A stainless steel patio heater is a square pyramid. The length of one side of the base is 21.6 in. The slant height of the pyramid is 88.6 in. What is the height of the​ pyramid? NEED ANSWERED ASAP! Its due tomorrow

Answer:

21,  22, 23   or

-23, -22 , -21

Step-by-step explanation:

The 3 consecutive integers are x, x + 1, and x + 2

Sum of the squares of the 3 consecutive integers:

x² + (x+1)² + (x+2)² = 1454     Expand this equation

x² + x² + 2x + 1 + x² + 4x + 4 = 1454   Combine like terms

3x² + 6x + 5 = 1454

3x² + 6x + 5 - 1454= 0

3x² + 6x - 1449 = 0

Use quadratic equation to solve for the roots of x:  (a = 3, b = 6,

c= -1449)

x = 21, -23

The consecutive numbers are: x, (x + 1), (x + 2)

21,  22, 23

-23, -22 , -21

The standard form of the equation of the conic is x² + y² - 16x - 16y - 192 = 0.

It is a type of curve with a curved line in the middle and two straight lines on the sides. Conic sections include circles, ellipses, parabolas, and hyperbolas.

The standard form of the equation of a conic is

Ax² + Bxy + Cy² + Dx + Ey + F = 0, where A, B, C, D, E, and F are constants.

In this case, the equation of the conic is x²  + y²  - 16x - 16y - 192 = 0.

To derive this equation, we'll use the distance formula to calculate the distance between the vertices and the foci. The distance between the vertices and the foci is given by

d = √((x_1 - x_2)²  + (y_1 - y_2)²)

where (x_1, y_1) is the coordinates of the first vertex and (x_2, y_2) is the coordinates of the first foci.

For the first vertex, (x_1, y_1) = (0, 8). For the first foci, (x_2, y_2) = (0, √48). Thus, the distance between the two points is

d = √((0 - 0)²  + (8 - √48)² )

= √(0 + (-8 - √48)² )

= √(-16 - 2√48 + 48)

= √(32 -2√48)

= 2√(16 - √48)

= 2√(16 - 6.9)

= 2√(9)

= 2(3)

= 6

So, the distance between the vertices and the foci is 6.

The equation of the conic can then be written as x² + y² - 16x - 16y - (-8)² = 0, which simplifies to x² + y² - 16x - 16y - 192 = 0.

Thus, the standard form of the equation of the conic is x² + y² - 16x - 16y - 192 = 0.

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Step-by-step explanation:

Vertex at  -4,3 would result in vertex form of parabola  

g(x) = (x+4)^2 + 3

Answer:

the answer will be A

Step-by-step explanation:

for the explanation the picture will do the best

mark me branliest as you promised

The trigonometric ratios for this problem are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the triangle, we have that:

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Answer:

To differentiate the given expression, we will need to use both the product rule and the quotient rule.

Let's first rewrite the expression using the reciprocal identity for x:

2y/5x = 2y * (5x)^(-1)

Now we can use the product rule and the quotient rule to find the derivative with respect to x:

d/dx [2y * (5x)^(-1)] = 2y * d/dx[(5x)^(-1)] + (5x)^(-1) * d/dx[2y]

Using the chain rule, we can find the derivative of (5x)^(-1) with respect to x:

d/dx[(5x)^(-1)] = -1/(5x)^2 * 5 * (dx/dx)

d/dx[(5x)^(-1)] = -1/(5x)^2

Using the chain rule again, we can find the derivative of 2y with respect to x:

d/dx[2y] = 2 * (dy/dx)

Substituting these expressions back into the original equation, we get:

d/dx [2y/5x] = 2y * (-1/(5x)^2) + (5x)^(-1) * 2 * (dy/dx)

Simplifying this expression, we get:

d/dx [2y/5x] = -2y/(5x)^2 + 2/(5x) * (dy/dx)

Therefore, the derivative of 2y/5x with respect to x is -2y/(5x)^2 + 2/(5x) * (dy/dx).

Answer:

The answer is 2√10

Step-by-step explanation:

Hyp²=opp²+adj²

let hyp be x

x²=6²+2²

x²=36+4

x²=40

square root both sides

√x²=√40

x=2√10

Let's denote the speed of the boat in still water as "b", and let's denote the distance between the two points as "d" (in this case, d = 24 miles).

When the boat is traveling upstream against the current, its effective speed is b - 2 mph (since the current is working against the boat). When the boat is traveling downstream with the current, its effective speed is b + 2 mph (since the current is helping the boat).

We know that the boat travels a total distance of 24 miles upstream and then 24 miles downstream, for a total distance of 48 miles. We also know that the total time it takes for the boat to make this round trip is 5 hours. So we can set up the following equation:

24/(b-2) + 24/(b+2) = 5

Multiplying both sides by (b-2)(b+2), we get:

24(b+2) + 24(b-2) = 5(b-2)(b+2)

Simplifying and rearranging, we get:

10b^2 - 96b - 208 = 0

We can solve this quadratic equation using the quadratic formula:

b = (-(-96) ± sqrt((-96)^2 - 4(10)(-208))) / (2(10))

b = (96 ± sqrt(96^2 + 8320)) / 20

b = (96 ± sqrt(9024)) / 20

b = (96 ± 96) / 20

So the possible values of b are b = 9.6 or b = -0.8. We can discard the negative value since it doesn't make sense as a speed, so we have:

b = 9.6 mph

Therefore, the speed of the boat in still water is 9.6 miles per hour

To find the inverse of the function f(x) = 7x - 5, we need to solve for x in terms of y (or f^(-1)(x)). First, let's replace f(x) with y:

Now, we need to solve for x:

1. Add 5 to both sides:

2. Divide both sides by 7:

Now we have the inverse function, f^(-1)(x) = (x + 5) / 7. We can use this to find f^(-1)(18):

Answer:

1.2974634e+14

Step-by-step explanation:

ye

yes is answer   for all option   .we can check it by rules of rounding off numbers .

what is rounding ?

Rounding is the process of approximating a number to a nearby value that is easier to work with or more appropriate for a given context. When rounding, we take a number with many decimal places or significant figures and adjust it to a simpler or more convenient value with fewer decimal places or significant figures.

In the given question,

Yes, each number is rounded correctly to the nearest hundred thousand based on the rules of rounding.

To round to the nearest hundred thousand, we look at the digit in the hundred thousand place and the digit to its right (i.e., in the ten thousand place).

If the digit in the ten thousand place is 5 or greater, we round up the digit in the hundred thousand place by adding 1.

If the digit in the ten thousand place is less than 5, we leave the digit in the hundred thousand place as it is.

Using these rules, we can see that:

350000 rounded to the nearest hundred thousand is 400000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.

555555 rounded to the nearest hundred thousand is 560000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.

137998 rounded to the nearest hundred thousand is 200000 because the digit in the ten thousand place is 7, so we round up the digit in the hundred thousand place.

792314 rounded to the nearest hundred thousand is 800000 because the digit in the ten thousand place is 3, so we leave the digit in the hundred thousand place as it is.

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This is an image of a histogram representing the number of hours a group of students spent studying for a test. The horizontal axis shows the number of hours studied, and the vertical axis shows the frequency or number of students who studied that number of hours.

A histogram is a graphical representation of data that displays the frequency distribution of a set of continuous or discrete data. It consists of a series of adjacent rectangular bars, where the area of each bar represents the frequency of occurrences of a particular range of values.

Based on the histogram, it appears that the majority of students studied for 5-7 hours, with a frequency of 14 students. Additionally, it appears that 8 students studied for 2-4 hours, and 10 students studied for 8-10 hours. Finally, it appears that only 1 student studied for more than 10 hours.

Histograms are a useful way to display and analyze data because they allow us to quickly see the distribution and frequency of the data. In this case, we can see that the data is roughly symmetric around the 5-7 hour range, with fewer students studying for fewer or more hours.

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There are 43,680 different ways to choose a President, Vice President, Treasurer, and Secretary from 16 students.

An arrangement of items in a particular order is referred to as a permutation. Permutations are frequently used in mathematics to count the number of possible configurations of a set of items. P(n,r) stands for the quantity of permutations of n items taken r at a time and is equal to n! / (n - r)!, where n! (also known as "n factorial") is the sum of all positive numbers from 1 to n.

Given that, the number of students = 16 and the positions are 4.

Thus, after every selection we have:

16 * 15 * 14 * 13 = 43,680

Hence, there are 43,680 different ways to choose a President, Vice President, Treasurer, and Secretary from 16 students.

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Answer:

y = 1/28(x²)

Step-by-step explanation:

Not totally sure about this, but here's what I think is the answer:

focus (0,7)

directrix y = -7

Always a good idea to plot the point (0,7) and the line y = -7 so you can visualize what the parabola looks like.

From the graph, you can see that p = 7  (halfway between the focus and the directrix).

The vertex of this parabola is (0,0), which are your (h, k) values.  You can see that from the graph.  The parabola opens UP.

4p(y-k) = (x-h)²  →  4p(y-0) = (x-0)²

4py = x²

y = x²/4p = x²/4(7) = x²/28

y = 1/28(x²)

sorry if this isn't the right answer, but I tried  (I'm not a paid expert, just a fellow student trying to learn math)!

Answer:

It is irrational, because the product of an irrational number and a rational number is irrational.

Step-by-step explanation:

sqrt 27 is  irrational =5.19615.......

3 is rational

  subtracting 3 from the irrational number just creates a smalller irrational number    ....then multiplying by 9 just creates a larger irrational number

Therefore, it will take 173 months to pay off the loan, or approximately 14 years and 5 months.

A percentage is a way of expressing a number as a fraction of 100. The symbol for a percentage is "%". For example, 50% is the same as 50/100 or 0.5 as a decimal. Percentages are often used to express a portion or share of a whole. For instance, if you scored 90% on a test, it means you got 90 out of 100 possible points. In finance, percentages are commonly used to express interest rates, returns on investments, or changes in stock prices.

First, we need to convert the monthly interest rate from a percentage to a decimal by dividing by 100.

0.25% / 100 = 0.0025

Now we can plug in the values into the formula:

N= (-log⁡ (1-0.0025*70000/250))/ (log⁡ (1+0.0025))

Simplifying the equation in the parentheses:

N= (-log⁡ (1-175))/ (log⁡ (1.0025))

N= (-log⁡ (0.9964))/ (0.002499)

N= 172.9

Rounding up to the nearest whole number since we can't make partial payments:

N= 173

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So according to the given figure ∠mah is right angle(90°), The value of x is 17, ∠mat is 38° and ∠tah is equal to 52°.

(A) ∠mah is right angle(90°) [GIVEN IN THE FIGURE]

(B) (2x+4)+(3x+1) = 90

5x+5 = 90

x= 17

(C) 2x+4 = 2×17 + 4 = 38°

(D) 3X + 1 = 3 × 17 + 1 = 52°

A graph is a visual representation or diagram that displays facts or values in an organised manner in mathematics. The points on a graph are typically used to depict the relationships between two or more things.

A graph in discrete mathematics is made up of vertices, which are groups of points, and edges, which are the connections between those vertices. There are numerous different types of graphs besides linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs.

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Answer:

The answer the runner who took 45 sec to run 400m

Step-by-step explanation:

let the runner who took 45 sec to run 400m be x

let the runner who took 48sec to run 400m be y

Average speed=Total distance(m)/time taken(s)

A(x)=400/45≈9m/s

A(y)=400/48≈8m/s

The minimum value of Jeri Dammers' total deductions is $200.68.

Based on the given information, we can calculate the total deductions for Jeri Dammers as follows:

Social Security: Jeri pays 6% of the first S$90,000 of her gross pay towards Social Security. As her gross pay is only $735.00, her Social Security deduction will be:

Medicare: Jeri pays 1.45% of all her income towards Medicare. As her gross pay is $735.00, her Medicare deduction will be:

Federal Income Tax: To calculate the federal income tax, we need to refer to the tax tables provided by the IRS. As the gross pay is only $735.00, Jeri's federal income tax deduction will be very minimal or possibly none.

State Tax: Jeri pays 2% of her gross pay towards state tax. As her gross pay is $735.00, her state tax deduction will be:

Local Tax: Jeri pays 1.5% of her gross pay towards local tax. As her gross pay is $735.00, her local tax deduction will be:

Medical: Jeri has a deduction of $32.00 towards medical expenses.

Union Dues and Others: No information is given about Jeri's union dues or other deductions.

Therefore, the total deductions for Jeri Dammers will be:

We cannot calculate the exact value of Total Deductions without information about Union Dues and Others.

However, the minimum value of Total Deductions would be:

= $44.10 + $10.65 + $88.20 + $14.70 + $11.03 + $32.00

= $200.68

Therefore, the minimum value of Jeri Dammers' total deductions is $200.68.

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See full text below

Find the total deduction The person pays Social Security 6 percent of the first S90,000. Medicare is 1.45 percent of all income Use the tax tables for federal tax The state tax is 2 percent of gross pay and the local tax is 1.5 percent of gross pay. (Remember to add the Medical; Union Dues, and Others for total deduction: FIT Federal Income Tax, FICA Social Security) .4. Jeri Dammers is married and claims 3 allowances.

Dept

Employee

Check Number -3205

Gross Pay -$735.00

Net Pay

44B Jeri Dammers

Tax Deductions

Other Deductions

FIT

FICA

Medicare

State

Local

Medical -32.00

Union

Dues

Others

f(x) = 8/2^3

Rewritten in radical form: f(x) = 2^(3/2)

f(x) = 8(21)

Rewritten in exponential form: f(x) = 2^3 * 21

Key features:

Initial value: 2^3

Exponential base: 21

Domain: All real numbers

Range: All real numbers greater than 0

f(x) = 8/2^3

Rewritten in radical form: f(x) = 2^(3/2)

Key features:

Initial value: 2^(3/2)

Radical base: 2

Domain: All real numbers

Range: All real numbers greater than 0

f(x) = (√10)

Rewritten in exponential form: f(x) = 10^(1/2)

Key features:

Initial value: 10^(1/2)

Exponential base: 10

Domain: All real numbers

Range: All real numbers greater than 0

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By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

What is the parallel lines?

Parallel lines are two lines in a plane that never intersect.

1. Orientation of Lines:

Parallel lines are lines that never intersect and remain equidistant from each other at all points.

When constructing parallel lines, the lines are drawn in the same direction and maintain the same distance between them throughout their entire length. They do not meet or cross each other.

On the other hand, perpendicular lines are lines that intersect at a right angle (90 degrees). When constructing perpendicular lines, the lines are drawn so that they intersect at a right angle, forming four right angles at the point of intersection.

2. Tools/Methods Used:

Constructing parallel lines and constructing perpendicular lines may require different tools or methods.

To construct parallel lines, one common method is to use a straightedge and a compass. A straightedge is used to draw a straight line, and a compass is used to measure and transfer distances to create additional parallel lines.

Therefore, By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

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With the given compound interest, Total amount paid is $5,593.20 and you paid $1,379.40 more for the loan due to your bad credit score.

What is Compound interest?

Compound interest is the interest calculated on the initial principal as well as on the accumulated interest from previous periods. In other words, it is the interest earned not only on the principal amount but also on the interest previously earned.

Now,

To find the monthly payment, we can use the loan payment formula:

P = (Pv*r)/(1-(1+r)⁻ⁿ)

where P is the monthly payment, Pv is the present value of the loan, r is the monthly interest rate, and n is the total number of payments.

For your loan with a 15% APR, the monthly interest rate is 15%/12 = 1.25%.

For a 5-year loan with monthly payments, the total number of payments is 5 x 12 = 60.

So, plugging in the values, we get:

P = (5000*0.0125)/(1-(1+0.0125)⁻⁶⁰)) = $116.21

Your total amount paid over 5 years is:

Total amount paid = P x n = $116.21 x 60 = $6,972.60

For your friend's loan with a 5% APR, the monthly interest rate is 5%/12 = 0.42%.

Using the same formula as above, we get:

P = (5000*0.0042)/(1-(1+0.0042)⁻⁶⁰) = $93.22

Your friend's total amount paid over 5 years is:

Total amount paid = P x n = $93.22 x 60 = $5,593.20

The difference in the total amount paid is:

$6,972.60 - $5,593.20 = $1,379.40

Therefore, you paid $1,379.40 more for the loan due to your bad credit score.

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Answer:

[tex]1. \: \: - 2 {a}^{2} [/tex]

[tex]2. \: \: 4ab[/tex]

[tex]3. \: \: - 2[/tex]

Step-by-step explanation:

-2a(a+b-5) +3(-5a+2b) +b(6a-b-8)

[tex] - 2 {a}^{2} - 2ab + 10a - 15a + 6b + 6ab + {b}^{2} - 8b[/tex]

collecting like terms

[tex] -2 {a }^{2} + {b}^{2} - 2ab + 6ab + 10a - 15a + 6b - 8b[/tex]

[tex] = - 2 {a}^{2} + {b }^{2} + 4ab - 5a - 2b[/tex]

The equations of line that are perpendicular to each other are:

A: y = (1/6)x + 6; y = -6x + 4

The general formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

Now, for two equations to be perpendicular, it means that their slope must be negative reciprocals of each other. Thus:

Looking at the equations, we can say the only ones that have slopes that are negative reciprocals of each other is option A.

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The domain of the function y=√x-4 is restricted by the square root of a non-negative number, which means that x-4 must be greater than or equal to zero. Thus, we have:

x-4 ≥ 0

x ≥ 4

Therefore, the domain of the function is x≥4.

The range of the function is determined by the output values of the function. Since the square root of any non-negative number is always non-negative, the output values of the function y=√x-4 will always be non-negative. Thus, the range of the function is y≥0.

Therefore, the correct answer is A. Domain: x≥−4, Range: y≥0.

The function is f(x)=115.[tex](1.58)^x[/tex] and number of people after 6 months is 1789.

What is exponential function?

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Here according to the table initial people f(0) = 115

Now using exponential formula

=> f(x) = f(0).[tex](1+r)^x[/tex]

If x = 1 then f(1)= 182 then,

=> 182 = 115.[tex](1+r)^1[/tex]

=> 1+r = 182/115

=> 1+r = 1.58

=> r = 1.58-1=0.58

Then the exponential function is

=> f(x)=115.[tex](1.58)^x[/tex]

Now x=6 then,

=> f(6) = 115.[tex]1.58^6[/tex] = 1789

Hence number of people after 6 month is 1789.

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Answer:

tanQ = 1

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ OPQ is an exterior angle of the triangle , then

∠ R + ∠ Q = 135°

90° + ∠ Q = 135° ( subtract 90° from both sides )

∠ Q = 45°

Then

tanQ = tan45° = 1

Answer:

The probability of picking a yellow envelope is 2/7

Step-by-step explanation:

red envelope =2

blue " " =1

green " "=2

yellow " " =2

Total envelope =2+1+2+2=7

Probability thay at least one envelope will be yellow

P=number of yellow envelope/Total envelope

P=2/7