Answer:
[tex]f(x)=x^2+2x-3[/tex]
Step-by-step explanation:
[tex]\textsf{General form of a quadratic function}:f(x)=ax^2+bx+c[/tex]
Equation 1
[tex]\begin{aligned}f(1) &=0\\ \implies a(1)^2+b(1)+c &=0\\ a+b+c &=0 \end{aligned}[/tex]
Equation 2
[tex]\begin{aligned}f(-1) &=-4\\ \implies a(-1)^2+b(-1)+c &=-4\\ a-b+c &=-4 \end{aligned}[/tex]
Equation 3
[tex]\begin{aligned}f(2) &=5\\ \implies a(2)^2+b(2)+c &=5\\ 4a+2b+c &=5 \end{aligned}[/tex]
Add Equation 1 and Equation 2:
[tex]\begin{array}{r l}a+b+c & =0 \\+\quad a-b+c & =-4 \\\cline{1-2} 2a+2c & =-4 \end{array}[/tex]
[tex]\implies a+c=-2[/tex]
Substitute [tex]a+c=-2[/tex] into Equation 1 and solve for b:
[tex]\begin{aligned}\implies a+b+c &=0\\ b-2 &=0\\ b &=2\end{aligned}[/tex]
Substitute [tex]a=-2-c[/tex] and [tex]b=2[/tex] into Equation 3 and solve for c:
[tex]\begin{aligned} \implies 4a+2b+c&=5\\ 4(-2-c)+2(2)+c &=5\\-8-4c+4+c &=5\\ -3c &=9\\ c &=-3\end{aligned}[/tex]
Substitute found value of c into [tex]a=-2-c[/tex] and solve for a:
[tex]\implies a=-2-(-3)=1[/tex]
Therefore, a = 1, b = 2 and c = -3
Substitute the found values into the general form of a quadratic function to form the final equation:
[tex]f(x)=x^2+2x-3[/tex]
HELP ME WITH THESE TWO QUESTIONS PLEASE.
Answer:
the answer for the first one is 141
and the answer for the second is 48
Answer:
First: -1628
Second: -16
Step-by-step explanation:
For the first problem, start by rewriting the equation by plugging in h and g as (4n-3)(-4n-4)
By FOILing this, you’ll end up with -16n^2-16n+12n+12
-16n^2-4n+12
Now you can plug in n, which is -10:
-16(10)^2-4(10)+12
-1600-40+12
-1628
For the second question, you’ll be plugging f(-2) into g, but I’ll leave -2 as n for simplicity until the end
g(n)=n^2+2n
f(n)=2n-4
g(n)=(f(n))^2+2(f(n))
(2n-4)^2+2(2n-4)
(4n^2-16n+16) + (4n-8)
4(-2)^2-16(-2)+16+4(-2)-8
16-32+16-8-8
-16
10. Enter the value of p so that the expression 8(n + 2) is equivalent to (n + p)8
Answer:
p=2
Step-by-step explanation:
8n + 16 = 8n + 8p
subtract 8n
16=8p
divide both sides by 8
p = 2
To find the value of p that sets the expression equal to each other:
⇒ must set both equations equal to each other, like such:
[tex]8(n+2)=(n+p)8\\8n+16=8n+8p\\8n+16-8n=8p\\16=8p\\8p=16\\p=2[/tex]
Thus the value of p so that the expression 8(n + 2) is equivalent to (n + p)8 is 2
Answer: 2
Hope that helps!
Find the radius of the circle given by this equation:
Answer:
8
Step-by-step explanation:
We know that
Equation
[tex] {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0[/tex]
Represents the equation of Circle
where
[tex]radius = \sqrt{ {g}^{2} + {f}^{2} - c } [/tex]
On comparing the given equation with general Equation of Circle
we get
[tex]g = - 5[/tex]
[tex]f = 3[/tex]
[tex]c = - 30[/tex]
On substituting these values We get
[tex]radius = \sqrt{ { (- 5)}^{2} + {3}^{2} - ( - 30) } [/tex]
[tex]radius = \sqrt{25 + 9 + 30 } = \sqrt{64 } = 8[/tex]
[tex]radius = 8[/tex]
A car travels at 30 1/5 miles in 2/3 of an hour. What is the average speed, in miles per hour
Answer:
45.3 miles/h
Step-by-step explanation:
The answer is 45.3 miles/h
ANSWER:
45 3/10 mph
decimal form: 45.3 mph
Step-by-step explanation:
30 1/5 /2 = 15 1/10
15 1/10 x 3 = 45 3/10 mph
So hence, your answer is 45 3/10 mph. In decimal format, it can be 45.3
Which statement best describe the product of 4/5x10
Answer:
4/5x10=8
Step-by-step explanation:
Not sure what the statements the question describes are since you didn't put them but the product is 8.
What is the value of K?
Find the missing value.
(√24-√k)(√24+√k)=5
Answer:
k = 19Step-by-step explanation:
Identity
(a + b)(a - b) = a² - b²Simplifying the LHS (Left Hand Side)
(√24-√k)(√24+√k)(√24)² - (√k)²24 - kEquating to the RHS
24 - k = 5k = 24 - 5k = 19Answer:
19
Step-by-step explanation:
[tex](\sqrt{24} -\sqrt{k} )(\sqrt{24} +\sqrt{k} )\\\\As,\\\\\hookrightarrow a^{2} -b^{2} =(a+b)(a-b)\\\\Subtitute:\\\\a=\sqrt{24} \\\\b=\sqrt{k} \\\\Now,\\\\\hookrightarrow (\sqrt{24} -\sqrt{k} )(\sqrt{24} +\sqrt{k} )=5\\\\\hookrightarrow (\sqrt{24} )^{2} -(\sqrt{k} )^{2} =5\\\\\hookrightarrow 24-k=5\\\\\hookrightarrow 24-5=k\\\\\hookrightarrow 19[/tex]
Step 1: –10 8x < 6x – 4 step 2: –10 < –2x – 4 step 3: –6 < –2x step 4: ________ what is the final step in solving the inequality –2(5 – 4x) < 6x – 4? x < –3 x > –3 x < 3 x > 3
The final step of the inequality equation –10 + 8x < 6x – 4 is x > 3. Then the correct option is D.
What is inequality?Inequality is simply a type of equation that does not have an equal sign in it. Inequality is defined as a statement about the relative size as well as is used to compare two statements.
The inequality equation is given below.
–10 + 8x < 6x – 4
This can be simplified as
–10 + 8x < 6x – 4
–10 < –2x – 4
–6 < –2x
–3 < –x
x > 3
More about the inequality link is given below.
https://brainly.com/question/19491153
A bicycle manufacturer wants to find out which features most cyclists prefer to have in the newest model of bicycles to be manufactured next year. What is the population from which the manufacturer should choose a sample?
A. Subscribers to a national bicycling magazine. B. Cyclists who purchased bicycles from this manufacturer before. C. Visitors to the manufacturer’s Web site. D. Members of a bicycling club.
Answer:
It's B
Step-by-step explanation:
I did the test
Vhich statements are true about the graph of the function f(x) = x7
- 8x + 5? Select three options.
J The function in vertex form is F(x) = (x - 4)2 - 11
- 11
The vertex of the function is (-8, 5).
O The axis of symmetry is X = 5.
O The y-intercept of the function is (0, 5).
O The function crosses the x-axis twice.
Answer:
A D E
Step-by-step explanation:
https://brainly.com/question/18143812
The net below shows a square pyramid. What is the lateral surface area?
A. 176 in^2
B. 112 in^2
C. 64 in^2
D. 210 in^2
Answer: B
Step-by-step explanation:
1/2 8 *7 = 28
because there is 4 triangles you do this 28+28+28+28
28+28+28+28 = 112
The lateral surface area of the pyramid is 112 sq. in.
The correct answer is an option (B)
From the attached figure of the net of a square pyramid, we can observe that the side length of the square base is 8 in and height of the lateral triangular face is 7 in.
Hence, The lateral surface area of the pyramid is equal to the area of the four triangular faces of the pyramid.
Using the formula of the area of triangle, the lateral surface area would be,
A = 4 × (1/2 × base × height)
A = 4 × (1/2 × 8 × 7)
A = 4 × (4 × 7)
A = 4 × 28
A = 112 sq. in.
Thus, This is the required lateral surface area.
So, The correct answer is an option (B) 112 in²
Learn more about the surface area here:
brainly.com/question/18727714
#SPJ2
The difference of two numbers is 3. Their sum is 13. Find the numbers.
Answer:
10 and 3
Ten and three have a difference of three, and their sum is thirteen, with that being said, this should be correct.
25 points!
7 and 8 Find the measurement of the missing interior angle
Answer:
7. x = 88
8. x = 59
Step-by-step explanation:
You're probably trying to equal 180° because that's what the triangle should equal so
7. 48° + (88° - 44°) + 88° = 180°
8. 73° + (59° - 11°) + 59° = 180°
I hope this is right :,)
Carl is having a party.
Each cake serves 4 people.
Does this situation represent a proportional relationship?
Answer:
Yes
Step-by-step explanation:
Use a table to multiply (-3a2)(a - b).
Answer:
-3a³ + 3ba²
Step-by-step explanation:
1) Distribute
-3a² (a-b)
-3a³ + 3ba²
Rewrite the following linear equation in slope-intercept form. Write your answer with no spaces.
V-5= 3(x+1)
Answer:
V=3x+6
Step-by-step explanation:
slope intercept form: y=mx+b
V-5=3(x+1)
[open parentheses]
V-5=3x+1
[combine like terms; add 5 to both sides]
V=3x+6
why is it v tho
if the compound ratio of 5:8 and 3:7 is 45:x. find x
Given:
5:8 and 3:7 = 45:X
Explanation:
15:56 = 45:x
15x. = 2520
X=2520/15
x= 168
Conclusion:
Thus the value of x is found to be 168.
5:8 and 3:7=45:x
15:56 = 45:x
Product of means. = product of extremes
15x. = 2520
X=2520/15
x= 168
Can someone answer these 2 questions, thanks!
Answer:
1, answer ..
b, 50% because add this
40+10=50
Step-by-step explanation:
and 2nd one i dont know but i studied it i did not remember
jayce runs 2 1/2 miles on monday. Each day after that, he runs the same 1 1/3 mile route every morning. His goal is to run at least 6 miles by the end of the week. Which inequality represents the least number of days after monday that jayce needs to run to reach his goal?
Answer:
Step-by-step explanation:
6 < 2 1/2 + 1 1/3R
Work out x 3
Give your answer in its simplest form.
1
1
4
4
4
Answer:
3/4
Step-by-step explanation:
Hey there!
When multiplying fractions, there is no need to make the denominators the same like how you do when adding fractions
So we can just straight multiply the numerators and the denominators together
[tex]\frac{1}{4}*\frac{3}{1}[/tex]
I made 3 to 3/1 so the multiplying process is easier
3 x 1 is 3 and 4 x 1 is 4
The numerator is 3
The denominator is 4
3/4
So 1/4 x 3 is 3/4
10. Find the surface area of the figure to the left.
13 m
9 m
Answer:
soz i need points n
Step-by-step explanation:
cuz
the time failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures. what is the probability that a randomly selected part will fail in less than 20 hours
Using the exponential distribution, it is found that there is a 0.3297 = 32.97% probability that a randomly selected part will fail in less than 20 hours.
Exponential distributionThe exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
In this problem, the mean and the decay parameter are, respectively, given by:
[tex]m = 50, \mu = \frac{1}{50} = 0.02[/tex].
The probability that a randomly selected part will fail in less than 20 hours is given by:
[tex]P(X \leq 20) = 1 - e^{-0.02 \times 20} = 0.3297[/tex]
0.3297 = 32.97% probability that a randomly selected part will fail in less than 20 hours.
More can be learned about the exponential distribution at https://brainly.com/question/18596455
The ratio of men to women working for a company is 5 to 4. If there are 234 employees total, how many women work for the company?
Answer:
104
Step-by-step explanation:
5 to 4 equals 9
divide 234 by 9 and you get 26
26 times 5 is 130
and 26 times 4 is 104
so 130 to 104 adding up gives you 234
and the number of women employees would be 104
Mr. Hollins determines that he gives away $800 each month. If he gives away 16% of his budget, then how much is his overall budget
Answer:
5000 dollars
Step-by-step explanation:
Let his budget be x
16% of x is 800 dollars
.16 * x = 800
Divide each side by .16
.16x/.16 = 800/.16
x=5000
His budget is 5000 dollars
Which formula below is used to find the volume of a shape?
A. length ÷ width ÷ height
B. length − width − height
C. length + width + height
D. length × width × height
Answer:
D. length × width × height
Step-by-step explanation:
That is how you calculate the volume of a shape.
em sa
1.
She bikes at a constant speed of 13 miles per hour for
the entire 20 minutes.
Hint 20 minutes is what fraction of an hour? Look back
at the answer to problem 4.
Answer:
4.33 miles
Step-by-step explanation:
20 minutes=1/3 of an hour
because 1 hour=60minutes
so 20/60 = 1/3
for your answer
13× 1/3=4.33
therefore she was able to bike 4.33 miles in 20 minutes at a constant speed
PLS answer and explain
Write the expression for the cubic function
Answer:
F(x) = ax3 + bx2 + cx1 + d.
Step-by-step explanation:
A, b, and c are the coefficients and d is the constant.
The measure of anglerst can be represented by the expression (6x 12)°. three lines extend from point s. the space between lines s r and s u is 78 degrees. the space between lines s u and s t is 3 x minus 12. what is manglerst in degrees? 78° 84° 120° 156°
Answer:
∠RST = 120°
Step-by-step explanation:
We assume the positions of the lines and angles will match the attached figure. The angle addition theorem gives a relation that can be solved for x, then for the value of angle RST.
∠RSU +∠UST = ∠RST
__
78° + (3x -12)° = (6x +12)° . . . . . substitute given values into the above
54 = 3x . . . . . . . . . . . . . . . . divide by °, subtract 3x+12
108 = 6x . . . . . . . . . . . multiply by 2
120° = (6x +12)° = ∠RST . . . . add 12, show units
The measure of angle RST is 120 degrees.
_____
Additional comment
Note that we don't actually need to know the value of x (18) in this problem. We only need to know the value of 6x.
is it true or false?
Answer:
True
Step-by-step explanation:
plug in numbers
4(-3)+15=3
-12+15=3
-3+15=12
rewrite the equation in standard form
Y= -3/4x + 7
rewrite the equation in slope intercept form
X+2y=-3
Answer:
Y= -3/4x + 7 in standard form is 3x + 4y = 28
x + 2y =-3 in slope intercept form is y= 1/2x - 3/2
Step-by-step explanation:
Hope this helps!!
Answer:
please see photo above for detailed analysis.