2. A rectangular plot of land is 0.4 kilometer long and 0.07 kilometer wide. What is its
area in square kilometers? Show your reasoning

Answer:

[tex]x=5,y=10[/tex]

Step-by-step explanation:

Given:

                      [tex]4x - 2y = 0[/tex]        equation:1

                 [tex]-x - 2y = -25[/tex]        equation:2

Terminating the equations by subtracting equation:2 from equation:1

                     [tex]4x - 2y -(-x - 2y)= 0-( -25)\\\\ 4x-2y+x+2y=25\\\\5x=25\\\\x=5[/tex]

Putting 'x' in equation :1

                                [tex]4(5) - 2y = 0\\\\20-2y=0\\\\2y=20\\\\y=10[/tex]

[tex]x=5,y=10[/tex]

The value of h(t) when [tex]t=\frac{15}{32}[/tex] is 10.02.

Solution:

Given function [tex]h(t)=-16t^2+15t+6.5[/tex]

To find the value of h(t) when [tex]t=\frac{15}{32}[/tex]:

[tex]h(t)=-16t^2+15t+6.5[/tex]

Substitute [tex]t=\frac{15}{32}[/tex] in the given function.

[tex]$h\left(\frac{15}{32} \right)=-16\left(\frac{15}{32} \right)^2+15\left(\frac{15}{32} \right)+6.5[/tex]

            [tex]$=-16\left(\frac{225}{1024} \right)+15\left(\frac{15}{32} \right)+6.5[/tex]

Now multiply the common terms into inside the bracket.

           [tex]$=-\left(\frac{3600}{1024} \right)+\left(\frac{225}{32} \right)+6.5[/tex]

Now, in the first term, the numerator and denominator both have common factor 16. So reduce the first term into the lowest term.

          [tex]$=-\left(\frac{225}{64} \right)+\left(\frac{225}{32} \right)+6.5[/tex]

To make the denominator same, take LCM of the denominators.

LCM of 64 and 32 = 64

        [tex]$=-\left(\frac{225}{64} \right)+\left(\frac{225\times2}{32\times2} \right)+6.5\times\frac{64}{64}[/tex]

        [tex]$=-\frac{225}{64} +\frac{450}{64}+\frac{416}{64}[/tex]

        [tex]$=\frac{-225+450+416}{64}[/tex]

       [tex]$=\frac{641}{64}[/tex]

       = 10.02

[tex]$h\left(\frac{15}{32} \right)=10.02[/tex]

Hence the value of h(t) when [tex]t=\frac{15}{32}[/tex] is 10.02.

The functions whose graphs include the point (16, 4) is y = x−12.

Option: D.

Step-by-step explanation:

To find the function that passes through the point (16,4).

Substitute the point in all the equations and equate the final values to find the correct equation.

A. y=2x.

Substitute (16,4).

4=2(16).

4≠32.

Thus the equation doesn't contains the point (16,4).

B. y=[tex]x^2[/tex].

Substitute (16,4).

4=[tex]16^2[/tex].

4≠ 256.

Thus the equation doesn't contains the point (16,4)

C. y=x+12.

4=16+12.

4≠28.

Thus the equation doesn't contains the point (16,4)

D. y=x−12.

4=16-12.

4=4.

Thus the equation contains the point (16,4)

E. y=14x.

4=14(16).

4≠224.

Thus the equation doesn't contains the point (16,4)

∴The functions whose graphs include the point (16, 4) is y = x−12.

Answer:

Step-by-step explanation:

There are 2 answers to this question. I know one of them wich is D but the other one I think it;s A

Answer:

Trapezium.

Step-by-step explanation:

Some of the properties of a trapezium include:

- A pair of opposite parallel sides (the long and short base)

- Has 4 sides (meaning it is a quadrilateral)

-

Answer:

rise

Step-by-step explanation:

Answer:

6x+8

Step-by-step explanation:

Answer:

6x + 8 is the answer

Step-by-step explanation:

on Edgenuity 2020

Answer:

1. 7/10 + 3 6/10= 4 13/10= 5 3/10

Answer:

He is correct.

Step-by-step explanation:

9÷4=2.25

The equivalent quarterly interest rate is 2.25%. The annual interest is converted quarterly by dividing the annual rate by 4.

Simple interest is a notion employed in various industries, including banking, finance, and automobiles.

Gavin put money into his savings account, which is compounded annually at an interest rate of 9%

The corresponding quarterly interest rate is, 2.25%.

The annual interest is converted quarterly as;

[tex]\rm n= \frac{9}{4} \\\\ n= 2.25\%[/tex]

Hence, the equivalent quarterly interest rate is 2.25%.

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Answer:

3/2

Step-by-step explanation:

Scale factor=side of second triangle/side of first triangle

Scale factor=12/8

=3/2

Step-by-step explanation:

[tex]Scale \: factor = \frac{8}{12} = \frac{2}{3} \\ [/tex]

Answer:

[tex]-0.8x + 4.8y + 16[/tex]          

Step-by-step explanation:

We have to simplify the given expression:

[tex]4(0.5x + 2.5y-0.7x-1.3y+4)[/tex]

First we group all the like terms of x.

