Answer:
The cost of 1 jar of peanut butter is $2.50 ⇒ answer B
Step-by-step explanation:
* Lets change the story problem to equations to solve it
- The cost of a jar of peanut butter is p dollars
- The cost of a jar of jelly is j dollars
- Winston purchased 3 jars of peanut butter and 2 jars of jelly for $11.50
- Peter purchased 2 jars of peanut butter and 4 jars of jelly for $13.00
* Lets write the equations
∵ The cost of a jar of peanut butter is p dollars and the cost of a jar
of jelly is j dollars
∵ Winston purchased 3 jars of peanut butter and 2 jars of jelly for $11.50
∴ 3p + 2j = 11.50 ⇒ (1)
∵ Peter purchased 2 jars of peanut butter and 4 jars of jelly for $13.00
∴ 2p + 4j = 13.00 ⇒ (2)
- Lets solve this system of equation by using elimination method
- Multiply equation (1) by -2
∴ -6p - 4j = - 23 ⇒ (3)
- Add equations (2) and (3)
∴ -4p = -10 ⇒ divide both sides by -4
∴ p = 2.5
∵ p is the cost of 1 jar of peanut butter
* The cost of 1 jar of peanut butter is $2.50
Final answer:
Using a system of equations based on the purchases of Winston and Peter, the price of one jar of peanut butter is calculated to be $2.50.
Explanation:
To determine the cost of one jar of peanut butter, we can set up a system of equations based on the information provided. Let p represent the price of one jar of peanut butter, and j represent the price of one jar of jelly.
The system of equations based on the purchases made by Winston and Peter are:
1) 3p + 2j = 11.50
2) 2p + 4j = 13.00
To solve for p, we can multiply equation 1) by 2 and equation 2) by 3 to eliminate j when we subtract one equation from the other.
2*(1): 6p + 4j = 23.00
3*(2): 6p + 12j = 39.00
Subtracting the first equation from the second, we get:
6p + 12j - (6p + 4j) = 39.00 - 23.00
8j = 16.00
j = 2.00
Now, substitute j = 2.00 into equation 1) to find p:
3p + 2(2.00) = 11.50
3p + 4.00 = 11.50
3p = 7.50
p = 2.50
Therefore, one jar of peanut butter costs $2.50, which corresponds with option B.
A 20m ladder and a 15m ladder were leaned against a building. The bottom of the longer ladder was 7m farther from the building than the bottom of the shorter ladder, but both ladders reached the same distance up the building. Find this distance.
6m
12m
10m
9m
Answer:
The correct answer is: d=9m
Step-by-step explanation:
Ok, the ladders leaned against a building make two right triangles with same the same height, which we will call h. For the 20m ladder, its leg is (7+d) and for the 15m ladder, its leg is d, and the two hypotenuses are 20 and 15 respectively.
Then, using the Pythagorean Theorem we have:
20m ladder:
20^2 = h^2 + (d+7)^2 (Eq. 1)
400 = h^2 + d^2 + 2*7*d + 7^2 (expanding the theorem)
400 = (h^2 + d^2) + 14*d + 49 (Eq. 2)
15m ladder:
15^2 = h^2 + (d)^2 (Eq. 3)
Since h^2 + (d)^2 is equal to 15^2, we can substitute (2) into (3):
400 = (15^2) + 14*d + 49
400 = 225 + 14*d + 49
14*d = 400 - 225 - 49 (clearing the variable d)
14*d = 126
d = 9 m
And since we now know that d is equal to 9m. For the longer ladder is (d+7)=(9+7)=16m.
And, then the shorter ladder is 9m from the building and the longer ladder is 16m from the building
7. Find the percent of decrease from 290 to 100. Round to the nearest tenth of a
percent, if necessary.
A 65.5%
B 190%
C 290%
D 1.9%
Answer:
A 65.5%
Step-by-step explanation:
Percent decrease = (original - new)/ original * 100 percent
= (290-100)/290 * 100 %
= 190/290* 100%
=.655172414 * 100%
=65.5172414%
To the nearest tenth percent %
65.5%
Suppose the probability that the Seahawks will defeat the Raiders is 0.55. What is the complement and what does it mean?
20/9 ; the probability that the Seahawks will not defeat the Raiders.
20/9 ; the probability that the Seahawks will defeat the Raiders.
11/20 ; the probability that the Seahawks will defeat the Raiders.
