Answer:
Step-by-step explanation:
y=x²+4x-7
=x²+4x+4-4-7
=(x+2)²-11
axis of symmetry is x=-2
vertex is (-2,-11)
x²+4x-7=0
[tex]x=\frac{-4 \pm\sqrt{4^2-4(1)(-7)} }{2(1)} \\=\frac{-4 \pm \sqrt{16+28} }{2} \\=\frac{-4 \pm 2\sqrt{11} }{2} \\=-2 \pm\sqrt{11}[/tex]
Answer:
Axis of symmetry is x = -2
(-2, -11) is the vertex
Roots are
-2 + [tex]\sqrt{11}[/tex], -2 - [tex]\sqrt{11}[/tex]
Step-by-step explanation:
a) Axis of symmetry equation is: x = -b/2a
Original equation: y = [tex]x^2+4x-7[/tex]
So...
x= -4/2(1) = -2
Axis of symmetry is x = -2
b) Vertex Point can be found by plugging into original equation.
[tex]y =x^2+4x-7[/tex]
=> y = [tex](-2)^2+4(-2)-7[/tex]
=> 4 - 8 - 7 = y
=> -11 = y
(-2, -11) is the vertex
c) quadratic formula is [tex]x = \frac{-b +-\sqrt{b^2-4ac} }{2a}[/tex]
Lets plug in the values.
[tex]\frac{-4 +- \sqrt{4^{2}-4(1)(-7) } }{2(1)}[/tex]
[tex]\frac{-4 +- \sqrt{16+28 } }{2}[/tex]
[tex]\frac{-4 +- \sqrt{44 } }{2}[/tex]
[tex]\sqrt{44} = 2\sqrt{11}[/tex]
-4 +- 2[tex]\sqrt{11}[/tex]
--------------
2
Here, i will factor out 2, and take out the +- and make it into two equations
2(-2 + [tex]\sqrt{11}[/tex]) / 2 = -2 + [tex]\sqrt{11}[/tex]
2(-2 - [tex]\sqrt{11}[/tex]) / 2 = -2 - [tex]\sqrt{11}[/tex]
x= -2 + [tex]\sqrt{11}[/tex]
or
x = -2 - [tex]\sqrt{11}[/tex]
Roots are
-2 + [tex]\sqrt{11}[/tex], -2 - [tex]\sqrt{11}[/tex]
determine whether it is a solution to 2+3x≥8
Please help me asap please! I need all the answers please!
[tex]See Solution Below;[/tex]
[tex]A. 6m - 2 = m + 13,\\6m - m = 13 + 2,\\5m = 15,\\m = 3;\\ OneSolution[/tex] [tex]F. 18x - 5 = 3 * ( 6x - 2 ),\\18x - 5 = 18x - 6,\\18x - 18x = - 6 + 5,\\0 = - 1 ; NoSolution[/tex]
[tex]B. 4y + 9 = 4y - 7,\\4y - 4y = - 7 - 9,\\0 \neq - 16 ; NoSolution[/tex]
[tex]C. 3c + 2 = 3c + 2,\\3c - 3c = 2 - 2,\\0 = 0 ; Infinite Solution[/tex]
[tex]E. - 8j + 14 = - 2 * ( 4j - 7 ),\\- 8j + 14 = - 8j + 14,\\- 8j + 8j = 14 - 14,\\0 = 0 ; InfiniteSolution[/tex]
[tex]D. 3 * ( x - 4 ) = 2x + 6,\\3x - 12 = 2x + 6,\\3x - 2x = 6 + 12,\\x = 18 ; OneSolution[/tex]
solution of the equation
3x/5+1=4x/15+7
Answer:
x = 18
Step-by-step explanation:
Given
[tex]\frac{3x}{5}[/tex] + 1 = [tex]\frac{4x}{15}[/tex] + 7 ( subtract 1 from both sides )
[tex]\frac{3x}{5}[/tex] = [tex]\frac{4x}{15}[/tex] + 6
Multiply through by 15 to clear the fractions
9x = 4x + 90 ( subtract 4x from both sides )
5x = 90 ( divide both sides by 5 )
x = 18
Answer only. What is the greatest possible sum of the digits of a six-digit number that is a multiple of 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11?
Answer: 36
The LCM of 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11 is 2 × 3 × 2 × 5 × 7 × 2 × 3 × 11 = 27720.
