Solve By Substitution
y=-3x
2x-3y=22

The diameter of the circular garden round to the nearest tenth will be 19.1 inches.

In a circle, an infinite number of diameters can be drawn. A diameter is a straight line passing through the center and joins two points of the circumference of a circle. The length of a diameter is twice the length of the radius.

The circumference of a circle is given by C = πd, where d is the diameter of the circle and π can be taken as 3.14.

Substitute C = 60 and π = 3.14 into the above formula and find d.

60 = 3.14×d

d = 60/3.14

≈ 19.108

≈ 19.1

Therefore, the obtained answer is 19.1 inches.

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The elevation of the diver after the dive can be found to be 42 feet below sea level or - 42 feet.

If the diver's elevation is -30 feet relative to sea level, and she dives down 12 feet, we can find her new elevation by adding the change in depth to her initial elevation:

New elevation = Initial elevation + Change in depth

New elevation = - 30 feet + ( - 12 feet )

New elevation = - 42 feet

Therefore, the diver's new elevation after the dive is -42 feet relative to sea level.

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The full question is :

A divers elevation is -30 feet below sea level. She dives down 12 feet. What is her elevation after the dive?

One cubic foot is equal to approximately 28.3168 liters. So to convert cubic feet to liters, you can multiply the number of cubic feet by 28.3168.

Unit conversion is the process of converting a value expressed in one unit of measurement to an equivalent value expressed in another unit of measurement. For instance, to convert 10 feet to meters, you would use the conversion factor 1 foot = 0.3048 meters.

For example, if you have a volume of 5 cubic feet, you can convert it to liters as follows:

5 cubic feet * 28.3168 liters/cubic foot = 141.584 liters

Therefore, 5 cubic feet is equivalent to 141.584 liters (approximately).

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Answer:

20,000

Step-by-step explanation:

I'm assuming your class is using this model of the exponential decay function:

f(x) = a(1 - r)^x

In this case, the equation would be:

f(x) = 20,000(1 - .15)^x

or, when 1 - r is calculated:

f(x) = 20,000(.85)^x

The "a" value is basically the starting value, because on a graph, the starting value would be where x = 0. Anything to the 0th power is 1, and anything multiplied by 1 is the same thing, making "a" the same as the starting value, or the y-intercept.

Therefore, a = 20,000.

Hope this helps!

Answer:

-7.988 or -2E

Step-by-step explanation:

The gallon is a unit of volume that represents the capacity of a liquid in both conventional and US imperial systems of measurement. 1 gallon is defined as 4.54609 liters.

Gallon:

The gallon is a common unit of volume in both English and US customary units. There are three types of gallons in use today: Imperial Gallon, US Gallon, and US Dry Gallon. There are 4 quarts in a gallon, for a total of 8 pints, and each system has a different volume.

Current use of the imperial gallon as of 2021 is still used as the standard unit of petrol in four British overseas territories. It is also the standard unit of measure for six countries: Antigua and Barbuda, Grenada and Saint Lucia.

Liter:

A liter is a metric unit of volume. A liter costs 1/1000 of a cubic meter. The liter was used as the base unit of the basic French metric system. 1 liter is the volume of a cube, i.e. 10 cm x 10 cm x 10 cm, so 1 liter = 1000 cm3 and 1 liter = 0. 2641720524 gallons.

This unit of volume can be used in the International System of Units even though it is not an SI unit. Current use of liters . The liters are primarily used for pourable items (these items can be solid or liquid). These items are measured by the size or capacity of the container. It is also used to measure non-liquid volumes such as backpacks, car trunks, etc.

Formula for Converting Gallons to liters

The formula for converting 1 gallon of water in liters is :

Liter = Gallon x 3.785411784

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9 is the value of C.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The three given angles are (3c)° 42° 111°

We need to find the value of C.

The figure might be a triangle because there are three angles.

From angle sum property , the sum of three angles of triangle is 180 degrees.

3c+42+111=180

3c+153=180

Substitute 153 from both sides

3c=27

Divide both sides by 3

c=9

Hence, the value of c is 9.

