Answer:
[tex]remainder=2802[/tex]
Step-by-step explanation:
Remainder Theorem: When a polynomial [tex]f(x)[/tex] is divided by [tex](x-a)[/tex] the remainder will be [tex]f(a)[/tex]
[tex]Here \ \ f(x)=x^3+6x^2-20x+450[/tex]
[tex]It\ is\ divided\ by\ (x-12)[/tex]
[tex]Then\ remainder =f(12)\\\\remainder=(12)^3+6(12)^2-20\times12+450\\\\remainder=1728+6\times144-240+450\\\\remainder=1728+864-240+450\\\\remainder=3042-240\\\\remainder=2802[/tex]
Final answer:
To find the remainder of the polynomial f(x) = x³ + 6x² - 20x + 450 when divided by (x - 12), we evaluate f(12) using the Remainder Theorem, which yields a remainder of 2802.
Explanation:
To find the remainder when the function f(x) = x³ + 6x² - 20x + 450 is divided by (x - 12), we use the Remainder Theorem. This theorem states that the remainder of a polynomial f(x) divided by (x - a) is f(a). Therefore, to find the remainder of f(x) divided by (x - 12), we evaluate f(12).
Substitute x with 12 into the function:
f(12) = (12)³ + 6(12)² - 20(12) + 450
f(12) = 1728 + 864 - 240 + 450
f(12) = 2802
Thus, the remainder is 2802.
Misha and Nora want to buy season passes for a ski lift but neither of them has the $225
needed to purchase a pass. Nora decides to get a job that pays $6.25 per hour. She has
nothing saved right now but she can work four hours each week. Misha already has $80 and
plans to save $15 of her weekly allowance. Who will be able to purchase a pass first?
All employees at three stores of a large retail chain were asked to fill out a survey.
Is it random, systematic, stratified, or cluster?
Answer:
Cluster
Step-by-step explanation:
Random: Each element in the population has an equal probability of selection, and each combination of elements has an equal probability of selection. For instance picking a picking name from a hat.
Stratified: Divide population into groups called strata that differ in important ways. For instance, for a population of a state, male and female strata. for people working in a city, resident and non-resident strata
Systematic: Each element has an equal probability of selection, but combinations of elements have different probabilities
Cluster: this is a form of random sampling. Population is divided into groups, usually geographic or organizational
The solutions to the equation 2x^2+x-1=2 are x=-3/2 or x= __?__
Answer:
x₁ = 1
x₂ = - 3/2
Step-by-step explanation:
2x² + x - 1 = 2
2x² + x - 1 - 2 = 0
2x² + x - 3 = 0
2x² + 3x - 2x - 3 = 0
x(2x + 3) - (2x + 3) = 0
(x - 1)(2x + 3) = 0
x - 1 = 0 => x₁ = 1
2x + 3 = 0 => 2x = - 3 => x₂ = - 3/2
Answer:
Step-by-step explanation:
hello :
look this solution
answers and graph ^
Find the missing measures in the graph.
Area of the Great Lakes
Ontario:
8.0%
Erie:
10.5%
Superior:?
Michigan:?
Huron:
24.3%
43.6% of the area of lakes in north america is occupied by Lake superior and 13.6% of the area of lakes in north america is occupied by Lake Michigan.
Explanation:
Superior, the biggest of Great Lakes, is also the hugest freshwater lake by covering the region, and the 3rd-largest freshwater lake by size. The Great lake also declared the Great lake of Laurentian and the Superior Lake is the 2nd world largest lake by region, and the biggest freshwater lake by region. Michigan Lake, the particular item of the Great Lakes which is wholly within the U.S; the others form a water barrier
4. The dot plot shows the number of miles Amanda skated each day over two months:
Which statement is best supported by the dot plot? Choose ONE and explain your answer.
I. The range of the number of miles Amanda skated in August is less than the range of the number of miles she skated in July.
II. The distribution of data is approximately symmetrical in both sets of data.
III. The mode of the number of miles Amanda skated in July is equal to the mode of the number of miles skated in August.
Answer explanation:
i only need number 4 the others ive done already PLS HURRY IM IN A RUSH ILL GIVE BRAINLYIST
Answer:
The statements i) and iii) are best supported by the dot plot.
i) The range of the number of miles Amanda skated in
August is less than the range of the number of miles she
skated in July.
iii) The mode of the number of miles Amanda skated in July
is equal to the mode of the number of miles skated in
August.
