Find the value of each variable. Round your answers to the nearest tenth. (Soh Coh Toa)

Answer:

[tex]85\:\mathrm{units^2}[/tex]

Step-by-step explanation:

All side lengths of a square are equal. The three squares create a right triangle, and the hypotenuse of this triangle represents the side length of the square.

All right triangles must follow the Pythagorean Theorem [tex]a^2+b^2=c^2[/tex] where [tex]c[/tex] is the hypotenuse of the triangle.

Therefore, let [tex]h[/tex] be the side length of this largest square. Since the area of a square with side length [tex]s[/tex] is given by [tex]s^2[/tex], [tex]h^2[/tex] will represent the area of the square:

[tex]\sqrt{35}^2+\sqrt{50}^2=h^2=\boxed{85\:\mathrm{units^2}}[/tex]

Answer:

85

Step-by-step explanation:

We can use the Pythagorean theorem (a^2+b^2=c^2) to find the area of square adjacent to the third side.

Area of a square=side^2

So, we can substitute the areas of the squares that share side lengths with the triangle for a^2, b^2, and c^2 in the Pythagorean theorem.

For example, in the diagram above, the area of the square that shares a side with side length a is 35 square units. So, a^2=35.

Let's fill in the remaining values:

a^2 + b^2 = x^2

35+50-x^2
85=x^2
The area of the square adjacent to the third side of the triangle is 85 units^2.

Answer:

The formula for finding the volume of a rectangular prism is the following: Volume = Length * Height * Width, or V = L * H * W. Ex: V = 5 in.

Hi there!

[tex]\large\boxed{\text{Gradient = -1}}[/tex]

We can find the slope using the slope formula:

Slope = (y2-y1)/(x2-x1)

Plug in the given coordinates:

Slope = (1 - 5)/(7 - 3)

Simplify:

Slope = -4/4

Slope = -1

Answer:

29,800

Step-by-step explanation:

that will be 149 x 2 which equals 298

149

 ×2         Multiply 9 × 2 = 18

------        Keep the 8 carry the 1 multiply 4 by 2 then add 1 finally multiply 2 by 1

298

Then add two zeros at the end since we're multiplying a number with two zeros. (This method only works for numbers that end with zeros)

Final answer: 29800

Answer: 1,2,3,5,6, and 10

Step-by-step explanation:

Answer:

F=0.46N

Step-by-step explanation:

[tex]F[/tex]∝[tex]\frac{1}{d^{2}}[/tex],

[tex]F=\frac{k}{d^{2} } \\[/tex]

[tex]F=0.35N, d=8m\\[/tex]

[tex]0.35=\frac{k}{8^{2} }[/tex]

[tex]k=0.35\times 8^{2} \\\\k=22.4\\F=\frac{22.4}{d^{2} } \\d=7m, F=\frac{22.4}{7^{2} } =0.46N[/tex]

Answer:

1) 40

2) 118

3) 71

Step-by-step explanation:

3) is the easiest. All interior angles add to 180

Angle 3 = 180 - 62 - 47

Angle 3 = 71

2) Angle 2 is on the same straight line as 62 and together they equal 180

Angle 2  = 180 - 62

Angle 2 = 118

1) Using 22, Angle 2 and the knowledge that all interior angles equal 180

180 - 22 - 118 = Angle 1

40 = Angle 1

Answer:

12 additional sticks of butter

Step-by-step explanation:

First, create an equation. Let y represent the number of additional sticks of butter needed, and let x represent the number of cakes made.

y = [tex]\frac{x}{2}[/tex] will be the equation.

Since she has already baked 17 cakes, she will need to bake 24 more cakes to make 41 cakes.

Plug in 24 as x into the equation, and solve for y:

y = [tex]\frac{x}{2}[/tex]

y = [tex]\frac{24}{2}[/tex]

y = 12

So, she will need 12 additional sticks of butter

Answer:

[tex]L=1+20i[/tex]

[tex]B=3+20i[/tex]

Step-by-step explanation:

From the question we are told that:

Area [tex]A=440cm^2[/tex]

Generally the equation for For Area is mathematically given by

 [tex]A=L*B[/tex]

 [tex]A=x*(x-2)[/tex]

Therefore

 [tex]x^2-2x-440=0[/tex]

 [tex]x=1+20i[/tex]

Therefore The Dimensions are

  [tex]L=1+20i[/tex]

 [tex]B=1+20i+2[/tex]

 [tex]B=3+20i[/tex]

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

start by squaring both sides:

[tex](\sqrt{-8+3x} )^2=(2)^2[/tex]

squaring a square root cancels it out:

[tex]-8+3x = 4[/tex]

solve for x by first adding 8 to both sides:

[tex]3x=12[/tex]

then divide both sides by 3:

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

Answer:

16

Step-by-step explanation:

mark it as the Brainliest

Answer:

The dependent variable is y (the amount paid)

Step-by-step explanation:

Given

[tex]y = 5x[/tex]

Where

[tex]x \to[/tex] number of movies

[tex]y \to[/tex] amount paid

Required

The dependent variable

From the question, we have:

[tex]y = 5x[/tex]

This means that the value of y is determined by the value of x.

