The expression for the area of the base of Prism is x2 – 2x – 9
The volume of a rectangular prism is this
Volume = Area x Height
Substituting the given expressions
x3 + 2x2 - 17x - 36 = Area x (x + 4)
Area = (x3 + 2x2 - 17x - 36) / (x + 4)
Now, let's use synthetic division
-4 | 1 2 -17 -36
---- __-4___8___36
1 -2 -9 0
The expression for the area is
Area = x2 - 2x - 9
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Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west at 20 mi/h. At what rate is the distance between the cars increasing two hours later
Rate is the distance between the cars increasing two hours later is 52 miles/hr
Let x(t) be distance of first car from starting point at time t
Let y(t) be distance of second car from starting point at time t
Let s(t) be distance between the two cars at time t. We need to evaluate ds/dt at time t = 2.
We know x2(t) + y2(t) = s2(t). Therefore 2x * dx/dt + 2y * dy/dt = 2s * ds/dt. The 2s cancel.
At t=2 hours, x = 96 miles. and y = 40 miles.
We will need the distance between the cars at t=2:
s(2) = √x(2)2 + y(2)2 = √96 2 + 40 2 = √10816 = 104.
Now fill in x * dx/dt + y * dy/dt = s * ds/dt at time t = 3 and solve for ds/dt:
96 * 48 + 40 * 20 = 104 * ds/dt
ds/dt = 5408/104 = 52 miles/hr
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A researcher gets a list of all 500 members of the National Association of Social Work in Yourtown that she wants to include in her study. She only has the funding and time to survey 50 members. She takes her list of members, randomly selects a starting point, and then selects every tenth name from the list to be included in her sample. In this example, the sampling interval is:
In this example, the sampling interval is 10.
A researcher gets a list of all 500 members of the National Association of Social Work in Yourtown that she wants to include in her study. She only has the funding and time to survey 50 members. She takes her list of members, randomly selects a starting point, and then selects every tenth name from the list to be included in her sample.
In this example, the sampling interval is 10.
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Determine the vertex of the quadratic relation y=2(x+2)(x-6).
Answer:
V = (2,-32)
Step-by-step explanation:
Hello!
The vertex of a quadratic lies on the Axis of Symmetry (AOS). The axis of symmetry is exactly in the middle of the roots of the Quadratic. We can solve for the AOS by finding the average of the two roots.
Rootsy = 2(x + 2)(x - 6)0 = 2(x + 2)(x - 6)0 = (x + 2)(x - 6)0 = x + 2: x = -20 = x - 6: x = 6The two roots of the quadratic are 6 and -2.
Solve for the AOS[tex]AOS = \frac{r_1 + r_2}{2}[/tex][tex]AOS = \frac{6-2}{2}[/tex][tex]AOS = \frac42[/tex][tex]AOS = 2[/tex]The Axis of symmetry of the quadratic is 2.
VertexSince the vertex lies on the AOS, we know the x-value of the vertex. We can solve for the y-value by plugging in the value of the AOS in the equation.
Find the Vertex
y = 2(x + 2)(x - 6)y = 2(2 + 2)(2 - 6)y = 2(4)(-4)y = 2(-16)y = -32The Vertex of the quadratic is at (2,-32).
Pat won the lottery!! She won 23 million dollars. Of course she had to pay the income tax of 33%. She decides to take the rest in monthly payments for twenty years. How much money will
Pat get each month?
Answer:
$64,208.33
Step-by-step explanation:
100% - 33% = 67%
Since she pays 33% in taxes, she will only get 67% of the $23 million.
1 year = 12 months
20 years = 20 × 12 months = 240 months
There are 240 months in 20 years.
monthly amount = 67% of $23 million / 240
monthly amount = 0.67 × $23,000,000 / 240
monthly amount = $64,208.33
1-secA+tanA/1+secA+TanA = secA+tanA-1/secA+tanA+1
It has been proven that the trigonometric Identity (1 - secA + tanA)/(1 + secA + TanA) is equal to; (secA + tanA - 1)/(secA + tanA + 1)
How to prove trigonometric Identities?
