Answer:
[tex]f(x)=-4(x-2)(x+7)[/tex]
Or, in standard form:
[tex]f(x)=-4x^2-20x+56[/tex]
Step-by-step explanation:
We can use the factored form of a quadratic equation:
[tex]f(x)=a(x-p)(x-q)[/tex]
Where a is the leading coefficient and p and q are the zeros of the quadratic.
We know that the x-intercepts are at (2, 0) and (-7, 0).
So, let's substitute 2 for p and -7 for q. This yields:
[tex]f(x)=a(x-2)(x+7)[/tex]
Now, we need to determine a.
We know that it passes through the point (1, 32). In other words, if we substitute 1 for x, we should get 32 for f(x). Therefore:
[tex]32=a(1-2)(1+7)[/tex]
We can now solve for a. First, compute:
[tex]32=a(-1)(8)[/tex]
Multiply:
[tex]32=-8a[/tex]
Divide both sides by -8:
[tex]a=-4[/tex]
So, the value of a is -4.
Therefore, our entire equation is:
[tex]f(x)=-4(x-2)(x+7)[/tex]
Notes:
We can expand this into standard form:
[tex]f(x)=-4(x-2)(x+7) \\ f(x)=-4(x^2+5x-14) \\ f(x)=-4x^2-20x+56[/tex]
pleaseeeee helpppppp
Answer:
BCE
Step-by-step explanation:
I hoped this helped and mark me as brainly pls
Answer:
a c b d
Step-by-step explanation:
A dressmaker needs to cut 6-inch pieces of ribbon from rolls of ribbon that are 9 feet in length. How many 6-inch pieces can the dressmaker cut from 15 of these rolls of ribbon? Before you try that problem, answer the question below. How many inches of ribbon does the dressmaker have, in total?
Answer:
Step-by-step explanation:
Answer:
60 pieces
Step-by-step explanation:
What we know:
There are 12 inches in a foot
There are 5 6-feet lengths of ribbon
So, we simply need to multiply.
Since there are 12 inches in a foot, and we only need 6 inches for each one, we can see that she makes 2 pieces for each foot.
Multiply
2*6=12
She makes 12 pieces for each length of ribbon.
Now multiply it by 5
12*5= 60
She can make 60 pieces from 5 of these length of ribbon.
Hope this helps!
Find the area of the shape above. Will give brainliest answer.
Answer: 3/5
Step-by-step explanation:
A=a+b/2h
Since the bottom width = 4 and the top length =2 and the length = 5
2+4=6
2(5)=10
so 6/10 = 3/5
URGENT SOMEONE HELP PLEASE!!
Rewrite the function by completing the square
f(x)=x^2-14x+63
Answer:
f(x) = (x - 7)² - 14
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Standard Form: ax² + bx + c = 0Vertex Form: f(x) = a(bx - c)² + dCompleting the Square: (b/2)²Step-by-step explanation:
Step 1: Define
f(x) = x² - 14x + 63
Step 2: Rewrite
Separate: f(x) = (x² - 14x) + 63Complete the Square: f(x) = (x² - 14x + 49) + 63 - 49Simplify: f(x) = (x - 7)² - 14Answer:
-7 and 14 on khan
Type the correct answer in the box. Use numerals instead of words. What value of x makes this equation true? -2x + 3 = -15
What does x =
Answer:x=9
Step-by-step explanation:
-2x+3=-15
Subtract 3 on both sides:
-2x+3-3=-15-3
-2x=-18
Divide -2 on both sides:
-2x/-2=-18/-2
x=9
If the expression (- 2x + 3) is equivalent to (- 15), then [x] is equivalent to 9.
What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is the equation as follows -
- 2x + 3 = - 15
The given equation is -
- 2x + 3 = - 15
Solving, we get -
- 2x = - 15 - 3
- 2x = - 18
2x = 18
x = 9
Therefore, if the expression (- 2x + 3) is equivalent to (- 15), then [x] is equivalent to 9.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
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The cost of a school banquet is $85 plus $12 for each person attending. Write an equation that gives the total cost of the number of people attending.
