Solve this system of linear equation.Separate the x- and y-values with comma. -6x=-4-y -7x=-22+y

Answer:

Step-by-step explanation:

Look at the picture.

ΔADC and ΔCDB are similar (AAA). Therefore corresponding sides are in proportion

[tex]\dfrac{15}{x}=\dfrac{x}{20-15}\\\\\dfrac{15}{x}=\dfrac{x}{5}[/tex]

cross multiply

[tex]x^2=(15)(5)\\\\x^2=75\to x=\sqrt{75}\\\\x=\sqrt{25\cdot5}\\\\x=\sqrt{25}\cdot\sqrt5\\\\x=5\sqrt5[/tex]

(5k^2)^3 simplifies to 125k^6.

To simplify the expression (5k^2)^3, we can apply the exponent rule. The rule states that when raising a power to another power, we multiply the exponents together.

In this case, we have (5k^2)^3. To simplify, we raise both the base, 5, and the exponent, k^2, to the third power.

First, let's raise the base, 5, to the third power:
5^3 = 5 x 5 x 5 = 125

Next, let's raise the exponent, k^2, to the third power:
(k^2)^3 = k^(2 x 3) = k^6

Therefore, (5k^2)^3 simplifies to 125k^6.

Answer:

The number of permutations of the letters in the word SMART are 120

Step-by-step explanation:

Permutations are events of multiplicative type, where the number of possibilities decreases and if the order of a permutation is an arrangement of a set of objects in a defined order.

The number of possible permutations when taking objects from the set of elements will be, following the same reasoning: [tex]P_{n} =n![/tex]

The number of permutations of the letters in the word SMART is:

[tex]P_{5} =5!=5.4.3.2.1=120[/tex]

.

Answer:

3.64

Step-by-step explanation:

65 + 66 + 70 + 58 + 61 = 319

319/5 = 63.8

65 - 63.8 = |1.2|

66 - 63.8 = |2.2|

70 - 63.8 = |6.2|

58 - 63.8 = |-5.8| = 5.8

61 - 63.8 = |-2.8| = 2.8

1.2 + 2.2 + 6.2 + 5.8 + 2.8 = 18.2

18.2/5 = 3.64

104.4...............................:::::::

Answer:

a lot

Step-by-step explanation:

You would get paid $1.25 per hour, you divide 50 by 40 and get 1.25. Hope this helps ʅ（◞‿◟）ʃ

the answers is 1.25

enjoy good grades!!!!!

Answer:

Mean : 95

Median : 85

Mode : 90

Part B : Impossible

Step-by-step explanation:

We can make an equation to find the mean using the first 5 history test scores.

[tex]85=\frac{80+75+90+75+95+n}{6} \\ \\ 85=\frac{415+n}{6} \\ \\ 510=415+n \\ \\ n=95[/tex]

So a 95 would be needed to have a mean of 85.

Next, the median.

First, we sort the first 5 history scores from least to greatest.

We get 75, 75, 80, 90, 95.

Since, 80 is the middle value, it will be used in the calculation of the median.

We can make an equation with this.

[tex]82.5=\frac{80+n}{2} \\ \\ 165=80+n \\ \\ n=85[/tex]

So a score a 85 would be needed to have a median of 82.5

Thirdly, the mode.

Since 90 is already in the set once, we can just have Maliah score another 90 to make 90 the mode (with the exception of 75 of course).

Finally, Part B.

We can use the equation we had for the first mean calculation but change 85 to 90.

[tex]90=\frac{80+75+90+75+95+n}{6} \\ \\ 90=\frac{415+n}{6} \\ \\ 540=415+n \\ \\ n=125[/tex]

So Maliah would need a score of 125 to make her mean score 90, but since the range is only from 0-100, it is impossible.

Answer:

Step-by-step explanation:

1 represent a candy bar with a  coupon and numbers 2 through 5 represent a candy bar without a coupon.

Now we are asked to find the probability that, if she buys 7 candy bars, more than 2 will include a coupon.

Total number of outcomes=16

Number of favorable outcomes(i.e. the outcome which have more than 2 one) = 3

( Since the outcomes are:  2113415 4341112   1455141 )

Hence, the probability is the ratio of Number of favorable outcomes to the total number of outcomes.

i.e.  [tex]Probability=\dfrac{3}{16}\\\\\\Probability=0.1875[/tex]

for (A^x)^y = A^xy

Thus for (3^-5)^-2 = 3^n

n = -5×-2 =10

Answer:

n=10

Step-by-step explanation:

We know that a^b^c = a^(b*c)

3 ^-5^-2 = 3^(-5*-2)

             = 3^(10)

3^n = 3^10

n = 10

Answer:

Part 1) The measure of the remaining angle is [tex]60\°[/tex]

Part 2) Is a 10 sided polygon (decagon)

Part 3) Yes, is possible for a triangle to have angles measures of 1°, 2° and 177°

Step-by-step explanation:

Part 1)

we know that

The sum of the measures of the interior angles of a polygon is equal to the formula

[tex]S=(n-2)180\°[/tex]

where

n is the number of sides of polygon

In this problem we have a hexagon

so

n=6 sides

Substitute

[tex]S=(6-2)180\°=720\°[/tex]

Let

x-----> the measure of remaining angle of the hexagon

[tex]6*(110\°)+x\°=720\°[/tex]

[tex]x=720\°-660\°=60\°[/tex]

Part 2) The sum of the measures of the interior angles of a polygon is [tex]1440\°[/tex]. What kind of polygon is it?

we know that

The sum of the measures of the interior angles of a polygon is equal to the formula

[tex]S=(n-2)180\°[/tex]

where

n is the number of sides of polygon

In this problem we have

[tex]S=1440\°[/tex]

substitute in the formula and solve for n

[tex]1440\°=(n-2)180\°[/tex]

[tex]n=(1440\°/180\°)+2=10\ sides[/tex]

therefore

Is a 10 sided polygon (decagon)

Part 3) Is it possible for a triangle to have angles measures of 1°, 2° and 177° ?

we know that

In any triangle the sum of the measures of the interior angles must be equal to 180 degrees

In this problem we have

1°+ 2°+ 177°=180°

therefore

Yes, is possible for a triangle to have angles measures of 1°, 2° and 177°

Answer:

Number the boxes on the left 1–8 from top to bottom. Then their correct order on the right is 3, 7, 8, 4, 6, 5, 2, 1

Step-by-step explanation:

Trade the cube root for a 1/3 power:

(875x^5y^9)^(1/3)

Distribute the 1/3 power:

(125·7)^(1/3)·x^(5/3)·y^(9/3)

Further distribute the powers, rewrite the improper fractions:

125^(1/3)·7^(1/3)·x^(3/3+2/3)·y^3

Write 125 as a cube and simplify 3/3:

(5^3)^(1/3)·7^(1/3)·x^(1+2/3)·y^3

Simplify the cube root of a cube and the x term:

5·7^(1/3)·x·x^(2/3)·y^3

Group the terms with fractional exponents:

5·x·y^3·(7^(1/3)·x^(2/3))

Factor out the 1/3 exponent:

5xy^3·(7x^2)^(1/3)

Trade the 1/3 exponent for a cube root symbol:

5xy^3·∛(7x^2)

Answer:

13/12

Step-by-step explanation:

B - 7/4 = -2/3

B = -2/3 + 7/4

B = 13/12

Answer:

20

Step-by-step explanation:

This reads mathematically exactly how it is stated in words.  The word "is" means =, the word "of" means multiply, and "what number" is x.  Therefore, the equation from that looks like this:  16 = .80x.  Don't forget that you cannot use a percent in an equation without first changing it to its decimal equivalency.  Solve that for x by dividing both sides by .80 to get that x = 20

The number that when 80 % is found of it, would give the result of 16 is the number 20.

To determine the number that 16 is 80% of, you can set up an equation using algebra.

Let's represent the unknown number with the variable "x." The equation can be written as:

16 = 80% of x

To solve for "x," we need to isolate it on one side of the equation.

Since 80% is equivalent to 0.8 as a decimal, we can rewrite the equation as:

16 = 0.8x

To solve for "x," divide both sides of the equation by 0.8:

16 / 0.8 = 0.8x / 0.8

Simplifying the equation:

20 = x

Therefore, the number that 16 is 80% of is 20.

Find out more on percentages at https://brainly.com/question/843074.

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Answer: The table that represents a function is table A

Step-by-step explanation: This is because every time the input goes down once with a change of output, where as a nonlinear function doesn't do this

Answer:

width = (x-1)

Step-by-step explanation:

The volume of the prisms is defined in the problem as

Volume = x^3 + 9x^2 + 6x − 16

Volume  = width*height* length

And we know that,

length = (x+2)

height = (x+8)

We can find the roots of the equation, which happen to be

x = -8

x = -2

x = 1

(See image below)

This means that the volume can be represented as

Volume = x^3 + 9x^2 + 6x − 16 = (x+8)(x+2)*(x-1)

Therefore,

The width = (x-1)

Answer:

b

Step-by-step explanation:

to find volume you have to multiply 12, 6 and 8.5

if it is right rate and thanks me so others know it is right

Answer:

[tex]v = \frac{i \: \times w \ \times h}{3} \\ \: \: \: \: = \frac{8.5 \times 6 \times 12}{3} \\ \: \: \: \: = 204 {in}^{3} [/tex]

Answer D is correct.