We want to prove that;
(1 - secA + tanA)/(1 + secA + TanA) = (secA + tanA - 1)/(secA + tanA + 1)
We know from trigonometric identities that;
(secA)² – (tanA)² = 1 ----(1)
Also, from algebra we know that;
a² - b² = (a + b)(a - b)
The numerator of LHS of the original given Identity is:
1 - sec A - tan A
Using equation 1, we can say that;
(secA)² – (tanA)² - (sec A + tan A)
⇒ (sec A + tan A)(sec A - tan A) - (sec A - tan A)
This can be factorized to get;
(sec A - tan A)(sec A + tan A - 1)
Similarly, the denominator can be expressed as;
(sec A - tan A)(sec A + tan A + 1)
Thus, combining the numerator and denominator together gives us:
[(sec A - tan A)(sec A + tan A - 1)]/[(sec A - tan A)(sec A + tan A + 1)]
⇒ (secA + tanA - 1)/(secA + tanA + 1)
That expression is equal to the Right hand side and as such the Trigonometric Identity is proved.
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what does the Symbol z- stands
two fifth grade classes raised money for their local animal shelters. there are 20 students in class a each student raised 12 there are 26 students in class b each student in class b rasied 1.5 times as much as each student in class a
The amount the first charity got is $10.
The amount the second charity got is $20.
How much did each charity get?The first step is to determine the amount raised by the second fifth grade class: 1.5 x $12 = $18
The total amount raised by the two classes : $18 + $12 = 30
Let x represent the amount gotten by the first charity
Amount gotten by the second charity : 2x
2x + x = $30
3x = $30
x = $30 / 3
x = $10
Amount gotten by the second charity : 2(10) = $20
Two fifth grade classes raised money for their local animal shelters. there are 20 students in class a each student raised $12. there are 26 students in class b each student in class b raised 1.5 times as much as each student in class a. The money raised went to two charity. One charity received two times as much as the other. How much money did each charity receive? Show your work and explain your answer.
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Solve the system of equations using elimination: -8x-4y=4 and -5x-y=-11.
The solutions to the given system of equations are x = 4 and y = -9
Simultaneous linear equationsFrom the question, we are to determine the solutions to the given system of equations
The given system of equations are
-8x-4y=4 --------- (1)
-5x-y=-11 --------- (2)
Multiply equation (2) by 4
4 ×[-5x-y=-11 ]
-20x -4y = -44 -------- (3)
Now, subtract equation (3) from equation (1)
-8x -4y = 4 --------- (1)
-(-20x -4y = -44) -------- (3)
12x = 48
x = 48/12
x = 4
Substitute the value of x into equation (2)
-5x -y = -11
-5(4) -y = -11
-20 -y = -11
-y = -11 + 20
-y = 9
∴ y = -9
Hence, the solutions to the given system of equations are x = 4 and y = -9
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The inequality are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Inequality expressionsInequality are expressions not separated by an equal sign. Given the inequality expression below;
–3(2x – 5) < 5(2 – x)
Expand
-6x + 15 < 10 - 5x
Collect the like terms
-6x + 5x < 10 - 15
-x < -5
x > 5
Hence the correct representations of the inequality are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
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The planetary boundary layer (PBL) is the lowest layer of the troposphere; its characteristics are influenced by contact with the ground. Wind speed, temperature, and moisture in the PBL all affect weather patterns around the globe. A random sample of days was obtained and the height of the PBL (in meters) above the Great Basin Desert was measured using weather radar. Assume the underlying distribution of PBL heights is normal.
Height(m)
1 673 2 664 3 906 4 956 5 751 6 752 7 654
8 610 9 816 10 667 11 690 12 657 13 920 14 741 15 646 16 682 17 715
18 618 a. Find a 95% confidence interval for the true mean height of the PBL above the Great Basin Desert. b. Is there any evidence to suggest that the true mean height of the PBL above the Great Basin Desert is different from 700 m? There is_____to suggest that the mean height is different from 700 m. The confidence interval_____the value 700 so it is_____as the true mean height of the PBL.
