Add the equations.

3x - y = -5
7x + y=15

A. -4x = 10
B. -4x = -20
C. 10x = 10
D. 10x-2y = -20

The midpoint of the line is (-2.5, -0.5)

From the question, we have the following parameters that can be used in our computation:

E(-2,5) and Q(-3,-6)

The midpoint of the line is calculated as

Midpoint = 1/2(E + Q)

Substitute the known values in the above equation, so, we have the following representation

Midpoint = 1/2(-2 - 3, 5 - 6)

Evaluate

Midpoint = (-2.5, -0.5)

Hence, the midpoint of the line is (-2.5, -0.5)

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Answer:

3/8 or 0.375

Step-by-step explanation:

............

Answer:

5/4

Step-by-step explanation:

Area of a rectangle = length * width

A = 3/4, W = 3/5, L = ?

3/4 = L * 3/5

\(\frac{3}{4}= L\frac{3}{5}\)

L * 3 * 4 = 3 * 5

12L = 15

L = 15/12 = 5/4

d. Expected life in years of the depreciable asset. The acceptable way to express the useful life of a depreciable asset is in terms of the expected life in years.

The useful life refers to the period of time over which the asset is expected to contribute to the revenue-generating activities of a business.

While options a, b, and c may be relevant factors for certain specific assets (such as units produced, hours of productivity, or miles driven), they do not encompass the overall concept of useful life. Useful life is a broader measure that takes into account the anticipated duration of productive use, regardless of specific output or activity metrics.

Expressing the useful life in years provides a common standard for comparison and allows for consistency in depreciation calculations and financial reporting. It is a practical and widely accepted approach to estimating the lifespan of a depreciable asset.

It is worth noting that the estimated useful life in years may vary depending on the nature of the asset and industry practices. It is typically determined based on factors such as technological advancements, physical wear and tear, economic obsolescence, and the intended purpose of the asset.

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The indicated sum is 1619.

To find the indicated sum, we need to evaluate fog(2) first.

fog(x) means we need to plug g(x) into f(x), so:

fog(x) = f(g(x)) = f(3x+4) = (3x+4) + 5 = 3x + 9

Therefore, fog(2) = 3(2) + 9 = 15.

Now that we have fog(2) = 15, we can use it to evaluate the final expression:

1604 + fog(2) = 1604 + 15 = 1619.

So the indicated sum is 1619.

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Refer to the attachments!!~

\(\rule{300pt}{3pt}\)

The exact value is found by making use of order of operations. The

functions can be resolved using the characteristics of quadratic functions.

Correct responses:

\(\displaystyle i. \hspace{0.1 cm} \underline{ f(x) = 2 \cdot \left(x - 1.25 \right)^2 + 4.875 }\)

ii. The function has a minimum point

iii. The value of x at the minimum point, is 1.25

iv. The equation of the axis of symmetry is x = 1.25

First part:

The given expression, \(\displaystyle \mathbf{ 1\frac{4}{7} \div \frac{2}{3} -1\frac{5}{7}}\), can be simplified using the algorithm for arithmetic operations as follows;

Second part:

y = 8 - x

2·x² + x·y = -16

Therefore;

2·x² + x·(8 - x) = -16

2·x² + 8·x - x² + 16 = 0

x² + 8·x + 16 = 0

(x + 4)·(x + 4) = 0

y = 8 - (-4) = 12

Third part:

(i) P varies inversely as the square of V

Therefore;

\(\displaystyle P \propto \mathbf{\frac{1}{V^2}}\)

\(\displaystyle P = \frac{K}{V^2}\)

V = 3, when P = 4

Therefore;

\(\displaystyle 4 = \frac{K}{3^2}\)

K = 3² × 4 = 36

\(\displaystyle V = \sqrt{\frac{K}{P}\)

When P = 1, we have;

\(\displaystyle V =\sqrt{ \frac{36}{1} } = 6\)

Fourth Part:

Required:

Solving for x in the equation; 2·x² + 5·x  - 3 = 0

Solution:

The equation can be simplified by rewriting the equation as follows;

2·x² + 5·x - 3 = 2·x² + 6·x - x - 3 = 0

2·x·(x + 3) - (x + 3) = 0

(x + 3)·(2·x - 1) = 0

Fifth part:

The given function is; f(x) = 2·x² - 5·x + 8

i. Required; To write the function in the form a·(x + b)² + c

The vertex form of a quadratic equation is f(x) = a·(x - h)² + k, which is similar to the required form

Where;

(h, k) = The coordinate of the vertex

Therefore, the coordinates of the vertex of the quadratic equation is (b, c)

The x-coordinate of the vertex of a quadratic equation f(x) = a·x² + b·x + c,  is given as follows;

\(\displaystyle h = \mathbf{ \frac{-b}{2 \cdot a}}\)

Therefore, for the given equation, we have;

\(\displaystyle h = \frac{-(-5)}{2 \times 2} = \mathbf{ \frac{5}{4}} = 1.25\)

Therefore, at the vertex, we have;

\(k = \displaystyle f\left(1.25\right) = 2 \times \left(1.25\right)^2 - 5 \times 1.25 + 8 = \frac{39}{8} = 4.875\)

a = The leading coefficient = 2

b = -h

c = k

Which gives;

\(\displaystyle f(x) \ in \ the \ form \ a \cdot (x + b)^2 + c \ is \ f(x) = 2 \cdot \left(x + \left(-1.25 \right) \right)^2 +4.875\)

Therefore;

ii. The coefficient of the quadratic function is 2 which is positive, therefore;

iii. The value of x for which the minimum value occurs is -b = h which is therefore;

iv. The axis of symmetry is the vertical line that passes through the vertex.

Therefore;

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Answer:

$109.53

Step-by-step explanation:

first, let's find 16.7% of 131.49:

131.49(0.167) = 21.95883

next, subtract the percentage from the sale, leaving the remainder for the company:

131.49 - 21.95883 = 109.53

hope this helped!

Points, lines, planes are all undefined terms of geometry

To do this, we draw a plane H (represented by a rectangle), and then add a point on the rectangle

To do this, we draw a plane I (represented by a rectangle), and then draw a line on the rectangle

This means that a line passes through points A, B and C or in other words, points A, B and C are on the same line

This means that point M is a common point on lines x and y or in other words, point M lies on both lines

This means that line JI lies on both planes

See attachment for the illustration of the 5 activities

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AREA OF A SQUARE= LENGTH* LENGTH

16900= L²

TAKE THE SQUARE ROOTS OF BOTH SIDES

√16900 =√L²

L= 130

THEREFORE THE LENGTH OF THE FIELD IS 130cm.

The volume of the solid of intersection is V = (2/3) × 2πr³ = V = (4/3)πr³.

To find the volume of the solid of intersection of the two right circular cylinders of radius r whose axes meet at right angles, we can use the formula:

V = (2/3)πr³

where r is the radius of the cylinders.

First, we need to find the height of the intersection. Since the axes of the cylinders meet at right angles, the height of the intersection will be equal to the diameter of each cylinder. So, the height of the intersection will be 2r.

Now, we can find the volume of the solid of intersection by multiplying the area of the base (which is a circle of radius r) by the height of the intersection (2r):

V = πr²(2r)

Simplifying this equation, we get:

V = 2πr³

So, the volume of the solid of intersection of the two right circular cylinders of radius r whose axes meet at right angles is 2/3 of the total volume of a cylinder with radius r and height 2r, which is 2πr³.

Therefore, the volume of the solid of intersection is:

V = (2/3) × 2πr³
V = (4/3)πr³

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Answer:

C

Step-by-step explanation:

y = a(x - h)² + k

a(x - h)² = y - k

a = (y - k)/(x - h)²

Answer: C

The range of the interval will be smaller, when we calculate a 90% confidence interval instead of a 95% confidence interval, the interval will be narrower, meaning that it will exclude more values from the sample.

When we want to estimate the true population mean with a certain degree of certainty, we use a confidence interval. This interval specifies a range of values that the true mean is likely to fall within.

The confidence level is the percentage of times that the interval will include the true population mean of the estimation process is repeated many times.

Suppose we have calculated a 95% confidence interval for the population mean of a variable based on a sample. This means that we are 95% confident that the true population mean falls within the interval we have calculated.

