The graph shows f(x). The absolute value function g(x) is described in the table.


The graph shows a v-shaped graph, labeled f of x, with a vertex at 0 comma 1, a point at negative 1 comma 2, and a point at 1 comma 2.
x g(x)
−4 0
−2 −2
0 −4
2 −2
4 0

If g(x) = f(x) + k, what is the value of k?
k = −5
k = −4
k = 4
k = 5

Answers

Answer 1

The value of k given the absolute value functions is (a) k = -5


Calculating the value of k

Given that

graph = f(x)

table = g(x)

Since the vertex of the function f(x) is at (0,1), we have f(0) = 1.

Also, from the given table, we have g(0) = -4.

Therefore, if g(x) = f(x) + k, we must have g(0) = f(0) + k = 1 + k.

But we also know that g(0) = -4. Thus, we have:

1 + k = -4

Solving for k, we get:

k = -5

Therefore, the value of k is -5.

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Related Questions

Solve for x in the equation 2x + 3 > 11

Answers

Hi !

[tex]2x + 3 > 11\\\iff 2x > 8\\\iff x > \frac{8}{2}\\ \iff x > 4[/tex]

Have a nice day ;)

Answer:

x > 4

Isolate the variable by dividing each side by the factors that don't contain the variable

7x-y=2. -21x-3y=5 por metodo de reduccion

Answers

The solution to the system of equations is:

x = -1/42

y = -11/6

What you understand by variables?

In mathematics, a variable is a symbol that represents a value that can vary or change. It is often represented by a letter, such as x, y, or z. Variables are used to write algebraic expressions and equations that can be solved to find unknown quantities. The value of a variable can be determined by solving an equation that involves the variable, or by assigning a specific value to the variable. In algebra,

To solve this system of equations by the method of elimination, we need to eliminate one of the variables by adding the two equations together. We can do this by multiplying the first equation by 3, which will make the y terms cancel out when we add the equations:

7x - y = 2 (multiply by 3)

-21x - 3y = 5

21x - 3y = 6 (first equation multiplied by 3)

-21x - 3y = 5

Now we can add the two equations together:

(21x - 3y) + (-21x - 3y) = 6 + 5

0x - 6y = 11

Simplifying, we get:

-6y = 11

Dividing both sides by -6, we get:

y = -11/6

Now that we have solved for y, we can substitute this value back into either equation to solve for x. Let's use the first equation:

7x - y = 2

7x - (-11/6) = 2

Multiplying both sides by 6 to eliminate the fraction, we get:

42x + 11 = 12

Subtracting 11 from both sides, we get:

42x = -1

Dividing both sides by 42, we get:

x = -1/42

Therefore, the solution to the system of equations is:

x = -1/42

y = -11/6

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Solid A and solid B are similar.
The ratio of the volume of solid A to the volume of solid B is 27:1000
The surface area of solid A is 810 cm²
Calculate the surface area of solid B.

Answers

The surface area of solid B is 9000 cm².

What is ratio?

A ratio is a comparison of two quantities or values, often expressed as a fraction. Ratios can be used to express the relationship between two or more quantities.

Since solids A and B are similar, their corresponding linear dimensions are proportional. Let the scale factor be k, such that the dimensions of solid A are k times larger than the corresponding dimensions of solid B.

The ratio of their volumes is given as 27:1000. Therefore:

(volume of A) / (volume of B) = 27/1000

Let the volume of solid B be V. Then the volume of solid A is (27/1000)V.

Since the surface area of a solid is proportional to the square of its linear dimensions, we have:

[tex]$\frac{surface\ area\ of\ A}{surface\ area\ of\ B} = \frac{k_{A}^{2}}{k_{B}^{2}}$[/tex]

where kA and kB are the linear dimensions of solids A and B respectively.

