Answers
f(-3) = 4(-3) -3 = -15
(f◦g)(0) = f(g(0)) = -15
Related Questions
The hypotenuse of an isosceles right triangle is 14 sqrt 2. How long is each leg of the triangle?
Answers
Hope this helps!
Answer:
14
Step-by-step explanation:
Let the legs of the triangle each have length $x$ (they are equal because it is an isosceles right triangle). Then
x^2 + x^2 = (14√2)^2 = 14^2 × (√2)^2 = 14^2 × 2, so x^2 = 14^2. Given that x must be positive, we have x = 14. So, the value of each leg is 14
(Hope this helped you!)
If i know a real root of f(x) = x3 -6x2 + 11x – 6 is neither 1, even, or negative, a good guess would be?
Answers
A good guess for the real root of the polynomial [tex]f(x) = x^3 - 6x^2 + 11x - 6[/tex] that is neither 1, even, nor negative, would be a positive odd integer such as 3 or 5, considering the constraints and the Rational Root Theorem.
The real root of the cubic equation [tex]f(x) = x^3 - 6x^2 + 11x - 6[/tex] that is neither 1, even, nor negative would most likely be a positive odd number (since all positive even numbers are, by default, also excluded). Considering the smallest odd numbers greater than 1 are 3 and 5, and given that we're working with integers, a good guess for the real root would be either 3 or 5. However, one can apply the Rational Root Theorem which states that any rational root, expressed in its lowest form p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient. In this case, the possible rational roots could be
divisors of 6 (constant term) over divisors of 1 (leading coefficient), which gives us only divisors of 6 itself
since the leading coefficient is 1. Among those divisors, the ones that fit the criteria of being neither 1, even, nor negative, would be 3 or positive odd integers.
By accident, 4 burned out bulbs have been mixed in with 20 good ones. ken is replacing old bulbs in his house. if he selects two bulbs at random from the box of 24, what is the probability they both work?
Answers
next, there are 23 left, including 19 good ones. So the probability is 19/23.
Multiply 19/23 and 5/6 to get 95/138, which is out answer.
HELP PLEASE
Determine the missing statements and reasons for the following proof.
Answers
Reason 3: Congruent supplements theorem
Statements:
Statement 4: Angle 1 is congruent with angle 2
Answer: Option D:
Reason 3: Congruent supplements theorem.
Statement 4: Angle 1 is congruent with angle 2
In a mathematical proof, missing statements and reasons are usually concluded from the given statements and the relevant geometric postulates or theorems. They could include establishing the congruency of angles or declaring the parallelism of lines.
Explanation:Without the concrete steps of the proof or the reasoning proposed, it is difficult to provide the exact missing statements and reasons. However, in a general mathematical proof, common reasons used include 'definition of congruent angles', 'definition of parallel lines', 'alternate interior angles theorem', etc.
For instance, if we have a proof that involves stating two angles are congruent, the missing statement might be 'Angle A is congruent to Angle B', and the missing reason could be 'Definition of Congruent Angles' or 'Angle Bisector Theorem', if an angle bisector comes into the picture.
Another missing statement might be 'Segment AB is parallel to Segment CD', with the reason being 'Corresponding Angles Postulate', or 'Alternate Interior Angles Theorem', if the proof involves parallel lines.
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which number correctly completes this equation 3/4%x75= A. 0.255 B. 0.5625 C. 2.55. D. 5.626
Answers
3/4 of a percent is .0075.
0.0075 times 75 = 0.5625
The answer is B) 0.5625.
What is the probability of rolling an even number or a prime number on a number cube? Write as a fraction in simplest form.
Answers
Final answer:
The probability of rolling an even number or a prime number on a six-sided die is 5/6, considering the unique favorable outcomes of 2, 3, 4, 5, and 6 against the total possible outcomes.
Explanation:
The question asks, "What is the probability of rolling an even number or a prime number on a number cube?" To answer this, first identify the outcomes on a six-sided die which are even and those that are prime.
