A rectangle is eight inches and diagonal is ten
inches. What's the width of the rectangle?

Answer:

XAE and EAY form a linear pair.

done

DE and XY are perpendicular.

XAE and DAY are vertical angles.

Step-by-step explanation:

This answer explains the mathematical concepts related to angles and lines i.e., vertical angles, perpendicular lines, complementary angles, and linear pair. Vertical angles are equivalent, perpendicular lines intersect at right angles, complementary angles sum to 90 degrees, and a linear pair of angles sum to 180 degrees.

Without the actual diagram presented in your question, I can only provide some general insights into your question which is related to angles and lines. Firstly, vertical angles are the angles opposite each other when two lines intersect. They are always equal.

Secondly, two lines are perpendicular if they intersect at a right angle(90 degrees). In terms of angles, two angles are complementary when they add up to 90 degrees. Finally, a linear pair refers to two angles that are adjacent (share a common vertex and side but have no common interior points) and whose non-common sides are opposite rays, i.e., they add up to 180 degrees.

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Answer:

  [tex]\sqrt{a^2+b^2+16}\text{ units}[/tex]

Step-by-step explanation:

The distance is found using the distance formula:

  [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]

Then the distance from the given point to the origin is ...

  [tex]d=\sqrt{(a-0)^2+(-b-0)^2+(-4-0)^2}\\\\=\boxed{\sqrt{a^2+b^2+16}\ \dots\text{ units}}[/tex]

Answer:

2/15in^2

Step-by-step explanation:

Area of rectangle is given by:

where

A is the area of rectangle

l is the length of the rectangle

w is the width of the rectangle

As per the statement:

a rectangle is 2/5 inches long and 1/3 inches wide

then using area formula we have;

Answer:

the answer is 325

Step-by-step explanation:

Answer:

51 inches of rope?

Step-by-step explanation:

If 17 inches is 1/3 if what he needs, then have 3 of 17 inches of rope which is

= 17 × 3= 51.. so it will be 3/3

Answer:

51 inches

Step-by-step explanation:

Total length of the rope possessed by Todd = 17 inches.

But what he has corresponds to [tex]\[\frac{1}{3}\][/tex]  of his actual requirement.

Let his total requirement be represented by x.

Then [tex]\[\frac{1}{3} * x = 17\][/tex]

Simplifying,

[tex]\[x = 17 * 3\][/tex]

[tex]\[x = 51\][/tex]

Hence the total length of the rope required by Todd is 51 inches which is 3 times what he has currently.

Final answer:

Pedro had 1,482 hits, while Ricky had 1,204 hits. We determined these numbers by setting up a system of linear equations and solving for both players' hits using substitution.

Explanation:

To solve the problem of determining how many base hits teammates Pedro and Ricky had last season, we can set up a system of linear equations. Let's let P represent the number of hits Pedro had, and R represent the number of hits Ricky had. According to the problem, together they had 2,686 hits, so we can write the first equation as:

P + R = 2,686

The second piece of information tells us that Pedro had 278 more hits than Ricky, which gives us the second equation:

P = R + 278

We can substitute the second equation into the first equation to find the value of R:

P = (R + 278)

(R + 278) + R = 2,686

2R + 278 = 2,686

2R = 2,686 - 278

2R = 2,408

R = 1,204

Now, we know Ricky had 1,204 hits. To find out how many hits Pedro had, we substitute R's value back into the second equation:

P = 1,204 + 278

P = 1,482

So, Pedro had 1,482 hits and Ricky had 1,204 hits.

x = 5

Solution:

Given equation is [tex]x+1=\sqrt{5x+11}[/tex].

[tex]\Rightarrow x+1=\sqrt{5x+11}[/tex]

Squaring on both sides of the equation to remove the square root.

[tex]\Rightarrow (x+1)^2=(\sqrt{5x+11})^2[/tex]

[tex]\Rightarrow (x+1)^2=5x+11[/tex]

Using algebraic identity: [tex](a+b)^2=a^2+2ab+b^2[/tex]

[tex]\Rightarrow x^2+2x(1)+1^2=5x+11[/tex]

[tex]\Rightarrow x^2+2x+1=5x+11[/tex]

Combine all terms in one side of the equation.

[tex]\Rightarrow x^2+2x+1-5x-11=0[/tex]

Arrange like terms together.

[tex]\Rightarrow x^2+2x-5x+1-11=0[/tex]

[tex]\Rightarrow x^2-3x-10=0[/tex]

Now solve by factorization.

[tex]\Rightarrow x^2-5x+2x-10=0[/tex]

[tex]\Rightarrow (x^2-5x)+(2x-10)=0[/tex]

Take common terms on left side of the term.

[tex]\Rightarrow x(x-5)+2(x-5)=0[/tex]

Now, take (x – 5) common on both terms.

[tex]\Rightarrow (x+2)(x-5)=0[/tex]

⇒ x + 2 = 0 (or) x – 5 = 0

⇒ x = –2 (or) x = 5

If we put x = –2 in the given equation,

[tex]-2+1=\sqrt{5(-2)+11}[/tex]

[tex]\Rightarrow-1=1[/tex]

It is false. So, x = –2 is not true.

If we put x = 5 in the given equation,

[tex]5+1=\sqrt{5\times5+11}[/tex]

[tex]5+1=\sqrt{36}[/tex]

[tex]\Rightarrow6=6[/tex]

It is true. So, x = 5 is true.

Hence x = 5 is the solution.

Answer:

Her weekly allowance is $8.

Step-by-step explanation:

Let the weekly allowance of Ming is $x.

If she spends half of her weekly allowance playing mini-golf and to earn more money her parents let her wash the car for $5, then the remaining amount of money that she has = [tex](\frac{x}{2} + 5)[/tex] dollars.

Now, given that [tex](\frac{x}{2} + 5) = 9[/tex]

⇒ [tex]\frac{x}{2} = 4[/tex]

⇒ x = $8

Therefore, her weekly allowance is $8. (Answer)

Answer:

n= -2

Step-by-step explanation:

Answer:

2x + 5

Step-by-step explanation:

 Make sure you remember the area of a square with side which is [tex]s^{2}[/tex]. Once you figure that out, you need to find the length of a​ side, make sure you factor the expression of the area as a​ perfect-square trinomial.

 An example of that is...

[tex]a^{2} +2ab+b^{2}[/tex] [tex]= (a +b)^{2}[/tex]

^^key point^^

Break it down and take the length out of the Square of Sum and you should get your answer.

Example: Use Square of Sum and get [tex](2x+5)^{2}[/tex]  then, get rid of parentheses >> 2x + 5 and you should get your answer :)

The length of the Little Drop is unknown. However, the question defines that the Big Drop is twice the length of the Little Drop. The exact length cannot be factually stated without more information.

The question states that the Big drop is twice as long as the little drop. Let's say that the length of Little Drop is represented as 'L'. We don't know the exact length of 'L', but we can say that the length of the Big Drop is twice this, which can be represented as 2L.

Since we don't have a specific measure given for either drops, the exact length of Little Drop can't be determined from the information provided. However, whatever it is, we understand that Big Drop is twice that length.

This question is a good demonstration of relative sizing in Mathematics, where we use one unknown quantity to express the size of another

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Answer:

The answer is -5.

Answer:

mean = -0.25

Step-by-step explanation:

Explanation:-

mean:- The sum of all the observations and then divided the number of observations and it is denoted by 'μ'

given data is -15 , -12 , 8 and 9

Given observations is '4' so n = 4

[tex]mean= \frac{-15-12+8+9 }{4}[/tex]

[tex]mean= \frac{-27+17}{4}[/tex]

[tex]mean = -0.25[/tex]

The mean of given data is - 0.25

The mean of -15, -12, 8, and 9 is calculated by summing the numbers to get -10 and then dividing by 4, leading to a mean of -2.5.

The mean of a set of numbers is calculated by summing up all the numbers and then dividing the total by the count of the numbers. In this case, to find the mean of -15, -12, 8, and 9, you would add these four numbers together and then divide by 4, because there are four numbers in this set.

The calculation would look like this:

(-15) + (-12) + 8 + 9 = -10

To find the mean, you would then divide -10 by the number of values in the set, which is 4:

Mean = -10 / 4 = -2.5

Therefore, the mean of the numbers -15, -12, 8, and 9 is -2.5.

