Drag the tiles to the correct boxes to complete the pairs. Match the one to one functions with their inverse functions.
Answers
Answer:
Part 1) [tex]f^{-1}(x)=3(x+17)/2[/tex] ----> [tex]f(x)=\frac{2x}{3}-17[/tex]
Part 2) [tex]f^{-1}(x)=x+10[/tex] -----> [tex]f(x)=x-10[/tex]
Part 3) [tex]f^{-1}(x)=\frac{x^{3}}{2}[/tex] ----> [tex]f(x)=\sqrt[3]{2x}[/tex]
Part 4) [tex]f^{-1}(x)=5x[/tex] ----> [tex]f(x)=x/5[/tex]
Step-by-step explanation:
Part 1) we have
[tex]f(x)=\frac{2x}{3}-17[/tex]
Find the inverse
Let
y=f(x)
[tex]y=\frac{2x}{3}-17[/tex]
Exchange the variables, x for y and y for x
[tex]x=\frac{2y}{3}-17[/tex]
Isolate the variable y
Adds 17 both sides
[tex]x+17=\frac{2y}{3}[/tex]
Multiply by 3 both sides
[tex]3(x+17)=2y[/tex]
Divide by 2 both sides
[tex]y=3(x+17)/2[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
so
[tex]f^{-1}(x)=3(x+17)/2[/tex]
Part 2) we have
[tex]f(x)=x-10[/tex]
Find the inverse
Let
y=f(x)
[tex]y=x-10[/tex]
Exchange the variables, x for y and y for x
[tex]x=y-10[/tex]
Isolate the variable y
Adds 10 both sides
[tex]y=x+10[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
so
[tex]f^{-1}(x)=x+10[/tex]
Part 3) we have
[tex]f(x)=\sqrt[3]{2x}[/tex]
Find the inverse
Let
y=f(x)
[tex]y=\sqrt[3]{2x}[/tex]
Exchange the variables, x for y and y for x
[tex]x=\sqrt[3]{2y}[/tex]
Isolate the variable y
elevated to the cube both sides
[tex]x^{3}=2y[/tex]
Divide by 2 both sides
[tex]y=\frac{x^{3}}{2}[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
so
[tex]f^{-1}(x)=\frac{x^{3}}{2}[/tex]
Part 4) we have
[tex]f(x)=x/5[/tex]
Find the inverse
Let
y=f(x)
[tex]y=x/5[/tex]
Exchange the variables, x for y and y for x
[tex]x=y/5[/tex]
Isolate the variable y
Multiply by 5 both sides
[tex]y=5x[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
so
[tex]f^{-1}(x)=5x[/tex]
The inverse of a function is shown in the picture we can calculate by interchanging the value of f(x) and 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:
Functions are shown in the picture.
We have to find the inverse of a function.
[tex]\rm f(x) = \dfrac{2x}{3}-17[/tex]
To find the inverse of a function plug in the place of f(x)→x and x→f(x) ⁻¹
[tex]\rm x = \dfrac{2f^-^1(x)}{3}-17[/tex]
f(x) ⁻¹ = 3(x + 17)/2
Similarly, we can find the rest of the inverse of the function as follows:
f(x) = x - 10
f(x) ⁻¹ = x + 10
f(x) = ∛2x
f(x) ⁻¹ = x³/2
f(x) = x/5
f(x) ⁻¹ = 5x
Thus, the inverse of a function is shown in the picture we can calculate by interchanging the value of f(x) and x.
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Related Questions
Guillermo earned $15.25 per hour for 25 hours of work. What was he paid?
Answers
Answer:
$381.25
Step-by-step explanation:
15.25*25=381.25
$381.25
you have to multiply $15.25 by 25
What is the remainder in the synthetic division problem below?
Answers
Answer:
B
Step-by-step explanation:
1 | 1 2 - 3 2
1 3 0
--------------------
1 3 0 2 ← remainder
Answer:
The remainder is 2
Option B is correct
Step-by-step explanation:
Given the synthetic division problem
we have to solve the problem
The steps are
Step 1: Set up the synthetic division.
