To use the elimination method, you can add the two equations in a system of equations to eliminate one of the variables.


Add the two equations.


{−9x+y=10
10x−y=−9


What is the resulting equation?



A 0 + 2y = 10 + 2, y = , 1


B x + 0 = 1x, + 0 = 1


C x + 0 = 19x, + 0 = 19


D 19x + 2y = 19

P.S its not C pls help asap

Answer:

0.89

Step-by-step explanation:

The probability that a randomly selected male's systolic blood pressure will be less than 108 is 0.25.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Here, mean  = 110, standard deviation = 8

P = \(\frac{x_{mean}-x }{SD}\)

P = (110 - 108)/8

P = 2/8 = 0.25

P(Z<0.25) = 0.5 - 0.25 = 0.25

Thus, The probability that a randomly selected male's systolic blood pressure will be less than 108 is 0.25.

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Answer-

The slope of the line that passes through the points is

Solution-

As there is a single line passing through all these points, so taking any two points and then applying the formula for slope will give the slope of the line.

The points are,

(-14, 8), (-7, 6), (0, 4), (7, 2), (14, 0)

Taking two points as, (0, 4), (7, 2)

x₁ = 0

y₁ = 4

x₂ = 7

y₂ = 2

Putting the values,

Therefore, the slope of the line that passes through the points is

Step-by-step explanation:

The slope of the line that passes through the points in the table is -2/7.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Given a table which shows the points on the line.

Slope of a line passing through two points (x, y) and (x', y') is,

Slope = (y' - y) / (x' - x)

Take any two points on the line.

(0, 4) and (7, 2).

Slope = (2 - 4) / (7 - 0) = -2/7

Hence the slope of the line is -2/7.

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Answer:

y=2x-A

Step-by-step explanation:

Answer:

After 4 years working for the company, he would make $79,000 of salary.

His salary after t years will be:

[te]S(t) = 69000 + 2500t\)

Step-by-step explanation:

David just accepted a job at a new company where he will make an annual salary of $69000. David was told that for each year he stays with the company, he will be given a salary raise of $2500.

This means that after t years, his salary will be given by:

[te]S(t) = 69000 + 2500t\)

How much would David make as a salary after 4 years working for the company?

[te]S(4) = 69000 + 2500*4 = 69000 + 10000 = 79000\)

After 4 years working for the company, he would make $79,000 of salary.

The solution set for all possible side lengths for side L is;

⇒ L < 7

What is Triangle?

A triangle is a three sided polygon , which has three vertices and three angles.

Given that;

The longest side of a triangle must be less than the sum of the other two sides.

Suppose a triangle is made up of lengths 2 inches, 5 inches and L. inches, where, L is the longest side.

Now, By the given condition;

''The longest side of a triangle must be less than the sum of the other two sides.''

We can formulate;

L < 2 + 5

L < 7

So, The solution set for all possible side lengths for side L is;

⇒ L < 7

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Answer:

$0.88

Step-by-step explanation:

cost per 1% = 22 ÷ 100 = 0.22

⇒ cost of 4% = 4 x 0.22 = 0.88

Or

4% = 4/100 = 0.04

⇒ 4% of 22 = 0.04 x 22 = 0.88

Step-by-step explanation:

Answer:

1% of 22 is 0.22, so 4% of 22 is 0.88

So top guy, you are wrong.

After answering the provided question, we can state that As a result, 145.62 square feet of glass are required to cover the entire pyramid.

A pyramid is a polygon formed by connecting points known as bases and polygonal vertices. For each hace and vertex, a triangle known as a face is formed. A cone with a polygonal shape. A pyramid with a floor and n pyramids has n+1 vertices, n+1 vertices, and 2n edges. Every pyramid is dual in nature. A pyramid contains three dimensions. A pyramid is made up of a flat tri face and a polygonal base that come together at a single point known as the vertex. A pyramid is formed by connecting the base and peak. The base's edges form triangle faces known as sides that connect to the top.

To determine how much glass is required to cover the entire pyramid, we must first determine the total surface area of the pyramid, including the base.

