Answer:
(x - 3)(x + 1)(x + 5)
Step-by-step explanation:
I'd use synthetic division instead. If we were to find the roots of the given polynomial, we could from them write the factors as well.
The divisor x + 5 corresponds to root x = -5. Setting up synthetic div.,
-5 ) 1 3 -13 -15
-5 10 +15
-----------------------------
1 -2 -3 0
Since the remainder is 0, we know that -5 is a root and (x + 5) is a factor. Moreover, we know that the coefficients of the quotient are 1, -2 and -3.
1x² - 2x - 3 can be factored: the factors are (x - 3) and (x + 1).
So the end result for this problem is (x - 3)(x + 1)(x + 5).
Which statement below is incorrect
The mean is not affected by the existence of an outler
(B) The median is not affected by the existence of an outlet
(c) the standard deviation
affected by the existence of an outler
Answer:
The Answer is A
Step-by-step explanation:
The mean or average is highly sensitive to outliers - and is one reason why the median is a more reliable statistic.
solve this system of linear equations. separate the x- and y- values with a comma. 6x +5y=-19 12x-8y=52
ANSWER
The solution is
(x,y)=(1,-5)
EXPLANATION
The equations are:
1st equation: 6x +5y=-19
2nd equation: 12x-8y=52
Multiply the first equation by 2:
3rd equation: 12x +10y=-38
Subtracy the 2nd equation from the 3rd equations.
12x-12x+10y--8y=-38-52
18y=-90
Divide both sides by 18.
y=-5
Put y=-5 into any of the equations and solve for x.
Preferably, the first equation will do.
6x +5(-5)=-19
6x -25=-19
6x=25-19
6x=6
x=1
The solution is
(x,y)=(1,-5)
Andrew is paid $4 per hour for the first 30 hours he works each week. He makes $5 per hour for each hour he works over 30 hours per week. In other words, total wages = fixed wages for 30 hours + additional wages at $5 per hour. Apply function notation to answer the following questions about Andrew’s wages. Part A Write a function that gives Andrew’s total wages when he works more than 30 hours. Use the variables w for wages and h for hours.
Answer:
f(w) = 120 + 5(30-h)
Step-by-step explanation:
It is given that, Andrew gets paid $4 for first 30 hours of the week
So,
For first 30 hours, his wage will be:
4(30) = $120
Now, let w denote wages and h denote total number or hours he works in the week
So he will be paid $5 for h-30 hours
So the function will be
f(w) = 120 + 5(30-h)
Where $120 is the fixed income for first 30 hours and the second term is the wage of hours more than 30 at the rate of $5 per hour..
What is the volume of this prism?
units3=
Answer:
240 units^3
Step-by-step explanation:
To find the volume of a rectangular prism you just multiply length times width times height. So, 8*6*5 which equals 240 units^3.
The dimensions of the prism is given as Length = 8 units, width = 6, Height = 5. Therefore, the volume of the prism is 240 units^3.
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units,
then its volume is given as:
[tex]V = a\times b \times c \: \: unit^3[/tex]
The dimensions of the prism is given as
Length = 8 units
width = 6
Height = 5
To find the volume of a rectangular prism
[tex]V = a\times b \times c \: \: unit^3[/tex]
V = 8 x 6 x 5
V = 240 units^3.
Therefore, the volume of the prism is 240 units^3.
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a circle has a circumfrence of 14mm. Find its area. Give an exact answer
Answer:
15.597 mm^2
Step-by-step explanation:
The formula for circumference of a circle 2πr, in which r is the circle's radius.
The formula for area of a circle π[tex]r^{2}[/tex]. This means that we can find the radius from the circle's circumference and use it to find the area.
First we have to equal 14 to 2πr because both are representations of circumference and we need to find r.
14 = 2πr
Solve:
14/2 = 2πr/2
7 = πr
7/π = πr/π
2.23 = r
Plug 2.23 into the formula for area as r and solve:
π(2.23)^2
π4.96
15.597
Find the value of x to the nearest tenth.
Answer:
x = 8.9 (nearest tenth)
Step-by-step explanation:
6^2 - 4^2 = 36 - 16 = 20
So
x = 2 * (√20)
x = 2 * 4.47
x = 8.94
Answer:
The value of x = 4√5
Step-by-step explanation:
Points to remember
For a right angled triangle
Hypotenuse² = Base² + Height²
To find the value of x
From the figure we can see a right angled triangle with,
hypotenuse = 6 and height = 4
Value of x = 2 * base
we have, Hypotenuse² = + Height²
Base² = Hypotenuse² - Height²
= 6² - 4²
= 36 - 16 = 20
Base = √20 = 2√5
x = 2 * 2√5 = 4√5
The value of x = 4√5
Which equation represents a line that is parallel to 2x-3y=9
A line parallel to 2x - 3y = 9 would have the same slope, 2/3, and a different y-intercept, represented as y = (2/3)x + b, where 'b' is any real number.
Explanation:The equation 2x - 3y = 9 represents a line in a standard form. To find a line that is parallel to it, we need another line with the same slope. The slope-intercept form of the given equation, by isolating y, is y = (2/3)x - 3. A parallel line must have the same slope, which is 2/3 in this case. Therefore, a line parallel to 2x - 3y = 9 could be represented as y = (2/3)x + b, where 'b' is any y-intercept. For example, if b = 5, a parallel line would be given by y = (2/3)x + 5.
What is the order of √5 , -0.1, -5/3 , 0.7, √2from least to greatest?
Answer:
-5/3, -0.1, 0.7, √2 and √5
Step-by-step explanation:
To start ordering these items, we first need to have a common point of comparison... so we'll get an approximation of their decimal value. No need to be very precise, just have a rough estimate:
√5: roughly 2.2
-0.1: -0.1
-5/3: -1.66
0.7: 0.7
√2: roughly 1.4
Now that we have the same comparing point (a decimal value), it's easy to sort them from the smallest value to the greatest value:
-5/3, -0.1, 0.7, √2 and √5
Of course, √2 is smaller than √5
Answer:
[tex]\large\boxed{-\dfrac{5}{3},\ -0.1,\ 0.7,\ \sqrt2,\ \sqrt5}[/tex]
Step-by-step explanation:
[tex]\sqrt5\\\\-0.1=-\sqrt{0.1^2}=-\sqrt{0.01}\\\\-\dfrac{5}{3}=-\sqrt{\left(\dfrac{5}{3}\right)^2}=-\sqrt{\dfrac{25}{9}}=-\sqrt{2\dfrac{7}{9}}\\\\0.7=\sqrt{0.7^2}=\sqrt{0.49}\\\\\sqrt2\\\\-\sqrt{2\dfrac{7}{9}}<-\sqrt{0.01}<\sqrt{0.49}<\sqrt2<\sqrt5[/tex]
The fish tank has side lengths 20in, 10in and height 15in. The water level is two inches below the top of the tank. A glass sphere of radius 1in is dropped in to the tank. What is the new distance from the water to the top of the tank? How many of these balls can be put into the tank with the tank not overflowing?
Answer:
Part 1) The new distance from the water to the top of the tank is [tex]1.979\ in[/tex]
Part 2) The maximum number of balls that can be put into the tank with the tank not overflowing is 95
Step-by-step explanation:
step 1
Find the total volume of the tank
[tex]V=20*10*15=3,000\ in^{3}[/tex]
step 2
Find the volume of the tank if the water level is two inches below the top of the tank
[tex]V=20*10*(15-2)=2,600\ in^{3}[/tex]
step 3
Find the volume of the glass sphere
The volume of the glass sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=1\ in[/tex]
assume
[tex]\pi=3.14[/tex]
substitute
[tex]V=\frac{4}{3}(3.14)(1)^{3}[/tex]
[tex]V=4.2\ in^{3}[/tex]
step 4
What is the new distance from the water to the top of the tank?
we know that
[tex]2 in -----> represent (3,000-2,600)=400\ in^{3}[/tex]
so
using proportion
Find how many inches correspond a volume of [tex]4.2\ in^{3}[/tex]
[tex]\frac{2}{400}\frac{in}{in^{3}}=\frac{x}{4.2}\frac{in}{in^{3}}\\ \\x=4.2*2/400\\ \\x=0.021\ in[/tex]
The new distance from the water to the top of the tank is
[tex]2-0.021=1.979\ in[/tex]
step 5
Find how many of these balls can be put into the tank with the tank not overflowing
we know that
The volume of one ball is equal to [tex]4.2\ in^{3}[/tex]
using proportion
[tex]\frac{1}{4.2}=\frac{x}{400}\\ \\x=400/4.2\\ \\x=95.23\ balls[/tex]
therefore
The maximum number of balls that can be put into the tank with the tank not overflowing is 95
Use the quadratic formula to determine the exact solutions to the equation.
222 – 50+1=0
Enter your answers in the boxes.
x=
or x =
Answer:
222- 50+1=0? 225 - 50 = 175 175+1 = 176 176+0 = 176
I don’t know the answer I need help
Answer:
[tex]-11b^2+8b-4[/tex]
Step-by-step explanation:
We can substitute in our expressions for P and Q to get
[tex]P=-4b^2+6b-9\\Q=7b^2-2b-5\\\\(-4b^2+6b-9)-(7b^2-2b-5)[/tex]
Next, we need to distribute the negative to the values within the parenthesis. Then we can combine like terms in order to get our answer
[tex](-4b^2+6b-9)-(7b^2-2b-5)\\\\-4b^2+6b-9-7b^2+2b+5\\\\-11b^2+8b-4[/tex]
Answer:
-11b^2 + 8b - 4
Step-by-step explanation:
(-4b^2 + 6b - 9) - (7b^2 - 2b - 5) =
Drop the first set of parentheses because it is unnecessary. To drop the second set of parentheses, you must distribute the negative sign. That means you must change every sign inside the second set of parentheses.
= -4b^2 + 6b - 9 - 7b^2 + 2b + 5
Now, group like terms.
= -4b^2 - 7b^2 + 6b + 2b - 9 + 5
Finally, combine like terms.
= -11b^2 + 8b - 4
Peta attempted to solve the following equation. Explain Peta's error.
x (x - 5) = 20
x = 20 and x - 5 = 20
x = 20 and x = 25
when you have a problem you can tell me and i can help you
The value of x is 7.63
The formula of the determinant is
x = -b ± √(b² - 4ac) / 2a
Where the equation is in the form of ax² + bx + c = 0
The error made by Peta is to use the determinant formula to find the root of the equation x (x - 5) = 20.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
We have,
x (x - 5) = 20
Removing the parenthesis.
x² - 5x = 20
x² - 5x - 20 = 0
This is in the form of ax² + bx + c = 0
Now,
a = 1
b = -5
c = -20
Using the determinant formula.
x = -b ± √(b² - 4ac) / 2a
x = 5 ± √(25 + 80) / 2
x = 5 ± √105 / 2
x = (5 + √105) / 2
x = (5 + 10.25) / 2
x = 15.25/2
x = 7.63
x = (5 - √105) / 2
x = (5 - 10.25) / 2
x = -5.25/2
x = -2.63 (neglected)
Thus,
The value of x is 7.63
The error made by Peta is to use the determinant formula to find the root of the equation x (x - 5) = 20.
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To fill an order, the factory dyed 851 yards of silk teal and 59 yards indigo How many yards of silk did it dye for that order?
Answer:
910 yards
Step-by-step explanation:
The total is the yards dyed teal plus the yards dyed indigo:
851 + 59 = 910
Total 910 yards of silk was dyed by the factory for that order.
What is addition?The addition is defined as a mathematical operation i.e. a method of adding numbers to get total.
We have,
Factory dyed silk teal = 851 yards,
Factory dyed silk indigo = 59 yards,
So,
To get the total we will add the given data,
i.e.
Total silk dyed = dyed silk teal + dyed silk indigo
= 851 + 59
= 910 yards,
So,
In total 910 yards of silk was dyed by the factory.
Hence, we can say that total 910 yards of silk was dyed by the factory for that order.
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What is the correct answer?
Answer:
160
Step-by-step explanation:
The top right quadrant is 90 and the given is 70, adding them equal 160. It is the only option that is greater than 90 degrees anyway.
True or False: 2y = -3x + 8 is an equation that represents a line parallel to the line 6x + 2y = 9.
For this case we have by definition, that if two lines are parallel then their slopes are equal.
We manipulate the equations algebraically to take them to the form y = mx + b.
Equation 1:
[tex]2y = -3x + 8\\y = - \frac {3} {2} x + 4[/tex]
Thus, the slope of this line is [tex]- \frac {3} {2}.[/tex]
Equation 2:
[tex]6x + 2y = 9\\2y = 9-6x\\2y = -6x + 9\\y = \frac {-6x + 9} {2}\\y = -3x + \frac {9} {2}[/tex]
The slope of this line is -3.
As the slopes are not equal, then the lines are not parallel.
Answer:
False
the equation 5x+2y=20 represents the cost for a family to attend a play where x is the number of adults and y is the number of children. find the intercepts and interpret the meaning of each one
Answer:
x-intercept: 4 This means that only 4 adults can come under the budjet of $20
y-intercept: 10 This means that only 10 children can come under the budjet of $20
Step-by-step explanation:
for y:
5(0) + 2y = 20
2y = 20
2y/2 = 20/2
y = 10
for x:
5x + 2(0) = 20
5x = 20
5x/5 = 20/5
x = 4
Help!!
Solve this 6x^3 - 8y^3 - 12x^2y^2 + 4xy
x=2/3 and y=1/2
Answer:
7/9
Step-by-step explanation:
6x^3-8y^3-12x^2y^2+4xy x=2/3 y=1/2
=6(2/3)^3-8(1/2)^3-12(2/3)^2(1/2)^2+4(2/3)(1/2)
=6(8/27)-8(1/8)-12(4/9)(1/4)+4(1/3)
=(16/9)-1-(4/3)+(4/3)
=(1 7/9)-1
=7/9
Solve for X in the following triangles.
X=
Answer:
The 51 and 62 triangle is 67°
The 43 triangle is 47°
Step-by-step explanation:
Angles in a triangle add to 180°
180 - ( 51 + 62 ) = 180 - ( 113 ) = 67°
180 - ( 43 + 90 ) = 180 - 133 = 47°
Find the value of the expression.
5200 – [40%(300 * 42.5)]
Answer:
The value of the expression is 100
Step-by-step explanation:
we have
5,200-[40%(300*42.5)]
we know that
(300*42.5)=3*100*42.5=3*4,250=12,750
40%=40/100=0.40
substitute
5,200-[0.40*12,750]
5,200-5,100=100
A manufacturer of shipping boxes has a box shaped like a cube. The side length is (5a + 4b). What is the volume of the box in terms of a and b? Show your work.
Answer:
125a^3 + 300a^2b + 240ab^2 + 64b^3
Step-by-step explanation:
The volume of a cube is the cube of the side length.
V = s^3
Here, the side length of the cube is 5a + 4b, so we cube 5a + 4b.
V = (5a + 4b)^3
V = (5a + 4b)(5a + 4b)(5a + 4b)
V = (25a^2 + 20ab + 20ab + 16b^2)(5a + 4b)
V = (25a^2 + 40ab + 16b^2)(5a + 4b)
V = 125a^3 + 100a^2b + 200a^2b + 160ab^2 + 80ab^2 + 64b^3
V = 125a^3 + 300a^2b + 240ab^2 + 64b^3
Given three collinear points, which of the following is true?
There is exactly one plane that contains all three points.
They form a triangle.
They are not coplanar.
They are contained in multiple planes.
Answer:
I think it is A.
Step-by-step explanation:
Hope my answer has helped you!
The true statement is:
They are contained in multiple planes. Step-by-step explanation:We are given three points such that they are collinear i.e. they lie in a straight line.Hence, such points could never form a triangle.
Because a triangle is formed with the help of three non-collinear points.
Also, we know that the line containing the three collinear points in a plane will always lie in a plane and there may be multiple or infinite planes that may contain this line.Hence, the points will be coplanar (i.e. they lie in the same plane)
Lewis has a bag of colored marbles. The bag contains 24 red marbles , 36 blue marbles , and 60 yellow marbles. What are the ratios of the number of red marbles , blue marbles , and yellow marbles to the total number of marbles?
Answer:
Step-by-step explanation:
The total number of marbles is 24 + 36 + 60 = 120
Red: 24/120 = 1/5
Blue: 36/120 = 6/20 = 3/10
Yellow: 60 / 120 = 1/2
A cylindrical shaped drum is used to store basketballs in a gymnasium. The hollow drum measures 48 inches high with a 24 inch radius. If the radius of a basketball is 6 inches, the maximum number of basketballs that the cylindrical drum contains is ______ (192, 48, 96)
Answer:
[tex]96\ basketballs[/tex]
Step-by-step explanation:
step 1
Find the volume of the cylinder (hollow drum)
The volume is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]h=48\ in[/tex]
[tex]r=24\ in[/tex]
substitute
[tex]V=\pi (24)^{2} (48)[/tex]
[tex]V=27,648\pi\ in^{3}[/tex]
step 2
Find the volume of one basketball
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=6\ in[/tex]
substitute
[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]
[tex]V=288\pi\ in^{3}[/tex]
step 3
Find the maximum number of basketballs that the cylindrical drum contains
so
Divide the volume of the cylinder by the volume of one basketball
[tex]27,648\pi/288\pi=96\ basketballs[/tex]
What is the amount of a $4,000.00 annuity due at 12 percent compounded semiannually for 3 years?
