Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
x + 2y = 12
- x = -y-6
A. (7.1)
B. (9,3)
C. (6,0)
D. (8,2)

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:

p v q = x < -3 or x > 3

Step-by-step explanation:

We are given

p: x < -3

q: x > 3

and we need to find p v q

v symbols represents disjunction and in simple terms it is called "or"

So, p v q represents either p holds or q holds

So, p v q = x < -3 or x > 3

[tex]x<-3 \vee x>3[/tex]

Answer:

x = 4 ± 3[tex]\sqrt{5}[/tex]

Step-by-step explanation:

Given

4(x - 4)² - 180 = 0 ( add 180 to both sides )

4(x - 4)² = 180 ( divide both sides by 4 )

(x - 4)² = 45 ( take the square root of both sides )

x - 4 = ± [tex]\sqrt{45}[/tex] = ± 3[tex]\sqrt{5}[/tex]

Add 4 to both sides

x = 4 ± 3[tex]\sqrt{5}[/tex]

The value of x is equal to [tex]4 +3\sqrt{5}[/tex] and [tex]4 -3\sqrt{5}[/tex] by solving the quadratic equation that is taking the square root of both sides and also by using the concept of transposition.

Given the quadratic equation [tex]4(x-4)^2-180=0[/tex] by taking the square root of both sides

To solve a quadratic equation [tex]4(x-4)^2-180=0[/tex] by taking the square root of both sides, follow steps:

Step 1: Consider the given quadratic equation:

[tex]4(x-4)^2-180=0[/tex]

Add by  18  on both sides, gives;

[tex]4(x-4)^2-180+180=0+180[/tex]

On operating algebra sum results:

[tex]4(x-4)^2=180[/tex]

Step 2: Isolate the LHS [tex]4(x-4)^2[/tex]  from number 4 by dividing both sides by 4 yields:

[tex]\frac{4(x-4)^2}{4} =\frac{180}{4}[/tex]

On cancelation of 4 on LHS and divide 180 by 4 on RHS results in :

[tex](x-4)^2=45[/tex]

Factorize RHS with a perfect square 9 :

[tex](x-4)^2=9\times5[/tex]

Step 3: Taking the square root of both sides results :

[tex]\sqrt{(x-4)^2} = \sqrt{9\times5}[/tex]

On taking square roots results:

[tex](x-4) = \pm3\sqrt{5}[/tex]

Add by 4 on both sides, gives:

[tex]x=4 \pm3\sqrt{5}[/tex]

Therefore, the value of x is equal to [tex]4 +3\sqrt{5}[/tex] and [tex]4 -3\sqrt{5}[/tex] by solving the quadratic equation that is taking the square root of both sides and also by using the concept of transposition.

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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:

B. Your didn't move but you went up to the C marking.

The  coordinates for point A of the square without using any new variables will be (O, d), i.e. option A.

Square is a 2D shape, having all sides equal and interior angles at 90 degrees.

We have,

A square on a graph with vertex at O, A, B, (c, d).

Now,

Side OB and A(c, d) are on x-axis,

While side OA and A(c, d) are on y-axis.

So,

We have to find the coordinates of A ,

So,

We know that sides of a squares are equal,

So,

OA = B(c, d)

So,

The coordinates of A will be (0, d).

Hence, we can say that the  coordinates for point A of the square without using any new variables will be (O, d), i.e. option A.

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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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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:

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:

2.6  cm

Step-by-step explanation:

7 - 4.4 = 2.6 cm

-

The difference between 7 cm and 4.4 cm is 2.6 cm. But since we need to round to the place value of the less precise measurement (7 cm), our final answer is 3 cm.

To find the difference between 7 cm and 4.4 cm, we simply subtract the smaller number from the larger one. So, we have 7 cm - 4.4 cm which equals 2.6 cm. However, we need to round to the place value of the less precise measurement. The least precise measurement here is 7 cm (as it's rounded to the nearest whole number), so we round our answer to the nearest whole number as well, which gives us 3 cm.

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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:

h(1) = 1.81 and h(2) = 21.44

Step-by-step explanation:

* Lets read the problem and solve it

- Evaluate means find the value, so evaluate h(x) means find the value

 of it at the given values of x

∵ h(x) = 2.8x³ + 0.01x² - 1

∵ x = 1 and x = 2

- Then find h(1) by substitute x by 1 and find h(2) by substitute x by 2

# At x = 1

∴ h(1) = 2.8(1)³ + 0.01(1)² - 1

∴ h(1) = 2.8(1) + 0.01(1) - 1

∴ h(1) = 2.8 + 0.01 - 1

∴ h(1) = 1.81

# At x = 2

∴ h(2) = 2.8(2)³ + 0.01(2)² - 1

∴ h(2) = 2.8(8) + 0.01(4) - 1

∴ h(2) = 22.4 + 0.04 - 1 ⇒ simplify

∴ h(2) = 21.44

* h(1) = 1.81 and h(2) = 21.44

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:

(3,2)

Step-by-step explanation:

y=4x-10 y=2

2=4x-10

12=4x

3=x , so that's (3, _)

y=2 is given, so (3,2)

Answer:

a

Step-by-step explanation:

[tex]\bf \underset{\stackrel{\textit{declining}}{\textit{so it's negative}}}{\stackrel{\textit{grade of 8\%}}{-\cfrac{8}{100}}}\implies \stackrel{\textit{slope}}{-\cfrac{\stackrel{rise}{8}}{\stackrel{run}{100}}}\implies -\cfrac{2}{25}[/tex]

a = interest rate of first CD

b = interest rate of second CD

and again, let's say the principal invested in each is $X.

[tex]\bf a-b=3\qquad \implies \qquad \boxed{b}=3+a~\hfill \begin{cases} \left( \frac{a}{100} \right)X=240\\\\ \left( \frac{b}{100} \right)X=360 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{a}{100} \right)X=240\implies X=\cfrac{240}{~~\frac{a}{100}~~}\implies X=\cfrac{24000}{a} \\\\\\ \left( \cfrac{b}{100} \right)X=360\implies X=\cfrac{360}{~~\frac{b}{100}~~}\implies X=\cfrac{36000}{b} \\\\[-0.35em] ~\dotfill\\\\[/tex]

[tex]\bf X=X\qquad thus\qquad \implies \cfrac{24000}{a}=\cfrac{36000}{b}\implies \cfrac{24000}{a}=\cfrac{36000}{\boxed{3+a}} \\\\\\ (3+a)24000=36000a\implies \cfrac{3+a}{a}=\cfrac{36000}{24000}\implies \cfrac{3-a}{a}=\cfrac{3}{2} \\\\\\ 6-2a=3a\implies 6=5a\implies \cfrac{6}{5}=a\implies 1\frac{1}{5}=a\implies \blacktriangleright 1.2 = x\blacktriangleleft[/tex]

[tex]\bf \stackrel{\textit{since we know that}}{b=3+a}\implies b=3+\cfrac{6}{5}\implies b=\cfrac{21}{5}\implies b=4\frac{1}{5}\implies \blacktriangleright b=4.2 \blacktriangleleft[/tex]

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

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

x-8= 15

x-8+8=15+8

x= 23

Check answer by using substitution method

x-8= 15

23-8= 15

15= 15

Answer is X= 23 (D.)

Answer

700 is 87.5% of 800

Step-by-step explanation:

Answer:

The equivalent trigonometric ratio in Quadrant I is [tex]-\cos (\frac{3\pi}{8})[/tex]

Step-by-step explanation:

The terminal side of [tex]\frac{27\pi}{8}[/tex] is in the 3rd quadrant.

The principal angle is [tex]\frac{3\pi}{8}[/tex]

In other words, the terminal side of [tex]\frac{27\pi}{8}[/tex]  makes an acute angle of [tex]\frac{3\pi}{8}[/tex] radian with the positive x-axis. Acute angles are in the first quadrant.

Since the cosine ratio is negative in the 3rd quadrant,

[tex]\cos (\frac{27\pi}{8})=-\cos (\frac{3\pi}{8})[/tex]

Answer:

c on edgen

Step-by-step explanation:

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:

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:

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.

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 < 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

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:

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:

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

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]