Since the solids are similar, we can write:

[tex]$k_{A} / k_{B} = \frac{(volume\ of\ A)^{\frac{1}{3}}}{(volume\ of\ B)^{\frac{1}{3}}}$[/tex]

kA / kB = (volume of A)^(1/3) / (volume of B)^(1/3)

Substituting the given volume ratio and solving for kA / kB, we get:

[tex]$k_A/k_B = \left(\frac{27}{1000}\right)^{1/3} = 0.3$[/tex][tex]$k_A/k_B = \left(\frac{27}{1000}\right)^{1/3} = 0.3$[/tex]

Therefore, kA = 0.3 kB.

Now we can substitute the given surface area of solid A and solve for the surface area of solid B:

(surface area of A) / (surface area of B) = (kA)² / (kB)²

810 / (surface area of B) = 0.3²

(surface area of B) = 810 / 0.09

(surface area of B) = 9000 cm²

Therefore, the surface area of solid B is 9000 cm².

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Prove that
sin0/(sec 0+tan 0-1)+cos0/ (cosec 0+ cot 0-1)=1​

Answers

Answer:

Prove the following identitics: tan 0 + cot 0 = I/(sin 0 cos 0) 0 + tan 0 sec 0 = cosec 0 'sec? 0. 18 cosec = cosec? 0 = tan? 0 cot2 19 sec? 0 sin ' 0 =cos? 0 'sin? 20 cos4 (sec 0 + tan 0) (sec 0 _ tan 0) = 1 2 sin? 0 = cOs? 0 _ 'sin? 0. 22 2 cos? 0_I=1 23 sec? 0 + cosec 0 = sec? 0 cosec? sin? , COs? 24 sec" 0 cosec" 0 = cos 0 sin" 0 25 =I tan 0 + 1 cot? 0 +4 26 (sec? 0 1) (cosec? 0 1) = [ 27 ((sec? 0 _0)+ V(cosec" 0 _ !) = sec € cosec 0 28 (sec? tan? 0) + V(cosec? 0 ~ cot? 0) = 2 cos? 0 29 =1 sin sec? 0 _ 1 sec 0 cosec 0 tan 0 + cot 0 30 tan 0 cot 0 sec 0 + cosec 0 cos 0 sin 0 31 =l V( + tan? 0) V( + cot? 0) Eliminate 0 from the following equations: 32 x = 4 cos 0, y = b sin 0. 33 x = 4 cot 0,y = b cosec 0. 34 x=a tan 0,y =b cos 0. 35 x = ] sin 0, y = [ + cos 0, 36 x =a sec 0,y = b +c cos 0. 37 x=a cosec 0, y = b sec 0. 38 X=l+ tan 0,y = cos 0. 39 x=sin 0 + cos 0,y = sin 0 40 cos X = sCc 0 + tan 0, y = sCc 0 ~ tan 0.

Rita’s adding 3+ -8+1 Siri writes the expression is 3+-1+8 what is Rita’s error

Answers

Answer: 3+(-8+1) or 3+-8+1

Step-by-step explanation: Rita rewrote the equation so instead of it being negative 8 it is negative 1.

ph,
ructure.com/courses/3695486/quizzes/10149308/take
D
Question 7
O 500
An ice cream factory makes 200 quarts of ice cream in 10 hours. How many quarts could be made
in 36 hours?
O 720
360
9
620

Answers

The ice cream factory could make 720 quarts of ice cream in 36 hours.

How many quarts could be made in 36 hours?

We can use a proportion to solve this problem:

quarts / hours = constant rate of production

Let x be the number of quarts that could be made in 36 hours. Then we have:

200 quarts / 10 hours = x quarts / 36 hours

Cross-multiplying, we get:

10x = 200 * 36

Simplifying, we get:

10x = 7200

Dividing both sides by 10, we get:

x = 720

Therefore, the ice cream factory could make 720 quarts of ice cream in 36 hours.

