Answers
f(x) = 5x^2 + 25x + 30
============================================================
Explanation:
The roots, aka x intercepts, of this curve are x = -3 and x = -2. This is where the graph crosses the x axis.
Since x = -3 is a root, this makes x+3 a factor of the quadratic. Similarly, x = -2 leads to x+2 as another factor. I'm using the zero product property.
So far we have found that the polynomial is (x+3)(x+2). This isn't the full factorization because if we plugged x = -1 into that expression, then we would get
y = (x+3)(x+2)
y = (-1+3)(-1+2)
y = (2)(1)
y = 2
But we want y = 10 instead. So we must multiply that factorization by 5 to jump from 2 to 10 (i.e. 5*2 = 10)
Therefore, the full factorization of this parabola is y = 5(x+3)(x+2)
Now let's expand everything out and simplify
y = 5(x+3)(x+2)
y = 5(x^2+2x+3x+6)
y = 5(x^2+5x+6)
y = 5x^2+5*5x+5*6
y = 5x^2 + 25x + 30
Choice C is the final answer
-------------------------
To check this, we can plug in x = -3 and we should get 0
y = 5x^2 + 25x + 30
y = 5(-3)^2 + 25(-3) + 30
y = 5(9) + 25(-3) + 30
y = 45 - 75 + 30
y = -30 + 30
y = 0
This proves that x = -3 is a root of y = 5x^2 + 25x + 30
I'll let you check x = -2. You should also get y = 0 when plugging this x value in.
Plugging x = -1 should lead to y = 10 as the last bit of confirmation. I'll let you check this one as well.
Related Questions
x - (-20) = 5 _________________
Answers
X - (-20) = 5
When you subtract a negative, change it to addition:
X + 20 = 5
Subtract 20 from both sides:
X = -15
Answer:
[tex]\boxed{x=-15}[/tex]
Step-by-step explanation:
[tex]x-(-20)=5[/tex]
[tex]\sf Distribute \ negative \ sign.[/tex]
[tex]x+20=5[/tex]
[tex]\sf Subtract \ 20 \ from \ both \ sides.[/tex]
[tex]x+20-20=5-20[/tex]
[tex]x=-15[/tex]
round off 3867 in nearest 100
Answers
Answer:
3900
Step-by-step explanation:
since its to the nearest 100th we use the common rule that if the number is greater than half way then we round up otherwise if it is less then we round down. In the number 3867, 867 is greater than 850 so we round up. It becomes 3900 then.
(a) An angle measures 40°. What is the measure of its complement?
(b) An angle measures 63°. What is the measure of its supplement?
Answers
Answer:
see below
Step-by-step explanation:
Complements add to 90 degrees
x+40 = 90
x = 90-40
x = 50
Supplements add to 180
y+63 =180
y = 180-63
y = 117
If the sum of the measures of two angles is 90° they are known as complementary angles.
Let the value of unknown angle be x.According to the question
⇨x + 40° = 90°
⇨x = 90° - 40° [Subtract]
⇨x = 50°
Complement angle is 50°
____________________(b)If the sum of the measures of two angles is 180° they are known as supplementary angles.
Let the value of unknown angle be x.According to the question
⇛x + 63° = 180°
⇛x = 180° - 63° [Subtract]
⇛x = 117°
Supplement angle is 117°
If the sum of the measures of two angles is 90° they are known as complementary angles.
Let the value of unknown angle be x.According to the question
⇛x + 40° = 90°
⇛x = 90° - 40° [Subtract]
⇛x = 50°
Complement angle is 50°
____________________(b)If the sum of the measures of two angles is 180° they are known as supplementary angles.
Let the value of unknown angle be x.According to the question
⇨x + 63° = 180°
⇨x = 180° - 63° [Subtract]
⇨x = 117°
Supplement angle is 117°
A local gym charges a $25 monthly membership fee plus $2 per hour for aerobics classes. What is the linear equation that describes the relationship between the total monthly cost (Y) and the number of class hours each month (X)
Answers
Answer:
The equation is same as the equation for a straight line Y= mx+cStep-by-step explanation:
The linear equation that describes the relationship between the total monthly cost Y and number of class hours in each month X is the same as the equation of line which is
[tex]Y= mx+c\\\\ Y= 2X+25[/tex]
where Y= the dependent variable, monthly cost
x= the independent variable, the number of hours for aerobic classes
c= the intercept, $25
I need help!!! Need it asap!!!!!
Answers
Answer:
Not enough infomation, you need to provide #12
Step-by-step explanation:
Chen is baking muffins and banana bread for a brunch buffet. He needs 3 and one-fifth cups of flour to make the muffins and 3 and two-thirds cups of flour to make the banana bread. Which is the best estimate of the number of cups of flour that Chen needs to bake both recipes?
Answers
Options :
A. 6 cups of flour
B.7 cups of flour
C.8 cups of flour
D.9 cups of flour
Answer:
B.7 cups of flour
Step-by-step explanation:
Given the following :
Cups of flour required to make muffins = 3 1/5
Cups of flour required to make banana = 3 2/3
Number of cups of flour required to make both recipe :
(cups of flour required to make muffins + cups of flour required to make bread)
(3 1/5 + 3 2/3) = 3+3+(1/5 + 2/3)
= 6 + (1/5 + 2/3) = (3 + 10)/15 = 6 + (13/15)
6 13/15 = 6.8666666
The best estimate is to round to the nearest whole number = 7
Answer: The answer is 7
Step-by-step explanation:
I got it right in my quiz! Hope this helps (:
Evalute n2+2N for N=5
Answers
Answer:
Hey there!
Do you mean- [tex]n^2+2n?[/tex]
If so, then your answer would be 5^2+2(5), or 35.
Let me know if this helps :)
In 2008, golfer Annika Sornestam had a driving accuracy of 71%. That is, on par 4 and par 5 holes, her tee shot landed in the fairway 71% of the time. Explain how to use a spinner to simulate Sorenstam’s performance in a round of golf where she attempts 15 drives. (Hint: What type of chart is a spinner? What does each piece represent?)
Answers
Answer:
Ok, we know that the driving accuracy is of 71%.
Then the first step is to get a spinner that is enumerated from 1 to 100 (in such way that each number is equispaced)
Now, we can mark a section between numbers 1 and 71. (this regio represents the cases where the shot lands in the fairway) and the unmarked region represents the cases where the shot does not land in the fairway.
Now, for each shot, we can spin our spinner next to a fixed pencil, depending on the section of the spinner that is marked by the pencil when the spinner fully stops, we can guess if the shot landed or not in the fairway.
In this way the shot has the region from 1 to 71 (71%) to land in the fairway
and the region from 72 to 100 to not land in the fairway.
If you want to simulate Sorenstam’s performance in a round of golf where she attempts 15 drives, you need to spin the spinner 15 times, and record the oucomes.
is the measure of how much the values in a data set vary, or deviate, from the mean; it tells us how spread out the data is from the mean.
Answers
Answer:
Standard deviation
Step-by-step explanation:
The standard deviation provides a measure of the overall variation in a data set. The standard deviation is always positive or zero. The standard deviation is small when the data are all concentrated close to the mean, exhibiting little variation or spread.
Helpppp please!!!!!!
Answers
Answer:
5/2
Step-by-step explanation:
tan&= 2/5(p/b)
here,
p=2,b=5
cot&=b/p
=5/2
in digging a pipe trench that measures 29 feet long, 2 feet 9 inches wide, and 3 feet 6 inches deep.
How many cubic yards of earth were removed from the site?
Answers
Answer:
10.34
Step-by-step explanation:
converting digits to feet,
3ft 6in = 3.5 ft
2ft 9in = 2.75 ft
now feet to yards
3.5ft = 1.16666667 yards (rounded)
2.75ft = 0.9166666667 yards (rounded)
29ft = 9.66666667 yards (rounded)
multiplying them, you'll get approximately 10.34 cubic yards (rounded), that's the volume.
or you can multiply the digits in feet,
3.5×2.75×29
= 279.125 cubic ft
now to convert to cubic yards from cubic ft,
279.125/3³
= 10.337963..
= 10.34 (rounded to the nearest hundredth)
fin the slope of the line that is perpendicular to y=1/3x
1. 3
2. -3
3. -1/3
4. 12
Answers
Answer:
-3
Step-by-step explanation:
When a line is perpendicular, the slope becomes the opposite to the original. If the slope is 1/3, the perpendicular line's slope would be -3.
The computer technician charges $20 per visit plus $35 per hour. If the computer technician works for 2 hours, what will be the cost?
$75
$90
$55
Answers
Answer:
90
Step-by-step explanation:
To solve this problem we need to set up an expression
35x+20
35 is the cost per hour, and 20 dollars is the visit fee.
x is the amount of hours the CT can work
So if we plug in the amount for the number of hours from the problem we get
35(2)+20
Which becomes 70+20 which is 90.
Hope thsi helps!
The computer technician works for 2 hours will take total charges equal to $90 .
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7
According to the question
The computer technician charges $20 per visit plus $35 per hour.
i.e
Let hours he work = x
therefore,
Total charge of computer technician in equation = 20 + 35x
Now,
As the computer technician works for 2 hours the cost will be
By using equation
Total charge of computer technician in dollars = 20 + 35x
where x = 2
so,
= 20 + 35*2
= $90
Hence, the computer technician works for 2 hours will take total charges equal to $90 .
To know more about equation here:
https://brainly.com/question/10413253
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The volume of a cube is 1000 blocks. What is the length of one side of the cube?
Answers
Answer:
A cube has 4 sides
1000÷4
=250
Find the distance between the points J( – 8,0) and K(1, 4).
The exact distance between the two points is
Answers
Answer:
The answer is
[tex] \sqrt{97} \: \: units[/tex]
Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } [/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
J( – 8,0) and K(1, 4)
The distance between them is
[tex] |JK| = \sqrt{ ({ - 8 - 1})^{2} + ({0 - 4})^{2} } \\ = \sqrt{ ({ - 9})^{2} + ( { - 4})^{2} } \\ = \sqrt{81 + 16} \\ [/tex]
We have the final answer as
[tex] \sqrt{97} \: \: \: units[/tex]
Hope this helps you
whats the squareroot of 18
Answers
Answer:
it should be 4.24264068712 looked it up
Answer:
18 doesn't have a square root but you can simplify it
[tex] \sqrt{18 } [/tex]
then you take 9 which is a square number and divide it to get 3 which you'll place on the outside
[tex] 3\sqrt{2} [/tex]
An object that weighs exactly 1
pound is placed on a digital scale that measures weight in ounces.
If the scale is accurate and precise, what weight might be shown on the scale?
Answers
Which graph best represents the function f(x) = 2(1.5)x? graph of increasing exponential function going through point 0, 2 graph of increasing exponential function going through point 0, 3 graph of increasing exponential function going through point 0, 1 graph of increasing exponential function going through point 0, 4
Answers
Graph of increasing exponential function going through point (0, 2)
=======================================================
Explanation:
Assuming you meant to say f(x) = 2(1.5)^x, then we can see the equation is an exponential and it is increasing. It is increasing because the base b = 1.5 is larger than 1.
Plug in x = 0 to find y
y = 2(1.5)^x
y = 2(1.5)^0
y = 2(1)
y = 2
We have x = 0 and y = 2 pair up together meaning (0,2) is on the function curve. This is the y intercept.
Answer:
A. graph of increasing exponential function going through point 0, 2
Step-by-step explanation:
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Answers
Answer:
A. (3,-4)
Step-by-step explanation:
Hi there!
When we reflect a point (x,y) across the y-axis, it will become the point (-x,y).
Right now we can see that point G has the coordinates (-3,-4). Therefore after reflecting about the y-axis, it would become (3,-4).
I hope this helps!
Answer for both pleaseeeeeeeeeee
Answers
Answer:
0 and yes
Step-by-step explanation:
Let a=6m where m is any integer since a is divisible by 6. (a+12)/3=(6m+12)/3=2m+4 which is also an integer. The remainder is 0.
Since n is divisible by 3, n can be written as 3a, where a is any integer and m can be written as 2b, where b is any integer. n*m+12=6ab+12 which is divisible by 2.
