Solve the following system of equations. Show your work.

−2x+5y=−2

4x−10y=4

Solution:

Answer:

linear

Step-by-step explanation:

equal slope throughout

y = -5x – 13 equation is the equation of a line that passes through (- 10 3 and is perpendicular to Y 5x 7 with slope

The equation of a line is y = mx + b, where m is the slope and b is the y-intercept. To find the equation of a line that passes through (-10, 3) and is perpendicular to y = 5x + 7, we need to find m, the slope of the line.

We can find the slope of the line by using the point-slope form of a line, which is y - y1 = m(x - x1). In this equation, m is the slope, (x1, y1) is a given point on the line, and (x, y) are the coordinates of any point on the line.

Plugging in the given point of (-10, 3) and the line y = 5x + 7 into this equation, we get:

3 - 3 = m(-10 - -10)

The left side of this equation is 0, so the right side must also be 0. That means that m = 0.

Now that we have the slope of the line, we can plug it into the equation of a line, y = mx + b, to get the equation of the line:

y = 0x + b

Next, we need to find the y-intercept, b. To do this, we can use the given point (-10, 3). Plugging this in to the equation above, we get:

3 = 0x + b

Simplifying, we get:

b = 3

Now that we have the slope and y-intercept, we can write the equation of the line in slope-intercept form:

y = 0x + 3

Finally, we can simplify this equation to get the final answer:

y = -5x – 13

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Answer: They will each get 6 and there will be 1 left over.

Step-by-step explanation:

6*4 is 24. 25-24=1

Answer: No.

Step-by-step explanation: In order for a motion to be considered "rigid", it must undergo a transformation or rotation in which the distance between the vertices does not change. The distance between the vertices becomes larger in the image, meaning this is not a rigid motion.

Good luck!

Slope-intercept form with slope and y-intercept can be written as y = mx + b.

The slope-intercept form of a straight line is one of the most common ways to show the equation of a line. The slope-intercept formula can be used to derive the equation of a line when the y-intercept and slope of the straight line are known.

Consider a straight line with y-intercept "b" and slope "m." The slope-intercept form equation of a straight line is given by y = mx + b. For example, the equation of the line with a y-intercept = 5 and slope = -1 is written as y = -x+5.

When two points (x1, y1) and (x2, y2) are given, then the slope-intercept form is written as (y2 - y1)/(x2 - x1).

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The diagram that models the ratio in the story is circled on the image given at the end of the answer.

If the students used 12 rolls of blue streamers, the number of rolls of yellow streamers that the students used was of:

8 rolls.

A ratio between two amounts a and b is given by the division of the amount a by the amount b.

The group used 3 rolls of blue paper streamers for every 2 rolls of yellow paper streamers, hence the ratio is given as follows:

blue streamers/yellow streamers = 3/2.

If the students used 12 rolls of blue streamers, the amount of yellow streamers is found applying the proportion as follows:

12/x = 3/2.

Applying cross multiplication, we have that:

3x = 2 x 12

3x = 24

x = 24/3

x = 8 rolls of yellow streamers.

The problem is given by the image shown at the end of the answer.

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An equation that has 3 variables is called a cubic equation.

In mathematics, the general form of a cubic equation is ax³+ bx² + cx + d=0. Here, a is the co-efficient of the cube of x, b is the co-efficient of the square of x and c is the co-efficient of x. We also have the constant term d.

This is also referred to as a trinomial equation.

The degree of a cubic equation is 3. The degree of an equation is the highest power the equation has. As we can clearly see that the degree here will have to be 3. It also has 3 roots namely, α, β, and γ.

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The equation of the line through (1, 2) so that the segment of the line intercepted between the axes is y+2x=4.

Let's use the slope-intercept form to find the equation of the line,

Hence the equation of the line would be of the form y=mx+c,

now the point at which the line intersects X-axis is (a,0), and the point at which it intersects Y-axis is (0,b).

⇒ m×a+c = 0

⇒a= − c/m

​and b=c+0 ⇒ b=c

Now, (1,2) is the midpoint of (a,0) and (0,b)

ie. 2=(0+b)/2​ ⇒ c/2 ​=2

                  ⇒c = 4

and  1=(a+0)/2​ ⇒ 1= −c/2m​

                       ⇒ m= −c​/2

                       ⇒ m= −2

∴ The equation of the line is given by y+2x=4.

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The complete question is-

What is the equation of the line through (1, 2) so that the segment of the line intercepted between the axes is?

