Answer:
Q(x) = 4
R(x) = 0
Step-by-step explanation:
Q(x) = 2x + 2 ----- (1)
R(x) = x² - 1 -------- (2)
i) For (R * Q)(5) and [(Q * R)], we have as follow:
[(x² - 1)(2x + 2)] (5)
= (2x³ + 2x² - 2x - 2)(5)
= x³ + x² - x - 1
When x = -1
x³ + x² - x - 1 = 0
∴ (x³ + x² - x - 1) ÷ (x + 1) = x² - 1
If x + 1 = 0
x = -1
and x² - 1 = 0
x = 1
From (1), when x= 1: Q(x) = 4
From (2), when x= 1 or -1: R(x) = 0
The half-life of a certain substance is 5.9 days. How many days will it take for 30g of the substance to decay to 12g?
Answer:
7.8 DAYS
Step-by-step explanation:
The time taken for the substance to reach 12g is 7.8 days
The half-life of a substance is the time taken for it to reach half it's initial value.
I will list some formula and concepts which are of importance to this topic but not necessarily this question.
In solving this problem, we may need the formula to calculate half life of a substance which is given as.
[tex]T_\frac{1}{2}= In2/[/tex]λ
where λ = Disintegration constant.
Disintegration ConstantBut to find this constant, we need to use another formula
[tex]N=N_oe^-yt\\\frac{N}{N_o}= e^-yt\\[/tex]
where the values are
N = Mass of sample at time (t)No = Initial mass of sampleλ = Disintegration constantt = time Time TakenHowever,
[tex]n=\frac{Log_e\frac{No}{N} }{Log_e2}[/tex]
Everything remains the same as above but only a slight change now
n = number of half livesSubstituting the values,
[tex]n = \frac{Log_e(\frac{30}{12}) }{log_e2}\\n = 1.32[/tex]
Since n stands for the half life passed within time (t)
The time taken would be
[tex]t = 1.32 * 5.9\\t =7.8[/tex]
The time taken for the substance to reach 12g is 7.8 days.
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The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the cone to the volume of the
prism?
base area = B
base area = B
A
1
volume of cone
volume of prism 2
O B.
volume of cone
volume of prism 3
C.
volume of cone 2
volume of prism 3
OD.
volume of cone
volume of prism
= 1
E.
volume of cone
volume of prism 2
الف لا
Answer:
C.
volume of cone 2
volume of prism 3
OD.
Step-by-step explanation:
Answer:
I just took the test and the correct option is B.
Step-by-step explanation:
what is the remainder when p(x) is divided by (x-3) please help
Answer:
1
Step-by-step explanation:
We will use polynomial remainder theorem or little Bézout's theorem. It states that reminder p(x) divided by (x - a) is p(a). In our case (a = 3) it is p(3) = 1
A car is traveling on Michigan Street towards Ward Street. The car planes to turn right into Ward Street. what is the angle measure of the turn.
Pls help ASAP
The area of this parallelogram is 120 ft2 find the value of h
Answer: 6
Step-by-step explanation:
A=bh plus 120 for A and 20 for B
120=20b
/20 divide by 20 each side
H=6
Quadrilateral DEFG is rotated 180° about the origin to create quadrilateral D'E'F'G'. In which quadrant does G' lie? A. I B. II C. III D. IV
Answer:
B. II
Step-by-step explanation:
G is in quadrant IV. The quadrant that is across the origin from that is quadrant II.
G' will lie in quadrant II
Answer:
B. 11
Step-by-step explanation:
Simplify completely, help me:(
Answer:
a.
[tex] \frac{3a}{7 {b}^{2} } [/tex]
b.
[tex] \frac{2}{x} [/tex]
Find an equation of the tangent line to the curve at the given point. y = x , (16, 4) Step 1 To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (16, 4), we know that (16, 4) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x = a can be found using the formula mtan = lim x→a f(x) − f(a) x − a . In this situation, the function is f(x) = and a =
The question is incomplete. The complete question is:
Find an equation of the tangent line to the curve y = [tex]\sqrt{x}[/tex] at the given point (16,4). To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (16,4) we know that (16,4) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x = a can be found using the formula m tan = lim x↔a f(x) - f(a)/ x - a.