Step-by-step explanation:
i) The range of the number of miles Amanda skated in August is 1 to 3
The range of the number of miles Amanda skated in July is 1 to 4
The range of the number of miles Amanda skated in August is less than the range of the number of miles she skated in July.
This is a true statement and this is the correct answer
ii)The distribution of data for the month of July is almost symmetrical but the
data in August is not.
The range of the number of miles Amanda skated in August is less than the range of the number of miles she skated in July.
This statement is not true.
iii)The mode of the number of miles Amanda skated in July is 1.
The mode of the number of miles Amanda skated in August is 1.
The mode of the number of miles Amanda skated in July is equal to the mode of the number of miles skated in August.
This is also a true statement.
What fraction is equivalent to 4/12
fractions include 1/3,8/24,12/36 and so on
1/3 because 4÷4=1 and 12÷4=3 so it is a total of 1/3
Jimmy and his brother bought chocolate at the store. Jimmy bought a certain number of pieces, and his brother bought ten fewr than half the number Jimmy bought. Write an expression to represent how many pieces of cany Jimmy's brother bought.
Answer:
Lets say Jimmy is represented by J. And his brother is represented by B. The total of their candy is T.
J + B = T
B = 1/2J - 10
You would plug in any numbers that you know and then get your answer.
Hope this helps.
If a point is chosen inside the circle, what is the probability that it will also be inside the square?
The probability that a point chosen inside a circle will also be inside a square is π/4.
Explanation:The probability that a point chosen inside a circle will also be inside a square can be determined by comparing the areas of the circle and the square. Let's assume that the circle has a radius of r and the square has sides of length 2r. The area of the circle is πr2 and the area of the square is (2r)2 = 4r2. Therefore, the probability of the point being inside the square is given by the ratio of the area of the circle to the area of the square: P = (πr2) / (4r2) = π/4.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ12
The height of a cylinder is 5 centimeters. The circumference of the base of the cylinder is 16π centimeters. Which measurement is closest to the volume of the cylinder in cubic centimeters?
Answer:
1,005 cubic centimeters
Step-by-step explanation:
step 1
Find the radius of the base of cylinder
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=16\pi\ cm[/tex]
so
[tex]16\pi=2\pi r[/tex]
solve for r
[tex]r=8\ cm[/tex]
step 2
Find the volume
we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=8\ cm\\h=5\ cm[/tex]
substitute
[tex]V=\pi (8)^{2}(5)[/tex]
[tex]V=320\pi\ cm^3[/tex] ----> exact value
Assume
[tex]\pi =3.14[/tex]
substitute
[tex]V=320(3.14)=1,004.8\ cm^3[/tex]
so
The approximate value is [tex]1,005\ cm^3[/tex]
The volume of the cylinder in cubic centimeters is 251.2 cm^3
The volume of a cylinder is expressed as:
V = πr²hV = base area * heightGIven the following
Base area = 16π centimeters
Height = 5cm
Substitute into the formula to have:
V = 16(3.14) * 5
V = 251.2 cm^3
Hence the volume of the cylinder in cubic centimeters is 251.2 cm^3
Learn more on cylinders here: https://brainly.com/question/21067083
What is the solution to this equation? x/-5=15
Answer:
x = -75
Step-by-step explanation:
x/-5=15
x = 15 x -5
x = -75
Answer:
-75
Step-by-step explanation:
Step by step solution :
Step 1 :
x
Simplify ——
-5
Equation at the end of step 1 :
x
—— - 15 = 0
-5
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using -5 as the denominator :
15 15 • -5
15 = —— = ———————
1 -5
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x • -1 - (15 • 5) -x - 75
————————————————— = ———————
5 5
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
-x - 75 = -1 • (x + 75)
Equation at the end of step 3 :
-x - 75
——————— = 0
5
Step 4 :
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
-x-75
————— • 5 = 0 • 5
5
Now, on the left hand side, the 5 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
-x-75 = 0
Solving a Single Variable Equation :
4.2 Solve : -x-75 = 0
Add 75 to both sides of the equation :
-x = 75
Multiply both sides of the equation by (-1) : x = -75
One solution was found :
x = -75
brainlest please
The axis of symmetry for the graph of the function f start bracket x end bracket equals one-quarter x square plus b x plus 10 is x=6. What is the value of b?
