Solve the system of equations using elimination.

2x + 3y = −8
3x + y = 2

To calculate the amount of money that needs to be set aside today to purchase a new piece of equipment in 3 years, we need to find the future value of the equipment and calculate the present value of that future amount.

First, let's find the future value of the equipment:

The cost of the equipment is expected to increase by 3% per year, so after 3 years the cost will be:

$75,000 * (1 + 0.03)^3 = $78,225

Next, let's find the present value of that future amount:

The money is expected to earn 9% interest compounded annually, so to find the present value, we need to discount the future amount by the interest rate. We can use the formula:

PV = FV / (1 + r)^t

where PV is the present value, FV is the future value, r is the interest rate, and t is the number of years.

Plugging in the values, we get:

PV = $78,225 / (1 + 0.09)^3 = $73,232.57

So, to purchase the equipment in 3 years, we need to set aside $73,232.57 today.

Answer:

see below

Step-by-step explanation:

Remember this definition:

A rhombus is a special case of a parallelogram. In a rhombus, opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles. The rhombus is also called a diamond or rhombus diamond.

so if you know only 1 angle, you'll know all of them

because  z is opposite to the given angle 69 so z=69

the other 2 angles are the same = 180 -69 =111

The size of angle ACB to the nearest degree is 88 degree.

Construction Steps:

Create a line segment BC with the property AC = 4 cm.

Draw two arcs that meet at point A by using B as the centre and a radius of 4 cm, and C as the centre and a radius of 7 cm.

Join AB and AC now. Consequently, the necessary triangle is ABC.

With the use of a compass, draw a line segment AB = 7 cm from A, cutting an arc AC = 4 cm.

Cut an arc of 3 cm from point B.

Embrace BC and AC

Triangle with  angle ABC is necessary.

< ACB = 88 degree

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The amount of sand that must be added to form a new mixture that is 80% sand by volume will be 90 cubic feet.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The thickness and strength of not entirely set in stone by the proportion of concrete and total. Assume that a project worker has 450 cubic feet of a dry substantial blend that is 60 % sand by volume.

The amount of sand that must be added to form a new mixture that is 80% sand by volume is given as,

⇒ 0.80 x 450 - 0.60 x 450

⇒ 360 - 270

⇒ 90 cubic feet

The amount of sand that must be added to form a new mixture that is 80% sand by volume will be 90 cubic feet.

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The axis of symmetry for each function is given as follows:

Hence the rank from smallest to largest axis of symmetry is given as follows:

f(x), h(x), g(x).

The axis of symmetry of a quadratic function is given by the x-coordinate of the vertex of the quadratic function.

For function f(x), considering the vertex-form definition, the x-coordinate of the vertex is given as follows:

x = -4.

For function g(x), considering the standard definition, the x-coordinate of the vertex is given as follows:

x = -(-16)/2(4).

x = 16/4.

x = 4.

For function h(x), considering the graph of the function, the x-coordinate of the vertex is given as follows:

x = 1.

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The value of the lesser integer is -9. The solution has been obtained by using algebra.

What is algebra?

In the area of mathematics known as algebra, abstract symbols rather than actual numbers are used to perform operations or manipulations.

Let the integer be 'x'.

We are given that when an integer is subtracted from 2 times the next consecutive integer, the difference is -7.

So, from this we can form the equation as

⇒2(x+1) - x = -7

⇒2x + 2 - x = -7

⇒x = -7 - 2

⇒x = -9

Hence, the value of the lesser integer is -9.

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Answer:

12

Step-by-step explanation:

The answer for your question is 12

Answer:

=12

Step-by-step explanation:

1(4×3)/3+ 8=

1(12)/3+8=

12/3 + 8=

4 + 8 = 12

I hope I help you in this ans and tq.

Based on the given trapeziums, each problem's answers are:

Let's discuss each problem we have:

1. The given trapezium is an isosceles trapezium, hence:

J = K = 7x  + 2

M = L = 25x - 14

Since trapezium is a part of parallelogram, then:

∠J + ∠K + ∠L + ∠M = 360°

2∠J + 2∠M = 360°

2(7x + 2) + 2(25x - 14) = 360°

14x + 4 + 50x - 28 = 360°

64x - 24 = 360°

64x = 384

x = 6

∠J = ∠K = 7x + 2

∠J = ∠K = 7(6) + 2 = 44°

∠M = ∠L = 25x - 14

∠M = ∠L = 25(6) - 14 = 136°

2. Since EFGH is an isosceles trapezoid, then:

EH = FG

4x - 27 = x + 9

3x = 36

x = 13

EG = FH

3y + 19 = 11y - 21

40 = 8y

y = 5

3. It was given that:

PQ = 27

SR = 39

WX?