Answer: y = [tex]\frac{x}{8} + 2[/tex]
Step-by-step explanation: The tangent line is a line that intercepts a curve in only one point. The point-slope formula for a line is [tex]y-y_{0} = m(x-x_{0})[/tex], where m is the slope of the line and can be calculated by the first derivative of the given curve. For this case:
y = [tex]\sqrt{x}[/tex]
f'(x) = [tex]\frac{dy}{dx} = \sqrt{x}[/tex]
f'(x) = [tex]\frac{1}{2\sqrt{x} }[/tex]
At point (16,4), the slope will be:
m = f'(16) = [tex]\frac{1}{2.\sqrt{16} }[/tex]
m = [tex]\frac{1}{8}[/tex]
With slope and a point, the line function will be:
[tex]y-y_{0} = m(x-x_{0})[/tex]
y - 4 = [tex]\frac{1}{8}[/tex](x - 16)
y = [tex]\frac{x}{8}[/tex] - 2 + 4
y = [tex]\frac{x}{8}[/tex] + 2
The tangent line to the curve is y = x/8 + 2
Find the length of a leg of a right triangle (in inches) if the other leg measures 9 in. and the hypotenuse measures 19 in. Round to the nearest thousandth. __________________ in
Answer:
a = 16.733
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
a^2 + 9^2 = 19^2
a^2 = 19^2 - 9^2
a^2 = 361-81
a^2 =280
Taking the square root of each side
sqrt(a^2) = sqrt(280)
a = 16.73320053
Rounding to the nearest thousandth
a = 16.733
Solve the one-variable equation using the distributive property and properties of equality.
-6(2 + a) = -48
What is the value of a?
O a = -6
O a = -3
O a = 5
Са= 6
Hey there! :)
Answer:
Last choice. a= 6.
Step-by-step explanation:
Starting with:
-6(2 + a) = -48
Distribute the -6:
-6(2) -6(a) = -48
Simplify:
-12 - 6a = -48
Add 12 to both sides:
-12 + 12 - 6a = -48 + 12
-6a = -36
Divide both sides by -6:
a = 6. Therefore, the last choice is correct.
Answer:
a = 6
Step-by-step explanation:
Solve the one-variable equation using the distributive property and properties of equality.
–6(2 + a) = –48
What is the value of a?
a = –6
a = –3
a = 5
a = 6
What is the solution to 8/x+2=2/x-4
Answer:
x=-1
Step-by-step explanation:
8/x+2=2/x-4
8/x=2/x-6
8=2-6x
6=-6x
-1=x
Answer:
x=6
Step-by-step explanation:
8/x+2=2/x-4
Using cross products
8*(x-4) = 2 (x+2)
Distribute
8x - 32 = 2x+4
Subtract 2x
8x-2x -32 = 2x-2x+4
6x-32 = 4
Add 32
6x-32+32 = 4+32
6x = 36
Divide by 6
6x/6 = 36/6
x = 6
Evaluate geometric series sigma1^20 4(8/9)^n-1
Answer:
32.5861
Step-by-step explanation:
I interpreted it this way:
20 - stop at n = 20 (inclusive)
1 - start at n = 1
4(8/9)^(n - 1) - geometric expression
how many different four letter permutations can be formed using four letters out of the first 12 in the alphabet?
Answer:
11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet
Step-by-step explanation:
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
Permutations of four letters from a set of 12 letters. So
[tex]P_{(12,4)} = \frac{12!}{(12-4)!} = 11800[/tex]
11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet
Answer: it’s 11,880
not 11800
graph the linear equation. Find three points that solve the equation, then plot on the graph. -3y=-x-6
Answer:
hope u get it.......!!
The oblique pyramid has a square base. What is the volume of the pyramid? 2.5 cm3 5 cm3 6 cm3 7.5 cm3
Take a look at the attachment below. It fills in for the attachment that wasn't provided in the question -
An oblique pyramid is one that has a top not aligned with the base. Due to this, the height of the pyramid connects with two vertices at its ends to form a right angle present outside the pyramid, knowing that it is always perpendicular to the base. There is no difference between the calculations of the volume of an oblique pyramid and a pyramid however -
[tex]\\Base Area = 2 cm * 2 cm = 4 cm^2,\\Volume ( Pyramid ) = 1 / 3 * ( Base Area ) * ( Height ),\\Volume = 1 / 3 * ( 4 ) * ( 3.75 ),\\-------------------------\\Volume = 5 cm^3[/tex]
And thus, you're solution is 5 cm^3, or in other words option b!
