Answer:
[tex]\large\boxed{f(x)=(x+8)^2-110}[/tex]
Step-by-step explanation:
[tex]\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\\text{We have the equation:}\\f(x)=x^2+16x-46=x^2+2(x)(8)-46=x^2+2(x)(8)+8^2-8^2-46\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\to x^2+2(x)(8)+8^2=(x+8)^2\\\\f(x)=(x+8)^2-64-46=(x+8)^2-110[/tex]
The function f(x)=x^2+16x-46 can be rewritten by completing the square to achieve the vertex form of the function: f(x)= (x+8)^2 - 110. After rewriting, we can determine the vertex of this parabola is located at (-8,-110).
Explanation:The problem asks you to rewrite the function f(x)=x^2+16x-46 by completing the square. This involves manipulating the quadratic formula to write it in the form f(x)=a(x-h)^2+k where (h,k) is the vertex of the parabola.
So, let's start by rearranging the original function:
f(x)=x^2+16x-46
The coefficient of x is 16; halving this, we get 8. Then we add and subtract (which means adding 0, so we don't change the equation) this within the square to complete the square:
f(x)= (x^2+16x+64) - 64 - 46
Then, the equation can be written as:
f(x)= (x+8)^2 - 110
This is the vertex form of the function. We can see that the vertex of the parabola is at (-8,-110).
Learn more about Completing the Square here:https://brainly.com/question/4822356
#SPJ3
Gina is the chairperson of a group. Last week, she set up 22 folding chairs for the group meeting. This week, some of the members could not attend the meeting, so she set up only 15 chairs. How many chairs did Gina set up in the past two weeks?
Answer:
37 Chairs
Step-by-step explanation:
Last week she set up 22 chairs.
This week, that amount was 15
Add those together, and you have 37.
Gina set up a total of 37 chairs in the past two weeks.
Explanation:To find the total number of chairs Gina set up in the past two weeks, we need to add the number of chairs she set up last week to the number of chairs she set up this week.
Last week, Gina set up 22 chairs for the group meeting.This week, she set up 15 chairs for the meeting.To find the total number of chairs she set up in the past two weeks, we add the number of chairs from last week and this week: 22 + 15 = 37.An architect built a scale model of a sports stadium using a scale in which 2 inches represents 30 feet. The height of the sports stadium is 180 feet.
What is the height of the scale model in inches?
A] 3in
B} 105 in
C[ 12in
D{ 60in
PLEASE HELP‼️ AND SHOW WORK‼️
A. 12 in
We know that the sports stadium is 180 ft tall and that in the scale model there is 2 in for every 30 ft. If we divide 180 by 30 we get 6. There is 2 in for every 30 ft, so the answer would be 6 x 2 or 12 in.
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
If 2 inches = 30 feet and the height of the sports stadium is 180 feet.
The height of the sports stadium in scale model in inches is 12 inches.
Option C is the correct answer.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
In 5 minutes a machine can cut 10 potato
In 1 minute a machine can cut 2 potato.
We have,
30 feet = 2 inches
Divide both sides by 30.
1 feet = 2/30 inches
Now,
1 feet = 2/30 inches
Multiply 180 on both sides.
180 feet = 180 x 2/30 inches
180 feet = 6 x 2 inches
180 feet = 12 inches
Thus,
If 2 inches = 30 feet and the height of the sports stadium is 180 feet.
The height of the sports stadium in scale model in inches is 12 inches.
Learn more about unit rates here:
https://brainly.com/question/11258929
#SPJ6
Please help me!!! QUICK!!!
Extra points and brainliest will be given :)
See the attached picture:
1) Jason flipped a penny many, many times to verify that it lands on heads half the time. He heard that if you apply a layer of clear coat to the tails side of a penny,it will land on heads more frequently. He decided to test this and coated the tails side of his penny. Jason flipped the coin 200 more times and it landed on heads 54.5% of the time. Do you think his trick worked? Use a 0.05
Answer:
yes theoretically it did work
Step-by-step explanation:
hypothetically it is supposed to land on each side half of the time, but as we all know it's a matter of luck. since after you put on the layer of coating and it landed on heads more thank half of the time (50%), it technically has worked but in a real world application it would be hard to tell/justify.
Carmen wants to paint the ceiling of her restaurant. The ceiling is in the shape of a square. Its side lengths are 39 feet. Suppose each can of paint will cover 169 square feet. How many cans will she need to paint the ceiling?
Answer:
The answer is 9
Step-by-step explanation:
39X39 is 1521
1521/169=9
so carmen needs 9 cans of paint
To paint the square ceiling of 1521 square feet, Carmen will need to round up from the approximately 9 cans of paint that would be required to cover it, so she will need to purchase 10 cans of paint.
