classify the triangle by its sides
a(3,-3), b(1,4), c(-1,-1)

In geometry, similar shapes have equal angles. If angle GHE (z) is 110 degrees, then angle CDA, in similar shapes, is also 110 degrees, simplifying angle-related problems.

In geometry, understanding the properties of similar and congruent shapes is essential. When two shapes are similar, it means that they have the same shape, and their angles are equal, but their sizes are proportionate. This concept provides a basis for solving problems involving angles in similar shapes.

In the given scenario, we are dealing with two shapes: GHE and CDA. When it's established that these shapes are similar, it means their corresponding angles are equal. Therefore, angle GHE (often denoted as 'z') is indeed equal to angle CDA.

Furthermore, the problem provides the measure of angle GHE (z) as 110 degrees. Using the information that angles in similar shapes are equal, we can confidently state that angle CDA is also 110 degrees.

In summary, the solution leverages the concept of similarity in geometry, where similar shapes have equal angles. Given that angle GHE (z) is provided as 110 degrees, it follows that angle CDA, being corresponding and equal in similar shapes, is also 110 degrees. This demonstrates how understanding similarity and congruence properties can simplify angle-related problems in geometry.

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Answer:

[tex]\large\boxed{B. \left\{\begin{array}{ccc}4x+2y=10\\10x+y=21\end{array}\right}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}4x-2y=6\\2x+y=5&\text{multiply both sides by 2}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}4x-2y=6\\4x+2y=10\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad8x=16\qquad\text{divide both sides by 8}\\.\qquad x=2\\\\\text{put the value of x to the second equation:}\\\\2(2)+y=5\\4+y=5\qquad\text{subtract 4 from both sides}\\y=1[/tex]

[tex]\text{Put the value of x and y to the each equation and check the equalities:}\\\\A.\\-4x-2y=10\\-4(2)-2(1)=10\\-8-2=10\\-10=10\qquad\bold{FALSE}\\\\B.\\4x+2y=10\\4(2)+2(1)=10\\8+2=10\\10=10\qquad\bold{CORRECT}\\10x+y=21\\10(2)+1=21\\20+1=21\\21=21\qquad\bold{CORRECT}\\\\C.\\-4x-5y=-1\\-4(2)-5(1)=-1\\-8-5=-1\\-14=-1\qquad\bold{FALSE}\\\\D.\\3x+2y=6\\3(2)+2(1)=6\\6+2=6\\8=6\qquad\bold{FALSE}[/tex]

Answer:

B

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

There are 64 people with brown eyes and black hair out of 303 total people; this is 64/303 = 0.211 = 21.1%.

There are 9 people with blue eyes and black hair out of 303 total people; this is 9/303 = 0.0297 = 2.97%.

This is a difference of 21.1-2.97 = 18.13, or 18%.

Answer:-38

Step-by-step explanation:

Answer:

-38

Explanation:

You're dealing with absolute value. Those little | | (lines) are absolute value. Absolute value is simply the distance of a number on the number line from 0 without considering which direction from 0 the number lies. Absolute value of a number is always positive (never negative). In your case you have to find the absolute value of |-38|, which is 38. Expect your problem includes a negative on the outside of the absolute value making the number a negative again.

-|-38|=?

Get rid of lines and you're left with

-38

Hope this helps a bit,

Flips

Answer:

13 Units-correct on edge

Step-by-step explanation:

The length of line segment VT in which SU and VT are chords that intersect at point R is 13 units

An equation is an expression that shows the relationship between two or more numbers and variables.

Using the intersecting chord theorem:

VR * RT = SR * RU

(x + 1)(x + 4) = x(x + 6)

x² + 6x = x² + 5x + 4

x = 4

VT = VR + RT = x + 1 + (x + 4) = 4 + 1 + 4 + 4 = 13 units

The length of line segment VT in which SU and VT are chords that intersect at point R is 13 units

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Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

so convert the equation -x + y = 5 into slope intercept form by adding x to both sides

(-x + x) + y = 5 + x

0 + y = 5 + x

y = 5 + x

To match the slope intercept formula switch the x and 5 around

y = x + 5

If lines are parallel then they have the same slope (m) but they have different b

This means that the slope of the line will be 1 (in front of the x is an invisible 1 which would be m)

This is what we have so far...

y =  x + b

Now we must find b

To do that you must plug in the point the line goes through in the x and y of the equation.

(2, -5)

-5 = 1(2) + b

-5 = 2 + b

-7 = b

y = x + (-7)

y = x - 7

Hope this helped!

~Just a girl in love with Shawn Mendes

USE y=mx+b

m=Slope

b= Y-intercept

So y=x-7

Answer:

56 tablets

Step-by-step explanation:

Jonah knows that Mr. Robinson needs 14 tablets for a week's supply of an anti-inflammatory drug.

Mr. Robinson is going on vacation and needs a 4-week supply.  

So multiplying 4 with the weekly supply will yield the required result.  

So, number of tablets Jonia needs to fill is,

=4\times 14

=56

Therefore, Jonah needs 56 tablets in order to fill his prescription

Final answer:

Jonah needs to fill Mr. Robinson's prescription with 56 tablets for a 4-week supply of the anti-inflammatory drug by multiplying the weekly need of 14 tablets by 4 weeks.

Explanation:

Jonah knows that Mr. Robinson needs 14 tablets for a week supply of an anti-inflammatory drug. Mr. Robinson is going on vacation and needs a 4 weeks supply. To calculate the total number of tablets needed for the 4-week supply, you multiply the weekly need by the number of weeks:

Determine the weekly need: 14 tablets.

Multiply the weekly need by the number of weeks: 14 tablets × 4 weeks = 56 tablets.

So, Jonah needs to fill Mr. Robinson's prescription with 56 tablets for a 4-week supply of the anti-inflammatory drug.

Answer:

The percent error is 12.5%.

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

The answer is 12.5%

Hope this helps

-Amelia The Unknown

Answer:

1. F(x) = 5/4 x - 1

2. F(x) = 3x - 9

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

(1)

let (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (4, 4), then

m = [tex]\frac{4+1}{4-0}[/tex] = [tex]\frac{5}{4}[/tex]

Note the line crosses the y- axis at (0, - 1) ⇒ c = - 1

y = [tex]\frac{5}{4}[/tex] x - 1 ← in slope- intercept form

(2)

let (x₁, y₁ ) = (4, 3) and (x₂, y₂ ) = (1, - 6), then

m = [tex]\frac{-6-3}{1-4}[/tex] = [tex]\frac{-9}{-3}[/tex] = 3, hence

y = 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 3), then

3 = 12 + c ⇒ c = 3 - 12 = - 9

y = 3x - 9 ← in slope- intercept form

Answer:

(-1, -9)

Step-by-step explanation:

Recall that for 2 points (x1, y1) and (x2,y2)

the midpoints are given by

x ordinate = [tex]\frac{x1+x2}{2}[/tex]

y ordinate = [tex]\frac{y1+y2}{2}[/tex]

In our case x1 = 8, y1 = -10, x2 = -10, y2=-8

x ordinate = [tex]\frac{x1+x2}{2}[/tex]  = [8 + (-10) ] / 2 = -1

y ordinate = [tex]\frac{y1+y2}{2}[/tex] = [-10 + (-8) ] / 2 = -9

hence midpoint is (-1, -9)

Answer:

The the midpoint of given line segment = (-1, -9)

Step-by-step explanation:

Points to remember

Midpoint formula

Midpoint of a line segment with end points (x₁, y₁) and (x₂, y₂) is given by,

Midpoint = [( x₁ + x₂)/2 , (y₁ + y₂)/2]

To find the midpoint of given line segment

Here (x₁, y₁) = (8, -10) and (x₂, y₂) = (-10, -8)

Midpoint = [( x₁ + x₂)/2 , (y₁ + y₂)/2]

 = [(8 + -10)/2 , (-10 + -8)/2]

 = [-2/2, -18/2]

 = (-1, -9)

Therefore the midpoint of given line segment = (-1, -9)

Answer:

Step-by-step explanation:

4 to 24 = 1 to 6

Answer:

4  to 24

Step-by-step explanation:

The bag in total has 24 fruit. So that means that the bag has 4 bannanas and 24 fruit in total its 4 to 24

Answer:

0.3333

Step-by-step explanation:

To get 5/15 converted to decimal, you simply divide 5 by 15.

Hope this helps!

Answer:

population standard deviation = √58.79857 =  7.6680

sample standard deviation = √63.32154 = 7.9575

Step-by-step explanation:

The question is on sample standard deviation and population standard deviation

Arrange data in ascending order

56, 65, 73, 66, 64, 58, 72, 52, 69, 71, 53, 66, 78, 58

52,53,56,58,58,64,65,66,66,69,71,72,73,78

Find the mean of the data set;

[tex](52+53+56+58+58+64+65+66+66+69+71+72+73+78) /14[/tex]

=[tex]\frac{901}{14} = 64.36[/tex]

Finding the deviations from the mean

              Deviations           square of deviations

52-64.36= -12.36                  152.77

53-64.36= -11.36                   129.05

56-64.36= -8.36                     69.89

58-64.36= -6.36                     40.45

58-64.36= -6.36                      40.45

64-64.36= -0.36                         0.13

65-64.36= 0.64                          0.41

66-64.36= 1.64                           2.67

66-64.36=  1.64                          2.67

69-64.36= 4.64                         21.53

71-64.36=6.64                           44.09

72-64.36=7.64                           58.37

73-64.36=8.64                            74.65

78-64.36=13.64                          186.05

Sum                                             823.18        

1. Treating the data set as an entire population;

population variance= 823.18/14 =58.79857

population standard deviation = √58.79857 =  7.6680

2. Treating the data set as a sample, the number of data points will be less by 1

n= 14-1 = 13

sample variance= 823.18/13 = 63.32154

sample standard deviation = √63.32154 = 7.9575

Answer:

C on edge

Step-by-step explanation:

PLEASE IGNORE THIS I MISREAD THE QUESTION AND AM NOT SURE HOW TO REMOVE MY ANSWER.

Answer:

D. 28

Step-by-step explanation:

ED2021

Answer:

0 ,2

Step-by-step explanation:

you are just looking for when f(x) and g(x) hold the same value and what x does it happen at...

so the first time I see it is when f(x) and g(x) are both -3 and that happens at x=0

the next time I see f(x) and g(x) are the same is when they are both 0 and that is at x=2

there are no other times when f(x) and g(x) 's values are the same

Answer:

Step-by-step explanation:

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

We have the equation of the line in the point-slope form:

[tex]y-4=\dfrac{3}{4}(x+8)[/tex]

Convert it to the standard form:

[tex]y-4=\dfrac{3}{4}(x+8)[/tex]        multiply both sides by 4

[tex]4y-16=3(x+8)[/tex]          use the distributive property

[tex]4y-16=3x+24[/tex]           add 16 to both sides

[tex]4y=3x+40[/tex]         subtract 3x from both sides

[tex]-3x+4y=40[/tex]        change the signs

[tex]3x-4y=-40[/tex]

Answer:

Option D. [tex]\frac{64}{25}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor and the ratio of its surface areas is equal to the scale factor squared

In this problem

The scale factor is equal to [tex]\frac{8}{5}[/tex]

therefore

The ratio of its surface areas is equal to

[tex](\frac{8}{5})^{2}=\frac{64}{25}[/tex]

Final answer:

The ratio of the surface areas of the two similar rectangular prisms, given the ratio of their edge lengths is 8.5, is the square of that ratio, which is 72.25.

Explanation:

If the rectangular prisms are similar, their corresponding sides are proportional. Given that the ratio of their edge lengths is 8.5, we know that the corresponding sides of the two prisms are in the ratio of 8.5:1.

Since surface area is determined by the area of each face, and the area of each face is proportional to the square of the length of the corresponding edge, we square the ratio of their edge lengths to find the ratio of their surface areas.

Let's denote the ratio of surface areas as S. We have:

S = (8.5)² = 72.25

Therefore, the ratio for the surface areas of the rectangular prisms is 72.25:1. This means that the surface area of the larger prism is 72.25 times greater than the surface area of the smaller prism.

Answer:

The value of x is 15 ⇒ answer D

Step-by-step explanation:

* Lets talk about dilation

- A dilation is a transformation that changes the size of a figure.  

- It can become larger or smaller, but the shape of the

 figure does not change.  