The confidence interval for the true mean height of the PBL above the Great Basin Desert is (651.48,748.52) and there is any sufficient evidence that the true mean is different from 700 m .
Given Heights in meters: 673,664,906,956,751,752,654,610,816,667,690,657,920,741,646,682,715,618 and confidence level of 95%.
We have to show the evidence that the true mean height is different from 700 m.
We have to first make hypothesis.
[tex]H_{0}:[/tex]μ=700
[tex]H_{1}[/tex]:μ≠700
We have to first find the population standard deviation.
σ=[tex]\sqrt{(x-x bar)^{2}/n-1 }[/tex]
=[tex]\sqrt{187375.1/17}[/tex]
=104.98
Z=(X-μ)/σ
=(700-728.78)/104.98 (μ=728.78 is calculated in figure)
=-0.2741
p value of -0.2741 =0.39358
0.39358
0.39358<0.90
so we reject the null hypothesis.
Which means that the true mean is different from 700m.
Confidence level=X±z*s/[tex]\sqrt{n}[/tex]
Upper level=700 +1.96*104.98/[tex]\sqrt{18}[/tex]
=700+48.52
=748.52.
Lower level=700-1.96*104.98[tex]\sqrt{18}[/tex]
=700-48.52
=651.48
Hence the confidence interval is (651.48,748.52).
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1. take away five from twelve times f. 2. one-half of the sum of k and six 3.x squared minus the sum of 5 4.the sum of the product of a and b, and three times c 5.twenty-four times the product of x and y, plus g.
The expressions formed are,
12f -5(k+6)/2x²-x+5ab+3c24xy+gFormation of expressions in 1, 2 and 3:
In 1, twelve times f is, 12f
Taking away 5, it becomes (12f-5)
In 2, sum of k and 6 is, (k+6)
One-half of the above quantity is, (k+6)/2
In 3, sum of 5 with x is, (x+5)
Now, x squared minus the above expression indicates (x²-x+5)
Formation of expressions in 4 and 5:
In 4, product of a and b, is ab and 3 times c is 3c
Sum of the expressions evaluated in the previous statement = ab+3c
In 5, 24 times the product of x and y is, 24xy
Adding, g in the above computed expression, we get, 24xy+g
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What is the smallest positive integer that has a square root that is greater than 10?
The smallest positive integer that has a square root that is greater than 10 is 101
How to determine the integer?Let the integer be represented by n
The square root is greater than 10.
So, we have:
[tex]\sqrt n > 10[/tex]
Square both sides
n > 100
The above means that the integer is greater than 100.
The smallest integer greater than 100 is 101
Hence, the smallest positive integer that has a square root that is greater than 10 is 101
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Need help (problem and directions in the image):
Triangle ABC is congruent to triangle CDE using the side - angle - side congruence theorem. The sink hole is 52.2 ft and the Perimeter of ABC is 172.2 ft
What are congruent triangles?Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent.
In the image shown:
AC = CE, BC = ED and they have the same angle (opposite angles are congruent).
Hence:
Triangle ABC is congruent to triangle CDE using the side - angle - side congruence theorem.
AB = DE = 52.2 ft
Perimeter of ABC = AB + BC + AC = 50 + 70 + 52.2 = 172.2 ft
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Consider the relation given by the graph below.
a) Is the relation a function? Why or why not?
b) Determine the domain and range of the graph.
(a) The relation is a function because each value of x maps onto only one value of y.
(b) Domain is [tex](-\infty, 3][/tex], range is [tex][-1, \infty)[/tex].
Help ON PLATO
Please I need help w more stuff too
Answer:
find the graph where y is 3 less than x in value
Step-by-step explanation:
the answer explains it if you showed us the graphs we would be able to answer it for you
can someone help me ?
