PQRST is a rectangular-based pyramid with a height of 10 cm.
P
4 cm S
10 cm
R
Find the angle between the line PT and the plane PQRS.
Give your answer correct to 1 decimal place.

The x-intercepts of the function are 10, and -8.

y-intercept is: -80.

The zeros are: x = 10 and x = -8

f(2) = -80

f(x) = -65 when x = 5 or -3.

The y-intercept of a function is the output (y) when the input value (x) is zero. On the other hand, the x-intercept is the input value (x), when the output value (y) is zero.

The zeros of a function are the x-intercepts of a function.

Given the function, f(x) = x² - 2x - 80, substitute f(x) = 0 to find the value of x, which is the x-intercept:

0 = x² - 2x - 80

x² - 2x - 80 = 0

Factorize

(x - 10)(x + 8)

x = 10 or x = -8

Substitute x = 0 into the function to find the y-intercept:

f(0) = 0² - 2(0) - 80

f(0) = -80

x-intercepts are 10, and -8.

y-intercept is: -80.

The zeros are: x = 10 and x = -8

Find f(2):

f(2) = (2²) - 2(2) - 80,

f(2) = 4 - 4 - 80

f(2) = -80

Find x when f(x) = -65:

-65 = x² - 2x - 80

-65 + 80 = x² - 2x

15 = x² - 2x

x² - 2x  - 15 = 0

Factorize

(x - 5)(x + 3) = 0

x = 5; x = -3

Therefore, f(x) = -65 when x = 5 or -3.

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Answer:

The mako shark swims first

Step-by-step explanation:

mako shark swim's at 40kilometre per hr

ablue whale swim's at 20km per hr

The proportional relationship between the number of centerpieces and the total cost for the centerpieces is graphed at the end of the answer.

A graph represents a proportional relationship if the output variable y in the y-axis is written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:

y = kx.

The constant k is called the slope of the unit rate of the situation, measuring by how much y changes when x changes by 1.

In the context of this problem, the cost of each centerpiece is of $5.50, hence the constant is given as follows:

y = 5.5x.

The number of centerpieces cannot be negative, hence the domain of the relation is given as follows:

x ≥ 0.

Considering this domain, the graph of the relation is given at the end of the answer.

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Answer: this should be more then 5 coins

Step-by-step explanation:

Answer:

√2 is between the integers 1 and 2.

Answer:

m∠R = 72°

Step-by-step explanation:

As ΔPQR and ΔUVW are congruent, m∠R = m∠W.

Equate the expressions for the two angles and solve for x:

⇒ m∠R = m∠W

⇒ 10x - 18 = 8x

⇒ 10x - 18 + 18 = 8x + 18

⇒ 10x = 8x + 18

⇒ 10x - 8x = 8x + 18 - 8x

⇒ 2x = 18

⇒ 2x ÷ 2 = 18 ÷ 2

⇒ x = 9

Substitute the found value of x into the expression for m∠R:

⇒ m∠R = 10x - 18

⇒ m∠R = 10(9) - 18

⇒ m∠R = 90 - 18

⇒ m∠R = 72°

Therefore, m∠R = 72°.

Answer: 8

Step-by-step explanation: 3.18 divided by 0.39 is 8 (without the decimals)

Answer:

A

Step-by-step explanation:

seventy and twenty-three thousandths = 70.023

Answer:

A

Step-by-step explanation:

thank

you

:D

Answer:

x + 2y = 5

Step-by-step explanation:

y = mx + b the m is the slope or gradient.  

y=2x+3  The slope is 2.

When lines are perpendicular,  the slopes are opposite inverses of each other.  So, the perpendicular slope to 2 is -1/2.  I would write the answer in the point slope of the line and then change the equation to the stand form

y -2 = -1/2(x -1)  Distribute the -1/2

y - 2 = -1/2x + 1/2  Add 1/2 x to both sides

1/2x + y -2 = 1/2  Add 2 to both sides

1/2x +y = 5/2  Multiply by 2 to clear the decimal

x + 2y = 5

Answer:

[tex]\angle K[/tex]

Step-by-step explanation:

When looking for corresponding angles, compare their order in the names. Since T and K are the first letters in the names of the triangles, they correspond.

