The function which is the vertex form of the equation whose first three steps shown in writing is f(x)=5(x +4)²- 80.
What is the vertex form of parabola?Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.
The standard equation of the vertex form of parabola is given as,
[tex]y=a(x-h)^2+k[/tex]
Here, (h, k) is the vertex point.
The first three steps in writing the function in vertex form are shown.
[tex]f(x) = 40x +5x^2[/tex]
Write the function in standard form.
[tex]f(x) = 5x^2+ 40x[/tex]
Factor out of the first two terms by taking out the common number 5 from the equation,
[tex]f(x) = 5(x^2 +8x)[/tex]
Form a perfect square trinomial with (8/2)² = 16,
[tex]f(x) = 5(x^2 +8x+ 16) - 5(16)\\f(x) = 5(x+4)^2 - 80[/tex]
Hence, the function which is the vertex form of the equation whose first three steps shown in writing is f(x)=5(x +4)²- 80.
Learn more about the vertex form of the parabola here;
https://brainly.com/question/17987697
Answer:
c
Step-by-step explanation:
(NEED EVIDENCE, NOT ONLY ANSWER)
Lily has a rectangular shaped shawl that is 75 inches wide and 18 inches long. What is the area of the shawl in square feet?
Find the number to add to x^2 + 14x to make it a perfect square trinomial. Write that trinomial as the square of a binomial.
Answer:
Option 2
Step-by-step explanation:
Divide the co efficient of 'x' by 2 and the square the result.
14 ÷2 = 7
7² = 49
To make it a perfect trinomial, 49 should be added
x² +14x + 49 = x² + 2*x *7 + 7² {Compare with a²+ 2ab + b² = (a +b)²}
= (x +7)²
big pts. no links pls help with explanation
AND BRAINLEST
James opens 2 different savings accounts and deposits $12,000 into each one.
Account I earns 2.2% interest compounded annually.
Account II earns 2.2% annual simple interest.
There are no additional deposits or withdrawals.
What is the sum of the total balances of these accounts at the end of 7 years?
Question 7 options:
$27,168.00
$27,696.00
$27,949.08
$27,822.53
Answer:
The answer to this is D $27,822.53
Step-by-step explanation:
Answer:
27,822.53
Step-by-step explanation:
When the research hypothesis predicts the direction of a relationship, the test is ______. a. direct b. two-tailed c. one-tailed d. positive
Answer:
c. one-tailed
Step-by-step explanation:
i think its this because i say so now trust :)
Find the new side lengths if the scale factor is 2/5. 35 inches 15 iches NEED ANSWER ASAP PLEASEEEE
Answer:
l = 14 inches , b = 6 inches
Step-by-step explanation:
multiply length l and breadth b by the scale factor , then
new length = [tex]\frac{2}{5}[/tex] × 35 = 2 × 7 = 14 inches
new breadth = [tex]\frac{2}{5}[/tex] × 15 = 2 × 3 = 6 imches
60 points) khan academy geometry practice. Need help i in any way cannot miss this question please help!!
A restaurant used 231 eggs last week. Of these, 46 were brown. The remaining eggs were white. Which equation can be used to solve for w, the number of white eggs used last week?
w = 231 - 46
hope it helps...!!
Answer:
185
Step-by-step explanation:
[tex]x + 46 = 231 \\ x = 231 - 46 \\ x = 185[/tex]
(3+1)(6x9)-23
Using Pemdas explain and answer this question
Answer:
193
Step-by-step explanation:
Parenthesis
Exponent
Multiply
Divide
Add
Subtract
3+1 can be simplified to 4
6 times 9 is 54
(4)(54)-23
216-23
193
if Tanya 's class starts at 11:50 but she gets off work at 12:10 how many minutes does Tanya miss of class?
Answer:
20 minutes
Step-by-step explanation:
Answer:
Tanya misses the class for 20 minutes
Step-by-step explanation:
11:50 to 12: 00 ⇒ 10 minutes
12:00 to 12: 10 ⇒ 10 minutes
20 minutes
i just need the answer and ill do the labels
By the vertical angle theorem, the two angles '5y + 12' and '82' are equal
⇒ [tex]5y + 12 = 82[/tex]
[tex]5y = 70\\y = 14[/tex]
Thus x = 14
Hope that helps!
p.s. Definition of Vertical Angle Theorem: angles that are opposite each other and formed by two intersecting straight lines, are congruent
p.s. Diagram for what is Vertical Angle Theorem:
Answer:
y = 14
Step-by-step explanation:
82° = (5y + 12)°
5y = 82 - 12
5y = 70
y = 14
{calculate carefully{
What is the simplified expression for:
−2x+3y=0
2x+2y=20
answer options
no solution
infinitely many soultions
(6,-4)
(6,4)
Answer:
(6,4)
Step-by-step explanation:
First we must cross out the -2x and 2x since they're both opposites of each other and thus they cancel each other out.
Now we have:
3y = 0
2y = 20
So next we add the 3 and 2 to get 5y, and then we add 20 and 0 to get 20.
So now we have:
5y = 20
And so we'll simply divide by 5 on both sides, and the answer is y = 4.
Now normally we would plug 4 back in to one of the equations to solve for x, but since only one of the answer choices has 4 in the y position, we can already tell that (6,4) is the answer.
Hope this helps you. Sorry if it doesn't though.
A circle has a circumference of 26 millimeters. What is the circle's
radius? Use 3.14 for pi and round your answer to the nearest tenth
PLS HELP!!! No links pls and ty <333
Answer:
22.5
Step-by-step explanation:
Radius = Circumference/(2*PI)
211,207,203,...
Find the 38th term.
Answer:
63
Step-by-step explanation:
Using the formula attached, we can setup the equation:
[tex]211 + (38 - 1) - 4[/tex]
Then using a calculator you can solve
The required 38th term of the given arithmetic sequence is 63.
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values
What is geometric progression?Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
here,
Given sequence,
211,207,203,...
First term, a = 211
Common difference, d = 207 - 211 = -4
Now.
Nth term of an arithmetic progression,
Nth term = a + (n -1)d
Nth term of given sequence
Nth term = 211 - (n - 1)4
Now, put n = 38
38th term = 211 - (38 - 1)4
38th term = 211 - [37](4)
38th term = 211 - 148 = 63
Thus, the required 38th term of the given arithmetic sequence is 63.
Learn more about arithmetic progression here: https://brainly.com/question/20334860
#SPJ2
5x + 3y -5.70 2x+10y+3.60
Answer:
I`m not really sure what i`s asking to solve but here`s my best answer.
5x + 3 - 5.70 = 2x + 10y + 3.60
3x + 3 - 5.70 = 10y + 3.60
3x + 3 = 10y + 9.30
3x = 10y + 6.30
^^^That`s the most it can be simplified without any new fractions or decimals
3x = 10y + 6.30
x = 3.33y + 2.10
^^^That`s the most it can be simplified to solve for x.
Need help 10 points
Answer:
have you missed out any option cause i doeant match with any of your options
An exponential function and a linear function are graphed below.
Over which interval does the growth rate of the exponential function continue to exceed the growth rate of the linear function?
Answer:
x = 1.79 to x = 3
Step-by-step explanation:
I think this is correct because the linear function grows at a constant rate so the point where the exponential function's line starts going up faster means that the growth rate is increasing. At the point (1.79,7.17) is when both lines intersect but the exponential function is growing at a faster rate than the linear function.
Answer:
x = 1.79 to x = 3
Step-by-step explanation:
help solve for number 5 please
:)
(x+2)/3 = (3x-2)/6
6(x+2) = 3(3x-2)
6x+12 = 9x-6
12+6 = 9x-6x
18 = 3x
x = 6
You are standing next to a really big circular lake. You want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! You decide to walk around the perimeter of the lake and measure its circumference, and find that it's 400\pi\text{ m}400π m400, pi, start text, space, m, end text.
What is the diameter of the lake?
Answer:
diameter = 400 m
Step-by-step explanation:
Perimeter of circle = pi * d
400 pi = pi * d
d = 400 meters
If the simple interest on $5,000 for 6 years is 1,200 then what is the interest rate?
Answer:
4%
Step-by-step explanation:
You can use the formula below to find the simple interest rate.
Simple interest = P r t / 100
Here,
P ⇒ Principle ⇒ $ 5000
r ⇒ rate ⇒ ??
t ⇒ time ⇒ 6 years
simple interest ⇒ $ 1200
Let us find it now.
Simple interest = P r t / 100
1200 = 5000 × r × 6 / 100
1200 × 100 = 30000r
120000 = 30000 r
Divide both sides by r.
4 = r
Therefore, the interest rate is 4%
Cos²(90° -X).tan(180°-X).cos(180°+X)/sin(180°-X)
Recall some identities:
tan(x) = sin(x) / cos(x)
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
cos(x - y) = cos(x) cos(y) + sin(x) sin(y)
sin(x - y) = sin(x) cos(y) - cos(x) sin(y)
This means we have
• cos²(90° - x) = [cos(90°) cos(x) + sin(90°) sin(x)]²
… = sin²(x)
• tan(180° - x) = sin(180° - x) / cos(180° - x)
… = [sin(180°) cos(x) - cos(180°) sin(x)] / [cos(180°) cos(x) + sin(180°) sin(x)]
… = sin(x) / (-cos(x))
… = -tan(x)
(and we also get sin(180° - x) = sin(x))
• cos(180° + x) = cos(180°) cos(x) - sin(180°) sin(x)
… = -cos(x)
So, the given expression reduces to
sin²(x) (-tan(x)) (-cos(x)) / sin(x) = sin²(x)
since tan(x) and cos(x)/sin(x) = 1/tan(x) will cancel.
If 32 superscript 2 c baseline = 8 superscript c 7, what is the value of c?
If 32 superscript 2 c baseline = 8 superscript c 7 is the given expression then the value of c is 3.
What are exponents?The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.
The given equation is 32 superscript 2 c baseline = 8 superscript c 7
[tex]32^{2c} = 8^{c+7}[/tex]
Write the expression in exponents form as
[tex](2^5)^{2c} = (2^3)^{c+7}[/tex]
[tex](2)^{10c} = (2)^{3c+21}[/tex]
Comparing the base,
10c = 3c + 21
10c - 3c = 21
7c = 21
c = 21/ 7
c = 3
Therefore, the value of c is 3.
Learn more about exponents;
https://brainly.com/question/5497425
What is the slope of a line that is parallel to the line y = 3/4x + 2?
-4/3
-3/4
3/4
4:3
Answer: The Slope Is 3/4
Step-by-step explanation:
y = 3/4x + 2
This is given in slope intercept form y = mx+b where m is the slope
Parallel lines have the same slope
The slope is 3/4y = 3/4x + 2
Answer:
x is - 7
Step-by-step explanation:
as you do 4+3=7 then there is a - sign in front of itPlease help guys much love
Step-by-step explanation:
1) Ans 3
2) Ans 6
3) Ans 4
4) Ans 1/5
5) Ans 1/23
Given the points (0, 5), (1, 7), and (-2, -5), find the equation of the quadratic polynomial that contains
these points. Show your work.
Answer:
y=-x²+3x+5.
Step-by-step explanation:
1) the common view of the quadratic function is y=ax²+bx+c, where a, b and c - numbers;
2) according to the equation above, it needed to substitute the given coordinates and to make up the system of the equations:
point (0;5): c=5;
poit(1;7): a+b+5=7 ('c' is already known, 5);
point(-2;-5): 4a-2b+5=-5 (c=5);
3) to solve the system:
[tex]\left \{ {{a+b+5=7} \atop {4a-2b+5=-5}} \right. \ = > \ \left \{ {{a=-1} \atop {b=3}} \right.[/tex]
4) finally, if a=-1, b=3 and c=5, then
y=-x²+3x+5.
A triangle has one side that measures 9 units, another side that measures x, and a third side that measures 2 units more than x. The perimeter is 29 units.
Which equation would we use to find the value of x?
Answer:
9+x+(x+2)=29
Step-by-step explanation:
9+x+(x+2)=29
Find the missing angle x
Answer:
144° or 36°- depends on what you are asking.
Step-by-step explanation:
Since there are 190° in a straight line and there is 36° on one side. I then substracted 190-36 to get 144°.
If you are asking for the missing side of the triangle then the answer is 36° since this triangle is an equilateral triangle.
PLEASE HELP this is a missing assignment i will mark brainliest
The polynomial a(x) = -18x² - 6x + 12 is the dividend of the polynomial division
The quotient q(x) is 0 and the remainder r(x) is -18x² - 6x + 12
How to divide the polynomial?The polynomial functions are given as:
a(x) = -18x² - 6x + 12
b(x) = 3x³ + 9x - 1
The quotient equation is given as:
a(x)/b(x) = q(x) + r(x)/b(x)
Since the degree of the dividend a(x) is less than the degree of the divisor b(x), then it means that the value of the quotient q(x) is:
q(x) = 0
And the remainder r(x) is:
r(x) = a(x)
Substitute known values
r(x) = -18x² - 6x + 12
Hence, the quotient q(x) is 0 and the remainder r(x) is -18x² - 6x + 12
Read more about polynomial division at:
https://brainly.com/question/25289437
Mariah needs to randomly select one of three groups of students to make their presentation first. Which simulation tools could she use in this
situation?
a full standard deck of cards
a spinner divided evenly into four sections, with each section a different color
a six-sided number cube
0 a bag containing 12 chips in three different colors, with four of each color
two coins
The simulation tool to use is (d) a bag containing 12 chips in three different colors, with four of each color
How to determine the simulation tool?From the question, we have the following parameter:
Group, n = 3
The probability of selecting a group is:
p = 1/3
This means that the simulation tool to select must have a probability value of 1/3
From the question, the option (d) has a probability of 1/3
This is so because, we have:
Chips = 12Colors = 3Chip of same color = 4So, the probability of selecting each color is 4/12 or 1/3
Hence, the simulation tool to use is (d)
Read more about probability at:
https://brainly.com/question/251701
Answer:
a bag containing 12 chips in three different colors, with four of each color
and i think
a six-sided number cube
Step-by-step explanation:
plato?
Suppose a is between 4 and 5, and b is between 2 and 4. Find all possible values of the expression a/b
first im guessing its 4 and 1/2
and the second is 3