The solution for x of the given equation ax + b = 0 is x = -b/a.
What is the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
A formula known as an equation uses the same sign to denote the equality of two expressions.
As per the given equation,
ax + b = 0
Add -b both side
ax + b - b = 0 - b
ax = -b
Divide by both side
ax/a = -b/a
x = -b/a
Hence "The solution for x of the given equation ax + b = 0 is x = -b/a".
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100%− 9/10 equals what
Answer: 100%-9/10= -0.8
Step-by-step explanation:
100%-9=-8
-8/10=-0.8
Need help solving these questions!! thank you :)
Answer:
1. 25+5c
2. -8y-16
3. (m+1)^9
4. -6a-15
5. 4y+12z
6. (2a+3b)^4
7. 23c
8. 8y+7x
9. 14a+16
10. 16m+16n
A spherical balloon is inflated so that its volume is increasing at the rate of 12 cubicfeet per minute. How fast is the radius of the balloon increasing when the radius is 6feet?
Given:
The rate of change in volume = 12 cubic feet per minute.
We need to find the rate of change of radius at radius = 6 feet.
Consider the formula to find the volume of the sphere.
[tex]V=\frac{4}{3}\pi r^3[/tex]Differentiate with respect to t.
[tex]\frac{dV}{dt}=\frac{4}{3}\pi\times3r^2\times\frac{dr}{dt}[/tex][tex]\text{ Substitute }\frac{dV}{dt}=12\text{ and r=6 in the formula.}[/tex][tex]12=\frac{4}{3}\pi\times3(6)^2\times\frac{dr}{dt}[/tex][tex]12=144\pi\times\frac{dr}{dt}[/tex]Dividing both sides by 144pi, we get
[tex]\frac{12}{144\pi}=\frac{dr}{dt}[/tex][tex]\frac{dr}{dt}=\frac{1}{12\pi}[/tex][tex]\frac{dr}{dt}=\frac{1}{37.68}=0.0265\text{ feet per minute}[/tex]Hence the radius of the balloon increases by 0.03 feet per minute.
Riley and Paul go to the driving range. Together, they hit 75 balls. Riley hit 17 more than Paul. How many
balls did each of them hit?
Riley hit 46 balls and Paul hit 29 balls at the driving range.
According to the question, let
Number of balls hit by Riley be x
Number of balls hit by Paul be y
Together Riley and Paul hit 75 balls
∴x+y=75 (1)
Riley hit 17 more balls than Paul
∴x= y + 17 (2)
Now we have to solve these simultaneous linear equations (1) and (2)
Replacing the value of x from equation (2) into equation (1) we get,
y+17+y=75
⇒2y + 17 = 75
⇒2y = 75 - 17
⇒2y = 58
⇒y = 58/2 (dividing both sides by 2)
⇒y = 29
∴No. of balls hit by Riley = x = y +17 = 29 + 17 = 46 (from equation (2))
Therefore, Riley hit 46 balls and Paul hit 29 balls at the driving range.
Another problem to solve simultaneous linear equation using algebra
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#10 Eastern Mountain Sports is offering 20%
off of your entire purchase. You have an
online code that will give you an additional
10% off of the sale price(s). You decide to
buy a Kayak, a seat, and a paddle. How
much will you pay after receiving the
discount and using your online code?
EASTERN MOUNTAIN SPORTS
PELICAN Summit Kayak $299.99
BB Adjustable Paddle $191.96
YAK GEAR Kayak Seat $99.99
Answer: $426.20
Step-by-step explanation:
The subtotal is [tex]299.99+191.96+99.99=\$ 591.94[/tex].
[tex](591.94)(0.8)=\$473.552\\\\(473.552)(0.9) \approx \$426.20[/tex]
What’s the answer plss
The length of the opposite side XY = 15.2cm
How to calculate the opposite side XY?
From the right- triangle XYZ,
[tex]sin \theta =\frac{opposite}{hypotenuse}\\\\sin 61 ^\circ=\frac{XY}{XZ} \\\\XY = sin 61 ^\circ *XZ\\\\XY = 0.875* 17.4 \\\\XY = 15.2cm[/tex]
The length of the opposite side XY = 15.2cm
What is opposite side of a right-triangle?
