9514 1404 393
Answer:
a. f(x) = (4x +5)(x -3)
b. x-intercepts: {-1.25, +3}
c. f(x) goes to +infinity as x goes to ±infinity
d. plot the x-intercepts, the vertex, and a few other points; draw a smooth curve through them
Step-by-step explanation:
a. Here, you're looking for factors of (4)(-15) = -60 that have a sum of -7. Those factors will be -12 and +5, so we can factor the function as ...
f(x) = (4x -12)(4x +5)/4
f(x) = (x -3)(4x +5)
__
b. The x-intercepts are the values of x that make the factors zero:
x -3 = 0 ⇒ x = 3 . . . . (add 3)
4x +5 = 0 ⇒ x = -5/4 . . . . (add -5, divide by 4)
__
c. As with all even-degree polynomials with positive leading coefficients, the end behavior of f(x) matches that of |x|:
as x → ∞, f(x) → ∞
as x → -∞, f(x) → ∞
__
d. The vertex of the function will be located halfway between the x-intercepts, at x = (3-5/4)/2 = (7/4)/2 = 7/8. The value of f(x) there is ...
f(7/8) = (4(7/8) +5)(7/8 -3) = -289/16 = -18.0625
Since the leading coefficient is 4, the normal x^2 function behavior is stretched vertically by a factor of 4. So, additional points would be
x = 7/8 ±1, f(x) = -18.0625 +4·1 = -14.0625
x = 7/8 ±2, f(x) = -18.0625 +4·2^2 = -2.0625
The answers of part B locate two points on the graph, and help find the vertex. The answer of part C confirms the graph as opening upward.
__
Additional comment
I find a graphing calculator to be very helpful finding the roots and making the graph.
A new pair of Air Jordan's that sells for $150 decreases at a rate of 14% each year. Find the value of the shoes after 5 years (round to the nearest cent).
Answer:
$45
Step-by-step explanation:
If it looses it value of 14 % every year, by the end of 5 years, the value would go down by 70%. So, 150x0.7= 105, 150-105=45, so it would be. worth. 45% in 5 years.
A bakery offers a sale price of $2.60 for 6 muffins. What is the price per dozen?
Answer:
$5.20
Step-by-step explanation:
A dozen is 12, so multiply by two.
2.60 * 2 = $5.20
Answer:
5.20 for 12
Step-by-step explanation:
2.60 for 6
2.60*2=12
5.20 for 12
Write an equation of the line that passes through (5,0) and is parallel to the line
y = -3x + 2
Answer:
y=-3x+15
is the equation that passes through the point (5,0) and is the parallel line to y=-3x+2
Step-by-step explanation:
find the slope of the original line and use the point-slope formula y-y₁=m(x-x₁) to find the parallel line of y=-3x+2, which if done correctly you should end up with y=-3x+15.
hope this helps
In 2016, the average SAT Math score was 510 with a standard deviation of 80 points. What is the probability of a student scoring less than 590?
a. 83.85%
b. 67.7%
c. 16.15%
d. 49.85%
Please help I’ll mark as brainliest !
Answer:
x = 0.6
Step-by-step explanation:
2(x+4)+8x = 14
2x+8+8x = 14
10x+8 = 14
10x = 6
(divide by 10)
x= 0.6
if p (x) = 3x^3+2x^2+4x^4+3 and q (x) = 3x^4-2-x+5^2 .find p (x) - q (x)
Answer:
4x⁴-3x⁴+5x³-3x²+1
Step-by-step explanation:
Given that p (x) = 3x^3+2x^2+4x^4+3 and q (x) = 3x^4-2-x+5x^2
p (x) - q (x) = 3x^3+2x^2+4x^4+3 - (3x^4-2-x+5x^2)
p (x) - q (x) = 3x^3+2x^2+4x^4+3 - 3x^4 + 2 + x - 5x^2
Collect the like terms
p (x) - q (x) = 4x⁴-3x⁴+3x³+2x²-5x²+x+3-2
p (x) - q (x) = 4x⁴-3x⁴+5x³-3x²+1
This givess the difference
ABCD is a rhombus. If the area of the rhombus is 16 cm2, and = 8 cm, what is ?
1 cm
4 cm
2 cm
8 cm
What is the radius of a hemisphere with a volume of 920 ft^3 to the nearest tenth of a foot?
