Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answer:

The equation is y=5/2x - 15 or if solving for X is -6

Step-by-step explanation:

In terms of y=mx+b, we are to make the Y by itself.

Step 1. -2y = -5x +30

Make y become positive!

Step 2. 2y = 5x - 30

Distribut the 2 over to make it 1y.

Step 3. 1y = 5/2x - 15

The equation is y=5/2x - 15

If you are to find X it would be....

-15 divided by 2.5 gets you x= -6

Answer:

(8,5)

Step-by-step explanation:

To find the y-value that corresponds to x=8 let's substitute this x-value in the equation.

5x-2y=30

5 x 8-2y=30

40-2y=30

10=2y

5=y

Therefore (8,5) is a solution of the equation.

Answer:

1/27 units cubed or 0.037037... units cubed

Step-by-step explanation:

Volume of a cube = s*s*s : Where s is a side length.

The volume of the first cube is 1 cubed, which means that each side length is 1. (s=1)

The volume of the second cube in relation to the first cube can be found by multiplying each side length by 1/3.

Volume of second cube= (1/3s)(1/3s)(1/3)s

Volume of second cube= (1/3)(1/3)(1/3)

Volume of second cube= 1/27

Answer:

answer 3

Step-by-step explanation:

point slope form is

\(y - y1 = m(x - x1)\)

Answer:

Find the exact value using trigonometric identities.

100

Step-by-step explanation:

The exact value of 2 divided by (0.01) 2 is 20000.

We are given that;

2 divided (0.01)2

Now,

To find the exact value of 2 divided by (0.01) 2, we can use the following steps:

Rewrite 0.01 as a fraction: 0.01 = 1/100

Square both the numerator and the denominator: (0.01) 2 = (1/100) 2 = 1/10000

Flip the fraction and multiply by 2: 2 / (0.01) 2 = 2 x 10000/1 = 20000

Therefore, by algebra the answer will be 20000.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ6

ΔABC  and ΔADC are congruent by SAS

We have,

From the figure,

We have,

ΔABC and ΔADC

∠BAC = ∠DAC = 51 ( given )

AB = AD = 4 ( given )

AC = AC ( common length )

This means,

ΔABC  and ΔADC are congruent by SAS

Thus,

ΔABC  and ΔADC are congruent by SAS

Learn more about triangle congruency here:

https://brainly.com/question/12413243

#SPJ1

The value of the inverse of the equation is this: x³ -3 = y

To find the inverse of the equation follow these steps:

1. Replace H(x) with y.

y = (x + 4)³ - 1

2. Interchange the values of X and Y.

X = (y + 4)³ - 1

3. Find the cube root of both sides

x³ = y + 4  - 1

4. Find the value of y

x³ - 4 + 1 = y

x³ -3 = y

Learn more about the inverse of an equation here:

https://brainly.com/question/3831584

#SPJ1

Answer:

B

D

A

Step-by-step explanation:

Given:

A. \(2x^3-x^{2} -6x\)

B. \(2x^3+8x+4\)

C. \(3x^4+x^{2} +x-7\)

D. \(3x^4-3x^{2} +5x-7\)

Now, let us evaluate the given expressions one by one.

\((4x^3-4+ 7x)-(2x^3-x-8)\\\Rightarrow 4x^3-4+ 7x-2x^3+x+8\\\Rightarrow 2x^3+8x+ 4\)

It is equation B.

So, \((4x^3-4+ 7x)-(2x^3-x-8)\) is equivalent to B.

\((-3x^2+x^4+x)+(2x^4-7+4x)\\\Rightarrow -3x^2+x^4+x+2x^4-7+4x\\\Rightarrow3x^4-3x^{2} +5x-7\)

It is equation D.

So, \((-3x^2+x^4+x)+(2x^4-7+4x)\)  is equivalent to D.

\((x^{2} -2x)(2x+3)\\\Rightarrow 2x^3-4x^{2} +3x^{2} -6x\\\Rightarrow 2x^3-x^{2} -6x\)

It is equation A.

So, \((x^{2} -2x)(2x+3)\) is equivalent to A.