0.45 ; the probability that the Seahawks will not defeat the Raiders.
Answer:
D: 0.45 ; the probability that the Seahawks will not defeat the Raiders.
Step-by-step explanation:
The complement of an event A is the set of all outcomes in the sample space that are not included in the outcomes of event A.
The Complement Rule states that the sum of the probabilities of an event and its complement must equal 1, or for the event [tex]A[/tex], and its complement event [tex]\overline{A}[/tex] always
[tex]Pr(A)+Pr(\overline{A})=1.[/tex]
If [tex]Pr(A)=0.55,[/tex] then
[tex]0.55+Pr(\overline{A})=1\\ \\Pr(\overline{A})=1-0.55=0.45.[/tex]
Event [tex]A[/tex] - the Seahawks will defeat the Raiders
Event [tex]\overline{A}[/tex] - the Seahawks will not defeat the Raiders
Hence, correct choice is D: 0.45 ; the probability that the Seahawks will not defeat the Raiders.
The complement of the probability of the Seahawks defeating the Raiders is 0.45, this represents the probability of the Seahawks not defeating the Raiders.
Explanation:In probability theory, a complement refers to the opposite event of whatever has been defined. If the probability of a certain event, in this case the 'Seahawks defeating the Raiders', is given as 0.55, then the complement of that event, 'the Seahawks not defeating the Raiders', is calculated by subtracting the given probability from 1. Hence, the probability of the Seahawks not defeating the Raiders is 1 - 0.55, which equals 0.45.
Thus, the correct answer is '0.45; the probability that the Seahawks will not defeat the Raiders'.
Learn more about Probability and Complement here:https://brainly.com/question/23528544
#SPJ12
Please help me out with this
Answer:
a. y = {x+1, x≤2; x+2, x>2}
Step-by-step explanation:
The open circle at (2, 4) means the function is not defined as y=x+2 at that point. Only one answer selection correctly uses the inequality symbol > for that part of the function definition.
___
Comment on the other answer choices.
One selection (b) uses the region definitions x < 2 and x ≥ 2. That would put the open circle at (2, 3) and the filled circle at (2, 4)—not a match with the graph. The other function definitions (c, and d) have the relation defined as two different values at x=2. Such a relation is not a function.
△ TUV undergoes the dilation: (x, y) → → (2x, 2y). Then it is translated: (x, y) → → (x - 10, y - 8). If vertex T was at (8, 6), what are its coordinates after these two transformations?
(16, 12)
(-2, -2)
(6, 4)
(-4, -4)
Answer:
(6, 4)
Step-by-step explanation:
step 1
we have
The vertex T (8,6)
First transformation
The rule of the dilation is
(x, y) → → (2x, 2y)
so
(8, 6) → → (16, 12)
step 2
Second transformation
The rule of the translation is
(x, y) → → (x - 10, y - 8)
so
(16, 12) → → (16 - 10, 12 - 8) → → (6, 4)
Lester was solving an equation but he made a mistake. What is the mistake and what is the correct answer? X + 17 = 22 –22 –22 x = 0
subtract 17, not 22, from both sides. 17 – 17 = 0 and 22 – 17 = 5. The answer should be x = 5.
Step-by-step explanation:
An equation between two variables that gives a straight line when plotted on a graph.
Lester made mistake in first steps he subtract 22 from the equation.
The correct solution of the equation is x =5.
GivenLester was solving an equation but he made a mistake.
The given equation is;
[tex]\rm x + 17 = 22[/tex]
What is a linear equation?An equation between two variables that gives a straight line when plotted on a graph.
The equation represents the linear equation and to solve the equation following all the steps given below.
Then,
The correct way to solve the equation is,
[tex]\rm x + 17 = 22\\\\x+17-17 = 22-17\\\\x +0=5\\\\x=5[/tex]
Hence, the correct solution of the equation is x =5.
To know more about the Linear equation click the link given below.
https://brainly.com/question/11897796
Students volunteering at a charity event work 1/2- hour shifts.Zack volunteered for 4 hours.He incorrectly divided one half by four to find the number of shifts he worked. How should zack have calculated the number of his shifts
Answer:
He should have divided 4 by [tex]\frac{1}{2}[/tex]:
[tex]shifts=\frac{4}{\frac{1}{2}}\\\\shifts=8[/tex]
Step-by-step explanation:
You know that the students work [tex]\frac{1}{2}[/tex]-hour shifts at the charity event and Zack worked in the event for four hours.