By using the concept of conversion of unit, it can be calculated that

There are 12075 milligrams in 12 grams 75 milligrams

What is conversion of unit?

The process of changing a value from one unit to the equivalent measurement in other unit is called conversion of unit.

Conversion of unit is a very important tools and is very much required in physics, maths and chemistry.

There are 1000 milligrams in 1 gram.

In 12 grams 75 milligrams, number of milligrams = [tex]12 \times 1000 + 75[/tex]

                                                                                = 12075 milligrams

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The correct option is a survey based on multidimensional scaling”.

What is multidimensional scaling?

Using multidimensional scaling (MDS), it is possible to see how similar the individual examples in a dataset are to one another. The pairwise "distances" between a group of items or people are translated using MDS into a configuration of points that are mapped onto an abstract Cartesian space.

Companies utilize multidimensional scaling (MDS) as a technique to visualize the degree of similarity between diverse goods or datasets.

Since the study asks participants to rate how similar two brands are. Consequently, it is regarded as multidimensional scaling (MDS).

Hence the correct option is a survey based on multidimensional scaling”.

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Complete Question
You are a customer taking a survey. It lists two brands and asks you to rate how similar they are. What type of survey are you taking?

A. a focus group application survey
B. a survey based on multidimensional scaling
C. a survey based on attributes
D. a conjoint analysis survey.

Answer:

16

Step-by-step explanation:

there are four of them and four spaces, so you would do 4x4. 4x4= 16

Answer:

See below.

Step-by-step explanation:

We can find three points by picking values of one of the variables and calculating the other.  I'll pick a few values of x:  -2, 0, 2, 4.  Now calculate the values of y with the equation x-y = 0.  We can rearrnage this to -y = -x, or y = x.  This tells us that y equals x, so the data points would be:

(-2,-2)

(0,0)

(2,2)

(4,4)

Plot these points on graph paper and then draw a straight line through them.  Or use an online graphing utility, such as the free DESMOS.  The graph is attached.

Answer:

Step-by-step explanation: 1/2 is the slope of the line

The approximate percentage of daily phone calls numbering between 37 and 47 is of:

68%.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

The mean and the standard deviation in this problem are given as follows:

Hence the percentage is of 68%, as these measures are within one standard deviation of the mean.

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Answer:

? = 5

Step-by-step explanation:

There are no like terms to 5, so it stays the same

Answer:

721.1 grams.

Step-by-step explanation:

To determine the mass of the sample on the 8th day of the experiment, you can use the formula for compound interest, which is given by the following equation:

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

where A is the final amount of the substance, P is the initial amount, r is the rate of decay, n is the number of time periods, and t is the number of time periods elapsed. In this case, the initial amount of the substance is 1400 grams, the rate of decay is 12%, and the number of time periods is 1 day. Therefore, the mass of the substance on the 8th day can be calculated as follows:

A = 1400(1 + 0.12/1)^(1*8) = 721.1 grams

Therefore, the mass of the radioactive sample at the beginning of the 8th day of the experiment is 721.1 grams.

Consecutive integers are a set of positive whole numbers which follows one another respectively. Thus the required proof to the question is as explained below:

The theorem states that:[tex]/hypotenuse/^{2}[/tex] = [tex]/adjacent/^{2}[/tex] + [tex]/opposite/^{2}[/tex]Thus a set of consecutive numbers which represent each side of a right angled triangle must obey the Pythagorean theorem.

Consecutive integers are a set of positive whole numbers which follows one another respectively. Examples are; 20, 21 and 22, 2, 3 and 4 etc.Therefore, the three consecutive integers that are also Pythagorean tribble are 3, 4 and 5.

So that let the adjacent side be 3, and the opposite side 4, then;[tex]/hypotenuse/^{2}[/tex] = [tex]/adjacent/^{2}[/tex] + [tex]/opposite/^{2}[/tex]                       = [tex]3^{2}[/tex] + [tex]4^{2}[/tex] = 9 + 16                       = 25

hypotenuse = [tex]\sqrt{25}[/tex] = 5

Therefore the common three consecutive integers that are Pythagoras tribble are 3, 4 and 5.

