Simplify completely quantity 8 x minus 16 over quantity x squared minus 13 x plus 22 and find the restrictions on the variable.

The value of x is given as follows:

x = 24.

The measure of angle DFE is given as follows:

<DFE = 62º.

To obtain the measures, we consider that the sum of the measures of the internal angles of a triangle is of 180º.

The internal angle measures for this problem are given as follows:

Hence the value of x is obtained as follows:

180 - 5x + 14 + 44 + 3x - 10 = 180

228 - 2x = 180

2x = 48

x = 24.

The measure of angle DFE is obtained as follows:

<DFE = 3(24) - 10

<DFE = 72 - 10

<DFE = 62º.

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Answer:

10(x+y)

Step-by-step explanation:

the sum is addition

Answer:

Functions: y = -x + 11, y = 2x^2 - 6x + 4, y = 7

Not Functions: x = 3, x^2 + y^2 = 81, y^2 = -5x - 12

Answer:

Factors of 63 ; 1 , 3 , 7 , 9 , 21 , 63

I hope I helped you^_^

Answer:

1, 3, 7, 9, 21, 63

Step-by-step explanation:

factors of 63 = 1, 3, 7, 9, 21 and 63

Answer:

37%

Step-by-step explanation:

2 dimes = 20 cents, or 20%

3 nickels = 15 cents, or 15%

2 pennies = 2 cents, or 2%

20+15+2 = 37

Answer:B

Step-by-step explanation:

Option B has more, if you want to have mathematical work just set each of the square side lengths to 1. In the first figure, you have 4 units square for each square so 2 units sq on the first and 4 on the second. Then since the other shapes are half circles or 1/4 circles we can put them together to get full and partial circles. The first shape had 2 full circles and the second shape has 1.5. SO using 1 as the radius, you get 3.14 units sq per circle. Leaving you with (circles) 6.28 + (squares) 2 leaving you with 8.28 units sq for figure 1 and (circles) 4.71  + (squares) 4 leaving you with 8.71 for figure 2. This leaves you with a .43 difference. Hope this helps

Answer:

The areas of all 3 shaded regions are equal: about 30.96 square units (144 - 36π square units). The area of the entire square is 144 square units, because 12⋅12=144. The area of the 1 large circle is approximately 113.04 square units, because 3.14⋅62=113.04. The area of the 4 medium circles is also 113.04 square units, because 3.14⋅32=28.26, and 28.26⋅4=113.04. The area of the 9 small circles is also 113.04 square units, because 3.14⋅22=12.56, and 12.56⋅9=113.04.

Step-by-step explanation:

Answer: y=5

Step-by-step explanation:

114+7y+y+26=180

8y+140=180

    -140   -140

8y=40

8     8

y=5

Answer:

None of them

Step-by-step explanation:

n+3<12

(Subtract 3 from both sides)

n<9

(n is less than 9, so n is everything left of 9)

(the inequality symbols: > and < are an open dot)

(none of the choices display n<9 with an open dot, so none of the options are correct)

(if you meant < with a line underneath it, then the dot would be filled, and the answer would be D)

Answer:i cant tell upside down

Step-by-step explanation:

so like huh

Answer:

Step-by-step explanation:

Method

Take the inverse Cos of both sides. That will give you the angle on the left.

From there you can solve for t

cos-1(1/11) = cos-1 cos ((2pi/3)t)

1.4798 = 2*pi*t/3                              Multiply both sides by 3/2

1.4798 * 3/2 = (2pi*t/3)*3/2

2.2196 = 2*pi*t                                 Divide both sides by 2*pi

2.2196 / (2*pi) = t

t = .3534

This was done by setting my calculator to radians. 1.4798 is a radian measure.

Answer:

Step 3

Step-by-step explanation:

The mistake was made in Step 3.

Step 1: Subtract the wholes. 4 - 1 = 3

Step 2: Subtract the fractions. 5/6 - 3/6 = 2/6

After Step 2, He should have added them instead of subtracting them:

3 + 2/6 = 3 2/6

So, step 3 was his mistake.

