Answers
The solutions are 3 and -3
Explanation:
To get the solution, we will need to isolate the x on one side of the equation as follows:
10x² - 56 = 88 - 6x²
10x² - 56 + 56 = 88 - 6x² + 56
10x² = 144 - 6x²
10x² + 6x² = 144 - 6x² + 6x²
16x² = 144
x² = 144/16
x² = 9
x = ±√9
either x = +√9 = 3
or x = -√9 = -3
Hope this helps :)
Related Questions
Find the pair of numbers whose sum is 46 and whose product is a maximum.
Answers
1. Let's call:
x the first number and and the other number 46-x
2. Then, the product of both numbers is:
y=x(46-x)
3. When you apply the distributive property, you obtain:
y=46x-x^2
4. As you can see, the coefficient of x^2 is negative, this means that the maximun value is at the vertex of the parabola.
5. Then, you have:
h=-b/2a
h=-46/2(-1)
h=23 (x coordinate)
6.Then:
y=46x-x^2
y=46(23)-(23)^2
y=529
Therefore the answer is: 23 and 529.
Explain how you can tell when a formula represents a length an area or a volume
Answers
Ex:
d = 2r (this would only involve multiplying by one dimension, therefore it is a length)
A = bh (this involves multiplying 2 dimensions, giving a measurement of area)
V = lwh (this involves multiplying 3 dimensions, giving a measurement of volume)
To determine if a formula represents a length, area, or volume, consider the units used in the formula.
Explanation:When determining if a formula represents a length, area, or volume, you need to consider the units used in the formula. Length is typically measured in units such as meters or feet. Area is measured in square units, such as square meters or square feet. Volume is measured in cubic units, such as cubic meters or cubic feet.
For example, suppose you have a formula that involves only one variable and it includes units such as meters. This formula would most likely represent a length. If the formula involves two variables and includes units like square meters, then it represents an area. And if the formula involves three variables and includes units like cubic meters, then it represents a volume.
It's important to pay attention to the units to determine whether a formula represents a length, area, or volume.
given the function, f(x)=(x^3)-(3x^2)+(64x)-192 find the zeros
Answers
NOTE: GCF = Greatest Common Factor
The function: [tex]f(x) = x^3 - 3x^2 + 64x - 192[/tex]
Lets group [tex]x^3 - 3x^2[/tex] and [tex]64x - 192[/tex]
Factor [tex]x^3 - 3x^2[/tex]
Find GCF
GCF = [tex]x^2[/tex]
Divide out the GCF [tex]x^2[/tex]
[tex]\frac{x^3 - 3x^2}{x^2} = (x - 3)[/tex]
Factor From:
[tex]x^2(x - 3)[/tex]
Now factor 64x -192
GCF of 64 and 192 = 64
Factor out 64 from 64x - 192
[tex]\frac{64x - 192}{64} = (x - 3)[/tex]
Factor Form:
[tex]64(x - 3)[/tex]
Now that we have factored the groups, bring them together.
[tex] x^2(x-3)[/tex]
[tex] 64(x-3)[/tex]
[tex]x^2(x-3) + 64(x-3)[/tex]
Since (x-3) is the GCF of [tex]x^2(x-3) + 64(x-3)[/tex], factor (x-3) out.
[tex]\frac{x^2(x-3) + 64(x-3)}{(x-3)} = x^2 + 64[/tex]
Factor Form:
[tex](x-3)(x^2 + 64)[/tex]
Now set [tex](x^2 + 64)(x-3)[/tex] to zero and solve for x.
[tex](x^2 + 64) = 0[/tex]
[tex]x^2 = - 64[/tex]
Take the square root of both sides of the equal sign:
[tex]\sqrt{x^2} = \sqrt{-64}[/tex]
[tex]x = \sqrt{-64}[/tex]
[tex]x = \pm 8i[/tex]
Now for (x-3)
x - 3 = 0
x - 3 + 3 = 3
x = 3
The zeros and answers:
[tex]x = -8i[/tex]
[tex]x = 8i[/tex]
x = 3
please help me with math
i need it soon
Answers
We are told that Mrs. Thymes is buying mulch for her gardens.