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Answer: x intercept: -4, y intercept: 2 (look at the image for the solution)

Step-by-step explanation:

Answer:

x intercept: -4, y intercept: 2

Step-by-step explanation:

Answer:

a = 9.114

Step-by-step explanation:

[tex]\frac{a}{2.1}[/tex] = 4.34 ( multiply both sides by 2.1 to clear the fraction

a = 2.1 × 4.34 = 9.114

The standard form, of the expression 3x³+7x-1+4x³-9x²-11x+1 is 7x³-9x²-4x

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, 3x³+7x-1+4x³-9x²-11x+1 we need to make it in a standard form,

To arrange this expression in a standard form, we will just have to perform operations in like terms and then arrange them in decreasing order of the power of the variables,

Therefore,

3x³+7x-1+4x³-9x²-11x+1

Adding the like terms

= 4x³+3x³+7x-11x-9x²+1-1

= 7x³-9x²-4x

Hence, the standard form, of the expression 3x³+7x-1+4x³-9x²-11x+1 is 7x³-9x²-4x

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10 degrees is the measure of angle x from the circle

In order to determine the value of x from the given circle, we will use the theorem ' angle at the centre of the circle is twice the angle at the circumference.

Mathematically;

360 - 140 = 2arcED

220 = 2arcED

arcED = 220/2

arcED = 110 degrees

Hence the measure of angle x from the given figure is 110 degrees

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The amount of square feet that will be needed is given as follows:

122 ft².

The amount of square feet needed is given by the total area of the figure, which is composed as follows:

The area of the rectangle is given by the multiplication of the dimensions, hence:

Ar = 6 x 15 = 90 ft².

The area of the trapezoid is given by half the multiplication of the sum of the bases and the height, hence:

At = 0.5 x 4 x (6 + 10) = 32 ft².

Hence the total area is given as follows:

A = Ar + At

A = 122 ft².

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The length of side x is 10 units

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

Segment AD bisects angle BAC.

Using the above as a guide, we have the following:

BD = DC

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

x = 20 - x

Evaluate the like terms

2x = 20

Divide by 2

x = 10

Hence, the value of x is 10

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Answer:

2,412

Step-by-step explanation:

[tex]\displaystyle E(X)=np=(36180)\biggr(\frac{14}{210}\biggr)=2412[/tex]

Therefore, we can expect 2,412 students at the university to speak 3 or more languages.

The correct answer is B. 2

Answer:

x = 9 , y = 5

Step-by-step explanation:

Consider the figure to be a parallelogram.

• the diagonals bisect each other

then

2x - 4 = x + 5 ( subtract x from both sides )

x - 4 = 5 ( add 4 to both sides )

x = 9

and

9y - 13 = 5y + 7 ( subtract 5y from both sides )

4y - 13 = 7 ( add 13 to both sides )

4y = 20 ( divide both sides by 4 )

y = 5

The following table contains the appropriate values for A, B, and C:

White 13 52 91 130 Black 9 36 63 90

The definition of a proportionate relationship is as follows:

y = kx.

where k is the proportionality constant.

The following are the input and output variables for this issue:

Number of black keys to enter.

Number of white keys is the output.

The constant k is then obtained using the formula:

91 = 63k

k = 91/63

k = 13/9.

Hence the equation is:

y = 13x/9.

Hence the values are given as follows:

A: when x = 9, y = 13.

B: when x = 36, y = 13 x 36/9 = 52.

C: when x = 90, y = 13 x 90/9 = 130.

Hence the first table is correct.

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An algebraic expression representing the amount Xavier will have in his savings account after w weeks is 43 + 15w.

Algebraic expressions consist of numbers, variables, and the mathematical operations, especially addition, subtraction, division, and multiplication.

An algebraic expression does not have the equation symbol (=) unlike an equation because it is not a complete mathematical statement.

The amount Xavier already has in his savings account = $43

The planned weekly savings = $15

The period of savings = w

43 + 15w

Thus, using an algebraic expression, after w weeks, Xavier will have 43 + 15w in his savings account.

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The cost of each large van is 22,323.53 and each small van is 36,117.65.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Let x be the cost of a large van and y be the cost of a small van.

The total cost of the vans for Location A is $228,500.

Location A buys 7 large and 2 small vans.

So we have a linear equation,

7x + 2y = 228,500

The total cost for Location B is $153,000.

Location B buys 2 large and 3 small vans.

So we have a linear equation,

2x + 3y = 153,000

Multiplying the first equation with 3 and the second equation with 2,

21x + 6y = 685,500

4x + 6y = 306,000

Subtracting,

17x = 379,500

x = 22,323.53

Substituting in one of the equation,

y = 36,117.65

Hence the cost of each large and small van are 22,323.53 and 36,117.65 respectively.

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The height of the school is approximately 5.96 meters.

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.

The mirror and the triangles formed by the mirror, the top of the school, and the ground are similar. This means that the corresponding sides of the triangles are proportional.

