complete the number bond and write the number sentence to match the tape diagram

The linear equation that passes through the points (14, 15) and (20, 24) crosses the y-axis at y = -6.

A general linear equation can be written as:

y = m*x + b

Where m is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:

m = (y₂ - y₁)/(x₂ - x₁).

In this case the line passes through (14, 15) and (20, 24) so the slope is:

m = (24 - 15)/(20 - 14) = 9/6 = 3/2

y = (3/2)*x + b

To find the y-intercept we can replace the values of one of the points, like (14, 15)

15 = (3/2)*14 + b

15 = 3*7 + b

15 = 21 + b

15 - 21 = b

-6 = b

The y-intercept is -6.

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If he National Research Council recommends keeping a 1 : 3 copper to zinc ratio in a horse’s diet. If the horse is getting 420 milligrams (mg) of zinc per day, The number of  milligrams of copper that the Council recommend the horse have is : 140 milligrams.

Given data:

Copper to zinc ratio  = 1 : 3

Zinc per day = 420 milligrams

Hence,

1 /3 = x / 420

x /420 = 1 / 3

Where x is the number of milligrams of copper

so,

x = 1 /3 × 430

x = 140  milligrams of copper

Therefore the  milligrams of copper is 140 milligrams.

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Answer:

[tex]\dfrac{x-7}{9}[/tex]

which corresponds to choice
C :   [tex]f^{\small -1}(x)\ =\ \frac{1}{9}x\ -\ \frac{7}{9}[/tex]

Step-by-step explanation:

The inverse of a function y = f(x) can be found by interchanging x and y and solving for y

Let y = f(x)

y = 9x + 7

Interchange x and y:

x = 9y + 7

9y + 7 = x  (switch sides)

subtract 7 both sides
→  9y + 7 - 7 = x - 9

→ 9y = x - 9

Divide both sides by 9

→ [tex]y = \dfrac{x - 7}{9} = \dfrac{x}{9} - \dfrac{7}{9}[/tex]

which corresponds to choice C

Surface area of a rectangular prism formula

where w is width, l is length, and h is height.

Substituting with w = 4 ft, l = 6 ft, and h = 10 ft, we get:

The solution set for the given inequality (2q/5 + 4 < 2q/-9) is q∈(-∞, - 45/7).

So, 2q/5 + 4 < 2q/ - 9:

Now, solve for the solution set as follows:

Therefore, the solution set for the given inequality is q ∈ ( -∞, - 45/7).

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Answer:

Step-by-step explanation:

0 mixed berry smoothies and 70 milkshakes

Answer:

1.25 hours.

68.75 miles from the city

Step-by-step explanation:

Eltan's train (E) is travelling 65mph west.

Dmitri's train (D) is travelling 55mph west.

In terms of vectors, we can write E as 65E and D as 55W

The miles travelled by each is a function of time, T, in hours.

Each train's distance is:

 E:  T*65E

 D:  T*55W

They are 150 miles apart.  They will meet with the combined miles travelled is 150 miles.

 150 miles = T*65E + T*55W

150 miles = T(120 miles/hour)

T = (150 miles/120 miles/hour)

T = 1.25 hours

Make Demitri's train mile 0 and Eitan's train at mile 150 at the start.

They will have travelled the following miles in 1.25 hours:

Demitri:  (1.25hr)(55 m/hr) = 68.75 miles

Eitan:      (1.25hr)(65 m/hr) = 81.25 miles

Total = 150 miles

Dimitri is headed away from the city.  After 1.25 hours, his train will have travelled 68.75 miles when he sees Eitan passing him on the adjacent track (hopefull) headed into the city.  They meet 68.75 miles from the city.

Answer:

question one is B and question 2 is C

Step-by-step explanation:

Answer:

x = 8 + 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

computation just means to calculate

x(2[tex]\sqrt{3}[/tex] - 3 ) = 4[tex]\sqrt{3}[/tex] ( divide both sides by (2[tex]\sqrt{3}[/tex] - 3 ) )

x = [tex]\frac{4\sqrt{3} }{2\sqrt{3-3} }[/tex]

rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator.

the conjugate of 2[tex]\sqrt{3}[/tex] - 3 , is 2[tex]\sqrt{3}[/tex] + 3

= [tex]\frac{4\sqrt{3}(2\sqrt{3}+3) }{(2\sqrt{3}-3)(2\sqrt{3}+3) }[/tex] ← expand denominator using FOIL

