The question involves setting up and solving an algebraic equation to find a number such that 12 less than 7 times this number equals 32 less than the product of -3 and the number. The solution to the equation 7x - 12 = -3x - 32 is x = -2.
The phrase '12 less than 7 times a number' can be represented as 7x - 12, where 'x' is the number in question. The phrase '32 less than the product of -3 and a number' translates to -3x - 32. Setting these two expressions equal to each other gives us the equation 7x - 12 = -3x - 32.
To solve for 'x', we can first add 3x to both sides of the equation, which will give us 10x - 12 = -32. Next, we add 12 to both sides to isolate the term with 'x', resulting in 10x = -20. Finally, we divide both sides by 10 to find the value of 'x', which yields x = -2.
Therefore, the number that satisfies the condition is -2.
DESCRIBE HOW TO USE THE SCALE FACTOR TO DILATE A POLYGON ON THE COORDINATE PLANE.
Answer:
Multiply the original points by the fraction or ratio of the dilution needed
Step-by-step explanation:
I'm less confident in this answer, but Scale factor is the ration between two geometric figures, like 1:2 is for every one unit on one figure is two on the other, so to dilute a figure, you multiply the points by 1/2 to make a smaller figure, or by 2 to get a bigger one. Plot the given answers and you have diluted :) Hope this helps!
Can you help me and please explain...
Explanation:
For each exponent inside the radical, you will divide it over the root index. The root index is the small number to the left and above the radical symbol. So the root index is 6 in this case.
Divide each exponent over 6
3/6 = 1/2 is the final exponent for x
18/6 = 3 is the final exponent for y
which is how we get to x^(1/2)*y^3
--------------------
note: x^(1/2) is the same as the square root of x
[tex]x^{1/2} = \sqrt{x}[/tex]
The more general rule is
[tex]x^{m/n} = \sqrt[n]{x^m}[/tex]
Your estimate that the length of a board is 24 feet. The actual length of the board is 22 feet. Find the percent error.
Answer:
9.09%
Step-by-step explanation:
You over estimated by 2 feet. Find out how much 2 feet of 22 is by dividing 2 by 22...
2/22 = 0.090909090909
To convert a decimal to a percent, multiply the decimal by 100%
0.0909090909(100%) = 9.0909090909% or 9.09%
Final answer:
The percent error in the student's estimate of the board's length is approximately 9.09%. The exercise demonstrates the value of precise calculations over rough estimates, although some thoughtful guesses can be quite close.
Explanation:
To find the percent error of the student's estimate, we'll use the following formula:
Percent Error = |(Actual Value - Estimated Value) / Actual Value| × 100%
The actual length of the board is 22 feet, and the estimated length is 24 feet. So we can calculate the percent error as follows:
|(22 - 24) / 22| × 100% = |(-2) / 22| × 100% = (2 / 22) × 100% ≈ 9.09%
The percent error in the student's estimate is approximately 9.09%. This calculation underscores the importance of making careful calculations rather than relying on rough guesstimates, which can lead to significant errors in certain situations. However, it can also show that even guesses made with some thought, like the example of 10 feet versus an actual of 12 feet, can sometimes be surprisingly close.
2 cars started to move at the same time, at the same direction but one was moving twice as fast as the other. 6 hours later, the 2 cars were 204 miles apart. Find the speed for each car.
Answer:
The speeds are 34 mph for the slower car and 68 mph for the faster car.
Step-by-step explanation:
speed = distance/time
Using s for speed, d for distance, and t for time, we have the equation for speed:
s = d/t
Solve for distance, d, by multiplying both sides by t.
d = st
Now we use the given information.
Speed of slower car: s
Speed of faster car: 2s
Distance traveled by faster car: d
Distance traveled by slower car: d - 204
time traveled by faster car = time traveled by slower car = 6
Distance equation for faster car:
d = st
d = 2s * 6
d = 12s <---- equation 1
Distance equation for slower car:
d = st
d - 204 = s * 6
d - 204 = 6s
d = 6s + 204 <----- equation 2
Now, using equations 1 and 2, we have a system of two equations in two unknowns.
d = 12s
d = 6s + 204
Since the first equation is already solved for d, we can use the substitution method. Substitute 12s for d in the second equation:
12s = 6s + 204
6s = 204
s = 34
The speed of the slower car is 34 mph.
