Answer:
C) f(x) = 2(x+2)² - 3
Explanation:
Given function:
f(x) = 2x² + 8x +5
Vertex form: y = a(x - h)² + kFor this function:
⇒ y = 2x² + 8x + 5
⇒ y = 2(x² + 4x) + 5
⇒ y = 2(x + 2)² + 5 - 2(2)²
⇒ y = 2(x + 2)² - 3
Is the sequence arithmetic? If so, identify the common difference.
11, 15, 19, 23, ...
Answer:
Yes, the common difference is 4
Step-by-step explanation:
In an arithmetic sequence, you are either adding or subtracting the same number. In this case, you are adding 4 each time. 11+4=15 15+4=19 19+4=23
Which relation is also a function?
A. ((10, 5), (5, 10), (15, 5), (20, 25),
(25, 15))
B. ((10, 5), (5, 10), (15, 10), (20, 25),
(20, 15))
C. x 5 10 20 10 25
y 10 5
15 15 20
5
2
D.
3
7
B
Answer:
A
Step-by-step explanation:
A because the vertical line test passes if you graph all the points.
Find the sum of the first 8 terms of the following series, to the nearest integer 48,60,75
The series is a geometric series and the sum of the first 8 terms of the series 48, 60, 75 is 952.32
How to determine the sum of the first 8 terms?The series is given as:
48, 60, 75
The above series is a geometric series with the following parameters:
First term, a = 48
Common ratio, r = 1.25
The sum of n terms is:
[tex]S_n = \frac{a(r^n - 1)}{r -1}[/tex]
So, we have:
[tex]S_8 = \frac{48 * (1.25^8 - 1)}{1.25 -1}[/tex]
Evaluate
[tex]S_8 = 952.32[/tex]
Hence, the sum of the first 8 terms of the series is 952.32
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Could someone please answer and explain the following question?
Answer:
see explanation
Step-by-step explanation:
the error in the question is that
sec²x = [tex]\frac{1}{cos^2x}[/tex] ≠ [tex]\frac{1}{sin^2x}[/tex] , and
csc²x = [tex]\frac{1}{sin^2x}[/tex] ≠ [tex]\frac{1}{cos^2x}[/tex]
have been used incorrectly in simplifying the expression
then
[tex]\frac{tan^2x+1}{1+cot^2x}[/tex]
= [tex]\frac{sec^2x}{csc^2x}[/tex]
= [tex]\frac{\frac{1}{cos^2x} }{\frac{1}{sin^2x} }[/tex]
= [tex]\frac{1}{cos^2x}[/tex] × [tex]\frac{sin^2x}{1}[/tex]
= [tex]\frac{sin^2x}{cos^2x}[/tex]
= tan²x
Find the area of a circle with radius, r = 76cm.
Give your answer rounded to 3 SF.
Answer:
17,700.00
Step-by-step explanation:
Area of a circle = 22
------ r2
7
=22
------ 76x76 =123,750
7 ---------- =1,768.571
7
1,768.571 rounded to 3 SF=17700.00
can someone help i is confused
Answer:
The answer is c (the one outlined in blue)
Step-by-step explanation:
1. Angelo is wrong. Just start with the 1st one. 1+1.25 DOES NOT EQUAL 1.25
2. Try all the other ones, they don't work.
3. 1*1.25=1.25 (it works!) 2*1.25=2.50 (it works!) 3*1.25=3.75 (it works!)
The volumes of two similar solids are 210 m3 and 1,680 m3. The surface area of the larger solid is 856 m2. What is the surface area of the smaller solid? 107 m2 214 m2 1034 m2 6848 m2.
The surface area of the smaller solid according to the task content is; 107m²
What is the surface area of the smaller solid?It follows from task content that the two solids are similar. On this note, the same formula applies for calculating their areas and volume.
Since, surface area is directly proportional to the volume in both shapes;
The surface area of the smaller solid is;
A = (210 × 856)/1680
A = 107m².
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Answer:
A
Step-by-step explanation:
can someone help me with this? Thank you!
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: c = 2\pi r[/tex]
r = 4 cm[tex]\qquad \sf \dashrightarrow \: c = 2 \times 3.14 \times 4[/tex]
[tex]\qquad \sf \dashrightarrow \: c = 25.12 \: cm[/tex]
The circumference of the given circle.
Solution:[tex]c = 2 {\pi}r[/tex]
[tex]c = 2 \times 3.14 \times r[/tex]
[tex]c = 2 \times 3.14 \times 4[/tex]
[tex]c = 25.12 \: cm[/tex]
Hence, the circumference of the given circle is 25.12 centimeters.