So, answer is:

B

D

A

Answer:

B D A

Step-by-step explanation:

Hope I Helped

Answer:

3/8

Step-by-step explanation:

1. Find common denominators, which is 7/8 and 4/8

2. 7/8 - 4/8 = 3/8

Answer:

7/4 or 1 3/4

Step-by-step explanation:

If Mira had spent the same total amount of time but an equal amount of time on each problem, each problem would have taken around 2.36 minutes.

In the given plot, Mira spent varying amounts of time on each of the 55 math problems. To find out how many minutes each problem would have taken if Mira had spent an equal amount of time on each problem, we need to calculate the total time she spent and divide it by the number of problems.

Looking at the plot, we can estimate the total time Mira spent by counting the dots above each tick mark and multiplying them by the corresponding time interval. Let's break it down step by step:

The tick marks on the plot are at 7, 7.5, 8, 8.5, 9, 9.5, and 10 minutes per problem.

There are 2 dots above the unlabeled tick mark between 8 and 8.5 minutes per problem. We can assume it represents 8.25 minutes.

There are 3 dots above the 9.5 minutes per problem tick mark.

Now, let's calculate the total time Mira spent:

(7 * 2) + (7.5 * 2) + (8 * 2) + (8.25 * 2) + (9 * 2) + (9.5 * 3) + (10 * 2) = 129.5 minutes.

Since Mira spent a total of 129.5 minutes on 55 problems, each problem would have taken approximately 2.36 minutes (rounded to two decimal places) if she had spent an equal amount of time on each problem.

for more such questions on amount

https://brainly.com/question/843074

#SPJ8

In order to solve the missing side for a right triangle, we can use the Pythagorean theorem

then, we rewrite the expression for on of the sides different from the hypotenuse

replace with the values

Answer:

9.98- 2.53 = 7.45

7.68 + 13.07 = 20.75

100.03 - 16.28 = 83.75

Step-by-step explanation:

 9.98

- 2.53

_____

7.45

  1   1        - Process of carrying 10's

   7.68

+ 13.07

_______

 20.75

0000 13 ⇔ What the number becomes after carrying

↑↑↑↑↑

100.03

- 16.28

______

83.75

Happy New Year!

for a study cvaluating the difference among three treatments with a separate sample of n-10 for cach treatment,the kruska-walis test statistic would have df - 2(3-1)=2

The Kruskal-Wallis test statistic has a degrees of freedom (df) equal to the number of groups minus one. In this case, there are three groups, so the df is 2 (3-1).The Kruskal-Wallis test statistic is a non-parametric test used to compare the means of a set of independent samples. In this case, we have three separate samples of n-10 for each treatment. To calculate the Kruskal-Wallis test statistic, we need to first calculate the sum of the ranks for each sample and then subtract the expected sum of ranks for each sample. The df for the Kruskal-Wallis test statistic is equal to the number of groups minus one. In this case, there are three groups, so the df is 2 (3-1). Finally, the Kruskal-Wallis test statistic is calculated by dividing the calculated sum of ranks by the expected sum of ranks and multiplying by the df. This will give us the Kruskal-Wallis test statistic for the data set.

Learn more about test statistic here

https://brainly.com/question/14128303

#SPJ4

The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

To know more about temperature refer to

https://brainly.com/question/24746268

Answer:

\(x=\sqrt{15,} -5\)

Step-by-step explanation:

The rate of the slower car is 77km/hr

Velocity is the rate of change of displacement with time. It is measured in meter per second and it is a vector quantity.

velocity = displacement/time

displacement = velocity × time

represent the faster car by v1 and the slower car by v2

v1 = v2+16

V2 = v1-16

Total displacement = 680km

680 =( v1+V2)t

680 = (v1+V2)4

v1+v2 = 680/4

v2+16+v2 = 170

2v2 = 170-16

2v2 = 154

v2 = 154/2

v2 = 77km/hr

therefore the rate of the slower car is 77km/hr

learn more about velocity from

https://brainly.com/question/80295

#SPJ1

Simplifying this equation, we get:

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

Therefore, the value of k is 1.

In mathematics, a polynomial is an expression consisting of variables (usually represented by x), coefficients, and non-negative integer exponents, which are combined using the operations of addition, subtraction, and multiplication. For example,

\(3x^2 + 2x - 1\)

is a polynomial with three terms, or a "trinomial," where the variable x is raised to the powers of 2 and 1, and the coefficients are 3, 2, and -1.

