solve x and y for 5x−y=44−3=−3x−y=−12

Answer:

cosΘ = [tex]\frac{\sqrt{7} }{4}[/tex]

Step-by-step explanation:

using the identity

sin²x + cos²x = 1 ( subtract sin²x from both sides )

cos²x = 1 - sin²x ( take square root of both sides )

cosx = ± [tex]\sqrt{1-sin^2x}[/tex]

given

sinΘ = [tex]\frac{3}{4}[/tex] , then

cosΘ = ± [tex]\sqrt{1-(\frac{3}{4})^2 }[/tex]

         = ± [tex]\sqrt{1-\frac{9}{16} }[/tex]

         = ± [tex]\sqrt{\frac{16}{16}-\frac{9}{16} }[/tex]

         = ± [tex]\sqrt{\frac{7}{16} }[/tex]

         = ± [tex]\frac{\sqrt{7} }{\sqrt{16} }[/tex]

since Θ is in quadrant 1 , then cosΘ > 0

cosΘ = [tex]\frac{\sqrt{7} }{4}[/tex]

The break-even points in terms of customers served = 14 customers

Charge per customer = 120

Let the Number of customers= n

So,

Income from serving n customers = 120n

Expenditure from serving n customers = Fixed cost + cost of preparation of meal per customer

= 1400 + 20n

For beak-even:

Income = Expenditure

Substituting values, we get:

120n = 1400 + 20n

So, we get:

100 n = 1400

So, we get:

n =1400/100

= 14

So,

The break-even points in terms of customers served = 14 customers

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The maximum volume of the box is approximately 128.0in³.

Since the cardboard has dimensions of 8 inches by 12 inches, the largest possible length and width of the box are both 8 inches (since 8 is the smaller of the two dimensions).

Then we can cut two 8-inch by 8-inch squares from the cardboard to make the top and bottom of the box, and then cut out four 8-inch by 2-inch rectangles from the remaining cardboard to make the sides of the box.

The height of the box will be the same as the width of the 8-inch by 2-inch rectangles, which is 2 inches. Therefore, the maximum volume of the box is:

V = l × w × h = 8 in × 8 in × 2 in = 128 in³

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The value of x is 4

Similar triangles are triangles that have the same shape, but their sizes may vary. For two triangles to be similar, the corresponding angles must be equal.

Also the ratio corresponding sides are equal in similar triangles.

3/11 = x+5/6x+9

11(x+5) = 3( 6x+9)

11x+55 = 18x +27

collecting like terms

18x-11x = 55-27

7x = 28

x = 28/7

x = 4

therefore the value of x is 4

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Answer: -44

Step-by-step explanation:

[tex]2(4)^2 -4(7) -4(4)(7-4) = ?\\2(16) - 28 - 16(3) =\\32 - 28 -48 = -44[/tex]

Answer:

m = 7√2/2

n = 7√2/2

Step-by-step explanation:

sin45 = m/7

√2/2 = m/7

m = 7√2/2

cos45 = m/7

√2/2 = m/7

m = 7√2/2

Answer:

C

Step-by-step explanation:

f(x) = 2 + x - x²

to obtain f(- 3) substitute x = - 3 into f(x)

f(- 3) = 2 + (- 3) - (- 3)²

        = 2 - 3 - 9

      = - 10

Answer:

Substituting -3 in the expression for f(x), we get:

f(-3) = 2 + (-3) - (-3)^2 = 2 - 3 - 9 = -10

Step-by-step explanation:

Therefore, the value of f(-3) is -10.

Option C is the correct answer.

We have the reasons given as;

<4 + <3 = 180 degrees; supplementary angles

m<1 + m<2 + m<3 = 180; sum of angles in a triangle

m<1 + m<2 = m<4; substitution of equality

Angle n and n are corresponding angles

angle n + <3 are supplementary angles

First, we need to know the following deductions;

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Answer:

Below

Step-by-step explanation:

There are many ways to write an equation using 1/4 and 1000, depending on the context and what you are trying to express. Here are a few examples:

To find out what 1/4 of 1000 is, you can use the equation:

1/4 * 1000 = 250

This equation multiplies 1/4 (or 0.25) by 1000 to get the result of 250.

