Using the distributive property what is 5(2y +1) in simplest form?

Answer:

Step-by-step explanation:

12 + 4b = 72

Subtract 12 on both sides

4b = 60

b = 15

Answer:

a. – 4 or –3

b. –4 or –2

c. 4 or –3

d. 7 or 4

Step-by-step explanation:

To factorize the above expression, multiply the first and last term together, then find two factors of the result such that their sum will result to the middle term of the expression.

Now, we shall give the answers to the question.

a. x² + 7x + 12 = 0

x² + 3x + 4x + 12 = 0

Factorise

x(x + 3) + 4(x + 3) = 0

(x + 4)(x + 3) = 0

x + 4 = 0 or x + 3 = 0

x = 0 – 4 or x = 0 – 3

x = – 4 or –3

Therefore, the roots of the equation are – 4 or –3

b. t² + 6t + 8 = 0

t² + 2t + 4t + 8 = 0

Factorise

t(t + 2) + 4(t + 2) = 0

(t + 4)(t + 2) = 0

t + 4 = 0 or t + 2 = 0

t = 0 – 4 or t = 0 – 2

t = –4 or –2

Therefore, the roots of the equation are –4 or –2

c. 2n² – 2n – 24 = 0

Divide through by 2

n² – n – 12 = 0

n² + 3n – 4n – 12 = 0

Factorise

n(n + 3) – 4(n + 3) = 0

(n – 4)(n + 3) = 0

n – 4 = 0 or n + 3 = 0

n = 0 + 4 or n = 0 – 3

n = 4 or n = –3

Therefore, the roots of the equation are 4 or –3

d. y² – 11y + 28 = 0

y² – 4y – 7y + 28 = 0

Factorise

y(y – 4) – 7(y – 4) = 0

(y – 7)(y – 4) = 0

y – 7 = 0 or y – 4 = 0

y = 0 + 7 or y = 0 + 4

y = 7 or 4

Therefore, the roots of the equation are 7 or 4.

Answer:

2. 38

3. 12

5. 7

9. 13

Answer:

620 milliliters

Step-by-step explanation:

1 milliliter= 0.001 liters

0.62L= move the decimal point 3 places to the left

0.62

06.2

062.

0620.

620 milliliters

Answer:

14 dimes and 4 quarters

Step-by-step explanation:

x= number of dimes

y=number of quarters

x-10=y

0.10x+0.25y=2.40

substitute for y

0.10x+0.25(x-10)=2.40

0.35x-2.50=2.40

0.35x=4.90

x=14

y=4

Answer:

We know,

Area of triangle = 1/2 * b * h

= 1/2 * 2x * 3x

= 1/2 * 6x

= 3x

Hope it helped

All the best !!

The area of the given triangle is 3x².

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Given a triangle.

Area of a triangle can be found using the formula,

Area = [tex]\frac{1}{2}[/tex] × base × height

Given,

Base = 3x and height = 2x

So using the formula,

Area = [tex]\frac{1}{2}[/tex] × 3x × 2x

        = 3x × x

        = 3x²

Hence the area of the triangle is 3x².

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Answer:

Era is x and number of wins is y

Edit: I would go up by two's on the y axis and .5 on the x axis

Answer:

th correct center is in B

9514 1404 393

Answer:

  a = 14.9

  b = 11.1

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relevant relationships.

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

In this triangle, that means ...

  sin(48°) = b/a

  cos(48°) = 10/a

Using the cosine relation, we can find 'a':

  a = 10/cos(48°) ≈ 14.9

Then using the sine relation, we have ...

  b = a·sin(48°) ≈ 11.1

_____

Additional comment

When computing 'b', the full precision value of 'a' should be used.

Answer:

y=9

Step-by-step explanation:

6y=79-25

= 6y= 54

= y=54/6

= y= 9

Answer:

The relationship between d, c and p is that [tex]p = \frac{4c^2}{9d}[/tex]

Step-by-step explanation:

Roots of a quadratic equation:

The roots [tex]r_1[/tex] and [tex]r_2[/tex] of a quadratic equation in the following format:

[tex]ax^2 + bx + c = 0[/tex]

Can be given by:

[tex]r_1 + r_2 = -\frac{b}{a}[/tex]

[tex]r_1r_2 = \frac{c}{a}[/tex]

In this question:

We have the following quadratic equation:

[tex]dx^2 - cx + p = 0[/tex]

So [tex]a = d, b = -c, c = p[/tex]

One of the roots is twice the other:

