Find AEAE on the rhombus below when AD=4x+2AD=4x+2, DC=7x-13DC=7x−13 and BD=34BD=34.

Using the Pythagorean theorem, we know that the roof of the building is 24 ft far from the ground.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

So, the Pythagorean theorem formula:

c² = a² + b²

Now, substitute the values in the formula to calculate the distance between the roofline and the ground.

c² = a² + b²

25² = a² + 7²

625 = a² + 49

a² = 625 - 49

a² = 576

a = √576

a = 24ft

Therefore, using the Pythagorean theorem, we know that the roof of the building is 24 ft far from the ground.

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Since 3 | 1+3 | = 3 |4|

                      = 3·4

                      = 12

and

since 3 | -7+3 | = 3 |-4|

                        = 3·4

                        = 12,

both 1 and -7 check as solutions,

so C: x = 1 or x = -7

There are 210 sequences for 7 church bells to rung with the given conditions. Using permutations, the required number of sequences is calculated.

A sequence or arrangement that can be framed by taking some or all of a finite set of things (or objects) is called a permutation.

The formula for finding the number of such arrangements is,

ⁿPₓ = n!/(n - x)!

It is given that, a church's bell tower has 7 bells. 3 of them will ring in a sequence before each service and no bell is rung more than once.

So, the number of sequences that the bells will form is calculated by using the permutations formula. I.e., ⁿPₓ = n!/(n - x)!

Here, n = 7; x = 3

Then,

ⁿPₓ = n!/(n - x)! ⇒ ⁷P₃ = 7!/(7 - 3)! = 7!/4!

⇒ ⁷P₃ = (7 × 6 × 5 × 4!)/4! = 7 × 6 × 5 = 210

Therefore, there are 210 sequences for ringing the bells.

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Answer: 150+30n ≤ p

Step-by-step explanation:

150 is your starting amount, and you add 30 lbs of how many ever boxes (n) onto your plane. So far, you have 150 + 30n. Because there is a limit of p amount that you can't exceed, you need a less than or equal to sign because it can be p amount but not over p amount. So your answer is 150 +30n ≤ p

Answer:

----------------------------------------

The perimeter is:

If the perimeter is less than 20, then the inequality is:

Answer:

x < 4

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

Therefore, from inspection of the triangle:

⇒ Perimeter = 4 + 9 + x + 3

⇒ Perimeter = x + 16

If the perimeter is less than 20 meters then:

⇒ x + 16 < 20

Solve the inequality:

⇒ x + 16 - 16 < 20 - 16

⇒ x < 4

Answer:

  1180 cm³

Step-by-step explanation:

You want the volume of a prism with an L-shaped base. It is 20 cm between bases. The outside dimensions of the L are 7 cm high by 11 cm wide; the inside dimensions are 3 cm high by 6 cm wide.

The formula for the volume of a prism is ...

  V = Bh

where B is the area of the base, and h is the distance between them. We know h, but we need to find B.

The area of an L-shape is the area of the rectangle with the outside dimensions, less the area of the rectangle with the inside dimensions.

  A = LW -lw

  A = (11 cm)(7 cm) -(6 cm)(3 cm) = 77 cm² -18 cm² = 59 cm²

Using the above formula, the volume is ...

  V = (59 cm²)(20 cm) = 1180 cm³

The volume of the prism is 1180 cubic centimeters.

__

Additional comment

The dimensions of the inside of the L are found by subtracting the given width of the legs from the outside dimensions.

 7 cm -4 cm = 3 cm . . . . inside height

  11 cm -5 cm = 6 cm . . . . inside width

You can also find the area of the base by extending one or the other of the lines to divide it into two rectangles. Extending the vertical line makes the left rectangle 7 cm high by 5 cm wide. The right rectangle is 4 cm high by 6 cm wide. Then the area is 7·5 +4·6 = 35+24 = 59, as above.

For the function, y = log₄ (x + 16) - 1, it has x-intercept of -12 and y-intercept of 1.

Logarithmic functions are functions expressed in another way for exponential functions. It is the power to which any number should be raised to yield other values.

Logₐ x = n can be written in exponential form as x = aⁿ.

y = log₄ (x + 16) - 1

x-intercept is the x-coordinate of the point when y = 0.

