Answer:
Step-by-step explanation:
x²+4xy+4y²-8x-16y-20=(x+2y)²-8(x+2y)-20
put x+y=t
t²-8t-20=t²-10t+2t-20=t(t-10)+2(t-10)=(t-10)(t+2)
substitute the value of t
x²-4xy+4y²-8x-16y-20=(x+2y-10)(x+2y+2)
i don't know what else you want.
Complete the table for the given rule.
Rule: y=\dfrac{x}{2}y=
2
x
y, equals, start fraction, x, divided by, 2, end fraction
xxx yyy
111
2.52.52, point, 5
3.53.53, point, 5
Using the proportional relationship, it is found that:
When x = 1, y = 0.5.When x = 2.5, y = 1.25.When x = 3.5, y = y = 1.75.What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
[tex]y = kx[/tex]
In which k is the constant of proportionality.
In this problem, the relationship is given by:
[tex]y = \frac{x}{2}[/tex]
Hence, when x = 1:
[tex]y = \frac{1}{2} = 0.5[/tex]
When x = 2.5:
[tex]y = \frac{2.5}{2} = 1.25[/tex]
When x = 3.5:
[tex]y = \frac{3.5}{2} = 1.75[/tex]
You can learn more about proportional relationships at https://brainly.com/question/10424180
Answer:
x y
___
12 4
3 1
18 6
Step-by-step explanation:
solve for x: 3x²-243
3x²–243=0 —> 3 (x²–81) = 0 —>
x²–81=0 —> (x-9)(x+9)=0
x-9=0 —> x=9
x+9=0 —> x=–9
I hope I helped you^_^
Please help me! I am trying to complete this question!
Answer:
131.25 in ^2
Step-by-step explanation:
Find the area of the rectangle on the left
A = l*w
A = 11.75 * 6 = 70.5 in ^2
Now find the area of the rectangle on the right
The length is 9 and the height is 11.75 - 5 = 6.75
A = 9 * 6.75
A = 60.75 in ^2
Add the areas together
70.5+60.75 = 131.25 in ^2
Answer:131.25
Step-by-step explanation:
11 3/4 x 6 = 70.5 (area of first rectangle)
11 3/4 - 5 = 6.75 (to find the height of the other figure)
6.75 x 9 = 60.75 (area of 2 figure)
60.75 + 70.5 = 131.25
To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use the alphaequals0.10 level of significance. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
Height of Father Height of Son
72.4 77.5
70.6 74.1
73.1 75.6
69.9 71.7
69.4 70.5
69.4 69.9
68.1 68.2
68.9 68.2
70.5 69.3
69.4 67.7
69.5 67
67.2 63.7
70.4 65.5
Which conditions must be met by the sample for this test? Select all that apply.
A. The sample size is no more than 5% of the population size.
B. The differences are normally distributed or the sample size is large.
C. The sample size must be large.
D. The sampling method results in a dependent sample.
E. The sampling method results in an independent sample.
Write the hypotheses for the test. Upper
H 0 :
H 1 :
Calculate the test statistic. t 0=?
(Round to two decimal places as needed.)
Calculate the P-value. P-value=?
(Round to three decimal places as needed.) Should the null hypothesis be rejected?
▼ Do not reject or Reject Upper H 0 because the P-value is ▼ less than or greater than the level of significance. There ▼ is or is not sufficient evidence to conclude that sons ▼ are the same height or are shorter than or are taller than or are not the same height as their fathers at the 0.10 level of significance. Click to select your answer(s).