Suppose we are asked to calculate a 90% confidence interval for the same population mean.

What will change?

The answer is that the range of the interval will be smaller.

The 95% confidence interval is wider because it needs to account for a higher probability of including the true population mean.

On the other hand, the 90% confidence interval is narrower because it needs to account for a lower probability of including the true population mean.

Therefore, the confidence level and the width of interval are inversely related. In other words, as the confidence level decreases, the width of the interval decreases, and vice versa.

In summary, when we calculate a 90% confidence interval instead of a 95% confidence interval, the interval will be narrower, meaning that it will exclude more values from the sample.

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Answer:

4x^2-27x+167-996/x+6

Step-by-step explanation:

Answer:

The Answer is D.

Step-by-step explanation:

If you have this on edge, then it is right.

The term used to describe the process of assigning values to responses in a research instrument and grouping them is called: coding.

In data analysis, before raw data can be processed, the researcher groups and assigns values to each response in the research instrument for easy collation and analysis.

This is referred to as coding, in research analysis.

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Answer:

\(d = 15.0\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Step-by-step explanation:

Step 1: Define

Point C (7, -4)

Point D (-8, -5)

Step 2: Find distance d

Maximize Z=10000C+12000E+5000M+15000T

Subject to 2C+4E+M+3T ≤ 0.6× 40× 24

2C+2E+M+3T ≤ 0.4× 40× 24

M ≤ 40/20

E ≥ 20/40 C, E, M, T ≥ 0

Let the number of regular cars, electric cars, motorbikes and trucks produced in 40 days be C, E, M and T respectively.

The objective is to maximize the profit. Therefore, the objective function is given by:

Maximize Z=10000C+12000E+5000M+15000T

Subject to,The manufacturing time constraint, which is given as 2C+4E+M+3T ≤ 0.6× 40× 24

This constraint ensures that the total time taken for parts assembly does not exceed 60% of the total time available for production.The finishing time constraint, which is given as 2C+2E+M+3T ≤ 0.4× 40× 24

This constraint ensures that the total time taken for finishing touches does not exceed 40% of the total time available for production.

The limit on the production of motorbikes, which is given as M ≤ 40/20

This constraint ensures that the number of motorbikes produced does not exceed one in every 20 days.The minimum production of electric cars, which is given as E ≥ 20/40

This constraint ensures that at least one electric car is produced in every 20 days.The non-negativity constraint, which is given as C, E, M, T ≥ 0

These constraints ensure that the number of vehicles produced cannot be negative.

The mathematical formulation for the problem is given by:

Maximize Z=10000C+12000E+5000M+15000T

Subject to 2C+4E+M+3T ≤ 0.6× 40× 24

2C+2E+M+3T ≤ 0.4× 40× 24

M ≤ 40/20

E ≥ 20/40 C, E, M, T ≥ 0

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Answer:

c = 20d + 15

Step-by-step explanation:

answer choices may help if the answer is not one of the choices; but here is the answer that it should be:

20 dollars per day is 20 times the length of rental.

15 is a cost that is added and does not change.

c = the total cost therefore:

c = 20d + 15

Answer:

Each bottle is 40 cents

Step-by-step explanation:

To find the answer you can do $2.80 / 7 bottles which would give you 0.4 or 40 cents

The cost of each bottle of juice is 0.4 dollars.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Aaliyah buys 7 bottles of apple juice at the corner store for a total cost of $2.80.

Cost of each bottle juice =Total cost of juice/Number of bottles

= 2.80/7

= $0.4

Therefore, the cost of each bottle of juice is 0.4 dollars.

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The t-score to be used to find the 90% confidence interval for the population mean is; \(t_{(0.05,27)}\) = 1.703

The t-score which is representative of a point with n - k (n, and k represents the sample size and the number of groups in the test respectively) degrees of freedom  from the Student's T-distribution is a standard test statistic obtained by applying a T-test

Therefore, the t-score used for a confidence interval is obtained by by making use of the the following information;

The number of degrees of freedom = n - k

Given,

The number of pizza orders in the sample, n = The sample size = 28

The number of samples used in the estimate, k = 1 group of 28 randomly sampled pizza

The level of confidence (the probability) that the interval contains the population mean = 90%

