Idk if ya still need it or if this will help but this is what i put for mine
Concepts that I had previously learned about are quite important because math goes hand and hand. if you try to skip something and go ahead you'll most likely get confused because there could of been something highly important to that would help you understand whats ahead. in the previous unit it tells you about triangles and their description like a right triangle-90 degree angle and where legs and hypotenuse is located, this unit has had a ton about right triangles.
Previous concepts learned in mathematics provide a necessary foundation for understanding more complex topics such as trigonometry and the properties of right triangles. This is exemplified in how the Pythagorean theorem and understanding of sine, cosine, and tangent in a right triangle, inform the understanding of trigonometric principles. Hence, learning in mathematics is a progressive and integrated process.
Explanation:Reflecting on working with right triangles and trigonometric concepts, it's clear that concepts learned previously were extremely important to success in this unit. Mathematics is interconnected, and concepts build upon one another. Take for example, the Pythagorean theorem, a fundamental principle in geometry that establishes a relationship between the sides of a right-angled triangle. This theorem set the stage for understanding trigonometric concepts.
Another important previous learning that helped in understanding trigonometry is the concept of the sine, cosine, and tangent of an angle in a right triangle. Knowledge of these terms and ability to calculate them, as represented in a right triangle, feeds into the understanding of trigonometric principles.
Furthermore, the problem-solving strategies applied in mathematics aid in integrating concepts. Identifying physical principles and solving for unknowns is crucial and this reasoning prowess comes from continuous practice over previous sections.
Learn more about Importance of previous concepts in understanding new mathematical learning here:https://brainly.com/question/33473920
#SPJ3
A vegetable garden and a surrounding path are shaped like a square that together are 12 ft wide. The path is 2 feet wide. The the total area of the path.
Answer:
80 ft²
Step-by-step explanation:
The area of the path is equal to the area of the overall square minus the area of the garden.
Area of a square is the side length squared:
A = s²
The overall square has a side length of 12 feet. The side length of the garden is 12 - 2 - 2 = 8 feet. So the area of the path is:
A = 12² - 8²
A = 144 - 64
A = 80
The area of the path is 80 ft².
42. What is the surface area of a sphere with a circumference of 50 feet round the answer to the nearest 10th.
43. The volume of a sphere is 2254 pi m^3. What is the surface of the sphere to the nearest 10th?
44. What is the scale factor of a cube with a volume of 729 m^3 to a cube with a volume of 6859?
Answer:
Part 42) The surface area of the sphere is [tex]SA=795.8\ ft^{2}[/tex]
Part 43) The surface area of the sphere is [tex]SA=1,781.6\ m^{2}[/tex]
Part 44) The scale factor is [tex]\frac{19}{9}[/tex]
Step-by-step explanation:
Part 42) What is the surface area of a sphere with a circumference of 50 feet round the answer to the nearest 10th
step 1
Find the radius of the sphere
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=50\ ft[/tex]
assume
[tex]\pi =3.14[/tex]
substitute and solve for r
[tex]50=2(3.14)r[/tex]
[tex]r=7.96\ ft[/tex]
step 2
Find the surface area of the sphere
The surface area of the sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
substitute the value of r
[tex]SA=4(3.14)(7.96)^{2}[/tex]
[tex]SA=795.82\ ft^{2}[/tex]
round to the nearest 10th
[tex]795.82=795.8\ ft^{2}[/tex]
Part 43) The volume of a sphere is 2254 pi m^3. What is the surface of the sphere to the nearest 10th?
step 1
Find the radius of the sphere
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]V=2,254\pi\ m^{3}[/tex]
substitute and solve for r
[tex]2,254\pi=\frac{4}{3}\pi r^{3}[/tex]
Simplify
[tex]1,690.5=r^{3}[/tex]
[tex]r=11.91\ m[/tex]
step 2
Find the surface area of the sphere
The surface area of the sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
substitute the value of r
[tex]SA=4(3.14)(11.91)^{2}[/tex]
[tex]SA=1,781.6\ m^{2}[/tex]
Part 44) What is the scale factor of a cube with a volume of 729 m^3 to a cube with a volume of 6859?
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
so
Let
z -----> the scale factor
x ----> the volume of the larger cube
y ----> the volume of the smaller cube
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]x=6,859\ m^{3}[/tex]
[tex]y=729\ m^{3}[/tex]
substitute
[tex]z^{3}=\frac{6,859}{729}[/tex]
[tex]z=\frac{19}{9}[/tex]
[tex](\frac{6,859}{729})[/tex]
Are all cubes similar? If so, explain why. If not, give an exapmle of two cubes that are not similar.
