Answer:
f^-1 (x)=1/2x+5
Step-by-step explanation:
y=2x-10
x=2y-10
2y=x+10
y=1/2x+10/2
y=1/2x+5
Byron's weekly salary is $ 650. He receives a 15% pay raise. What is Byron's new weekly salary?How much was his raise?
Answer:
$747.50
Step-by-step explanation:
650×15/100=$97.50 which is then added to 650 Becoz his pay is 15% rising=747.50
x + y = -1 when x = -1
Answer:
-2
Step-by-step explanation:
Answer:
-1+y=-1
y=0
Step-by-step explanation:
cuz you basically add 1 to both sides
Cora made a scale drawing of the middle school. The scale of the drawing was
7 inches
Could I get more context about the question? If I had more numbers then I could solve it.
How to solve -5x(-7xcubed)
-5x(-7x^3)
Because -7x^3 is in parentheses, you add the degrees together:
35x^4
What is the value of x and y I’m stuck!!!
Answer:
x = 4 and y = 8
Step-by-step explanation:
Using the tangent and cosine ratios in the right triangle and the exact values
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex], cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{4\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] x = 4[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
x = 4
-------------------------------------------------------------------
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4\sqrt{3} }{y}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] y = 8[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
y = 8
orthocenter of the triangle with vertices J(1,0) H(6,0) I(3,6)
Answer:
(3, 1)
Step-by-step explanation:
The orthocenter is the point where the altitudes meet. Since all three altitudes meet there, it is only necessary to look at two of them. A graph helps immensely.
In the attached graph, we notice that segment HJ is horizontal, so the x-coordinate of the orthocenter will be that of point I (x=3).
The segment IJ has a rise of 3 for a run of 1, so its perpendicular through point H will have a rise of 1 for a run of -3. That gets you to point (3, 1) from point H, so (3, 1) is the orthocenter.
Find the perimeter of the polygon
The perimeter of a polygon is found by adding up the lengths of all its sides. The given polygon has a perimeter of 600,000 km. A side labeled 'mfi' would be 300,000 km.
Explanation:To find the perimeter of a polygon, you add up the lengths of all its sides. In this case, the given sides of the polygon are 200,000 km, 100,000 km, and 300,000 km. So adding these together gives you a perimeter of 600,000 km for this polygon.
If you're asked to find the length of a missing side (e.g., the side labeled as 'mfi'), you can subtract the lengths of the known sides from the total perimeter. So, 600,000 km (total perimeter) - 100,000 km - 200,000 km = 300,000 km. Therefore, the length of 'mfi' is 300,000 km.
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The perimeter of the polygon shown is approximately 84.91 centimeters.
According to the given image
∠B = ∠D and AB = AD.
To find the perimeter, break the polygon into smaller shapes and find the perimeters of those shapes.
Note that triangle ABD is isosceles since AB = AD, so ∠ABD = ∠ADB. Draw imaginary segments BC and DC, which create two right triangles, ABC and ADC. Since ∠B = ∠D, it is clear that ∠ABC = ∠ADC. Additionally, it is given that BC = 8.5 cm and DC = 7.5 cm.Now, the Perimeter of triangle ABD is calculated in the following way:
AB = AD (given) = 6.5 cm
We can use the Pythagorean theorem on triangle ABD to find BD:
[tex]BD^2 = AB^2 - (\frac{1}{2} \times AD)^2\\BD^2 = 6.5^2 - (\frac{1}{2} \times 6.5)^2\\BD^2 = 25.5625\\BD \approx 5.05 cm[/tex]
So, the Perimeter of triangle ABD is
= AB + AD + BD
[tex]\approx 6.5 cm + 6.5 cm + 5.05 cm \\ \approx 18.05 cm[/tex]
Again, the Perimeter of triangle ABC is
AC = BC + AB = 8.5 cm + 6.5 cm = 15 cm
As ∠ABC is a right angle and AC is the hypotenuse, use the Pythagorean theorem to find AB:
[tex]AB^2 + BC^2 = AC^2\\AB^2 + 8.5^2 = 15^2\\AB^2 = 81\\AB = 9 cm[/tex]
Perimeter of triangle ABC
= AB + BC + AC = 9 cm + 8.5 cm + 15 cm = 32.5 cm
Perimeter of triangle ADC:
Similar to triangle ABC, find AD using the Pythagorean theorem:
[tex]AD^2 + DC^2 = AC^2\\AD^2 + 7.5^2 = 15^2\\AD^2 = 135\\AD = 3\sqrt{5} cm \approx 11.86 cm[/tex]
Perimeter of triangle ADC
= AD + DC + AC = 11.86 cm + 7.5 cm + 15 cm = 34.36 cm
Finally, to find the perimeter of the entire polygon, add the perimeters of the three triangles:
Perimeter of polygon = Perimeter of triangle ABD + Perimeter of triangle ABC + Perimeter of triangle ADC
Perimeter of polygon is
[tex]\approx 18.05 cm + 32.5 cm + 34.36 cm \approx 84.91 cm[/tex]
Therefore, the perimeter of the polygon is approximately 84.91 centimeters.
