The required quadratic function in the standard form is f(x) = -1.25 x² + 5x.
What is a quadratic equation ?
A quadratic equation is an equation which contains a single variable of degree 2 and its general form is ax² + bx + c = 0.
The x - intercepts of the quadratic equation are (-5, 0) and (0 , -8). That meant (x + 5) and (x -0) are two factors of quadratic equation.
f(x) = a (x + 5) (x - 0)
f(x) = ax² + 5x
The graph of quadratic equation passes through (4 , 0). So we need to substitute x = 4 , f(x) = 0 in equation 1.
0 = a × 4² + (5 × 4)
0 = a × 16 +20
a = -20/16
We know that quadratic equation is in form ax² + bx + c = 0.
f(x) = [tex]\frac{-20}{16}[/tex] × x² + 5x
f(x) = [tex]\frac{-5}{4}[/tex]x² + 5x
f(x) = -1.25 x² + 5x
Therefore , the required quadratic function in the standard form is f(x) = -1.25 x² + 5x.
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QUICKLY!!!!!!!!!
In the figure to the right, AB=7 1/2m, BC=2 1/4 m, and DE=1 1/4m. Find the perimeter of the figure if all angles are right.
Answer:
22m
Step-by-step explanation:
You're welcome, just trust me it's right.
Please help me with my homework :)
Step-by-step explanation:
x = 36
y = 48
z = 72
hope it helps
Identify the property illustrated. (Commutative, Associative, Identity, Property of Zero, Property of -1)
1. -1 • (-6) =6
2. 0 • (-76.3) =0
3. (3x) y = 3 (xy)
4. 0.3 • (-3) = -3 • 0.3
-1 × (-6) = 6 ( because of multiplicative property of -1)
0 ×(-76.3) = 0 (zero property of multiplication)
(3x)y = 3(xy) (commuative property)
0.3 × (-3) = -3 × 0.3 ( commutative property)
As we know that,
The commutative property is a math rule that says that the order in which we multiply numbers does not change the product.
The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.
Identity property states that a number, known as the identity, can be added to, subtracted from, multiplied by, or divided into a number without changing the number.
Zero property of multiplication is defined as “when we multiply any number by zero, the resulting product is always a zero”.
Multiplicative property of -1 atates that any number multiplied by -1 gives the same but with its opposite sign.
From the given example we can say that
-1 × (-6) = 6 ( because of multiplicative property of -1)
0 ×(-76.3) = 0 (zero property of multiplication)
(3x)y = 3(xy) (commuative property)
0.3 × (-3) = -3 × 0.3 ( commutative property)
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I will mark brainiest to whoever answers this!
Answer:
2
Step-by-step explanation:
......... . ........ .......
why is 10 x 10 is 1 less than 9 x 11
Answer: It's the other way around and it is because 10 x 10 is adding 10+10+10+10+10+10+10+10+10+10, while 11x9 is just 9 11s added together.
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 55 pounds each, and the small boxes weigh 25 pounds each. There are 125 boxes in all. If the truck is carrying a total of 4775 pounds in boxes, how many of each type of box is it carrying?
There are 70 small boxes and 55 big boxes.
How to calculate the equation?Let x = small box
Let y = large box
The equation will be:
x + y = 125 ....i
25x + 55y = 4775 ..... ii
From equation i, y = 125 - x.
25x + 55y = 4775
25x + 55(125 - x) = 4775
25x + 6875 - 55x = 4775
Collect like terms
25x - 55x = 4775 - 6875
30x = 2100
x = 2100/30
x = 70
Since x + y = 125
y = 125 - 70 = 55
Therefore, there are 70 small boxes and 55 big boxes.
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A line through (4,-8) with a slope of -8 has y intercept at (0,?)
Answer:
so y intercept is 24
Step-by-step explanation:
Using y = mx + b
m = -8
y = -8
x = 4
then -8 = -8(4) + b
-8 = -32 + b
b = 32 - 8 = 24
The median of 4 numbers is 48
3 of the numbers are:
42, 51, and 52
what is the other number
Answer:
45!
Step-by-step explanation:
Henri's bill at a restaurant is $19.62. He wants to leave a tip of 20%, or , of the bill. To find the exact amount of the tip, he should multiply the bill by ____. A good estimate for the amount of the tip is
$4.00. A good estimate for the total bill, including the tip, is
$24.00.
Answer:
0.2
Step-by-step explanation:
19.62*0.2
Multiply by 0.2
Hope this helps plz hit the crown :D
Expand $(2t - 7)^2.$
Answer:
4t^2 - 28t + 49
Step-by-step explanation:
(2t - 7)^2
Use FOIL.
(2t - 7)^2 =
= (2t - 7)(2t - 7)
= 4t^2 - 14t - 14t + 49
Combine like terms.
= 4t^2 - 28t + 49
(2t - 7)² on expansion results in 4t² - 28t + 49.
What are Algebraic Identities?The algebraic equations which can be used for all variables in the equation is called Algebraic identities. These identities used in factorization of polynomial expressions as well as in the computation of algebraic expressions.
Some of the standard algebraic identities are:
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
a² - b² = (a + b) (a - b)
Here we have the expression (2t - 7)².
Using the second identity (a - b)² = a² - 2ab + b², we can write,
(2t - 7)² = (2t)² - (2 × 2t × 7) + 7²
= 4t² - 28t + 49
Hence the expression (2t - 7)² is expanded to 4t² - 28t + 49 using the algebraic identity (a - b)² = a² - 2ab + b².
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The lifetime of a 2-volt nonrechargeable battery in constant use has a Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Of all batteries, 90% have a lifetime shorter than
It should be noted that when the lifetime of a 2-volt non-rechargeable battery in constant use has a Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Ninety percent of all batteries have a lifetime less than 541.60 hours. This is true.
What is standard deviation?A measure of a set of values' variance or dispersion is called the standard deviation. Because it aids in comprehending measurements when the data is scattered, standard deviation is significant. The greater the distribution of the data, the higher its standard deviation will be..l
It should be noted that the Z value will be computed thus:
Z = X - U / SD
Z = 541.6 - 516 / 20
Z = 1.28.
This will be looked in the distribution table and it illustrated that 90 percent of all batteries have a lifetime less than 541.60 hours
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The lifetime of a 2-volt non-rechargeable battery in constant use has a Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Ninety percent of all batteries have a lifetime less than 541.60 hours. True or false?
Rebecca has 6 yards of ribbon. It takes 3/8 yard to wrap one package. How many packages can rebecca wrap
Answer:
16
Step-by-step explanation:
6 x 8 = 48
48 / 3 = 16
Rebecca can only wrap 16 packages with 6 yards of ribbon.
Help please!!!!!!!!!!
[tex]3x+15y=45[/tex]
[tex]x+5y=15[/tex] ↦ Divide the whole equation by 3.
[tex]5y=15-x[/tex] ↦ Move the x to another side.
[tex]y=\frac{15-x}{5}[/tex] ↦ Move 5 to divide 15-x
[tex]y=\frac{15}{5}-\frac{x}{5}[/tex] ↦ Separate
[tex]y=3-\frac{x}{5}[/tex] ↦ Divide 15 by 5 as we get 3.
[tex]y=-\frac{x}{5}+3[/tex] ↦ Arrange in the form of y = mx + b or the slope-intercept form.
That's the answer.
Consider a total of 1,000 people. If it was said that within 1 deviation (of the mean) of all people like MATH 123, how many of the group should like MATH 123?
Answer:
680 students
Step-by-step explanation:
The 68 - 95 - 99.7 rule (empirical rule) states that 68% of the population lies within one standard deviation of the mean, 95% of the population lies within two standard deviations and 95% of the population lies within three standard deviations.
Hence since it was said that within 1 deviation (of the mean) of all people like MATH 123, therefore the number of people that like MATH 123 is:
number of people that like MATH 123 = 68% of the population
number of people that like MATH 123 = 0.68 * 1000
number of people that like MATH 123 = 680 students
Select the points that are solutions to the system of inequalities. Select all that apply. A(–2, 0)B (0, 10)C(–10, 10)D(1, 2)
Answer:
b and c
Step-by-step explanation:
i took the test
What is the answer for this
Answer:
B
Step-by-step explanation:
For what values of x and y must ABCD be a parallelogram?
Use vector operations to draw the resultant vector
Answer:
Draw an arrow from the origin to (4, 0)
Step-by-step explanation:
u-v+w
= <-3, -4> - <-4, -1> + <3, 3>
= <4, 0>
We want to perform a sum of vectors and draw the resultant vector. The resultant vector will be <4, 0> and its graph can be seen at the end.
If we see the image, we can write the vectors as:
w = <3, 3>u = <-3, -4>v = <-4, -1>Now we want to sum:
u - v + w
Remember that in the sum of the vectors we just add (subtract) the correspondent components, then we will have:
u - v + w = <-3, -4> - <-4, -1> + <3, 3> = <-3 + 4 + 3, -4 + 1 + 3> = <4, 0>
The graph of the resultant vector can be seen below.
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A player throws a bean bag from the height of 3 feet with an initial velocity of 34 feet per second at an angle of 30º.
The parametric equation that represents this situation is __
A. x = (34cos(30°)t and y = –16t2 + (34sin(30°))t
B. x = (34cos(30°)t and y = –16t2 + (34sin(30°))t + 3
C. x = (34cos(30°)t + 3 and y = –16t2 + (34sin(30°))t + 3
The bean bag’s path is part of a curve that is a __
To the nearest second, the bean bag was in the air for __
second(s).
Answer:
B, parabola, 1
Step-by-step explanation:
right on edge
The bean bag’s path is part of a curve that is a parabola and to the nearest second, the bean bag was in the air for 1 second(s).
What is projectile motion?Projectile motion is the motion of the body, when it is thrown in the air taking the action of gravity on it.
The parametric equation for x and y can be given as,
[tex]x =x_o+ v_o\cos(\theta)t \\y =y_o -\dfrac{1}{2}at^2 + (v_o\sin(\theta))t[/tex]
Here, (vo) is the initial speed, (h) is the height and θ is the angle of throw.
The player throws a bean bag from the height of 3 feet with an initial velocity of 34 feet per second at an angle of 30º.
Let suppose the time is t second. Thus, the parametric equation that represents this situation are,
[tex]x = (34\cos(30^o)t \\y = -16t^2 + (34\sin(30^o))t + 3[/tex]
The bean bag’s path is part of a curve. This path is in the form of parabola.
To the nearest second, the bean bag was in the air for 1 second(s).
Thus, the bean bag’s path is part of a curve that is a parabola and to the nearest second, the bean bag was in the air for 1 second(s).
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A process produces a certain part with a mean diameter of 3 inches and a standard deviation of 0.05 inches. The lower and upper engineering specification limits are 1.80 inches and 3.05 inches. What is the Cp (measure of potential capability)
Answer:
The correct answer is 4.167
Step-by-step explanation:
According to the given scenario, the calculation of the Cp i.e. measure of potential capability is as follows;
= (USL - LSL) ÷ 6 × standard deviation
= (3.05 inches - 1.80 inches) ÷ 6 × 0.05
= 1.25 ÷ 0.3
= 4.167
hence, the calculation of the Cp i.e. measure of potential capability is 4.167
solve this one please I will mark brainlist
The only decimal that contains a digit that represents ten times the value of the digit to its' right is; 33.458
How to Interpret Decimals?From the question, we want to find the digit that represents ten times the value of the digit to its' right.
Now, when it comes to decimals, there is the whole number part which is the left side of the decimal while there is a fraction part which is the right side of the decimal.