Answer:
1) B. The differences are normally distributed or the sample size is large
C. The sample size mus be large
E. The sampling method results in an independent sample
2) The null hypothesis H₀: [tex]\bar x_1[/tex] = [tex]\bar x_2[/tex]
The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] < [tex]\bar x_2[/tex]
Test statistic, t = -0.00693
p- value = 0.498
Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers at 0.10 level of significance
Step-by-step explanation:
1) B. The differences are normally distributed or the sample size is large
C. The sample size mus be large
E. The sampling method results in an independent sample
2) The null hypothesis H₀: [tex]\bar x_1[/tex] = [tex]\bar x_2[/tex]
The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] < [tex]\bar x_2[/tex]
The test statistic for t test is;
[tex]t=\dfrac{(\bar{x}_1-\bar{x}_2)}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}[/tex]
The mean
Height of Father, h₁, Height of Son h₂
72.4, 77.5
70.6, 74.1
73.1, 75.6
69.9, 71.7
69.4, 70.5
69.4, 69.9
68.1, 68.2
68.9, 68.2
70.5, 69.3
69.4, 67.7
69.5, 67
67.2, 63.7
70.4, 65.5
[tex]\bar x_1[/tex] = 69.6
s₁ = 1.58
[tex]\bar x_2[/tex] = 69.9
s₂ = 3.97
n₁ = 13
n₂ = 13
[tex]t=\dfrac{(69.908-69.915)}{\sqrt{\dfrac{3.97^{2}}{13}-\dfrac{1.58^{2} }{13}}}[/tex]
(We reversed the values in the square root of the denominator therefore, the sign reversal)
t = -0.00693
p- value = 0.498 by graphing calculator function
P-value > α Therefore, we do not reject the null hypothesis
Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers at 0.10 lvel of significance
THIS IS THE HARDEST WORK ON EART SOMEONE HELP ME
Answer:
a) 2 h 45 min
b) 2 h 50 min
c) 2 h 20 min
d) 3 h 20 min
Step-by-step explanation:
Answer:
a) hours: 9 hours 15 minutes
minutes: 555
b) hours: 9hours 10 minutes
minutes: 550
c) hours: 2hours 20 minutes
minutes: 140
d) hours: 3 hours 20 minutes
minutes: 200
Step-by-step explanation:
While sailing, Jacob is 150 feet from a lighthouse. The angle of elevation from his feet on the boat (at sea level) to the top of the lighthouse is 48°
What can you conclude about the height of the lighthouse, with respect to Jacob's distance from the lighthouse? Explain your answer.
Answer:
The height of the lighthouse is approximately 166.6 feet.
Step-by-step explanation:
Let the height of the lighthouse be represented by s, then;
Tan 48° = (opposite) ÷ (adjacent)
Tan 48° = s ÷ 150
⇒ s = 150 × Tan 48°
= 150 × 1.1106
= 166.59
s ≅ 166.6 feet
Therefore, the height of the lighthouse is approximately 166.6 feet.
Answer:
The height of the lighthouse is approximately 42.
Step-by-step explanation:
This situation forms a right triangle so the angles would be 90 and 48
90+48+x=180
138+x=180
x=180-138
x=42
water needs to be removed from an underground chamber before work can commence. when the water was at a depth of 3m five suction pipes were used and emptied the chamber in 4 hours. if the water is now at a dpeth of 5 m and you want to empty the chamber in 10 hours time how many pipes need to be used
Answer:
8 pipes
Step-by-step explanation:
given that when height increases also time increases and automatically no of pipes will be decreased Mathematically;
h∝t•1/p
remove proportionality symbol and we will get
h=kt
p
make k as subject and we'll get
k=hp
t
find the value ok k
k=3×5
4
k=15
4
k=3.75
from h=kt. make p as subject and the answer should be
p=kt. find p
h
p=3.75×10
5
p=37.5
5
p=7.5 or 8
hence 8 pipes should be used
Find the nth term of the arithmetic
sequence - 1,2,5, ....
A. 3n - 2
B. -2n + 1
C. 2n + 2
D. 3n - 4
Answer:
3n -4
Step-by-step explanation:
We are adding 3 each time
-1+3 =2
2+3 = 5
The formula for an arithmetic sequence is
an = a1+d(n-1) where a1 is the first term and d is the common difference
an = -1+3(n-1)
= -1 +3n -3
= 3n -4
Find the difference of functions s and r shown
below.
r(x) = -x2 + 3x
s(x) = 2x + 1
(s - r)(x) =
Answer:
[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle r(x) = -x^2 + 3x \text{ and } s(x) = 2x + 1[/tex]
And we want to find:
[tex]\displaystyle (s-r)(x)[/tex]
This is equivalent to:
[tex]\displaystyle (s-r)(x) = s(x) - r(x)[/tex]
Substitute and simplify:
[tex]\displaystyle \begin{aligned}(s-r)(x) & = s(x) - r(x) \\ \\ & = (2x+1)-(-x^2+3x) \\ \\ & = (2x+1)+(x^2-3x) \\ \\ & = x^2 +(2x-3x) + 1 \\ \\ & = x^2 - x + 1 \end{aligned}[/tex]
In conclusion:
[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]
On a survey, 6 students reported how many minutes it takes them to travel to school. Here are their responses.
Find the mean travel time for these students.
