Which choice could be used in proving that the given triangles are similar?

Oscar and Eli can sell 368 1-cup servings of lemonade because there are 16 cups in 1 gallon, and they have 23 gallons of lemonade.

Oscar and Eli have prepared 23 gallons of lemonade and want to know how many 1-cup servings they can sell. First, we need to know the equivalent of gallons to cups. There are 16 cups in 1 gallon. Therefore, we multiply 23 gallons by 16 cups per gallon to find the total number of cups available:

23 gallons x 16 cups/gallon = 368 cups. Thus, they can sell 368 1-cup servings of lemonade.

To summarize the conversion:

1. Identify the conversion rate between gallons and cups (1 gallon = 16 cups).

2. Multiply the total gallons of lemonade by the conversion rate to get the total cups (23 gallons x 16 cups/gallon).

Answer:

residual = - 4

Step-by-step explanation:

The residual is the difference between the actual mass of the falcon chick and the mass our regression line would have predicted.

residual = actual mass - predicted mass

actual mass = 29 grams

The predicted mass of 40 mm breadth of egg can be calculated by using the regression equation Danila came up with.

predicted mass

y = -47 + 2(40)

y = -47 + 80

y = 33 grams

residual = actual mass - predicted mass

residual =  29 - 33

residual = - 4

Answer:

-4

Step-by-step explanation:

trust me.

Answer:

it would be A and C because they are the lowest

Step-by-step explanation:

The correct option is C

Percentage point : It is defined as a unit for the arithmetic difference of two percentages and greater the difference more will be the error range.

So, the most reliable error range is the one whose percentage point is minimum.

Now, among the provided options , 2 percentage points is minimum so it will be the most reliable error range.

Hence, Option C. 2 percentage points is correct

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Answer:

7 units

Step-by-step explanation:

use the distnce formula to get the riangles legs, multiply them and divide by two

Given:

The diameter of the cylinder = 34 m

So, the radius (r) = 17 m

The height (h) of the cylinder = 12 m

The slant height (l) of the cone = 20 m

To find the surface area of the given figure.

Surface area of the given fig = surface area of cylinder + surface area of the cone

Formula:

The surface area of the cylinder is [tex]2 \pi r(r+h)[/tex]

The surface area of the cone is [tex]\pi rs[/tex]

Now,

The surface area of the cylinder is given by

[tex]SA=2 \pi 17(17+12)[/tex]

     [tex]=2 \pi 17(29)[/tex]

     [tex]=2 \pi (493)[/tex]

[tex]SA=986 \pi[/tex]

The surface area of the cylinder is 986π m²

The surface area of the cone is given by

[tex]SA=\pi rs[/tex]

[tex]SA=\pi (17)(20)[/tex]

     [tex]=340 \pi[/tex]

Thus, the surface area of the cone is 340π m²

The surface area of the composite figure is given by

Surface area = Surface area of cylinder + Surface area of cone

Substituting the values, we get;

[tex]SA=986\pi +340 \pi=1326 \pi \ m^2[/tex]

Thus, the surface area of the composite figure is 1326π m²

Answer:

72 feet

Step-by-step explanation:

This is an example of a regular hexagon. A hexagon is  a polygon that has 6 sides. It is regular because all the sides are equal.

Perimeter of a Regular Hexagon=6l

Length of one side, l=12 feet

Therefore:

Perimeter of the deck = 6 X 12 =72 feet

Answer:

y = 4[tex](9)^{x}[/tex]

Step-by-step explanation:

Using the given points to find a and b

Using (0, 4), then

4 = a[tex]b^{0}[/tex] ⇒ a = 4, thus

y = 4[tex]b^{x}[/tex]

Using (3, 2916), then

2916 = 4 b³ ( divide both sides by 4 )

729 = b³ ( take the cube root of both sides )

b = [tex]\sqrt[3]{729}[/tex] = 9

Thus

y = 4 [tex]9^{x}[/tex] ← is the exponential function

Answer: 72 in

Step-by-step explanation:

If the area is 96 inches the it would be 72

Answer:

67

Step-by-step explanation:

A linear pair is two angles which form a straight angle when combined (or 180 degrees). Thus do 180 - 113 to get 67 degrees for Angle 2

The measure of angle 2 is 67°.

It is required to find the measure of angle 2.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.

Given :

<1=113°

We know that

A linear pair adds to 180 degrees.

<1 + <2 =180°

113°+ <2 = 180°

<2 = 180°-113°

<2 =67°

Hence, the measure of angle 2 is 67°.

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Answer: a line parallel to one side of a triangle divides the other two sides proportionally. you’re welcome :)

The range of the function y=|x-1|+7 is all real numbers greater than or equal to 7, as the absolute value ensures non-negative values to which 7 is added.

The range of the function y=|x-1|+7 can be determined by analyzing the nature of the absolute value function and the constant term. The absolute value function, |x-1|, ensures that the output is always non-negative for any value of x, since it represents the distance from 1 on the number line, which cannot be negative. Therefore, when we add 7 to this non-negative value, the smallest value y can take is when |x-1|=0, which is when x=1. So, at x=1, y will be 7 since we have 0+7. For any other value of x, |x-1| will be positive, and when adding 7, y will be greater than 7. Hence, the range of y is all values greater than or equal to 7.

The other root is 1, and the correct answer is: c. 1

The quadratic equation [tex]x^2 - 3x + a = 0[/tex] has two roots, and given that one of the roots is 2, we can use the fact that the sum of the roots is equal to the coefficient of the linear term (-b/a).  

In this case, the linear term is −3x, so the sum of the roots is 3. Since we know one root is 2, the other root must be such that when added to 2, the sum equals 3.

Therefore, the other root is 3 − 2 = 1.

This demonstrates the application of the sum of roots formula in solving for the other root when one root is known. Hence, the correct answer is 1, which is option (c).

A picture and the board it is mounted on are not mathematically similar because their corresponding sides do not have the same proportions, with the board generally having extra space around the picture that alters the length-to-width ratio. Additionally, artistic elements like tension and abstractness in images disrupt dimensional consistency that similarity requires.

To show that a picture and the board it is mounted on are not mathematically similar, we must understand similarity in a mathematical context. For two figures to be similar, they must have the same shape but not necessarily the same size, meaning their corresponding angles are equal, and their corresponding sides are in proportion. When we mount a picture on a board, the picture itself has dimensions that are different from that of the board - the board is usually larger to provide a border or frame around the picture. Since the additional border provided by the board changes the overall dimensions, the two objects cannot be considered mathematically similar.

The concept of similarity also involves dimensional consistency. If the picture and the board were to be similar, the ratio of the length to width in the picture would have to be the same as that of the board. However, in most scenarios, a picture needs to be mounted with additional space around it, thus altering the ratio.

Additionally, from an artistic point of view, tension within a painting or an abstract representation might disrupt the dimensional consistency that mathematical similarity requires. Various factors such as perspective can create a visual illusion that skews perceived dimensions, making it impossible for the two to be similar. When a picture includes a pattern that has a specific repetition with variation, it does not satisfy the conditions of mathematical similarity when placed on a uniform board.

Answer:

C. 6x² -45x + 21

Step-by-step explanation:

( x - 7) (6x - 3)

= x(6x - 3) -7 ( 6x - 3)

= 6x² - 3x - 42x + 21

= 6x² - 45x + 21

Hope it will help you :)

Answer

the answer is c

Step-by-step explanation:

Answer:

The number is 6

Step-by-step explanation:

Let the number be x

3 times a number plus 5 =  3x +5

Same number increased by 17 = x + 17

3x + 5 = x + 17

3x -x  + 5 = 17

2x + 5 = 17

2x = 17 - 5

2x = 12

x = 12/2

x = 6

The solution to the problem 3x + 5 = x + 17 is x = 6. This involves setting up an algebraic equation using the given conditions and then solving for x.