Let x be the distance from the mirror to the top of the school. Then:

[tex]\dfrac{x} {7.95} = \dfrac{(x + h) }{ 2.3}[/tex]

We can simplify this equation by cross-multiplying and solving for x:

2.3x = 7.95(x + h)

2.3x = 7.95x + 7.95h

5.65x = 7.95h

[tex]x = \dfrac{7.95h} { 5.65}[/tex]

Now we can use the measurement of the distance from Ai Mi's eyes to the ground to find h. Let d be the distance from the mirror to Ai Mi's eyes. Then:

d = 1.15 meters

The triangles formed by Ai Mi's eye, the mirror, and the ground are similar, so:

[tex]\dfrac{h} { d} =\dfrac{ x} { (d + 2.3)}[/tex]

We can substitute the value of x from earlier:

[tex]\dfrac{h} { 1.15} = \dfrac{(\dfrac{7.95h} { 5.65)}} { 3.45}[/tex]

Simplifying:

[tex]h = \dfrac{(1.15 \times 7.95\times 3.45)}{ 5.65}[/tex]

h = 5.96 meters

Therefore, the height of the school is approximately 5.96 meters. Rounded to the nearest hundredth of a meter, the answer is 5.96 meters.

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Using inferential statistics, it is found that the option that is best surveyed from the collected in the survey is given by:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

An inferential statistic is one that makes inference or predictions about a population based on a sample.

From the table, we have that cookies and cream is the most popular flavor, hence the correct option is:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

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We can determine the radius of the container using the formula for a sphere's surface area because it resembles an orange and has a surface area of roughly 50.3 square inches:

A sphere's surface area equals [tex]4 r^2[/tex].

where r denotes the sphere's radius.

50.3 sq. = 4πr²

By multiplying both sides by 4, we obtain:

r² = 50.3 sq. / (4π)

r² ≈ 4

When we square the two sides, we obtain:

r ≈ 2

Hence, the spherical container has a radius of around 2 inches.

The volume of the container can now be calculated using the following formula:

A sphere's volume equals [tex](4/3)r^3[/tex].

Container volume = (4/3) X(23)

The container's volume is 33.5 cubic inches.

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Answer:

First off that is my name.

y=-0.5x+5 is the first equation. I don't know the second.

Sorry

Step-by-step explanation:

Answer: 70.08

Step-by-step explanation:

0.96*73=

The statement "If point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, -x)." is incorrect.

The origin of the coordinate plane is the point (0, 0), and it is the center of rotation for many geometric transformations.

When a point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, x). This is because rotation by 90 degrees counterclockwise causes the x-coordinate to become the negative of the original y-coordinate and the y-coordinate to become the original x-coordinate.

To see this, imagine the point (x, y) on the coordinate plane and draw a line segment connecting the point to the origin. The length of this line segment is given by the Pythagorean theorem as the square root of x² + y². After rotating the point 90 degrees about the origin, the line segment will be perpendicular to the original line segment and have a length equal to y and -x.

In summary, rotating a point (x, y) at 90 degrees about the origin results in the point (-y, x) due to the change in the direction and length of the line segment connecting the point to the origin.

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To reflect a point across the y-axis, you multiply the x-coordinate of the original point by -1 while keeping the y-coordinate the same. So, reflecting the point (-9, -5) across the y-axis results in the point (9, -5).

Answe

To reflect a point across the y-axis, you multiply the x-coordinate of the original point by -1 while keeping the y-coordinate the same. So, reflecting the point (-9, -5) across the y-axis results in the point (9, -5).

Step-by-step explanation:

The correct answer is option D. We can be 95% confident that the sample proportion is captured by the confidence interval.

The margin of error of plus or minus three percentage points at a 95% confidence level means that the true proportion of people who jog regularly in the population is estimated to be between 15% and 21%. We can be 95% confident that the true proportion of people who jog regularly falls within this interval.

Therefore, option B is correct. Option A is incorrect because it implies that the margin of error always holds true for any sample size, which is not the case. Option C is incorrect because it presents a range of values for the population, not for the estimate. Option E is incorrect because it refers to the proportion of samples that would find the same sample proportion, not the range of values within which the true proportion lies.

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Answer:

(4,0)

Step-by-step explanation:

I will assume the fiorst equation is missing an "x," so I'll assume it was meant to be:  y = -x + 4

See the attached graph.  The lines cross at (4,0).

Answer:

[tex]-0.281250[/tex]

Step-by-step explanation:

The given number has [tex]5[/tex] after the decimal point, so add a trailing zero.