WX is the mig segment, where:

Mid segment = (base + top) / 2

WX = (PQ + SR) /2

WX = (27 + 39) / 2

WX = 66/2

WX = 33

4. It was given that:

MN = 22

DC = 29

AB ?

MN is mid segment

MN = (AB + DC) / 2

22 = (AB + 29) / 2

44 = AB + 29

AB = 15

5. JK = 3x + 11

NP = 45

ML = 10x - 12

NP is mid segmet

NP = (JK + ML) / 2

45 = [(3x + 11) + (10x - 12)] / 2

90 = (3x + 11) + (10x - 12)

90 = 13x - 1

13x = 91

x = 7

ML = 10x - 12

ML = 10(7) - 12

ML = 58

6. BC = 19

GH = 9x - 3

FE = 5x + 1

GH is mid segment

GH = (BC + FE) / 2

(9x - 3) = (19 + (5x + 1)) / 2

18x - 6 = 19 + (5x + 1)

18x - 6 = 20 + 5x

13x = 26

x = 2

GH = 9x - 3

GH = 9(2) - 3

GH = 15

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Answer:

Step-by-step explanation:

To find the number of hours David has to work at each job, we can set up an equation. Let's say David works x hours at the first job and y hours at the second job. Then, we have:

14x + 11y = 1000

Next, we need to find the possible combinations of x and y that satisfy this equation. To do this, we can use trial and error, or use the substitution method. Let's use the latter method. Solve for x in terms of y:

14x = 1000 - 11y

x = (1000 - 11y) / 14

Now, we can substitute this expression for x into the original equation to get a new equation in terms of y:

11y = 1000 - 14x

y = (1000 - 14x) / 11

We can use this equation to find possible values of y. For example, if x = 40 hours, then y = (1000 - 14 * 40) / 11 = (1000 - 560) / 11 = (440) / 11 = 40. So, David could work 40 hours at the first job and 40 hours at the second job to earn $1000.

We can repeat this process for other values of x to find more combinations. Some possible combinations of the numbers of hours David could work at each job to earn $1000 are:

40 hours at the first job and 40 hours at the second job

45 hours at the first job and 35 hours at the second job

50 hours at the first job and 30 hours at the second job

55 hours at the first job and 25 hours at the second job

60 hours at the first job and 20 hours at the second job, etc.

Input Variable: Height (h), Output Variable: Temperature (T)

Axes: h (km) | 0 | 1 ,  T (°C) | 10 | 10

Slope: 0 (The temperature does not change with increasing height)

The theory used in this question is the ideal gas law, which states that the pressure, volume, and temperature of an ideal gas are directly proportional.

As the dry air moves upward, it expands and the temperature decreases. This is why the temperature at a height of 1 km is 10°C.

Determine the input and output variables:

The input variable is the height (h) and the output variable is the temperature (T).

Draw and label two axes: On the x-axis, label it "h (km)" and on the y-axis, label it "T (°C)".

Plot and label the two points you were given:

Plot a point at (0, 10) and another point at (1, 10).

Determine the slope of the line between your two points:

The slope of the line between the two points is 0, indicating that the temperature does not change with increasing height.

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In standard position, 2.280° refers to an angle in the Cartesian plane with its beginning side on the positive x-axis and its terminal side establishing an angle of 2.280° with the positive x-axis counterclockwise.

An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are known as dihedral angles. An angle is formed by joining two rays (half-lines) that have a shared terminal. The latter is referred to as the angle's vertex, while the rays are referred to as the angle's sides, legs, and arms.

Here,

The measure of 2.280° in standard position refers to an angle in the Cartesian plane, with its initial side on the positive x-axis and its terminal side making an angle of 2.280° with the positive x-axis in a counterclockwise direction.
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The exponential equation is P = 7000 * (1 + 0.08)ᵗ  and the nearest whole number.

What is the exponential equation?

