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[tex]\huge\bold{Given :}[/tex]

Product of two integers = - 112

One of the integer = -8

[tex]\huge\bold{To\:find :}[/tex]

The other integer.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

[tex]\sf\blue{The \:other \:integer\:is\: 14.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

Let the other integer be [tex]x[/tex].

As per the question, we have

[tex]Product \: \: of \: \: two \: \: integers = - 112[/tex]

➼ [tex] \: - 8 \times x = - 112[/tex]

➼ [tex] \: x = \frac{ - 112}{ - 8} [/tex]

➼ [tex] \: x = 14[/tex]

[tex]\sf\purple{Therefore,\:the\:other\:integer\:x\:is\:14.}[/tex]

[tex]\huge\bold{To\:verify :}[/tex]

[tex] - 8 \times 14 = - 112[/tex]

➺ [tex] \: - 112 = - 112[/tex]

➺ L. H. S. = R. H. S

Hence verified.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]

Answer:

If the product of two integers is -112 and one of them is -8, that means the value of the second integer would be 14.

Step-by-step explanation:

The product of two integers equals -112 means that there are two numbers that, when multiplied, were equivalent to -112. Since you know one of the integers is -8, you can infer that the second integer is both a positive number AND the remainder of [tex]\frac{-112}{-8}[/tex] or 14.

Answer:

Rational.

Step-by-step explanation:

2/18=0.1 repeating.

3/3 = 1

Multiplying these together get you 0.1 repeating.

There is only one rule that makes a number irrational.

This is a number that is not divisiable by two integers, and is not capable of being expressed as a fraction.

0.1, as we know, can be written as 2/18, or 1/9.

So it must be a rational number.

Something you may not know - Rational numbers CAN be infinitly repeating numbers.

For instance, 0.111 like shown above is repeating, and its rational.

However, pi is a repeating number...but its irrational.

This is not because its infinitly repeating, this is actually becuase it is not divisiable by two numbers, and cannot be put into fraction form.

Some people think infinitly repeating numbers are irrational, however this is not correct, for some fractions are actually repeating.

Hope this helps!

Answer:

6√7=15.874507866387543=√252

Step-by-step explanation:

hope this is helpful

The expression that are equivalent to √252 are [tex]252^{\frac{1}{2} }[/tex] and 6√7.

Applying the surd rule,

√a = [tex]a^{\frac{1}{2} }[/tex]

Hence,

[tex]\sqrt{252}=252^{\frac{1}{2} }[/tex]

using surd rule, we can also decompose √252

Therefore,

√252 = √36 × 7 = 6√7

Hence, the equivalent expression of √252 are as follows:

learn more on expression here: https://brainly.com/question/27768447

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Answer with Step-by-step explanation:

We are given that

[tex]3\times (2\div 3)^2+(2\div 3)^2-20\times 2\div 3+12[/tex]

[tex]3\times (\frac{2}{3})^3+(\frac{2}{3})^2-20\times \frac{2}{3}+12[/tex]

[tex]3\times \frac{8}{27}+\frac{4}{9}-\frac{40}{3}+12[/tex]

[tex]\frac{24}{27}+\frac{4}{9}-\frac{40}{3}+12[/tex]

[tex]\frac{24+12}{27}-\frac{40}{3}+12[/tex]

[tex]\frac{36}{27}-\frac{40}{3}+12[/tex]

[tex]\frac{4}{3}-\frac{40}{3}+12[/tex]

[tex]\frac{4-40}{3}+12[/tex]

[tex]-\frac{36}{3}+12[/tex]

[tex]-12+12[/tex]

[tex]=0[/tex]

Answer:

y = 45

Step-by-step explanation:

y = 9x

input = 5

y = 9(5)

9(5) = 45

y = 45

Answer:

The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient of consecutive terms is the same. The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term and [tex]q[/tex] is the common ratio.

A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again.

This means that:

[tex]q = 0.7, a_1 = 25*0.7 = 17.5[/tex]

Then

[tex]a_n = a_1q^{n-1}[/tex]

[tex]a_n = 17.5(0.7)^{n-1}[/tex]

First 5 terms:

[tex]a_1 = 17.5[/tex]

[tex]a_2 = 17.5(0.7)^{2-1} = 12.25[/tex]

[tex]a_3 = 17.5(0.7)^{3-1} = 8.58[/tex]

[tex]a_4 = 17.5(0.7)^{4-1} = 6[/tex]

[tex]a_5 = 17.5(0.7)^{5-1} = 4.2[/tex]

Find the total distance the ball has travelled after it hits the ground the 5th time.

[tex]T = 17.5 + 12.25 + 8.58 + 6 + 4.2 = 48.53[/tex]

The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.

