The values of a and b are a = -3 and b = 42. The solutions for x can be written as:
x = -3 - √42
x = -3 + √42
To solve the quadratic equation 2x² + 12x = 66 by completing the square, we need to follow these steps:
Step 1: Move the constant term to the right side:
2x² + 12x - 66 = 0
Step 2: Divide the equation by the leading coefficient (2):
x² + 6x - 33 = 0
Step 3: To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation:
x² + 6x + (6/2)² = 33 + (6/2)²
x² + 6x + 9 = 33 + 9
x² + 6x + 9 = 42
Step 4: Rewrite the left side as a perfect square:
(x + 3)² = 42
Step 5: Take the square root of both sides:
√(x + 3)² = ±√42
x + 3 = ±√42
Step 6: Solve for x:
x = -3 ± √42.
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a. Find the value of x
below
#The x side is same with 80° so
11x + 3 = 80°
11x = 80 - 3
11x = 77
x = 7
Answer : 73x-4y=11
3x+2y=2
please help, I need to find what the answer is for x and y
Answer:
I have attached a picture of me solving the equation.
Now you must be wondering how I got the answer, well first simplify the expression in y = mx + b. Then graph it on demos. Do the same thing for the other expression. Pick any point that lies on the line. That is your solution to the equation.
The green line is the expression of 3x - 4y = 11. I simplify the equation in y = mx + b giving me y = 3/4x - 11/4.
The orange line is the expression of 3x + 2y = 2. I simplify the equation in y = mx + b giving me y = -3/2x + 1.
Hope this helps, thank you !!
Please help!!! (Look at picture)
Answer:
20,000 17000 17200.
Step-by-step explanation:
That's your answer.
Subtract Write your answer in simplest form. 11/12 - 3/6
Answer:
5/12 cannot simplify more further
Step-by-step explanation:
11/12 - 6/12 = 5/12
Answer:
5/12
Step-by-step explanation:
hope this helps have a nice day
If a cross section of a rectangular prism is cut perpendicular to the base, what would be the shape of the resulting cross section
Answer:
Step-by-step explanation:
We are given a rectangular prism as shown.
Part A: After slicing the rectangular prism with a plane parallel to the base, we see that the cross-sectional region will be similar to a rectangle.
Thus, the cross-sectional region is a RECTANGLE.
Answer:
triangle
Step-by-step explanation:
Write an equation for the line in slope-intercept
form.
(Use integers or fractions for any numbers in the
equation.)
find the area of EFG
Answer:
12ft
Step-by-step explanation:
Find the length of the missing side. Round answers to the nearest tenth it
necessary. *
8
8
the sum of 2 integers are -396, if one is 64, find the other
PLEASE HELP!!!
Find the common difference for the arithmetic sequence. -55, -50, -45, -40.....
Answer:
5
Step-by-step explanation:
Just grap any two consecutive terms in the sequence. lets say -55 and -50
-50-(-55) = 5
you can check this by picking two other terms
Simplify -3a + 5b - c given a = 2, b = -1 and c= 10
Answer:
-21
Step-by-step explanation:
-3a + 5b - c
-3(2)+5(-1)-(10)=-21
Find the area of the triangle.
4ft
ift
8ft
[? ] ft2
help me PLZ LUV YOU ALL
Answer:
1) AB = 10cm
2) 70 degrees
3) 12m
4) 10m
5) 32 degrees
6) 9 + 9 = 18m
A girl is 6 years younger than her brother. The
product of their ages is 135. Find their ages.
=============================================================
Work Shown:
x = brother's age, which is some positive whole number
x-6 = sister's age, since she is 6 years younger than her brother
The product is the result of multiplication, so we multiply x and (x-6) to get 135
x*(x-6) = 135
x^2-6x = 135
x^2-6x-135 = 0
Use the quadratic formula to solve from here
We plug in a = 1, b = -6, c = -135
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-6)\pm\sqrt{(-6)^2-4(1)(-135)}}{2(1)}\\\\x = \frac{6\pm\sqrt{576}}{2}\\\\x = \frac{6\pm24}{2}\\\\x = \frac{6+24}{2}\ \text{ or } \ x = \frac{6-24}{2}\\\\x = \frac{30}{2}\ \text{ or } \ x = \frac{-18}{2}\\\\x = 15\ \text{ or } \ x = -9\\\\[/tex]
x represents the brother's age, in years. So x must be positive.