A multiple of 27720 will end in 0, and the sum of its digits will be a multiple of 9.
The largest 6-digit number which is multiple of 9 with last digit of 0 is 999990, and the sum of its digits is 45. 45 is not a multiple of 27720, and there is no other way to get a digit sum of 45.
We now look at the next biggest multiple of 9, 9 × 4
= 36.
The largest 6-digit multiple of 27720 is 27720 × 36 = 997920, and the sum of its digits is 36.
I need help, I need an explanation for the answer
Answer:
3) The function's leading coefficient is negative.
Explanation:
(1) Is not the answer because when x = 3, f(x) = 0.
(2) Is not the answer because when f(x) = -3,
x = 0.
(4) Is also not the answer because the y-values on both sides of (1, -4) are mirroring each other.
Therefore,
(3) is the answer, by elimination, but also because there is not proof of the leading coefficient being negative, as we don't see the original equation.
I hope this helped! :)
The table gives two options for online music clubs which is also given by the system of equations:
y = 0.4x + 15 and y = 0.2x + 25
For what number of songs will the monthly charge be the same?
Answer:
50 songs at $35
Step-by-step explanation:
Answer:
x = 50, y = 35
Step-by-step explanation:
Solve this system of linear equations by using substitution. Equate the two equations to one another, thus eliminating y:
0.4x + 15 = 0.2x + 25
subtract 0.2x from both sides, obtaining: 0.2x + 15 = 25, or, after combining the constants, 0.2x = 10.
Finally we divide both sides by 0.2, which results in x = 50.
Use the first equation to find y: y = 0.4(50) + 15 = 20 + 15 = 35
The graph shown here is the graph of which of the following rational
functions?
Answer:
B
Step-by-step explanation:
From the graph you see point (1, -2) is on f(x)
So substitute x = 1 and the resuult should be -2.
The only function that is valid, is function B.
HELP MATH!
You have a frame that holds three pictures. You pulled out your favorite five photos. How many sets of three are there?
Make a list of all the possible combinations using the numbers 1 to 5 to represent the photos.
Answer:
theres 1 set of 3
Step-by-step explanation:
What is the difference between using a sample and using a census (population survey)? When is it appropriate to use one or the other?
Answer:
census is a total of the population of a county and/or state.
samples are random selections of people or things
Step-by-step explanation:
If Sky wanted to get a survey from 100 kids who liked baseball or softball in her school. She would not pick the first 100 because it is not random. She would choose choose kids at random till she got her quota.
AWARDING BRANLIEST TO FIRST CORRECT ANSWER!!! A train was carrying 560 passengers. This was 4/5 of its capacity. How many passengers could the train carry if it was full?
Answer:
700 passengers
Step-by-step explanation:
4/5 = 560
(÷4) (÷4)
1/5 = 140
560 + 140 = 700
I hope this helps <3
Answer:
700 passengers
Step-by-step explanation:
let total be x
560= 4/5 of total
therefore=
equating
560=4/5x
560*5/4=x
700=x
therefore answer is 700 passengers
Gary can ride his bike 6 miles in 20 minutes. At this rate, how many miles can he ride in 100 minutes?
Answer:
30 miles
Step-by-step explanation:
We can use a ratio to solve
6 miles x miles
------------ = -------------
20 minutes 100 minutes
Using cross products
6 * 100 = 20 x
Divide each side by 20
600/20 = 20x/20
30 =x
Answer:
30 miles
Step-by-step explanation:
First you want to divide 100mins by 20mins which will equal 5
Then multiply 5 by 6 which will equal 30
The solution of g+h≤11 is g≤4. What is the value of h?
Answer:
H≤7
Step-by-step explanation:
Substitution Property of Equality
Answer:
B. 7x-5 = 11
Step-by-step explanation:
you're putting -5 instead y in equation 7x+y = 11 so 7x+(-5) =11
Simplify the expression completely. 7b+3(4b−2)+6÷3
Answer:
19b-4
Step-by-step explanation:
7b+3(4b-2)+6÷3
Bracket comes first so we distribute 3 over the terms in the bracket
= 7b + 12b -6 +6 ÷ 3
First we solve division
= 7b + 12b -6 +6 ÷ 3
= 7b + 12b -6 +2
= (7b+12b)+(-6+2)
= 19b -4
This can't be simplified further as it can't be solved anymore
Answer:
19b - 4
Step-by-step explanation:
Distribute the 3 to (4b - 2), like so:
3(4b - 2)
12b - 6
→ 7b + 12b - 6 +6 ÷ 3
Add like terms:
→19b - 6 + 6 ÷ 3
Following PEMDAS, you divide 6 by 3 first:
→19b - 6 + 2
Add like terms:
→19b - 4
Using the attached image, find the value for x.
