Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.

[tex]5\sqrt{2}[/tex]
[tex]\frac{5\sqrt{2} }{2}[/tex]
[tex]5\sqrt{3}[/tex]
[tex]\frac{5\sqrt{3}}{2}[/tex]

Answer:

PY = 14.5

Step-by-step explanation:

The diagonals of a rectangle are congruent and bisect each other, thus

XZ = WY , that is

4x - 1 = x + 7 + x + 7

4x - 1 = 2x + 14 ( subtract 2x from both sides )

2x - 1 = 14 ( add 1 to both sides )

2x = 15 ( divide both sides by 2 )

x = 7.5

Thus

PY = x + t = 7.5 + 7 = 14.5

Step-by-step explanation:

x+7+x+7= 4x-1

2x+14=4x-1

14= 2x-1

15= 2x (divide)

x = 7.5

wp= 7.5cm

not really sure

Answer:

D. sum of these edges is increased by 24 inches -- True

Step-by-step explanation:

Given a cube and its edge is increased by 2 inches.

To study the effect of this increase in the Volume, area of each face, diagonal and sum of edges.

Solution:

Let the side of original cube = a inches.

Formula for volume of cube:

[tex]V =side^3 = a^3[/tex]

If the side is increased by 2 inches, the side becomes (a+2) inches.

So, new volume, [tex]V' = (a+2)^3[/tex]

Using the formula:

[tex](x+y)^3 =x^3+y^3+3xy(x+y)[/tex]

[tex]V' = (a+2)^3 = a^3+8+3\times 2 \times a(a+2)=a^3+8+6a(a+2)[/tex]

So, [tex]V' = V + 8+6a(a+2)[/tex]

Volume increased by 8+6a(a+2) [which is not equal to 8]

So, statement is false:

A. volume is increased by 8 cubic inches  -- False

Each face in a cube is a square.

Area of each face, A = [tex]side^2 = a^2[/tex]

New area, A' = [tex](a+2)^2[/tex]

Using the formula: [tex](x+y)^2 =x^2+y^2+2xy[/tex]

[tex]A' = a^2+4+4a[/tex]

Area increased by 4+4a [which is not equal to 4 sq inches]

B. area of each face is increased by 4 square inches -- False

Diagonal of each face = [tex]a\sqrt2[/tex]

Increase of 2 in the edge:

New diagonal = [tex](a+2)\sqrt2 = a\sqrt2+2\sqrt2[/tex]

So, increase of [tex]2\sqrt2[/tex] not 2.

C. diagonals of each face is increased by 2 inches -- False

There are 12 number of edges in a square.

So sum of all 12 edges  = 12a

When edge is increased by 2, sum of all edges = 12(a+2) = 12a + 24

An increase of 24.

D. sum of these edges is increased by 24 inches -- True

Answer:

[tex]\boxed{y=2x-2}[/tex]

Step-by-step explanation:

Pick values from the table.

When x = 1, y = 0.

The third option seems right.

[tex]y=2(1)-2[/tex]

[tex]y=2-2[/tex]

[tex]y=0[/tex]

True.

Answer:

The correct option is;

D. 6,5

Step-by-step explanation:

TS and TU are midsegments

Segment PR = 18.2

Segment TS = 6.5

Given that TS is the midsegment of PR and PQ, therefore, TS = 1/2×QR

Which gives;

Segment QR = 2×TS = 2 × 6.5 = 13

Segment QR = 13

Given that TU is a midsegment to PQ and QR, we have that QU = UR

Segment QR = QU + UR (segment addition postulate)

Therefore, QR = QU + QU (substitute property of equality)

Which gives;

QR = 2×QU

13 = 2×QU

Segment QU = 13/2 = 6.5

The length of segment QU is 6.5.

Answer:

Step-by-step explanation:

The triangle inequality theorem states that the sum of any two sides of a triangle os greater than the third side.

■■■■■■■■■■■■■■■■■■■■■■■■■■

First triangle:

Let a,b and c be the sides of the triangle:

● a = 10

● b = 20

● c = 30

Now let's apply the theorem.

● a+b = 10+20=30

That's equal to the third side (c=30)

●b+c = 50

That's greater than a.

● a+c = 40

That's greater than b.

These aren't the sides of a triangel since the first inequality isn't verified.

■■■■■■■■■■■■■■■■■■■■■■■■■

Second triangle:

● a = 122

● b = 257

● c = 137

Let's apply the theorem.

● a+b = 379

That's greater than c

● a+c = 259

That's greater than b

● b+c = 394

That's greater than a

So 122,257 and 137 can be sides of a triangle.

■■■■■■■■■■■■■■■■■■■■■■■■■■

The third triangle:

● a = 8.6

● b = 12.2

● c = 2.7

Let's apply the theorem:

● a+b = 20.8

That's greater than c

● b+c = 14.9

That's greater than a

● a+c = 11.3

That isn't greater than b

So theses sides aren't the sides of triangle.

■■■■■■■■■■■■■■■■■■■■■■■■■■

● a = 1/2

● b = 1/5

● c = 1/6

Let's apply the theorem.

● a+b = 7/10

That's greater than c

● a+c = 2/3

That's greater than b

● b+c = 11/30

That isn't greater than a

So these can't be the sides of a triangle.

Answer:

7 sqrt(2)/2 =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin 45 = x/7

7 sin 45 =x

7 sqrt(2)/2 =x

Answer:

[tex]\large \boxed{\mathrm{D. \ \displaystyle \frac{7\sqrt{2} }{2 }}}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trigonometric functions to solve the problem.

[tex]sin \theta = opp/hyp[/tex]

The opposite side to the angle 45 degrees is x and the hypotenuse of the triangle is 7.

[tex]sin 45 = x/7[/tex]

Multiply both sides of the equation by 7.

[tex]7 sin 45 = x[/tex]

Simplify the value.

[tex]\displaystyle \frac{7\sqrt{2} }{2 }=x[/tex]

Answer:

As property of a rectangle:

1. AC = 13

AC = 2 x EC (E is midpoint of AC and BD)

13 = 2 x (3x - 11)

13 = 6x - 22

35 = 6x

x = 35/6 m

2. DB = AC = 13 m( two diagonals are equal)

3. BAE = ABE = 40 degree

4. BDA = 90 - ABE = 90 - 40 = 50 (triangle ABD is a right triangle at A)

5. BC = AD = 5m (two opposite sides are equal)

6. AB = sqrt(BD^2 - AD^2) = sqrt(13^2 - 5^2) = sqrt(144) = 12 m

Perimeter = 2 x (AD + AB) = 2 x (5 + 12) = 2 x 17 = 34 m

7. Area= AD x AB = 5 x 12 = 60 m2

Answer:

When radius is doubled:

Circumference becomes double.

Area becomes four times.

When diameter is doubled:

Circumference becomes double.

Area becomes four times.

Step-by-step explanation:

Given that

Radius of a circle is doubled.

Diameter of circle is doubled.

To study:

The effect on circumference and area on doubling the radius and diameter.

Solution/explanation:

Let us discuss about the formula for circumference and area.

Formula for Circumference of a circle in form of radius:

[tex]C =2\pi r[/tex]

It is a linear equation in 'r'. So by doubling the radius will double the circumference.

Formula for Area of a circle in form of radius:

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

It is a quadratic equation in 'r'. So by doubling the radius will make the area as four times the earlier area.

Testing using example:

Let the initial radius of a circle = 7 cm

Initial circumference = [tex]2 \times \frac{22}{7} \times 7 = 44 cm[/tex]

Initial area = [tex]\frac{22}{7} \times 7 \times 7 =154 cm^2[/tex]

After doubling:

Radius = 14 cm

circumference = [tex]2 \times \frac{22}{7} \times 14 = 88 cm[/tex]   (Twice the initial circumference)

area = [tex]\frac{22}{7} \times 14 \times 14 =616 cm^2[/tex] (4 times the initial area)

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

Formula for Circumference of a circle in form of Diameter:

[tex]C =\pi D[/tex]

It is a linear equation in 'D'. So by doubling the diameter will double the circumference.

Formula for Area of a circle in form of diameter:

[tex]A =\dfrac{1}{4}\pi D^2[/tex]

It is a quadratic equation in 'D'. So by doubling the Diameter will make the area as four times the earlier area.

Testing using example:

Let the initial diameter of a circle = 28 cm

Initial circumference = [tex]\frac{22}{7} \times 28 = 88 cm[/tex]

Initial area = [tex]\frac{1}{4}\times \frac{22}{7} \times 28 \times 28 =616cm^2[/tex]

After doubling:

Diameter = 56 cm

circumference = [tex]\frac{22}{7} \times 56= 176 cm[/tex]   (Twice the initial circumference)

area = [tex]\frac{1}{4}\times \frac{22}{7} \times 56 \times 56 =2464cm^2[/tex] (4 times the initial area)

So, the answer is justified:

When radius is doubled:

Circumference becomes double.

Area becomes four times.

When diameter is doubled:

Circumference becomes double.

Area becomes four times.

Answer:

Hey there!

Part A. This is a proportional relationship because the amount of dollars she earns per hour is constant. We can divide her total income by the number of hours she works to find that she earns 12.50 dollars per hour.

Part B. Joslyn will always earn more money than Kate because she earns more money per hour, and the slope of Joslyn's line is greater.

Let me know if this helps :)

The measure of angle Q in the triangle QMN is 52.83°

An equation is an expression that shows the relationship between two or more variables and numbers.

For a triangle with sides a, b, c and respective opposite angles A, B, C, cosine rule is:

a² = b² + c² - 2bc * cos(A)

In triangle QMN, QM = 18, MN = 17, QN = 20, hence:

17² = 18² + 20² - 2(18)(20) * cos(Q)

Q = 52.83°

The measure of angle Q in the triangle QMN is 52.83°

Find out more on equation at: https://brainly.com/question/2972832

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Answer:

53

Step-by-step explanation:

its rounded

Answer:

Which term is a term in this expression?

Step-by-step explanation:

Which term is a term in this expression?Which term is a term in this expression?Which term is a term in this expression?Which term is a term in this expression?Which in this expression?Which term is a term in this expression?

Answer:

x = 1.5

Step-by-step explanation:

6 - 2x = 3

→ Minus 6 from both sides to isolate -2x

-2x = -3

→ Divide -2 from both sides to isolate x

x = 1.5

Answer:

A. 10.125 minutes

Step-by-step explanation:

A stopwatch measures time to the hundredth of a second. Which of the following quantities is not possible using this measurement tool?

A. 10.125 minutes

B. 10.125 seconds

C. 10.12 seconds

D. 10.1 seconds

The stopwatch measures time to the hundredth of a second.

Option A. Measures the time to thousandth of a minutes

Option B. Measures time to thousandth of a second

Option C measures time to hundredth of a second

Option C measures time to tenth of a second.

Option A. 10.125 minutes is the quantity which is not possible using the stopwatch because it is in MINUTES.

Option B 10.125 seconds can be rounded up to 10.13 seconds (hundredth of seconds).

Answer:

[tex]\Large \boxed{\mathrm{78 \ units^2 }}[/tex]

Step-by-step explanation:

The area of the trapezoid can be found by adding the area of the triangle and the area of the rectangle.

Area of rectangle = base × height = 2 × 12 = 24 units²

Area of triangle = base × height × 1/2

The base is missing for the triangle. Apply Pythagorean theorem to solve for the base.

12² + b² = 15²

b = 9

9 × 12 × 1/2 = 54 units²

Adding the areas.

54 units² + 24 units² = 78 units²

Answer:

its 78 units on khan academy :)))

Step-by-step explanation:

Answer:

1232.000

Step-by-step explanation:

Estimated distance across the river=1,232 meters

Find the approximate distance across the river to

the nearest thousandth of a meter

Note: Thousandth is having 3 values after the decimal point

This means we will round 1,232 meters to the nearest thousandth

1,232 is an whole number and decimal point can only be added at the end like this 1,232.

So we need 3 values after the decimal point.

We must add only values that wouldn't change the original 1,232 meters.

Therefore, zero (0) will be added

1232.000

Is to the nearest thousandth

Answer:

The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2

Step-by-step explanation:

Let the number of mangoes bought by the grocery store be n. Also let the number of mango sold for $3 in one stack be x and the number of mango sold for $6 in the second stack be y.

Therefore:

x + y = z                                  (1)

Also, the mangoes was sold at break even price, that is the cost of the mango and the price it was sold for was the same. Therefore:

Cost of buying = Price it was sold for

The cost of the mango = 5z and the price it was sold for = 3x + 6y

3x + 6y = 5z                            (2)

Substituting z = x + y in equation 1

3x + 6y = 5(x + y)

3x + 6y = 5x + 5y

6y - 5y = 5x - 3x

y = 2x

x / y = 1/ 2 = 1 : 2

The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2

Answer: Hi!