Even numbers on a die: 2, 4, 6. Prime numbers on a die: 2, 3, 5. Notice that 2 is both even and prime, and it only needs to be counted once. Therefore, the unique favorable outcomes are 2, 3, 4, 5, 6.
The die has a total of 6 sides, making the total number of possible outcomes 6. The probability of rolling an even number or a prime number is therefore the number of favorable outcomes (5) divided by the total number of outcomes (6), which simplifies to 5/6.
Solve for y.
a.10
b.12
c.15
d.18
Answers
Angle ABD=90°
3x°=90°
3x=90
Solving for x:
3x/3=90/3
x=30
Angle CBD=90°
(2x+3y)°=90°
2x+3y=90
x=30
2(30)+3y=90
60+3y=90
Solving for y:
60+3y-60=90-60
3y=30
3y/3=30/3
y=10
Answer: Option a. 10
How can you find the perimeter of the rhombus? Find 1/2 (QS)(RT). Find 1/2(QT)(TS). Use the distance formula to find QT, then multiply by 4. Use the distance formula to find QT and QR, add the distances, then multiply by 4.
Answers
Yes C is correct which would be
Use the distance formula to find QT, then multiply by 4.
The perimeter of the rhombus can be found by C. use the distance formula to find QT and then multiply by 4.
What is Rhombus?A rhombus is a two dimensional shape which consists of four equal sides with opposite side being parallel and opposite angles being equal.
Perimeter of a straight sided figures or objects is the total length of it's boundary.
Actual perimeter = QR + RS + ST + TQ
That is add all the sides.
Now since the polygon is rhombus, all the sides are of equal length.
So, it is enough to find any side length of the rhombus and then multiply by 4.
The length of a side can be found using the distance formula.
So the correct way is use the distance formula to find QT and then multiply by 4.
Hence the correct option is C.
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Your question is incomplete. The complete question is as given below.
Hey can you please help me posted picture of question
Answers
Of the six faces numbered 1 to 6, there is only one five. The probability therefore of rolling a die and getting a five is equal to 1/6. This approach is the theoretical. Hence, the answer to this item is the first option, A Theoretical.
So basically if you think about it the answer is Empirical.
Question partpointssubmissions usedverify that the divergence theorem is true for the vector field f on the region
e. give the flux.f(x, y, z) = 3xi + xyj + 5xzk,e is the cube bounded by the planes x = 0, x = 2, y = 0, y = 2, z = 0, and z = 2.
Answers
By the divergence theorem, the flux across the boundary of the given region [tex]\mathcal E[/tex] is
[tex]\displaystyle\iint_{\partial\mathcal E}\mathbf f(x,y,z)\cdot\mathrm d\mathbf S=\iiint_{\mathcal E}\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV[/tex]
[tex]=\displaystyle\int_{z=0}^{z=2}\int_{y=0}^{y=2}\int_{x=0}^{x=2}(3+6x)\,\mathrm dx\,\mathrm dy\,\mathrm dz=72[/tex]
7.
Find the amount of the payment for the sinking fund.
Amount Needed: $58,000
Years Until Needed: 2
Interest Rate: 6%
Interest Compounded: Semiannually
$13,863.74
$8,620.68
$28,155.52
$13,258.22
Answers
Substituting,
SFF = (0.06/2)/{(1+0.06/2)^2*2 -1} = 0.239
PMT = A*SFF = 58,000*0.239 = $13,863.57 ---- The closest answer is $13,863.74
The sum of the squares of two numbers is 18. the product of the two numbers is 9. find the numbers.
Answers
Answer:
x=3 y=3
Step-by-step explanation:
The sum of the squares of two numbers is 18, and the product of those two numbers is 9, you just need to create an equation:
So the sum of the squares is 18, the first number will be represented as X and the second as Y:
[tex]x^{2}+ y^{2} =18[/tex]
And the other one is that the product of the two numbers is 9:
[tex]xy=9[/tex]
We have a system of equations here, we clear X from the first one:
[tex]x=\frac{9}{y}[/tex]
And instert that value of x in the first one:
[tex]x^{2}+ y^{2} =18\\(\frac{9}{y} )^{2}+ y^{2} =18\\81=y^2(18-y^2)\\y^4-18y^2+81=0\\(y^2-9)(y^2-9)=0\\Y^2-9=0\\y^2=9\\y=3[/tex]
By solving this equation we get that the first number is 3.
