Given that ACAB - ACED, lind the value of y to 1 dermal place

 Given That ACAB - ACED, Lind The Value Of Y To 1 Dermal Place

Answers

Answer 1

Answer:

y = 15

Step-by-step explanation:

The triangles CAB and CED are similar (Using the case AA), so we can write the following relations:

[tex]\frac{12}{28} =\frac{15}{x}=\frac{y}{35}[/tex]

Using the first two fractions, we can find the value of x:

[tex]\frac{12}{28} =\frac{15}{x}[/tex]

[tex]12x = 28*15[/tex]

[tex]12x = 504[/tex]

[tex]x = 504/12 = 42[/tex]

Using the first and last fractions, we can find the value of y:

[tex]\frac{12}{28} =\frac{y}{35}[/tex]

[tex]28y = 12*35[/tex]

[tex]28y = 420[/tex]

[tex]y = 420/28 = 15[/tex]


Related Questions

Can somebody plz help me 15-[7+(-6)+1]^3

Answers

Answer:

7.

Step-by-step explanation:

15 - [7 + (-6)+ 1]^3

Using PEMDAS:

= 15 - [ 7-6+1]^3

Next work out what is in the parentheses:

= 15  - 2*3

Now the exponential:

= 15 - 8

= 7.

Step-by-step explanation:

Hi,

I hope you are searching this, right.

=15[7+(-6)+1]^3

=15[7-6+1]^3

=15[2]^3

=15-8

=7...is answer.

Hope it helps..

Please help fast! 25 points and brainliest!!

Let f(x) = 36x5 − 44x4 − 28x3 and g(x) = 4x2. Find f of x over g of x

Answers

Answer:

The answer is

9x³ - 11x² - 7x

Step-by-step explanation:

f(x) = 36x^5 − 44x⁴ − 28x³

g(x) = 4x²

To find f(x) / g(x) Divide each term of f(x) by g(x)

That's

[tex] \frac{f(x)}{g(x)} = \frac{ {36x}^{5} - {44x}^{4} - {28x}^{3} }{ {4x}^{2} } \\ \\ = \frac{ {36x}^{5} }{ {4x}^{2} } - \frac{ {44x}^{4} }{ {4x}^{2} } - \frac{ {28x}^{3} }{ {4x}^{2} } \\ \\ = {9x}^{3} - {11x}^{2} - 7x[/tex]

Hope this helps you

Answer:

9x³ - 11x² - 7x

Step-by-step explanation:

guy abpove is right or bwlowe

Please answer this in two minutes

Answers

Z EQUALS 73


There are 5 sides so we know the sum of the interior angles is 540.
Then create an equation. z+2z+2z-6+117+64=540.
Simplify. 5z+175=540.
Subtract both sides by 175 then divide both sides.

1.) Which movie had the Lower Q3 as shown in the box plot?

Movie A

Movie B

Both about the same


Answers

Answer: Movie A

Q3, or third quartile, is visually located at the right edge of the box. Movie A shows to have a smaller Q3 value as it is to the left of Q3 for movie B.

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Answers

Answer:

1. 24 x

Step-by-step explanation:

Area = (6x +1)(6x-1)

which means

length = 6x+1

width = 6x -1

as perimeter = 2 (length + width)

                     = 2 (6x +1+6x -1)

                     = 2(12x)

                    =24x

what is 2.267676767 as a fraction

Answers

Answer:

2267676767/1000000000

Step-by-step explanation:

To write 2.267676767 as a fraction you have to write 2.267676767 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

2.267676767 = 2.267676767/1 = 22.67676767/10 = 226.7676767/100 = 2267.676767/1000 = 22676.76767/10000 = 226767.6767/100000 = 2267676.767/1000000 = 22676767.67/10000000 = 226767676.7/100000000 = 2267676767/1000000000

And finally we have:

2.267676767 as a fraction equals 2267676767/1000000000

Hope it helps.. If yes mark me BRAINLIEST!!

TYSM!

Answer:

2267676767/1000000000

Step-by-step explanation:

when converting a decimal to fraction,

write down the decimal divided by 1 and than add as many zeros as the digits after the decimal point.

since we have nine digits after the decimal point  nine zeros are put after the '1'

The side lengths of a triangle are 9, 12, and 15. Is this a right triangle?

