Answer:
y = 2(x - 1)² - 3
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (1, - 3), thus
y = a(x - 1)² - 3
To find a substitute (- 1, 5) into the equation
5 = a(- 1 - 1)² - 3
5 = (- 2)²a - 3 ( add 3 to both sides )
8 = 4a ( divide both sides by 4 )
a = 2
Thus
y = 2(x - 1)² - 3 ← in vertex form
when 7 is subtracted from 3 times a certain number , the result is 28. What is the number
7 multiply by three u get 21 then add it to the number 28 add u get the answer 49
Which translation maps the graph of the function f(x)=x2 onto the function g(x)=x2+_2x+6?
Answer:
idk
Step-by-step explanation:
Which of these is an example of a literal equation?
A. 12 = 9 + 3x
B. 6 + 30 = 62
C. ax - by = k
D. 3x - 4y
Complete the sentence.
The bases of a circular cylinder are two ___
ao circles.
Answer:
congruent & parallel
Step-by-step explanation:
The bases of a circular cylinder are congruent and parallel to each other. If you need more explanation, reply to my answer.
What is the radius of this cone ? V=16cm3 and 12 cm
Answer:
1.13 cm
Step-by-step explanation:
V=1/3 * pi*r^2*h
h=12 cm (assuming, since that's what you gave)
V=16
r=1.13 cm
BRAINLIEST WILL BE MARKED(THAT MEANS- 3 EXTRA POINTS) HERE! GRAPHING HELP 101
The graph of f(x)=x2 is shown.
Use the parabola tool to graph the function g(x)=(1/5x)2.m
The 1/5 is a fraction.
The graph with the blue highlight is my answer. LET ME KNOW IF MY ANSWER IS RIGHT OR WRONG! ASAP PLEASE AND THANK YOU WILL MARK BRAINLIEST!
Answer:
I think its wrong. For g(5)=(5/5)^2=1 and in your graph is something close to 3. The correct graph for [tex]g(x)=(\frac{1}{5}x)^2[/tex] is
Answer:
False
Step-by-step explanation:
Took the test and this is what I got
Please help me I need to finish today!
Answer:
C
Step-by-step explanation:
For Youfang, the time spent running is equal to 15 times the week
A farmer finds that if she plants 25 trees per acre, each tree will yield 41 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 1 bushel. How many trees should she plant per acre to maximize her harvest?
Answer:
17
Step-by-step explanation:
Let F be the number of fruit per acre
F = (25 + x) × (41 - x)
F=1025 -25x + 41x -x²
F=-x²+16x+1025
The maximum yield is at the maximum of that expression, which is at
[tex]x=-\frac{b}{2a} =>-\frac{16}{-2\times1}[/tex]
x=8
So apparently she currently has far too many trees per acre. To get the maximum yield, she needs to reduce the number of trees per acre by 8.
So the number of trees per acre for maximum yield is 25-8 = 17.
5 + 3 + 2 = 151022
9 + 2 + 4 = 183652
8 + 6 + 3 = 482466
5 + 4 + 5 = 202541
Then ...
7 + 2 + 5 = ??????
Answer:
7 + 2 + 5 = 143547
Step-by-step explanation:
This question needs to identify the pattern
the pattern
is
5 + 3 + 2 = 151022
First two digits: 5*3 = 15 multiple of first and second term
third and fourth digit: 5*2 = 10 multiple of first and third term
last two digit = First two digits + third and fourth digit - second term
= 15+10 - 3 = 22
similarly
9 + 2 + 4 = 183652
9*2 = 18
9*4 = 36
18+36 - 2 = 52
____________________________________
5 + 4 + 5 = 202541
5*4 = 20
5*5 = 25
20+25-4 = 41
_______________________
7 + 2 + 5 = ??????
7*2 = 14
7*5 = 35
14+35-2 = 49-2 = 47
thus, 7 + 2 + 5 = 143547
Question 1 (1 point)
Solve
- +13 > 10
(Blank 1 is <,>, S, or 2. Blank 2 the number)
Recall that < and > are on the keyboard. You can get S and respectively by doing Alt < and Alt > on the keyboard. You may also copy the
symbols from the instruction page or the Copy Symbol and Keyboard Shortcuts Page.
Blank 1:
Blank 2:
Sammy wants to deposit into a 7% annual simple interest account she will also deposit twice as much in a certificate of deposit earning 5% annual simple interest to earn $390 of annual interest how much should she invest in each account?