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By using trigonometry, it can be concluded that

sin 60° = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{\sqrt{3}}{2}[/tex]

cos 60° = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{1}{2}[/tex]

tan 60° = [tex]\frac{BC}{AC}[/tex] = [tex]\sqrt{3}[/tex]

cot 60° = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{1}{\sqrt{3}}[/tex]

What is Trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are

[tex]sin \theta, cos \theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

[tex]sin\theta = \frac{perpendicular}{hypotenuse}[/tex]

[tex]cos\theta = \frac{base}{hypotenuse}[/tex]

[tex]tan\theta = \frac{perpendicular}{base}[/tex]

[tex]cot\theta = \frac{base}{perpendicular}[/tex]

[tex]sec\theta = \frac{hypotenuse}{base}[/tex]

[tex]cosec\theta = \frac{hypotenuse}{perpendicular}[/tex]

Trigonometry is a very important tool in mathematics.

Here, [tex]\Delta ACB[/tex] is a right angled triangle whose base is AC, Perpendicular is BC and hypotenuse is AB

By using Trigonometry,

sin 60° = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{\sqrt{3}}{2}[/tex]

cos 60° = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{1}{2}[/tex]

tan 60° = [tex]\frac{BC}{AC}[/tex] = [tex]\sqrt{3}[/tex]

cot 60° = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{1}{\sqrt{3}}[/tex]

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Answer: To solve for an area of something, we must first multiply the length by the width, something that is 5 inches long and 2 inches wide has an area of 10 square inches. It's basically multiplying the numbers together in order to find the amount of area it has.

Step-by-step explanation:

a) The average cost of the promotion is $0.01 per tire.

b) The probability that Greer will refund more than $25 for a tire is 0.9

According to the Question:

Greer Tire Company has:

Lifetime mileage = 33500

Standard Deviation = 3500 miles

a)

Meal lifetime mileage : $33,500

Standard deviation of mileage $3,500

Observed miles 30,000 miles

100 miles failed $1.00

Hence :

The average cost of the promotion:

= (33,500 – 30,000) / 3500

= 3500 /3500

= 1

Therefore,

Cost of production

100 miles = $1.00

= 1 * 1 / 100

= $0.01 per tire

b)

 P (z < 25000 -33500/ 3500

= P (z < -8500/ 3500)

= z < -2.4

Hence:

= 1 - 0.1

= 0.9

Therefore, the Probability that gear will refund more than $25.00 per tire is: 0.9

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a) The proportion of the students scored at least 26 points on this test is 0.02275.

b) The 71 percentile of the distribution of test scores is 24.073

A low standard deviation suggests that values are often close to the mean of the collection, whereas a large standard deviation suggests that values are dispersed over a wider range.

Standard deviation, often known as SD, is most frequently represented in mathematical texts and equations by the lower case Greek letter (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

Let the scores be X and X is normally distributed with a mean of 22 and standard deviation of 2.

μ=22

σ=2

X≈N(22,2)

a) P(X≥26)=P(((X-μ)/σ)≥(26-μ)/σ)

=1-P(Z≥2)

=1-P(Z<2)

=1-0.97725

=0.02275

b) Let a is the 71th percentile of X,

P(X≤a)=0.71

P((X-μ)/σ)≤(a-μ)/σ)=0.71

P(Z≤z)=0.71

From the standard normal table by calculating with z value, we get

a=24.073

Therefore,

a) The proportion of the students scored at least 26 points on this test is 0.02275.

b) The 71 percentile of the distribution of test scores is 24.073.

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Applying the trend in the table the population in 2023 is predicted to be

Exponential function  is a type of function that are of 3 main parts

Considering the given problem,  f(x) = 80(b)^x

the starting = 80

the base = b

the exponents = x

f(x) = 80(b)^x using the table again

132 = 80b

b = 132/80

b = 1.65

after 2023 the exponents will be

x = 2023 - 2016

x = 7

The predicted population

= 80(b)^x

= 80(1.65)^7

= 2898

the predicted population is 2898

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It would cost $1804.86 to buy concrete for repavement of the driveway if 1 cubic yard of concrete costs $130 .

Given,

Width of driveway = 30 ft = [tex]\frac{30}{3}[/tex] = 10 yard

Length of driveway  = 50ft = [tex]\frac{50}{3}[/tex] = 16.667 yard

As the driveway is repaved by pouring concrete then it's height will increase

Height of driveway = 3 inch = [tex]\frac{3}{36}[/tex] = 0.0833 yard

Volume of driveway = length x breadth x height

Volume of driveway = 10 x 16.667 x 0.0833

Volume of driveway = 13.8836 cubic yard

Cost of 1 cubic yard of concrete = $130.00

then cost of 13.8836 cubic yards of concrete  will be

130.00 x 13.8836 = $1804.86

Thus, the cost of concrete will be $1804.86.