Answers

Answer:

Yes, this is a right triangle.

Step-by-step explanation:

Hypotenuse always have the highest number than base and perpendicular.

Hypotenuse ( h ) = 15

Base ( b ) = 9

Perpendicular ( p ) = 12

Let's see whether the given triangle is a right triangle or not

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

Plugging the values,

[tex] {15}^{2} = {12}^{2} + {9}^{2} [/tex]

Evaluate the power

[tex]225 = 144 + 81[/tex]

Calculate the sum

[tex]225 = 225[/tex]

Hypotenuse is equal to the sum of perpendicular and base.

So , we can say that the given lengths of the triangle makes a right triangle.

Hope this helps..

Best regards!!

Answer:

[tex]\boxed{Yes.}[/tex]

Step-by-step explanation:

To solve this equation, we can use the Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are regular side lengths and [tex]c[/tex] is the hypotenuse.

The hypotenuse is the longest side of a triangle and is assigned to the [tex]c[/tex]-variable.The other two side lengths can be assigned to either [tex]a[/tex] or [tex]b[/tex] because of the commutative property: [tex]a + b = b + a[/tex].

Now, just substitute the side lengths into the formula and solve!

[tex]9^2 + 12^2 = 15^2[/tex]    Simplify the equation by taking each value to its power.

[tex]81 + 144 = 225[/tex]    Simplify by adding like terms.

[tex]225 = 255[/tex]

Therefore, this is indeed a right triangle.

The area of circle Z is 64 ft^2.
What is the value of r?
Or= 4 ft
O r= 8 ft
O r= 16 ft
O = 32 ft

Answers

Answer:

The answer is

r =4 ft

Step-by-step explanation:

Area of a circle is given by πr²

Where r is the radius

From the question

Area = 64 ft²

So the radius is

64 = πr²

Divide both sides by π

[tex] {r}^{2} = \frac{64}{\pi} [/tex]

Find the square root of both sides

[tex]r = \sqrt{ \frac{64}{\pi} } [/tex]

r = 4 ft

Hope this helps you

Answer: 8

The answer is 8 not 4.5 or 4!!!!!!!!

Step-by-step explanation: It's not just "64" its 64pi. when you posted the question your device could not put the pi symbol so people were thinking that it was just 64.

The following sphere has a diameter of 11 inches.

What is the volume of the sphere? Use 3.14 for it and round your answer to the nearest tenth.
O 5,572.5 in.3
O 696.6 in.)
O 174.1 in."
O 126.6 in.3

Answers

Answer:

[tex]\boxed{Volume = 696.9 \ in.^3}[/tex]

Step-by-step explanation:

Diameter = 11 inches

Radius = 11/2 = 5.5 inches

[tex]Volume \ of \ a \ sphere = \frac{4}{3} \pi r^3[/tex]

Where r = 5.5

V = [tex]\frac{4}{3} (3.14)(5.5)^3[/tex]

V = [tex]\frac{4}{3} (3.14)(166.375)[/tex]

V = [tex]\frac{2090.7}{3}[/tex]

V = 696.9 in.³

Solve with long division method 31/27​

Answers

Answer:

1.148 repetent

Step-by-step explanation:

hope this helps

A zookeeper weighed an African elephant to be 9 × 103 pounds and an African lion to be 4 × 102 pounds. How many times greater is the weight of the elephant than the weight of the lion? A. 2.25x 10 B. 5 C. 13x10 D. 3.6x10

Answers

Answer:

2.25 x 10

Step-by-step explanation:

In the above question, we were given :

The weight of the Elephant = 9 × 10³ pounds

The weight of the African Lion = 4 × 10² pounds

We would compare both weights to determine which size is bigger

Weight of Elephant : Weight of Lion

9× 10³ : 4 × 10²

= 9 × 10³/4 × 10²

= 2.25 × 10¹

= 2.25 × 10

The weight of the elephant is 2.25 × 10 times greater than the weight of the lion.

