The sandbox at a local playground is shaped like a square. The length of one side of the sandbox is 8 feet. What is the area of the sandbox, written as an expression with exponents? 24 ft² 28 ft² 8² ft² 88 ft²

Answer:

m∠A=m∠D=60°, m∠B=m∠C=120°

Step-by-step explanation:

Consider isosceles trapezoid ABCD with midsegment MN. Draw two trapezoid heights BF and CE. Then quadrilateral FBCE is rectangle and EF=BC=17 units.

By the trapezoid midsegment theorem,

[tex]MN=\dfrac{AD+BC}{2},\\ \\30=\dfrac{AD+17}{2},\\ \\60=AD+17,\\ \\AD=60-17=43\ units.[/tex]

Segments FA and ED are equal to [tex]\dfrac{43-17}{2}=13\ units.[/tex]

In right triangle ABF, the hypotenuse AB is twice greater than the leg FA, then m∠FBA=30°.

m∠B=m∠FBA+m∠CBF=30°+90°=120°.

In isosceles trapezoid

m∠B=m∠C=120°,

m∠A=m∠D and m∠A=180°-m∠B=180°-120°=60°=m∠D.

In a trapezoid with equal bases and a midsegment, the angle measures of the trapezoid can be determined using the properties of the figure. In this case, the angle measures are 90 degrees for each angle.

In a trapezoid ABCD, the midsegment MN is parallel to the bases AB and CD, and its length is equal to the average of the lengths of the bases. Given that AB = 26, CD = 26, and MN = 30, we can set up the equation: MN = (AB + CD) / 2. Substituting the given values, we get 30 = (26 + 26) / 2. Solving for the angle measures, we can use the fact that the opposite angles in a trapezoid are congruent. So, m∠A = m∠C and m∠B = m∠D. Since the sum of the interior angles of a trapezoid is always 360 degrees, we can use the equation: m∠A + m∠B + m∠C + m∠D = 360. Substituting the angle measures we found, we get 2(m∠A) + 2(m∠B) = 360. Solving for the angle measures, we get m∠A = m∠C = 90 degrees and m∠B = m∠D = 90 degrees.

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Answer:

2 minutes 40 sec

Step-by-step explanation:

Recall that distance = rate times time.

Thus, time = distance / rate.

Here,

time = 280 ft / (1.75 ft/sec) = 160 sec, or 2 minutes 40 sec

To calculate the time it takes to travel 280 feet on a moving walkway at an airport moving at a pace of 1.75 feet per second, we use the formula time = distance/pace. This equates to approximately 160 seconds.

The question is asking about the time it takes to transport someone along a distance of 280 feet by a moving walkway in an airport, given that the pace of the walkway is 1.75 feet per second. To answer this, you use the formula of time = distance/pace. So we have time = 280 feet / 1.75 feet per second. This calculation will give you the answer in seconds. When you do this calculation, you will find that it takes approximately 160 seconds to cover that distance on the moving walkway.

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Answer:

Alright well Convert fraction to an decimal, then multiply by 100

0.02714285% Hope this helps have a nice day :)

Step-by-step explanation:

Answer:

Y= -3

Step-by-step explanation:

5y-10=-25     Add 10 on both sides

5y=-15      Divide by 5 on both sides

y=-3

Answer:

sooo sorry im in the third grade and notised that this is not my onw level but i really thought i could help u sorry ;(

Step-by-step explanation:

Answer:

The slope is 3

Step-by-step explanation:

To find the slope we can use the formula

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

Using the points (5,14) and (-5,-16)

m= (-16-14)/ (-5-5)

  = -30/-10

 = 3

Answer:

21 ft

Step-by-step explanation:

Diameter = Circumference/Pi

Diameter = 66/(22/7)

Diameter = 21

Answer:

(- 3, 0), (2 + [tex]\sqrt{2}[/tex], 0), (2 - [tex]\sqrt{2}[/tex], 0)