= [tex]\frac{24+12\sqrt{3} }{12-9}[/tex]

= [tex]\frac{24+12\sqrt{3} }{3}[/tex]

= [tex]\frac{24}{3}[/tex] + [tex]\frac{12\sqrt{3} }{3}[/tex]

= 8 + 4[tex]\sqrt{3}[/tex]

Answer:

y axis-(0,6) x axis-(5,0) quad 1-(8.7,2.3) quad 2-(-1,10)  quad 3-(-1/4,-6 1/2) quad 4-(5,-2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

PLUG IN THE VALUES OF THE VARIABLES IN THE RIGHT POSITIONS AND SIMPLIFY.

[tex] \frac{1}{2} (12 - 4) \times \frac{1}{4} \\ = \frac{1}{2} (8) \times \frac{1}{4} \\ = \frac{8}{2} \times \frac{1}{4} \\ = \frac{8}{8} \\ = 1[/tex]

THE ANSWER IS OPTION B.

From the ellipse equation

the length of the major axis is equal to 2a. By comparing this equation with the given one, we can note that

Then, the length of the major axis is 2x7 = 14

In the given figure, m∠2 and m∠7 are "Alternate Exterior Angles" and they are always congruent (equal).

So we can equate them and solve for x.

So, m∠2 is

According to the straight-line angle property, the sum of m∠1 and m∠2 must be equal to 180°

Therefore, the measure of m∠1 is 147°

30

Given the expression for the instantaneous voltage expressed as:

Given the following parameter:

θ = 30⁰

Substitute the given parameter into the formula to have:

Therefore the instantaneous voltage when θ = 30⁰ is 30.

Answer:

10^2 + 15^2 = 20^2

100+225≠400

so no, it's not a right angled triangle

:)

Remember that to model this kind of problems, we can use the equation of a straight line

Where:

• b, are the fixed costs

• x ,represents what varies

• m, is the cost of what varies

1. Therefore, using the data provided, we can model the cost of production with a function where:

• x ,is the numbers of CD's produced

• C, is the cost of producing those CD's

2. To model the revenue, we'll have to take into account that every CD sells at $68. Therefore, the money collected by selling the x CD's produced is:

Where:

• x ,its the number of CD's produced and sold

• R, is the total revenue

3. To get the profit, we'll have to substract the production cost to the money collected by the sale. Remember we already have two expressions, in terms of x, that describe both situations. Therefore,

Where:

• x ,its the number of CD's produced and sold

• P, is the total revenue

4. In order to break even, the revenue (R) has to be equal to the cost of production (C), Thus,

Therefore, 546 CD's would have to be produced to break even.

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following function:

We calculate the inverse function as follows:

The cutoff score so that only 5% of the population has a higher score is 124.7.

If 5% of the population has a higher score, then the probability of selecting these is 0.05.

Find the z-score that corresponds to the probability in the z-table. (see attached images)

probability = 1 - 0.05 = 0.95

z-score = 1.647

Using the formula for the z-score below, determine the cutoff score.

z-score = (x – μ) / σ

where x = individual data value = cutoff score

μ = mean = 100

σ = standard deviation = 15

1.647 = (x - 100) / 15

1.647(15) = x - 100

x = 24.705 + 100

x = 124.705

cutoff score = 125

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Answer: slope = [tex]\frac{y}{x}[/tex]

Step-by-step explanation:
Slope means gradient which is given by change in y
                                                                      change in x
on the graph, change in y = 100-0 = 100
                        change in x = 95-45 = 50
so, gradient is 100/50
                      = 2

The equation of the line in slope-intercept form would be; y = -12x + 18

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

y = MX +c

To find the slope of a line, we the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.

We have been given the point (1,6) and (2,-6)

y-y₁ = m(x-x₁)

m = (-6-6)/(2 -1)

m = -12/1

Now substitute;

y-y₁ = m(x-x₁)

y- 6 = -12(x- 1)

y- 6 = -12x + 12

y = -12x + 18

Hence, the equation of the line in slope-intercept form would be; y = -12x + 18

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Jane decides to randomly interview 10 freshmen from each of the dorms, these people are her Sample.

What is Sample?

Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.

A little sample or amount of someone or something that is inspected, analyzed, or otherwise investigated to learn more about the rest.

Given: Jane wants to know what percentage of freshmen at her college purchase clothing with college logos. She decides to randomly interview 10 freshmen from each of the dorms.

Therefore, by the above information, these people are her Sample.

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The associated number of degrees of freedom for reading the t-value is 58.

The aim is to determine an interval for the mean of a population.

The standard deviation is unknown to us. The sample consists of 59 items. The mean of the sample is determined to be 32. We need to calculate the associated number of degrees of freedom for reading the t value.

We know that the degree of freedom is one less than the number of items in the sample space.

The associated number of degrees of freedom for reading the t-value is 59-1.

The associated number of degrees of freedom for reading the t-value is 58.

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Taking into account the definition of a system of linear equations, the first number is x= -14 and the second number y= -13.

A system of linear equations is a set of linear equations (that is, a system of equations in which each equation is of the first degree) in which two or more unknowns are related.

Systems of linear equations have as a solution set all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers. That is, solving a system of equations consists of finding the values of the unknowns, with which, when replaced in the equations, they must give the proposed solution.

In this case, a system of linear equations must be proposed taking into account that

You know:

The system of equations to be solved is

x-y= -1

x+y= -27

It is decided to solve the system of equations using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "x" from the first equation:

x= -1 +y

Replacing this expression in the second equation:

-1 +y +y= -27

Solving:

y +y= -27 +1

2y= -26

y= (-26)÷2

y= -13

Remembering that x=-1 +y, you get

x= -1 -13

x= -14

Finally, the numbers are -13 and -14.

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The values of the first and second numbers are - 13 and - 14 respectively.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let us assume that the two numbers are x and y.

Given, The difference between the two numbers is -1.

∴ x - y = - 1...(i)

And, Their sum is - 27 which is,

x + y = - 27...(ii)

Now, if we add eqn (i) to eqn (ii)

    x + y = - 27

+  x - y =     -1

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

  2x     = - 28

+ y and - y get canceled and we get

∴ 2x = 26.

x = - 13.

Now, substitute the value of x in any of the eqn(i). we get y = - 14.

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Answer:

Step-by-step explanation:

x y

2 12

6 8

10 4

14 0

18 -4

The slope is the Rise/Run, or change in y over the change in x.  Pick any two points.  I'll choose (2,12) and (18,-4),

Rise = (-4 - 12) = -16

Run = (18 - 2) = 16

Slope = Rise/Run = -16/15, or -1

The equation becomes y = -1x + b

To find b, use any of the points in the equation and solve for b.  I'll use (14,0):

y = -1x + b

0 = -1(14) + b

b = 14

The equation is y = -x + 14

See the attached graph.

Answer:

Step-by-step explanation:

triangle area formula: A = 1/2 × b × h

7 +3 = 10 ft

1/2 10 × 4 =

5 × 4 =

20 feet²

1) We need to consider that whenever we have a variable its exponent is raised to the 1st power, even when we don't write it as a superscript.

2) So we can write out the following steps to get that product as x²:

That's why we can write that, applying the property of exponents.

We have the next information

When he left the library he read 8/8-7/8= 1/8

then he read 1/10

after dinner, he read 2/5

First, we need to sum the fraction of the book he read

we need to have the same denominator in order to sum the fractions

the book complete represent 8/8 so we need to subtract 5/8 from the fraction of the complete book

the fraction of the book does he have left to read is 3/8

The ascending order of the set of numbers is √3 - 1, 2√10 ÷ 5, √14, 3√2, √19 + 1, 6

Given,

A set of numbers;

3√2, √3 - 1, √19 + 1, 6, 2√10 ÷ 5, √14

We have to arrange this numbers from least to greatest. That is, in ascending order.

Ascending order;

Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.

Here,

First we have to find the values of the square roots in the numbers.

3√2 = 4.24

√3 - 1 = 0.73

√19 + 1 = 5.36

6

2√10 ÷ 5 = 1.26

√14 = 3.74

Then,

6 is the greatest number and √3 - 1 is the least number.

That is,

The ascending order of the set of numbers is √3 - 1, 2√10 ÷ 5, √14, 3√2, √19 + 1, 6

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55.557 + 121.4474 + 6.3

we have that

55.557=55.5570

121.4474

6.3=6.3000

so

55.5570

121. 4474

6. 3000

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