The data in this table represents a linear function.

What is the slope of this line?
Y
-16
-24
-44
X -48
6
8
13
14

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Answer:  [tex]\textsf{y = -3/4x - 5}[/tex]

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Given: [tex]\textsf{Slope = -3/4 and passes through (4, -8)}[/tex]

Find:  [tex]\textsf{Determine the equation of the line that fits the criteria}[/tex]

Solution:  The first thing that we need to do is plug the information that was provided into the point-slope formula, distribute, and solve for y.

Plug in the values

Distribute and simplify

Solve for y

Therefore, the final equation of the line that passes through the point (4, -8) and has a slope of -3/4 is [tex]\textsf{y = -3/4x - 5}[/tex]

Answer:

[tex]x=\frac{1}{10}[/tex]

Step-by-step explanation:

[tex]\frac{30x^1}{3}=1[/tex]

Multiply both sides by 3

[tex]\frac{3\cdot \:30x^1}{3}=1\cdot \:3[/tex]

Simplify

[tex]30x=3[/tex]

divide both sides by 30

[tex]\frac{30x}{30}=\frac{3}{30}[/tex]

Simplify

[tex]x=\frac{1}{10}[/tex]

Answer:

a. 117. b. 9 c. 0. d. 22

Step-by-step explanation:

this composite function is calculated as: (f o g) (x) = f (g (x))

Answer:

[tex]270.33\%[/tex]

Step-by-step explanation:

so generally when we want to calculate how much "percent" a number is of another number we do, [tex]100(\frac{part}{whole})[/tex]

In this question, it's asking what percent of 182 is 492, and this wording might be a bit tricky at first. It might help a bit to reword it into, "492 is what percent of 182"

So in this question, the 492 is the part (despite it being bigger), and 182 is the whole

So now we use the equation: [tex]100(\frac{part}{whole})=100(\frac{492}{182})\approx270.33\%[/tex]

Answer:

-11

Step-by-step explanation:

I think it helps you

The probability that a boy selected at random is a Junior is 0.23 and the probability of randomly choosing a student who is a Junior and a boy is 0.14

The probability of an event is the chance or the likelihood that the event would occur.

Note that the chance or the likelihood is represented as a numerical value

The table that completes the question is added as an attachment

From the table, we have the following values

n(Boys and Junior) = 65

n(Boys) = 285

So, the probability that a boy selected at random is a Junior is

P = n(Boys and Junior)/n(Boys)

This gives

P = 65/285

Evaluate

P = 0.23

From the table, we have the following values

n(Boys and Junior) = 65

Total = 465

So, the probability of randomly choosing a student who is a Junior and a boy is

P = n(Boys and Junior)/Total

This gives

P = 65/465

Evaluate

P = 0.14

Hence, the probability of randomly choosing a student who is a Junior and a boy is 0.14

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Answer:

x > -6.

Step-by-step explanation:

-3x < 18

Divide both sides by -3.

x > -6.

(Note that the sign is flipped as we are dividing by a negative quantity).

The true statements about the integer are:

The statement is given as

The sum of -5 and another integers is a positive integer

Let the other integer be x

So, we have

The sum of -5 and x is a positive integer

A positive integer is greater than 0

So, we have

-5 + x > 0

Add 5 to both sides of the inequality

So, we have

x > 5

The above means that x is greater than 5

Hence, the sign of the integer is positive

The statement is given as

The sum of -5 and another integers is a positive integer

Let the other integer be x

So, we have

The sum of -5 and x is a positive integer

A positive integer is greater than 0

So, we have

-5 + x > 0

Add 5 to both sides of the inequality

So, we have

x > 5

The above means that x is greater than 5

Hence, the value of the integer is greater than 5

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The answer is 3 ft-lb.

Beyond its natural length:

Work done to strech the spring to a lentgh x = 0.5 * k * x^2

Now;

12  = 0.5 * k * 9

k = 8/3 = 2.667

9 in = 1.5 ft

Work needed to stretch it 9 in. beyond its natural length = 0.5 * 2.667 * 1.5*1.5 = 3 ft-lb

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Statement 2 is true. The contrapositive of a biconditional statement is always true.

A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, it typically has the form "if P then Q."

Where:

P and Q represent sentences.

A biconditional statement can be defined as a statement which combines a conditional statement with its converse. This ultimately implies that, a biconditional statement is generally created when a conditional statement is combined with its converse.

In Mathematics, a biconditional statement typically has the form "P if and only if Q." Therefore, the biconditional statement, "p if q," is true whenever the two statements have the same truth value. Otherwise, the biconditional statement is false.

In this context, we can reasonably infer and logically deduce that since statement 2 is true because the contrapositive of a biconditional statement is always true.

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According to the question, to write the solution for the logarithmic function, the concept of indices is also needed.

Therefore, the given expression is [tex]ex^{-2}=12[/tex]

The values get multiplied in addition. Therefore, the above expression can be written as by taking log on both the sides:

[tex]ln(ex^{-2} )=ln(12)\\-2(ln(e)+ln(x)) = ln(4)+ln(3)= 2ln(2)+ln(3)[/tex]

Using logarithmic definition, we can write:

The solution for the given expression is [tex]-2(1+ln(x)) = 2+ln(3)[/tex]

What is logarithmic function?

