Answer:
[tex]y=\frac{2}{3}x +\frac{4}{3}[/tex]
Step-by-step explanation:
[tex]-2x+3y=-6\\3y=2x-6\\y=\frac{2}{3}x-2\\ \\\\Then\\y-0=\frac{2}{3}(x-(-2)\\ y-0=\frac{2}{3}x+\frac{4}{3} \\Therefore, the answer is y=\frac{2}{3}x+\frac{4}{3}[/tex]
If [tex]f(x) = -4x^{5} and g(x) = 10x^9 - 12x^4 + 6[/tex] (what is f x g) x?
A.) [tex]-40x^{14} + 48a^{3} x^{9} +6[/tex]
B.) [tex]40x^{14} - 12x^{4} + 6[/tex]
C.) [tex]-40x^{14} + 48x^{9} - 24x^{5}[/tex]
D.) [tex]-40x^{9} + 48x^{4} - 24[/tex]
Answer:
C
Step-by-step explanation:
(f×g)x just means
f(x) × g(x)
Multiply the two given functions together. Use distributive property. To multiply terms with the same base, add the exponents.
see image.
Montraie drove 220 miles in 5 hours. If he continued at the same rate, how long would it take to travel 88 miles?
The time taken for Montraie to travel a distance of 88 miles is 2 hours.
How long would it take for Montraie to travel 88 miles?Speed is simply referred to as distance traveled per unit time.
It expressed mathematically as;
Speed = Distance ÷ time.
Given the data in the question;
Distance covered = 220 milesTime elapsed = 5 hoursSpeed = ?First, we determine the speed of Montraie.
Speed = Distance ÷ time.
Speed = 220 miles ÷ 5 hours
Speed = 44 miles per hour.
Now, time spent in traveling a distance of 88 miles will be;
Speed = Distance ÷ time
Time = Distance / Speed
Time = 88 miles / 44 miles per hour
Time = 2 hours
Therefore, the elapsed time is 2 hours.
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If Montraie drove 220 miles in 5 hours. If he continued at the same rate, then it takes 2 hours to travel 88 miles.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that,
Montraie drove 220 miles in 5 hours.
We need to find how long it would take to reach 88 miles.
Let us form a equation based on given data.
Let x be the time to reach 88 miles.
We need to find value of x.
220/5=88/x
Apply cross multiplication
220x=440
x=440/220
x=2
Hence it takes 2 hours to travel 88 miles with same rate.
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a spherical snowball is melting in such a way that its volume is decreasing at a rate numerically equal to twice the surface area. how quickly is the radius of the snowball decreasing?
The radius of the snowball decreasing by -2.
What is rate?
A rate is the ratio of two related values expressed in various units. [1] If one of these numbers is used as the ratio's denominator and it is assumed that this quantity can be altered in a predictable way (i.e., is an independent variable), then the numerator of the ratio represents the rate of change in the other (dependent) variable.
Let r(t) be a function of the radius of the sphere over time.
The volume of the sphere over time is then [tex]v(t) = \frac{4}{3} \pi r(t)^3[/tex]
The rate of change of the volume is then [tex]v'(t) = 4\pi r(t)^2r'(t)[/tex]
Comparing is to the surface area of the sphere [tex]s(t) = 4\pi r(t)^2[/tex], it seems perfectly possible for the volume to decrease at a rate equal to 2s(t).
That just means that
[tex]v'(t) = -2s(t)\\4\pi r(t)^2r'(t) = -8\pi r(t)^2\\r'(t) = -2[/tex]
Therefore, the radius must shrink by two units of distance every unit of time, it is now obvious.
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Which of the following service providers may use credit reports and/or credit scores to decide whether a person can buy a service and/or what price he or she will pay?Group of answer choicesLandlordMortgage lenderCell phone companyAll of the aboveCredit card issuer
Answer:
All of the above
Explanation:
All the given options make use of credit scores and/or credit reports to decide whether a person can buy a service and/or to decide what price he or she will pay. landlords may use credit scores to decide if they will require a security deposit and, if so, how much it should be. Also, other service providers like Mortgage lender, Cell phone company and Credit card issuer makes use of credit scores and/or credit reports in making certain decisions.
Find the area of the trapezoid shown above. [?] square inches The measurements are 36in the base. 20in the height. 30 in the top.
