Answers
Using synthetic division:
[tex]\begin{gathered} k+5=0 \\ k=-5 \end{gathered}[/tex]Therefore:
[tex]\frac{k^3-17k+32}{k+5}=k^2-5k+8-\frac{8}{k+5}[/tex]
Related Questions
5. Aiden wrote the interval (-5, 4] and claimed it was equivalent to the graph below. Explain what he did wrong and correct his mistake.
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Aidan did wrong because the number -5 is closed and 4 is open, he did the opposite.
The right way is [-5, 4).Suppose we want to choose 5 letters, without replacement, from 16 distinct letters.(a) If the order of the choices is taken into consideration, how many ways can this be done?0(b) If the order of the choices is not taken into consideration, how many ways can this be done?
Answers
Explanation:
a) Given: Order is important and replacement is not allowed.
This is a permutation.
Number of ways =
[tex]\begin{gathered} N\text{ = }\frac{n!}{(n-r!)} \\ N\text{ = }\frac{16!}{(16-5)!} \\ \text{ =524160} \end{gathered}[/tex]Answer: 524160
b) Order is not important, replacement is not allowed.
This is a combination.
[tex]\begin{gathered} N\text{ = }\frac{n!}{(n-r)!*r!} \\ N\text{ = }\frac{16!}{(16-5)!*5!} \\ N\text{ = 4368} \end{gathered}[/tex]Answer: 4
What is the probability of either event occurring when you roll adie?Event A: Rolling a 6Event B: Rolling a number greater than 3Express your answer as a simplified fraction.Enter the answer
Answers
Given:
Roll a die.
Required:
We need to find the probability that rolling a 6 and rolling a number greater than 3.
Explanation:
A)
A die had six sides and numbered 1 to 6.
The sample space, S=(1,2,3,4,5,6)
[tex]n(S)=6[/tex]Let event A be rolling a 6.
A={6}.
[tex]n(A)=1[/tex]The probability that rolling a 6 is P(A).
[tex]P(A)=\frac{n(A)}{n(S)}[/tex][tex]P(A)=\frac{1}{6}[/tex]B)
Let B be the event of rolling a number greater than 3.
[tex]B=\lbrace4,5,6\rbrace[/tex][tex]n(B)=3[/tex]The probability of rolling a number greater than 3 is P(B).
[tex]P(B)=\frac{n(B)}{n(S)}[/tex][tex]P(B)=\frac{3}{6}[/tex][tex]P(B)=\frac{1}{2}[/tex]Final answer:
The probability of rolling a 6 is 1/6.
The probability of rolling a number greater than 3 is 1/2.
Please help me with the question below(also please try to answer the question in a maximum of 2-4 minutes).
Answers
Given the equation
[tex]7p+15.89=19.32[/tex]solving for p
[tex]7p+15.89=19.32[/tex][tex]7p=19.32-15.89[/tex][tex]7p=3.43[/tex][tex]p=\frac{3.43}{7}[/tex][tex]p=0.49[/tex]p=0.49
Hi can you help please?Why do we divide 6 by 6 and not do 6-6 to isolate n
Answers
we have the expression
[tex]-1=\frac{-2+n}{6}[/tex]Solve for n
step 1
Multiply by 6 on both sides, to remove the fraction
-6=-2+n
step 2
subtract 2 on both sides
-6-2=n
n=-82) Keira wants to make an open-top box by cutting out corners of a square piece of cardboard andfolding up the sides. The cardboard is 12 centimeters by 12 centimeters. The volume V(x) incubic centimeters of the open-top box is a function of the side length x in centimeters of thesquare cutouts.a) Write an expression for V(x).b) What is the volume of the box when x = 4?c) What is a reasonable domain for the Volume in this context?yes
Answers
Keira wants to make the open-top box as described in the problem.
The card box is 12 x 12 centimeters. Keira will cut 4 corners of side x and fold up the sides.
This means the base of the box is (12-2x) by (12-2x) and the height of the box is x.
