Graph the solution set to the inequality: 8x - 7y ≥ 42​

Answer:

289560

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equations in order from least to greatest unit rate are y = 13/6x,y = 11/5x, y = 21/9x and y = 19/8x

On a graph, the unit rate is obtained by calculating the slope of the line. The slope is the change in y divided by the change in x:

Slope = y2-y1 / x2-x1  

Thus, we can any two convenient points on the graph and use it calculate the slope:

Let's pick points (5, 10) and (12, 25)

This implies x1 = 5, y1 = 10 and  x2 = 12, y2 = 25

Slope = y2-y1 / x2-x1

Slope = 25-10 / 12-5 = 15/7

Thus,  the unit rate of the graph is 15/7 = 2.143

Find the equations with unit rates greater than the unit rate of the graph:

y = 19/8x: unit rate = 19/8 =  2.375

y = 27/13x: unit rate = 27/13 = 2.077

y = 21/9x: unit rate = 21/9 = 2.333

y = 11/5x: unit rate = 11/5 = 2.200

y = 15/17x: unit rate = 15/17 = 0.882

y = 31/15x: unit rate = 31/15 = 2.067

y = 13/6x: unit rate = 13/6 = 2.167

The equations with unit rates greater than the unit rate of the graph are y = 19/8x, y = 21/9x, y = 11/5x and y = 13/6x

Therefore, the equations in order from least to greatest unit rate are y = 13/6x,y = 11/5x, y = 21/9x and y = 19/8x. Drag each tile to the correct box accordingly

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The measure of the intercepted arc, [tex]\widehat{XY}[/tex], formed by the secants ZW and ZV is 30°

A secant line is a straight-line which has two points of intersection with a circle.

From a similar question on the internet, the figure consists of an outside angle of 41° formed by two secants and two intercepted consisting of [tex]\widehat{XY}[/tex]and [tex]\widehat{VW}[/tex] which measures 112°

The outside angles of a circle theorem states that the outside angle formed by two secants or two tangent or a combination of a secant and a tangent is the difference of the measure of the difference of the angles of the intercepted arcs divided by two.

Mathematically;

[tex]m\angle z = \dfrac{\widehat{VW} - \widehat{XY}}{2}[/tex]

Where;

The outside angle formed by the secant ZW and ZV, m∠z = 41°

[tex]\widehat{VW}[/tex] = 112°

Which gives;

[tex]41^{\circ}= \dfrac{112^{\circ}- \widehat{XY}}{2}[/tex]

2 × 41° = 112° - [tex]\widehat{XY}[/tex]

82° = 112° - [tex]\widehat{XY}[/tex]

[tex]\widehat{XY}[/tex] = 112° - 82° = 30°

[tex]\widehat{XY}[/tex] = 30°

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Answer:

  D(8, -11)

Step-by-step explanation:

You want the coordinates of end point D if C is (2, -3) and the midpoint of CD is M(5, -7).

The midpoint is the average of the endpoint coordinates:

  M = (C +D)/2

Solving for D, we find ...

  D = 2M -C

Then point D is ...

  D = 2(5, -7) -(2, -3) = (2·5-2, 2(-7)+3)

  D = (8, -11)

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{3}}x+7\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is -1/3 and that it passes through (-2 , 5.5)

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5.5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5.5}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{(-2)}) \implies y -5.5= -\cfrac{1}{3} (x +2)[/tex]

[tex]y-5.5=-\cfrac{1}{3}x-\cfrac{2}{3}\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+5.5\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{55}{10} \\\\\\ y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{11}{2}\implies {\Large \begin{array}{llll} y=-\cfrac{1}{3}x+\cfrac{29}{6} \end{array}}[/tex]

The rational zeros for F(x)=3x^4-4x^3+x^2+6x-2 are x= -1 and x= 1/3 while the linear factors are (x+1) and (3x-1)

Synthetic division has to do with dividing polynomials.

The process involves:

Step 1: Set up the synthetic division.

Step 2: The leading coefficient should be brought down to the bottom row.

Step 3: Multiply this by the value just written on the bottom row.

Step 4: Then, add the column created in step 3.

This can be illustrated thus:

Given: f(x) = 3x⁴-4x³+x²+6x-2

3x⁴-4x³+x²+6x-2 = 0

We will try x = -1 in f(x). In this case, replace x with -1. This will be:

= 3x⁴-4x³+x²+6x-2 = 0

Since f(-1)= 0 so (x+1) is a factor

Using synthetic division:

-1)....3....-4....1....6....-2

.........3.....-7...8....-2..|..0

Remainder = 0

Quotient = 3x³ -7x² + 8x -2

For 3x³ -7x² + 8x -2,  f(1/3) = 0 so (x- 1/3) is a factor

1/3)....3....-7....8....-2

..........3.....-6...6...|..0

Remainder = 0

Quotient = 3x²-6x+6

= 3(x²-2x+2)

Since there are no more rational zeros or linear factors for x²-2x+2. Therefore, the rational zeros are x= -1 and x= 1/3.

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The value of C (8,5) is 56.

A combination is made up of n different items that are taken one at a time without repeating itself.

The given expression is C(8,5).

The expression C (8,5) can be denoted as ₈C₅.

The formula for selecting x thins from n things is:
ₙCₓ = n!/( (n-x)! x!)

Therefore, the value of ₈C₅ is:

₈C₅ = 8!/( (8-5)! 5 !)

     = 8!/( 3! ×5!)

      = (8×7×6×5!)/( 3! ×5!)

      = (8×7×6)/(3!)

      = (8×7×6)/(6)

      = 8×7

      =56

Hence, the value of C (8,5) is 56.

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By doing addition and subtraction of integers, the result obtained is

Mohammed had $5290 at the end of the month

What is addition and subtraction of integers?

At first it is important to know about integers

Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.

Suppose there are many integers, and we need to find the sum total of all those integers, then the operation used in this case is called addition.

To find how big or small one integer is from the other, then the operation used is called subtraction of integers.

Here we will use addition and subtraction of integers

Bank balance of Mohammed = $8376

Amount of money taken out by Mohammed next month to buy a car = $4595

Amount of money needed to buy new tires for his car = $1200

Amount of salary received by Mohammed next day = $2709

Amount of money Mohammed had at the end of the month =

$(8376 - 4595 - 1200 + 2709)

= $5290

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The dividend is 35286 and the divisor is 7. The value of the division is $540.8571

When dividing, it's important to note that the number that is being divided in this case 35286 is the dividend.

On the other hand, the number that is being divided by which is in this case 7 is the dividend.

The division will be:

= $35286 ÷ 7

= $540.8571

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Answer:

[tex]34.8w+5.2x[/tex] cm

Step-by-step explanation:

If the width of a rectangle measures [tex](9.6w+4.7x)[/tex] cm and its length measures [tex](7.8w-2.1x)[/tex] cm, then the perimeter of the rectangle is:

[tex]2(9.6w+4.7x)+2(7.8w-2.1x)[/tex]

[tex](19.2w+9.4x)+(15.6w-4.2x)[/tex]

[tex]19.2w+9.4x+15.6w-4.2x[/tex]

[tex]19.2w+15.6w+9.4x-4.2x[/tex]

[tex]34.8w+5.2x[/tex]

Answer:

amount owed = $7434.57

Step-by-step explanation:

To solve this problem, we have to use the following formula:

[tex]\boxed{A = P(1 + \frac{r}{n})^{nt}}[/tex],

where:

• A = final amount

• P = principal (initial) amount

• r = annual interest rate

• n = amount of times the interest is compounded per time period

• t = number of years the money is kept for

In this case, the principal amount, P = $5000 and the money is owed for two years, so t = 2. The annual interest rate, r = 0.20 (20% = [tex]\frac{20}{100}[/tex] = 0.2). The interest is compounded monthly, which means it is compounded 12 times per year. Therefore, n = 12.

Using the above information and formula, we can calculate the amount owed after 2 years:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

   [tex]= 5000(1 + \frac{0.2}{12})^{12 \times 2}[/tex]

   [tex]=[/tex] $7434.57

Therefore, the amount Edgar owes after 2 years is $7434.57.

From the graph,

a. Friend runs at constant rate because of the straight line graph

b. the domain of the function representing your run 0 ≤ x ≤ 60

the domain of the function representing your friend's run 0 ≤ x ≤ 60

The graph of a straight line shows that the variables are constantly varying hence the graph that has a straight line which is your friend's graph is the graph at constant rate.

The domain is controlled by the x direction, it consist of all the values that the s coordinate ca get to

The graph shows that both you and your friend has similar x coordinate and will have same domain

The x coordinate from the beginning of the graph is at 0. At the end it is at at point 60

point 60 is not marked but reading the graph it can be deduced that the last line is point 60. hence the domain is 0 ≤ x ≤ 60

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Answer: 7

Step-by-step explanation:

Answer:

7 is the GCF of 21 and 28

Step-by-step explanation:

The GCF of 21 and 28 is 7. To calculate the greatest common factor (GCF) of 21 and 28, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest factor that exactly divides both 21 and 28, i.e., 7.

Answer:

he read 9 chapters

Step-by-step explanation:

4:30 pm to 6:00 pm is 1:30 hours, which is 90 minutes

90/10=9

Answer:

[tex]\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)[/tex]

[tex]\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=3x^3-2x^2-11x+10[/tex]

If (x + 2) is a factor then:

[tex]\implies f(x)=(x+2)(ax^2+bx+c)[/tex]

Expand:

[tex]\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c[/tex]

[tex]\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c[/tex]

[tex]\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c[/tex]

To find a, compare the coefficients of x³:

[tex]\implies a=3[/tex]

To find b, substitute the found value of a into the coefficient for x² and compare:

[tex]\implies 2a+b=-2[/tex]

[tex]\implies 2(3)+b=-2[/tex]

[tex]\implies b=-8[/tex]

To find c, compare the constants:

[tex]\implies 2c=10[/tex]

[tex]\implies c=5[/tex]

Therefore:

[tex]\implies f(x)=(x+2)(3x^2-8x+5)[/tex]

Now factor (3x²-8x+5):

[tex]\implies 3x^2-3x-5x+5[/tex]

[tex]\implies 3x(x-1)-5(x-1)[/tex]

[tex]\implies (3x-5)(x-1)[/tex]

Therefore the factored function is:

[tex]\implies f(x)=(x+2)(3x-5)(x-1)[/tex]

Zero Product Property

[tex]\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}[/tex]

To find the zeros, set each factor equal to zero and solve for x:

[tex]\implies x+2=0 \implies x=-2[/tex]

[tex]\implies 3x-5=0 \implies x=\dfrac{5}{3}[/tex]

[tex]\implies x-1=0 \implies x=1[/tex]

Therefore, the zeros of the function are:

[tex]x=-2, \quad x=\dfrac{5}{3},\quad x=1[/tex]

Answer:

D.) 11

Step-by-step explanation:

-9=-k^2-7k+k Plugging in k for x

-9=k^2-6k Combine like terms

0=k^2-6k+9 Add 9 to both sides

0=(k-3)(k-3) Factor

k=3

The equation is now

f(x)=x^2-7x+3

so

f(-1)=(-1)^2-7(-1)+3

f(-1)=1+7+3

f(-1)=11

The value of  x is 26.125°

The measures of each angle are as shown below:

∠P  = 115.625°

∠Q =21.125°

∠R=43.25°

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

In ∆PQR

∠P is 14 less than five times x = 5x-15

∠Q is five less than x=x-5

∠R is nine less than twice x=2x-9

Angle sum property of triangle : The sum of all angles of triangle is 180°

So,5x-15+x-5+2x-9=180

8x-29=180

8x=180+29

x=( 180+29 )/8

x=26.125

So,∠P  = 5x-15 =5(26.125)-15=115.625°

  ∠Q =x-5=26.125-5=21.125°

 ∠R=2x-9=2(26.125)-9=43.25°

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The critical values of the chi statistic are; χ²R = 8.643 and χ²L = 42.796

The confidence interval estimate of σ is; 0.20 < σ < 0.45

We are given the following data;

Sample size; n = 23

Degree of freedom; df = n - 1 = 23 - 1 = 22

Confidence level; α - level = 99%

Sample standard deviation; s = 0.25 mg

For χ²R;

The significance level is; 1 - (1 - 0.99)/2= 0.995

The degree of freedom is; df = 22

From critical value tables, we know that; χ²R = 8.643

For χ²L ;

The significance level is; (1 - 0.99)/2 = 0.005

The degree of freedom is; df = 22

From critical value tables, we know that; χ²L = 42.796

The confidence interval estimate of σ is;

s * √[(n-1)/χ²L] < σ < s * √[(n-1)/χ²R)]

Plugging in the relevant values gives;

0.28 * √(22/42.796) < σ < 0.28 * √(22/8.643)

0.2008 < σ < 0.4467

0.20 < σ < 0.45

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Answer: no slope

Step-by-step explanation:
m= y2-y1/x2-x1

m= 6-(-6)/4-4

m=12/0

m= no slope

Answer:

y = 0.8x - 0.8

Step-by-step explanation:

Δy ÷ Δx = gradient (x)

4 - -4 = 8

6 - -4 = 10

8 ÷ 10 = 0.8

equation of line; y = mx + c

substitute one of the coordinates into the equation

(6, 4) y  = 4, x = 6

4 = 0.8(6) + c

4 = 4.8 + c

- 4.8 to get the y intercept on it's own

-0.8 = y intercept (c)

confirmation

substitute the new values to get the other y

(-4, -4) y = -4 <-- should be the answer, x = -4

y = mx + c

y = 0.8(-4) - 0.8

y = -3.2 - 0.8

y = -4 the gradient and the y intercept have been proven right

The number of tongue depressors = 56

The number of Band-Aids = 128

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let x be the number of tongue depressors.

Let y be the number of Band-Aids

Convert cents to dollars

1 cent = $0.01

So, 4 cents = 0.01*4 = $0.04

     8 cents = 0.01* = $0.08

The materials are worth $12.48 .

This means, 0.04x+0.08y=12.48......(1)

There are 184 individual packages in total.

This means,  x+y=184.......(2) => x=184-y.....(3)

Substitute (3) in (1),

0.04(184-y)+0.08y=12.48

7.36-0.04y+0.08y=12.48

=> y= 128

(3) => x=184-128=56

So, the number of tongue depressors = 56

     The number of Band-Aids = 128

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The integer +3 describes the statement, 3 inches above average.

What is an average?

A single number chosen to represent a group of numbers is called an average, and it is typically calculated by dividing the total number of numbers in the group by the number of numbers in the group. As an illustration, the sum of the integers 2, 3, 4, 7, and 9 is 5.

One point in the average refers to the amount of 1 inch.

If the average is above 3 inches, it means that the value of the average is above 3 inches. It further implies that the total value has gained 3 inches on that average.

Inches mainly describe the gains and losses in short-time investments. A positive sign (+) shows the above average, and a negative sign (-) represents the below average.

Therefore, the integer +3 describes the statement, 3 inches above average.

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the answer to that question is 34cm² of the circumference

The y-intercept of a line that has a slope of and passes through points (8, 3) is (0,1).

what is the slope-intercept?

A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.

The slope-intercept form: y = mx + b

m - a slope

b - y-intercept

Here, we have

A slope m = 1/4.

Substitute: y = 1/4 x + b

We know that

the line passes through the point (8, 3) → x = 8, y = 3.

Put the values of x and y into the slope of the line:

1/4 · 8 + b = 3

2 + b = 3 |-2

b = 1

Hence, the y-intercept is (0, 1)

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The probability that X will be greater than 25 is 0.42

Given,

The sample size, n = 39

The mean of the population, μ = 23

The standard deviation of the population, σ = 10

We have to find the probability for X > 25.

Here,

Z score = (X - μ) / σ

Z score = (X - 23) / 10

Now,

We have to find P(X > 25)

Then,

P(X > 25) = P(z >  (25 - 23) / 10)

P(X > 25) = P(z > 2/10)

That is,

P(X > 25) = P(z > 0.2)

Here,

0.5 - P(0 ≤ z ≤ 0.2)

= (0.5 - 0.0792)

= 0.42

Therefore,

The probability that X will be greater than 25 is 0.42

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The expression equivalent to [tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m[/tex] is m - 2.

Equivalent expressions are expressions that work the same even though they look different.

In other words, equivalent expressions are expressions that have the same value.

Therefore, the expression that is equivalent can be calculated as follows:

[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m[/tex]

Hence, let's simplify the expression to find it's equivalent,

open the bracket

[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = -\frac{21}{2}+2m+\frac{17}{2}-m[/tex]

[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = -\frac{21}{2}+2m+\frac{17}{2}-m = -\frac{21}{2}+\frac{17}{2}+2m-m[/tex]

[tex]-\frac{21}{2}+\frac{17}{2}+2m-m=-\frac{4}{2} + m[/tex] = m - 2

Therefore,

[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = m-2[/tex]

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