In combinatorial mathematics, the exponential formula (called the polymer expansion in physics) states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected structures.

a. To write the exponential equation, let t be the number of years and let P be the amount of money in the account after t years. The exponential equation can be written as:

P = 7000 * (1 + 0.08)ᵗ

b. To solve for t, we need to find the number of years it takes for P to reach $30,100. We can set up an equation and solve for t:

30,100 = 7000 * (1 + 0.08)ᵗ

Dividing both sides by 7000:

30,100 / 7000 = (1 + 0.08)ᵗ

Taking the natural logarithm of both sides:

ln (30,100 / 7000) = t * ln (1 + 0.08)

Solving for t:

t = ln (30,100 / 7000) / ln (1 + 0.08)

Using a calculator, we get:

t = 21.1397

Rounding up to the nearest whole number, it will take Fred 22 years to have $30,100 for a new car.

Hence, the exponential equation is P = 7000 * (1 + 0.08)ᵗ  and the nearest whole number.

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The rule for the function is P(t) = 170 + 680t

Let's call Julia's final position after t hours as P.

If she drove at a constant speed v (in miles per hour), then the distance traveled can be given as:

P - P0 = vt

Given that she was 170 miles east from Denver after driving for a quarter of an hour (0.25 hours), we can write the first equation:

170 = v * 0.25

v = 680

This means that her speed was 680 miles per hour.

Using this speed, we can write the second equation:

P = 680 * t

100 = 680 * t

t = 100 / 680 = 0.147

Combining the two equations, we can find the function that gives Julia's position east from Denver after t hours as:

P(t) = P0 + v * t ----- P0 = 170 i.e. her initial position

P(t) = 170 + 680 * t

So, the rule for the function P(t) is:

P(t) = 170 + 680t

P^-1(16) is the inverse of the function P(t) at the value 16.

In other words, it gives us the time t after which Julia is 16 miles east from Denver.

To find its value, we can use the equation of the function P(t):

P(t) = 170 + 680 * t

16 = 170 + 680 * t

-154 = 680 * t

t = -154 / 680

Time cannot be negative.

So, it does not exist

P^-1(-141) is the inverse of the function P(t) at the value -141.

In other words, it gives us the time t after which Julia is 16 miles east from Denver.

So, we have

-141 = 170 + 680 * t

-311 = 680 * t

t = -311 / 680

Time cannot be negative.

So, it does not exist

We simply make t the subject in P(t)

So, we have

P^-1(t) = (t - 170) / 680

The graph is attached

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a) The amount of the supplies is $70

b) The number of the plants is 3

c) The rate of change is 1/20.

A proportional relationship is a mathematical relationship between two variables where their ratio is constant. In other words, as one variable increases or decreases, the other variable also increases or decreases in the same ratio.

We have to note that we can read up the relationship from the graph. The amount of the supplies for 9 plants is $70. If the total budget is $60 then we can only have three plants. The rate of change is therefore 1/20.

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The required number of ice blocks that fit in the storage box is 80 ice blocks.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

The volume of the storage box is,
= 7.5 feet × 6 feet × 6 feet
= 270 cubic feet.

Each ice block has a volume,

= 1.5 feet × 1.5 feet × 1.5 feet
= 3.375 cubic feet.

Therefore, the number of ice blocks that fit in the storage box is,
= 270 / 3.375
= 80 ice blocks.

Thus, the required number of ice blocks that fit in the storage box is 80 ice blocks.

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The required range of the given data set is 42 and defined for the interval (14, 56).

Statistics is the study of mathematics that deals with relations between comprehensive data.

Range: The range is the difference between the largest and smallest values in a set of data.

Here,
The largest value is 56 and the smallest is 14, so the range is given as,
= 56 - 14 = 42.

Interquartile range (IQR): The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.

Quartile deviation (QD): The QD is also known as the semi-interquartile range, and is half the interquartile range (IQR).

Mean Absolute Deviation (MAD): The MAD is a measure of variability that is calculated by finding the average of the absolute deviations of each data point from the mean.

Population Variance: The population variance is a measure of how much the data points in a population deviate from the mean.

Population Standard Deviation: The population standard deviation is the square root of the population variance, and is a measure of how spread out the data points in a population are.

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Note: The calculation of IQR, QD, MAD, population variance, and population standard deviation would require more steps, but these calculations are beyond the scope of this answer.

The required cost of the construction of a 4.5-inch tower is $114.75.

Algebraic word problems are defined as questions that require translating sentences to equations, and thereafter solving those equations. and a single variable.

The parameters given are;

The cost of construction = $25.50 per inch.

The cost of 4.5 inches of construction = 25.50 * 4.5

= $114.75.