The degree of a polynomial is the highest power of the variable in the expression. For example, the polynomial above has a degree of 2, since the highest power of x is 2.

Polynomials are used in many areas of mathematics, including algebra, calculus, and geometry, and are used to model many real-world phenomena.

We can use the remainder theorem, which states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). In this case, we know that when the polynomial\(l x^3 + kx^2 + 2kx\) + 6 is divided by (x - 2), the remainder is 30. So, we can set up the following equation:

\(x^3 + kx^2 + 2kx + 6 = (x - 2)q(x) + 30\)

where q(x) is the quotient when. \(x^3 + kx^2 + 2kx + 6\) is divided by (x - 2). We don't need to know what q(x) is, since we're only interested in finding k.

Now, let's substitute x = 2 into the equation above:

\(2^3 + k(2^2) + 2k(2) + 6 = (2 - 2)q(2) + 30\)

Simplifying the left-hand side, we get:

\(8 + 4k + 4k + 6 = 30\)

\(16k = 16\)

\(k = 1\)

OR

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

To know more about equation visit:

https://brainly.com/question/10413253

#SPJ1

The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51  19. 17 < 23  20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)

To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.

To indicate that the first value is less than the second value, write <.

Alternatively, to indicate that the first value is greater than the second value, write >.

Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36

To determine the direction of inequality, we need to compare the values.

We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.

For more questions on comparisons

https://brainly.com/question/30097421

#SPJ8

The correct question would be as

Write > or < to make each statement true.

11. -5 0

12. 9 -8

13. -7 7

14. 55 -75

15. -32 -24

16. 89 73

17. -58 -51

18. -32 4

19. 17 23

20. 18 -36​

Answer:

980.95

Step-by-step explanation:

A = $ 980.95

A = P + I where

P (principal) = $ 800.00

I (interest) = $ 180.95

Formula:

Compound Interest Equation

A = P(1 + r/n)^nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

Given:

A car travels 180 miles in 3 hrs and 45 min

As we know, 1 hour = 60 minutes

so, 45 minutes = 45/60 hours = 0.75 hour

so, the car travels 180 miles in 3.75 hrs

To find the number of miles per hour, we will divide the number of miles by the number of hours

so, the number of miles per hour =

so, the answer will be:

The car travels 48 miles per hour.

The requried, local minimum and maxium for the given function is √2 and -√2.

We need to find the local maximum and local minimum of the function \(f(x) = 2x + 4x^{(-1)}.\)

First, we find the derivative of f(x):

\(f'(x) = 2 - 4x^{(-2)} = 2 - 4/x^2\)

Setting f'(x) = 0 to find the critical points:

\(2 - 4/x^2 = 0\)

Solving for x, we get:

x = ±√2

To determine whether these critical points are local maxima or minima, we need to examine the sign of the second derivative:

\(f''(x) = 8x^{(-3)}\)

When x = √2, f''(√2) = 8/(√2)³ = 8√2 > 0, so x = √2 is a local minimum.

When x = -√2, f''(-√2) = 8/(-√2)³ = -8√2 < 0, so x = -√2 is a local maximum.

Learn more about local maximum and minimum here:

https://brainly.com/question/28983838s

#SPJ1

By the Mean Value Theorem for Integrals, there exists a value c in the interval [0,2] such that the average value of the function f(x) = x^2 over [0,2] is equal to f(c).

The average value of f(x) over [0,2] is given by:

(1/(2-0)) * ∫[0,2] x^2 dx

= (1/2) * [x^3/3] from 0 to 2 interval.

= (1/2) * (8/3)

= 4/3

Therefore, there exists a value c in [0,2] such that f(c) = 4/3.

To find the specific value(s) of c, we can solve the equation f(c) = 4/3, which gives:

c^2 = 4/3

c = ±\(\sqrt{(4/3)}\)

So the value(s) of c guaranteed by the Mean Value Theorem for Integrals are c = \(\sqrt{4/3}\) and c = - \(\sqrt{4/3}\)

You can learn more about interval at

https://brainly.com/question/28272404

#SPJ4

Answer:

None

Step-by-step explanation:

Truly, I'm not sure what type of problem this is, but most people don't favor all the seasons. If there is more to the problem, I would be glad to help further.