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Answer:

Q+R+S=180

30°+R+129°=180

R=180-159

R=21..

is the answer

A person who invests $3,500 in a bank paying 6.75% interest compounded quarterly, must leave it for a period of 53 quarters (13 years) to reach a future value of $8,500.

The future value is the product of the compounded present value at an interest rate for some periods.

Compounding involves charging interest on the accumulated interest and principal, unlike the simple interest system.

When we are given the interest rate, and present and future values, we can determine the period from an online finance calculator as follows:

I/Y (Interest per year) = 6.75%

PV (Present Value) = $3,500

PMT (Periodic Payment) = $0

FV (Future Value) = $8,500

Results:

N (# of periods) = 53.023

Total Interest = $5,000.00

Thus, the investor needs 53 quarters (13 years) to accumulate a future value of $8,500.

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The required length of one of the longest sides is 29 in the given pentagon.

The pentagon has 3 sides of length (2x - 1) and 2 sides of length (x + 5) and the perimeter of the pentagon is 127.

We know that the perimeter of the pentagon is the total length of all its sides, so we can set up the following equation:

3(2x - 1) + 2(x + 5) = 127

Apply the distributive property of multiplication,

6x - 3 + 2x + 10 = 127

Combine the likewise terms of the equation,

8x + 7 = 127

Finally, we can solve the equation by subtracting 7 from both sides and dividing both sides by 8:

8x = 120

x = 15

Therefore, the length of one of the longest sides is (2 × 15 - 1) = 29.

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The distance of the [x] - coordinate between the endpoints → R(-3,-3) and S(5,2), that is equal to 3/4 of RS is 7.08 units away.

        [tex]$d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

       [d] = distance

        (x₁, y₁) = coordinates of the first point

        (x₂, y₂) = coordinates of the second point

Given is that a line segment has endpoints R (-3,-3) and S (5,2).

Using the distance formula -

RS² = (2 + 3)² + (5 + 3)²

RS² = (5 x 5) + (8 x 8)

RS² = 25 + 64

RS² = 89

RS = √(89)

RS = 9.44

Now, 3/4 of RS will be -

{3/4} x 9.44

7.08

Therefore, the distance equivalent to 3/4 of RS is 7.08 units away.

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The estimated population is 114.74 microorganisms after three hours.

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases with time.

a type of growth when the values' logarithms rise linearly with time. This indicates that the value increases faster than it would with linear development. A population that increases by 10% of its value each unit of time would be an example of exponential growth.

let A(f) = number of bacterial 'I' now. in

A(t) = Ao × e^kt

= 71 × e^(0.16XA)

For t = 3 hours

A(t) = 71 × e^(0.16×3)

= 114.74 bacteria

Complete question:

The number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a relative rate of 16% per hour. Suppose that a sample culture has an initial population of 71 bacteria. Find the predicted population after three hours Do not round any intermediate computations, and round your answer to the nearest tenth bacteria

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according to the question

given data in the question,

the type of sample-

random stratified sampling

The usage of satisfied sampling may be required for a variety of distinct features.

The population is first split into two or more strata or subgroups in this kind of random sampling. Beginning with the sampling procedure, each unit is assigned to one stratum based on the unit's historical performance. Following that, separate random samples are chosen using a basic random sampling technique from each stratum, which contains a percentage of the population. that is, they are both mutually and jointly exhaustive.

The traits that we are evaluating are distinct from those of members of another stratum and similar to those of the sample unit stratum.

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the type of sample that proportionately reflects the relevant diversity of opinions in the population from which it is drawn is random stratified sampling

A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.

The sample size in statistics is a measurement of the total number of samples utilized in an experiment. The sample size is 50, for instance, if we are evaluating 50 samples of city dwellers who watch TV. It's also known as sample statistics.

Considering the query

the information in the query

a sample's type-

stratified sampling at random

For a number of unique traits, satisfied sampling may be necessary.

In this type of random sampling, the population is initially divided into two or more strata or subgroups. Each unit is categorized into a stratum at the start of the sampling process depending on its prior performance. A basic random sampling approach is then used to select distinct random samples from each stratum, which represents a portion of the population. they are mutually and jointly exhaustive, in other words.

The characteristics that we are examining are different from those of members of one stratum and comparable to those of the stratum that contains the sample unit.

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