Step 2: Put down the leading coefficient to bottom row.
Step 3: Multiply divisor which is on left by the value just written on the bottom row.
Step 5: Repeat the above steps.
The synthetic division is shown in attachment.
The remainder is 2
Option B is correct
Find the value of x. 4(x-7)= 3(9- 1/3x)
Answers
Answer:
x = 11
Step-by-step explanation:
distribute: 4x - 28 = 27 - x
add x to both sides: 5x - 28 = 27
add 28 to both sides: 5x = 55
divide 5 to both sides: x = 11
PLEASE HELP ASAP
Emily plans to roll a standard six-sided die 3 times and record the result after each roll.
What is the probability that she rolls an odd number for all 3 rolls?
Answers
Answer:
Emily has a 1 in 9 chance of rolling an odd number for all 3 rolls
Step-by-step explanation:
If there are three odd numbers, you’d simply multiply one sixth three times. One sixth because the dice has six sides and three times because there are three possibilities of getting an odd number
Brett is paid $18.95 per hour with time and a half
for overtime. What will his gross pay be for a pay
period in which he worked 42 hours one week and
36 hours the next week for a total of 78 hours?
$1,478.10
$1,876.05
$2,217.15
$1,497.05
Answers
Answer:
$1,497.05
Step-by-step explanation:
Brett had 2 hrs OT his first week which would be (40 hr × 18.95 )+ (18.95 ×3) add the total to (36×18.95).
Please help I will mark brainliest
Answers
20-3=17
B) Incorrect
6(16) =96
C) Incorrect
11 does not equal 12
Answer:
A = True
B = False
C = true
Step-by-step explanation:
Consider the functions.
f(x)= square root x
g(x)= square root x-3+1
h(x)= square root x+1-2
Which statement compares the relative locations of the minimums of the functions?
1.The minimums of g(x) and h(x) are both in the first quadrant.
2.The minimums of g(x) and h(x) are both in the third quadrant.
3.The minimum of h(x) is farther right and up from the minimums of f(x) and g(x).
4.The minimum of h(x) is farther left and down from the minimums of f(x) and g(x).
Answers
Answer:
The minimum of h(x) is farther left and down from the minimums of f(x) and g(x) ⇒ answer 4
Step-by-step explanation:
* Lets revise the meaning of the minimum of the function
- The minimum of a function is the lowest point of a vertex
- The minimum value is the y-coordinate of the lowest point
* Now lets solve the problem
∵ f(x) = √x
- The domain of the function is all the real numbers ≥ 0, because
there is no square root for negative numbers
- We will use the first value of x to find the range of the function
∵ x = 0 ⇒ first value of the domain
∴ f(0) = √0 = 0
∴ The minimum of f(x) is point (0 , 0)
∵ g(x) = √(x - 3) + 1
- Lets find the domain of the function
∵ x - 3 ≥ 0 ⇒ add 3 for both sides
∴ x ≥ 3
∴ The domain of the function is all real values of x ≥ 3
- We will use the first value of x to find the range of the function
∵ x = 3 ⇒ the first value of the domain
∴ g(3) = √(3 - 3) + 1 = 0 + 1 = 1
∴ The minimum of g(x) is point (3 , 1)
∵ h(x) = √(x + 1) - 2
- Lets find the domain of the function
∵ x + 1 ≥ 0 ⇒ subtract 1 for both sides
∴ x ≥ -1
∴ The domain of the function is all real values of x ≥ -1
- We will use the first value of x to find the range of the function
∵ x = -1 ⇒ the first value of the domain
∴ h(-1) = √(-1 + 1) - 2 = 0 - = -2
∴ The minimum of h(x) is point (-1 , -2)
* To find the correct answer look to the minimum points of the
functions (0 , 0) , (3 , 1) , (-1 , -2)
- The minimum of f(x) lies on the origin
- The minimum of g(x) lies in the 1st quadrant
- The minimum of h(x) lies in the 3rd quadrant
∴ The minimum of h(x) is farther left and down from the minimums
of f(x) and g(x)
- Look to the attached graph to more understand
- The red curve is f(x)
- The blue curve is g(x)
- The green curve is h(x)
Final answer:
The minimums of f(x) and g(x) are in the first quadrant, and h(x) is in the fourth quadrant, making the minimum of h(x) farther right and up from the minimums of f(x) and g(x).
Explanation:
To compare the relative locations of the minimums of the functions f(x) = √x, g(x) = √x - 3 + 1, and h(x) = √x + 1 - 2, we need to consider how transformations affect the graph of the square root function.
The function f(x) is the parent square root function. Its minimum is at the origin (0,0), which is in the first quadrant.
The function g(x) is a horizontal translation 3 units to the right and a vertical translation 1 unit up from the function f(x). Hence, its minimum would also be in the first quadrant.
The function h(x) is a horizontal translation 1 unit to the right and a vertical translation 2 units down from f(x), which places its minimum in the fourth quadrant because the downward translation moves it below the x-axis.
Thus, the correct statement is: 3. The minimum of h(x) is farther right and up from the minimums of f(x) and g(x).
The net of a storage box is shown. The outside surface of the box was painted green.
What is the area that was painted green?
Answers
When this net is assembled, it will form a box. To calculate the area of the outside surface, find the area of each section and add them together. The formula for area of a rectangle is A=lw:
A1=4(2)=8
A2=4(3)=12
A3=4(2)=8
A4=2(3)=6
A5=4(3)=12
A6=2(3)=6
8+12+8+6+12+6=52
The area that was painted green is 52cm2.
Hope this helps!!
2. What is the center and the radius of a circle given by the equation
x2 + y2 + 4x - 10y + 20 = 0?
A.(-2,5) and r=square root of 25
B.(2,-5) and r=square root of 20
C.(-2,5) and r=3
D.(2,-5) and r=3
Answers
Answer:
C
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given x² + y² + 4x - 10y + 20 = 0
Collect x and y terms and subtract 20 from both sides. that is
x² + 4x + y² - 10y = - 20
To obtain standard form use the method of completing the square
add ( half the coefficient of the x/y term )² to both sides
x² + 2(2)x + 4 + y² + 2(- 5)y + 25 = - 20 + 4 + 25
(x + 2)² + (y - 5)² = 9 ← in standard form
with centre = (- 2, 5) and r = [tex]\sqrt{9}[/tex] = 3 → C
By rearranging the given equation to match the standard form of circle equation, we can determine the center of the circle to be (-2,5), and the radius to be 3.
Explanation:The equation provided can be rewritten in the form (x - h)² + (y - k)² = r², wherein (h, k) denote the center coordinates of the circle, and r is the radius. To arrange it in this form, we group terms to complete the square for both x and y:
x² + 4x + y² - 10y = -20
⇒ (x² + 4x + 4) -4 + (y² - 10y + 25) - 25 = -20
⇒ (x + 2)² + (y - 5)² = 9
With this, we can identify the center of the circle to be at point (-2,5), and the radius is the square root of 9 which equals to 3. Hence, the correct answer is option C.
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PLEASE HELP! Which best describes the shape of this distribution?
skewed left
skewed right
uniform
normal
Answers
The term that best describes the distribution is uniform.
The distribution shown in the image appears to be uniform. The bars are relatively similar in height, indicating that all outcomes are equally likely or nearly so.
A distribution where most of the data points are concentrated on the right, with the tail extending to the left is said to be skewed. While A distribution where most of the data points are concentrated on the left, with the tail extending to the right is said to be skewed right. A symmetrical, bell-shaped distribution where most data points are concentrated around the mean, with fewer points as you move away from the center. is said to be normal.
Therefore, the term uniform best describes the given distribution in the image.
A dog and a cat are 200 meters apart when they see each other. The dog can run at a speed of 30 m/sec, while the cat can run at a speed of 24 m/sec.
a
How soon will they meet if they simultaneously start running towards each other?
Please help with this question! I need the answer by tomorrow. Thank you!
