What value for c will make the expression a perfect square trinomial? x2 – 7x + c
Answers
Answer:
Final answer is [tex]\frac{49}{4}[/tex].
Step-by-step explanation:
Given expression is [tex]x^2-7x+c[/tex].
Now we need to find about what value for c will make the given expression [tex]x^2-7x+c[/tex], a perfect square trinominal.
Coefficient of middle term that contains x, in [tex]x^2-7x+c[/tex] -7.
Take half of that so we get [tex]-\frac{7}{2}[/tex].
Then take square of the half value.
We get [tex]\left(-\frac{7}{2}\right)^2=\frac{49}{4}[/tex].
We add the square value to make perfect square trinomial.
Hence final answer is [tex]\frac{49}{4}[/tex].
Answer:
D. [tex]\frac{49}{4}[/tex].
Step-by-step explanation:
We have been given a trinomial [tex]x^2-7x+c[/tex]. We are asked to find the value of c, which will make the expression a perfect square trinomial.
We know that a perfect trinomial is in form [tex]a^2\pm2ab+b^2[/tex].
We will use complete the square process to solve for c.
To complete a square, we need to add square of half the coefficient of x term. We can see that coefficient of x is -7, so the value of c would be:
[tex](\frac{b}{2})^2=(\frac{-7}{2})^2=\frac{(-7)^2}{2^2}=\frac{49}{4}[/tex].
Therefore, the value of c required to make the given expression a perfect trinomial is [tex]\frac{49}{4}[/tex] and option D is the correct choice.
Related Questions
Adriana's computer code 20% less than jocelyn's computer. Adriana's computer cost $640. Adriana's computer cost 15% more than corbins computer. Write an equation that could be used to find the cost of jocelyn's computer
Answers
Answer:
640 = 0.80·j
Step-by-step explanation:
Let j represent the cost of Jocelyn's computer (in dollars). Adriana's computer cost 20% less, so has a cost that is 0.80·j. We are told that amount is $640, so we can write the equation ...
640 = 0.80·j
For which intervals is the function negative? Select each correct answer.
Answers
ANSWER
(1,4)
(-∞,-3)
EXPLANATION
The interval where a portion of the graph is below the x-axis is where the graph is negative.
From the graph , the curve is below the x-axis on the interval (-∞,-3). Hence the graph is negative on this interval.
Also the graph is below the x-axis on the interval (1,4). This is also another interval where the graph is negative.
What is the sum of the infinite geometric series represented by
A. 240
B. 135
C. 360
D. 720
Answers
Answer:
the answr is a 240
Step-by-step explanation:
beacuse you have to desept the question
Answer:
240 is the answer
Ameekah is working with consecutive integers
Answers
Consecutive numbers: 1, 2, 3, 4, 5.
As we can see it's the latest plus 1
So,
x, x + 1, x + 1 + 1, x + 1 + 1 + 1
x, x + 1, x + 2, x + 3 and so on
So it's x + 1.
For this case we have that by definition, a consecutive number is obtained by adding a unit to the previous one.
Example:
n, n + 1, n + 2, n + 3 ...
So:
If "x" is the first number of Ameekah, its second number to form a series of consecutive integers must be:
x + 1, that is, add "1" to the previous number.
Answer:
x + 1
Option B
How many solutios are there for the following triangle:
A=9 C=4 c=12*
Answer Choices:
a. 0 solutions
b. 1 solution
c. 2 solutions
d. infinite solutions
Answers
I would personally go w/ b or c
There is exactly one solution for this triangle, and the correct answer is: b. 1 solution
To determine the number of solutions for the given triangle with angles A, C, and side c, we can use the Law of Sines, which states that in any triangle:
[tex]\[\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}\][/tex]
Given:
- Angle A = 90 degrees (since it is a right angle, we assume A is the right angle for the purpose of this solution)
- Angle C = 4 degrees
- Side c = 12 units (opposite to angle C)
Since angle A is 90 degrees, we know that this triangle is a right-angled triangle. In a right-angled triangle, the other two angles must add up to 90 degrees. We are given one of those angles, C, which is 4 degrees. Therefore, the third angle, B, which is opposite side b, can be calculated as:
[tex]\[B = 90^\circ - C = 90^\circ - 4^\circ = 86^\circ\][/tex]
Now, we have all three angles: A = 90°, B = 86°, and C = 4°. The sum of angles in any triangle is 180 degrees, and in this case:
[tex]\[A + B + C = 90^\circ + 86^\circ + 4^\circ = 180^\circ\][/tex]
This confirms that the angles are consistent with the angles of a triangle.