Let us check the price for each option:
[tex]\boxed {Option \ A}[/tex]
3 yd³ for $165
Divide 165 by 3, to find the price per cubic yard:
[tex] \frac{165}{3} [/tex] = $55 per cubic yard
[tex]\boxed {Option \ B }[/tex]
4 yd³ for $240
Do the same:
[tex] \frac{240}{4} [/tex] = $60 per cubic yard
[tex]\boxed {Option \ C }[/tex]
6 yd³ for $300
[tex] \frac{300}{6} [/tex] = $50 per cubic yard
[tex]\boxed {Option \ D }[/tex]
8 yd³ for $360
[tex] \frac{360}{8} [/tex] = $45 per cubic yard
Therefore, we can see that 8 yd³ for $360 is the best price
[tex]\boxed {Your \ Answer \ will \ be \ Option \ D }[/tex]
A. $165/(3 yd³) = $55/yd³
B. $240/(4 yd³) = $60/yd³
C. $300/(6 yd³) = $50/yd³
D. $360/(8 yd³) = $45/yd³ . . . . . . . this is the best price per cubic yard.
Please help me!!!! Help me find the dimensions. :(
Answers
Volume=πr²h
Area=2πr²+πdh
Ratio of SA to volume=Area/volume
π=3.14
Thus using the above formula:
1.
a]
Radius: 3 inches
Height: 2 inches
Volume=πr²h
volume=π×3²×2=56.52 in³
b]
Area=2πr²+πdh
2×π×3²+π×2×3×2
=56.55+37.68
=94.23 in²
c]
Ratio=area/volume
=94.23/56.52
=1.6672
1.
Radius: 2 inches
Height: 9 inches
a]
V=πr²h
V=3.14*2^2*9
V=113.04 in³
b]
Area=2πr²+πdh
=2*3.14*2^2+3.14*2*2*9
=25.12+113.04
=138.16 in²
c]
Ratio=area/volume
=138.16/113.04
=11/9
3.
Diameter=4 inches
Height= 9 inches
a]
V=πr²h
V=3.14×2²×9
V=113.04
b]
Area=2πr²+πdh
=2*3.14*2^2+3.14*4*9
=25.12+113.04
=138.16 in²
c]
Ratio=area/volume
=138.16/113.04
=11/9
4]
Diameter: 6 inches
Height: 4 inches
a]
Volume=πr²h
=3.14×3²×4
=113.04 in³
b]
Area=2πr²+πdh
=2×3.14×3²+3.14×6×4
=56.52+75.36
=131.88 in²
c] Ratio
131.88/113.04
=7/6
1. For the surface area to volume to be small it means that the area is smaller than the volume, for surface area to volume be larger it means that the surface area is larger than the volume. It is more economical for the surface area to volume to be small because it will mean that small amount of materials make cans with large volume. This means cost of production is cheaper.
2. To evaluate this process let's use one of the dimensions:
Radius: 3 inches
Height: 2 inches:
i. add radius and height:
3+2=5 inches
ii. Multiply radius and height:
3×2=6
iii. Dividing the result from step 1 by the result in step 2:
5/6
iv. Multiply the result from step 3 by 2:
5/6×6
=5
This result does not seem to add up to the result in our earlier ratio. Thus we conclude that Khianna was wrong. This method can't work with 3-D figures.
A group of 4 friends likes to bowl together, and each friend keeps track of his all-time highest score in a single game. Their high scores are all between 180 and 220, except for Adam, whose high score is 250. Adam then bowls a great game and has a new high score of 290. How will increasing Adam's high score affect the mean and median?
A
Both the mean and median will increase.
(Choice B)
B
The median will increase, and the mean will stay the same.
(Choice C)
C
The mean will increase, and the median will stay the same.
(Choice D)
D
The mean will increase, and the median will decrease.
Answers
Option: C is the correct answer.
C The mean will increase, and the median will stay the same.
Step-by-step explanation:We know that the mean of scores is the average value of the scores of the score obtained by 4 friends.
i.e. it is the ratio of sum of scores of 4 friends to the total number of person i.e. 4.
Hence, if the score of any of the person will increase then the mean will also increase
( Since, the denominator remains the same and the numerator is increasing so , the resultant value will increase )
Also, we know that the median of the score lie between the data set, i.e. the change in the score of the last score won't affect the median :
Since, here we have 4 data points and the median lie between the 2nd and 3rd data point so change in the 4th data point won't affect the median.
Hence, increasing Adam's high score affect the mean and median as:
Mean will increase and Median remains the same.
The mean and median will increase as Adam's high score rises, while the median will remain unchanged. Then the correct option is C.
What is Mean?Mean is simply defined as the average of the given set of numbers. The mean is considered one of the measures of central tendencies in statistics.
What is a median?The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.
A group of 4 friends likes to bowl together, and each friend keeps track of his all-time highest score in a single game.
Their high scores are all between 180 and 220, except for Adam, whose high score is 250.
Adam then bowls a great game and has a new high score of 290.
If any of the individuals' scores improve, the mean will improve as well.
We also observe that the median of the scoring lies inside the data set, implying that a change in the last score will have no effect on the median.
Because we have four data sets and the median is between the second and third, a change in the fourth data point will have no effect on the median.
More about the mean and the median link is given below.
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2) Use spherical coordinates to find the integral of f(x,y,z) = z over x^2 + y^2 + z^2 < 4 and x,y,z < 0
Answers
[tex]\begin{cases}x=r\cos u\\y=r\sin u\\z=v\end{cases}[/tex]
and [tex]\mathcal D[/tex] is obtained by varying the parameters over [tex]0\le r\le3[/tex], [tex]0\le u\le2\pi[/tex], and [tex]0\le v\le6[/tex]. The volume element is
[tex]\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm du\,\mathrm dv[/tex]
so the integral becomes
[tex]\displaystyle\iiint_{\mathcal D}xz\,\mathrm dV=\int_{v=0}^{v=6}\int_{u=0}^{u=2\pi}\int_{r=0}^{r=3}r^2v\cos u\,\mathrm dr\,\mathrm du\,\mathrm dv=0[/tex]
2. Now let [tex]\mathcal D[/tex] denote the region bounded by the sphere [tex]x^2+y^2+z^2=4[/tex] and the coordinate planes in the octant in which each coordinate of the point [tex](x,y,z)[/tex] is negative.
Converting to spherical coordinates, we set
[tex]\begin{cases}x=\rho\cos u\sin v\\y=\rho\sin u\sin v\\z=\rho\cos v\end{cases}[/tex]
where we obtain [tex]\mathcal D[/tex] by varying over [tex]0\le\rho\le2[/tex], [tex]\pi\le u\le\dfrac{3\pi}2[/tex], and [tex]\dfrac\pi2\le v\le\pi[/tex]. The volume element is now
[tex]\mathrm dV=\rho^2\sin v\,\mathrm d\rho\,\mathrm du\,\mathrm dv[/tex]
so the integral becomes
[tex]\displaystyle\iiint_{\mathcal D}z\,\mathrm dV=\int_{v=\pi/2}^{v=\pi}\int_{u=\pi}^{u=3\pi/2}\int_{\rho=0}^{\rho=2}\rho^3\cos v\sin v\,\mathrm d\rho\,\mathrm du\,\mathrm dv=-\pi[/tex]
The ball game begins at 2pm. It takes ying 30 minutes to get to the ballpark. At what time should ying leave home to get to the the game 30 minutes before it starts
Answers
Find the area of the regular trapezoid. The figure is not drawn to scale. The top side is 4, the bottom side is 7, and both side sides are 5.
