Answer:
y = 3x² - 21x + 30Step-by-step explanation:
Given is the factored form of a quadratic function.
The standard form is:
y = ax² + bx + cOpen parenthesis to convert it into standard form:
y = 3(x - 2)(x - 5) = 3(x² - 7x + 10) = 3x² - 21x + 30Answer:
3x² - 21x + 30Step-by-step explanation:
Keep in mind that the equation in standard form is y = ax² + bx + c
[Where "a, b, and c" are the constants.]
Simplify the distibutive property:
⇒ y = 3(x - 2)(x - 5)
⇒ y = (3x - 6)(x - 5)
Simplifying the R.H.S using the rule (a + b)(c - d) = ac - ad + bc - bd:
⇒ y = (3x - 6)(x - 5)
⇒ y = (3x² - 15x - 6x + 30)
⇒ y = (3x² - 21x + 30)
⇒ y = 3x² - 21x + 30
If possible, reorganize the equation in standard form:
⇒ y = 3x² - 21x + 30 (In standard form)
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A bag of oranges weighs 3/5 pounds. How much do
1 3/5 bags weigh?
.......................................................
The sum of the interior angle of a polygon is 1260 degrees. How many sides does the polygon have?
Answer: 9 sides
Step-by-step explanation:
If this is a perfect polygon then the answer is 9 sides. A perfect polygon is a polygon where all the sides and angles are congruent to each other.
180°(n-2) = 1,260°
n - 2 = 7
n = 9
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[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
In the given figure, Angle y is equal to Angle adjacent to 52° and 90° by Vertical opposite angle pair
And since they for straight line, their Angle sum will be equal to 180°
that is :
[tex]\qquad \tt \dashrightarrow \:y + 52 + 90 = 180[/tex]
[tex]\qquad \tt \dashrightarrow \:y + 142 = 180[/tex]
[tex]\qquad \tt \dashrightarrow \:y = 180 - 142[/tex]
[tex]\qquad \tt \dashrightarrow \:y =38 \degree[/tex]
Answer:
y = 38°
Step-by-step explanation:
We know that the angles in a straight line are added up to 180°.
So,
90 + y + 52 = 180
142 + y = 180
y = 180 - 142
y = 38°
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Answer:
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Step-by-step explanation:
ty sa points
cercaughters A mother says to her 5 years ago I 5 times as old as you were but 10 years Hence shall be only twice as old as you will find the posent age of mother T and daughter
Answer:
Daughter is now 10 The mother is 30
Step-by-step explanation:d
d=daugter
5d=mother
5d = 2d +5 +10
3d =15
d=5
5 years ago d=5 m=25
now d=10 m=30
in10 years d=20 m=40
What is the sum of the solutions to the equation below?
8x^2 + 2x - 3 = 0
A) 3/8 B) 1/4 C) -1/4 D - 3/8
Answer:
(x−1)43x3−8x2+10 can be resolved into partial fraction as x−1A+(x−1)2B+(x−1)3C+(x−1)4D
So , 3x3−8x2+10=A(x−1)3+B(x−1)2+C(x−1)+D
Put x=1 , we get 3−8+10=D
D=5
Comparing the coefficient of x3 on both sides we get , A=3 .
So equation reduces to 3x3−8x2+10=3(x−1)3+B(x−1)2+C(x−1)+5
Now compare the constant on both sides , 10=−3+B−C+5
=>8=B−C - (1)
Comparing the coefficent of x2 we get −8=−9+B
=>B=1
So , put B=1 in (1) , we get C=−7
Therefore , (x−1)43x3−8x2+10=x−13+(x−1)21−(x−1)37+(x−1)45
Step-by-step explanation:
hope it helps
what number equals 2/9?
Which of the following steps would you perform to the system of equations
below so that the equations have opposite y-coefficients?
4x+2y - 4
12x - y - 26
O A. Divide both sides of the top equation by 3
O B. Multiply both sides of the top equation by 2
O C. Multiply both sides of the bottom equation by 2
O D. Divide both sides of the bottom equation by 3
Step-by-step explanation:
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A cylinder has a diameter of 6 cm and a height of 3 cm. What is the surface area of the cylinder? Enter your answer, in exact form, in the box.
If the diameter and height of the cylinder are 6 cm and 3 cm. Then the surface area of the cylinder is 56.55 square cm.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
A cylinder has a diameter of 6 cm and a height of 3 cm.
Then the surface area of the cylinder will be
[tex]\rm SA = \pi d h[/tex]
We have
d = 6 cm
h = 3 cm
Then the surface area will be
[tex]\rm SA = \pi \times 6 \times 3 \\\\SA = 56.55[/tex]
More about the cylinder link is given below.
https://brainly.com/question/3692256
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please help
Find the volume of each prism. Round to the nearest tenth if nessary
What is the area under the normal curve between the z-scores of −1 and 0?
Enter your answer as a decimal, rounded to the nearest hundredth, like this: 0.42
Answer:
0.34
Step-by-step explanation:
You know from the empirical rule that 68% of the area of the normal distribution lies in the range z=-1 to z=1. The distribution is symmetrical, so half that area lies in the range z = -1 to z = 0.
area = 68%/2 = 34% = 0.34
__
Your calculator can tell you the same thing.
What is the scale factor of the enlargement of shape A to shape B?
Answer:
scale factor = 6
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, shape B to shape A
base of shape A = 1 , base of shape B = 6 , then
scale factor = [tex]\frac{6}{1}[/tex] = 6
After finding the ratio of their corresponding sides of triangles the scale factor we get is 6.
The difference in scale between an original item's scale and a new object that is its representation but is larger or smaller is known as a scale factor.
From figure
For small triangle:
base = 1 units
For large triangle:
base = 6 units
Now the scale factor = ratio of adjacent sides
Scale factor = (Base of large triangle)/(Base of small triangle)
Scale factor = 6/1
Scale factor = 6
Hence,
The scale factor is 6.
To learn more about the triangle visit;
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0.07 x what equals 441 ???
Step-by-step explanation:
[tex]0.07 \times x = 441[/tex]
[tex]x = \frac{441}{0.07} [/tex]
[tex]x = 6300[/tex]
An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 4057 feet and Plane B is at an altitude of 5000 feet. Plane A is gaining altitude at 60.75 feet per second and Plane B is gaining altitude at 40.25 feet per second.
How many seconds will pass before the planes are at the same altitude?
What will their altitude be when there’re at the same altitude?
Answer:
46 seconds6851.5 feetStep-by-step explanation:
The altitude of each plane can be expressed by an equation that adds the initial altitude and the product of time and its rate of climb.
plane A: y = 4057 +60.75t
plane B: y = 5000 +40.25t
__
We want to find the time when their altitudes are the same:
4057 +60.75t = 5000 +40.25t . . . . equate the expressions for y
20.50t = 943 . . . . . . . . . subtract (40.24t +4057)
t = 46 . . . . . . . . . . . . divide by the coefficient of t
At t=46, the altitude of the planes will be ...
y = 5000 +40.25(46) = 5000 +1851.5 = 6851.5
The planes are at the same altitude after 46 seconds.
Both planes will be at an altitude of 6851.5 feet.
Simplify the following expression.
6.64 ÷ 8
A.
1.245
B.
0.664
C.
0.83
D.
0.93
Answer:
[tex]0.83[/tex]
Step-by-step explanation:
[tex]6.64 \div 8[/tex]
[tex]0.83[/tex]
Answer:
The answer should be C.)0.83, hope this helps.
Height of a Toy Rocket A toy rocket (not internally powered) is launched straight up from the top of a building 50 ft tall at an initial velocity of 200 ft per sec. a. Give the function that describes the height of the rocket in terms of timet b. Determine the time at which the rocket reaches its maximum height and the maximum height in feet. c. For what time interval will the rocket be more than 300 ft above ground level? d. After how many seconds will it hit the ground?
The height of the toy is an illustration of the height function
The function of the toy velocityThe given parameters are:
Initial velocity, Vo = 200 ft per secInitial height, H = 50 ftThe function of the height is calculated as:
h(t) = -16t² + Vot + H
This gives
h(t) = -16t² + 200t + 50
Hence, the velocity function is h(t) = -16t² + 200t + 50
The time of maximum heightIn (a), we have:
h(t) = -16t² + 200t + 50
Differentiate
h'(t) = -32t + 200
Set to 0
-32t + 200 = 0
Subtract 200 from both sides
-32t = -200
Divide both sides by -32
t = 6.25
Substitute 6.25 for t in h(t)
h(6.25) = -16 *6.25² + 200 * 6.25 + 50
h(6.25) = 675
Hence, the time to reach the maximum height is 6.25 seconds and the maximum height is 675 feet
When the rocket will be at a height more than 300This is represented as
h(t) >300
So, we have:
-16t² + 200t + 50 > 300
Subtract 300 from both sides
-16t² + 200t - 250 > 0
Using a graphical calculator, we have:
t = 11.09s and t = 1.41 s
Hence, the rocket will be at a height more than 300 at 11.09s and 1.41 s
When it will hit the ground?This means that
h(t) = 0
So, we have:
-16t² + 200t + 50 = 0
Using a graphical calculator, we have:
t = 12.75
Hence, the rocket will hit the ground at 12.75s
Read more about height function at:
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Question 5 of 10
Which of the following is most likely the next step in the series?
