elogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find the length of BD. A. 6 B. 16 C. 18 D. 32

Answer:

x = 2, x = -10

Step-by-step explanation:

(x+4)^2 = 36

(x+4) = 6, -6

x = 2, x = -10

Answer:

She saved $48; She had $72 remaining

Step-by-step explanation: She started off with $120. 20% of $120= $24, 25% of $96= $24. $24 + $24= $48.  $120(total) - $48(total money saved) = $72(money left).

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The amount of money left is $72

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Amount = $120

Amount spend on food.

= 20% of 120

= 20/100 x 120

= $24

Amount remaining.

= 120 - 24

= $96

Amount spend on clothes.

= 25% of 96

= 1/4 x 96

= $24

Amount remaining.

= 96 - 24

= $72

Thus,

The amount of money left is $72

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ5

Round this however you need to.

===========================

Work Shown:

Check out the diagram below. We have the following points

Based on those points, we know that

Which allows us to find the distance from C to D. Focus solely on triangle EDC. Use the sine ratio to find x.

sin(angle) = opposite/hypotenuse

sin(angle EDC) = CE/CD

sin(56) = 7130/x

x*sin(56) = 7130

x = 7130/sin(56)

x = 8600.33397283284 approximately

Make sure your calculator is in degree mode.

Answer:

10

Step-by-step explanation:

It's the $10 that is to be added to the cost for each produced item.

Answer:

86.55 ft

Step-by-step explanation:

First find the perimeter for 3 sides of the rectangle that are solid

24+15+24 = 63

The we find the circumference for 1/2 of the circle

C = pi d

The diameter is 15 and pi = 3.14

But we only want 1/2

1/2 C = 1/2 pi d

        = 1/2 ( 3.14) * 15

       =23.55

Add the lengths together

23.55+63 =86.55 ft

Answer:

[tex]\boxed{\sf \frac{15}{22} }[/tex]

Step-by-step explanation:

The radius of the circle is 7 cm.

The two legs of the triangles are 7cm as well.

Area of a trinagle is ( base × height )/2.

[tex]\frac{7 \times 7}{2} =24.5[/tex]

Multiply the value by 2 since there are two triangles.

[tex]24.5 \times 2 = 49[/tex]

Calculate the area of the circle.

[tex]\pi r^2[/tex]

The radius is given.

[tex]\pi (7)^2[/tex]

Take [tex]\pi[/tex] as [tex]\frac{22}{7}[/tex]

[tex]49(\frac{22}{7} )[/tex]

[tex]=154[/tex]

Subtract the area of the two triangles from the area of the whole circle.

[tex]154-49=105[/tex]

The area of the shaded part is 105 cm². The total area of the shape is 154cm².

[tex]\frac{105}{154} =\frac{15}{22}[/tex]

Answer:

Part A: check B, E and F.

Part B: check E and G.

Step-by-step explanation:

The equation [tex]y = a(x - b)^2 + c[/tex] is the equation of a parabola written in the vertex form, where the vertex will be (b, c).

So, if the vertex is (2, -1), we have that b = 2 and c = -1

To find the c value, we use the information that the y-intercept is 3, so we have the point (0, 3). Using x = 0 and y = 3, we have:

[tex]3 = a(0 - 2)^2 - 1[/tex]

[tex]3 = 4a - 1[/tex]

[tex]4a = 4[/tex]

[tex]a = 1[/tex]

So we have a = 1, b = 2 and c = -1.

Part A: check B, E and F.

To find the x-intercepts, we need to find the values of x where y = 0:

[tex]0 = (x - 2)^2 - 1[/tex]

[tex]x^2 - 4x + 4 - 1 = 0[/tex]

[tex]x^2 - 4x + 3 = 0[/tex]

Solving using Bhaskara's formula (a = 1, b = -4 and c = 3), we have:

[tex]\Delta = b^2 - 4ac = 16 - 12 = 4[/tex]

[tex]x_1 = (-b + \sqrt{\Delta})/2a = (4 + 2)/2 = 3[/tex]

[tex]x_2 = (-b - \sqrt{\Delta})/2a = (4 - 2)/2 = 1[/tex]

So the x-intercepts are 1 and 3

Part B: check E and G.