In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.

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After solving the given inequality the answer is x = 0.7/5log.

So,

Then,

Therefore, after solving the given inequality the answer is x = 0.7/5log.

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Step-by-step explanation:

the area of a triangle is

baseline × height / 2

now we also know that

the height in that triangle is twice its baseline.

so,

height = 2×baseline

so, for the given area we have

49 = baseline × 2 × baseline / 2 = baseline²

baseline = 7 ft.

therefore,

height = 2×baseline = 2×7 = 14 ft.

and now we run into a problem. as we don't have any further information about the triangle, the lengths of the sides cannot be determined.

the reason is that the height can be placed anywhere on the baseline (from the left end point all the way over to the right end point). all these triangles created by the moving height have the same area (49 ft²), but different lengths of the legs.

the lengths of the legs are calculated via Pythagoras, because the height splits the main triangle into 2 smaller right-angled triangles.

so, if I assume e.g. an isoceles triangle (both legs are equally long), then I know that the height splits the triangle into 2 equal triangles and the baseline in half.

then I can calculate :

leg² = (baseline/2)² + height² = 3.5² + 14² =

= 12.25 + 196 = 208.25

(each) leg = 14.43086969... ft

if I assume the height is at an endpoint of the baseline then the whole triangle is by itself a right-angled triangle.

and the height is one leg and the other leg is again via Pythagoras

leg² = baseline² + height² = 7² + 14² = 49 + 196 = 245

leg = 15.65247584... ft

all the possible solutions for the leg lengths are between 14 ft (the height) and 15.65247584... ft.

According to the question, the polynomial equation that is [tex]x^{4}+3x^{3}+16x^{2} -19x+8[/tex] is divided by the binomial [tex]x-1[/tex]. And in this, the coefficient of [tex]x^{2}[/tex] in the quotient is [tex]2[/tex].

The given expression can be written as:

Expression = [tex]\frac{x^{4}+3x^{3}+16x^{2} -19x+8}{x-1}[/tex]

Now, find the factors of the numerator term:

f(x) = [tex]x^{4}+3x^{3}+16x^{2} -19x+8 = (x-1)(x^{3}+4x^{2} -11x-30 )[/tex]

From the above equation, the coefficient of [tex]x^{2}[/tex] is [tex]4[/tex].

The solution for the given expression is [tex]4[/tex].

What is polynomial function?

Polynomial functions are those function whose variables contains varying degrees as well as non-zero coefficients and positive integers. It has different forms like quadratic equation or cubic equation etc.

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The possible values of x < 21.6.

When two mathematical statements or two numbers are compared in an unequal way, it is known as inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical or as a combination of the two. When a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression. Different types of linear inequalities can be represented in a number of different ways. As with multi-step linear equations, start by separating the variable from the constants when resolving multi-step linear inequalities with one variable. According to the laws of inequality, it is crucial that we remember to flip the inequality sign when multiplying or dividing with negative values while resolving multi-step linear inequalities.

so, from the question, the equation becomes,

x+15.5+14.2<51.3

x= 51.3-29.7

x= 21.6 Inches

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Explanation:

CCW = counter-clockwise

The rule for a 90 degree CCW rotation is this

[tex](\text{x}, \text{y})\to(-\text{y}, \text{x})[/tex]

it only works if the center of rotation is the origin.

The x and y coordinates swap places. Then you change the sign of the first coordinate after the swap occurred.

Applying that rotation rule to point C(5, 6) gets us to C ' (-6, 5).

Then to reflect over the x axis, we flip the sign of the y coordinate. The x coordinate stays the same. The notation would be [tex](\text{x}, \text{y})\to(\text{x}, -\text{y})[/tex]

So we go from C ' (-6, 5) to C '' (-6, -5)

There is a 35% increase in the number of seats.

Let us try to carry out each of the calculations as shown;

1) 7/8 + 1/6 ÷  2/9

Applying BODMAS

7/8 + (1/6 * 9/2)

7/8 + 9/12 = 39/24

2) 8/ 0.4^3 = 125

3) 75/100 * 15400 = 11550 people

4) Percentage increase in the number of seats = New capacity - Old capacity/Old capacity * 100/1

= 20790 seats - 15400 seats/15400 seats * 100/1

= 35 % increase

4) If it flashes 5 times every 10 seconds

Then in 1 second it flashes 0.5 times in every second

In a day there are 86400 seconds

Thus the light flashes 86400 seconds  * 0.5 times = 43200 times in a day.