Step-by-step explanation:

rearrange the equation equating to zero

x³ - x² - 10x + 6 = 0

note that when x = - 3

(- 3)³ - (- 3)² - 10(- 3) + 6 = - 27 - 9 + 30 + 6 = 0, hence

x = - 3 is a root and (x + 3) is a factor of the polynomial

dividing x³ - x² - 10x + 6 ÷ (x + 3) gives

(x + 3)(x² - 4x + 2) = 0

solve x² - 4x + 2 = 0 using the quadratic formula

with a = 1, b= - 4 and c = 2

x = (4 ± [tex]\sqrt{16-(4(1)(2)}[/tex])/ 2

  = (4 ± [tex]\sqrt{8}[/tex]) / 2

  = (4 ± 2[tex]\sqrt{2}[/tex]) / 2

  = 2 ±[tex]\sqrt{2}[/tex], hence

x = 2 + [tex]\sqrt{2}[/tex], x = 2 - [tex]\sqrt{2}[/tex]

intersect at (- 3, 0), (2 +[tex]\sqrt{2}[/tex], 0), (2 - [tex]\sqrt{2}[/tex], 0)

Answer: [tex]\bold{x=-3,\quad x=2+\sqrt{2}, \quad x=2-\sqrt{2} }}[/tex]

Step-by-step explanation:

First, move all terms to one side with zero on the other side so the Zero Product Property can be applied:

x³ - x² - 10x + 6 = 0    Possible rational roots are: ±{1, 2, 3, 6}

Use synthetic division to find one of the roots.  Let's try x = -3

-3 |  1    -1    -10    6

   |  ↓   -3    12    -6

      1    -4     2     0  ← remainder is zero, so x = -3 is a root/intercept

Next, evaluate the reduced polynomial x² - 4x + 2 = 0

This can not be factored so use the quadratic formula to find the remaining roots/intercepts: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

a = 1, b = -4, c = 2

[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(2)}}{2(1)}[/tex]

 [tex]=\dfrac{4\pm\sqrt{16-8}}{2}[/tex]

 [tex]=\dfrac{4\pm\sqrt{8}}{2}[/tex]

 [tex]=\dfrac{4\pm2\sqrt{2}}{2}[/tex]

 [tex]=2\pm\sqrt{2}[/tex]

[tex]x=2+\sqrt{2}\qquad x=2-\sqrt{2}[/tex]

Intercepts are [tex]x=-3,\quad x=2+\sqrt{2}, \quad x=2-\sqrt{2}}[/tex]

Answer:

They drove 300 miles on the first day

Step-by-step explanation:

They drove 1200 miles

They drove 1/4 on the first day

1200 * 1/4 = 300 miles

They drove 300 miles on the first day

Answer:

C) ∠6 and ∠7

Step-by-step explanation:

We have been given that lines a and b are parallel. We are asked to find the angle on line b that will be congruent to angle 3.

We can see that angle 3 is under the line a and on the left side of transversal.

We know that the corresponding angles and alternate interior angles formed by two parallel lines are equal.

We can see that angle 7 corresponds to angle 3 and angle 6 is alternate interior angle of angle 3.

Therefore, angle 7 and angle 6 will be congruent with angle 3 and option C is the correct choice.

Answer:

1. y = 2/3 x +2

2.  y = -x -8

Step-by-step explanation:

The slope intercept form of a line is y = mx+b where m is the slope and b is the y intercept

1. y = 2/3 x +2

2.  y = -x -8

ANSWER:

1. y = 2/3x + 2

2. y = -1x + -8

ABOUT SLOPE INTERCEPT FORM:

Hope this helps you!!! :)

Answer:

Option B is correct.

Value of cos(a+B) is,  [tex]\frac{16}{65}[/tex]

Step-by-step explanation:

Using the formula:

[tex]\cos(a+B) = \cos a \cos B -\sin a \sin B[/tex]

Given the values:

[tex]\cos a = \frac{3}{5}[/tex] and [tex]\sin B = \frac{5}{13}[/tex]

Using trigonometric identity:

[tex]\sin^2 \theta + \cos^2 \theta =1[/tex]

or

[tex]\sin \theta = \sqrt{1-\cos^2 \theta}[/tex]

or

[tex]\cos \theta = \sqrt{1-\sin^2 \theta}[/tex]

Find the value of sin a and cos B;

Using trigonometric identity:

[tex]\sin a = \sqrt{1-\cos^2 a}[/tex]

[tex]\sin a = \sqrt{1-(\frac{3}{5})^2}[/tex] = [tex]\sqrt{1-\frac{9}{25}} = \sqrt{\frac{25-9}{25}}=\sqrt{\frac{16}{25} } =\frac{4}{5}[/tex]

Similarly;

[tex]\cos B = \sqrt{1-\sin^2 B}[/tex]

