Answer:
B
Step-by-step explanation:
A) The function in factored form is -5(x - 1)² and the vertex is (1, 0).
B) The zeroes are x = 1, the axis of Symmetry is x = 1 and the direction of the opening is downward.
C) The domain of the function is all real numbers and the range is
(-∞, 0].
We have,
A)
Factoring out the common factor (-5):
f(x) = -5(x² - 2x + 1)
The equation x² - 2x + 1 can be factored as (x - 1)(x - 1) or simply (x - 1)²:
f(x) = -5(x - 1)²
The equation of a quadratic function:
f(x) = a(x - h)² + k
In this case,
a = -5, h = 1, and k = 0 (since there is no constant term).
So, the vertex of the function is (h, k) = (1, 0).
B)
To find the zeros of the function, we set f(x) = 0 and solve for x:
-5(x - 1)² = 0
(x - 1)² = 0
Taking the square root of both sides:
x - 1 = 0
x = 1
The axis of symmetry is a vertical line that passes through the vertex of the parabola.
In this case, the axis of symmetry is x = 1.
The direction of the Opening:
Since the coefficient of the x² term is negative (-5), the parabola opens downward.
C)
The domain of the function f(x) is all real numbers since there are no restrictions or limitations on the possible input values of x.
The parabola opens downward and the vertex is at (1, 0), the range of the function is all real numbers less than or equal to 0.
The range can be expressed as (-∞, 0].
Thus,
A) The function in factored form: -5(x - 1)², Vertex: (1, 0).
B) Zeros: x = 1, Axis of Symmetry: x = 1, Direction of Opening: Downward.
C) Domain: All real numbers, Range: (-∞, 0].
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GIVING BRAINLIST TO THE CORRECT ANSWER PLS ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
a = -1/2 & k = 3/7
Step-by-step explanation:
Solve for a over the real numbers:
24 a^3 + 8 a^2 + 6 a + 4 = 0
The left hand side factors into a product with three terms:
2 (2 a + 1) (6 a^2 - a + 2) = 0
Divide both sides by 2:
(2 a + 1) (6 a^2 - a + 2) = 0
Split into two equations:
2 a + 1 = 0 or 6 a^2 - a + 2 = 0
Subtract 1 from both sides:
2 a = -1 or 6 a^2 - a + 2 = 0
Divide both sides by 2:
a = -1/2 or 6 a^2 - a + 2 = 0
Divide both sides by 6:
a = -1/2 or a^2 - a/6 + 1/3 = 0
Subtract 1/3 from both sides:
a = -1/2 or a^2 - a/6 = -1/3
Add 1/144 to both sides:
a = -1/2 or a^2 - a/6 + 1/144 = -47/144
Write the left hand side as a square:
a = -1/2 or (a - 1/12)^2 = -47/144
(a - 1/12)^2 = -47/144 has no solution since for all a on the real line, (a - 1/12)^2 >=0 and -47/144<0:
Answer: a = -1/2
______________________________________
Solve for k over the real numbers:
(7 k - 3) (k^2 - 2 k + 7) = 0
Split into two equations:
7 k - 3 = 0 or k^2 - 2 k + 7 = 0
Add 3 to both sides:
7 k = 3 or k^2 - 2 k + 7 = 0
Divide both sides by 7:
k = 3/7 or k^2 - 2 k + 7 = 0
Subtract 7 from both sides:
k = 3/7 or k^2 - 2 k = -7
Add 1 to both sides:
k = 3/7 or k^2 - 2 k + 1 = -6
Write the left hand side as a square:
k = 3/7 or (k - 1)^2 = -6
(k - 1)^2 = -6 has no solution since for all k on the real line, (k - 1)^2 >=0 and -6<0:
Answer: k = 3/7
50+50+5050 + 50 + 50 + 50 + 50 + 50 + 50 + 50 + 30
Answer:
5530
Step-by-step explanation:
Answer:
5530Step-by-step explanation:
50 times 9 equals 450
then add the 5050 and 30 to get 5080
then add up 5080 and450 and get your answer of 5530
A calculator screen displays 3.294E6. Write this number in standard form.
Answer:
3.294
Step-by-step explanation:
The standard form of the given number is [tex]3294000[/tex].
Important information:
The calculator screen displays 3.294E6.Standard form:in a calculator, the numbers on the right side of E are the exponent of 10. So, the scientific notation of the given number is:
[tex]3.294E6=3.294\times 10^6[/tex]
It can be written as:
[tex]3.294E6=3.294\times 1000000[/tex]
[tex]3.294E6=3294000[/tex]
Therefore, the standard form of the given number is [tex]3294000[/tex].
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Write an equation in slope-intercept form for the line with slope 4 and y-intercept - 2
Answer:
The slope intercept form is typically in the form of
y=mx+c
c=-2
m=4
The slope intercept form of the equation is
y=4x-2
Answer each question about the following
arithmetic sequence:
-20,-16, -12,-8,-4, ...
What is the 30th term of the sequence?
a30
=
Answer:
1) a30=96
2) 30(-20+96)/2
3) 1140
Step-by-step explanation:
I just did on Edg 2020
The solution is, the 30th term of the sequence a_30 = 96.
What is Arithmetic progression?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.
The nth term of AP : a_n = a + (n – 1) × d
here, we have,
the given sequence is,
-20,-16, -12,-8,-4, ...
so, here, we have,
a = -20
d = 4
so, the 30th term of the sequence is,
a_30 = a + (30-1) d
= -20 + 29*4
= 96
Hence, The solution is, the 30th term of the sequence a_30 = 96.
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what is 7=2m-1 plz helps
Answer:
m=4
Step-by-step explanation:
7=2m-1
+1 +1
8=2m
÷2 ÷2
m=4
Estimate the sum of 381 and 22 by rounding both values to the nearest ten. What is the best estimate of the sum?
400
410
420
430
The best estimate for my answer is 410 to the nearest ten
Answer:
410
Step-by-step explanation:
solve for a side in right triangles
Answer:
2.88?
Step-by-step explanation:
There are 7 red 3 green 2 blue and 8 purple marbles in a bag if a marble is randomly chosen 250 times predict how many times it should be red or green
Answer:
It should be red or green 125 times
Step-by-step explanation:
The first thing to do here is to calculate the probability of selecting a red or a green marble
Total number of marbles = 7 + 3 + 2 + 8 = 20
Probability of selecting a red marble is 7/20
Probability of selecting a green marble is 3/20
The probability of selecting a red or a green marble = Probability of selecting a red marble + Probability of selecting a green marble = 7/20 + 3/20 = 10/20 = 1/2
Now our selection spans 250 times, the number of times it should have been a green or a red marble = The probability of selecting a green or a red marble * number of selection times = 1/2 * 250 = 125 times
February 2, the temperature at 11 AM was 5°F. At
10 PM, it had dropped to 3°F. To find the number of
degrees the temperature dropped, which equation
could you use? Let x be the number of degrees the
temperature changed.
Answer: x = 2 degrees Fahrenheit
Step-by-step explanation:
5-3= 2 it’s a pretty simple equation
Can someone please help me
Answer:
I think its G, I'm not 100% sure...
Find the quartiles for these data values:
5,7,7,8,10,11,12,15,17
Answer:
The median {Q2} is 10
Q1 is 7+7/2 which is 7
Q3 is 15+12/2 which is 13.5
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
its coreect
Brainliest question please help please help me now plz
Answer:
13/b I think
Step-by-step explanation:
Brainliest for the correct answers!
Answer:
didn't i answer this on your last post?
5 + x = -2
I need work and answer!!!!
We need to get x by itself.
We do that by subtracting 5 from both sides.
This leaves us with x = -7.
So x = -7 is the solution.
Answer:
The final answer is [tex]x = -7[/tex] .
Step-by-step explanation:
Solve the equation:
[tex]5 + x = -2[/tex]
Subtract both sides by 5:
[tex]5 - 5 + x = -2 -5[/tex]
[tex]x = -7[/tex]
So, therefore, [tex]x = -7[/tex] is the final answer.
If 80% of an item is $144.00, what is the original price?
Answer:
180
Step-by-step explanation:
Answer:
180
Step-by-step explanation:
the original price * 80% = 144
Change to decimal form
the original price * .80 = 144
Divide each side by .80
the original price * .80/.80 = 144/.80
the original price =180
Bartolo is running a race. He determines that if he runs at an average speed of 15 feet/second, he can finish the race in 6 seconds. If he runs at an average speed of 18 feet/second, he can finish the race in 5 seconds. Which equation represents this inverse variation?
Answer:
The Equation that represents these inverse variation is:
Speed is inversely proportional to Time
Speed (S) ∝ 1/ Time(T)
And the constant of proportionality = Distance(D)
Therefore, Speed = Distance/ Time
Step-by-step explanation:
For an inverse variation, one element increases while the other element decreases. In this question, the element or variable that increases is the speed while the element or variable that decreases is the time.
We can see from the question that
a) If he runs at an average speed of 15 feet/second, he can finish the race in 6 seconds.
b) If he runs at an average speed of 18 feet/second, he can finish the race in 5 seconds
Speed is inversely proportional to Time because the higher the speed, the lesser the time it takes to go or move in a particular direction or to go in a particular distance.
Hence, the Equation that represents these inverse variation is:
Speed is inversely proportional to Time
Speed (S) ∝ 1/ Time(T)
For inverse variation or proportionality, a constant is always needed
And the constant of variation or proportionality = Distance(D)
Therefore, Speed = Distance/ Time
HELP ME ASAP PLS ! Marianne’s box for camp measures 24 inches by 24 inches by 14 inches. Will her field hockey stick , which is 1 yard long , fit in the box ? Explain your answer
Answer:
Yes
Step-by-step explanation:
24²+24²=x², x = 33.94
33.94²+14²=x², x = 36.71 inches
1 yard is about 36 inches, so it should just fit.
Write the quadratic equation in general form. (x-5)2
Answer:
x^2 - 10x + 25
Step-by-step explanation:
I'm hoping that the 2 means squared.
x^2 - 10x + 25
Answer:
x^2 -10x+25
Step-by-step explanation:
(x-5)^2
(x-5)(x-5)
FOIL
first = x*x = x^2
outer:-5x
inner: -5x
last: -5*-5 = 25
Add them together
x^2 -5x-5x+25
Combine like terms
x^2 -10x+25
Standard form is ax^2 +bx +c so this is standard form
3 ft
4 ft
What is the length of the hypotenuse
Write 34.996 to:
i. 2 decimal places
Answer:
34.996 to 2 dcp is 35.00
Step-by-step explanation:
6 rounds up 9 goes to 10 add the 1 left over to make the units number equal 5 but as it is decimal place remember to add the 0's
Answer:
35.00
Step-by-step explanation:
just don't leave the zeros.
Which answer represents a geometric sequence?
A. {1,3,9,27,…}
B. {17,10,3,−4,…}
C. {0,2,4,8,…}
D. {5,10,15,20,…}
Answer:
A.
Step-by-step explanation:
in A. your q is 3 so: a1=1 a2= a1*q=3 a3=a2*q=9 and so on.
i C. its almost the right answer too,but notice that a1 is 0. so 0*2 is still 0 so though it looks almost perfect the first number ruins it
Mark is comparing prices of different brands before he goes shopping. Who has the best deal on ice cream? Brand Size & Price Turkey Hill $4.50 for 30 ounces Breyers $15.36 for 128 ounces Ben & Jerrys $2.88 for 16 ounces
Answer:
Breyers is the correct answer
Step-by-step explanation:
$4.50/30 oz = .15
$15.36/128 oz = .12
$2.88/16 oz = .18
will mark brainliest!! 20 points!! i just need a short paragraph on this....look at attachment
A restaurant advertises that its burritos weigh 250 g 250 g250, start text, space, g, end text. A consumer advocacy group doubts this claim, and they obtain a random sample of these burritos to test if the mean weight is significantly lower than 250 g 250 g250, start text, space, g, end text.
Answer: C) H0 : μ = 250 , Ha: μ < 250
Step-by-step explanation:
The questions is incomplete. The correct question is
A restaurant advertises that its burritos weigh 250 g. A consumer advocacy group doubts this claim, and they obtain a random sample of these burritos to test if the mean weight is significantly lower than 250 g. Let u be the mean weight of the burritos at this restaurant and ĉ be the mean weight of the burritos in the sample. Which of the following is an appropriate set of hypotheses for their significance test? Choose 1 answer:
A) H0 : x = 250 , Ha : x < 250
B) H0 : x = 250 , Ha : x > 250
C) H0 : μ = 250 , Ha: μ < 250
C) H0 : μ = 250 , Ha: μ > 250
Solution:
The null hypothesis is the hypothesis that is assumed to be true. The restaurant advertises that its burritos weigh 250. This is the null hypothesis. 250 is the population mean,μ . Thus, the null hypothesis is
H0 : μ = 250
The alternative hypothesis is what the researcher expects or predicts. The consumer advocacy group tests if the mean weight is significantly lower than 250g. This is the alternative hypothesis. It is expressed as
H0 : μ < 250
Answer:
Yes, because 0.002 < 0.01
Step-by-step explanation:
Super Strength Inc. has found that the relationship between their sales and their net profit can be described by a polynomial function G(x) in which x is their sales (in thousands of dollars) and G(x) is their net profit (in thousands of dollars). What would be an appropriate domain for this function?
Answer:
x ≥ 0
Step-by-step explanation:
The domain of the profit function G(x) is the set of all possible values that "x" could assume. In this function, "x"represents the sales in thousand of dollars, therefore the minimum possible value is zero (scenario in which there are no sales). Assuming an hypothetical scenario in which the company has an infinite supply capacity, there is no upper limit for what their sales might be. Thus, the domain for the function is x ≥ 0.
Answer:
x > or equal to 0
Step-by-step explanation:
Two step equations. Please help
Y=7
Step-by-step explanation:
Move all terms not containing y to the right side of the equation.
4y=22+6
Then add 22 and 6.
4y=28
Divide each term in 4y=28 by 4
4y÷4=28÷4
Cancel the common factor of 4 in the first part of the equation so it looks like this...
y=28÷4
Divide 28 by 4.
Therefore y=7
Hope this helps! If you have any more questions or you need further clarification on anything then please comment down below! Good luck!
The graph shown can be used to convert between kilometres and miles....
Answer:
where's the picture I can't see it
According to the graph, I can see
42 Miles = 68 Kilometers
32 Miles = 22 Kilometers
The distance between London and Cardiff is 240 Kilometers
Is mile in the metric system?
Mile is under the Imperial System and
Kilometers is under the metric system.
What is metric system?The metric units used for measuring length, mass, area and capacity. For example, millimeters, centimeters, meters, and kilometers are the metric units of the measurement of length. Grams and kilograms are the units for measuring weight.
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solve for a side in right triangles
Answer:
? =8.77
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opposite side/ hypotenuse
sin 20 = 3 / ?
? = 3/ sin 20
? = 8.7714132
To the nearest hundredth
? =8.77
Michelle bought 2 soccer balls priced at $24.95 each. She paid for her purchase with three $20 bills. How much change did she receive?
Answer:
$35.05
Step-by-step explanation:
3 $20 bills turns into $60 and 60-24.95=35.05