The coordinates of the point that is 2/4 the way from A to B are (1, 7).

The coordinates of the point that divides a segment into a fractional component, n (n+m), or an arbitrary ratio, n:m, are given by:

   x = [n ⁄ (n+m)] (x₂ - x₁) + x₁  and y = [n ⁄ (n+m)] (y₂ - y₁) + y₁

Given:

For this problem, n = 2 and m = 2 since (2 ⁄ (2+2) = 2 ⁄ 4,  ( x,₁ y₁) =(-2, 5) and ( x₂, y₂) = (4, 9)

Where n and m are both positive integers, [n (n+m)] is the required distance ratio from the beginning position, (x₁, y₁)  are the coordinates of one endpoint, and (x₂, y₂) are the coordinates of the other endpoint.

x = [n ⁄ (n+m)] (x2 - x1) + x1

  = (2/4 ) (4 - (-2)) + (-2)

  =  (2/4 ) (4 + 2) + (-2)

  = (2/4 ) × 6 + (-2)

  =  3 - 2 = 1

y = [n ⁄ (n+m)] (y2 - y1) + y1

  =  (2/4 ) (9 - 5) + 5

  =  (2/4 ) (4) + 5

   =  2 + 5 = 7

Therefore, the coordinates of the point are (1, 7).

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With the annual interest of 1%, the total saving after 5 years is $6060.

Interest:

Interest is the amount for a particular principal amount of money at some rate of interest.

Given,

You earn $100 per month and want to save 10% in a savings account.

Here we have to use the savings calculator to find out how much your total savings would be in 5 years if your account has an annual interest rate of 1%.

Through the given details we have identified that,

Monthly earning = $100

Saving per month = 10%

So, in amount it can be

=> 100 x 10/100 = $10

So, for one year the saving without interest is

=> 10 x 12 = 1200

So, When we add the interest of 1% for the year,

Then the interest amount for one year will be,

=> 1200 x 1/100 = 12

So, the total amount including interest for one year,

=> 1200 + 12 = 1212

So, the savings after 5 years will be,

=> 5 x 1212

=> 6060.

Therefore, the total saving amount after 5 years is $6060.

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Answer:

3x+5?

Step-by-step explanation:

Not 100% sure but yh

The distance between the two points (2, 6) and (7, -6) will be 13 units.

Let one point be (x, y) and another point be (h, k). Then the distance between the points will be

D² = (x - h)² + (y - k)²

A right triangle with the two points forming the hypotenuse. The two points are given below.

(2, 6) and (7, -6)

Then the distance between the points (2, 6) and (7, -6) will be given as,

D² = (7 - 2)² + (-6 - 6)²

D² = 5² + (-12)²

D² = 25 + 144

D² = 169

D = 13 units

The distance between the two points (2, 6) and (7, -6) will be 13 units.

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Answer:

3 x 3 x 3 or 3 to the 3rd power :)

Step-by-step explanation:

Lets solve! :)

3 x 3 x 3

9 x 3

27

The volume of the tank would be 27s :)

Have an amazing day!!

Please rate and mark brainliest!

The temperature when the plane reaches an altitude of 4,000 will be 560°F.

It should be noted that temperature simply means the degree of hotness and coldness of a body.

In this case, there is a 14°F drop in temperature for every thousand feet that an alplane climbs into the sky.

Since the the temperature on the ground is 616, the temperature when the plane reaches an altitude of 4,000 will be:

= 616 - 14(4000/1000)

= 616 - 14(4)

= 616 - 56

= 560°F

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The equivalent rates for each of the given options are;

A) 1 goal in 2 games

10 goals in 20 games

B) 1 km jogged in 6 min

5 km jogged in 12 min

C) 1 pizza eaten in 5 minutes

2 pizzas eaten in 10 minutes

D) 2 penalties in 5 games​

20 penalties in 50 games​.

We want to write two equivalent rates for the given rates.

It should be noted that different rates that have the same value are equivalent rates. You can find an equivalent rate the same way you find equivalent ratios which is to divide or multiply the numerator and the denominator by the same number.

A) 5 goals in 10 games can also be written as;

5/10 = 1/2 = 10/20

These equivalent rates are;

1 goal in 2 games

10 goals in 20 games

B)  10 km jogged in 60 min;

10/60 = 1/6 = 5/12

These equivalent rates are;

1 km jogged in 6 min

5 km jogged in 12 min

C) 6 pizzas eaten in 30 min;

6/30 = 1/5 = 2/10

These equivalent rates are;

1 pizza eaten in 5 minutes

2 pizzas eaten in 10 minutes

D)  10 penalties in 25 games​;

10/25 = 2/5 = 20/50

These equivalent rates are;

2 penalties in 5 games​

20 penalties in 50 games​.

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The equilateral triangular prism has a surface area of 1997.321 square inches

From the question, the given parameters are

The total surface area of an equilateral triangular prism is calculated using the following formula

Surface area = a(√3/2) + 3(a × h);

Substitute the known values in the above equation

So, we have the following equation

Surface area = 20 * (√3/2) + 3(20 × 33);

Evaluate the product

So, we have the following equation

Surface area = 1997.321

Hence, the surface area of the equilateral triangular prism is 1997.321 square inches

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In the given angle, the value of x is 18°.

So, first label the lines as A, B, C, and D as follows:

Refer to the image attached below.

Line DC cuts the angle ∠ADB in two parts, so the equation can be:

Now, solve for x as follows:

Therefore, in the given angle, the value of x is 18°.

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The strategy used by Dr. Chang for the research study of undergraduate students is c. stratified sampling.

Stratified sampling can be defined as the type of sampling in which a population is divided into subpopulations and then random samples are taken from these subpopulations. These subpopulations or subgroups are also called strata.

The strategy used by Dr. Chang is stratified sampling because she divided all the undergraduate students into subgroups based on grade level and then from these subgroups she randomly selected 50 students.

Contrastingly, in simple random sampling, no subgroups are involved and the subset of individuals are chosen from a single large population randomly. On the other hand, quota sampling and accidental sampling are not a type of random sampling.

In cluster sampling, the subgroups are internally heterogeneous but in this case, the subgroups are internally homogenous as they are made based on grade level.

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Answer:

[tex]\textsf{3.} \quad \dfrac{5}{6}x+ 10=y[/tex]

4.  See below.

[tex]\textsf{5.} \quad \dfrac{10}{3}x-2=y[/tex]

Step-by-step explanation:

Given equation:

[tex]\dfrac{1}{3}x-\dfrac{2}{5}y=-4[/tex]

[tex]\textsf{Add \;$\dfrac{2}{5}y$ \; to both sides}:[/tex]

[tex]\implies \dfrac{1}{3}x-\dfrac{2}{5}y+\dfrac{2}{5}y=-4+\dfrac{2}{5}y[/tex]

[tex]\implies \dfrac{1}{3}x=\dfrac{2}{5}y-4[/tex]

Add 4 to both sides:

[tex]\implies \dfrac{1}{3}x+4=\dfrac{2}{5}y-4+4[/tex]

[tex]\implies \dfrac{1}{3}x+4=\dfrac{2}{5}y[/tex]

[tex]\textsf{Multiply both sides by \; $\dfrac{5}{2}$}:[/tex]

[tex]\implies \dfrac{5}{2} \cdot \dfrac{1}{3}x+ \dfrac{5}{2} \cdot4=\dfrac{5}{2} \cdot \dfrac{2}{5}y[/tex]

[tex]\implies \dfrac{5}{6}x+ 10=y[/tex]

[tex]\boxed{\begin{minipage}{3cm}$\dfrac{1}{3}x-\dfrac{2}{5}y=-4\\\\\underline{\phantom{\dfrac{1}{3}x}+\dfrac{2}{5}y\phantom{=-4}\dfrac{2}{5}y}\\\\\dfrac{1}{3}x=\dfrac{2}{5}y-4\\\underline{+4 \phantom{)=3y}+4\phantom{)))))}}\\\\\dfrac{1}{3}x+4=\dfrac{2}{5}y\\\\\underline{\phantom{)}\times\dfrac{5}{2}\phantom{))))}\times \dfrac{5}{2}}\\\\\dfrac{5}{6}x+10=y$ \end{minipage}}[/tex]

See the attachment for the highlighted mistake.

The mistake Mike made is that he did not divide 10x by 3.

Given equation:

[tex]10x-3y=6[/tex]

Add 3y to both sides:

[tex]\implies 10x-3y+3y=6+3y[/tex]

[tex]\implies 10x=6+3y[/tex]

Subtract 6 from both sides:

[tex]\implies 10x-6=6+3y-6[/tex]

[tex]\implies 10x-6=3y[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{10x}{3}-\dfrac{6}{3}=\dfrac{3y}{3}[/tex]

[tex]\implies \dfrac{10}{3}x-2=y[/tex]

[tex]\boxed{\begin{minipage}{3cm}$10x-3y=6\\\underline{\phantom{10x}+3y\phantom{=6}+3y}\\\\10x=3y+6\\\underline{-6 \phantom{)=3y}-6\phantom{)))))}}\\\\\dfrac{10x-6}{3}=\dfrac{3y}{3}\\\\\dfrac{10}{3}x-2=y$ \end{minipage}}[/tex]

When Eva advanced to the next round of the contest, the inequality that describes the number of questions will be 3x + 5y > 60

It should be noted that an inequality will simply used to illustrate the expressions that aren't equal. This is illustrated with the use of greater than, less, than, etc.

In this case, the contestants receive 3 points for each correct multiple choice question and 5 points for each correct free response question, and they must score more than 60 points to advance to the next round.

Therefore, the inequality that describes the number of questions will be:

= 3(x) + 5(y) > 60

= 3x + 5y > 60

where x = number of multiple choice questions,

y = number of free response questions,

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By using Distribution of the sample mean,  “It will have less variation”. So option B is correct.

With Large numbers of successive random samples, the mean of the sampling distribution is equal to the mean population (µ). The variability of each sampling distribution decreases in increase of sample size..

so that they become increasingly more Leptokurtic distribution .

As a sample size increases, sample variance (variation between observations) increases but the variance of the standard error decreases.

The mean of the sample means would be equal to μ (approx.), the mean  from which the samples were drawn. However,  the sample means will depend on the size of the samples, since big  samples are more likely to give estimated means that are equal to the true mean of the population(Approx. )

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By considering the areas of the two rectangles, we have shown that 2x² - 5x - 18 = 0

The value of length AB is 4.5 cm

From the question, we are to show that 2x² - 5x - 18 = 0

From the given information,

The total area of the compound shape ABCDEF is 36 cm²

That is,

Total area = 36 cm² = Area of small rectangle + Area of big rectangle

From the given diagram, we can write that

Area of small rectangle = x(x -4)

Area of small rectangle = x² - 4x

and

Area of big rectangle = (2x + x)(x -2)

Area of big rectangle = 3x(x - 2)

Area of big rectangle = 3x² - 6x

∴ 36 = x² - 4x + 3x² - 6x

36 = 4x² -10x

4x² -10x - 36 = 0

Divide through by 2

2x² - 5x - 18 = 0

Thus, we have shown that 2x² - 5x - 18 = 0

Now, we are to determine the value of length AB

The value of length AB is x cm.

Therefore, we will solve for x

From,

2x² - 5x - 18 = 0

2x² + 4x - 9x - 18 = 0

2x(x + 2) -9(x + 2) = 0

(2x - 9)(x + 2) = 0

2x - 9 = 0 OR x + 2= 0

2x = 9 OR x = -2

x = 9/2 OR x = -2

x = 4.5 OR x = -2

Since x cannot be negative, the value of x is 4.5

Thus,

AB is 4.5 cm

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Answer:

-4.9, negative four and eight ninths, four and seven tenths, 490%

Step-by-step explanation:

4 7/10 =approx. 4.7

-4 8/9 = -4.888889

490% = 4.9

-4.9

Answer:

first find 40 squared

[tex] {40}^{2} \\ = 1600[/tex]

1598,1599, 1600, 1601,1602

You can see that 1600 is between 1599 and 1601

The cost of each land is 120,000 dollars.

The mountain cabin on 1 acre of land costs 30,000 dollars.

The land cost 4 times as much as the cabin.

Therefore, the cost of each land can be calculated as follows:

cost of each land = 4 (30, 000)

cost of each land = 4 × 30000

cost of each land = 120,000 dollars

Therefore, the land that cost 4 times as much as the cabin cost 120000 dollars for each.

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