Yes, all cubes are similar.
Similarity in geometry refers to the property where two shapes have the same shape but not necessarily the same size. In the case of cubes, all cubes share the same shape characteristics: they have six square faces, with each face having four equal sides and all angles being right angles. The only difference between one cube and another is their size, or the length of their sides. Similarity does not depend on size; it is solely based on shape. Therefore, regardless of how large or small a cube is, it maintains its geometric properties and thus, all cubes are similar to each other. This means any two cubes you pick, regardless of their size, will be similar as they share these fundamental properties.
What is the rate of change between the interval x= pi and x= 3pi/2
Answer:
[tex]\frac{6}{\pi }[/tex] or 1.9099
Step-by-step explanation:
Look for y values at each of those given values of "x" and apply the slope formula. When x = pi. y = -1 so the coordinate is [tex](\pi,-1)[/tex]. When x = 3pi/2, y = 2 so the coordinate is [tex](\frac{3\pi }{2},2)[/tex]
Plug those values into the slope formula:
[tex]\frac{2-(-1)}{\frac{3\pi }{2}-\pi}[/tex]
You need a common denominator of pi:
[tex]\frac{3}{\frac{3\pi-2\pi}{2} }=\frac{3}{\frac{\pi }{2} }[/tex]
Do the math on that to get a slope of [tex]\frac{6}{\pi } =1.9099[/tex]
The dimensions of a square are altered so that one dimension is increased by 7 feet and the other is decreased by 2 feet. The area of the resulting rectangle is 90 square feet. Find the original area of the square
I got 64 square feet.
My work is shown in the image.
For possible questions:
1: you can find x+7 and x-2 because the sides of the square can be measured as x, and x+7 means 7 more than the original; x-2 means 2 less than the original.
2: solved via factoring. Not sure if you've learned it or not.
3: reject the negative numbers because you can't have negative sides in a square.
Area of rectangle is multiplication of length and width.
Original area of square will be 64 square feet.
Let us consider the each side of square is x feet.
Since, one dimension is increased by 7 feet and the other is decreased by 2 feet . then, it become a rectangle have length (x + 7) and width (x - 2) feet.
Area of resulting rectangle = (x + 7)(x - 2)
[tex](x + 7)(x - 2)=90\\\\x^{2} +5x-104=0\\\\x^{2} +13x-8x-104=0\\\\x(x+13)-8(x+13)=0\\\\(x-8)(x+13)=0\\\\x=8,x=-13[/tex]
Since, length can not be negative. So x = 8 feet
Original are of square = [tex]x^{2} =8^{2}[/tex]
= 64 square feet
Learn more:
https://brainly.com/question/23148123
Find z 1 ÷ z 2 for z 1 = 9(cos225° + isin225°) and z 2 = 3(cos45° + isin45°).
Express the quotient in a + bi form.
[tex]\bf \qquad \textit{division of two complex numbers} \\\\ \cfrac{r_1[cos(\alpha)+isin(\alpha)]}{r_2[cos(\beta)+isin(\beta)]}\implies \cfrac{r_1}{r_2}[cos(\alpha - \beta)+isin(\alpha - \beta)] \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \begin{cases} z1=9[cos(225^o)+i~sin(225^o)]\\\\ z2=3[cos(45^o)+i~sin(45^o)] \end{cases}\implies \cfrac{z1}{z2}\implies \cfrac{9[cos(225^o)+i~sin(225^o)]}{3[cos(45^o)+i~sin(45^o)]} \\\\\\ \cfrac{9}{3}[cos(225^o-45^o)+isin(225^o-45^o)]\implies 3[cos(180^o)+i~sin(180^o)] \\\\\\ 3[(-1)+i~(0)]\implies -3+0i[/tex]
Answer:
-1
Step-by-step explanation:
Use DeMoivre's Theorem for division of complex polar numbers. Set it up like this:
[tex]\frac{9(cos225+sin225i)}{3(cos45+sin45i)}[/tex]
The rule is
[tex]\frac{z_{1} }{z_{2} }cis(\theta_{1}-\theta _{2} )[/tex]
Our z1 is 9 and our z2 is 3, so the division of those gives you 3. The subtraction of the angles 225 - 45 = 180, therefore:
3 cis 180° = 3(cos 180 + sin 180 i)
The cos of 180 is -1 and the sin of 180 is 0, so 3(-1 + 0) = -3
On a protractor there are two scales.Read one scale to find 44.What is the measure on the other side
Answer:
136
Step-by-step explanation:
The two scales are supplementary, so the value on the second scale is ...
180° -44° - 136°
A game is played with two for spinners. One spinner has four sections numbered one through eight. The second spinner has five sections, each with a different color: Red, blue, green, orange, and brown. What is the probability of spinning a number less than four on the first spinner in the color brown on the second spinner?
Answer:
3/40
Step-by-step explanation:
3/8 numbers less than four
1/5 chance for brown
And=Multiplication
Or=Addition
3/8×1/5=3/40
Based on a poll of 100 citizens, a community action group claims that 38% of the population is in favor of the construction of a senior center using tax dollars. A business group claims that the poll is not valid and that 65% of the citizens favor the construction of the senior center using tax dollars.
To determine whether this sample supports the population proportion of 0.38, a simulation of 100 trials is run, each with a sample size of 200 and a point estimate of 0.65. The minimum sample proportion from the simulation is 0.42, and the maximum sample proportion from the simulation is 0.72.
The margin of error of the population proportion is found using an estimate of the standard deviation.
What is the interval estimate of the true population proportion?
Answer:
(0.55, 0.75)
Step-by-step explanation:
The range can be estimated to be 6 standard deviations wide. Therefore, the standard deviation is:
σ = (0.72 - 0.42) / 6
σ = 0.05
The margin of error is ±2σ, so:
ME = ±0.10
Therefore, the interval estimate is:
(0.65 - 0.10, 0.65 + 0.10)
(0.55, 0.75)
The standard deviation is a measure of a collection of values' variance or dispersion. The interval estimate of the true population proportion is (0.55, 0.75).
What is a standard deviation?The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
A.) The range is around 6 standard deviations broad. As a result, the standard deviation is:
σ = (0.72 - 0.42) / 6
σ = 0.05
B.) Because the margin of error is ±2σ, therefore, we can write,
Margin Of Error = (±0.05)×2 = ±0.10
C.) The interval can be estimated as,
Interval = 0.65±0.10
= 0.65-0.10, 0.65+0.10
= 0.55, 0.75
Hence, the interval estimate of the true population proportion is (0.55, 0.75).
Learn more about Standard Deviation:
https://brainly.com/question/16555520
#SPJ2
A contractor records all of the bedroom areas, in square feet, of a five-bedroom house as: 100, 100, 120, 120, 180 what is the variance? what is the standard deviation?
Variance = 864
Standard Deviation= 29.4
Answer:
Standard Deviation = 29.40
Variance = 864
Step-by-step explanation:
A contractor records all of the bedroom areas, in square feet of a 5 bedroom house as : 100, 100, 120, 120, 180
To calculate the standard deviation first we have to calculate the mean of the data
( 100 + 100 + 120 + 120 + 180 ) / 5
= 620 / 5 = 124
Then for each number subtract the mean and square the result :
-24, -24, -4, -4, 56
square the result = 576, 576, 16, 16, 3136
Now work out the mean of these squared differences.
( 576 + 576 + 16 + 16 + 3136 ) / 5 = 4320 / 5 = 864
This value is Variance, so the variance = 864
Now we take the square root of 864 to get standard deviation
[tex]\sqrt{864}[/tex] = 29.39 rounded to 29.40
Standard Deviation = 29.40
Variance = 864
ANSWER INCLUDED: What is the solution of log3x + 4 4096 = 4?
x=-1
x=0
x=4/3
x=3
We solve for x by simplifying both sides of the equation, then isolate the variable.
ANSWER:
C (x=4/3)
Answer:
C [tex]x=\frac{4}{3}[/tex]
Step-by-step explanation:
The given logarithmic equation is:
[tex]\log_{3x+4}(4096)=4[/tex]
We rewrite in exponential form; to get;
[tex]4096=(3x+4)^4[/tex]
We rewrite the LHS as a certain natural number exponent 4.
[tex]8^4=(3x+4)^4[/tex]
The exponents are the same, hence the bases must also be the same.
[tex]\implies 3x+4=8[/tex]
[tex]\implies 3x=8-4[/tex]
[tex]\implies 3x=4[/tex]
Divide both sides by 3;
[tex]\implie x=\frac{4}{3}[/tex]
The correct answer is C
Help please!!!!!!!!!!!!!!!!
Answer:
3
Step-by-step explanation:
1 person eats 2/5 of a pizza
6 people eat 2/5 * 6 pizzas
But what value is 2/5 * 6?
You could do it this way
12/5 = 2 2/5
This number is telling you that you need 2/5 of a pizza over 2.
The group should order 3 pizzas. There will be left overs, but that won't matter. Everyone will get at least 2/5 of a pizza.
Janis is helping organize the school dance. She asked 30 randomly selected students to select their favorite theme for the dance. The top choice for 6 students was Glow-in-the-Dark. The total number of students in the middle school is 200. Based on the results of the survey, how many students should Janis expect to choose Glow-in-the-Dark as their favorite theme?
Answer:
Step-by-step explanation:
6 of 30 chose Glow in the Dark
That is 1/5 of the students
Out of 200, 40 would choose glow in the dark
40 is 1/5 of 200
The answer is 40
Out of 200, 40 students should Janis expect to choose Glow-in-the-Dark as their favorite theme.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
6 of 30 chose Glow in the Dark.
So, if there are 200 middle school students then the number of students choose Glow-in-the-Dark as their favorite theme
= 6/30 x 200
= 1/5 x 200
= 40
Learn more about Unitary Method here:
https://brainly.com/question/22056199
#SPJ6
Please help me with this please
Answer:
338 in
Step-by-step explanation:
Tangents to a circle from an external point are congruent, thus counting from the bottom left in a clockwise direction gives
perimeter = 98 + 22 + 22 + 27 + 27 + 22 + 22 + 98 = 338 in
Two similar figures have a side ratio of 3:4. The area of the larger figure is 100 square units. What is the area of the smaller figure?
[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{small}{large}\qquad \stackrel{ratio}{\cfrac{3}{4}}\qquad \qquad \cfrac{3}{4}=\stackrel{areas}{\cfrac{\sqrt{a}}{\sqrt{100}}}\implies \cfrac{3}{4}=\cfrac{\sqrt{a}}{10}\implies 30=4\sqrt{a} \\\\\\ \cfrac{30}{4}=\sqrt{a}\implies \left( \cfrac{30}{4} \right)^2=a\implies \cfrac{900}{16}=a\implies \cfrac{225}{4}=a[/tex]
The area of the smaller figure is 225/4 or 56.25 square units if the two similar figures have a side ratio of 3:4.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
Let's suppose the area of the smaller figure is x
Area of larger figure = 100 square units
The ratio of the areas:
= x/100
We also have:
Two similar figures have a side ratio of 3:4
= 3/4
Square it we will get ratio of the area
= 9/16
x/100 = 9/16
x = 900/16 = 225/4 or 56.25 square units
Thus, the area of the smaller figure is 225/4 or 56.25 square units if the two similar figures have a side ratio of 3:4.
Learn more about the ratio here:
brainly.com/question/13419413
#SPJ2
In regression analysis, which statements are true?
I. Data sets that include an influential point are nonlinear.
II. Influential points always reduce the coefficient of determination.
III. All outliers are influential data points.
A) I only
B) II only
C) III only
D) None are true
Answer:
D) None are true
Step-by-step explanation:
- Data sets with influential points can be linear or nonlinear.
- Influential points can increase the coefficient of determination.
- Outliers are influential only if they have a big effect on the regression equation.
Hope his helps
-Amelia
In regression analysis, statement III is not true. All outliers are not necessarily influential data points. And statement II is not always true
Hence, option I is correct.
What is statistics?Statistics is a discipline of mathematics that deals with all aspects of data. Statistical knowledge aids in the selection of the appropriate technique of data collection and the use of those samples in the appropriate analysis process in order to effectively create the results. In short, statistics is an important procedure that assists in making data-driven decisions.
Since we know that,
A point with a significant residual is considered an outlier.
An influential point is one that has a significant impact on the regression. Surprisingly, these are not synonymous. A point can be an outlier without having any influence. Without being an anomaly, a point can be influential.
Therefore,
statement I can be true - data sets with influential points can indeed be non-linear.
And statement II is not always true - influential points can either increase or decrease the coefficient of determination, depending on whether they are positively or negatively correlated with the response variable.
To learn more about statistics visit:
https://brainly.com/question/30765535
#SPJ2
Molly went to her grandma's house for 16 hours last weekend. This was four times longer than the last time she spent at her grandma's this weekend. How many minutes was Molly at her grandma's house this weekend?
Answer: 240 minutes should be it
Answer:
Step-by-step explanation:240 minutes should be it
Solve the following quadratic-linear system of equations. y=x^2-x-6 and y=2x-2
You can do substitution 2x-2=x^2 -x -6; isolate all terms on one side 0= x^2 -x-2x -6+2; combine like terms x^2 -3x -4=0; factor the quadratic (x-4)(x+1)=0; each term is zero x-4=0 so x=4 and x+1=0 so x=-1. Now, y=2•4-2=6 and y=2•(-1) -2= -4 ; solutions for the system are ( 4,6) and ( -1, -4)
Answer:
(4,6) or (-1,-4)
Step-by-step explanation:
since both equations about x are equal to y, you can make x^2-x-6=2x-2
solve this quadratic equation, you get x=4 or -1
substitute x into y=2x-2
you get y=6 when x=4, or y= -4 when x=-1
Elizabeth is going to flip a fair coin 100100100 times. what is the best prediction for the number of times that the coin will land tails up
Answer:
50050050
Step-by-step explanation:
There is a 50% chance for the coin to either land on heads or tales so you divide 100100100 by 2 to get 50050050 this would work with anything else say you need to figure out the chance of a coin landing on heads and the coin flips 550 times to figure out the chance you do 550 divided by 2 and you get 225. But anyways the answer is 50050050. the reason you divide by two is because the coin has 2 sides, if it were a dice, for instance, you would divide by 6 because it has 6 sides
Simplify the polynomial expression.
3x(-2x+7)-5(x-1)(4x-3)
Answer:
The simplified form is -26x^2 + 56x -15
Step-by-step explanation:
We need to solve the expression:
3x(-2x+7)-5(x-1)(4x-3)
Multiplying the terms outside the bracket with the terms inside the bracket.
=-6x^2+21x-5(x(4x-3) -1(4x-3))
= -6x^2+21x-5(4x^2-3x-4x+3)
= -6x^2+21x-5(4x^2-7x+3)
Now multiply -5 with the terms inside the bracket
= -6x^2+21x -20x^2 +35x -15
Now, Combining the like terms:
= -6x^2 -20x^2 +21x+35x -15
Adding the like terms
= -26x^2 + 56x -15
So, the simplified form is -26x^2 + 56x -15
Answer: [tex]-26x^2+56x-15[/tex]
Step-by-step explanation:
The first step is to apply Distributive property.
You also need to remember the Product of powers property, which states the following:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Applying these properties:
[tex]3x(-2x+7)-5(x-1)(4x-3)=\\=-6x^2+21x-5(4x^2-3x-4x+3)\\=-6x^2+21x-20x^2+15x+20x-15[/tex]
And finally, you need to add the like terms.
Therefore, you get:
[tex]=-26x^2+56x-15[/tex]
Use the formula to evaluate the infinite series. Round to the nearest hundreth if necessary.
25 + 5 + 1 + . . .
Answer:
31.25
Step-by-step explanation:
The initial term is 25 and the common ratio is 5/25 = 1/5. The formula tells you the sum is ...
25/(1 -1/5) = 25/(4/5) = 31.25
If we factor 25 from the sum, we have
[tex]\displaystyle 25\left(1+\dfrac{1}{5}+\dfrac{1}{25}+\ldots\right)=25\sum_{i=0}^\infty \left(\dfrac{1}{5}\right)^i = 25 \dfrac{1}{1-\frac{1}{5}} = 25\dfrac{1}{\frac{4}{5}}=25\cdot \dfrac{5}{4} = \dfrac{125}{4}[/tex]
What is the area of the regular hexagon shown in the image?
Answer:
1,595.34
Step-by-step explanation:
A=33
2a2=3·3
2·24.782≈1595.34454
Does each situation describe a survey, an experiment, or an observational study?
Select Survey, Experiment, or Observational Study for each situation.
Answer:
Experiment, observational study, survey
Step-by-step explanation:
The first one is an experiment. The vet selects random samples and compares the effects of the injection to the nose drips.
The second one is an observational study. The reaction of the dogs to the treats is being observed.
