Mathematics High School

A parabola has two x intercepts at (-2 , 0) and (3 , 0) and passes through the point (5 , 10). Find the equation of this parabola.

Answers

Answer 1
y = a(x + 2)(x - 3) : equation of the parabola in factored form 10 = a(5 + 2)(5 - 2) : (5 , 10) is a point on the graph of the parabola and therefore satisfies the equation of the parabola. a = 5/7: solve the above equation for a.

Related Questions

I need help math Brainliest

Answers

the answer is a. you have a large monthly car payment

that is the reason you would want a larger than normal financial reserve

Suppose that x=6 and y=8. If y is inversely related to x, what it y when x=3?

4
5
16
18

Answers

X equals 6 and y equals 8 and y is complete buddies with x, Y would definitely be 4 when x is 3 because they are halved. Half of 6 is 3 and half of 8 is four. If we half them both we get our answer. 5, 16, and 18 would all be classified as incorrect answers.

Credit to: Jdoe0001.

C. 16

Matt is saving to buy a new motorcycle. If he deposits $60 at the end of each month in an account that pays an annual interest rate of 3.5%, how much will he have in 15 months? Assume that the compounding is being done monthly.,

Answers

This is a problem of compound interest because the interest received one month is added to the money deposited on which you calculate the interest the next month.

You need to apply the following formula:
C = P[ [tex] (1+r)^{t} [/tex] - 1]
where:
C = compound interest you need
P = original amount of money deposited
r = is the rate, written as a rational number
t = number of months

Pluggin in numbers:
C = 60[ [tex] (1+0.035)^{15} [/tex] - 1] = 40.52$

Now, you need to add this amunt to the original amunt:
(60+40.52) = 100.52$

Therefore, Matt will have 100.52$ after 15 months.

How do I solve this? Please explain.

Answers

Volume is the product of base area and height.

The first candle will have a volume of
.. V = Bh = (21 cm^2)*(8 cm) = 168 cm^3

The second candle will have a volume of
.. V = Bh = (7 cm^2)*(14 cm) = 98 cm^3

The total volume of the two candles is
.. 168 cm^3 +98 cm^3 = 266 cm^3

Josie is 6 cm^3 short of the amount required for the two candles she has in mind.

No, the base area of the second candle cannot be 7 cm^2. There is not enough wax to make a candle with that area 14 cm tall.

25 points!

Answer both! please leave explanation!

Answers

1) To solve for x you'll use the sine formula

sin 27 = 34/x
x = 34/sin27
x = 74.89

2) to find the value of x you'll use the tangent formula

tan 49 = x/55
55(tan49) = x
63.270

What is the volume of a cylinder with base radius 3 and height 8?

Answers

Answer is provided in the image attached.

Final answer:

The volume of a cylinder with a base radius of 3 and a height of 8 is approximately 226.195 cubic units, using the formula V = πr²h.

Explanation:

The volume of a cylinder is calculated using the formula V = πr²h, where π is the constant pi (approximately 3.14159), r is the radius of the cylinder's base, and h is the height of the cylinder. For a cylinder with base radius 3 and height 8, we use the values directly in the formula:

V = π×(3²)×8

V = π×9×8

V = π×72

V = 3.14159×72

V ≈ 226.195 cubic units

Therefore, the volume of the cylinder is approximately 226.195 cubic units.

The focal length, F, in a camera is given by the following function, where d is the distance from the lens in the camera to the object being photographed.

F = 2.24d/ d +2.24

Write an equation that expresses distance, d, as a function of the focal length, F.

Answers

You are asked to solve the equation given for d. As it is a proportion you can cross multiply and then isolate the d.

[tex]F= \frac{2.24d}{d+2.24} [/tex]
[tex]F(d+2.24)=2.24d[/tex]
[tex]Fd+2.24F=2.24d[/tex]

Next factor out d to obtain

[tex]2.24F=d(2.24-F)[/tex]
[tex]d= \frac{2.24F}{2.24-F} [/tex]

Using function notation: [tex]G(d)= \frac{2.24F}{2.24-F} [/tex]

Answer: D) d = -2.24F/F-2.24

This figure shows circle Z with chords AB and RS .

mAR=55°
mRB=66°
AB=8 m
RS=8 m

What is ​ mRS ​ ?

Enter your answer in the box

Answers

We have that since the chords are equal, the arcs are equal too. Hence AB=RS. We also have that AB=AR+RB and RS=RB+BS. By equating these two, we have that AR=BS. Hence BS=55 degrees. Substituting back, since we know RB and BS, we get: RS=55+66=121 degrees

Answer:

121 degrees

Step-by-step explanation:

I took the test peeps

On a rombus AB=27, m

Answers

Angle ADC = 180- 74 = 106 degrees

PLEASE SOMEONE HELP ME WITH THIS
Hurryyy!!!!
ASAP~ BRAiNLiEST AVAILABLE TO CORRECT ANSWER

1st Blank options : +6, +1, +7, +13
2nd blank options: 7,13, 6, 1
3rd blank options: +6 , -1 , +7 , +1
4th blank options: 71 ,59, 69, 61

Answers

Look at the beginning of the recursive formula:

[tex]\sf f(1)=7,f(n)=f(n-1)[/tex]

It gives us the first value, which is 7. The second part means that for whatever term we want to find, we plug that in for 'n'. Say we want to find the second term, let's plug in 2 for 'n':

[tex]\sf f(2)=f(2-1)=f(1)[/tex]

We are left with f(1), which is given as 7. So the second term is 7 and then we have the leftover blank. We already know that the second term is 13. 13 - 7 = 6. Therefore, what must be missing from this recursive formula is + 6.

[tex]\sf f(n)=f(n-1)+6[/tex]

For the explicit function, we want to know what will give us these same values if we plugged in which term we want for 'n'. So if we plugged in 1 for 'n', we want to get 7, and if we plugged in 2 for 'n' we want to get 13, and so on. I can spot the similarity that all of these are additions of 1 to the multiples of 6. 6 * 1 = 6 + 1 = 7, 6 * 2 = 12 + 1 = 13, and so on. We could just write this as:

[tex]\sf 6n+1[/tex]

If you tried plugging in 1, you'd get 7, if you plugged 2 in, you'd get 13, and so on. So this is our explicit formula, the 2nd blank should be 6, and the 3rd blank should be + 1.

For the fourth blank, f(10) would just be plugging in 10 for 'n' into our formula, let's do this:

[tex]\sf 6n+1[/tex]

[tex]\sf 6(10)+1[/tex]

Multiply:

[tex]\sf 60+1[/tex]

Add:

[tex]\sf 61[/tex]

So the 4th blank should be 61.
1st blank: each term is 6 more than the previous one, so the appropriate choice is "+6"

2nd blank: The way we write the generic term of an arithmetic sequence is
  a[n] = a[1] +d*(n -1)
You have a[1] = 7 and d = 6, so this is
  a[n] = 7 +6*(n -1) = 6 +6n -6 = 6n +1
The appropriate choice for the 2nd blank is "6"

3rd blank: see the discussion for the 2nd blank. The appropriate choice is "+1"

4th blank: a[10] = 6*10 +1 = 61. The appropriate choice is "61"

Find the number of sides of a regular polygon if the interior angle is 150

Answers

180-150= 30

360/30= 12.

remember that no matter what is the polygon the sum of EXTERIOR angle is 360.
and 1 exterior angle + 1 interior angle = 180.

which trig functions have a period of 2pi?

Answers

Tangent and its inverse, cotangent, have a period of pi. The others have a period of 2π.

54 is 60% of what number?


Enter your answer in the box.

Answers

60% of 90 = 54!
I hope I helped!

Answer:The answer would be 90

Step-by-step explanation:


Look at the figures. How can you prove these triangles are congruent?



∆ABC ≅ ∆DEF by the SAS Postulate.

∆ABC ≅ ∆DEF by the SSS Postulate.

It is not possible to determine if the triangles are congruent.

Answers

It is not possible to determine if the triangles are congruent

by SSS, you need to know AC=DF, but there is no way to know it.

by SAS, you need to know ∠ABC=∠DEF, no way to know as well.

The sum of two numbers is 240. the larger number is 6 less than twice the smaller. find the numbers. the smaller number is , and the larger number is

Answers

The sum of two numbers is 240. The larger number is 6 less than twice the smaller. Find the numbers.
----------
Let the smaller be "x" ; Larger is "2x-6"
EQUATION:

x + 2x-6 = 240

3x= 246

x = 82 (smaller)

2x-6 = 158 (larger)

The smaller number is 82 and the larger number is 158.

Given that, the sum of two numbers is 240.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the smaller number be x.

The larger number is 6 less than twice the smaller.

Larger number = 2x - 6

Now, the sum of two numbers is 240.

So, x+2x-6 = 240

⇒ 3x - 6 =240

⇒ 3x = 246

⇒ x = 82

Larger number = 240 - 82

= 158

Therefore, the smaller number is 82 and the larger number is 158.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ5

what is the answer too......5(x+9)

Answers

Hi there!

To solve for x in this problem, we need to distribute the 5 using the distributive property and then simplify.

