Answer:
r = 1
Step-by-step explanation:
8 - 6r + 3 = 5
Combine like terms
11 - 6r = 5
Subtract 5 from both sides
6 - 6r = 0
Add 6r to both sides
6 = 6r
Divide both sides by 6
1 = r
bens owns two cars, car 4 and car B. This year, car A is 9 years old and car B is x years old. 5 years ago, the ratio of the age of car 4 to the age of car B was 2:5 Calculate the value of x.
Answer: 45 yrs old
Step-by-step explanation:
Car A = 9 yrs old
Car B = X yrs old
The ratio for the cars are
Car A : Car B
or
2 : 5
You want to make it easier to read so you make both the ratio number and the given age number (9) the same number.
Multiply Car A age by 2 to make it 18 and the Ratio 2 by 9 to make it 18. This makes them the same number. Since you did this to one side, you have to do it on the other side by multiplying the 5 by 9 which is 45.
Your new ratio is now
18 : 45
This means Car B is 45 yrs old
Question: Can it be simplified? If NO, explain why. If YES, simplify completely or rewrite as a simplified radical expression. SHOW ALL WORK.
Expression: (x^4y)^2/3
Please help me with this!
Answer:
Step-by-step explanation:
1) Use multiplication distributive property [tex](xy)^a=x^ay^a[/tex]
= [tex]\frac{(x^4)^2y^2}{3}[/tex]
2) Use Power rule [tex](x^a)^b = x^{ab}[/tex]
= [tex]\frac{x^8y^2}{3}[/tex]
a house at the bottom of a hill is fed by a full tank of water 5.pm deep and connected to the house by a pipe that is 110m long at an angle of 58 degrees from the horizontal
The water gauge pressure at the house will be 9.63×10⁵ N/m².
Firstly we will be calculating the total height which will comprise of height from tank to house and elevated height. The formula for total height will be -
Total height = 5 + 110 sin 58°
Keep the value of sin 58° in formula and performing multiplication followed by addition
Total height = 5 + 110×0.848
Total height = 5 + 93.28
Total height = 98.28 meters
Now, calculating the water gauge pressure at house. The formula to be used is -
P = ρ×g×h, where P is pressure, ρ is density of water, g refers to acceleration due to gravity and h represents total height. We are aware that density of water is 1000 kg/m³ and accelerate due to gravity is 9.8 m/s².
Keep the values in formula to find the gauge pressure.
P = 1000 × 9.8 × 98.28
Performing multiplication
P = 963,144 N/m² or 9.63×10⁵ N/m²
Hence, the water gauge pressure at the house will be 9.63×10⁵ N/m².
The complete question is -
A house at the bottom of a hill is fed by a full tank of water 5m deep and connected to the house by a pipe that is 110m long at an angle of 58 degrees from the horizontal. Determine the water gauge pressure at the house.
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solve for x32=10+ x/2
Answer:
x=44
Step-by-step explanation:
x32=10+x/2
Multiply the 2 from x over 2 to reverse the division equation.
2*x32=10+x/2*2
That results in 2 multiplying 32x and 2 multiplying the 2 in x over 2.
Because multiplication is the reverse of division, the 2's will cancel out and reduce x over to 2 to simply x.
2*32 is 64, include the x before the 64 just like the given equation exemplifies with the x before the 32.
The equation looks like the following once put together: x64=10+x
Subtract the x from the 10+x side of the equation underneath the x64.
x64=10+x
-x -x
Which equals x63=10.
To receive the answer to this question, you have to divide the 63 on both sides.
63 divided by 63x leaves you with just the x.
63 divided by 10 leaves you with 6.3 in decimal form.
Thus, x equals 6.3.
To check if it's right, insert 6.3 for both x's.
(6.3)*32=10+(6.3)/2
Solve.
201.6=10+3.15
201.6=13.15
Clearly, this doesn't work.
So, I'm assuming you actually meant: 32=10+x/2.
Hence, you would multiply 2 on both sides.
2*32=10+x/2*2
We've established that 32*2 is 64 and the 2's would cancel out.
64=10+x
Subtract the 10 on both sides.
54=x
To see if this one is correct, plug in 54 to the x.
32=10+(54)/2
Divide 54 by 2 which equals 27.
32=10+27
32=37
Nope, that doesn't work either.
Thus, instead of multiplying by 2, we would first need to subtract the 10.