The dimensions given are as follows;
Base a = 36
Base b = 30
Height = 20
The area is derived as follows;
[tex]\begin{gathered} A=(\frac{a+b}{2})\times h \\ A=(\frac{36+30}{2})\times20 \\ A=(\frac{66}{2})\times20 \\ A=33\times20 \\ A=660in^2 \end{gathered}[/tex]The area therefore is 660 square inches
Solve the trig equation on the interval [tex]0 \leqslant theta \: \ \textless \ 2\pi[/tex][tex]3 sec \: \: theta \: - 2 \sqrt{3 } = 0[/tex]
Answer:
pi/6 and 11pi/6
Explanation
Given the trigonometry equation:
[tex]\begin{gathered} 3\text{sec}\theta\text{ - 2}\sqrt[]{3}=0 \\ \end{gathered}[/tex]Add 2\sqrt[3] to both sides as shown;
[tex]\begin{gathered} 3\sec \theta-2\sqrt[]{3}=0+2\sqrt[]{3} \\ 3\sec \theta\text{ = 2}\sqrt[]{3} \\ \sec \text{ }\theta\text{ = }\frac{2\sqrt[]{3}}{3} \\ \frac{1}{\cos \theta}=\frac{2\sqrt[]{3}}{3} \\ \cos \theta\text{ =}\frac{3}{2\sqrt[]{3}} \\ \cos \text{ }\theta\text{ = }\frac{3\sqrt[]{3}}{2\cdot3} \\ \cos \text{ }\theta\text{ = }\frac{\sqrt[]{3}}{2} \\ \end{gathered}[/tex]Take the cos inverse of both sides
[tex]\begin{gathered} \cos ^{-1}(\cos \theta)=cos^{-1}\frac{\sqrt[]{3}}{2} \\ \theta=cos^{-1}\frac{\sqrt[]{3}}{2} \\ \theta=30^0 \end{gathered}[/tex]Since theta is between 0 and 2pi
theta = 360 - 30
theta = 330^0
Convert to radians
180^0 = pi rad
30^0 = x
180x = 30pi
x = 30pi/180
x = pi/6
Similarly;
180^0 = pi rad
330^0 = x
180x = 330pi
x = 330pi/180
x = 11pi/6
Hence the value of thets between 0 and 2pi are pi/6 and 11pi/6
Before a piece of steel can be sold for its maximum price, it must be 35 feet long with an absolute error of 1 foot. Find the range of acceptable heights for steels that are to be sold at full price by writing an absolute value inequality to represent this situation then solving it.
Let's call x to the height. The inequality that represents an acceptable range is:
|x - 35| ≤ 1
Solving it, we get:
x - 35 ≤ 1 or x - 35 ≥ -1
x ≤ 1 + 35 x ≥ -1 + 35
x ≤ 36 x ≥ 34
which is equivalent to 34 ft ≤ x ≤ 36 ft
is there a right triangle in which two side lengths are simple fractions (ratios of integers such as 2/7 or 2/3), and the other side length is an integer?
Yes , there can be a Right triangle with two side lengths as simple fraction and other side length as an integer .
In the question ,
we have to find , whether a Right Triangle can be made by two fractions and an integer length .
yes, we can make a Right Triangle with two lengths as fractions and other length as integer .
let us prove it with the help of an example .
Consider the triplet 7 , 24 , 25 .
let the two fractions side be 7/25 and 24/25 , and the hypotnuse of the right triangle be 1 .
We know that for the Right Triangle
(side1)² + (side2)² = hypotnuse²
(7/25)² + (24/25)² = 1²
49/625 + 576/625 = 1
(49+576) / 625 =1
625/625 = 1
1 = 1
hence ,it is a Right Triangle .
Therefore , Yes , there can be a Right triangle with two side lengths as simple fraction s and other side length as an integer .
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1/2 (7/10-3/5) + -1.9
Answer: -1 17/20
Step-by-step explanation: use order of operations to solve, parenthesis, multiplication, addition/subtraction
Low flow showerheads use 2 1/2 gallons of water per minute. If family members shower a total of 2 1/3 hours per week, how much water does the family use for showers each week? Write an expression that represents the problem. Then solve the problem.
The expression that represents the situation is 5/2(x) and the family uses 350 gallons of water for each week.
Showerheads:
The showerhead is a bathroom fixture that directs the flow of water in a bathroom shower.
Given,
Low flow showerheads use 2 1/2 gallons of water per minute.
And the family uses 2 1/3 hours per week.
Here we need to find the expression for this situation and we also need to find the amount of water used by the family.
First, we have to convert the mixed fraction into improper fraction, then we get,
2 1/2 =5/2
So, for one minute the showerhead use 5/2 gallon of water.