Answer: [tex]P=61.93\°[/tex]

Step-by-step explanation:

You know that:

[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]

And the arctangent is:

[tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]

You can observe a right triangle in the figure.

Since you need to find the measure of the angle P, then:

[tex]\alpha=P\\opposite=15cm\\adjacent=8cm[/tex]

Knowing this, you can substitute these values into [tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]:

[tex]P=arctan(\frac{15cm}{8cm})[/tex]

Therefore, the measure of the angle P to the nearest hundreth is:

[tex]P=61.93\°[/tex]

Answer:

Step-by-step explanation:

L is 2* W so L=2W

perimeter= 2w+2l

plug in whats given to get

perimeter=2w+4w   4w is because L is *2 of W so that makes L=2w

36=6w

36/6=6

6w/6=w

w=6

6*2=12=L

now we have 6*12=72=Area

Answer:

C

Step-by-step explanation:

The scale factor is a quantity that "scales" another quantity.

Since, the dimensions of large is "3 times" that of the smaller box, the scale factor is 3.

This means, that we can multiply any dimension (length, width, or height) of the small box by 3 to get respective dimension of large box.

Remember, to get area, we need to multiply by scale factor squared. To get volume, we need to multiply by scale factor cubed.

Since, surface area is given of smaller box, we need to multiply by scale factor squared (3^2 = 9) to get surface area of larger box.

Hence, 79 * 9 = 711 cm^2

C is the correct answer.

Answer:

∠ADC and ∠BDC are supplementary

A pair of complementary angles is angles ACD and DCB.

<ADC and <BDC are supplementary angles

<ACD and <BCD are complementary angles)

Complementary Angles: Two angles that add up to 90 degrees, complementing each other to form a right angle, e.g., 30 and 60 degrees.

Supplementary Angles: Two angles that add up to 180 degrees, forming a straight line, e.g., 120 and 60 degrees.

From the figure

ED is a ray that bisects AB and <ACB

<ACB is 90⁰(given)

<ADC + <BDC = 180( linear angles)

Linear angles are supplementary

Therefore

<ADC and <BDC are supplementary angles

Since <ACB = 90⁰

ED is a bisector

Therefore

<ACD + <BCD = 90⁰

<ACD and <BCD are complementary angles)

learn more about bisector here

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Answer:

2n-12 ( n is the unknown number)

Answer:

12-2n

Step-by-step explanation:

12 less which means you have to subtract 12 from twice a number n so 2 times n

so 12-2n

Answer:

204

Step-by-step explanation:

To find the volume of a rectanguar prism, you must multiply legnth x width x height to get the volume.

Before we multiply, first lets convert the fractions into improper fractions to make multiplying a little easier.

6 3/8 = 51/8

10 2/3 = 32/3

Now, we multiply.

[To multiply fractions, multiply the numerators and denominators.]

51/8 x 32/3

51 x 32 = 1632

8 x 3 = 24

1632/24 = 68

Now that we've multiplyed the length and height, multiply 68 by the width, 3.

68 x 3 = 204

Therefore, the volume of the rectangular prism is 204. I hope this helps!

About 204 inches.

Hope this helps!

Answer:

1/9

Step-by-step explanation:

Separate the fraction (1/9) from the variable x:

y = (1/9)x.

1/9 is the constant of proportionality.

The constant of proportionality in the equation y=x/9 is 1/9.

A constant of proportionality is a constant that is multiplied by a variable to make two variables equal.

The equation is given as:

y=x/9

Observe the given equation. Here, we can see that x and y are variables.

This means that 1/9 is the constant of proportionality.

A constant of proportionality is a constant that is multiplied by a variable to make two variables equal.

Therefore, the constant of proportionality is found. The value of the constant of proportionality is 1/9.

Therefore, we have found the constant of proportionality in the equation y=x/9 is 1/9.

