The product of two consecutive even number is 12 more than the square of the smaller number. Find the smaller number

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[tex]-9 (y-13) = 16[/tex]

This is called a linear equation. Let's distribute:

[tex]-9y + 117 = 16[/tex]

Now we need to subtract 117 from both sides

[tex]-9y +117-117=16-117[/tex]

[tex]-9y = -101[/tex]

Now divide both sides by -9

[tex]\frac{-9y}{-9} = \frac{-101}{-9}[/tex]

[tex]y = \frac{101}{9}[/tex]

Happy to help! All the best this semester!

Equation f (x) = |x| represent the Absolute Value Functions.

Parent functions are the simplest form of a given family of functions. A family of functions is a group of functions that share the same highest degree and, consequently, the same shape for their graphs.

Absolute Value Functions :

The parent function of absolute value functions is y = |x|. Absolute value functions are expected to return V-shaped graphs.

The vertex of y = |x| is found at the origin as well. Since it extends on both ends of the x-axis, y= |x| has a domain at (-∞, ∞).  Absolute values can never be negative, so the parent function has a range of [0, ∞].

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Answer: [tex]-7^2 * 5^4[/tex]

Step-by-step explanation:

The evaluation of the subtraction operation using the number line is 2/3. The correct option is the last option 2/3

From the question, we are to evaluate the subtraction operation using the number line

From the number line we can observe that the magnitude of the distance between two successive mark is 1/3

Now, we are subtract

-2/3 - (-1 1/3)

If we count from - 1 1/3 to -2/3, we will observe that there are two marks.

Thus,

1/3 + 1/3 = 2/3

Hence, the evaluation of the subtraction operation using the number line is 2/3. The correct option is the last option 2/3

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Answer: i think it might be 72

Answer:72

Step-by-step explanation:

The least common multiple is the smallest common(of equal value) number. we get this number by multiplying the two numbers by a number value till we get a common number between the two.

The ratio of area of the ball bearings will be equal to 4 / 9.

We are given the volume of the ball bearings as:

Volume 1 = 1.6 cm³

Volume 2 = 5.4 cm³

Now, the ratio of their volumes will be equal to:

r = 1.6 / 5.4

r = 16 / 54

r = 8 / 27

Now, we know that, the scale factor will be:

k = ∛8 / 27

k = 2 / 3

Also, we know that, the ratio of their areas is the square of their scale factor.

So, the ratio of area will be equal to:

R = (2 / 3)²

R = 4 / 9

Therefore, we get that, the ratio of area of the ball bearings will be equal to 4 / 9.

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The ratio of their areas is 4 / 9.

The scale factor for the linear dimensions of the ball bearings will be the cube root of the volume scale factor:

[tex]$$k=\sqrt[3]{(1.6 / 5.4)}=2 / 3$$[/tex]

Then the scale factor for the areas will be the square of this scale factor: ratio of surface area =(2 / 3)^2=4 / 9

The area is the product of two linear dimensions, so its scale factor is the product of the linear dimension scale factors. That is, the scale factor for area is the square of the linear dimension scale factor.

Similarly, volume is the product of three linear dimensions, so its scale factor is the cube of the linear dimension scale factor.

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized. It is employed to change the size of an item.

If the original figure's dimensions and the dilated (increased or lowered) figure's dimensions are known, the scale factor can be determined. A rectangle, for instance, has dimensions of 5 units in length and 2 units in breadth.

The sides of this rectangle will change to 10 units and 4 units, respectively, if the size of the rectangle is increased by a scale factor of two. Therefore, we may use the scale factor to determine the modified figures' dimensions.

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Answer:Cylinder B has the radius r and the height as h. The lateral surface area of cone is. The lateral surface area of cylinder is. 1/2 × lateral surface area of cylinder B, ⇒. ⇒ = lateral surface area of cone A. Hence we can conclude that the lateral surface area of cone A is exactly 1/2 the lateral surface area of cylinder B is option (A) true.

Hope this helped you :)

False, the statement that: The lateral surface area of cone A is equal to the lateral surface area of cylinder B. is not true.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Since, Lateral area of cone is given by: πrl

where r is the radius and l is the slant height

Here r = r and l = h

Hence, lateral area of cone A= π × r × h

                                           = πrh

And, Lateral area of cylinder is given by:

= 2πrh

where r is the radius and h is the height

Hence, Lateral area of cylinder B=2πrh

Clearly, both the lateral areas are not equal.

Hence, the statement that: The lateral surface area of cone A is equal to the lateral surface area of cylinder B. is not true.

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Answer:

its c

Step-by-step explanation:

Answer:

3.69

Step-by-step explanation:

Answer:

3.69

Step-by-step explanation:

when the nearest number from the right side is lower than 5 it just disappears and all of the numbers after that will disappear as well.

