What is the slant height x of this square pyramid? The figure shows a square pyramid. The slant height is shown as a dashed line perpendicular to the base edge and is labeled as x. The length of the lateral edge is 4 meters. The lateral edge makes a 60 degree angle with the base edge. Enter your answer in the box. Express your answer in radical form.

Answers

Answer 1

The side adjacent to the 60° angle in the right triangle consisting of x, the lateral edge, and half the base edge is half the base edge, 2 m. The side opposite that angle is x. Thus you have
tan(60°) = x/(2 m)
(2 m)*tan(60°) = x = 2√3 m

The slant height is 2√3 meters.

Answer 2

Based on the information given, it should be noted that the slant height will be 2✓3 meters.

From the information given, the slant height is shown as a dashed line perpendicular to the base edge and is labeled as x as the length of the lateral edge is 4 meters and the lateral edge makes a 60 degree angle with the base edge.

Therefore, the calculation of the slant height goes thus:

Tan 60° = x/2

x = 2 × tan 60°

x = 2 × ✓3

x = 2✓3

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Related Questions

a rectangle box is twice as long as it is wide. the height of the box is 3 feet less than the width. if the box is x feet wide, what polynominal represents its volume in cubic feet

Answers

The width is given as x.
The length is twice the width, so is 2x.
The height is 3 less than the width, so is x-3.

The volume is (length)*(width)*(height), so is (2x)(x)(x -3). Eliminating parentheses, the volume in cubic feet is represented by the polynomial ...
2x³ -6x²

What is the length of AA' , rounded to the nearest hundredth? Type a numerical answer is the space provided. Do not type spaces in your answer

Answers

Coordinate of A are (0,0)
Coordinates of A' are (5,2)

We can find the distance from A to A' using the distance formula:

[tex]AA'= \sqrt{(5-0)^{2}+ (2-0)^{2} } \\ \\ AA'= \sqrt{25+4} \\ \\ AA'= \sqrt{29} \\ \\ AA'=5.39 [/tex]

Thus, rounded to nearest hundredth, AA' is equal to 5.39

What is the length of the hypotenuse of the triangle?
sides 7cm and 3cm

A. sqrt 20cm
B. sqrt 23cm
C. sqrt 40cm
D. sqrt 58cm

Answers

So use the Pythagorean theorem formula - a² + b² = c²

7² + 3² = c²
49 + 9 = c²
49 + 9 = 58
58 = c²
Sqrt of 58 = 7.6 cm

So the answer is D) Sqrt 58 cm.

Hope this Helps!!

The length of the hypotenuse of the triangle is √58 cm (Option D).

To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's label the sides of the triangle:

Side a = 7 cm (one of the legs)

Side b = 3 cm (the other leg)

Side c = ? (the hypotenuse)

The Pythagorean theorem is:

[tex]c^2 = a^2 + b^2[/tex]

Substitute the given values:

[tex]c^2 = 7^2 + 3^2\\\\c^2 = 49 + 9\\\\c^2 = 58[/tex]

Now, we can find the square root of both sides to solve for c:

c = √58 cm

So, the length of the hypotenuse of the triangle is √58 cm.

The correct answer is: D. √58 cm

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If the train that Megan is riding covers 80 miles in 2 hours, how fast is the train traveling?

Answers

The train is traveling at 40 mph (miles per hour).

To find this, you divide both 80 and 2 by 2 to find how many miles in a single hour the train travels. Thus giving you 40 miles in an hour (40 mph) as a ginal answer.

I hope this helps!

Final answer:

The average speed of the train Megan is traveling on is 40 miles per hour. It's obtained by dividing the total distance of 80 miles by the total time of 2 hours.

Explanation:

To find the average speed of the train that Megan is riding, which covers 80 miles in 2 hours, we will use the formula for average speed, which is total distance divided by total time. The train travels 40 miles one way and 40 miles back, totaling 80 miles.

Here is the step-by-step calculation:

Calculate the total distance the train travels: 40 miles one way + 40 miles back = 80 miles.

Calculate the total time of the journey: 2 hours.

Divide the total distance by the total time to find the average speed: 80 miles / 2 hours = 40 miles per hour.

This means the average speed of the train is 40 miles per hour.

In a woodworking you are planing boards to make shelves. The planer is set to remove 1/16 inch from a board on each pass the board makes through the planer. If a board starts out at 3/4 inch thick, how many times will you need to send it through the planer to get it down to 5/8 inch?

Answers

Material removed per pass = 1/16 in
Initial thickness = 3/4 in
Final thickness = 5/8 in

If x is the number of passes,
The material removed = (1/16)x in.
Therefore,
3/4 - (1/16)x = 5/8
3/4 - x/16 = 5/8
x/16 = 3/4 - 5/8 = 1/8
x = 16*1/8 = 2

Therefore, the board will be passed through the plane twice.

which word best describe 8(2x+4)

Answers

Hope it helped you.
~~~~~~~~~~~~~~~~~~

8*2 is 16

Then 8*4 is 32.

Answer is 16x+32

Distribution it should be used 8(2x+4).

-Charlie

The answer you are looking for is A. Coefficient.

A coefficient is a number that is in front of a variable. Examples of this are 6 in 6x, 100 in 100s, and 45 in 45h. Thus making 8 the coefficient of the problem.

There are also no like terms (like 4 and 6 or 5x and 9x), there is no inequality sign (greater than, less than, etc), and there are no constant variables (like 2 and 7 in the equation " 2x - 2 = 7).

I hope this helps!

A round table top has a diameter of 2.6 meters.What is its surface area

Answers

Hello!

To find the area of a circle you use the equation

[tex] \pi r^{2} [/tex]

r is radius which is half the diameter

r = 2.6 / 2

r = 1.3

Put in the values you know

[tex] \pi 1.3^{2} [/tex]

Square the number

[tex]1.69 \pi = 5.31[/tex]

The answer is [tex]1.69 \pi [/tex] or ≈5.31

Hope this helps!

that's just area of a circle

remmber that [tex]A=\pi r^2[/tex] where r=radius and A is area and pi is pi or about 3.14159265

so if diameter is 2.6, ah, tricky, they give you dameter
rmemeber that d/2=r so 2.6/2=d/2=r=1.3

so
[tex]A=\pi r^2[/tex]
[tex]A=\pi (1.3)^2[/tex]
using your calculator
[tex]A=5.309 m^2[/tex]

the surface area is [tex]5.309 m^2[/tex]

HI :) I NEED HELP PLEASE BEFORE 12 AM

Answers

See, please, the solution for the task number 2.

The total cost of a prescription is $119.25. Mr. Jones's co-insurance plan requires him to contribute 15 percent of the cost. What's Mr. Jones's out-of-pocket cost for this prescription?

Answers

Final answer:

To find Mr. Jones's out-of-pocket cost for his prescription, calculate 15% of the total cost of $119.25, resulting in $17.89 after rounding.

Explanation:

The question asks us to calculate Mr. Jones's out-of-pocket cost for his prescription if his co-insurance plan requires him to pay 15% of the total cost. The total cost of the prescription is $119.25.

To find out Mr. Jones's out-of-pocket expense, we calculate 15% of $119.25:

Out-of-pocket cost = 15% of total cost
= 0.15 × $119.25
= $17.8875

So, Mr. Jones's out-of-pocket cost will be $17.8875, which we can round to $17.89 for practical purposes.

hey can you please help me posted picture of question

Answers

The number of roots of a quadratic function can be determined from its discriminant.

If Disc> 0, the function has two distinct roots
If Disc = 0, the function has a repeated root
If Disc < 0, the function has no real root.

The discriminant can be calculated as:

Disc = b² - 4ac

For the given equation:

Disc = 9 - 4(2)(1) =1

Since the value of discriminant is positive, the function will have two distinct roots.

So, the answer to this question is option B

One 16-ounce bottle of an energy drink has an average of 400 mg of caffeine with a standard deviation of 20 mg. What is the probability that the average caffeine in a sample of 25 bottles is no more than 395 milligrams?

Answers

That probability is about 10.6%.

What type of conic section is the following equation? 4x2 + y2 = 36

Answers

The terms are both squares, so it is not a parabola.

The signs of the terms are both positive, so it is a circle or an ellipse.

The coefficients of the terms are different, so it is not a circle, it is an ELLIPSE.

Answer:

Ellipse

Step-by-step explanation:

The signs of the terms are both positive, so it is either a circle or an ellipse.

The coefficients of the terms are different, so it can not be a circle.

Therefore it is an Ellipse.

If P(A or B)equals=0.60.6, P(A)equals=0.40.4, and P(A and B)equals=0.350.35, find P(B).

Answers

Answer:

P(B) = 0.55 .

Step-by-step explanation:

We are given that P(A or B) = 0.6 , P(A) = 0.4 , and P(A and B) = 0.35 .

As we know that;

P(A or B) = P(A) + P(B) - P(A and B)

0.6 = 0.4 + P(B) - 0.35

P(B) = 0.35 + 0.6 - 0.4 = 0.55

Therefore, P(B) = 0.55 .

need help please.I forgot this.

Answers

The associative property lets you move the parentheses.

6. (-20×50)×-29 = -1000×-29 = 29,000

7. (5×10)×18 = 50×18 = 900

8. 400 + (60 + 98) = 400 +158 = 558

9. 3×(20×5) = 3×100 = 300

10. (18 + 9) +91 = 27 +91 = 118

find the unit price rounded to the nearest cent: $12.35 for 11 lb

Answers

The unit price is 1.12.

All you have to do is divide $12.35 / 11 = 1.12

Hope this Helps!!

Answer:
unit price = $1.1

Explanation:
We are given that 11 lb cost $12.35. To know how much does 1 lb cost (unit price), all you have to do is cross multiplication as follows:
11 lb .......................> 12.35
1 lb .........................> ??
unit price = (1*12.35) / 11 = $1.122 which is approximately $1.1 (to the nearest cent)

Hope this helps :)

Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it is 8 inches. How far did Chubby run? Give your answer in terms of pi. (prize is 99 points)

Answers

Answer: 800pi inches

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

Explanation:

The formula to find the circumference of a circle is
C = pi*d
where
C = distance around the circle (aka circumference)
pi = 3.14 approximately
d = diameter

We know that the diameter of the wheel is d = 8, so
C = pi*d
C = pi*8
C = 8pi
is the circumference of the wheel

One full rotation will have the wheel cover a distance of 8pi inches. Imagine that wet paint is on the outer surface of the wheel. If the wheel is rolled out in a straight line, then the wet paint would cover a linear distance of 8pi inches along the flat ground. This is one full rotation, so 100 rotations covers 100*8pi = 800pi inches

Note: if we use pi = 3.14 as the approximation, then the hamster ran approximately 800*pi = 800*3.14 = 2512 inches if the wheel could move

Answer:

6280

Step-by-step explanation:

It's 6280

Use the Change of Base Formula to evaluate log3 58. Then convert log3 58 to a logarithm in base 4. Round to the nearest thousandth.

Answers

[tex]\log_ab=\dfrac{\log_cb}{\log_ca}[/tex]
[tex]\log_358=\dfrac{\log_458}{\log_43}\approx\dfrac{2.929}{0.792}\approx3.698[/tex]

simplify completely 3x^2+21x-54 over x^2+3x-54

Answers

[tex]\bf \cfrac{3x^2+21x-54}{x^2+3x-54}\implies \cfrac{3(x^2+7x-18)}{x^2+3x-54}\implies \cfrac{3\underline{(x+9)}(x-2)}{\underline{(x+9)}(x-6)} \\\\\\ \cfrac{3(x-2)}{x-6}[/tex]

Answer: 3(x-2) / x-6

Step-by-step explanation: find gcf..

A rectangular dartboard has an area of 648 square centimeters. The triangular part of the dartboard has an area of 162 square centimeters. A dart is randomly thrown at the dartboard. Assuming the dart lands in the rectangle, what is the probability that it lands inside the triangle?

To the nearest whole percent, the probability is

A) 18
B) 25
C) 35
D) 50

Answers

The answer is B) 25.
Hope this helps!!

Answer: B) 25

Step-by-step explanation:

Given: A rectangular dartboard has an area of 648 square centimeters.

The triangular part of the dartboard has an area of 162 square centimeters.

If a dart is randomly thrown at the dartboard. Assuming the dart lands in the rectangle, the probability (in percent) that it lands inside the triangle will be :

[tex]\dfrac{162}{648}\times100=25\%[/tex]

Hence, the probability that it lands inside the triangle = 25%.

[tex] \sqrt[3]{ 3x + 1 - 4 = - 6} [/tex]

Answers

i'm not sure if -6 is out or inside the cubic root but i will solve it for both cases

In case of [tex] \sqrt[3]{3x+1-4} =sqrt[3][-6][/tex] --> (by multiplying the power by 3)
[tex] 3x+1-4 = -6[/tex]
[tex] 3x -3 = -6 [/tex] ---> by adding 3 for the both sides
[tex] 3x = -3 [/tex] ---> by dividing both sides by 3
[tex] x = -1 [/tex]

in case of [tex] \sqrt[3]{3x+1-4} = -6[/tex] ----> we will repeat the first step again
therefore,
[tex] 3x + 1 -4 = (-6)^{3} = -216 [/tex]
[tex] 3x -3 = -216 [/tex] ----> by adding both sides by 3
[tex] 3x = -213 [/tex] ----> by dividing both sides by 3
[tex] x = \frac{-213}{3} = -71 [/tex]
then x = -71
I hope that helps ;)

a company observes the lifespan of 560 lightbulbs and finds that their data follows a normal distribution. what is the approximate number of light bulbs that fall within two standard deviations from the mean?

Answers

Empirical rule can be used to estimate the number of values that lie with 1, 2 or 3 standard deviations of a Normally distributed population.

According to the empirical rule, 95% of the values lie within 2 standard deviations of the mean.

Total number of bulbs = n = 560
95% of n = 0.95 x 560 = 532

This means, 532 bulbs will lie within 2 standard deviations from the mean

Daisy is cooking pasta. The recipe says she needs 480 grams of pasta for 4 people. How many kilograms will she need for 14?

Answers

480 grams of pasta = 480 grams x (1 kilogram / 1,000 grams) = 0.48 kilograms

Rule of three:

Pasta People
(kilograms)
0.48 → 4
x ← 14

x=(14 * 0.48)/4
x=1.68

Answer: She will need 1.68 kilograms of pasta for 14 people

Answer:

1.68 kilo grams are required for 14 people.

Step-by-step explanation:

First of all the answer is required in kilo grams and the data given is in grams.

Lets convert the given value to kilo grams;

480 grams = 0.48 kilo grams

If 0.48 kilo grams are required to cater 4 people then how many kilo grams are required to cater 14 people?

⇒[tex]\frac{0.48}{4} *14[/tex] kilo grams

1.68 kilo grams.

-7y to the third (4y + y - 3)

Answers

Hello,

So if we have the equation: -7y^3(4y + y - 3), we're essentially distributing "-7y^3" to everything of what's in the parenthesis. When you distribute -7y^3, know that you add exponents but you multiply the numbers. After simplifying you get:

-28y^4 - 7y^4 + 21y^3

**We can still simplify this expression because there are still like terms:

-35y^4 +21y^3

Hope this helps!

May

Caleb bought a car for $6,900. He agreed on a five-year loan at a 5.4% interest rate. Calculate what Caleb's monthly payments will be.

Answers

Final answer:

To calculate Caleb's monthly car payments, use the loan amortization formula that deals with compound interest, not simple interest. Input the loan amount of $6,900, the monthly interest rate (annual rate of 5.4% divided by 12), and the total number of payments (5 years times 12 payments per year) into the formula to find the monthly payment.

Explanation:

Caleb's car loan scenario comes under financial mathematics, specifically, it deals with loan amortization using the concept of compound interest. Since the car loan spans multiple years, compound interest is the accurate model to use, not simple interest. As opposed to simple interest which only accrues on the original amount or principal, compound interest accrues on the principal and all interest previously added.

The formula to calculate the monthly payment, P, on a loan is given by, where PV represents t

[tex]P = [r*PV] / [1 - (1 + r)^-n][/tex]

he present value or the amount of loan, which is $6,900 in this case; r is the monthly interest rate which can be calculated as annual interest rate divided by 12, translating to 0.054/12 in this case; and n is the total number of payments (i.e., 5 years of payments with 12 payments per year, hence, 5*12).

To calculate the monthly payment, plug these values into the formula which should give you the monthly payment amount that Caleb needs to pay for his car loan.

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Factor completely the following quadratic expression 16x^2-25y^2

Answers

[tex]16x^2-25y^2 [/tex]

[tex](4x)^2-(5y)^2[/tex]

[tex](4x+5y)(4x-5y)[/tex]

Answer:

(4x+5y)(4x-5y)

Step-by-step explanation:

it is correct i got it right

Suppose f(x)=x^2-2. Find the graph of f(5x).

Answers

The function f (x) = x ^ 2 - 2 is given
It is asked to find the graph of f (5x)
So where the x goes we must now place "5x"
In this way the function is as shown below:
f (5x) = (5x)² -2
f (5x) = 25x² -2
The graph of this function is shown in the attached image.

What is the annual rate of productivity advance implied by moore's law? (assume linear growth from the base.) instructions: enter your response rounded to the nearest whole number. %?

Answers

The annual rate of productivity is 34%. Moor's law sates that it i sequal to 34%.

What is one possible solution for the triangle below?

Answers

Answer:

The correct answer is C, i can promise you that

Step-by-step explanation:

the only one with Angle Z as 94.6 degrees.

One possible solution for the triangle below is:

Option D:

YZ = 95.4

∠X = 26.7°

∠Z = 85.3°

How use law of sines and cosines?

If only one of these is missing, the law of cosines can be used.

3 sides and 1 angle. So if the known properties of a triangle are SSS (side-side-side) or SAS (side-angle-side), then this law applies.

If you want the ratio of the sine of an angle and its inverse to be equal, you can use the law of sine. This can be used if the triangle's known properties are ASA (angle-side-angle) or SAS.

Using Law of sine:

40/sin 68 = 43/sin Z

sin Z = (43/40) * sin 68

sin Z = 0.9967

Z = sin⁻¹0.9967

Z = 85.3°

The only option with the correct value of angle Z is Option D with:

YZ = 95.4

∠X = 26.7°

∠Z = 85.3°

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What is the median of the data set represented by the dot plot? A number line with line with two dots above the number 10, one dot above the number 12, one dot above the number 13, one dot above the number 14, one dot above the number 15, one dot above the number 18, and two dots above the number 19.

Answers

There are 4 dots either side of the dot above 14, so 14 is the middle value.

The median of the data set is 14.

Answer:

The median of the data set is 14.

PLEASE PLEASE HELP WITH THIS

Answers

Since triangles ABC and BCD are similar, we can establish a proportion between the lengths of corresponding sides:
[tex] \frac{AC}{BC} = \frac{BC}{CD} [/tex]

We can infer from our picture that [tex]BC=m[/tex]. Also we can find the length of AC by adding AD and CD:
[tex]AC=AD+CD[/tex]
[tex]AC=11+7[/tex]
[tex]AC=18[/tex]

Lets replace the values in our proportion:
[tex] \frac{AC}{BC} = \frac{BC}{CD} [/tex]
[tex] \frac{18}{m} = \frac{m}{7} [/tex]
Solving for [tex]m[/tex]:
[tex]m^2=(18)(7)[/tex]
[tex]m^2=126[/tex]
[tex]m= \sqrt{126} [/tex]

We can conclude that the correct answer is: D [tex] \sqrt{126} [/tex]

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Which of the pairs of compounds below is most likely to form a solution when mixed?view available hint(s)which of the pairs of compounds below is most likely to form a solution when mixed?water and ammonia (nh3)sodium chloride (nacl) and pentane (c5h12)? Read the following speech excerpt and then select the correct answer to the question below: President George W. Bushs speech to the troops on the USS Abraham Lincoln Our mission continues. Al-Qaida is wounded, not destroyed. The scattered cells of the terrorist network still operate in many nations, and we know from daily intelligence that they continue to plot against free people. The proliferation of deadly weapons remains a serious danger. The enemies of freedom are not idle, and neither are we. Our government has taken unprecedented measures to defend the homeland and we will continue to hunt down the enemy before he can strike. The war on terror is not over, yet it is not endless. We do not know the day of final victory, but we have seen the turning of the tide. No act of the terrorists will change our purpose, or weaken our resolve, or alter their fate. Their cause is lost. Free nations will press on to victory. Other nations in history have fought in foreign lands and remained to occupy and exploit. Americans, following a battle, want nothing more than to return home. And that is your direction tonight. After service in the Afghan and Iraqi theaters of war after 100,000 miles, on the longest carrier deployment in recent history you are homeward bound. Some of you will see new family members for the first time 150 babies were born while their fathers were on the Lincoln. Your families are proud of you, and your nation will welcome you. Which line from the text suggests the president feels other governments have handled wars poorly? A. Other nations in history have fought in foreign lands and remained to occupy and exploit. B. 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