[tex]\cos B = \sqrt{1-(\frac{5}{13})^2}[/tex] = [tex]\sqrt{1-\frac{25}{169}} = \sqrt{\frac{169-25}{169}}=\sqrt{\frac{144}{169} } =\frac{12}{13}[/tex]

Substitute these given values equation [1] we have;

[tex]\cos(a+B) =\frac{3}{5} \cdot \frac{12}{13}-\frac{4}{5} \cdot \frac{5}{13}[/tex]

[tex]\cos(a+B) =\frac{36}{65}-\frac{20}{65}[/tex]

then;

[tex]\cos(a+B) =\frac{36-20}{65}=\frac{16}{65}[/tex]

Since, the angles a and B are in first quadrant angles therefore the value of cos(a+B) is, [tex]\frac{16}{65}[/tex]

To find cos(a + B), use the formula cos(a + B) = cos(a)cos(B) - sin(a)sin(B). Substitute the given values of cos(a) = 3/5 and sin(B) = 5/13, and solve for cos(B) using the Pythagorean identity. Then substitute all the values into the formula and simplify to find cos(a + B) = 16/65.

To find cos(a + B), we can use the formula:

cos(a + B) = cos(a)cos(B) - sin(a)sin(B)

Given that cos(a) = 3/5 and sin(B) = 5/13, we can substitute these values into the formula:

cos(a + B) = (3/5)(cos(B)) - (sin(a))(5/13)

To find cos(B), we can use the Pythagorean identity:

cos²(B) + sin²(B) = 1

Substituting the given value of sin(B), we can solve for cos(B):

cos(B) = √(1 - (5/13)²)

Now we can substitute the values of cos(a), sin(B), and cos(B) into the formula for cos(a + B):

cos(a + B) = (3/5)(√(1 - (5/13)²))) - (5/13)(5/13)

Simplifying this expression gives us the final answer: cos(a + B) = 16/65.

Answer:

-21

Step-by-step explanation:

3(-7)

3*7 =21

A positive times a negative is a negative

-21

Answer:

3x-7=21 ( i think )

Step-by-step explanation:

when you have a parenthesis beside a number you always multiply. A negative times a positive is a negative,

Answer:

It will take 12 minutes

Step-by-step explanation:

We can use ratio's to solve the problem

2/3 mile          1 miles

------------   = ------------------

8 minutes      x minutes

Using cross products

2/3 * x = 8*1

Multiply each side by 3/2 to isolate x

3/2 * 2/3 x = 3/2 * 8

x = 12

Answer:

78

Step-by-step explanation:

Answer in #1 it ads up by 8

Number 1 is Add by 8

& I'm not sure about number 2

This question is asking us to find the sum.

8,792 + 9,491 + 9,629 =  27, 912

They lay 27, 912 bricks in all.

Hope helps!-Aparri

Answer: Three bricklayers from the Emerald Construction Company are working on the new addition to an office building. The first bricklayer laid 8,792 bricks; the second laid 9,491 bricks; and the third laid 9,629 bricks this week. They lay a total of 8,792 + 9,491 + 9,629 = 27, 912 bricks.

Step-by-step explanation:

First Brick Layer Laid: 8,792

Second Brick Layer Laid: 9,491

and lastly the

Third Brick Layer Laid 9,629

Now if you take all the bricks that each Brick layer has laid and add them all up (break down)

8,792+9,491+9,629= 27,912 bricks laid in all

that's the break down I hope this helps you all

Answer:

x= 6.6

LM= 33

MN= 17.2

LN=50

Step-by-step explanation:

10x-16= 5x+2x+4 (LN=LM+MN)

10x-16=7x+4

3x-16=4

3x=20

x=6.6

then plug 6.6 back into equation and round to the nearest whole number.

Answer: Inconsistent

Step-by-step explanation:

y = 3x + 4   → m = 3, b = 4

y = 3x + 3   → m = 3, b = 3

These equations have the same slope but different y-intercepts so they are parallel lines which means they will never intersect.

NOTES

Answer:

Inconsistent

Step-by-step explanation:

Answer:

8 teams

5 girls and 4 boys

Step-by-step explanation:

To determine how many teams we can have , we need to determine the greatest common factor.

 girls:40 = 5*8

boys:32 = 4*8

The greatest common factor is 8

So we will have 8 teams

There will be 5 girls and 4 boys on each team

Jeff's net pay is $1,065.70 per week.

To calculate Jeff Jones's net pay, we need to consider several deductions from his gross pay.