Since x must be positive, this means we rule out x = -9
The value x = 15 is the only practical solution.
If x = 15, then x-6 = 15-6 = 9
The brother is 15 years old and the sister is 9 years old.
The product of their ages is 15*9 = 135, which confirms the answers.
Just as you are about to estimate a regression (due tomorrow), massive sunspots cause magnetic interference that ruins all electrically powered machines (e.g., computers). Instead of giving up and flunking, you decide to calculate estimates from your data (on per capita income in thousands of U.S. dollars as a function of the percent of the labor force in agriculture in 10 developed countries) using methods like those used in Section 2.1 (Yi = B0 + B1Xi + Ei) without using a computer. Your data are:Country A B C D E F G H I JPer Capita Income 6 8 8 7 7 12 9 8 9 10% in Agriculture 9 10 8 7 10 4 5 5 6 7a.) Calculate Beta-hat zero and Beta-hat one.b.) Calculate R2(r-squared) and R`2 (adjusted r-squared).c.) If the percent of the labor force in agriculture in another developed country was 8 percent, what level of per capita income (in thousands of U.S. dollars) would you guess that country had?
Answer:
A) Beta-hat one = -0.547
Beta-hat zero = 12.2837
b) attached
C) y = $7.904
Step-by-step explanation:
hello attached below is the detailed solution and the table
A) Calculate Beta-hat Zero and Beta-hat one
Beta-hat one :
∑ ( xi - x ) (yi - y ) / ∑ (xi - x )^2
= -22.4 / 40.9 = -0.547
Beta-hat zero :
Y - Beta-hat one * X
= 8.4 - (-0.547 )(7.1 ) = 12.2837
B) Calculate R^2 and R^2
attached below
C) using Regression equalia to determine the level of per capita income
y = 12.28 - 0.547 * x
where x = 8
hence Y = $7.904
According to an AP-Ipsos poll (June 15, 2005), 42% of 1001 randomly selected adult Americans made plans in May 2005 based on a weather report that turned out to be wrong.
a. Construct and interpret a 99% confidence interval for the proportion of Americans who made plans in May 2005 based on an incorrect weather report.
b. Do you think it is reasonable to generalize this estimate to other months of the year
Answer:
a) The 99% confidence interval for the proportion of Americans who made plans in May 2005 based on an incorrect weather report is (0.3798,0.4602). This means that we are 99% sure that the true population proportion is in this interval.
b) No, since May is a month with a wide range of possible weather.
Step-by-step explanation:
a)
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
42% of 1001 randomly selected adult Americans made plans in May 2005 based on a weather report that turned out to be wrong.
This means that [tex]p = 0.42, n = 1001[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 2.575\sqrt{\frac{0.42*0.58}{1001}} = 0.3798[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 + 2.575\sqrt{\frac{0.42*0.58}{1001}} = 0.4602[/tex]
The 99% confidence interval for the proportion of Americans who made plans in May 2005 based on an incorrect weather report is (0.3798,0.4602). This means that we are 99% sure that the true population proportion is in this interval.
b. Do you think it is reasonable to generalize this estimate to other months of the year
No, since May is a month with a vast number of possible outcomes, as it is in the spring, not being in the winter(cold) or summer(hot), which means that it can be both hot or cold, wet or dry,...
A construction worker drops a hammer while building the Grand Canyon skywalk 4,000ft above the Colorado River. Use the formula t=h−−√4 to find how many seconds it takes for the hammer to reach the river. Round your answer to the nearest tenth of a second.
Answer:
15.8
Step-by-step explanation:
We are asked to find how many seconds it takes for an object to fall from a height of 4,000ft. We will use the given formula, t=h−−√4. Substituting h=4,000, we find
t=4000−−−−√4=15.8
So, the hammer reaches the river after 15.8 seconds.
F(x)=2x^3-3x^2+7 f(-1)=
Answer:
f(x)=6x^2-6x
Step-by-step explanation:
Now select point D, and move it around. You will notice that moves with point D but remains parallel to . Check the box labeled Show Ratios of Intersected Segments to see the ratios AD : DB and AE : EC. What do you notice about the ratios as you move point D?
Answer: The ratios change as the position of D changes, but the two ratios remain equal to each other.
Step-by-step explanation:
Answer:
The ratios change as the position of D changes, but the two ratios remain equal to each other
Step-by-step explanation:
what is dimension of work done?
Answer:
ML2T-2
Step-by-step explanation:
please help it’s due!!!
Answer:
33
Step-by-step explanation:
46/22=46+23/x
46x=22 times 69
46x=1518
x=33
1. What is the LCM of 15 and 100?
a. 400
b. 300
c. 200
d. 100
Answer:
b. 300
i need 20 words this is filler
Which operation should you perform first when evaluating the expression:
3 to the power of 2+2
Answer: the power so ans should be 81
Step-by-step explanation:
what was the main difference between the French and British armies in the French and Indian War
What does decreased mean in math?
Answer:
becoming less or fewer; diminishing. Mathematics. (of a function) having the property that for any two points in the domain such that one is larger than the other, the image of the larger point is less than or equal to the image of the smaller point; nonincreasing.
Step-by-step explanation:
BRAINLIST PLEASE!
Meaning of decreased in math is, get smaller in size, number or quantity.
We have to given that,
To defined decreased mean in math.
We know that,
We use minus sign to denote subtract, decreased by, take away, etc.
For example, Minus sign also means how much is one value more than the other value.
Hence, Meaning of decreased in math is, get smaller in size, number or quantity.
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Keith earns $42.00 in 3 hours. How much would he earn in 10 hours? A. $135.00 B. $140.00 C. $84.00 D. $112.00
Answer:
B.$149.00
Step-by-step explanation:
=$42.00÷3=$14.00
=$14.00×10=$140.00
Im sorry if this not helpfull
Have a nice day
Solve 5x ≥ 25. Graph the solution.
Answer:
Step-by-step explanation:
Alright so we are going to solve
5x ≥ 25 Divide both sides by 5
x≥5
Which statement is an example of the symmetric property of congruence?
A. If AKLM = APQR, then APQR = AKLM.
B. If AKLM = APQR, then APQR - ASTU.
X Х
C. If AKLM = APQR, and APQR - ASTU, then AKLM - ASTU.
D. AKLM = AKLM
Answer:
D.AKLM = AKLM
Step-by-step explanation:
because D.AKLM = AKLM is an example of the symmetric property of congruence
The statement which represents the symmetric property of congruence is given by if ΔKLM ≅ ΔPQR , then ΔPQR ≅ ΔKLM
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be represented as ΔKLM
Let the second triangle be represented as ΔPQR
Now , the measure of sides and angles be congruent
So , ΔKLM ≅ ΔPQR
From the symmetric property of congruence ,
If the first figure is congruent to second figure , the second figure is congruent to first figure
ΔKLM ≅ ΔPQR , then ΔPQR ≅ ΔKLM
Hence , the ΔKLM ≅ ΔPQR and they are congruent triangles
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What is 25% of 60? I need this answer right away
Answer:
15
Step-by-step explanation:
Answer:
2.4
Step-by-step explanation:
60÷25=2.4
Shani has 2 chocolate bas. One has 60% cacao and the other 92% calco
What mass of each bar must she mix to obtain 400g of chocolate
with 72% cacao
Answer:
250 grams of the 60% cocoa bar and 150 grams of the 92% cocoa bar should be used.
Step-by-step explanation:
Given that Shani has 2 chocolate bars, one that had 60% cocoa and the other that had 92% cocoa, to determine what mass of each bar must she mix to obtain 400g of chocolate with 72% cocoa, the following calculation must be performed:
100 x 0.6 + 0 x 0.92 = 60
90 x 0.6 + 10 x 0.92 = 63.2
80 x 0.6 + 20 x 0.92 = 66.4
70 x 0.6 + 30 x 0.92 = 69.6
65 x 0.6 + 35 x 0.92 = 71.2
63 x 0.6 + 37 x 0.92 = 71.84
62.5 x 0.6 + 37.5 x 0.92 = 72
400 x 0.625 = 250
Thus, 250 grams of the 60% cocoa bar and 150 grams of the 92% cocoa bar should be used.