Answer:
62 in
Step-by-step explanation:
the Hypotenuse of a triangle is always longer than the two other sides, 27 + 32 is larger than all but one of the options, 62. Making 62 the answer by process of elimination.
Given that f(x) is a cubic function with zeros at -3, 0, and 7, find an equation for f(x) given that f(-8) = -5.
Answer:
[tex]\huge\boxed{f(x)=\dfrac{1}{120}x^3-\dfrac{1}{30}x^2-\dfrac{7}{40}x}[/tex]
Step-by-step explanation:
[tex]f(x)=a(x+3)(x-0)(x-7)=ax(x+3)(x-7)\\\\=ax\bigg((x)(x)+(x)(-7)+(3)(x)+(3)(-7)\bigg)\\\\=ax(x^2-7x+3x-21)=ax(x^2-4x-21)\\\\=(ax)(x^2)+(ax)(-4x)+(ax)(-21)\\\\=ax^3-4ax^2-21ax\qquad(*)\\\\f(-8)=-5[/tex]
[tex]\text{substitute}\ x=-8\\\\f(-8)=(a)(-8)^3-(4a)(-8)^2-(21)(-8)a=-512a-(4a)(64)+168a\\\\=-512a-256a+168a=-600a\\\\f(-8)=-5\\\\\text{therefore}\\\\-600a=-5\qquad|\text{divide both sides by (-600)}\\\\a=\dfrac{-5}{-600}\\\\a=\dfrac{1}{120}[/tex]
[tex]\text{Substitute to}\ (*):\\\\f(x)=\dfrac{1}{120}x^3-4\cdot\dfrac{1}{120}x^2-21\cdot\dfrac{1}{120}x=\dfrac{1}{120}x^3-\dfrac{1}{30}x^2-\dfrac{7}{40}x[/tex]
Help please
Answer question 2 please
On the list of facts, the second fact says "A quarter of the nuts are walnuts.".
A quarter of 956 is => 239 <= .
If Jaime wants to find 60% of 320, which table should he use?
A 2-column table with 11 rows. Column 1 has entries 10 percent, 10 percent, 10 percent, 10 percent, 10 percent, 10 percent, 10 percent, 10 percent, 10 percent, 10 percent, Total 100 percent. Column 2 has entries blank, blank, blank, blank, blank, blank, blank, blank, blank, blank, Total blank.
A 2-column table with 5 rows. Column 1 has entries 25 percent, 25 percent, 25 percent, 25 percent, Total 100 percent. Column 2 has entries blank, blank, blank, blank, Total blank.
A 2-column table with 4 rows. Column 1 has entries 30 percent, 30 percent, 30 percent, Total 100 percent. Column 2 has entries blank, blank, blank, Total blank.
A 2-column table with 3 rows. Column 1 has entries 50 percent, 50 percent, Total 100 percent. Column 2 has entries blank, blank, Total blank.
Answer: The answer is A. Six 10% and total 100% (I hope ya'll understand what I'm saying)
Answer:
it is A
Step-by-step explanation:
just finished
A contractor uses a scale drawing of an office floor to determine the amount of carpet he needs to buy 1/4 inch = 4.5 feet the width in the scale drawing of the office floor is 6.4 inches what is the actual width of the office floor
A scale drawing is a method of drawing that requires either increasing or decreasing the dimensions of a given object. So then, the actual width of the office floor is: 115.2 feet.
A representative factor is a factor the can be used to either increase or decrease the dimensions of an object. It is sometimes referred to as a scale factor.
In the given question, the scale factor is given as:
[tex]\frac{ 1 }{4}[/tex] inch = 4.5 feet
Given that the width in the scale drawing of the office floor is 6.4 inches, let the actual width be represented by x.
So then;
[tex]\frac{ 1 }{4}[/tex] inch = 4.5 feet
6.4 inches = x
x = [tex]\frac{6.4 *4.5}{\frac{1}{4} }[/tex]
= [tex]\frac{28.8}{0.25}[/tex]
x = 115.2
Therefore, the actual width of the office floor is 115.2 feet.
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Answer:
115.2 /\
Step-by-step explanation: / \
What the person above me said. / \
given the equation 3x-2y=-10, identify the slope and the y-intercept
Answer:
3/2 is the slope and (0,5) is the y-intercept
Step-by-step explanation:
We need slope-intercept form for this question, so we simplify the equation into:
-2y=-10-3x which is just
y=5+3/2x =
y=3/2x+5
When we compare this to y=mx+b, we see that 3/2 is the slope and (0,5) is the y-intercept.
Answer: The slope is [tex]\frac{3}{2}[/tex] and the y-intercept is 5.