Explanation:Carmen would be dealing with a mathematical concept related to area and division. Since the ceiling is a square, we can find the total area by squaring the length of one side. This means multiplying 39 (feet) by itself: 39*39 = 1521 square feet.
Each tin of paint can cover 169 square feet, so if we divide the total square feet of the ceiling by what one tin can cover, we get the amount of tins needed. This means 1521 divided by 169: approximately 9 cans of paint. Since you cannot buy a fraction of a can, Carmen will need to purchase 10 cans of paint to ensure she can cover the entire area of the ceiling.
Learn more about Area and Division here:https://brainly.com/question/34784610
#SPJ3
perform the indicated operation (3x^3-2x^2+4x-3)(x+2)
Answer:
3x^{4} + 4x³ + 5x - 6
Step-by-step explanation:
Given in the question is an expression
(3x³ - 2x² + 4x - 3)(x + 2)
Apply distributive law
(3x³ - 2x² + 4x - 3)(x) + (2)(3x³ - 2x² + 4x - 3)
3[tex]x^{4}[/tex] - 2x³ + 4x² -3x + 6x³ - 4x² + 8x - 6
Rearrange the like terms
3[tex]x^{4}[/tex] + x³(-2+6) +x²(4-4) +x(-3+8) - 6
3[tex]x^{4}[/tex] + 4x³ + 5x - 6
After performing indicated operation the result is
[tex]3x^{4}+4x^{3}+5x-6[/tex]
Use the quadratic formula to formula to find both solutions to the quadratic equation given below. 3x^2-x+6=0
Final answer:
To find the solutions of the quadratic equation 3x^2 - x + 6 = 0, we can use the quadratic formula. The solutions are complex numbers: x = (1 ± i√71) / 6.
Explanation:
To find the solutions of the quadratic equation 3x^2 - x + 6 = 0, we can use the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
By comparing the given equation to the standard quadratic equation form ax^2 + bx + c = 0, we can determine that a = 3, b = -1, and c = 6. Substituting these values into the quadratic formula, we get:
x = (-(-1) ± √((-1)^2 - 4(3)(6))) / (2(3))
Simplifying further, we have:
x = (1 ± √(1 - 72)) / 6
Finally, evaluating the expression under the square root, we get:
x = (1 ± √(-71)) / 6
Since the square root of a negative number is not a real number, the solutions to the quadratic equation are complex numbers. Hence, the solutions are:
x = (1 ± i√71) / 6
In a class of 32 students, 25% of the students wear glasses. How many students wear glasses?
32×.25=8
so 8 students wear glasses
I need help please and thank you.
Answer:
0
Step-by-step explanation:
The formula gives you a relation between S and n. For every n, you can perform the calculation and obtain an S.
So, for n=0 we get 0/2 (0+1) which equals 0. So (0,0) is an (n,S) pair.
114.4 is 65% of what amount
65% × 114.4 =
(65 ÷ 100) × 114.4 =
(65 × 114.4) ÷ 100 =
7,436 ÷ 100 =
74.36
and how you can check yourself kinda do the opposite of what you did to get the answer
74.36 ÷ 114.4 =
0.65 =
0.65 × 100/100 =
0.65 × 100% =
(0.65 × 100)% =
65%
An equation is shown below. 12 - 9 + c = 12 What value of c makes the equation true?
The correct answer is C = 9.
Step by step:
Subtract 12 - 9 = 3
3 + 9 = 12.
It’s that simple. Hold this helps!
The value of c is 9 makes the equation true.
It is given that the equation 12 - 9 + c =12.
It is required to find the value of c that makes the equation true.
What is a linear equation?It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
If in the linear equation one variable is present then the equation is known as the linear equation in one variable.
We have a linear equation in one variable:
12 - 9 + c = 12
-9 + c =0 (subtract 12 on both sides)
c = 9 ( add 9 on both sides)
Thus, the value of c is 9 makes the equation true.
Learn more about the linear equation here:
brainly.com/question/11897796
Two values of x that are roots of xsquared+2x-6=0
The two values of x are
1.65 , -3.65
Answer:
Two values of x that are :
[tex]x=-\sqrt{7}-1[/tex]
[tex]x=\sqrt{7}-1[/tex]
Step-by-step explanation:
Given= [tex]x^2+2x-6=0[/tex]
To find = Two values of x
Solution :
[tex]x^2+2x-6=0[/tex]
Adding and subtracting 1 in the equation :
[tex]x^2+2x+1-1-6=0[/tex]
[tex](x^2+2\times x\times 1+1^2)-1-6=0[/tex]
[tex](x+1)^2-7=0[/tex]
[tex](x+1)^2=7[/tex]
[tex](x+1)=\pm \sqrt{7}[/tex]
Two values of x that are :
[tex]x=-\sqrt{7}-1[/tex]
[tex]x=\sqrt{7}-1[/tex]
What is the distance between the points (-7, 3) and (4, -5) in the coordinate plane?