5 * x + 5 * 9
= 5x + 45

So, the most simplified form of this expression would be 5x + 45.

Hope this helps!
5(x+9) distribute the 5 to the x and 9.
5*x + 5*9 =
5x + 45
You have to get the x alone so divide both of them by 5
5x/5 + 45/5 = 
x + 9 
To get the x alone subtract it. 
x - x + 9 = 
9 = -x  can't leave x a negative so dived both sides by -1
9/-1 = -x/-1 =
-9 = x or x = -9
Hope this Helps!

A baker has three banana muffin recipes. Recipe A uses 3 bananas to make 12 muffins. Recipe Buses 5 bananas to make 24 muffins. Recipe C uses 11 bananas to make 48 muffins.

Answers

Answer:

From least to Greatest: B, C, A

Step-by-step explanation:

For each recipe, dividing the number of bananas needed by the number of muffins  will give us the number of bananas per muffin.

A: 3/12 = 0.25B: 5/24 = 0.21C: 11/24 = 0.23

As you can see here, Recipe A gives you 0.25 Bananas per muffin, Recipe B gives you 0.21 Bananas per muffin and recipe C will give you 0.23 Bananas per muffin.

Hope this helps!

Answer:

B,C,A

Step-by-step explanation:

Medal will be given to the best answer.


Which of the following is a solution to the equation y = 3x - 1 ?
A. (4,1)
B. (2,5)
C. (4,3)
D. (0, -3)

Answers

B. (2,5)  
For this problem, simply plug in the X values and calculate the Y value and verify that the Y value matches the value given. 
 A. (4,1); X = 4: 3x - 1 = 3*4 - 1 = 12 - 1 = 11. 11 does not match 1.
 B. (2,5); X = 2: 3x - 1 = 3*2 - 1 = 6 - 1 = 5. 5 matches 5.
 C. (4,3); X = 4: 3x - 1 = 3*4 - 1 = 12 - 1 = 11 does not match 3
 D. (0,-3); X = 0: 3x - 1 = 3*0 - 1 = 0 - 1 = -1 does not match -3
 
 And of the above, only option "B. (2,5)" matches.

A man 50 years old has 8 sons born of equal intervals. The sum of the ages of the father and sons is 186. What is the age of the eldest son if the youngest is 3 years old.,

Answers

To find the age of the eldest son in a family where the father is 50 and has 8 sons with a total age sum of 186, and the youngest son is 3, one can determine the age difference between siblings and use the formula for the sum of an arithmetic series.

The question is asking us to determine the age of the eldest son, given that the sum of the ages of a 50-year-old father and his 8 sons is 186 years and the youngest son is 3 years old. Let's assume that the sons are born at equal intervals; we can denote the age difference between each son as 'd' years.

The sequence of the sons' ages forms an arithmetic series where the youngest son is 3 years old (the first term of the series, or 'a1'), and the eldest son's age will be 'a1 + 7d' (since there are 8 sons).

Since the sum of an arithmetic series is given by the formula 'n/2 * (a1 + an)', where 'n' is the number of terms, 'a1' is the first term and 'an' is the last term, we can set up the equation:
8/2 * (3 + (3 + 7d)) = 186 - 50 (subtract the father's age from the total sum).
This simplifies to 4 * (3 + 3 + 7d) = 136, or '4 * (6 + 7d) = 136'. Dividing both sides by 4, we get '6 + 7d = 34', which leads to '7d = 28' and thus 'd = 4'.

Therefore, the age of the eldest son will be '3 + 7*4', which equals 31 years old.

Hi need this done fast, please
Andrea is planting a rectangular garden with a length of 6 feet and a width of 5 feet. Her mother is planting another garden that is 60% of the length of Andrea's garden and 150% of the width of Andrea's garden.

The length of her mother's garden is--- feet, and the width is---- feet.

Answers

Length:
60% of 6 is 3.6

3.6 x 6 = 21.6


Width:
150% of 5 is 7.5

7.5 x 5 = 37.5

So her mothers garden should be 21.6 feet in length, and 37.5 feet in width.

The answer is 3.6 and 7.5

A certain drug is made from only two ingredients: compound a and compound
b. there are 7 milliliters of compound a used for every 4 milliliters of compound
b. if a chemist wants to make 748 milliliters of the drug, how many milliliters of compound b are needed?

Answers

272, i just kept on adding 7 and 4 equally untill i got 748 and figured out you need 272 b and if it asks for a, the answer is 476

Can someone explain the Pythagorean theorem to me, please?

Answers

Pythagorean theorem is applied to the right triangles. 

Pythagorean theorem is a²+b²=c².

a is the length is the leg, b is also a leg and c is the hypotenuse

hey I really need help its a test -3x=48


5x-1=29



4(x-6)+7=23






3(x-4)+5x=4





Answers

 -3x=48 ---> x=-16
5x-1=29 --> x=6
4(x-6)+7=23 --> x=10
3(x-4)+5x=4 --> x=2

At 9:00 am two cars started from the same town and traveled north on the same road. one ca traveled at a rate of 35 mph and the other at a rate of 40 mph. after how many hours will the cars be 30 miles apart

Answers

35 x 6 = 210 
40 x 6 = 240 

240 - 210 = 30 

so after 6 hours the cars will be 30 miles apart 

am i correct?

Which of the following describes how to translate the graph of y = |x| to obtain the graph of y = |x + 1| - 2?


shift right 1 and down 2
shift left 1 and down 2 <<<
shift right 1 and up 2,

Answers

You are actually incorrect, as setting x=0 shows that the shifted graph needs to hit the y-axis at -2 (a downshift of 2). Similarly setting y=0, we find that x then becomes -1, since the absolute value of x +1 =0 implies that x=-1. So the correct answer is actually a shift down of 2 and left of 1.

Answer: both of u are wrong its one unit shift up one unit shift down


How do I solve this?

Answers

This problem can be worked with units of feet in the vertical direction and units of inches in the horizontal direction, as long as you maintain that relationship.

I find it convenient to draw a graph of a line that represents the ladder. I choose to have the y-intercept be where the ladder touches Catie's head (5.5 feet above the ground), and the x-intercept to be where the ladder touches the ground, 16 inches away from Catie.

Then the wall is 4.5 feet (54 inches) from the ladder's base, or 38 inches in the other direction from Catie. The graph shows the ladder hits the wall at a height of about 18.6 feet.

The graph shows the calculations for the position of the wall and for the equation of the line. (The line is written in "intercept form.") The graphing calculator shows the intercept points, so no "work" is required except to highlight them.

the leg of each isosceles right triangle when the hypotenuse is of the given measure. Given = 5sqrt6

Answers

so, the triangle is a right-triangle and is an isosceles one, namely, it has twin legs, thus, check the picture below.

I would like help with the question. It's part of my assigment, but I have trouble with this type of math. If someone understands, can you explain it to me as well? For future reference?

In Panama City in January, high tide was at midnight. The water level at high tide was 9 feet and 1 foot at low tide. Assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in January for Panama City as a function of time (t).,

Answers

The cosine function cos(x), as you know, has a peak at x=0, a minimum at x=π, and another peak at x=2π. That is, its period is 2π. Its amplitude is 1, meaning the peak is +1 and the minimum is -1.

Problems where sine or cosine functions are used to model periodic behavior are problems in scaling. You need to match the period and amplitude of your scaled cosine function to the period and amplitude of the phenomenon you are modeling.

Here, high tides are 12 hours apart, so we need to scale x by a factor that turns 12 hours into 2π. That might be x ⇒ 2πx/12 or (π/6)x.

The high tide is 9 ft, and the low tide is 1 ft, so we need to do vertical offset and scaling to make the peak of our transformed cosine function be 9 and its minimum be 1. That difference is 8, so has an amplitude of ±4 around a midline of (9+1)/2 = 5.

Then our tide model is
.. water level = 5 +4*cos((π/6)t)

Identify the 25th term of the arithmetic sequence 2, 1 and 3 over 5,
1 and 1 over 5 …
@ranga

Answers

First, you have to transform your numbers into proper fractions:
1 and 3/5 = (5+3)/5 = 8/5
1 and 1/5 = (5+1)/5 = 6/5

Therefore your arithmetic sequence is 2, 8/5, 6/5, ...

In an arithmetic sequence, the difference between a given term and the preceding one is equal to the difference between the following term and the given one. In your case:
d = 8/5 - 2 = (8-10)/5 = -2/5
As a prove: d = 6/5 - 8/5 = -2/5

Now, in order to find the 25th term you need to apply the formula:
an = a + (n - 1)d
where an is the number you are looking for, a is the first term, n is the term you are looking for and d is the distance.
Hence, 
a₂₅ = 2 + (25-1)(-2/5) = 2 - 24·2/5 = 2 - 48/5 = (10-48)/5 = -38/5

-7 3/5 is the correct answer simplified.

100p for an answer please

Answers

n+8
 For n=5.3
 5.3+8=13.3
 All that apply:

 1) First, write an expression.
 2) the correct expression is: n + 8
 3) second, substitute 5.3 for the variable, n. 
 4) third, simplify by adding 5.3 and 8
 5) the answer is 13.3 
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