Answers
We know that:
DC = minor base = 4
AB = major base = 7
AD = BC = lateral sides or legs = 5
Since the two legs have the same length, the trapezoid is isosceles and we can calculate AH by the formula:
AH = (AB - DC) ÷ 2
= (7 - 5) ÷ 2
= 2 ÷ 2
= 1
Now, we can apply the Pythagorean theorem in order to calculate DH:
DH = √(AD² - AH²)
= √(5² - 1²)
= √(25 - 1)
= √24
= 2√6
Last, we have all the information needed in order to calculate the area by the formula:
[tex]A = \frac{(AB + CD)DH}{2} [/tex]
A = (7 + 5) × 2√6 ÷ 2
= 12√6
The area of the regular trapezoid is 12√6 square units.
The trash can is in the shape of a cylinder that has a radius of 2 ft and a height of 5 feet what is the volume of the trash can round to the nearest tenth
Answers
(2)^2 * 5 * 3.14 = V
4 * 5 * 3.14 = V
20 * 3.14 = V
V = 62.8
Volume is a three-dimensional scalar quantity. The volume of the trash can is 62.8318 ft³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the trash can = π×r²h = π×(2ft)²×(5ft) = 62.8318 ft³
Hence, the volume of the trash can is 62.8318 ft³.
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Form a sequence that has two arithmetic means between -13 and 89. a. -13, 33, 43, 89 c. -13, 21, 55, 89 b. -18, -36, -72, -144 d. -18, -81, -144
Answers
Solution:
Since it has to be between -13 and 89, letter d and b are not anymore considered to be the answer.
for a:
33-(-13)=46=d
43-33=10=d the value for this d is different from the two sequence,
89-43=46=d
they have different value for d, thus this is not the answer!
for c:
21-(-13)=34=d
55-21=34=d
89-55=34=d
they have the same value for d, thus the correct answer is c. -13, 21, 55, 89
how do I solve 9y+3=6y+15 then y =
Answers
Using the photo I have provided, you can see the steps. I performed these steps as you need to isolate the variable, Y. Once you do that, you must preform a one or two step equation to then get what said variable equals.
Hope this helps!
9y-9y+3=6y-9y+15
3=-3y+15
3-15=-3y+15-15
-12=-3y
-12/-3=-3y/-3
y=4
Apply the commutative property to 13 × 7 × 21 to rearrange the terms and still get the same solution
Answers
13 × 21 × 7
7 × 13 × 21
7 × 21 × 13
21 × 7 × 13
21 × 13 × 7
Any of these arrangements will give the same answer, 1,911.
The commutative property in mathematics says that the order in which numbers are multiplied doesn't change the product. For example, using the commutative property, the product of 13 x 7 x 21 will be the same as 7 x 21 x 13, which is 1911.
Explanation:The commutative property is a fundamental concept in Mathematics which states that for multiplication and addition, numbers can be moved around (or commuted) without changing the result. For example, if you have the multiplication problem 13 * 7 * 21, thanks to the commutative property, you can rearrange this problem to: 7 * 21 * 13 or 21 * 13 * 7 or any other arrangement of these three numbers, and the result will remain the same.
Let’s see this in action:
Original arrangement: 13 * 7 * 21 = 1911
Changed arrangement: 7 * 21 * 13 = 1911
As you can see, regardless of how the terms were rearranged, the answer remained the same, thus demonstrating the commutative property.
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what is the point slope form of a line with a slope 4/5 that contains the point (-2,1)
Answers
[tex]We\ have:\\\\m=\dfrac{4}{5}\\\\(-2;\ 1)\to x_1=-2\ and\ y_1=1[/tex]
[tex]Substitute:\\\\y-1=\dfrac{4}{5}(x-(-2))\\\\\boxed{B.\ y-1=\dfrac{4}{5}(x+2)}[/tex]
hey can you please help me posted picture of question
Answers
There are 5 ways to select the pant, 7 ways to select a shirt and 3 ways to select the shoes.
Total number of combinations will be the product of all these ways the dress items can be selected.