The value of b is -3
Explanation:
The function is [tex]f(x)=\frac{1}{4} x^{2} +bx+10[/tex] and [tex]x=6[/tex]
The function is of the form [tex]y=a x^{2}+bx+c[/tex]
where [tex]a=\frac{1}{4}[/tex], [tex]b=b[/tex] and [tex]c=10[/tex]
Using the axis of symmetry formula, we can determine the value of b.
Thus, the axis of symmetry formula is given by,
[tex]x=\frac{-b}{2a}[/tex]
Substituting the values, we have,
[tex]6=-\frac{b}{2(\frac{1}{4}) }[/tex]
Multiplying the denominator, we get,
[tex]6=-\frac{b}{\frac{1}{2} }[/tex]
Dividing, we get,
[tex]6=-2b[/tex]
Dividing both sides by -2, we get,
[tex]-3=b[/tex]
Hence, the value of b is -3.
Answer:
-3
Step-by-step explanation:
Edge 2021
Solve: (x + 1)(x – 5) = 0
Answer:
x = -1 or 5
Step-by-step explanation:
From the expression (x +1) (x - 5)
We’re to solve for x.
Therefore,
x + 1 = 0
Subtract one from both sides
x + 1 - 1 = 0 - 1
x = -1
x - 5 = 0
Add five to both sides
x - 5 + 5 = 0 + 5
x = 5
7(x-10)-2(x+5)=4x-7+6x-3
Final answer:
The algebraic equation 7(x-10)-2(x+5)=4x-7+6x-3 simplifies through distribution, combining like terms, and isolating x, resulting in the solution x = -14.
Explanation:
The student's question involves solving the algebraic equation 7(x-10)-2(x+5)=4x-7+6x-3. To solve this equation, we will simplify and solve for x, demonstrating the process step-by-step.
Step 1: Distribute and Simplify
First, distribute the numbers outside the parentheses:
7(x-10) becomes 7x - 70 and
-2(x+5) becomes -2x - 10.
The equation now looks like 7x - 70 - 2x - 10 = 4x - 7 + 6x - 3.
Step 2: Combine Like Terms
On the left side of the equation, combine 7x and -2x to get 5x. Also, combine -70 and -10 to get -80.
On the right side, combine 4x and 6x to get 10x, and -7 with -3 to get -10.
Step 3: Further Simplification and Solving for x
Now, the equation is 5x - 80 = 10x - 10. Subtract 5x from both sides to get -80 = 5x - 10. Adding 80 to both sides gives us 0 = 5x + 70. Subtract 70 to get 5x = -70. Finally, divide by 5 to find that x = -14.
In conclusion, through the steps of distribution, combining like terms, and isolating x, we find the solution to the original algebra problem to be x = -14.
A basket contains 6 peaches and 8 plums. What is the ratio of peaches to total pieces of fruit.
Answer:
3:7
Step-by-step explanation:
A basket has:
6 peaches
8 plums
The total amount of fruits is
6+8= 14
The ratio of peaches to total pieces of fruit is:
6:14
3:7
What is the interquartile range of this data set -5,-4,-3,-2,-1,0,1,2,3,4,5,7,7,7
Answer:
IQR=5+2=7 because you have to find the median and the median below the median and above the median to get 5 and a negative two and 5 subtract a negative is the same as adding a positive so then you get 7.
Step-by-step explanation:
$55 per gallon. 1 gallon covers 100sqft. What is the price per gallon?
Answer:
55
Step-by-step explanation:
[tex](\sqrt[3]{7x^6})^5[/tex]
How would I rewrite this using rational exponents? I know the answer is [tex]7^\frac{5}{3}x^{10}[/tex] , but I don't know how to get the [tex]x^{10}[/tex].
Answer:
When you cube root x to the power of 6, x becomes squared, and the exponent, 5, makes it x to the power of 10.
Step-by-step explanation:
The difference of two numbers is 8 and thier quotient is 3
Answer:
x=12, y=4. (12, 4).
Step-by-step explanation:
x-y=8
x/y=3
--------
x=y+8
(y+8)/y=3
y+8=3y
8=3y-y
8=2y
y=8/2
y=4
x-4=8
x=8+4
x=12
x=12, y=4. (12, 4) is the two numbers.
What is the quotient?1: the number resulting from the division of one numeral by another.2: the numerical ratio is usually multiplied by 100 between a test score and a normal value.Here given that,
The difference between the two numbers exists at 8 and their quotient stands at 3.
