Please select the best answer from the choices provided:
A. Unbounded
B. Infeasible
C. One optimal solution.
D. Alternate optimal solutions

The solution to the given simultaneous equation; x + 2y = -4, 2x + 5y = 1 using substitution method is x = -22 and y = 9

x + 2y = -4

2x + 5y = 1

Using Substitution method

From equation (1)

x = -4 - 2y

Substitute x = -4 - 2y into equation (2)

2x + 5y = 1

2(-4 - 2y) + 5y = 1

-8 - 4y + 5y = 1

- 4y + 5y = 1 + 8

y = 9

Substitute y = 9 into

x + 2y = -4

x + 2(9) = -4

x + 18 = -4

x = -4 - 18

x = - 22

Therefore, the solution to the given simultaneous equation; x + 2y = -4, 2x + 5y = 1 using substitution method is x = -22 and y = 9

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Answer:

you better give me brainliest

Step-by-step explanation:

The answer is the first two

Answer:

36

Step-by-step explanation:

75/100

75/100=0.75

0.75*48 =36

Answer:

c

Step-by-step explanation:

By the Pythagorean theorem,

[tex]28^2 + 15^2 = s^2 \\ \\ s^2 = 1009 \\ \\ s = \sqrt{1009}[/tex]

Step-by-step explanation:

answer=18^2/3

according to the congruent triangles are present there.

so divide corresponding sides

Answer:

False

Step-by-step explanation:

Consider an isoscles trapezoid with angles 75° and 105°.

The dependent variable in this situation is; the speed at which the car travels.

Speed = Distance / Time

The dependent variable in this situation is; the speed at which the car travels.

The independent variable; The distance the car has traveled.

This is the variable whose value depends on one or more variables in the equation.

Independent variable

This is the variable whose value is not dependent on any other in the equation.

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The remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76

The function is given as:

f(x)=−2x3+x2−4x+1 is divided by x+3.

Set the divisor to 0

x + 3 = 0

Solve for x

x = -3

Calculate f(-3)

f(-3)=−2(-3)^3+(-3)^2 − 4(-3) + 1

Evaluate the expression

f(-3)= 76

Hence, the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76

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Step-by-step explanation:

x = number of heavy equipment operators

y = number of general laborers

x + y = 37 (37 people were hired)

out if this we get e.g.

x = 37 - y

124x + 82y = 3916 (daily rate for each role, in total 3916)

now we use the first equation in the second :

124(37 - y) + 82y = 3916

4588 - 124y + 82y = 3916

672 - 42y = 0

672 = 42y

y = 16

x = 37 - y = 37 - 16 = 21

21 heavy equipment operators were hired.

16 general laborers were hired.

Answer:

.00476

Step-by-step explanation:

Answer:

45%

Step-by-step explanation:

Simply, 25/55 which gives you 0.454545.

Convert that to a percentage and you get 45%

The theorem used and the angle measures are:

D. corresponding angles postulate

m∠1 = 150°, m∠2 = 150°

According to the corresponding angles postulate, if two angles lie on same relative corner along a transversal that cuts two parallel lines (corresponding angles), then their measures are equal.

Thus, ∠1 and ∠2 are corresponding angles, therefore:

m∠1 = m∠2 [corresponding angles postulate]

Given the following:

m∠1 = (50x − 50)∘,

m∠2 = (20x + 70)∘

Therefore, we would have:

50x − 50 = 20x + 70

Subtract 20x from both sides

50x − 50 - 20x = 20x + 70 - 20x

30x − 50 = 70

Add 50 to both sides of the equation

30x − 50 + 50 = 70 + 50

30x = 120

Divide both sides by 30

30x/30 = 120/30

x = 4

Plug in the value of x

m∠1 = (50x − 50) =  50(4) − 50 = 150°

m∠2 = (20x + 70)∘ = 20(4) + 70 = 150°

Thus, the answer is: D. corresponding angles postulate

m∠1 = 150°, m∠2 = 150°

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Using translation concepts, the transformations are described as follows:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, the parent function is:

[tex]f(x) = 2^x[/tex]

The transformed function is:

[tex]g(x) = -2^x + 4[/tex]

We have that the transformations in this problem can be described as follows:

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Based on the given coordinate grid, and the increment for each grid line, the coordinates of point A is ( fraction negative 1 and 1 over 4, fraction 3 over 4) or (-1¹/₄, ³/₄).