Answer:
Step-by-step explanation:
(x +13) + (4x + 2 ) = 180
5x + 15 = 180
Subtract 15 from both sides
5x = 180 - 15
5x = 165
Divide both sides by 5
x = 165/5
x = 33
Check
x + 13 = 33 +13 = 46
And
4x + 2 = 4*33 + 2 = 132 + 2 = 134
For which x is f(x)?=_3
-7
-4
4
5
given 4x+6/2=9 prove x=3
Steps:
Step 1: Simplify both sides of the equation.
4x+3=9
Step 2: Subtract 3 from both sides.
4x+3−3=9−3
4x=6
Step 3: Divide both sides by 4.
4x /4 = 6 /4
Answer: x= 3/2
Please mark brainliest
Hope this helps.
Answer:
4(3)+6/2=9
12+3[tex]\neq[/tex]9
4x+6/2=9
4x=6
x=3/2
Step-by-step explanation:
Jose sells portraits for $300 each. Each portrait costs him $150 in supplies and he spends $2,100 per year on fixed costs. Last year Jose sold 140 portraits. He believes that he made more than $20,000 in profit. Is this true? WILL GIVE BRAINLIEST PLEASE HELP! a) Write an expression to represent José's yearly profit. Use x to represent the number of portraits sold. b) Simplify the expression from Part I. Then, evaluate the expression for the 140 portraits José sold last year to determine if he actually made $20,000 dollars in profit. Write your answer as a complete sentence.
Answer:
a) y=(300-150)x-2100
b) y=150x-2100
c) y=150(140)-2100
y=18900
Jose was wrong. He did not make 20000 dollars last year.
Answer:
A: ((300-150) * 140) - 2100
B: 21000-2100= $18,900 profit.
Jose made 18,900 dollars worth of profit. He did not make $20,000 worth of profit.
What is the value of k?
k = 28
k= 29
k= 31
(5k - 3)°/(9 + k)°
k = 42
Answer:
k=29
Step-by-step explanation:
(5K-3)+(9+k)=180
6k+6=180 add like numbers
6x=174 subtract 6 from 180
x=29 divide by 6
The solution is : k=29, is the value of k.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
Here, we have,
from the given diagram, we get,
(5K-3)+(9+k)=180
6k+6=180 [add like numbers]
6x=174 [ subtract 6 from 180]
x=29 [ divide by 6]
Hence, The solution is : k=29, is the value of k.
To earn more on addition click:
brainly.com/question/29560851
#SPJ7
Simplify and solve this equation for q 3q+5+2q-5+65
Answer:
5q +65
Step-by-step explanation:
3q+5+2q-5+65
We can only simplify since there is no equals sign
Combine like terms
5q +65
Answer:
55
Step-by-step explanation:
3q+5+2q-5+65
-2q -2q
q+5-5+65
+5 +5
q+10+65
-10 -10
q+55
q=55
Need help with this pls
(Show work pls!!)
Answer:
Given below
Step-by-step explanation:
M is Mikey and B is Betty in,
Current ages:
M= x
B= 3x (cuz she is 3 times older)
After 5 years
M= x+5
B= 3x+5 (5 years added to present age)
It says the ages of Betty after 5 years (3x+5) will be twice as much as Mikey (2(X+5))
So,
3x+5 = 2(x+5)
3x+5 = 2x+10
3x -2x = 10-5
x = 5
Therefore,
The current ages are
Betty : 3x = 3*5 = 15
Mikey: 5 (x)
You can verify by checking with the criterias or clues given in the question.. hope this helps..mark as brainiest if this was helpful:)
Answer: The current ages are
Betty : 3x = 3*5 = 15
Mikey: 5 (x)
Step-by-step explanation:
Hoped this helped
Find (3m^2n)^3 show work
The right answer is 3m^6n^3
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
[tex] = 27 {m}^{6} {n}^{3} [/tex]
Step-by-step explanation:
[tex](3 {m}^{2} n)^{3} \\ {3}^{3} \times {m}^{2 \times 3} {n}^{3} \\ = 27 {m}^{6} {n}^{3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
find a_(1) if d = 2.5, a_(15) = 33.5, S_(15 )= 240
Answer:
Value of d is 20.
I hope it will help you.
Step-by-step explanation:
Answer:
[tex]a_{1}=-19[/tex]
Step-by-step explanation:
It is sum of arithmetic progression again.
[tex]$S_{15}=\frac{15}{2} [2a_{1}+(15-1)\cdot 2.5]$[/tex]
[tex]$240=\frac{15}{2} [2a_{1}+35]$[/tex]
[tex]$240=15a_{1}+535$[/tex]
[tex]-285=15a_{1}[/tex]
[tex]a_{1}=-19[/tex]
I want to take my 5 friends to the movie theater. It costs $8.25 a ticket and I want to buy a pound of gummy bears to share with my friends. If I have $50, how much change should I get back?
Answer:
Whatever the gummy bears cost minus the amount left
Step-by-step explanation:
50= 8.25(5) + gummy bears
50=41.25 + gummy bears
8.75= gummy bears
2 Points
Which type of statement has the form "If A, then B"?
O A. True
OB. Conditional
O C. Deductive
O D. False
SUBMIT
This is a conditional: if the condition A is satisfied (true), then the result B is also satisfied (true).
Answer:
Its conditional , as the A decides what B has to do , whether this or that
A person invests 5000 dollars in a bank. The bank pays 4% interest compounded
annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 8200 dollars?
A= P(1+ r over n)^nt
Answer: 12.6 years
Step-by-step explanation:
Hi, to answer this question we have to apply the compounded interest formula:
A = P (1 + r/n) nt
Where:
A = Future value of investment (principal + interest)
P = Principal Amount
r = Nominal Interest Rate (decimal form, 4/100= 0.04)
n= number of compounding periods in each year (1)
t = years
Replacing with the values given
8200= 5000(1+ 0.04/1)^1(t)
Solving for t
8200 =5000 (1.04)^t
8200/5000 =(1.04)^t
1.64 =(1.04)^t
log 1.64 =log (1.04)^t
log 1.64 = t log (1.04)
log 1.64/ log (1.04) =t
t = 12.6 years
I need help to solve this proportion
Answer:
5
Step-by-step explanation:
cross multiply
isolate x
12x=7.5(8)
12x=60
12x/12=60/12
5 is the answer
A ball is dropped from the top of a building that is 1,000 feet high. Its height, in feet, as a function of the
time, x, in seconds, after the ball was dropped, is given by the following equation, f(x) = 1,000 - 16x2.
Which set of numbers is appropriate as the domain for this function?
Positive Integers
Positive Real Numbers
Natural Numbers
Positive Rational Numbers
Answer:
Positive real numbers
Step-by-step explanation:
The time is not limited to rational numbers or integers. Natural numbers are a subset of integers. So the domain is positive real numbers.
HELP! ASAP! with the 2 pleasee
Answer:
8.106
Step-by-step explanation:
Use Pythagorean Theorum for this question, a^2+b^2=c^2
If you put the numbers into the equation you get 6.3^2+5.1^2=c^2.
Simplify and get 65.7=c^2
To get rid of the square, you square root both sides, which will get you 8.106=c (since the answer wants round to 3 numbers behind the decimal point)
Therefore the missing length is 8.106cm. (For estimation just write a random number you think it would be before actually solving the problem.
Answer for #2:
Right Triangle
Not Right Triangle
Not Right Triangle
Right Triangle
Not Right Triangle
Step-by-step explanation:
Just use the pythagorean thereum for each of the questions to see if the values match up
Suppose that the mean number of chocolate chips in 30 cookies is 19 chocolate chips. Explain what this means.
Answer: It means that there are 570 chocolate chips in all the 30 cookies
Step-by-step explanation:
The mean also referred to as the average of a data set is calculated by adding all numbers in a data set and dividing by number of values in the set.
Since the mean number of chocolate chips in 30 cookies is 19 chocolate chips, this means that there are:
= (30 × 19) = 570 chocolate chips in the cookies.