Answer:
∠ C = 26°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180° , that is
∠ A + ∠ B + ∠ C = 180°
120° + 34° + ∠ C = 180°
154° + ∠ C = 180° ( subtract 154° from both sides )
∠ C = 26°
A budweiser delivery truck in west texas has driven 1,386 miles in 4 days. he leaves the distributor and stops at 24 stores during this period. between stops the driver averages ___ miles. do not count the driving back to the distributor.
Using proportions, it is found that between stops the driver averages 57.75 miles.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In 1,386 miles, the driver had 24 stops, hence the number of miles per stop is found as follows:
1386/24 = 57.75 miles.
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Erin had 555555 stuffed bears. she took out her favorite 777 bears and then equally divided the other bears among her 333 sisters. erin's youngest sister, su, already had 151515 stuffed bears. how many stuffed bears does su have now?
The number of stuffed bears with Su=153181
What is the number of stuffed bears Su has?Total number of bears Erin has=555555
The number of bears Erin took out=777
Remaining number of bears with Erin=555555-777
=554778
Now, these remaining stuffed bears are to be divided equally among 333 sisters.
So, each sister gets [tex]\frac{554778}{333}[/tex]=[tex]1666[/tex] stuffed bears.
To find the number of stuffed bears Su has, find the sum of her share of stuffed bears and the number of stuffed bears she already had.
Number of stuffed bears Su already has=151515
Total number of bears she has at present=151515+1666
=153181
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3. Find the point of intersection of the graphs for each system. a) x - y = 1 and 3x - y = -1
Answer:
the point of intersection is (-1 , -2)
Step-by-step explanation:
[tex]\begin{cases}x-y=1&(1)\\ 3x-y=-1&(2)\end{cases}[/tex]
(2) - (1) ⇒ (3x - y) - (x - y) = (-1) - 1
⇒ 3x - y - x + y = -2
⇒ 3x - x = -2
⇒ 2x = -2
⇒ x = -1
……………………………
Now ,we can determine the value of y
by substituting x by its value -1 in the first equation (1) :
(1) x - y = 1 ⇒-1 - y = 1 ⇒ -y = 2 ⇒ y = -2
========================
Conclusion:
x = -1
y = -2
Then ,the point of intersection of the graphs is (-1 , -2)
Hello !
[tex]\begin{cases} x - y &=1 \\ 3x-y &= - 1 \end{cases} \\\Leftrightarrow \begin{cases} x =y + 1 \\ 3x-y = - 1 \: \: \: \: \: (a)\end{cases} [/tex]
We replace x by y+1 in (a) :
[tex]3(y + 1) - y = - 1 \\ 3y + 3 - y = - 1 \\ 2y = - 4 \\ y = \frac{ - 4}{2} = - 2[/tex]
Now we replace x by -1 in the first equation.
[tex]x + 2 = 1 \\ x = -1[/tex]
The point of intersection is (-1;-2).
Have a nice day
Name two monomials with a quotient of 12
Victor borrowed money at 5.25 percent simple annual interest. At the end of the year, the interest on the loan is $255.94. What was the amount of the loan?
Identity the construction that the figure represents
The construction is the construction of the Perpendicular bisector.
How to illustrate the information?The steps for the construction of perpendicular bisectors are as follows:
Open the compass more than half of the distance between A and B, and scribe arcs of the same radius centered at A and B.
Call the two points where these two arcs meet X and Y. Draw the line between X and Y.
So, the point where this line meets the line segment; M is called the mid point and the line XY is the perpendicular bisector of the line AB.
The figure is a construction of perpendicular bisector.
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Find the sum of the geometric sequence. (7 points) 1 divided by 3, 2 divided by 3, 4 divided by 3, 8 divided by 3, 16 divided by 3
The sum of the geometric sequence is 31/3
How to determine the sum?The sequence is given as:
1/3, 2/3, 4/3, 8/3, 16/3
The sum of the sequence is;
Sum = 1/3+ 2/3+ 4/3+ 8/3+ 16/3
Evaluate
Sum = 31/3
Hence, the sum of the geometric sequence is 31/3
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how many centigram are equal to 9.95 milligram
Answer:
0.995 centigram
Step-by-step explanation:
divide the mass value by 10
pls help asap..............