Answer:

One possible way to estimate how many people out of 20 would say that they like all seasons is to use a simple random sample. A simple random sample is a subset of a population that is selected in such a way that every member of the population has an equal chance of being included. For example, one could use a random number generator to assign a number from 1 to 20 to each person in the population, and then select the first 20 numbers that appear. The sample would then consist of the people who have those numbers.

Using a simple random sample, one could ask each person in the sample whether they like all seasons or not, and then calculate the proportion of positive responses. This proportion is an estimate of the true proportion of people in the population who like all seasons. However, this estimate is not exact, and it may vary depending on the sample that is selected. To measure the uncertainty of the estimate, one could use a confidence interval. A confidence interval is a range of values that is likely to contain the true proportion with a certain level of confidence. For example, a 95% confidence interval means that if the sampling procedure was repeated many times, 95% of the intervals would contain the true proportion.

One way to construct a confidence interval for a proportion is to use the formula:

p ± z * sqrt(p * (1 - p) / n)

where p is the sample proportion, z is a critical value that depends on the level of confidence, and n is the sample size. For a 95% confidence interval, z is approximately 1.96. For example, if out of 20 people in the sample, 12 said that they like all seasons, then the sample proportion is 0.6, and the confidence interval is:

0.6 ± 1.96 * sqrt(0.6 * (1 - 0.6) / 20)

which simplifies to:

0.6 ± 0.22

or:

(0.38, 0.82)

This means that we are 95% confident that the true proportion of people who like all seasons in the population is between 0.38 and 0.82. Therefore, based on this sample and this confidence interval, we would expect between 8 and 16 people out of 20 to say that they like all seasons in the population.

MARK AS BRAINLIEST!!!

The true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.

It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.

To get to the current positioning, a rotation might not be sufficient.

It could be required to include a fictitious translation known as the object's location (or position, or linear position).

Together, the position and orientation completely explain where the object is situated in space.

Therefore, the true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

Know more about orientation here:

https://brainly.com/question/3520971

#SPJ1

Answer:

10 servings

Step-by-step explanation:

5 pound= 80 ounce

80/8=10

10

Answer:

10 servings

Step-by-step explanation:

There are 16 ounces in 1 pound.

So, 5 times 16 gives you the total number of ounces.

5 x 16 = 80

Since you want to know how many 8 ounce servings you have, divide your answer by 8.

80 divided by 8 = 10

Your answer is 10 servings.

The answer is that we fail to reject the null hypothesis and cannot conclude that the variance is greater than 0.4 at α = 0.05.

The question asks us to test if the variance of the distance between door and jamb is greater than 0.4 at α = 0.05 for a random sample of 28 cars. To do this, we will use the chi-square test for variance.

Step 1: State the null and alternative hypotheses.
H0: σ2 = 0.4
H1: σ2 > 0.4

Step 2: Calculate the test statistic.
The test statistic for the chi-square test for variance is given by:
χ2 = (n - 1)s2 / σ2
where n is the sample size, s2 is the sample variance, and σ2 is the population variance under the null hypothesis.
Plugging in the values from the question, we get:
χ2 = (28 - 1)(0.7) / 0.4
χ2 = 18.9

Step 3: Find the critical value.
The critical value for the chi-square test for variance is found using the chi-square distribution table. For a one-tailed test at α = 0.05 and degrees of freedom = n - 1 = 28 - 1 = 27, the critical value is 40.113.

Step 4: Make a decision and draw a conclusion.
Since the test statistic (18.9) is less than the critical value (40.113), we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the variance of the distance between door and jamb is greater than 0.4 at α = 0.05.

Therefore, the answer is that we fail to reject the null hypothesis and cannot conclude that the variance is greater than 0.4 at α = 0.05.

Learn more about Variance

brainly.com/question/4725561

#SPJ11

Answer:

See explanation below.

Step-by-step explanation:

Given transformed function:

\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)

The parent function of the given function is:  y = sin(x)

The five key points for graphing the parent function are:

(See attachment 1)

Standard form of a sine function:

\(\text{f}(x)=\text{A} \sin\left[\text{B}(x+\text{C})\right]+\text{D}\)

where:

Therefore, for the given transformed function:

\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)

See attachment 2.

Answer:

c is your answer

Step-by-step explanation: