If using the method of completing the square to solve the quadratic equation
x^2 + 8x – 4 = 0, which number would have to be added to "complete the square"?
Answers
Step-by-step explanation:
everything can be found in the picture
Related Questions
Which graph represents the function f(x)=|x|-4?
Answers
See the graph in the attached image.
HELP TIMER Write the equation of a hyperbola centered at the origin with x-intercept +/- 4 and foci of +/-2(squareroot 5)
Answers
Given:
x-intercepts of the hyperbola are ±4.
The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].
Center of the hyperbola is at origin.
To find:
The equation of the hyperbola.
Solution:
The general equation of a hyperbola:
[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex] ...(i)
Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, [tex](\pm c,0)[/tex] are foci.
Center of the hyperbola is at origin. So, h=0 and k=0.
x-intercepts of the hyperbola are ±4. So,
[tex]\pm a=\pm 4[/tex]
[tex]a=4[/tex]
The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].
[tex]\pm c=\pm 2\sqrt{5}[/tex]
[tex]c=2\sqrt{5}[/tex]
We know that,
[tex]a^2+b^2=c^2[/tex]
[tex](4)^2+b^2=(2\sqrt{5})^2[/tex]
[tex]16+b^2=20[/tex]
[tex]b^2=20-16[/tex]
[tex]b^2=4[/tex]
Taking square root on both sides, we get
[tex]b=\sqrt{4}[/tex] [b>0]
[tex]b=2[/tex]
Substituting [tex]h=0,k=0,a=4,b=2[/tex] in (i), we get
[tex]\dfrac{(x-0)^2}{4^2}-\dfrac{(y-0)^2}{2^2}=1[/tex]
[tex]\dfrac{x^2}{4^2}-\dfrac{y^2}{2^2}=1[/tex]
Therefore, the correct option is (d).
The manager of a local car dealership wants to conduct a customer satisfaction survey. Which group of people should make up a sample of the population?
A. sales people in the dealership
B. mechanics who work at the dealership
C. people who bought cars from the dealership
D. prospective buyers who visit the dealership
Answers
Answer:
Step-by-step explanation:
A customer satisfaction survey refers to a questionnaire that's designed by a company in order for businesses to know what customers think about their products.
Since the manager of a local car dealership wants to conduct a customer satisfaction survey, then the group of people should make up a sample of the population will be the people who bought cars from the dealership
Answer:
c
Step-by-step explanation:
One batch of trail mix can be made by mixing 3 cups of granola with 0.75 cup of raisins. Hamid needs to make a bigger batch of trail mix. He makes a graph to be sure the mixture will be correct.
On a coordinate plane, the point (3, 0.75) is plotted.
How can he use the graph to find an equivalent ratio?
He can draw a straight line from the origin that passes through (0, 0.75).
He can draw a straight line from (3, 0.75) that passes through (6, 2).
He can draw a straight line from (3, 0.75) that passes through (6, 1).
He can draw a straight line from the origin that passes through (3, 0.75).
put it in the comments im out of answers
Answers
the graph that he needs to do is a straight line from the origin that passes through (3, 0.75), the correct option is the last one.
How can he use the graph to find an equivalent ratio?He knows the relation:
3 cups of granola ⇒ 0.75 cups of raisins.
Assuming this is a proportional relation of the form:
y = k*x
Where k is a constant.
Then when x = 0, we also have y = 0, so the line also passes through the point (0, 0), which is the origin.
Then the graph that he needs to do is a straight line from the origin that passes through (3, 0.75), the correct option is the last one.
If you want to learn more about proportional relationships:
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Point Q is the midpoint of GH¯¯¯¯¯¯. GQ=2x+3, and GH=5x−5 .
What is the length of GQ¯¯¯¯¯?
Answers
Answer:
[tex]GQ =25[/tex] --- GoTV
Step-by-step explanation:
Given
[tex]GQ = 2x + 3[/tex]
[tex]GH= 5x - 5[/tex]
Required
Find GQ
Since Q is the midpoint, then:
[tex]GH = 2 * GQ[/tex]
This gives:
[tex]5x - 5 = 2[2x+3][/tex]
Open bracket
[tex]5x - 5 = 4x+6[/tex]
Collect like terms
[tex]5x - 4x = 5+6[/tex]
[tex]x =11[/tex]
We have:
[tex]GQ =2x+3[/tex]
This gives:
[tex]GQ =2*11+3[/tex]
[tex]GQ =25[/tex]
In a certain year, 86% of all Caucasians in the U.S., 77% of all African-Americans, 77% of all Hispanics, and 84% of residents not classified into one of these groups used the Internet for e-mail. At that time, the U.S. population was 64% Caucasian, 11% African-American, and 10% Hispanic. What percentage of U.S. residents who used the Internet for e-mail were Hispanic
Answers
Answer:
Percentage of U.S resident who used the Internet for e-mail were Hispanic=9.19%
Step-by-step explanation:
We are given that
Population was Caucasian=64%
Population was African-American=11%
Population was Hispanic=10%
Let the population of U.S=10000
Now,
Population was Caucasian=[tex]\frac{64}{100}\times10000=6400[/tex]
Population was African-American=[tex]\frac{11}{100}\times 10000=1100[/tex]
Population was Hispanic=[tex]\frac{10}{100}\times 10000=1000[/tex]
Population of others=10000-(6400+1100+1000)=1500
Population of Caucasians used the Internet for e-mail=86% of 6400
Population of Caucasians used the Internet for e-mail=[tex]\frac{86}{100}\times 6400[/tex]
Population of Caucasians used the Internet for e-mail=5504
Population of African-American used the Internet for e-mail=77% of 1100
Population of African-American used the Internet for e-mail=[tex]\frac{77}{100}\times 1100=847[/tex]
Population of Hispanics used the Internet for e-mail=77% of 1000
Population of Hispanics used the Internet for e-mail=[tex]\frac{77}{100}\times 1000=770[/tex]
Population of others used the Internet for e-mail=84% of 1500
Population of others used the Internet for e-mail=[tex]\frac{84}{100}\times 1500=1260[/tex]
Total population used the Internet for e-mail=5504+847+770+1260
Total population used the Internet for e-mail=8381
Percentage of U.S resident who used the Internet for e-mail were Hispanic
=[tex]\frac{Population \;of \;Hispanics \;used \;the \;Internet \;for \;e-mail}{total\;population\; used \;the \;Internet \;for\; e-mail}\times 100[/tex]
Percentage of U.S resident who used the Internet for e-mail were Hispanic=[tex]\frac{770}{8381}\times 100[/tex]
Percentage of U.S resident who used the Internet for e-mail were Hispanic=9.19%
its my final, please help!!!!!!!!!!
Answers
Answer:
both apply
Step-by-step explanation:
i guessed just do it
This exercise involves the formula for the area of a circular sector. The area of a circle is 700 m2. Find the area of a sector of this circle that subtends a central angle of 3 rad.
Answers
Answer:
334.4 m²
Step-by-step explanation:
The formula for the area of a sector is given as:
1/2 × r² × θ
Where θ = Central angle
Area of a Circle = 700 m²
The formula for the area of a circle = πr²
r = Radius of a circle
r² = Area / π
r = √Area / π
r = √700/π
r = 14.927053304 m
Approximately, r = 14.93 m
Therefore, the area of the sector
= 1/2 × r² × θ
= 1/2 × 14.93² × 3 rad
= 334.35735 m²
Approximately, Area of the sector = 334.4 m²
Plz help me solve this
Answers
Name this triangle by its sides and angles. This is a(n) ____________________ triangle.
a triangle with one right angle and three non-congruent sides
Answers
right triangle
Hope this helps! :)
High School Dropouts
Number of Dropouts
1990
2000
Male
Female
MAMD.M.D.3: Which of the
following is true about the graph?
Answers
Answer:
There are more females dropping than males each year and that there are more females than males
Leila buys candy that costs 8 dollars per pound. She will spend more than 40 dollars on candy. What are the possible numbers of pounds she will buy?
Answers
Answer:
She must buy more than 5 lbs
Step-by-step explanation:
First write the inequality
cost per pound * number of pounds > total cost
8 * lbs > 40
Divide each side by 8
8 lbs /8 > 40/8
lbs > 5
She must buy more than 5 lbs
An English teacher needs to pick 4 books to put on his reading list for the next school year. He has narrowed down his choices to 8 novels and 6 plays.
a. How many different ways can he choose the books to put on the list if he wants to include at least two plays?
b. Find the standard deviation.
Answers
Answer:
A) 3 ways
B) sorry don't know.
Step-by-step explanation:
2 P and 2 N
3P and 1 N
4P
So 3 ways.
If the number of orders at a production center this month is a Geom(0.7) random variable, find the probability that we'll have at most 3 orders.
Answers
Answer: 0.973
Step-by-step explanation:
The probability mass function of geometric distribution is
[tex]f(x)=(1-p)^{x-1}p,\ \ \ x=1,2,3,...[/tex], p= probability of success on a trial.
As per given, we have
p=0.7
The probability that we'll have at most 3 orders [tex]P(X\leq3)=P(x=1)+P(x=2)+P(x=3)[/tex]
[tex]=(1-0.7)^{1-1}(0.7)+(1-0.7)^{2-1}(0.7)+(1-0.7)^{3-1}(0.7)\\\\=0.7+0.21+0.063\\\\=0.973[/tex]
hence, the required probability = 0.973
The probability that we'll have at most 3 orders will be "0.973".
According to the question,
→ [tex]x \sim Geometric (p)[/tex]
here,
p = 0.7
then,
→ [tex]P(X=x) = (1-p)^{x-1}\times p[/tex]
By putting the given values, we get
[tex]= (1-0.7)^{x-1}\times 0.7[/tex]
hence,
The probability that we'll have at most 3 orders will be:
→ [tex]P(X \leq 3)=P(X=1)+P(X=2)+P(X=3)[/tex]
[tex]=0.7+0.21+0.063[/tex]
[tex]=0.973[/tex]
Thus the above response is correct.
Learn more about probability here:
https://brainly.com/question/6981569
Find the area of rectangle whose length is -3/7 and breadth is 16/3
Answers
Answer:
I'm gonna guess your length is positive and you made a typing mistake. If that's so....
Step-by-step explanation:
Area= length x breadth
=[tex]\frac{3}{7\\}[/tex] x [tex]\frac{16}{3}[/tex]
=[tex]\frac{16}{7}[/tex]
=2.29 [tex]unit^{2}[/tex]
Element X is a radioactive isotope such that its mass decreases by 73% every
hour. If an experiment starts out with 680 grams of Element X, write a
function to represent the mass of the sample after t hours, where the rate of
change per minute can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the
percentage rate of change per minute, to the nearest hundredth of a percent.
Mi
Answers
Answer:
Step-by-step explanation:
The element decay percentage rate of change 2.22% per minute.
What is radioactive isotope?
Radioisotope, radionuclide, or radioactive nuclide, any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha, beta, and gamma rays.
Here, mass decreases by 73% every hour.
Weight of element X is 680 grams.
According to question,
f(t) = 680 (1 - 73%)ⁿ
f(t) = 680 (1 - 0.73)ⁿ
f(t) = 680 X 0.27ⁿ
f(t) = 680 X 0.9778ⁿ
f(t) = 680 X (1 - 0.02322)ⁿ
Thus, the element decay percentage rate of change 2.22% per minute.
Learn more about radioactive isotope from:
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Determine if each proportion on the left is True or False. Answer options on the right side may be used more than once.
True
False
28/16=14/8
3/5=9/15
4/32=10/78
3/4=12/16
Answers
Answer:
28/16=14/8 true
3/5=9/15 true
4/32=10/78 false
3/4=12/16 true
Step-by-step explanation:
DID IT ON BRIDGE
Find value a when the angle between vectors U=(2,a) and V = (-6;8) is pie/4
Answers
Answer:
Step-by-step explanation:
The formula to find the angle between 2 vectors is
[tex]cos\theta=\frac{u*v}{|u||v|}[/tex] which is the dot product of u*v over the (magnitude of u times the magnitude of v). We also know that θ = [tex]\frac{\sqrt{2} }{2}[/tex]. Filling in that formula requires us to find the dot product of u and v, which is
u·v = (2×(-6)) + (a×8) so
u·v = -12 + 8a. Then we need the magnitudes of both u and v:
[tex]|u|=\sqrt{2^2+a^2}=\sqrt{4+a^2}[/tex] and
[tex]|v|=\sqrt{(-6)^2+8^2}=\sqrt{100}=10[/tex]
Putting all of together looks like this:
[tex]\frac{\sqrt{2} }{2}=\frac{-12+8a}{10\sqrt{4+a^2} }[/tex] . Cross multiply to get
[tex]10\sqrt{2}(\sqrt{4+a^2})=2(-12+8a)[/tex] which is tricky to simplify. You really need to know the rules for multiplying radicals to do this correctly. The simplification is
[tex]10\sqrt{8+2a^2}=-24+16a[/tex] and we need to solve for a. Begin by squaring both sides to get rid of the square root to get:
100(8 + 2a²) = 256a² - 768a +576 and simplify some more by distributing through the parenthesis to get
800 + 200a² = 256a² -768a + 576. Combine like terms to come up with
0 = 56a² - 768a - 224 and we need to factor that. Assuming since you're this far in math (pre-calc or maybe late algebra 2) you know how to factor, when you do, you get values for a of - .285714... and 14.
Therefore, the value for a is 14. I checked it...it works
Answer:
a = 14, U = (2, 14)
Step-by-step explanation:
the other answer is correct.
just to add the solution path for the quadratic equation
0 = 56a² - 768a - 224
in general, a quadratic equation usually expressed in x
0 = ax² + bx + c
has its solution as
x = (-b ± sqrt(b² - 4ac))/(2a)
for us here this looks like this then
a = (768 ± sqrt(768² - 4×56×-224))/(2×56) =
= (768 ± sqrt(589824 + 4×56×224))/112 =
= (768 ± sqrt(589824 + 50176))/112 =
= (768 ± sqrt(640000))/112 = (768 ± 800)/112
a1 = (768 + 800)/112 = 1568/112 = 14
a2 = (768 - 800)/112 = -32/112 = -0.29
and the negative solution would be for a vector solution in the wrong direction (down instead of up). as V is pointing up left, and the angle is only 45 degrees (pi/4), also U has to point up.
so, 14 is the solution for U.
If f(x)=2x+3 and g(x)= x^2-8find (f+g (x)
Answers
[tex] \large \boxed{(f + g)(x) = f(x) + g(x)}[/tex]
Use the following property above to find the value. Substitute f(x) and g(x) in.
[tex] \large{(2x + 3) + ( {x}^{2} - 8)} \\ \large{2x + 3 + {x}^{2} - 8}[/tex]
Evaluate/Combine like terms.
[tex] \large{2x + {x}^{2} - 5}[/tex]
This step is optional but it's the best to arrange the degree.
[tex] \large{ {x}^{2} + 2x - 5} \\ \large{(f + g)(x) = {x}^{2} + 2x - 5}[/tex]
Answer
(f+g)(x) = x²+2x-5Let me know if you have any doubts!
Can someone please answer this
Answers
A local salesman has forty-five stacks of magazines. If the salesman plans to sell three-fifths of the stacks, how many stacks will he have left?
Answers
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
The total cost of a truck rental, y, for x days, can be modeled by y=24x+39. What is the rate of change for this function?
Answers
Answer:
24 per day
Step-by-step explanation:
'x' = days, so since 24 is with x, the rate of change is 24
what is 1 6/9 +5 9/7
Answers
[tex]\longrightarrow{\green{7 \frac{20}{21}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]1 \frac{6}{9} + 5 \frac{9}{7} \\ \\ = \frac{15}{9} + \frac{44}{7} \\ \\ = \frac{15 \times 7}{9 \times 7} + \frac{44 \times 9}{7 \times 9} \\ \\ = \frac{105 + 396}{63} \\ \\ = \frac{501}{63} \\ \\ = \frac{167}{21} \\ \\ = 7 \frac{20}{21} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
Find the value of x. Round to the nearest 10th
Answers
Answer:
44.94
Step-by-step explanation:
Dan has an old lawn mower! It takes him 1 hour to mow the whole lawn. How many square yards does Dan cut in one minute? Hints: There are 60 minutes in 1 hour. To find the unit rate divide the area of the lawn by the amount of time it takes Dan to mow the whole lawn.
40 square yards per minute
400 square yards per minute
2400 square yards per minute
240 square yards per minute
Answers
Answer: You didnt mention how much Dan mows in 1 hour, but just do that divided by 60
Step-by-step explanation:
How many quarts of pure antifreeze must be added to 8 quarts of a 40% antifreeze solution to obtain a 60% antifreeze solution
Answers
Let q be the number of quarts of pure antifreeze that needs to be added to get the desired solution.
8 quarts of 40% solution contains 0.40 × 8 = 3.2 quarts of antifreeze.
The new solution would have a total volume of 8 + q quarts, and it would contain a total amount of 3.2 + q quarts of antifreeze. You want to end up with a concentration of 60% antifreeze, which means
(3.2 + q) / (8 + q) = 0.60
Solve for q :
3.2 + q = 0.60 (8 + q)
3.2 + q = 4.8 + 0.6q
0.4q = 1.6
q = 4
GIVING OUT BRAINLIEST HELP ME PLSS !!
Answers
Answer:
C) 5.66
Step-by-step explanation:
For a 45-45-90 triangle, the length of each leg length (not including the hypotenuse) is congruent to each other. If 8=y√2, then y=8/√2=4√2=5.66
Answer:
5.66
Step-by-step explanation:
take 45 degree as reference angle
using cos rule
cos 45 =adjacent /hypotenuse
[tex]\frac{1}{\sqrt{2} }[/tex] =y/8
[tex]\frac{1}{\sqrt{2} } *8=y[/tex]
[tex]\frac{8}{\sqrt{2} }=y[/tex]
[tex]4\sqrt{2} =y[/tex]
5.66=y
El opuesto y el semejante de 8xy
Answers
Answer:
No entiendo
Step-by-step explanation:
Use the grouping method to factor this polynomial.
x^3 + 2x^2 + 12x +24
A. (x^2+6)(x+2)
B. (x^2 +2)(x+6)
C. (x^2 +2)(x+12)
D. (x^2 +12)(x+2)
Answers
Answer:
[tex]( {x}^{2} + 12)(x + 2)[/tex]
Step-by-step explanation:
[tex] {x}^{3} +2 {x}^{2} +12x+24[/tex]
[tex]( {x}^{3}+2 {x}^{2} )+12x+24[/tex]
[tex] {x}^{2} (x+2)+12(x+2)[/tex]
[tex]( {x}^{2} + 12)(x + 2)[/tex]
Hope it is helpful...A high school has 32 players on the football team. The summary of the players' weights is given in the box plot. Approximately, what is the percentage of players weighing greater than or equal to 233 pounds
Answers
Answer:
[tex]\% = 11.96\%[/tex]
Step-by-step explanation:
Given
See attachment for box plot
Required
Percentage greater than or equal to 233
From the box plot, the maximum is:
[tex]Max = 244[/tex]
The minimum is:
[tex]Min = 152[/tex]
Percentage greater than 233 is calculated as:
[tex]\% = \frac{Max - 233}{Max - Min}[/tex]
[tex]\% = \frac{244 - 233}{244-152}[/tex]
[tex]\% = \frac{11}{92}[/tex]
Express as percentage
[tex]\% = \frac{11}{92}*100\%[/tex]
[tex]\% = \frac{1100}{92}\%[/tex]
[tex]\% = 11.96\%[/tex]