This problem seems to be a basic algebra problem. You can begin by setting up the equation based on the sentence given. The sentence translates into the equation: 3x + 5 = x + 17 where x is the unknown number you’re solving for. Then, you need to solve for x by isolating it on one side of the equation.

Step-by-step explanation: Subtract x from both sides of the equation to get 2x + 5 = 17. Then, subtract 5 from both sides to get 2x = 12. Finally, divide by 2 to solve for x. This will give you: x = 6. Therefore, the number that fits the condition in the problem is 6.

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Answer:

4(6)+12=36

Step-by-step explanation:

The required, Tracy has a total of 36 ounces of juice in her refrigerator.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,

The expression for the total ounces of juice Tracy has in her refrigerator is:

4(6) + 12

The expression shown above shows the sum of the ounces of juice in the four cans that have 6 ounces each, plus the ounces of juice in the fifth can that has 12 ounces.

Evaluating this expression:

4(6) + 12 = 24 + 12 = 36

Therefore, Tracy has a total of 36 ounces of juice in her refrigerator.

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Answer:

  98,790

Step-by-step explanation:

The given relation is ...

  0.248 · (total employees) = 24,500

Dividing by the coefficient of the variable, we have ...

  (total employees) = 24,500/0.248 = 98,790

The company has 98,790 employees in total.

Answer:

You get $5727.27

Step-by-step explanation:

At the start, you have 2000

After you are attacked, stampeded and have trouble finding water, you have lost 10% of your cattle

2000 * 10% is 200

2000 - 200 is 1800

Multiply 1800 cattle by $35 per cow

1800 * $35 = $63000

10 cowboys + 1 (you) is 11 people

Divide $63000 by 11

63000 / 11 = $5727.27

You get $5727.27

Answer:

9 degrees.

Step-by-step explanation:

For ALL polygons, the exterior angles add up to 360 degrees.

Therefore the 8th exterior angle = 360 - (42+110+13+67+55+11+53)

= 360 - 351

= 9 degrees.

Answer:

9°

Step-by-step explanation:

Always some of exterior angle of any polygon is 360

42 + 110 + 13 + 67 + 55 +11 + 53 + x = 360

351 +x = 360

x = 360 - 351

x = 9

Answer:

f(x) should shifted Right by 4 units to obtain g(x) ⇒ B

Step-by-step explanation:

Let us put g(x) in the form of g(x) = (x - h)² + k, where h is the the horizontal shift (x - h) to right, (x + h) to left and k is the vertical shift (k) up and (-k) down

In the quadratic function y = ax² + bx + c, h = [tex]-\frac{b}{2a}[/tex]  and k = y at x = h

∵ g(x) = x² - 8x + 1

∵ a is the coefficient of x² and b is the coefficient of x

∴ a = 1 and b = -8

∵ h = [tex]-\frac{b}{2a}[/tex]

∴ h = [tex]-\frac{-8}{2(1)}=\frac{8}{2}[/tex]

∴ h = 4

∵ k = g(x) at x = h

- Substitute x by 4 in g(x) to find k

∴ k = (4)² - 8(4) + 1 = 16 - 32 + 1

∴ k = -15

- Substitute them in the form of g(x) = (x - h)² + k

∴ g(x) = (x - 4)² + (-15)

∵ h is the horizontal shift

∵ (x - h) means shift to right h units

∵ f(x) = x²

∵ g(x) = (x - 4)² + (-15)

- That means f(x) is shifted 4 units to the right

∴ f(x) should shifted right by 4 units to obtain g(x)

Answer:

B. Right by 4 units

Step-by-step explanation:

Answer:

I think it's supposed to be 8x+2=14

Answer:

42.5

Step-by-step explanation:

so you start with adding 15 to the equations because that is how many days

1.5 15 +20

1.5 x 15 =22.5

22.5+20=42.5

so 42.5 is the answer

The predicted height of the plant 15 days from today is 42.5 cm.