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Answer: The answer is 9 i am 100% sure

Step-by-step explanation:

It would be

B.9 I hope this helps

For this case we have the following functions:

[tex]f (x) = x + 7\\g (x) = \frac {1} {x}[/tex]

We must find [tex](f_ {0} g) (x):[/tex]

By definition:

[tex](f_ {0} g) (x) = f (g (x))[/tex]

So, evaluating g(x) in f(x) we have:

[tex](f_ {0} g) (x) = f (g (x)) = \frac {1} {x} +7[/tex]

ANswer:

[tex]\frac {1} {x} +7[/tex]

Option D

Answer:

Rational number/integer

Answer:

b

Step-by-step explanation:

Answer:

[tex]\large\boxed{(81m^6)^\frac{1}{2}=9m^3}[/tex]

Step-by-step explanation:

[tex]81=9^2\\\\m^6=m^{3\cdot2}=(m^3)^2\qquad\text{used}\ (a^n)^m=a^{nm}\\\\\left(81m^6\right)^\frac{1}{2}=\bigg(9^2\left(m^3\right)^2\bigg)^\frac{1}{2}\qquad\text{use}\ (ab)^n=a^nb^n\\\\=\left(9^2\right)^\frac{1}{2}\bigg(\left(m^3\right)^2\bigg)^\frac{1}{2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=9^{2\cdot\frac{1}{2}}\left(m^3\right)^{2\cdot\frac{1}{2}}=9^1(m^3)^1=9m^3[/tex]

Other method:

[tex]Use\ a^\frac{1}{n}=\sqrt[n]{a}\to a^\frac{1}{2}=\sqrt[2]{a}=\sqrt{a}\\\\\left(81m^6\right)^\frac{1}{2}=\sqrt{81m^6}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ \text{and}\ (a^n)^m=a^{nm}\\\\=\sqrt{81}\cdot\sqrt{m^{3\cdot2}}=9\sqrt{(m^3)^2}\qquad\text{use}\ \sqrt[n]{a^n}=a\to\sqrt{a^2}=a\\\\=9m^3[/tex]

Answer:

Surface area = [tex]261.6cm^2[/tex]

Volume = [tex]281.2cm^3[/tex]

Step-by-step explanation:

To find the surface area of our cone, we are using the formula for the surface area of a cone:

[tex]A=\pir(r+\sqrt{h^2+r^2} )[/tex]

where

[tex]A[/tex] is the surface area

[tex]r[/tex] is the radius

[tex]h[/tex] is the height

Notice that the height, radius, and slant height make a right triangle, so to find the height, [tex]h[/tex], we can use the Pythagorean theorem:

[tex]s^2=r^2+h^2[/tex]

[tex]14^2=4.5^2+h^2[/tex]

[tex]196=20.25+h^2[/tex]

[tex]h^2=196-20.25[/tex]

[tex]h^2=175.75[/tex]

[tex]h=\sqrt{175.75}[/tex]

[tex]h=13.26[/tex] cm

We have all we need now to find the surface area of our cone:

[tex]A=\pir(r+\sqrt{h^2+r^2} )[/tex]

[tex]A=\pi(4.5)(4.5+\sqrt{13.26^2+4.5^2} )[/tex]

[tex]A=261.6cm^2[/tex]

Now, to find the volume of our cone, we are using the formula for the volume of a cone:

[tex]V=\frac{\pi r^2h}{3}[/tex]

where

[tex]V[/tex] is the volume

[tex]r[/tex] is the radius

[tex]h[/tex] is the height

Replacing values

[tex]V=\frac{\pi (4.5^2)(13.26)}{3}[/tex]

[tex]V=281.2cm^3[/tex]

We can conclude that the surface area of our cone is 261.6 square centimeters and its volume is 281.2 cubic centimeters.

Answer:

Surface area [tex]= 261.405 cm^2\\[/tex]

Volume of the cone [tex]= 177.19 cm^3\\[/tex]

Step-by-step explanation:

Slant height of cone [tex]= (r + \sqrt{r^2 + h^2}) \\[/tex]

Height of the cone will be derived from this slant height

[tex]14 = 4.5 + \sqrt{4.5^2 + h^2} \\9.5 = \sqrt{4.5^2 + h^2}\\90.25 = 20.25 + h^2\\h = 8.36\\[/tex]

Surface Area of Cone

[tex]= \pi r (r + l)\\= (3.14) (4.5) (4.5 + 14)\\= 261.405[/tex]

Volume of the cone

[tex]= \frac{1}{3} \pi r^2h\\= \frac{1}{3} (3.14)(4.5^2) (8.36)\\= 177.19 cm^3\\[/tex]

B. Interquartile Range