The value of x is ±√(42 - y² - z²).
What is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators.
Given:
x² + y² + z²=k
As, it is given that k = 42.
So, x² + y² + z²=k
x² + y² + z²= 42
x² = 42 - y² - z²
x=±√(42 - y² - z²)
Hence, the value of x is ±√(42 - y² - z²).
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1.5.PS-21 Challenge Yossi used to have a square garage with 314 ft² of floor space. He recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side? One side of the garage was originally 17.7 ft long. (Round to the nearest tenth as needed.) ft long. Question Help One side of the garage is now (Round to the nearest tenth as needed) Enter your answer in the answer box and then click Check Answer. -
Required values:
The length of one side of the garage was originally 17.7 ft long
The length of one of the sides of the garage is now 21.7 ft long
The percentage increase in length is 22.5%.
Given parameters are;
The area of the square garage is 314 ft.²
The area of the new garage has 50% more space
Required;
Initial side length:
The initial side length, given to the nearest tenth, s, is the square root of the area, A, given as follows;
s = √(314 ft.²) ≈ 17.7 ft.
New Side length:
The side was increased by 50%, to give,
314 + 0.5×314 = 471
The new area of the garage = 471 ft.²
The side length of the new garage, s = √(471) ≈ 21.7 ft
The side of the garage now is 21.7 ft.
Percentage increase in length:
The percentage increase is given as follows;
% increase in length
= new side length - old side length / old side length * 100
= 21.7 - 17.7 / 17.7 *100
= 22.5 %
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find the number represented by the prime factorization 2^3 10^2
Answer:800
Step-by-step explanation:
2×2×2×10×10=800
Answer:
2^3*3^2=72
Step-by-step explanation:
First 4 solve for x
Last 4 solve for x AND y
Step-by-step explanation:
find the value of 8x³-y³if 2x-y and xy=-1
1) 2 + x = 22 3) -6 + p = -18 5) -29 = -20 + n 7) -5 + r = -23 9) 11 = x + 13 11) 101 = n +55 2) -15 = -18 + n 4) -18 + v = -9 6) -19 = n - 13 8) -12 = k +5 10) 11 = -1 + x 12) x - 36 = -68
Answer:
1)x=20
3)p=−12
5)n=−9
7)r=−18
9)x=−2
11)n=46
2)n = 3
4)v=9
6)n=−6
8)k=−17
10)x=12
12)x=−32
Step-by-step explanation:
Let's solve your equation step-by-step.
1) 2+x=22
Step 1: Simplify both sides of the equation.
x+2=22
Step 2: Subtract 2 from both sides.
x+2−2=22−2
x=20
3) −6+p=−18
Step 1: Simplify both sides of the equation.
p−6=−18
Step 2: Add 6 to both sides.
p−6+6=−18+6
p=−12
5) −29=−20+n
Step 1: Simplify both sides of the equation.
−29=n−20
Step 2: Flip the equation.
n−20=−29
Step 3: Add 20 to both sides.
n−20+20=−29+20
n=−9
7) −5+r=−23
Step 1: Simplify both sides of the equation.
r−5=−23
Step 2: Add 5 to both sides.
r−5+5=−23+5
r=−18
9) 11=x+13
Step 1: Flip the equation.
x+13=11
Step 2: Subtract 13 from both sides.
x+13−13=11−13
x=−2
11) 101=n+55
Step 1: Flip the equation.
n+55=101
Step 2: Subtract 55 from both sides.
n+55−55=101−55
n=46
2) −15=−18+n
Step 1: Simplify both sides of the equation.
−15=n−18
Step 2: Flip the equation.
n−18=−15
Step 3: Add 18 to both sides.
n−18+18=−15+18
n=3
4) −18+v=−9
Step 1: Simplify both sides of the equation.
v−18=−9
Step 2: Add 18 to both sides.
v−18+18=−9+18
v=9
6) −19=n−13
Step 1: Flip the equation.
n−13=−19
Step 2: Add 13 to both sides.
n−13+13=−19+13
n=−6
8) −12=k+5
Step 1: Flip the equation.
k+5=−12
Step 2: Subtract 5 from both sides.
k+5−5=−12−5
k=−17
10) 11=−1+x
Step 1: Simplify both sides of the equation.
11=x−1
Step 2: Flip the equation.
x−1=11
Step 3: Add 1 to both sides.
x−1+1=11+1
x=12
12) x−36=−68
Step 1: Add 36 to both sides.
x−36+36=−68+36
x=−32
The marine center has 150 parking spaces in front of its building.