The ratio of the side lengths of the triangle will be 3:10 or 3/10.
How to illustrate the ratio?From the information given, the first triangle has sides 6 and 9 while the large triangle has sides 20 and 30.
Based on this, the ratio will be:
= 6/20 = 9/20
= 3/10 = 3/10
Therefore, the ratio is 3:10.
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True or False. Both distributions are bell-shaped and symmetric but where the peak falls on the number line is determined by the mean.
Both distributions are bell-shaped and symmetric but where the peak falls on the number line is determined by the mean.
The given statement is false.
A bell curve is a graph depicting the ordinary distribution, which has a shape harking back to a bell. The top of the curve suggests the mean, mode, and median of the records accrued.
The everyday distribution is a bell-fashioned and symmetrical distribution this is used to calculate the opportunity. in the everyday distribution, the mathematics means, mode, and median are usually the same, and the normal distribution is likewise called the Gaussian distribution.
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1. Which statement about this figure is true?
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
A group of high school students were surveyed about which type of movie they enjoy watching most. The results are shown in the two-way
relative frequency table below.
Female
Male
Total
Comedy
64
54
118
Drama
16
6
22
Action
20
22
42
Sci-Fi
6
27.2% 57.4% 5.7%
12
18
Use the information provided in the table to match each description with the correct percentage of students.
Total
106
94
200
18.9%
6.4%
percentage of female students who prefer sci-fi
45.8% 33.3%
percentage of students who prefer comedies that are male
percentage of male students who prefer dramas
percentage of students who prefer action movies that are female
47.6%
Answer:
a) 5.7%
b) 45.8%
c) 6.4%
d) 47.6%
Step-by-step explanation:
remember, we find percentage as:
specific / total
(ex. if we have 2 dogs and 2 cats, and we want to find what percentage of total animals are dogs, we divide 2/4 to get 0.5, or 50%)
percentage of female students who prefer sci-fi
here, we know we have 106 female students (total: 106)
and we have 6 of those students who prefer sci-fi (specific: 6)
6 / 106 = 0.05660..
which we can round to: 0.0566
So, the first percentage is 5.66%
(5.7%)
percentage of students who prefer comedies that are male
we have 118 students who prefer comedies (total: 118)
and 54 of those students that are male (specific: 54)
54 / 118 = 0.4576...
which we can round to 0.4576
So, the second percentage is 45.76%
(45.8%)
percentage of male students who prefer dramas
we have 94 male students (total: 94)
and 6 who prefer dramas (specific: 6)
6 / 94 = 0.0638298...
which we can round to 0.0638
So, the third percentage is 6.38%
(6.4%)
percentage of students who prefer action movies that are female
we have 42 students who prefer action movies (total: 42)
and 20 of those who are female (specific: 20)
20 / 42 = 0.47619..
which we can round to 0.4762
So, the fourth percentage is 47.62%
(47.6%)
hope this helps! have a lovely day :)
In a function why berries directly with X in the constant of variation is two which table could represent the function
The correct option is (D)
What is a function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
the complete question is attached below
As, per the data given we can say that
the variation of quantity is 2.
So, the equation can be
y=2x
This equation defined by part (4) of the question.
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What is the center of MN given M(3, -1) and N(7,-5)
Answer:
(5, -3)
Step-by-step explanation:
So the center of the two points, or a line can be defined using the equation: [tex]midpoint=(\frac{x_2+x_1}{2}, \frac{y_2+y_1}{2})[/tex]. So using the two points you gave, you simply plug the values in to get
[tex]midpoint=(\frac{3+7}{2}, \frac{-1+(-5)}{2})\\[/tex]
Add numerators:
[tex]midpoint=(\frac{10}{2}, \frac{-6}{2})[/tex]
Simplify fraction:
[tex]midpoint=(5, -3)[/tex]