If you want to express a ratio between 1/4 and 1000, you can use the equation:

(1/4) : 1000 = x : 1

This equation sets up a proportion where x is the unknown value that represents the ratio between 1/4 and 1000. By cross-multiplying and solving for x, you can find the answer. For example:

(1/4) : 1000 = x : 1

1000x = 1/4

x = (1/4) / 1000

x = 0.00025

So the ratio of 1/4 to 1000 is 0.00025 to 1.

Another example of an equation using 1/4 and 1000 could be:

1/4 + 1000 = x

This equation adds 1/4 to 1000 to find the value of x. The result would be:

1/4 + 1000 = 1000.25

So x is equal to 1000.25.

The value of the logarithmic expression is:

log₅(5¹´²) = 1/2

Remember the two rules for logarithms:

logₐ(x) = ln(x)/ln(a)

ln(xⁿ) = n*ln(x)

Then we can rewrite the expression:

log₅(5¹´²) as:

ln(5¹´²)/ln(5)

Using the second rule we can take out the exponent to get:

ln(5¹´²)/ln(5) ]= (1/2)*ln(5)/ln(5) = 1/2

That is the value.

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Janet has 630 options to customize a car based on the given features.

How to solve the question?

To determine the number of ways Janet can customize a car, we need to multiply the number of choices she has for each feature. Therefore, the total number of ways Janet can customize a car can be calculated as:

10 car models x 7 exterior colors x 9 interior colors = 630

Thus, Janet has 630 options to customize a car based on the given features.

It's worth noting that this calculation assumes that each feature (car model, exterior color, and interior color) can be combined with any other feature, without any restrictions or dependencies. However, in reality, certain car models may not be available in certain exterior or interior colors, or there may be other restrictions on the customization options.

Additionally, there may be other features that Janet can customize, such as the type of engine, transmission, or other options. Therefore, the total number of customization options may be even greater than what we have calculated here.

In summary, based on the given information, Janet has 630 ways to customize a car, but in reality, the actual number of options may be more limited or varied depending on other factors.

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Answer:

$2.50

Step-by-step explanation:

6% of $16.90 is $1.014

$16.90 + $1.014 is $17.914

14% of $17.914 is $2.50796

Which we then round down to $2.50

Hope this helps!

Answer:

The range is the difference between the greatest and least values in a set of data.

For Contest 1, the greatest kite height is 170 feet and the least kite height is 112 feet, so the range is:

170 - 112 = 58 feet

For Contest 2, the greatest kite height is 160 feet and the least kite height is 85 feet, so the range is:

160 - 85 = 75 feet

The difference between the ranges is:

75 - 58 = 17 feet

Therefore, the answer is B. 17.

The area of the shape ABCD and EFGH are 64cm² and 25cm²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

Since the sides of a square are equal. The area of a square is given as;

A = l²

For square ABCD,

one grid square represents 1 square cm

Therefore ,ABCD represents 8 square centimeters.

This means the area of square ABCD is given as;

A = 8²

= 64cm²

For square EFGH,

EFGH has 5 grid squares, therefore the area of the square is given as;

A = 5²

A = 25cm²

therefore the area of squares ABCD and EFGH are 64cm² and 25cm²

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Based on the angle of two-tangent theorem, the value of x in the image is: x ≈ 4.

The angle of two-tangent theorem states that when two tangent lines intersect outside of a circle, the angle that they form has a measure equal to half the positive difference between the measures of the arcs intercepted by the angle.

Applying the theorem, we have:

70 = 1/2[(360 - 27x + 2) - (27x + 2)]

140 = 360 - 27x + 2 - 27x - 2

140 = 360 - 54x

140 - 360 = -54x

-220 = -54x

-220/-54 = x

x ≈ 4

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The area of ​​the triangular pyramid is 787.27 mm²

The volume of a right-angled triangular pyramid  is given by the formula V = 1 3 × B × h, where B is the area of ​​the base of the triangle and h is the height (the distance from the apex to the base).