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Can someone show me step by step correctly for a better grade
There are approximately 7.48 liquid gallons in a cubic foot. If a cylindrical water tank holds 1,100 liquid gallons and has a radius of 3.2 feet, what is the approximate height of the water tank? Approximate using π = 3.14 and round to the nearest tenth.

4.6 feet

14.4 feet

46.0 feet

147.1 feet

Answers

The height of the cylindrical water tank is 4.6 feet. Therefore, the answer is A.

How to find the height of the water tank?

The cylindrical water tank holds 1,100 liquid gallons and has a radius of 3.2 feet.

Therefore, the height of the tank can be calculated as follows:

7.48 liquid gallons = 1 ft³

1100 liquid gallons = ?

cross multiply

volume of the tank = 1100 / 7.48 = 147.058823529 ft³

Therefore, let's find the volume of the cylindrical tank.

volume of the cylindrical tank = πr²h

where

r = radiush = height

Therefore,

r = 3.2 feet

h = ?

The volume of the cylindrical tank in feet cube is 147.058823529 ft³

Let's find the height, h

volume of the cylindrical tank = 3.14 × 3.2² × h

147.058823529 = 3.14 × 10.24 × h

32.1536h = 147.058823529

divide both sides by 32.1536

h = 147.058823529 / 32.1536

h = 4.57363405653

Therefore,

height of the water tank = 4.6 feet

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find fy , the y-component of force that the wall exerts on the beam ( f ), using the axis shown. remember to pay attention to the direction that the wall exerts the force.

Answers

The y-component of the force that the wall exerts on the beam (f) is -400.5 N.

The y-component of the force that the wall exerts on the beam (f) can be found using the following steps:

Step 1: Calculate the magnitude of the force (f):

f = √[f_x² + f_y²]

f = √[(-500 N)² + (-300 N)²]

f = 600 N

Step 2: Calculate the angle of the force relative to the y-axis:

θ = tan-1(-300 N/500 N)

θ = -53.13°

Step 3: Calculate the y-component of the force (fy):

fy = f × sin(θ)

fy = 600 N × sin(-53.13°)

fy = -400.5 N

Therefore, the y-component of the force that the wall exerts on the beam (f) is -400.5 N.

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Please could you help its due tommorow

Answers

Answer:

x = 52.5

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360.

2x+100 +95+60 = 360

Combine like terms.

2x+255=360

Subtract 255 from each side

2x+255-255= 360-255

2x = 105

Divide each side by 2

2x/2 = 105/2

x = 52.5

Answer:

x = 52.5

Step-by-step explanation:

The sum of the interior angles of a quadrilateral is 360°.

Accordingly, let us find the value of x.

2x + 100 + 95 + 60 = 360

2x + 255 = 360

Subtract 255 from both sides.

2x = 360 - 255

2x = 105

Divide both sides by 2.

x = 52.5

2. Given: MNOP is a rectangle.
Show: The diagonals bisect each other, and the diagonals are congruent.
M
-5
N

Answers

The answer of the given question based on the rectangle is , The MNOP congruence is shown by  Side-Angle-Side (SAS) and the steps are given below.

What is Diagonal?

In geometry, a diagonal is a straight line that connects two non-adjacent vertices of a polygon or a polyhedron. In other words, a diagonal is a line segment that joins two corners or vertices of a shape that are not next to each other. For example, in a rectangle, the diagonals are the line segments that connect opposite corners of the rectangle.

To show that the diagonals of a rectangle bisect each other and are congruent, we can use the following steps:

Draw the diagonal MO and the diagonal NP.Since MNOP is a rectangle, we know that angles M and N, as well as angles O and P, are right angles. Therefore, we have four right triangles: triangle MNO, triangle NOP, triangle OPM, and triangle PMN.Since each of these triangles shares side OP, we can use the Side-Angle-Side (SAS) congruence criterion to show that triangles MNO and OPM are congruent, and triangles NOP and PMN are congruent.Since these triangles are congruent, we know that their corresponding sides are congruent. In particular, we know that segment MP is congruent to segment NO.Since MO and NP intersect at point Q, we know that Q is the midpoint of both segments MO and NP. Therefore, the diagonals of rectangle MNOP bisect each other.