Answer:step 3

Step-by-step explanation: he should have added

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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The slope of the line passing through A(0,-5) and B(3,1) is 2.

what is slope?

In mathematics, slope is a measure of how steep a line is. It is the ratio of the change in the y-coordinates to the change in the x-coordinates between two points on the line.

The slope formula is given by:

slope = (change in y)/(change in x)

The change in y is the difference between the y-coordinates of two points on the line, while the change in x is the difference between the x-coordinates of the same two points. The slope is a single number that represents the degree of steepness of the line.

To find the slope of the line passing through two given points A(0,-5) and B(3,1), we can use the slope formula:

slope = (change in y)/(change in x)

We first need to find the change in y and the change in x between the two points:

change in y = y-coordinate of B - y-coordinate of A

= 1 - (-5)

= 6

change in x = x-coordinate of B - x-coordinate of A

= 3 - 0

= 3

Now, we can substitute these values into the slope formula:

slope = (change in y)/(change in x)

= 6/3

= 2

Therefore, the slope of the line passing through A(0,-5) and B(3,1) is 2.

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Answer: \(x=0, -\frac{3}{2}\)

Step-by-step explanation:

\(4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}\)

The body surface area is given by the equation A = 1.6865 m²

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the body surface area be represented as A

Now , the equation will be

A = ( HW / 3600 )^1/2

A = √( HW / 3600 )   be equation (1)

where H is the height in centimeters and W is the weight in kilograms

Now , the value of H = 160 cm

The value of W = 64 kg

Substituting the values in the equation , we get

A = √ [ ( 160 x 64 ) / 3600 ]

On simplifying the equation , we get

A = √ ( 10240/3600 )

A = √ ( 2.8444 )

A = 1.6865 m²

Therefore , the body surface area is 1.6865 m²

Hence , the equation is A = 1.6865 m²

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Answer:

Answers

1.  4     3/4 is closer to 1, so 3 + 1 = 4

2.  1     11 is more than half of 20, so 11/20 is closer to 1.

3.  2     1/2 or more, we round up, so we round up to 1.  1 + 1 = 2

4.  4       2/5 is less than 1/2, so round down—0 + 4 = 4

5.  7     7/10 is close to 1, so 6 + 1 = 7

your welcome plus can you mark mr brainlest pls

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

The probability that 75% or more of the women in the sample have been on a diet is 0.0371 or 3.71 %.

Here, n = 267, p = 0.7, 1 = 0.3

Mean, \(m_p = p\)

⇒ \(m_p = 0.7\)

Standard deviation, \(\sigma_p = \sqrt(\frac{pq}{n})\)

⇒ \(\sigma_p\) = 0.028

The conditions for a sampling distribution to be normal distribution, it must satisfy

1. Randomization condition(SRS)

2. logo condition

3. success/failure condition

Hence, the given sampling distribution in the problem statement is approximately normal distribution.

n×p = 267×0.7 = 186.9 ≥ 10

n×q = 267×0.3 = 80.1 ≥ 10

Norm cdf = (0.75, 999, 0.7, 0.028) ≈ 0.0371 ≈ 3.71%

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The required length of AC in triangle ABC is b = 119.57 units.

In triangle ABC, we have:

\($\angle B = 85^\circ$\)

\($\angle C = 53^\circ$\)

\($BC = 85 units\)

AB = c

AC = b (we need to find the value of b)

We know that the sum of the interior angles of a triangle is \($180^\circ$\). Therefore:

\($\angle A = 180^\circ - \angle B - \angle C$\)

\($\angle A = 180^\circ - 85^\circ - 53^\circ$\)

\($\angle A = 42^\circ$\)

Using the law of sines, we have:

\($\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$\)

Substituting the given values, we get:

\($\frac{c}{\sin 85^\circ} = \frac{b}{\sin 53^\circ}$\)

Solving for $c$, we get:

\($c = b \cdot \frac{\sin 85^\circ}{\sin 53^\circ}$\)

We also know that:

\($\frac{a}{\sin A} = \frac{85}{\sin 42^\circ}$\)

Solving for a, we get:

\($a = 85 \cdot \sin 42^\circ$\)

Now we can use the law of cosines to find b:

\($b^2 = a^2 + c^2 - 2ac \cdot \cos B$\)

Substituting the known values, we get:

\($b^2 = (85 \cdot \sin 42^\circ)^2 + \left[b \cdot \frac{\sin 85^\circ}{\sin 53^\circ}\right]^2 - 2 \cdot 85 \cdot b \cdot \sin 42^\circ \cdot \sin 85^\circ/(\sin 53^\circ)$\)

Simplifying and solving for b, we get:

b = 119.57 units

Therefore, the length of AC in triangle ABC is b = 119.57 units.

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SOLUTION

(a) To break even, total revenue must be equal to total cost.

So we equate the revenue function to the cost function and find x which is the number of units, we have

Hence number of units sold to break even is 504 units

Amount coming and going out, we put x for 504 into any of the equation, we have

Hence the answer is 143,640

The profit function, we subtract cost function from revenue, we have

Hence the answer is

P(x) = 140x - 70,560

Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

The equation for g (x) is,

⇒ g(x) = x² -3

Since, The function is,

⇒ f (x) = x²

when x = 0, f(x) = 0

hence it has vertex at (0,0)

Since, g(x) is shifter version of f(x) and has vertex at (-1, 4),

Then, g(x) must be shifted along y axis.

So, We get;

g(x)= x²+c

when x = - 1, g(x)= 4

4 = (-1)² + c

4 = 1 + c

c = 3

Thus, The equation for g (x) is,

g(x) = x² -3

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Answer:

4 and 9

Step-by-step explanation:

x+(x+5)=13

2x+5=13

2x=8

X=4

Answer:

the smaller value is 2.2

the larger value is 10.8

Step-by-step explanation:

5a + a = 13

6a = 13

a = 2.2

5(2.2) = 10.8

10.8 + 2.2 = 13

The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can calculate the distances between each pair of consecutive points as follows:

Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards

Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards

Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards

Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards

Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.

We got x = 16.54 by using Pythagorean theorem .

What is the Pythagorean theorem in plain English?

angle of semicircle is always be 90° .

   18² = 7.1² + x²

    324 = 50.41 + x²

     x² = 324 - 50.41

          = 273.59

    x = √ 273.59

    x = 16.54

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The simplified form of the function f(x) = (x² - 4x + 4) / (x² - 4) will be f(x) = (x - 2) / (x + 2).

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

f(x) = (x² - 4x + 4) / (x² - 4)

Simplify the equation, then we have

f(x) = (x² - 4x + 4) / (x² - 4)

f(x) = (x - 2)² / [(x - 2)(x + 2)]

f(x) = (x - 2) / (x + 2)

The simplified form of the function f(x) = (x² - 4x + 4) / (x² - 4) will be f(x) = (x - 2) / (x + 2).

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The length of the base of the triangle is 8 yards whose height is half of 28 yards.

A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. These three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.

The following formula provides the area of a triangle:

Area = (1/2) x base x height

We are given that the height of the triangle is half of 28 yards, which is:

height = 1/2 x 28 = 14 yards

We are also given that the area of the triangle is 56 square yards. Substituting these values into the formula for the area, we get:

56 = (1/2) x base x 14

Simplifying this equation, we get:

56 = 7 x base

Dividing both sides by 7, we get:

base = 8

Therefore, the length of the base of the triangle is 8 yards.

The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.

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Given: The table showing the number visitors in 4 parks

To Determine: The percentage of the visitors in each park

Solution

Let us find the total number of visitors in all the parks

Let us now find the percentage for each

Hence, each percentage is as inputed in the table below

Given that Bill saves 1/8 of his $92 income, the amount of money he saves is $11.5.

Given that;

Let the amount saved by be be represented by the variable x.

Hence,

1/8 of Bill's income = Amount saved

1/8 × $92 = x

Multiply the numerators

x = 1/8 × $92

x = $92/8

Divide 92 by 8

x = $11.5

Given that Bill saves 1/8 of his $92 income, the amount of money he saves is $11.5.

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