Therefore, the significance level, α = 1 - 90% = 1 - 90/100 = 0.1

∴ The α-level for the upper and lower limit of the interval are α/2 = 0.1/2 = 0.05 long

The degrees of freedom, df = n - k

∴ For the estimation, DF = 28 - 1 = 27

The t-statistic is therefore the t-value at the intersection of the row for DF = 27 and the 0.05 (one-tail) column (0.05 two-tail column) which gives;

\(t_{(\alpha /2, DF)}\) = \(t_{(0.05, 27)}\) = 1.703

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Answer:

  see the attachment for graphs of these

Step-by-step explanation:

You want the general form equation and graph of circles with the given center and (1) radius 4, and (2) through point (0, 0).

The standard-form equation of a circle with radius r and center (h, k) is ...

  (x -h)² +(y -k)² = r²

The general form equation will be a rearrangement of this:

  x² +y² -2hx -2ky +(h² +k² -r²) = 0

The center is (h, k) = (3, 2), and the radius is r = 4. Put these values in the above equation:

  (x -3)² +(y -2²) = 4² . . . . standard form

  x² +y² -6x -4y -3 = 0 . . . . general form

For this one, you don't know the radius, but you know a point that satisfies the equation. Using the point coordinates for x and y, you can find the necessary radius (squared).

The center is (h, k) = (5, -2), and point (x, y) = (0, 0) satisfies the equation.

  (x -5)² +(y -(-2))² = (0 -5)² +(0 -(-2))² = 25 +4

  (x -5)² +(y +2)² = 29 . . . . standard form

  x² +y² -10x +4y = 0 . . . . general form

Answer:

D) *the last one*

Step-by-step explanation:

-8 - (-6) = -2 and the last one is the only one that seems to show -2

Answer:

C = 43.98 inches; A = 153.94 square inches

Step-by-step explanation:

2*pi*(7)=43.98

pi*(7)^2=153.94

If Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

So, the probability that the base construction company did not bid:

\(\begin{aligned}& P(A \mid B)=\frac{P(B \mid A) P(A)}{P(B \mid A) P(A)+P\left(B \mid A^{\prime}\right) P\left(A^{\prime}\right)} \\& P\left(B^{\prime} \mid O\right)=\frac{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)}{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)+P(O \mid B) P(B)} \\& P\left(B^{\prime} \mid O\right)=\frac{(0.5)(0.3)}{(0.5)(0.3)+(0.25)(0.7)} \\& P\left(B^{\prime} \mid O\right)=\frac{0.15}{0.15+0.175} \\& P\left(B^{\prime} \mid O\right)=0.4615\end{aligned}\)

Therefore, if Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.

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The restriction on x when x³ - 4x² + 5x - 6 is divided by x - 1 is x = 1.

When we divide x³ - 4x² + 5x - 6 by x - 1, we perform polynomial long division or synthetic division to find the quotient and remainder.

In this case, the remainder is zero, indicating that (x - 1) is a factor of the polynomial.

To find the restriction on x, we set the divisor, x - 1, equal to zero and solve for x.

Therefore, x - 1 = 0, which gives us x = 1.

Hence, the value of x that satisfies the restriction when x³ - 4x² + 5x - 6 is divided by x - 1 is x = 1.

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We can conclude that an integer a is divisible by 8 if and only if the last three digits of a in base 10 form a 3-digit number that is divisible by 8.

1) To prove that an integer a is divisible by 8 if and only if the last three digits of a in base 10 form a 3-digit number that is divisible by 8, we can use the fact that a number is divisible by 8 if and only if the number formed by its last three digits is divisible by 8.

For example, let's consider the number 123456. The last three digits are 456, which is divisible by 8. Therefore, 123456 is divisible by 8.

Conversely, if a number is divisible by 8, its last three digits must also be divisible by 8. For instance, if we have the number 876, which is divisible by 8, the entire number formed by its last three digits (876) is also divisible by 8.

Therefore, we can conclude that an integer a is divisible by 8 if and only if the last three digits of a in base 10 form a 3-digit number that is divisible by 8.

2) To prove the equation (a + b)' = a' + b' mod 5, which is a special case of the "Freshman's Dream" equation, we need to use the concept of modular arithmetic.

