Two runners start from the same point at the same time. They will be 4 miles apart at the end of two hours if running in the same direction, and they will be 16 miles apart at the end of one hour if running in opposite directions. Find their speeds.

Answer:

ans: -4( x-3 )( x-4 ) I.e -4( x² + x - 12 )

Step-by-step explanation:

as per question

1- (2x-7)²

= (1 + 2x - 7)(1- 2x + 7)

= ( 2x - 6)(-2x +8)

= -4(x-3)(x+4)

The simplified form of [tex](2x-7)^{2}[/tex] is [tex]4x^{2} +49-28x[/tex].

And we get, [tex]-4x^{2} -48+28x[/tex] when we subtract [tex](2x-7)^{2}[/tex] from 1.

Polynomials are algebraic expressions that consist of variables and coefficients.

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

According to the given question

We have a polynomial [tex](2x -7)^{2}[/tex].

Therefore, the simplified form of [tex](2x-7)^{2}[/tex] is given by

[tex](2x-7)^{2} =(2x)^{2} +(7)^{2} -2(2x)(7)[/tex]

⇒[tex](2x-7)^{2} =4x^{2} +49-28x[/tex]

Therefore, the simplified form of [tex](2x-7)^{2}[/tex] is [tex]4x^{2} +49-28x[/tex].

Now,

[tex]1-(4x^{2} +49-28x)= 1-4x^{2} -49+28x[/tex]

⇒[tex]1-(4x^{2} +49-28x)=-4x^{2} -48+28x[/tex]

Hence, we get [tex]-4x^{2} -48+28x[/tex] when we subtract [tex](2x-7)^{2}[/tex] from 1.

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Answer:

[tex]4p + 9[/tex]

Step-by-step explanation:

Commutative property of addition:

Changing the order of addends does not change the sum.

Answer:

4p+9

Step-by-step explanation:

Addition is the same reversed.

For example,

7+5=12

AND

5+7=12

Answer:

slope = 1/-7

Step-by-step explanation:

We have two points which are (3,2) and (-4,3) .

To find slope , use the slope formula

m = ( y² - y¹ ) / ( x² - x¹)

Where,

substitute the values

m = ( 3 - 2 ) / ( - 4 - 3)

m = 1/-7

Hence, slope of line is 1/-7

Answer:

In could be mean inches? otherwise there is not enough context to know sorry :/

Step-by-step explanation:

Answer:the answer is 90

Answer:

10

Step-by-step explanation:

Do HCF of 40,50,60 and the answer is 10

Answer:

1.95

Step-by-step explanation:

Answer: Martina's margin of error is 1.5.

Step-by-step explanation:

Given: Average graduate student (upper limit) = 33

Random sample graduate student (lower limit) = 30

Formula to calculate margin of error is as follows.

Margin of error = [tex]\frac{upper limit - lower limit}{2}[/tex]

Substitute the values into above formula as follows.

[tex]Margin of error = \frac{upper limit - lower limit}{2}\\= \frac{33 - 30}{2}\\= \frac{3}{2}\\= 1.5[/tex]

Thus, we can conclude that Martina's margin of error is 1.5.

Answer:

p = 1.25

Step-by-step explanation:

varies inversely

p (q + 2)² = k

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

Find k

p=5 when q = 3

5(3 + 2)² = k

5(25) = k

125 = k

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

Find p when q = 8​

p(8 + 2)² = 125

p(100) = 125

divide both sides by 100

p = 1.25

Answer:

Option (1)

Step-by-step explanation:

From the graph of the piecewise function,

There are two pieces of the function,

1). Segment (1) having x < 0

2). Segment (2) having x ≥ 0

Segment (1),

Segment starts with a hollow circle at x = 0 and passes through two points (0, 1) and (-2, 2)

Slope of the segment = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                                     = [tex]\frac{2-1}{-2-0}[/tex]

                                     = [tex]-\frac{1}{2}[/tex]

Equation of the segment passing through (-2, 2) with slope = [tex]-\frac{1}{2}[/tex],

[tex]y-y'=m(x-x')[/tex]

[tex]y-2=-\frac{1}{2}(x+2)[/tex]

[tex]y=-\frac{1}{2}x-1+2[/tex]

[tex]y=-\frac{1}{2}x+1[/tex]

[tex]y=-0.5x+1[/tex] For x < 0

Segment (2),

Segment starts with a solid circle at x = 0 and passes through (0, -2) and (2,2)

Slope of the segment = [tex]\frac{2+2}{2-0}[/tex]

                                    = 2

Equation of the segment passing through (0, -2) and slope = 2,

y - y' = m(x - x')

y + 2 = 2(x - 0)

y = 2x - 2 For x ≥ 0

Therefore, Option (1) will be the correct option.

Answer:

930=9 hundreds 3 tens

93times10

80=8 tens

320= 3 hundreds 2 tens

8000=8 thousands

Answer:

8.8%

Step-by-step explanation:

We first divide the new amount by the original and close it with brackets.

Our one year will be shown as 1/1 as an indices

(761.60/700)^1/1

= 1.088

We then convert it to 0.088 and times it by 100.

0.088×100= 8.8% Compound interest rate.

This is correct as:

700×1.088= 761.6

Have a nice day! :)

25√2

Step-by-step explanation:

Since angle BAC and angle ABC are equal, AB = BC.