Answer: B

Step-by-step explanation:

f(2) = 2, and is defined/exists. Holes (and asymptotes) like the hole at (2, -2) ruins continuity. The limit exists, but is not equal to f(2) which is why continuity is ruined at x=2

Answer: B

Step-by-step explanation:

f(2) = 2 and exists/is defined Holes (and asymptotes) such as the one at (2, -2) destroy continuity. The limit exists, but it is not equal to f(2), hence continuity is broken at x=2.

Answer:

x - 4

Step-by-step explanation:

The quickest way to do this is to Factor and "cancel". (Cancelling is not a mathematical term--it really is dividing)

x^2 - 16 is the difference of two squares. Its super-beneficial to recognize a difference of two squares and its factored form:

(x - 4)(x + 4)

Now you have:

(x - 4 )(x + 4) / x+4

The x+4 term "cancels" and you end up with x-4 as your answer.

You could also do this division problem using long division or synthetic division. You will get the same answer.

Applying the triangle proportionality theorem, the value of x and the value of y are:

C. y = 5, x = 10.

Since lines m and n are said to be parallel lines, therefore, according to the triangle proportionality theorem, the ratios below can be created.

4/12 = y/15 [proportional sides]

Cross multiply

(y)(12) = (4)(15)

12y = 60

Divide both sides by 12

12y/12 = 60/12

y = 5

x = 15 - y

Plug in the value of y

x = 15 - 5

x = 10

Thus, applying the triangle proportionality theorem, the value of x and the value of y are:

C. y = 5, x = 10.

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Answer:

80 percent

Step-by-step explanation:

4/5 = 80 percent (4/5 = .8, .8*100= 80)

Answer:

339.15

Step-by-step explanation:

5% is equal to 1/20, so we can use 1/20 in place of 5%. All that needs to be done is to determine 1/20 of 357 and subtract the result (we subtract because Tapiwa raked more than Adam)

357 x 1/20 = 17.85

357 - 17.85
339.15

Answer:

15.6 in² (nearest tenth)

Step-by-step explanation:

Circumference of a circle

[tex]\large\boxed{C=2\pi r}[/tex]

Where r is the radius of the circle.

Given:

Substitute the given value into the equation for the circumference and solve for r:

[tex]\begin{aligned}\implies 14 & = 2 \pi r\\\\ r & = \dfrac{14}{2 \pi}\\\\ r & = \dfrac{7}{ \pi}\end{aligned}[/tex]

Area of a circle

[tex]\large\boxed{A=\pi r^2}[/tex]

Where r is the radius.

Substitute the found radius into the equation for area and solve for A:

[tex]\begin{aligned}\implies A&=\pi \left(\dfrac{7}{\pi}\right)^2\\\\ A&=\pi \cdot \dfrac{7^2}{\pi^2}\\\\ A&=\dfrac{49\pi}{\pi^2}\\\\ A&=\dfrac{49}{\pi}\\\\A & = 15.6\;\sf in^2\;(nearest\:tenth)\end{aligned}[/tex]

Therefore, the area of the circle with a circumference of 14 in is 15.6 in².

Answer: 35/4

Step-by-step explanation:

7/11 ÷ 4/5 》7/11 × 5/4 = 35/44

Reason:

It is impossible to pass a single vertical line through more than one point on the graph. This relation passes the vertical line test.

The other graphs fail the vertical line test. For instance, in the upper right corner we have a vertical line through x = -1 which passes through more than one point. The input x = -1 leads to multiple outputs y = -1 and y = 3 at the same time.

A function is only possible when each input leads to exactly one output.

The greatest common multiple of 60 and 72 is 6.

The given numbers are 60 and 72.

The greatest common factor (GCF) is a term used to describe the biggest number that can divide evenly into two or more numbers. Sometimes, this is also referred to as the greatest common divisor (GCD) or highest common factor (HCF). A factor is a smaller number that can divide evenly into that number.

Now, 60 = 2×2×3×5 and 72 = 2×2×2×3×3

The common factors are 2 and 3

So, the greatest common factor =2×3=6

Therefore, the greatest common multiple of 60 and 72 is 6.

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Answer:

Step-by-step explanation:

The value is 102.

Here the expression is 2x² - 5x.

We have to find the value of the algebraic expression for x = -6.

Expression = 2x² - 5x

Now put the value of x = -6 in the expression, we get

2x² - 5x = 2(-6)² - 5(-6)

             = 2×36 + 30

             = 72 + 30

             = 102

Therefore the value of an algebraic expression is 102.

