Answer:
f(-2) = 30Step-by-step explanation:
[tex]f(x)=x^4-3x^3+5x=1x^4-3x^3+0x^2+5x+0[/tex]
The Remainder Theorem states that when we divide a polynomial f(x)
by x − a the remainder R equals f(a).
a = -2
Syntetic substitution.
1. Write only the coefficients of x in the dividend inside an upside-down division symbol.
[tex]\underline{\begin{array}{c|ccccccc}\ &1&-3&0&5&0\\\ \end{array}}[/tex]
2. Put the divisor at the left.
[tex]\underline{\begin{array}{c|ccccccc}-2&1&-3&0&5&0\\\ \end{array}}[/tex]
3. Drop the first coefficient of the dividend below the division symbol.
[tex]\underline{\begin{array}{c|ccccccc}-2&1&-3&0&5&0\\\ \end{array}}\\\begin{array}{ccccccccc}\ \ \ \ &1\end{array}[/tex]
4. Multiply the drop-down by the divisor, and put the result in the next column.
[tex]\underline{\begin{array}{c|ccccccc}-2&1&-3&0&5&0\\\ &&-2\end{array}}\\\begin{array}{ccccccccc}\ \ \ \ &1\end{array}[/tex]
5. Add down the column.
[tex]\underline{\begin{array}{c|ccccccc}-2&1&-3&0&5&0\\\ &&-2\end{array}}\\\begin{array}{ccccccccc}\ \ \ \ &1&-5\end{array}[/tex]
6. Repeat 4 and 5 until you can go no farther
[tex]\underline{\begin{array}{c|ccccccc}-2&1&-3&0&5&0\\\ &&-2&10&-20&30\end{array}}\\\begin{array}{ccccccccc}\ \ \ \ &1&-5&10&-15&30\end{array}[/tex]
The remainder is 30, so f(-2) = 30.
Check:
[tex]f(x)=x^4-3x^3+5x\\\\f(-2)=(-2)^4-3(-2)^3+5(-2)=16-3(-8)-10=16+24-10=30[/tex]
What number must you add to complete the square x^2-16=23
Answer:
6,24
Step-by-step explanation:
6,24^2-16= 22,9376 -> 23
The length of a rectangular garden is 10 yards and it’s width is 10 feet. What is the perimeter of the garden in feet
Answer: 80 feet
Step-by-step explanation:
10 yard= 30 feet
2[l + b]
2{30+10}
(17 Leon uses 3/4 cup water to make a serving of iced tea.
Part A
If Leon makes 17 servings of iced tea, how many cups of water does
he use?
-cups
Part B
If the water cooler holds 88 servings of iced tea, how many cups of tea
does the cooler have?
cups
Answer:
A.) 12 3/4 cups
B.) 117 1/3
Step-by-step explanation:
Part A
If one serving of ice tea contains 3/4 cup of water, how much does 7 serving have?
To answer this, you must multiply 3/4 and 17
17 is the same as 17/1, so multiply the numerators and denominators
17 x 3 = 51
1 x 4 = 4
51/4 = 12 3/4
So, Leon used 51/4 or 12 3/4 cups of water
Part B
If the cooler has 88 servings of tea, how many cups of water does it have?
To solve this, divide 88 by 3/4
Dividing 88 by 3/4 is the same as multiplying 88 by 4/3.
Again, 88 is the same as 88/1 so multiply the numerators and the denominators.
88 x 4 = 352
1 x 3 = 3
352/3 = 117 1/3
So, there are 352/3 or 117 1/3 cups of water in the cooler
I hope this helps!
To make 17 servings of iced tea, Leon uses 12.75 cups of water. If the water cooler holds 88 servings of iced tea, it contains 66 cups of water.