Answer:

[tex]c =\sqrt{a^{2}+b^{2} }[/tex]

Step-by-step explanation:

You clear c, wich is the hypotenuse

[tex]c =\sqrt{a^{2}+b^{2} }[/tex]

Answer:

This graph represents the function above.

Answer:

[tex]x + 0.05x = 15[/tex], solution is $14.29

Step-by-step explanation:

We can create an equation for this scenario to try and solve it.

Assuming the cost of the CD is x, it’s sale tax will be 0.05x (as that is 5% of x, 0.05.)

We can write the equation in two ways:

[tex]x + 0.05x = 15[/tex] or [tex]1.05x = 15[/tex].

Assuming we take the second one (easier to work with), we can divide both sides by 1.05. The equation simplifies to x = 14.289... which rounds to x = 14.29.

Therefore, the equation is [tex]x + 0.05x = 15[/tex] and the solution is $14.29.

Hope this helped!

Answer:

x + 0.05x = 15; x = $14.29

Step-by-step explanation:

Answer:

{ 1,2}

Step-by-step explanation:

The ∩ means intersection, or what is in common for the two sets

The intersection of A and B is what is in the overlapping circles

The intersection of A and B is { 1,2}

Answer:

x-intercept → (-5, 0)

Step-by-step explanation:

Let the equation of the line having pairs given in the table is,

y - y' = m(x - x')

m = slope of the line

(x', y') is a point lying on the line.

From the given table,

Two points (33, -22) and (52, -33) lie on the line.

Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                        m = [tex]\frac{-33+22}{52-33}[/tex]

                        m = [tex]-\frac{11}{19}[/tex]

Equation of the line passing through (33, -22) and slope = [tex]-\frac{11}{19}[/tex] will be,

y + 22 = [tex]-\frac{11}{19}(x - 33)[/tex]

For x-intercept y = 0,

0 + 22 = [tex]-\frac{11}{19}(x-33)[/tex]

-38 = x - 33

x = -38 + 33

x = -5

Therefore, x-intercept of the line is (-5, 0).

Answer:

-5,0

Step-by-step explanation:

khan academy

Answer:

Step-by-step explanation:

The first thing we are going to do is to fill in the other angles that we need to solve this problem. You could find ALL of them but all of them isn't necessary. So looking at the obtuse angle next to the 35 degree angle...we know that those are supplementary so 180 - 35 = the obtuse angle in the small triangle. 180 - 35 = 145. Within the smaller triangle we have now the 145 and the 10, and since, by the Triangle Angle-Sum Theorem all the angles have to add up to equal 180, then 180 - (10 + 145) = the 3rd angle, so the third angle is 180 - 155 = 25. Now let's get to the problem. If I were you, I'd draw that out like I did to keep track of these angles cuz I'm going to name them by their degree. In order to find d, we need to first find the distance between d and the right angle. We'll call that x. The reference angle is 35, the side opposite that angle is 12 and the side we are looking for, x, is adjacent to that angle. So we will use the tan ratio to find x:

[tex]tan(35)=\frac{12}{x}[/tex] Isolating x:

[tex]x=\frac{12}{tan(35)}[/tex] so

x = 17.1377 m

Now we have everything we need to find d. We will use 25 degrees as our reference angle, and the side opposite it is 12 and the side adjacent to it is

d + 17.1377, so that is the tan ratio as well:

[tex]tan(25)=\frac{12}{d+17.1377}[/tex] and simplifying a bit:

[tex]d+17.1377=\frac{12}{tan(25)}[/tex] and a bit more:

d + 17.1377 = 25.73408 so

d = 8.59, rounded

Answer:

Remember to round!

Answer:

m ∠DBC=80−10=70

m ∠ABC=80+30=110

Step-by-step explanation:

m ∠DBC+m ∠ABC=180

( x−10)+(x+30.)=180

2x+20=180

2x=180-20

2x=160

x=80

>>m ∠DBC=80−10=70

>>m ∠ABC=80+30=110

Answer:

[tex]\boxed{<DBC = 70 degrees}\\\boxed{<ABC = 110 degrees}[/tex]

Step-by-step explanation:

∠ABC and ∠DBC are supplementary which means that the sum of these two angles is equal to 180.