Next, we can find the length of side b using the Law of Sines:
[tex]\[\frac{\sin(B)}{b} = \frac{\sin(C)}{c}\][/tex]
[tex]\[\frac{\sin(86^\circ)}{b} = \frac{\sin(4^\circ)}{12}\][/tex]
Since 86° and 4° are acute angles and sine of an acute angle is unique, there will be a unique positive value for b. This means there is only one possible length for side b that will satisfy the conditions of the triangle.
Therefore, there is exactly one solution for this triangle, and the correct answer is:
b. 1 solution
Find the Geometric Mean of 8 and 50. Be sure to show your work!
Answers
Answer:
20
Step-by-step explanation:
The geometric mean of n numbers is the n-th root of their product. For two numbers, it is the square root of their product:
geometric mean = √(8·50) = √400 = 20
The answer is: 20
My work: √8*50 = √400 = 20
You have to take the square root of 8 multiplied by 50. With that, you would get 400, which is still squared because you have to get the numbers inside of the square root to one number. After that, you can now take the square root of the number that is inside of it, which in this case it is 400. The square root of 400 is 20.
I hope this helps!
For every pound a company spends on advertising, it spends ?0.75 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form.
Answers
Answer:
The ratio is equal to [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Let
x----> the amount spent on advertising
y----> the amount spent on its website
The ratio is equal to x/y
Remember that
[tex]0.75=\frac{3}{4}[/tex]
so
[tex]\frac{1}{(3/4)}=\frac{4}{3}[/tex]
Need help ASAP!! Use the graph to find the solution of the system of equations what is the solution?
A.(0,-4)
B.(0,-1)
C.no solution
D.(4,-3)
Answers
The solution is the point where the two lines meet. The answer is D.
The probability of winning a prize at a school raffle is 0.62. What is the probability of not winning a prize
at the raffle?
a. 0.48 c. 3.8
b. 0.38 d. 38
Answers
We will see that the probability of not winning the prize is equal to 0.38, so the correct option is b.
How to get the probability of not winning?
In this experiment, we have two possible outcomes.
One outcome is winning the prize, with a probability P and the other outcome is losing, with a probability Q.
Because there are only two outcomes we will have that:
P + Q = 1
We know that P = 0.62, replacing that we get:
0.62 + Q = 1
Q = 1 - 0.62 = 0.38
So we conclude that the probability of not winning the prize is 0.38, then the correct option is b.
If you want to learn more about probability, you can read:
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PLEASE HELP ME ON THESE 2 QUESTIONS!!!
THANK U!!!
Answers
Answer:
Step-by-step explanation:
You might see this a bit easier if you change the 5/4 * pi into degrees.
pi/180 = 5/4*pi / x This is the proportion. Change 5/4 into a decimal
pi/180 = 1.25 *pi / x Cross multiply
x * pi = 1.25 pi * 180 Divide by pi
x = 1.25 * 180
x = 225 degrees.
The fraction of the area of the sector is angle/360
The fraction of the area of the sector is 225/360
The fraction of the area area of the sector is 5/8 Reduced.
225: 3*3*5*5
360 = 2*2*2*5*3 *3
Cancel out the common factors
3 * 3 * 5
which leaves 5/8
Two
-3x^2 + 5x - 2 - 2x^2 + 4x + 2
- 5x^2 + 9x (the 2's cancel)
a = - 5
b = 9
c = 0
John and George together raked 7/8 if the yard. John raked 3/4 of that amount. What part of the yard did john raked?
Answers
Answer:
1
8
Step-by-step explanation:
What do we know:
John and George raked 7/8 of the yard.
John raked 3/4 of 7/8
What we need to know is:
How much did George rake?
How? Subtract the fractions given.
7 - 3
8 4
To do this we must make the denominator (bottom) number the same. How? Find the least common denominator for 8 and 4. Basically what is the lowest number that both 8 and 4 can be divided.
Answer is 8
8 divided by 8 is 1
4 divided by 8 is 2
so
7 - 3 ×2 6
8 4 ×2 = 8
7 _ 6 = 1
8 8 8 is how much George raked.
I need help ty ty ty :-)
Answers
Answer:
First Answer: y + 4 = -3(x - 3)
Second Answer: y - 5 = (-3/4)(x - 4)
Step-by-step explanation:
That answer was correct :)
Answer:
1. y + 4 = -3(x - 3)
2. Second Answer: y - 5 = (-3/4)(x - 4)
:)))
Which of these is an example of a final good?
Answers
Answer:
The answer on Plato is C as this is a final product
Step-by-step explanation:
These are the choices on Plato
A. wood
B. steel
C. needle
True or false:
1) If f'(c)=0, then f has a local maximum or minimum at x=c.
I think this one is false, but I'm not sure.
2) If f is continuous on [a, b] and differential on (a, b) and f'(x) = 0 on (a, b), then f is constant on [a, b].
3) The Mean Value Theorem can be applied to f(x) = 1/x^2 on the interval [-1, 1].
I'm pretty sure the last one is false.
Answers
1. False. [tex]f'(c)=0[/tex] does not necessarily mean that [tex]f(c)[/tex] is a maximum or minimum. It could just as easily be a saddle point. For example, consider the function [tex]f(x)=x^3[/tex] with [tex]f'(x)=3x^2=0[/tex] when [tex]x=0[/tex], yet [tex]f(x)<0[/tex] for [tex]x<0[/tex] and [tex]f(x)>0[/tex] for [tex]x>0[/tex].
2. True. If [tex]f'(x)=0[/tex] for all [tex]x[/tex] in [tex](a,b)[/tex], then [tex]f[/tex] must be constant on that interval.
3. False. In order for the MVT to apply, [tex]f[/tex] must be continuous on the closed interval. But [tex]\dfrac1{x^2}[/tex] does not exist at [tex]x=0[/tex].
The first statement about f'(c)=0 implying a local maximum or minimum is true. The second statement that if f'(x)=0 on an interval implies the function is constant is also true. Lastly, the Mean Value Theorem cannot be applied to f(x) = 1/x² on the interval [-1, 1] because the function is not continuous at x=0.
Explanation:True or false:
The statement 'If f'(c)=0, then f has a local maximum or minimum at x=c' is true. As part of calculus, this is the concept of the first derivative test. If the derivative of a function at a given point is zero, it means that point is a local minimum or maximum, or it could also be a point of inflexion.The statement 'If f is continuous on [a, b] and differential on (a, b) and f'(x) = 0 on (a, b), then f is constant on [a, b]' is true. This is based on the fact that if the derivative of a function is zero over an interval, the function will be constant in that interval.The statement that 'The Mean Value Theorem can be applied to f(x) = 1/x² on the interval [-1, 1]' is indeed false. The Mean Value Theorem requires the function to be continuous over the closed interval and differentiable over the open interval. The function f(x) = 1/x² is not defined at x=0, hence it is not continuous in the interval [-1,1].Learn more about Calculus here:https://brainly.com/question/32512808
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PLEASE HELP ASAP 60 POINTS + BRAINLIEST TO RIGHT/BEST ANSWER!
Answers
Answer:
see explanation
Step-by-step explanation:
Given
P(x) = x³ + 7x² + 4x, then
P(a) = a³ + 7a² + 4a ← substitute x = a into polynomial
To evaluate P(- 2) substitute a = - 2 into P(a)
P(- 2) = (- 2)³ + 7(- 2)² + 4(- 2) = - 8 + 28 - 8 = 12
Since P(- 2) ≠ 0 then (x + 2) is not a factor of P(x)
Answer:
12
Step-by-step explanation:
(-2)³ + 7(-2)² + 4(-2)
12
99 PLZ HELP BRAINLIEST Which strategy would not correctly solve this story problem?
There are 14 bikes for sale at a bicycle store. Four of the bikes are black, 5 are white, and the rest are red. How many bikes are red?
A.
Translate into an equation. 4 + 5 + r = 14
B.
Use logical reasoning. There were 14 bikes to start with. Subtract the number of black bikes (4) and subtract the number of white bikes (5). The remaining bikes must be red.
C.
Work backward. Start with 14 bikes and add 4. Then subtract 5. The number left is the number of red bikes.
D.
Draw a diagram. Draw 14 circles. Cross out 4 of the circles and then cross out 5 more circles. Color the remaining circles red.
Which strategy would not correctly solve this story problem?
Billy put up some balloons for a party. He had 4 times as many green balloons as red ones. There were 3 red balloons. During a game, 2 green balloons popped. Then another 5 green balloons popped. How many green balloons did Billy have left?
A.
Use objects to model the problem. Use toothpicks to represent the green balloons. Count out a total of 4 groups of 3 toothpicks. Remove 2 toothpicks and then 5 more. Count the remaining toothpicks to find the number of green balloons left.
B.
Work backwards. Start by adding the number of green balloons that popped (5 + 2) Then multiply the sum by 4. Subtract the number of red balloons (3) and that gives the number of green balloons that were left.
C.
Use logical reasoning. Step 1. Multiply 3 × 4 to figure out the total number of green balloons. Step 2. Add 2 + 5 to figure out how many green balloons popped. Step 3. Subtract the sum in Step 2 from the product in Step 1 to find out the number of green balloons that were left.
D.
Translate into an equation. (3 × 4) – (2 + 5) = g
Which strategy would not correctly solve this story problem?
Comic books cost $1, paperback books cost $3, and hardcover books cost $5 at the used book store. Sara bought 2 comic books, 5 paperbacks, and 2 hardcover books. How much money did Sara spend?
A.
Use objects to model the problem. Use coins to represent $1. Drop 1 coin into a jar 2 times for the cost of comic books. Drop 3 coins into the jar 5 times for the cost of the paperbacks. Drop 5 coins into the jar 2 times for the cost of the hard cover books. Count the coins in the jar.
B.
Draw a diagram. Draw 2 squares and write $1 inside each. Draw 5 circles and write $3 inside each. Draw 2 triangles and write $5 inside each. Add all the dollar amounts inside the shapes to find the total Sara spent.
C.
Use logical reasoning. Sara bought 2 comic books at $1 each for a total of $2. She bought 5 paperbacks at $3 each for a total of $15. She bought 2 hard cover books at $5 each for a total of $10. So Sara adds $2 + $15 + $10 to find the total amount she spent.
D.
Translate into an equation. (1 + 3 + 5) × (2 + 5 + 2) = n
Answers
Answer:
is this all apart of the answers or separate questions??
Step-by-step explanation:
1. B
2.C
3.C
4.A
5.D
A chord of a circular clock is 48 inches long, and its midpoint is 7 inches from the center of the circle. What is the radius of the clock to the nearest whole number?
Answers
ANSWER
The radius is 25 inches
EXPLANATION
From the diagram, the radius of the circle is AC.
From the Pythagoras Theorem,
[tex] {r}^{2} = {7}^{2} + {24}^{2} [/tex]
[tex]r^{2} = 49 + 576[/tex]
Simplify
[tex]r^{2} = 625[/tex]
Take positive square root,
[tex]r = \sqrt{625} [/tex]
[tex]r = 25[/tex]
Hence the radius is 25 inches
Please help me?????????
Answers
Given an implication of the form [tex]P\implies Q[/tex]
The equivalent implication is [tex]\lnot Q \implies \lnot P[/tex]
So, you have to negate both propositions and invert the order:
If a triangle is not isosceles, then it's not equilateral.
lim (-x^2 + 6x-8)
x->-3
Answers
[tex]\bf \lim\limits_{x\to 3}~-x^2+6x-8\implies \lim\limits_{x\to 3}~-(3)^2+6(3)-8\implies 1[/tex]
Answer:
2///////////////////////////
if m AD=98 and m CD=120 Whats is m
Answers
Answer:
The measure of arc BC is 44°
Step-by-step explanation:
we know that
m arc AD+m arc DC+m arc BC+m arc AB=360° ----> by complete circle
substitute the given values and solve for m arc BC
98°+120°+m arc BC+98°=360°
m arc BC+316°=360°
m arc BC=360°-316°=44°
Answer:
109Step-by-step explanation:
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Simplify.
Answers
Answer: [tex]\bold{B)\quad \dfrac{x-2}{x+1}}[/tex]
Step-by-step explanation:
[tex]\dfrac{x^2+5x-14}{x^2+8x+7}\\\\\\=\dfrac{(x+7)(x-2)}{(x+7)(x+1)}\\\\\\=\dfrac{x-2}{x+1}[/tex]
Please please help me
Answers
Answer:
BF = 30
Step-by-step explanation:
Each midsegment is half the length of the parallel side of the triangle. CE is 60 and is parallel to BF, so BF = 60/2 = 30.
Please help with this question!! I am out of points now!! I need this!
Answers
Answer:
m∠QRS = 30°
Step-by-step explanation:
An inscribed angle has half the measure of the intercepted arc.
(arc QS)/2 = 60°/2 = 30°
The measure of angle QRS is 30°.
Juanita and Nina are bowling together. The probability of Juanita getting a strike next game is 24%. The probability of Nina getting a strike next game is 0.17. Which of these events is more likely?
(Choice A)
A
Juanita gets a strike next game.'
(Choice B)
B
Nina gets a strike next game.
(Choice C)
C
Neither. Both events are equally likely.
Answers
Answer:
Step-by-step explanation:
0.24 is greater than 0.17, and therefore J's getting a strike next game is more likely.
The event that is more likely is Juanita gets a strike next game.
What is a probability?
Probability is the likelihood that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that Juanita would have a strike is higher than that of Nina. Thus, it is more likely that Juanita gets a strike next game.
To learn more about probability, please check: https://brainly.com/question/13234031
Rewrite sqr-100 +26 in complex number notation
Answers
Answer:
26 + 10i is your answer.
Subtract (5x + 3) from (9x – 7).
A. 4x – 4
B. 4x + 10
C. 4x – 10
D. –4x + 10
Answers
D is the correct answer
the result of subtracting (5x + 3) from (9x - 7) is 4x - 10. Therefore, the correct option is C: 4x - 10.
To subtract (5x + 3) from (9x - 7), we need to distribute the negative sign to all the terms in (5x + 3) and then perform the subtraction term by term.
(9x - 7) - (5x + 3)
= 9x - 7 - 5x - 3
Now, combine like terms:
= (9x - 5x) + (-7 - 3)
= 4x - 10
So, the result of subtracting (5x + 3) from (9x - 7) is 4x - 10. Therefore, the correct option is C: 4x - 10.
Learn more about subtraction here
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What is the value of term a^4?
Answers
Answer:
135Step-by-step explanation:
[tex]\text{We have the recursive formula of a series:}\\\\a_1=5\\a_n=3a_{n-1}\\\\a_2=3a_{2-1}=3a_1\to a_2=3(5)=15\\\\a_3=3a_{3-2}=3a_2\to a_3=3(15)=45\\\\a_4=3a_{4-1}=3a_3\to a_4=3(45)=135[/tex]
Solve this absolute value equation and show all work.
1) 9 + |2x - 3| = 7
2) 3 + |2x - 4| = 15
Answers
Answer:
For the equation
1) [tex]9 + | 2x - 3 | = 7[/tex]
x=0.5 and x=2.5
For the equation
2) [tex]3 + | 2x - 4 | = 15[/tex]
x=8 and x=-4
Step-by-step explanation:
For the equation
1) [tex]9 + | 2x - 3 | = 7[/tex]
we have 2 cases
Case 1 [tex](2x - 3)> 0[/tex]
[tex]9 + 2x - 3 = 7\\2x = 7 + 3-9\\2x = 1\\x = 0.5[/tex]
Case 2 [tex](2x - 3) <0[/tex]
[tex]9 - (2x - 3) = 7\\-2x + 3 = 7-9\\-2x = 7-9-3\\-2x = -5\\x = 2.5[/tex]
For the equation
2) [tex]3 + | 2x - 4 | = 15[/tex]
we have 2 cases
Case 1 [tex](2x - 4)> 0[/tex]
[tex]3 + 2x - 4 = 15\\2x = 15 + 4-3\\2x = 16\\x = 8[/tex]
Case 2 [tex](2x - 4) <0[/tex]
[tex]3 - (2x - 4) = 15\\-2x +4 = 15-3\\-2x = 15-3-4\\-2x = 8\\x = -4\\[/tex]
Please help me out please
Answers
Answer:
400 units³
Step-by-step explanation:
The volume (V) of the square pyramid is
V = [tex]\frac{1}{3}[/tex] area of base × height (h)
where h is the perpendicular height.
Consider the right triangle formed by a segment from the vertex to the midpoint of the base and the slant height ( the hypotenuse )
Using Pythagoras' identity on the right triangle
h² + 5² = 13²
h² + 25 = 169 ( subtract 25 from both sides )
h² = 144 ( take the square root of both sides )
h = [tex]\sqrt{144}[/tex] = 12
Area of square base = 10² = 100, hence
V = [tex]\frac{1}{3}[/tex] × 100 × 12 = 4 × 100 = 400
Identify the measure of arc HD◠.
Answers
Answer:
The measure of arc HD is 20°
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
In the triangle of the figure , the measure of the third interior angle is equal to
180°-92°-38°= 50°
50°=(1/2)[(102+18)°-arc HD]
100°=[120°-arc HD]
arc HD=120°-100°=20°
Answer:
arc HD = 20°
Step-by-step explanation:
Let point N be the point where secant RL intersect the circle, point M be the point of intersection for chords NL and KH, and point S be the vertex of the triangle formed by secants KH and RD.
It is given that m∠SRM = 38∘ and m∠RMS = 92∘. Use the Triangle Sum Theorem to determine m∠MSR.
m∠MSR = 180° − 92∘ − 38∘ = 50∘
It is also given that mPN = 18∘ and mNK = 102∘. So, mPK = 18∘ + 102∘ = 120∘.
If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs. So,
m∠MSR= 1 /2 (mPK − mHD)
Substitute the known values and solve for mHD.
50∘ = 1/2 (120∘ − mHD)
Multiply by 2.
100 = 120∘ − mHD
Simplify.
mHD = 20
Therefore, the measure of arc HD is 20∘.