Thus, the volume of the box is:
V = (12-2x)(12-2x)x
a) To write an expression for V(x), we'll multiply the expression in parentheses:
[tex]\begin{gathered} V\mleft(x\mright)=(144-24x-24x+4x^2)x \\ \text{Simplifying:} \\ V(x)=(144-48x+4x^2)x \end{gathered}[/tex]Now multiply the last term:
[tex]V(x)=144x-48x^2+4x^3[/tex]This is the required expression for V(x)
b) The volume of the box for x=4 is calculated by substituting the value into the expression above:
[tex]\begin{gathered} V(4)=144(4)-48(16)+4(64) \\ \text{Calculating:} \\ V(4)=64 \end{gathered}[/tex]The volume is 64 cubic centimeters
c) To find a reasonable domain for V(x), we'll return to the first expression:
V = (12-2x)(12-2x)x
The domain can be obtained by assuming the volume cannot be negative. Neither of the sides of the box can be negative, so the conditions that define the domain are:
12 - 2x > 0
and
x > 0
The first condition results in:
x < 6
Thus, the domain of the Volume function is all the numbers greater than 0 and less than 6, or: (0,6)
If the volume is allowed to be zero, then the endpoints are included: [0,6]
Can you please help me out with a question
Answers
From Thales's theorem, which states that in a inscribed triangle, where its hypotenuse its the diameter of a circle, its angle opposite to the hypotenuse is a right angle, so we get
[tex](2x+9)+90+(4x-3)=180[/tex]because interior angles of a triangle add up to 180 degrees. By combining similar terms, from our last relation, we get
[tex]\begin{gathered} 2x+4x+9-3+90=180 \\ 6x+6+90=180 \\ 6x+96=180 \end{gathered}[/tex]By moving 96 to the right hand side, we have
[tex]\begin{gathered} 6x=180-96 \\ 6x=84 \end{gathered}[/tex]Then, x is given by
[tex]\begin{gathered} x=\frac{84}{6} \\ x=14 \end{gathered}[/tex]Therefore, the answer is option B.
Answer:
Therefore, the answer is option B.
hey could u help me with a question (s) pls, im new to this app and in 7th grade.
Answers
2)
Given data
First, list the original price and discounted price
Original price = $199
Discounted price = $139
Discount = 199 - 139 = $60
Next, you will apply the formula for a percentage discount
[tex]\begin{gathered} \text{Percentage discount = }\frac{Discount}{\text{Original price}}\text{ x 100\%} \\ =\text{ }\frac{60}{199}\text{ }\times100 \\ =\text{ }\frac{6000}{199} \\ \text{= 30.15\%} \end{gathered}[/tex]Final answer
Percentage discount = 30%
4)
A cube has 6 faces.
A cube outcomes = ( 1,2,3,4,5,6 )
For two cubes
Possible outcomes
Part EComplete the table for different values of x in the polynomial expression - 7x2 + 32x + 240.Then, determine the optimal price that the taco truck should sell its tacos for. Assume wholedollar amounts for the tacos.*need help with daily revenue when the value of x is at 6*
Answers
The given polynomial expression is
[tex]\begin{gathered} -7x^2+\text{ 32x + 240} \\ \text{When x = 6, the daily revenue would be} \\ -7(6)^2+\text{ 32(6) + 240} \\ -\text{ 262 + 192 + 240 } \\ =\text{ 170} \end{gathered}[/tex]The daily revenue when the value of x is at 6 is 170
If you read the information in the picture. Here’s the 2nd part to the question. Name the coordinates of point B after it is reflected over the x-axis and then the y-axis.
Answers
Solutions:
• Given the coordinates of point B = (x;y) =(-1;-4)
• reflect over the ,x -axis, (x;y) →(x;-y) , then ,B' = ( -1;4)
,• reflect B'(-1;4) over the ,y -axis, (x;y) →(-x;y) , the,, B''= ( 1;4)
the graph below will show the B'' reflected over the y -axis
Solve the equation for y.cy – h= -21
Answers
Solve for y:
[tex]\begin{gathered} c\cdot y-h=-21 \\ c\cdot y=-21+h \\ y=\frac{h-21}{c} \end{gathered}[/tex]The solution is y=(h-21)/c.
Hi, I need help solving this equation using the 'Product Rule', thanks
Answers
Given:
[tex]y=2x(x+3)^2[/tex]Where:
Gradient = 14
Let's find the exact values of x for which the gradient of the tangent line to the curve is 14.
Let's first simplify the equation:
[tex]y=2x((x+3)(x+3))[/tex]Expand using the FOIL method:
[tex]\begin{gathered} y=2x(x(x+3)+3(x+3)) \\ \text{ } \\ \text{ Apply distributive property:} \\ y=2x((x(x)+x(3)+3(x)+3(3)) \\ \\ y=2x(x^2+3x+3x+9) \\ \\ y=2x(x^2+6x+9) \\ \\ y=2x(x)+2x(6x)+2x(9) \\ \\ y=2x^3+12x^2+18x \end{gathered}[/tex]Now, let's find the first derivative of the equation:
[tex]\begin{gathered} \frac{d}{dx}(y)=\frac{d}{dx}(2x^3+12x^2+18x) \\ \\ y^{\prime}=6x^2+24x+18 \end{gathered}[/tex]Set the derivative to 14 and solve for x.