A. Y=85x-12
B. Y=12x+85
C. Y=85x+12
D. Y=12x-85
Answer: I think that the answer is B
Step-by-step explanation:
Segment AB is the diameter of circle M. The coordinates of A are (1,6). The coordinates of M are (-3, 8). What are the coordinates of B
1) (-7,10)
2) (5,4)
3) (-1,7)
4) (-2,1)
Step-by-step explanation:
Let the midpoint formula be expressed as;
M(X,Y) = {x2+x1/2, y2+y1/2}
X = x2+x1/2
Y = y2+y1/2
Get x2
-3 = x2 + 1/2
-6 = x2 + 1
x2 = -6-1
x2 = -7
Get y2;
Y = y2+y1/2
8 = y2+6/2
16 = y2+6
Y2 = 16-6
y2 = 10
hence the coordinate of B is (-7, 10). Option A is correct
simplify the expression -9x-8+4x+7
Answer: 5x - (-1)
Step-by-step explanation:
Answer:
-5x-1
Step-by-step explanation:
First combine like terms
-9x-8+4x+7 combine -9 and 4
-5x-8+7 then combine -8 and 7
-5x-1
descending order 20,-30,4,0,-3,10
Answer:
20,10,4,0,-3,-30
Step-by-step explanation:
HELP ASAP PLS BRAINLIEST
Answer:
for the 10 column it is $150.00 the next column is 15 and for 200 it is $250.00
Step-by-step explanation:
Need help and exact locations please, very confused
Answer:
here you go ;d
Step-by-step explanation:
Scientists have found that the relationship between the area of an island and the number of species can be modeled approximately by S=-3.404+103.2ln(A) S=−3.404+103.2ln(A), where AA is the area in km^2km 2 and SS is the number of species.
Answer:
[tex]A=e^{(S+3.404/103.2)[/tex]
Step-by-step explanation:
Step one:
we are told that the relationship between the number of species and the island area is given as
[tex]S=-3.404+103.2ln(A)[/tex]-----------------1
based on any given value for either area or number of species, we can find the other.
say we want to find the land area for a given amount of specie
Step two:
we first make area A subject of the formula.
[tex]S=-3.404+103.2ln(A)[/tex]
let us isolate [tex]ln(A)[/tex]
[tex]S + 3.404 = 103.2ln(A)[/tex]
Divide both sides by 103.2 we have
[tex](S + 3.404)/103.2 = ln(A)[/tex]
Now, exponentiate both sides using the base e.
[tex]A=e^{(S+3.404/103.2)[/tex]----------------2
for a given value of "S" we can find the area A based on the above expression.
How are ROC (rate of change) and slope related AND different
Answer:
Rate of change and slope is the same since they are both terms of every rate, but rate of change can be said in any terms as in exponential and linear, etc. While slopes are only for linear equations.
Step-by-step explanation:
Hope this helps :)
i need this asap, will give brainliest to fast answers!! :)
Answer: $22.50, but rounded to the nearest dollar its $23.00 Hope this helps :)
Step-by-step explanation: The unit rate it 1/0.75
World's Finest Coffee (Decaf) is sold by the case where one case contains 48 6-ounce packages. A restaurant uses 36 pounds of this coffee each month. How many cases must be ordered per month?
Answer:
The number of cases to be purchased is 2.
Step-by-step explanation:
Giving the following information:
World's Finest Coffee (Decaf) is sold by the case where one case contains 48 6-ounce packages.
First, we need to calculate how many pounds are in each case.
1 pound = 16 ounces
1 case= (48*6)/16
1 case= 18 pounds
Now, the number of cases required each month:
36 pounds = 18*x
x= number of cases
x= 36/18
x= 2
The number of cases to be purchased is 2.
A circle has a diameter of 50 cm. Which of these is closest to it's circumference.
A) 157 cm
B) 314 cm
C) 7,850 cm
D) 1,963 cm
Answer:
i know the circumference is 1.57 so it is A)
Step-by-step explanation:
Mya creates the
table below to
show how much
fruit to put in her
shake. How much
fruit should she
use if she is
making 5 servings?
which situation could be represented by the equation 15.5 = x/2
Answer:
C. Julie drive 15.5 miles from her home to the grocery store. Julie drives the same path going back home. What is x, the total amount of miles traveled to the grocery store and back home?
Step-by-step explanation:
The situation in the 3rd option represents the equation, 15.5 = x/2.
Distance driven by Julie to the grocery store = 15.5 miles
Distance driven by Julie back home following the same path = 15.5 miles
Total amount of miles travelled to and fro the store, x, = 2*15.5
This means, the mile's covered going to the store or coming back home can be expressed as ½ the total amount of miles, x, covered. Which is: 15.5 = ½x
Therefore, the third option represents the equation, 15.5 = x/2.