Triangle A B C is shown with its exterior angles. Angle B A C is (p + 4) degrees and angle A C B is 84 degrees. Exterior angle X B C is (3 p minus 6 degrees).
What is the measure of ∠XBC?

m∠XBC = m∠BAC + m∠BCA
3p – 6 = p + 4 + 84
3p – 6 = p + 88
2p – 6 = 88
2p = 94
m∠XBC =
°

Answers

Answer: 135

Step-by-step explanation:

took it on edg2020

Answer:

135

Step-by-step explanation:

Just took the test and got it right

Triangle ABC has vertices at A(2,5), B(4,11) and C(-1,6). Determine the angles in this triangle.
I need this solved using vectors please

Answers

Answer:

The angles are

∠A = 90°, ∠B = 26.56°, ∠C = 63.43°

Step-by-step explanation:

We have that the angles of a vector are given as follows;

[tex]cos\left ( \theta \right ) = \dfrac{\mathbf{a\cdot b}}{\left | \mathbf{a} \right |\left | \mathbf{b} \right |}[/tex]

Whereby the vertices are represented as

A= (2, 5, 0), B = (4, 11, 0), C = (-1, 6, 0),

AB =(4, 11, 0) - (2, 5, 0) = (2, 6, 0) ,  BA = (-2, -6, 0)

BC = (-1, 6, 0) - (4, 11, 0) = (-5, -5, 0), CB = (5, 5, 0)

AC = (-1, 6, 0) - (2, 5, 0) = (-3, 1, 0), CA = (3, -1, 0)

θ₁ = AB·AC

a·c = a₁c₁ + a₂c₂ + a₃c₃ = 2×(-3) + 6×1 = 0

Therefore, θ₁ = 90°

BA·BC = (-2)×(-5) + (-6)×(-5) = 40

[tex]{\left | \mathbf{}BA \right |\left | \mathbf{}BC \right |}[/tex] = (√((-2)² + (-6)²)) × (√((-5)² + (-5)²)) = 44.72

cos(θ₂) = 40/44.72 = 0.894

cos⁻¹(0.894) =θ₂= 26.56°

CA·CB = 5×3 + 5×(-1) = 10

[tex]{\left | \mathbf{}CA \right |\left | \mathbf{}CB \right |}[/tex] = (√((3)² + (-1)²)) × (√((5)² + (5)²)) = 22.36

10/22.36 = 0.447

cos(θ₃) = 0.447

θ₃ = cos⁻¹(0.447) = 63.43°.

Help urgently please❤️

Answers

Answer:

1. 677 inches = 18.056 yards

677 inches  = 56.416 feet

677 inches = 677 inches

2. QP = 23.5 cm

3. The perimeter = 53.5 cm

Step-by-step explanation:

1. To convert, 677 inches to yards, we have;

1 inch = 0.0277778 yards

677 inches = 677*0.0277778 = 18.056 yards

To convert, 677 inches to feet, we have;

1 inch = 0.083333 feet

677 inches = 677*0.083333  = 56.416 feet

To convert, 677 inches to inches, we have;

1 inch = 1 inch

677 inches = 677*1  = 677 inches

2. We have that ∠PRQ and ∠PRS are supplementary angles (angles on a straight line

Given that ∠PRS = 90°, ∠PRQ = 180° - 90° = 90°;

∠PRQ + ∠PQR + ∠RPQ = 180°, sum of angles in a triangle

∠PQR = 24° given

∠PRQ = 90°

∴  ∠RPQ = 180° - 90° - 24° = 66°

∴∠SPQ = ∠SPR + ∠RPQ = 36° + 66° = 102°

∠QSP + ∠SPQ + ∠PQS = 180° (sum of angles in a triangle)

∠QSP = 180° -∠SPQ - ∠PQS = 180° -102° - 24 = 54°

By sine rule, we have;

a/(sin(A)) = b/(sin(B))

Therefore, we have;

11.8/(sin(24)) = QP/(sin(54°))

QP = (11.8/(sin(24))) × (sin(54°)) = 23.5 cm

3. From trigonometric ratios, we have;

tan(43°) = BC/CA = BC/(16.2 cm)

BC = 16.2 cm × tan(43°) = 15.1

By Pythagoras theorem, we have;

AB = √(15.1² + 16.2²) = 22.2

The perimeter = 15.1 + 16.2 + 22.2 = 53.5 cm

If 18% of q is 27 , what is 27% of 2q

Answers

In this problem, there are two parts. We will need to find what q is if 18% of q is 27, and what 27% of 2q is.