We have:
[tex]y^{\prime}^{\prime}=12x+24[/tex]Now, set the second derivative to 14:
[tex]12x+24=14[/tex]Solve for x:
Subtract 24 from both sides:
[tex]\begin{gathered} 12x+24-24=14-24 \\ \\ 12x=-10 \\ \\ x=-\frac{10}{12} \\ \\ x=-\frac{5}{6} \end{gathered}[/tex]Therefore, the exact value of x for which the gradient of the tangent to the curve is given is:
[tex]-\frac{5}{6}[/tex]ANSWER:
[tex]x=-\frac{5}{6}[/tex]Perform the indicated operations on the following polynomials.Divide: 6x3 + 27x - 19x2 - 15 by 3x -5
Answers
EXPLANATION:
Given;
We are given the polynomial below;
[tex]6x^3+27x-19x^2-15[/tex]Required;
We are required to divide the polynomial by;
[tex]3x-5[/tex]Step-by-step solution;
We shall apply the synthetic division method of dividing polynomials.
The first step would be to re-arrange the polynomial in standard form. This is shown below;
[tex]6x^3-19x^2+27x-15[/tex]Next step, we list out the coefficients of the polynomial;
[tex]6,-19,27,-15[/tex]Next step, we identify the zeros of the denominator;
[tex]\begin{gathered} 3x-5=0 \\ \\ 3x=5 \\ \\ x=\frac{5}{3} \end{gathered}[/tex]We can now write down the question in synthetic division format;
Next step, we carry down the leading coefficient below the division symbol.
Next step, we multiply this value by the zero of the denominator that is, 5/3.
That gives us;
[tex]6\times\frac{5}{3}=10[/tex]Now we write 10 right under the next coefficient and that is -19. We add both together (-19 + 10 = -9) and write the result below the division symbol. Next we multiply this too by the zero of the denominator and we have;
[tex]-9\times\frac{5}{3}=-15[/tex]We write this too under the next coefficient and we have;
[tex]27-15=12[/tex]We multiply this too by 5/3 and we have 20. Write this right under the next coefficient and add up and we now have;
[tex]-15+20=5[/tex]The result we have come up with are the coefficients beneath the division symbol and that is;
[tex]6,-9,12,5[/tex]The last number is the remainder and the result of the division carried out will be;
[tex]6x^2-9x+12\text{ }Rem\text{ }5[/tex]This is otherwise written out as follows;
ANSWER:
[tex]6x^2-9x+12+\frac{5}{(3x-5)}[/tex][15-(|-6+2|+ squareroot9)]^2and what are the steps to solve it. i’m confused!!
Answers
The given expression is as given below
[tex]\frac{\lbrack15-(I-6+2I+\sqrt[]{9})\rbrack^2}{3-3^2}[/tex][tex]\frac{\lbrack15-(I-4I+\sqrt[]{9})\rbrack^2}{3-3^2}[/tex][tex]\begin{gathered} \frac{\lbrack15-(4+3)\rbrack^2}{3-3^2} \\ \frac{\lbrack15-(7)\rbrack^2}{3-3^2} \end{gathered}[/tex][tex]\begin{gathered} \frac{\lbrack15-7\rbrack^2}{3-3^2} \\ =\frac{8^2}{3-27} \\ =\frac{64}{-24} \\ =\frac{-8}{3} \end{gathered}[/tex][tex]=-2\frac{2}{3}[/tex]Use the fact that the sum of the 3 angles in a triangle is 180° to answer this question.One angle in a triangle has a measure that is three times as large as the smallest angle. Themeasure of the third angle is 45° more than that of the smallest angle. Find the measure of the eachof the angles.The SMALLEST angle has a measure of0The MIDDLE angle has a measure ofloThe LARGEST angle has a measure of0
Answers
The SMALLEST angle has a measure of 27°
The MIDDLE angle has a measure of 72°
The LARGEST angle has a measure of 81°
Explanations:Let the smallest angle in the triangle = x
Let the third(middle) angle = y
Let the largest angle = z
The first angle is three times as large as the smallest angle
z = 3x
The third angle(middle) is 45 more than the smallest angle
y = x + 45
Sum of angles in a triangle is 180
x + y + z = 180
x + (x + 45) + 3x = 180
x + x + 3x = 180 - 45
5x = 135
x = 135 / 5
x = 27
y = x + 45
y = 27 + 45
y = 72
z = 3x
z = 3(27)
z = 81
A certain game involves tossing 3 fair coins, and it pays 12¢ for 3 heads, 9¢ for 2 heads, and 4¢ for 1 head. Is 9¢ a fair price to pay to play this game? That is, does the 9¢ cost to play make the game fair?