Answer: $2294 should be invested in the simple interest account while $4588 should be invested in the certificate of deposit.
Step-by-step explanation:
Let x represent the amount that he would deposit in the simple interest account.
Let y represent the amount that he would deposit in the certificate of deposit.
she will deposit twice as much in the certificate of deposit. It means that
y = 2x
Interest from the simple interest account would be 7%. This mean that the interest would be 7/100 × x = $0.07x
Interest from the certificate of deposit account would be 5%. This mean that the interest would be 5/100 × y = $0.05y.
The total interest from both accounts would be $390. It means that
0.07x + 0.05y = 390- - - - - - - - - - 1
Substituting y = 2x into equation 1, it becomes
0.07x + 0.05 × 2x = 390
0.07x + 0.1x = 390
0.17x = 390
x = 390/0.17 = $2294
y = 2x = 2 × 2294
y = 4588
please help a struggling man
Answer:
x is all real numbers
Step-by-step explanation:
The domain is the input to the function. It is the values that x can take.
For this function, x can be any real value
How many cubes with a side length of 1/2 unit would it take to fill a rectangular prism with a volume of 2 cubic units?
Answer:
16
Step-by-step explanation:
1/2*1/2*1/2 = 1/8 cubic units
2/(1/8) = 16
Answer:
16
Step-by-step explanation:
[tex](\frac{1}{2})^3 = \frac{1^3}{2^3} = \frac{1}{8}\\\frac{2}{\frac{1}{8}} = 2 \cdot 8 = 16[/tex]
Which of the following pair of angles is the complementary angle? 25 and 65 31 and 71 60 and 40 145 and 35
Answer:
Step-by-step explanation:
If the sum of a pair of angles is 90, then they are complementary angles.
25 + 65 = 90
So, 25 and 65 are complementary angles
Answer:
25 and 65
Step-by-step explanation:
complementary angle= either of two angles whose sum is 90°
25 and 65, sum = 90°
yes31 and 71, sum = 102°
no60 and 40, sum = 100°
no145 and 35, sum = 180°
noWhat is the equation of a line with a slope of six and passes through the coordinates 0,1
Answer:
y = 6x + 1
Step-by-step explanation:
Use the point slope equation:
y - y1 = m( x - x1 )
y - 1 = 6 ( x - 0)
y - 1 = 6x
y = 6x + 1
I need help with this problem.
Answer:
D
Step-by-step explanation:
[tex]f(x)=3x+5 \\\\g(x)=x^2 \\\\(f-g)(x)=(3x+5)-(x^2)=-x^2+3x+5[/tex]
Therefore, the correct answer is choice D. Hope this helps!
Help pls :/.
The net of a triangular prism and its dimensions are shown. What is the total surface area, in square inches, of the triangular prism?
A) 240 sq inches
B) 120 sq inches
C) 96 sq inches
D) 24 sq inches
Answer:
120 sq inches
Step-by-step explanation:
I just did the quiz just now
Four college roommates rented an apartment together. When they
moved out, they were charged $1500 for damages to the carpet
and walls. The roommates agreed to equally share the cost.
What integer represents how much each person will have to pay?
Answer:
Step-by-step explanation:
What we do is to divide 1500 by 4 = $1500/4 = $375
Answer:375
Step-by-step explanation:
1500/4=375
Part 3. Identify the X intercepts for
y = (x+4)^2-9
Answer:
x = -1 or x = -7
Step-by-step explanation:
y = (x + 4)^2 - 9
To find x-intercept, set y = 0
=> (x + 4)^2 - 9 = 0
=> ( x + 1)( x + 7) = 0
=> x = -1 or x = -7
To find the x intercepts, plug in y = 0 and solve for x
y = (x+4)^2 - 9
0 = (x+4)^2 - 9 ... replace y with 0
9 = (x+4)^2
(x+4)^2 = 9
x+4 = plus/minus sqrt(9)
x+4 = sqrt(9) or x+4 = -sqrt(9)
x+4 = 3 or x+4 = -3
x = 3-4 or x = -3-4
x = -1 or x = -7 You have the correct answers. Nice work.-----------------------------------------------------------------
Checking each answer:
Plug x = -1 into the original equation. You should get y = 0 as a result
y = (x+4)^2 - 9
y = (-1+4)^2 - 9
y = (3)^2 - 9
y = 9-9
y = 0 .... so this confirms x = -1 as a solution
The same should apply for the other potential solution x = -7
y = (x+4)^2 - 9
y = (-7+4)^2 - 9
y = (-3)^2 - 9
y = 9-9
y = 0 .... this confirms x = -7 as well
At the start of the week, Ladasha’s checking account had a balance of $34. She deposited $50 each day for three days. She made a $60 withdrawal on the fourth day. Ladasha also wrote a check for $22. Explain how you can write an expression to show the account balance at the end of the week.