Therefore, we have shown that the diagonals of a rectangle bisect each other and are congruent.

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A figure which has a sphare and cylinder. The total height of figure is 102mm and the height of cylinder is 76mm. Find Volume and Surface Area of the figure

Answers

The volume of the figure is approximately 50101mm^3 and the surface area is approximately 8253mm^2.

The figure consists of a sphere and a cylinder. We can find the volume and surface area of the figure by calculating the volume and surface area of each component separately and adding them together.

The height of the cylinder is given as 76mm, which means the remaining height of the figure must be occupied by the sphere. Thus, the radius of the sphere can be calculated as half the difference between the total height of the figure and the height of the cylinder:

Radius of sphere = (102mm - 76mm)/2 = 13mm

Now we can calculate the volume and surface area of each component:

Volume of cylinder = πr^2h = π(13mm)^2(76mm) ≈ 40899mm^3

Surface area of cylinder = 2πrh + 2πr^2 = 2π(13mm)(76mm) + 2π(13mm)^2 ≈ 6128mm^2

Volume of sphere = (4/3)πr^3 = (4/3)π(13mm)^3 ≈ 9202mm^3

Surface area of sphere = 4πr^2 = 4π(13mm)^2 ≈ 2125mm^2

Finally, we can find the total volume and surface area of the figure by adding the values for the cylinder and sphere:

Total volume = Volume of cylinder + Volume of sphere ≈ 50101mm^3

Total surface area = Surface area of cylinder + Surface area of sphere ≈ 8253mm^2

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The circumference of a circle is 7(pie)cm. What is the area, in square centimeters?
Express your answer in terms of TT(pie).

Answers

Let’s begin by writing our area formula for pie : A=R^2.
Let’s now divide our circumference by 2, because our radius is half of our diameter.
7 divided by 2 is 3.5.
Now, let’s plug in our formula. A= 3.5^2
3.5 x 3.5 = 12.25
Add your pie symbol and 12.25cm pie is your answer.

Can someone please help me on this?

Answers

Answer: angle(s) A on the left.

Step-by-step explanation:

Complementary angles are angles whose sum equals 90, which is a righ angle (forms a corner)

To landscape his 70 ft by 60 ft backyard, Austin is planning first to put down a 4 inch layer of topsoil. He can buy bags of topsoil at $2.50 per 3-ft3 bag, with free delivery. Or he
can buy bulk topsoil for $22.00/yd, plus a $20 delivery fee. Which option is less expensive?
I need volume of soil, cost of bags and cost of bulk

Answers

Answer:

To calculate the volume of soil needed, we first convert the dimensions of the backyard to feet:

Length = 70 ft

Width = 60 ft

Depth = 4 in = 4/12 ft = 1/3 ft

Volume = Length x Width x Depth

Volume = 70 ft x 60 ft x (1/3) ft

Volume = 1400 ft³

Option 1: Bags of topsoil

Each bag of topsoil contains 3 ft³ of soil, so the number of bags needed is:

Number of bags = Volume / Bag size

Number of bags = 1400 ft³ / 3 ft³ per bag

Number of bags = 467 bags

The total cost of bags of topsoil is:

Cost = Number of bags x Cost per bag

Cost = 467 bags x $2.50 per bag

Cost = $1167.50

Option 2: Bulk topsoil

The volume of topsoil needed is 1400 ft³, which is equivalent to:

Volume = 1400 ft³ / 27 ft³ per yd³

Volume = 51.85 yd³ (rounded to two decimal places)

The cost of bulk topsoil is:

Cost = Volume x Cost per yd³ + Delivery fee

Cost = 51.85 yd³ x $22.00 per yd³ + $20.00 delivery fee

Cost = $1153.70

Therefore, buying bulk topsoil is less expensive than buying bags of topsoil. The cost of bulk topsoil is $1153.70, while the cost of bags of topsoil is $1167.50

Answer:

Bulk is less expensive

Step-by-step explanation:

First convert inches to feet:  4 in x 1 ft/12 in =0.333 ft

Volume of topsoil needed = 70 x 60 x 0.333 = 1400 ft³

Bagged topsoil:   1400 ft³ x $2.50/3 ft³ = $1166.67

Bulk: 1400 ft³ x 1 yd³/27 ft³ x $22.00/yd³ + $20 = $1160.74

Bulk is just a little cheaper

The function y=5. 45+1. 05(x+7) can be used to determine the cost in dollars for a prepaid cell phone plan of x minutes​ What is the rate of change with respect to the number of minutes purchased

Answers

According to the function, the rate of change with respect to the number of minutes purchased is $1.05 per minute.

The function given in the problem is y = 5.45 + 1.05(x + 7), where y represents the cost in dollars for a prepaid cell phone plan of x minutes. This means that if you want to know how much it will cost to purchase a certain number of minutes, you can simply plug in that number for x and the equation will give you the corresponding cost in dollars.

Now, the rate of change with respect to the number of minutes purchased is also known as the slope of the function. This tells us how much the cost will change for each additional minute purchased. To find the slope, we need to take the derivative of the function with respect to x.

The derivative of y with respect to x is given by:

dy/dx = 1.05

This means that for each additional minute purchased, the cost will increase by $1.05.

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Please solve number 7 I do not understand it at all. Please and thank you so much.

Answers

The equation of the largest circle is given as follows:

x² + y² = 9².

What is the equation of a circle?

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.

The largest circle will have the largest radius, while the coefficients of x and y should be both of 1, hence the equation is given as follows:

x² + y² = 9².

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What is the value of x in the equation 2x + 3 = 11?

Answers

Answer: x=4

Step-by-step explanation:

Isolate x using opposite operations.

2x + 3 = 11

2x = 8

x = 4

Answer:

4

Step-by-step explanation:

subract 3 from 11

2x=8

divide by 2

x=4

Which question requires gathering numerical data?
A
What are my favorite TV shows?
B.
How many goldfish are in the pet store?
What breeds of dogs are in the dog show?
D. What are the seven tallest mountains in the world?

Answers

it’s the best day for the new generation and it’s not a big day

How do you find the legs of a 45-45-90 triangle if you know the length of the hypotenuse?

Answers

Each leg of the triangle has a length of 5√(2) units

Since the triangle is 45-45-90, each of the two legs has the same length, which we'll call x. By the Pythagorean theorem, we know that:

x² + x² = h²

Simplifying this equation, we get:

2x² = h²

To solve for x, we can divide both sides by 2 and then take the square root:

x = h / √(2)

This tells us that each leg of a 45-45-90 triangle is equal to the hypotenuse divided by the square root of 2.

Let's say you have a 45-45-90 triangle with a hypotenuse of length 10. To find the length of each leg, you would use the formula:

x = h / √(2)

Substituting h = 10, we get:

x = 10 / √(2)

To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √(2):

x = (10 / √(2)) * (√(2) / √(2))

= 10√(2) / 2

= 5√(2)

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What is the slope of (1,9) and (-1,6)

Answers

Answer: the slope of line = y2-y1÷x2-x1

Step-by-step explanation:x1=1 x2=-1 y1=9 y2=6

                                              slope=(6-9)÷(-1-1)

                                               slope= (-3)÷(-2)

                                                answer= 3

                                                               2

The rainfall in a town, measured in inches over the last 7 days has been: 1 , 3 , 0 , 2 , 2 , 1 , 3 Find the median rainfall.

Answers

Answer: 2

Step-by-step explanation:  0 1 1 2 2 3 3  order

011 2 middle one  233

What is the area of this square?

Answers

Answer: 81mi^2

Step-by-step explanation:

Area Formula for Square: side * side

9*9 = 81

In the equation A = P(1 + r)t, A is the total amount, P is the principal amount, r is the annual interest rate,and t is the time in years. Which statement correctly relates information regarding the annual interestrate for each given equation?
(A) For A = P(1.025), the principal amount of money is increasing at a 25% interest rate.
(B) For A = P(1.0052), the principal amount of money is increasing at a 52% interest rate.
(C) For A = P(0.86)t, the principal amount of money is decreasing at a 14% interest rate.
(D) For A = P(0.68)t, the principal amount of money is decreasing at a 68% interest rate.

Answers

The correct statement regarding the annual interest rate for the given equations is (A) For A = P(1.025), the principal amount of money is increasing at a 2.5% interest rate.

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=).

In the equation A = P(1 + r)t, the annual interest rate is represented by the variable "r". It is not correct to directly interpret the value of (1 + r) as the interest rate, as it represents the factor by which the principal amount is multiplied over time to yield the total amount.

Let's analyze each given equation to see which statement correctly relates information regarding the annual interest rate:

(A) For A = P(1.025), the equation does not have a term for time (t), so it cannot represent the growth of a principal amount over time. It simply represents the total amount (A) as 102.5% of the principal amount (P), which means that the interest rate is 2.5% per year.

(B) For A = P(1.0052), similar to the previous equation, this equation does not have a term for time (t), so it cannot represent the growth of a principal amount over time. It simply represents the total amount (A) as 100.52% of the principal amount (P), which means that the interest rate is 0.52% per year.

(C) For A = P(0.86)t, the value of (0.86) represents the factor by which the principal amount is multiplied over time to yield the total amount. Since (0.86) is less than 1, it means that the principal amount is decreasing over time, not increasing. The interest rate in this case is -14% per year (negative because the principal amount is decreasing).

(D) For A = P(0.68)t, similar to the previous equation, the value of (0.68) represents the factor by which the principal amount is multiplied over time to yield the total amount. Since (0.68) is less than 1, it means that the principal amount is decreasing over time, not increasing. The interest rate in this case is -32% per year (negative because the principal amount is decreasing).

Therefore, the correct statement regarding the annual interest rate for the given equations is:

(A) For A = P(1.025), the principal amount of money is increasing at a 2.5% interest rate.

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What is the value of x when -3x + 7x = -12?
A -6/5
B -3
C 6/5
D 4/7
E 3
I NEED AN ANSWER ASAP!

Answers

Answer is B. -3

Explanation:

-3x + 7x = -12

1) Collect like terms

4x = -12

2) Divide both sides 4

3) The answer

x= -3

Find the volume of a cone that has a height of 9 inches and a diameter of 12 inches. Use 3. 14 for pi and round to the nearest tenth

Answers

The volume of the cone with height of 9 inches and a diameter of 12 inches is approximately 339.3 cubic inches.

To find the volume of a cone, we need to use the formula V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone.

Since the diameter of the cone is given as 12 inches, we can find the radius as half of the diameter, which is 6 inches. The height of the cone is given as 9 inches.

Now, we can substitute the values of r and h in the formula to get the volume as follows

V = (1/3)πr^2h

= (1/3)×3.14×6^2×9

= 339.12 cubic inches (rounded to the nearest tenth)

Therefore, the volume of the given cone is approximately 339.1 cubic inches.

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through ten games of basketball this season, jevonte has made 7 out of 8 of his free-throws. which word or phrase describes the probability that jevonte will hit his next free throw?

Answers

The probability that Jevonte will hit his next free throw is "likely" or "high".