Then, to calculate the number of shifts he worked, he should not have divided [tex]\frac{1}{2}[/tex] by 4. He should have divided 4 by [tex]\frac{1}{2}[/tex].
Let's make the correct procedure to calculate the number of shifts Zack worked at the charity event. This is:
[tex]shifts=\frac{4}{\frac{1}{2}}\\\\shifts=8[/tex]
Therefore, he worked 8 shifts.
To calculate the number of shifts Zack worked, we need to follow these steps:
1. Determine the length of one shift. According to the information provided, one shift lasts 1/2 hour.
2. Determine the total amount of time Zack volunteered. Zack volunteered for 4 hours.
3. To find out the total number of shifts Zack worked, we need to divide the total number of hours he volunteered by the length of one shift.
So, we take the total volunteer time (4 hours) and divide it by the shift length (1/2 hour):
\[ \text{Number of shifts} = \frac{\text{Total volunteer time}}{\text{Shift length}} \]
\[ \text{Number of shifts} = \frac{4}{1/2} \]
Now, when dividing by a fraction, you can multiply by its reciprocal. The reciprocal of 1/2 is 2/1, or just 2.
\[ \text{Number of shifts} = 4 \times 2 \]
\[ \text{Number of shifts} = 8 \]
So Zack should have determined that he worked 8 shifts in total during his volunteer time.
The sums that appear when two fair? four-sided dice? (tetrahedrons) with sides 1?, 2?, 3?, and 4 are tossed
When two four-sided dice are tossed, the combined outcome ranges from 2 to 8. The probability for each outcome can be calculated by counting the number of combinations that sum to that outcome and dividing by the total number of possible outcomes (16). For example, there's one way to get a sum of 2 (1+1), so the probability is 1/16.
Explanation:The subject of this question is probability, particularly, the sums of outcomes when tossing two fair four-sided dice (or tetrahedrons). Each dice has sides 1, 2, 3, and 4. When these dice are tossed together, the combined outcome is anywhere between the minimum value 2 (1 from each dice) to the maximum value 8 (4 from each dice).
The probability of each combined outcome can be calculated based on the total possible different outcomes (4 outcomes from each die, 4 * 4 = 16 total possibilities). To determine the probability for each combined outcome, we'd need to count the number of ways to get that particular sum:
To get a sum of 2 or 8, there's only one possible way (1+1 or 4+4), so the probability is 1/16 To get a sum of 3 or 7, there are two combinations (1+2, 2+1 or 3+4, 4+3), so the probability is 2/16 = 1/8 Similarly for other sums, count the combinations and divide by 16Learn more about Probability here:
https://brainly.com/question/32117953
#SPJ11
A box without a top is made from a rectangular piece of cardboard, with dimensions 6 ft by 8 ft, by cutting out square corners with side length x. Which expression can be used to determine the greatest possible volume of the cardboard box? (8−2x)(6−2x)x (6−x)(8−x)x (8x−6)(6x−8) (8−6x)(6−8x)
The answer is:
The first option:
[tex]Volumen_{max}=(8-2x)(6-2x)*x[/tex]
Why?From the statement, we know the dimensions of the box, and the length of the sides to be cut (x).
So,
Working with the length of the box, we have:
Let be 8 the length of the cardboard for the length of the box, so, if we cut out the side of length "x", we have:
[tex]Length=(8-(x+x))=(8-2x)[/tex]
Now,
Working with the width of the box, we have:
Let be 6 the length of the cardboard for the width of the box, so, if we cut out the side of length "x", we have:
[tex]Length=(6-(x+x))=(6-2x)[/tex]
Now that we already know the length and the width of the box, we know that the bottom of the box will have the same length "x", so, the greatest possible volume of the cardboard box will be:
[tex]Volumen_{max}=Length*Width*Bottom=(8-2x)(6-2x)*x[/tex]
Have a nice day!
The price of a sweatshirt at a local shop is twice the price of a pair of shorts. The price of a T-shirt at the shop is $4 less than the price of a pair of shorts. Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for a total cost of $136.
19Let w represent the price of one sweatshirt, t represent the price of one T-shirt, and h represent the price of one pair of shorts. Write a system of three equations that represents the prices of the clothing.
20= Solve the system. Find the cost of each item.