Answer:

52

Step-by-step explanation:

f(n) is purely based on the previous value of f(n), or f(n-1), so we can start with f(1) and work our way up. We know f(1) = 2, so to find f(2), we plug f(1) into

f(n-1)²+3 to get

f(1)²+3 = 2²+3 = 4+3=7

Thus, f(2) =7. Similarly,

f(3) = f(3-1)²+3 = f(2)² + 3 -= 7² + 3= 52

Answer:

A)4/5

Step-by-step explanation:

7/9=0.778

so you need to convert the other fractions into decimals as well. The one that's greater than 0.778 will be your answer.

a)4/5=0.8

b)2/3=0.667

c)13/18=0.722

d)3/5=0.6

The decimal that's greater than 0.778 is A=0.8 so that's the answer.

Answer:

Yes, the triangles are similar ([tex]\triangle HMG \sim \triangle KMJ[/tex]).

Step-by-step explanation:

We're given that the two triangles share at least one angle, angles H and K. The two angles in the triangles at point M, [tex]\angle HMG[/tex] and [tex]\angle KMJ[/tex] are vertical angles, meaning they are on opposite sides of a point of intersection between two lines. Since vertical angles are always equal, these two angles are also equal.

If two triangles share two angles, they must share all three, because all triangles have a total sum of interior angles of 180 degrees. Therefore, the triangles share all 3 angles. AAA (Angle-Angle-Angle) is a proof of similarity, where two triangles share all three of their angles. Thus, the two triangles are similar.

Similarity statement (vertices should correspond):

[tex]\triangle HMG \sim \triangle KMJ[/tex]

Answer:

60

Step-by-step explanation:

Given: 1/2a + 2/3b =50

(Since b is equal to 30 we will automatically replace b with 30)

Step 1: Simplify both sides of the equation.

1/2a+20=50

Step 2: Subtract 20 from both sides.

1/2a=50-20

1/2a=30

Step 3: Multiply both sides by 2.

2(1/2a) 2(30)

a=60

Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?  

Answer:

a = 15

Step-by-step explanation:

1/2(a) + (2/3 x 30) = 50

2/3 x 30 = 20

1/2(a) + 20 = 50

Rearrange > 20 to -20

-20 + 50 = 30

1/2(a) = 30

Rearrange 1/2 to 2

2 > 30/2

30/2 = 15

a = 15

Hope this helps, and please let me know if it is correct or isn't.

Have a nice day

Step-by-step explanation:

See you know the area of rectangle that is base x perpendicular

When you cut half the area of rectangle, it becomes a triangle

That is why the formula is 1/2 x base x perpendicular

Answer:

[tex](x -y)^2 = -1[/tex]

Step-by-step explanation:

[tex](x - y)^2 = x^2 + y^2 - 2xy[/tex]

           [tex]= (x^2 + y^2 ) - 2(xy)\\\\=(9) - 2( 5)\\\\= 9 - 10 \\\\ = -1[/tex]

The binomial expansion of (x - y)² is

(x - y)² = x² - 2xy + y²

Substitute the given values to the equation

(x - y)² = x² - 2xy + y²

(x - y)² = x² + y² - 2xy

(x - y)² = 9 - 2(5)

(x - y)² = 9 - 10

(x - y)² = -1

Therefore the value of (x - y)² is -1.

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Answer:

She will need to fill her spoon twice, once adding in the full amount, and the second adding half the amount.

3/4  ÷ 4/8

=3/4 * 2/1

=6/4

=1.5

So, that much amount would be needed o be added to the recipe during the two times

Answer:31

Step-by-step explanation:

Answer:

y=31

Step-by-step explanation:

-21 + y= 10

-21 + y + 21 =10 + 21

y = 10+21

y = 31

HOPE THIS ANSWER HELPS YOU :)))

Answer:

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

[tex]2)y=-x-1[/tex]

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

Step-by-step explanation:

Hope this helps

Answer:

Average rate of change = 0.6

Step-by-step explanation:

Average rate of change of a function between x = a and x = b is given by,

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

From the graph attached,

f(-5) = 0

f(0) = 3

Average rate of change of the graph between x = -5 and x = 0,

Average rate of change = [tex]\frac{3-0}{0-(-5)}[/tex]

                                        = [tex]\frac{3}{5}[/tex]

                                        = 0.6

Therefore, average rate of change of the given function between x = -5 and x = 0 is 0.6.

Answer:

C

Step-by-step explanation:

Given

[tex]\frac{4}{x^3}[/tex] - [tex]\frac{2x-1}{3x}[/tex]

Multiplying the numerator/ denominator of the first fraction by 3 and the numerator/denominator of the second fraction by x² will ensure that the fractions have a common denominator.