∠ABC + ∠DBC = 180

Given that: ∠ABC = x+30 and ∠DBC = x - 10

So,

=> x+30+x-10 = 180

=> 2x+20 = 180

=> 2x = 180-20

=> 2x = 160

Dividing both sides by 2

=> x = 80

Now, Finding measures of the angles.

=> ∠DBC = x-10 = 80-10 = 70 degrees

=> ∠ABC = x+30 =80+30 = 110 degrees

Answer:

C

Step-by-step explanation:

Given

2x² + x - 1 = 2 ( subtract 2 from both sides )

2x² + x - 3 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 3 = - 6 and sum = + 1

The factors are - 2 and + 3

Use these factors to split the x- term

2x² - 2x + 3x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(2x + 3) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex]

Answer:

[tex]\large \boxed{\sf \ \ \dfrac{5-\sqrt{3}}{2} \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex]\dfrac{1+2\sqrt{3}}{1+\sqrt{3}}=\dfrac{(1+2\sqrt{3})(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\ \text{... to eliminate the root in the denominator ...} \\\\=\dfrac{1-\sqrt{3}+2\sqrt{3}-2*3}{(1-3)}\\\\=-\dfrac{1+\sqrt{3}-6}{2}\\\\=-\dfrac{\sqrt{3}-5}{2}\\\\=\dfrac{5-\sqrt{3}}{2}\\[/tex]

Do not hesitate if you have any question

Answer:

4(2x^3+ x^2-2x-1)

Step-by-step explanation:

the explanation is given above in the picture

pls do mark me the brainliest.

Answer:

4(2x^3+x^2-2x-1)

Step-by-step explanation:

Mulitply each term:

8x^3+4x^2-8x-4

Now simplify: 4(2x^3+x^2-2x-1)

Please mark me brainliest!!

Answer:

x = 1, x = 2

Step-by-step explanation:

Given

f(x) = g(x) - 1, that is

x² - 2x - 1 = x - 1 - 2

x² - 2x - 1 = x - 3 ( subtract x - 3 from both sides )

x² - 3x + 2 = 0 ← in standard form

(x - 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

Answer:

11.7

Step-by-step explanation:

Let H be the heipotenys of the big triangle:

H= 28.04

Let's calculate the third side using the pythagorian theorem:

H²= 26²+ d²(the third side)

d² = 28.04²-26²= 110.24

d= 10.49

let's calculate x now

x= 11.65 ≈ 11.7

Answer:

The coordinates of the vertices are;

(200, 200), (300, 200), (300, 0), (0, 500)

Step-by-step explanation:

The vertices are the corners of a polygon. It is the point where an angle is formed by the intersection of two lines

The feasible region is the solution space of the points of the variables that meet the specification of the problem set by means of a constant or the definition of inequalities or equations

From the graph of the function of inequalities, we have that the four vertices are the four points where the lines bounding the area of the feasible region of the inequalities meet

The coordinates of the vertices are (200, 200), (300, 200), (300, 0), (0, 500).

Answer:

A, B, A

Step-by-step explanation:

(3)

Given

- 2x² + 10x + 12 ← factor out - 2 from each term

= - 2(x² - 5x - 6) ← factor the quadratic

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 5)

The factors are - 6 and + 1, since

- 6 × 1 = - 6 and - 6 + 1 = - 5, thus

x² - 5x - 6 = (x - 6)(x + 1) and

- 2x² + 10x + 12 = - 2(x - 6)(x + 1) → A

(4)

[tex]x^{4}[/tex] - 81 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

[tex]x^{4}[/tex] - 81

= (x² )² - 9²

=(x² - 9)(x² + 9) ← note that x² - 9 is also a difference of squares

= (x - 3)(x + 3)(x² + 9) ← in factored form

x² - 3 is not a factor → B

(5)

Given

5[tex]x^{4}[/tex] - 320 ← factor out 5 from each term

= 5([tex]x^{4}[/tex] - 64) ← difference of squares

= 5(x² - 8)(x² + 8) → A

Answer:

28

Step-by-step explanation:

We divide the shape covenientely, like this, and area 1 is 4*4=16

area 2=4*4/2=8

area 3= 2*4/2=4

Area total = Area 1 + Area 2 + Area 3=16+8+4=28

Answer:

a) $26.4

b) $324

Step-by-step explanation:

Hire purchase is the purchase of an item which can be paid instalmentally.