Since Jevonte has made 7 out of 8 of his free throws so far, he has a success rate of 87.5%, which is quite high. Therefore, it is reasonable to expect that he will continue to make his free throws at a similar rate, making it likely that he will hit his next free throw.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. A probability of 0.5 (or 50%) means the event is just as likely to occur as it is not to occur. Probability is used extensively in fields such as mathematics, statistics, physics, engineering, economics, and many other areas to model and analyze uncertain events or situations.

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Time plots are special scatterplots where the explanatory variable, x, is a measure of time

Answers

The statement " Time plots are special scatterplots where the explanatory variable, x, is a measure of time" is true because time plots are scatterplots where the x-axis represents time, and they are commonly used to visualize trends and patterns in time series data.

A time plot is a type of scatterplot where the x-axis represents time and the y-axis represents a response variable. Time plots are useful for displaying data that change over time and can reveal trends, patterns, and seasonality in the data. They are commonly used in fields such as economics, finance, and social sciences to analyze time series data.

By visualizing data over time, time plots can help to identify relationships, outliers, and potential forecasting models. Overall, time plots are a powerful tool for analyzing and understanding trends and patterns in time series data.

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The given question is incomplete, the complete question is:

Time plots are special scatterplots where the explanatory variable, x, is a measure of time. True or false

(I NEED THIS ASAP)

3. Select all the transformations that produce congruent images.

(A.) dilation
(B.) horizontal stretch
(C.) reflection
(D.) rotation
(E.) translation

Answers

(C.) reflection and (D.) rotation produce congruent images.

What three transformations are congruent?

We can generate congruent shapes by combining the three types of transformations: rotations, reflections, and translations. Actually, using a combination of one or more of these three transformations, any pairs of congruent shapes can be matched to one another.

(A) Dilation, (B) horizontal stretch, and (E) translation do not produce congruent images because they change the size, shape, and/or orientation of the original object.

(C) Reflection produces congruent images because the resulting image is a mirror image of the original object, and therefore has the same size and shape.

(D) Rotation produces congruent images because the resulting image is the same shape and size as the original object, just rotated to a different orientation.

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ASAP PLEASE!

1.

Triangle D has been dilated to create triangle D′. Use the image to answer the question.

image of a triangle labeled D with side lengths of 3.8, 4.8, 4.2 and a second triangle labeled D prime with side lengths of x, 2.4, 2.1

Determine the scale factor used.

one half
2
one fourth
3

2.

Question 4(Multiple Choice Worth 2 points)
(Dilations MC)

Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−9, −9), B(9, 9), C(0, 9). Determine the scale factor used.

6
one sixth
3
one third

Answers

The first option, "one half," corresponds to the scale factor of 0.5.

How to find the scale factor?

Scale factor = Dimensions of the new shape Dimensions of the original shape is the fundamental formula used to calculate it. The formula is expressed as Scale factor = Larger image dimensions Smaller figure dimensions in the event that the original figure is enlarged.

We can contrast the side lengths of triangles D and D′ to determine the scaling factor.

Let's contrast the side lengths for the two triangles.

Triangle D has sides that are 4.2 in length, and triangle D′ has sides that are 2.1 in length.

Scale factor = (Side length of triangle D′) / (Side length of triangle D)

Scale factor = 2.1 / 4.2

Scale factor = 0.5

The first option, "one half," corresponds to the scale factor of 0.5.

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The time $t$t​ (in seconds) it takes a dropped object to fall h$h$h​ feet is given by t is equal to square root of h over 16 end root$t=\sqrt{\frac{h}{16}}$t=√
h
16​​ .

A building of height 55 feet.
a. Estimate how long it takes an earring to hit the ground when it falls from the roof of the building. Round your answer to the nearest hundredth.

about ____ seconds

b. Estimate how much sooner the earring hits the ground when it is dropped from two stories (22 feet) below the roof. Round your answer to the nearest hundredth.

about seconds

Answers

a. About 3.01 seconds.b. The earring hits the ground about 0.69 seconds sooner when dropped from two stories below the roof.
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