Please help me. Thank you...
9514 1404 393
Answer:
V = (x)(10-2x)² . . . . factored form
V = 4x³ -40x² +100x . . . . standard form
Step-by-step explanation:
A square with corners cut out has no volume. It is a plane figure.
__
We presume you are interested in the volume of the open-top box obtained by folding up each "ear" of the cut figure. The length of each side of its square bottom is 10-2x. The depth of the box is x. So, the volume is ...
V = LWH = (10-2x)(10-2x)(x)
V = x(10 -2x)²
_____
The graph shows the volume is a maximum when x = 1 2/3 cm.
Find x
27 degrees and 32 degrees will give brainlist
Answer:
x = 121°
Step-by-step explanation:
If you add up all the angles of a triangle, you get 180°.
So you must add up all the angles.
[tex]27+32+x=180\\\\59+x=180[/tex]
Next you subtract 59 on both sides.
[tex]x=121[/tex]
x should be 121°.
If you would like to check your answer, you can add up 27, 32, and 121. If it all equals to 180, then your answer is correct.
The table below shows the relationship between the number of gallons of fremaining in a truck and the number of hours the truck has been driven.
Driving a Truck
Time Driven (h) 0 2.5 5 7.5 10
Fuel (gal)
175
125 100
200
150
Which of the following best represents the rate of change for the number of gallons of fuel remaining with respect to the number of hours the truck has been driven?
-200 gal/h
-10 gal/h
0-1 gal/h
O-to galh
Answer:
-10 gal/h
Step-by-step explanation:
Rate of change for the number of gallons of fuel remaining and the number of hours the truck has driven is (-10) gallons per hour.
Option (2) will be be the answer.
Average rate of change of a function is given by the expression,
Average rate of change = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
From the table given,
Two points are (0, 200) and (2.5, 175),
Average rate of change = [tex]\frac{175-200}{2.5-0}[/tex]
= [tex]-\frac{25}{2.5}[/tex]
= -10 gallons per hour
Therefore, average rate of change for the given table will be Option 2. (-10) gallons per hour.
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What is the combined length of all the buttons longer than 1 inch
Answer:
Where is the problem to solve?
Step-by-step explanation:
Find the slope of the line through each pair of points
(1, -19), (19, -2)
For a submarine cable, the range of signalling is governed by the function
f(r) = r^2 ln(1/r)
where 0
Find df/dr.
Answer:
[tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]
Step-by-step explanation:
Explanation
Given function f(r) = r² log r ....(i)
Apply derivatives formula
[tex]\frac{d}{dx} UV = U^{l} V + V^{l} U[/tex]
[tex]\frac{d}{dx}x^{n} = nx^{n-1}[/tex]
[tex]\frac{d}{dx}log x = \frac{1}{x}[/tex]
Differentiating equation (i) with respective to 'r' , we get
[tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )\frac{d}{dr} (\frac{1}{r } )+ log(\frac{1}{r} ) 2 r[/tex]
[tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )(\frac{-1}{r^{2} } )+ log(\frac{1}{r} ) 2 r[/tex]
Final answer:-
[tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]
Mia is making pickles. She uses 3/4 cup of salt when she has 9 pounds of cucumbers. How much salt will Mia use when she has 3 pounds of cucumbers?
Answer:
1/4 cup of salt. .........
a rectangle with a length of 3x and a width of x+1 has the same perimeter as a rectangle with a width of x and a length of 2x-2. find the actual dimensions of each figure.
Answer:
8
Step-by-step explanation:
value
Is the following equation proportional or non-proportional?
y = -4x - 3
Answer:
proportional
Step-by-step explanation:
Why do you think most people who have lived
on our planet would have been suspicious of negative
numbers?
Answer:
I do not know
Step-by-step explanation:
I guess because negative represents going down :/
Francis heard that a car stereo system was on sale for 30% off. If the original price was $62.40, what was the sale price of the stereo?
Answer:
89.14
Step-by-step explanation:
Determine the input value for which the statement
f(x) = g(x) is true.
From the graph, the input value is approximately .
f(x) = 3 and g(x) = x – 2
3 = x – 2
5 = x
The x-value at which the two functions’ values are equal is .
Answer:
The x-value at which the two functions' values are equal is 5.
Step-by-step explanation:
Let [tex]f(x) = 3[/tex] and [tex]g(x) = x-2[/tex], if [tex]f(x) = g(x)[/tex], then:
[tex]x - 2 = 3[/tex]
[tex]x = 3+2[/tex]
[tex]x = 5[/tex]
The x-value at which the two functions' values are equal is 5.
Which set of ordered pairs represents a function?
{(-3,1), (8, -2), (0,0), (8,6)}
{(-1,-8),(-8, –3), (-8,-7), (4,1)}
{(-3,-8),(-3,-7), (2,-7), (6,-4)}
{(1,-1),(-3,-8), (8, -1),(0,5)}
B.
explanation:
whhdhdhdhehehgaahakkabdvdvhabs
Please help me with this Its kind of frustrating
Answer:
you have too see what makes 36, 42 ,48 and 27
Step-by-step explanation:
What is the slope of the line below?
