Consider the expressions below. for each expression below, select the letter that corresponds to the equivalent expression given above. is equivalent to expression . is equivalent to expression . is equivalent to expression . is equivalent to expression .

The value of the expression is 0.0265. Using exponents and power rules, the required value is calculated.

The important exponent and power rules are:

The given expression is [tex]126^{-3/4}[/tex]

Using calculator: [tex]126^{-3/4}[/tex] = 0.0265

Applying the exponent rule for evaluating the given expression:

[tex]126^{-3/4}[/tex]

Applying the negative power rule;

I.e., a⁻ⁿ = 1/aⁿ

⇒ [tex]126^{-3/4}=\frac{1}{126^{3/4}}[/tex]

Applying fractional exponent rule;

I.e., [tex]a^{\frac{x}{y} } = \sqrt[y]{a^x}[/tex]

⇒ [tex]\frac{1}{126^{3/4}}=\frac{1}{\sqrt[4]{126^3} }[/tex]

⇒ 1/[tex]\sqrt[4]{2000376}[/tex]

⇒ 1/37.6077

⇒ 0.0265

Therefore, the value of the given expression is 0.0265.

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If they work together, they need 15/8 hours to assemble one shelving unit.

What does work mean in math?

According to tittle, we know worker A can  assemble a shelving unit in 5 hours , which means worker A can finish 1/5 of work in 1 hour . And worker B can finish 1/3 of work in 1 hour.

If A & B work together , they will spend the same time t to assemble only one shelving .

That means,                  1/5t + 1/3 t = 1                         (equation)

1/5 t is worker A's workload during time t , 1/3 t is worker B workload.

So,   1/5 t + 1/3t = 1  is the answer

     ⇒ 5t + 3t = 15

     ⇒ t = 15/8 hours

If they work together, they need 15/8 hours to assemble one shelving unit.

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Answer:

Letter C is the correct answer or  1/5 t + 1/3t = 1

The quotient in lowest term exists 2/3.

An improper fraction exists as a fraction whose numerator exists equivalent to, larger than, or of equivalent or higher degree than the denominator.

Given the quotient: [tex]$4\frac{2}{3} \div 7[/tex]

Write [tex]$\frac{2}{3}[/tex] in improper fraction

[tex]$4\frac{2}{3}= \frac{14}{3}[/tex]

Dividing throughout by 7 on both sides of the equation, we get

[tex]$4\frac{2}{3} \div 7 = \frac{14}{3}\div 7[/tex]

Change the division sign to multiplication by taking the reciprocal of 7

[tex]$\frac{14}{3}\div 7 = \frac{14}{3} \times \frac{1}{7}[/tex]

Simplifying the above equation, we get

[tex]$\frac{14}{3}\div 7 = \frac{2}{3}[/tex]

Therefore, the quotient in lowest term exists 2/3.

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Work Shown:

m = (y2 - y1)/(x2 - x1)

-4/3 = (a - (-3))/(-3 - 3)

-4/3 = (a+3)/(-6)

-4*(-6) = 3(a+3)

24 = 3a+9

3a+9 = 24

3a = 24-9

3a = 15

a = 15/3

a = 5

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

Let's solve ~

Area of shaded region is equal to :

Area of rectangle - Area of two triangles ~

1. Area of rectangle :

[tex]\qquad \sf  \dashrightarrow \: length \times width[/tex]

[tex]\qquad \sf  \dashrightarrow \: 20 \times 15[/tex]

[tex]\qquad \sf  \dashrightarrow \: 300 \: \: cm {}^{2} [/tex]

2. Area of first triangle :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (base) \times (height)[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (20 - 18) \times (15)[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (2) \times (15)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 15 \: \: cm {}^{2} [/tex]

3. Area of second triangle :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (base) \times (height)[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (6) \times(20)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 \times 20[/tex]

[tex]\qquad \sf  \dashrightarrow \: 60 \: \: cm {}^{2} [/tex]

Area of shaded region is :

[tex]\qquad \sf  \dashrightarrow \: 300 - (15 + 60)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 300 - 75[/tex]

[tex]\qquad \sf  \dashrightarrow \: 225 \: \: cm {}^{2} [/tex]

The point of intersection of the two lines is at (1,-1)

The given system of expression is shown below

x - 2y = 3

5x + 3y = 2

The solution to the system of equation is the point of intersection

From equation 1

x = 3 + 2y

Substitute into 2

5(3+2y) + 3y = 2

15 +10y + 3y = 2

13y = -13

y = -1

Substitute y = -1 into 3

x = 3 + 2y

x = 3+(-2)

x = 1

Hence the point of intersection of the two lines is at (1,-1)

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Answer:

35-17=3y

Step-by-step explanation:

3y+17=35

    -17  -17

3y=35-17

The domain of the exponential function shown in the graph is -oo < x < oo

The function on the graph is an exponential function.

The domain is the set of x values the function can take

From the graph, we have the following x values

This means that the domain of x in the graph is -oo < x < oo

Hence, the domain of the exponential function shown in the graph is -oo < x < oo

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Solution -:

[tex] \bold{ \underline{ \underline{Given}}}[/tex]

-3x7x7x7x7x7x7

[tex]\bold{\underline {\underline{lets \: begin}}}[/tex]

We have,,

[tex] -3 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \\ = - 3¹ \times {7}^{6} [/tex]

As like example→ 2⁴

here 2 is base and 4 is power , index or exponent. and 2⁴ is known as Exponential form.

Formula for finding area of rhombus: [tex]\frac{d1 * d2}{2}[/tex]

d₁ = 16 yd

Area = 72 yd²

Rhombus Area =>

[tex]\frac{16 * d2}{2} = 72[/tex]

16*d₂ = 144

d₂ = 9

AC = 9 yd

Hope it helps!

Step-by-step explanation:

A.

the height, the 17cm leg and half of the baseline (16/2 = 8cm) create a right-angled triangle.

so, Pythagoras applies.

c² = a² + b²

c being the Hypotenuse (side opposite of the 90° angle).

so, we get

17² = height² + 8²

289 = height² + 64

225 = height²

height = sqrt(225) = 15cm

B.

the answer to this is the surface area of the whole box.

it has 5 sides :

bottom : 20×16 rectangle = 320 cm²

left and right : 20×17 rectangles = 340×2 = 680 cm²

front and back : 16×15/2 triangles = 120×2 = 240 cm²

in total that is

320 + 680 + 240 = 1,240 cm² of cardboard

Answer:

true

Step-by-step explanation:

thats really it i believe its true

The cell phone carrier had 250 subscribers before the strategy was introduced. After the new strategy is introduced, the number of staffs increased by a factor of 1.4.

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

An exponential function is in the form:

y = abˣ

Where a is the initial value of y and b is the multiplication factor.

Let f(t) represents the number of subscribers and t represents the time in months. Hence:

[tex]f(t) = 250(1.4)^t[/tex]

a = 250, b = 1.4

The cell phone carrier had 250 subscribers before the strategy was introduced. After the new strategy is introduced, the number of staffs increased by a factor of 1.4.

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Answer: 250,      1 month,      and    1.4

The average rate of change of [tex]f(x)[/tex] on [tex]12\le x\le36[/tex] is the difference quotient

[tex]\dfrac{f(36) - f(12)}{36 - 12} = \dfrac{28 - 34}{24} = \boxed{-\dfrac14}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{(x + 3)^0}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{(x + 3)^0}[/tex]

[tex]\text{Anything raised to the 0 power it automatically equal to 1.}[/tex]

[tex]\huge\text{So, this mean that your answer should be: \boxed{\mathsf 1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

18

Step-by-step explanation:

The arrows on lines AB and CD indicate that these 2 shapes are similar and these 2 lines are corresponding so :

Linear scale factor :

12 ÷ 10 = 1.2 or 6/5

Let's use the fraction form

Using the linear scale factor we can make an equation to solve for x :

2x+4 = 6/5(x+8)

Expand the brackets :

2x+4 = 6/5x + 9.6

Subtract 4 from both sides :

2x = 6/5x + 5.6

Subtract 6/5x from both sides :

4/5x = 5.6

Divide both sides by 4/5 :

x = 7

Now substitute this value into the expression for the length of AE :

AE = 2(7) + 4

AE = 14 + 4

AE = 18

Hope this helped and have a good day

Answer:

116 units

Step-by-step explanation:

AE + ED = 180 because they make a straight angle and a straight angle is 180 degrees or half of a circle 360/2.

AE = 2x + 4 and ED = x +8 added together they equal 180

2x + 4 + x + 8 = 180  Combine the like terms

3x + 12 = 180  Subtract 12 from both sides of the equation

3x = 168  Divide both sides by 3

x = 56

Now that we know that x is 56 we can plug that in for AE to find its length

2x + 4

2(56) + 4

112 + 4

116

we can conclude that the last digit of the product of all the numbers between 11 and 29 is 0.

Here we want to find the last digit of the product between all the whole numbers larger than 11 and smaller than 29.

Then we have the product:

P = 12*13*14*15*16*17*18*19*20*21*22*23*24*25*26*27*28

Now, notice that there is a 20 there.

Any number times 20 will end with a zero, then:

P = 20*(12*13*14*15*16*17*18*19*21*22*23*24*25*26*27*28)

Only with that, we can conclude that the last digit of the product of all the numbers between 11 and 29 is 0.

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The surface area of the cylinder with the given height and radius is 835.2 square inches

The given parameters are

The surface area is then calculated using the following formula

A = 2πr² + 2πrh

Substitute the given values in the above equation

So, we have:

A = 2 * 3.14 * 7^2 + 2 * 3.14 * 7 * 12

Evaluate the exponents

A = 2 * 3.14 * 49 + 2 * 3.14 * 7 * 12

Evaluate the products

A = 307.72 + 527.52

Evaluate the sum

A = 835.2

Hence, the surface area of the cylinder with the given height and radius is 835.2 square inches

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Answer:

12√2.

Step-by-step explanation:

You can do this by the Pythagoras theorem:

20^2 = x^2 + (4sqrt7)^2    where  x is the distance required.

x^2 = 20^2 - (4sqrt7)^2

      = 400 - 112

      =  288

x  = √288

   =  √144 *√2

   =   12√2.

The building is 151 meters tall

From the question, we have the following parameters about the building and the man

Man's height = 138 cm

Man's shadow = 149 cm

Building's shadow = 163 m

Based on the above parameters, we have the following equivalent ratio:

Ratio = Height : Shadow

So, we have:

Man's height : Man's shadow = Building's height : Building's shadow

Substitute the known values in the above equation

138 cm : 149 cm = Building's height : 163 m

Remove the units

138 : 149 = Building's height : 163

Express as fraction

138 /149 = Building's height/163

Multiply both sides by 163

Building's height = 163 * 138 /149

Evaluate the product

Building's height = 151 m

Hence, the building is 151 meters tall

So, the complete parameters are:

Man's height = 138 cm

Man's shadow = 149 cm

Building's shadow = 163 m

Building's height = 151 m

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Equivalent to tan A =[tex]\frac{y}{x}[/tex]

Equivalent to tan A:

A right triangle ABC so that m∠C = 90°

The lengths are:

                           Side a is opposite ∠A,

                           Side b is opposite ∠B,

                           Side c (the hypotenuse) is opposite ∠C

Because cos A = x, therefore

[tex]x =\frac{b}{c}[/tex]  => [tex]b = cx[/tex]                  (1)

Because sin A = y, therefore

[tex]y =\frac{a}{c}[/tex] => [tex]a = cy[/tex]                 (2)

By definition,

tan A = a/b

         [tex]=\frac{cy}{cx}[/tex]

        [tex]=\frac{y}{x}[/tex]

Equivalent to tan A =[tex]\frac{y}{x}[/tex]

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Step-by-step explanation:

that is a huge gas tank. that car is practically a tank.

the volume of the gas tank is

4×3×3 = 36 m³

I assume you use liters for liquid mass.

remember

1 meter (m) = 100 centimeter (cm)

10 cm = 1/10 m = 1 decimeter (dm)

1 liter = 10×10×10 cm³ = 1000cm³ = 1 dm³

1 m³ = 10×10×10 dm³ = 1000 dm³ = 1000 liters

so, his gas tank contained 36,000 liters.

he used the 36,000 liters in 45 hours.

his corresponding rate of gas consumption was

36,000 liters / 45 hours = 800 liters / hour

Answer: 3

Step-by-step explanation:

The missing number in the simplified ratio ?/4 is 3.

Here, we have to find the missing number in the simplified ratio ?/4, we need to determine the ratio of girls to boys in Mr. Stevenson's class.

Given that there are 6 girls and 8 boys in the class, the ratio of girls to boys can be expressed as:

Number of girls : Number of boys = 6 : 8

To simplify the ratio, we can divide both the number of girls and the number of boys by their greatest common divisor (GCD).

In this case, the GCD of 6 and 8 is 2.

Dividing both 6 and 8 by 2, we get:

Number of girls : Number of boys = 6/2 : 8/2 = 3 : 4

So, the simplified ratio of girls to boys is 3/4.

Therefore, the missing number in the simplified ratio ?/4 is 3.

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Answer:

-65

Step-by-step explanation:

23-2(17+3^3)

23-2(17+27)

23-2(44)

23-88

=-65

The discriminant of the given quadratic equation as in the task content can be evaluated by means of the formula; D = b²-4ac and it's value is; 13.

According to the task content, it follows that the quadratic equation whose discriminant is to be determined is; x²-5x+3=0.

By comparison with the standard form equation of a quadratic graph which goes thus; ax²+bx +c = 0, in which case, the determinant is given by the expression; b² - 4ac.

We can consequently evaluate the determinant of the quadratic equation in discuss as follows;

Determinant = b² -4ac = (-5)² - (4×1×3) = 25 - 12

Hence, the determinant in this case is; 13.

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Answer:

The first option:

[tex]x^2-5x+9[/tex]

Step-by-step explanation:

Trust me I am right.

If you need work please ask!

Have a nice day!