First, let's set up and solve the equation for 18% of q is 27.

18 / 100 = 27 / q

100q = 486

q = 4.86

Next, we'll find the value of 2q.

2(4.86) = 9.72

Finally, we'll set up a proportion and solve for 27% of 2q.

27 / 100 = x / 9.72

100x = 262.44

x = 2.6244

If 18% of q is 27, then 27% of 2q is 2.6244 (round to tenths/hundredths place as needed).

Hope this helps!! :)

Answer:

81

Step-by-step explanation: Let's first find the value of q

[tex]18/100 \times q = 27\\\frac{18q}{100} = \frac{27}{1}\\18q = 2700\\\frac{18q}{18} = \frac{2700}{18} \\q= 150.\\[/tex]

Now we can find 27% of 2q

[tex]27 \% \times 2q = \\27 \% \times 2(150)\\\frac{27}{100} \times 300\\\\= \frac{8100}{100} \\= 81[/tex]

At the shop near the beach, ice cream is offered in a cone or in a cylindrical cup as shown
below. The ice cream fills the entire cone and has a hemisphere on top. The ice cream
levelly fills the cylindrical cup.
radius of cone= 3 cm
radius of cylinder= 4.5 cm
height of cone = 10 cm
height of cylinder = 5 cm
Determine how much more ice cream the larger option has. Show your work. ( 19)

Answers

Answer:

B

Step-by-step explanation:

Select the equation that could represent the relationship between f(x) and g(x).

Answers

Answer:

C

Step-by-step explanation:

First, f(x) and g(x) are mirror image over the x-axis. so add a -ve in front.

Second, f(x) is about 2x steeper than g(x), that is its slope is doubled. so add a 2 in front.

Thus, f(x) = -2 g(x)

What the answer now

Answers

Answer:

  57°

Step-by-step explanation:

There is a right angle at the point of tangency, so the angle of interest is the complement of the one given:

  m∠K = 90° -m∠J = 90° -33°

  m∠K = 57°

the angle of elevation of the top of a tree from a point 27m away on the same horizontal ground as the foot on the tree is 30 degrees .find the height of the tree.

Answers

Answer:

The height of the tree = 15.59m

Step-by-step explanation:

let's make the height of the tree = x

tan30=x/27

x = 27 x tan30

x = 15.59m

Solve the inequality. 12x – 3x + 11 > 4x – (17 – 9x)

Answers

Answer:

20>4

Step-by-step explanation:

12-3 forget about the x 12-3=9 . 9+11=20

(17-9)=8 . 8-4 =4

so your answer is correct

Answer:Subtract 3x from 12x

9 x + 11 > 4 x − ( 17 − 9 x )

 

Simplify  4 x − ( 17 − 9 x ) .

9 x + 11 > 13 x − 17

Move all terms containing  x  to the left side of the inequality.

−4 x + 11 > − 17

Move all terms not containing  x  to the right side of the inequality.

− 4 x > − 28

Divide each term by  − 4  and simplify

x < 7

Interval Notation:

( − ∞ , 7 )

Solve for $x$, where $x > 0$ and $0 = -21x^2 - 11x + 40.$ Express your answer as a simplified common fraction.[tex]Solve for $x$, where $x \ \textgreater \ 0$ and $0 = -21x^2 - 11x + 40.$ Express your answer as a simplified common fraction.[/tex]

Answers

Answer:

[tex]\large \boxed{\sf \ \ \dfrac{8}{7} \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

The solutions are, for a positive discriminant:

   [tex]\dfrac{-b\pm\sqrt{\Delta}}{2a} \ \text{ where } \Delta=b^2-4ac[/tex]

Here, we have a = -21, b = -11, c = 40, so it gives:

[tex]\Delta =b^2-4ac=11^2+4*21*40=121+3360=3481=59^2[/tex]

So, we have two solutions:

[tex]x_1=\dfrac{11-59}{-42}=\dfrac{48}{42}=\dfrac{6*8}{6*7}=\dfrac{8}{7} \\\\x_2=\dfrac{11+59}{-42}=\dfrac{70}{-42}=-\dfrac{14*5}{14*3}=-\dfrac{5}{3}[/tex]

We only want x > 0 so the solution is

   [tex]\dfrac{8}{7}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y + 1 = 0?