0 = log₄ (x + 16) - 1

For the left hand side to be equal to 0, the term log₄ (x + 16) must be equal to 1.

log₄ (x + 16) = 1  

⇒ x + 16 = 4       (∵ logₐ a = 1)

⇒ x = -12

y-intercept is the y-coordinate of the point where x = 0.

y = log₄ (0 + 16) - 1

y =  log₄ (16) - 1

y =  log₄ (4²) - 1

logₐ mⁿ = n logₐ m

⇒ y = 2 log₄ (4) - 1

⇒ y = 2 - 1     (∵ log₄ (4) = 1)

⇒ y = 1

Hence, the function y = log₄ (x + 16) - 1 has x-intercept of -12 and y-intercept of 1.

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As per the congruence theorem, we have proved that ΔABC ≅ΔDEF.

In math congruence theorem states that if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other.

Here we need to prove ΔABC ≅ΔDEF by using the congruence theorem.

Here we have given that ΔABC and ΔDEF,

=> ∠B≅∠E [right angle]

So, we have obtained that

=> ∠A≅∠D

As we know that there is two angles and one non included side of ΔABC is congruent the two corresponding angles and one non- included side of ΔDEF, therefore, by AAS congruence rule.

So, based on the given fact we have identified that

=> ΔABC ≅ΔDEF

Therefore, the AAS congruence postulate defined that the triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.

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Answer:

Step-by-step explanation:

P = F/a

Pa = F

a = F/P

Answer:

a = [tex]\frac{F}{p}[/tex]

Step-by-step explanation:

P =[tex]\frac{F}{a}[/tex]  multiple both sides by a

aP = [tex]\frac{F}{a}[/tex] [tex]\frac{a}{1}[/tex]  On the right side of the equal sign, the a's cancel each other out

aP = F  Divide both sides by P

[tex]\frac{aP}{P}[/tex] = [tex]\frac{F}{P}[/tex]  The P's cancel out on the left side of the equal sign.

a = [tex]\frac{F}{P}[/tex]

When x²-3x-2 is divided by x-7, the remainder is 26, and the quotient is x+4.

Sums of terms of the form k-x^n, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Here

f(x)=x²-3x-2

divisor=x-7

When x²-3x-2 is divided by x-7,

The quotient is x+4.

The remainder is 26.

The remainder will be 26 when x²-3x-2 is divided by x-7 and the quotient will be x+4.

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Answer:q<-6.87

Step-by-step explanation:

isolate q by adding 2.01 to both sides

-q>6.87

divide by side by -1, and since it is negative flip the sign

q<-6.87

To test the null hypothesis that there is no difference in parents' wealth for the different levels of schooling, a one-way ANOVA (analysis of variance) test should be used.

To compare the means of two or more groups, statisticians employ the analysis of variance (ANOVA) test. It is used to assess whether there are any significant variations in the means of the groups and to pinpoint which group or groups have significantly different means. The null hypothesis, according to which there is no difference between the group means, is evaluated using the ANOVA test using the F-statistic. If the F-statistic is significant, at least one of the groups has a mean that differs from the others in a meaningful way. To examine how several treatments or circumstances affect a response variable, investigations frequently utilize an ANOVA. It can also be used in non-experimental research to compare the means of different groups.

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The rate at which the distance from the plane to the station is increasing when it has a total distance of 3 mi away from the station is 313.05 mi/h .

Given :

a plane flying horizontally at an altitude of 2 mi and a speed of 420 mi/h passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it has a total distance of 3 mi away from the station .

Here ,

h = 2

d = 3

we know that ,

x = [tex]\sqrt{d^2 - h^2}[/tex]

= [tex]\sqrt{3^2 - 2^2}[/tex]

= [tex]\sqrt{9 -4}[/tex]

= [tex]\sqrt{5}[/tex]

d = [tex]\sqrt{5}[/tex] * 420 / 3

= [tex]\sqrt{5}[/tex] * 140

= 313.05 mi/h

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Answer:

7x - y = 5

Step-by-step explanation:

(y - y1) = m(x - x1)

Here, (x1, y1) = (1, 2) and m = 7

(y - 2) = 7(x - 1)

y - 2 = 7x - 7

7x - y - 7 = - 2

7x - y = -2 + 7

7x - y = 5

Answer:The standard form of the equation of the line through the given point with the given slope through:(1, 2), slope = 7 is 7x - y = 5.

Step-by-step explanation:

Answer:

36%

Step-by-step explanation:

People with size 7 shoes = 5

People with size 7½ = 7

People with size 8 = 9

People with size 8½ = 3

People with size 9 = 1

To find out the total, you have to add all the people up:

5 + 7 + 9 + 3 + 1 = 25

The total amount of students = 25

Since you're trying to find the percentage of students who have a shoe size of 8, you have to look at how many people have that size:

People with size 8 = 9

To find out the percentage you do:

9/25 × 100 = 36%

Therefore 36% of students have a shoe size of 8

:)

Option A) Buying a laptop will be most affordable among all the options as per the Selling price with Sales tax included.