The speed of the faster car is
2s = 2(34) = 68
The speed of the faster care is 68 mph.
Two cars started moving simultaneously where one was twice as fast as the other. After setting x as the speed of the slower car, the equations showed the slower car traveled at 34 mph and the faster car at 68 mph, based on being 204 miles apart after 6 hours.
Two cars started moving at the same time and direction where one car's speed was twice as fast as the other. After 6 hours, they were 204 miles apart. To solve for the speed of each car, let's set up an equation where the speed of the slower car is x miles per hour and the faster car is 2x miles per hour.
The distance covered by each car after 6 hours would then be:
Slower car: 6x milesFaster car: 6(2x) = 12x milesSince the cars are 204 miles apart after 6 hours, the equation can be set up as:
12x - 6x = 204
So the distance difference is:
6x = 204
Divide both sides by 6 to find the speed of the slower car:
x = 34
Therefore, the slower car travels at 34 mph and the faster car travels at 68 mph (twice the speed of the slow car).
find the constant of variation k for the direct variation x -1 0 2 5 f(x) 2 0 -4 -10
Answer:
k = -2
Step-by-step explanation:
x -1 0 2 5
f(x) 2 0 -4 -10
ƒ(x) = kx
Substitute a pair of values for x and ƒ(x)
-10 = k×5
Divide each side by 5
k = -2
The constant of variation k = -2.
(25 Points) What is the area of a triangle that has a base of 3 feet and a height of 6 feet?9 ft?or4.5ft?
Let's start with the formula for the area of a triangle
[tex] \frac{1}{2} bh[/tex]
And for the first one, insert the numbers
[tex] \frac{1}{2} 3 \times 6[/tex]
To make this easier, 3×6=18, 1/2 of 18 is 9, so the answer is 9 square feet. There's all you need to complete the rest, good luck .
The value 5pi/2 is a solution for the equation 2sin^2x -sin x -1=0
Answer:
5π/2 it is not a solution for the equation 2sin²x - sinx - 1 = 0
Step-by-step explanation:
∵ 2sin²x - sin x - 1 = 0
* Lets factorize it as a quadratic equation
∴ ( 2sinx + 1)(sinx - 1) = 0
∴ 2sinx + 1 = 0 ⇒ 2sinx = -1 ⇒ sinx = -1/2
* ∵ The value of sinx is -ve
∴ x is in the 3rd or 4th quadrant ⇒ According to ASTC Rule
- ASTC Rule: 1st all +ve , 2nd sin only +ve ,
3rd tan only +ve , 4th cos only +ve
* Let sinα = 1/2 where α is an acute angle
∴ α = π/6
∵ x is in 3rd or 4th quadrant
∴ x = π + α = π + π/6 = 7π/6 or
∴ x = 2π - π/6 = 11π/6
OR
∴ sinx - 1 = 0 ⇒ sinx = 1
∴ x = π/2
∴ ALL values of x are π/2 , 7π/2 , 11π/2 if 0 ≤ x ≤ 2π
∴ 5π/2 it is not a solution for the given equation
Answer:
5pi/2 is a solution for the equation 2sin²x -sin x -1=0
Step-by-step explanation:
We need to check 5pi/2 is a solution for the equation 2sin²x -sin x -1=0.
Substituting 5pi/2 in equation
[tex]2sin^2x-sin x-1=2sin^2\left (\frac{5\pi}{2} \right )-sin\left (\frac{5\pi}{2} \right )-1\\\\=2sin^2\left (2\pi +\frac{\pi}{2} \right )-sin\left (2\pi +\frac{\pi}{2} \right )-1\\\\=2sin^2\left (\frac{\pi}{2} \right )-sin\left (\frac{\pi}{2} \right )-1\\\\=2\times 1-1-1=0[/tex]
So 5pi/2 is a solution for the equation 2sin²x -sin x -1=0.
what is the value of x?
Answer:
2
Step-by-step explanation:
The rule for secants from an external point is that the product of the near and far distance to the intersection with the circle is a constant.
EA·EB = EC·ED
(x+12)·(x+1) = (x+4)·(x+5)
x^2 +13x +12 = x^2 +9x +20 . . . . . . eliminate parentheses
4x = 8 . . . . . . . . . . . . subtract x^2+9x+12 from both sides
x = 2 . . . . . . . . . . . . . divide by 4
The value of x is 2.
Princess peach has a cell phone plan that charges $50 a month and $0.12 for every minute that she uses the phone beyond what her plan allows. One month she was billed $63.32
she was 111 minutes over what her plan allowed.
Brett is making a fruit salad. The recipe calls for 1 1 2 cups of apple, 3 4 cup of oranges, and 2 3 cup of grapes. How many cups of fruit salad will Brett's recipe make?
Answer:
35/12 cups
Step-by-step explanation:
Brett's recipe will make [tex]\( \frac{35}{12} \)[/tex] cups of fruit salad, which is approximately 2.92 cups when rounded to two decimal places.
To find the total number of cups of fruit salad Brett's recipe will make, we add the amounts of each fruit together:
1. Apples: 1 1/2 cups
2. Oranges: 3/4 cup
3. Grapes: 2/3 cup
To add these fractions, we need a common denominator. The least common denominator (LCD) of 2, 4, and 3 is 12.
[tex]1. Apples: \(1 \frac{1}{2} = \frac{3}{2}\) cups[/tex]
[tex]2. Oranges: \(\frac{3}{4}\) cup[/tex]
[tex]3. Grapes: \(\frac{2}{3}\) cup[/tex]
Now, we convert each fraction to have a denominator of 12:
[tex]1. Apples: \(\frac{3}{2} \times \frac{6}{6} = \frac{9}{6}\) cups[/tex]
[tex]2. Oranges: \(\frac{3}{4} \times \frac{3}{3} = \frac{9}{12}\) cups[/tex]
[tex]3. Grapes: \(\frac{2}{3} \times \frac{4}{4} = \frac{8}{12}\) cups[/tex]
Now, we add these amounts:
[tex]\(\frac{9}{6} + \frac{9}{12} + \frac{8}{12} = \frac{18}{12} + \frac{9}{12} + \frac{8}{12} = \frac{35}{12}\) cups[/tex]
So, Brett's recipe will make [tex]\( \frac{35}{12} \)[/tex] cups of fruit salad, which is approximately 2.92 cups when rounded to two decimal places.
A bag contains 4 red, 3 green and 2 blue marbles. What is the probability of selecting a green marble and then a blue marble assuming you replace the first marble?
1st of all, this makes my brain hurt
2nd of all, which one was the first marble?
Find the value of x and y.
A) x=109, y=108
B) x=108, y=109
C) x=108, y=108
D) x=109, y=109
Answer:
B
Step-by-step explanation:
Since a quadrilateral has an angle sum of 360 degrees you just add the three angle measures together and subtract them from 360 leaving you with 108.
The angle which is outside is supplementary which means it adds to 180 degrees. All you have to do here is subtract 71 from 180 which gives you 109.
It’s B) x=108,y=109
Es la respuesta
The graphs below have the same shape. What is the equation of the blue graph?
Answer:
C. G(x) = (x - 1)² - 3Step-by-step explanation:
f(x) + n - shift the graph of f(x) n units up
f(x) - n - shift the graph of f(x) n units down
f(x - n) - shift the graph of f(x) n units to the right
f(x + n) - shift the graph of f(x) n units to the left
===================================
Look at the picture.
The graph of F(x) shifted 1 unit to the right and 3 units down.
Therefore the equation of the function G(x) is
[tex]G(x)=(x-1)^2-3[/tex]
What is the degree measure of the angle formed by the hands of a clock when the time is 12:00
Answer:
0 degrees
Step-by-step explanation:
when it is hour 12 and 0 minutes, the hour and minute hand will be on top of each other, so therefore it does not form an angle
Given the system of equations, what is the solution?
x + 2y = 7
x - 2y = -1
{(-8, -12)}
{(3, 2)}
{(-4, 6)}
Answer:
[tex]\large\boxed{x=3\ and\ y=2\to(3,\ 2)}[/tex]
Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}x+2y=7\\x-2y=-1\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=6\qquad\text{ivide both sides by 2}\\.\qquad x=3\\\\\text{Put the value of x to the first equation:}\\\\3+2y=7\qquad\text{subtract 3 from both sides}\\\\2y=4\qquad\text{divide both side by 2}\\\\y=2[/tex]
The solution to the given system of linear equations is (3, 2), which is found by eliminating y and solving for x, then substituting back to find y.
Given the system of equations:
x + 2y = 7
x - 2y = -1
To find the solution to the system, we can add the two equations to eliminate y:
(x + 2y) + (x - 2y) = 7 + (-1)
2x = 6
x = 3
Substituting x = 3 into the first equation:
3 + 2y = 7
2y = 4
y = 2
So, the solution to the system of equations is (3, 2). None of the other provided options, {(-8, -12)} or {(-4, 6)}, match this solution.
An item has a listed price of $ 60 . If the sales tax rate is 6 % , how much is the sales tax (in dollars)?
Answer:
$3.6
Step-by-step explanation:
6%=.06
60*.06=3.6
Identify the graph of 3x^2+y^2=9 for T(-1,3) and write an equation of the translated or rotated graph in general form.
ANSWER
D. Ellipse;
[tex]3{x}^{2} +{y}^{2} + 6x - 6y + 3= 0[/tex]
EXPLANATION
The given equation is
[tex]3 {x}^{2} + {y}^{2} = 9[/tex]
Dividing through by 9 gives
[tex] \frac{ {x}^{2} }{ 3} + \frac{ {y}^{2} }{9} = 1[/tex]
This is the equation of an ellipse centered at the origin.
If this ellipse has been translated, so that its center is now at (-1,3), then the equation of the translated ellipse becomes
[tex]\frac{ {(x + 1) }^{2} }{ 3} + \frac{ {(y - 3)}^{2} }{9} = 1[/tex]
We multiply through by 9 to get,
[tex]3 {(x + 1)}^{2} + {(y - 3)}^{2} = 9[/tex]
Expand to obtain;
[tex]3( {x}^{2} + 2x + 1) + {y}^{2} - 6y + 9 = 9[/tex]
Expand to obtain;
[tex]3{x}^{2} + 6x + 3+ {y}^{2} - 6y + 9 = 9[/tex]
Regroup and equate to zero to obtain;
[tex]3{x}^{2} +{y}^{2} + 6x - 6y + 3= 0[/tex]
If g(x)=3/4x+2,find g(-12)
Answer:
g(-12) = -7
Step-by-step explanation:
Answer: g(-12)=-7
Step-by-step explanation:
g(x)= 3/4x+2
g(-12)= 3/4(-12)+2
g(-12)=-9+2
g(-12)=-7
Find the length and width of a rectangle whose area is 56 units squared and whose length is 10 units less than it's width
Answer:
l = 4, w = 14
Step-by-step explanation:
[tex]A_r = 56 = l * w[/tex]
l - length;
w - width;
l = w - 10;
We substitute the 'l' using the previous formula =>
[tex][tex]A_r = (w -10) \cdot w = w^2 - 10w = 56 =>\\w^2 - 10w - 56 = 0\\[/tex]
By the quadratic formula we solve for 'w':(we will use the positive value, because we're talking about lengths of planes in a Euclidean space)
[tex]w = \frac{10 + \sqrt{100+224} }{2} = \frac{10+18}{2} = \frac{28}{2} = 14[/tex]
l = w - 10 = 14 -10 = 4
Please help with this!!!!
Answer: 7
Step-by-step explanation:
[tex]\dfrac{\overline{CD}+\overline{A F}}{2}=\overline{BE}\\\\\\\dfrac{(18)+(6x-12)}{2}=2x+10\\\\\\(18)+(6x-12)=2(2x+10)\\\\\\6x +6 = 4x +20\\\\2x+6=20\\\\2x=14\\\\\large \boxed{x=7}[/tex]
[tex]Z_{1}[/tex]=3cisπ [tex]Z_{2}[/tex]=5cis(π/2) If [tex]Z_{1}[/tex]*[tex]Z_{2}[/tex]=a1+b2 than a= blank, and b=blank
Answer:
a = 0b = -15Step-by-step explanation:
z1 = -3
z2 = 5i
z1·z2 = (-3)(5i) = -15i = 0 + (-15)i
Then the real and imaginary parts are a = 0, b = -15.
A certain four-cylinder combination lock has 55 numbers on it. to open it, you turn to a number on the first cylinder, then to a second number on the second cylinder, and then to a third number on the third cylinder and so on until a four-number lock combination has been affected. repetitions are allowed, and any of the 55 numbers can be used at each step to form the combination. (a) how many different lock combinations are there
Answer:
9,150,625.
Step-by-step explanation:
Any one of the 55 numbers can be combined with any one of the 55 in the other cylinders.
So the number of different combinations are 55^4
= 9,150,625.
The total number of different combinations that can be made with a four-cylinder combination lock that has 55 numbers on each cylinder is 9,150,625. This is calculated using the multiplication principle of counting.
Explanation:This question involves the principle of counting or combinatorics in mathematics. Specifically, it relates to the multiplication principle, which says that if event A can occur in m ways, and after it happens, event B can occur in n independent ways, then the total number of ways in which both events can occur is calculated as m times n.
In the case of the four-cylinder combination lock with 55 possible numbers for each cylinder, there are 55 ways to choose a number for the first cylinder. Since repetitions are allowed and each choice is independent, there are also 55 ways to choose a number for the second cylinder, 55 ways for the third cylinder, and 55 ways for the fourth cylinder. Using the multiplication principle, we can find the total number of possible lock combinations by calculating 55 * 55 * 55 * 55 = 9,150,625 possible combinations.
Learn more about Combination Lock here:
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HELP ASAP PLEASE !!! WILL MARK BRAINLEST!!
Use the slope-intercept form of a line, y = mx + b, to answer the following.
Find the equation of the line that has these features:
Slope= 2/5
Passes through the point (-10, -5)
Answer: [tex]y=\frac{2}{5}x-8[/tex]
Step-by-step explanation:
By definition, the equation of the line in slope-intercept form of is:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
Then, given the slope 2/5 and the point, (-10, -5), you can calculate the value of b by susbtituting and solve for it:
[tex]-10=\frac{2}{5}(-5)+b\\ -10=-2+b\\b=-8[/tex]
Substitute this value and the slope into the equation. THerefore, you obtain:
[tex]y=\frac{2}{5}x-8[/tex]
hey this text is just for min word requirement the problem is in the picture
Answer:
(-2, 0)
Step-by-step explanation:
Because both equations are to find Y, set them equal to each other to solve:
3x+6 = x+2
Subtract x from both sides:
2x + 6 = 2
Subtract 6 from both sides:
2x = -4
Divide both sides by 2:
x = -4 /2
x = -2
Now you have a value for x, replace X with -2 in one of the equations and solve for y:
y = 3x +6 = 3(-2) +6 = -6 +6 = 0
X = -2 and Y = 0
(-2,0)
Jenna brought in $25,000 to her startup firm at the beginning of the year. During the year, she withdrew $2,500 for her personal expenses. The business earned $10,000 at the end of the accounting period after paying off all its expenses. What is the value of Jenna’s capital account at the end of the accounting year?