The x-value of point A is said to be 5 grid lines to the left of y-axis. This means that the x value will be negative.

The increments are 1/4 so the x-value is:
= -1/4 x 5

= -1¹/₄

The y-value is given by the 3 grid lines above the x-axis which means that this value is positive:

= 1/4 x 3

= 3 /4

The coordinates of A are:

(-1¹/₄, ³/₄)

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The algebraic expression that represents the number of hours Anna and Tamara traveled the first two days is (2x - 1) hours.

We are told that;

On the first day, Anna and Tamara stop for sightseeing and lost 2 hours of travel time.

On the second day, they did not stop for lunch and gained 1 hour.

Now, we are told that x is the number of hours driven per day. Thus, for two days, number of hours driven is expressed as 2x.

Now, since they lost 2 hours on the first day, then total hours travelled is;

2x - 2 hours

On the second day, they gained 1 hour. Thus;

Final total number of hours traveled = 2x - 2 + 1

Final total number of hours traveled = (2x - 1) hours

Thus, we can conclude that the algebraic expression that represents how many hours Anna and Tamara traveled the first two days is (2x - 1) hours.

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Answer:

42 - 24 = 18

18/24 = 3/4

the answer would be 1 and 3/4 days

Answer:

1 and 3 over 4 days

Step-by-step explanation:

Since 24 hours is 1 day  all we have to do is divide 42 into 24 and see what the resulting fraction is

42/24 = 7/4  (reducing to lowest fraction)

7/4 = 1 3/4 days (7 ÷ 4 gives quotient 1 and remainder is 3)

Answer:
1 and 3 over 4 days

The percentage of people who preferred cheesecake if 50% prefferd fruit cake 1/5 preferred sponge is 40%.

Percentage remaining = 100% - 50%

= 50%

Sponge cake = 1/5

Percentage of sponge cake = 1/5 × 50%

= 1/5 × 0.5

= 10%

Percent that likes cheesecake = Total - (fruits cake + sponge cake)

= 100% - (50% + 10%)

= 100% - (60%)

= 40%

Therefore, the percentage of people who preferred cheesecake if 50% prefferd fruit cake 1/5 preferred sponge is 40%.

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Answer: C: 12-7x

Step-by-step explanation:

This expression is a good example of the difference of two squares, as 144 is the square of 12, while 49x² is the square of 7x.

Any difference of two squares [tex]a^2-b^2[/tex] can be factored into the sum of their square roots times the difference of their square roots [tex](a+b)(a-b)[/tex].

Let's factor our expression.

[tex]144-49x^2=(12+7x)(12-7x)[/tex]

Out of all the options given, only [tex]12-7x[/tex] is a factor. Hence, option C is correct.

Answer:

i think 10 because in triangle there is 180 and 180-170 = 10

Answer:

Step-by-step explanation:

hjhj

Answer:

9900

Step-by-step explanation:

You start with 300, and add 300 32 times (once for every 3 months in 8 years).

[tex]300+9600=9900[/tex]

(730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15. This can be obtained by using formula for confidence interval and using statistical table for values.

The formula for finding the confidence interval for population variance is:

[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]

where n is the size of the sample, (n - 1) is the degrees of freedom, s is the standard deviation, α is the significance level.

Here it is given that,

α/2 = 0.02/2 = 0.01

1 - α/2 = 1 - 0.01 = 0.99

For (n - 1) degrees of freedom,

[tex]\chi^{2}_{\frac{\alpha}{2} }[/tex] = 29.141 , and  [tex]\chi^{2}_{1-\frac{\alpha}{2} }[/tex] = 4.660 (Using statistical table)

Using the formula we get,

[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]

[tex]\frac{(14)39^{2} }{29.141} < \sigma^{2} < \frac{(14)39^{2} }{4.660}[/tex]

[tex]730.72 < \sigma^{2} < 4569.53[/tex]

The confidence interval for the population variance is (730.72, 4569.53)

Hence (730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15.

