Answer:
x^2 - 5x + 8 = (x - 5/2)^2 + 7/4
Step-by-step explanation:
(x - a)^2 + b = x^2 - 2ax + a^2 + b
equate to your quadratic :
x^2 - 5x + 8 = x^2 - 2ax + (a^2 + b)
equating coefficients (ignoring x^2 as the coefficient is 1 for both)
for x :
-5 = -2a --> a = 5/2
for x^(0) : 8 = a^2 + b , note a = 5/2
thus,
8 = (5/2)^2 + b
8 = 25/4 + b
b = 8 - 25/4 = 32/4 - 25/4 = (32 - 25)/4 = 7/4
hence a = 5/2 , b = 7/4
thus,
x^2 - 5x + 8 = (x - 5/2)^2 + 7/4
Doroteo determined that the correlation coefficient for a set of data was -.9 what percent of the total variation in the Y values is not explained by the regression line
Answer: 10%
Step-by-step explanation:
(1 - 0.9) × 100 = 10%
With a correlation Coefficient of -0.9. This signifies a strong negative correlation between the x and y variables. That is an increase in the x variable leads to a corresponding decrease in the y variable and vice versa. The correlation Coefficient could also be interpreted to mean that about 90% of the variation in the y variable is explained by the regression line or equation. With the the remaining 10% being unexplained. This is why a correlation Coefficient of 1 or - 1 refers to a perfect relationship, meaning 100% variation in y is explained by the regression line.
Please help me with this question is hard and i will give you a Brainiest
Answer:
0
Step-by-step explanation:
10(x-2)=-20
10x-20=-20
10x=0
x=0
Rewrite the equation by completing the square.
x^2+ 12x + 36 = 0
Answer:
(x+6)^2 =0
Step-by-step explanation:
x^2+ 12x + 36 = 0
Subtract 36 from each side
x^2+ 12x + 36-36 = 0-36
x^2 +12x = -36
Take the coefficient of x
12
Divide by 2
12/2 =6
Square it
6^2 =36
Add this to each side
x^2+ 12x + 36 = -36+36
(x+12/2)^2 = 0
(x+6)^2 =0
The given quadratic equation [tex]x^2+ 12x + 36 = 0[/tex] is written in squaring form as [tex](x + 6)^2 = 0[/tex].
Used the concept of a quadratic equation that states,
An algebraic equation with the second degree of the variable is called a Quadratic equation.
Given that the equation is,
[tex]x^2+ 12x + 36 = 0[/tex]
Now completing the square as
[tex]x^2+ 12x + 36 = 0[/tex]
It can be written as,
[tex]x^2+ 12x + 6^2 = 0[/tex]
[tex]x^2+ 2\times 6\times x + 6^2 = 0[/tex]
[tex](x + 6)^2 = 0[/tex]
Therefore, the equation is written as [tex](x + 6)^2 = 0[/tex].
To learn more about the quadratic equation visit:
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Correct answer only please!
Elizabeth deposited $4,530 in a savings account earning 11% interest, compounded annually.
To the nearest cent, how much will she have in 5 years?
Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer: Elizabeth earned $7270.91.
Step-by-step explanation:
The formula given to us is the formula for compounded interest.
You can substitute the values given in the first part of the problem into the equation to find B, the final amount:
[tex]B = p*(1+r)^t\\\\B = 4530 * (1 + 0.11)^5[/tex]
Note that 11% interest is expressed as 0.11 because it is a percentage of a whole number.
Now, use a calculator to raise 1.11 to the fifth degree to get this:
[tex]B = 4530 * 1.605058\\B = 7270.912[/tex]
As such, Elizabeth earned $7270.91 in interest after 5 years.
A scientist is measuring the temperature change in a decimal compound. The temperature dropped 11 f per hour from the original temperature. After four hours the temperature was 90 f find the compounds original temperature.
Answer:
[tex] F = mt +b[/tex]
From the info given we know that m =-11 and we have a condition given:
[tex] F =90 , t =4[/tex]
Using this condition we have:
[tex] 90 = -11*4 +b[/tex]
And solving for b we got:
[tex] 90 +4*11 = 90 +44= 134[/tex]
So then the original temperatue for this case is 134 F
Step-by-step explanation:
For this case we know that after four hours the temperature was 90 f and the temperature dropped 11 f per hour.
We can use a linear model to solve the problem given by:
[tex] F = mt +b[/tex]
Where F represent the temperature, t the time in hours and m the slope and b the intercept.
From the info given we know that m =-11 and we have a condition given:
[tex] F =90 , t =4[/tex]
Using this condition we have:
[tex] 90 = -11*4 +b[/tex]
And solving for b we got:
[tex] 90 +4*11 = 90 +44= 134[/tex]
So then the original temperatue for this case is 134 F
Help please!!!!
Amara has taken out a fixed rate mortgage for $125,000 at 4.04% for 20 years, or 240 months. Her payments are $730. What is the total cost of the loan?
A. $130,050
B. $175,200
C. $211,680
D. $226,000
Answer:
B. $175,200
Step-by-step explanation:
Monthly payment
$730Number of payments
240Total cost of the loan is:
$730*240 = $175200Correct answer choice is: B
Answer:
Hello, the total cost of the loan is $175,200 i have the same question on my previous exam and did the work to double check
What is the length of side AB
Answer:
5 units
Step-by-step explanation:
Using the distance formula:
[tex]AB=\sqrt{(-3-(-8))^2+(-6-(-6))^2}=\sqrt{5^2}=5[/tex]
Hope this helps!
The principal uses a computer to randomly select the name of a student from all the students in
the school. With the computer program, it is possible to draw the name of the same student
twice. If the principal selects the name of a student from the Voyagers on the first try, what is
the probability she will draw the name of another student from the Voyagers on the second try?
answer choices
81/399
41/200
1/82
21/100
Complete Question
Stillwater Junior High divides students into teams taught by a group of teachers. The table shows the number of students in each team.
Team{Number of Students}
Acers{78}
Blazers{80}
Outbacks{83}
Quasars{77}
Voyagers{82}
Total-400
Answer:
(A)81/399
Step-by-step explanation:
The probability that the Principal selects a voyager on the first try is:
82/400
Since another student is to be selected, the total population has reduced by 1 and the number of voyagers likewise has been reduced by 1.
Therefore:
Probability that another voyager is selected on the second try =
81/399
The correct option is A.
Answer:
41/200 B
Step-by-step explanation:
The student never gets taken away from the count so.
first pull probability is.. 82/400 second is... 82/400 simplify by dividing by 2. Equals 41/200
PLZ HELP MEH!! it would mean a lot! :) thx
Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?
-15m = -4m
-7m - 8 = m - 4
-3m - 8 = 4 - m
m - 4 = -7m - 8
-8 - 7m = -4 + m
-8 - 3m = 4 - m
Step-by-step explanation:
-2m - 5m - 8 = 3 - 7 + m
Solving like terms
-7m - 8 = - 4 + m
Rearranging
-7m - 8 = m - 4
ZA=
Round your answer to the nearest hundredth.
B
9
?
С
3
A
Answer:
∠A ≈ 71.57
Step-by-step explanation:
You use inverse tangent since it gives you the opposite and adjacent sides: [tex]tan^-1[/tex]
[tex]tan^-1(9/3)[/tex]
≈ 71.565
Round to nearest hundredth:
≈ 71.57
A circular table top has a radius of 3 feet. Enter the area in square feet or the table top. Round your answer
Answer:
28.26 square feet
Step-by-step explanation:
A=πr²
A=(3.14)(3)²=28.26 square feet
Find the sum of the geometric series 3+12+48+...+12,288
Answer:
I think that you need to add obvoiusly.
12351 Thats what I got. But Im not sure if its correct. I hope his helps
Step-by-step explanation:
Answer:
16383
Step-by-step explanation:
12288+3072+767+192+48+12+3 =
please help me quickly !!
Answer:
A ... [tex]\frac{3}{4} (\frac{4}{3})x=-6 (\frac{4}{3})[/tex]
Step-by-step explanation:
Multiplying 4/3 on both sides gets x by itself
In a study done in Miami's economically disadvantaged community, it was determined that 38 out of 62 children who attended preschool needed social services later in life compared to 49 out 61 children who did not attend preschool. Test the claim that the proportion of children who need social services later in life is greater amongst the children who did not attend preschool compare to the ones who did attend preschool. Use a 0.05 level of significance.
Answer:
Step-by-step explanation:
This is a test of 2 population proportions. Let 1 and 2 be the subscript for the children who attended preschool and need social services later in life and children who did not attend preschool and need social services later in life. The population proportion for the children who attended preschool and children who did not attend preschool would be p1 and p2 respectively.
p1 - p2 = difference in the proportion of proportion of the children who attended preschool and children who did not attend preschool .
The null hypothesis is
H0 : p1 = p2
p1 - p2 = 0
The alternative hypothesis is
Ha : p1 < p2
p1 - p2 < 0
it is a left tailed test
Sample proportion = x/n
Where
x represents number of success(number of complaints)
n represents number of samples
For children who attended preschool,
x1 = 38
n1 = 62
p1 = 38/62 = 0.61
For children who did not attend preschool,
x2 = 49
n2 = 61
p2 = 49/61 = 0.8
The pooled proportion, pc is
pc = (x1 + x2)/(n1 + n2)
pc = (38 + 49)/(62 + 61) = 0.71
1 - pc = 1 - 0.71 = 0.29
z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)
z = (0.61 - 0.8)/√(0.71)(0.29)(1/62 + 1/61) = - 0.19/0.08183139728
z = - 2.32
Since it is a left tailed test, we would determine the probability for the area below the z score from the normal distribution table. Therefore,
p = 0.01
Since alpha, 0.05 > than the p value, 0.01, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the the proportion of children who need social services later in life is greater amongst the children who did not attend preschool compare to the ones who did attend preschool.
A quadrilateral is circumscribed around a circle. The sum of the lengths of two of its opposite sides is 15 cm. Find the perimeter of the quadrilateral.
Answer:
The perimeter of the quadrilateral is 30 cm.
Step-by-step explanation:
To circumscribe implies drawing a required figure around a given figure, while to inscribe means drawing a required figure inside a given figure. From the question, the quadrilateral is circumscribed around the circle.
And given that the sum of the lengths of its two opposite sides is 15 cm.
The perimeter of a figure is the sum of the length of the sides of the figure. For this quadrilateral, the sum of opposite sides are equal.Thus;
Perimeter of the quadrilateral = 2(l+b)
= (l + b) + (l + b)
= 15 + 15
= 30
The perimeter of the quadrilateral is 30 cm.
Shantanu bought more apples than bananas, and he bought more bananas than cantaloupes. Let a represent the number of apples Shantanu bought, let b represent the number of bananas, and let c represent the number of cantaloupes. Let's compare the expressions b+c and a. Which statement is correct?
Answer:
There is not enough information to tell
Step-by-step explanation:
We are given that:
a>b
b>c
Therefore:
a>c
However, we are not given enough information to draw a relationship between b+c and a.
In order to better understand this situation, try applying values. Let a=4, b=2, and c=1.
In this case, a > b+c. However if a = 9, b=8 and c=7, then a < b+c.
In both stipulated cases, the given conditions are met, but no conclusion can be reached regarding the relationship between b+c and a.
Can somebody help me on this one?
Answer:
I pretty sure the answer is Nervous
nervous, because it sends signals to your brain and it’s basically the main thing that makes you move.
for example, when the oven is hot you can feel the heat and notice how you don’t touch it, that’s because your brain knows that if you touch the oven you’re going to burn yourself and your brain stops you from touching the surface of the oven.
Can some one help me plz with step by step
x^2 + x - 42
Answer:
x = 6 or x = -7
Step-by-step explanation:
Solve for x over the real numbers:
x^2 + x - 42 = 0
The left hand side factors into a product with two terms:
(x - 6) (x + 7) = 0
Split into two equations:
x - 6 = 0 or x + 7 = 0
Add 6 to both sides:
x = 6 or x + 7 = 0
Subtract 7 from both sides:
Answer: x = 6 or x = -7
18 = -4x -9 + 3 resolver
Answer:
The answer is X=-4 hope this helps.
Answer:
Hope it helps! Mark as brainlist.
Which is greater or less then 2/3 Or 1 3/4
Answer:
2/3 < 1 3/4
Step-by-step explanation:
2/3 is less than 1 3/4
2/3 as a decimal is 0.6666667
1 3/4 as a decimal is 1.75
So, 1.75 is more than 0.6666667
What is the best next step in the constructed of a line that passes through point C and is parallel to AB? (Assume that the arc drawn with the compass placed at point A was the result of the last step performed.)
Answer:
B
Step-by-step explanation:
using the same compass setting, place the point of the compass at C and draw an arc that intersects ĀB
B. using the same compass setting, place the point of the compass at C and draw an arc that intersects ĀB
Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.
So, the next step should be using the same compass setting, place the point of the compass at C and draw an arc that intersects ĀB.
Therefore the correct option is C.
Learn more:https://brainly.com/question/9018125
The table shows the height in feet, y, of a pebble dropped from a tall bridge after x seconds.
Which descriptions are true of the function shown in the table? Check all that apply.
quadratic
linear
rational
y = –16x + 150
y = –16x2 + 150
y = + 150
nvm . jus got it wrong and it's A and E
Answer:
The answer is A & E
Step-by-step explanation:
quadratic
y=-16x^2 + 150
Answer: A and E
Step-by-step explanation:
edge 2023
Quadrilateral EFGH is inscribed in a circle. If m∠F = 114° and m∠G = 78° then which of the following is the measure of ∠H?
Answer:
m∠H=66°
Step-by-step explanation:
Since Quadrilateral EFGH is inscribed in a circle, it is a Cyclic quadrilateral.
Theorem: Opposite Angles of a Cyclic Quadrilateral are Supplementary.
Angles F and H are opposite angles of a cyclic quadrilateral and by the theorem above:
m∠F+m∠H=180 degrees
114° +m∠H=180°
m∠H=180° - 114°
m∠H=66°
Solve the following equation 3x-1=2x -2/3
Answer:
1/3
Step-by-step explanation:
3x-1 = 2x -2/3
Collect like terms.
3x -2x = 1 - 2/3
x=1/3
HELPZZZZ PLEZZZZZZZ
The height of a pyramid is doubled, but its length and width are cut in half. What is true about the volume of the new pyramid?
A) The new pyramid has a volume that is One-fourth the volume of the original pyramid.
B) The new pyramid has a volume that is One-half the volume of the original pyramid.
C) The new pyramid has the same volume as the volume of the original pyramid.
D) The new pyramid has a volume that is 2 times the volume of the original pyramid.
It's only one answer!!!
Answer:it is B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
I got it correct
What is 3x10^7 x 8x10^4 in standard form
Answer:
They are already in standard form.
Step-by-step explanation:
Which Postulate/Theorem below would prove that the triangles shown below are congruent?
a. SSS
b. SAS
c. AAS
d. ASA
Answer:
Correct answer is D. ASA
Step-by-step explanation:
Let us first define ASA congruence rule:
2 triangles are called congruent according to ASA congruence rule if 2 angles of the triangle and the corresponding side between these two angles are equal to each other.
In the question figure, we can figure out following conclusions from Triangles [tex]\triangle SRT\text{ and }\triangle WXY[/tex] respectively:
[tex]\angle TRS = \angle YXW[/tex]Side RS = Side WX[tex]\angle TSR = \angle YWX[/tex]As per the definition of option d) ASA congruence, the triangles are congruent.
Answer:
D. ASAStep-by-step explanation:
Divide ( 4x2 - 24x + 35 ) / ( 2x - 5 )
Answer:
the closest i got is [tex]\frac{43-24x}{2x-5}[/tex]
Step-by-step explanation:
How many solutions does the equation 8x-4=10 have ? PLEASE HELP QUICK
Answer:
one solution
Step-by-step explanation:
8x-4=10
Add 4 to each side
8x - 4+4 = 10+4
8x = 12
Divide by 8
8x/8 = 12/8x
x = 3/2
Answer:
one solution
Step-by-step explanation:
[tex]8x - 4 = 10 \\ 8x = 10 + 4 \\ 8x = 14 \\ \frac{8x}{8} = \frac{14}{8} \\ x = \frac{7}{4} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Determine the intercepts of the line
Answer:
x-intercept (-7,0)
y-intercept (0,2)
Step-by-step explanation:
Answer:
x-intercept (-7 , 0)
y-intercept (2 , 0)
x intercept is where on the x - aces a point is sitting on on the line
-------------------------- <--- this one is x
y intercept is where on the y- aces a point is sitting on the line
║ <---- this one is y