= [tex]\frac{3(4)}{3x^3}[/tex] - [tex]\frac{x^2(2x-1)}{3x^3}[/tex]

= [tex]\frac{12}{3x^3}[/tex] - [tex]\frac{2x^3-x^2}{3x^3}[/tex] ← combine terms on numerator

= [tex]\frac{12-2x^3+x^2}{3x^3}[/tex]

= [tex]\frac{-2x^3+x^2+12}{3x^3}[/tex] → C

Answer:

Step-by-step explanation:

The discriminant is used to determine the number and nature of the zeros of a quadratic. If the discriminant is positive and a perfect square, there are 2 rational zeros; if the discriminant is positive and not a perfect square, there are 2 rational complex zeros; if the discriminant is 0, there is 1 rational root; if the discriminant is negative, there are no real roots.

The roots/solutions/zeros of a quadratic are where the graph goes through the x axis. Those are the real zeros, even if they don't fall exactly on a number like 1 or 2 or 3; they can fall on 1.32, 4.35, etc. They are still real. If the graph doesn't go through the x-axis at all, the zeros are imaginary because the discriminant was negative and you can't take the square root of a negative number. As you can see on our graph, the parabola never goes through the x-axis. Therefore, the zeros are imaginary because the discriminant was negative. Choice C.  Get familiar with your discriminants and the nature of quadratic solutions. Your life will be much easier!

Answer:

$26.84

Step-by-step explanation:

We have to find 10% of 268.40. To do that, we multiply it by 0.10:

268.40 * 0.1 = 26.840, or $26.84

Answer: C

Step-by-step explanation:

Answer:

[tex]( 5 + 6b^3)^2 = 36b^6 + 60b^3 + 25[/tex]

Step-by-step explanation:

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

So,

        [tex](5 + 6b^3)^2 = (5)^2 + (6b^3)^2 + 2 (5)(6b^3)[/tex]

                       [tex]= 25 + 36b^6 + 60b^3[/tex]

Answer:

One quarter= 1/4

5 3/4= 23/4

Number of quarters in 5 3/4= 23/4 divided by 1/4

23/4 ÷ 1/4

= 23/4 × 4

=23

I hope this helps!

Answer:

23

Step-by-step explanation:

5x4 + 3

5 x 4 = 20

20 + 3 (3 Is the fraction part)

Answer:

8

Step-by-step explanation:

5x-8 = 2x+16

Move 2x to the left side and you get 3x-8 = 16

Move -8 to the right side and you get 3x = 24

Divide 3 on both sides and you get x = 8

Answer: x = 19

Hi! I was studying for the NYC SHSAT when this exact problem came up a year ago. I will do my best to try to answer it correctly!

Step-by-step explanation:

To start, we have to notice the similar properties of the angles. They are alternate exterior angles (?). Therefore, I think that you just have to put the angles on opposite sides of the equation!

(6x + 6) = 120

-6              -6

6x/6 = 114/6

x = 19

Answer:

49

Step-by-step explanation:

The average is calculated as

average = [tex]\frac{sum}{count}[/tex] Given the average of 7 numbers is 45 , then

[tex]\frac{sum}{7}[/tex] = 45 ( multiply both sides by 7 )

sum of 7 numbers = 315

Subtract 27, 43 from the sum to obtain the sum of first 5 numbers

315 - (27 + 43) = 315 - 70 = 245 , then

average of first 5 numbers = [tex]\frac{245}{5}[/tex] = 49

Answer:

[tex]x^4+2x^3+2x^2+2x+1[/tex]

Step-by-step explanation:

Given that,

[tex](x+1)^2 . (x^2+1) = 0[/tex]

We know that, [tex](a+b)^2=a^2+b^2+2ab[/tex]

So,

[tex](x+1)^2=x^2+1+2x[/tex]

So,

[tex](x+1)^2 . (x^2+1) = (x^2+1+2x)(x^2+1)\\\\=x^2\times x^2+x^2+2x^3+x^2+1+2x\\\\=x^4+2x^3+2x^2+2x+1[/tex]

So, the value of the given expression is equal to[tex]x^4+2x^3+2x^2+2x+1[/tex]

Answer:

2x + y = 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

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

with (x₁, y₁ ) = C (1, 3) and (x₂, y₂ ) = D (4, - 3)

m = [tex]\frac{-3-3}{4-1}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2 , then

y = - 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (1, 3 )

3 = - 2 + c ⇒ c = 3 + 2 = 5

y = - 2x + 5 ← equation in slope- intercept form

Add 2x to both sides

2x + y = 5 ← equation in standard form