So, the expression for this situation is,
=> 5/2(x).
Where x represents the amount of time in minutes.
Now, we know that the family uses the showerhead for 2 1/3 hours per week.
So, we have to convert this mixed fraction into improper fraction,
2 1/3 = 7/3
We know that, 1 hour = 60 minutes.
So, 7/3 hours is equal to,
=> 7/3 x 60 = 7 x 20 = 140
Then, the amount of water used by the family is,
=> 5/2 (140)
=> 5 x 70
=> 350
Therefore, the amount of water used by the family is 350 gallons per week.
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triangle ABC has coordinates A(1,4) B(3.-2) and C(4,2) . Find the coordinates of the image ABC after a reflection over the x axis.
The given vertices are A(1,4), B(3,-2), and C(4,2).
The reflection over the x-axis is expressed as
[tex](x,y)\rightarrow(x,-y)[/tex]This means we have to multiple each y-coordinate with -1. Let's do it!
[tex]\begin{gathered} A(1,4)\rightarrow A^{\prime}(1,-4) \\ B(3,-2)\rightarrow B^{\prime}(3,2) \\ C(4,2)\rightarrow C^{\prime}(4,-2) \end{gathered}[/tex]Therefore, the vertices of the new triangle are A'(1,-4), B'(3,2), and C'(4,-2)
Gabrielle and Joni each wrote a fraction equivalent to 60/105 using the
greatest common factor. Gabrielle says the equivalent fraction is 12/21
Joni says the equivalent fraction is 4/7. Who is correct? Explain. Use the
GCF of the numerator and denominator of 60/105 to justify your answer.
Gabrielle is the correct one.
What are greatest common factor?The largest positive integer m that divides both x and y is the GCF of two or more non-zero integers, x, and y. The GCF stands for the greatest common factor. Here, greatest might be changed to highest, and factor to divisor. Therefore, the greatest common factor is often referred to as the highest common divisor )(HCD), highest common factor (HCF), or greatest common divisor (GCD.
Fractions, which are frequently employed in daily life, are almost always utilized with GCF. Finding the GCF of the denominator and numerator will allow you to obtain the necessary reduced form for simplifying a fraction or ratio. The greatest number that can divide two numbers x and y is their GCF.
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URGENT 50 points
WRITE AS AN ORDER OF OPERATIONS EXPRESSION, THEN SIMPLIFY IT.
Chloe owed the bank $3500 after taking out a small loan. She currently works and
makes $24 per hour. She works for 6 hours a day. After 25 days, will Chloe still owe the
bank money?
Answer:
She will no longer owe the bank any money. She will have 100 dollars in profit.
Step-by-step explanation:
$24 x 6 hours a day means she makes 144 dollars a day.
144 dollars times 25 means she makes 3600 dollars over the 25 day period.
3600-3500(the amount she owed) is 100 dollars
Solve for x and y in the problem below. Then, find m
Given the Cyclic Quadrilateral Theorem,
Opposite angles of a Cyclic Quadrilateral are supplementary(that is, they add up to 180°).
Therefore,
[tex]\begin{gathered} 17x+78^o=180^o \\ 17x=180^o-78^o \\ 17x=102^o \\ x=\frac{102^o}{17} \\ x=6^o \end{gathered}[/tex]To obtain y,
[tex]\begin{gathered} 9y+6y=180^o \\ 15y=180^o \\ y=\frac{180^o}{15} \\ y=12^o \end{gathered}[/tex]Thus,
[tex]\begin{gathered} m\angle X=9y \\ =9\times12 \\ =108^o \end{gathered}[/tex][tex]\begin{gathered} m\angle V=6y \\ =6\times12 \\ =72^o \end{gathered}[/tex][tex]\begin{gathered} m\angle W=17x \\ =17\times6 \\ =102^o \end{gathered}[/tex]Therefore, the values are
m
m
m
Solve for b
-73 = b/7- 81
Solve for b
-73 = b/7- 81
b= 56
-511=b-567
b-567=-511
b=-511+567
b=56
Solution 2
Add 81 to both sides.
-73+81= b/7
simplify -73+81 to 8
8=b/7
8*7=b
simplify 8*7 to 56
56=b
switch sides b= 56
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If the equation be -73 = b/7- 81 then the value of b is 56.
What is meant by Linear equations?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."Solve for b
-73 = b/7- 81
b= 56
-511=b-567
b-567=-511
Hence,
b=-511+567
b=56
Solution 2
Add 81 to both sides.
