A pair of pants costs twice as much as a shirt. The total cost of 1 pair of pants and 1 shirt is $18. If s represents the cost of 1 shirt, which equation could you use to find the cost of 1 shirt?

Answer:

[tex]x=4, y=8[/tex]

Step-by-step explanation:

step 1

Find the value of y

we know that

In the right triangle of the figure

[tex]cos(30\°)=\frac{4\sqrt{3}}{y}[/tex]

Remember that

[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]

so

[tex]\frac{\sqrt{3}}{2}=\frac{4\sqrt{3}}{y}[/tex]

Simplify

[tex]y=8\ units[/tex]

step 2

Find the value of x

In the right triangle of the figure

[tex]sin(30\°)=\frac{x}{8}[/tex]

Remember that

[tex]sin(30\°)=\frac{1}{2}[/tex]

so

[tex]\frac{1}{2}=\frac{x}{8}[/tex]

[tex]x=4\ units[/tex]

Answer:

V1 / T1 = V2 / T2

0.67 / (273 + 89) = 1.12 / (273 + t )

t = 332 °C

Given values:

Volume,

Temperature,

We know the relation,

→ [tex]\frac{V_1}{T_1} = \frac{V_2}{T_2}[/tex]

By substituting the values, we get

→ [tex]\frac{0.67}{362} = \frac{1.12}{T_2}[/tex]

→   [tex]T_2 = \frac{1.12\times 362}{0.67}[/tex]

          [tex]= 332^{\circ} C[/tex]

Thus the answer above is right.

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Answer:

All 4 four angles of the rectangle are 90°

Answer:

Opposite sides of a rectangle are the same length (congruent). The angles of a rectangle are all congruent (the same size and measure.) Remember that a 90 degree angle is called a "right angle." So, a rectangle has four right angles.

four- 90 degrees

Answer:

Derek:

Mean:1929

Median: 1930

range: 54

IQR: 48

MAD: 23.75

Paul:

Mean: 1929

Median: 1929.5

range: 15

IQR: 6

MAD: 3.5

Step-by-step explanation:

For the Derek's collection:

1.  Mean =  1930.375

2. Median =  1930

For the Paul's collection:

1.  Mean = 1929.75

2. Median = 1931

For Derek's collection:

Mean:

Add up all the numbers and divide by the total number of numbers:

Mean = (1950 + 1952 + 1908 + 1902 + 1955 + 1954 + 1901 + 1910) / 8

          = 1930.375

Median:

The median is the middle value of the set, so we first need to put the numbers in order:

1901, 1902, 1908, 1910, 1950, 1952, 1954, 1955

The median is the average of the middle two numbers, which are 1910 and 1950:

Median = (1910 + 1950) / 2

             = 1930

For Paul's collection:

Mean:

Add up all the numbers and divide by the total number of numbers:

Mean = (1929 + 1935 + 1928 + 1930 + 1925 + 1932 + 1933 + 1920) / 8

          = 1929.75

Median:

The median is the middle value of the set, so we first need to put the numbers in order:

1920, 1925, 1928, 1929, 1930, 1932, 1933, 1935

The median is the average of the middle two numbers, which are 1930 and 1932:

Median = (1930 + 1932) / 2

            = 1931

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D. Y= - 4/3 x Rise over run

The equation of the line is:

  C.     [tex]y=\dfrac{-3}{4}x[/tex]

The line passes through the point (0,0) and (4,-3).