The formula for calculating the surface area of each triangular face is:

(1/2) x width x height

27.31 square feet = (1/2) x 7 feet x 7.79 feet

24 square feet = (1/2) x 6 feet x 8 feet

Simply multiply the length and width to find the area of the rectangular base:

7 feet by 6 feet equals 42 square feet

As a result, the total surface area of the pyramid is:

145.62 square feet = 2 (27.31 square feet) + 2 (24 square feet) + 42 square feet

As a result, 145.62 square feet of glass are required to cover the entire pyramid.

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Answer: 102.53

Step-by-step explanation:  I calculated all the numbers you gave me and then added them to get 102.53

The area of the shaded portion in the equilateral triangle with sides 6 is 9√3 - 36π.

To find the area of the shaded portion in the equilateral triangle, we need to determine the area of the three arcs and subtract it from the area of the equilateral triangle.

First, let's find the area of one arc. Each arc has a radius equal to the length of the side of the equilateral triangle, which is 6. The formula for the area of a sector is A = (θ/360)πr², where θ is the central angle in degrees.

In an equilateral triangle, each interior angle measures 60 degrees, so the central angle of the arc is 120 degrees (360 degrees divided by 3). Plugging these values into the formula, we get A_arc = (120/360)π(6)² = (1/3)π(6)² = 12π.

Since there are three identical arcs, the total area of the arcs is 3 times the area of one arc, which is 3(12π) = 36π.

Now, let's find the area of the equilateral triangle. The formula for the area of an equilateral triangle is A_triangle = (√3/4)s², where s is the length of a side.

Plugging in the value of the side length, we have A_triangle = (√3/4)(6)² = (√3/4)(36) = 9√3.

Finally, we subtract the area of the arcs from the area of the equilateral triangle to find the shaded portion's area: A_shaded = A_triangle - A_arc = 9√3 - 36π.

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None of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

To find the slope of the red line given that it is perpendicular to the green line with a slope of 2, we can use the property that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the green line is 2. To find the slope of the red line, we take the negative reciprocal of 2. The negative reciprocal is obtained by taking the reciprocal (flipping the fraction) and changing the sign.

Reciprocal of 2: 1/2

Negative reciprocal: -1/2

Therefore, the slope of the red line is -1/2.

However, none of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

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Let f(x) = lnx and g(x) = log₂x. for all 0 < x < 1, f(x) < g(x): True.

In this scenario and exercise, we would determine the corresponding output value for the functions f(x) and g(x) under the given mathematical operation and independent variables.

When x = 1, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(1) = ln(1).

f(1) = 0.

When x = 2, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(2) = ln(2).

f(2) = 0.69314718

When x = 1, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(1) = log₂(1)

g(1) = 0.

When x = 2, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(2) = log₂(2)

g(2) = 1.

In this context, we can logically deduce that the function f(x) is less than function g(x) for all 0 < x < 1.

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Answer:

x=34    y=-87     (34,-87)

Step-by-step explanation:

3x+y=15              rewrite to solve for y  ----->    y=15-3x

5x+2y=-4

Plug y=15-3x into 5x+2y=-4

So, 5x+2 (15-3x)=-4

Distribute: 5x+30-6x=-4

Combine like terms: 30-x=-4

Solve for x   -x=-34

Solve for x   x=34

Then, to solve for y, plug "x" into 3x+y=15

So, 3(34)+y=15

Distribute: 102+y=15

Solve for y  y=-87

Answer:

we can get the difference by just subtracting -1 and +1 which will give us 0

After 10 years the depreciation value of the vehicle will be $12700.

What is percentage(%)?

A %(percentage) is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

\(V(t) = V0*(1-rate)^t\)

V(t) is the value at year t (we want t =10 years)

V0 is the starting value = $20,700

rate is the depreciation rate expressed as a decimal = 0.05

t = years = 10

\(V(10) = $20700*(1 - 0.05)^{10}\)

= 20700*(0.95)^10

= 20700*(0.598)

= 12,393.85

= 12,394

therefore after 10 years the vehicle will cost $12700.