(4,5)
(-2,2)
Answer:
1/2 or one half
Step-by-step explanation:
Answer:
The slope is 1/2.
Step-by-step explanation:
To find the slope of a line, divide yB - yA by xB - xA.
(yB - yA)/(xB - xA)
(2 - 5)/ (-2 - 4)
-3/-6
Dividing two negatives make a positive.
0.5
The slope is 0.5, or 1/2.
Witch fraction is equivalent to 2/3
Answer: 4/6, 6/9, 8/12, 10/15, 12/18, 14/21
Step-by-step explanation:
These r just a few hope this helps ;)
A baker has 2 2/3 cups of flour for her recipe, but she only has a 1/3 cup scoop. How many scoops will she need for the recipe?
Need help if u do I will put brainliest
Find the Value of “Y”.
Answer:
26
Step-by-step explanation:
7x - 28 = 5x + 12 and 5x + 12 + y = 180
The angle (7y - 28) and angle y are supplementary angles which means their sum is 180°
7y - 28 + y = 180 add like terms
8y - 28 = 180 add 28 to both sides
8y = 208 divide both sides by 8
y = 26
please help ASAP pleassssseeeee
Answer:
4 miles.
Step-by-step explanation:
We know that Molly travels 20 miles in 5 hours, so we can divide by 5 to find out how many miles she travels in 1.
20/5 = 4/1
Therefore, Molly travels 4 miles per hour.
Answer: 4 miles in one hour
Step-by-step explanation:
If molly goes 20 miles in 5 hours divide 20 miles by 5 hours and you get 4 miles in 1 hour
-7(2-3x) help solve please
Answer:
-14+21x
Step-by-step explanation:
Distrubute
-7 times 2= -14
-7 times 3x= -21x
Answer:
The answer is -14 + 21x
Step-by-step explanation:
Distribute -7 to 2 and -3x
-7 × 2 = -14
-7 × - 3x = 21x
= -14 + 21x
Find the slope of the line.
Answer:
79
Step-by-step explanation:
it is 556
4x-4y+4z=8
9x+3y+z=6
16x+4y+z=2
9514 1404 393
Answer:
(x, y, z) = (-1, 3, 6)
Step-by-step explanation:
The augmented matrix for the system is ...
[tex]\left[\begin{array}{ccc|c}4&-4&4&8\\9&3&1&6\\16&4&1&2\end{array}\right][/tex]
Your graphing or scientific calculator can tell you the solution to this system is ...
(x, y, z) = (-1, 3, 6)
__
If you want to solve this by hand, it can work well to divide the first equation by 4 to get ...
x -y +z = 2
This can be subtracted from the other two equations to eliminate z.
(9x +3y +z) -(x -y +z) = (6) -(2) ⇒ 8x +4y = 4
(16x +4y +z) -(x -y +z) = (2) -(2) ⇒ 15x +5y = 0
These two equations can be reduced to standard form:
2x +y = 13x +y = 0Subtracting the first equation from the second, we have ...
(3x +y) -(2x +y) = (0) -(1) ⇒ x = -1
Substituting into the first gives y:
2(-1) +y = 1
y = 3 . . . . . . . add 2
Then we can find z from the reduced first equation above:
z = 2 -x +y = 2 -(-1) +3 = 6
Then the solution is (x, y, z) = (-1, 3, 6).
Find the scale factor of PQRS to JKLM and the values of w, x, and y.
The scale factor of PQRS to JKLM is 4/5 and the values of w, x and y are 20, 12.5 and 20 respectively.
What is Scale Drawing?A scale drawing is a drawing made by enlarging or reducing the size of the original object.
The factor by which the drawing is enlarged or reduced is called the scale factor.
Given two quadrilaterals PQRS and JKLM.
Since the shape is similar, the angles are equal and thus are similar figures.
The corresponding sides of two similar figures are proportional.
Scale factor of PQRS to JKLM = QR / KL = 12 / 15 = 4/5
Using the proportional rule for similar figures,
KL / QR = LM /RS = MJ / SP = JK / PQ
15 / 12 = x / 10 = y / 16 = 25 / w
Scale factor = 15/12 = 5/4
Consider 15 / 12 = x / 10.
12x = 150
x = 12.5
Consider 15 / 12 = y / 16
12y = 15 × 16
y = 20
Consider 15 / 12 = 25 / w
15w = 12 × 25
w = 20
Hence the option d is the correct answer.
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PLEASE HELP
The vertex of this parabola is at (-2, 1). Which of the following could be its
equation?