So, number of combination of outfits = 5 x 7 x 3 = 105
Therefore, option B gives the correct answer
Factor completely 121x2 − 16.
Answers
(11x+4)(11x-4)
HELP ME PLEASE WILL PICK BRAINLYEST
Answers
AB ≅ AC . . . . . . . . . . given
∠BAY ≅ ∠CAY . . . . given
AY ≅ AY . . . . . . . . . . reflexive property
ΔBAY ≅ ΔCAY . . . .. SAS congruence
XY ≅ XY . . . . . . . . . . reflexive property
∠AYB ≅ ∠AYC . . . . CPCTC
BY ≅ CY . . . . . . . . . . CPCTC
ΔXYB ≅ ΔXYC . . . .. SAS congruence
Therefore ...
∠XCY ≅ ∠XBY . . . . CPCTC
A ball is thrown upward and outward from a height of 77 feet. the height of the ball, f(x), in feet, can be modeled by f left parenthesis x right parenthesis equals negative 0.2 x squared plus 1.4 x plus 7f(x)=−0.2x2+1.4x+7 where x is the ball's horizontal distance, in feet, from where it was thrown. use this model to solve parts (a) through (c).
Answers
f(x)=-0.2x^2+1.4x+7
A] The maximum height of the ball will be given by:
At max height f'(x)=0
from f(x),
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
thus the maximum height would be:
f(3.5)=-0.2(3.5)^2+1.4(3.5)+7
f(3.5)=9.45 ft
b]
How far from where the ball was thrown did this occur:
from (a), we see that at maximum height f'(x)=0
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
This implies that it occurred 3.5 ft from where the ball was thrown.
c] How far does the ball travel horizontally?
f(x)=-0.2x^2+1.4x+7
evaluationg the expression when f(x)=0 we get:
0=-0.2x^2+1.4x+7
Using quadratic equation formula:
x=-3.37386 or x=10.3739
We leave out the negative and take the positive answer. Hence the answer 10.3739 ft horizontally.
HI, PLEASE HELP ASAP~(no one is helping me ;-;) + BRAINLIST!!
Janelle is at the movie theater and has $20 to spend. She spends $8 on a ticket and wants to buy some snacks. Each snack costs $4.99 . How many snacks, x , can Janelle buy? Inequality that represents this situation: 20≥8+4.99x Drag each number to show if it is a solution to both the inequality and the problem situation, to the inequality only, or if it is not a solution
Answers
Answer:
Part A : 2 snacks
Part B : Solution to both the inequality and the problem situation ⇒ 1 , 2
Solution to the inequality only ⇒ -4 , 3/4 , 2.3
Not a solution ⇒ 2.5
=================================================================
Step-by-step explanation:
Part A :
Janelle has $20 to spend
She spends $8 on a ticket, so , the remaining = 20 - 8 = $12
Each snack costs $4.99
So, the number of snacks =
the integer of ( 12 / 4.99 ) = integer of (2.4) = 2 snacks
Part B:
Inequality that represents this situation: 20 ≥ 8 + 4.99x
Solve for x
∴ 20 - 8 ≥ 4.99 x
12 ≥ 4.99 x
divide both sides by 4.99
∴ (12/4.99) ≥ x
∴ x ≤ 2.4048
The given options are : -4 , 3/4 , 2.3 , 2.5 , 1 , 2
So,
Solution to both the inequality and the problem situation ⇒ 1 , 2
solution to the inequality only ⇒ -4 , 3/4 , 2.3
Not a solution ⇒ 2.5
Answer:
Solutions to Both:
1
2
Solutions to the Inequality Only;
3/4
-4
2.3
Not a Solution:
2.5
Step-by-step explanation:
On the 4th of July, the probability of a person having a car accident is 0.08. What is the probability of a person driving while intoxicated or having a car accident if the probability of a person driving while intoxicated is 0.25 and the probability of a person having a car accident while intoxicated is 0.13?
