Find the value of each variable

Answer:

Step-by-step explanation:

If a line is parallel to another it must have the same slope

The slope/intercept form of a line is y = mx + b where m is the slope and b the y intercept

The line y = 2x + 5 has slope 2

So the slope of the line that passes through (2,3) must also have the slope 2

We have
y = 2x + b; Substituting x =2, y =3 in this equation gives us
3 = 2 (2) + b or b = -1

Hence the equation of the line is
y = 2x -1

Cross-check

Substitute for x = 2 ==> y = 2(2) - 1 = 3 which is consistent

Answer:

18.86

Step-by-step explanation:

5 ⟌94.3

90 ÷ 5 = 18

   18

5 ⟌94.3

    -90

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

      4.3

cant divide by 4 so add a decimal

5 × 0.8 = 4

   18.8

5 ⟌4.3

   - 4.0

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

     0.3

5 × 0.06 = 0.3

  18.86

5 ⟌0.3

  - 0.3

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

     0

I hope this helps!

Answer:

The answer is D = 9/57

Step-by-step explanation:

Get the variable D by itself as stated to solve for D.

I got the other numbers to the other side.

70D + 6 - 9D = 35 + 4D - 20.

(70D - 9D - 4D) = (35 - 20 - 6)

57D = 9

D = 9/57

Answer:

[tex]x=4,\:x=-2[/tex]

Step-by-step explanation:

Both equations are equal to y, so we can simply set them equal to each other and solve for x:

[tex]x^2-5=2x+3\\\\x^2-8=2x\\\\x^2-2x-8=0\\\\(x-4)(x+2)=0\\\\x=4,\:x=-2[/tex]

Answer:

324

Step-by-step explanation:

Formula: [tex]a_{n} =a_{1} +(n-1)d[/tex]

=> [tex]a_{46} =9_{1} +(n-1)7\\[/tex]

          = [tex]9_{1} +(46-1)7\\[/tex]

          = [tex]9+(45)7\\[/tex]

          = [tex]9+315[/tex]

          = [tex]324[/tex]

:D

The solutions for the following system of equations will be (–1, 6) and (1, 6). Then the correct option is B.

The equations are given below.

–3x² + 4y = 21 ...1

   4x² + y = 10  ...2

Multiply equation 1 by 4 and equation 2 by 3, then we have

–12x² + 16y = 84

   12x² + 3y = 30  

Add both equations, then we have

19y = 114

   y = 6

From equation 2, we have

4x² + 6 = 10

      4x² = 4

        x² = 1

         x = ±1

         x = 1, –1

Then the correct option is B.

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The liters of smoothies sold is 9 7/8 liters.

An equation is a statement formed when two algebraic expressions are equated by an equal sign.

The volunteer prepares 12 1/2 = 25/2 liters of smoothies

The remaining amount of smoothies is 2 5/8 = 21/8 liters of smoothies

Let the amount of smoothies sold is x liters

Then the equation formed to determine the value of x is

x = (25/2) - (21/8)

x = 79/8

x = 9 7/8 liters

Therefore, the liters of smoothies sold is 9 7/8 liters.

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Let's solve

Multiply- on both sides

Multiply 24 on boths sides

Solution set

Answer:

Step-by-step explanation:

Given inequality:

[tex]\sf \dfrac{h}{-24} < 18[/tex]

Eliminate the denominator of the fraction by multiplying both sides by -24, remembering to flip the relation (inequality symbol) as the factor is negative.

[tex]\implies \sf \dfrac{h}{-24} \cdot -24 > 18 \cdot -24[/tex]

[tex]\implies \sf h > -432[/tex]

Therefore, the solution is [tex]\sf h > -432[/tex]

P(A | B) is 2/10 = 0.2.

P(A | B) means the probability that a students pays both basketball and football. It is the intersection of both circles on the venn diagram.

P(A | B) = number of students that play both games / total number of students

2/10 = 0.2

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[tex]\left(\sqrt[3]{-3} \right) \left(\sqrt[3]{-5}\right)\\\\=\left( \sqrt[3]{-1}\right \sqrt[3]{3}) \left(\sqrt[3]{-1} \sqrt[3]{5} \right)\\\\=\sqrt[3]{(-1)(-1)} \cdot \sqrt[3]{(3)(5)}\\\\=\sqrt[3]{1} \cdot \sqrt[3]{15}\\\\=1\cdot \sqrt[3]{15}\\\\=\sqrt[3]{15}[/tex]

The factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)

The expression is given as:

x^3 + 4x^2 +5x + 20

Group the expression into two

(x^3 + 4x^2) + (5x + 20)

Factorize each group

x^2(x + 4) + 5(x + 4)

Factor out x + 4

(x^2 + 5)(x + 4)

Hence, the factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)

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The point (3, -4) lie on the line y + 4 = 4(x - 3) because the point (3,-4) satisfy the line option (A) is correct.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have an equation of a line:

y + 4 = 4(x - 3)

A (3,-4)  

Plug the above points in the equation of the line.