Step-by-step explanation:
The equation is 3x - 2y = -10
We need to turn 3x - 2y = -10 into slope intercept form.
y = mx + b → slope-intercept form
m = the slopeb = the y-intercept3x - 2y = -10
-3x -3x
-2y = -3x - 10
Divide the whole equation by -2
y = [tex]\frac{3}{2}[/tex]x + 5
The slope of the equation is [tex]\frac{3}{2}[/tex] and the y-intercept is -2.
How to solve this question? Adding algebraic fractions
Answer:
it should be 2/12 and 9/11
Step-by-step explanation:
answer fully /// /////////////////////
Answer:
Step-by-step explanation:
Yes, but like they say in Vegas, you're trying to make your point the hard way.
8 * (8 - 4) So the distributive property is means remove the brackets.
8*8 - 4*8 What you have done is multiply the numbers on either side of the - sign by 8. It is a good practice NOT to destroy the minus sign just yet.
64 - 32
32 The answer is 32. That's how the distributive property works
With this question only It might be easier to do what is inside the brackets first. That's making your point the easy way.
8*(8-4) = 8* 4 = 32
Select all the statements that are true for △ABC.A. AH is an altitude.
B. IH is a median.
C. JC is a median.
D. The medians and altitudes intersect at the same point.
E. The altitudes intersect outside of the triangle.
The relationships between the two medians and an altitude marked on
ΔABC can be used to determine the true statements.
The true statements are;
A. AH is an altitudeC. JC is a medianReasons:
A median line is a line that extends from the vertex to the midpoint of the
opposite side, bisecting the opposite side.
In the figure, we have;
The median of ΔABC are; JC, and BI
The point of intersection is the point K
The altitude is a perpendicular line from a vertex to the opposite side
known as the base of the triangle.
The given altitude of ΔABC is; AH
Therefore, the statements that are true are;
A. AH is an altitude
C. JC is a median
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A 11 foot ladder is placed against a building. If the base of the ladder is 7 feet away from the building, how far up the building will the ladder reach? Round the answer to the nearest tenth.
Check the picture below.
Emily took an airplane trip. Her plane flew an equal number of miles each hour. Write an equation to represent one way you can find how many miles Emily's plane flew each hour.
Use this to help you:
Air travel time: 12 hours
Destination: 2,184 miles
182.00 miles per hour
y = 182x will be the equation to represent one way you can find how many miles Emily's plane flew each hour.
What is the equation?A formula that expresses the connection between two words on each side of an indication. A calculation with an integer multiple is referred to as an equation. Algebra is widely used in equations. In performing calculations but unsure of the precise amount, algebra is utilized.
The information that is provided is
the air travel time is 12 hours
The destination miles will include 2,184 miles
Assuming the values of x and y
x = number of hours n
y = distance covered
The equation that will be made will be:
y = (2184 / 12)x
y = 182x
Therefore, the equation will be y = 182x.
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Kelly worked on a straight 8 % commission. Her friend worked on a salary of $850 plus a 6% commission. In a particular month, they both sold $21,700 worth of
merchandise
Step 1 of 2: How much did Kelly earn for this month? Follow the problem-solving process and round your answer to the nearest cent, if necessary.
The total amount of money Kelly earned for the month is $1,736
Commission refers to a sum of money paid to a salesperson for every sale that he or she makes. It is usually a percentage of the total sales.Given:
Kelly
Worth of goods sold = $21,700
commission = 8%
Total earned = 8% of $21,700
= 8/100 × 21,700
= 0.08 × 21,700
= $1,736
Approximately, $1,736.00
Therefore, the amount of money Kelly earned for this month is $1,736
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Mr. D math
Find the distance between (12,5) and (3,4) approximated to the 1 decimal place.
select the correct response
0.2
9.3
9.1
9.4
The distance between (12,5) and (3,4) approximated to the 1 decimal place is 9.1.
To find the distance between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we will use the distance formula:
Distance = [tex]\(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)[/tex]
In this case, [tex]\((x_1, y_1) = (12, 5)\)[/tex] and [tex]\((x_2, y_2) = (3, 4)\)[/tex].
Substituting these values:
Distance = [tex]\(\sqrt{(3 - 12)^2 + (4 - 5)^2}\)[/tex]
Distance = [tex]\(\sqrt{(-9)^2 + (-1)^2}\)[/tex]
Distance = [tex]\(\sqrt{81 + 1}\)[/tex]
Distance = [tex]\(\sqrt{82}\)[/tex]
Now, approximate value of [tex]\(\sqrt{82}\)[/tex] to 1 decimal place:
[tex]\(\sqrt{82} \approx 9.1\)[/tex]
So, the correct response is 9.1.
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How do you know if a relationship between two quantities is not proportional
Answer:
Step-by-step explanation:
Recall that a proportional relationship is a relationship between two quantities in which the ratio of one quantity to the other quantity is constant. ... When ratios between quantities are not constant, a relationship may be linear but not proportional and the graph does not pass through the origin.
