Solve for the unknown variable. -7x + 5 = 61

A) -66/7

B) 8

C) -8

D) 66/7

Answer:

Since the screw is smaller than 3/4 mm and larger than 5/8 mm,

we can make an inequality from the given data

3/4 > x > 2.5/4

where x is the width of the screw

So since the value is greater than 2.5/4 and less than 3/4,

the approximate value will be the mean of the two values

(2.5/4) + (3/4) = 5.5/4 = 11/8 mm

Answer:

5 and 24

Step-by-step explanation:

1) replace the x's with 125 | c(x)=120+4(125)/(125)

620/125=5 simplify numerator

x=5

2) replace c(x) with 9 | 9=120+4x/x

9x=4x+120 multiply both sides by x

9x-4x=4x+120-4x subtract both sides by -4x

5x=120 divide both sides by 5

x=24

so, it costs about 5 dollars per book when 125 are printed

and, if it costs 9 dollars per book, 24 should be printed

The given function for the cost of printing is a linear function that has a

fixed (set up) cost and a variable cost component.

The correct responses are;

Reasons:

Given that the function for the cost of printing x books is; c(x) = 120 + 4·x, we have;

1. The cost of printing 125 books is c(125) = 120 + 4 × 125 = 620

2. The amount the author plans to charge per book = $9

The number of books, n, that should be printed is given as follows;

\(\displaystyle 9 = \mathbf{ \frac{120 + 4 \times n}{n}}\)

Which gives;

9·n = 120 + 4·n

9·n - 4·n = 120

5·n = 120

\(\displaystyle n = \frac{120}{5} = \mathbf{24}\)

The number of books that should be printed, n ≥ 24 books

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The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

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Answer: The value of h that maximizes the volume of the box is h = 3.36

Step-by-step explanation:

First, the volume of a box of length L, width W, and height H is:

V = L*W*H.

in this case, we start with a rectangle of measures AxB.

We can define that the side with length A will be the length, and the other side will be the width.

As we cut squares of length h in the corners, now we will have that the measures of the box are:

Length = A - 2*h

Width = B - 2*h

Height = h.

And we know that A = 17 and B = 27.

So we can replace those values and get:

Length = 17 - 2*h

Width = 27 - 2*h

Height = h

The volume of this box will be:

V = (17 - 2*h)*(27 - 2*h)*h = 459*h -54*h^2 - 34*h^2 + 4*h^3.

Now we want to maximize this.

V(h) = 4*h^3 - 88*h^2 + 459*h

To find the maximum, let's look at the first derivation of V(h)

V'(h) = 3*4*h^2 - 2*88*h + 459.

We need to look for which values of h this is zero.

0 = 12*h^2 - 176*h + 459

The solutions are given by the Bhaskara equation:

\(h = \frac{176 +- \sqrt{(176)^2 - 4*12*459} }{2*12} = \frac{176 +- 95.33}{24}\)

Then the two solutions are:

h = (176 + 95.33)/24 = 11.3

h = (176 -95.33)/24 = 3.36

Now, the problem with the first solution is that if we cut two squares of length 11.3 in side A (2*11.3 > 17) , the amount of material cut is larger than A, so that option can be discarded.

Then the only option is h = 3.36

The value of h that maximizes the volume of the box is h = 3.36

The domain and range of the function in interval notation are (-∞, ∞) and [-5, ∞) respectively. Option D is correct.

The given function is y = (x+3)^2 - 5.

The domain of the function is all real numbers, since any value of x can be plugged into the function.

To find the range of the function, we can consider the vertex of the parabola, which is (-3,-5) since the coefficient of x^2 is positive. The lowest value of the function occurs at the vertex, which is -5. Therefore, the range of the function is y ≥ -5, meaning that the function can output any value greater than or equal to -5.

Therefore, the domain of the function is all real numbers and the range of the function is y ≥ -5.

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Answer:

A  =  139.25

Step-by-step explanation:

Answer:

(p)60/100     :)

Step-by-step explanation:

Answer:

\(1-\frac{2+13+25}{100} = 0,6\)

Here is one solution to the puzzle:

Squares: 2, 8, 16

Circles: 5, 7, 14

Total: 26

You can verify that each row of three numbers adds up to 26: 2 + 8 + 16 = 26, 5 + 7 + 14 = 26.