-4 + 4 = 4(3 -3)

0 = 0    (true)

The point lies on the line

Similarly checking for others points we will find that points (2,9), (0,0) , (1,-11), (1,11), and (-2, 3) does not lie on the line y + 4 = 4(x - 3)

Thus, the point (3, -4) lie on the line y + 4 = 4(x - 3) because the point (3,-4) satisfy the line option (A) is correct.

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The bank which will charge a customer more in fees if she writes 18 checks per month, and by how much is Bank A by $0.30

let

Bank A = 2.50 + 0.15x

= 2.50 + 0.15(18)

= 2.50 + 2.7

= $5.20

Bank B = 4 + 0.05x

= 4 + 0.05(18)

= 4 + 0.9

= $4.9

Difference in charges = $5.20 - $4.90

= $0.30

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Answer: x = 0

Step-by-step explanation:

Given:

   x + 4x = 0

Combine like terms:

   5x = 0

Divide both sides of the equation by 5:

   x = 0

We can also check our work by graphing. See attached, intercepts of the x-axis are solutions.

Answer:

352

Step-by-step explanation:

it repeated more than once

to get the equation of any straight line, we simply need two points off of it, let's use the ones in the table.

[tex]\begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} -1&-10\\ 3&14\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{14 +10}{3 +1}\implies \cfrac{24}{4}\implies 6[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{6}(x-\stackrel{x_1}{(-1)}) \\\\\\ y+10=6(x+1)\implies y+10=6x+6\implies y=6x-4[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

We need to find volume of the given Cylinder, with information :

[tex]\qquad \sf  \dashrightarrow \:Volume_{(Cylinder)} = \pi r²h[/tex]

[tex]\qquad \sf  \dashrightarrow \:Volume_{(Cylinder)} = \pi \sdot(12) {}^{2} \sdot17[/tex]

[tex]\qquad \sf  \dashrightarrow \:Volume_{(Cylinder)} = \pi \sdot144{}^{} \sdot17[/tex]

[tex]\qquad \sf  \dashrightarrow \:Volume_{(Cylinder)} = 2448 \pi \: \: unit {}^{3} [/tex]

So, correct choice is B

The volume of the given cylinder is 2448π cubic units

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

We have to find the volume of the given cylinder

Radius is 12 units

Height is 17 units

Volume of cylinder= πr²h

Plug in the values of radius and height

Volume = π×12²×17

=π×144×17

=2448π cubic units

Hence, the volume of the given cylinder is 2448π cubic units

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The complete question is

"A solid sphere is cut into 12 equal wedges. The volume of each wedge is V= 4/3πr³. Solve the formula for r."

A solid sphere is cut into 12 equal wedges. The volume of each wedge is V= 4/3πr³. The value of r is (9V/π)^1/3.

It is given that;

The  Volume of a sphere = V = 4/3πr³

Dividing into 12

4/3 x 1/12 πr³ = 1/9πr³

V = 1/9πr³

Cross multiply

9V = πr³

Divide both sides by π

9V/ π = πr³/ π

9V/ π = r³

Take the cube root of both sides

r = (9V/π)^1/3

Thus, The value of r is (9V/π)^1/3.

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g(x) = ¹/₂f(x - 2) -------> y-intercept at (0, - ¹/₂)

h(x) = f(x - ¹/₂) ------->  x-intercept at (1.5, 0)

j(x) = f(x) - ¹/₂ ------->  vertical asymptote at x = 0

m(x) = function decreases as x increases

We are given the function;

f(x) = In (x)

Now, from the given tiles and when we punch the respective values for the given functions, we can say that;

g(x) = ¹/₂f(x - 2) -------> y-intercept at (0, - ¹/₂)

h(x) = f(x - ¹/₂) ------->  x-intercept at (1.5, 0)

j(x) = f(x) - ¹/₂ ------->  vertical asymptote at x = 0

m(x) = function decreases as x increases

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Answer:

1203.6 ---- the six is recurring ( .666666...)