Answer:
7.6 ft
Step-by-step explanation:
The volume of a sphere is
V = 4/3 pi r^3
A hemisphere is 1/2 of a sphere
V = 1/2 (4/3 pi r^3)
V = 2/3 pi r^3
920 = 2/3 pi r^3
Multiply each side by 3/2
920 * 3/2 = 3/2 * 2/3 pi r^3
1380 = pi r^3
Divide each side by pi
1380/pi = pi r^3 / pi
1380/ pi = r^3
Using pi as 3.14
1380/3.14 = r^3
439.4904459= r^3
Taking the cube root of each side
(439.4904459)^(1/3)= r^3^(1/3)
7.602967711=r
To the nearest tenth
7.6 = r
radius=7.6ft
Answer:
Solution given:
radius [r]=?
Volume of hemisphere=920ft³
⅔*πr³=920
r³=920*3/(2π)
r³=439.267
r=[tex]\sqrt[3]{439.267}=7.6ft[/tex]
Find the equation with a line with slope 7
_
2 passing through the point (-2,9).
Answer:
y = 7/2 x+16
Step-by-step explanation:
The equation for a line is y = mx+b where m is the slope and b is the y intercept
y = 7/2 x+b
Substitute the point into the equation
9 = 7/2(-2)+b
9 = -7+b
9+7 = b
16 = b
y = 7/2 x+16
ASAP
Help pls
Answer as fast as you can
Plsss help
Thank you
Answer:
42
Step-by-step explanation:
From the question, we have it that 63 cups were emptied
That means the sum of both cup sizes is 63
Thus;
x + y = 63 ••••••(i)
Since each small cup is of size 8 oz and a total of x was used. The total volume from the small sized cup is 8 * x = 8x oz
similarly for the medium sized, we have 12 * y = 12y oz
The sum of both is 4(147)
8x + 12y = 4(147 )•••••(ii)
We want to get the value of x
from equation i;
y = 63-x
Substitute this into equation ii
8x + 12(63-x) = 4(147)
8x + 756 - 12x = 4(147)
12x-8x = 756-4(147)
4x = 168
x = 168/4
x = 42 small sized cups
Using distributive property What expression is equivalent to (p-q)(3)
[tex]\longrightarrow{\green{3p-3q}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex](p - q)(3)[/tex]
Using distributive property which states that [tex]a(b - c) =( a \times b) - (a \times c)[/tex], we have
[tex] = (3 \times p) - (3 \times q)[/tex]
[tex] = 3p - 3q[/tex]
[tex]\pink{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]
Answer:
3p - 3q
Step-by-step explanation:
( p - q ) ( 3 )
use distribute property which means multiply each terms in the parantheses by 3.
3 × p - 3 × q
3p - 3q
please answer no links pls
Answer:
i cant read it..
Step-by-step explanation:
Please help its urgent quick fast Lighting McQueen!
Answer:
Option A
Step-by-step explanation:
x-7>2
x>9
Therefore, A is correct since 9 isn't included in the solution set.
Answer:
First option is correct
Step-by-step explanation:
x-7 > 2
x > 7+2
x > 9
Hope it is helpful....Pleas help this is due today!!
Find the surface area of the rectangular prism
Answer:
472
Step-by-step explanation:
the table below does not represent a function why?
Answer:
Because X (10) repeats
Step-by-step explanation:
A function has no repeated X but here in your x variable 10 is there twice so therefore it is NOT a function
You can use the pencil test also in a graph, align your pencil vertically and see if there are multiple points that have the same X and if there isn't any repeated its a function.
Answer:
The function is a relation between two sets that associates to each element of the first set exactly one element of the second set.
We have x = 10 twice with different f(x) associated, 5 and 20.
If we plot those points they will be on same vertical line, thus the vertical line test is failed.
Ray is constructing a flowerbed for the zoo and wants to
know if he has enough edging. A sketch of the flowerbed
is shown below. What is the perimeter of the triangle?
Round to the nearest whole number.
72 ft
41 ft
12 ft
24 ft
12 H
48 ft
Answer:
Option (3)
Step-by-step explanation:
Since, flowerbed is in the shape of a right triangle,
By applying Pythagoras theorem in the given right triangle,
(Hypotenuse)² = (leg 1)² + (leg 2)²
(Hypotenuse)² = (12)² + (12)²
(Hypotenuse)² = 144 + 144
Hypotenuse = √288
Hypotenuse = 16.97
≈ 17 ft
Perimeter of the triangle = Sum of the measures of three sides of the triangle
= 12 + 12 + 17
= 41 ft
Therefore, Option (3) will be the correct option.
Answer:
41ft
Step-by-step explanation:
because i got 100% on the lesson
Please help quadratic equation!! 20 points
Answer:
x=4,−2
Step-by-step explanation:
Because Step 1. Move all terms to one side.
{x}^{2}-2x-8=0
x
2
−2x−8=0
2 Factor {x}^{2}-2x-8x
2
−2x−8.
1 Ask: Which two numbers add up to -2−2 and multiply to -8−8?
-4−4 and 22
Step 2. Rewrite the expression using the above.
(x-4)(x+2)
(x−4)(x+2)
and going to;
(x-4)(x+2)=0
(x−4)(x+2)=0
And Step 3. Solve for xx.
1 Ask: When will (x-4)(x+2)(x−4)(x+2) equal zero?
When x-4=0x−4=0 or x+2=0x+2=0
2 Solve each of the 2 equations above.
x=4,-2
x=4,−2
x=4,-2
Our Answer is:
x=4,−2
I Hope It's Helps
Answer:
2 and -4
tso numbers when added gives -2 and 8 incase it's not clear enough.
Could someone please help me with this?
Answer:
Equal
Equal
Equal
Supplementary
Step-by-step explanation:
Just learn the angles tbh, you will need them in the future
Show that x^2 + 5x = 3
Answer:
[tex]area = length \times width \\ 9 = (x + 3)(x + 2) \\ {x}^{2} + 2x + 3x + 6 = 9 \\ {x}^{2} + 5x + 6 = 9 \\ {x}^{2} + 5x + (6 - 9) = 0 \\ {x}^{2} + 5x =3[/tex]
If there are 10 marbles in a bag 1/5 of them are red and the others are blue. What is the ratio of red marbles to blue marbles ?
Answer:
4:1
Step-by-step explanation:
We know 1/5 of the marbles are red.
There are 10 marbles.
1/5 is also 2/10, so:
2 of the 10 marbles are red.
To find the blue marbles, lets subtract the red marbles from the total marbles:
10-2=8
So 8 of the marbles are blue.
This is a ratio of 8 blue to 2 red marbles.
Or
4 blue to 1 red marbles.
This can be shown as:
4 : 1
Hope this helps!
Select the correct answer.
What is in simplest form?
A. 8√4
B. 17√2
C. 4√ 17
D. 2√17
Answer the question. Will give Brainliest to whoever gets it right.
Answer:
27 feet
Step-by-step explanation:
they go 27 feet because 15+6+6=27
Find the area of this parallelogram
Given: CA bisects BAD and CA bisects BCD.
Prove: ABC - ADC.
By AAS criteria, ΔABC ≅ ΔADC.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is CA bisects ∠BAD, AB ⊥ BC and AD ⊥ DC.
In ΔABC and ΔADC -
∠ABC = ∠ADC = 90°
∠ACB = ∠ACD {bisected angle ∠BCD}
AC = AC {Common}
By AAS criteria, ΔABC ≅ ΔADC.
Therefore, by AAS criteria, ΔABC ≅ ΔADC.
To solve more questions on 2 -D figures, visit the link below-
brainly.com/question/25950519
#SPJ2
[Complete questions
Given: CA bisects ∠BAD, AB ⊥ BC and AD ⊥ DC . Prove: △ABC≅△ADC.]
Analyzing angle pair relationships
Angle 3 and 4 are ____.
The equation _____ can be used to solve for x.
m 5 = __
Answer:
Angle 3 and 4 are supplementary angles.
The equation (3x+4) + (2x+11) = 180 can be used to solve for x.
m 5 = 77
Step-by-step explanation:
find the value of n
3n-10
n=
10-3=N
N=7
Step-by-step explanation:
hope you like it
what is the value of the expression 6ab - b3 , if a=1 and b=2?
Answer:
6
Step-by-step explanation:
6(1×2) - 3(2)
6×2 - 6
12-6
= 6
here you go
please help with mine
what is the length of the diagonal of the screen,in feet?
Answer:
12.2
Step-by-step explanation:
Pick ALL the options below that make g > 21 true
g = 21 1.
g = 17 2.
g = 12 3.
g = 34 4.
g = 25 5.
Answer:
correct answers that make g > true
g = 21.1
g = 34.4
g = 25.5
In short words , the 1st , 4th and 5th option make , g > 21 true .