2. Evaluate the polynomial two ways: by substituting in the given
value of x, and by using long division.
Find P(-3)for P(x)= 4x2 +10x - 8.
Answers
Answer:
P(-3) = -2
Step-by-step explanation:
Substitution
P(-3) = 4(-3)^2 +10(-3) -8 = 36 -30 -8
P(-3) = -2
__
Long Division
See the working below. The remainder is -2, so ...
P(-3) = -2
Related Questions
The following frequency table shows the number of hours each of the staff members at Eroy's Electronics slept Thanksgiving night. Find the mean number of hours of sleep.
Answers
Answer:
Mean
=Sigma (Number of sleep ×Number of employees) / Sigma Number of employees
= (3×1) + (4×0) + (5×0)+ (6×2)+(7×1)+(8×1) / 1+0+0+2+1+1
= 3+0+0+12+7+8/ 1+0+0+2+1+1
= 30 / 5
= 6
So the mean of number of hour sleep is 6 hours.
I hope this helps
if u have question let me know in comments ^_^
Answer:
Step-by-step explanation:
Mean
=Sigma (Number of sleep ×Number of employees) / Sigma Number of employees
= (3×1) + (4×0) + (5×0)+ (6×2)+(7×1)+(8×1) / 1+0+0+2+1+1
= 3+0+0+12+7+8/ 1+0+0+2+1+1
= 30 / 5
= 6
So the mean of number of hour sleep is 6 hours.
I hope this helps
The area of a rectangle is 36 square centimeters. Give all possible whole-number dimensions of the rectangle. Which rectangle has the greatest perimeter?
Answers
Answer:
ALL POSSIBLE DIMENSIONS OF THE RECTANGLE (whole numbers):
1 cm and 36 cm (Perimeter = 74 cm)
2 cm and 18 cm (Perimeter = 40 cm)
3 cm and 12 cm (Perimeter = 30 )
4 cm and 9 cm (Perimeter = 26)
6 cm and 6 cm Perimeter= 24 (squares are also considered rectangles, this is a square because of equal sides)
The rectangle with the greatest perimeter consists of the dimensions 1 cm and 36 cm.
EXPLANATION:
I listed all possible factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
And have come up with 5 possible dimensions with numbers from the listed factors above (when the dimensions of each rectangle are multiplied the result will be 36/the area)
Multiplication is used because the area of a rectangle is length x width
And I used the formula for perimeter:
2 (l + w)
And found the greatest perimeter (74 cm) that belongs to the rectangle with the dimensions 36 cm and 1 cm.
Which mean the same as 60%? Check all that apply
a.3/5
b. 0.06
c. 0.60
d. 6/10
e. 6/100
Answers
step by step explanation:
3/5 can be 60%. Why? If you multiply 20 with 5 and 3, it would be 60/100. It is basically the same thing as 69%.
0.60 is the same as 60% because if you made it into a fraction, it would become 60/100. In result, 60%.
6/10 is the same as 60% because if you multiplied both numbers by 10, it would be 60/100. And again, it would become 60%.
if alan had bought a figure at a discount of 5%, he would pay $20 less. How much would he pay if he had bought it at a discount of 20%
Answers
Answer:
80
Step-by-step explanation:
5%-->20% is increased by x4, therefore you multiply 20 by 4 which is 80 or you can set an proportion
5/20=20/x5x=400x=80The first step in solving this is hidden in the sentence “discount of 5%, he would pay $20 less”. This informs us that 5% of the price and $20 are the same
Our next step is to find how much 100% of the price is
Multiplying 5 and 20 gets us 100, so multiplying 5% by 20 will get us 100%
We already know that 5% is $20, so we can multiply $20 by 20 to get to 100% percent of the price
(20*20=400)
Now that we know the total price, we can find a discount of any percent. Since we know that a five percent discount will give you $20 dollars off, we can deduce that a 20% discount will give us $80 off.
(20/5=4)
(4*20=80)
(400-80=320!)
Hopefully this helps, if you need me to explain anything again I’ll try my best!
Find an equation of the line with the slope m= 3 that passes through the point (2,2). Write the equation in the form Ax+By = C.
Answers
Answer:
[tex]y = 3x-4[/tex]
Step-by-step explanation:
We know that if we were to write an equation with the slope of 3, it would be [tex]y=kx[/tex], where k is the constant (in this case 3.)
So right now, we have [tex]y=3x[/tex].
However, this will not pass through the point (2,2). To do this, we need to add a y-intercept in which (2,2) will be crossed through.
If we have a y-intercept of -4, the points will be:
(0, -4)
(1, -1)
(2, 2)
So our final equation is [tex]y = 3x-4[/tex].
Hope this helped!
Answer: 3x-1y=4 in Ax+By=C form
Step-by-step explanation:
the intercept form is y=3x-4
subracting 3x from both sides would get -3x+y=-4
distributing -(-3x+y=-4) would get 3x-y=4.
The number of oranges that Joe has is a multiple of 6. When he sells one orange, the number of oranges is a multiple of n. If n is a positive integer less than 10, how many possible values are there for n?
Answers
Answer:
2
Step-by-step explanation:
The number of oranges he has is a multiple of 6, so the number can be
6, 12, 18, 24, 30, 36, 42, 48, 54, etc.
He sells one orange, so now he an have:
5, 11, 17, 23, 29, 35, 41, 47, 53, etc.
All numbers above up to 53 are multiples of 1, so n can be 1.
Also 5 and 35 are multiples of 5, so n can be 5.
All numbers other than 5 and 35 are prime.
Answer: 2
Machine A can fill 1 box of nails in 6 minutes. Machine B can fill 1 box of nails in 9 minutes. They started to work at the same time and they stopped also at the same time. In all they filled 100 boxes. How many were filled by machine A?
Answers
A-
1 box --- 6 minutes
y boxes --- 1 minute
y = 1/6
B-
1 box --- 9 minutes
t boxes --- 1 minute
t = 1/9
So...
r - used time
r(1/9 + 1/6)=100
r=(100.18)/5
r= 360 minutes
1/6 . 360 = 60 boxes
answer: 60 boxes
In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.
Let's use the concept of the rate of work to solve this problem. The rate of work is the amount of work done per unit of time.
Machine A's rate of work is 1 box of nails every 6 minutes.
Machine B's rate of work is 1 box of nails every 9 minutes.
Let's assume that machine A filled x boxes, and machine B filled y boxes. Since they worked for the same amount of time, the total number of boxes filled by both machines is 100.
So, the equation representing the total work is:
x (boxes filled by A) + y (boxes filled by B) = 100
Now, let's use their rates of work to form two more equations:
Rate of work of A = 1 box every 6 minutes
Rate of work of B = 1 box every 9 minutes
Since work = rate × time, we can write two equations:
x (boxes filled by A) = (1/6) * t (time in minutes)
y (boxes filled by B) = (1/9) * t (time in minutes)
Since they both worked for the same time, we can set the time for both machines as equal:
t = t
Now, we have a system of equations:
x + y = 100
x/6 = y/9
t = t
Let's solve the system of equations. We can start by substituting the value of y from the second equation into the first equation:
x + (x/6)*3 = 100
x + (x/2) = 100
Multiply both sides by 2 to eliminate the fraction:
2x + x = 200
3x = 200
x = 200/3
Now, let's find the value of y using the second equation:
y = (x/6)*3
y = (200/3)/6 * 3
y = 200/3
So, machine A filled 200/3 boxes of nails, which is approximately 66.67 boxes.
Machine B filled 200/3 boxes of nails, which is also approximately 66.67 boxes.
Since they cannot fill a fraction of a box, we can distribute the remaining 2/3 box between machine A and machine B, giving one extra box to each.
In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.
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hey im sry if im asking to many questions i really want help
Answers
Answer:
V= 6,000 cm^3
Step-by-step explanation:
(15*20*10) + (10*20*15)
3000 + 3000
6000 cm^3
Answer:
6000 cm³
Step-by-step explanation:
20 * 10 * 15 + (20 * 10 * 15) = 6000 cm³
If you apply the changes below to the absolute value parent function, f(x)=x, what is the equation of the new function? Shift 2 units to the right shift 3 units down
Answers
Answer:
f(x) = Ix - 2I -3
Step-by-step explanation:
f(x) = IxI
f(x) = Ix - 2I -3
The equation is f(x) = | x – 2 | + 3 Then the vertex of the absolute function will be at (2, 3).
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x – h | + k
If you apply the changes below to the absolute value parent function
f(x) = |x|
Then the equation of the new function will be
Shift 2 units to the right, shift 3 units down
f(x) = | x – 2 | + 3
Then the vertex of the absolute function will be at (2, 3).
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A shop sells “Gello” pens and “Inko” pens. A “Gello” pen costs £5 and an “Inko” pen costs £7. One day the shop sold 17 pens and recieved £109. How many of each type of pen were solved? Form a pair of simultaneous equations to solve this question.
Answers
Answer:
5 Gello Pens and 12 Inko Pens.
12 Inko Pens adds up to 84.
5 Gello Pens adds up to 25.
84 + 25 = 109.
I hoped this helped :)
what is -4 as a fraction
Answers
Answer:
-4/1
Step-by-step explanation: whenever you have a whole number you just put a 1 as the denominator to make it a fraction.
Rearrange the tiles so that it shows the proper steps of solving this quadratic equation using square property
Answers
Answer:
see explanation
Step-by-step explanation:
Given
(x + 2)² = 25 ( take the square root of both sides )
x + 2 = ± [tex]\sqrt{25}[/tex] ← Step 1
x + 2 = ± 5 ← Step 2 ( subtract 2 from both sides )
x = - 2 ± 5 ← Step 3
On a certain map, 3 inches represents 15 miles. Briarwood and Middletown are 5 inches apart on the map. What is the actual distance between Briarwood and Middletown? A. 25 mi B. 30 mi C. 50 mi D. 75 mi
Answers
Answer:
i think the answer is a. 25
Calculate the area of the circle to the nearest hundredth of a square unit. Approximate as 3.14. a. 124.63 cm 2 b. 124.6 cm 2 c. 39.56 cm 2 d.19.78 cm 2
Answers
Answer:
[tex]124.63[/tex]
Step-by-step explanation:
[tex]a = \pi \times r {}^{2} = \pi \times (6.3) {}^{2} = \pi \times 39.69[/tex]
[tex]\pi \times 39.6 = 3.14 \times 39.69 = 124.63[/tex]
Hope this helps ;) ❤️❤️❤️
The area of circle will be;
⇒ 124.63 cm²
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The radius of circle = 6.3 cm
Now,
Since, The radius of circle = 6.3 cm
We know that;
Area of circle = π r²
Hence, We get;
⇒ Area of circle = 3.14 × 6.3²
= 3.14 × 39.69
= 124.63 cm²
Thus, The area of circle will be;
⇒ 124.63 cm²
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L-Lcosθ=v^2/2 solve for L
Answers
Answer:
[tex]$L=\frac{v^2}{2-2\cos(\theta)}$[/tex]
Step-by-step explanation:
Solve for [tex]L[/tex] in
[tex]$L-L \cos(\theta)=\frac{v^2}{2} \Longrightarrow L(1-\cos(\theta))=\frac{v^2}{2}$[/tex]
[tex]$L=\frac{v^2}{2(1-\cos(\theta))}=\frac{v^2}{2-2\cos(\theta)}$[/tex]
help me please real quick
Answers
Volume of cuboid = L x b x h = 8 x 5 x 9 = 360.
Answer:
D) [tex]360 m^{3}[/tex]
Step-by-step explanation:
Let's review the formula for finding the volume of a cube or rectangular prism.
[tex]V = (l)(h)(w)[/tex] - Basically saying "Volume = length × height × width".
In this case, you can consider 9 meters as the length, 5 meters as the height, and 8 meters as the width (but it doesn't really matter which dimensions are which since you are just multiplying them all together).
Now, let's multiply our dimensions together.
[tex]9 * 5 * 8 = 360[/tex]
That's your answer! Make sure to not forget your units (in this case, meters) cubed.
Hope that helps and maybe earns a brainliest!
Have a splendid day! <3
Describe the transformations that will map triangle A to triangle B and illustrate the similarity between the two triangles.
A) reflect triangle a across the y-axis and then translate triangle a 5 units down. B) reflect triangle A across the x-axis and then reflect triangle a across the y-axis.
C) translate triangle a 4 units down and then rotate triangle A 180° counterclockwise about the origin.
D) reflect triangle a across the x-axis and then rotate triangle A 90° counterclockwise about the origin
Answers
The triangle is shifted 4 units downwards and then is rotated about the origin.
What is image rotation?A rotation is a type of transformation which is a turn.A figure can be turned clockwise or counterclockwise on the coordinate plane.In both transformations the size 3 shape of the figure stays exactly the same.Given are triangles A and B.
Transformation 1 : The triangle is shifted 4 units downwards.
Transformation 2 : The figure is rotated about the origin.
Therefore, the triangle is shifted 4 units downwards and then is rotated about the origin.
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calculate the size of angle x. the sides are 8cm, 11cm and 15cm
Answers
Answer:19.93
Step-by-step explanation:
11 x 8 x 15 = 1320
then u would simplify
The value is: angle x is approximately 103.95 degrees.
Here, we have,
To calculate the size of angle x, you can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.
In this case, the sides of the triangle are given as follows:
a = 8 cm (adjacent to angle x)
b = 11 cm (opposite to angle x)
c = 15 cm (hypotenuse)
The Law of Cosines states:
c² = a²+ b² - 2ab*cos(x)
Substituting the given values:
15² = 8² + 11² - 2(8)(11)*cos(x)
225 = 64 + 121 - 176*cos(x)
Simplifying:
225 = 185 - 176*cos(x)
Rearranging the equation:
176cos(x) = 185 - 225
176cos(x) = -40
Now, divide both sides by 176 to isolate the cosine term:
cos(x) = -40/176
cos(x) ≈ -0.2273
To find the value of angle x, take the inverse cosine (cos⁻¹) of -0.2273:
x ≈ cos⁻¹(-0.2273)
x ≈ 103.95 degrees
Therefore, angle x is approximately 103.95 degrees.
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In which pair do both decimals represent rational numbers?
A. 0.397 and 0.8999...
B. 2.28182845904523536... and 0.8999
C. 9.1426535893793238... and 0.397
D. 9.1426535893793238... and 0.8999...
Answers
Answer:
Option b
step by step explanation:
Answer:
Option (A)
Step-by-step explanation:
0.296 and 0.9888 is correct because rational no are terminating and repeating ..
What is the volume of the right triangular prism shown?
Answers
Answer:
C. 567yd^3
Step-by-step explanation:
To find the volume of the right triangular prism, it is: 1/2a c h.
In this case, 1/2✖️9✖️6✖️21=567yd^3
So this means that option C is the correct answer.
Hope this helps!
Have a nice day:)
Answer:
567 cu. yard
Step-by-step explanation:
will make it simple and short.
Vol = area of a triangle x length
Vol = (1/2 * 6 * 9 ) * 21
Vol = 567 cu. yard
Find the value of x.
Answers
Answer:
D. 15
Step-by-step explanation:
Both equations need the same end result because this is a square:
3x - 15 = 45 - x =
3x - 3x = 45 - x - 3x
0 = 45 - 4x
4x = 60
4x/4 = 60/4 =
X = 15
Check:
3(15) - 15 = 45 - 15
45 - 15 = 45 - 15
30 = 30
please help
a(8x + 2y) = 8ax +
Answers
a(8x + 2y) = 8x
Answer x=-2/0
The number of radians in a 720-degree angle can be
written as an, where a is a constant. What is the
value of a ?
Answers
Answer:
a=4
Step-by-step explanation:
When going from degrees to radians, 180 degrees is always going to equal π radians
That means 2π would be 360 degrees, and 4π would be 720
And since we're trying to find a in aπ when it's a 720 degree angle, we can conclude that a=4
Answer:
4
Step-by-step explanation:
We know that:
π rad= 180°Then:
720° = 4*180° = 4π radianThe value of a:
4π = aπ ⇒ a= 4Name five fractions whose values are between 1/8 and 1/5
Answers
The five fractions whose values are between 1/8 and 1/5 will be 13/100, 7/50, 3/20, 4/25, and 9/50.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
The fraction numbers are given below.