The third one is a survey. The owners are given specific questions to answer.
The terms 'survey', 'experiment', and 'observational study' are methods of data collection in mathematics, specifically in statistics. A 'survey' collects data systematically from a group of individuals, an 'experiment' tests hypotheses in controlled conditions, and an 'observational study' records data without influencing the subjects of the study.
Explanation:The terms 'survey', 'experiment, and 'observational study' represent distinct methods of data collection in statistics. A survey is a data collection tool used to gather information about individuals systematically. An experiment involves carrying out a procedure under controlled conditions to test a hypothesis. An observational study refers to a study where researchers observe and record data without influencing the subjects of the study.
Now let’s identify each of the provided situations:
If the situation is about systematically gathering information from a group of individuals through questioning, it describes a survey.If the situation describes a procedure being performed under controlled conditions to test a hypothesis, it's referring to an experiment.But, if the situation illustrates a process in which data is collected by observing and recording specific variables of interest without any interference by the researchers, it's an observational study.Learn more about Data Collection Methods here:https://brainly.com/question/35917278
#SPJ11
Given that (-6,5) is on graph of f(x) find the corresponding point for the function f(x)-4
The new graph will go down 4 point so y coordinate will go down 4. (-6,5) becomes ( -6, 1)
The corresponding point for the function f(x)-4 is (-6, 1) if the point (-6,5) is on the graph of f(x).
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a point (-6, 5) is on graph of f(x) find the corresponding point for the function f(x)-4
As we know, if f(x) is subtracted by 4 the function f(x) will go down by 4 units.
The corresponding point on the function f(x)-4 will be:
= (-6, 5-4)
= (-6, 1)
Thus, the corresponding point for the function f(x)-4 is (-6, 1) if the point (-6,5) is on the graph of f(x).
Learn more about the function here:
brainly.com/question/5245372
#SPJ2
A concession stand has crates of bottled water to sell at a sporting event. Each crate holds 48 bottled waters and costs the concession stand $9.20. If the concession stand wants to make exactly $34.00 profit per crate of bottled water, customers should be charged $ for each bottled water.
Answer:
90 cents
Step-by-step explanation:
If a crate holds 48 bottles and you want to make exactly $34 on selling them, before you find out exactly how much to charge for each bottle, you have to subtract the amount you paid for the crate from the profit. The unknown here is the cost per bottle that you have to make in order to reach your goal of $34. If you have 48 bottles of water and you want to know how much to charge PER bottle, the algebraic expression for that would be 48x. Now from that profit of 48x you need to subtract the $9.20 and set it equal to what you'd like to earn:
48x - 9.20 = 34.00
Solve this by adding 9.2 to both sides, and then dividing by 48. That gives you a cost per bottle of 90 cents. Plug .90 in for x in the equation above and see that the left side does indeed equal the right side.
To make a profit of $34 per crate along with the original cost of $9.20, the concession stand should charge $0.90 per bottled water.
Explanation:The question is asking for the price the concession stand should charge per bottle of water in order to make a profit of $34.00 per crate. We start by determining the total desired income from each crate, which is cost plus profit ($9.20 cost + $34.00 profit = $43.20 total income per crate). Next, we divide the total income per crate by the number of bottles in each crate, which is 48. So, $43.20 / 48 = $0.90. Therefore, the concession stand should charge customers $0.90 per bottle of water to achieve the desired profit of $34.00 per crate.
Learn more about Profit Calculation here:https://brainly.com/question/29785281
#SPJ3
Which of the following tables shows the correct steps to transform x2 + 8x + 15 = 0 into the form (x - p)2 = q?
[p and q are integers] (5 points)
Step 1x2 + 8x + 15 - 1 = 0 - 1
Step 2x2 + 8x + 14 = -1
Step 3(x + 4)2 = -1
Step 1x2 + 8x + 15 - 2 - 0 - 2
Step 2x² + 8x + 13 = -2
Step 3(x + 4)2 = -2
Step 1x2 + 8x + 15 + 1 = 0 + 1
Step 2x2 + 8x + 16 = 1
Step 3(x + 4)2 = 1
Step 1x2 + 8x + 15 + 2 = 0 + 2
Step 2x2 + 8x + 17 = 20
Step 3(x + 4)2 = 2
Answer:
Step 1: x^2 + 8x + 15 + 1 = 0 + 1
Step 2: x^2 + 8x + 16 = 1
Step 3: (x + 4)^2 = 1
Step-by-step explanation:
You want the constant on the left to be the square of half the x-coefficient.