Answer:
A. [tex]x = 4\cdot (y-1)^{2}-2[/tex]
Step-by-step explanation:
From the image attached below statement we understand that a parabola with a horizontal axis of symmetry and whose vertex is centered at [tex]V(x,y) = (h,k)[/tex] is defined by the following expression:
[tex]x-h = C\cdot (y-k)^{2}[/tex] (1)
Where [tex]C[/tex] is the parabola factor, when [tex]C > 0[/tex], the parabola is oriented in the +x direction, otherwise is oriented in the -x direction. Hence, we may conclude that equation of the parabola is of the form:
[tex]x+2 = C\cdot (y-1)^{2}[/tex]
[tex]x = C\cdot (y-1)^{2}-2[/tex], where [tex]C > 0[/tex]
The correct answer is A.
Answer:
A
Step-by-step explanation:
Hopefully this helps
A ball is launched into the sky at 54.4 feet per second from a 268.8 meter tall building. The equation for the ball’s height, h, at time t seconds is h = -3.2t^2 + 54.4t + 268.8. When will the ball strike the ground?
Answer:
7.41
Step-by-step explanation:
Vertical component:
S = 268.8
U = 0
V =?
A = 9.8
T=?
S = ut + 0.5at^2. u = 0
268.8 = 0.5x9. 8xt^2
T = 7.41 seconds
Answer:
4.42 seconds is the correct answer
Step-by-step explanation:
Bo, Ryan and Zachary went for a walk. They walked 1/4 miles from school to Bocas House. Then they walked 4/6 miles From Paul’s house to the park. What is the total distance with the boys walked?
Answer:
Total distance walked by boys = [tex]\frac{11}{12}[/tex] miles
Step-by-step explanation:
Given that:
Distance walked from school to Bocas house = 1/4 miles
Distance walked from Paul's house to the park = 4/6 miles
Total distance walked = [tex]\frac{1}{4}+\frac{4}{6}[/tex]
Total distance walked = [tex]\frac{3+8}{12}[/tex]
Total distance walked = [tex]\frac{11}{12}[/tex] miles
Hence,
Total distance walked by boys = [tex]\frac{11}{12}[/tex] miles
A roofer leaned a 16-foot ladder against a house. If the base of the ladder is 5 feet from the house, how high up the house does the ladder reach?
Answer:
15.20feet
Step-by-step explanation:
Length of the ladder = 16foot (hypotenuse)
BAse of the ladder from the house = 5feet (adjacent)
height of the house = x (opposite)
Using the pythagoras theorem
hyp^2 = opp^2 + adj^2
16^2 = 5^2 + opp^2
256 = 25 + opp^2
opp^2 = 256-25
opp^2 = 231
opp =√231
opp = 15.20
Hence the house is 15.20feet high up the house
Simplify 6(5x-1)-3(2x-10)
Answer:
30x-6-6x-30
30x-30x-6-6
0-12
-12
Suppose that populations of men and women have the following summary statistics for their heights (in
centimeters):
Mean
Standard deviation
Men
HM = 172
M = 7.2
Women
Uw = 162
ow = 5.4
Both distributions are approximately normal. Suppose we randomly select a man and a woman from each
population, and calculate the difference between their heights. We can assume that their heights are
independent
Find the probability that the woman is taller than the man
You may round your answer to two decimal places
IN
P woman taller
Answer:
.13
Step-by-step explanation:
172-162 = 10
We can find the standard deviation of D by adding the variances of the heights and taking the square root:
σ
D
2
σ
D
2
σ
D
=σ
M
2
+σ
W
2
=7.2
2
+5.4
2
square root of 81
=9
Representing probability with area
When D= M-W =0, their heights are equal. When the man is taller, D is positive, and when the woman is taller, D is negative. Since we know the distribution of the difference D is normally distributed, the probability that the woman is taller than the man can be found by calculating the shaded area below D=0, in the corresponding normal distribution:
A standard normal curve is plotted on a horizontal axis representing D, that goes from negative 17 to 37. The mean, or mu sub D, = 10. The standard deviations, or sigma sub D = 9. The value 0 is marked. The area under the curve to the left of 0 is shaded, representing the probability that the woman is taller. The area to the right represents the probability that the man is taller.
normalcdf:
lower bound: −9999
upper bound: 0
μ=10
σ=9
Using subtraction of normal variables, it is found that there is a 0.1335 = 13.35% probability that the woman is taller than the man.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. When two measures are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the variances.In this problem:
Men have mean weight of 172 cm, women of 162 cm, hence, for the distribution of the differences, the mean is [tex]\mu = 162 - 172 = -10[/tex].The standard deviation is the square root of the sum of the variances, hence [tex]\sigma = \sqrt{7.2^2 + 5.4^2} = 9[/tex]The probability of the women being taller is P(X > 0), which is 1 subtracted by the p-value of Z when X = 0.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - (-10)}{9}[/tex]
[tex]Z = 1.11[/tex]
[tex]Z = 1.11[/tex] has a p-value of 0.8665.
1 - 0.8665 = 0.1335
0.1335 = 13.35% probability that the woman is taller than the man.
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