A. $25,000
B. $22,500
C. $35,000
D. $32,500
➷ 25,000 - 2500 = 22500
22500 + 10,000 = 32,500
The correct answer would be option D. $32,500
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
Step-by-step explanation:
I would have to go with D. The 25,000 is what you start with minus the 2,500 she withdrew which would leave her at 22,500. She then receives 10,000 for the business leaving her with 32,500
For the function F(x)= [tex]\frac{1}{x+1}[/tex], which of these could be a value of F(x) when x is close to -1?
A. -1
B. -10,000
C. 0.01
D. -0.01
Answer:
C
Step-by-step explanation:
Answer:
it is B
Step-by-step explanation:
Write the sum using summation notation, assuming the suggested pattern continues. 2 - 6 + 18 - 54 + ... summation of two times negative three to the power of n from n equals zero to infinity summation of two times three to the power of n from n equals zero to infinity summation of two times three to the power of the quantity n plus one from n equals zero to infinity summation of two times negative three to the power of the quantity n minus one from n equals zero to infinity
Answer:
It's the first choice.
Step-by-step explanation:
The common ratio is -6/2 = 18/-6 = -3.
2*(-3)^0 = 2*1 = 2.
2*(-3)^1 = -6
2*(-3)^2 = 18
2*(-3)^3 = -54.
So in summation notation is
∞
∑ 2(-3)^n
n=0
The sum using summation notation is given by:
Summation of two times negative three to the power of n from n equals zero to infinity.
i.e. numerically it is given by:
[tex]\sum_{n=0}^{\infty} 2(-3)^n[/tex]
Step-by-step explanation:The alternating series is given by:
[tex]2-6+18-54+........[/tex]
The series could also be written in the form:
[tex]=2+(2\times (-3))+(2\times (-3)\times (-3))+(2\times (-3)\times (-3)\times (-3))+....\\\\i.e.\\\\=2\times (-3)^0+2\times (-3)^1+2\times (-3)^2+2\times (-3)^3+.....\\\\i.e.\\\\=\sum_{n=0}^{\infty} 2(-3)^n[/tex]
Please help me out!!!!!
(132°-x)+(6x-12°) = 180°(Co-interior Angles)
132°-12°-x+6x = 180°
120° + 5x = 180°
5x = 180° - 120°
5x = 60°
x = 12°
(132°-x)+(6y+18°) = 180°(Co-interior Angles)
132°-x+6y+18°=180°
132°-12°+18°+6y=180°
138°+6y=180°
6y=180°-138°
6y=42°
y = 7°
HOPE THIS WILL HELP YOU
Which type of graph would be best for showing the height of a sapling tree over the span of several weeks?
a bar graph
a circle graph
a histogram
a line graph
Answer:
A line graph
Step-by-step explanation:
A line graph will be the best option because it can show the exact height based on time as a data point. Connecting each data point will then reveal the trend in how the sapling grows and average growth rate among other information can be found.
Final answer:
A line graph is the best choice for displaying the continuous growth of a sapling tree over a period of several weeks, as it shows trends over time effectively.
Explanation:
The best type of graph for showing the height of a sapling tree over several weeks is a line graph. A line graph is designed to show trends over time and is particularly useful when you want to display changes in a variable continuously, such as the growth of a tree's height. The line graph will clearly depict the gradual increase in height with each passing week, allowing for an easy visual interpretation of the data. Other graphs such as a bar graph, circle graph (or pie chart), or a histogram are not as suitable for representing data over time in the same continuous and clear manner as a line graph.
Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.
y=csc (x) -9
Answer:
The answer is vertical translation down 9 units ⇒ answer (d)
Step-by-step explanation:
* Lets talk about the transformation
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) - k
* Lets study the problem
- The basic function is y = csc(x)
∵ y = csc(x) - 9
- That means the function translated vertically 9 units down
* Vertical translation 9 units down
* Look to the graph
-The red graph is y = csc(x)
- The green graph is y = csc(x) - 9