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Answer:

$5.75

Step-by-step explanation:

price of the two hot dogs = 1.50 × 2 = $3

Then

The total payment = 3 + 2.75 = $5.75

Answer:

C. -5/6x+(8)

Step-by-step explanation:

mmmm math, love me some math, love me math, mmmm

From the given table, the equations that represent the relationship between the amount of money, A, and the number of months, m are:

First, find the slope of the line:
= (1,300 - 1,200) / (6 - 5)

= 100 / 1

= 100

The slope is 100. We can use this to find the y-intercept:

y = mx + b

1,400 = 100(7) + b

b = 1,400 - 700

b = 700

The form of the relationship between the amount of money and the number of months is:

y = mx + b

y = 100x + 700

The variants of this equation are:

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The answer to the following listed algebra questions are below:

6 = a/4 + 2

substract 2 from both sides

6 - 2 = a/4

4 = a/4

cross product

4 × 4 = a

a = 16

-6 + x/4 = -5

x/4 = -5 + 6

x/4 = 1

x = 4 × 1

x = 4

9x - 7 = -7

Add 7 to both sides

9x = -7 + 7

9x = 0

x = 0/9

0 = 4 + n/5

0 - 4 = n/5

-4 = n/5

-4 × 5 = n

-20 = n

-4 = r/20 - 5

-4 + 5 = r/20

1 = r/20

1 × 20 = r

r = 20

-1 = (5+x) / 6

-1 × 6 = (5 + x)

-6 = 5 + x

-6 - 5 = x

x = -11

(v+9)/3 = 8

v + 9 = 8 × 3

v +9 = 24

v = 24 - 9

v = 15

2(n + 5) = -2

2n + 10 = -2

2n = -2 - 10

2n = -12

n = -12/2

n = -6

-9x + 1 = -80

-9x = -80 - 1

-9x = -81

x = -81/-9

x = 9

-6 = n/2 - 10

-6 + 10 = n/2

4 = n/2

4 × 2 = n

n = 8

-2 = 2 + v/4

-2 - 2 = v/4

-4 = v/4

-4 × 4 = v

-16 = v

144 = -12(x + 5)

144 = -12x - 60

144 + 60 = -12x

204 = -12x

x = 204 / -12

x = 17

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The expression given as -15 + 0 is a representation of the identity property of integer

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

-15 + 0

The identity property of integer states that

x + 0 = x

This means that

-15 + 0 is a representation of the identity property of integer

Hence,  the expression given as -15 + 0 is a representation of the identity property of integer

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The formula for density is d = M/V,

where d is density, M is mass, and V is volume.

Density is commonly expressed in units of grams per cubic cm. For example, the density of water is 1 gram per cubic cm, and Earth's density is 5.51 grams per cubic cm.

The quantity per unit volume, unit area, or unit length: as. a : the mass of a substance per unit volume. b : the distribution of a quantity (as mass, electricity, or energy) per unit usually of space.

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The required value of base x is -4, 3.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is

ax^2 + bx + c = 0,

where a and b are the coefficients, x is the variable, and c is the constant term.

Now it is given that,

221x = 25base10

Converting them into quadratic equation we get,

2x^2 + 2x + 1x^0 = 2*10^1 + 5*10^0

Solving we get,

2x^2 + 2x + 1*1 = 2*10 + 5*1

Multiplying we get,

2x^2 + 2x + 1 = 20 + 5

Adding we get,

2x^2 + 2x + 1 = 25

Subtracting 25 both the side we get,

2x^2 + 2x + 1 - 25 = 25 - 25

Solving we get,

2x^2 + 2x - 24 = 0

Dividing whole equation by 2 we get,

x^2 + x - 12 = 0

factorizing we get,

x^2 + (4 - 3)x - 12 = 0

Expanding the bracket we get,

x^2 + 4x - 3x - 12 = 0

Taking common we get,

x(x + 4) - 3(x + 4) = 0

Again taking common we get,

(x + 4)(x - 3) = 0

Thus the value of x are,

x = -4

and x = 3

this is the required value of base x.

Thus, the required value of base x is -4, 3.

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The unit price of strawberries at the grocery mart is $1.5, the unit price of strawberries at the Baldwin hills is $1.30

In order to get the unit price of an item, you would have to divide the cost of the item by the total quantity bought.

With this definition, at the grocery mart

price = 2.99 dollars

quantity bought = 2

unit price = 2.99 / 2

= 1.5 dollars

At the Baldwin hills

price = 3.99 dollars

quantity bought = 3

unit price = 3.99 / 3

= $1.30

Hence the unit prices at the two markets are $1.5 and $1.30

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At Grocery Mart,strawberries cost $2.99 for 2lb., and at Baldwin Hills Market strawberries are $3.99 for 3 lb.What is the unit price of strawberries at each grocery store? If necessary , round to the nearest penny.

Answer:

[tex]\begin{array}{| c | c | }{ \rule{3cm}0cm}&{ \rule{3cm}0cm} \\ \bf Height, h cm& \bf Frequency\\{ \rule{3cm}0cm}&{ \rule{3cm}0cm}\\ \\ 0 < h \leqslant 5 & 2 \\{ \rule{3cm}0cm}&{ \rule{3cm}0cm} \\5 < h \leqslant 10& 7 \\{ \rule{3cm}0cm}&{ \rule{3cm}0cm} \\ 10 < h \leqslant 15&8 \\{ \rule{3cm}0cm}&{ \rule{3cm}0cm} \\ 15 < h \leqslant 20&3 \\ { \rule{3cm}0cm}&{ \rule{3cm}0cm}\end{array}[/tex]

According to the topic,

We know the number of following height, h cm :-