By using the two point formula to find the equation of the line.

i.e. any line passing through two points (a,b) and (c,d) is calculated by using the formula:

[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]

Here (a,b)=(0,0) and (c,d)=(4,-3)

Hence, the equation of line is calculated as follows:

[tex]y-0=\dfrac{-3-0}{4-0}\times (x-0)\\\\i.e.\\\\y=\dfrac{-3}{4}\times x\\\\i.e.\\\\y=\dfrac{-3}{4}x[/tex]

Hence, the correct answer is:  Option: C

Answer:

((2 x + 1) (4 x^2 - 2 x + 1))/8

Step-by-step explanation:

Factor the following:

x^3 + 1/8

Put each term in x^3 + 1/8 over the common denominator 8: x^3 + 1/8 = (8 x^3)/8 + 1/8:

(8 x^3)/8 + 1/8

(8 x^3)/8 + 1/8 = (8 x^3 + 1)/8:

(8 x^3 + 1)/8

8 x^3 + 1 = (2 x)^3 + 1^3:

((2 x)^3 + 1^3)/8

Factor the sum of two cubes. (2 x)^3 + 1^3 = (2 x + 1) ((2 x)^2 - 2 x + 1^2):

((2 x + 1) ((2 x)^2 - 2 x + 1^2))/8

1^2 = 1:

((2 x + 1) ((2 x)^2 - 2 x + 1))/8

Multiply each exponent in 2 x by 2:

((2 x + 1) (2^2 x^2 - 2 x + 1))/8

2^2 = 4:

Answer:  ((2 x + 1) (4 x^2 - 2 x + 1))/8

[tex]x^3+\dfrac{1}{8}=\\ \\ =x^3+2^{-3} = \\ \\ =x^3+(2^{-1})^3 =\\ \\ = (x+2^{-1})(x^2-2^{-1}x+2^{-2}) = \\ \\ = \Big(x+\dfrac{1}{2}\Big)\Big(x^2-\dfrac{x}{2}+\dfrac{1}{4}\Big)\\ \\ \\ \boxed{a^3+b^3 = (a+b)(a^2-ab+b^2)}[/tex]

Answer:

b) -6x - 3

Step-by-step explanation:

3(-2x-1)=3*(-2x)+3*(-1)= -6x - 3

B. -6x - 3

Distribute the 3, or multiply it by everything in the parentheses.

You multiply 3 times -2x to get -6x, and you multiply 3 times -1 to get -3.

Put these together to get -6x-3.

Answer:

3x+6y^3

Step-by-step explanation:

-First you add all the Xs

2x+x+x

-Then you multiply all the Ys

2y * 3y * y

* the Y has a 1 as an exponent by multiplying the Ys the exponents are added making the Y a Y^3

*the numbers are multiplied making it a 6

Together it forms 6y^3

-Ys and Xs cannot be added because they are different values so your answer would be 3x+ 6y^3

The simplification of the given algebraic expression 2x+x+x+(2y × 3y × y) is 4x + 6y³.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The simplification of 2x+x+x+(2y × 3y × y) can be done as,

2x + x + x + (2y × 3y × y)

= 4x + (2y × 3y × y)

= 4x + 6y³

Hence, the simplification of the given algebraic expression 2x+x+x+(2y × 3y × y) is 4x + 6y³.

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Answer:

m<A = m<D

Step-by-step explanation:

This is the correct answer to your question.

Hope this helps!!!

Kyle.

Answer:

log (y)+ 8 log (z)

Step-by-step explanation:

use the rules of logarithm

The expanded form of the given function is log (x)+ 8 log (y).

When you raise a number with an exponent, there comes a result.

Let's say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Given;

[tex]log(xy^8)[/tex]

use the rules of the logarithm;

log (x)+ 8 log (y)

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57-12= 3x+12-12

45=3x

Divide by 3

x=15

Check answer

57= 3(15)+12

57=57

Answer is correct.

x= 15

Answer:

The answer is 1.2

Step-by-step explanation:

1/5 it basicly stands for 1 ÷ 5

1 ÷ 5 = 0.2

plus the one you already have

1 + 0.2 = 1.2

1.2

Hope this helped!

~Lunar Rose. Moon

Answer:

1.2

Step-by-step explanation:

Take 1/5, or make it larger into 2/10 and divide those.

2/10 is obviously .2, while 1/5 is also .2.

now take the .2+ the 1 we had and you get 1.2

B is correct. Hope I helped yah.

Answer:

144 gold bars

Step-by-step explanation:

first you fine the area gold bars take up in cubic inches by multiplying the 3, 2, and 6 to get 36

once you have the space 1 gold bar takes up you divide the total space by that the total space is 5184 so you divide 5184 by 36 to get 144

Answer:

c. 144

Step-by-step explanation:

:)

Answer:

The baby

Step-by-step explanation:

If you count the baby inside the pregnant woman, then he is the youngest.

hahha funny the baby of course

Subtract 4x from both sides

24 = 5x + 1 - 4x

Simplify 5x + 1 - 4x to x + 1

24 = x + 1

Subtract 1 from both sides

24 - 1 = x

Simplify 24 - 1 to 23

23 = x

Switch sides

x = 23

Answer:

Step-by-step explanation:

Subtract 4x from both sides

24 = 5x + 1 - 4x

Simplify 5x + 1 - 4x to x + 1

24 = x + 1

Subtract 1 from both sides

24 - 1 = x

Simplify 24 - 1 to 23

23 = x

Switch sides

x = 23

Answer:

the radius is 13

the diameter is 40.82 inches squared

the area is 530.66

Step-by-step explanation:

well, the radius is 13

Answer:

(x − 7)² + (y + 2)² = 52

Step-by-step explanation:

The equation of a circle is:

(x − h)² + (y − k)² = r²

where (h, k) is the center and r is the radius.

We know that (h, k) = (7, -2).  But we need to find the radius.  To do that, find the distance from the center to a point on the edge:

r² = (x₁ − x₂)² + (y₁ − y₂)²

r² = (7 − 1)² + (-2 − -6)²

r² = 6² + 4²

r² = 36 + 16

r² = 52

So the equation of the circle is:

(x − 7)² + (y + 2)² = 52

The equation of the circle is (x-2)^2 + (y-(-3))^2 = 5^2.

To write the equation of a circle, we need to know the center and the radius of the circle. We can see from the diagram that the center of the circle is the point (2, -3), and the radius is 5 units.

The equation of a circle is given by the formula (x-h)^2 + (y-k)^2 = r^2,

where (h, k) is the center and r is the radius. Therefore, the equation of the circle is (x-2)^2 + (y-(-3))^2 = 5^2.

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Answer:

The best possible answer for this would be: D. Mode.

This is because mode measures how many times each number appears.

Answer:

mine said c is the correct answer

Step-by-step explanation:

First, we have to isolate the t, or keep it by itself, to solve. To do that, we need to move everything with t in it to on side.

-5 - 2t + 2t = 3t + 2t

The -2t and + 2t cross out, leaving us with t on one side, which is exactly what we want!

-5 = 5t

But t isn't alone yet. We need to get rid of its five. To do that, we need to use the same process: use the opposite symbol. In 5t, 5 is being multiplied by t. To get rid of, we need to divide 5. BUT the mega rule in algebra... what you do to one side you must do to the other, or else the equation would not be true anymore, so...

-5/5 = 5t/5

-1 = t

There's your answer! Hope this helps!

Answer:

Louise is missing the term [tex]30x^3[/tex]

Step-by-step explanation:

Remember that the formula for squaring a binomial is:

[tex](a+b)^2=a^2+2ab+b^2[/tex]

Where

[tex]a[/tex] is the first term of the binomial

[tex]b[/tex] is the second term of the binomial

Our binomial is [tex](5x^3+3)^2[/tex], so [tex]a=5x^3[/tex] and [tex]b=3[/tex].

Replacing values

[tex](5x^3+3)^2=(5x^3)^2+2(5x^3)(3)+3^2[/tex]

[tex](5x^3+3)^2=5^2x^6+6(5x^3)+9[/tex]

[tex](5x^3+3)^2=25x^6+30x^3+9[/tex]

Since Louise’s answer is [tex](5x^3+3)^2=25x^6+9[/tex], we can conclude that she is missing the term [tex]30x^3[/tex]

Answer:

Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.