Take for instance:

[tex]x = 2[/tex]

The value of y will be:

[tex]y =5*2 = 10[/tex]

If x changes (say; x = 12), y will also change

[tex]y =5*12 = 60[/tex]

Hence, y is the dependent variable

Answer:

-168

Step-by-step explanation:

because  f(x) = 8 - 10xg(x) = 5x + 4

(fg)(x) = (8 - 10x)(5x + 4)(fg)(x) = 40x + 32 - 50x^2 - 40x(fg)(x) = 32 - 50x^2

(fg)(-2) = 32 - 50(-2)^2(fg)(-2) = 32 - 200(fg)(-2) = -168

Answer:

253 miles

Step-by-step explanation:

Ratio:

115:5 and x:11

Method 1:

115/5 = x/11

1265 = 5x                     (cross multiplying)

x = 253 miles

Method 2:

11/5 = 2.2

2.2 x 115 = 253

253 miles

Method 3:

115 / 5 = 23

23 x 11 = 253

253 miles

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

√73

Step-by-step explanation:

d = √(x2 - x1)² + (y2 - y1)²

√[-6 - (-3)]² + (-7 - 1)²

√(-3)² + (-8)²

√(9) + (64)

√73

8.5

Answer:

Step-by-step explanation:

25 x 6/5 = 30

Answer:

1

Step-by-step explanation:

The mode is the number that appears most often

1 appears twice in the data list and that is the mode

Answer:

Step-by-step explanation:

The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!

Answer:

3 + ( -7 )

7 - 3

= 4 is the answer

Answer: 9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Nice to see someone from Canada asking a question.

Set up a proportion

4/24 = x/54            Cross Multiply

4*54 = 24*x           Combine the left  

216 = 24x               Divide by 24

x = 216/24

x = 9

She should expect 9 prizes

Answer:

(i) interest = $1680

(ii) total amount = 13680

Step-by-step explanation:

Interest.

12000 × 14/100

=168000/100

=1680

Total amount.

Interest + Loan

1680 + 12000

=13680

Answer:

Step-by-step explanation:

If the diagonals of the rectangle are congruent,

AC = BD

By using formula to calculate the distance between two points,

Distance between two points = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance between A(0, -3) and C(2, 8),

AC = [tex]\sqrt{(8+3)^2+(2-0)^2}[/tex]

     = [tex]\sqrt{125}[/tex]

     = [tex]5\sqrt{5}[/tex]

Similarly, distance between two points B(-4, 0) and D(6, 5),

BD = [tex]\sqrt{(5-0)^2+(6+4)^2}[/tex]

     = [tex]\sqrt{125}[/tex]

     = [tex]5\sqrt{5}[/tex]

Therefore, both the diagonals are congruent.

Hence, given quadrilateral ABCD is a rectangle.

Answer:

x=40

Y= 35

Angle AEC= 55

Step-by-step explanation:

Answer:

[tex]x = 40 \\y = 35 \\\angle AEC = 55^\circ[/tex]

Step-by-step explanation:

Find x :

[tex]( 3x + 5)^{\circ} + ( x +15)^{ \circ} = 180 ^{\circ}[/tex]                    [tex][ \ straight \ line \ angles \ ][/tex]

[tex]3x + 5 + x + 15 = 180\\\\4x + 20 = 180 \\\\4x = 160 \\\\x = 40[/tex]

[tex]\angle AED \ = 3x + 5 = 125 ^{ \circ}[/tex]

[tex]\angle DEB = (x + 15 ) = 40 + 15 = 55^{ \circ}[/tex]

Find y :

[tex]( y + 20)^{ \circ} + (4y - 15)^{ \circ} = 180^{\circ}\\\\y + 20 + 4y - 15 = 180\\\\5y + 5 = 180\\\\5y = 175\\\\y = 35[/tex]

[tex]\angle AEC = ( y + 20 ) = 35 + 20 = 55^\circ\\\\\angle BEC = (4y - 15) = 4(35) -15 = 140 - 15 = 125^\circ[/tex]

Answer:

No solution

Step-by-step explanation:

x = -5 +- √5^2 -4 x 2 x 4/ 2 x 2

x = -5 +- √-7/4

d = -7

The square root can't be a negative number so it is no solution.

Answer:

1/3+(-1)

Step-by-step explanation:

Answer:

i think its c

Step-by-step explanation:

Answer:

Charlene claim is true.

Step-by-step explanation:

Max claims that a point on any line that is perpendicular to a segment is equidistant from a segment's endpoints.

It is not necessary as  shown in the diagram (a).

Charlene claims that the line must be a perpendicular bisector for a point on the line to be equidistant from a segment's endpoints.

It is true as shown in the diagram (b).

So, Charlene claim is true.

Answer:

y = 4 x + 24 i think thats the answer if not im sorry

Step-by-step explanation:

Answer:

3^6, 3^-4 * 3^10, 3^3 * 3^3, and (3*3) * (3*3*3*3) are the answers that are equivalent!

Step-by-step explanation:

These four are correct:-

Answer:

I think it is option 1

Step-by-step explanation:

11/4 x 1/2

[tex]\frac{11 *1}{4 * 2} = \frac{11}{8}[/tex]

which would equal: [tex]1\frac{3}{8}[/tex]

I might be wrong.