The second number is solved by inserting the value of Y into one of the equations, in this case we will use the second:
[tex]xy=9\\x=\frac{9}{y} \\x=\frac{9}{3} \\x=3[/tex]
So we get that x and y are both 3.
Q#2 Graph the relation in the table.Then use the vertical-line test.Is the relation a function
Answers
x y
-1 3
1 -1
2 2
1 3
We observe that the graph shown in the question shows a scattering of points that do not obey any behavior of known function.
Therefore, the table does not represent any function.
Answer:
The table does not represent a function.
By applying the vertical line test we find that the relation is not a function because there are two points which are (1,-1) , (1,3) have the same value of x with different values of y which contradicts with with the rule of function.
What is the mode of the data set? 61, 92, 61, 89, 92, 61 Enter your answer in the box.
Answers
Hope that helped:)!!!!!!!
Answer:
61 is the Answer
Step-by-step explanation:
K12 for life
PLZ HELP ASAP WRITE STANDERED EQAUTION OF A CIRCLE
Answers
(x-xo) ^ 2 + (y-yo) ^ 2 = r ^ 2
Where,
(xo, yo): coordinate of the center of the circle
r: radius of the circle.
Substituting values we have:
(x-9.2) ^ 2 + (y + 7.4) ^ 2 = (5/3) ^ 2
Rewriting:
(x-9.2) ^ 2 + (y + 7.4) ^ 2 = 25/9
Answer:
The equation of the circle is:
(x-9.2) ^ 2 + (y + 7.4) ^ 2 = 25/9
C(9.2, -7.4)
r^2 = (x-h)^2 + (y-k)^2
(5/3)^2 = (x - 9.2)^2 + (y + 7.4)^2
a company that manufactures and ships canned vegetables is designing boxes in the shape of rectangular prisms to meet specific requirements. The vegetables are packed into cans that are 3 inches in diameter and 5 inches in height. Company regulations state that boxes must be filled in with two layers of 12 cans each, and be completely closed with no overlapping material. What is the smallest amount of cardboard needed to meet the company's requirements
Answers
Therefore, you need to understand how the cans are positioned in order to find the dimensions of the boxes: two layers of cans mean that the height is
h = 2 · 5 = 10 in
The other two dimensions depend on how many rows of how many cans you decide to place, the possibilities are 1×12, 2×6, 3×4, 4×3, 6×2, 12×1.
The smallest box possible will be the one in which the cans are placed 3×4 (or 4×3), therefore the dimensions will be:
a = 3 · 3 = 9in
b = 3 · 4 = 12in
Now, you can calculate the total surface area:
A = 2·(a·b + a·h + b·h)
= 2·(9·12 + 9·10 + 12·10)
= 2·(108 + 90 + 120)
= 2·318
= 636in²
Hence, the smallest amount of carboard needed for the boxes is 636 square inches.
Answer:
636
Step-by-step explanation:
trust
Find the area of the surface. the part of the surface z = 9 + 5x + 2y2 that lies above the triangle with vertices (0, 0), (0, 1), (2, 1).
Answers
The area of the surface is [tex]\rm \dfrac{1}{54}(53\sqrt{53} -17\sqrt{17} )[/tex] and this can be determined by doing the integration.
Given :
The part of the surface [tex]\rm z = 9+5x+2y^2[/tex] that lies above the triangle with vertices (0, 0), (0, 1), (2, 1).