Answers
0.25 + 0.08 - 0.13 = 0.20
what does life expectancy measure
Answers
Hope this helps! :)
please help I need a good grade
Answers
Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (-1+i)+(21+5i)
Answers
Answer:
c
Step-by-step explanation:
edge 2020
Answer:
The correct answer is C.
Step-by-step explanation:
Two samples are randomly selected from each population. if a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
Answers
The equation of a parabola is given.
y=−14x2+4x−19
What are the coordinates of the vertex of the parabola?
Enter your answer in the boxes.
Answers
Answer:
vertex ( [tex]\frac{1}{7}[/tex], [tex]\frac{131}{7}[/tex]).
Step-by-step explanation:
Given : The equation of a parabola is given.
y=−14x²+4x−19
To find : What are the coordinates of the vertex of the parabola.
Solution : We have given that
y = −14x²+4x−19
we will be "completing the square" .
Factor out -14 to make leading coefficient 1
y = -14 ([tex]x^{2} -\frac{2x}{7} +\frac{19}{14}[/tex])
Add and subtract [tex](\frac{-1}{7}) ^{2}[/tex]
y = -14 ([tex]x^{2} -\frac{2x}{7} +\frac{19}{14}+\frac{-1}{7}) ^{2} - (\frac{-1}{7})^{2})[/tex] .
Complete the square
y = -14 ( [tex](x -\frac{1}{7}) ^{2} +\frac{19}{14}- (\frac{-1}{7})^{2})[/tex].
y = -14 ( [tex](x-\frac{1}{7}) ^{2} -\frac{131}{7}[/tex]
Standard form of parabola vertex form y = a(x - h)²+ k,
Where, ( h, k) are vertex
On comparing a = -14 , h= [tex]\frac{1}{7}[/tex], k = [tex]\frac{131}{7}[/tex]
Therefore, vertex ( [tex]\frac{1}{7}[/tex], [tex]\frac{131}{7}[/tex]).
hey can you please help me posted picture of question
Answers
r = f (t)
Where,
Independent variable is t.
Dependent variable is r.
To find the inverse we solve for the independent variable, that is, the data entry variable.
Answer:
FALSE
option B
How do you divide a decimal
Answers
Solve the rational equation 8/x+1/5=3/x
Answers
To solve the equation 8/x + 1/5 = 3/x, we multiply the entire equation by 5x to get rid of the fractions to get 40 + x = 15. Solving for x we get x = -25.
Explanation:To solve the given rational equation 8/x + 1/5 = 3/x, we first need to find a common denominator to combine the fractions. Hence, we multiply the entire equation by 5x to get rid of the denominators:
5 * 8 + x = 15
which simplifies to
40 + x = 15.
Then by subtracting 40 from both sides to solve for x, we get:
x = -25.
That is the solution to the rational equation.
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The rational equation 8/x + 1/5 = 3/x is solved by finding a common denominator, simplifying the equation and then factoring the resulting polynomial to find the roots.
Explanation:To solve the given rational equation 8/x + 1/5 = 3/x, we first find a common denominator for the fractions. Seeing x and 5, we can take the common denominator as 5x.
Next, we rewrite each term with the common denominator: (40/5x) + (x/5x) = (15/5x). This simplifies to 40/5x + x/5x - 15/5x = 0. Simplifying further we have 8/x - 3/x + 1/5 = 0.
After setting the equation to zero, one may notice that this equation can be solved by bringing the terms together and then trying to factorize the resulting polynomial. The solution of the equation are the roots of the factored polynomial.
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if i had 7 apples and someone took away 5 how many would i have left
Answers
Hey can you please help me posted picture of question
Answers
A. G(x)=(x+3)^2-2
The explanation is shown below:
1. As you can see in the graph shown in the picture attached, there is two parabolas. The red parabola has the patern function F(x)=x^2, which means that is the most basic function of the quadratic functions. The blue parabola is shifted 3 units on the -x axis and 2 units on the -y axis, therefore, the correct option is the Option A.