The student is asking how to calculate the total amount of water needed for 17 servings of iced tea, with each serving using 3/4 cup of water. To find the total, we multiply the number of servings by the amount of water per serving:
17 servings times 3/4 cup/serving = 12.75 cups
For part B, to find out how many cups are in 88 servings:
88 servings times 3/4 cup/serving = 66 cups
Give the terms that best describes arc BC
Answer:
Option D. minor arc
Step-by-step explanation:
we know that
In a circle the measure of minor arc plus the measure of major arc is equal to 360 degrees
The measure of minor arc is less than 180 degrees
The measure of major arc is greater than 180 degrees
In this problem
Arc BDC is a major arc
Arc BC is a minor arc
Determine if these three equations are simplified correctly. You will earn 15 points to solve all of them!
1. (3x+7)÷(7)=3x
2.(6x)÷(2x^2)=(6)÷(2x+1)
3. (5+x)÷(5+2x)=(1)÷(x)
Thank you so Much!
Answer:
1. Not simplified correctly. It is (3/7)x + 1
2. Not simplified correctly. It is (3/x)
3. Not Simplified correctly. I believe it is as simplified as it can get
Step-by-step explanation: When a polynomial is over a denominator, ALL elements of the polynomial is affected
PLS HELP ASAP!!!! BRAINLIEST AND 20 POINTS!
Aisha can use the expression 120 divided by 10 to determine the solution to which problem?
A.What is 10% of 120?
B.What is 10% of 12?
C.What is 25% of 120?
D.What is 25% of 12?
Answer:
The answer would be A.
Step-by-step explanation:
This is because when you divde 120 by 10, you will be given an answer of 12. This shows that 10% of 120 is 12.
Answer:
A. What is 10% of 120?
Step-by-step explanation:
did it on edge and the other person is correct :] Hope this helps
How do I find AB. of a triangle on a graph?
If you are looking for a line measurement then I suggest using the distance formula. Which is [tex]\sqrt({x2-x1)^{2} +(y2-y1)^{2} }[/tex]
a shoe box measures 15 in. by 7 in. by 4 1/2 in. What is the surface area of the box?
Answer:
408 in²
Step-by-step explanation:
Given in the question that,
length of a show box = 15 in
width of a show box = 7 in
height of a show box = 4.5 in
Formula to calculate the surface area of shoe box is as following
2*(L*W + L*H + W*H)Plug values in the formula
2*(15*7 + 15*4.5 + 7*4.5)
2(105 + 67.5 + 31.5)
408 in²
The surface area of the box = 408 in²
Kevin's sock drawer contains 6 white socks, 4 black socks, 3 grey socks, and 5 red socks. If Kevin randomly picks two socks, what is the probability that they are both white?
Answer:
5/51
Step-by-step explanation:
The probability of Kevin choosing a white sock on the first pick, there are 6 white socks and 18 socks total so the chances are 6/18. But 6/18 simplified is 1/3. On the second choice he has to pick another sock and there are 5 left out of 17 socks total remaining. So the chances of him picking another sock are 5/17. If you multiply 1/3 by 5/17 you will end up with your answer, 5/51.
Probabilities are used to determine the chances of an event.
The given parameters are:
[tex]\mathbf{White = 6}[/tex]
[tex]\mathbf{Black = 4}[/tex]
[tex]\mathbf{Grey = 3}[/tex]
[tex]\mathbf{Red = 5}[/tex]
So, the total is:
[tex]\mathbf{Total = 6 + 4 + 3 + 5}[/tex]
[tex]\mathbf{Total = 18}[/tex]
The probability that both selections are white socks is:
[tex]\mathbf{Pr = \frac{White}{Total} \times \frac{White - 1}{Total - 1} }[/tex]
1 is subtracted from the fractions of the second factor, because it is a selection without replacement.
So, we have:
[tex]\mathbf{Pr = \frac{6}{18} \times \frac{6 - 1}{18 - 1} }[/tex]
[tex]\mathbf{Pr = \frac{1}{3} \times \frac{5}{17} }[/tex]
So, we have:
[tex]\mathbf{Pr = \frac{5}{51} }[/tex]
Hence, the probability that both selections are white socks is 5/51
Read more about probabilities at:
https://brainly.com/question/11234923
Which point has coordinates (4.9,3.9)
Point C is the answer
Answer:
Point C
Step-by-step explanation:
MATH :((
how do the chart??