A rectangular garden 50 m long by 34 m wide is surrounded by a sand path of uniform width. Calculate the width of this path if it is known that it has an area of 540 cm2.
Considering a width x of the sand path, we have a larger rectangle of dimensions 50+2x by 34+2x, as indicated in the figure. Now, the area of the sand path is expressed.
[tex]\boldsymbol{\sf{ (50+2x)(34+2x)-50\times 34=540\Longrightarrow\quad 0=4x^2+168x-540 }}[/tex]
[tex]\boldsymbol{\sf{ 0=4(x^2+42x-135)=4(x-3)(x+45) }}[/tex]
Therefore, the path is 3 m long.
Show all work necessary to solve each problem.
1. Solve the following equation step by step. Write a reason for each step-
2(x-18)+ 3x = 24
Answer:
x = 12
Step-by-step explanation:
2(x-18)+ 3x = 24
distribute the 2
2x - 36 + 3x = 24
combine like terms
5x - 36 = 24
+ 36 on both sides
5x = 60
divide by 5
x = 12
if there are 95 students in a school and there are 12 classes how many students are in each class
Answer:
11 classes will have 8 students, 1 class will have 7 students
Step-by-step explanation:
Take the total number of students and divide by the number of classes
95 / 12 =7.916666
Most classes will have 8 students, 1 class will have 7 students
What is the value of the expression shown? (1 point)
4 x (2 + 4)
Group of answer choices
12
24
32
48
Answer:
24
Step-by-step explanation:
first you have to add 2 and 4; 6. then multiply it by 4; 24
The box plot below represents the lengths, in inches, of fish a group of friends caught.
What is the interquartile range of the data?
Answer:
3.5Step-by-step explanation:
According to the box plot we have
Q1 = the 25% mark of data = 4.5 and Q3 = the 75% mark of data = 8The IQR is the difference of the two numbers above
IQR = Q3 - Q1 = 8 - 4.5 = 3.5Answer:
IQR = 3.5
Step-by-step explanation:
Explanation of the given box plot:
The closed circles at either end are the minimum and maximum The middle vertical line of the box is the medianThe left side of the box is the first quartileThe right side of the box is the third quartileTherefore, the Five-number summary of the given box plot is:
Minimum = 3First quartile (Q₁) = 4.5Median (Q₂) = 6Third quartile (Q₃) = 8Maximum = 13[tex]\begin{aligned}\textsf{Interquartile range (IQR)} & = \sf Q_3-Q_1\\& = \sf 8 - 4.5\\&= \sf 3.5\end{aligned}[/tex]
Math question 10 points
Answer: (a)
Step-by-step explanation:
the last step is
clear x
X=15.9/6.36
the answer is 5/2 or 2.50
Can someone help please!!
I need help, please and thank you!
Answer:
6,251
Step-by-step explanation:
First you have to multiply 65 by 7 you will get 455
Then you have to multiply 144.9 by 40 you will get 5,796
At last add the two values:
5,796+455=6,251
The expression "-280" + 18 represents a submarine that began at a depth of feet below sea level and ascended at a rate of 18 feet per minute. What was the depth of the submarine after 5 minutes?
Can someone solve this now please
Answer:
The answer is B.
Step-by-step explanation:
f(6) = 146 & g(6) = 731 /// The difference of the two is 585.
Answer answer please please
Answer:
The answer is B) <
Step-by-step explanation:
Just looking at the Base 10 to the power of -5. we can just ignore it since they both have the base.
Now compare 3.2 with 4.6 which one is greater than or less than or equal to.
3.2 < 4.6
Answer: the answer is b . The second choice is correct .
Step-by-step explanation:
the second one is bigger than the fist one . Hopeit helps you .Please give brainliest .thanks .
A cylinder has a radius of 4.5 inches and a height of 15 inches. If the radius is doubled, how would it affect the original volume of the cylinder?
Answer:
The volume will be increased 4 times.
Step-by-step explanation:
Short mathy expl:
If the radius is "doubled" that is 2 times bigger. But in the volume formula, the radius is squared. So 2 times bigger AND squared makes it FOUR times bigger.
See the volume calculations:
original--
Vol = pi•r^2•h
= (3.14)•4.5^2•15
= 953.775
new/bigger radius--
Vol = 3.14•9^2•15
= 3815.1
So when the radius is doubled, going from 4.5 to 9, the volume goes from 953.775 to 3815.1
3815.1 is 4 times 953.775
Tanvi opened a savings account and deposited $400.00 as principal. the account earns 13%
interest, compounded annually. what is the balance after 7 years?
p(1+)",
use the formula a = p 1 + where a is the balance (final amount), p is the principal
(starting amount), r is the interest rate expressed
as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years.
round your answer to the nearest cent.
The amount of the money after 7 years with a rate of 13% with an initial amount of $400 will be $ 941.04.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
Tanvi opened a savings account and deposited $400.00 as principal.
The account earns 13% interest, compounded annually.
Then the balance after 7 years will be
We know the compound interest formula.
A = P (1 + r)ⁿ
We have
P = $ 400
r = 13%
n = 7 years
Then we have
A = 400 x (1 + 0.13)⁷
A = 400 x 1.13⁷
A = 400 x 2.3526
A = $ 941.04
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which functions have a maximum and are transformed to the left and down of the parent function, f(x)=x²? check all that apply
p(x)=14(x+7)²+1
q(x)=-5(x+10)²-1
s(x)=-(x-1)²+0.5
g(x)=2x²+10x-35
t(x)=-2x²-4x-3
Answer:
q(x) and t(x)
Step-by-step explanation:
p(x) has no maximum (bc it's an upward parabola) and is shifted up from the parent equation
q(x) has a maximum (downward parabola) and is shifted left and down from the parent equation
s(x) has a maximum (downward parabola), but is shifted right and up of the parent equation
g(x) has no maximum (upward parabola) but is shifted left and down
t(x)has a maximum (downward parabola) and is shifted left and down from the parent equation
See the attached image for details :) hope this helps!
if 39 is 5% of a number, what is that number? How did you get your answer?
Answer:
780
Step-by-step explanation:
☞ To find the solution, divide 39 by 5% and multiply by 10
P = 39 * 5%(0.5) = 78
P = 78 * 10 = 780
a
a
1) Jimmy invests $8,540 in a retirement
account with a fixed annual interest rate of
6.03% compounded continuously. What
will the account balance be after 14 years?
A) $16,422.64 B) $19,865.03
C) $18,522.03 D) $17,525.57
Answer:
B) $19,865.03
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amountP = Principal amountr = annual interest rate (in decimal form)t = time (in years)Given:
P = $8,540r = 6.03% = 0.0603t = 14 yearsSubstituting given values into the formula and solving for A:
[tex]\large \implies \text{$ \sf 8540e^{0.0603 \times 14}=19865.03215 $}[/tex]
Please help I have no idea what I'm doing.
Answer:
Okay so your numbers are:
0, 2, 2, 4, 5, 1, 3, 4, 2, 4, 5, 0, 0, 1, 3, 4
You have to put them in order first:
0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5
Now that its all in order you have to pull out the middle number.
Since there are 16 numbers its an even pile so you have to get the 2 middle numbers:
2, 3
Add them both together:
2 + 3 = 5
Then divide by 2:
5 ÷ 2
= 2.5
Step-by-step explanation:
Hope this helps!
From your neighborhood sofite.
Answer: Median is 78
Step-by-step explanation: What you have to do in this stem and leaf plot is for example 6|0 is 60, 9|4 is 94, etc. To find the median height, ignore the stem (the number by itself) and do the median how you usually do it. Sorry if its a bit complicated
Can somebody help please and thank you!!
Answer:
(3x+12)+X=180
Step-by-step explanation:
Supplementary angles always equal 180
Answer:
C. (3x + 12) + x = 180 is the correct answer.
Step-by-step explanation:
The angle of any straight line is 180*, and since thats a sraight line, then the acute angle (x) plus the obtise angle (3x + 12) must equal 180*.
Hope this helps!
Also x = 42* for reference.
10. In a library, Jolly deaned and arranged 4599 books on the shelf. Gopal arranged 1945 less books than Jolly. How many books were arranged in all by Gopal?
Answer: 2654
Step-by-step explanation:
you take jolly's number 4599 and subtract Gopal's number of 1945
Which is NOT a solution
of the inequality
9 - 3x ≥ -36 ?
A. 0
B. -22
C. 50
D. 11
Angles A and B are supplementary. If the measure of A= x-10 and the measure of B = x + 4, find the measure of each angle.
Answer:
10x - 15 + 5x = 180
Step-by-step explanation:
Solve for x
Convert the fraction below into a decimal using
long division. Round any repeating decimals to
the thousandths.
13/15
Answer:
0.86666666666667
Step-by-step explanation:
What we have to do is do 13 divided by 15 which equals 0.86666666666667.