Let x = AB = BC

By the Pythagorean theorem,

AB² + BC² = AC²

x² + x² = 50²

2x² = 2500

x²= 1250

x = √1250

x = √(2 • 625)

x = √2 • √625

x = √2 • 25

x = 25√2

x = AB = 25√2

the reciprocal of 9 is 1 divided by 9, i.e. 1/9

Answer:

the think the answer is €170

because 15000+20/100

Answer:

42 units²

Step-by-step explanation:

the area = (11-4) × (9-3)

=7×6 = 42 units²

Answer:

Área de un rectángulo = 150 cm²

El perímetro de un rectángulo = 50 cm

Step-by-step explanation:

Área de un rectángulo = largo × ancho (alto)

= 15 cm × 10 cm

= 150 cm²

El perímetro de un rectángulo = 2L + 2W

Donde L = longitud = 15 cm

W = Ancho = 10 cm

= 2 (15 cm) + 2 (10 cm)

= 30 + 20

= 50cm

Answer:

gracias por los puntos xd

Answer:

C

Step-by-step explanation:

To convert from point-slope form to slope-intercept form, we can simplify and isolate the y.

We have the equation:

[tex]\displaystyle y-3=\frac{1}{2}(x-1)[/tex]

Distribute the right-hand side:

[tex]\displaystyle y-3=\frac{1}{2}x-\frac{1}{2}[/tex]

Add 3 to both sides:

[tex]\begin{aligned} \displaystyle y&=\frac{1}{2}x-\frac{1}{2}+3\\\\&=\frac{1}{2}x-\frac{1}{2}+\frac{6}{2}\\\\&=\frac{1}{2}x+\frac{5}{2}\end{aligned}[/tex]

Our answer is C.

Answer:

Step-by-step explanation:

Answer:

(- 3, - 5 ) , (3, 7 )

Step-by-step explanation:

Given the 2 equations

y = 2x + 1 → (1)

y = x² + 2x - 8 → (2)

Substitute y = x² + 2x - 8 into (1)

x² + 2x - 8 = 2x + 1 ( subtract 2x + 1 from both sides )

x² - 9 = 0 ( add 9 to both sides )

x² = 9 ( take the square root of both sides )

x = ± [tex]\sqrt{9}[/tex] = ± 3

Substitute these values into (1) for corresponding values of y

x = - 3 : y = 2(- 3) + 1 = - 6 + 1 = - 5 ⇒ (- 3, - 5 )

x = 3 : y = 2(3) + 1 = 6 + 1 = 7 ⇒ (3, 7 )

There are (5 C 1) = 5! / (5 - 1)! = 5 ways of drawing a red marble, and (11 C 1) = 11! / (11 - 1)! = 11 ways of drawing any marble, so that the probability of drawing a red marble is 5/11.

After putting back the first marble, the probability of drawing another red is again 5/11.

So the probability of drawing 2 red marbles with replacement is (5/11)² = 25/121.

Answer:

x > 5.5

Step-by-step explanation:

4(x - 3) - (2x - 1) > 0

4x - 12 - 2x + 1 > 0

4x - 2x - 11 > 0

2x - 11 > 0

2x - 11 + 11 > 0 + 11

2x > 11

2x ÷ 2 > 11 ÷ 2

x > 5.5

Answer:

x>13/2

Step-by-step explanation:

4x-12-2x-1>0

2x-13>0

2x>13

X>13/2

Answer:

Step-by-step explanation:

Correct choice is D

Answer:

D. 270°

Step-by-step explanation:

Answer: x = 22

Step-by-step explanation: Since x is unknown, we want to isolate it and determine what it equals. We know that x - 3 gives us 19, but we don't want to know what x - 3 is, just x. So we can add three to both sides of the equation, to get our answer and keep it balanced. As a result, we get x = 22

Answer:

x = 22

Step-by-step explanation:

19 = x - 3

Add 3 to each side

19 + 3 = x - 3 + 3

Simplify

22 = x

The none of no irrational number in the given option.

Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is referred to as an irrational number.

In another word, irrational numbers are those numbers that can not terminate.

For example, √2, and √3 are irrational numbers because they cannot be written as p/q where p and q both should be integers.

Among the given option

A) √100 = 10 which is integer.

B) 1/8 were 1 and 8 both integer.

C)  -2.2675 here also it is an integer.

D)  [tex]0^{12}[/tex] which is 0 so it is also a rational number.

Hence none of the irrational numbers. It might be possible that there is a typing mistake in the question or in option D there is something else.

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Answer:

timely, timely,measurable

Step-by-step explanation:

Answer:

specific, timely, measurable

Step-by-step explanation:

i took the test on plato

Answer:

[tex] {x }^{o} = {130}^{o} [/tex]

Step-by-step explanation:

[tex] {50}^{o} + {x}^{o} = {180}^{o} [/tex]

[tex] {x}^{o} = {180}^{o} - {50}^{o} [/tex]

[tex] {x }^{o} = {130}^{o} [/tex]

Answer:

x= 130°

Step-by-step explanation:

hope it helps

Answer:

67.77$ Kevin use to pays for the items.

Step-by-step explanation:

According To the Question, We have

Kevin buys the item listed below at a grocery store

Now, Kevin Pays for the items and receives 0.45$ in Change.

Amount of Money Kevin Pays

6.48$+23.76$+37.08$+0.45$ = 67.77$

Answer:

6

Step-by-step explanation:

2x+2y=2*(-2)+2*5=6

Answer:

6

Step-by-step explanation:

Substitute x = - 2, y = 5 into the expression

2x + 2y

= 2(- 2) + 2(5)

= - 4 + 10

= 6