Step-by-step explanation:

volume of hemisphere= [tex]\frac{2}{3}[/tex] x 3.14 x r^3

volume of cylinder= 3.14 x r^3 x h

1. Volume of hemisphere= 2/3 x 3.14 x 5^3 = 261.6 recurring

2. volume of cylinder = 3.14 x 5^2 x12 = 942

3. add the two together -----------> 1203.6

answer 2/3

check the attachments for more info

hope it helps :)

The functions f(x) and g(x) are equal for the x = 2/3

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given that, are two functions, f(x) = -3x + 4 and g(x) = 2, we need to find the value of x for which both are equal,

So,  

For f(x) = g(x) we should equate the two functions to get the value of x.

f(x) = g(x)

-3x + 4 =  2

-3x + 4 - 4 = 2 - 4

-3x = -2

Dividing by -3 on both sides;

(-3x)/-3 = (-2)/-3

x = 2/3

Hence, the  functions f(x) and g(x) are equal for the x = 2/3

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Answer:

0.93x

Step-by-step explanation:

the total amount is:

x(1-15%+8%)=0.93x

so the answer is 0.93x

Answer:

Second option

Step-by-step explanation:

Given the following question:

We are given four choices and we need to determine which choice is a rational number. In order for any integer to be a rational number you have to be able to write it as a fraction.

In this case, options one and four are immediately excluded since they are repeating decimals. They cannot be written as a fraction which leaves us with the second option or the third option.

[tex]\sqrt{36}[/tex]
[tex]\sqrt{36} =6\times6[/tex]
[tex]=6=\frac{6}{1}[/tex]
[tex]=\frac{6}{1}[/tex]

Your answer is the second option or "sqrt36."

Hope this helps.

Answer: D (82, 84, 90, 80, 74)

Finding Range:

To find range, you must subtract the smallest number to the highest number in that number pattern.

For example, the highest in D is 90, and the smallest is 74. 90-74 is 16, which matches the range for a possible price (16 = 16).

Range is basically the most easiest to find out of median, mean, and mode. You just have to find the greatest-smallest = range.

Finding Mean:

To find mean, you must add all the numbers up then divide the sum by the QUANTITIY of all the numbers.  

For example, if we add 82, 84, 90, 80, and 74, we would get 410. Since there are 5 numbers that make up 410, we divide 410 by 5, and therefore getting 82. This matches the mean of the price of a textbook (82 = 82).

Mean is basically easy to find as you just add all the numbers and divide it by how much numbers make that sum.

Conclusion:

In conclusion, the mean and range all match a possible price of the textbook, having a range of $16 and a mean of $82. Thus, D is the right answer.

The correct option is D (82, 84, 90, 74)

Range is subtract the smallest number to the highest number in that number pattern.

Mean is addition of all the numbers up then divide the sum by the quantities of all the numbers.  

The highest in D is 90, and the smallest is 74. 90-74 is 16, which matches the range for a possible price (16 = 16).

Addition of 82, 84, 90, 80, and 74, we would get 410. Since there are 5 numbers that make up 410, we divide 410 by 5, and therefore getting 82. This matches the mean of the price of a textbook (82 = 82).

Therefore, the possible prices for the textbook is the possible prices for the textbook is  (82, 84, 90, 74).

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Answer:

Step-by-step explanation:

Note

Answer: Jane's question

Howard merely asked if a visit had taken place. There isn't a number anywhere or one that can be implied.

Jane asked for a number. It requires that the responder gives a number with no embellishment. The question asks for the number of times something has occurred and there is a time frame for the answer. That usually is the characteristic of a statistical survey.

[tex]~~~~~~|x-4| = 17\\\\\implies x -4 = 17~~~~ \text{or}~~~~~ x -4 = -17\\\\\implies x = 17+4~~~~\text{or}~~~~~ x = -17+4\\\\\implies x = 21~~~~~~~~~\text{or}~~~~~x = -13[/tex]

Answer:

(5*10^3)*(9*10^7) = 4.5*10^11

(7*10^5) / (2*10^2) = 3.5*10^3

Step-by-step explanation:

calculate 5 multiply by 9

5*9=45

the multiple of the power in the same base of number is calculated by using addition(+)

(10^3)*(10^7) = 10^(3+7)

= 10^10

in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so

45*(10^10)

= (4.5*10^1) * (10^10)

= 4.5*10^(1+10)

= 4.5*10^11

calculate 7 divide by 2

7/2=3.5

the dividing of the power in the same base of number is calculated by using subtraction(-)

(10^5)/(10^2)

= 10^(5-2)

= 10^3

in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so

3.5*10^3

Answer:

Step-by-step explanation:

(5×10³)×(9×10⁷)

= 5×10³×9×10⁷

= 5×9×10³×10⁷      (commutative property)

= (5×9)×(10³×10⁷)  (associative property)

= 45 × 10³⁺⁷

= 45 × 10¹⁰.           (Exponent property)

= 4.5 × 10¹¹

…………………………………………

(7×10⁵) / (2×10²)

= (7/2) × (10⁵/10²)

= 3.5 × 10⁵⁻²

= 3.5 × 10³