4 x + y + 6 = 0
4 x + y - 6 = 0
4 x - y - 6 = 0

Answers

Answer:

The answer is

4x + y - 6 = 0

Step-by-step explanation:

Equation of a line is y = mx + c

where m is the slope

c is the y intercept

4x + y + 1 = 0

y = - 4x - 1

Comparing with the above formula

Slope / m = - 4

Since the lines are parallel their slope are also the same

That's

Slope of the parallel line is also - 4

Equation of the line using point ( 1 , 2) is

y - 2 = -4(x - 1)

y - 2 = - 4x + 4

4x + y - 2 - 4

We have the final answer as

4x + y - 6 = 0

Hope this helps you

PLEASSE HELP
If a line crosses the y-axis at (0, 1) and has a slope of 4/5, what is the equation of the line?
A 4y - 5x=5
B.y - 4x = 5
C. 5y + 4x = 5
D. 5y - 4x = 5

Answers

Answer:

The answer is option D.

Step-by-step explanation:

Equation of the line using point (0, 1) and slope 4/5 is

[tex]y - 1 = \frac{4}{5} (x - 0) \\ \\ 5y - 5 = 4x \\ \\ 5y - 4x = 5[/tex]

Hope this helps you

Answer:

D. [tex]\boxed{5y-4x=5}[/tex]

Step-by-step explanation:

Slope = m = 4/5

y - intercept = b = 1 (As from the point (0,1) , y-intercept is when x = 0)

So, the equation becomes

=> [tex]y = mx+b[/tex]

=> [tex]y = \frac{4}{5} x +1[/tex]

=> [tex]y - \frac{4}{5} x = 1[/tex]

Multiplying both sides by 5

=> [tex]5y-4x = 5[/tex]

dentify which of these types of sampling is​ used: random,​ systematic, convenience,​ stratified, or cluster. To determine her air qualityair quality​, MirandaMiranda divides up her day into three​ parts: morning,​ afternoon, and evening. She then measures her air qualityair quality at 33 randomly selected times during each part of the day. What type of sampling is​ used?

Answers

Answer:

The sampling method used is a stratified sampling method

Step-by-step explanation:

sampling is the selection of a predetermined representative subpopulation from a larger population, to estimate the characteristics of the whole population.

Stratified sampling: Here, the total population are divided into subcategories (strata) before sampling is done. The strata are formed based on some common characteristics. In our example, the times of the day (morning, afternoon and evening) has widely varying atmospheric conditions which will add biases to the measurement of air quality. For example, the air in the morning if compared to the afternoon in an industrial area may be purer because of minimal industrial activity, hence effective comparison will be made by stratification.

From the top of a vertical cliff 75.0m high, forming one bank of a river, the angles of depression of the top and bottom of a vertical cliff which forms the opposite bank are 22° and 58° respectively. Determine the height of the second cliff and width of the river

Answers

Answer:

a. 46.9 m b. 56.1 m

Step-by-step explanation:

a. Width of the river

The angle of depression of the bottom of the second vertical cliff from the first vertical cliff = angle of elevation of the top of the first vertical cliff from the bottom of the second vertical cliff = 58°.

Since the height of the vertical cliff = 75.0 m, its distance from the other cliff which is the width of the river, d is gotten from

tan58° = 75.0 m/d

d = 75.0/tan58° = 46.87 m ≅ 46.9 m

b. Height of the second cliff

Now, the difference in height of the two cliffs is gotten from

tan22° = h/d, since the angle of depression of the top of second cliff from the first cliff is the angle of elevation of the top of the first cliff from the second cliff = 22°

h = dtan22° = 18.94 m

So, the height of the second cliff is h' = 75.0 - h = 75.0 m - 18.94 m = 56.06 m ≅ 56.1 m

6. Find d.


Please help

Answers

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

The graphed line shown below is y = negative 2 x minus 8. Which equation, when graphed with the given equation, will form a system that has infinitely many solutions? y = negative (2 x + 8) y = negative 2 (x minus 8) y = negative 2 (x minus 4) y = negative (negative 2 x + 8)

Answers

Answer: A y = -(2x+8)

Step-by-step explanation:

The first line is y=-2x-8

Thus, the answer that simplifies to y = -2x-8 is the answer.  

a) y=-(2x+8)

Distribute

y=-2x-8

Because it works, no need to try the others.

Hope it helps <3

Answer:

[tex]\boxed{y = -(2x + 8)}[/tex]

Step-by-step explanation:

For the two lines to have infinite [tex]\infty[/tex] solutions, the two equations must be the same.

First equation : y = -2x - 8

A. y = -(2x + 8)

   y = -2x - 8 correct

B. y = -2(x - 8)

   y = -2x + 16 incorrect

C. y = -2(x - 4)

   y = -2x + 8 incorrect

D. y = -(-2x+8)

    y = 2x - 8 incorrect

y = -2x - 8 and y = -(2x + 8) when graphed are the same, they intersect at infinite points and there are infinite solutions.

The Patel, Lopez, and Russo families all had parties recently. There were 152 adults at the Lopez party. The ratio of adults to children at the Russo party was 5 to 4. What was the ratio of adults to children at the Patel party

Answers

Answer:

[tex]\frac{4}{5}[/tex]

Step-by-step explanation:

The Patel, Lopez, and Russo families all had parties recently. There were 152 adults at the Lopez party. The ratio of adults to children at the Russo party was 5 to 4. What was the ratio of adults to children at the Patel party?

(1) The Russo party had 31 more adults than children, and 47 more adults than did the Patel party.

(2) The Patel party had 40 more children, though 4 fewer people in total, than did the Lopez party, where the ratio of adults to children was 8 to 5.

Answer: Let the number of children in Russo party be x, The Russo party had 31 more adults than children, therefore the number of adults at the Russo party = x + 31. The ratio of adults to children at the Russo party was 5 to 4, we can find the number of children using:

[tex]\frac{5}{4}=\frac{x+31}{x}\\ 5x=4x+124\\x=124[/tex]

The number of children at the Russo party is 124 and the number of adult is 155 (124 + 31).

They  are 47 more adults at the Russo party than the Patel party, the number of adult at the Patel party = 155 - 47 = 108

the ratio of adults to children was 8 to 5 at the Lopez party, There were 152 adults at the party. Let x be the number of children at the Lopez party therefore:

[tex]\frac{8}{5}=\frac{152}{x}\\ 8x=760\\x=95[/tex]

The Patel party had 40 more children than the Lopez, the number of children at the Patel party = 135 (95 + 40).

The ratio of adults to children at the Patel party is [tex]\frac{108}{135} =\frac{4}{5}[/tex]

The real numbers $x$ and $y$ are such that \begin{align*} x + y &= 4, \\ x^2 + y^2 &= 22, \\ x^4 &= y^4 - 176 \sqrt{7}. \end{align*}Compute $x - y.$

Answers

You get everything you need from factoring the last expression:

[tex]x^4-y^4=-176\sqrt7[/tex]

The left side is a difference of squares, and we get another difference of squares upon factoring. We end up with

[tex]x^4-y^4=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)[/tex]

Plug in everything you know and solve for [tex]x-y[/tex]:

[tex]-176\sqrt7=(x-y)\cdot4\cdot22\implies x-y=\boxed{-2\sqrt7}[/tex]

Answer:

-2sqrt(7)

Step-by-step explanation:

Solution:

From the third equation, $x^4 - y^4 = -176 \sqrt{7}.$

By difference of squares, we can write

\[x^4 - y^4 = (x^2 + y^2)(x^2 - y^2) = (x^2 + y^2)(x + y)(x - y).\]Then $-176 \sqrt{7} = (22)(4)(x - y),$ so $x - y = \boxed{-2 \sqrt{7}}.$

Which quadrilaterals have diagonals that are always
perpendicular to each other?

Answers

Answer:

rhombus and square

Answer:

Rhombus and square

Step-by-step explanation:

The quadrilaterals that satisfy this condition are rhombi and squares.

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