Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression.

-7.5 and 5.4

In decimal form, this is equivalent to 1.25

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Work Shown:

The given equation 2x^2-10x+13 = 0 matches the form ax^2+bx+c = 0

We see that a = 2, b = -10, c = 13. Plug those values into the quadratic formula to solve for x.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-10)\pm\sqrt{(-10)^2-4(2)(13)}}{2(2)}\\\\x = \frac{10\pm\sqrt{-4}}{4}\\\\x = \frac{10\pm2i}{4}\\\\x = \frac{2(5\pm i)}{2*2}\\\\x = \frac{5\pm i}{2}\\\\x = \frac{5}{2} \pm \frac{1}{2}i\\\\x = \frac{5}{2} + \frac{1}{2}i \ \text{ or } \ x = \frac{5}{2} - \frac{1}{2}i\\\\[/tex]

The two solutions are in the form [tex]a \pm bi[/tex] where a = 5/2 and b = 1/2

Therefore a*b = (5/2)*(1/2) = 5/4 = 1.25

Answer:

For question 1 you can try dividing each of the value

For instance, you can divide 9 by 25 and see if you get a nice number

e.g. 1/8=0.125, numbers like these

For the second question, you can find the fraction by dividing 1000 starting with the decimal points

e.g 0.650, you would be plotting 650/1000 and you would simplify the fraction to the lowest value any value above the decimal point you can multiply by the denominator and add the nominator value to get your final answer.

Step-by-step explanation:

Answer:

Write the denominator in its prime factors. If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expression terminates.  If there is any prime factor in the denominator other than 2 or 5, then the decimal expression repeats.

example: 9/25

25 = 5*5, so it will be terminating

example: 7/12

12 = 3*2*2, which contains a 3, so it will be repeating.

Answer:

(x + 1)^2 + (y - 1)^2 = (8.5)^2

Step-by-step explanation:

Consider the general equation of a circle:

(x - h)^2 + (y - k)^2 = (r)^2

Where (h,k) represent the center point of the circle, and r represents the radius of the circle.  

For this circle, our center point appears to be at (-1,1) and the circle has a radius of 8.5.

Using this information, we simply plug these values into the general equation to get the following:

(x + 1)^2 + (y - 1)^2 = (8.5)^2

Cheers.

Answer:

a. 9

b. 9.

Step-by-step explanation:

a) √1098 = 33.136

33^3 = 1089

So the answer is 1098 - 1089

= 9.

b) √4498 = 67.067

67^2 =  4489

Answer = 9.

Answer:

a). 9

b). 9

Step-by-step explanation:

a) If you try to subtract 1 to 8 from 1098, it won't make a perfect square. But if you subtract 9 from 1098 (that will make it 1089), it will make a perfect square.

√1089 = 33

33² = 33 × 33 = 1089

So the answer is 9.

b). If you try to subtract 1 to 8 from 4498, it won't make a perfect square. But if you subtract 9 from 4498 (that will make it 4489), it will make a perfect square.

√4489 = 67

67² = 67 × 67 = 4489

So the answer is 9.

Hope you understand ◉‿◉ (◠‿◕)

Answer:

see attachement

Step-by-step explanation:

Answer:

A Yes

Step-by-step explanation:

the ratio is 2:1

Answer:

A. yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]6\sqrt{x-2}+4<28\\6\sqrt{x-2}<28-4\\\sqrt{x-2}<\frac{24}{6}\\\sqrt{x-2}<4\\\\x-2 <16\\x<16-2\\x<14x-2 \geq 0\\x\geq 2\\so~2 \leq x < 14[/tex]

Answer:

Step-by-step explanation:

(9-5)/6-4)= 4/2= 2

y - 5 = 2(x - 4)

y - 5 = 2x - 8

y = 2x - 3 is the solution

Answer:

the answer is y = –2x – 5 hope this helps:) give brainliest if it does

Step-by-step explanation:

i got it right on edge

[tex]-25(x - 4) = -55(x - 10)\\-25x+100=-55x+550\\30x=450\\x=\dfrac{450}{30}=15[/tex]

Answer:

x=15

Step-by-step explanation:

Answer:

81

Step-by-step explanation:

First find the amount decrease

90 * 10 %

90 * .10

9

90 decreased by 9

90 -9

81

Answer:

81

Step-by-step explanation:

Turn into decimal.