An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.

Therefore, the correct answer is as given above

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Answer:

Step-by-step explanation:

ST=SU

5x=3x+32

5x-3x=32

2x=32

x=32/2=16

ST=5×16=80

TU=80

SU=2×80=160

Therefore,

But, we do not have the dimension for the hypotenuse, In order to find the hypotenuse, we need to apply the Pythagorean theorem

Hence,

Therefore,

Answer:

Slope= 2

Y-intercept= -5

Step-by-step explanation:

This inequality is in slope-intercept form which means we can get both striaght from the inequaltiy. Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. In this inequality m would be 2 and b would be -5, so those are your answers.

Answer:

12.7  ==> distance of RS

24.2 ==> distance of RT

Step-by-step explanation:

Distance is always positive. So if you get a negative value, take the absolute value of the negative number:

For example, between point R and S:

-17.2 - (-4.5) =

-17.2 + 4.5 =  ==> subtracting a negative number is equivalent to adding a

                           positive number

-(17.2 - 4.5) = -12.7

-12.7 ==> |-12.7| = 12.7  ==> distance of RS

For RT:

-17.2 - 7 =

-(17.2 + 7) = -24.2

-24.2 ==> |-24.2| = 24.2 ==> distance of RT

The area of the sidewalk is 388 square feet.

To find the area of the sidewalk you can find the area of each individual shape and add them together.

Area of the first triangle T = (1/2) x 6 ft x 11 ft = 33 sq. ft.

Area of the second triangle = (1/2) x 6 ft x 18 ft = 54 sq. ft.

Area of the rectangle = 6 ft x 30 ft = 180 sq. ft.

Area of the square = 11 ft x 11 ft = 121 sq. ft.

Therefore, the total area of the sidewalk is:

33 sq. ft. + 54 sq. ft. + 180 sq. ft. + 121 sq. ft. = 388 sq. ft.

So, the area of the sidewalk is 388 square feet.

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Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

Answer:

f(x)'=3x^2-4x

Step-by-step explanation:

dy/ dx or f(x)'=3x^2-4x

Please make answer as brainliest

Answer:

The first option is correct. Option A is correct.

LCL = 0.270, and UCL = 0.397

80% Confidence interval = (0.270, 0.397)

Step-by-step explanation:

The data for Y and N for the 90 companies is attached to this solution provided.

Y represents companies with at least 1 bilingual operator and N represents companies with no bilingual operator.

The number of Y in the data = 30

Hence, sample proportion of companies with at least one bilingual operator = (30/90) = 0.3333

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = 0.3333

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 80% confidence level for sample size of 90 is obtained from the z-tables.

Critical value = 1.280

Standard error of the mean = σₓ = √[p(1-p)/n]

p = sample proportion

n = sample size = 90

σₓ = √[0.3333×0.6667)/90] = 0.0496891568 = 0.04969

80% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.3333 ± (1.28 × 0.04969)

CI = 0.3333 ± 0.0636021207

80% CI = (0.2696978793, 0.3969021207)

80% Confidence interval = (0.270, 0.397)

Hope this Helps!!!

Answer:

i believe its 5,-2

Step-by-step explanation:

sry if im incorrect

Answer:

1/5x

Step-by-step explanation:

1/5x

Answer:

B,C,D, and E

Step-by-step explanation:

Inequality tells us about the relative size of two values.

Mathematics is not always about "equals", sometimes we only know that something is greater or less than.

Example: Alex and Billy have a race, and Billy wins!

What do we know?

We don't know how fast they ran, but we do know that Billy was faster than Alex:

Billy was faster than Alex

We can write that down like this:

b > a

(Where "b" means how fast Billy was, ">" means "greater than", and "a" means how fast Alex was)

Inequalities: Symbols and Vocabulary

Algebra rules / General Rules:

 Isolate a positive x on the left side using algebra

 Reverse the inequality sign when mult/divide by a negative

 Less than: The symbol that:  Looks like an L () for ess than

< ○ )  Points to the Left



● ]  Caps the arrow pointing towards smaller numbers

on the number line

 Points towards the smaller of two numbers (4 < 7)

> Greater than: The symbol that: Looks like the top of an R ( >

)for GReater than

> ○ (  Points to the Right



● [  Caps the arrow pointing towards larger numbers on

the number line

 Open end is by the larger number (7 > 4)

Compound inequalities: usually in the form -4 < x < 4

but can also be x > -4 and x < 4

Answer:

Option D

Step-by-step explanation:

Given the following question:

\((7^5)^3\)

To find the answer we simply have to apply the exponent rule and multiply the exponents.

\((7^5)^3\)
\((a^b)^c=a^{bc}\)
\(5\times3=15\)
\(=7^{15}\)

Your answer is "7^15" or option D.

Hope this helps.

Answer:

7^15

Step-by-step explanation:

We know that a^b^c = a^(b*c)

7^5^3

7^(5*3)

7^15

The given linear equation, 5x - 8 = 11 - 7x + 12x , has no solution

From the question, we are to solve the given linear equation.

From the given information,

The given linear equation is

5x - 8 = 11 - 7x + 12x

To solve the linear equation, we would determine the value of the unknown variable.

In the given equation, the unknown variable is x. Thus, we would solve for x.

Solving for x

5x - 8 = 11 - 7x + 12x

Simplify

5x - 8 = 11 + 5x

Add 8 to both sides of the equation

5x - 8 + 8 = 11 + 8 + 5x

5x = 19 + 5x

Subtract 5x from both sides

5x - 5x = 19 + 5x - 5x

0 = 19

Hence, no solution

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To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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If an item has a listed price of $65 and the sales tax rate is 5%, the sales tax will be $3.25 and the total cost will be $68.25.

If the item has a listed price of $65, the sales tax rate is 5%, we can first calculate the amount of sales tax as follows:

Sales Tax = Listed Price x Sales Tax Rate

Sales Tax = $65 x 0.05

Sales Tax = $3.25

So the sales tax on the item is $3.25.

To calculate the total cost, we simply add the sales tax to the listed price:

Total Cost = Listed Price + Sales Tax

Total Cost = $65 + $3.25

Total Cost = $68.25

So the total cost of the item with sales tax is $68.25.

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Answer: a = 47.3;

              p = 0.65

Step-by-step explanation: A power function is of the form \(y=ax^{p}\) and passes through points (2,5) and (3,81), i.e.:

\(5=a.2^{p}\)

\(81=a.3^{p}\)

To determine the two unknows, solve the system of equations:

\(log5=log(a.2^{p})\)

\(log81=log(a.3^{p})\)

Using multiplication and power rules:

\(log5=loga+plog2\)

\(log81=loga+plog3\)

Giving values to constants:

0.7=loga+0.3p

2=loga+0.5p

This system of equations can be solved by subtracting each other:

\(-1.3=-0.2p\)

p = 0.65

Substituting p into one of the equations above:

\(loga+0.5(0.65)=2\)

\(loga=1.675\)

\(a=10^{1.675}\)

a = 47.3

The constants a and p of the power function which passes through points (2,5) and (3,81) are 47.3 and 0.65, respectively.

Step-by-step explanation:

36^3/4   *    36 ^-1/4    =   36 ^( 3/4 - 1/4 )  =  36 ^1/2 = sqrt (36 ) = 6

Refer from RD Sharma

RS Aggarwal or ask your teacher

The amount of force used to pull the cart from 60 N to 90 N, the new acceleration of the cart is, 1.5 m/s²

The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.

Formula of force,

F = ma

Given that,

A man pulled a cart filled with stones that had a total mass of 60 kg

He increased the amount of force used to pull the cart from 60 N to 90 N

New acceleration of cart = ?

F  = ma

Old acceleration,

60  = 60a

a   =  1 m/s²

New acceleration,

90 = 60a

a   = 90/60

a   =  3/2

a   =  1.5 m/s²

Hence, the new acceleration is 1.5 m/s²

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