Answers
The fair price of the game will be : 6.37 cents .
This is not fair game .
What is probability?A probability is just a number that represents the likelihood or chance that a specific event will occur. Probabilities can also be expressed as proportions ranging from 0 to 1, as well as percentage distribution ranging from 0% to 100%.Probability seems to be a number ranging from 0 to 1 that defines the likelihood of an event occurring. An event is a predefined set of random variable outcomes. Only one mutually exclusive event can occur at a time. Exhaustive events encompass or include all possible outcomes.A fair game is one in which both winning and losing are equally likely. A game is said to be fair if the probability of winning equals the probability of losing.Based on the question,
The probability of getting 2 heads = 3/8
The probability of getting 3 heads = (1/2)² = 1/8
The probability of getting 1 heads = 3/8
The expected earnings = 1/8(12 cents) + 3/8 (9 cents) + 3/8 (4 cents)
= 6.37 cents
Therefore the fair price of the game will be : 6.37 cents .
∴ This is not a fair game.
To learn more about probability refer to :
https://brainly.com/question/26924886
#SPJ1
a 15 ft ladder leans against the side of a house. the bottom of the ladder is 8 ft away from the side of the house. Find x, the angle of elevation of the ladder. round your answer to the nearest tenth of a degree
Answers
Answer:
57.8°
Explanation:
We can represent the situation as:
So, we can relate, the given measurements with the trigonometric function cosine, so:
[tex]\begin{gathered} \cos x=\frac{Adjacent\text{ side}}{Hypotenuse} \\ \cos x=\frac{8}{15} \end{gathered}[/tex]Then, solving for x, we get:
[tex]\begin{gathered} \cos x=0.533 \\ x=\cos ^{-1}(0.533) \\ x=57.8 \end{gathered}[/tex]Therefore, the angle of elevation of the ladder is 57.8°
Find the midpoint of the line segment from (2,2) to (-3,-3)
Answers
Answer: (-0.5, -0.5)
Given:
(2,2) and (-3, -3)
To find the midpoint, we will use the following formula:
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]From the given, we know that:
x1 = 2
x2 = -3
y1 = 2
y2 = -3
Substitute these to the equation
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex][tex]M(\frac{2+(-3)}{2},\frac{2+(-3)}{2})[/tex][tex]M(\frac{2-3}{2},\frac{2-3}{2})[/tex][tex]M(\frac{-1}{2},\frac{-1}{2})[/tex][tex]M(-\frac{1}{2},-\frac{1}{2})=(-0.5,-0.5)[/tex]The midpoint of the points (2,2) to (-3,-3) is at (-0.5, -0.5)
Solve the problems.1 A computer performs a calculation in 45 X 10-5 seconds to solve a math problem.How long does the computer need to calculate the solutions to 3 x 100 math problems?Write your answer in standard form,Show your work.Answer in seconds
Answers
time per math problem = 4.5 x 10 ^-5
number of math problems= 3 x 10^6
Multiply both expressions:
4.5 x 10^-5 x 3x 10 ^6
(4.5 x 3 ) ( 10^[-5+6] )
13.5 x 10^1 = 135
135 seconds
Imani's grandmother's house is 5 miles west of her own house down Main Street. While at hergrandmother's, Imani decides to ride her bike farther west down Main Street at 10 miles perhour. Which equation best describes the distance, d, in miles, Imani is from home after t hours?Ad=5+10tB.d= 5 – 10tC.d= 5t +10Dd= 5t – 10
Answers
Since the house is to the west and Imani will also ride to the west, the initial position (5 miles) and the speed (10 miles per hour) will have the same signal (positive).
Then, we can use the following equation to describe the distance d after t hours:
[tex]d=d_0+v\cdot t[/tex]Where d0 is the initial position and v is the speed. Using d0 = 5 and v = 10, we have:
[tex]d=5+10t[/tex]So the correct option is A.
15. What are the terms of the expression -102+2y-6z?
Answers
In mathematics, often the value of a certain number may be unknown. A variable is a symbol, usually a letter, which is used to represent an unknown number.
[tex]-102+2y-6z[/tex]In this expression we have a total of 3 terms
pls help me!! it's due tomorrow and I have a lot of homework rn.