What is the numerator of the simplified sum?
x/x^2 +3x+2 + 3/x+1
Question:
What is the numerator of the simplified sum?
x/x^2 +3x+2 + 3/x+1
Answer & Step-by-step explanation:
The given equation is as follows.
\frac{x}{x^{2}+3x+2} + \frac{3}{x+1}
Taking L.C.M, the equation will become as follows.
\frac{x(x+1)+ 3(x^{2}+3x+2)}{(x^{2}+3x+2)(x+1)} ........ (1)
Factorize the equation x^{2}+3x+2 in the denominator as follows.
x^{2}+3x+2
= x^{2} + 2x + x + 2
= x(x+2) + 1(x + 2)
= (x+1)(x+2) ........ (2)
Put the factors in equation (2) in to equation (1), then the equation will become as follows.
\frac{x(x+1)+ 3(x^{2}+3x+2)}{(x^{2}+3x+2)(x+1)}
= \frac{x^{2}+x +3x^{2}+9x+6)}{(x+1)(x+2)(x+1)}
= \frac{4x^{2}+10x+6}{(x+1)^{2}(x+2)}
Now, factorize the numerator as follows.
\frac{4x^{2}+10x+6}{(x+1)^{2}(x+2)}
= \frac{4x^{2}+4x+6x+6}{(x+1)^{2}(x+2)}
= \frac{4x(x+1) + 6(x+1)}{(x+1)^{2}(x+2)}
= \frac{(4x+6)(x+1)}{(x+1)^{2}(x+2)}
Cancelling (x+1) from both numerator and denominator. Then the equation will be written as follows.
\frac{(4x+6)(x+1)}{(x+1)^{2}(x+2)}
= \frac{(4x+6)}{(x+1)(x+2)}
The numerator of simplified sum is (4x+6).
4x+6
C on Edge 2022
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The diameter of a circle is 18 kilometers. What is the length of a 120° arc?
Final answer:
The length of a 120° arc in a circle with an 18-kilometer diameter is approximately 18.85 kilometers.
Explanation:
The question asks to find the length of a 120° arc, given the diameter of a circle is 18 kilometers. To solve this, we first find the radius of the circle by dividing the diameter by 2, which gives us 9 kilometers.
Knowing the circumference formula is 2πr, we calculate the circumference as 2π(9) or 18π kilometers. Since 360° represents the full circumference, a 120° arc represents one-third of the circle.
Thus, the arc's length is one-third of the circumference: ⅓(18π) = 6π kilometers, which is approximately 18.85 kilometers.
Callie thinks of a number. She adds 6 to the number, multiplied the result by 2, and then subtracts 4. The number she ends up with is 46. what number did callie start with?
Answer:
20
Step-by-step explanation:
Add 4 to 46 = 52
Divide 52 by 2 = 26
Finally, subtract 6 to get 20
The two triangles below are similar. Triangle A B C. Side A B is 4 centimeters and B C is 9 centimeters. Angle A is 104 degrees, B is 50 degrees, C is 26 degrees. Triangle A prime B prime C prime. Side A prime B prime is 2 centimeters and B prime C prime is 4.5 centimeters. Angle A prime is 104 degrees, B prime is 50 degrees, C prime is 26 degrees. What is the ratio of the corresponding side lengths? 4:9 4:2 26:26 4.5:2
Answer:
4 : 2
Step-by-step explanation:
The two triangles Δ ABC and Δ A'B'C' are similar.
Here, ∠ A = ∠ A' = 104°, ∠ B = ∠ B' = 50° and ∠ C = ∠ C' = 26°.
Now, the length of AB and the length of A'B' are 4 cm and 2 cm respectively.
Again, the length of BC and the length of B'C' are 9 cm and 4.5 cm respectively.
Therefore, [tex]\frac{AB}{A'B'} = \frac{BC}{B'C'} = \frac{CA}{C'A'} = \frac{4}{2} = \frac{9}{4.5} = 2[/tex]
Hence, the ratio of the corresponding side lengths is 4 : 2. (Answer)
Answer:
4:2
Step-by-step explanation:
What is an equivalent fraction for 5/10
Answer:
1/2
Step-by-step explanation:
5/10, 5 is HALF of ten so 1/2
11. Circle all of the examples that are perfect square. (You must circle all correct responses to receive credit)
2
4
0
8
10
12
14
16
18
120
Good evening ,
Answer:
Circle 0 , 4 , 16
Step-by-step explanation:
→ 0 = 0²
→ 4 = 2²
→ 16 = 4²
:)
5(w-4) in distributive property
Answer:
the answer would be 5w-20 after distribution
Answer: 5w + (-20)
Step-by-step explanation: So let's simplify this problem using the distributive property. The first thing we want to do is change the minus to plus a negative.
Now we can distribute or multiply the 5 by each of the terms inside the set of parentheses.
So we get 5(w) + 5(-4) and this simplifies to 5w + (-20).
g(x) = 5 - 2.7
What is the domain of g?
Answer:
3
Step-by-step explanation:
John scored 5:7 of the goals he attempted at the soccer game. During three games, if John scored 20 goals, how many did he attempt
Answer:
John scored 20 goals he attempted 28.
Step-by-step explanation:
Given:
John scored 5:7 of the goals he attempted at the soccer game.
During three games, if John scored 20 goals.
Now, to find the number of attempts.
Let the number of attempts be [tex]x.[/tex]
The number of goals = 20.
As, given John scored 5:7 of the goals he attempted at the soccer game.
So, 5 is equivalent to 7.
Thus, 20 is equivalent to [tex]x.[/tex]
Now, to solve by using cross multiplication method:
[tex]\frac{5}{7} =\frac{20}{x}[/tex]
By cross multiplying we get:
[tex]5x=140[/tex]
Dividing both sides by 5 we get:
[tex]x=28.[/tex]
Therefore, he attempt 28.
What is the equation, in slope-intercept form, of the line that is perpendicular to the line
y – 4 = –Two-thirds(x – 6) and passes through the point (−2, −2)?
Answer:
[tex]y=\frac{3}{2}x +1[/tex]
Step-by-step explanation:
We are given;
The equation of a line;
[tex]y-4 = -\frac{2}{3}(x-6)[/tex]
We are required to determine the equation of a line perpendicular to the above line and passing through (-2, -2).
We can get the gradient of a line when given its gradient and a point where it is passing through.In this case;We need to know that the product of gradient of two parallel lines is -1
Therefore, we can get the gradient of the unknown line;m₁× m₂ = -1
Thus;
m₂ = -1 ÷ -2/3
= 3/2
Thus, the gradient is 3/2 and the line passes through (-2,-2)
Thus, to get its equation, we take another point (x,y)
We get;
[tex]\frac{y+2}{x+2}= \frac{3}{2}[/tex]
Then;
[tex]2(y+2)=3(x+2\\2y + 4 = 3x + 6[/tex]
Combining the like terms,
[tex]2y=3x+2[/tex]
In the form of slope-intercept;
[tex]y=\frac{3}{2}x +1[/tex]
Chen’s report will take 8 and one third hours to complete. He has worked for three fifths of the time doing research. How long has he worked?
Answer:
5 Hours
Step-by-step explanation:
Given:
Chen’s report will take 8 and one third hours to complete.
He has worked for three fifths of the time doing research.
Question asked:
How long has he worked = ?
Solution:
Total hour required to complete the report = [tex]8\frac{1}{3}[/tex] = [tex]\frac{25}{3}[/tex]
He has worked of the total hour = [tex]\frac{3}{5}[/tex]
He has worked = three fifth of the total time doing research.
= [tex]\frac{3}{5} \times\frac{25}{3}[/tex]
= [tex]\frac{75}{15}[/tex]
= [tex]5 hours[/tex]
Thus,he has worked 5 hours doing his research.
what is an equation that passes the points (4,-1) and (8,5) in fully reduced form
Answer:
y=3x-13
Step-by-step explanation:
1) find slope
5--1/8-4=6/2=3
2) (y--1)=3(x-4)
y+1=3x-12
y=3x-13
noah has 4 bags of marbles with the same number in each bag. if there are 536 marbles altogether,how many marbles are in each bag?explain how u know
Answer:
There are 134 marbles in each bag.
Step-by-step explanation:
536/4=134
Answer:536 divided by 4 equals 134 marbles in each bag
Step-by-step explanation:
Look at attached photo!! Please answer asap!!
Answer:
C 1
Step-by-step explanation:
BC is perpendicular to AB, so has a slope that is the negative reciprocal of that of AB:
BC slope = -1/(AB slope) = -1/-1 = 1
Dilating the triangle has no effect on the slope.
The slope of B'C' is 1.
The graph of f(x) is shown. Estimate f(–3).
f(–3) =
The value estimated for f ( -3 ) from the graph is 12.5
Step-by-step explanation:
The function (f) in the graph defines all point sets in plane as (x, f(x)) form. The graph of equation to be the graph of function. I.e. y = f (x). Hence, graph of f is if the special case for graph of equation.
Given x = - 3 and asked to find f (-3). So, we have to see the point of y mapped (meeting point of y) on the point x = -3. In the graph, the point marked on y straight away to x = - 3 is 12.5.
Answer: 12.5
Step-by-step explanation:
it is the same as the g (x) problem. we sub -3 for x and see what the y value is on graph. At -3, y = 12.5
Brainliest? :)
Complete the square x squared +18x-64=0
Answer:
x = -9±√145 (= 3.04 or -21.04)
Step-by-step explanation:
x²+18x-64 = 0 (move the constant to the right side, add 64 to both sides)
x²+18x = 64 (divide the x-term by 2, square it, then add it to both sides)
x²+18x + (18/2)²= 64 + (18/2)² (simplify)
x²+18x + 9²= 64 + 9²
x²+18x + 9²= 64 + 81
x²+18x + 9²= 145 (simplify left side using the property (a+b)² = a²+ 2ab+b²)
(x+9)² = 145 (take square root of both sides)
x+9 = ±√145
x = -9±√145 (= 3.04 or -21.04)
Fraction 45/100 what the decimal
Answer:
.45
Step-by-step explanation:
Answer:
0.45
Step-by-step explanation:
If you divide 45 by 100, the decimal point will move two times to the left because there is two 0's in 100, making it 0.45
2b + 8 - 5b + 3 = -13 + 8b - 5
Answer:
The final value of [tex]b=\frac{29}{11}[/tex] .
Step-by-step explanation:
Given:
[tex]2b + 8 - 5b + 3 = -13 + 8b - 5[/tex]
We have to find the value of [tex]b.[/tex]
[tex]2b + 8 - 5b + 3 = -13 + 8b - 5[/tex]
Steps to be followed:
Step 1:Bring all the variables one left side of the equation.Subtract 8b both side.
[tex]2b + 8 - 5b + 3-8b = -13 + 8b - 5-8b[/tex]
[tex]2b - 5b -8b+ 3 +8= -13 - 5[/tex]
Step 2:Add the variable and constants on each side.[tex]2b - 5b -8b+ 3 +8= -13 - 5[/tex]
[tex]-11b+11=-18[/tex]
Step 3:Subtract 11 on both side.[tex]-11b+11=-18[/tex]
[tex]-11b+11-11=-18-11[/tex]
[tex]-11b=-29[/tex]
Step 4:Divide -11 on both sides of the equation.[tex]-11b=-29[/tex]
[tex]b=\frac{-29}{-11} =\frac{29}{11}[/tex]
So the final value of b is 29/11.
Ed has two dogs the smaller dog weighs 1 1/3 lb the larger dog weighs 1 1/2 times as much as a smaller dog how much does the larger dog weigh
Can someone please help me
a^2 + b^2 = c^2
65^2 + 34^2 = c^2
4225 + 1156 = c^2
5381 = c^2
c ≈ 73.3552997404
Hope this helps! ;)
Line k passes through (2, -3) and (8,1). Which equation represents a line that is parallel to k? A. y = -2/3 x - 5/3 B. y = 2/3 x - 13/3 C. y = 3/2 x - 6 D. y = -3/2 x
Answer: B. y = 2/3 x - 13/3
Step-by-step explanation:
two lines are said to be parallel if they have the same slope.
To find the slope of line K we will use the formula fro calculating slope which is :
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = 2
[tex]x_{2}[/tex] = 8
[tex]y_{1}[/tex] = -3
[tex]y_{2}[/tex] = 1
substituting into the values into the formula , we have :
m = [tex]\frac{1-(-3)}{8-2}[/tex]
m = [tex]\frac{4}{6}[/tex]
m = [tex]\frac{2}{3}[/tex]
Therefore : the slope of line K = [tex]\frac{2}{3}[/tex] , this means that any line that will be parallel to K must have a gradient of [tex]\frac{2}{3}[/tex].
The only line that has a gradient of [tex]\frac{2}{3}[/tex] is the line y = 2/3x - 13/ 3 ,this means that the line is parallel to Line K
The tables below show four sets of data:
Set A
x
1
2
3
4
5
6
7
8
9
y
10
9
8
7
6
5
4
3
2
Set B
x
1
2
3
4
5
6
7
8
9
y
3
4
5
6
7
8
9
10
11
Set C
x
1
2
3
4
5
6
7
8
9
y
8
6
5
4
3.5
3
2.5
2
2
Set D
x
1
2
3
4
5
6
7
8
9
y
1
2.5
2.5
3
4
5
6
8
9
For which set of data will the scatter plot represent a positive linear association between x and y?
Set A
Set B
Set C
Set D
Answer:
B? sorry if its wrong
Step-by-step explanation:
Answer:
The answer is not set c!
Step-by-step explanation:
Write the following as an exponential expression?
Answer:
Step-by-step explanation:
recall that for a radical expression, the following apply
[tex]\sqrt[x]{y} = y^{\frac{1}{x} }[/tex]
compare this with our case, we can clearly see that
x = 4 and y = 10,
substituting into the above equation gives:
[tex]\sqrt[4]{10} = 10^{\frac{1}{4} }[/tex]
The expression [tex]$\sqrt[4]{10}[/tex] can be written as an exponent as [tex]$(10)^{\frac{1}{4} }[/tex].
What is the general equation of exponential function? What is the general equation of a quadratic equation?The general equation of a exponential relationship is -
y = Aeˣ
The general equation of a quadratic equation is -
y = ax² + bx + c
Given is the following expression -
[tex]$\sqrt[4]{10}[/tex]
We can write the given expression in the form of exponential expression as -
y = [tex]$(10)^{\frac{1}{4} }[/tex]
Therefore, the expression [tex]$\sqrt[4]{10}[/tex] can be written as an exponent as [tex]$(10)^{\frac{1}{4} }[/tex].
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