Answer:

200

Step-by-step explanation:

200 × 33% = 66 so

200 is answer

Answer:

A) 200

Step-by-step explanation:

33% of x is 66

33/100 = 66/x

33x = 6600

x = 6600/33

x = 200

The width of the canyon is 315 ft.

An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.

Given that, Jim owns a restaurant on the edge of a canyon. He wants to install a cable car over the canyon. He needs to know the width of the canyon. (please refer to the figure attached)

m ∠ ABC = 180°-80°  (Linear pair)

m ∠ ABC = 100°

In Δ ABC,

∠ A + ∠ B + ∠ C = 180°  (sum of interior angles of a triangle)

∠ A = 180°-(100°+40°)

∠ A = 40°

Since, ∠ A = 40° and ∠ C = 40°

Therefore, ∠ A = ∠ C

Therefore, AB = BC (Side opposite to equal angles are equal)

That means,  Δ ABC is an isosceles triangle

∵ BC = 315 ft

∴ AB = 315 ft

AB is the width of the canyon.

Hence, The width of the canyon is 315 ft.

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Answer:

Therefore,

[tex]y=2x+6[/tex] and

[tex]6y=2x+9[/tex] are not Perpendicular.

Step-by-step explanation:

Given:

[tex]y=2x+6[/tex]         ............................Equation of line( 1 )

[tex]6y=2x+9\\y=\dfrac{1}{3}+\dfrac{3}{2}[/tex]     ............................Equation of line( 2 )

Solution:

So the Equations are written in

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

Where m is the slope of the line

On Comparing we get

[tex]Slope = m1 = 2[/tex]

[tex]Slope = m2 = \dfrac{1}{3}[/tex]

So for the lines to be Perpendicular.

Product of slopes = - 1

m1 × m2 = -1

So Product of slopes of the given lines are

[tex]m1\times m2=2\times \dfrac{1}{3}=\dfrac{2}{3}[/tex]

Which is not equal to -1

Therefore,

[tex]y=2x+6[/tex] and

[tex]6y=2x+9[/tex] are not Perpendicular.

Answer:

Step-by-step explanation:

A linear expression has the highest power of the variable to 1, i.e ax+b

Then only the first option is in a linear expression format

9x-2

The linear expression from the given options is 9x - 2.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given are four expressions consisting of variable x.

Linear expressions are those expressions for which the highest degree of the variable in the expression is 1.

Look at the expressions with the power of the variable equals one and no other term in the expression has power of the variable more than 1.

The expression is 9x - 2.

In 3x² + 4x - 5, the highest degree of the variable is 2.

In 5x³ + 6x² - 7x + 8, highest degree of the variable is 3.

In 4x⁴ - 5x³ + 6x² - 7x + 8, highest degree of the variable is 4.

Hence the linear expression is 9x - 2.

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Answer: 9.84 x 10²

Step-by-step explanation: To write 984 in scientific notation, first write a decimal point in the number so that there is only one digit to the left of the decimal point.

So here we have 9.84.

Next, count the number of places that we would need to move the decimal point in 9.84 in order to get back to the original number, 984.

Since we would need to move the decimal point two places to the right to get back to the original number, we have an exponent of 2.

Notice that our exponent is positive because we would need to move the decimal point to the right.

Now, scientific notation is always expressed as a power of 10. In this case, we have 10 to the 2nd or 10 to the 2nd power.

So 984 can be written in scientific notation as 9.84 x 10².

Answer:

A

Step-by-step explanation:

A horizontal translation of - 3 means to subtract 3 from the original x- coordinate.