So [tex]r_2 = 2r_1[/tex]

First relation:

[tex]r_1 + r_2 = -\frac{b}{a}[/tex]

[tex]r_1 + 2r_1 = -\frac{(-c)}{d}[/tex]

[tex]3r_1 = \frac{c}{d}[/tex]

[tex]r_1 = \frac{c}{3d}[/tex]

Second relation:

[tex]r_1r_2 = \frac{c}{a}[/tex]

[tex]r_1*2r_1 = \frac{p}{d}[/tex]

[tex]2r_{1}^{2} = \frac{p}{d}[/tex]

[tex](\frac{2c}{3d})^2 = \frac{p}{d}[/tex]

[tex]\frac{4c^2}{9d^2} = \frac{p}{d}[/tex]

[tex]p = \frac{4c^2}{9d}[/tex]

The relationship between d, c and p is that [tex]p = \frac{4c^2}{9d}[/tex]

Answer: A

Step-by-step explanation: both triangle have a congruent side, angle, and second side

Answer:

2h-2=92 and h-2=92-h.

Step-by-step explanation:

Hannah, h, is the older sibling and their ages are consecutive odd integers. This means that Anthony's age will be 2 less than Hannah's, or h-2.

The sum of these would be h+(h-2), giving us the equation h+(h-2)=92.

Combining like terms we would have the first correct choice, 2h-2=92.

Our first equation can be transformed, however, to have (h-2) by itself. To do this, we would subtract h from both sides, giving us h-2=92-h.

The equation that will represent the sum of the age of Hannah and Anthony will be 2x+2=92.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the age of Hannah be x. and Since the age of Hannah and Anthony are two consecutive odd integers, therefore, the age of Anthony will be (x+2).

As it is given that the sum of the ages of the two other person is 92, therefore, the equation that will represent the sum of the age of the two persons can be written as,

[tex]x+(x+2)=92\\\\x+x+2=92\\\\2x+2=92[/tex]

Thus, the equation that will represent the sum of the age of Hannah and Anthony will be 2x+2=92.

Learn more about Equation:

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Answer:

1/5(a+b)

Step-by-step explanation:

Answer:

1/4,5/9,6/8,4/5

Step-by-step explanation:

Answer:

(1)

Karen: [tex]y = 2x +3[/tex]

Alice: [tex]y = 2x +1[/tex]

(2): Slope is 2

(3) y intercept

[tex]b = 3[/tex] --- For Karen

[tex]b = 1[/tex] --- For Alice

(4) They do not intersect

(5) No solution

(6) No

Step-by-step explanation:

Given

[tex]x = loaves[/tex]

[tex]y = amount[/tex]

Solving (1): Complete the equation.

For Karen:

[tex]m = 2[/tex] --- the rate

[tex]b = 3[/tex] --- additional spendings

For Alice:

[tex]m = 2[/tex] --- the rate

[tex]b = 1[/tex] --- additional spendings

The general equation is;

[tex]y = mx +b[/tex]

For Karen, it becomes

[tex]y = 2x +3[/tex]

For Alice, it is:

[tex]y = 2x +1[/tex]

(2): The slopes.

In (1), we have:

[tex]m = 2[/tex] --- the rate (for both Karen and Alice).

This rate implies the slope.

Hence, the slope is 2

(3): The y intercept.

The additional spendings in (1) means the y intercept.

So, we have:

[tex]b = 3[/tex] --- For Karen

[tex]b = 1[/tex] --- For Alice

(4) Because they have the same slope, they do not intersect

(5) Number of solutions.

[tex]y = 2x +3[/tex]

[tex]y = 2x +1[/tex]

Subtract both equations

[tex]y-y = 2x-2x +3-1[/tex]

[tex]0 = 2[/tex]

This means there is no solution

(6) Can they spend the same amount on the same number of loaves

In (5), the equations have no solution

Hence, it is not possible to spend the same amount for the same number of loaves

Answer: 7.83 years

:)))

Answer: 1296π

Step-by-step explanation:

To find the surface are if a square, we have to use the formula:

= 4πr²

= 4 × π × 18²

= 4 × π × 324

= 1296π

Therefore, the surface area of the sphere is 1296π

Answer:

C

Step-by-step explanation:

I did the test right

Answer:

879

Step-by-step explanation:

Because C is greater than A, C has to be the largest possible number so that A can be as large as possible. because C is the largest possible number, which is 9, the next largest number is 8, which in this case is A. The next biggest number is 7 which is B.

To sum it all up, the number is 879.