Answers
Answer:
The dog will catch the cat at 33.33 sec
Step-by-step explanation:
Let
x------> distance the cat runs before being caught by the dog,
Remember that
The speed is equal to divide the distance by the time
v=d/t
solve for t
t=d/v
so
equate the time
x/24=(200+x)/30
30x=24(200+x)
30x=4,800+24x
30x-24x=4,800
x=4,800/6=800 m
t=d/v=800/24=33.33 sec
or
t=(800+200)/30=1,000/30=33.33 sec
Answer:
3.(703)
Step-by-step explanation:
Find the missing length of the triangle.
Answers
Using the Pythagorean theorem the formula would look:
[tex]c^2=b^2+a^2\Longrightarrow3.4^2=3^2+a^2[/tex]
Now just solve for a.
[tex]a^2=3.4^2-3.0^2\Longrightarrow a=\sqrt{3.4^2-3.0^2} \\
a=\sqrt{11.56-9}=\sqrt{2.56}=\boxed{1.6}
[/tex]
Side a is 1.6 inches long.
Hope this helps.
r3t40
Find the slope of a line given the following points: (-1, 4) and (-5, 4). 0 1 4
Answers
Answer:
0
Step-by-step explanation:
The y-coordinates of the points are the same, so it is a horizontal line with a slope of 0.
___
slope = (change in y)/(change in x) = (4 -4)/(-5-(-1)) = 0/-4 = 0
ANSWER
0
EXPLANATION
The slope of a straight line is calculated using the formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
The given line passes through (-1,4) and (-5,4).
We substitute the points into the formula to get:
[tex]m = \frac{4 - 4}{ - 5 - - 1} [/tex]
[tex]m = \frac{4 - 4}{ - 5 + 1} [/tex]
This simplifies to:
[tex]m = \frac{0}{ - 4} [/tex]
Zero divided by any number is zero.
Therefore, the slope is:
[tex]m = 0[/tex]
What is .4 converted into a fraction?
Answers
4/10 or 2/5
Hope this helps!
Great Question!
First, 0.4 Is The Same Thing As 0.4/1
Next, Do 0.4/1 Multiplied By 10 And That Equals 4/10.
Finally, Simplify 2/5
In Conclusion, 0.4 Converted To A Fraction Is 2/5
Question 1 (Essay Worth 10 points)
(08.01 MC)
The graph shows two lines, A and B.
A graph is shown with x- and y-axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 2, 6 with the ordered pair 5, 0. Another straight line labeled B joins the ordered pair 0, 2 with the ordered pair 6, 6.
Part A: How many solutions does the pair of equations for lines A and B have? Explain your answer. (5 points)
Part B: What is the solution to the equations of lines A and B? Explain your answer. (5 points)
Answers
The pair of equations has one solution and the solution is (30/11, 20/11).
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
The coordinates on one line are (2, 6) and (5, 0)
Here, m=(0-6)/(5-2)
= -2
Substitute m=-2 and (2, 6) in y=mx+c, we get
6=-2(2)+c
c=10
So, the equation of a line is y=-2x+10 -----(i)
The coordinates on another line are (0, 2) and (6, 6)
Here, m= (6-2)/(6-0)
= 2/3
Substitute m=2/3 and (0, 2) in y=mx+c, we get
2=2/3(0)+c
c=0
So, the equation is y=2/3 x -----(ii)
Substitute equation (ii) in (i), we get
2/3 x=-2x+10
2x/3 +3x =10
11x=30
x=30/11
Substitute x=30/11 in equation (ii), we get
y =2/3 × 30/11
y= 20/11
So, the solution is (30/11, 20/11)
Therefore, the pair of equations has one solution and the solution is (30/11, 20/11).
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the two figures are similar. write the similarity. justify your answer.
Answers
Answer:
The corresponding sides are in proportion. so they are similar triangles.
The similarity statement is: Triangle ALB ~ Triangle EBR
Similarity statement:
Triangle ALB ~ Triangle EBR
Justification:
Two triangles are similar if they have the same shape, but different sizes. This means that the corresponding angles of the two triangles are equal, and the corresponding sides are proportional.