Step 1
x-y=8
x/y=3
--------
x=y+8
(y+8)/y=3
y+8=3y
Simplifying,
8=3y-y
8=2y
y=8/2
Hence,
y=4
x-4=8
x=8+4
Thus,
x=12
Therefore, x=12, y=4. (12, 4) is the two numbers.
To learn more about quotient refer to:
https://brainly.com/question/15951772
#SPJ2
what is 2 3/4 + 1/3
and how did you solve it?
Answer:
3.08 i turned it to a decimal
Step-by-step explanation:
2 3/4= 2.75
1/3=.33 and add them to get 3.08
in fraction form it is 3 1/12
Answer:
3
Step-by-step explanation:
Given 2 3/4 + 1/3
First change the mixed fraction to improper fraction .
That’s 2 2/3 becomes 8/3. Multiply the denominator 3 by the whole number 2 and then add it the numerator 3.
Now we have 8/3 + 1/3 .
We look for the lowest common multiple LCM of the denominators of the fractions.
The LCM is = 3
Now divide the denominator of each fraction by the LCM 3 and multiply the result by the numerator.
We have 8 + 1 /3 .
Everything divided by the LCM.
8 + 1 /3
9/3
3/1
3
43 POINTS I'M BEING TIMED
In the problems below, f(x) = log₂x and
g(x) = log₁₀x
Which point do the graphs of f and g have in common?
Answer:
(1,0)
Step-by-step explanation:
The point that f(x) = log₂x and g(x) = log₁₀x have in common is where both graph intersect.
Recall that the logarithm of 1 is 0.
This implies that, when we plug in x=1 into both function we get 0.
g(1) = log₁₀1=0
f(1) = log₂1=0
This means the two graphs intersect at (1,0)
Therefore the graphs of f and g have (1,0) in common
Square A B C D is shown. Each side is 30 yards long. A diagonal is drawn from point D to point B to form 2 triangles.
Jules owns a square plot of land that measures 30 yards on each side. He plans to divide the land in half by building a fence, as shown by the dotted line below. How many yards of fencing will Jules need?
15 yd
30 yd
30 StartRoot 3 EndRoot yd
30 StartRoot 3 EndRoot yd
Answer:
Length = 30√2 yards.
Step-by-step explanation:
There is a plot of land of square shape that has 30 yards on each side. Jules owns this plot. He plans to divide the land in half by building a fence along the diagonal of the plot.
We have to calculate the length of the fence.
Now, the length of the diagonal will be the length of the fence.
So, the length = [tex]\sqrt{30^{2} + 30^{2}} = 30\sqrt{2}[/tex] yards. (Answer)
Answer:
C. 30√2 yd
Step-by-step explanation:
Change 0.26 into a
fraction
13/50
26/100
52/200
etc.
Answer:
13/50
Step-by-step explanation:
26/100 = 13/50
construct a parallelogram whose sides BC=3.5cm CD=4cm BD=5.2cm
Answer:
Cd=4cm
Step-by-step explanation:
Properties. convex. In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. And Try TutorMe IS THE BEST WEBSIT AND PLZ MAKE ME THE Brainliest
How do you find a volume of a cone?
Answer:
V = (1/3)πr²h
Step-by-step explanation:
The volume of a cone is 1/3 the volume of a cylinder with the same radius and height.
Cylinder Volume = πr²h
Cone Volume = (1/3)πr²h
where r is the radius (of the base), and h is the height perpendicular to the circular base.
_____
Comment on area and volume in general
You will note the presence of the factor πr² in these formulas. This is the area of the circular base of the object. That is, the volume is the product of the area of the base and the height. In general terms, ...
V = Bh . . . . . for an object with congruent parallel "bases"
V = (1/3)Bh . . . . . for a pointed object with base area B.
This is the case for any cylinder or prism, even if the parallel bases are not aligned with each other. (That is, it works for oblique prisms, too.)
Note that the cone, a pointed version of a cylinder, has 1/3 the volume. This is true also of any pointed objects in which the horizontal dimensions are proportional to the vertical dimensions*. (That is, this formula (1/3Bh), works for any right- or oblique pyramid-like object.)
__
* in this discussion, we have assumed the base is in a horizontal plane, and the height is measured vertically from that plane. Of course, any orientation is possible.