What is the reciprocal of 150?
The reciprocal of 150 will be 1/150.
We have a marine center has 150 parking spaces in front of its building.
We have to find the reciprocal of 150.
What do you understand by the reciprocal of a number ?The reciprocal of a number is a number such that the product of both the numbers is equal to 1. Mathematically, if the original number is a, then its reciprocal will be 1/a , such that -
a x 1/a = 1
According to the question -
Let us assume that A = 150
Now, from the definition of reciprocal, the reciprocal of A will be -
1/A. Therefore, the reciprocal of 150 will be = 1/150
Hence, the reciprocal of 150 will be 1/150.
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A rectangular swimming pool is 15 meters long, 14 1/2 meters wide, and 5 1/2 meters deep. What is its volume?
Answer:
length x width x height (or depth) = volume
Step-by-step explanation:
761.25 or 761 1/4 is the answer
janice wants to put a fire at the mid point between two of her trees in her backyard. the coordinates of tree A are (3, 5) and the coordinates of tree b are (-3,-3). How far is the fire from tree b?
Answer:
janice wants to put a fire at the mid point between two of her trees in her backyard. the coordinates of tree A are (3, 5) and the coordinates of tree b are (-3,-3). step by step thinking we want tree A is coordinat at 35. three b coordinate is -3-3 .janice stand between centre that from A mark 6feet so At B is 3
The graph below represents how much money Lana will make babysitting in one night. How much money will Lana make at the start of the night?
i think its 8. is the x days and y money?
4 divided by 8/9 - 1/2
Answer:
-0.28
Step-by-step explanation:
4 ÷ 8/9 -1/2
BODMAS
8/9 ÷ 4
8/9 x 1/4
2/9 x 1
2/9 - 1/2
= -0.2777
= -0.28
Mr.letter has 80 sheets of colored paper. seven of his students need the paper for a project. how many sheets does each student get. how many sheets are left over?
Answer:
11
Step-by-step explanation:
80 /7=11.428
so each gets 11 so 77 so u do 80-77=3 so u would have 3 left over
HELP...............................! !
Answer:
-1 31/65
Step-by-step explanation:
I did this before trust me
Answer:
[tex] \sf \large - 1 \frac{31}{65} [/tex]
Step-by-step explanation:
6 2/5/-4 1/3
6 2/5/−4 1/3
=32/5/−4 1/3
= 32/5 −13/3
=32/5/−13/3
=−96/65
= −1 /31/65
help a real one out i need help with this
1. A(2,8) A'(6,7)
2. B(5,2) B'(9,1)
3. C(2,2) C'(6,1)
4. P(x,y) P'(x ₊ 4 , y ₋ 1)
5. x units to x ₊ 4 units.
y units to y ₋ 1 units.
6. triangle A'B'C' (6 , 4)
7. triangle A'B'C' (7 , 5)
8. triangle ABC ( 3,2)
9. triangle ABC (4 , 4)
Given,
A set of values called coordinates helps to display a point's precise location in the coordinate plane.
we can observe the points from the graph we get the values for B' and C'.
P(x,y) P'(x₊,y₋)
P(2,5) P'=(6,4) ⇒(2₊4,5₋1)
P(3,6) P' = (3₊x' , 6₋y') ⇒ (3₊4 , 6₋1) = (7,5)
P'(7,1) P = (x'₋4 , y'₊1) ⇒ (7₋4 , 1₊1) = (3,2)
P'(8,3) P = (x'₋4 , y'₊1) ⇒ (8₋4 , 3₊1) = (4,4)
hence we acquired the desired values of the points from the graph given.
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3 charles can type 675 words in 9 minutes how many words can charles type in 3 minutes
In one minute, Charles can type in 3-minute 225 words.
How many words can Charles type in 3 minutesIn one minute, Charles can type
675/9 = 75 words.
Hence, in 3 minutes Charles can tape [tex]75\times3[/tex] = 225 words (if works with the same rate).
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To win the annual read-a-thon at his school, Ronald has to read more books than any of his
classmates over winter break. He starts by reading a lot of sports books. Then, he reads 7
mystery books. In all, Ronald reads 25 books for the read-a-thon.
Which equation can you use to find the number of sports books n Ronald reads?
n+ 7 = 25
n - 7 = 25
Submit
7n = 25
7
= 25
Solve this equation for n to find the number of sports books Ronald reads.
sports books
Answer:
The equation for this question should be n+7=25
where n=18
Step-by-step explanation:
Can someone help me
The given table of the values of f(x) is used to complete the table for the function [tex]y = f \left( \frac{1}{5} \cdot x \right) [/tex], to give;
The following values of x and y as follows;
x: -0.8, -0.2, 0, 0.6, 1.2
y: 7, -2, 3, -4, 5
Please also see the attached table
How can the function, f(x) be scaled to give the function, [tex]y = f \left( \frac{1}{5} \cdot x \right) [/tex]?The question is with regards to scaling a graph horizontally.
Using the rule of scaling a graph, we have;
Given that a point on the graph of f(x) is (x, y), the corresponding point in the graph of f(C•x) is (C•x, y).
The given modification of the function is presented as follows;
[tex]y = f \left( \frac{1}{5} \cdot x \right) = f \left( 0.2 \cdot x \right)[/tex]
The points on the graph that completes the table are therefore;
(0.2×(-4), 7) = (-0.8, 7)(0.2×(-1), -2) = (-0.2, -2)(0.2×0, 3) = (0, 3)(0.2×3, (-4)) = (0.6, -4)(0.2×6, 5) = (1.2, 5)The completed table is therefore;
x y
-0.8 7
-0.2. -2
0 3
0.6. -4
1.2. 5
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help needed ASAP. high school geometry
Answer:
9 u^2
Step-by-step explanation:
there's 2 ways to solve this problem
easy way
plot every coordinate and youll see it's a square
square area = side^2
3^2 = 9 answer
and this method
working with 3 points (triangle)
W - X - Y
0 0
0 3
-3 3
0 0
--------------
2
--------------------------------------
0 0
0 -9
0 0
-----------
l-9/2l
4.5
since a square is made of 2 triangles
4.5 * 2 = 9 u^2
Evaluate the expression if m = − 4 , n = 1 , p = 2 , q = − 6 , r = 5 , and t = − 2 . − | 10 − 7 r + 8 m + 2 p |
Answer:
-53
Step-by-step explanation:
if m = − 4 , n = 1 , p = 2 , q = − 6 , r = 5 , and t = − 2
-| 10 - 7r + 8m + 2p |
Substitute the given values into the equation.
-| 10 - 7(5) + 8(-4) + 2(2) |
Simplify
-| 10 - 35 + -32 + 4) |
-| -53 |
= -53
Absolute value of -53 is 53 however there is a negative sign outside of it, so the answer is -53
Solve for × 3×+2=32
Answer: x = 10
Step-by-step explanation:
3(10) = 30 +2 + 32
Given x is the midpoint of line WY, wx is congruent to xz
Prove line xy is congruent to line xz
Give statements and reasons
The two column proof is completed by the substitution property of equality, which gives;
WX = XZ
XY = XZ
[tex] \overline{XY} \cong \overline{XZ}[/tex]How can the congruency of the required segments be proven?The completed two column table is presented as follows;
Statement. Reasons
1. X is the midpoint of [tex] \overline{WY}[/tex]. 1. Given
2. WX = XY 2. Definition of midpoint
3. [tex] \overline{WX} \cong \overline{XZ}[/tex]. 3. Given
4. WX = XZ 4. Definition of midpoint
5. XY = XZ 5. Substitution property of equality
6. [tex] \overline{XY} \cong \overline{XZ}[/tex] 6. Definition of congruency
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Although it is much larger in reality, when we
see Saturn from Earth, it looks like it has a
diameter of 20 μm. Through a telescope, the
diameter looks 9,000 um long. What
magnification scale was used?
The magnification scale used was 450:1
Saturn from Earth, it looks like it has a diameter of 20 μm.
d₁=20μm
Through a telescope, the diameter looks 9,000 μm long.
d₂= 9,000 μm
magnification scale = d₂/d₁
= 9,000 μm/20μm
= 450/1
magnification scale used was 450:1
A scale factor is a number that can be used to adjust the size of any geometrical figure or object in relation to its original size. It's used to draw the enlarged or reduced shape of any given figure, as well as to calculate the missing length, area, or volume of an enlarged or reduced figure. It should be noted that the scale factor only affects the figure's size and not its shape.
A scale factor is a number or conversion factor used to adjust the size of a figure without changing its shape. It is used to enlarge or reduce the size of an object. If the dimensions of the original figure and the dimensions of the dilated (increased or lowered) figure are known, the scale factor can be determined. A rectangle, for example, has a length of 5 units and a width of 2 units. If we raise the size of this rectangle by a factor of two, the sides will become 10 and 4, respectively. As a result, we can use the scale factor to determine the dimensions of the altered figures.
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Write an equation in point-slope form
Answer:
y = -4/3x + 2
Step-by-step explanation:
Point slope form is this:
y - y1 = m (x - x1)
Where m is the slope. y1 and x1 are where you put your coordinates.
so now we just plug it in.
y - (-2) = -4/3 (x - 3)
We should clean it up in order to make it look like this equation: y = mx + b
y + 2 = -4/3x -4/3(-3)
y + 2 = -4/3x + 4
y = -4/3x + 2
Simplify.
[tex]\sqrt{20+5}[/tex]
Answer: 5
Step-by-step explanation:
[tex]\sqrt{20+5}[/tex]=
[tex]\sqrt{25}[/tex]=5
Answer:
√(20 + 5) = 5
Step-by-step explanation:
Let's solve the problem,
→ x = √(20 + 5)
→ x = √25
→ [ x = 5 ]
Hence, the answer is 5.
answer the question in the image
Answer:
[tex]\frac{211}{500}[/tex]
Step-by-step explanation:
[tex].4\bar{2}[/tex] means the 2 repeats till infinity
[tex].4\bar{2}[/tex] = .4222222222.....
To convert to fraction just take the first three decimal place digits 422 and divide by 1000 to convert to fraction
[tex].4\bar{2} = \frac{422}{1000}[/tex]
Dividing numerator and denominator of this fraction by 2 gives
[tex]\frac{422/2}{1000/2} =\frac{211}{500}[/tex]
This cannot be simplified further and therefore
[tex].4\bar{2} = \frac{211}{500}[/tex]
If we had chosen first 4 decimal digits then it would be[tex].4\bar{2} = \frac{4222}{10000} = \frac{2111}{5000}[/tex]
i.e. we divide by 10,000
[tex]- \sqrt{64}[/tex]
The value of the square root of 64 is -8
Square root integersAn integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.
The square root of a number is the values that will can multiply twice to give the resulting value in the root.
Given the expression below:
- √64
Since the square root of 64 is 8, hence;
-√64 = -1 * √64
-√64 = -8
Hence the value of the square root of 64 is -8
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A survey was carried out among 120 school children looked at which type of meat they preferred. 55%said they preferred lamb,20% said they preferred chicken, 15% preferred duck and 10% turkey . calculate the number of children in each category
No. of children in lamb, chicken, duck, and turkey category is 66, 24, 18 and 12 respectively.
What is percentage ?Percentage is the value per hundredth.
According to the given question a survey was carried out among 120 school children looked at which type of meat they preferred. 55% said they preferred lamb,20% said they preferred chicken, 15% preferred duck and 10% turkey and we have to calculate no. of children in each category.
55% said they preferred lamb, So the no. of students i this category is
= (55/100)×120
= 66 children.
20% said they preferred chicken, So the no. of children in this category is
= (20/100)×120
= 24 children.
15% said they preferred duck, So the no. of children in this category is
= (15/100)×120
= 18 children.
10% said they preferred turkey, So the no. of children in this category is
= (10/100)×120
= 12 children.
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25 POINTS AND BRAINLIEST
NO EXPLANATION NEEDED JUST ANSWER
Answer: 35.
Step-by-step explanation: 33 + 34 + 35 is 102. Your 35 is the largest of the three.
On a map with a scale of 1 inch to 12 feet, the area of a restaurant is 60 in². Han says that the actual area of the restaurant is 720 ft²
O True
O False
Answer:
False
Step-by-step explanation:
The scale is for length only, when converting to area scale, you have to square both sides of the scale.
1 in² = 144 ft²
5| c + 7 | = -45
Absolute Volume
Answer:c=16
Step-by-step explanation:5c+35=-45=5c=-45-35=5c=-80. C=16
During a snowstorm, Snowfill an a constant rate for a number of hours. Then it stoped snowing for a number of hours. then it started Up again at a different constant rate Andrew Madie graph showing the edges of the snow on the ground over time using the data he collected. After how many hours were there 7 inches of snow on the ground
Answer: Unable to answer
Step-by-step explanation: If you do not show what the constant rate is, I am unable to solve it for you.
-4x+1.5x-2.5x-2 x-6.5= evaluate the expression when x=4
could someone do this :(
Answer:
-34.5
Step-by-step explanation:
Put together like terms:
-7x-6.5
-28-6.5
-34.5