32=10+x/2
-10 -10
32-10 is 22 and it would leave the other side with just x over 2.
22=x/2
Now, we would have to multiply the 2 on both sides.
22*2=44 and x/2*2 gives us x.
So, 44=x.
Let's check.
32=10+(44)/2
32=10+22
32=32
Finally, we have our match.
In conclusion, x=44.
Hope this helps.
Solve the simultaneous equations:
x+y=9
x²-3xy + 2y² = 0
The solutions are (4.5, 4.5) and (6, 3).
Here,
The equations are;
x + y = 9
x²- 3xy + 2y² = 0
We have to solve the equations.
What is Expression?
Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division
Now,
The equations are;
x + y = 9
x²- 3xy + 2y² = 0
Since, x + y = 9 ⇒ y = 9 - x
And, solve the equation as;
x²- 3xy + 2y² = 0
x²- 2xy - xy + 2y² = 0
x (x - 2y) - y (x - 2y) = 0
(x - y) (x - 2y) = 0
(x - y) = 0 or (x - 2y) = 0
For, (x - y) = 0
Given, x + y = 0
Hence, Solve equation (x - y) = 0 and (x + y) = 9 we get;
2x = 9
x = 4.5
And, y = 4.5
For (x - 2y) = 0
x = 2y put in equation (x + y) = 9 we get;
(x + y) = 9
2y + y = 9
3y = 9
y = 3
And, x = 6
Therefore, The solutions are (4.5, 4.5) and (6, 3).
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Solutions are (4.5,4.5) and (6,3)
What are Quadratic equations ?
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
Given,
x + y = 9 => y = 9-x equation 1
x^2 - 3xy + 2y^2 = 0 equation 2
(x - y)(x - 2y)=0
x - y = 0 or x - 2y = 0
1. Equating x-y=0 and x + y = 9,
x + y = 9
x - y = 0
2x = 9
x = 4.5
y = 4.5
because y = x
2. Equating x - 2y = 0 and x + y = 9,
2x + 2y = 18
x - 2y = 0
3x = 18
x = 6
y = 9 - x = 3
therefore, possible solutions are (4.5,4.5) and (6,3)
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-2 1/2 divided 2 6/7
Answer:
Exact Form -- -7/8 Decimal Form -- -0.875
Step-by-step explanation:
I Didn't Now If U Wanted It Explained So...
Answer: -7/8
Step-by-step explanation:
convert from mixed number to fraction:
-5/2 ÷ 20/7
use the fraction rule
[tex]\frac{a}{b}[/tex]÷[tex]\frac{c}{d} = \frac{a}{b}[/tex]×[tex]\frac{d}{c}[/tex]
-5/2 x 7/20
cross cancel
- 1/2 x 7/4
from there multiply numerators together and denominators together
(-1*7) / (2*4)
-7/8
Calculate the value of the x (with reason)
in fig. 3.1 the value of x is 20° , in fig. 3.2 the value of x is 40° , in fig. the value of 3.3 x is 10° , in fig. 3.4 the value of x is 120°.
WHAT IS ANGLE?In planar geometry, an angle is a shape made up of two rays or lines that share an endpoint. The English word "angle" derives from the Latin word "angulus," which means "corner." The vertex and the two rays are referred to as the sides of an angle, respectively, and are the shared termini of two rays.
CALCULATION3.1
straight lines makes an angle of 180° thus ,
x + 2x + 120 = 180
3x = 60
x = 20°
3.2
sum of the angles of triangle is = 180°
105 + 35 + x = 180
140 + x = 180
x = 40°
3.3
since it is an isoceles triangle so the opposite angles to equal sides are equal
140 + 4x = 180
4x = 40
x = 10°
3.4
parallel line theorem state that alternate angles are equal
so ,
180= x + 60
x = 120 °
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Find the focus and the directrix of the parabola with the equation y = -¹/2 (x-8)² -
6.
A) Focus = (-8,-5¹/2), directrix is y=-6¹/2
B) Focus = (8,-6¹/2), directrix is y= -5¹/2
○ C) Focus = (-8,-6¹⁄2), directrix is y= −5¹/2
D) Focus = (8,-5¹/2), directrix is y=-6¹/2
Answer:
focus
Step-by-step explanation:
Answer:
Step-by-step explanation:
Focus = (8,-6¹/2), directrix is y= -5¹/2
statistical considerations for use of composite health-related quality-of-life scores in randomized trials
Statistical considerations for the use of composite health-related quality-of-life scores in randomised trials
This is a research paper whose author is Andrew J. Vickers.