The formula of the surface area is given by:
[tex]\rm A(S) = \int \int_D\sqrt{1+\left(\dfrac{\delta z}{\delta x}\right)^2 +\left(\dfrac{\delta z}{\delta y}\right)^2 }[/tex]
Now, the values of D varies from:
D = {(x,y): 0 [tex]\leq[/tex] y [tex]\leq[/tex] 1 , 0 [tex]\leq[/tex] x [tex]\leq[/tex] 2y}
Now, the area of the surface is given by:
[tex]\rm A(S) = \int \int_D\sqrt{1+4^2+(6y)^2 }\;dA[/tex]
[tex]\rm A(S) = \int^1_0 \int^{2y}_0\sqrt{17+36y^2 }\;dx\;dy[/tex]
[tex]\rm A(S) = \int^1_02y\sqrt{17+36y^2 }\;dy[/tex]
Now, let [tex]u=17+36y^2[/tex]
[tex]du = 72y dy[/tex]
[tex]\rm \dfrac{du}{36}=2ydy[/tex]
Now, the integral becomes:
[tex]\rm A(S)= \dfrac{1}{36}\sqrt{u} \; du[/tex]
[tex]\rm A(S) = \dfrac{1}{54}\times u^{3/2}+C[/tex]
Now, substitute the value of u in the above expression.
[tex]\rm A(S) = \dfrac{1}{54}\times \left[\left[\sqrt{17+36y^2} \right]^{3/2}\right]^1_0[/tex]
Now, simplify the above expression.
[tex]\rm A(S) = \dfrac{1}{54}(53\sqrt{53} -17\sqrt{17} )[/tex]
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To calculate the surface area of the part of the surface z = 9 + 5x + 2y² lying over a triangle, the limits of the variables are determined by triangle vertices. Then, the double integral of the surface area formula, which integrates the square root of 1 plus the squares of the partial derivatives of the function over these limits, is computed.
Explanation:The problem presented is leading us to calculate the surface area of a part of z = 9 + 5x + 2y² that lies above a right triangle whose vertices are (0, 0), (0, 1), (2, 1). The first step in resolving this is to recognize the given formula of the surface, it is a quadratic surface in three-dimensional space, also known as a paraboloid.
The vertices of the triangle give as a hint to define the limits of the variables. Given that this triangle is defined in the xy plane, owing to the vertices of the triangle provided, the limits for x would range from 0 to 2, the limits of y would range from 0 to 1 (since for x = 0, y = 1 and for x = 2, y = 1).
Finally, the area S of a part of the surface z = f(x, y) that lies above the region D in the xy plane is defined by the double integral: S = ∫∫D √(1 + (fx)² + (fy)²) dA where fx and fy are partial derivatives of the function f(x, y) with respect to x and y respectively. The integral needs to be computed over the region D which is defined by triangle vertices.
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YOU HAVE TO KNOW FOR SURE THE ANSWER. (: 15 points?!
Which fraction is equivalent to 95%
A. 0.95/10
B. 0.95/100
C. 95/10
D. 95/100
Answers
Answer:
D)
Step-by-step explanation:
Percent means "per hundred" or "out of one hundred." While B) is out of one hundred, turn it into a percent, and the percentage would be .95%. A) and C) are not out of 100, so those answers are not applicable. The only answer left is D), which is correct, because 95/100 is equivalent to 95%.
The Length of a rectangle is 5 times the width. The area is 125 square centimeters. What is the length?
Answers
length = 5x
Area = width*length
125=x*5x
5x²=125
x²=25
x=5
width= x = 5 cm
Length =5x=5*5=25 cm
Length=25 cm
A laterally loaded single pile is shown below. use the elastic pile solutions (based on the winkler's model) to calculate the displacement and rotation at pile head ????. assume free headed condition. pile length ???? = 30 ft; young's modulus ???????? = 3 × 10 6 psi; ????ℎ = 30 lb/in3 ; and the eccentricity ???? = 60 in.
Answers
Josiah has 3 packs of toy animals. Each pack has the same number of animals. Josiah gives 6 animals to his sister stephanie. Then josiah has 9 animals left.how many animals were in each pack?
Answers
Total number of animals will be 3x
after Josiah gave 6 animals to his sister the remaining animals were:
3x-6=9
thus sloving for x we have:
3x-6=9
add 6 on both sides
3x-6+6=9+6
3x=15
divide both sides by 3
(3x)/3=15/3
x=5
Answer:
There were 5 animals in each pack
Each gallon of shingle stain covers 120 square feet. How many gallons should you buy to cover 658 square feet?