A vertical translation of - 3 means to subtract 3 from the original y- coordinate, thus

M(2, 2 ) → M'(2 - 3, 2 - 3 ) → M'(- 1, - 1 ) → A

Answer:

21 feet (20.977)

Step-by-step explanation:

1. Draw a picture, it makes it much easier. Draw a right triangle with the vertical labeled 25 and the horizontal labeled X, then label the angle adjacent to the horizontal and hypotenuse 40°

2. Use tangent because X is opposite of 40 and 25 is adjacent to angle 40. the equation would be Tan40/1 = X/25

3. You then cross multiply to get 25Tan(40) = X

4 You then plug it into a calculator and get the full answer of 20.97749078, but I always round up to either 20.98 or 21 feet, whatever your teacher allows

Answer:

18 servings each pint being 1/3 serving size that 3 servings per pint 3×6 =18

1 second = 2 megabytes

[tex]1\frac{1}{2}\ seconds=3\ megabytes[/tex]

2 seconds = 4 megabytes

Step-by-step explanation:

Given,

Time taken to download 5 megabytes = [tex]2\frac{1}{2}=\frac{5}{2}[/tex] seconds

[tex]\frac{5}{2}\ seconds = 5\ megabytes[/tex]

Multiplying both sides by [tex]\frac{2}{5}[/tex] to find unit rate

[tex]\frac{2}{5}*\frac{5}{2}\ second = \frac{2}{5}*5\\1\ second = 2\ megabytes[/tex]

1 second = 2 megabytes

[tex]1\frac{1}{2}\seconds = \frac{3}{2}\ seconds[/tex]

[tex]\frac{3}{2}\ seconds = \frac{3}{2}*2[/tex]

[tex]\frac{3}{2}\ seconds = 3\ megabytes[/tex]

[tex]1\frac{1}{2}\ seconds=3\ megabytes[/tex]

2 seconds = 2*2 megabytes

2 seconds = 4 megabytes

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Answer: 7.6, 22/7, 1.01

Step-by-step explanation:

c = (x + 3)^2

Step-by-step explanation:

(6/2)^2 = (36/4)

           = 9

=x^2 + 6x + 9

= (x + 3)(x + 3)

c = (x + 3)^2

Answer:

27 paper fortune tellers

Step-by-step explanation:

fortune tellers = time

3 = 6

6 = 9

9 = 12

12 = 15

15 = 18

18 = 21

21 = 24

24 = 27

27= 30

so 30 fortune tellers will be made in 30 minutes

hope this helps!!!

Answer:

Actually, it's 25 paper fortune tellers.

Step-by-step explanation:

15 = 18

15 divided by 3 = 18 divided by 3

5 = 6

5 x 5 = 6 x 5

25 = 30

Answer: Dilation by a scale factor of 0.75

Step-by-step explanation:

Answer:

Cost per Apple is $0.75

Step-by-step explanation:

Step 1:  Divide cost by the apples

$6.00 / 8 = x

$0.75 = x

Cost per Apple is $0.75

Answer:

0.75

Step-by-step explanation:

Just divide $8.00 by $6.00

Answer:

20%

Step-by-step explanation:

If there are 25 marbles in the bag and 5 of them are red then you just divide 25 by 5 which is 5 which is 1/5 the 25 witch 20%

Answer:

20%

Step-by-step explanation:

Nice seeing you a year later <3

[tex]\boxed{-2\left(z+5\right)+20>6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:z<2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:2\right)\end{bmatrix}}[/tex]

Solution:

Given inequality is:

[tex]-2(z+5)+20>6[/tex]

We have to solve the given inequality

[tex]-2\left(z+5\right)+20>6\\\\\mathrm{Subtract\:}20\mathrm{\:from\:both\:sides}\\\\-2\left(z+5\right)+20-20>6-20\\\\\mathrm{Simplify}\\\\-2\left(z+5\right)>-14[/tex]

[tex]Multiply\ both\ sides\ by\ -1\ \left(reverse\:the\:inequality\right)[/tex]

Whenever we multiply or divide an inequality by a negative number, we must flip the inequality sign

[tex]\left(-2\left(z+5\right)\right)\left(-1\right)<\left(-14\right)\left(-1\right)\\\\\mathrm{Simplify}\\\\2\left(z+5\right)<14\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{2\left(z+5\right)}{2}<\frac{14}{2}\\\\\mathrm{Simplify}\\\\z+5<7\\\\\mathrm{Subtract\:}5\mathrm{\:from\:both\:sides}\\\\z+5-5<7-5\\\\simplify\ the\ above\\\\\boxed{z < 2 }[/tex]

Thus the solution to inequality is:

[tex]-2\left(z+5\right)+20>6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:z<2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:2\right)\end{bmatrix}[/tex]