Answer:
option A
Step-by-step explanation:
Answer os option a
You roll a 6-sided die two times.
What is the probability of rolling a 5 and then rolling a 3?
Write your answer as a fraction or whole number.
Answer:
1/36
Step-by-step explanation:
The chance of you rolling a 5 is 1/6
While the chance of you rolling a 3 is a 1/6
If you want both a 5 then a 3 then you multiply the fractions
1/6 * 1/6 = 1/36
The number of jelly beans placed in jars by a class of kindergarteners is normally distributed with an unknown population
mean and standard deviation. A random sample of 20 jars is taken and results in a sample mean of 43 jelly beans and
sample standard deviation of 6 jelly beans.
Using the t-distribution, the 80% confidence interval for the mean number of jelly beans is (41.22, 44.78).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 80% confidence interval, with 20 - 1 = 19 df, is t = 1.3277.
The other parameters are given as follows.
[tex]\overline{x} = 43, s = 6, n = 20[/tex].
Hence, the bounds of the interval are given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 43 - 1.3277\frac{6}{\sqrt{20}} = 41.22[/tex]
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 43 + 1.3277\frac{6}{\sqrt{20}} = 44.78[/tex]
The 80% confidence interval for the mean number of jelly beans is (41.22, 44.78).
More can be learned about the t-distribution at https://brainly.com/question/16162795
Barry's income can be calculated as $17 times the number of hours worked (h) added to his commission of $200. If he subtracts $300 to pay a bill, his income totals $580. Which expression represents Barry's income?
One group (A) contains 765 people. Three-fifths of the people in group A will be selected to win $50 fuel cards. There is another group (B) in a nearby town that will receive the same number of fuel cards, but there are 716 people in that group. What will be the ratio of nonwinners in group A to nonwinners in group B after the selections are made? Express your ratio as a fraction or with a colon.
Answer:
There are 1.07 non winners in group A for every 1 non winner in group B
Or: 1.07:1
Or: 7% more non winners in group A
Step-by-step explanation:
Group A:
765*3/5 = 459 non winners
Group B:
716*3/5 = 429 non winners
Final Calculation:
459/429 = 1.07
Help answer question
Answer:
Yes and yes
Step-by-step explanation:
complete the ordered pair so that it is a solution of 2/3x + y -1 = 0
Answer:
Step-by-step explanation:
No solution; 3x+y-1 =/ 0
You would use a back-to-back stem-and-leaf plot when you want to analyze the heights of the boys on the basketball team.
False
True
Answer:
true because there are going to be many heights already
Step-by-step explanation:
i it's true
this is because already there will be
so many heights
The area of circles
Answer:
Formula for the area of a circle;
A = π[tex]r^{2}[/tex]Where 'π' represents pi(3.14 or 22/7), and 'r' represents the radius which is being squared.
Plug in the radius into this formula:-
A = π[tex]r^{2}[/tex]
Note: I will be using 3.14 as pi(π).A = 3.14(4^2)
A = 3.14(16)
A = 50.24 centimetres is the area for this circle.
How many solutions does the equation
below contain?
-4-3t+ 1) - 7+ = 51 - 4
A.
no solution
B.
one solution
C. two solutions
D. infinitely many solutions
Answer:
A.no solution
Step-by-step explanation:
[tex]12t- 4 - 7t = 5t - 4[/tex]
[tex]12t - 7t = 5t - 4[/tex]
[tex]5t = 5t - 4[/tex]
[tex]5t - 5t = - 4[/tex]
[tex]0 = - 4[/tex]
if Bill
deposits $3000 in an account that earns 6.5% compound interest annually for 3.5 years.
How much interest will he have earned?
Answer:
$3,623.84 Exact answer without rounding | $3,623.85 ~ (Approximent Answer with rounding.)
Step-by-step explanation:
Compound Interest Has a Specific Formula:
This case is Exponential Growth.
Formula: y= ab^x
You need to set up the equation.
First we need to define the rate of growth meaning what do you have to do for the 6.5%.
You need to do 100% + 6.5% = 106.5%
You need to convert the percent to a decimal which will be 1.065
Now we need to start plugging things into our formula to solve.
Your initial Starting amount was $3000
So you need to have y=3000(b)^x
We now know that the rate of growth is 1.065 so the b would be 1.065
y=3000(1.065)^x
Our power to x is our 3.5 years.
Our Equation now:
y=3000(1.065)^3
Now you need to use a calculator to do this due to the amount of decimals and digits.
Remember pemdas when doing this!!!
The answer should result to $3,623.84 but if rounded then: $3,623.85
find the value of x and y in the figure below
Step-by-step explanation:
First find out the value of X and second find the value of Y and where is figure