[tex] - x ^{2} - 9 \geqslant 0[/tex]
Answer:
no solutionStep-by-step explanation:
[tex]-x^2-9\geq0\qquad\text{change the signs}\\\\x^2+9\leq0\\\\\text{the parabola}\ x^2\ \text{is op}\text{en up and shifted 9 units up. Therefore is whole}\\\text{over the x-axis (only positive values)}.\\\\\bold{CONCLUSION}:\\\\\bold{no\ solution}[/tex]
Find an equation for the nth term of the arithmetic sequence. a15 = -53, a16 = -5
Answer:
an = -773 + 48n
Step-by-step explanation:
an = a + (n -1)d
a15 = a + (15 - 1)d = -53
a + 14d = -53 .........1
a16 = a + (16 - 1)d = -5
a + 15d = -5 ............2
subtract equation 2 from 1
a - a + 14d - 15d = -53 + 5
-d = -48
d =48
substitute d =48 in equation 1
a + 14(48) = -53
a +672 = -53
a = -53 -672
a = -725
an = -725 + (n -1)48
an = -725 + 48n - 48
an = -773 +48n
8 1/2 + 7 2/3 = Write the answer as a mixed number.
let's firstly convert the mixed fractions to improper fractions, and then add them up.
[tex]\bf \stackrel{mixed}{8\frac{1}{2}}\implies \cfrac{8\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{17}{2}}~\hfill \stackrel{mixed}{7\frac{2}{3}}\implies \cfrac{7\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{23}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{17}{2}+\cfrac{23}{3}\implies \stackrel{\textit{using the LCD of 6}}{\cfrac{(3)17~~+~~(2)23}{6}}\implies \cfrac{51+46}{6}\implies \cfrac{97}{6}\implies 16\frac{1}{6}[/tex]
Point B is reflected over the x-axis to create B'. Where is B' on the coordinate plane?
Answer:
3,-5
Step-by-step explanation:
To rationalize the denominator 2 sqrt 10/ 3 sqrt 11 you should multiply the expression by which fraction
Answer:
B
Step-by-step explanation:
To rationalise the denominator.
Multiply the numerator/denominator by the radical on the denominator.
The radical on the denominator is [tex]\sqrt{11}[/tex], thus
Multiply the fraction by
[tex]\frac{\sqrt{11} }{\sqrt{11} }[/tex] → B
The expression (√11 /√11 ) needs to be multiplied to rationalize the denominator.
What are Rational Numbers ?Those numbers which can be written in the form p/q such that q > 0 ae called Rational Numbers.
The expression given is
( 2 √10) /( 3 √11 )
To rationalize the denominator , the radical √11 needs to be rationalize
( 2 √10) /( 3 √11 ) * (√11 /√11 )
(2√110) / 33
Therefore (√11 /√11 ) needs to be multiplied to rationalize the denominator.
Option B is the answer.
To know more about Rational Number.
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The sum of the present ages of George and his father is 60 years. In 6 years his father will be twice as old as George will be. Find their present ages.
Answer:
60+6= 66, 66/3= 22 in 6 years time his father will be 44 years. now his father age will 38 and George age will be 22
The present age of the father is 42 years and George is 18 years.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the sum of the present ages of George and his father is 60 years. In 6 years his father will be twice as old as George will be.
Make the two linear equations and solve them to get the present ages.
G + F = 60
2 ( G + 6 ) = F + 6
2G + 12 = F + 6
2G + 12 = 60 - G + 6
3G = 54
G = 18 years
Father's age will be,
F = 60 - 18
F = 42 years
To know more about an expression follow
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Help me help me help me help me help me help me
Answer:
Step-by-step explanation:
find the volume of each figure
PLEASE HELP A square has an area of 64 square units. Which set of coordinates could be the vertices of the square?