-73+81= b/7
simplify -73+81 to 8
8=b/7
8*7=b
simplify 8*7 to 56
56=b
switch sides b= 56
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The headlights of an automobile are set such that the beam drops 2.00 in. for each 28.0 ft in front of the car. What is the angle between the beam and the
Road?
The most appropriate choice for trigonometry will be given by -
Angle between beam and road is 0.33°
What is Trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are [tex]sin\theta, cos\theta, tan\theta, cos\theta, sec\theta, cosec\theta[/tex]
[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}\\[/tex]
Trigonometry is a very important tool in mathematics.
Here,
The headlights of an automobile are set such that the beam drops 2.00 in. for each 28.0 ft in front of the car.
According to the figure attached here, 2.0 inch forms the height of the triangle and 28.0 ft forms the base of the triangle
Let the angle be [tex]\theta[/tex]. Now trigonometry is applied here
[tex]tan\theta = \frac{\frac{2}{12}}{28}\\tan\theta = \frac{1}{6 \times 28}\\tan\theta = \frac{1}{168}\\\theta = tan^{-1}\frac{1}{168}\\\theta = 0.33^{\circ}[/tex]
Angle between beam and road is 0.33°
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Select all ratios equivalent to 3:6
18:9. 4:8. 11:12
Answer:
4:8
Step-by-step explanation:
Equivalent ratios have the same simplified ratio.
The simplified ratio of 3:6 is 1:2. We can get it by dividing both sides of the ratio by a common factor of 3.
18:9 is incorrect because its simplified ratio is 2:1. Equivalent ratios have the same order.
4:8 is correct because dividing both sides of the ratio by 4 gives us 1:2.
11:12 is incorrect because it can not be simplified to give 1:2.
The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, hcf). the cost for using 18 hcf of water is $39.67, and the cost for using 37 hcf is $69.12. what is the cost for using 21 hcf of water?
The monthly cost of water use can be represented using a linear equation y = 1.55 x + 11.77 and the cost of using 21 hcf is $44.32.
A linear equation can be represented by a line equation:
y = mx + c
Where:
m = slope
c = constant
From the problem, we have 2 equations:
39.67 = 18 m +c
69.12 = 37 m + c _
29.45 = 19 m
m = 1.55
Substitute m = 1.55
39.67 = 18 . (1.55) + c
c = 11.77
Hence, the linear equation is:
y = 1.55 x + 11.77
Substitute x = 21
y = 1.55 . (21) + 11.77 = 44.32
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Help me answer this what’s wrong with this problem
Answer:
See below
Step-by-step explanation:
The equation is
y = [tex]x^{2}[/tex] + x
x equals the step
We see steps: 1, 2,3 and 4
y equals the number of squares that you see in each step.
If you look at step 1, you see [tex]1^{2}[/tex] + 1 = 2
Step 2: [tex]2^{2}[/tex] + 2 = 6
Step 3: [tex]3^{2}[/tex] + 3 = 12
Step 4: [tex]4^{2}[/tex] + 4 = 20
Can you see at each step there is a square of the number and then a little extra? That little extra equals the number of the stop.
In the equation
y = 4x -2
Step 1
y = 4(1) -2
y = 2 It works!
Step 2:
y = 4x -2
y = 4(2) - 2
y = 8 - 2
y = 6 It works!
Step 3:
y = 4x -2
y = 4(3) - 2
y = 12 - 2
y = 10 It does not work!
Step 4:
y = 4x -2
y = 4(4) - 2
y = 16 - 2
y = 14 It does not work!
The equation y= 4x -2 only worked for the first 2 steps.
2x+y = -7
-4x -5y =23
Answer:
x = -2
y = -3
Step-by-step explanation:
If it is a simultaneous equation.
2x+y = -7-----equation 1
-4x -5y =23-----equation 2
5(2x+y = -7)
-4x -5y =23
10x+5y = -35
-4x -5y =23 +5y cancel -5y
10x= -35
-4x=23
6x = -12
x = -2
Solving for Y
Substitute the value of x in equation one or two.
equation two = -4x -5y =23
-4x -5y =23
-4(-2) -5y =23
8-5y=23
-5y = 23-8
-5y = 15
y = -3
A woman is training for a cycling event. In the first week she cycles 20 km. In each subsequent week, she cycles 5 km more than she cycled the previous week.
How many kilometres has she cycled in total by the end of the 18th week?
The kilometres that she has cycled in total by the end of the 18th week is 105.
How to calculate the number of kilometers?Based on the information, this is an arithmetic sequence and the formula is illustrated as
= a + (n - 1)d
where a = first term = 20
d = common difference = 5
n = numbers = 18
Therefore, the 18th term will be:
= a + (n - 1)d
= 20 + (18 - 1)5
= 20 + (17 × 5)
= 20 + 85
= 105
The number of kilometers is 105 kilometers.
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Olivia purchased two blouses for $12.50 each and a shirt for $11.25.The sales tax rate is *8.5 %. How much will Olivia pay including tax?
Answer:
$39.33
Step-by-step explanation:
11.25 + 12.50 +12.50 = 36.25
36.25 + 8.5% = 39.33
The length of a rectangle is twice its width. If the area of the rectangle is 162in^2, find its perimeter.
We know that the length of a rectangle is twice its width. Then:
The area of a rectangle is the product of its width and length. Then:
[tex]A=2x\cdot x=2x^2[/tex]Additionally, we know that the area is 162 in². Using the expression above we can obtain the value of x:
[tex]\begin{gathered} 162=2x^2 \\ 81=x^2 \\ x=9\text{ in} \end{gathered}[/tex]Finally, the perimeter (2P) is just twice the sum of the width and the length of the rectangle:
[tex]2P=2\cdot(2x+x)=6x=6\cdot9=54\text{ in}[/tex]Please help! I have no idea what I’m doing and I’m super behind, I absolutely suck at math!
The function f(x) is graphed below.
(Picture below)
A) what is f(0)
B)what is f(3)
C) what is f(2)
Answer: 0, 3, 0
Step-by-step explanation:
f(a) represents the value of f(x) at x=a.
Using the numbers 8, 6, 4, and 2, write an expression that equals 6.
Answer:
6+4,8-6, 4x2,8-2
Step-by-step explanation:
giving brainliest to first person who answers!
Evaluate.
7 x 5 + 4² − 2³ / 4
Which number line and equation show how to find the distance from -2 to 5? O O A. 1-2-(-5) 2 3 12-1-5) sing O c. 1-2-5 D. 2-5
To find the distance between two numbers on the number line, you have tu use absolute value
So, if I want to know the distance from -2 to 5, all I have to do is to substract 5 from -2 and then apply absolute value, like this:
[tex]\mleft|-2-5\mright|\text{ = }\mleft|-7\mright|\text{ = 7}[/tex]And the number line should look like this:
Determine the relative frequency for the third class as a simplified fraction
GIVEN:
We are given a frequency distribution table showing different classes of hours of study and the frequency of each class of data.
Required;
To determine the relative frequency for the third class
Step-by-step solution;
For a relative frequyency, we need to find the number of times an event occurs and express it as a fraction of the total events that occured in the survey/experiment.
The events in this case are hours of study and the occurrence is the total frequency for all classes of hours of study.
The total frequency is;
[tex]3+10+6+15+6=40[/tex]The relative frequency for the third class therefore would be;
[tex]\begin{gathered} Relative\text{ }Frequency_3=\frac{6}{40} \\ \\ Relative\text{ }Frequency=\frac{3}{20} \end{gathered}[/tex]ANSWER:
The relative frequency of the third class therefore is
[tex]\frac{3}{20}[/tex]The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?.
Percentage of the student body exists at least 21 years old exists 50%.
What is meant by normal distribution?A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
As one moves away from the center, values start to taper off and the majority of values are concentrated in this area. In a normal distribution, the mean, mode, and median are identical measures of central tendency.
When given a normal or Symmetric distribution, the mean of the distribution exists at the center with 0.5 or 50% of the distribution to either side (right and left) of the distribution.
Therefore, if the mean = 21 ; then the percentage of student body with at least 21 years is the percentage to the left of the distribution, which exists 50%.
P(x ≤ 21) = 0.5 = 50%
Therefore, 50 percentage of the student body exists at least 21 years old
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Assuming a direct proportion between the distance and time, how far would they travel in 5 hours?
A family taking a road trip vacation travels 126 miles in 3 hours.
We can calculate the constant of proportionality as:
[tex]\frac{126\text{ miles}}{3\text{ hours}}=42\text{ miles/hour}[/tex]Then, in 5 hours they would travel:
[tex]d=5\text{ hours}\cdot\frac{42\text{ miles}}{1\text{ hour}}=210\text{ miles}[/tex]In 5 hours they would travel 210 miles.