A. Square root of 125
B. Square root of 57
C. Square root of 13
D. Square root of 185
the correct answer is d
please find the unknown with all steps
Answer:
see explanation
Step-by-step explanation:
Since AC = BC then ΔABC is isosceles with base angles
∠BAC =∠ABC, thus
3x + x = 70
4x = 70 ( divide both sides by 4 )
x = 17.5
----------------------------------------------------
∠ADC is an external angle of ΔABD and the external angle is equal to the 2 opposite interior angles, hence
y = 70 + x = 70 + 17.5 = 87.5
Please help lol ............
Answer:
1 X 16 and 8 X2
Step-by-step explanation:
1 X 16 = 16
2 X 8 = 16
3 X nothing = 16
4 X 4 = 16
5 X nothing = 16
6 X nothing = 16
7 X nothing = 16
8 X 2 = 16
etc.
[tex]\bold{Hey\ there!} \\ \\ \bold{Choose\ all\ of\ the\ correct\ factors\ of\ 16}[/tex]
[tex]\bold{It \underline{CAN'T} \ be\downarrow} \\ \bullet\ \bold{3\times5\ because\ it\ equals\ to\ 15} \\\bullet\ \bold{4\times3\ because\ it \ equals\ to\ 12} \\ \\ \\ \\ \bold{It\ \underline{CAN} \ be\downarrow} \\ \bullet \ \bold{1\times16\ because\ it\ equals\ to \ 16} \\ \bullet \ \bold{8\times2\ because\ it\ equals\ to\ 16} \\ \\ \\ \boxed{\boxed{\bold{Answer(s):1\times16\ \& \ 8\times2}}}\checkmark[/tex]
[tex]\bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your \ day!} \\ \\ \frak{LoveYourselfFirst:)}[/tex]
Please help me out on this question I been stuck on it
Answer:
B, C
Step-by-step explanation:
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{3^2 - 4(1)(-5)}}{2(1)} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{9 + 20}}{2} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{29}}{2} [/tex]
Answer: B, C
The life expectancy of a certain tire is a normal distribution with the mean = 40,000 miles, standard deviation is 1,000 miles. Find the probability that a tire will last more than 39,000 miles.
Answer:
[tex]P = 84\%[/tex]
Step-by-step explanation:
The average is:
[tex]\mu = 40,000\ miles[/tex]
The standard deviation is:
[tex]\sigma = 1,000\ miles[/tex]
We want the probability that a tire lasts more than 39,000 miles.
This is:
[tex]P (X>39,000)[/tex]
Now we must transform these values to those of a standard normal distribution to facilitate calculation by using the probability tables.
[tex]P (X> 39,000)\\\\P (X-\mu> 39,000-40,000)\\\\P (\frac{X-\mu}{\sigma}> \frac{39,000 -40,000}{1,000})\\\\P (Z> -1)[/tex]
This is:
[tex]P(Z> -1) = P(Z<1)[/tex] ---------- (For the symmetry of the standard normal distribution)
When you search for the normal standard table, you get the following value:
[tex]P(Z <1) = 0.8413\\\\P(Z> -1) = 0.8413[/tex]
WILL GIVE BRAINLIEST
What is the period of a wave if the wavelength is 100m and the speed of 200m/s
A. 100s
B. 200,000s
C. 0.5s
D. 2s
Answer:
C. O.5s
Step-by-step explanation:
If the wave length is 100m and it goes at a speed of 200m/s then it will only take 0.5 seconds because 100 is half of the speed of 200
Answer:
C
Step-by-step explanation:
The formula we use to solve this would be: [tex]T=\frac{\lambda}{v}[/tex]
Where
T is the period in seconds
[tex]\lambda[/tex] is the wavelength in m, and
v is the speed of the wave in m/s
We have [tex]\lambda[/tex] equal to 100, and v = 200 m/s. Plugging these into the equation, we get the period:
[tex]T=\frac{\lambda}{v}\\T=\frac{100}{200}\\T=0.5[/tex]
C is the right answer.
Find the distance d. (2,4) and (7,2)
Answer:
The answer is d = [tex]\sqrt{29}[/tex]
Step-by-step explanation:
To find the distance, use the distance formula.
d = [tex]\sqrt{(x1 - x1)^{2} + (y1 - y2)^{2} }[/tex]
d = [tex]\sqrt{(7 - 2)^{2} + (2 - 4)^{2} }[/tex]
d = [tex]\sqrt{(5)^{2} + (-2)^{2} }[/tex]
d = [tex]\sqrt{25 + 4 }[/tex]
d = [tex]\sqrt{29}[/tex]
(i really need help with this , and you can get branliest
If s = unit and A = 12s2, what is the value of A, in square units? square unit(s). (Input whole number only.)
The equation below shows the total volume (V), in cubic units, of 5 identical boxes with each side equal to s units:
V = 5s3
If s = 1.4 units, what is the value of V?
13.72 cubic units
19.21 cubic units
21 cubic units
25 cubic units
Answer:
13.72 cubic units
Step-by-step explanation:
The equation below shows the total volume (V), in cubic units, of 5 identical boxes with each side equal to s units: V = 5s3
If s = 1.4 units, what is the value of V?
Substitute s = 1.4 into V = 5s³ = 5(1.4)³ = 13.72 cubic units.
Simplify. Rewrite the expression in the form 10^n
10^5 x 10 = ?
10 to the power of 6
10^5 × 10 = 10^6
--------------------------
list the fractions from least to greatest and a picture to show your answers
a 1/5,1/7,1/3
b 2/5,2/7,2/3
c 5/6,3/6, 1/6
d 5/12,8/12,4/12
Answer:
Below, the fractions organized from least to greatest:
a. 1/7, 1/5, 1/3
b. 2/7, 2/5, 2/3
c. 1/6, 3/6, 5/6
d. 4/12, 5/12, 8/12
if f(x) = (1/7), what is F(3)
A.343
B.1/49
C.49
D.1/343
Answer:
Step-by-step explanation:
None of them
Perhaps the original question was f(x) = (1/7)^x or f(x)=(1/7)^-x
The first one would give A as an answer
The second one would give D as an answer.
A similar answer could be worked out for B and C
In any event correct your question, please
Answer:
49
Step-by-step explanation:
Please help me and please don't answer if you're not 100% sure!
The answer choices are
A. 1120 people
B. 280 people
C. 100 people
D. 112 people
Answer:a
Step-by-step explanation:
it just looks like it
Which expression shows the total price including tax?
Answer:
1.04p
Step-by-step explanation:
You will pay the whole price of the item which is p or 1p. Then you will add 4% tax or 0.04p. So the total will be 1p + 0.04p = 1.04p.
Timothy drove his race car 10% farther using the gasoline from Smith's Station compared to gasoline from Jack's Station. After Timothy filled his gas tank at Jack's Station, he traveled 480 miles. How far did he travel on a tank of gas from Smith's Station?
Answer:
528
Step-by-step explanation:
x = 480
1.1 x = 480 * 1.1
480 + 48 = 528
Timothy traveled 528 miles using the gasoline from Smith's Station, which is 10% farther than the 480 miles he traveled with gasoline from Jack's Station.
Explanation:To calculate how far Timothy traveled using the gasoline from Smith's Station, we need to determine what 10% more than the 480 miles he traveled using gasoline from Jack's Station is. First, let's find 10% of 480 miles:
10% of 480 miles = 0.10 × 480 miles = 48 miles.Now, let's add this additional distance to the original 480 miles to find the total distance traveled with gas from Smith's Station:
480 miles + 48 miles = 528 miles.Therefore, Timothy traveled 528 miles on a tank of gas from Smith's Station.
25 points for answer!! Consider the circle graph below of the type of flowers planted in a garden. If 57 carnations are in the garden, how many roses are in the garden?
The ratio of carnations to roses in the garden is 19:31.
Since there are 57 carnations in the garden, there are 57 * 31/19 = 93 roses in the garden.
Answer:
The answer is 93
Step-by-step explanation:
The zeros of a quadratic function are -8 and 5. Write the quadratic function in Standard Form.
Answer:
y = x² + 3x - 40
Step-by-step explanation:
Given the zeros are x = - 8 and x = 5, then the factors are
(x + 8) and (x - 5) and
y = (x + 8)(x - 5) ← expand factors
y = x² - 5x + 8x - 40, hence
y = x² + 3x - 40 ← in standard form
Find a number that is square number and also a cube number
Answer:
64
Step-by-step explanation:
4 x 4 x 4 = 64
8 x 8 = 64
what is equivalent to the expression below?
(-6) to the -5 power
a. 6 to the 5 power
b. (1/6) to the 5 power
c. (-1/6) to the 5 power
d. 30