10% = 0.1

Multiply

90 * 0.1 = 9

Subtract

90 - 9 = 81

Best of Luck!

Answer:

2/5

Step-by-step explanation:

First for the sum:

3/5 + 1/5 i + 4/5 - 2/5 i = 7/5 - 1/5 i

Now for the difference

9/5 - 1/5 i - (7/5 - 1/5 i)

= 9/5 - 1/5 i - 7/5 + 1/5 i

= 2/5 , which is the answer :)

The answer is  2/5.

To find the fraction bar in the box.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given that:

First for the sum:

3/5 + 1/5 i + 4/5 - 2/5 i = 7/5 - 1/5 i

Now substract the sum,

9/5 - 1/5 i - (7/5 - 1/5 i)

= 9/5 - 1/5 i - 7/5 + 1/5 i

= 2/5

So, the answer is  2/5.

Learn more about fraction here:

https://brainly.com/question/17154057

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Answer:

Step-by-step explanation:

AREA OF CIRCLE = 660.185CM^2

HOPE IT HELPS

Answer: [tex]y=\dfrac12 x[/tex] .

Step-by-step explanation:

We know that [tex]a f (x)[/tex]  compresses f(x) vertically such that

If we vertically compress the linear parent function, F(x) = x, by multiplying by [tex]\dfrac12[/tex].

Then, the equation of the new function is [tex]y=\dfrac12 F(x)=\dfrac12 x[/tex] .

i.e. [tex]y=\dfrac12 x[/tex] .

Answer:

52°

Step-by-step explanation:

360 - 33 - 165 - 20 - 90 = x

x = 52

Answer:

Step-by-step explanation:

Let's find the size of angle x

The angle in a complete turn add up to 360°

[tex] \mathsf{x + 20 + 165 + 33 + 90 = 360}[/tex]

Add the numbers

[tex] \mathsf{x + 308 = 360}[/tex]

Move constant to R.H.S and change it's sign

[tex] \mathsf{x = 360 - 308}[/tex]

Calculate the difference

[tex] \mathsf{x = 52}[/tex] °

Hope I helped!

Best regards!

Answer:

6.9263 × 109

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

x=13, 16(x-1)

Step-by-step explanation:

For 38, you have to first divide both sides by 2.

This becomes, x-6=7

Add 6 to both sides

x=13.

For 40. You can can distribute the 8.

This makes it 16x-16.

With this you can than, factor out the 16.

16(x-1).

Answer:

Step-by-step explanation:

38.

[tex]2(x - 6) = 14\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{2\left(x-6\right)}{2}=\frac{14}{2}\\\mathrm{Simplify}\\x-6=7\\\mathrm{Add\:}6\mathrm{\:to\:both\:sides}\\\\x-6+6=7+6\\\\x=13[/tex]

40.

[tex]8(2x - 2)\\\mathrm{Apply\:the\:distributive\:law}:\\\quad \:a\left(b-c\right)=ab-ac\\\\a=8,\:b=2x,\:c=2\\\\=8\times \:2x-8\times \:2\\\\=16x-16[/tex]

Answer:

c

Step-by-step explanation:

The expression (9⁶ x 7⁻⁹)⁻⁴ is equivalent to expression 7³⁶ / 9²⁴. Then the correct option is D.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ (9⁶ x 7⁻⁹)⁻⁴

Simplify the expression, we have

⇒ (9⁻⁶ x 7⁹)⁴

⇒ 9⁻²⁴ x 7³⁶

⇒ 7³⁶ / 9²⁴

Then the correct option is D.