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\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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Step-by-step explanation:

a. z = 5.5

25 ^( 5.5 - 4 ) = 125

25 ^ (1.5) = 125

125 = 125

z = 5.5

PlZzzzz follow me

Answer:

122 degrees

Step-by-step explanation:

The two intersecting lines are parallel for this problem, which means that the angle next to angle3 is the same degree measure as the one that is 58 degrees.

Also, remember that two angles next to each other on a straight line are supplementary, meaning that they add to 180 degrees.

When keeping these two things in mind, you can solve like this:

180 = angle3 + 58

180 - 58 = angle3

angle3 = 122

122 degrees

Using a confidence interval of 90%, note that the Margin of Error is computed to be: 4.171

The margin of error is a statistic that expresses the degree of random sampling error in survey data. The greater the margin of error, the less confident one should be that a poll result would accurately represent the results of a population census.

The margin of error for a 90% confidence interval for the population mean can be calculated using the following formula:

Margin of Error = z* (σ/√n)

where:

z* is the z-score corresponding to the level of confidence,

σ is the population standard deviation, and n is the sample size.

For a 90% confidence level, the corresponding z-score can be found using a standard normal distribution table or calculator.

The z-score for a 90% confidence level is 1.645.

Plugging in the values, we get:

Margin of Error = 1.645 * (19/√43)

Margin of Error ≈ 4.171

Rounded to three decimal places, the margin of error is approximately 4.171.

Therefore, we can say with 90% confidence that the true population mean lies within the range of the sample mean plus or minus 4.171.

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The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is 34650 ways.

We have,

By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.

Here, the differences between permutation and combination are described in detail.

The number of ways in which we can select a committee of 4 democrats from ten democrats is:

P = 10C 4 = 10! / (4)! (10 - 4)!

P = 210

The number of ways in which we can select a committee of 3 Republicans from 11 Republicans is:

P = 11C 3 = 11! / 3! (11 - 3)!

P = 165

The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is:

P = (210) (165) = 34650

The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is 34650 ways.

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Answer:

x > 2

Step-by-step explanation:

when a line has an open circle it is greater/less than the number it is on, a closed circle means it could be than number, so greater than or equal to. This equation is an open circle (so it's not equal to) and is on the 2. So you know the equation is x < or > 2. To find if it's < or >, you look at what direction the line goes. This one is to the right. If you notice the > looks like an arrow pointing to the right, so you can know > is the right symbol to use. The full equation will be read, x is greater than 2. Hope this was helpful!

Answer:

14 bags

Step-by-step explanation:

Dimension of lawn : 230 feet by 180 feet

area of rectangle is given by length * width

Since lawn is rectangular area of lawn = 230 feet * 180 feet = 41,400 sq. feet

Given that one bag of fertilizer covers 3000 square feet of lawn.

Thus , to find no. of bags required to cover whole lawn will be

total area of lawn/area which one bag of  fertilizer covers

no. of bags required to cover whole lawn = 41,400 sq. feet/3000 sq. feet

    = 13.8 bags.

As no. of bags cannot be fractional , hence rounding bag to nearest unit place is 14 bags.

Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

Answer:

  see below (both 2nd and 3rd choices)

Step-by-step explanation:

One way to tell if the functions are inverses is to look at f(g(x)). If the functions are inverses, then f(g(x)) = x.

A: f(g(x)) = 2^((log2(x -1) -1) -1) +1 = (2^(log2(x-1))(2^-2) +1 = (1/4)(x -1) +1 ≠ x

__

B: f(g(x)) = (1/2)(ln((2e^(2x+1))/2) -1) = (1/2)(ln(e^(2x+1)) -1) = (1/2)(2x +1 -1) = x

__

C: f(g(x)) = 4ln(e^((e^2x/8))^2)/e^2 = 8(e^2x/8)/e^2 = x

__

D: f(g(x)) = 10^((log(x+10)-10) -10)-10 = (10^log(x+10))(10^-10) -10

  = (x +10)(10^-10) -10 ≠ x

_____

The 2nd and 3rd pairs of functions listed are inverses of each other.