Answer:
10
Step-by-step explanation:
Plug in "6" for each x value.
3(6) - 8
18 - 8
10
Show all work to factor x^4-10x^2+9 completely
Answer:
[tex](x^{2}-9)(x^{2} -1)[/tex]
Step-by-step explanation:
Step 1: Find what adds to _ and multiples to_
It needs to multiple to the 'c' term or 9
It needs to add to the 'b' term or -10
Step 2: Find the numbers
We know -9 and -1 make 10 and multiple to 9
-9 x -1 = 9
-9 + (-1) + -10
Step 3: Write equation in form a(x-r)(x-s)
a = 1
r = -9
s = -1
Plug in the equation to get the factored form of the equation:
[tex](x^{2}-9)(x^{2} -1)[/tex]
Therefore the factored form of the equation is [tex](x^{2}-9)(x^{2} -1)[/tex]
Quadratic equations are also a type of algebraic fractions that have factors.
The factor of [tex]x^{4} - 10x^{2} + 9 = (x -3)(x + 3)(x - 1)(x + 1)[/tex]
In order to completely factor [tex]x^{4} - 10x^{2} + 9[/tex] we would apply the formula:
a(x-r)(x-s)
To find the variables a, x, r and s, we have to love at the coefficients of [tex]x^{2}[/tex] which is -10 and the term 9 and find out what can we multiply together to give us 9 and add together to give us -10
That would be , -9 and - 1 because:
-9 x -1 = 9
-9 + (-1) = -10
Hence: the value for a = 1
, r = -9 and s = -1
Putting this into the equation:
1(x -(-9)(x - (-1))
Hence, we have:
[tex](x^2-9)( x^{2} - 1)[/tex]
Factorizing the above expression further, we have
[tex](x - 3)(x + 3)(x - 1)(x + 1)[/tex]
Therefore, the factor of [tex]x^{4} - 10x^{2} + 9 = (x -3)(x + 3)(x - 1)(x + 1)[/tex]
To learn more, visit the link :
https://brainly.com/question/22763163
The crosssectional areas of triangular prism and a night cylinder are congruent. The triangular prism has a helght of 5 units, and the right cylinder height of 3 unitsconclusion can be made from the given Information? The volume of the prism half the volume of the cylinder The volume of the prism is twice the volume of the cylinder The volume of the premis equal the volume of the cylinder. The volume of the is not equal to the volume of the cylinder
Answer:
The volume of the triangular prism is not equal to the volume of the cylinder
Step-by-step explanation:
Given that:
The cross sectional area of triangular prism and a night cylinder are congruent. The term 'congruent' means when two objects or shapes are placed above each other , they should both overlap exactly.
It was given that:
The triangular prism has a height of 5 units
and the right cylinder height of 3 units
The conclusion that can be drawn from this is that:
The volume of the triangular prism is not equal to the volume of the cylinder.
This is because, they do not occur in the same family. A triangular prism is a three - dimensional shape that has identical, parallel ends and parallel faces.
A triangular prism has two triangles at it ends and three rectangular faces.
The volume of the triangular prism is calculate by using the formula:
[tex]V= \dfrac{1}{2}\times b \times h\times l[/tex]
On the other hand, a cylinder is a shape with two circular ends and a curved surface.The two circular ends are congruent and both circular end posses the same cross section from one end to the other in the cylinder.
The volume of a cylinder is calculated by using the formula:
V = πr²h
Thus, we conclude that irrespective of the nature of their congruency, since the heights are different which will definitely affects their volume, the the volume of the triangular prism is not equal to the volume of the cylinder.
Calculate the slope of a line that passes through the points (2, 6) and (4, 2) *
Answer:
-2
Step-by-step explanation:
Given:
Points (2, 6) and (4, 2)Slope formula:
m = (y2-y1)/(x2-x1)Using the given points:
m = (2- 6)/(4 - 2) = -4/2 = -2Find the midpoint of the line segment joining the points R(3,2) and S(-5,5).
The x coordinates are 3 and -5. They add to 3+(-5) = -2
Cut this in half to get -2/2 = -1
The x coordinate of the midpoint is x = -1
-------------------
The y coordinates are 2 and 5. They add to 2+5 = 7.
Then we cut this in half to get 7/2 = 3.5
The y coordinate of the midpoint is y = 3.5
-------------------
Overall, the midpoint is (-1, 3.5)
Answer: (-1, 3.5) which is the same as (-1, 7/2)Question 4
20 pts
Graph the points X(-4,5) and Y(1,-1) on the coordinate plane. What type of
slope would the segment XY have?
O positive slope
O undefined slope
O negative slope
O zero slope
Answer:
Negative slope Hopefully
Step-by-step explanation:
Slope formula : (5 - (-1)) / (-4 - 1)
6/-5 = a negative slope
Evaluate 5/8-(1/4)2=
Answer:
0.125
Step-by-step explanation:
(5 divided by 8) - ((1 divided by 4) x 2) = 0.125
Answer:
1/8
Step-by-step explanation:
Because of BEDMAS, we first multiply, then subtract.
We multiply 1/4 and 2, getting 2/4, or 1/2.
Then, our expression becomes 5/8 - 1/2.
We can evaluate:
5/8 - 1/2 = 5/8 - 4/8 and simplify, getting 1/8.
One card is to be drawn from a deck of 52 cards.The deck includes four types of cards.Red heart, red stars , black triangles , black circles .Each type has 13 cards numbered 1-13.What is the probability of drawing a red one a, black three , or a six of hearts.Give your answer in the simplify form .
Answer:
red one = 1/26
black three = 1/26
six of hearts = 1/52
Graph x≥−1, plz amswer. from khan
Draw a number line. Plot -1 on the number line and make this a filled in circle. Shade to the right of the filled in circle to indicate the set of values x such that [tex]x \ge -1[/tex]
So x could be -1 or it could be larger. The fact that x = -1 is possible is why we have a closed or filled in circle (instead of an open hole) at this endpoint.
Type the correct answer in each box. Use numerals instead of words. Consider the equation below. x/h+1=-2 The value of x in terms of h is ___. The value of x when h=4 is ___.
Answer:
x = -3h
x = -12
Step-by-step explanation:
Given equation is [tex]\frac{x}{h}+1=-2[/tex]
To find the value of x in terms of h we will solve the expression to isolate x on one side of the equation.
by subtracting 1 from both the sides of the equation,
[tex]\frac{x}{h}+1-1=-2-1[/tex]
[tex]\frac{x}{h}=-3[/tex]
Multiplying 'h' on both the sides of the equation,
[tex](\frac{x}{h})\times h = (-3)h[/tex]
x = -3h
If h = 4,
x = (-3)(4)
x = -12
Answer:
x = -3h
Given equation is
To find the value of x in terms of h we will solve the expression to isolate x on one side of the equation.
by subtracting 1 from both the sides of the equation,
Multiplying 'h' on both the sides of the equation,
x = -3h
If h = 4,
x = (-3)(4)
x = -12
Step-by-step explanation:
The house Trevor's family lives in has 666 people (including Trevor) and 333 bathrooms. In the past month, each person showered for an average of 480480480 minutes and used an average 727272 liters of shower water (over the entire month). Water costs 0.200.200, point, 20 dollars per liter. How much did Trevor's family pay per minute on shower water?
Using proportions, we find that: Trevor's family paid $0.03 per minute on shower water.
---------------------------------
This question is solved using proportions.
There are 6 people in the house.There are 3 bathrooms in the house.Each person used an average of 72 liters of shower.Thus, the total amount of liters used is:
[tex]L = 72 \times 6 = 432[/tex]
---------------------------------
432 liters used.Each liter costs $0.2.Thus, the total amount paid was of:
[tex]A = 432 \times 0.2 = 86.4[/tex]
---------------------------------
Total of 86.4 dollars.Total of 6x480 = 2880 minutes.The amount of dollars per minute is:
[tex]D = \frac{86.4}{2880} = 0.03[/tex]
Trevor's family paid $0.03 per minute on shower water.
A similar question is given at https://brainly.com/question/24342347
Trevor's family paid $ 1.33 per minute on shower water.
Since the house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms, and in the past month, each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the entire month), and water costs 0.20 dollars per liter, to determine how much did Trevor's family pay per minute on shower water, the following calculation must be performed:
You must multiply the number of liters by its value, and divide that result by the number of minutes that each person consumed, in order to obtain the value per minute on shower water.
((480 x 6) x 0.2) / (6 x 72) = X(2880 x 0.2) / 432 = X576/432 = X1.333 = XTherefore, Trevor's family paid $ 1.33 per minute on shower water.
Learn more in https://brainly.com/question/13643409.
what's the square root of 57?
Answer:
the square root of 57 is 7.549834435
=7.5
Step-by-step explanation:
press square root followed by 57 on your calculatorWhich value of n makes the equation true?
-1/2n = -8
A. -16
B.-4
C.4
D.16
Answer:
16
Step-by-step explanation:
Lets do a Step-by-step:
You must Solve for n:
-n/2 = -8
Multiply both sides of -n/2 = -8 by -2:
(-2 (-n))/2 = -2 (-8)
-2×(-1)/2 = (-2 (-1))/2:
(-2 (-1))/2 n = -2 (-8)
(-2)/2 = (2 (-1))/2 = -1:
--1 n = -2 (-8)
(-1)^2 = 1:
n = -2 (-8)
-2 (-8) = 16:
Answer: n = 16
Hope this helps
Write 1/64 as an expression with a negative exponent other than -1.
Answer:
[tex]8^{-2}[/tex]
Step-by-step explanation:
Remember, if there is a negative within the power sign, you must put the power and base under 1:
8^-2 = 1/(8^2).
Simplify:
1/(8^2) = 1/(8 * 8) = 1/(64)
1/64 = 1/64, ∴ [tex]8^{-2} = 1/64[/tex]
Which mathematical symbol would best fill in the blank to compare the two real numbers?
Answer:
<
Step-by-step explanation:
If we compare the 2 values
[tex]\sqrt{7}[/tex] ≈ 2.65
[tex]\frac{14}{5}[/tex] = 2.8
Thus we can see that 2.65 is less than 2.8, then
[tex]\sqrt{7}[/tex] < [tex]\frac{14}{5}[/tex]
THE SEVEN APPLEWOMEN
Seven apple women, possessing respectively 20, 40, 60, 80, 100, 120, and 140
apples, went to market and sold all their apples at the same price, and each
received the same sum of money. What was the price?
Answer:
zero
Step-by-step explanation:
If the same sum is received for the sale of 20 apples at price p as is received for the sale of 140 apples at price p, then we must have ...
20p = 140p
120p = 0 . . . . . . subtract 20p
p = 0 . . . . . . . . . divide by 120
The price was zero.
Answer:
Price was 1 unit of money per each 7 apples and 3 units of money per each extra appleEach woman received 20 unit of moneyStep-by-step explanation:
This is the tricky one
I think 'The Seven Apple' is the hint. Let's see what the numbers have to do with 7:
20 = 7*2 + 640 = 7*5 + 560 = 7*8 + 480 = 7*11 + 3100 = 7*14 + 2120 = 7*17 + 1140 = 7*20 + 0Assume each '7 apples' sold for a fixed price x and each 'extra' apple sold for a different price y. Since all add up to make same amount, we get:
2x + 6y = 5x + 5y = ... = 20xLet x = 1, then we get y = 3
So we get the sold price:
20 apples cost: 2*1 + 6*3 = 2040 apples cost: 5*1 + 5*3 = 20...140 apples cost: 20*1 = 20So each apple woman got 20 units of money for their apples.
Price was 1 unit of money per each 7 and 3 units of money per each extra apple
If you drove a bus with 43 people on board from Chicago and stopped at Pittsburgh to
pick up 7 more people and drop off 5, and then at Cleveland to pick up 4 more people
and drop off 8, and arrive at Philadelphia 20 hours later. How old is the bus driver?
If I'm correct im sure I'd be 41
If you drove a bus with 43 people on board from Chicago and stopped at Pittsburgh. the bus driver is 41 old.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
If you drove a bus with 43 people on board from Chicago and stopped at Pittsburgh.
To pick up 7 more people and drop off 5,
So, 43 + 7
= 50 -5
= 45
then at Cleveland to pick up 4 more people and drop off 8, and arrive at Philadelphia 20 hours later.
= 45 + 4
= 49 - 8
= 41
Therefore, the bus driver is 41 old.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ2
Three Bears
In the land of Plentiful Honey, lived three bears: Papa
Bear, Mama Bear and Baby Bear. They had three pots
of honey: one large, one medium, and one small. One
day they found themselves carrying the pots of honey
down a path. Papa was carrying the medium pot, while
Mama was carrying the small pot, and Baby was
carrying the large pot. This was clearly inequitable and they decided to trade pots, so that
each was proportional to the size of the bear. It may seem there is a simple solution to their
dilemma, however, the rules for transferring pots in the land of Plentiful Honey are quite
complicated. They are:
a) Only one pot of honey can be passed at a time.
b) fa bear is holding two pots of honey, only the smaller pot may be transferred.
• A honey pot may not be transferred to a bear that is holding a smaller pot.
d) Pots may not be set on anything, such as the ground or a stump.
Diagram or explain the sequence of the transferring of honey pots, so that Papa Bear has the
large pot, Mama Bear the medium pot, and Baby Bear the small pot.
Answer:
m→B, s→P, m→M, s→M, l→P, s→B
Step-by-step explanation:
The initial state is ...
(Baby, Mama, Papa) = (Large, Small, Medium)
The large pot can only be transferred from someone holding only that pot, and only to someone holding no pots. The small pot can go anywhere any time.
Transfer the medium pot to Baby.
(B, M, P) = ({L, M}, S, –)
Transfer the small pot to Papa.
(B, M, P} = ({L, M} –, S)
Transfer the medium pot to Mama.
(B, M, P) = (L, M, S)
Transfer the small pot to Mama.
(B, M, P) = (L, {M, S}, –)
Transfer the large pot to Papa.
(B, M, P) = (–, {M, S}, L)
Transfer the small pot to Baby.
(B, M, P) = (S, M, L) . . . . . . desired end condition
there are 8 knives and 12 forks in a package of plastic utensils. Which ratio is equivelent to 8/12?
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
If you divide [tex]\frac{8}{12}[/tex] by 4 (both numerator and denominator)
You get [tex]\frac{2}{3}[/tex] which is equivalent to the given ration
What word also means to put or replace a variable with a number?
Answer:
Hey there!
Substitute would be your answer.
Let me know if this helps :)
An object in geometry with no width, length or height is an:
A. Point
B. Line
C. Ray
D. Angle
Answer:
A. Point
Step-by-step explanation:
It has no size. It tells about the location only.
Answer:
A. Point
Step-by-step explanation:
A point is a zero- dimensional object as it has no length, width, or height. It also has no size and tells about location only.
( solving proportions ) solve for x .
Answer:
Your would need too add and subtract and find the least common multipule
X= 72/5 =14.400
Answer:
14.4
Step-by-step explanation:
By multiplying each side by 9x, you cancel out the denominators on each side. On the left what you have left is 9 x 8. On the right you have 5x. You can figure out the rest of the work for yourself. :)
Given the function ƒ(x ) = 3x + 1, evaluate ƒ(a + 1).
Answer:
[tex]\Huge \boxed{3a+4}[/tex]
Step-by-step explanation:
The function is given.
[tex]f(x)=3x+1[/tex]
To find : [tex]f(a+1)[/tex]
The input for the function f(x) is (a + 1).
Replace x with (a + 1).
[tex]f(a+1)=3(a+1)+1[/tex]
Expand brackets.
[tex]f(a+1)=3a+3+1[/tex]
Simplifying.
[tex]f(a+1)=3a+4[/tex]
Jayden is a waiter at a restaurant. Each day he works, Jayden will make a guaranteed wage of $30, however the additional amount that Jayden earns from tips depends on the number of tables he waits on that day. From past experience, Jayden noticed that he will get about $14 in tips for each table he waits on. How much would Jayden expect to earn in a day on which he waits on 16 tables? How much would Jayden expect to make in a day when waiting on
Answer:
$254
$30 + $14x
Step-by-step explanation:
Jayden:
Guaranteed wage= $30
Tips per table = $14
Number of tables = 16
Total revenue = fixed revenue + variable revenue
Fixed revenue= $30
Variable revenue change with quantity= $14 × number of tables Jayden waits on
Total earnings of Jayden for the day = $30 + $14(16)
= $30 + $224
= $254
When Jayden waits on x number of tables
Total earnings of Jayden for the day = $30 + $14(x)
= $30 + $14x
Where x = number of tables Jayden waits on
Answer:
$254
30 + 14t
Step-by-step explanation:
Evaluate -1 -3- (-9) + (-5).
Answer:
The evaluated answer to the given expression is 0.
Step-by-step explanation:
-1 - 3 - (-9) + (-5)
Subtract -1 from 3.
-4 - (-9) + (-5)
Distribute the negative to -4.
-4 + 9 + (-5)
Add 9 to -4.
5 + (-5)
Add 5 to -5.
0
mona started making oatmeal cookies at 11:40 A.M. It took her 1 hour and 10 minutes to make the dough and 1 hour and 50 minutes to bake all of the cookies. What time was it when mona finished making cookies.
Answer:
14:40 P.M or 2:40 P.M
Step-by-step explanation:
Mona started making oatmeal cookies at 11:40 A.M. What time did she finish:
Making the dough = 1 hour and 10 minutes (1:10)
Baking all the cookies = 1 hour and 50 minutes (1:50
11:40 + 1:10 = 12:50 P.M
12:50 + 1:50 = 14:40 P.M
She finished making cookies at 14:40 P.M or 2:40 P.M
Terry is filling spherical water balloons with a faucet that puts out 100 cm^3 of water per second. At least rate, it takes Terry 6 seconds to fill a balloon. What is the radius of a filled balloon?
Answer:
its 5 cm
Step-by-step explanation:
its what I got off of Khan
The radius of a filled balloon is approximately 5.22 cm.
What is the volume of a sphere?The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius.
Let's first find the volume of a filled balloon.
Since Terry can fill a balloon in 6 seconds and the faucet puts out 100 cm³ of water per second, the volume of a filled balloon is:
V = 6 × 100 = 600 cm³
Now we can use the formula for the volume of a sphere to find the radius.
Rearranging the formula, we get:
[tex]r = [\dfrac{3V}{4\pi}]^{(1/3)}[/tex]
Substituting V = 600 cm³, we get:
[tex]r = [\dfrac{3\times600}{4\pi}]^{(1/3)}[/tex]
r ≈ 5.22 cm
Therefore, the radius of a filled balloon is approximately 5.22 cm.
Learn more about the sphere here:
https://brainly.com/question/12390313
#SPJ2
Carlo used this number line to find the product of 2 and −3. A number line going from negative 7 to positive 3. An arrow goes from negative 2 to negative 4, and from negative 4 to negative 6. What errors did Carlo make? Select two options.
Answer:
The errors are;
a. negative 4 to negative 6
b. negative 2 to negative 4
Step-by-step explanation:
The number line is the mathematical representation of numbers in the horizontal line or the x-axis.
The result of the multiplication of a positive 2 and a negative 3 is;
2 x -3 = -6 , gives a negative 6.
So the number line should scale to accommodate the operands and the result, which is from negative 7 to positive 3, in the option given.
Answer:
the answer is a and c :)
Step-by-step explanation:
Add. Write your answer as a fraction in simplest form. 9/10+(−4/5)=
Answer:
1/10
Step-by-step explanation:
9/10+(-4/5)
= 9/10-4/5
=9/10-8/10
=1/10
The simplified form of the expression as a fraction is 1/10.
We have,
Expression:
9/10 + (-4/5)
Remove the parenthesis.
9/10 - 4/5
Simplify the fraction.
(9 - 8)/10
1/10
Thus,
The simplified form of the expression is 1/10.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ6
Jimmy has 2 times as many twenty-five paisa coin as fifty-paisa coins . If he has total of Rs. 3.00, how many coins of each kind does he have ? Please answer will mark you the brainest!
Answer:
x = 6
y = 3
6 twenty-five paisa coin
3 fifty-paisa coins
Step-by-step explanation:
x -----> twenty-five paisa coin
y -----> fifty-paisa coins
0.25x + 0.5y = 3.00 per 100
x = 2y
25x + 50y = 300
x = 2y
25(2y) + 50y = 300
50y + 50y = 300
100y = 300
y = 300/100
y = 3
x = 2y
x = 2(3)
x = 6
help me plz and ty....
Answer: c
Step-by-step explanation:
The two angles combine to form a straight angle which is 180 degrees. Therefore, the two angles are supplementary.