Answer:
$ 5674.076
Step-by-step explanation:
The question is on compound interest
The formulae = A= P(1+ r/n) ^nt .......where P is the principal amount, r is the rate of interest in decimal, n is number of compoundings per year and t is the total number of years.
Given; P= $4,000.00 , r=12/100=0.12, n=2 and t=3
Substituting values in the equation A= P(1+ r/n) ^nt
A= 4000 ( 1+0.12/2)^2×3
A=4000(1.06)^6
A=$ 5674.08
20% of 180ft what is the quantity
Answer: 36ft
Step-by-step explanation: 180*.2=36
Answer:
36 ft
Step-by-step explanation:
to find 20% of 180 ft, multiply 180 ft by 0.20: 0.20(180 ft) = 36 ft
if f(x)=2x-6 and g(x)=x^3 what is (g f)(0)
The answer is:
[tex](g\circ f)(0)=-216[/tex]
Why?To composite functions, we need to evaluate functions in another function(s), for example:
Given f(x) and g(x), if we want to calculate f(x) composite g(x), we need to evaluate g(x) into f(x).
So, we are given the functions:
[tex]f(x)=2x-6\\g(x)=x^{3}[/tex]
And we are asked to calculate g(x) composite f(x), and then evaluate "x" to 0, so, calculating we have:
[tex](g\circ f)(x)=g(f(x))\\\\(g\circ f)(x)=(2x-6)^{3}[/tex]
Now that we have the composite function, we need to evaluate "x" equal to 0, so:
[tex](g\circ f)(0)=(2x-6)^{3}\\\\(g\circ f)(0)=(2*(0)-6)^{3}=(0-6)^{3}=-6*-6*-6=-216[/tex]
Hence, we have that:
[tex](g\circ f)(0)=-216[/tex]
Have a nice day!
Answer:
Step-by-step explanation:216
Ashley has already walked 0.5 miles this week, plus she plans to walk 1.5 miles during each trip to school. If she plans to take 3 trips to school for a total of 5 miles, what is the slope of the equation?
0.5 miles
1.5 miles
5 miles
3 trips
Answer:
Step-by-step explanation:
The slope is 1.5 miles / day
Final answer:
The slope of the equation that represents Ashley's walking distance over the number of trips is 1.5, which indicates that she walks 1.5 miles for each trip to school.
Explanation:
Ashley has already walked 0.5 miles this week and plans to walk 1.5 miles each trip to school for a total of 3 trips. To find the slope of the equation that represents her walking distance as a function of the number of trips, we use the slope formula, which is rise over run, or in this context, the change in distance over the number of trips.
Let's calculate her total planned distance. Since she plans on walking 1.5 miles for each trip and takes 3 trips, that's 1.5 miles/trip × 3 trips = 4.5 miles. Including the 0.5 miles she has already walked, her total distance for the week would be 0.5 miles + 4.5 miles = 5 miles, which matches with her goal.
Now, the slope is the distance she covers per trip, which is consistent and equal to 1.5 miles per trip. Therefore, the slope of the line that represents her distance over the week as a function of each trip is 1.5.
name the angles that are complements to SWT
Answer:
Option C
Step-by-step explanation:
we know that
Two angles are complements if their sum is equal to 90 degrees
we have that
∠SWT=50°
so
Its complement must be equal to 40 degrees
we know that
∠USP=40°
∠TSV=40°
therefore
∠USP and ∠TSV are complements to ∠ SWT
PLEASE HELP ME I WILL MARK!!
Answer:
3.2
Step-by-step explanation:
Calculate the length using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (A(2,2) and (x₂, y₂ ) = B(5, 1)
d = [tex]\sqrt{(5-2)^2+(1-2)^2}[/tex]
= [tex]\sqrt{3^2+(-1)^2}[/tex]
= [tex]\sqrt{9+1}[/tex] = [tex]\sqrt{10}[/tex] ≈ 3.2 ( nearest tenth )
Answer:
3.2
Step-by-step explanation:
Distance formula = √ (x₂ - x₁ )² + (y₂ - y₁ )²
Distance = [tex]\sqrt{(5-2)}^{2} + (1-2)^{2}[/tex]
Distance = [tex]\sqrt{ {3}^{2} + ( - 1 )^{2}[/tex]
Distance = 3.16227766
3x+5y=105
6x+2y=114
Answer:
3x + 5y = 105
3x + y = 57
------------------
4y = 48
y = 12, x = 15
{(15, 12)}