More about the equivalent link is given below.

https://brainly.com/question/889935

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Answer:

Step-by-step explanation:

  [tex]9xy\cdot(\frac{2}{3}x)^3=3^2xy\cdot\dfrac{2^3x^3}{3^3}\\\\=\dfrac{8}{3^{3-2}}x^4y=\boxed{\dfrac{8}{3}}x^4y[/tex]

__

The applicable rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)/(a^c) = 1/(a^(c-b))

Answer:

(2,0)    ( -1,0)

Step-by-step explanation:

y =3x^2-3x-6

Let y = 0 and solve for x to find the x intercepts

0 =3x^2-3x-6

Factor out a 3

0 =3(x^2-x-2)

Factor inside the parentheses

0 = 3( x-2) (x+1)

Using the zero product property

x-2 =0    x+1 = 0

x=2      x = -1

(2,0)    ( -1,0)

Answer:

[tex]\large \boxed{\mathrm{a. \ x-intercepts: (-1,0) \ and \ (2,0)}}[/tex]

Step-by-step explanation:

The x-intercept(s) is when y = 0.

3x² - 3x - 6 = 0

Factor left side of the equation.

3(x + 1)(x - 2) = 0

Set factors equal to 0.

x + 1 = 0

x = -1

x - 2 = 0

x = 2

The x-intercepts are (-1, 0) and (2, 0).

Answer:

The number of minutes Nikki needs to listen to the radio to hear 20 commercials is 63.275 minutes

Step-by-step explanation:

The given dependent and independent variables are;

The number of minutes spent by Nikki listening = x

The number of commercials aired = y

The relationship between the independent variable, x ans the dependent variable, y, was given by the Nikki's graphing tool line of best fit as follows;

y = 0.338·x - 1.387

Therefore, the number of minutes, x, Nikki needs to listen to the radio to hear 20 commercials, y is given as follows;

20 = 0.338·x - 1.387

20 + 1.387 = 0.338·x

0.338·x  =20 + 1.387 = 21.387

x =  21.387/0.338 = 63.275 minutes

The number of minutes, x, Nikki needs to listen to the radio to hear 20 commercials, y = 63.275 minutes.

Answer:

C. 63 minutes

Step-by-step explanation:

Answer:

[tex]Average = 12\frac{4}{7}\ lb[/tex]

Step-by-step explanation:

Given

Number of jars = 14

Weights = 2, 2, 2, 1, 11, 12, 12, 2, 24, 22, 24, 3, 37, 22  in pounds

Required

What is the weight of each jar if the sea glass is evenly distributed

What this question implies is that, the average weight of the sea glass is calculated;

[tex]Average = \frac{Sum\ of\ weights}{Number\ of\ jars}[/tex]

[tex]Average = \frac{2+ 2+ 2+ 1+ 11+ 12+ 12+ 2+ 24+ 22+ 24+ 3+ 37+ 22}{14}[/tex]

[tex]Average = \frac{176}{14}[/tex]

[tex]Average = 12\frac{8}{14}[/tex]

Divide the numerator and denominator by 2

[tex]Average = 12\frac{4}{7}[/tex]

Hence, the weight of each jar would be [tex]12\frac{4}{7}\ lb[/tex]

Answer:

3 tens   or 30

£12.35

Step-by-step explanation:

41,039

ten thousand thousands, hundreds tens ones

The three is in the tens place

3 tens   or 30

£12 and 35

1p = £0.01

£12.35

square ?

although this statement doesn't make any sense.

Answer:

Square!

Step-by-step explanation:

A rectangle is a parallelogram with all its interior angles being 90 degrees. A rhombus is a parallelogram with all its sides equal. This means that for a rectangle to be a rhombus, its sides must be equal. When this is satisfied, we have a square.

Hope helped.. If yes mark me BRAINLIEST

TYSM!