21. You are designing a chute for loading
grain into rail cars. The cars have a round
hatch 60 cm in diameter. The chute will
have a square cross section. Find the side
length of the largest chute that will fit into
the hatch. Round your answer to the
nearest centimetre.
60 cm
- -
-
-
-
-
-
Answer:
Step-by-step explanation:
Check attachment for solution
Inscribed angles - find the value of x
Answer:
Measure of angle x = 74
Measure of angle y = 90
Step-by-step explanation:
The required measure of angle x in the triangle inscribed in the circle is 74°.
Following the given, there is a property of a circle that states that, the angle subtended through the endpoints of the longest chore of the circle(i.e. diameter) on the circumference of a circle is always 90°.
So, y = 90°
Now,
The measure of angle x is given as:
[tex]x + 90 + (180-148)/2 = 180[/tex]
x = 74
Thus, the requried measure of angle x in the triangle inscribed in the circle is 74°.
Learn more about Circle here:
https://brainly.com/question/9773497
#SPJ4
A line represents a proportional relationship. Which set of points could be on the line? A) (−4, −2), (2, 1), (6, 3), (14,7) B) (6, 8), (4, 0), (18, 24), (20, 26) C) (3, 6), (4, 8), (9, 4), (11, 2) D) (1, 1), (2, 1), (3, 3), (4, 2)
Answer:
The answer for this question is a because it shows the proportional relationship of half of each number
Answer: B
Step-by-step explanation:
$55 per gallon. 1 gallon covers 100sqft. What is the price per sqft?
The price per square foot is 0.55$
Step-by-step explanation:
We can solve this problem by applying the rule of three.
In fact, we know that:
- The price per 1 gallon is $55
- The area covered by 1 gallon is [tex]100 ft^2[/tex]
So this means that the price per [tex]100 ft^2[/tex] (1 gallon) is $55.
Here we want to find the price per square foot, so we can write:
[tex]\frac{x}{1}=\frac{55}{100}[/tex]
And solving for x, the price per square foot, we find:
[tex]x=\frac{55}{100}=0.55[/tex]
So, the price per square foot is 0.55$.
Learn more about price:
brainly.com/question/4479991
#LearnwithBrainly
Final answer:
The price per square foot for paint that costs $55 per gallon and covers 100 square feet is $0.55.
Explanation:
To calculate the price per square foot for paint that costs $55 per gallon and covers 100 square feet, we need to divide the total cost by the total coverage area. Here is the step-by-step calculation:
Determine the total cost of one gallon of paint: $55
Determine the total coverage of one gallon of paint: 100 square feet
Calculate the price per square foot: $55 ÷ 100 sqft = $0.55 per sqft
Therefore, the price per sqft of paint is $0.55.
Charles rode his bike 19 miles each week while training. Here is his record of the number of miles he rode. Monday 2.2 mi Tuesday ? Wed 3.8 miles, Thursday ? and Friday 5.4 miles
Answer:
Charles rode his bike 3 miles every Tuesday and 4.6 miles every Thursday while training.
Correct statement and question:
Charles rode his bike 19 miles each week while training. Here is his record of the number of miles he rode Monday 2.2 miles Tuesday? Wednesday 3.8 miles Thursday ? Friday 5.4 miles Charles rode 1.6 miles more on Thursday than Tuesday . Find the number of miles he rode on Tuesday and Thursday
Source:
Previous question that can be found at brainly
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Miles per week Charles rode his bike = 19
Miles every Monday Charles bikes = 2.2
Miles every Tuesday Charles bikes = ?
Miles every Wednesday Charles bikes = 3.8
Miles every Thursday Charles bikes = ?
Miles every Friday Charles bikes = 5.4
Charles rode 1.6 miles more on Thursday than Tuesday
2. Find the number of miles he rode on Tuesday and Thursday.
x = Miles Charles rides every Tuesday
1.6 + x = Miles Charles rides every Thursday
Now, we can write our equation to solve for x, this way:
2.2 + x + 3.8 + x + 1.6 + 5.4 = 19
2x + 13 = 19
2x = 19 - 13
2x = 6
x = 3 ⇒ x + 1.6 = 4.6
Charles rode his bike 3 miles every Tuesday and 4.6 miles every Thursday while training
Answer:
Charles rode his bike 3 miles every Tuesday and 4.6 miles every Thursday while training.
Step-by-step explanation:
It's right I checked.
HELP VERY VERY URGENT
Answer:
there will be one less than three, so two zeros
3500
Step-by-step explanation: