Solve the Inequality and graph the solution set.

-8-8(2x-4)>-5(4x-5)-21

Answer:

instead of X, we replace 9.

So we have: f(9)=4*9^2-2*9+4.

Again, f(9)= 4*81-18+4=324-14=310.

Answer:

I believe the first one is log8(5/3), the second is log5(3), and the third is -2log2(5)

Step-by-step explanation:

I got this by applying the properties of logarithms which are:

logₐ mn = logₐ m + logₐ n (product property)

logₐ m/n = logₐ m - logₐ n (quotient property)

logₐ mn = n logₐ m (power property)

logb = (log꜀ a) / (log꜀ b) (change of base property)

Equation of the perpendicular line in slope intercept form is [tex]y = \frac{5}{2}x + 2[/tex]

Option A is correct

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here, the given line is

2x + 5y = 10

5y = -2x + 10

[tex]y = -\frac{2}{5}x + \frac{10}{5}\\y = -\frac{2}{5}x + 2[/tex]

Slope of the given line is [tex]-\frac{2}{5}[/tex]

Slope of the line perpendicular to this given line is [tex]\frac{5}{2}[/tex]

The line passes through (-2, -3)

Equation of the required line

[tex]y - (-3) = \frac{5}{2}(x - (-2))\\y + 3 = \frac{5}{2}(x + 2)\\2y + 6 = 5x + 10\\2y = 5x + 10 - 6\\2y = 5x + 4\\y = \frac{5}{2}x + \frac{4}{2}\\y = \frac{5}{2}x + 2[/tex]

Equation of the perpendicular line in slope intercept form is [tex]y = \frac{5}{2}x + 2[/tex]

Option A is correct

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The value of the test statistic of the given problem is; -17.969

In statistics, hypothesis testing is simply a method used to test a claim about a population.

We are given;

Sample size; n = 1160

Sample proportion; p^ = 88% = 0.88

The percentage of 97% represents the proportion of a population and this tells us that we are making a claim about the population proportion (p) in the hypotheses.

We claim "fewer then 97%", which indicates less than 97% or 0.97:

p<0.97

The null hypothesis states that the population proportion is equal to the value mentioned in the claim.

H₀: p = 0.97

The claim is either the null hypothesis or the alternative hypothesis. If the null hypothesis is the claim, then the alternative hypothesis states the opposite of the null hypothesis.

Hₐ: p < 0.97

The value of the test-statistic is gotten from the formula;

z = (p^ - p)/(√(p(1 - p)/n))

z = (0.88 - 0.97)/(√(0.97(1 - 0.97)/1160))

z = -17.969

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Answer:

x = 147°

Step-by-step explanation:

To find x, we have to find the angle measures in the small triangle.

180 - 61 = 119° (sum of adjacent angles on straight line=180)

The other angle measure in the triangle is 28° because they are vertically opposite angles.

We subtract 119° and 28° to find the angle measure next to x.

180 - 119 - 28 = 33° (sum of angles in a triangle=180)

x = 180 - 33

= 147° (sum of adjacent angles on straight line=180)

The spoon holds 1250 milligrams of sugar if Kenneth needs to remove 12 spoonfuls.

We are given;

Kenneth is making a cake for the first time.

His recipe calls for 280 grams of sugar, but he accidentally pours 295 grams on his first try.

He uses a small spoon to remove the extra sugar.

He needs to remove 12 spoonfuls.

We need to find the quantity of sugar his spoon hold.

First, let us find the extra amount of sugar;

Extra sugar = 295 - 280 = 15 grams.

We will find each spoon by using the unitary method;

Since 12 spoonfuls hold 15 grams.

So, 1 spoonful holds 15 / 12 grams = 1.25 grams = 1250 milligrams.

So, 1 spoonful holds 1250 milligrams of sugar.

Thus, the spoon holds 1250 milligrams of sugar if Kenneth needs to remove 12 spoonfuls.

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Answer:

18.0833333333

Step-by-step explanation:

online calculator

Potential rational solution(s) to the above polynomial equation is ±1, ±2.

Actual rational solution are ±1, +2.

What is  polynomial equation?

Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree.

Main Body:

Given:

x³ - 2x² - x +2 = 0

We will use the Rational Root Theorem:

If the rational number r/s is a root of a polynomial whose coefficients are integers, then the integer r is a factor of the constant term, and the integer s is a factor of the leading coefficient.

So, if the constant therm is 2 and the leading factor is 1, candidates for roots are:

±1,±2

Dividing x³ - 2x² - x +2 = 0 by x-1, we get

x²-x-2 as quotient.

Splitting the middle term ,

⇒x² - 2x + x - 2

⇒x(x- 2) + 1(x-2)

⇒(x+1)(x-2)

so x= -1 , 2

Hence the rational solution to the equation are ±1, 2.

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The graph of the linear equation can be seen in the image at the end.

Here we have the linear equation:

y = -2x - 1

To graph this, we need to evaluate from x = -2 to x = 2, this means replacing the value of x by the correspondent number.

if x = -2, then:

y = -2*(-2)  - 1 = 4 - 1 = 3

So we have the point (-2, 3)

if x = -1

y = -2*-1 - 1 = 2 - 1 = 1

We have the point (-1, 1)

If x = 0

y = -2*0 - 1 = -1

We have the point (0, -1)

If x = 1

y = -2*1 - 1 = -3

We have the point (1, -3)

If x = 2

y = -2*2 - 1 = -5

We have the point (2, -5)

Now we just need to graph these 5 points on a coordinate axis and then connect them with a line, the graph of the linear equation can be seen below.

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The mean of the data is 3.85 using the stem-and-leaf plot.

It means the average feet that the heavy ball was thrown is 3.85 feet, which is the typical number.

To find the mean of a data set that is represented by a stem-and-leaf plot, first, list out all the data values that are represented on the stem-and-leaf plot, add all the values, and divide by the number of values that were represented on the stem-and-leaf plot.

Given the stem-and-leaf plot, using the key, the data points represented are:

2.0, 2.1, 2.4, 3.1, 3.2, 3.6, 4.1, 4.3, 4.7, 5.1, 5.1, 6.5

Mean = [2.0 + 2.1 + 2.4 + 3.1 + 3.2 + 3.6 + 4.1 + 4.3 + 4.7 + 5.1 + 5.1 + 6.5]/12

Mean = 46.2/12

Mean = 3.85 feet

The mean of 3.85 feet means that the average distance that the heavy ball was thrown in feet is 3.85.

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According to the scatterplot (graph) provided, the weight for someone who is 1.4 meters tall is predicted to be 34.8 kilograms.

A scatterplot is also referred to as scatter diagram, scattergram, or scatter chart and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association between the data set.

For this exercise, the height (M) was plotted on the x-axis of the scatterplot (graph) while the weight (in kg) would be plotted on the y-axis of the scatterplot (graph).

From the scatterplot which models the relationship between the height (M) and weight (in kg) of a person, an equation for the line of best fit is given by:

Weight, kg = -114.3 + 106.5M

When M = 1.4 meters, we have the following weight:

Weight, kg = -114.3 + 106.5(1.4)

Weight, kg = -114.3 + 149.1

Weight, kg = 34.8 kg.

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Complete Question:

According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be close to ____ kilograms.

The value of x so the the the function has the given value is as follows:

A function relates an input to an output.

In other words, a function is a special relationship among the inputs and their outputs codomain) where each input has exactly one output value.

Therefore, let's find the value of x so that the function has the given values.

m(x) = -3/5x - 4;  m(x) = 2

let's find the value of x when  m(x) = 2

2 = - 3/5x - 4

2 + 4 = - 3/5x

6 = - 3/5 x

cross multiply

-3x = 30

x = 30 / - 3

Hence,

x = - 10

w(x) = 5/6x - 3; w(x) = -18

let's find the value of x when  w(x) = -18

- 18 = 5/6x - 3

- 18 + 3 = 5 / 6 x

- 15 = 5 / 6 x

5x = - 90

x = -90 / 5

Hence,

x = - 18

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The unit rate of the equation y = -4x + 2 is -4

From the question, we have the following equation

y = -4x + 2

The above equation is a linear equation

Linear equations are represented as

y = mx + c

Where

When the equations y = mx + c and y = -4x + 2 are compared, we have

Unit rate, m = -4

Y-intercept, c = 2

Note that all linear equations have a constant rate of change

Hence, the unit rate in the linear equation is -4

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Answer:

this is how to do it. Now find the answer

Step-by-step explanation:

find the common factor for the denominators, which is 30.

then × the numerator by however much you ×tl the denominator by to get 30

Answer:

x=2 and =-4

Step-by-step explanation:

The required volume of the given shape is given as 432 cubic feet.

Given that,
A 3-dimensional shape with a hexagonal profile is given with dimension,
a = 6 in, H = 6 in and h = 4 in as shown in figure.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

here,
The volume of the given shape is,
Volume = 6/2[ah] × H
Substitute the value in the above expression,
Volume = 3 [4×6] × 6
Volume = 432 cubic feet,

Thus, the required volume of the given shape is given as 432 cubic feet.

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Answer:

16

Step-by-step explanation:

The x's go up by 1 (1, 2, 3, 4, 5)

The y's go up by 4's. 0, 4, 8, 12, 16

There is a rule to find the y's from the x's instead:

times by 4 and minus 4.

y = 4x - 4

y = 4(5) - 4

y = 20 - 4

y = 16

x-3=0

so x = 3

-(y-2)=0

so y = 2

vertex = (3,2)

Using the points (5, 1273) and (10, 2546), equation for the line is 5y =  1273x.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

Given,

Coordinates (5, 1273) and (10,2546)

For slope, m

m = y₂ - y₁/ x₂ - x₁

m = 2546 - 1273/10 -5

m = 1273/5

Equation in y = mx form,

y = 1273/5 x

Cross multiplying,

5y =  1273x

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Answer:

Step-by-step explanation:

Answer:

[tex]d=-8[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]258[/tex] and the second term is [tex]250[/tex], then each successive term in the sequence is [tex]8[/tex] less than the previous term. Therefore, the common difference is [tex]-8[/tex] ( [tex]d=-8[/tex] ).

The formula representing the arithmetic sequence is:

[tex]a_n=-8n+266[/tex]

Therefore:

Term 1: [tex]a_1=-8(1)+266=-8+266=258[/tex]

Term 2: [tex]a_2=-8(2)+266=-16+266=250[/tex]

Term 3: [tex]a_3=-8(3)+266=-24+266=242[/tex]

…

Term 9: [tex]a_9=-8(9)+266=-72+266=194[/tex]

The equation of the parabola exists y = 3/80(x - 20)² - 15

In the coordinate plane, a parabola exists algebraically represented using the standard equation. A parabola's general equation exists written as,

y = a(x - h)² + k

where (h, k) signifies the vertex.

y² = 4ax is the typical equation for a normal parabola.

substitute the values in the above equation, we get

y = a(x - 20)² - 15

simplifying the above equation, we get

0 = a(0 - 20)² - 15

0 = 400a - 15

a = 15/400

a = 3 / 80

Therefore, the equation of the parabola exists y = 3/80(x - 20)² - 15.

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The time spent exercising for a student who spends 6 hours texting is 6 hours.

The scatter plot is given in the question,

As per the given scatter plot, we take the two points (9, 1) and (3,7).

The equation of the line of best fit:

Let the approximate equation would be as:

y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 9, y₁ = 1

x₂ =3, y₂ = 7

y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

y - 1 = (7 - 1)/(3 - 9)](x - 9)

y - 1 = (- 6/6)(x - 9)

y - 1 =  -1(x - 9)

y = -x + 9+ 1

y = -x + 10 ...(i)

The time spent exercising by a student who spends 4 hours texting

This means that x = 4.

Substitute the value x =4 in the equation (i), and solve for y

y = -4 + 10

y = 6

Hence, the time spent exercising for a student who spends 6 hours texting is 6 hours.

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120 ounces of 35% salt and 90 ounces of water is needed to obtain 210 ounces of a mixture that is 20% salt.

An equation shows the relationship between two or more numbers and variables.

Let x represent the amount of water and y represent the amount of 35% solution.

She wants to obtain 210 ounces of a mixture that is 20% salt. Hence:

x + y = 210   (1)

Also:

0% of x + 35% of y = 20% of 210

0.35y = 42

y = 120

x + y = 210

x + 120 = 210

x = 90

120 ounces of 35% salt and 90 ounces of water

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Answer:

The graph of a function f is the set of points which satisfy the equation y = f(x). ... However, of these two answers, only x = −2 fits in the domain.

Step-by-step explanation:

The equation to solve when the three angles of a triangle measure x,y and 39 is x + y + 39 = 180°.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

It is important to note that the total angles in a triangle is 180°.

Therefore, in this case, the angles will be illustrated thus:

x + y + 39 = 180. This illustrates the equation.

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$17690 is the amount Michael owed his dad .

 Equations and equations of maximum degree 1 are also called "linear equations". The linear equation formula can be written as Y = mx + b. where m is the slope of the line, b is the y-intercept, and x and y are the variables. Slope indicates the direction and slope of the line. . This is because (0,y) is the point where the line intersects the y-axis.

The amount Michael owes is given by :

y = - 290x +18,560

x = number of months ; y = amount owed

Amount owed after 3 months :

Put x = 3 in the equation :

y= - 290(3) +18,560

y = - 870 + 18560

y = 17690

According to the general form of a linear equation :

y = mx + c

Where, m = slope ; c = intercept

The slope = - 290 ; Intercept = 18560

Slope is the change in y per unit change in x ; The slope means that amount owed, y decreases by 290 per month

The intercept shows that the original amount borrowed is 18560

Amount Michael owes his father decreases by 290 per month.

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Answer:

c. 7/12

Step-by-step explanation:

There are 36 possible outcomes when you roll a die twice.

11, 12, 13, 14, 15, 16

21, 22, 23, 24, 25, 26

31, 32, 33, 34, 35, 36

41, 42, 43, 44, 45, 46

51, 52, 53, 54, 55, 56

61, 62, 63, 64, 65, 66

The desired outcomes are the ones whose first number is greater than or equal to the second number. They are shown in bold and underline above.

There are 21 desired outcomes.

p(first number ≥ second number) = 21/36 = 7/12

Answer: c. 7/12