- The scale factor, measures how much larger or smaller  

  the image will be

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

- If the scale factor is negative then the figure will reflected

* Now lets solve the problem

∵ D (o, k) (x , 9) → (-10 , -6)

- D means dilation

- o means the center of dilation is the origin

- k means the scale factor of dilation

∵ The y-coordinate of the point is 9

∵ The image has y-coordinate -6

∵ The image = The scale factor × the coordinates

∴ -6 = k × 9 ⇒ divide both sides by 9

∴ k = -6/9 = -2/3

- Lets find x by same way

∵ -10 = -2/3 × x ⇒ divide both sides by -2/3

∴ x = -10 ÷ (-2/3) ⇒ change the division to multiplication

∴ x = -10 × (-3/2) = 30/2 = 15

∴ The x-coordinate of the point before dilation is 15

* The value of x is 15

Hello There!

We know that Maria earned $450 in a total of 5 days so we need to find out how much money she earns in just 1 day.

To find this, we just divide 450 “the amount of money Maria earns in 5 days” by 5 “number of days it takes for Maria to earn $450”

“450 ÷ 5 ≈ 90”

Maria earns around $90 in just 1 day.

Answer:

A) b= 29(d)+13.95(d)+3.80(12)

B) $432.15

Step-by-step explanation:

29(9)= 261

13.95(9)= 125.55

3.80(12)= 45.60

$261+$125.55+$45.60=$432.15

Answer:

x = 1

Step-by-step explanation:

They intersect at ONE point.

Answer:

x=1.

Step-by-step explanation:

f(x) = g(x) in the point where the two graphs intersect. In this case, when x=1 and y=0 both graphs intersect.

Answer:

Choice B

Step-by-step explanation:

For a function to be a function, one of the easiest ways to tell is if an x-value has more than one y-value, because then it wouldn't pass the Vertical Line Test

But for choices A, C, and D, each x-value has 2 different y-values, failing the test

Out of the given options, the relation that describes a Functions is B) {(-2, −3), (-3, −2), (2, 3), (3, 2)}, as in this set, each x-value is only paired once with a unique y-value.

In the context of functions in Mathematics, a function is a relation where every domain (input) has exactly one unique range (output).

Looking at these four relations, the relation that describes a function would be B) {(-2, −3), (-3, −2), (2, 3), (3, 2)} because each x-value is paired with a unique y-value.

In other words, no x-value has more than one corresponding y-value.

For example, -2 is only paired with -3, -3 is only paired with -2, 2 is only paired with 3 - all unique pairs.

This is the definition of a function.

The other options (A, C, and D) all have x-values that are paired with more than one y-value, which violates the definition of a function.

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Answer:

Part 1) Monkey A [tex]42\ vegetables[/tex]

Part 2) Monkey B [tex]50\ fruits[/tex]

Step-by-step explanation:

Let

x -----> the number of fruits

y ----> the number of vegetables

we know that

The ratio of fruits  and vegetables is equal to

[tex]\frac{x}{y} =\frac{5}{7}[/tex]

Part 1) Find the number of vegetables Monkey A

we know that

[tex]\frac{x}{y} =\frac{5}{7}[/tex]

[tex]x=30\ fruits[/tex]

substitute and solve for y

[tex]\frac{30}{y} =\frac{5}{7}[/tex]

[tex]y=30*7/5=42\ vegetables[/tex]

Part 2) Find the number of fruits Monkey B

we know that

[tex]\frac{x}{y} =\frac{5}{7}[/tex]

[tex]y=70\ vegetables[/tex]

substitute and solve for x

[tex]\frac{x}{70} =\frac{5}{7}[/tex]

[tex]x=70*5/7=50\ fruits[/tex]

From the given picture , it can be seen that the ratio of the fruits to the vegetables is 5:7

Let x be the number of vegetables corresponds 30 fruits for Monkey A.

Then , by using proportional relationships between fruits and vegetables , we have :-

[tex]\dfrac{x}{30}=\dfrac{7}{5}\\\\\Rightarrow\ x=\dfrac{30\times7}{5}=42[/tex]

So, the number of vegetables for Monkey A = 42

Let y  be the number of vegetables corresponds 70 vegetables for Monkey B.