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Answer:

0.06(50h)

Step-by-step explanation:

Tax is usually computed by taking a percentage of the cost of a good or service. In the expression, we see that h represents the number of hours worked that are being paid for. Naturally, the cost of a service is the price times the hours worked. Therefore, 50 must represent the number of hours worked, and 50h represents the price Deborah must pay before tax. Knowing all this, we can deduce that the expression 0.06(50h) represents the tax that she must pay as it is a tax rate (6%) being multiplied by the cost before tax.

Answer:

124.59

Step-by-step explanation:

Answer:

the answer would be 20,313,04

Step-by-step explanation:

last place = 8 rounds up makes the thousandth place 5 which rounds up and makes the hundreth place 0 which doesnt change tyhe 4 giving us our aanswer. PLEASE MARK BRAINLIEST.

Answer:

-8

Step-by-step explanation:

If x = -2, then plug -2 into the equation where the x is:

y = 3(-2) - 2

Then solve:

3 * -2 = -6

-6 - 2 = -8

So, y = -8

Answer: All the answers you need are attached in the file.

Step-by-step explanation: Hope it helps!

Answer:

d

Step-by-step explanation:

Answer:The answer would most likely be c Read the problem carefully,find the question,understand the problem and find out what you know.

a) The work done is 3.3 J

b) The new force would  stretch it  1.9 cm beyond its natural length.

Hooke's law states that, the force of elasticity that tends to stretch a spring is directly proportional to the extension that is caused by the force as long as we do not by any means exceed the elastic limit of the material. This implies that the Hooke's law can only be found to hold when the elastic limit of the material has not been exceeded and the material has not become plastic.

Now;

F = Ke

W =1/2 Fe

F = 2W/e

W = work done

F = force exerted

e = extension

F = 2 * 23 /(44 - 30) * 10^-2

F = 328.6 N

a) To stretch  34 cm to 36 cm;

W = 1/2 *  328.6 N * 2 * 10^-2

W = 3.3 J

The work done is 3.3 J

b) F = Ke

328.6 N/(44 - 30) * 10^-2 = K

K = 2347 N/m

Then;

45 N =  2347 N/m * e

e = 45 N/ 2347 N/m

e = 0.019 m or 1.9 cm

New length = 30 cm + 1.9 cm = 31.9 cm

The new force would stretch it to a distance of 31.9 cm or 1.9 cm beyond its natural length.

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The solution of the equation for y is y = 5 - 2x and the values of y are 9, 5 and -1

The equation is given as

y + 2x = 5

Subtract 2x from both sides of the equation

So, we have

y + 2x - 2x = 5 - 2x

Evaluate the like terms

y = 5 - 2x

Next, we solve the function for the values of x

When x = -2, we have:

y = 5 - 2 * -2

Evaluate

y = 9

When x = 0, we have:

y = 5 - 2 * 0

Evaluate

y = 5

When x = 3, we have:

y = 5 - 2 * 3

Evaluate

y = -1

Hence, the solution of the equation for y is y = 5 - 2x and the values of y are 9, 5 and -1

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The value of y when x = -2 , 0 , 3 are 9, 5 and -1 respectively.

Given the equation;

y + 2x = 5

Make 'y' the subject of formula

y = 5 - 2x    (1)

When x = -2

Let's substitute the value of x as -2 in equation (1)

y = 5 - 2(-2)

expand the bracket

y = 5 + 4

y = 9

When x = 0

Substitute the value of x = 0

y = 5 -2(0)

y = 5 - 0

y = 5

When x = 3

Substitute the value of x = 3

y = 5 - 2(3)

y = 5 - 6

y = -1

Thus, the value of y when x = -2 , 0 , 3 are 9, 5 and -1 respectively.

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40,60,80,100,120,140,160,180,200 are the class boundaries.

The lower class boundary (LCB) is the LCL minus one-half the tolerance, and the upper class boundary (UCB) is the UCL plus one-half the tolerance. Class borders are the end points of an open interval that contains the class interval.

given that

8 classes for n = 75measurements

minimum value = 40

maximum value = 195

from the question

smallest class boundary = (maximum - minimum value) / n classes

= (195 - 40) / 75 = 19.375 = 20

round off the value means 20

using minimum value and smallest class boundary.

Hence, the 40,60,80,100,120,140,160,180,200 are the class boundaries.

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Disclaimer: the question is incomplete on portal. Here is the complete question.

Question: Use the information given to find a convenient class width. Then list the class boundaries that can be used to create a relative frequency histogram. (Round your class width up to the nearest multiple of 5. Use the minimum value as the smallest class boundary. Enter your class boundaries as a comma separated list.)

8 classes for  n = 75 measurements; minimum value = 40; maximum value = 195.