1. Gross Pay: Jeff earns $1,200 per week.

2. Social Security Deduction: Social Security tax is 6.2% of the first $118,500 of earnings. Jeff's earnings are below this threshold, so his Social Security deduction is 6.2% of his gross pay.

Social Security deduction = 6.2% of $1,200 = 0.062 * $1,200 = $74.40

3. Medicare Deduction: Medicare tax is 1.45% of all earnings.

  Medicare deduction = 1.45% of $1,200 = 0.0145 * $1,200 = $17.40

4. Health Insurance Deduction: $42.50 is deducted for health insurance.

5. Total Deductions: Add up all deductions.

Total deductions = Social Security deduction + Medicare deduction + Health insurance deduction

= $74.40 + $17.40 + $42.50

= $134.30

6. Net Pay: Subtract total deductions from gross pay.

Net pay = Gross pay - Total deductions

= $1,200 - $134.30

= $1,065.70

Therefore, Jeff's net pay is $1,065.70 per week.

Answer:

It is NOT a right triangle.

Step-by-step explanation:

You must figure out the slopes of the segments of the triangle to see if it is a right triangle. If they are perpendicular (meaning the slopes are negative reciprocals of each other), they form a right angle, making it a right triangle.

[tex]\frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex] This formula finds slope using two points.

Let's figure out the slope of JK.

(-1-1)/(-5-0) = m

Simplify.

-2/-5 = m

A negative divided by a negative makes a positive.

2/5 = m

Now LK.

(-5-1)/(2-0) = m

Simplify.

-6/2 = m

Divide.

-3/1 = m

Now JL.

(-1+5)/(-5-2) = m

Simplify.

4/-3 = m

None of these slopes are negative reciprocals of each other, thus deeming it not a right triangle.

Answer:

4X + 30 = TOTAL AMOUNT OF MONEY

Step-by-step explanation:

All of them bought a ride ticket (that explains the 4x)

3 of them also bought a game pass thet costs $10 each. That explains the 30

going deeper: If the total amount of money was $70

The tickets would've costed $10 each.

Look:

4x + $30 = $70

4x = 70 - 30

4x = 40

x = 40/4

x =$10

Answer:

D. 7 1/5

Step-by-step explanation:

We would calculate the amount of pounds she used by multiplying the total amount of cat food = 9 to the amount she has used = 4/5

= [tex]9 * \frac{4}{5}[/tex]

= [tex]\frac{36}{5}[/tex]

= [tex]7 \frac{1}{5}[/tex]

(An image is attached for the calculation)

The inequality y ≥ x^2-4 satisfies (0,0) but the inequality y < 2x-1

does not satisfy (0,0).  

          Substitute (x,y)=  (0,0) in the above inequality

                                   0 ≥ (0^2)-4

                                         0 ≥ -4

              The above inequality is true.

             Hence, (0,0) is the solution of inequality (i)

          Substitute (x,y)=  (0,0) in the above inequality

                                0 < 2(0) - 1

                                0 <  -1

                The above inequality is not true.

          Hence (0,0) does not satisfy the above inequality (ii).

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Answer:  Total: 30 + 20y + 85 + 17y  This is the not simplified version.

37y+115 This is the simplified version. Hope this helps

Step-by-step explanation: I really don't know the steps.?

Answer:

The sale price is $13.43

Step-by-step explanation:

In order to find the sale price of an item, we multiply it by the remaining percentage of cast left. Since we are subtracting 44% of the cost, that means that we are paying 56% of it. Therefore, we can multiply the cost by 56%

23.99 * .56 = $13.43

Answer: $13.43

Step-by-step explanation:

make your 22% a decimal by dividing it by 100 equaling 0.22 then since its markDOWN you subtract 1.00 - 0.22 equaling 0.88 then multiply 0.88 by $23.99 which is supposed to equal $13.43

Answer:

They are equivalent

Step-by-step explanation:

2x+14 = 8

Lets solve for x

Subtract 14 from each side

2x+14-14 = 8-14

2x = -6

Divide by 2

2x/2 = -6/2

x = -3

They are the same

Answer:

Yes

Step-by-step explanation:

Solving for 2x+14=8

Subtract 14 on both sides: 2x= 8-14

2x = -6

Divide by 2: x = -3

-3 = -3

Hope this helps!!

Answer:

D

Step-by-step explanation:

From the box- plot the left hand side of the box represents the lower quartile

that is [tex]Q_{1}[/tex] = 2 → D