Plz help me well mark brainliest! Only if correct!.
Answer:
[tex]6(\frac{5}{6}x+\frac{2}{3}) =-9(6)[/tex][tex]5x- -58[/tex][tex]5x+4=-54[/tex]Step-by-step explanation:
Hope this helps!
what is 20% of 30? how would you calculate it? please answer asap
Answer:
Working out 20% of 30
If you are using a calculator, simply enter 20÷100×30 which will give you 6 as the answer.
Step-by-step explanation:
Answer:
6Step-by-step explanation:
what is 20% of 30? how would you calculate it?
30 : 100 * 20 = 6
or
30 * 0.20 = 6
Can someone help me please
Answer:
40 students earned a B on this paper.
40%×80=32 people who chose action as their fav.
Evaluate the triple integral.
E
y dV, where E = {(x, y, z) | 0 ≤ x ≤ 6, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y}
The definition of the set E gives you a natural choice for the limits in the integral:
[tex]\displaystyle \iiint_E y \, dV = \int_0^6 \int_0^x \int_{x-y}^{x+y} y \, dz \, dy \, dx[/tex]
Computing the integral, we get
[tex]\displaystyle \iiint_E y \, dV = \int_0^6 \int_0^x y ((x+y)-(x-y)) \, dy \, dx = 2 \int_0^6 \int_0^x y^2 \, dy \, dx[/tex]
[tex]\displaystyle \iiint_E y \, dV = 2 \int_0^6 \frac13 (x^3 - 0^3) \, dx = \frac23 \int_0^6 x^3 \, dx[/tex]
[tex]\displaystyle \iiint_E y \, dV = \frac23 \cdot \frac14 (6^4 - 0^4) = \boxed{216}[/tex]
The evaluation of the triple integral ∭E y dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y} is 216
What is triple integral?Triple integral integrates the integrand over three dimensions.
Given that:
E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y}
Evaluating the integral:
[tex]I = \int \int \int _E y \: dV[/tex]
[tex]I = \mathlarger{\int_0^6 (\int_0^x (\int_{x-y}^{x+y} y\: dz)dy)dx}\\\\I = \int_0^6 (\int_0^x [yz]_{z=(x-y)}^{z=(x+y)}dy)dx\\\\I = \int_0^6 (\int_0^x y( (x+y) - (x-y)) \: dy)dx\\\\ I = \int_0^6 (\int_0^x y(2y) \: dy)dx\\\\I =2 \int_0^6 \left [\dfrac{y^3}{3}\right ]_{y=0}^{y=x} dx\\\\I = 2 \int_0^6 (x^3/3) dx\\\\I = \dfrac{2}{3} \left[\dfrac{x^4}{4} \right]_{x=0}^{x=6} = \dfrac{2}{3} \times \dfrac{6^4}{4} =216[/tex]
Thus, the evaluation of the triple integral ∭E y dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y} is 216
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The scatter plot shows the relationship between the average number of nightly customers and the number of mouths since a restaurant opened. The equation represents the linear model for this date
y = 5x + 120
what does the number 5 in the equation mean in this context?
A: There were 5 customers per night when the restaurant opened
B: The average number of costumers per night increased by 5 each month
C: The average number of customers per night decreased by 5 each month
D: The restaurant has been open for 5 months
At Arnold's Arcade, a child can buy 21 tokens for $6. At this rate, how many tokens would $20 get someone?
Based on the information given, the number of tokens that will be bought if a child has $20 will be 70.
Since a child can buy 21 tokens for $6, the cost of one token will be:
= $6 / 21 = $0.2857143
Therefore, if a child has $20, the number of tokens that will be gotten will be:
= $20 / $0.2857143
= 70
Therefore, 70 tokens will be bought.
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(X-y^2)(6x-y^2) find the product
what is the equation of the line in the slope-intercept? write your answer in simplest form.
Answer:
y=-6x
Step-by-step explanation:
Slope intercept form is y=mx+b where b is the y intercept and m is the slope. In this particular example, the y intercept is at (0,0), the origin, so b=0. y=mx+0 or just y=mx. Now, to determine the slope, we must look at the graph. It appears the graph intersects the point (-10, 60) as well as the point (0,0). Other than just calculating it quickly in your head, the way to get slope from that is y1-y2/x1-x2. Setting that up, 60-0/-10-0, which is 60/-10, which is equal to -6. Put that into the equation and you get y=-6x
Ella needs to buy 43 party favors that cost $2.75 each. Estimate the total cost by rounding the number of favors to the nearest ten and cost of each favor to the nearest dollar
A. $118.25
B. $120
C.$129
D.$135
Answer:
b.$120
Step-by-step explanation:
Party Favors rounded= 40
Dollars rounded= 3
40x3= 120
Sebastian is 3 years older than twice Amy's age. Sebastian is 33 years old. How old is Amy?
Answer:
15 years old
Step-by-step explanation:
You would have to create a equation. 2x+3=33, 2x=30, x=15.
geomtry plzzzz help 15 points
Step-by-step explanation:
RV = QV but also = PV = 26
because RVQ and RVP are both isoceles triangles.
TR = QR/2 = 24/2 = 12
because T is the middle point of RQ.
A table is on sale for 32% off. The sale price is $459.
What is the regular price?
the regular price is "x", which of course is the 100%, but we also know that $459 is 32% off that, hmmmmm well 100% - 32% = 68%, so $459 is really 68% of "x", because $459 is whatever "x" is minus 32%.
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 459&68 \end{array}\implies \cfrac{x}{459}=\cfrac{100}{68}\implies \cfrac{x}{459}=\cfrac{25}{17} \\\\\\ 17x = 11475\implies x = \cfrac{11475}{17}\implies x = 675[/tex]
có 100 công nhân sản xuất trong một ngày được 1200 đợn vị sản phẩm với tổng chi phí là 2400 USD
Answer:
4 better inbox
Step-by-step explanation:
The table shows the results for spinning the spinner 80 times. What is the relative frequency for the event "spin a 3"?
Answer:
0.267
Step-by-step explanation:
the answer is 0.267
The table shows the results for spinning the spinner 80 times. The relative frequency for the event "spin a 3" is 0.32.
How to find the relative frequency?Relative frequency is the ratio of the considered sub-group's count to the total count. (so its frequency of the considered subgroup relative to the total frequency).
In the problem given,
The table shows the results for spinning the spinner 80 times.
Number of Outcomes of "Spin a 3"=16
Total Number of Trials =50
Therefore,
The relative frequency for the event "spin a 3" = 16/50
= 0.32
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Find the inequality represented by the graph in the picture
(Khan academy)
Answer:
[tex]y < 3x - 4[/tex]
Step-by-step explanation:
We can tell right away, that the line has a positive slope, since it goes upwards and to the right. To find the slope exactly, we will use rise/run. We will count the units from the first given point until we reach the next point.
So we can tell that the slope is 3/1 or just 3.
Also, since the line crosses the y-axis at -4, this will be the y-intercept.
Next, since the line is dotted, we know that the inequality sign will either be the "greater than" sign, or the "lesser than" sign. In this case, since the shaded area is below the line, we will use the "lesser than" sign.
So all together, we have y < 3x - 4.
Hope this helps you :)
Combined, there are Asians, Africans, Europeans, and Americans in a village. The number of Asians exceeds the number of Africans and Europeans by . The difference between the number of Europeans and Americans is . If the number of Africans is doubled, their population exceeds the number of Europeans and Americans by . Determine the number of Asians, Africans, Europeans, and Americans in this village
There are 123 Asians, 25 Africans, 21 Europeans and 8 Americans in the village.
To determine the number of Asians, Africans, Europeans, and Americans in the village, the following calculation must be performed:
A.S + A.F + E.U + A.M = 177 A.S = A.F + E.U + 69 E.U - A.M = 13 E.U = A.M + 13 2A.F = E.U + A.M + 29 A.F + E.U + 69 + A.F + E.U + A.M = 177 A.F + A.M + 13 + 69 + A.F + A.M + 13 + A.M = 177 2A.F + 3A.M = 177 - 13 - 13 - 69 E.U + A.M + 29 + 3A.M = 82 A.M + 13 + A.M + 29 + 3A.M = 82 5A.M = 82 - 13 - 29 A.M = 40/5 A.M = 8 E.U = 8 + 13 = 21 A.F = (21 + 29) / 2 = 25 A.S = 177 - 25 - 21 - 8 = 123
Therefore, there are 123 Asians, 25 Africans, 21 Europeans and 8 Americans in the village.
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Simplify the expression, ((p^(-2)+1/p)^1 )^p, when p=3/4, in both radical and rational exponents forms.
Radical form: Rational exponent form:
this question requires two answers please
Answer:
(1/27)252^(3/4)(1/27)fourth root(252^3)Step-by-step explanation:
The exponent of 1 can be ignored. This means we're simplifying ...
[tex]\left(\left(\dfrac{3}{4}\right)^{-2}+\dfrac{1}{\left(\dfrac{3}{4}\right)}\right)^{3/4}=\left(\dfrac{16}{9}+\dfrac{4}{3}\right)^{3/4}=\left(\dfrac{28}{9}\right)^{3/4}\\\\=\left(\dfrac{28\cdot9}{3^4}\right)^{3/4}=\boxed{\dfrac{252^{3/4}}{27}}\qquad\text{rational exponent form}\\\\=\boxed{\dfrac{\sqrt[4]{252^3}}{27}=\dfrac{\sqrt[4]{16003008}}{27}}\qquad\text{radical form}[/tex]