Now, the decimal values given are;
36.295
33.458
37.889
Let us analyze each of them;
1) 36.295 = 30 + 6 + 2/10 + 9/100 + 5/1000
We can see that there is no number that is ten times the number to it's immediate right.
2) 33.458 = 30 + 3 + 4/10 + 5/100 + 8/1000
We can see that 30 is ten times the number to it's immediate right which is 3.
3) 37.889 = 30 + 7 + 8/10 + 8/100 + 9/1000
We can see that there is no number that is ten times the number to it's immediate right.
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5. Find JK to the nearest whole number.
A
Answer:
JK ≈ 63 units
Step-by-step explanation:
Using the sine ratio in the right triangle
sin44° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{JK}{JL}[/tex] = [tex]\frac{JK}{90}[/tex] ( multiply both sides by 90 )
90 × sin44° = JK , that is
JK ≈ 63 ( to the nearest whole number )
Answer:
Sin(x) = Opposite ÷ Hypotenuse
Sin(44) = JK ÷ 90
0.6946583705 = JK ÷ 90
0.6946583705 × 90 = JK
JK = 62.5192533413
Rounding JK to the nearest whole number:
JK = 63
Factor the following expression.
x^2- 9x + 14=
Suppose lines EF and GH are reflected over the line y = x to form the lines JK and LM. Which statement would be true about the lines?
A.
Line JK and line LM will be parallel.
B.
Line JK and line LM will be perpendicular.
C.
The slope of line JK will be the same as the slope of line EF.
D.
The slope of line LM will be the negative reciprocal of the slope of line GH.
Answer:
A.
Step-by-step explanation:
I believe the answer is A. (Line JK and line LM will be parallel) because lines EF and GH are parallel. Therefore if the are just reflected, the new set of lines will also be parallel.
EF: (-9,1) (-4,9)
[tex]\frac{1-9}{-9+4}[/tex] = [tex]\frac{-8}{-5}[/tex] = [tex]\frac{8}{5}[/tex] or 1.6
GH: (-5,-2) (0,6)
[tex]\frac{-2 - 6}{-5-0}[/tex] = [tex]\frac{-8}{-5}[/tex] = [tex]\frac{8}{5}[/tex] or 1.6
Same slope and different y-intercept means the lines a parallel
which table represents linear function?
Answer: The third option
Step-by-step explanation: You have to look for a pattern, as the x value increases by 1, the y value decreases by 8, every single time.
rs= 4x-9, st= 19, rt=8x-14
The value of x is 6
How to determine the valueFrom the information given, we have that;
Line RS = 4x - 9Line ST = 19Line RT = 8x - 14It is important to note that line RT is a line with segments RS and ST and S and the line between R and T
This can be expressed as;
RS + ST = RT
substitute the values into the equation, we have;
4x - 9 + 19 = 8x - 14
collect like terms
4x - 8x = -14 + 9 - 19
subtract like terms
-4x = -24
make 'x' the subject of formula
-4x/-4 = -24/-4
x = 6
Thus, the value of x is 6
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Can sum1 help plz!!
Answer:
5
Step-by-step explanation:
The rate is 5p/m
200 / 40 = 5 and so on...
Answer:
5 calories/minute.
Step-by-step explanation:
To find the rate, take one of the data sets (in my example, 40, and 200) and just divide the number of calories by the minutes to find your unit rate.
200/40
= 5
There are 3 boys for every 4 girls in Mrs. G.'s math class.
Find the constant of proportionality and write an equation to determine the number of boys in Mrs. G.'s class if you know the number of girls in Mrs. G's
class
Answer:
12 Step-by-step explanation:
Which point is located at (0.25,-0.5)?
The answer that you're looking for is point C.
Hope this helps! <3
Answer:
The person above me is correct it is C
Step-by-step explanation:
Because it is the only one with a positive and negative. And of course coordinates are correct.
Hope this helps! :)
answer the following
Step-by-step explanation:
–(11/4) = 11 : (–4) = –11/4 = 11/-4