Answer:

Manuel made his first mistake in step 2 leading to the continuous mistakes

Final answer=185

Step-by-step explanation:

Manuel made at least one error as she found the value of this expression. 2(-20) + 3[5/4(-20)] + 5[2/5(50)] + 4(50) Step 1: 2(-20) + 3(-25) + 5(20) + 4(50) Step 2: (3 + 2)(-20 + -25) + (5 + 4)(20 + 50) Step 3: 5(-45) + 9(70) Step 4: -225 + 630 Step 5: 405 Identify the step in which Chris made her first error. After identifying the step with the first error, write the corrected steps and find the final answer.

2(-20) + 3[5/4(-20)] + 5[2/5(50)] + 4(50)

Step 1: 2(-20) + 3(-25) + 5(20) + 4(50)

Step 2: -40 - 75 + 100 +

200

Step 3: -115 + 300

Step 4: 185

Manuel made his first error in step 2 by combining two different terms into one as he has done

(3 + 2)(-20 + -25) and also (5 + 4)(20 + 50)

Step 2: (3 + 2)(-20 + -25) + (5 + 4)(20 + 50)

Step 3: 5(-45) + 9(70) Step 4: -225 + 630 Step 5: 405

He should have evaluated the terms separately as I have done above, giving us 185 as the final answer in contrast to his 405 final answer.

Answer:

4ny²+4n²-4n-8+y⁴-2y²

Answer:

3,781

Step-by-step explanation:

To solve this problem, we will find the area of the whole circle and use that to find teh area of the 60º section.

First, recognize the formula for the area of a circle:

A = 3.14[tex]r^{2}[/tex]

In this scenario, the radius (r) is 85 feet:

A = 3.14(85[tex])^{2}[/tex]

A circle is 360º and we only require the area of 60º. 360º / 60º = 6 so we will divide by 6:

A = [tex]\frac{3.14(85)^{2} }{6}[/tex]

Finally, we will simplify and round:

A = 3,781

Answer:

[tex]\boxed{\sf QS = 98}[/tex]

Step-by-step explanation:

QP = PS   [Diagonals are bisected(Divided into two equal parts) by the other diagonal of parallelogram]

So,

3x - 11 = 2x + 9

3x - 2x = 9 + 11

x = 20

Now,

QS = QP + PS

QS = 3x-11+2x+9

QS = 3(20)-11+2(20)+9

QS = 60 - 11 + 40 + 9

QS = 49 + 49

QS = 98

Answer:  QS=98

Step-by-step explanation: diagonals are bisected by the other diagonal parallelogram

Answer: Because of PEMDAS, the way Morgan rewrote the expression would change the the order of the steps to simplify it.

Step-by-step explanation: PEMDAS is the order of operations and it stands for Parenthesis, Exponents, Multiply, Divide, Addition, and Subtraction. If we simplify Morgan's version of the expression, we would add 90+10 first, which makes 100, then add 4.8 which makes 104.8. We come to the same conclusion when simplifying the original expression, 104.8. The difference is that we add 10+4.8 first and then add it to 90. While in this situation, the outcome was not different, the order of operations was changed.

Answer:

a = 1

Step-by-step explanation:

Given that both ax³ + 3x² - 3 and 2x³ - 5x + a have the same remainder when divided by x - 4.

x - 4 = 0

x = 4

When ax³ + 3x² - 3 is divided by x - 4, the remainder is gotten by substituting x = 4:

a(4)³+3(4)²-3 = 64a + 48 - 3 = 64a + 45

The remainder is 64a³ + 45

For 2x³ - 5x + a we find the remainder by substituting x = 4:

2(4)³ - 5(4) + a = 128 - 20 + a = 108 + a

Since they both have the same remainder, therefore:

64a + 45 = 108 + a

64a - a = 108 - 45

63a = 63

a = 1

Step-by-step explanation:

since, x = 5 and y = 5

we substitute the values to the equation 6x - 6y

So:

6(5) - 6(5)

= 30 - 30

= 0

I hope this helps!

Step-by-step explanation:

IS 0 thanks me latter:))!