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Answer:

1 and 4

Step-by-step explanation:

x-1 = 0

x = 1

x^2 - 5x + 4

(x-4)(x-1) = 0

x can't be 1 or 4

Answer:  1 and 4

Step-by-step explanation:

1. To find excluded values, we need to make the denominator equal to zero.

x² - 5x + 4 = 0

2. Then we need to find the x the product of them was 4, but they add up to -5, which are -4 and -1. We get:

(x - 4)(x - 1) = 0

x - 4 = 0          x - 1 = 0

    x = 4               x = 1

These two numbers will make the denominator equal to 0, the denominator cannot be equal to 0, so they are excluded numbers.

Answer:

[tex]\displaystyle{1.) \ \ f(x) = \dfrac{2}{3}x-8}\\\\\displaystyle{2.) \ \ f(x) = -4x+11}[/tex]

Step-by-step explanation:

- Range is a set of all y-values in a set of coordinate points.

A linear equation or function always have range equal to set of real number because you can substitute f(x) as any numbers and you'll still be able to solve for x-variable.

An quadratic equation or function may have range equal to set of positive real number or negative real number depending whether if the coefficient of x² is in positive or negative but consider this:

Suppose we have f(x) = x², f(x) cannot be negative number because that'd make the equation not real. Therefore, a quadratic function does not have [tex]\displaystyle{\mathbb{R}}[/tex] range.

For an exponential function, it's same as quadratic equation. It depends whether if a base is in negative or positive. You can consider like this:

Suppose we have [tex]\displaystyle{f(x)=2^x}[/tex], f(x) cannot be negative number because there are no x-values that make the equation true. Therefore, an exponential function does not have [tex]\displaystyle{\mathbb{R}}[/tex] range as well.

The 4.2 inches base length and 36 in.² area of the given triangle and the 5.6 inches base length of the similar triangle gives the area of the similar triangle as 64 square inches

Area of a triangle = (Base length × Height)/2

Area of the given triangle = 36 in.²

Base length of the given triangle = 4.2 inches

Base length of the similar triangle = 5.6 inches

Therefore;

Area of the given triangle = (Base length × Height)/2

Which gives;

36 = (4.2 × h)/2

Where;

h = Height of the given triangle

36 × 2 = 4.2 × h

[tex]h = \mathbf{\frac{36 \times 2}{4.2}} = 17 \frac{1}{7} [/tex]

Height of the given triangle, h = 17+ 1/7

The ratio of corresponding sides of similar triangles are the same, which gives;

[tex] \frac{5.6}{4.2} = \frac{h'}{17 \frac{1}{7}} [/tex]

Where;

h' = The height of the similar triangle

Which gives;

[tex] h' = \frac{5.6}{4.2} \times 17 \frac{1}{7} = 22 \frac{6}{7} [/tex]

The area, A', of the similar triangle is therefore;

[tex] A' = \frac{1}{2} \times 5.6 \times 22 \frac{6}{7} = 64 [/tex]

The area can also be obtained using the scale factor of area as follows;

Which gives;

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Answer:

1.05

Step-by-step explanation:

Because 30% of 70 is [tex]30\% \times 70 = \frac{30}{100} \times 70 = 0.3 \times 70 = 21[/tex], so the question becomes "21 is what percent of 2000?"

To answer this, we can solve for [tex]x[/tex] in the equation [tex]21 = x\% \times 2000[/tex], which is:

[tex]21 = x\% \times 2000\\21 = \frac{x}{100} \times 2000\\21 = 20x\\x=\frac{21}{20}=1.05[/tex]

So the answer is 1.05 percent.

Answer: No

Step-by-step explanation:  proportional means corresponding in size or amount to something. However, the number of her sit-ups isn't consistent, so it isn't proportional to the time she spends doing them.

Answer:

D is the correct answer -3+8=5 ,1+4=5