The value of x is [tex]\frac{3a}{4b}[/tex] and [tex]-\frac{2b}{3a}[/tex]
Explanation:
The expression is [tex]12abx^{2} -(9a^{2} -8b^{2} )x-6ab=0[/tex]
Multiplying the term x withing the bracket, we get,
[tex]12abx^{2} -9a^{2} x+8b^{2} x-6ab=0[/tex]
Grouping the terms, we have,
[tex](12abx^{2} -9a^{2} x)+(8b^{2} x-6ab)=0[/tex]
Taking out the common terms in each bracket, we get,
[tex]3ax(4bx -3a)+2b(4bx-3a)=0[/tex]
Simplifying, we get,
[tex](3ax+2b)(4bx -3a)=0[/tex]
Equating each term to zero, we get,
[tex]\begin{aligned}3 a x+2 b &=0 \\3 a x &=-2 b \\x &=-\frac{2 b}{3 a}\end{aligned}[/tex] and [tex]\begin{aligned}4 b x-3 a &=0 \\4 b x &=3 a \\x &=\frac{3 a}{4 b}\end{aligned}[/tex]
Hence, the values of x is [tex]\frac{3a}{4b}[/tex] and [tex]-\frac{2b}{3a}[/tex]
(c) Mez bought 9 tubes of paint. She
received $16 change from $70.
How much did each tube of
paint cost?
Answer:
$6
Step-by-step explanation:
9 tubes of paint costs
$70 - $16 = $54
1 tube of paint cost
$54 : 9 = $6
Explain the steps you take to graph an inequality.
Arrange the following fractions in order from smallest to largest.
3/4, 1/8, 9/16, 1, 1/4, 3/8
Answer:
1/8, 1/4, 3/8, 9/16, 3/4, 1
Step-by-step explanation:
The fractions have been arranged in order from smallest to largest as 1/8< 1/4< 3/8< 9/16< 3/4< 1.
How to compare fractions with different denominators?Fractions with different denominators can be compared by making the denominators the same. For example, take 1/4 and 1/2. The LCM of these fractions is 4. Now we can alter the fractions so that they have the same denominators as follows:
1/4 and 2/4
We can see that 2/4 is greater than 1/4.
We can arrange the given fractions in order from smallest to largest as shown below:The given fractions are: 3/4, 1/8, 9/16, 1, 1/4, 3/8
The lowest common multiple of these fractions is 16.
We can convert the fractions as shown below:
12/16< 2/16< 9/16< 16/16< 4/16< 6/16
Now we can arrange them in ascending order easily as shown below:
2/16, 4/16, 6/16, 9/16, 12/16, 16/16
or 1/8< 1/4< 3/8< 9/16< 3/4< 1
Therefore, we have arranged the fractions in order from smallest to largest as 1/8< 1/4< 3/8< 9/16< 3/4< 1.
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A store owner bought hats for 6.50 each and sold them for 12.00 the overhead was 2.50. What was the profit on each hat?
(a,1/b) and (b,1/a) find the slope of the line joining the points whose coordinates are
Answer:
[tex]m=\frac{1}{ab}[/tex]
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have the points
(a,1/b) and (b,1/a)
substitute
[tex]m=\frac{1/a-1/b}{b-a}[/tex]
[tex]m=\frac{\frac{b-a}{ab}}{b-a}[/tex]
[tex]m=\frac{1}{ab}[/tex]
The slope of the line joining the points (a,1/b) and (b,1/a) is calculated using the slope formula and is found to be 1 divided by the product of a and b, assuming a and b are not equal and neither is zero.
Explanation:To find the slope of the line joining the points with coordinates (a,1/b) and (b,1/a), we use the slope formula, which is the change in y divided by the change in x. We can write the formula as:
slope (m) = (y2 - y1) / (x2 - x1)
Substituting the given points into the formula gives us:
slope (m) = (1/a - 1/b) / (b - a)
If we assume that a does not equal b and neither a nor b is zero, the slope can be calculated by simplifying the numerator and the denominator:
slope (m) = ((b - a) / (ab)) / (b - a)
The (b - a) terms cancel out, leaving us with:
slope (m) = 1 / (ab)
Therefore, the slope of the line is the reciprocal of the product of a and b.
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A Greenland whale can hold its break three times as long as a beaver, and a hippopotamus can hold its breath for five minutes long than a beaver. If you added the time the Greenland whale,beaver and hippopotamus can hold their breath you would get 95 minutes. How long can a beaver hold its break
Answer:
18 minutes
Step-by-step explanation:
the beaver is 18 minutes so multiply that by 3 which equals 54 then add those two together then you get 72 then add 23 qhich then you end up with 95 minutes total.
To solve the problem, we create an equation representing the total time all three animals can hold their breath. Solving it reveals that a beaver can hold its breath for 18 minutes.
Explanation:Let's denote the time a beaver can hold its breath as 'x' minutes. According to the problem, a Greenland whale can hold its breath three times as long as a beaver, so that's '3x' minutes. A hippopotamus can hold its breath for five minutes more than a beaver, making it 'x+5' minutes.
The combined time for all three animals is given as 95 minutes, so we can set up the following equation:
x (beaver) + 3x (Greenland whale) + x + 5 (hippopotamus) = 95
Simplified, it becomes:
5x + 5 = 95
Next, you subtract 5 from both sides:
5x = 90
Finally, divide by 5:
x = 18
So, a beaver can hold its breath for 18 minutes.
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For questions 6-8, evaluate the
expression and give the exact value, if
possible. Otherwise, approximate to the
nearest tenth.
64
31
16
(6) The value of [tex]\sqrt{64}[/tex] is 8.
(7) The value of [tex]-\sqrt{31}[/tex] is -5.6
(8) The value of [tex]-\sqrt{16}[/tex] is -4
Explanation:
(6) The expression is [tex]\sqrt{64}[/tex]
Since, 64 is a perfect square, this can be written as [tex]8 \times 8[/tex].
Thus, the expression can be written as
[tex]\sqrt{64}=\sqrt{8 \times 8}=\sqrt{8^{2} }[/tex]
The square root gets cancelled. Thus, we have,
[tex]\sqrt{64}=8[/tex]
Thus, the value of [tex]\sqrt{64}[/tex] is 8.
(7) The expression is [tex]-\sqrt{31}[/tex]
Since, 31 is not a perfect square and solving the expression using a calculator, we get,
[tex]-\sqrt{31}=-5.56776[/tex]
Rounding off to the nearest tenth, we get,
[tex]-\sqrt{31}=-5.6[/tex]
Thus, the value of [tex]-\sqrt{31}[/tex] is -5.6
(8) The expression is [tex]-\sqrt{16}[/tex]
Since, 16 is a perfect square, this can be written as [tex]4\times 4[/tex]
Thus, the expression can be written as
[tex]-\sqrt{16}=-\sqrt{4\times 4}=-\sqrt{4^{2} }[/tex]
The square root gets cancelled. Thus, we have,
[tex]-\sqrt{16}=-4[/tex]
Thus, the value of [tex]-\sqrt{16}[/tex] is -4.
dentify the Pythagorean triple. A) 3, 6, 12 B) 8, 16, 32 C) 12, 34, 30 D) 28, 45, 53
Answer:
Therefore (28,45,53) is a Pythagorean triple.
Step-by-step explanation:
A Pythagorean triple consists of three positive integers a,b and c such that
a²+b²=c²
1.
3²+6²=45 and 12²=144
∴3²+6²≠144
Therefore (3,6,12) is not a Pythagorean triple.
2.
8²+16²= 330 and 32²= 1024
∴8²+16²≠32²
Therefore (8,16,32) is not a Pythagorean triple.
3.
12²+34²=1024 and 34²=5611
∴12²+34²≠34²
Therefore (12,34,30) is not a Pythagorean triple.
4.
28²+45²=2809 and 53²=2809
∴28²+45²=53²
Therefore (28,45,53) is a Pythagorean triple.
What is the product? 3 x [1 -4 5 -7]
Answer:
A
Step-by-step explanation:
3,-12,15,-21
The product 3 x [1 -4 5 -7] of [ -3 12 -15 21 ]
In mathematics, when we multiply a scalar (a single number) by a vector, the result is a new vector where each element of the original vector is multiplied by that scalar.
In this case, we have the scalar 3 and the vector [1 -4 5 -7].
1. Multiply each element of the vector by the scalar 3:
3 x 1 = 3
3 x (-4) = -12
3 x 5 = 15
3 x (-7) = -21
2. Arrange the results in order:
-3 12 -15 21
So, the product of 3 and the vector [1 -4 5 -7] is the new vector [-3 12 -15 21].
In this process, we essentially scaled each component of the original vector by a factor of 3, either increasing or decreasing the magnitude based on the sign of the original component.
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What is the product? 6 [ 4 -2 1 7 3 0]
Answer:
-130356
Step-by-step explanation:
solve for bracket first
4-21730 = -21726 then multiply by 6 =
-130356
Answer:
C
Step-by-step explanation:
EDGE 2020
24 -12 6
42 18 0
Please help now !! I’ll give u brainliest ..
Answer:
x = 0 AND x = -1
Step-by-step explanation:
You find the solution by finding where the two graphs meet. Then you can pull the x-coordinate off the points of intersection which is at 0 and -1
If B=80°, a=4.1, c=7.1, find the area of the triangle.
Answer:
14.2 squared units
Step-by-step explanation:
Always draw a diagram for the question. Capital letters are usually angles, and their opposite side is the same letter as a lowercase. (See diagram) The opposite side of angle B is side b.
The formula for area of a triangle is A = bh/2
"A" is for area.
"b" is for base (usually bottom side)
"h" is for height (perpendicular to base).
We know the measurement for the base c = 7.1. We need to find the height.
Notice when you draw in the height, it form two right triangles. We can use trigonometric ratios for right triangles.
Remember the trigonometric ratios using SohCahToa:
sinθ = opposite/hypotenuse;
cosθ = adjacent/hypotenuse and;
tanθ = opposite/adjacent, where θ means the angle of reference.
Focus on the triangle on the left side. We know one angle (∠B = 80°) and one side (a = 4.1). We can find "h", the missing side.
Since ∠B is our angle of reference, "h" is opposite. Since "a" is a longest side, it's the hypotenuse. Use the sine ratio because it uses the opposite and hypotenuse sides.
sinθ = opp/hyp General sine ratio formula
sinB = h/a Variables you use in this problem
sin80° = h/4.1 Isolate "h". Multiply both sides by 4.1
h = 4.1(sin80°) Multiply with calculator
h = 4.1(0.98480775...) Unrounded sin80
h = 4.03771178... Round this number
Note the number of decimal places given in the question.
h ≈ 4.0 Round to one decimal place
Now we can use the formula for the area of a triangle.
A = bh/2 Don't confuse side "b" with the base in this question
A = (7.1)(4.0)/2 Simplify the division
A = (7.1)(2.0) Multiply
A = 14.2 Final answer for area
Since we don't know what the units are, you can say the answer is:
A = 14.2u² or 14.2 squared units
Hours Spent at Water Park A 2-column table with 4 rows titled Hours Spent at Water Park. Column 1 is labeled Hours with entries 4, 5, 6, 7. Column 2 is labeled Tally with entries 4, 5, 3, 4. Write a statistical question that might have been asked to gather the data. Then explain why it is statistical.
Answer:
The question is: How much time do people spend in the water park?It is a statistical because the answer comes from a sample instead of from the entire population.
Explanation:
Rewrite the table
Hours Spent at Water Park
Hours Tally
4 4
5 5
6 3
7 4
These data could be the results of a survey whose target was to detemine how many hours people spent at a water park.
The size of the sample should be the number of tally, which is 4 + 5 + 3 + 4 = 16.
And the question most likely was made at the exit of a water park, when the people were leaving the park.
Thus, the statistical question could be How much time do people spend in the water park?
It is a statistical because the survey is made to a sample of the people who went to the water park instead to all the people. All the people who go to the water park is the population about whom you want to determine how much time they spend in the water park, but,since it is impossible to survey all the people, you need to survey a sample.
The resulting values from a sample are named statistical. The values for an entire population are named parameters. A statistical permits to draw conclusions for populations using just one or more samples, which should be random samples.
Answer:
sample responce
Step-by-step explanation:
“How many hours did you spend at the water park today?” It is statistical because the responses will vary among individuals and the responses will be numeric.
the sum of a number z divided by three and the number
Answer:
z ÷ 3 + z
Step-by-step explanation:
The cost of a jacket increased from $65.00 to $72.15. What is the percentage increase of the cost of the jacket?
Answer:
11%
Step-by-step explanation:
$72.15 - $65.00=$7.15 /$65.00=.11 or 11%
simplify the following expression(-5)(-3)(4)
Answer:
[tex]\displaystyle 60[/tex]
Step-by-step explanation:
All you do is multiply the terms straight across to get the above answer.
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(10,0)
V(0-8)2+(0-y)2 = 10
V(+8) +(-2)2 = 10
64+y? = 100
Which is the coordinate of point A?
(6,8)
Find the area of the shape shown below.
Answer: 10
Step-by-step explanation:
2 * 4 = 8
8/2 = 4
2 * 2 = 4
4/2 = 2
4 + 2 = 6
2 * 2 = 4
4 + 6 = 10
What dose 8 1/5 - 3 5/9 =
Answer:1 8/45
Step-by-step explanation:73-20/45
53/45
1 8/45
Answer:
4 29/45
Step-by-step explanation:
Kelly has a rock garden with a length of 6 feet. She constructs a scale model of the rock garden using the scale 1 inch:2 feet.
Questions:
(a) What is the length of the garden in her model? Show your work, including your proportion.
(b) If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?
Answer:
Part a) 3 inches
Part b) Yes, her scale model drawing will fit on the piece of paper 8.5 by 7 inches
Step-by-step explanation:
we know that
The scale drawing is
[tex]1\ inch:2\ feet[/tex]
That means
1 inch in the model represent 2 feet in the actual
Part a) What is the length of the garden in her model?
we know that
The length of the garden is 6 feet in the actual
so
Find out the length of the garden in her model, using proportion
[tex]\frac{1}{2}\ \frac{in}{ft}=\frac{x}{6}\ \frac{in}{ft}\\\\x=6/2\\\\x=3\ in[/tex]
Part b) If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?
we know that
The model width is described as 5 inches. Both the 3-inch length and the 5-inch width are less than the 8.5 inch and 7 inch dimensions of the paper Kelly is using.
therefore
She can easily draw her model on that size paper.
the area of a rectangular painting is 5346cm square. if the width of the painting is 66 centimeters what is its lenght
The area of a rectangle is length*width
Since we have the width, we can do 5346/66 to get the length
So the length is 81 cm
Hope this helped
Answer:
81 cm
Step-by-step explanation:
Area = Length × Width
5346cm² = length × 66cm
Length = 5346 ÷ 66
Length = 81cm
Choose a linear function for the line represented by the point-slope equation y-5= 3(x - 2).
f(x) = 3x + 1
f(x) = 3x - 1
f(x) = 8x + 10
f(x) = 8x – 10
f(x) = 3x - 1 is the linear function for the line represented by the point-slope equation
Solution:
Given point slope equation is:
[tex]y - 5 = 3(x-2)[/tex]
We have to find the linear function for the line
The formula y = mx + b is said to be a linear function
Rearrange the given equation
[tex]y - 5 = 3(x-2)\\\\y - 5 = 3x - 6\\\\Move\ the\ varibale\ y\ to\ one\ side\ and\ constants\ and\ x\ to\ other\ side\\\\y = 3x - 6 + 5\\\\y = 3x - 1[/tex]
Let y = f(x)
Then we get,
f(x) = 3x - 1
Thus the linear function is found
Answer:
the answer will be B. f(x)=3x-1
Tina ordered a replacement part for her desk. It was shipped in a box that measures 4inches By 4inches by 14 inches. What is the greatest length in whole inches that the part could have been
(Answer you get 15 points)
Answer:
15 inches
Step-by-step explanation:
The space diagonal of a rectangular prism is the root of the sum of the squares of the edge lengths. The longest straight part that will fit in the box will be at most ...
l = √(4² +4² +14²) = √228 ≈ 15.10 . . . . inches
The greatest length the part could have been is 15 inches.
Can you find the equation in standard form when given 3 or more orders pairs on a parabola
Answer:
Yes, you can
Step-by-step explanation:
The standard form of the equation of a parabola is [tex]y=ax^2+bx+c[/tex]
When given three points, you substitute each point into the equation to obtain 3 simultaneous linear equations.
You then solve the three equations simultaneously to find the values of the constants a,b, and c.
You then substitute these constants into [tex]y=ax^2+bx+c[/tex]
What is the angle of AFB
456cm^2
Step-by-step explanation:
AFB is 152 and times 3 it is 456cm^2
Find the area of the square as a single expression.
A) 6x + 4
B) 2x2 + 4x
Eliminate
C) 2x + x + 2
D) x2 + 2x + 2
Yo sup??
Area of the figure=A
A=l*b
=2x(x+2)
=2x^2+4x
Therefore the correct answer is option B
Hope this helps
solve for -6(w+1) < 2(w+5)
Answer:
Step-by-step explanation:
hello :
-6(w+1) < 2(w+5)
-6w-6< 2w+10
-6w-2w< 6+10
-8w < 16
8w > -16
w > -2
What is the answer to 2/3 (12x-9)
Answer:
8x-6
Step-by-step explanation:
Justin has $7.50 more than Eva ,and Emma has 12$ less than Justin. Together, they have a total of $63.00 How much money does each person have?
Eva has $20.00, Justin has $27.50 and Emma has $15.50
Step-by-step explanation:
The given is:
Justin has $7.50 more than EvaEmma has 12$ less than JustinTogether, they have a total of $63.00We need to find how much money each person has
Assume that Eva has $x
∵ Eva has $x
∵ Justin has $7.50 more than Eva
- Add 7.50 to x
∴ Justin has = x + 7.50
∵ Emma has $12 less than Justin
- Subtract 12 from (x + 7.50)
∴ Emma has = x + 7.50 - 12 = x - 4.50
∵ Together, they have a total of $63.00
- Add x , (x + 7.50) and (x -4.50), then equate the sum by 63.00
∴ x + (x + 7.50) + (x - 4.5) = 63.00
- Add like terms
∴ (x + x + x) + (7.5 - 4.5) = 63.00
∴ 3x + 3 = 63.00
- Subtract 3 from both sides
∴ 3x = 60.00
- Divide both sides by 3
∴ x = 20.00
Substitute x by 20.00 in each expression above
∴ Eva has = $20.00
∴ Justin has = 20.00 + 7.50 = $27.50
∴ Emma has = 20.00 - 4.50 = $15.50
Eva has $20.00, Justin has $27.50 and Emma has $15.50
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What is 6b plus 7b subtract 19
Answer:
13b - 19
Step-by-step explanation:
Because 6b and 7b are like terms so we add them. And 19 is not a like term so we connot add them.