Step-by-step explanation: The account started at $34. Three $50 credits were added. Indicate the withdrawal by subtracting $60 or adding –$60. The check is also represented by subtracting $22 or by taking the additive inverse and adding –$22.
Sample Response: The account started at $34. Three $50 credits were added. Indicate the withdrawal by subtracting $60 or adding –$60. The check is also represented by subtracting $22 or by taking the additive inverse and adding –$22.
The units of the subway map at the right are in miles. Suppose the routes between stations are straight, find the distance you would travel between each the Elm and Symphony Stations. Round your answer to the nearest tenth of a mile. The distance between the Elm and Symphony Stations is how many miles?
Answer:
Distance between 2 stations= 8.94 miles
Step-by-step explanation:
The coordinates of Symphony Station is given by:
Symphony Station: (x₁ , y₁) : (1,2)
The coordinates of Elm station is given by:
Elm Station: (x₂ ,y₂) : (-3,-6)
We know that the distance formula can be used to find distance between these 2 points. Distance formula is given as
d= √((x₂ - x₁)² + (y₂ - y₁) ²)
Substitute values
d= √((-3 - 1)² + (-6 - 2) ²)
d= √((-4)²+(-8)²)
d= √(16+64)
d=√80
d= 8.94 miles
i need help im too lazy still :)
Answer:
w=-16
Step-by-step explanation:
divide -192 by 12 to isolate w
Answer:
w=-16
Step-by-step explanation:
The price of an item has been reduced by 15%. The original price was $17
Answer:
17/100*85= $14.45
Step-by-step explanation:
Divide by 100 and multiply by (100-15) 85 to get the result.
Ms Adams shares out 21 pencils between Niamah and Jack in the ratio 2:5 how many pencils does each child get
Answer:
niamah : jack
2 : 5
2×3 : 5×3
6 : 15
niamah gets 6 pencils
jack gets 15 pencils
*6+15 = 21
Answer:
Step-by-step explanation:
If the ratio of Niamah to Jack is 2:5, that means that for every 2 pencils that N gets, J gets 5. If there are a total of 21 pencils, then
2x + 5x = 21 and
7x = 21 so
x = 3.
That means that N gets 2(3) which is 6, and J gets 5(3) which is 15. Notice that 6:15 is the same ratio as 2:5 when it is reduced.
Part 2:
1. Make sure your answers and work is SHOWN please and steps are in order.
2. List all possible rational roots.
3. Use synthetic division to test possible rational roots
4. Identify complex roots, if possible.
5. Sketch a graph of the function, please show:
a. the end behavior correctly
b. the shape of the near x-intercepts
c. (if possible) anything you can learn by considering symmetry and transformations
2a. p(x)= x^4 + 4x^3 + 13x^2 + 36x + 36
Answer:
2. ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±36
3. see below for synthetic division
4. complex roots: ±3i
5. see the second attachment for a graph (has no symmetry)
Step-by-step explanation:
2. The Rational Root Theorem tells you possible rational roots are the form of ...
±(divisor of constant term) / (divisor of leading coefficient)
Here, we're lucky in that the leading coefficient is 1. The constant is 36, and its divisors are 1, 2, 3, 4, 6, 9, 12, 18, 36. Possible rational roots, according to the Rational Root Theorem are ...
±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±36
__
3. When actually searching for possible roots, it is useful to narrow down this list of 18 candidates. We can do this using Descarte's Rule of Signs and a couple of other simple tests. The rule of signs has us look at the signs of the coefficients. They are ...
+ + + + +
There are no sign changes, hence no positive real roots. This means we're looking at negative roots only.
We know that p(0) = 36, the constant term. We can evaluate p(-1) simply, by reversing the signs of the odd-degree coefficients and adding them up:
1 -4 +13 -36 +36 = 10
So p(0) = 36 and p(-1) = 10. The average rate of change is -26, so we expect p(-2) to be zero or less. That value (-2) may be a good first choice for a possible root.
The synthetic division for the root -2 is shown in the first attachment. It shows a remainder of 0, so -2 is a root. The polynomial with the corresponding factor divided out is ...
q(x) = x^3 +2x^2 +9x +18
__
We can apply the above steps to this polynomial. It will have no positive real roots. The value of q(0) is 18, and the value of q(-1) is -1 +2 -9 +18 = 10. The average rate of change between these points is (18 -10)/(0 -(-1)) = 8, so we expect the function to be zero or negative between x=-2 and x=-3.
Further, we observe that the ratio of the first two coefficients is 1 : 2, the same as the 9 : 18 ratio of the last two coefficients. This suggests we can factor this polynomial by "grouping."
q(x) = (x^3 +2x^2) +(9x +18) = x^2(x +2) +9(x +2) = (x^2 +9)(x +2)
So, without doing any more synthetic division, we have found a second root at x = -2. This means -2 is a double root.
Our factorization so far is ...
p(x) = (x +2)^2(x^2 +9)
__
4. The remaining polynomial factor (x^2 +9) has only complex roots:
x^2 +9 = 0
x^2 = -9
x = ±√(-9)
x = ±3i . . . . the complex roots
__
5. The graph is shown in the second attachment, along with the graph of the final quadratic factor.
The leading coefficient is positive and p(x) is of even degree, so it will have a general U shape, going to +∞ for large positive and negative values of x.
Since x = -2 is a double root, the graph touches the x-axis there, but does not cross it.
The graph of p(x) shows no symmetry.
______
Comment on the graph
With modern graphing calculator software it is entirely feasible to start by graphing the polynomial, then reading the (rational) roots from the graph. The same calculator can effectively divide out those roots. If the result is a quadratic, its vertex form equation can be read from the graph, making it easy to find any additional real or complex roots.
This graph shows ...
p(x) = (x +2)^2·q(x)
q(x) = x^2 +9
4x+2/2 -(-2) find the answer
Answer:
[tex]4x+3[/tex]
Step-by-step explanation:
[tex]4x+2/2 -(-2)[/tex]
[tex]4x+1 -(-2)[/tex]
[tex]4x+1 +2[/tex]
[tex]4x+3[/tex]
Answer: =4x+3
Step-by-step explanation:
4x+ 2 /2 −(−2)
=4x+1+2
then you Combine the Like Terms:
=4x+1+2
=(4x)+(1+2)
=4x+3
Hope this helps :)
What is the perimeter of the triangle?
Answer:
To find the perimeter of the triangle, you need to add up the three sides of the triangle
/\
1 /__\ 5
9
1+5+9
_________________________________
Hey!!
The formula to find perimeter of triangle is a+b+c
For example:
If a triangle has the sides of 5,4 and 3 respectively,then to find the perimeter of triangle,we have to use the formula a+b+c which equals to 12.
Hope it helps
Good luck on your assignment
___________________________________
Solve the following inequality. Then place the correct answer in the box provided. Answer in terms of a mixed number.
2(P +1) + 3(P + 2 ) > 2
Answer: [tex]-1\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]2(P +1) + 3(P + 2 ) > 2[/tex]
Distribute 2 and 3
[tex]2P+2+3P+6>2[/tex]
Combine like terms;
[tex]5P+8>2[/tex]
Subtract 8
[tex]5P>2-8[/tex]
[tex]5P>-6[/tex]
Divide by 5
[tex]P>-\frac{6}{5}[/tex]
Convert to a mixed number by dividing. However, when we have the numerator greater than the denominator, we must find a way to make the numerator lower. We can achieve this by separating it into 2 fractions.
[tex]-\frac{6}{5}=-\frac{5}{5}-\frac{1}{5}[/tex]
When we do this, we can see that 5/5 = 1
[tex]-1-\frac{1}{5}=-1\frac{1}{5}[/tex]
20% of a number is 58
Answer:
290
Step-by-step explanation:
The reason this is the answer is because if you divide 100% by 20% it will give you 5% so then you have to multiply 58 times 20 which will give you 290.
Answer:
290
Step-by-step explanation:
any suggestions on how to solve this? thanks
Answer: x = 4
Step-by-step explanation:
You basically want to solve for the angle A. Do arcsin of 1/3, which is approximately 19.47 degrees. In this triangle, we are missing the adjacent and opposite, but we do have the angle luckily. Lets use SOH-CAH-TOA.
[tex]sin(theta) = \frac{opposite}{hypotenuse}[/tex]
We can see here that doing sine will give us the length of the opposite
[tex]sin19.47 = \frac{x}{12}[/tex]. Do sine of 19.47, then multiply by 12. I got 4