The given expression for the height of a plant is 1.5t + 20, where t represents the number of days from today. To find the predicted height of the plant 15 days from today, we need to substitute t = 15 into the expression.

        height of the plant 15 days from today = 1.5(15)+20 cm

        height of the plant 15 days from today = 22.5 + 20 cm = 42.5 cm

Therefore, the predicted height of the plant 15 days from today is 42.5 cm.

Answer:

b

Step-by-step explanation:

Answer:

do u have a pic?

Step-by-step explanation:

Given:

For cylinder A:

Radius = 3 unit

Height = 4 unit

For cylinder B:

Radius = 4 unit

Height = 3 unit

To find the ratio of the volume of cylinder A to the volume of cylinder B.

Formula

The volume of a cylinder is,

[tex]V = \pi r^{2} h[/tex]

where, r be the radius and

h be the volume of the cylinder.

Now,

For cylinder A

Putting, r = 3 and h = 4 we get,

Volume [tex]V_{A}[/tex] = [tex]\pi (3^{2} )(4)[/tex]

or, [tex]V_{A} = 36\pi[/tex]

For cylinder B

Putting, r = 4 and h = 3 we get

Volume [tex]V_{B}=\pi (4^{2} )(3)[/tex]

or, [tex]V_{B}= 48\pi[/tex]

Now,

The ratio [tex]\frac{V_{A} }{V_{B}} = \frac{36\pi}{48\pi}[/tex]

or, [tex]\frac{V_{A} }{V_{B}} = \frac{3}{4}[/tex]

Hence,

The ratio of the volume of Cylinder A to the volume of Cylinder B is [tex]\frac{3}{4}[/tex]. Option A

Given:

Given that the triangle ABC has vertices A(-2,3), B(0,3) and C(-1,-1).

We need to determine the coordinates of the image after a reflection over the x - axis.

Let A'B'C' denote the coordinates of the triangle after a reflection over the x - axis.

Coordinates of the point A':

The general rule to reflect the coordinate across the x - axis is given by

[tex](x,y)\rightarrow (x,-y)[/tex]

Substituting the point A(-2,3), we get;

[tex](-2,3)\rightarrow (-2,-3)[/tex]

Thus, the coordinates of the point A' is (-2,-3)

Coordinates of the point B':

The general rule to reflect the coordinate across the x - axis is given by

[tex](x,y)\rightarrow (x,-y)[/tex]

Substituting the point B(0,3), we get;

[tex](0,3)\rightarrow (0,-3)[/tex]

Thus, the coordinates of the point B' is (0,-3)

Coordinates of the point C':

The general rule to reflect the coordinate across the x - axis is given by

[tex](x,y)\rightarrow (x,-y)[/tex]

Substituting the point C(-1,-1), we get;

[tex](-1,-1)\rightarrow (-1,1)[/tex]

Thus, the coordinates of the point C' is (-1,1)

Hence, the coordinates of the image after a reflection over the x - axis is A'(-2,-3), B(0,-3) and C(-1,1)

Answer:

A - (-2,-3)

B - (0,-3)

C - (-1,1)

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

if you do 6^3 you get 216

6*6*6=216

6*6=36

36*6=216

2*2*2*3*3*3=216

2*2=4

4*2=8

8*3=24

24*3=72

72*3=216

Answer:

(x - 1)² = 0

Step-by-step explanation:

Given

x² - 2x + 1 = 0 ( subtract 1 from both sides )

x² - 2x = - 1

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 1)x + 1 = - 1 + 1

(x - 1)² = 0

Answer: A2, B3, E1, C5, D4

Step-by-step explanation:

1. A is Maxium because it is the highest point on the graph

2.B is Midline because it is the “middle”

3.C is Peroid because the graph in a way ends or meets back in the middle

4.D is Minimum because it is the lowest point on the graph

5.E is Amplitude

Answer:

I believe the answer is 8.

Step-by-step explanation:

8.02 rounded to the nearest tenth is 8