In modular arithmetic, we work with remainders. The modulus 5 means that we are working with remainders when dividing by 5.

To prove the equation, we need to show that (a + b) and a + b have the same remainder when divided by 5.

Let's consider two numbers, a and b, such that a has a remainder of a' when divided by 5 and b has a remainder of b' when divided by 5.

When we add a and b, we get a + b. The remainder of (a + b) when divided by 5 is equal to (a' + b') mod 5.

Therefore, we can conclude that (a + b)' = a' + b' mod 5.

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The angles between 0° and 360° in standard position that have a reference angle of 25° can be determined by adding or subtracting multiples of 360° from the reference angle. In this case, since the reference angle is 25°, the angles can be calculated as follows: 25°, 25° + 360° = 385°, 25° - 360° = -335°.

To determine the angles between 0° and 360° in standard position with a reference angle of 25°, we can add or subtract multiples of 360° from the reference angle. Starting with the reference angle of 25°, we can add 360° to it to find another angle in standard position. Adding 360° to 25° gives us 385°. This means that an angle of 385° has a reference angle of 25°.

Similarly, we can subtract 360° from the reference angle to find another angle. Subtracting 360° from 25° gives us -335°. Therefore, an angle of -335° also has a reference angle of 25°.

To visualize these angles, we can sketch them in their standard positions on a coordinate plane. The reference angle, which is always measured from the positive x-axis to the terminal side of the angle, can be labeled for each angle. The angles 25°, 385°, and -335° will be represented on the sketch, with their respective reference angles labeled.

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Answer:

\(x=-1+\sqrt{6 }\)

\(x=-1-\sqrt{6 }\)

Step-by-step explanation:

\(x=\frac{-b±\sqrt{b^{2}-4ac } }{2a}\)

Ignore the A before the ±. It wouldn't let me type it correctly.

x² + 2x - 5 = 0

a = 1

b = 2

c = - 5

\(x=\frac{-2±\sqrt{2^{2}-4((1)(-5)) } }{2(1)}\)

\(x=\frac{-2±\sqrt{4-4((1)(-5)) } }{2(1)}\)

\(x=\frac{-2±\sqrt{4+20 } }{2(1)}\)

\(x=\frac{-2±\sqrt{24 } }{2}\)

\(x=\frac{-2±\sqrt{(2)(12) } }{2}\)

\(x=\frac{-2±\sqrt{(2)(2)(6) } }{2}\)

\(x=\frac{-2±\sqrt{(2)(2)(2)(3) } }{2}\)

\(x=\frac{-2±(\sqrt{2} )(\sqrt{2})(\sqrt{(2)(3) )} }{2}\)

\(x=\frac{-2±2\sqrt{6 } }{2}\)

Two separate equations

\(x=\frac{-2+2\sqrt{6 } }{2}\)

\(x=\frac{-2-2\sqrt{6 } }{2}\)

\(x=-1+\sqrt{6 }\)

\(x=-1-\sqrt{6 }\)

Answer:

TSU is the correct for answer

Another way to name ∠UST is ∠TSU.

Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.

Angles are usually measured in degrees or radians.

The angle mentioned in the figure is at the point S.

This angle is the smaller angle formed at the point S.

An angle can be represented in two ways, from left to right or from right to left.

Suppose, an angle is ∠ABC.

We can represent this as ∠CBA.

So, the angle represented is ∠TSU.

Hence the angle is ∠TSU.

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Answer:

1/ 75

Step-by-step explanation:

I think, because 1/ 125-1/ 5=75 and then the the 1 stays the same

The expression is equal to 26y² - 20y/4(y - 1)

First, we need to know that algebraic expressions are described as expressions that are made up of terms, variables, constants and factors.

These algebraic expressions are also made up of arithmetic operations, such as;

From the information given, we have that;

y + 1/4y(y -1) + 5/6y²

find the lowest common multiple, we have;

6y²(y + 1) + 5(4y² - 4y) /4y(y -1)(6y²)

expand the bracket, we get;

6y³ + 6y² + 20y² -20y/24y⁴ - 24y³

collect the like terms, we get;

6y³ + 26y² - 20y/24y³(y - 1)

26y² - 20y/4(y - 1)

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