Answers
5.483 gallons bought to cover 658 square feet.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Each gallon of shingle stain covers 120 square feet.
We have to find gallons should be bought to cover 658 square feet.
We have to perform division
= 658/120
= 5.483 gallons
Hence, 5.483 gallons bought to cover 658 square feet.
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The area of a rectangle is 53.3 in2. If the width is 6.5 in, what is the perimeter of the rectangle?
Answers
A = LW
53.3 in² = L×(6.5 in)
(53.3 in²)/(6.5 in) = L = 8.2 in
The perimeter is twice the sum of length and width.
P = 2(L +W)
P = 2(8.2 in +6.5 in) = 29.4 in
The perimeter of the rectangle is 29.4 inches.
l × w
6.5 is our width you already know but 53.3 isn't the length so really
you are trying to solve for l, so l × 6.5 = 53.3
when you get that answer you should get 8.2
Now .. you already have the width and the length so you hook in 6.5(w) + 6.5(w)+ 8.2 (l)+ 8.2(l)
6.5 + 6.5 gives you 13 and
8.2 + 8.2 gives you 16.4
Adding both up you get the final answer/ perimeter 29.4 inches
a coin is tossed , then a number 1-10 is chosen at random.what is the probability of getting heads then a number less than 4?
Answers
The probability of tossing a coin and getting heads is 50%, or 0.5, and the probability of selecting a number less than four from 1-10 is 40%, or 0.4.
The overall probability can then be expressed as:
0.5 x 0.4 = 0.2 or 20%
There is a twenty percent chance that a heads would be tossed and a number less than four selected.
K+1=3k-1 what us the answer
Answers
2k = 2
Divide by 2:
k = 1
If you want to check your work:
1 + 1 = 3 - 1
2 = 2
Together, two people earn $28,000. One earns $2,000 more than the other. How much is the smaller income?
$30k
$26k
$14k
$13k
Answers
2x+$2,000=$28,000
2x=$28,000-$2,000
2x=$26,000
x=26,000 divided by 2
x=$13,000
P1+2= P2 . -------Equation 2 . I abbreviate the thousands of $
Using substitution
P1+(P1+2)=28
2P1 +2=28
P1=13
then substitute into equation 2 we get
13+2=p2
P2=15
Therefore one is $15,000
and the other is 13,000
Smaller is 13,000!!!
What is the range of the function in interval notation?
Answers
The range is negative infinity to positive infinity.
In interval notation it is
[tex] (-\infty, \infty) [/tex]
Enrique earns 101010 points for each question that he answers correctly on a geography test. Write an equation for the number of points, yyy Enrique scores on the test when he answers xxx questions correctly.
Answers
[tex]y = 101010 \times x[/tex]
In the question it must be 10 instead of 101010, y instead of yyy and x instead of xxx.
Since, Enrique earns 10 points for each question that he answers correctly on a geography test.
We have to write an equation for the number of points, 'y' Enrique scores on the test when he answers 'x' questions correctly.
So, Number of points scored = Points scored for one question [tex] \times [/tex] Number of questions answered correctly.
So, Number of points scored = [tex] 10 \times x [/tex]
[tex] y=10 \times x [/tex]
y = 10x is the required equation.
A, B, C, and D have the coordinates (-8, 1), (-2, 4), (-3, -1), and (-6, 5), respectively. Which sentence about the points is true?
A, B, C, and D lie on the same line.
AB and CD are perpendicular lines.
AB and CD are parallel lines.
AB and CD are intersecting lines but are not perpendicular.
AC and BD are parallel lines.
Answers
We observe that the slopes of both lines are different (they are not reciprocal opposites).
Therefore, the lines are not perpendicular.
Answer:
AB and CD are intersecting lines but are not perpendicular.
See attached image.
Answer:
AB and CD are intersecting lines but are not perpendicular.
See attached image.
Step-by-step explanation:
Jorge owes his father $60. After raking the lawn for the month, he has paid him $12, $8, and $9. How much money does Jorge still has owes his father?
Answers
60 - 29= 31
Jorge owes his father $31