Answer:
The answer is B
Step-by-step explanation:
How does a perpendicular bisector divide a triangle
In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Jim, George, Helen, and Maggie. The possible outcomes can be represented as follows: JG JH JM GJ GH GM HJ HG HM MJ MG MH Here, for example, JG represents the outcome that Jim receives the first prize and George receives the second prize. The event A is defined as follows: A = event that Helen gets first prize List the outcomes that comprise the event ~A (not A).
Answer:
1. JG (Jim gets first prize, George gets second prize)
2. JH (Jim gets first prize, Helen gets second prize)
3. JM (Jim gets first prize, Maggie gets second prize)
4. GH (George gets first prize, Helen gets second prize)
5. GJ (George gets first prize, Jim gets second prize)
6. GM (George gets first prize, Maggie gets second prize)
7. MJ (Maggie gets first prize, Jim gets second prize)
8. MG (Maggie gets first prize, George gets second prize)
9. MH (Maggie gets first prize, Helen gets second prize)
Step-by-step explanation:
The question asks for the list of outcomes in the event "Not A". We are looking for the reverse or negative of Event A.
The above given list is the list of outcomes in the event where Helen DOES NOT get first prize.
PLS HELP (pic included)
hope it helps uh.......
Add and write the fraction or mixed number in its simplest form: 2/5 + 1/4 + 7/10
Answer:
The LCM of 5, 4, and 10 is 20 so we can rewrite this expression as:
8/20 + 5/20 + 14/20 = (8 + 5 + 14) / 20 = 27 / 20 = [tex]1\frac{7}{20}[/tex]
Adding all the three fractions ,
Simplest form is
[tex]1\frac{7}{20}[/tex]
Given :
[tex]\frac{2}{5}+\frac{1}{4} +\frac{7}{10}[/tex]
Step-by-step explanation:
To add all the fractions , the denominators should be same
Lets find out LCD of 5,4 and 10
[tex]5= 1,5\\4=2,2\\10=5,2\\LCD=5\cdot 2\cdot 2=20[/tex]
Least common denominator = 20
Multiply the first fraction by 4 and second fraction by5 and third fraction by 2 to get same LCD 20
[tex]\frac{2}{5}+\frac{1}{4}+\frac{7}{10}\\\frac{8}{20}+\frac{5}{20}+\frac{14}{20}\\\\\frac{8+5+14}{20}\\\frac{27}{20}[/tex]
We cannot simplify the fraction further . So we write it in mixed form
[tex]1\frac{7}{20}[/tex]
Learn more : brainly.com/question/22881654
Not sure how to solve this
Answer:
The x-intercepts as shown on this graph are: (-3,0), (1,0), and (3,0). The y-intercept as shown on this graph is: (0,2).
Step-by-step explanation:
The intercepts refer to where the function intersects with either the x-axis or y-axis. Since the line crosses the y-axis at (0,2), that's the y-intercept. The same thing applies to the x-intercepts. On this graph, it's easier to identify because the intercepts are marked with dots.
There were 35,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold, nine times as many paperback copies as hardback copies were sold. If a total of 448,000 copies of the novel were sold in all, how many paperback copies were sold
Answer:
3,717,000
Step-by-step explanation:
The calculation of paperback copies is shown below:-
Let us assume hardback copies is x, so paperback copies will be 9x
now the equation is
35,000 + x + 9x = 448,000
10x = 448,000 - 35,000
10x = 413,000
[tex]= \frac{413,000}{10}[/tex]
= 41,300
Therefore, the paperback copies are
= [tex]9\times 41,300[/tex]
= 3,717,000
Hence, the paperback copies is 3,717,000
Chloe has a budget of $800 for costumes for the 18 members of her musical theater group. What is the maximum she can spend for each costume?
Answer:
$42.10
Step-by-step explanation:
Assuming that she did not yet buy a costume for herself, 800 dollars divided among 18 people plus herself is equal to $42.10 maximum per person.
Answer:
44.44
Step-by-step explanation:
800 didvided by 18.
please tell ans of attached photo
Answer:
192 m^2.
Step-by-step explanation:
We can split this up into 3 rectangles:
Area of the bottom rectangle = 27 * (9-3)
= 27 * 6 = 162 m^2.
Area of rectangle on the left = (18-6)*2
= 24 m^2
Area of small rectangle on the right = 3*2
= 6 m^2
Total area = 162+24+6
192 m^2.