 To calculate the  area of ​​a triangular pyramid, we need to find the area and base of the four triangles.

First, we find the area of ​​the base of an equilateral triangle. The formula for the area of ​​an equilateral triangle is (sqrt(3)/4)*a², where a is the side length. Substituting a=19, we get:

Area of ​​base = (√(3)/4)*19²

= 207.39 mm²

Then we find the area of ​​one triangular surface. We can use the formula for the area of ​​a triangle, which is (1/2) the height of the base. The base of the triangle is the other side of an equilateral triangle with a length of 19 mm. The height of the triangle is the  height of the diagonal of the pyramid, which is 17 mm. Using the Pythagorean theorem, we can find the length of the height of the triangle:

h = √ (slope² - (1/2 base)²)

= √(17² - (1/219)²)

= 15.27 mm

Thus, the area of ​​one triangular surface is:

Area of ​​triangle = (1/2)1915.27

= 144.97 mm²

Since there are four triangular faces, the total area of ​​the triangular faces is:

Total area of ​​triangular surfaces = 4 × 144.97

= 579.88 mm²

Finally, the  area of ​​the pyramid is the sum of the area of ​​the base and the area of ​​the four triangular sides:

Area = area  of ​​base Total area of ​​triangular surfaces

= 207.39 + 579.88

= 787.27 mm²

Therefore the  area of ​​the triangular pyramid is 787.27 square millimeters.

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Based on simple interest, the solution to the question is that his friend will ultimately owe Darrel $2,875.

A loan or investment's interest can be calculated using simple interest using the principal, interest rate, and duration of the transaction. Because it just considers the original principal and does not account for any compounded interest, it is known as "simple" interest.

Darrel will be indebted to his friend for the following sum if he lends him $2,500 and receives repayment with 15% simple interest after a year:

Interest = Principal x Rate x Time

Interest = $2,500 x 0.15 x 1

Interest = $375

Thus, the total sum his friend will be required to pay Darrel is:

Total amount = Principal + Interest

Total amount = $2,500 + $375

Total amount = $2,875

Thus, the total amount his friend owes Darrel is $2,875.

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Required value of angle CMG is 53°.

What is supplementary angle?

Supplementary angles are angles whose sum is 180 degrees. For example, an angle of 130° and an angle of 50° are cause the sum of 130° and 50° equals 180°. Similarly, complementary angles add up to 90 degrees. Two supplementary angles, when joined together, form a right and a right angle.

But it should be noted that two complementary angles do not have to be adjacent. Thus, any two angles can be supplementary angles if their sum is 180°.

Geometry is one of the important branches of mathematics that deals with the study of different shapes. This will trigger the exploration of lines and angles. A straight line is a line without curves and is defined as the shortest distance between two points. An angle is formed when line segments meet at a point.

From the figure, it is clear that value of angle DMF is 180°.

Now angle DMF = angle CMD + angle CMG + angle GMF

So, 180° = 63° + angle CMG + 64°

Angle CMG = 180° - 64° - 63° = 180° - 127° = 53°.

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Correct question is "Find the angle CMG from the given picture".

Answer:

y = 4x + 11

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x + 9 ← is in slope- intercept form

with slope m = 4

• Parallel line have equal slopes , then

y = 4x + c ← is the partial equation of line A

to find c substitute (- 2, 3 ) into the partial equation

3 = 4(- 2) + c = - 8 + c ( add 8 to both sides )

11 = c

y = 4x + 11 ← equation of line A

To evaluate x=50+0.35m to find the amount Mr. Parker will pay if he drives 80 miles, we substitute m with 80 and simplify the expression as follows:

[tex]x = 50 + 0.35m[/tex]

[tex]x = 50 + 0.35(80)[/tex]

[tex]x = 50 + 28[/tex]

[tex]x = 78[/tex]

Therefore, Mr. Parker will pay $78 if he drives 80 miles.

I'm sorry to bother you but can you please mark me BRAINLEIST if this ans is helpfull

The given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.

Equation is a mathematical expression that consists of variables, symbols, and numbers, and shows the relationship between different quantities. An equation can involve one or more unknowns, and can be represented as an equality or as an inequality. Solving an equation requires understanding the relationship between the different elements in the equation, and manipulating the equation to isolate the unknowns. Common types of equations include linear equations, quadratic equations, and polynomial equations.

From this diagram, we can conclude that $\angle ABC$ is an isosceles triangle. This is because the angles opposite equal sides of a triangle must be equal. Since $\angle BAC=24^\circ$, $\angle ABC$ must be $24^\circ$. Furthermore, the sides $AB$ and $AC$ are equal, so $ABC$ is an isosceles triangle.

This conclusion can be verified by using the Pythagorean Theorem. If $AB=AC$, then it follows that $BC = \sqrt{AB^2 + AC^2} = \sqrt{2AB^2}$. Since $AB=3$, it follows that $BC=\sqrt{2*3^2}=6$. Therefore, the triangle $ABC$ is a right triangle with legs of length 3 and hypotenuse of length 6. Since $\angle BAC = 24^\circ$, it follows that $\angle ABC = 24^\circ$, verifying that the triangle is isosceles.

In conclusion, the given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.

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Answer:

78

Step-by-step explanation:

According to the given data the equation of the new function is (D) f(x) = 2x - 4.

An equation is a mathematical statement that indicates that two expressions are equal. It contains an equals sign "=" and may involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc.

If we translate the function h(x) = 2x - 9 up by 5 units, the new function f(x) will have the form:

f(x) = h(x) + 5

Substituting the definition of h(x) into this equation, we get:

f(x) = 2x - 9 + 5

Simplifying, we have:

f(x) = 2x - 4

Therefore, the equation of the new function is (D) f(x) = 2x - 4.

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Answer:

3(x - 4) + 5x can be simplified to 8x - 12.

Answer: 8x - 12

Step-by-step explanation:

3(x - 4) + 5x

distribute = 3x - 12 + 5x

simplify = 8x - 12

Answer:To determine the possible scales of the map, we need to calculate the ratio of the distance on the map to the corresponding distance on the ground in the actual state. We can do this using the following formula:scale = distance on map ÷ distance on groundFirst, we need to convert the dimensions of Kansas from miles to inches using a common scale factor. Since 1 mile is equal to 63,360 inches, we have:Length of Kansas: 410 miles × 63,360 inches/mile = 25,984,600 inchesWidth of Kansas: 210 miles × 63,360 inches/mile = 13,315,200 inchesNow we can calculate the possible scales of the map based on the dimensions of the page in Jada's book, which is 5 inches by 8 inches:For the length of Kansas:scale = 5 inches ÷ (25,984,600 inches ÷ 2.54 cm/in) = 0.0000484scale = 8 inches ÷ (25,984,600 inches ÷ 2.54 cm/in) = 0.0000774For the width of Kansas:scale = 5 inches ÷ (13,315,200 inches ÷ 2.54 cm/in) = 0.0000962scale = 8 inches ÷ (13,315,200 inches ÷ 2.54 cm/in) = 0.0001539Therefore, the possible scales of the map are 1:20,655, and 1:10,326.

Answer:

674

Step-by-step explanation:

50 miles would make the two choices equivalent in cost.

The following formula is used to determine a line's slope:

slope is equal to y2 - y1 / x2 - x1.

where the two points on the line are (x1, y1) and (x2, y2). The steepness or rate of change of the line is indicated by the slope. A line with a positive slope is increasing from left to right, whereas a line with a negative slope is dropping from left to right. An undefined slope denotes a vertical line, while a slope of zero denotes a horizontal line.

To determine the choice where the two miles are equivalent we take x as the number of miles:

For the first company:

Total cost = 25 + 0.8x

For the second company:

Total cost = 35 + 0.6x

Setting the equations as equal:

25 + 0.8x = 35 + 0.6x

0.2x = 10

x = 50

Hence, 50 miles would make the two choices equivalent in cost.

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