solve similar triangles (advanced) khan academy. solve for x

The inequality in vertex form represents the region containing the results of the year is y < -2(x - 25)² + 200 option (D) is correct.

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

From the graph:

The vertex is:

(25, 200)

The vertex form of the parabola:

y = a(x - h)² + k

y = a(x - 25)² + 200

Plug x = 30 and y = 150

a = --2

y = -2(x - 25)² + 200

The inequality will be:

y < -2(x - 25)² + 200

Thus, the inequality in vertex form represents the region containing the results of the year is y < -2(x - 25)² + 200 option (D) is correct.

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Check the picture below.

so is more or less the figure of a rectangular prism with a right-cylinder underneath that has a radius of 1, since it has a diameter of 2.

now, if we just get the volume of the prism, and then the volume of half of the cylinder, because only half-cylinder is really inside the prism, and then subtract that half-cylinder volume from that of the prism, what's leftover is the volume of the figure only.

[tex]\stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}\hspace{5em}\stackrel{\textit{volume of half a cylinder}}{V=\cfrac{1}{2}\pi r^2 h} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE volumes}}{\stackrel{prism}{(4)(4)(8)}~~ - ~~\stackrel{half~cylinder}{\cfrac{1}{2}\pi (\underset{r}{1})^2(\underset{h}{8})}}\implies 128~~ - ~~4\pi ~~ \approx ~~\text{\LARGE 115.43}~cm^3[/tex]

The measure of angle PSR is 105°.

An arc's angle at the center of the circle is twice as large as its angle at any other point on the circumference.

Given:

The centre of the circle is O.

P, R, and S are points on a circle.

∠POR = 150°

Let Q be a point on the circumference of the circle with centre O.

By half angle property,

∠POR = 2∠PQR

∠PQR = [tex]\frac{1}{2} * 150[/tex] = 75°

In the figure, the points on the circle PQRS form a cyclic quadrilateral.

A cyclic quadrilateral has opposite angles that measure a total of 180 degrees.

∠PQR + ∠PSR = 180°

∠PSR = 180° - 75°

∠PSR = 105°

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P (-5), replace x by (-5).

Solve the parentheses:

Combine like terms:

the error in the equation is 3 is not multiplied by 4 which gives wrong value of x .

A linear equation is a first-order (linear) term and a constant in an algebraic equation of the type y=mx+b, where m is the slope and b is the y-intercept. The previous equation, which has the variables y and x, is sometimes referred to as a "linear equation with two variables."

The typical form for linear equations with two variables is Ax+By=C. For instance, the linear equation 2x+3y=5 is in standard form. Finding both the intercepts of an equation in this way is quite easy (x and y).

3 (x + 4) = 13

3x + 12 = 13          \\the place where the error was occurred in the question\\

3x = 1

x = 1/3

this is correct value of x

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Answer:

HI

Step-by-step explanation:

HOW ARE

So,

The temperature was -10 degrees in the morning. Given that it dropped 15 degrees by midnight, we could substract 15 to -10 to find the temperature at midnight:

The temperature at midnight was -25 degrees.

b. Clearly,

c. The absolute value of the morning temperature is:

That's because:

The verdict on whether the frequency distribution given appears to be normal is; No, the distribution is not symmetric.

It follows from the task content that it is required to determine if the frequency distribution as given appears to be normal.

On this note, since a major distinctive feature of a normal distribution is that; there is a concentration of frequency in the middle and additionally, a normal distribution infers symmetry in the frequency distribution.

Therefore, since none of the data values (speed) can be chosen as the middle value, and the distribution is not symmetric, it follows that;

The frequency distribution in discuss is not a normal distribution because the distribution is not symmetric.

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The equation of the form [tex]f(x)=ax^2+bx+c[/tex] that must solve algebraically and f(1)=4, f(2)=13 and, f(4)=46 is [tex]\frac{5}{2}x^2+\frac{3}{2}x+5[/tex].

Putting x = 1 in the given equation, we get

[tex]f(1)=a(1)^2+b(1)+c[/tex]

f(1) = a + b + c = 4 ...(1)

Putting x = 2 in the given equation, we get

[tex]f(2)=a(2)^2+b(2)+c[/tex]

f(2) = 4a + 2b + c = 13 ...(2)

Putting x = 4 in the given equation, we get

[tex]f(4)=a(4)^2+b(4)+c[/tex]

f(4) = 16a + 4b + c = 46 ...(3)

Using elimination method to solve the set of linear equations, we get

(2) - (1), we get

3a + b = 9  ...(4)

(3) - (2), we get

12a + 2b = 33  ...(5)

Multiplying (4) by 2, we get

6a + 2b = 18 ...(6)

(5) - (6), we get

6a = 15

a = 15/6 = 5/2

Putting a = 5/2 in (4), we get

3(5/2) + b = 9

15/2 + b = 18/2

b = 3/2

Putting the values of a and b in (1), we get

5/2 + 3/2 + c = 9

4 + c = 9

c = 9 - 4

c = 5

Hence, the equation is [tex]\frac{5}{2}x^2+\frac{3}{2}x+5[/tex].

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The appropriate choice of ratio will be given by

Jonas got 30 oranges

What is ratio?

Ratio determines the comparision among many quantities with the same unit.

Here,

Let Mary got 3x oranges and Rejoice got 2x oranges

By the Problem,

                           [tex]2x = 24[/tex]

                             [tex]x = \frac{24}{2}[/tex]

                             [tex]x = 12[/tex]

Number of oranges Mary got = [tex]12 \times 3[/tex]

                                                 = [tex]36[/tex]

Number of oranges shared between Mary and Rejoice = [tex]24 + 36[/tex]

                                                                                            = [tex]60[/tex]

Fraction of oranges shared between Mary and Rejoice = [tex]1 - \frac{1}{3}[/tex]

                                                                                            = [tex]\frac{3 - 1}{3}[/tex]

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

Total number of oranges = [tex]\frac{60}{\frac{2}{3} }[/tex]

                                          = [tex]60 \times \frac{3}{2}[/tex]

                                          = [tex]90[/tex]

Number of oranges Jonas got = [tex]90 \times \frac{1}{3}[/tex]

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We are going to evaluate for the giving values

x | y | x + 3y

0 | 4 | 0 + 3(4) = 3(4) = 12

2 | 3 | 2 + 3(3) = 2 + 9 = 11

4 | 2 | 4 + 3(2) = 4 + 6 = 10

3 | 6 | 3 + 3(6) = 3 + 18 = 21

Simplification of the given problems without absolute value sign:

1.  |5-x|-|x+8|, if x>5 is equal to -13.

2.  |x − 2| + |8 − x| + 2, if 2 ≤ x < 8 is equal to 8.

3.  |x − 5| − |2 − x| + |x + 1|, if x ≥ 5 is equal to x -2.

4.  |7 − x| + |4 − 2x| − |x − 8, if x < 2 is equal to 3 -2x.

As given,

Simplification of the given problems without absolute value sign:

1. |5-x|-|x+8|, if x>5

 = x - 5-(x+8)

 = x-5 -x-8

 = -13

2. |x − 2| + |8 − x| + 2, if 2 ≤ x < 8

= x -2+ 8 -x+2

=8

3. |x − 5| − |2 − x| + |x + 1|, if x ≥ 5

 = x-5-(x-2)+(x+1)

=x-5-x+2+x+1

=x-2

4. |7 − x| + |4 − 2x| − |x − 8, if x < 2

= 7-x +4-2x-8 +x

=3-2x

Therefore, simplification of the given problems without absolute value sign:

1.  |5-x|-|x+8|, if x>5 is equal to -13.

2.  |x − 2| + |8 − x| + 2, if 2 ≤ x < 8 is equal to 8.

3.  |x − 5| − |2 − x| + |x + 1|, if x ≥ 5 is equal to x -2.

4.  |7 − x| + |4 − 2x| − |x − 8, if x < 2 is equal to 3 -2x.

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The constant of proportionality on the equation is 5.

What is constant of proportionality?

Constant of proportionality is defined as the ratio that relates two given value. When two values are directly or indirectly proportional to one another, there relation is expressed as y = kx.

We compare the general direct proportionality relation with the equation given.

The equation given : y = 5x

The direct relationship between y and x is :

y α x

y = kx - - - (1)

Where, y and x are variables and k is the constant of proportionality.

Comparing equation (1) with the equation given :

y = kx

y = 5x

We can observe that, k in the equation (1) equals to 5 in the given equation.

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Probability of an experiment consists of rolling a fair 15 -sided die with an event of rolling a number divisible by 3 is P(E)=(1 /3).

As given ,

Total number of outcomes of an experiment consists of rolling a fair 15-sided die 'n'

={1, 2, 3, …., 14, 15}

=15

Number of outcomes of an event 'E' showing rolling a number divisible by 3 'n(E)'

={3,6,9,12,15}

=5

Probability of event showing rolling a number divisible by 3 'P(E)'

=(Total number of favourable outcomes)/(Total number of outcomes)

=n(E)/n

= 5/15

=1/3

Therefore, probability of an experiment consists of rolling a fair 15 -sided die with an event of rolling a number divisible by 3 is P(E)=(1 /3).

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2.5% of 8 = .2

5/8 + .2/8 = 5.2/8

5.2/8 = .65 x 100 = 65%

65% of games cost 1 or 2 dollars

100% - 65% = 35%

!! after doing it i did realize I could've just converted 5/8 into a percent than added it.

or

5/8 = .625 + .025 = .65 x 100 = 65%; 100% - 65% = 35%

Answer:

5 times the length of the short piece = 75 inches

The length of the short piece =75 / 5 = 15 inches

Length of the long piece = 4 times the length of the short piece = 60 inches

Check: 15 + 60 = 75 inches

yay

Let x be the number of game he can finish in 1 hour

1/4 = 1/3 hour

x = 1 hour

cross-multiply

1/3 x = 1/4

Multiply both-side of the equation by 3

x = 3/4 of his level game

He can finish 3/4 of his level game in an hour

The length of the rectangle is 30 feet and the width of the rectangle is 15 feet.

Let l be the length l the rectangle and w be the width of the rectangle.

The area of a rectangular living room is 450 square feet.

⇒ A = l × w

⇒ 450 = l × w                     ................(1)

The length of the room is 15 feet less than three times the width.

So we get an expression,

l = 3w - 15

Substitute above vale of l in equation (1)

450 = (3w - 15) × w        

450 = 3w² - 15w

3w² - 15w - 450 = 0

w² - 5w - 150 = 0

(w - 15)(w + 10) = 0  

w - 15 = 0  or w + 10 = 0

w = 15    or    w = -10

But width of the rectangle cannot be -10

So, w = 15 feet

and l = 3(15) - 15

l = 30 feet

Therefore, the length of the rectangular living room is 30 feet and the width is 15 feet.

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A total of 8 cups of mix is needed for a Gatorade recipe calls for 2 cups of mix for every 4 cups of water if you have a total of 16 cups of water.

The unitary technique in actuality involves first determining the actual value of a single unit, alongside followed by the value of the necessary number of units.

The unitary approach is a kind of a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

2 mix for 4 cups of water

⇒ 1 mix for 2 cups

⇒ for 1 cup = 1/2 mix

so for 16 cups = 8 mix

A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit.

The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one liter of gas if it travels 44 km on two liters of fuel.

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The results based on divisibility rules are given below -

A divisibility rule is a convenient shorthand for checking if an integer is divisible by a given set divisor without actually doing the division, typically by looking at the digits of the number.

Rule of Divisibility for 2: The given integer's final/unit digit must be an even number or a multiple of two, i.e., 0, 2, 4, 6, and 8.

Dividend Rule for Number 5: The provided number should have a unit digit of 0 or 5.

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Step-by-step explanation:

Answer:

Danladi is correct

Step-by-step explanation:

Danladi is correct because 2^3×4^2 equals 128

8 to the 6th is 262144 and to the 5th is 32768

The measure of largest exterior angles is 150 degrees

Exterior angles are defined as angles of a polygon formed or created by two the sides of that polygon and sharing a common endpoint.

It is important to note that the exterior angle of a triangle is congruent to the sum of the two non-adjacent interior angles that are opposite to each other.

They are also known to be angles formed by a transversal line as it cuts through one of two lines and it is located on the outside part of the line.

Given the angles as;

Note that the sum of exterior angles are 360degrees

5x° + 9x° + 10x° = 360°

collect like terms

24x = 360

Make 'x' the subject of formula by dividing both sides by 24

x = 360/24

x = 15

But the largest angle is 10x = 10(15) = 150°

Hence, the value is 150°

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When you're reading a study that reports selecting a random sample of hospitals and estimating admission delay times, it's an example of C. probability sampling.

Probability sampling is the process of selecting a sample from a population when the selection is based on the randomization principle, often known as chance or random selection. In general, probability sampling is more difficult, time-consuming, and expensive than non-probability sampling.

Using a method based on probability theory, probability sampling is a strategy in which the researcher selects samples from a larger population.

Researchers can produce a sample that accurately represents the relevant real-world population by using probability sampling.

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You are reading a study that reports selecting a random sample of hospitals and estimating admission delay times. You know this is an example of:

a. Quota sampling

b. Convenience Sampling

c. Probability sampling

d. Sampling bias

The linear equation of given point (1, -7) and slope -1 is y = -x - 6.

Given:

Point(x₁ , y₁) = (1, -7)

Slope = -1

By using the Point-slope form of the linear equations, we get

y - y₁ = m(x - x₁)

⇒ y - (-7) = -1(x - 1)

⇒ y + 7 = -x + 1

⇒ y = -x + 1 - 7

⇒ y = -x - 6

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Answer:

She will have 23.1 gallons left after 3 days.

Step-by-step explanation:

We know Margaret uses an average of 1.3 gallons of gas every day and her car holds 27 gallons total. In three days, she would use 3 times her daily average, or 3 * 1.3 = 3.9 gallons consumed in 3 days. To find how many gallons are left in her tank after 3 days, we would subtract 3.9 gallons from 27 gallons. This equals exactly 23.1 gallons of gas.

The height of the ball be after 3 seconds will be 72.2 feet.

From the information given, it should be noted that the astronaut on the moon throws a baseball upward and the height of the ball in feet

(y) is related to the number of seconds since the ball was thrown (x).

In this case, it should be noted that the function is illustrated as:

y = -2.7x² + 30x + 6.5

Therefore, it was given that x = 3. It should be noted that this will be put back into the function. This will be:

y = -2.7x² + 30x + 6.5

y = -2.7(3)² + 30(3) + 6.5

y = -24.3 + 90 + 6.5

y = 72.2

The height is 72.2 feet.

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The ball reaches a maximum height of 96 feet and it spent 0 seconds in the air

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The quadratic equation is given as

h(t) = -16t^2 + 96

Differentiate the equation of the function

So, we have

h'(t) = -32t

Set the differentiated function to 0

So, we have

-32t = 0

Divide both sides by -32

So, we have

t = 0

Substitute t = 0 in the equation h(t) = -16t^2 + 96

So, we have

h(0) = -16(0)^2 + 96

Evaluate

h(0) = 96

This means that the maximum height of the ball is 96 feet

Recall that the quadratic equation is given as

h(t) = -16t^2 + 96

Next, we differentiate the equation of the function

So, we have

h'(t) = -32t

Set the differentiated function to 0

So, we have

-32t = 0

Divide both sides by -32

So, we have

t = 0

Hence, the ball spent a total of 0 seconds in the air

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