From a particular angle, the opposite side is across. The legs of a right triangle are its adjacent and opposite sides, together, they make up the triangle. The opposing (shorter) side is the side that is shorter and perpendicular to the angle from which you are observing it.The angle from which we are looking does not include this side.An opposite side in a right triangle is the one that is across from a given angle, while an adjacent side is the one that is next to a given angle and the hypotenuse is the longest side in a right triangle.To learn more about opposite side, refer:
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3 Violet's Videos
clients. One week after launching the website, she had posted a total of 6 videos. At the end
Violet is a yoga instructor who regularly posts new exercise videos on a website for her
of week 2, she had a total of 10 videos. At the end of week 3, she had a total of 14 videos. At
the end of week 4, she had a total of 18 videos.
Find the Term Value
The completed table is:
Term Number 1 2 3 4 5 6
Term Value 6 10 14 18 22 26
What are the term values?In order to determine the term values, the rate of increase in the number of videos that Violet has at the end of each week has to be determined.
Rate of increase in the number of videos can be determined by dividing the change in the number of videos per week by the change in the number of weeks.
Rate of increase = change in the number of videos / change in the number of weeks
(10 - 6) / (2 - 1)
4 / 1 = 4 videos per week
Number of videos in week 5 = 18 + 4 = 22
Number of videos in week 6 = 22 + 4 = 26
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In ΔTUV, UV = 14, VT = 19, and TU = 9. Which statement about the angles of ΔTUV must be true?
In ΔTUV, UV = 14, VT = 19, and TU = 9, The statement about the angles of ΔTUV that must be true is [tex]m \angle U > m \angle T > \angle V[/tex] Option 5
This is further explained below.
What are angles?Generally, A triangle's angle is a measurement of the length of the side that is perpendicular to it.
This indicates that if one of the sides is longer in length, then the measure of the angle opposite to it will also be longer.
The angles in the triangle TUV are denoted by the symbols T, U, and V.
The side that is UV, TV, and T U correspondingly is the side that is opposite to these angles.
The length of the opposing sides will immediately determine the measure of the angles, which will be directly proportionate to those angles.
since V T>U V>T U, the arrangement of angles will correspond to this as follows: [tex]m \angle U > m \angle T > \angle V[/tex] Option 5
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CQ
In $\triangle T U V$, UV $=14, V T=19$, and $T U=9$. Which statement about the angles of $\triangle T U V$ must be true?
$\mathrm{m} \angle V>\mathrm{m} \angle T>\mathrm{m} \angle U$
$\mathrm{m} \angle T>\mathrm{m} \angle U>\mathrm{m} \angle V$
$\mathrm{m} \angle U>\mathrm{m} \angle V>\mathrm{m} \angle T$
$m \angle V>m \angle U>m \angle T$
$m \angle U>m \angle T>m \angle V$
$\mathrm{m} \angle T>\mathrm{m} \angle V>\mathrm{m} \angle U$
Custard is heated to a temperature of 180°F. It is then allowed to cool in a refrigerator whose temperature is 30°F. The custard cools to 120°F in 30 minutes. Determine how long will it take for the custard to cool to 50°F.
Answer: About 65 minutes.
It changes an average of about 60 degrees Fahrenheit every half hour.
180 120 60 50
0 30 60 65
Now it is about ten degrees until it's fifty. Since it takes thirty minutes to go down sixty degrees, divide sixty by ten to get six. Then divide thirty by six to get five. So, it should take about 65 minutes to cool down to 50 degrees.
It will take approximately 35 minutes for the custard to cool from 120°F to 50°F.
To determine how long it will take for the custard to cool to 50°F, we need to consider the rate at which it cools. From the given information, we know that the custard cools from 180°F to 120°F in 30 minutes.
To find the rate of cooling, we can calculate the temperature change per minute.
The temperature decreases by 180°F - 120°F = 60°F over 30 minutes. So, the rate of cooling is 60°F / 30 minutes = 2°F per minute. Now, let's use this rate to calculate how long it will take for the custard to cool from 120°F to 50°F.
The temperature difference between 120°F and 50°F is 120°F - 50°F = 70°F. To cool from 120°F to 50°F at a rate of 2°F per minute, it will take 70°F / 2°F per minute = 35 minutes.
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Rotate the shape as described.
The ordered pair for A' is
. The ordered pair for B' is
. The ordered pair for C' is
. The ordered paid for D' is
By applying a rotation of 90° clockwise to square ABCD, we have the following:
The ordered pair for A' is (5, -3).The ordered pair for B' is (-2, 7).The ordered pair for C' is (8, 8).The ordered pair for D' is (10, 4).What is a rotation?A rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise direction.
In Mathematics, rotating a point 90° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (y, -x).