Okay. So this equation we will solve using something called the distributive property. We use the distributive property to multiply the terms inside the parentheses (x and -2) by the term outside and in front of the parentheses (4). First, we would multiply 4 * x, which is 4x. Then, we would multiply 4 * -2, which is -8. Out equation now looks like this:

4x - 8 = 14

Our goal is to isolate the x, so now we'll use inverse operations to remove the -8 from the equation. The inverse operation for subtraction is addition, so we would add 8 to both sides:

4x - 8 = 14

   + 8  + 8

The eights cancel out, so we're left with this equation:

4x = 22

Last step! We're almost done. All we have to do now is divide 4 on both sides; in the term 4x, 4 is being multiplied by x, so the inverse operation would be division.

4x ÷ 4 = x

22 ÷ 4 = 5.5

Our equation now looks like this:

x = 5.5

So, 5.5 is equal to x! This would be your answer!

Hope this helps!

Answer:

2/5 =x

Step-by-step explanation:

4/10 = x/1

4/10 =x

Simplify

2/5 =x

Answer:

x=0.4

Step-by-step explanation:

4/10=0.4

x/1 has to equal 0.4 too

0.4/1

HOPE I HELPED

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DESPERATELY TRYING TO LEVEL UP

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JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

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Answer:

is it 2

Step-by-step explanation:

Answer:

18 feet

Step-by-step explanation:

to find the frame around the widow means need to find the perimeter around the window:

P=2l+2w

P= 2(5+4)

P=18 feet

Answer:

[tex] \boxed{\sf {18}^{2} + {24}^{2} = {x}^{2}} [/tex]

To Find:

Length of hypotenuse of the right triangle i.e. x

Step-by-step explanation:

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

[tex] \therefore [/tex]

[tex] \sf \implies {18}^{2} + {24}^{2} = {x}^{2} [/tex]

Answer:

18²+24²=x²

Step-by-step explanation:

to answer this question you must know Pythagorean theorem

a^ 2+b^2 =c^2

a and b stands for the sides with length 24 and 18 and c stands for the HYPOTENUSE . so the correct answer for the above question is 18²+24²=x²

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

Explanation:

Start with the parent function [tex]y = |x|[/tex]

Replacing x with x-1 shifts the graph 1 unit to the right

Tack a -1 at the end to get [tex]y = |x-1|-1[/tex] which will shift everything down 1 unit.

The vertex started at (0,0) and moved to (1,-1)

Answer:

275 miles

Step-by-step explanation:

I assume all towns are on the same line. Then, town C is 5.5 cm from town A on the map since 3.5 cm + 2 cm = 5.5 cm.

The real distance can be calculated with a proportion.

2/100 = 5.5/x

2x = 5.5 * 100

2x = 550

x = 275

Answer: 275 miles

Answer:

d. appears most

Step-by-step explanation:

Mode is the number that appears the most often in a set of data

Answer:

  range = {5, 2, -1, -4}

Step-by-step explanation:

Maybe you want the corresponding range.

  f({-1, 0, 1, 2}) = 2 -3{-1, 0, 1, 2} = 2 +{3, 0, -3, -6} = {5, 2, -1, -4}

Answer:

  28 inches

Step-by-step explanation:

The point of intersection of the angle bisectors is the incenter. It is the center of a circle tangent to the three sides of the triangle. The circle has radius 2.

In the attached figure, we have labeled the points of tangency D, E, and F. We know that CE and CF are both of length 2, and we know that the points of tangency are the same distance from an external point where the tangents intersect. That means DA = FA and DB = EB.

The perimeter of the triangle is ...

  P = DA +DB +FA +EB +CF +CE

Using the above relations, this can be written as ...

  P = DA +DB +DA +DB +CF +CE = 2(DA +DB) +2(CE)

We are told that AB is 12 inches, so DA +DB = 12 inches. We also know that CE = 2 inches, so the perimeter is ...

  P = 2(12 in) + 2(2 in) = 28 in

The perimeter of triangle ABC is 28 inches.

Answer:

[tex]\huge \boxed{x=30}[/tex]

Step-by-step explanation:

[tex]\sf We \ can \ use \ ratios \ to \ solve.[/tex]

[tex]\displaystyle \frac{45}{27} =\frac{x}{18}[/tex]

[tex]\sf Multiply \ both \ sides \ by \ 18.[/tex]

[tex]\displaystyle \frac{45}{27}(18) =\frac{x}{18}(18)[/tex]

[tex]\sf Simplify \ the \ equation.[/tex]

[tex]\displaystyle \frac{810}{27} =x[/tex]

[tex]30=x[/tex]

Answer:

Step-by-step explanation:

70% of students are female

70/100* 75%= you get your answer

then subtract the percentage of the males and the females and then you get your answer

false. range of [tex] \cos^{-1}(x)[/tex] is $[0,\pi]$