In the given image, we can see that the two triangles have the same shape. The corresponding angles are also equal:
Angle ALB = Angle EBR
Angle LAB = Angle EBE
Angle BAL = Angle BRE
To show that the corresponding sides are proportional, we can calculate the ratios of the corresponding sides:
AL/EB = 13/5 = 2.6
AB/ER = 15/36 = 5/12 = 0.417
BL/BR = 12/39 = 4/13 = 0.308
We can see that the ratios of the corresponding sides are all equal to 2.6. This means that the corresponding sides are proportional, and therefore the two triangles are similar.
Therefore, the similarity statement is: Triangle ALB ~ Triangle EBR
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Which function has real zeros at x = −10 and x = −6? f(x) = x2 + 16x + 60 f(x) = x2 − 16x + 60 f(x) = x2 + 4x + 60 f(x) = x2 − 4x + 60
Answers
Answer:
[tex]\large\boxed{f(x)=x^2+16x+60}[/tex]
Step-by-step explanation:
The factored form of a quadratic function:
[tex]f(x)=ax^2+bx+c=a(x-x_1)(x-x_2)[/tex]
x₁, x₂ - the zeros
We have x₁ = -10 and x₂ = -6.
Substitute:
[tex]f(x)=(x-(-10))(x-(-6))=(x+10)(x+6)[/tex]
Use FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex]f(x)=(x)(x)+(x)(6)+(10)(x)+(10)(6)\\\\f(x)=x^2+6x+10x+60\\\\f(x)=x^2+16x+60[/tex]
Answer:
Its A on edge
Step-by-step explanation:
2. What is the equation of the line parallel to the line whose
equation is 5y + 9 = -2x ?
[1] y=-2x +3 [2] y = 2x + 1
B] y = x+4
[4] y=-x-1
Answers
Step-by-step explanation:
Paralle lines have the same slope.
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have
[tex]5y+9=-2x[/tex]
Convert to the slope-intercept form:
[tex]5y+9=-2x[/tex] subtract 9 from both sides
[tex]5y=-2x-9[/tex] divide both sides by 5
[tex]y=-\dfrac{2}{5}x-\dfrac{9}{5}\to m=-\dfrac{2}{5}[/tex]
Each of the answers to choose from is not the line equation sought.
The equation:
[tex]y=-\dfrac{2}{5}x+b[/tex] where b is any real number.
Parallel lines share the same slope. The slope of the given line is -2/5, so none of the provided options are correct as none have this slope.
Explanation:To find the equation of a line that is parallel to another, it's important to know that parallel lines have the same slope. So firstly, we need to find the slope of the given equation. Starting with 5y + 9 = -2x, we will rearrange this into slope-intercept form (y = mx + b), where 'm' is slope and 'b' is y-intercept.
Subtract 9 from both sides to get 5y = -2x - 9.Divide every term by 5 to get y = -2/5x - 9/5.So, the slope of the given line is -2/5. This means a parallel line will also have the slope -2/5. Therefore, neither [1] y=-2x +3 nor [2] y = 2x + 1, [3] y = x+4 and [4] y=-x-1 can be parallel to the given line because all of them have different slopes not equal to -2/5.
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I need help with this math question. It is really hard.
What is 2x+20=100
Answers
The answer for this math equation is x = 40 or just 40
Step-by-step explanation: You just need to solve this problem in the normal algebraic equation format, applying the rules too.
2x + 20 = 100
2x + 20 - 20 = 100 - 20
2x = 80
2x/2 = 80/2
x = 40
Step 1: Bring 20 to the right side of the equation by subtracting 20 to both sides (subtraction is the opposite of addition and will cancel 20 from the left side and bring it over to the right)
2x + (20 - 20) = 100 - 20
2x + 0 = 80
2x = 80
Step 2: To isolate x divide 2 to both sides (division is the opposite of multiplication and will cancel 2 from the left side and bring it over to the right)
2x ÷ 2 = 80 ÷ 2
x = 40
Check (plug in 40 for x and solve it like normal):
2(40) + 20 = 100
80 + 20 = 100
100 = 100 --------------------------------------> Correct!