The selling price is the price at which a thing is sold. Typically, it is identified as SP. also known as a selling price on occasion.

Shop owners essentially mark this as a promotional item to give discounts to customers in a way that,

When a product is sold to a buyer, the government levies sales tax (abbreviated as ST). This tax will be collected by the merchant and paid to the government. As a result, it is added to the bill after being charged on the item's selling price.

For Laptop,

Selling Price = (100-40)% of 2399.99

                     = 60% of 2399.99 = $ 1439.99

Total bill = 1439.99 + 8.2% of 1439.99

              = 1439.99 + 118.08 = $ 1558.07

For Smart TV,

Selling Price = (100-10)% of 1799.99

                     = 90% 0f 1799.99 = $ 1619.99

Total bill = 1619.99 + 4.5% of 1619.99

               = 1619.99 + 72.9 = $ 1692.89

For Iphone,

Selling Price = (100-5)% of 1699.99

                     = 95% 0f 1699.99 = $ 1614.99

Total bill = 1614.99 + 6.8% of 1614.99

               = 1614.99 + 109.82 = $ 1724.81

For GeForce RTX 3090 Graphics Card,

Selling Price = 2199.99 - 500 = $ 1699.99

Total bill = 1699.99 + 7.5% of 1699.99

               = 1699.99 + 127.5 = $ 1827.49

Total bill

Graphics Card > Iphone > Smart TV> Laptop.

Option A) Buying a laptop will be most affordable among all the options.

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The answer to the given function -1 . f(-8) -4 . g(4) is -7.

What are functions?

The core concept of mathematics calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.

According to question, we see that f(-8)=-5, and g(4)=3

Now substituting in the given equation:

-1 . f(-8) -4 . g(4)

=(-1 . -5) - (4 . 3)

=5-12 = -7

Therefore the answer to -1 . f(-8) -4 . g(4) is -7

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[tex]\cfrac{2}{3}-\cfrac{5}{12}\implies \cfrac{(4)2~~ - ~~(1)5}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{8~~ - ~~5}{12}\implies \cfrac{3}{12}\implies \cfrac{3\cdot 1}{3\cdot 4}\implies \cfrac{1}{4} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{4}{5}+\cfrac{11}{12}\implies \cfrac{(12)4~~ + ~~(5)11}{\underset{\textit{using this LCD}}{60}}\implies \cfrac{48~~ + ~~55}{60}\implies \cfrac{103}{60}\implies 1\frac{43}{60}[/tex]

Answer:

11

Step-by-step explanation:

-5 + 8 x 2

Do multiplication first because PEMDAS -5 + 16

Then add: 11

Answer:

11

Step-by-step explanation:

8x2 = 16
-5+16 = 11

If you do a question like this always use PEMDAS. Do it in order.

P arenthesis

E exponents

M ultiplcation

D ivision

A ddition

S ubtraction

Answer:

[tex]60=4x\\\\15=x[/tex]

I hope this helped.

Answer: y = -4x+60

y is -4 times x plus 60

Answer:

142.10 units²

Step-by-step explanation:

[tex] A = \dfrac{n}{360^\circ}\pi r^2 [/tex]

[tex] A = \dfrac{134^\circ}{360^\circ}\pi \times 6^2 [/tex]

[tex] A = \dfrac{134^\circ}{360^\circ}\pi \times 6^2 [/tex]

[tex] A = 142.10~units^2 [/tex]

Using the the Distributive Property to express 64 + 24 is 88.

This property states that multiplying the sum of two or more addends by a number produces the same result as multiplying each addend separately by the number and then adding the products together.

When you multiply a value by a sum, the distributive property of multiplication over addition is used. For instance, suppose you want to multiply 5 by the sum of 10 + 3. When we have similar terms, we usually add the numbers first and then multiply by 5. 5(10 + 3) = 5(13) = 65.