Then , we have :-

[tex]\dfrac{y}{70}=\dfrac{5}{7}\\\\\Rightarrow\ x=\dfrac{70\times5}{7}=50[/tex]

So, the number of fruits for Monkey B = 50

Angle a is opposite to angle b because they're vertical angles.

It should be noted that vertical angles mean the angle that are opposite each other.

In this case, angle a is opposite to angle b because they're vertical angles. This means they are congruent. In the image of the intersecting roads, angles 'a' and 'b' are opposite, and angles 'c' and 'd' are opposite. Another name for opposite angles is vertical angles because the two angles share the same vertex or corner.

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Answer:

x = -2 and y = 3

Step-by-step explanation:

It is given that,

4x + 5y = 7  ----(1)

3x – 2y = –12    ---(2)

To find the value of x and y

eq(1) * 3 ⇒

12x + 15y = 21   ----(3)

eq(2) * 4 ⇒

12x - 8y = -48  ---(4)

eq(3) - eq(4) ⇒

12x + 15y = 21   ----(3)

12x - 8y = -48  ---(4)

0 + 23y = 69

y = 69/23 = 3

y = 3

Substitute the value of y in eq(1)

4x + 5y = 7    ----(1)

4x + 5*3 = 7

4x = 7 - 15 = -8

x = -8/4 = -2

Therefore x = -2 and y = 3

ANSWER

x=-2,y=3

EXPLANATION

The system of equations is:

[tex]4x + 5y = 7...(1)[/tex]

and

[tex]3x - 2y = - 12...(2)[/tex]

We multiply the first equation by 2.5 to get:

[tex]7.5x - 5y = - 30...(3)[/tex]

We add equations (1) and (3)

[tex]4x+7.5x=-30+7[/tex]

[tex]11.5x = - 23[/tex]

Divide both sides by 11.5

[tex]x = - \frac{23}{11.5} [/tex]

[tex]x = - 2[/tex]

Put x=-2 into the first equation or any other equation and solve for y.

[tex]4( - 2) + 5y = 7[/tex]

[tex] - 8 + 5y = 7[/tex]

[tex]5y = 7 + 8[/tex]

[tex]5y = 15[/tex]

[tex]y = 3[/tex]

Kara should use Box C. The correct answer is OC) Box C.

To determine which shipping box Kara should use, we need to compare the volume of her gift box with the volumes of the available shipping boxes.

The volume of Kara's cube-shaped gift box is given by the formula:

Volume of cube=[tex]Side length^3[/tex]

For Kara's gift box:

Volume of Kara’s box=[tex]6^3 =216in^3[/tex]

Now, let's compare this with the volumes of the available shipping boxes:

Volume of Box A= [tex]64in^3[/tex]

Volume of Box B= [tex]125in^3[/tex]

Volume of Box C= [tex]343in^3[/tex]

Volume of Box D=[tex]729in^3[/tex]

Kara should choose the shipping box that is large enough to accommodate her gift. In this case, Box C has a volume of 343 in³, which is more than enough to fit Kara's gift (216 in³). Therefore, Kara should use Box C. The correct answer is OC) Box C.

Answer:

Scale factor is 0.25

Step-by-step explanation:

To find the scale factor, we have to do division of the shorter sides of the first and second rectangle, that is

1.5/6

=0.25

Answer:

4

Step-by-step explanation:

Assuming that the frog is consistent with its performance, the correct answer can be calculated. It can be noticed that the ability to jump upwards is 3 feet and the sliding back down is 2 feet. This means that the gain is greater than the loss. The net gain is 1 foot for each jump. This will continue until the distance of 6 feet has been achieved. It will be: 3 ft - 2 ft = 1 ft (1 jump); 1 ft + 3 ft - 2 ft = 2 ft (2 jumps); 2 ft + 3 ft - 2 ft = 3 ft (3 jumps). At the end of the 3 jumps, the frog has already covered the distance of 3 feet. This means that when the frog jumps from this height, it will achieve the height of 6 feet, by which it will get out of the hole. This means that the frog requires 4 jumps to get out of the tunnel.

Answer:

x < 11

Step-by-step explanation:

5x<55​

Divide each side by 5

5x/5 < 55/5

x < 11

Any number less than 11 will be a solution