Answers
ANSWER
The percentage of total budget spent on entertainment is 15%
STEP-BY-STEP EXPLANATION:
Given information
Rent = $350
Utilities = $125
Child care = $100
Food = $175
Entertainment = $150
Transportation = $50
Other = $50
Step 1: Find the total amount of the budget
Total amount = $(350 + 125 + 100 + 175 + 150 + 50 + 50)
Total amount = $ 1000.
The next thing is to find the percentage of the total budget spent on entertainment using the below formula
[tex]\begin{gathered} \text{ \% of total budget spent on entertainment = }\frac{amount\text{ spent on entertainment}}{\text{total budget}}\times\text{ 100\%} \\ \text{Amount spent on entertainment = \$150} \\ \text{ \% of total budget spent on entertainment = }\frac{150}{1000}\text{ }\times\text{ 100 \%} \\ \text{ \% of total budget spent on entertainment = 0.15 x 100\%} \\ \text{ \% of total budget spent on entertainment = 15\%} \end{gathered}[/tex]Hence, the percentage of total budget spent on entertainment is 15%
In a highschool 28% of the students are freshmen. 26% are sophmores, 22% are juniors, 24% are seniors. The amount lf students are 1600 How many more freshmen are there then juniors
Answers
We can find how many freshmen and juniors are with the following expression:
[tex]\begin{gathered} f=1600(28\text{ \%)=1600(0.28)=448} \\ j=1600(22\text{ \%)=1600(0.22)=352} \end{gathered}[/tex]then we can find the difference:
[tex]f-j=448-352=96[/tex]therefore, there are 96 more freshmen than there are juniors.
Helllo I need help with part b and part c but part c comes up after b
Answers
Part b
Decreasing intervals
The vertex is (0,0)
so
Interval (-infinite, 0)
Part c
Function is constant
Interval -----> DNE (not exist)
Alicia has 10 paintings she wants to hang side by side on her wall. if she only wants to display 3 of the paintings, how many ways can she choose to display the paintings? show your work.
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The number of ways she can choose to display the paintings is given by:
[tex]\frac{10!}{(10-3)!}=\frac{10!}{7!}=10\cdot9\cdot8=720[/tex]10b-2x+6 True Or False What Is The Expression Contains 2 Variables?
Answers
Sometimes we do not know the specific value of a quantity, in those cases we can represent it with a letter a, b, c, d, ..., x, y ,z, A, B, C, ..., Y, Z, those are called variables
Answer: TRUE. The expression 10b-2x+6, contains b and x, that is, it contains two variables
Solve the following formula for the indicated variable,7 Presolve for P
Answers
Given the formula
[tex]I=Prt[/tex]Solve for P, we divide by rt on both sides:
[tex]\begin{gathered} \frac{I}{rt}=\frac{Prt}{rt} \\ P=\frac{I}{rt} \end{gathered}[/tex]Answer:
[tex]\frac{I}{rt}[/tex]From the diagram below, if the tree is 61 ft. tall, and the angle of elevation from point B to the top of the tree is 29 °, find the distance that the tree is from point B. (Round to the nearest whole foot.)
Answers
So from the question, we get the height of the tree 61 ft and the angle of elevation in the B point 29°.
Now we going to use the trigonometric functions
We have the opposite side and an angle, and we going to find the adjacent side
The function that relates to all of this is tan
[tex]\tan(B)=\frac{opposite}{adjacent}[/tex][tex]\tan(29°)=\frac{61}{adjacent}[/tex]Solving for adjacent
[tex]\begin{gathered} adjacent=\frac{61}{\tan(29°)} \\ adjacent=110.04 \end{gathered}[/tex]Answer: 110 ft
find the slope of the line through each pair of points (-4,7) ,(-6, -4)
Answers
we have the ordered pairs
(-4,7) ,(-6, -4)
Applying the formula to calculate the slope
m=(-4-7)/(-6+4)
m=-11/-2
m=11/2A six sided die is rolled and a coin is tossed at the same time. What is the probability that the die will land on a number less than or equal to 5 AND the coin will land on tails? Write the answer is a fraction in lowest terms
Answers
Initi
We have two independent events:
A: the die will land on a number less than or equal to 5
B: the coin will land on tails
We have that
"A and B" mean the die landing on a number less than or equal to 5 AND the coin ladning on tails.
We want to find the probability of "A and B" to occur, this is
P(A and B) = P
We have that the probability of both to happen is given by their product, since they do not depend on each other:
P(A and B) = P(A) x P(B)