Hope this helped!
~Just a girl in love with Shawn Mendes
How to find a decimal equivalent to 39/50
Answers
Answer:
0.78
Step-by-step explanation:
The decimal equivalent to 39/50 is 0.78
Finding a decimal equivalent to 39/50from the question, we have the following parameters that can be used in our computation:
39/50
To find the decimal equivalent of 39/50, you can divide the numerator (39) by the denominator (50).
This can be done using long division
So, we have
0.78
50 | 39.00
| 350
-------
400
| 400
-------
Hence, the decimal equivalent to 39/50 is 0.78
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What is ittttt someone please help me
Answers
Answer:
3 choices for the first color, 2 choices for the second color, 1 choice for the third color.
3 × 2 × 1 = 6 different flags are possible.
What is the definition of net pay
Answers
It’s your pay after taxes and other expenses.
Answer:Net pay is the amount of pay remaining for issuance to an employee after deductions have been taken from the individual's gross pay. This is the amount paid to each employee on payday.
Step-by-step explanation:
hope it helps!
On a school
trip, the ratio of
teachers to pupils
is 2:11. If there are
132 pupils, how
on many teachers
o are there?
HELP PLEASE
Answers
Answer:
24
Step-by-step explanation:
132 pupils are represented by 11 parts of the ratio
Dividing 132 by 11 gives the value of one part of the ratio
132 ÷ 11 = 12 ← value of 1 part of the ratio, hence
2 parts = 2 × 12 = 24 ← number of teachers on trip
Answer:
24
Step-by-step:
132/11 (132 divide by 11)
=12
12*2 (12multiply by 2)
=24
What is the area of parallelagram ABCD
Answers
Answer:
The answer is 20 square units
Step-by-step explanation:
A=bh
A=5 times 4
A=20 units^2
Find the rectangular coordinates of the point (squareroot3, pi/6)
Answers
Answer:
The rectangular coordinates of the point are (3/2 , √3/2)
Step-by-step explanation:
* Lets study how to change from polar form to rectangular coordinates
- To convert from polar form (r , Ф) to rectangular coordinates (x , y)
use these rules
# x = r cos Ф
# y = r sin Ф
* Now lets solve the problem
∵ The point in the rectangular coordinates is (√3 , π/6)
∴ r = √3 and Ф = π/6
- Lets find the x-coordinates
∵ x = r cos Ф
∵ r = √3
∵ Ф = π/6
∴ x = √3 cos π/6
∵ cos π/6 = √3/2
∴ x = √3 (√3/2) = 3/2
* The x-coordinate of the point is 3/2
- Lets find the y-coordinates
∵ y = r sin Ф
∵ r = √3
∵ Ф = π/6
∴ y = √3 sin π/6
∵ sin π/6 = 1/2
∴ y = √3 (1/2) = √3/2
* The y-coordinate of the point is √3/2
∴ The rectangular coordinates of the point are (3/2 , √3/2)
Answer: B on edge
Step-by-step explanation:
A storehouse contains food for cows during the winter, when they cannot graze. Let y = 960/x, where x is the number of days and y is the number of cows the food will feed.
How many cows could be fed for 4 days?
How many cows could be fed for 12 days?
If farmer Bill has 85 cows, for how many days could he feed his herd and his neighbors herd of 35 cows?
Answers
a) 240 cows
b)80 cows
c) 8 days
Answer:
1) 240 cows.
2) 80 cows.
3) 8 days.
Step-by-step explanation:
1) To find the number of cows that could be fed for 4 days, you need to substitute [tex]x=4[/tex] into the equation, then:
[tex]y=\frac{960}{x}\\\\y=\frac{960}{4}\\\\y=240[/tex]
2) To find the number of cows that could be fed for 12 days, you need to substitute [tex]x=12[/tex] into the equation, then:
[tex]y=\frac{960}{x}\\\\y=\frac{960}{12}\\\\y=80[/tex]
3) Farmer Bill has two feed his 85 cows and 35 cows of his neighbors, then the total number of cows he needs to feed is:
[tex]y=85+35\\y=120[/tex]
Substitute this value into the equation and solve for "x" to find the number of days he could feed them:
[tex]120=\frac{960}{x}\\\\120x=960\\\\x=\frac{960}{120}\\\\x=8[/tex]
If m angle B=m angle D=41, find m angle C so that quadrilateral ABCD is a parallelogram
Answers
ANSWER
139°
EXPLANATION
One of the interior angle properties of a parallelogram is that adjacent interior angles are supplementary.