A) (3, –35) and (3, –28)
B) (21, –14) and (21, –22)
C) (32, –42) and (32, –7)
D) (74, 19) and (82, 27)
Answer:
B
Step-by-step explanation:
it is 64 units so 8 units long each
Answer:
B) (21, -14) and (21, -22)
Step-by-step explanation:
Given,
The area of the square = 64 square unit,
Let x be the side of the square,
[tex]\implies x^2 = 64[/tex]
[tex]\implies x = 8[/tex]
Hence, the side of the square = 8 unit,
⇒ The distance between the adjacent vertices in the square = 8 units,
By the distance formula,
The distance between (3, -35) and (3, -28) is,
[tex]\sqrt{(3-3)^2+(-28-(-35))^2[/tex]
[tex]=\sqrt{0+(-28+35)^2}[/tex]
[tex]=\sqrt{7^2}[/tex]
[tex]=7\neq 8[/tex]
Thus, (3, -35) and (3, -28) can not be the vertices of the square.
The distance between (21, -14) and (21, -22) is,
[tex]\sqrt{(21-21)^2+(-22-(-14))^2[/tex]
[tex]=\sqrt{0+(-22+14)^2}[/tex]
[tex]=\sqrt{8^2}[/tex]
[tex]=8[/tex]
Thus, (21, -14) and (21, -22) are the vertices of the square.
The distance between (32, -42) and (32, -7) is,
[tex]\sqrt{(32-32)^2+(-7-(-42))^2[/tex]
[tex]=\sqrt{0+(-7+42)^2}[/tex]
[tex]=\sqrt{35^2}[/tex]
[tex]=35\neq 8[/tex]
Thus, (32, -42) and (32, -7) can not be the vertices of the square.
The distance between (74, 19) and (82, 27) is,
[tex]\sqrt{(82-74)^2+(27-19)^2[/tex]
[tex]=\sqrt{8^2+8^2}[/tex]
[tex]=\sqrt{64+64}[/tex]
[tex]=\sqrt{128}[/tex]
[tex]=8\sqrt{2}\neq 8[/tex]
Thus, (74, 19) and (82, 27) can not be the vertices of the square.
A car rental company charges an initial fee plus a constant fee per kilometer driven.
The table compares the total distance driven on the trip (in kilometers) and the price of the rental (in dollars).
What is the cost of each kilometer driven?
Answer:
The cost of each kilometer driven is $0.6
Step-by-step explanation:
Let
x ------> the total distance driven on the trip (in kilometers)
y -----> the price of the rental (in dollars)
we have
(110,186) and (170,222) ----> see the table
step 1
Find the slope of the linear function
m=(222-186)/(170-110)
m=36/60
m=0.6 $/km
The slope of the linear equation is equal to the unit rate
so
The cost of each kilometer driven is $0.6
Answer:$120
Step-by-step explanation:
how do i factor 6x squared-12x?
Answer:
6x(x - 2)
Step-by-step explanation:
Find the common factors of 6x² - 12x, which is 6x.
A car wash cleans 3 cars in 24 min.
How many cars does the car wash clean in 56 min?
168 cars
8 cars
Jong
18 cars
7 cars
Help me please on c it would help so much
Answer: the answer is D
Step-by-step explanation:
20+25= 45 minutes already used up. there are 120 minutes in 2 hours that she has.
120-45= 75
75/120= .625
.625x100 to get you your percentage = 62.5%
Answer:
The answer is B
super easy points for you guys :) just need an answer
Answer:
3. Additive
4. [tex]x<2[/tex]
5. Graph the linear line. Then, make the line dotted and shade below the line.
Step-by-step explanation:
3. Adding -15 to both sides to isolate the variable.
4.
[tex]-3x+8>2x-2\\5x<10\\x<2[/tex]
Now I want to cover the curved area of the vase in paper. I do not want to cover the bases. My vase has a 6” diameter and is 12” tall. How many square inches of paper will I need?
Answer:
[tex]226.08\ in^{2}[/tex] or [tex]72\pi\ in^{2}[/tex]
Step-by-step explanation:
we know that
The lateral area of a cylinder ( curved area of the vase) is equal to
[tex]LA=2\pi rh[/tex]
we have
[tex]r=6/2=3\ in[/tex] ------> the radius is half the diameter
[tex]h=12\ in[/tex]
substitute the values
[tex]LA=2\pi (3)(12)=72\pi\ in^{2}[/tex] -----> exact value
assume
[tex]\pi=3.14[/tex]
[tex]72(3.14)=226.08\ in^{2}[/tex] ----> approximate value
What is the ratio for the volumes of two similar Pyramids, given that the ratio of the edge lengths is 8:3?