Step-by-step explanation:

Answer: 121.5 pi in^3 or 381.7 in^3

Step-by-step explanation:

Volume of a cylinder = pi r^2(h)

Radius = 4.5 in, Height = 6 in

pi (4.5)^2(6)

pi(20.25)(6)

121.5 pi in^3 or 381.7 in^3

The exact volume of a cylindrical cake with a diameter of 9 inches and a height of 6 inches is 121.5π cubic inches.

The volume of a cylinder can be found using the formula V = πr^2h, where V stands for volume, r is the radius of the base of the cylinder, and h is the height of the cylinder. Given the diameter of the cake is 9 inches, the radius is half of that, which is 4.5 inches. Therefore, the exact volume of the cake is calculated as follows:

V = π × (4.5 )² ×2 × 6

Which simplifies to:

V = π × 20.25 ×2 × 6

So, the exact volume of the cake is:

V = 121.5π  in^3

Answer:

B

Step-by-step explanation:

Answer:

It all depends on how long you have the bike for if you have it for only 1 hour it will be $22 dollars. If you have it for 2 hours it will be $24 dollars.

Answer:

Option B. [tex]116\ m[/tex]

Step-by-step explanation:

Let

x------> the height of the building

we know that

using proportion

[tex]\frac{2}{6}=\frac{x}{348} \\ \\x=348*2/6\\ \\x=116\ m[/tex]

Answer:

Step-by-step explanation:

the expression is equivalent to (cd)5 : c^5×d^5

Answer:

Then tan(x) = 4/3

Step-by-step explanation:

Given that we have a rectangle ABCD, we can affirm the following:

AD = BC = 4

AB = DC = 3

Now, we now that tan = Opposite Side / Adjacent Side

Then the opposite side to the angle x is AB = 4, and the adjacent side to angle x is DC = 3.

Then tan(x) = Opposite Side / Adjacent Side = 4/3 = 1,3333.

Answer: E

Step-by-step explanation:

Answer:

the answer is y=  9/2  x+7

Did you mean the interception or solve for? Anyway I'll do both.

Solve for y:

[tex]

2y-9x=14\Longrightarrow 2y=14+9x \\

2y=14+9x\Longrightarrow y=\frac{14+9x}{2} \\ \boxed{y=7+\frac{9x}{2}, x\in\mathbb{R}}

[/tex]

Intercept: [tex]2y-9x=14\Longrightarrow2y=14\Longrightarrow y=7[/tex]

Answer:

a) The formula for the sequence is

[tex]a_n = 67,000 -3,000(n-1)[/tex]

b) [tex]a_7 = 49,000[/tex]

Step-by-step explanation:

Note that the difference between any two consecutive terms in the sequence is always equal to $3,000

[tex]67,000-70,000= -3,000\\\\64,000-67,000=-3,000[/tex]

Then we have an arithmetic sequence where each term increases by a magnitude of 3,000 with respect to the previous term.

The explicit formula for an arithmetic sequence is:

[tex]a_n = a_1 +d(n-1)[/tex]

Where d is the common difference between the consecutive terms of the sequence

[tex]d = -3,000[/tex]

[tex]a_1[/tex] is the first term, or the value of the house after year 1 [tex]a_1= 67,000[/tex]

n represents the number of years since the house was purchased

With

n={0, 1, 2, 3, 4, 5, 6, 7,.., n}

a) Then the formula for the sequence is

[tex]a_n = 67,000 -3,000(n-1)[/tex]

With

n={0, 1, 2, 3, 4, 5, 6, 7,.., n}

---------------------------------------------------------------------------------------------

b) Now we can use the formula to find the price of the house after 7 years

[tex]a_7 = 67,000 -3,000(7-1)[/tex]

[tex]a_7 = 67,000 -3,000(6)[/tex]

[tex]a_7 = 49,000[/tex]

Answer:

No

Step-by-step explanation:

No it is not the correct answer.