1/8 and 1/5
Convert the fraction number into decimal numbers. Then we have
0.125 and 0.20
The five fractions whose values are between 1/8 and 1/5 will be given as,
0.13, 0.14, 0.15, 0.16, 0.18
13/100, 14/100, 15/100, 16/100, 18/100
13/100, 7/50, 3/20, 4/25, 9/50
The five fractions whose values are between 1/8 and 1/5 will be 13/100, 7/50, 3/20, 4/25, and 9/50.
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Which equation represents an ellipse with foci at (3, 2) and (-9, 2)
that passes through the point (-3, 10)?
Answers
Answer:
D, since it horizontal ellipse, a is greater than b
An ellipse has two foci. The correct option is D.
What is the equation of ellipse if its major and minor axis and centre are given?Suppose that the major axis is of the length 2a units and that the minor axis is of 2b units, and let the ellipse is centred on (h,k) with a major ellipse parallel to the x-axis, then the equation of that ellipse would be:
[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]
Coordinates of its foci would be: (h±c, k) where c² = a² - b²
If its major axis is parallel to the y-axis, then,
coordinates of its foci would be: (h, k±c) where c² = a² - b² and its equation would be:
[tex]\dfrac{(x-h)^2}{b^2} + \dfrac{(y-k)^2}{a^2} =1[/tex]
Given the foci at (3, 2) and (-9, 2) that pass through the point (-3, 10), therefore, the equation of the ellipse will be,
[tex]\dfrac{\left(x+3\right)^{2}}{100}+\dfrac{\left(y-2\right)^{2}}{64}=1[/tex]
Hence, the correct option is D.
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**TIMED** I REALLY NEED HELP
Answers
Answer:
24 students
Step-by-step explanation:
(20 + 23 + 25 + 28)/4
= 94/4
= 24
hope it helps!
Pls help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!please I’m begging u
Answers
Answer:
7. 36 8. 1 9. 21
Step-by-step explanation:
You plug in the variables in the equation.
7.[tex]5^{2} +-4^{2} = 41[/tex]
8. [tex](5-4)^{2} = 81[/tex]
9. [tex]5+4^{2} =21[/tex]
Answer:
See explanation
Step-by-step explanation:
1. 8^5 = 32768
2. a^6
3. 5^5*9^3 = 2278125
5. (-3)^5 = -243
6. (3/4)³ = 27/64
7. a² + b² = 5² + (-4)² = 25 + 16 = 41
8. (a + b)² = (5 + 4)² = 9² = 81
9. a + b² = 5 + 4² = 5 + 16 = 21
How would I solve this question? y = -1 1/8 - 7/8x -4x + 9y = -22 x = ?, y = ?
Answers
-32= -7n-12+3n please help thanks
Answers
Answer:
5
Step-by-step explanation:
-32=-7n-12+3n
-32=-7n+3n-12
-32=-4n-12
-4n=-32+12
-4n=-20
n=-20/-4
n=5
Answer:
[tex]n=5[/tex]
Step-by-step explanation:
[tex]-32=-7n-12+3n\\\text{Combine Like Terms}\\-32=-7n+3n-12\\-32=-4n-12\\\text{Isolate the Variable}\\-32+12=-4n-12+12\\-20=-4n\\\text{Divide each side by -4}\\n=5[/tex]
Please help me on this question
Answers
Answer:
DE = 13.4 cm (to 1 decimal place)
Step-by-step explanation:
Given: ABCD is a square
BC = AC = 12 cm (opposite sides of a square are congruent)
E is midpoint of BC (given)
BE = EC = 12/2 = 6 cm
CD = AB = 12 cm (opposite sides of a square are congruent)
angle ECD is a right angle (interior angles of a square are 90 deg.)
Consider right triangle ECD
DE = sqrt(EC^2+CD^2) ............. pythagorean theorem
= sqrt(6^2+12^2)
= sqrt ( 36+144 )
= sqrt (180)
= 2 sqrt(45)
= 13.416 (to three dec. places)