[tex]4((0.5x-0.7x) + 2.5y-1.3y+4))\\=4(-0.2x+ 2.5y-1.3y+4)[/tex]

Next we group all the like terms of y.

[tex]4(-0.2x+ (2.5y-1.3y)+4)\\=4(-0.2x+1.2y+4)[/tex]

Now, we use distributive property for the multiplication,

[tex]4(-0.2x+1.2y+4)\\=(4\times -0.2x) + (4\times 1.2y) + (4\times 4)\\=-0.8x + 4.8y + 16[/tex]

is the required simplified expression.

Answer:

-0.8x + 4.8y + 16

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

92÷4=23

There are a total of 92 barrettes and 4 sisters so you divide the total amount of barrettes with the total amount of people present.

Answer:

23 barrettes

Step-by-step explanation:

92 divided by 4=23 There are a total of 92 barrettes and 4 sisters so you divide the total amount of barrettes with the total amount of people present.

In another way :

So you have 92 then you divide 92 by 4 and that equals 23

Answer:

Option A

Step-by-step explanation:

We want to find an expression that is equivalent to

[tex] {16}^{ \frac{3}{4}x } [/tex]

Recall that:

[tex] {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } [/tex]

We apply this property of exponents to rewrite our expression:

We set a=16, n=4 and m=3x

This implies that:

[tex]{16}^{ \frac{3x}{4} } = \sqrt[4]{ {16}^{3x} } = (\sqrt[4]{ {16} })^{3x} [/tex]

The first choice is correct.

Answer:

A

Step-by-step explanation:

edg review 2020

Answer:

That's a very dumb question, because some of her friends could be fakers and users. But, I'll answer it.

86 subtracted by 2 is 84.

It says she gave 3 to each friend so:

84 divided by 3 is 28.

She has 28 friends.

Answer:infinitely many solutions

Step-by-step explanation: 4*2x= 8x and (7*4)+3 = 31. 8x+31 is equal to itself, therefore any value of x makes the equation true.

Answer:

3353

Step-by-step explanation:

1. Simplify 960 + 2 to 962.

4 · (962 − 125) + 5

2. Simplify 962 − 125 to 837.

4 · 837 + 5

3. Simplify 4 · 837 to 3348.

3348 + 5

4. Simplify

3353

Answer: 3353

Step-by-step explanation:

4 × 960 = 3840

4 × 2 = 8

4 × -125 = -500

-500 + 8 + 3840 = 3348

3348 + 5 = 3353

Answer:

The solution is -5 or 11

Step-by-step explanation:

We are given the equation;

[tex]4(3-x)^\frac{4}{3}-5=59[/tex]

We are supposed to solve the equation;

Taking 5 to the other side;

[tex]4(3-x)^\frac{4}{3}=59+5[/tex]

[tex]4(3-x)^\frac{4}{3}=64[/tex]

Dividing both sides by 4

[tex](3-x)^\frac{4}{3}=\frac{64}{4}[/tex]

[tex](3-x)^\frac{4}{3}=16[/tex]

We can cube both sides;

[tex]((3-x)^\frac{4}{3})^3=16^3[/tex]

[tex](3-x)^4=4096[/tex]

Then we can get the fourth root on both sides of the equation;

[tex]\sqrt[4]{ (3-x)^4} =\sqrt[4]{4096}[/tex]

We get;

[tex]3-x=+8 or -8[/tex]

Solving for x

[tex]3-x=8 and 3-x=-8[/tex]

Therefore;

[tex]x=-5 or 11[/tex]

Therefore, the solution is -5 or 11

Answer:

(y + 5) = -7(x + 3)

Step-by-step explanation:

Point Slope Form:  (y - y1) = m(x - x1)

Step 1:  Find Slope

m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

m = [tex]\frac{-19 - (-5)}{-1 - (-3)}[/tex]

m = [tex]\frac{-19 + 5}{-1 + 3}[/tex]

m = [tex]\frac{-14}{2}[/tex]

m = -7

Step 2:  Put into point slope form

Point Slope Form:  (y - y1) = m(x - x1)

(y - (-5)) = -7(x - (-3))

(y + 5) = -7(x + 3)

Answer:

Step-by-step explanation:

First, we can convert feet to inches

1 foot=12 inches

7 feet=84 inches

Next, we find out inches per hour

84 inches/27 1/2 hours

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

27 1/2 27 1/2

=3.054 inches/hour

Answer:

375 meters

Step-by-step explanation:

We use the tangent ratio to determine the height of the height of the cliff.

We have that, the boat is 600 meters from the base of a cliff.

We also know that, the angle of elevation to the top of the cliff is 32°

Using the tangent ratio, we have:

[tex] \tan(32) = \frac{h}{600} [/tex]

We solve for h to obtain:

[tex]600\tan(32) = h[/tex]

[tex]h = 374.92[/tex]

Therefore the height of the cliff is approximately 375 meters

The angle of elevation is an angle that is formed between the horizontal line and the line of sight, hence the Height of the cliff is

374.4 meters

Given Data

Opposite/Height of cliff = ??

Adjacent/Distance of boat from base = 600 meters

Angle of elevation ∅  = 32°

By applying SOH CAT TOA

Tan  ∅ = Opp/Adj

Substituting our given Data we have

Tan 32 = Opp/600

0.624 = Opp/600

Cross multiply we have

Opp = 0.624*600

Opp = 374.4 meters

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Answer:

-27 and -18

Step-by-step explanation:

Solve algebraically. Use a variable and an expression to represent the numbers.

let the smaller number be "x"

The bigger number is x + 9.

The two numbers are "x" and "x + 9".

The sum of two numbers means when you add them together. If their number is −45, then:

x + x + 9 = −45

Simplify and isolate "x" to solve in the equation.

x + x + 9 = −45        Collect like terms (numbers that have "x") to simplify

2x + 9 = −45        Isolate "x"

2x + 9 - 9 = −45 - 9        Subtract 9 from both sides

2x = −54

2x/2 = −54/2        Divide both sides by 2

x = -27       Value of smaller number

The bigger number is x + 9. Substitute "x" for -27 and solve.

x + 9

= -27 + 9        Add together

= -18        Value of bigger number

Therefore the two numbers are -27 and -18.

Answer:

if -45 + -9 = -54 that means - 54 + 9 = -45

Step-by-step explanation:

Answer:

2x((3x-2)x(3x+2))²

Final answer:

The correct equivalent expressions for 162x⁴-144x²+32 are 2(81x⁴ - 72x² + 16) and 2(9x² - 4)², which correspond to options A and C.

Explanation:

The expression 162x⁴-144x²+32 can be factored by first taking out the greatest common factor (GCF), which is 2, resulting in 2(81x⁴ - 72x² + 16). If we look at the inside expression, we can recognize that it is a perfect square trinomial because 81x⁴ is the square of 9x² and 16 is the square of 4, and the middle term (-72x²) is twice the product of 9x² and 4. Consequently, the expression inside the parentheses can be written as the square of a binomial, resulting in 2(9x² - 4)². Therefore, the equivalent expressions for 162x⁴ - 144x² + 32 are:

Thus, the answers are A and C from the options provided.

Answer:

16272

Step-by-step explanation:

just use mutiplication

Answer:

20 per min

Step-by-step explanation:

Answer: 1200 boxes per 1 hour

Step-by-step explanation: 15 divided by 3 is 5. 300 divided by 100. 100 boxes in 5 minutes. 5 times x is 60. 60 is a hour. 60 divided by 5 is 12. 100 times 12 is 1200. 1200 boxes per 1 hour.

With y-x=0, add x to both sides to get y=x.

Now you can substitute either x or y

7x-9x=8 or 7y-9y=8 which is the same thing

-2x=8 or -2y=8

x=-4 or y=-4

Hope this helped!

Final answer:

It will take Shaun 156 hours to mow 78 lawns based on his current rate of mowing 3 lawns in 6 hours.

Explanation:

To determine how many hours it will take Shaun to mow 78 lawns based on the rate at which he mows 3 lawns in 6 hours, we will use a proportion. First, we find the rate at which Shaun mows lawns per hour, which is 3 lawns / 6 hours = 0.5 lawns per hour. Next, we set up a proportion where the total number of lawns he needs to mow (78 lawns) is set equal to the product of the number of hours it takes (which we are trying to find) and the rate at which he mows lawns (0.5 lawns per hour).

So, the proportion is:
78 lawns = x hours ( 0.5 lawns/hour.)

Dividing both sides of the equation by 0.5 lawns/hour gives us:

x hours = 78 lawns / 0.5 lawns/hour

x hours = 156 hours.

Therefore, it will take Shaun 156 hours to mow 78 lawns at his current rate.

Final answer:

The weight gain in days per pound for Lin's puppy is 8 days per pound.

Explanation:

The weight gain in days per pound can be calculated by taking the reciprocal of the rate of weight gain. In this case, Lin's puppy is gaining weight at a rate of 0.125 pounds per day. To find the weight gain in days per pound, we can take the reciprocal of 0.125, which is 1/0.125 = 8 days per pound.

Answer:

0.525

Step-by-step explanation:

It's easy

Answer:

0.53

Step-by-step explanation:

(x²-3²)(x+5) is the binomial that is a factor of the polynomial P(x) = x³ + 5x² − 9x − 45

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is P(x) = x³ + 5x² − 9x − 45.

Factor out the greatest common factor from each group.

x³ + 5x² − 9x − 45.

x cube plus five times of x square minus nine times of x minus forty five.

x² (x+5)-9(x+5)

(x²-9)(x+5)

We can write 9 as a square of three

(x²-3²)(x+5)

A mathematical expression consisting of two terms connected by a plus sign or minus sign

Hence, (x²-3²)(x+5) is the binomial that is a factor of the polynomial P(x) = x³ + 5x² − 9x − 45

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