I AM GIVING + 20 POINTS !!!!! PLEASE ANSWER SOON!!!!! Which is NOT a good reason to perform step 1 in the solution shown? equation: 4x = 88 step 1: 4x/4 = 88/4 step 2: x = 22 a. divide by 4, because 4 is a factor of 88. b. dividing 4x by 4 isolates x on one side of the equation. c. dividing is the inverse of multiplying d. dividing both sides by 4 keeps the equation balanced
Answer:
c. dividing is the inverse of multiplying because it doesn't really relate the equation like the others do.
Will give brainliest answer
Answer:
Radius = 6.5cm
Diameter = 13cm
Step-by-step explanation:
The diameter is given (13)
Radius is half the diameter (13/2=6.5)
Answer:
Radius = 13 / 2 = 6.5 cmDiameter = 13 cmExplanation
RadiusThe straight line is drawn from the centre of a circle to a point on its circumference is called radius of the circle. The radius of a circle is half of its diameter.
DiameterThe chord that passes through the centre of a circle is called diameter of circle. Diameter is also called the largest chord of any circle. The length of diameter of a circle is two times it's radius.
Hope this helps...
Good luck on your assignment...
Find the surface area of this composite solid.
Answer:
C. 120 m²
Step-by-step explanation:
The surface area is equal to the area of 4 rectangles + area of 4 triangles + area of base.
Area of 4 rectangles:
4(5 × 4)
4(20) = 80
Area of 4 triangles:
4(3 × 4 × 1/2)
4(6) = 24
Area of base:
4² = 16
Add the areas.
16 + 24 + 80
= 120
The surface area of the composite solid is 120 m².
The surface area of this composite solid would be, 136 m². Hence, option D is true.
Used the formula for the surface area of the cuboid and the surface area of the 4 triangles,
The surface area of the cuboid = 2 (LW + LH + HW)
And, The surface area of the 4 triangles = 4 (1/2 × Base × Height)
Given that,
In a triangle,
Base = 4 m
Height = 3 m
And, In a Cuboid,
Length = 4 m
Width = 4 m
Height = 5 m
Hence, we get;
The surface area of the 4 triangles = 4 (1/2 × Base × Height)
= 4 (1/2 × 4 × 3)
= 4 × 6
= 24 m²
The surface area of the cuboid = 2 (LW + LH + HW)
= 2 (4 × 4 + 4 × 5 + 5 × 4)
= 2 (16 + 20 + 20)
= 112 m²
Therefore, The surface area of this composite solid would be,
24 m² + 112 m² = 136 m²
So, Option D is true.
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Factor completely
7a^2+53a+28
Hello! :)
____________ ☆ ☆____________________
Answer:
(7a+4)⋅(a+7)
Step-by-step explanation:
First you have to multiply... 7x28=196
Now find the factors of 196
Factor: 53
Add the first two terms
Add up the four terms and you get your answer
ANSWER: (7a + 4) • (a + 7)
_____________ ☆ ☆___________________
Hope this helps! :)
By BrainlyMember ^-^
Good luck!
If possible, find AB. & State the dimension of the result.
Answer:
Step-by-step explanation:
[tex]A=\begin{bmatrix}0 &0 &5 \\ 0 &0 &-3 \\ 0 &0 &3 \end{bmatrix}[/tex]
[tex]B=\begin{bmatrix}8 &-12 &5 \\ 7 &19 &5 \\ 0 &0 &0 \end{bmatrix}[/tex]
A.B = A × B
[tex]A.B=\begin{bmatrix}0 &0 &0 \\ 0 &0 &0 \\ 0 &0 &0 \end{bmatrix}[/tex]
Dimension of the resultant matrix is (3 × 3)
Using a Graph to Find Positive or Negative Intervals
Answer:
Step-by-step explanation:
The second is correct
f(x) <0 on ( _ infinit, -2.7) and ( -1, 0.8)
The following display from a graphing calculator presents the least-squares regression line for predicting the price of a certain commodity (y) from the price of a barrel of oil (x).
Y = a + bx
a = 4.95
b = 0.29
r2 = 0.53045
r = 0.72832
Predict the commodity price when oil costs $107 per barrel.
Answer:
35.98
Step-by-step explanation:
Fill in the numbers and do the arithmetic.
y = a + bx . . . . . . a=4.95, b=0.29, x=107
y = 4.95 + 0.29(107) = 35.98
The predicted price is 35.98.