We conclude that, the figure above is the amount to fund 4.6 inhces

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Complete question is;

A ratio station collects donations for a new board cast tower. The cost of construction is $25.50 per inch. How much does it cost to fund 4.5 inches of the construction?

The total surface area painted black = 90.5 square feet to the nearest tenth.

A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.

Given:

Three large cones hang from the ceiling in an office building in front of a bank of windows.

The height of each cone is 12 feet, and the circumference of the base of each cone is 8π feet.

The base and 40% of the lateral surface of each cone is painted red, and the rest of each cone is painted black.

Circumference of the base of the cone = 8π feet.

2πr = 8π

πr = 4π

The surface area of the cone = πr x height

The surface area of the cone = 12 x 4π

The surface area of the cone = 48π.

The total surface area painted black = 60% of 48π.

The total surface area painted black = 90.5 square feet to the nearest tenth.

Therefore, the result is 90.5 square feet to the nearest tenth.

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Answer:

oaxaca

oacaxa

xaoaca

xacaoa

caoaxa

caxaoa

aoaxac

axaoac

aoacax

acaoax

axacao

acaxao

aoxaca

aocaxa

acoaxa

acxaoa

axoaca

axcaoa

aoaxca

axaoca

aoacxa

axacoa

acaoxa

acaxoa

Looks like 24 to me.

6 arrangements of “oa” “xa” and “ca”

those same 6 reversed

those same 6 with the first pair reversed

those same 6 with the first two pairs reversed.

reversing the last pair or the last two pairs only is illegal, so this is comprehensive.

Step-by-step explanation:

The period of the sinusoidal function in this problem is given as follows:

10 units.

A periodic function is a function that has the behavior repeating in intervals over the domain.

Then the period of the function is defined as the difference between two points in which the function has the same behavior.

For this problem, the function has the same behavior at x = 8 and at x = -2, hence the period of the sinusoidal function is calculated as follows:

Period = 8 - (-2)

Period = 8 + 2

Period = 10 units.

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The choice that had statements that are all true is (a) Point B = -2 1/2, Point D = 1 3/4 and 1 3/4 > -2 1/2

The complete question is added as an attachment

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

The number line

On the number line, we have the following

A = -4

B = -2 1/2

C = 1

D = 1 3/4

When the above values are compared with the list of options, we have

Option (A) = true

This is so because in (a)

Point B = -2 1/2, Point D = 1 3/4 and 1 3/4 > -2 1/2

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The correct statement regarding the continuity of the function is given as follows:

All three conditions for continuity are true, so f(x) is continuous.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

For this problem, we must look at the turning point at x = 3, hence:

Hence all conditions are satisfied and the correct option is given by the fourth option.

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The maximum amount of weight, a human being could lift is  0.0002 kilograms.

Since an average ant can lift a maximum of 50 times its own body weight, and it weighs 4 milligrams,

The maximum weight it can lift is

50 * 4 milligrams = 200 milligrams.

To convert milligrams to kilograms, we divide by 10^6:

200 milligrams / 10^6 = 0.0002 kilograms

So, the maximum amount of weight a human being could lift if it could lift as much as an average ant is 0.0002 kilograms.

Therefore, the answer is 0.0002 kilograms or 0.2 grams

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Answer:51

Step-by-step explanation:

9+7+7+7+7+7+7

(or 9+7^6)

The graph of the function is given by the image presented at the end of the answer.

The minimum value on the interval [-2,0] is given as follows:

y = -1 at x = -2.

The maximum value on the interval [-2,0] is given as follows:

y = 1 at x = 1.

The minimum value of a function in an interval is the lowest value of y assumed by the function.

The maximum value of a function in an interval is the lowest value of y assumed by the function.

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The formula for the function obtained when the graph is shifted is f(x)=(x+7)^3+3.

Suppose the considered function whose graph is to be made is function f(x). The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values f(x) are plotted on the vertical axis.

They are together plotted on the point

(x,y) = (x, f(x))

This is why we usually write the functions as:

y = f(x)

Given;

f(x)=x^3 is shifted up 3 unit and to the left 7 units.

Now,

To shift upwards, we will add outside of the argument

To shift to the left, we will add inside of the argument

Therefore, the function will be f(x)=(x+7)^3+3

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Answer: 30

Step-by-step explanation:

Vertical angles are congruent.

[tex]x+30=2x \implies x=30[/tex]