4, 11, 14, 9, 4, 8
Giải các bất phương trình và biểu diễn tập nghiệm trên trục số
(X-1)(x+2)>(x-1)(x-1) +3
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Answer:
A. 314 in^3
Step-by-step explanation:
To solve the volume of a cone:
[tex]v = \pi r^2\frac{h}{3}[/tex]
Manipulate the radius and height of the cone, setting different values for each. Record the radius, height, and exact volume of the cone (in terms of π). The first one has been done for you. Also calculate the decimal value of the volume, and verify that it matches the volume displayed by the tool. (You might see some discrepancies in the tool due to rounding of decimals.)
Answer:
The decimal value of the volume already given= 1885.2 unit³
For radius 11 unit height 12 unit
Volume= 484π unit³
Volume= 1520.73 unit ³
For radius 4 unit height 6 unit
Volume= 32π unit³
Volume= 100.544 unit³
For radius 20 unit height 15 unit
Volume= 2000π unit³
Volume= 6284 unit³
Step-by-step explanation:
The decimal value of the volume already given= 600π
The decimal value of the volume already given= 600*3.142
The decimal value of the volume already given= 1885.2 unit³
For radius 11 unit height 12 unit
Volume= πr²h/3
Volume= 11²*12/3 *π
Volume= 484π unit³
Volume= 1520.73 unit ³
For radius 4 unit height 6 unit
Volume = πr²h/3
Volume= 4²*6/3(π)
Volume= 32π unit³
Volume= 100.544 unit³
For radius 20 unit height 15 unit
Volume= πr²h/3
Volume= 20²*15/3(π)
Volume= 2000π unit³
Volume= 6284 unit³
Here's the right answer.
As above, let
$$f(x) = 3\cdot\frac{x^4+x^3+x^2+1}{x^2+x-2}.$$Give a polynomial $g(x)$ so that $f(x) + g(x)$ has a horizontal asymptote of $y=0$ as $x$ approaches positive infinity.
Answer:
Hello,
Step-by-step explanation:
[tex]\dfrac{f(x)}{3} =\dfrac{x^4+x^3+x^2+1}{(x-1)(x+2)} \\\\=\dfrac{(x^2+3)(x-1)(x+2)-3x+7}{(x-1)(x+2)} \\=x^2+3-\dfrac{3x-7}{(x-1)(x+2)} \\\\=x^2+3-\dfrac{3}{x-1} +\dfrac{1}{(x-1)(x-2)} \\\\\dfrac{f(x)}{3}-\dfrac{3x^2+9}{3} =-\dfrac{3}{x-1} +\dfrac{1}{(x-1)(x-2)} \\\\\\ \lim_{x \to +\infty} (\dfrac{f(x)}{3}-\dfrac{3x^2+9}{3} )\\\\=0+0=0\\\\\\P(x)=-x^2-3[/tex]
Answer:
[tex]g(x)=-3x^2-9[/tex]
Explanation:
[tex]3\frac{x^4+x^3+x^2+1}{x^2+x-2}[/tex]
+[tex]\frac{p(x)(x^2+x-2)}{x^2+x-2}[/tex]
We need p(x) need to be a degree 2 polynomial so the numerator of the second fraction is degree 4. Our goal is to cancel the terms of the first fraction's numerator that are of degree 2 or higher.
So let p(x)=ax^2+bx+c.
[tex]3\frac{x^4+x^3+x^2+1}{x^2+x-2}[/tex]
+[tex]\frac{p(x)(x^2+x-2)}{x^2+x-2}[/tex]
Plug in our p:
[tex]3\frac{x^4+x^3+x^2+1}{x^2+x-2}[/tex]
+[tex]\frac{(ax^2+bx+c)(x^2+x-2)}{x^2+x-2}[/tex]
Take a break to multiply the factors of our second fraction's numerator.
Multiply:
[tex](ax^2+bx+c)(x^2+x-2)[/tex]
=[tex]ax^4+ax^3-2ax^2[/tex]
+[tex]bx^3+bx^2-2bx[/tex]
+[tex]cx^2+cx-2c[/tex]
=[tex]ax^4+(a+b)x^3+(-2a+b+c)x^2+(-2b+c)-2c[/tex]
Let's go back to the problem:
[tex]3\frac{x^4+x^3+x^2+1}{x^2+x-2}[/tex]
+[tex]\frac{ax^4+(a+b)x^3+(-2a+b+c)x^2+(-2b+c)x-2c}{x^2+x-2}[/tex]
Let's distribute that 3:
[tex]\frac{3x^4+3x^3+2x^2+3}{x^2+x-2}[/tex]
+[tex]\frac{ax^4+(a+b)x^3+(-2a+b+c)x^2+(-2b+c)x-2c}{x^2+x-2}[/tex
So this forces [tex]a=-3[/tex].
Next we have [tex]a+b=-3[/tex]. Based on previous statement this forces [tex]b=0[/tex].
Next we have [tex]-2a+b+c=-3[/tex]. With [tex]b=0[/tex] and [tex]a=-3[/tex], this gives [tex]6+0+c=-3[/tex].
So [tex]c=-9[tex].
Next we have the x term which we don't care about zeroing out, but we have [tex]-2b+c[/tex] which equals [tex]-2(0)+-9=-9[/tex].
Lastly, [tex]-2c=-2(-9)=18[/tex].
This makes [tex]p(x)=-3x^2-9[/tex].
This implies [tex]g(x)\frac{(-3x^2-9)(x^2+x-2)}{x^2+x-2}[/tex] or simplified [tex]g(x)=-3x^2-9[/tex]
Which inequality represents the following situation ; times 5 less than a number is no more than 272
0
A 3(x - 5) = 27
B. {x-5527
C 3 (5 – ) 2 27
D.(x - 5) 27
Answer:
A.
Step-by-step explanation:
from what the question states im assuming it was 3 times 5 less than a number is no more than 272.
if we look at a it fits it perfectly.
3 times 5 less than a number is no more than 272 =
3(x-5) = 272.
Hope it helps <3
The width of a rectangle is 5x -9.5 feet and the length is 9.5x + 10 feet. Find the perimeter of the
rectangle
Answer:
Perimeter of the rectangle is 29x + 1 feet
Step-by-step explanation:
Length of the rectangle = 9.5x + 10 feet
Width of the rectangle = 5x - 9.5 feet
perimeter of rectangle = 2 ( length + width )
perimeter = 2 { (9.5x + 10) + (5x-9.5) }
perimeter = 2 ( 9.5x + 5x + 10 - 9.5 )
perimeter = 2 (14.5x + 0.5)
perimeter =29x + 1 feet
Please help will give 5 stars with 1 thanks and 15 points
Answer:
mean is adding up all the numbers.
range means the difference between the Lowest and highest value.
Step-by-step explanation:
when we add the answer is 240.6.
divide it to 12..do the final answer is 20.05
range is 25.4_16.3
9.1
Answer:
Mean: 20.05
Range: 9.1
Step-by-step explanation:
To find the mean in this problem, first you add all the following numbers together then subtract by the quantity.
20.1 + 19.6 + 18.0 + 17.8 + 25.2 + 18.7 + 21.9 + 16.3 + 25.4 + 20.5 +17.8 + 19.3
= 240.6
Now, divide by the quantity which is 12 since there's 12 numbers.
240.6 divided by 12 = 20.05.
The mean is 20.05.
To find the range in the problem, you must subtract the smallest value from the largest value.
In this case, 16.3 is the smallest value and 25.4 is the largest.
25.4 - 16.3 = 9.1
9.1 is the range.
Hope this helps you!
the adult human brain represents 2% of total body weight. write this percentage as a decimal.
Answer:
2% = 0.02Step-by-step explanation:
[tex]2\%=2\cdot\frac1{100}=\frac2{100}=0.02[/tex]
Answer:
2% as a decimal is 0.02
Step-by-step explanation:
Find the distance d dd between z 1 = ( 6 + 2 i ) z 1 =(6+2i)z, start subscript, 1, end subscript, equals, left parenthesis, 6, plus, 2, i, right parenthesis and z 2 = ( 6 + 10 i ) z 2 =(6+10i)z, start subscript, 2, end subscript, equals, left parenthesis, 6, plus, 10, i, right parenthesis. Express your answer in exact terms and simplify, if needed. D =
Answer:
8
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = z₁(6, 2) and (x₂, y₂ ) = z₂(6, 10)
d = [tex]\sqrt{(6-6)^2+(10-2)^2}[/tex]
= [tex]\sqrt{0^2+8^2}[/tex]
= [tex]\sqrt{64}[/tex] = 8
The growth of a population of mountain lions can be described by the function f(x) = 500(1.015)^x, where x is the number of years after the first census. How do the mathematical domain and range compare to the reasonable domain and range? Check all that apply. Thank you!
Answer:
B E
Step-by-step explanation:
Answer:
B. The mathematical domain is the set of real numbers, while the reasonable domain only includes real numbers greater than or equal to 0.