By applying a rotation of 90° clockwise to square ABCD, the coordinate of the image of square A'B'C'D' is given by:
(x, y) → (y, -x)
Points at A = (-3, 5) → Points at A' = (5, -(3)) = (5, -3)
Points at B = (-7, -2) → Points at B' = ((-2), -(-7)) = (-2, 7).
Points at C = (-8, 8) → Points at C' = (8, -(-8)) = (8, 8).
Points at D = (-4, 10) → Points at D' = (10, -(-4)) = (10, 4).
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A driver travels 55km in 1 hour. He then drives at a speed of 35 km/h for 2 hours. Next, he drive 175km in 3 hours. What was his average speed
Answer:
108.333 km/hour
Step-by-step explanation:
See attached worksheet.
Evaluate : (12.5)³
find the answer
Answer:
1953.125
Step-by-step explanation:
(12.5)³
= 12.5 × 12.5 × 12.5
= 1953.125
Answer: 1953.125
(12.5)³
so 12.5 multiplied to itself thrice
12.5x12.5x12.5
which is 1953.125
how long does it take ella to run 7.5 kilometers
What is the probability of
spinning a yellow?
[?]%
Answer:
12.5
Step-by-step explanation:
there are eight triangles and one yellow so 1/8=12.5%
Answer: 12.5%
Step-by-step explanation:
There are 8 sections and 1 of them is yellow so 1 divided by 8 is 0.125 or 12.5%
Kara currently makes $12 per hour. If she receives a
50% raise, what is her new rate?
What would a 75% raise be equal to????
K
TO
160
Sign out
simplify:-
(-4)3
this is the chapter of exponents and power
PLEASE HELP DUE IN 4 MINUTES, THANK YOU!!
Answer:
A 100% increase in a total means the final amount is 200% of the initial amount.
A 100% decrease in a total means the final amount is 0% of the initial amount.
Error means that you were a way off from the real value
Step-by-step explanation:
The steps at the right show cam's works in solving an equation. Circle the line where he makes a mistake. Then, find the correct solution to the equation.
The correct solution to the equation is -13.
-12x + 12 = -3(5x + 8)
Split the right-hand side,
-12x + 12 = -15x + 24 (This line have error, instead of + there will be - )
Shifted the values of x to the left-hand side and the constant values to the right-hand side,
3x + 12 = 24
3x = 12
x= 4, which is the incorrect value of x.
The correct solution to the equation,
-12x + 12 = -3(5x + 8)
Split the right-hand side,
-12x + 12 = -15x - 24
Shift the values of x to the left-hand side and the constant values to the right-hand side,
3x = -36
The final value of x,
x = -13
Therefore, the value of x is -13.
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i have been working to become a major in math and i need some help with what this second word might be for this problem from last weeks exam
Find the Properties to graph this Rational Expression. DO NOT GRAPH. If an answer is "none" type in "none" for the answer blank. Make sure to type in your Asymptotes correctly(x=y=)F(x)=-4x+8/x^2-x-2Need to answer:Hole:(___,___)Vertical asymptote:______X-intercept:(___,___)Y-intercept:(___,___)Horizontal asymptote:____
Given data:
The given expression is f(x)= (-4x+8)/(x^2 -x-2).
The hole of the graph is x=2.
The expression for the vertical asymptode is,
[tex]x=-1[/tex]The expression for the horizontal asymptode is,
[tex]y=0[/tex]There is no x-intercept, and y-intercept is,
[tex](0,\text{ -4)}[/tex]Thus, the
Assume that each circle shown below represents one unit. Express the shaded
amount as a single fraction and as a mixed number.
Shaded portion in single fraction is [tex]\frac{37}{10}[/tex] and mixed number is 3[tex]\frac{7}{10}[/tex] .
What is difference between fraction and mixed number?
Single fraction is represented as [tex]\frac{p}{q}[/tex] form where p is numerator and q is denominator and value of q can't be zero. Example [tex]\frac{5}{9}[/tex] .
Mixed number contains two part one is an integer and other is fractional part. It is represented as N [tex]\frac{p}{q}[/tex]. Example 5[tex]\frac{1}{2}[/tex] .
According to figure, one shaded circle is equal to one unit and one shaded circle contain 10 sector.
There are three shaded circle and a circle with 7 sector shaded.
So, Total shaded area in single fraction = 1 + 1 + 1+ [tex]\frac{7}{10}[/tex] = [tex]\frac{37}{10}[/tex]
and total shaded area in mixed number = 1 + 1 + 1 + [tex]\frac{7}{10}[/tex] = 3 + [tex]\frac{7}{10}[/tex] = 3[tex]\frac{7}{10}[/tex] .
Hence, shaded portion in single fraction is [tex]\frac{37}{10}[/tex] and mixed number is 3[tex]\frac{7}{10}[/tex] .
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48,384 - 2,904 divided by 48,384 multiplied by 100
The cost of manufacturing a cake is directly proportional to the volume of the cake.
The baker makes a 70% profit when he sells a large rectangular cake.
The baker sells a large rectangular cake for £6.80 The baker decides to sell smaller rectangular cakes.
The length, width, and height of the smaller cakes are all half of those of the large rectangular cake.
He sells a pack of 6 of the smaller cakes for £6.50
How much profit does he make on the pack of smaller cakes?
Answer:
The baker makes £3.50 profit on smaller cakes================================
GivenLarge cake:
Price = £6.80,Profit = 70%Small cake:
Number = 6,Price = £6.50,Dimensions = each side is 1/2 of the large cakeSolutionThe profit is the difference of the cost and selling price.
Find the cost x of large cake:
x + 70% = 6.801.7x = 6.80x = 4Find the volume of the pack of smaller cakes, taking the volume of the large cake as a unit:
6*(1/2)³ = 6*1/8 = 3/4Cost of the pack of smaller cakes is proportional to the volume:
4*3/4 = 3Profit made on smaller cakes:
6.50 - 3 = 3.50Find the value of angle A in the triangle below:
angle A =
A
B
95°
55
PLEASE HURRY
a function is said to have a horizontal asymptote if either the limit at infinity exists or the limit at negative infinity exists. show that each of the following functions has a horizontal asymptote by calculating the given limit.
A function can only have two horizontal asymptotes, hence the answer is no. By examining the degrees of the numerator and denominator, one can find the horizontal asymptote of a rational function.
If limxf(x)=L or limxf(x)=L, a function f(x) will have the horizontal asymptote y=L. Therefore, we simply calculate the function's limit as it approaches infinity and again as it approaches negative infinity to locate horizontal asymptotes. Based on the degree of the numerator, n, and the degree of the denominator, m, horizontal asymptotes adhere to three principles. The horizontal asymptote is y = 0 if n m. The horizontal asymptote is y = a/b if n = m. There is no horizontal asymptote if n > m. As x gets closer to 0, we say that f(xlimit )'s is infinite. A boundary or a limit is now a number.
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How can you justify that the function is
exponential?
Answer:
Since the y axis is increasing at an exponential rate. You can see that it goes from 0.06 to 0.125 to 0.25. If you were to graph that it would be a exponential curve. You can see that it jumps alot.
0.0625 to 0.0625*2 to 0.0625*2*2 to 0.0625*2*2*2
Please simplify this equation and find what y is
Answer: y=7
Step-by-step explanation:
We need to combine like factors in this term by adding up all the exponents and copying the base.
No exponent implies the value of 1.
If this helped you please consider marking my answer as the brainliest! How? Once you get more than 1 answer of a question. A message is shown above each answer that is "Mark as brainiest". Thank you!
Answer:
y =7
Step-by-step explanation:
Find the future value, using the future formula and a calculator. (Round your answer to the nearest cent.)$901 at 3.5% compounded semiannually for 6 years
To calculate the future value we need to use the compound formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where P is the principal, r is the interest rate in decimal form, n is the number of times the interest is compound in any given time t.
In this case we have that P=901, r=0.035 and since the interest is compound semiannually this means that n=2. Finally t=6. Plugging this values into the equation above we have that:
[tex]\begin{gathered} A=901(1+\frac{0.035}{2})^{2\cdot6} \\ A=1109.53 \end{gathered}[/tex]Therefore the future value would be $1109.53
8+2x3²
= 8+6²
= 8+36
= 44
What are his mistakes?
Solve the equation.
-3x + 1 + 10x = x + 4
HN
0 x = -1/
5/6
0 x = 2/1/2
O x = 12
O x = 18
Value of x for equation -3x + 1 + 10x = x + 4 is 1÷2.
Given equation,
-3x + 1 + 10x = x + 4
Shifting the variables to the left-hand side and constant to the right-hand side,
-3x - x + 10x = 4 - 1
Simplifying the equation,
10x - 4x = 3
6x = 3
x = 1÷2
When x from the right side shifts to the left side, its sign changes, and similarly, when 1 from the left side shifts to the right side, its sign changes.
x = 0.5
Therefore, value of x = 1÷2 that is 0.5
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