a parabola passes through the points (2,8), (6,2), and (8,8). what is the x-coordinate of its vertex?
a) 4
b) 5
c) 7
d) cannot be determined

Answer:

x = 2

Step-by-step explanation:

The left side would be (3x - 12)
The right side would be (-4x+2)

In an equation, 3x - 12 = -4x+2

Combine all the letters on the left and plain numbers on the right,

3x + 4x = 12 + 2

Note: When you transfer to the other side of the equal sign, the number will change its sign.

Simplify the 3x + 4x = 12 + 2,

                     7x = 14

                      [tex]x=\frac{14}{7}[/tex]

                      x = 2

⊱________________________________________________________⊰

Answer:

Step-by-step explanation:

[tex]\large\begin{gathered} \sf{Simplify \ using \ the \ distributive \ property:} \\ \sf{3(x-4)=2(-2x+1)} \\ \ \sf{3x-12=-4x+2} \\ \rm{Move \ 12 \ to \ the \ right, \ with \ the \ opposite \ sign} \\ \ \sf{ 3x=-4x+2+12} \\ \rm{Move \ -4x \ to \ the \ left, \ wth \ the \ opposite \ sign.} \\ \sf{3x+4x=14} \\ \rm{Collect \ the \ like \ terms} \\ \sf{7x=14} \\ \rm{Divide \ the \ entire \ equation \ by 7.} \\ \sf{\dfrac{7x}{7}=\dfrac{14}{7} \\ \sf{x=2} \ \bigstar \end{gathered}[/tex]

Done!!

⊱______________________________________________________⊰

Answer:

A. Scalene

E. Obtuse

Step-by-step explanation:

Obtuse are angles that are greater than 90°

Scalene is not congruent sides.

Answer:

awnser D is the only function

The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.

The solution of the equation means the value of the unknown or variable.

The equation is given below.

x – 2 = √(2x – 1)

Square on both side, then we have

               (x – 2)² = 2x – 1

         x² – 4x + 4 = 2x – 1

         x² – 6x + 5 = 0

   x² – 5x – x + 5 = 0

x(x – 5) – 1(x – 5) = 0

       (x – 5)(x – 1) = 0

                         x = 1, 5

The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.

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Answer:

Hence the expression [tex]$(y+7)(y+4)=y^{2}+11 y+28$[/tex]

Step-by-step explanation:

- The given expression is (y+7)(y+4).

- We have to multiply the given expression.

- Multiply the (y+7) by 4 , multiply the (y+7) by y then add like terms.

[tex]\begin{array}{r}y+7 \\\underline {\times \quad y+28} \\4 y+28 \\\underline {y^{2}+7 y }\\y^{2}+11 y+28\end{array}[/tex]

Answer:

well the value of x is 2 and the value of y is 1##

Step-by-step explanation:

I hope it will help you

Answer:

[tex]y=\frac{3}{4}x+2[/tex]

Step-by-step explanation:

So when you express a linear function in slope-intercept form it's given in the form of y=mx+b, where m is the slope, and b is the y-intercept. This is because as x increases by 1, the y-value will increase by m (because multiplication), and since the slope is defined as rise/run, the rise will be m, and run will be 1, giving you a slope of m/1 or m. The reason b is the y-intercept, is because whenever the linear function crosses the y-axis, the x-value will always be 0. Meaning that mx will be 0 because m * 0 will equal 0... and that leaves b by it self, so b will determine the y-intercept.

So if you look at the graph, the linear function crosses the y-axis as (0, 2) so the value of b will be 2. This gives you the equation y=mx+2.

Now to calculate the slope, we can take any two points and see how much the rise was and how much the run was. It can also be more formally defined in the equation: [tex]y=\frac{y_2-y_1}{x_2-x_1}[/tex]. So let's take the points (0, 2) and (8, 8). As you can see the x-value increases by 8 or "ran" by 8, and the y-value increased by 6. So the rise over run in this case is 6/8 which can simplified as 3/4. That is the slope. This gives you the complete equation of: [tex]y=\frac{3}{4}x+2[/tex]

Answer:

39

Step-by-step explanation:

37 = 96 %

x  = 100%

[tex]x =\frac{37(100)}{96} =38.54= 39[/tex]

[tex]\huge\boxed{39\ \text{students}}[/tex]

Note: The numbers in this problem are a little weird and don't work out perfectly. I'll demonstrate at the end of this answer how something seems a little off in the problem, but we'll get as close as possible.

We know from the problem that 37 students are equal to 96% of the class.

Let's write this as an equation:

[tex]37=0.96x[/tex]

Divide both sides of the equation by [tex]0.96[/tex] to isolate [tex]x[/tex].

[tex]38.54\approx x[/tex]

We'll round this to [tex]39[/tex] as the final answer.

It's important to note that you can't have partial students, only whole numbers.

If we do the math here, 37 out of 39 students is about 95%.
Also, 37 out of 38 is about 97%.

I'm not sure how the original writer of the question got 96%, but I suppose 39 is the best answer with what's been given.

The equation which is equivalent to -i among the answer choices is; i^(15), option A

It follows from the concept of complex numbers that the representation -i stands for √-1 and on this note, it follows that;

i² = -1

i³ = -i

i⁴ = 1

Hence, it follows that;

i^(15) = i⁴ × i⁴ × i⁴ × i³ = 1 × 1 × 1 × -i = -i.

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The conditional probability illustrates that's there's a 2/8 that the event A occurs.

It should be noted that probability simply means the likelihood of the occurence of an event.

In this case, it can be delivered that P(AID) and P(DIA) aren't equal.

Hence, P(D|A) has event A as its given event, resulting in 2/8 for a probability.

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Answer:

h(x) = 2^(x) - 1.

Step-by-step explanation:

Let's look at each equation:

f(x) = -3x +7, Well as x increases, since it's multiplication, there are "going to be more" -3's, so it's going to be decreasing.

g(x) = -4(2^x). While 2^x is increasing, because "there are going to be more 2's multiplied by each other" as x increases, it's being multiplied by a negative number, so it's actually going to be decrasing

h(x) = 2^(x) - 1. Here's it's going to be increases as x goes towards infinity because "there are going to be more 2's multiplied by each other", and there isn't any negative sign, while there is a negative 1, it's constant, so the overall value will be increasing

Answer:

It's either 16 or -16

Step-by-step explanation:

Subtract 41 and 57 and you get one of those two.

My bet is 16 due to you not being able to have a negative amount of bills in your wallet in real life.

Using the given information, the percent error is 52%

From the question, we are to calculate the percentage error

From the given information,

Prediction = 23 people

Actual = 48 people

Using the formula,

[tex]Percent \ error = \frac{|Prediction - Actual|}{|Actual|}\times 100\%[/tex]

[tex]Percent \ error = \frac{|23 - 48|}{|48|}\times 100\%[/tex]

[tex]Percent \ error = \frac{|-25|}{|48|}\times 100\%[/tex]

[tex]Percent \ error = \frac{25}{48}\times 100\%[/tex]

Percent error = 52.083%

Percent error ≈ 52%

Hence, the percent error is 52%

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Answer:

  a) 2.5

  b) 6.25

Step-by-step explanation:

For similar figures, the ratio of any corresponding linear dimensions is the same. The ratio of areas is the square of that.

The ratio of linear dimensions, larger to smaller, is ...

  (30 yd)/(12 yd) = 2.5

Perimeter is a linear dimension, the sum of side lengths. The ratio of perimeters is 2.5.

The ratio of areas, larger to smaller, is the square of the scale factor for side lengths:

  (2.5)² = 6.25

The ratio of the areas of the larger to smaller figure is 6.25.

Answer:

area = 78

Step-by-step explanation:

Area of triangle = 1/2  x  base  x  perpendicular height

                            ⇒ 1/2  x  13  x  12

                            ⇒ 78 units²

Answer: This really depends on how long you have to reach this goal.

Let’s say you want to make this amount in one month.

There is about 4 weeks in a month so you’ll need to divide 2112.24 by 4.

That would be 528.06 per week.

To find an amount per day you’ll need to divide 528.06 by 7.

That would be about 75.5 per day.

Please let me know if this doesn’t help.

Answer: the total area with the extension S≈82,3 foot²,  S>S'.

Step-by-step explanation:

D₁=8 foot    D₂=10 foot    a wide extension = 4 foot.

1) Let the total area with the extension S is the area of the circular table S₁

plus a wide extension S₂.

Considere S₁:

[tex]R_1=\frac{D_1}{2} \\R_1=\frac{8}{2} \\R_1=4 foot.\\S_1=\pi* R_1^2\\S_1=\pi *4^2\\S_1=16*\pi \\S_1\approx50,3\ foot^2.\\[/tex]

[tex]S_2=8*4\\S_2=32 \ foot^2.[/tex]

[tex]S\approx50,3+32\\S\approx82,3 \ foot^2.[/tex]

2)\ Considere S':

[tex]R_2=\frac{D_2}{2} \\R_2=\frac{10}{2} \\R_2=5 \ foot.\\S'=\pi *R^2\\S'=\pi *5^2\\S'=25*\pi \\S'\approx78,5\ foot^2.[/tex]

S>S'.

Good luck an' have a nice day!

Answer:

147

Step-by-step explanation:

Angles in a triangle add up to 180:

x + 23 + 10 = 180

x = 147

The correct answer is option A which is ZA = 3 cm

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

The triangle is shown below.

From the triangle, A is the concurrency point of angle bisectors of all vertices.

Consider ΔAYD,

Using the Pythagorean theorem,

AD² = AY² + YD²

5² = AY² + 4²

25 = AY² + 16

AY² = 25 - 16

AY² = 9

AY = √9 = 3 cm

Consider triangles ADY and ADZ.

∠AYD ≅∠AZD=90

∠ADY≅∠ADZ ( Angle bisector)

AD ≡ AD (common side)

The two triangles are congruent by the AAS postulate.

Therefore, by CPCTE, AY=ZA=3 cm

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Answer: 3cm

Step-by-step explanation: Trust Me! Answer is correct on Edge quiz!

Good Luck! :)

ZA= 3cm

Answer:

The highest number that divides each of the two or more numbers is the HCF or Highest Common Factor.

Step-by-step explanation:

Example: What is the HCF of {12,42,14}

Answer: The HCF is 2 as the biggest number they can all be divided by is 2. {12,42,14} = {2^2*3,2*3*7,2*7} The factors in each number is 2.

Answer: Option 2

Step-by-step explanation:

The vertex must have a y-coordinate of 5, so eliminate options 3 and 4.

Also, since there must be a maximum, the coefficient of [tex]x^2[/tex] must be negative. So, eliminate option 1.

This leaves us with option 2.

Answer:

(x - 4)^2 + (y + 1)^2=9

Step-by-step explanation:

The equation of a circle can be written using a kinda of fill-in-the-blank method if you know the coordinates of the center and the radius.

If the center is (h,k) and the radius is r, then fill in those given numbers into:

(x-h)^2 + (y-k)^2 =r^2

The center of your circle is (4, -1).

Fill in 4 for the h, -1 for the k and 3 for the r.

(x-4)^2+(y- -1)^2= 3^2

Simplify.

(x-4)^2+(y+1)^2=9

The equivalent expression to2-1/y/3+1/y is [tex]\mathbf{=\dfrac{(2y-1)}{(3y+1)}}[/tex]

Equivalent expressions are expressions does not look the same but when a value is being replaced with their variable, they end up giving the same result.

From the information given:

We have are to determine the equivalent expression to:

[tex]\mathbf{=\dfrac{(2-\dfrac{1}{y})}{(3+ \dfrac{1}{y})}}[/tex]

So if we multiply both the numerator and the denominator with 1/y, we have:

[tex]\mathbf{=\dfrac{(2y-1)}{(3y+1)}}[/tex]

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The expected number of pairs of adjacent cards which are both black is  650 / 51

For each pair of cards, the probability that they are both black is 26/52 * 25/ 51 = 25 / 102,

So since there are 52 pairs in the circle, the expected number of pairs which are both black is

25 / 102 * 52 = 650 / 51

Probability is genuinely how probable something is to happen. Every time we're unsure about the final results of an occasion, we can speak approximately the chances of sure results—how probably they're.

The evaluation of occasions governed by chance is referred to as statistics.

A sequence of movements where the outcomes are constantly unsure. The tossing of a coin, deciding on a card from a deck of playing cards, throwing a cube. It's far a single final results of an experiment. Getting a Heads even as tossing a coin is an event.

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Answer: 5

Step-by-step explanation:

By the inscribed angle theorem.

[tex]\frac{9}{15}=\frac{2x-1}{3x}\\\\27x=30x-15\\\\-3x=-15\\\\x=5[/tex]

Answer:

cos=24/25

tan=7/24

Step-by-step explanation:

sin=opposite/hypotenuse

therefore 7 is the opposite and 25 is the hypotenuse.

using pythagorean theorem we can find the adjacent. i.e hypotenuse squared= sum of adjacent squared and opposite squared.

h^2= a^2+ O^2

25 squared - 7 squared= 576

which is equal to 24 squared.

therefore adjacent=24

cos=adjacent/hypotenuse

cos=24/25

tan=opposite/adjacent

tan=7/24.

Answer:

[tex]\cos(\theta)= \dfrac{24}{25}[/tex]

[tex]\tan(\theta)=\dfrac{7}{24}[/tex]

Step-by-step explanation:

Definitions of primary trig functions

For a given acute angle in a right triangle :

...where the hypotenuse is the side across from the right angle, the opposite side is the side not touching the angle theta, and the adjacent side is the side touching the angle theta (but that isn't the hypotenuse).

We are already given the ratio for the Sine function, so we need to find the Cosine and Tangent function ratios.  It will be helpful to visualize what this triangle looks like.

The given equation states [tex]\sin(\theta)=\frac{7}{25}[/tex], so there is some right triangle, with a specific angle theta, that has a ratio of sides (opposite to hypotenuse) of 7 to 25.  For ease, we'll consider the triangle that has actual side lengths of 7 and 25 for those sides.  (See attached diagram)

Given that information, we can identify that the unknown side length is the adjacent side length.  Since the triangle is a right triangle, this value can be found through the Pythagorean Theorem.

The Pythagorean Theorem states that for any right triangle, [tex]a^2+b^2=c^2[/tex] where "c" is the length of the hypotenuse of the triangle, and "a" and "b" are the lengths of the other two sides of the triangle (often called "legs").  It does not matter which leg is chosen to be side "a" or side "b" due to the commutative property of addition, but "c" must be the hypotenuse.

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

Substituting known values, and simplifying...

[tex]a^2+(7)^2=(25)^2[/tex]

[tex]a^2+49=625[/tex]

Subtracting 49 from both sides to begin to isolate "a", and simplifying...

[tex](a^2+49)-49=(625)-49[/tex]

[tex]a^2=576[/tex]

Applying the square root property to isolate "a", and simplifying/calculating...

[tex]\sqrt{a^2}=\pm \sqrt{576}[/tex]

[tex]a=\pm 24[/tex]

[tex]a=24[/tex]  or  [tex]a=-24[/tex]

Under the assumption that the triangle is an acute triangle, the adjacent side length is a positive value, so we reject the negative solution, deducing that the adjacent side length must be 24.

Side note:  If there is more information in the context of the question that suggests that theta may be larger than 90°, then other factors will need to be taken into account.

Returning to the trig ratio definitions, we can identify the requested cosine and tangent ratios

[tex]\cos(\theta)=\dfrac{\bold{adjacent} \text{ side length}} {\bold{hypotenuse} \text{ length}} = \dfrac{24}{25}[/tex]

[tex]\tan(\theta)=\dfrac{\bold{opposite} \text{ side length}} {\bold{adjacent} \text{ side length}}=\dfrac{7}{24}[/tex]

Answer:

55

Step-by-step explanation:

To find the average you add up all numbers given then divide by the amount of numbers there were. The mean, or average, of the original 5 people was 13 since their ages added was 65, which you divide by 5 for 13. The new mean once the 6th person entered the room was 20. So, you do 6 [number of people] times 20 [average] to get 120. Taking 65 [added amount of original ages of the 5 people] away from 120 [the new added up ages of all 6 people], you get 55. This means 55 would be the 6th person's age.

Sorry if the explanation is confusing!

Call the total ages of the 6 people, x

To calculate the mean age of 6 people, we take the total age (x) and divide by the amount of people (6)

So, x : 6 = 20

-> The total ages of the 6 people are 20 x 6 = 120

We can calculate the 6th person's age by taking 120 and minus the total age of the other 5

-> 120 - (13+12+13+15+12) = 55

So, the 6th person's age is 55.

Answer:

3

Step-by-step explanation:

Start with the amount that he wants to pay with gigabytes and subtract the amount of his bill without gigabytes.

58.50-46.50=12

 Then divide that amount by the price of each gigabyte to determine how many gigabytes he can use while staying in budget.

12/4=3

Answer: 3

Inequalities help us to compare two unequal expressions. The gigabytes of data that Elijah should use while staying within his budget is 3 gigabytes.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given that Elijah pays a flat cost of $46.50 per month and $4 per gigabyte. He wants to keep his bill at $58.50 per month. Therefore, we can write the inequality for this condition as,

$46.50 + $4(x) ≤ $58.50

46.50 + 4x ≤ 58.50

4x ≤ 58.50 - 46.50

4x ≤ 12

x ≤ 12/4

x ≤ 3

Hence, the gigabytes of data that Elijah should use while staying within his budget is 3 gigabytes.

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An airplane flying at a constant speed of 600 miles per hour, will travel 1350 miles in 135 minutes.

The average speed of any object is the ratio of the total distance the object travels, and the total time taken by the object to cover that distance.

Thus, Average speed = Total Distance/Time taken.

In the question, we are asked the distance traveled by airplane in 135 minutes at the constant speed of 600 miles per hour.

First, we need to convert the time from minutes to hours as our speed is given in miles per hour.

To convert minutes to hours, we divide it by 60.

Thus, the time = 135/60 hours = 2.25 hours.

Now, we substitute the speed = 600 miles per hour, and time = 2.25 hours in the formula:

Average speed = Total Distance/Time taken

or, 600 = Distance/2.25,

or, Distance = 600*2.25 miles,

or, Distance = 1350 miles.

Thus, an airplane flying at a constant speed of 600 miles per hour, will travel 1350 miles in 135 minutes.

The question is incomplete. The complete question is:

"An airplane flies with a constant speed of 600 miles per hour. How far can it travel in 135 minutes".

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Answer:

We know,

Distance,d = speed × time

d = 600 × 2.25

d = 1350km

Hence, the airplane can travel 1350km in 135 minutes with a speed of 600 miles.