E. The mathematical range has a minimum value greater than 0, while the reasonable range is limited to whole numbers and has a minimum value greater than or equal to 500.
Step-by-step explanation:
Edge 2021
Gretchen made a paper cone to hold a gift for a friend. The paper cone was 11 inches high and had a radius of 5 inches. Find the volume of the paper cone to the nearest tenth. Use 3.14 for π.
Answer:
91.67inch^3
Step-by-step explanation:
The volume of a cone can be calculated using below formula
V= 1/3 π.r^2h
Where h= height of the cone
r= radius of the cone
V= volume of the cone
Given :
height= 11inches
radius= 5inches
π= 3.14
Then substitute into the formula we have
V= 1/3 × 3.14× 5^2 ×11
V= 91.67inch^3
Therefore volume of the cone is 91.67inch^3
Please answer this question now
Answer:
113 degrees
Step-by-step explanation:
Measure of arc ADCB = 58+108+60 = 226 degrees
Measure of angle B = 226/2 = 113 degrees
Answer:50
Step-by-step explanation:
Divisibility by 10 of number 7236
7236 is NOT divisible by 10
Step-by-step explanation:
any number that ends with zero is divisible by 10 but 7236 dosent end with zero so 7236 isnt divisible by 10
What is the scale factor of abc to def
Answer:
[tex]\large \boxed{\mathrm{B. \ 6}}[/tex]
Step-by-step explanation:
Length AB is similar to length DE.
Scale factor = DE/AB
Scale factor = 12/2
Scale factor = 6
The required Scale factor would be 6 to transform triangle ΔABC to triangle ΔDEF which is the correct option (B).
What is a scale image?Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.
Length AB is similar to length DE.
Here triangle ΔABC is dilated to form triangle ΔDEF
Length of the side DE = 12
Length of the side AB = 2
As we know scale factor is the ratio of sides in the original image and the image after dilation.
Scale factor = DE/AB
Substitute the values of the length of the side DE and AB,
Scale factor = 12/2
Apply the division operation, and we get
Scale factor = 6
Therefore, the required Scale factor would be 6 to transform triangle ΔABC to triangle ΔDEF.
Learn more about the Scale images here:
brainly.com/question/13194929
#SPJ5
4(3−y)=6−2(1−3y) Enter your answer in the box. y=
Answer:
12-4y=4-12y
8y=-8
y=-1
Answer:
y= 0.8
Step-by-step explanation
4(3−y) = 6−2(1−3y)
12−4y = 6−2(1−3y)
12−4y = 6−2+6y
12−4y = 4+6y
12 = 4+10y
8 = 10y
0.8 = y
This is correct i just took the test. I hope this helps :)
Morgan jogged 51.2 kilometers one week. Karen jogged 53.52 kilometers the same week. How many more kilometers did Karen jog that week than Morgan?
Answer:
Karen jogged 2.32 kilometers more than Morgan.
Step-by-step explanation:
Calculate the difference:
53.52 - 51.2 = 2.32
Answer:
2.32 km
Step-by-step explanation:
Take the amount that Karen jogged and subtract the amount that Morgan jogged
53.52 - 51.2
2.32
What is the numerical coefficient of the linear term of the quadratic equation 3x2 − 9 =0?
Answer:
0
Step-by-step explanation:
The numerical coefficient of the linear term of the quadratic equation is 0 because there is no linear term, and 0 times any number or term is 0, or nothing.
Solve y=x2-5 for x.
What is the set of x-intercepts of this graphed function ? A.{-3,-1} B. {-3,-1,3} C. {-3,3} D.{-3}
Answer:
second option
Step-by-step explanation:
The x- intercepts are the values on the x- axis where the graph crosses.
These are
x = - 3, x = - 1 and x = 3
Algebra!! In the triangle to the below, the measure of ∠A equals the measure of ∠B. Find the value of x.
Answer:
x=21
Step-by-step explanation:
45=2x+3
Subtract 3 from both sides of the equation.
42=2x
Divide 2 from both sides of the equation.
21=x
Hope this helps!
Answer:
x=21°
Step-by-step explanation:
Angle A = Angle B
Angle A = 45°
2x+3 =45°
To work out what x is, you would have to do inverse operations.
45-3=42°
2x=42°
42÷2=21° (We divide by 2 because, in algebra, whenever a number is next to a letter, it means times, so then we have to do the opposite and divide).
So, x=21°
Hope this helps :)