Rachael earned $42 for 3 1/2 hours at her job today. How much does Rachel earn per hour ?
Answer:
$12
Step-by-step explanation:
It is given that,
Rachael earned $42 for [tex]3\dfrac{1}{2}[/tex] hours at her job today. It means,
For 7/2 hours, earning is $42
For 1 hour, we divide $42 by 7/2 as follows :
[tex]1\ h=\dfrac{42}{\dfrac{7}{2}}\\\\=\dfrac{42\times 2}{7}\\\\=\$12[/tex]
So, he will earn $12 per hour.
Plssss helpppp ASAPP
will mark BRAINLIEST!!!
Answer:
4th and 5th option
Step-by-step explanation:
you can easily add eqn 1 and 2 to get rid of the y term for 4th option and get rid of x term by addition as well for the 5th option
this is a topic on simultaneous equation. If you wish to explore more into this topic you can give me a follow on Instagram (learntionary) I'll be posting the notes for this topic and some other tips :)
Answer:
the last two
Step-by-step explanation:
The sum of ten consecutive whole even numbers is 1190
Answer:In other words, since even numbers are the multiples of 22, we can represent an even integer nn by 2k2k, where kk is also an integer. So if we have the even integers 1010 and 1616, we can rewrite them asn=2k→10=2(5)
n = 2k\, \to \,\,16 = 2\left( 8 \right)\,n=2k→16=2(8)
Step-by-step explanation:
Consecutive Even Integers
The best way to illustrate what consecutive even integers are through the use of examples. Observe that any pair of two consecutive even integers are 22 units apart. In other words, if you pick any even integer in the set of consecutive even integers then subtract it by the previous one, you will always get the difference of \bold{+2}+2 or simply \bold{2}2, written without the \bold{+}+ symbol.
Graph the linear equation
Answer:
I added a screenshot. ;)
Step-by-step explanation:
Which is equivalent to
^3*square root* 8^1/4x ?
pls hurry it’s a timed test
Answer:
[tex]12\sqrt{8} ^{x}[/tex]
Step-by-step explanation:
The equation y = 13x represents the rate, in gallons per minute, that Tank A at an aquarium fills with water. The table represents the rate that Tank B fills with water. Determine which tank fills faster.
Answer:
Tank A fills up faster.
Step-by-step explanation:
Tank A is y = 13x
Tank B is y = 11x
Plz mark as Brainliest!
How can ΔABC be mapped to ΔXYZ? First, translate vertex A to vertex . Next, ΔABC to align the sides a
The correct answer is vertex B to vertex Y
What is transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
Given are two triangles ABC and XYZ.
We have AB = XY = 25 cm, AC = YZ = 29 cm
and also angle A = angle X = 36 degrees
Thus, we find that corresponding congruent sides are
AB and AC with angles A and X
To map ABC onto XYZ,
Vertex B to Y, side AB to side XY with AC coinciding with XZ
Now all vertices x, y, z will perfectly match with transformed ABC
Hence, The correct answer is vertex B to vertex Y
For more references on transformation, click;
https://brainly.com/question/11709244
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Answer:
x and rotate
Step-by-step explanation:
i need help with this asap please
The ratio of BMX bikes in a sporting goods store to mountain bikes is 3 to 2 . The store has 90 BMX bikes . How many mountain bikes does the store have ?
Answer: 60
Step-by-step explanation:
From the question, we are informed that the ratio of BMX bikes in a sporting goods store to mountain bikes is 3 to 2 and that the store has 90 BMX bikes .
To calculate the number of mountain bikes that the store has goes thus:
= 2/3 × 90
= 2 × 30
= 60 mountain bikes
Don’t mind the question at the bottom but I need to know if this is right or not please help!
Answer:
the answer is d.
Answer:
no its not correct, the answer is d
Step-by-step explanation:
too long to explain, just trust me man
What is the slope of y=-3x - 2?*
Answer:
-3!
Step-by-step explanation:
The slope is always listed right before the x in any slope-intercept form. It can be negative or positive, or even a fraction. In this case, it's -3!
I really hope this helps!
Answer:
-3 is the slope
Step-by-step explanation:
y = mx + b.
The variable m represents the slope. So, what ever number replaces the variable m(-3) is the slope.