In this case, 64 + 24 will be;

= 8(8 + 3)

= 88

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Answer:

(2, -7)

Step-by-step explanation:

4x + y = 1                   3y= 6x + 27

y = 1 - 4x

3(1 - 4x) = 6x + 27

3 - 12x = 6x + 27

-12x = 6x + 24

-18x = 24

6/3

2

y = 1 - 4x

y = 1 - 4(2)

y = 1 - 8

y = -7

4x + y = 1

Answer:

Step-by-step explanation:

4x + y = 1
Divide 4x by 4, then do the same to the 1

4x/4 + y = 1/4

= x + y = 0.25

If you are solving for x, then the equation will look like this.

x = 0.25 - y (minus because you are moving the variable to the other side of the = sign)

If you are solving for y, then the equation will look like this.

y = 0.25 - x (minus because you are moving the variable on the other side of the = sign)

Answer solving for x = x = 0.25 - y

Answer solving for y = y = 0.25 - x

-------------------------------------------------------------------------------------------------------------

3y = -6x + 27

3y/3 = -6x + 27/3

y = -6x + 9

Bring -6x to the other side of the =.

6x + x = 9

6x/6 + y = 9/6

x + y =  1.5

Then you have to move the variable depending on which one you are going to solve for.

Answer solving for x = 1.5 - y

Answer solving for y = 1.5 - x

Hope this helps!

Answer: 4

Step-by-step explanation:

This is Peter equation 5x − 4 = 16

This is Andres equation 20x − 16 = 64

To get from Andres's equation, you multiply every number in Peter's equation by 4

5x times 4 = 20x

-4 times 4 = -16

16 times 4 = 64

If you can, please give me a Brainliest; thank you!

Answer:

4

Step-by-step explanation:

So if you look closely at the equations, you will find out that Andres equation is the same as Peter but 4 times bigger

5x-4=16

20x-16=64

20x-16=64/5x-4=16

= 4

Now let's check

4(5x-4)=4(16)

Therefore, 4 is the answer.

Andres equation is 4 times as big as Peter (but it has the same result)

Please, give me the brainliest if you can

a) The percentile of the phone that sold for $330 is; 29%

b) The sales price at 75th percentile is; $425

In statistics, a percentile is a term that describes how a score compares to other scores from the same set.

From the given set of data showing the sales prices, let us sort them out from smallest to largest;

Sort the data values from smallest to largest:

235, 299, 300, 304, 325, 325, 330, 345, 355, 355, 370, 400, 400, 405, 415, 415, 425, 430, 449, 450, 495

It should be noted that 6 of the 21 data values are smaller than 325.

The percentile is then the number of data values that are less than the individual's data value divided by the number of data values in total, written as a percentage.

Thus;

Percentile = (Total number of data values/Number of data values that are less than the individual’s data value) × 100%

= 6/21  × 100%

≈ 0.2857 × 100%

= 28.57 % ≈ 29%

At 75th percentile, we have;

0.75 = x/21

x = 21 * 0.75

x = 15.75

Thus, the selling price of the phone at the 75th percentile is greater than 16 of the 21 phones. This phone has a selling price of at least $425

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Answer: 56

Step-by-step explanation: 23+5=56

f(x) and g(x) are not inverses because f(g(x)) and g(f(x)) do not both equal x.

For a function f:X—>Y, its inverse f^{-1}:Y—>X  admits an explicit description,

it sends each element y∈Y to the special element x∈X

such that, f(x)=y.

Hence, f(x) and g(x) are not inverses because f(g(x)) and g(f(x)) do not both equal x.

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The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.

What is the scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2. The new figure we receive will resemble the first figure, but every dimension will be double that of the first rectangle. The scale factor in this case will be denoted by the number 2.

Let us take the radius of the circle to be r

We know that circumference = 2πr and the area of a circle is πr²

As, Scale factor = Original circle / Scaled circle

From the question, scale factor = 2

Thus,

2 = Circumference of the Original circle / Circumference of the Scaled circle.

⇒ Circumference of the Scaled circle = (1/2) * Circumference of the Original circle

For the area as well, scale factor = 2

2 = Area of the Original circle / Area of the Scaled circle

⇒ Area of the scaled circle = (1/2) * Area of the original circle

Thus,

The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.

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The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.

What is the scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2. The new figure we receive will resemble the first figure, but every dimension will be double that of the first rectangle. The scale factor in this case will be denoted by the number 2.

Let us take the radius of the circle to be r

We know that circumference = 2πr and the area of a circle is πr²

As, Scale factor = Original circle / Scaled circle

From the question, scale factor = 2

Thus,

2 = Circumference of the Original circle / Circumference of the Scaled circle.

⇒ Circumference of the Scaled circle = (1/2) * Circumference of the Original circle

For the area as well, scale factor = 2

2 = Area of the Original circle / Area of the Scaled circle

⇒ Area of the scaled circle = (1/2) * Area of the original circle

Thus,

The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.

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