The bicycle costs $300 for an instant purchase.

For a hire purchase, a $60 deposit must be made and the rest paid instalmentally over 10 months. An interest of 10% is included in the outstanding balance

The outstanding balance after paying deposit= $300 - $60 = $240

Hence, 10% of 240 = 10/100 × 240 = 24

An interest of $24 is added.

Therefore, a total of $240 + $24 = $264 will be paid for the next 10 months.

a) Hence, the amount to be paid in instalment each month is $264/10 = $26.4

b) the total cost of buying the bicycle by hire purchase= deposit amount + instalment price

= $60 + $264

= $324

Hence, a total of $324 will be paid for the bicycle by hire purchase.

N.B: $300 is the sale price + $24 interest

Answer:  60.1

Step-by-step explanation:  If you did 13/15 and then took  sin-1  and got 60.07356513, you did everything right.

But sometimes they want the answer rounded to one decimal point.

So try 60.1

Answer:

432 aquariums

Step-by-step explanation:

To determine the number of aquariums the factory made, find the volume of 1 aquarium, then divide the total volume of water required.

Solution:

Volume of triangular prism aquarium = triangular base area × length of triangular prism

Volume = ½*b*h*l

Where,

b = 8 ft

h = 4 ft

l = 3 ft

Volume = ½*8*4*3 = 4*4*3

Volume = 48 ft³

Number of aquarium made = Volume of water required ÷ volume of 1 aquarium

= 20,736 ÷ 48 = 432 aquariums

Answer:

1) 4a + 8

2) 12a² - 8a

3) 2a² + 8a

4) 4 - 6a

Step-by-step explanation:

The GCF of two numbers is the greatest common number each of the original two numbers can be divided by to get a whole number.

Hope it helps <3

Answer:

4     4a+8

4a   [tex]12a^{2}[/tex]+8a

2a   [tex]2a^{2} +8a[/tex]

2     4-6a

Step-by-step explanation:

Okay basicly you wand to find the biggest number that can go into both numbers

like the greatest common fact for 4a+8 would be 4 since only one of the numbers have an a you would just leave that out

Since you can take a 4 and an a out of [tex]12a^{2} \\[/tex] and out of 8a the greatest common factor would be 4a

Since you are able to take a 2 and an a out of [tex]2a^{2} +8a[/tex] your greatest common factor would be a

Since the largest number that can go into 4 and 6 is 2 your answer would be 2

Hope this helps you understand!

Answer:

31x² - 2

Step-by-step explanation:

5(2x²-1)+3(7x²+1) = 5*2x² - 5*1 + 3*7x² + 3 = 10x² - 5 + 21x² + 3 = 31x² - 2

Answer:

Step-by-step explanation:

Thank you for providing the details of the question.

Unfortunately none of the results you have to choose from will give you 44%

The problem resembles the first probability question you were likely asked. "What is the probability of getting a heads on every throw of a fair coin?" The answer is 1/2 no matter how many times you throw the coin or what has happened before any point in the throws.

The answer should be 6/50.  If this turns out not to be the answer and you have an instructor your safest course of action is to ask how 44% was obtained. Tell me in a comment.

Answer:

fraction 6 over 50

Step-by-step explanation:

In the question it says she pulls a tile out of the bag and records the color 50 times which means she pulled out 50 tiles.

Now the table says that she recorded 6 purple tiles.

Probability is equal to [tex]\frac{number of favorable outcomes}{number of possible outcomes}[/tex]

Number of favorable outcomes here is the number of purple tiles she pulled out (6) since we want to find the probability of choosing a purple tile and the number of possible outcomes is the total number of tiles she pulled out (50)

So the probability = [tex]\frac{6}{50}[/tex]