Abstract:
background: In randomised studies, first-rate of life measures are mechanically utilised as outcomes. contraptions with several subscales provide researchers the choice of combining a few or all scales right into a unmarried composite score. There is probably diverse clinically and scientifically sound alternative subscale combinations for the predominant outcome degree.foremost findings: The statistical effectiveness of diverse subscale combinations is decided with the aid of the relative effect size of the intervention on every subscale as well as the correlation between the subscales. easy formulae may be installed to determine the relative statistical efficiency of each clinically appropriate subscale aggregate. Hypothetical situations imply that the variety of participants required in a scientific trial is probably twice as huge for a few subscale combinations as for others.Conclusions:
Ina randomised examine, there are often robust scientific or scientific reasons to pick a positive subscale or composite.whilst there are several viable picks, statistical performance can help in guiding the choice of endpoint.To learn more about statistics, visit :
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40 POINTS! Classify the function as even, odd or neither. Be sure to include your work to justify your classification.
Answer:
this is the answer of about the image is even
For each part of each exercise copy the equation and show each step that leads to
your answer
x + 2 = 7
The equation x + 7 = 2 will have the value of x as 5.
We are given the equation:
x + 2 = 7
We need to solve the equation to find the value of x.
We will first subtract 2 from both the sides:
x + 2 - 2 = 7 - 2
So, subtracting 2 from both the sides, we get that:
x = 5
the value of x for the equation will be 5.
Therefore, the equation x + 7 = 2 will have the value of x as 5.
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find the coordinates of the midpoint segment with the given endpoints: (12,-7) and (-6,15) midpoint (blank
Find the approximate side length of a square game board with an area of 105 in2.
Answer:
Rounded to the nearest inch: 10
Rounded to the nearest tenth: 10.2
Rounded to the nearest hundredth: 10.25
Step-by-step explanation:
To find the area of a square, we multiply the side length by itself, or in other words, SQUARE the side length!
[tex]A=s^2[/tex]
We are given the area, so plugging that into our equation looks like this:
[tex]105=s^2[/tex]
To eliminate the exponent, take the square root of both sides of the equation!
[tex]\sqrt{105}=s[/tex]
From here, there are a few paths to take, depending on what your teacher is looking for. I will evaluate the approximate of the square root by finding the nearest perfect squares.
The nearest perfect square less than √105 is √100, and the nearest perfect square greater than √105 is √121.
105 is closer to 100 than to 121, so √105 is closer to √100.
√100 is equal to 10, so the √105 is approximately 10 inches!
Using a calculator to check:
[tex]\sqrt{105}=10.247[/tex] inches
brainliest if answerd correctly x³+y³+z³=k
Answer:
Uhh the answer should be x^3 + y^3 + z^3 for k
Step-by-step explanation:
That's what it says in question, which is the answer.
Pls brainlieset :0?
Four friends went out to lunch and the bill came to $54.55 They decided to add enough tip to make a total of
$67.51, so that they could easily split the bill evenly among themselves. What percent tip did they leave?
Round your answer to two decimal places.
The percent tip is
%?
Answer: four friends went out for dinner. the bill , including tax , totaled $64.00 if they want to leave a 15% tip and want to share the bill and tip equally
Step-by-step explanation:
Find the perimeter and area of the figure if each unit on the graph measures 1 centimeter. Round answers to the nearest tenth, if necessary.
The Perimeter of polygon ABCD = 21.6 units.
What is the Perimeter of a Figure?The perimeter of figure ABCD = sum of all its sides = AB + BC + CD + AD.
To find each of the sides, apply the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
A(-5, 5)
B(0, 3)
C(-2, -2)
D(-7, 0)
AB = √[(0−(−5))² + (3−5)²]
AB = √29
AB ≈ 5.4 units
BC = √[(0−(−2))² + (3−(−2))²]
BC = √29
BC ≈ 5.4 units
CD = √[(−7−(−2))² + (0−(−2))²]
CD = √29
CD ≈ 5.4 units
AD = √[(−7−(−5))² + (0−5)²]
AD = √29
AD ≈ 5.4 units
The Perimeter of polygon ABCD = 5.4 + 5.4 + 5.4 + 5.4 = 21.6 units.
Therefore, the Perimeter of polygon ABCD = 21.6 units.
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How are rays and angles related?
ieiejeieieiweisns xx xnsiwiwksniz
−4xy(5x² – 9xy – y²)
The abbreviated formula is -4xy (5x(x-y) - y(4x + y)).
The answer to the question is that common words outside of the brackets can be used to simplify the supplied equation.
Therefore,
Required expression is -4xy(5x2 - 9xy -y2), which is equivalent to -4xy(5x2 - 5xy - 4xy -y2).
The final formula will be: -4xy(5x(x-y) - y(4x + y)).
Therefore, the abbreviated formula is: -4xy(5x(x-y) - y(4x + y)).
How does simplification work?In mathematics, simplification is a technique that makes a complex equation simpler in a less complex way. This approach makes expression calculation possible.
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PLEASE HELP ME
Solve the inequality. Graph the solution, if possible.
24. |m|greater than or equal to 10
We can use inequality, 24. |m| greater than or equal to 10 then the possible to value is = |14|.
What is Inequality :A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Based on the given conditions, formulate,
24. |m| greater than or equal to 10
So, we can write,
24 + m ≥ 10
m ≥ 10 - 24
We can sum or difference,
m ≥ -14
Then,
|m| ≥ |-14|
Hence,
|m| ≥ |14|
Therefore,
24. |m| greater than or equal to 10 then the possible to value is = |14|.
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6) Jessica’s cat is stuck in a tree. The fire department comes to help rescue the cat. Using a 25 foot ladder that is 10 feet away from the base of the tree, how high will the firefighter climb to reach the cat?
The firefighter needs to climb a height of 22.91 foot to reach the cat.
What is the Pythagorean Theorem ?
Pythagorean Theorem states that the square of the hypotenuse of a right triangle equals the sum of squares of the lengths of the other two sides.
It is given that the hypotenuse of the ladder is 25 foot and it's base is 10 feet away from base of tree.
Using the Pythagorean theorem which states that :
H² = P² + B²
where ;
H = Hypotenuse , P = Perpendicular and B = base
We can find out the height up to which the firefighter needs to climb to reach the cat. And it is given by :
25² - 10² = P²
625 - 100 = P²
or
P = √525
P = 22.91 foot
Therefore , the firefighter needs to climb a height of 22.91 foot to reach the cat.
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Rewrite, using the distributive
property.
1(19c+30) = [?]c + [ ]
Answer:
[tex] \sf \: 19c + 30 [/tex]
Step-by-step explanation:
Given expression,
→ 1(19c + 30)
Let's simplify the expression,
→ 1(19c + 30)
→ 1(19c) + 1(30)
→ (1 × 19)c + (1 × 30)
→ (19)c + (30)
→ 19c + 30
Hence, answer is 19c + 30.
Triangle EFG is similar to triangle HIJ. Find the measure of side HI.
Round your answer to the nearest tenth if necessary. Figures are not
drawn to scale.
The measure of side HI is 10.74 for the triangle EFG which is similar to HIJ.
Similar triangles are those triangles which have corresponding sides in proportion to each other and the corresponding angles of two triangles are equal to each other. Similar triangles look the same but they differ in terms of the sizes of the two triangles.
In short, If two triangles are similar that means,
All corresponding angle pairs of triangles will be equal.
All corresponding sides of triangles will be proportional.
Now, it is given in the question that ΔEFG is similar to ΔHIJ then, their corresponding sides will be in proportion.
⇒ GE/EF = HJ/HI
⇒ 19/34 = 6/HI
⇒ HI = 6 x 34/19
⇒ HI = 10.74
Therefore, the measure of side HI is 10.74.
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PLEASE HELP
SHARKS Deep Blue, one of the largest great white sharks ever recorded, measures about 6.1 meters in length. If 1 meter = 3.28 feet, how long is Deep Blue in inches? Round to the nearest tenth.
Can someone help me out
Answer:
A
Step-by-step explanation:
(6*10^4*3^3)/(6^5*5^6)
Answer: (1/75)
Step-by-step explanation:
[{6*(10^4)*(3^3)}/{(6^5)*(5^6)}]
= (1/75)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{6\times10^4\times3^3}{6^5\times5^6}}[/tex]
[tex]\mathsf{= \dfrac{6\times10\times10\times10\times10\times3\times3\times3}{6\times6\times6\times6\times6\times5\times5\times5\times5\times5\times5}}[/tex]
[tex]\mathsf{= \dfrac{6\times100\times100\times9\times3}{36\times36\times6 \times25\times25\times25}}[/tex]
[tex]\mathsf{= \dfrac{6\times 10,000\times9\times3}{1,296\times6 \times 625\times5}}[/tex]
[tex]\mathsf{= \dfrac{60,000\times 27}{7,776\times 15,625}}[/tex]
[tex]\mathsf{= \dfrac{1,620,000}{12,150,000}}[/tex]
[tex]\mathsf{= \dfrac{1,620,000\div 1,620,000}{12,150,000\div1,620,0000}}[/tex]
[tex]\mathsf{= \dfrac{1}{75}}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{1}{75}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
What are the coordinates of the point on the directed line segment from (-1, -8) to (5, -2)(that partitions the segment into a ratio of 1 to 2?
The coordinates of the point on the directed line segment will be (1, -6).
What is the section of the line?Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
The coordinates of the point on the directed line segment from (-1, -8) to (5, -2). The ratio is 1: 2.
Then the coordinates of the point will be
x = (1(5) + 2(-1)) / (1 + 2)
x = (3 / 3)
x = 1
y = (1(-2) + 2(-8)) / (3)
y = - 18 / 3
y = - 6
The coordinates of the point on the directed line segment will be (1, -6).
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I need help with this question please
Answer:
The true statements are the 1st, 2nd, and 4th statement.
Students in 3 art classes cut 728 inches of ribbon into 8-inch long pieces. Two of the classes together cut 656 inches of ribbon. How many 8-inch long pieces of ribbon did the other class cut?
The number of 8-inch long pieces of ribbon that the other class cut is 9.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
Given that Students in 3 art classes cut 728 inches of ribbon into 8-inch long pieces. Therefore, the number of ribbon that 3 classes together cut is,
Number of ribbon cut by 3 classes together = 728 inches / 8 inches = 91
Further, it is given that two of the classes together cut 656 inches of ribbon. Therefore, the number of ribbon that 2 classes together cut is 656.
Number of ribbon cut by 2 classes together = 656 inches / 8 inches = 82
Now, the number of 8-inch long pieces of ribbon that the other class cut can be written as,
Number of pieces cut by other class
= Number of ribbon cut by 3 classes together - Number of ribbon cut by 2 classes
= 91 - 82
= 9
Hence, the number of 8-inch long pieces of ribbon that the other class cut is 9.
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Describe and correct the error in solving the equation below. (2 pts)
Answer: 3x=13
Step-by-step explanation:
The person is blind. They did what they were supposed to except the fact that they didn't multiply the 8 by the -1.
Answer: The error is in step 3
Explanation:
In step 2, they multiplied both sides by 8 to clear out the fractions. In step 3, they forgot to distribute the 8 to each term inside the parenthesis.
This is what the steps should look like
[tex]\frac{3\text{x}}{8}-1=\frac{5}{8}\\\\\\8\left(\frac{3\text{x}}{8}-1\right)=8\left(\frac{5}{8}\right)\\\\\\3\text{x}-8 = 5\\\\\\3\text{x} = 13\\\\\\\text{x} = \frac{13}{3}\\\\\\[/tex]
In step 4, we added 8 to both sides. Afterward, divide both sides by 3 to fully isolate x.
The improper fraction 13/3 is the same as the mixed number 4 & 1/3.
Use the graphs of F and G to evaluate the functions.
Someone please explain how you would solve this. This was all the info given with the problem.
The value of the functions are:
(a) ( f - g )( 1 ) = - 1
(b) ( f · g )( 4 ) = 0
Before performing operations on functions, we must first comprehend the various function rules and how to get the function value at a given x-value. By applying this concept, we can determine the function value.
From the graphs, we have the functions,
f(x) = 2( | x - 2 | )
g(x) = - x + 4
Now,
(a) ( f - g )( 1 )
( f - g )( 1 ) = f( 1 ) - g( 1 )
( f - g )( 1 ) = 2 ( | 1 - 2 | ) - ( - 1 + 4 )
( f - g )( 1 ) = 2 ( | - 1 | ) - ( 3)
( f - g )( 1 ) = 2 - 3
( f - g )( 1 ) = - 1
(b) ( f · g )( 4 )
( f · g )( 4 ) = f( 4 ) · g( 4 )
( f · g )( 4 ) = 2( | 4 - 2| ) · ( - 4 + 4 )
( f · g )( 4 ) = 0
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