Answer:
Price of sweatshirt = $24
Price of t-shirt=$8
Price of shorts= $12
Step-by-step explanation:
Let
w be the price of one sweat shirt
t be the price of t-shirt
h be the price of shorts
The first statement is:
The price of a sweatshirt at a local shop is twice the price of a pair of shorts.
w=2h Eqn 1
Then,
The price of a T-shirt at the shop is $4 less than the price of a pair of shorts.
t=h-4 Eqn 2
And
Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for a total cost of $136.
3w+2h+5t=136 Eqn 3
Putting the value of w and t in equation 3
3w+2h+5t=136
3(2h)+2h+5(h-4)=136
6h+2h+5h-20=136
13h=136+20
h=156/13
h=12
So the price of pair of shorts is $12.
Putting the value of h in equation 1
w=2(12)
w=24
Price of sweatshirt is: $24
Putting the value of h in eqn 2:
t=12-4
t=8
Price of T-shirt is $8 ..
Match each term with the appropriate example
1.
Absolute value
2.
All real numbers
3.
x = -5
4.
No solution
5.
Adding the opposite to both sides of the equation.
a.
|2x| = -10
b.
3x = 3x
c.
5x = -25
d.
| - 7| = 7
e.
Canceling
Answer:
1. Absolute value : d. | - 7| = 7
2. All real numbers : b. 3x = 3x
3. x = -5 : c. 5x = -25
4. No solution : a. |2x| = -10
5. Adding the opposite to both sides of the equation. : e. Canceling
Step-by-step explanation:
1. Absolute value : d. | - 7| = 7
The absolute value is considered the distance to 0... so if there's a negative sign in the value, the negative sign disappears.
2. All real numbers : b. 3x = 3x
If we divide both sides by 3, we have x = x, which will always be true.
3. x = -5 : c. 5x = -25
If we multiply each side by 5, we have 5(x) = 5(-5) thus 5x = -25
4. No solution : a. |2x| = -10
The result of an absolute value cannot be a negative number. So, that has no solution since there's no value of x that would make this true.
5. Adding the opposite to both sides of the equation. : e. Canceling
If you have for example (x = -5) and you add 5 on both sides, you cancel the value on the right side... (becomes x + 5 = 0).
Find an equation in standard form for the hyperbola with vertices at (0, ±4) and asymptotes at y = ±2/3x.
Check the picture below.
so the hyperbola looks more or less like so, is a hyperbola with a vertical traverse axis, with a = 4 and h = 0, k = 0.
[tex]\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ asymptotes\quad y= k\pm \cfrac{a}{b}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \stackrel{\textit{the asymptotes are}}{\pm\cfrac{2}{3}x}\implies \pm\cfrac{2}{3}x=k\pm \cfrac{a}{b}(x- h)~~ \begin{cases} h=0\\ k=0\\ a=4 \end{cases} \\\\\\ +\cfrac{2}{3}x=0+\cfrac{4}{b}(x-0)\implies \cfrac{2x}{3}=\cfrac{4x}{b}\implies 2bx=12x \\\\\\ b=\cfrac{12x}{2x}\implies b=6 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(y-0)^2}{4^2}-\cfrac{(x-0)^2}{6^2}=1\implies \cfrac{y^2}{16}-\cfrac{x^2}{36}=1[/tex]
Final answer:
The standard form for the hyperbola with vertices at (0, ±4) and asymptotes at y = ±2/3x is \(\frac{y^2}{16} - \frac{9x^2}{64} = 1\).
Explanation:
Finding the Standard Form Equation of a Hyperbola
The student has asked for the standard form of a hyperbola given certain characteristics such as vertices and asymptotes.
The vertices at (0, ±4) indicate that this is a hyperbola centered at the origin with its major axis along the y-axis, while the asymptotes given by y = ±2/3x help determine the relationship between the semi-major axis a and semi-minor axis b.
General Structure of a Hyperbola
For a hyperbola centered at the origin with a vertical transverse axis, the standard form is:
[tex]\(rac{y^2}{a^2} - \frac{x^2}{b^2} = 1\)[/tex]
Given that the asymptotes have slopes of ±2/3, the relationship between a and b is b/a = 2/3. Since the vertices are at (0, ±4), a = 4. Solving for b gives us b = (2/3) × 4 = 8/3.
Standard Form Equation
The standard form equation of the hyperbola is therefore:
[tex]\(rac{y^2}{16} - \frac{x^2}{(8/3)^2} = 1\)Or simplified:\(rac{y^2}{16} - \frac{9x^2}{64} = 1\)[/tex]
F=7gh solve the formula for the variable h
Answer:
[tex]\large\boxed{h=\dfrac{F}{7g}}[/tex]
Step-by-step explanation:
[tex]F=7gh\to7gh=F\qquad\text{divide both sides by}\ 7g\neq0\\\\\dfrac{7gh}{7g}=\dfrac{F}{7g}\\\\h=\dfrac{F}{7g}[/tex]
The formula for the variable h is F/7g.
What is the variable?A variable is an alphabet or term that represents an unknown number of unknown value or unknown quantity.
The given equation is;
F=7gh
The formula for the variable h is determined in the following steps given below.
[tex]\rm F=7gh\\\\ h =\dfrac{F}{7g}[/tex]
Hence, the formula for the variable h is F/7g.
Learn more about variables here;
https://brainly.com/question/12783247
#SPJ2
The diagram shows a scale drawing of a lacrosse field. The diagram is 5 1/2 inches long and 3 inches wide. If 1 inch represents 20 yards, what is the area of the field?
Answer:
6600 yd²
Step-by-step explanation:
The area of the scale drawing is ...
(5.5 in)(3 in) = 16.5 in²
Each square inch represents an area of the field that is ...
(20 yd)×(20 yd) = 400 yd² . . . . per square inch of drawing
Then the scale drawing represents a field with an area of ...
(16.5 in²)×(400 yd²/in²) = 6600 yd²
Write the equation of the line that contains the point (-6 7) and the midpoint of the segment connecting (4 -6) and (8 -4)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{8+4}{2}~~,~~\cfrac{-4-6}{2} \right)\implies (6,-5) \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{7})\qquad \stackrel{\textit{the midpoint}}{(\stackrel{x_2}{6}~,~\stackrel{y_2}{-5})}[/tex]
[tex]\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-5-7}{6-(-6)}\implies \cfrac{-12}{6+6}\implies \cfrac{-12}{12}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-7=-1[x-(-6)]\implies y-7=-1(x+6) \\\\\\ y-7=-x-6\implies y=-x+1[/tex]
Please please help me out
Answer:
26.6 m
Step-by-step explanation:
Given the figures are similar
linear ratio = a : b
area ratio = a² : b²
here
area ratio = 16 : 25, then
linear ratio = 4 : 5 ( square root of both area ratio parts )
let the perimeter of the larger figure be x, then by proportion
[tex]\frac{4}{21.3}[/tex] = [tex]\frac{5}{x}[/tex] ( cross- multiply )
4x = 106.5 ( divide both sides by 4 )
x ≈ 26.6
Hence perimeter of larger figure is approximately 26.6 m
Please help me out!!! :)
Answer:
x = 26°
Step-by-step explanation:
The measure of the secant- secant angle x is one- half the difference of the measures of the intercepted arcs , larger subtract smaller
x = [tex]\frac{1}{2}[/tex] (66° - 14°) = 0.5 × 52° = 26°
For the function defined by y = 1/x4, y varies inversely as what quantity
ANSWER
y varies inversely as x exponent 4.
EXPLANATION
The inverse variation equation is given as:
[tex]y = \frac{1}{ {x}^{4} } [/tex]
We can see that there is an inverse relation between the quantity y and x.
If the it were [tex]y = \frac{1}{ {x}^2 } [/tex], we say y varies inversely as the square of x.
Hence for the given relation,the precise definition is that, y varies inversely as x exponent 4.
Answer:
d. x^4
Step-by-step explanation:
Just got it right
If the parent function f(x)=\root(3)(x) is transformed to g(x)=\root(3)(x+2-4), which is the graph of g(x)?
(Photos of graphs included)
(15 points)
ANSWER
A.
EXPLANATION
The parent function is
[tex]f(x) = \sqrt[3]{x} [/tex]
This function is transformed to obtain
[tex]g(x) = \sqrt[3]{x + 2} - 4[/tex]
The +2 is a horizontal translation, that shifts the graph of the parent function to the left by 2 units.
The -4 is a vertical translation, that shifts the graph of the parent function down by 4 units.
The correct option is A.
Answer:
A)
Step-by-step explanation:
First we will graph th parent function which is a cube root and we can see it in the attachment #1.
In this excercise there are two types of transformations of the parent function:
[tex]f(x)=\sqrt[3]{x}[/tex]
First:
[tex]f(x+b)[/tex] shifts the function b units to the left.(Attachment #2 )
[tex]f(x)=\sqrt[3]{x+2}[/tex]
[tex]b=2[/tex]
Second:
[tex]f(x)-c[/tex] shifts the function c units downward. (Attachment #3)
[tex]f(x)=\sqrt[3]{x+2}+4[/tex]
[tex]c=4[/tex]
Help me with this please !
Answer:
True
Step-by-step explanation:
The formula for the circumference of a circle is:
C=2πr
So we can substitute in the numbers we have:
Radius=4, so:
C=8π (we multiplied the radius by 2)
So the statement is true.
Hope I... yeah you get it y now I've been answering your questions a lot.
I'm still gonna copyright it.
Copyright Potato 2019.
Answer:
True
Step-by-step explanation:
The circumference (C) of a circle is
C = 2πr ← r is the radius
For C = 8π, then
2πr = 8π ( divide both sides by 2π )
r = 8π ÷ 2π = 4
Hence the radius must be 4
This results when you flip the numerator and denominator of a fraction. what do you call this?
Answer:
the multiplicative inverse or reciprocal.
Step-by-step explanation:
calculate cosine to two decimal places
Answer:
Final answer is approx -0.07.
Step-by-step explanation:
We have been given a picture of the triangle whose sides are 7, 8 and 11.
Apply cosine formula to find the value of [tex]\cos\left(\theta\right)[/tex].
[tex]a^2=b^2+c^2-2\cdot b\cdot c\cdot\cos\left(a\right)[/tex]
[tex]11^2=7^2+8^2-2\cdot 7\cdot 8\cdot\cos\left(\theta\right)[/tex]
[tex]121=49+64-112\cdot\cos\left(\theta\right)[/tex]
[tex]121=113-112\cdot\cos\left(\theta\right)[/tex]
[tex]121-113=-112\cdot\cos\left(\theta\right)[/tex]
[tex]8=-112\cdot\cos\left(\theta\right)[/tex]
[tex]\frac{8}{-112}=\cos\left(\theta\right)[/tex]
[tex]-0.0714285714286=\cos\left(\theta\right)[/tex]
Hence final answer is approx -0.07.
The answer is C. -0.07.
Please please help me out
Answer:
angle x will be 17
Step-by-step explanation:
ATP,
3x+4=72–x
3x+x=72–4
4x=68
x=68/4
x=17
Answer:
x = 17
Step-by-step explanation:
Since triangles are similar then corresponding angles are congruent.
∠I and ∠ P are corresponding and congruent, hence
3x + 4 = 72 - x ( add x to both sides )
4x + 4 = 72 ( subtract 4 from both sides )
4x = 68 ( divide both sides by 4 )
x = 17
Which transformation represents a reflection over the y-axis? (x, y) → (−x, y) (x, y) → (x , −y) (x, y) → (y, x) (x, y) → (−y, x)
Answer:
(x, y) → (−x, y)(x, y)
Step-by-step explanation:
To do a transformation over the Y-axis, you just have to change the sign on the x in order to create a matching point on the other side of the Y axis, for example if you wish to make a reflection of the point (8,9), the reflection over the Y axis would be (-8,9), the same with X and Y, if you wish to make a reflection of (x,y) you just change the sign of the x like this: (-x,y)
The correct answer is option 1. [tex](x,y) \rightarrow (-x,y)[/tex]
To determine which transformation represents a reflection over the y-axis, we examine the options provided:
[tex](x,y) \rightarrow (-x,y)[/tex][tex](x,y) \rightarrow (x,-y)[/tex][tex](x,y) \rightarrow (y,x)[/tex][tex](x,y) \rightarrow (-y,x)[/tex]A reflection over the y-axis transforms the x-coordinate of a point to its opposite while keeping the y-coordinate unchanged. Therefore, the correct transformation is [tex](x,y) \rightarrow (-x,y)[/tex].
Reflection over the y-axis results in the point (x, y) being mapped to (−x, y). This is because the x-coordinate is negated while the y-coordinate remains the same.
The complete question is:
Which transformation represents a reflection over the y-axis?
1. [tex](x,y) \rightarrow (-x,y)[/tex]
2. [tex](x,y) \rightarrow (x,-y)[/tex]
3. [tex](x,y) \rightarrow (y,x)[/tex]
4. [tex](x,y) \rightarrow (-y,x)[/tex]
Internet provider A charges $9.95 per month for the first 10 hours of use and $1.69 per hour for all those over 10. Provider B charges a flat fee of $19.95.What would be the maximum number of hours you could use each month for Provider A to be the best value for you?
15 hours is the answer to this
1.69×5+9.95
Answer:
15 hours.
Step-by-step explanation:
In order to solve this, we just have to create an inequality, for ti to be more convenient for us to work with the first company we shouldn´t be spending more than 19.95 a month, otherwise we would be better off with the second one, so the total would be 19.95, and the base fee is $9.95 for the first ten hours, so X would be the number of extra hours we will use:
[tex]Base+Extra,hours=Budget[/tex]
Now we just insert the values in to the formula:
[tex]10+1.68x=19.95\\[/tex]
We clear X:
[tex]10+1.68x=19.95\\[/tex]
[tex]1.68x=19.95-10\\[/tex]
[tex]1.68x=9.95\\[/tex]
[tex]x=\frac{9.95}{1.69}[/tex]
[tex]x=5.91\\[/tex]
So the as the number of extra hours that we could use without going over the budget is 5.91, and the company wouldn´t charge us the .91, the number of extra hours is 5, plus the base hours, the total number of hours would be 15.
Write an equation in slope-intercept form, y=mx+b, for the lines with the following information:
y-intercept 3 and slope -6
Slope intercept formula: y = mx + b where m equals slope and b equals the y-intercept.
Answer: y = -6x + 3
Final answer:
The equation in slope-intercept form for a line with y-intercept 3 and slope -6 is y = -6x + 3, showing a line decreasing by 6 units in y for each unit increase in x.
Explanation:
To write an equation in slope-intercept form, which is y = mx + b, we need to know the slope (m) and the y-intercept (b). In this case, we have a y-intercept of 3 and a slope of -6. Plugging these values into the slope-intercept form, we get the equation of the line:
y = -6x + 3
This equation tells us that the line crosses the y-axis at (0, 3) and for each unit increase in x, the value of y decreases by 6 units, since the slope is negative. This is a direct application of the algebra of straight lines and the concepts of slope and y-intercept.
Determine if triangle XYZ with coordinates X(1, 1), Y(5, 6), and Z(6, 2) is a right triangle.
Answer:
Yes.
Step-by-step explanation:
If you graph it you can see that they all the points match up to the perfect right triangle. You may have to rotate it to see it though. Point Z is the angle of the triangle that is the corner of the 90 degree triangle.
Please please help me
Answer:
Your numbers are +7, -9, and 25
Step-by-step explanation:
Reverse the values of -7 and +9
Then you get +7 and -9
And also take radius squared which is 25
So, [tex](x--7)^{2} +(y-9)^{2} = 25[/tex]
The graph of a system of two linear equations has no solution. What is true about the lines? A. The lines are perpendicular. B. The lines have the same slope, but different intercepts. C. The lines have the same intercept, but different slopes. D. The lines are on top of each other.
Answer:
B. The lines have the same slope, but different intercepts.
Step-by-step explanation:
The solution of a system of linear equations doesn't exist if the lines do not intersect each other at any point. So if there is no solution that means the lines of both equations will not intersect.
Lets look at the options one by one.
For option A:
If the lines are perpendicular, they might intersect at any point so this is not the correct option.
For Option B:
If the lines have same slop and different intercepts that means the lines are parallel. We know that parallel lines never cross each other so option B is the correct answer.
For Option C:
The lines with same intercept and different might also intersect so option C is not correct.
For Option D:
The lines being on top of each other means that the lines intersect on all points. So option D is also not correct.
Please help me with this
Answer:
[tex]\frac{\sqrt{51} }{10}[/tex]
Step-by-step explanation:
Using the Pythagorean identity
sin²x + cos²x = 1 ⇒ cosx = ± [tex]\sqrt{1-sin^2x}[/tex], hence
cosΘ = [tex]\sqrt{1-(7/10)^2}[/tex]
= [tex]\sqrt{1-\frac{49}{100} }[/tex]
= [tex]\sqrt{\frac{51}{100} }[/tex]
= [tex]\frac{\sqrt{51} }{\sqrt{100} }[/tex] = [tex]\frac{\sqrt{51} }{10}[/tex]