Consider the equation.
12 - 4x
3
Choose the correct option from each box to make the sentence true.
y =
The range of the function is
The domain of the function is
The y-intercept of the function is
The rate of change of the function is

Equation of the line that passes through (7, 10) and is perpendicular to the line y = x - 9 is y = -x + 17.

Given,

The equation, y = x - 9

Slope = m = 1

Slope of line perpendicular to given line = -1/m = -1/1 = -1

Let the equation of line be y = mx + c

Passes through A(7,10)

10 = -1(7) + c

10 = -7 + c

c = 10 + 7

= 17

Therefore, the equation of line is y = -x + 17

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The yield on a corporate bond with a face value of $1000 after removal of discount would be =$60.

Interest rate can defined as the payment received by an individual after investing a particular amount of money for a given period of time.

The principal amount after removal of $950 discount = $1000

The rate of interest (R) = 6%

The time of investment (T) = 1

Then the simple interest;

= P × T × R/100

= 1000 × 1 × 6/100

= 6000/100 = $60

Therefore, the yield of the corporate bond would be extra $60.

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Answer:

x = 7, y = 4

Step-by-step explanation:

simultaneous equation:

3x-y=17

4x+y=-3

The lower limit of the confidence interval is 18.80 and the upper limit of the confidence interval is 25.19

Confidence interval = sample mean ± margin of error

Margin of error = z*population standard deviation/[tex]\sqrt{n}[/tex]

The level of confidence is represented by z==2.12

the size of the sample n=11

sample mean= 22

confidence interval = sample mean ± z*population standard deviation/[tex]\sqrt{n}[/tex]

upper limit of confidence interval = sample mean + z*population standard deviation/[tex]\sqrt{n}[/tex]

=22+2.12*5/[tex]\sqrt{11}[/tex]=25.19

lower limit of confidence interval = sample mean - z*population standard deviation/[tex]\sqrt{n}[/tex]

=22-2.12*5/[tex]\sqrt{11}[/tex]=18.80

Therefore, the lower limit of the confidence interval is 18.80 and the upper limit of the confidence interval is 25.19

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The statements are true or false.

The standard form of 4.4 x 10-4 is 0.00044.

= 4.4 * 10^-4

= 4.4/10^4

= 4.4/10000

0.00044 = 0.00044

This statement is true.

The standard form of 6.39 x 10^5

= 6.39 * 100000

= 639*1000

639000 ≠ 63,900,000

This statement is false

The standard form of 3.02 x 10^10 is 3,020,000,000.

= 3.02 * 10^10

= 3.02 *10000000000

= 3,020,000,0000

This statement  is false.

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The solution of the given function is x < 3 + 4a.

What is a function?

A function is uniquely represented by the set of all pairings (x, f (x)), known as the function graph, which is a popular way of visualizing the function. When the domain and codomain are real number sets, each pair may be thought of as the Cartesian coordinates of a point in the plane. Functions are frequently employed in science, engineering, and the majority of mathematical areas. Most disciplines of mathematics say that functions are "the major subjects of investigation." If the domain and codomain set of two functions f and g are the same and their output values agree over the whole domain, they are equivalent.

The solution of the given function is

-4(-x+a)+5<8

or, 4x - 4a + 5 < 8

or, x < 8 - 5 + 4a

or, x < 3 + 4a

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An equation in slope-intercept form that represents the total cost of the membership is y = 5x + 265.

The number of aerobics classes that Carly took at $500 one year is 47 aerobics classes.

In order to write the equation in slope-intercept form, we would have to determine the slope of the line representing the total cost of the membership.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Substituting the given parameters into the formula, we have;

Slope, m = (290 - 270)/(5 - 1)

Slope, m = 20/4

Slope, m = 4

At point (1, 270), an equation of this line in slope-intercept form can be calculated by using this standard formula:

y = mx + c

Where:

Substituting the given points into the formula, we have;

y = mx + c

270 = 5(1) + c

Intercept, c = 270 - 5

Intercept, c = 265.

Therefore, the required equation is given by:

y = 5x + 265

For the number of aerobics classes at $500 one year, we have:

500 = 5x + 265

5x = 500 - 265

5x = 235

x = 235/5

x = 47 aerobics classes.

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Answer:

u = 15

Step-by-step explanation:

It appears that you have already created an equation to solve for u and just need help solving it

So we have 8² + u² = 17²

==> simplify exponents

64 + u² = 289

==> subtract 64 from both sides

u² = 225

==> take the square root of both sides

u = 15

Answer:

9 More Pages Per Minute

Step-by-step explanation

Printer A: 400/40 = 10

Printer B: 760/40= 19

Difference Between Printers: 19-10= 9

Answer: x = -10.8666667

Step-by-step explanation:

The equation of the line passing through (4,1) and perpendicular to y=1/2x-1 is y = -2x+9.

According to the question,

We have the following information:

A line passes through (4,1) and perpendicular to y=1/2x-1.

Now, the slope of the given line is 1/2.

We know that the slope of the perpendicular line is given by -1/m.

Slope of perpendicular line = -1/(1/2)

Slope of perpendicular line = -2

Equation of the required line:

(y-y') = m(x-x')

(y-1) = -2(x-4)

y-1 = -2x+8

y = -2x+8+1

y = -2x+9

Hence, the equation of the line passing through (4,1) and perpendicular to y=1/2x-1 is y = -2x+9.

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Answer:

"Centi"  means hundred so, a centimeter is a meter times 100. Divide 165 centimeters by 100 to convert it to meters. 165/100=1.65. If you are 1.65 meters, and Roberto is 1.7 meters tall, Roberto is taller.

Hope this helped!

Step-by-step explanation:

One cable company charges $50 per month for their basic plan, plus $75 installation. A second company charges $55 per month, but offers free installation. For what number of months is the first plan cheaper than the second plan?

50m + 75 < 55m

subtract 50m from both sides:

50m + 75 -50m < 55m - 50m

75 < 5m

divide both sides by 5:

75/5 < 5m/5

15 < m

or m > 15

so:

The first plan cheaper than the second plan after 16+ months

The coefficients of the quadratic equation are:

a = 2, b = 4, c = -12

The general quadratic equation is:

a*x^2 + b*x + c = 0

In this case, we have the quadratic equation:

x^2 + 4x - 5 = -x^2+ 7

Let's move all the terms to the left side, then we will get:

x^2 + 4x - 5 + x^2 - 7  =0

Now group like terms:

x^2 + x^2 + 4x - 5 - 7  =0

2x^2 + 4x - 12 = 0

Comparing this with the general quadratic equation we can see that:

a = 2

b = 4

c = -12

These are the coefficients.

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Answer:

−2x (x² + 2x + 3)

The solution to the statement is 2.591

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

what is 28.5dived by 11 equal

Rewrite the statement properly

So, we have

what is 28.5 divided by 11 equal

This means that we divide 28.5 by 11

So, we have the following representation

28.5/11

Evaluate the quotient

28.5/11 = 2.591

Hence, the result is 2.591

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Answer:

8.56

Step-by-step explanation:

d=2

r=d/2

r=1

area of the circle=πr², but we also have to subtract the square from it

a=π2²

a= 12.56

now the area of the square is 2*2

the area of the shape 12.56-(2*3)

the area of the shape is 8.56

Answer: 3

Step-by-step explanation:

You are solving a system of equations y1 = abx1 and y2 = abx2, so plug the x and y coordinates into the equations to solve for a and b:6 = ab1 & 3/4 = ab-2Since a = 6/b, we can use this in the second equation to solve for b:3/4 = (6/b)b-23/4 = 6/b36/(3/4) = b38 = b32 = b,which means that a = 3.Now we just input our a and b values into y = abx, so our equation is y = 3*2x.                 I hope this helps

The correct statement is "Similar, due to SSS and a scale factor of 0.29. Triangle QRS is similar to triangle VUT".

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.

Given that, two triangles Δ QRS and Δ VUT

We have,

QR/VU = RS/UT = QS/VT = 2/7 = 0.29

Hence, the two triangles are similar by SSS property with a scale factor of 0.29

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If "add" = 9 , "bad" = 7 , "cad" = 8 , then the value of "ada" is 6  .

In the question ,

alphabets are given ,

the alphabets are a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z .

and the value of "add"  is 9,

form above we can see that , the alphabet "a" is in the first position , so value of "a" =  1 ,

"d" is at 4th position , so the value of "d" = 4 .

So , "add" = a + d + d = 1+4+4 = 9

similarly we have , "bad" = b + a + d = 2+1+4 = 7

and "cad" = c + a + d = 3+1+4 = 8

hence , the value of "ada"

"ada" = a + d + a = 1+4+1 = 6 .

Therefore , the value of "ada" is 6 .

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The solution of numbers in their ascending order is Option C.

−5 3/5 , −27/5 , −4.1 , −3

What is Ascending Order?

When numbers are arranged in ascending order, they are done so from least to largest. We must first compare the numbers before we may arrange them in any order. Compare first, then order. Numbers arranged in ascending order: Determine how many digits each number has.

Given data ,

The numbers in the set S is S = { -27/5 , -4.1 , -5 3/5 , -3 }

Now , the fractions  -27/5 and -5 3/5 can be simplified as

-27/5 = -5.4

-5 3/5 = -28/5

          = -5.6

And , the numbers in the set S = { -5.4 , -4.1 , -5.6 , -3 }

The larger negative numbers are smaller in value

So , the numbers in their ascending form will be

-5.6 < -5.4 < -4.1 < -3

And ,

-5 3/5 < -27/5 < -4.1 < -3

Hence , the ascending form of the numbers is -5 3/5 , -27/5 , -4.1 , -3

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The sample size for estimating the proportion is 2637.

Given,

How many people should be included in the sample if we want to have 96% confidence that our sample proportion will be within 0.02 of the true fraction of the voting population given the data?

E = 0.02

c = 96% = 0.96

[tex]\hat p[/tex] or P = 0.5 (We have no idea about P, in this case, take P = 0.5)

[tex]\hat p[/tex]  = 1 - [tex]\hat p[/tex]  = 0.5

Now,

α = 1 - c = 1 - 0.96 = 0.04

α/2 = 0.04/2 = 0.02

⇒ α/2 = 2.054 (using z table)

The sample size for estimating the proportion is given by,

[tex]n = Z^2_\alpha _/_2P(1-P)/E^2[/tex]

   = (2.054/0.02)2 * 0.5 * 0.5

   = 2636.8

   = 2637

Hence, the size of sample is 2637.

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600 milliliters of the solution will be needed.

Given:

Let x be the solution needed.

A neonate order is 0.03 mg/kg of a 1:10,000 solution. the patient weighs 4.4 lb.

4.4 lb = 1.99581 kg

4.4 lb ≈ 2 kg

neonate order = 2*0.03

= 2*3/100

= 6/100

= 0.06 mg

1 : 10000 = 0.06 : x

1/10000 = 0.06/x

x = 0.06 * 10000 / 1

= 0.6*1000

= 6*100

= 600 milliliters.

Therefore 600 milliliters of the solution will be needed.

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Answer:

the area for the entire scale is 8 inches

the area for one of the triangles is 6.2 inches

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area of the triangle is:

A = 1/2 * (Base * Height)

A = 1/2 * (b * h)

A = 1/2 * (8 * 6.2)

A = 1/2 * 49.6

A = 24.8

Area of the square is:

A = Base * Height

A = b * h

A = 8 * 6.2

A = 49.6

Answer:

2x X 6 = 11x - 7/6

12x = 11x - 7/6

12x - 11x = -7/6

x = - 7/6

Step-by-step explanation:

let the unknown be x

twice of the number is 2x multipled by 6

2x(6) equating to eleven times the number 11x minus 7/6

gives an equation as in step 1

multiply 6 by 2x to give a more simple equation

collect like terms so you have an equation as in step 3

simplify to get your final answer

Answer:

Step-by-step explanation:

A is an integer by 10 as even and by 3 as odd as timed would be in power also by 3 then, B, in scientific writing is.... 140 OBVI

Answer:7.07 m

Step-by-step explanation:

ab=5

ab=bc

bc=5

(ab)^2+(bc)^2=(ac)^2

25+25=50

ac^2=50

ac=7.07