Answer:

2/7

Step-by-step explanation:

Hope that helps! (Brainliest please!)

Answer:

The probability that two unqualified applicants are interviewed before finding the fourth qualified applicant = 0.164

Step-by-step explanation:

Let,

The number of unqualified applicants are interviewed before finding the fourth qualified applicant = x

So,

X be the negative Binomial (n = 4 , P = [tex]\frac{20}{100} = 0.2[/tex] )

As , we know that

P(X = n ) = ⁿ⁺⁴⁻¹Cₙ × (1 - 0.2 )⁴ × (0.2)ⁿ  for n = 0, 1, 2, ....

As we have to find the probability that two unqualified applicants are interviewed before finding the fourth qualified applicant

⇒n = 2

∴

P(X = 2 ) = ²⁺⁴⁻¹C₂ × (1 - 0.2 )⁴ × (0.2)²  for n = 0, 1, 2, ....

               = ⁵C₂ × (0.8 )⁴ × (0.2)²  

               = [tex]\frac{5!}{2! (5-2)!}[/tex] × 0.41 × 0.04

               = [tex]\frac{5.4.3!}{2.1! (3)!}[/tex] × 0.0164

               = [tex]\frac{5.4}{2}[/tex] × 0.0164

               = 10 × 0.0164 = 0.164

∴ we get

The probability that two unqualified applicants are interviewed before finding the fourth qualified applicant = 0.164

Answer:

9

Step-by-step explanation:

according to the condition it is possible to make up a system of two equations (if to suppose 'l' - the larger number and the 's' - is the smaller one):

1. 'two numbers have a sum of 7' means s+l=7;

2. 'When the smaller number is subtracted from twice the larger number, the result is 20' means 2*l-s=20.

3. the system of two equations is:

[tex]\left \{ {{s+l=7} \atop {2l-s=20}} \right. \ => \left \{ {{s=-2} \atop {l=9}} \right.[/tex]

4. the larger number is 9.

The larger number would be as follows:

[tex]9[/tex]

Let the two numbers (larger and smaller) be [tex]= x ; y[/tex] respectively.

[tex]x + y = 7[/tex]

So, [tex]y = 7 - x[/tex]

Given that,

The Smaller number subtracted from twice large number gives 20. Thus,

[tex]2x - y = 20[/tex]

Putting the value of [tex]y, 2x - (7 - x) = 20[/tex]

[tex]2x - 7 + x = 20[/tex]

[tex]3x - 7 = 20[/tex]

[tex]3x = 27[/tex]

[tex]x = 27 / 3[/tex]

∵ [tex]x = 9[/tex] [The larger Number]

The smaller number [tex]'y' = 7 - 9 = -2[/tex]

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Answer:

The distance between the points

d = LM = 10.24

Step-by-step explanation:

Step(i):-

Given that the points are L ( 7,-1) and M (-2,4)

The distance formula

  LM = [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} -y_{1} )^{2} }[/tex]

Step(ii):-

[tex]LM= \sqrt{(-2-7)^{2} +(4-(-1) )^{2} }[/tex]

LM = [tex]\sqrt{(-9)^{2} +(5)^{2} }[/tex]

LM = √106

LM = 10.29

The distance between the points

d = LM = 10.24

Answer

Step-by-step explanation:

 yl grafica

Answer:

The slope would be -7

Step-by-step explanation:

To find the slope, you find two points on a line and find the difference between x-values and y-values. Then divide the difference of y-values by the difference of x-values to acquire the slope. [tex]\frac{8-1}{-4+3}[/tex] = [tex]\frac{7}{-1}[/tex] or -7, so that would be the slope.

Answer:

Step-by-step explanation:

There are five dice, so whatever the first die rolls there is a 1/6 chance that the second die is the same number. If that occurs, there's a 1/6 chance that the third die is the same, ditto the fourth and the fifth. So probability of Yahztee in one roll is 1/6 x 1/6 x 1/6 x 1/6 = 1/1296.

Answer:

A 60% chance

Step-by-step explanation:

Answer:

15

Step-by-step explanation: I believe that's the answer because the hypotenuse in a 30 60 90 is x2 and 15x2=30

Answer:

15

Step-by-step explanation:

Answer:

3 2/5

I converted these into decimals, because I find it easier ^.^

We have an 8 feet board, and we twice remove 2 1/3 from that number.

8 - 2 1/3 = 5.7

5.7 - 2 1/3 = 3.4 or 3 2/5

~Hope this helps~