(8/2)^2 = 4^2 = 16
You already have a constant that is 15, so you need to add 1 to both sides of the equation. That is the Step 1 shown here. Step 2 is simplifying the result of Step 1. Step 3 is rewriting the trinomial as the square of a binomial.
Answer:
Step 1 x2 + 8x + 15 + 1 = 0 + 1
Step 2 x2 + 8x + 16 = 1
Step 3 (x + 4)2 = 1
Step-by-step explanation:
took the test
A recent hailstorm caused $900 worth of body damage to Kristen’s car. Based on Kristens insurance policy given below, how much will Karen receive after she files her claim.
Answer:
525
Step-by-step explanation:
the equation of a parabola is given. y=-1/12x^2-2x-1
What are coordinates of the focus?
[tex]-(x^2+24x+144)=12y+12...[/tex]Answer:
(-12, 8)
Step-by-step explanation:
The standard form of this parabola, the one we can use to determine the vertex coordinates and the value of p is:
[tex](x-h)^2=4p(y-k)[/tex]
where h and k are the coordinates of the vertex and p is the distance between the vertex and the focus. We need that p value to determine how far above the vertex the focus is. In this case, the focus will lie on the same x-coordinate as the focus, we just need to find how far that distance away is. That requires us to do some algebraic gymnastics on that original equation. Putting it into vertex form.
Begin by multiplying everything by 12 to get rid of the pesky fraction:
[tex]12y=-x^2-24x-12[/tex]
Now we need to complete the square. The easiest way to do this is to have just the x terms on one side of the equals sign and everything else on the other side, so we will add 12 to both sides:
[tex]-x^2-24x=12y+12[/tex]
The leading coefficient when you complete the square has to be a positive 1; ours is a negative 1, so factor out the negative:
[tex]-(x^2+24x)=12y+12[/tex]
The rules for completing the square are as follows: Take half the linear term (ours is a 24), square that half, then add it into the parenthesis.
Half of 24 is 12 so
[tex]-(x^2+24x+144)=12y+12[/tex]
BUT...since this is an equation, if we add something to one side we have to add it to the other side too. BUT we didn't just add in a 144, we have to take into account the -1 sitting outside the parenthesis that will not be ignored. So we didn't add in 144, we added in -1(144) which is -144.
[tex]-(x^2+24x+144)=12y+12-144[/tex]
What we have done on the left by completing the square is to create a perfect square binomial. Rewriting it as such and combining like terms on the right:
[tex]-(x+12)^2=12y-132[/tex]
Don't forget the purpose of this is to find the value of p. We're almost there. On the right, factor out a 12:
[tex]-(x+12)^2=12(y-11)[/tex]
From this we can determine the coordinates of the vertex and the value of p. The vertex sits at (-12, 11).
The equation for p is 4p = 12 so p = 3
That means that the focus is 3 units below the vertex on the same x coordinate. The focus then is at (-12, 8)
Choose the correct answer. Two cars leave phoenix and travel along roads 90 degrees apart. If car 1 leaves 60 minutes earlier than car 2 and averages 40 mph and if car 2 averages 50 mph, how far apart will they be after car 1 has traveled 3.5 hours? Miles.
Answer:
251.047804213 miles
Step-by-step explanation:
c1 t=3.5+1 speed 40 mph
c2 t=3.5 speed 50 mph
c1 40 *4.5= 180
c2 50 *3.5= 175
a^2+ b^2= c^2
180^2+175^2=c^2
32400+30625=c^2
63025=c^2
251.047804213=c
Answer:
It is 188 miles
Step-by-step explanation:
This is correct on Odyssey :)
What is the trigonometric ratio for sin Z ?
Enter your answer, as a simplified fraction, in the boxes.
In all right triangles, the ratio between a leg and the hypothenuse is the sine of the angle opposite to the leg.
So, in your case, we have
[tex]\sin(Z) = \dfrac{XY}{XZ}[/tex]
In order to find XY, we have
[tex]XY = \sqrt{XZ^2-YZ^2} = \sqrt{1600-1024}=\sqrt{576} = 24[/tex]
So, the ratio for the sine is
[tex]\sin(Z) = \dfrac{XY}{XZ} = \dfrac{24}{40} = \dfrac{3}{5}[/tex]