Answer:
D
Step-by-step explanation:
Given that the ratio of side lengths = 8 : 3, then
ratio of volumes = 8³ : 3³ = 512 : 27 → D
ANSWER
The correct answer is option D.
EXPLANATION
The given pyramids are similar and the side lengths are in the ratio 8:3
Volume is in cubic units, therefore the volume of the two similar pyramids are in the ratio;
[tex] {8}^{3} : {3}^{3} [/tex]
This simplifies to
[tex]512 : 27[/tex]
The correct answer is option D.
the sum of the interior angle measures of a convex 130 gon
(N-2)180
(130-2)180
128 x 180
23040
Final answer:
The sum of the interior angles of a convex 130-gon is 23040 degrees, calculated using the formula S = (n - 2) × 180° with n equal to the number of sides.
Explanation:
The sum of the interior angles of any polygon can be calculated by using the formula S = (n - 2) × 180°, where S is the sum of the interior angles and n is the number of sides in the polygon. In the case of a convex 130-gon, with n = 130, the calculation would be S = (130 - 2) × 180°. This simplifies to S = 128 × 180°, which is S = 23040°. Therefore, the sum of the interior angles of a convex 130-gon is 23040 degrees.
Since opening night, attendance at play A has increased steadily, while attendance at play B first rose and then fell. Equations modeling the daily attendance y at each play are shown below, Where x is the number of days since opening night. On what day(s) was the attendance the same at both plays? What was the attendance? Play A: y=15x+76 play B: y=-x^2+36x-4
Answer:
(5,151) and (16,316) are days with equal attendance for both plays.
Step-by-step explanation:
https://brainly.com/question/8102047
The correct answer is 5,101
I am a little stuck I just don’t really get expressions
Answer:
$66.50
Step-by-step explanation:
lets break this down a bit:
the tickets are $16 each
there is an additional $2.50 added when tickets are bought online, its a one time fee and does not apply to every ticket
n represents the amount of tickets bought
you're on the right track so far, the expression is as follows:
16n +2.50 <---n is placed next to the 16 because we are calculating the amount of tickets bought and their price plus the one time service fee of $2.50
we are then told that 4 tickets were bought
in this expression, n = 4, so we substitute 4 into the equation for n
16(4) + 2.50
16 x 4 = 64
instead of multiplying like you did on the worksheet, you would add since the original expression we wrote plus 2.50, not times 2.50
64 + 2.50 = 66.50
so, the total price for 4 tickets bought online is $66.50
you were on the right track! let me know if you need anything else cleared up about expressions
what is the equation of the circle that has center (0,-8) and passes through (9,7)?
Answer: x² + y² + 16y - 242 = 0
Step-by-step explanation: The equation of circle is given in the form (x -a)² + (y - b)² = r², where (a,b) is the center of the circle and r is the radius. But r is the distance from (0,-8) to (9,7)
the equation is (x-0)² + (y + 8)² = r²
x² + (y + 8)² = r²
hence r² = (x₁ - x₂)² + (y₁ - y₂)²
r² = (0 - 9)² + (-8 - 7)² = 81 + 225 = 306
hence the equation is
x² + y²+16y+64 = 306
x² + y² + 16y - 242 = 0
Find the volume of the prism.
Answer: 120 units3
Explanation: When finding the base of a prism, you must always multiply the side with the right angle. So basically, 5 is ignored because it does not have a right angle.
1st step: 3*4=12
2nd step: 12/2=6 (because the tringle which is the base is half a square)
3rd step: 6*20=120
The ending is unit 3 because it is volume. Area is unit 2 and we don't know if the prism is in cm so it is not A, or B, and D is the incorrect answer.
In conclusion:
120 units 3
Hope this helped!
Alin