This means that, the adjacent interior angles add up to 180°.
If
[tex]m \angle \: B = m \angle \: D = 41[/tex]
Then
[tex]m \angle \: C + m \angle \: D = 180 \degree[/tex]
OR
[tex]m \angle \: B + m \angle \:C= 180 \degree[/tex]
[tex] \implies41 \degree + m \angle \:C= 180 \degree[/tex]
[tex]\implies m\angle \:C= 180 \degree - 41 \degree = 139 \degree[/tex]
Answer:
193
Step-by-step explanation:
Find the height of the cone when the volume=300(pie) and the radius is 12
Answers
Answer:
The height of this cone is
[tex]\displaystyle \frac{25}{4}[/tex],
which is the same as 6.25 in decimals.
Step-by-step explanation:
Consider the formula for the volume [tex]V[/tex] of a cone:
[tex]\displaystyle V = \frac{1}{3} \pi\cdot r^{2}\cdot h[/tex],
where
[tex]r[/tex] is the radius of the base of the cone, and[tex]h[/tex] is the height of the cone.For this cone,
[tex]V = 300\;\pi[/tex],[tex]r = 12[/tex], and[tex]h[/tex] is to be found.Rearrange the equation to find the height of this cone.
[tex]\displaystyle V = \frac{1}{3} \pi\cdot r^{2}\cdot h[/tex],
[tex]3\;V = \pi \cdot r^{2}\cdot h[/tex],
[tex]\displaystyle \frac{3\;V}{\pi\cdot r^{2}} = h[/tex].
Therefore,
[tex]h = \displaystyle \frac{3\;V}{\pi\cdot r^{2}} = \frac{3\times 300\;\pi}{{12}^{2}\; \pi} = \frac{25}{4} = 6.25[/tex].
answer the question in the picture.
Answers
Answer: 6
Remember: 0.3 repeated = [tex]\frac{1}{3}[/tex]
[tex]3 \frac{2}{3} + 2 \frac{1}{3} = 5\frac{3}{3}\\\\5\frac{3}{3} = 6[/tex]
Answer:
6
Step-by-step explanation:
2.333... = 7/3
3 and 2/3 = 11/3
7/3 + 11/3 = 18/3 = 6
Francine has $4.35 in dimes and quarters. The number of dimes is five more than the number of quarters. How many of each coin does she have?
Answers
344676 I hope that helps
Answer:
Franchise has 11 quarters and 16 dimes.
Step-by-step explanation:
Let d represent number of dimes and q represent number of quarters.
We have been given that the number of dimes is five more than the number of quarters. We can represent this information in an equation as:
[tex]d=q+5...(1)[/tex]
We are also told that Francine has $4.35 in dimes and quarters. We can represent this information in an equation as:
[tex]0.10d+0.25q=4.35...(2)[/tex]
Now, we will substitution method to solve linear equations. Upon substituting equation (1) in equation (2), we will get:
[tex]0.10(q+5)+0.25q=4.35[/tex]
[tex]0.10q+0.50+0.25q=4.35[/tex]
[tex]0.35q+0.50=4.35[/tex]
[tex]0.35q+0.50-0.50=4.35-0.50[/tex]
[tex]0.35q=3.85[/tex]
[tex]\frac{0.35q}{0.35}=\frac{3.85}{0.35}[/tex]
[tex]q=11[/tex]
Therefore, Franchise has 11 quarters.
Upon substituting [tex]q=11[/tex] in equation (1), we will get:
[tex]d=11+5[/tex]
[tex]d=16[/tex]
Therefore, Franchise has 16 dimes.