PLEASEEEE HELPPPPP!!!

Select the correct answer. Simplify the expression.

Answer:

Step-by-step explanation:

Given the equation 4n^2 +28n +49, to get the factors of the equation, we need to factorize the equation completely as shown;

= 4n² +28n +49

Using the general formula n = -b±√b²-4ac/2a

from the equation: a = 4, b = 28 and c = 49

n =  -b±√b²-4ac/2a

n = -28±√28²-4(4)(49)/2(4)

n =  -28±√784-784/8

n = -28±√0/8

n = -28/8

n = -7/2

The factor of the given function is -7/2

The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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Answer:

t = 15

Step-by-step explanation:

t - 12 = 3

t = 3 + 12

t = 15

Answer:

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

g.

The quotient of p and q is p/q, at most means less or equal:

h.

The reciprocal of w is 1/w, at least means equal or greater:

i.

The absolute value of x is |x|:

Answer:

g. 1.  p/q ≤ 6

h. 2.  1/w ≥ 8

i.4. |x| > 6

Step-by-step explanation:

To express the given statements as an inequality, we need to determine the relationship between the given quantities.

g. The statement "The quotient of p and q is at most 6" means that p divided by q is less than or equal to 6. Mathematically, we can represent this as p/q ≤ 6.

h. The statement "The reciprocal of w is at least 8" means that the value of 1/w is greater than or equal to 8. Mathematically, we can represent this as 1/w ≥ 8.

i. The statement "The absolute value of x is greater than 6" means that the distance of x from 0 is greater than 6. This means that x is either greater than 6 or less than -6. Mathematically, we can represent this as |x| > 6.

Individual: Males between the ages of 40 and 59 in the U.S.

Variable: Amount of fat eaten per day

Type of variable: Continuous

Random variable X: Amount of fat eaten per day by a random sample of 32 men age 40-59 in the U.S.

The random variable X can be represented as:

X = amount of fat eaten per day by a randomly selected man between the ages of 40 and 59 in the U.S.

Note that this is a random variable because the amount of fat eaten per day can vary from person to person, and we don't know in advance what value X will take.

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The solution to the equation is given as \(a = \frac{2n}{(d + g)}\)

The equation is given as 2n= a(d+g), we are to make a the subject of the equation

in order to have a stand on its own we would have to divide the two sides of the equation by d + g

hence we would have:

\(\frac{2n}{(d + g)} =\frac{a(d+g)}{(d+g)}\)

this would cancel out on the right hand side such that we would have:

\(\frac{2n}{(d + g)} =a\)

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Answer:

radius = √13

Step-by-step explanation:

Forming the equation :

(x - h)² + (y - k)² = r²

Solving :

An equation for the total cars and trucks for dealership A is: x + y = 164.

An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.

The number of cars that dealership A sold is: 98 cars.

The number of trucks that dealership B sold is: 66 trucks.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:

Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;

x + y = 164.

Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;

2x + 0.5y = 229.

By solving the systems of linear equations simultaneously, we have:

2x + 0.5(164 - x) = 229

1.5x + 82 = 229

x = 98 cars.

For the y-value, we have;

2(98) + 0.5y = 229

0.5y = 229 - 196

y = 33/0.5

y = 66 trucks.

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Answer:

0.2 is the answer .

Hope it helps..

Answer:

4

Step-by-step explanation:

the factors are 1,2,4

Answer:

f + g=9x^2 +x-9

The domain is all real values

Step-by-step explanation:

f(x) = x - 9

g(x) = 9 x^2

f + g=x-9+9x^2

      = 9x^2 +x-9

The domain is the values that x can take

The domain is all real values

Answer:

D

Step-by-step explanation:

Answer:

Now he earns $11.66 per hour.

Step-by-step explanation:

6% raise

This means that now the employees will earn 100% + 6% = 106% = 1.06 of the previous amount they earned, that is, their previous earnings will be multiplied by 1.06.

Paul used to earn $11 an hour now he earns

Multiplying by 1.06

11*1.06 = 11.66

Now he earns $11.66 per hour.

The expression of the given statement is 2y - 3  = -1

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. The operations of mathematics include multiplication, division, addition, and subtraction.

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Let's look at how expressions are written.

The expression of the given statement is 2y - 3  = 4.

Here, let the unknown number = y

Now, product of y and 2 =  2 times  y   =   2y

Also, three less than the product   =  Product - 3

So, three less than the product  of 3 and y =  2 y - 3

Now, this above expression is equivalent to -1.

⇒2 y - 3  = -1

Hence the expression of the given statement is 2y - 3  = -1

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The sentence "Three less than the product of 2 and a number is 4" can be translated into the equation: 2x - 3 = 4

A mathematical statement that demonstrates the equivalence of two expressions is known as an equation.

It has two sides that are divided by the equals sign (=).

Variables, constants, coefficients, operators, and functions can all be used in the expressions on either side of the equation.

Here, x represents the unknown number that we are trying to solve for. The expression "the product of 2 and a number" is represented by 2x, and "three less than" is represented by the subtraction of 3 from that product. This expression is set equal to 4, which is the result given in the original sentence.

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Answer:

d/ ( a+b) = x

Step-by-step explanation:

d=ax+bx

Factor out x

d = x( a+b)

Divide each side by (a+b)

d/ ( a+b) = x (a+b)/ (a+b)

d/ ( a+b) = x

The value of x in the triangle is determined as 45.

The value of x in the triangle is calculated by applying the following formula,.

The measure of angle ABD = 0.2x + 52

The measure of angle CBD = 0.2x + 42

From the diagram, we can set-up the following equations;

x + 16 = 0.2x + 52

Simplify the equation above, by collecting similar terms;

x - 0.2x = 52 - 16

0.8x = 36

Divide both sides of the equation by " 0.8 "

0.8x / 0.8 = 36/0.8

x = 45

Thus, the value of x in the triangle is calculated by equating the appropriate values to each other.

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Intersection of 2 lines, and a circle

Find loci

Circle radius = 3 inches

Theres a given line AB

4 points are

2 intersections

1 center point

DRAWING. Points are 1,2,3,4

Then can be used a formula here, to find loci

A2x A1 = B3 x B4

Answer:

Proof is shown below.

Step-by-step explanation:

Use quadratic Formula, where from the standard form ax^2 + bx + c = 0, where a is not zero, we identify a = p-1, b=4, c = p-5, and since the given equation has no real roots, the discriminant b^2 - 4ac < 0, so that substituting we have that,

4^2 - 4(p-1)(p-5) < 0

16 - 4(p^2 - 6p + 5) < 0

16 - 4p^2 +24p - 20 < 0

-4p^2 + 24p - 4 < 0,

p^2 - 6p + 1 > 0, by dividing both sides of the inequality by -4.  

Chastity, this is the solution:

As you can see in the image of the double-line, we have:

3/5

6/10

9/15

12/20

15/25

Therefore, the simplest terms are:

3/5

The average rate of change of the function over the interval is 4

From the question, we have the following parameters that can be used in our computation:

y = 4x + 1

The interval is given as

[-1, 1)

The function is a linear function

This means that it has a constant average rate of change

From y = 4x + 1, we have

Rate = 4

Hence, the rate is 4

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The length of AB is AB = 8 units.

What is distance between two points?

The length of a straight line in the coordinate plane that connects two points in space is what is referred to as their distance. We use the absolute value to calculate the distance between any two points because it is impossible for this distance to be negative.

Consider, the given points A (-4, -3), B (4, -3), C (4, -7), D (-4, -7).

We have to find the length of AB.

Consider, the distance formula,

\(d = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}\)

where,

\((x_1, y_1)\) and \((x_2, y_2)\) are the points.

Here,

\((x_1, x_2) = (-4, -3)\\(x_2, y_2) = (4, -3)\)

Plug these values in the above formula,

\(d = \sqrt{(4-(-4))^2+(-3-(-3))^2} \\d = \sqrt{8^2 +0^2} \\d = \sqrt{8^2} \\d = 8\)

Hence, the length of AB is AB = 8 units.

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Answer:

Exterior angle = 45° each

Step-by-step explanation:

Given:

Number of side n = 8

Find:

Exterior angle

Computation:

Exterior angle =360° / n.

Exterior angle =360° / 8

Exterior angle = 45° each

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

the value of a is 3

hope it helps

Answer:

Step-by-step explanation:

Let x be the cost of the bench. Then the cost of the garden table is 3x.

The combined cost of the bench and the table is 1000, so x + 3x = 1000.

Combining like terms, we get 4x = 1000.

Dividing both sides by 4, we get x = 250.

The cost of the bench is 250.

Answer:

250.

Step-by-step explanation:

Let's call the cost of the bench "x".

The cost of the garden table is then 3x.

So the combined cost of both is x + 3x = 4x = 1000

So x = 250, and the cost of the bench is 250.

The volume of cylinder is,

V = 26,940.59 cm³

We have to given that,

The height of a cylinder is 24.8cm

And, the ratio of the diameter of the cylinder to the height of the cylinder is 3:2

Hence, Lenght of height = 2x

And, Diameter of cylinder = 3x

Since, The height of a cylinder is 24.8cm

So,

2x = 24.8

x = 24.8 / 2

x = 12.4 cm

Hence, Diameter of cylinder is,

d = 3x

d = 3 (12.4)

d = 37.2 cm

So, Radius = 37.2 / 2 = 18.6 cm

Thus, Volume of cylinder is,

V = πr²h

V = 3.14 × 18.6² × 24.8

V = 26,940.59 cm³

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Answer:

0 hundreds

0 tens

7 ones

.

4 tenths

0 hundredths

8 thousandths

Standard form=7.408

Step-by-step explanation:

Lets first solve (7x1)+(4x1/10)+(8x1/1000)

7+0.4+0.008

Simplify:

7.408

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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The amount that you will have in 3 years, given the interest rate and the amount won, is 1, 195, 618. 17 currency units

To find the amount earned in three years as a result of your lottery being invested, use the future value formula which is:

= Amount won x ( 1 + periodic  rate ) ^ number of periods

Periodic rate :

= 6 % / 4 quarters per year

= 1. 5 %

The number of periods is:

= 3 years x 4 quarters per year

= 12 quarters

The amount you will have in 3 years is:
= 1,000,000 x ( 1 + 1. 5 %) ¹²

= 1, 195, 618. 17 currency units

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