If a is divisible by 6 it is also divisible by 3 which when added to 12 which is also divisible by 3 will result in a number divisible by three which means remainder will be 0
if n is divisible by 3, m is divisible by 2 then n.m + 12 will always be divisible by 2 because any number multipled by a number mutiple of 2 will be always divisible by 2 and when 12 added to it will also be divisible by 2.
Must click thanks and mark brainliest
2×+16=12(..........+...........)
Answers
Answer:
The answer is 2x+16=12(1/6x +1/192 )
Step-by-step explanation:
What adds to be the bottom numbers but also multiplies to be the top?
39 at the bottom and 25 on the right above 39
Answers
Answer:
well i cant answr it if i oont have more inforomartion
Step-by-step explanation:
Answer:
Step-by-step explanation:
if we add 11,36,61,... to the bottom we get bottom as a multiple of numerator.
Tell whether the line for x = -5 is horizontal, vertical, or neither.
Answers
Answer:
vertical
Step-by-step explanation:
The line x = -5 includes all points where the value of x is -5, regardless of the value of y. This can be graphed as a vertical line going through (-5, 0), as the line represents the only place where x is the value -5.
Type the expression that results from the following series of steps:
Start with
y
, times by 4, then subtract 9.
Answers
Answer:
4y - 9
Step-by-step explanation:
y×4= 4y
4y-9
what is an equation in point-slope form of the line that passes through (-5,-3) and has a slope of negative 1
Answers
Answer:
Y= -x-8
Step-by-step explanation:
Hope this helps
Answer:
y + 3 = - (x + 5)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - 1 and (a, b ) = (- 5, - 3 ) , then
y - (- 3) = - 1 (x - (- 5) ) , that is
y + 3 = - (x + 5)
Atlantic Hurricanes
Number
1925
1930
1935
1940
1945
1950
1955
1960
1965
1970
1975
Year
Between which years was
the biggest change in the
number of hurricanes?
Answers
Answer:
1950
Step-by-step explanation:
because 1950 column has the most highest number which is 11
Answer:
Between 1945 and 1950 ( from 5 to 11 ),
Step-by-step explanation:
Geometry, please answer question ASAP
Answers
Answer:
144.5 in ^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2) h where the b1 and b2 are the lengths of the bases and h is the height
A = 1/2 ( 9.7+24.3) * 8.5
= 1/2 ( 34)*8.5
=144.5
Factor the polynomial completely using the
X method.
x2 + 16x + 48
An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression x squared + 16 x + 48.
Answers
The factors of the polynomial x² + 16x + 48 are ;
-4 and -12.
Given the polynomial :
x² + 16x + 48
To factorize :
x² + 16x + 48 = 0
Two numbers whose addition gives 16 and product gives 48
The two numbers are : 12 and 4
x² + 12x + 4x + 48 = 0
x(x + 12) + 4(x + 12)
Hence,
(x + 12) = 0
(x + 4) = 0
Hence,
x = -4 or x = -12
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Graph the relation shown in the table. Is the relation a function? Why or why not? PLEASE HELP THANKYOU
Answers
Answer:
Yes, no verticle line passes through two graphed points
Step-by-step explanation:
A function is when 1 input only has 1 output. None of the inputs have different outputs. So, this is a function.
The perimeter of a rectangle is 10 feet. If twice the width is equal to half of the length , find the dimensions of this rectangle.
WRITE AS AN EQUATION
Answers
w = 1ft
l = 4ft
Step-by-step explanation:P =2w + 2l
2w = l/2 => l = 4w
10ft = 2w + 2×4w
10ft = 2w + 8w
10ft = 10w
w = 10ft/10
w = 1 ft
l = 4w
l = 4×1ft
l = 4 ft
Answer:
length = 4 ft
Width = 1 ft
Step-by-step explanation:
Let length = l ft
Width = w feet
[tex]\frac{1}{2}l = 2w\\\\l = 2w*2\\\\l = 4w[/tex]
Perimeter = 10 ft
2*(l +w)= 10
2*( 4w + w ) = 10
2*5w = 10
10w = 10
Equation: 10w = 10
Divide both sides by 10
10w/10 = 10/10
w = 1 ft
Plug in the value of w in l = 4w
l = 4 *1
l = 4 ft