Answers
cosine is adjacent over hypotenuse.
there is an acronym for this: soh-cah-toa
soh: sine is opposite over hypotenuse
cah: cosine is adjacent over hypotenuse
toa: tangent is opposite over adjacent
Answer:
[tex]\text{cos}(B)=\frac{c}{a}[/tex]
Step-by-step explanation:
We have been given a triangle. We are asked to find [tex]\text{cos}(B)[/tex].
We know that cosine relates adjacent side of a right triangle to its hypotenuse.
[tex]\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]
We can see that side AB is adjacent side and CB is hypotenuse of our given right triangle.
[tex]\text{cos}(B)=\frac{AB}{CB}[/tex]
[tex]\text{cos}(B)=\frac{c}{a}[/tex]
Therefore, our required value is [tex]\text{cos}(B)=\frac{c}{a}[/tex]
Related Questions
Nadia has 20 more postcards then Pete. After Nadia gives Pete some cards Pete has 2 more postcards than Nadia. How many postcards does Nadia give to Pete?
Answers
Nadia gave Pete 11 postcards to balance the numbers as described. This means Pete ended up with 2 more postcards than Nadia after the exchange.
To find out how many postcards Nadia gave to Pete, let's set up some equations based on the information given.
First, let's define the number of postcards Pete has as P.
Since Nadia has 20 more postcards than Pete, we know:
N = P + 20
Now, let's define the number of postcards Nadia gives to Pete as x.
After Nadia gives x postcards to Pete, Nadia will have N - x postcards and Pete will have P + x postcards.
According to the problem, after the exchange, Pete has 2 more postcards than Nadia: P + x = (N - x) + 2
Substitute the first equation (N = P + 20) into the second equation: P + x = ((P + 20) - x) + 2
Simplify the equation:
P + x = P + 20 - x + 2
P + x = P + 22 - x
Now, isolate x on one side of the equation by subtracting P from both sides:
x + x = 22
2x = 22
Divide both sides by 2: x = 11
A wildfire is spreading at an alarming rate. The wildfire begins at a size of 8 square feet. It then doubles its width every x hours, and doubles its length every y hours. After a period of time, the wildfire covers 14,000 square feet.
Which equation correctly represents the area of the wildfire in terms of x and y?
A. 14,000 = 16^xy
B. 14,000 = 16xy
C. 14,000 = 8 ⋅ 2^x+y
D. 14,000 = 8 ∗ 2^xy
Answers
The equation [tex]\(14,000 = 8 \cdot 2^{x+y}\)[/tex] correctly represents the area of the wildfire in terms of x and y (option C).
How to find the correct equation for the area in terms of x and y?
The initial size of the wildfire is 8 square feet.
It doubles its width every x hours, so the width grows by a factor of [tex]\(2^{\frac{1}{x}}\)[/tex] each hour.
It doubles its length every y hours, so the length grows by a factor of [tex]\(2^{\frac{1}{y}}\)[/tex] each hour.
The area (A) of a rectangle is given by the formula [tex](A = \text{length} \times \text{width}\))[/tex].
So, after a period of time, the area of the wildfire is given by:
[tex]A = 8 \times 2^{\frac{1}{x}} \times 2^{\frac{1}{y}}[/tex]
Combine the exponents:
[tex]A = 8 \times 2^{\frac{1}{x} + \frac{1}{y}}[/tex]
Now, if the area is 14,000 square feet, we can set up the equation:
[tex]14,000 = 8 \times 2^{\frac{1}{x} + \frac{1}{y}}[/tex]
To make it match one of the given options, we can express 8 as 2³:
[tex]\[ 14,000 = 2^3 \times 2^{\frac{1}{x} + \frac{1}{y}} \][/tex]
Combine the exponents again:
[tex]\[ 14,000 = 2^{3 + \frac{1}{x} + \frac{1}{y}} \][/tex]
So, the correct equation that represents the area of the wildfire in terms of x and y is:
[tex]\[ 14,000 = 8 \times 2^{x+y} \][/tex]
Therefore, option C. [tex]\(14,000 = 8 \cdot 2^{x+y}\)[/tex] is the correct representation.
The pressure at sea level is 11 atmosphere and increases at a constant rate as depth increases. When Sydney dives to a depth of 23 meters, the pressure around her is 3.3 atmospheres. The pressure p in atmospheres is a function of x, the depth in meters.
Answers
Answer:
The function [tex]p(x) = 0.1x+1[/tex] , where x is the depth in meters.
Step-by-step explanation:
As per the statement: The pressure at sea level is 1 atmosphere and increases at a constant rate as depth increases.
Then, we have the two points i,e (0, 1) and (23, 3.3).
An equation of the line is in the form of y=mx+b where m is the slope or rate of the line and b is the y-intercept.
Let x represents the depth in meters and p(x)= y represents the pressure in atmosphere.
Calculate slope of the line:
Slope of line(m) is given by:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given point we have;
[tex]m = \frac{3.3-1}{23-0} = \frac{2.3}{23} = 0.1[/tex]
Then, our equation of line become:
y = 0.1x + b .....[1]
To solve for b;
Substitute the point (0, 1) in [1];
[tex]1 = 0.1(0)+b[/tex]
[tex]1 = b[/tex]
Our equation for this line become: y = 0.1x +1
Now, we write this for x as a function of p,
i.e, p(x) = 0.1x + 1
Then, the function formula become;
[tex]p(x) = 0.1x+1[/tex] where x is the depth in meters.
manager needs to buy chairs for his office the price for 1 chair is 79.99 dollars. If the manager buys 2 or more chairs then he get's a 40% discount on each chair. Approximately how much will the manager save on each chair if he buys 2?
Answers
40% discount
79.99 ÷ 100 =0.7999
0.7999 × 60 = 47.994
47.994 rounded down is $47.99
79.99-47.99=30.00
he saved $30
If the manager buys 2 or more chairs then he saves 31.99 dollars on each chair.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, A manager needs to buy chairs for his office the price for 1 chair is 79.99 dollars.
If the manager buys 2 or more chairs then he get's a 40% discount on each chair.
Therefore, He saves 40% of the original cost of 1 chair which is,
= (40/100)×79.99.
= 31.99 dollars.
So, The manager saves 31.99 dollars on each chair if he buys 2 or more at a time.
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There is typically a significant difference in loan interest rates between _______.
A. new cars and used cars
B.There is no significant difference in loan interest rates.
C. used cars and refinanced cars
D. new cars and refinanced cars
Answers
Answer:
option A) New cars and used cars is correct option.
Step-by-step explanation:
loan Interest rate can be defined as the percentage of a loan paid by borrowers to lenders. For most loans, interest is paid in addition to principal repayment in order to compound over time.
since new cars have more price than old cars that's why new cars have more greater loan interest than old cars
hence option a is correct
There is generally a significant difference in loan interest rates between new cars and used cars, with new cars usually having lower rates. Institutions regard new cars as less risky than used or refinanced cars, hence, they tend to offer lower interest rates to encourage new car loans.
Explanation:There is typically a significant difference in loan interest rates between new cars and used cars. This is mainly because new cars tend to have lower interest rates than used cars. Financial institutions, such as banks and credit unions, usually perceive new cars as less risky because they have not been subjected to any wear and tear compared to used cars which could potentially have mechanical issues. Consequently, these institutions lower the interest rates for new car loans to encourage more borrowers.
Whereas, in the case of used cars and refinanced cars, the interest rates are significantly higher due to the increased risk that the lender has to take on.
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Group Radii of Tomatoes (centimeters)
Fertilized 0.8, 1.1, 0.9, 0.8, 1.0, 1.2, 0.9, 1.1, 1.0, 1.2
Unfertilized 1.4, 1.6, 1.3, 1.5, 1.1, 1.5, 1.6, 1.2
Todd randomly divided some tomato plants into two groups. He applied fertilizer to one group, but did not apply fertilizer to the other group. Then he measured the radii of the tomatoes produced by the plants in each group. His data is shown in the table.
What is the difference in the mean radius of the tomatoes from the fertilized plants and the mean radius of the tomatoes from the unfertilized plants?
A) 0.3 centimeters
B) 0.4 centimeters
C) 0.5 centimeters
D) 0.6 centimeters
Answers
Answer: Option 'B' is correct.
Step-by-step explanation:
since we have given that
Group radii of fertilized tomatoes is given by
[tex]0.8, 1.1, 0.9, 0.8, 1.0, 1.2, 0.9, 1.1, 1.0, 1.2[/tex]
Group radii of unfertilized tomatoes is given by
[tex]1.4, 1.6, 1.3, 1.5, 1.1, 1.5, 1.6, 1.2[/tex]
So, we will first find the mean of both the group i.e.
Mean radii of fertilized tomatoes is given by
[tex]=\frac{0.8+1.1+0.9+0.8+1.0+1.2+0.9+1.1+1.0+1.2}{10}\\\\=1[/tex]
Similarly,
Mean radii of unfertilized tomatoes is given by
[tex]\frac{1.4+1.6+1.3+1.5+1.1+1.5+1.6+1.2}{8}\\\\=\frac{11.2}{8}\\\\=1.4[/tex]
So, the difference between the mean radii of fertilized and unfertilized tomatoes will be
[tex]1.4-1=0.4\ cm[/tex]
Hence, Option 'B' is correct.
The area of window measures 96 square inches. If the window is 8 inch wide, how long is the window
Answers
If we rearrange this equation to find the length we get - L = A/B
Substitute your information and you get 96/8 = 12
So the length of the window is 12 inches
Hope this helps :)
A parallelogram has an area of 285 square centimeters and a base length of 19 centimeters. What is the height of the parallelogram? 16 centimeters 28 centimeters 15 centimeters 14 centimeters
Answers
Final answer:
To find the height of the parallelogram with an area of 285 square centimeters and a base of 19 centimeters, divide the area by the base, resulting in a height of 15 centimeters.
Explanation:
The question pertains to finding the height of a parallelogram given the area and the base length. The formula for the area of a parallelogram is Area = base × height. Given an area of 285 square centimeters and a base length of 19 centimeters, we can solve for the height by rearranging the formula:
Height = Area / base
By substituting the given values:
Height = 285 cm² / 19 cm = 15 cm
So, the height of the parallelogram is 15 centimeters.
If one jar of glue weighs 1/12 pound, how many jars can Rickie getfrom 2/3 pound if glue?
Answers
Answer: 8
Step-by-step explanation:
2/3 divided by 1/12
2/3 * 12/1
24/3=8
hope i helped angel!
Answer:
I think it would be 8
Step-by-step explanation:
Divide 2/3 by 1/12.
(2/3) / (1/12) = 2/3 * 12/1 = 24/3 = 8
The length of an aquarium, which has the form of a rectangular solid, is equal to 5 decimeters, and the width is 4/5 the length. When you put 40 liters of water into the aquarium, it was full to 2/3 its volume. What part of the length makes up the height of the aquarium? (1 liter is equal by volume to 1 decimeter3)
Answers
Answer:
[tex]\dfrac{3}{5}[/tex] of the height makes up the height.
Step-by-step explanation:
The length of an aquarium, which has the form of a rectangular solid, is [tex]5\ dm[/tex]
The width is [tex]\dfrac{4}{5}[/tex] of the length, so teh width is,
[tex]=5\times \dfrac{4}{5}=4\ dm[/tex]
Let us assume the height is 'h' dm.
So the volume will be,
[tex]=\text{Length }\cdot \text{ Width }\cdot\text{ Height}[/tex]
[tex]=5\times 4\times h[/tex]
[tex]=20h\ dm^3[/tex]
As 1 liter of water occupies volume of 1 dm³, so volume of 40 liters of water will be,
[tex]=40\times 1=40\ dm^3[/tex]
This [tex]40\ dm^3[/tex] is the [tex]\dfrac{2}{3}[/tex]th of total volume.
Hence total volume will be,
[tex]=\dfrac{40}{\frac{2}{3}}=40\times \dfrac{3}{2}=60\ dm^3[/tex]
Therefore,
[tex]\Rightarrow 20h=60[/tex]
[tex]\Rightarrow h=3\ dm[/tex]
So the part of length makes up to the height will be,
[tex]=\dfrac{3}{5}[/tex]
In Las Vegas, Nevada, stores charge a 4.6\%4.6% state sales tax and a 3.65\%3.65% county sales tax. Yuki is purchasing a handbag priced at \$220$220 before tax. How much sales tax does Yuki pay for her handbag purchase?
Answers
Answer:
$18.15
Step-by-step explanation:
We have been given that in Las Vegas, Nevada, stores charge a 4.6% state sales tax and a 3.65% county sales tax. Yuki is purchasing a handbag priced at \$220$220 before tax.
To find total sales tax paid by Yuki for her handbag purchase we will find 4.6% of $220 and 3.65% of $220 and add amount of both taxes.
[tex]\text{Total sales tax amount}=\text{State sales tax amount+ County sales tax amount}[/tex]
[tex]\text{States sales tax amount for handbag}=\frac{4.6}{100}*220[/tex]
[tex]\text{States sales tax amount for handbag}=0.046*220[/tex]
[tex]\text{States sales tax amount for handbag}=10.12[/tex]
Now let us find county sales tax for handbag purchase.
[tex]\text{County sales tax amount for handbag}=\frac{3.65}{100}*220[/tex]
[tex]\text{County sales tax amount for handbag}=0.0365*220[/tex]
[tex]\text{County sales tax amount for handbag}=8.03[/tex]
Now let us add both amount to get total tax paid by Yuki.
[tex]\text{Total sales tax}=10.12+8.03[/tex]
[tex]\text{Total sales tax}=18.15[/tex]
Therefore, Yuki paid $18.15 sales tax for her handbag purchase.
Delaney would like to make a 5 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds. Let p represent the number of pounds of peanuts needed to make the new mixture, and let m represent the number of pounds of the 20% peanuts-80% almonds mixture.
(a) What is the system that models this situation? (8 points)
(b) Which of the following is a solution to the system
2 lb peanuts and 3 lb mixture;
2.5 lb peanuts and 2.5 lb mixture;
4 lb peanuts and 1 lb mixture? Show your work. (7 points)
ONLY ANSWER WITH WORK AND ANSWER IF YOU KNOW, MAKE IT EASY TO UNDERSTAND BTW 20 POINTS
Answers
The system that models the situation relates to the weights of peanuts and almond mixture.
The solution to the system can be determined by substituting the values of peanuts and mixture into the equations and checking if they hold true.
(a) The system that models this situation is:
p + m = 5
0.6p + 0.2m = 5 * 0.6
(b) To determine if a solution is valid, we need to substitute the values of p and m into the equations and check if the equations are true. For the solution 2 lb peanuts and 3 lb mixture:
p + m = 5
2 + 3 = 5 (true)
0.6p + 0.2m = 5 * 0.6
0.6(2) + 0.2(3) = 3 (true)
Therefore, 2 lb peanuts and 3 lb mixture is a valid solution.
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PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!
Multiply.
(3x + 2)(4x - 7)
Answers
Answer: 12x^2 - 13x - 14
Choice D
==========================================
Work Shown:
Let y = (3x+2)
Replace (3x+2) with y and we go from (3x+2)(4x-7) to y(4x-7)
Distribute this y through: y(4x-7) = 4xy - 7y
--------------
Now replace y with (3x+2), distribute again, and simplify
4xy - 7y
4x(3x+2) - 7(3x+2)
4x(3x)+4x(2) - 7(3x) - 7(2)
12x^2 + 8x - 21x - 14
12x^2 - 13x - 14
Answer:
Alternative D
Step-by-step explanation:
(3x + 2)(4x - 7)
12x² - 21x + 8x - 14
12x² - 13x - 14
I hope I helped you.
Nikki earned $185 at her summer job. She already had savings of $125.75. She buys a T-shirt for $23.50. How much money does she have left? A. $161.50 B. $287.25 C. $334.25 Reset Next
Answers
310.75-23.50=287.25
answer is B
Find the LCM (10,22,99)
Answers
Answer: 990
Step-by-step explanation:
10 22 99 ∧ ∧ ∧ 2 5 2 11 11 9 ∧ 3 310: 2 * 5
22: 2 * 11
99: 3 * 3 * 11
GCF: 1
LCM: 2 * 5 * 11 * 3 * 3
= 990
The Least Common Multiple (LCM) of the numbers 10, 22, and 99 is found by prime factorization and taking the highest power of all prime factors that appear, which results in an LCM of 990.
To find the Least Common Multiple (LCM) of the numbers 10, 22, and 99, we need to prime factorize each number and then take the highest power of all the prime factors that appear.
Prime factorization of 10 = 2 x 5
Prime factorization of 22 = 2 x 11
Prime factorization of 99 = 32 x 11
Now, identify the highest powers of all prime factors, which are 2, 32, 5, and 11. Then, multiply these together:
LCM = 2 x 32 x 5 x 11 = 2 x 9 x 5 x 11 = 990
Therefore, the LCM of 10, 22, and 99 is 990.
According to Adams survey,54 sixth graders, or 36% of the students in sixth grade, would like to take art or music electives. How many sixth grade students are there in Adams school?A.90b.150c.162d.194
Answers
[tex] \frac{54}{x} \: = \: \frac{36}{100} [/tex]
[tex]x \: = \: \frac{54 \times 100}{36} [/tex]
x = 150.
Therefore, B) 150.
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $3,169 was collected on the sale of 1,325 tickets. How many of each type of ticket were sold?
Answers
Answer:
461 adults and 864 students
Step-by-step explanation:
We can set-up a system of equations to find the number of adults. We know students and adults attended. We will let s be the number of students and a be the number of adults. Since 1,325 tickets were purchased, then s+a=1325.
We also know that a total of $3,169 was collected and adult tickets cost $5 each and students cost $1 each. We can write 1s+5a=3169.
We will solve by substituting one equation into the other. We first solve the first equation for s which is s=1325-a. Substitute s=1325-a into 1s+5a=3169. Simplify and isolate the variable a.
1(1325-a)+5a=3169
1325-a+5a=3169
1325+4a=3169
1325-1325+4a=3169-1325
4a=1844
a=461
This means that 461 adults attended and 864 students attended since 864+461=1325.
What is the solution to this system of equations?
Use the linear combination method (aka elimination method).
Answers
Answer:
A) (-2, 12)
Step-by-step explanation:
Just multiplied the second equation by -1
then eliminated the y
Then solved for x and you get x = -2
then you plug in x = -2 and figure out y
and you get y = 12
Hope this helped and plz mark as brainliest!
Can someone please help me with this? Thanks if you do!
Answers
Answer:
154 square cm (choice B)
Step-by-step explanation:
The diameter is 14 cm, so the radius is half that at 7 cm. Let r = 7
Use the formula
A = pi*r^2
to find the area of the circle. Let pi = 3.14 be the approximation for pi
So,
A = pi*r^2
A = 3.14*7^2
A = 3.14*49
A = 153.86
A = 154
Answer: B.
Step-by-step explanation:
3.14*r2
3.14*7(2)
153.9
What type of exponential equation is shown?
y = C(1 - r)t
Exponential growth
Compound interest
Exponential decay
Quadratic
Answers
Answer:
Exponential Decay or Growth
Step-by-step explanation:
[tex]y=C(1-r)^t[/tex] represents an exponential.
When r is greater than 0 but less than 1, the function decays by decreasing the values through the rate.
When r is less than 0 or negative, the function grows by increasing the values through the rate.
The length of a rectangle is one inch less than three times its width. If the perimeter of the rectangle is 54 inches, find the length
Answers
w - width
3w - 1 - length
54 in - perimeter
w + w + (3w - 1) + (3w - 1) = 8w - 2 - perimeter
The equation:
8w - 2 = 54 add 2 to both sides
8w = 56 divide both sides by 8
w = 7
3w - 1 = 3(7) - 1 = 21 - 1 = 20
Answer: The length = 20 in.The perimeter of the rectangle is twice the sum of the length and the width.The length of the rectangle is 20 inches long.
Given information-
The length of a rectangle is one inch less than three times its width.
The perimeter of the rectangle is 54 inches.
What is the perimeter of rectangle?The perimeter of the rectangle is the boundary by which the rectangle is covered. The perimeter of the rectangle is twice the sum of the length and the width.
It can be given as,
[tex]P=2(a+b)[/tex]
Here,[tex]a[/tex] is the length of the rectangle and [tex]b[/tex] is the width of the rectangle.
Now it is given that the length of a rectangle is one inch less than three times its width. Suppose the length of the rectangle is [tex]x[/tex] inches long. Thus the width [tex]y[/tex] of the rectangle is,
[tex]=\dfrac{x+1}{3} =\dfrac{x}{3} +\dfrac{1}{3}[/tex]
Thus the perimeter of the rectangle is,
[tex]\begin{aligned}\\P&=2(x+\dfrac{x}{3}+\dfrac{1}{3} )\\54-\dfrac{2}{3} &=2\times\dfrac{3x+x}{3} \\\dfrac{160}{3} &=\dfrac{8x}{3}\\160&=8x\\x&=20\\\end[/tex]
Hence the length of the rectangle is 20 inches long.
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The music club is having a bake sale as a fundraiser. They sell xx brownies at $5 each and yy cookies at $8 each. They will sell at least 26 brownies and 15 cookies. They need to make at least $250. Which system describes this situation?
Answers
Step-by-step explanation:
We are told that the music club is having a bake sale as a fundraiser. They sell x brownies at $5 each and y cookies at $8 each. They will sell at least 26 brownies and 15 cookies.
We can represent this information as:
[tex]x\geq 26[/tex]
[tex]y\geq 15[/tex]
They need to make at least $250. We can represent this information as:
[tex]5x+8y\geq 250[/tex]
Therefore, our system of inequalities will be:
[tex]x\geq 26[/tex]
[tex]y\geq 15[/tex]
[tex]5x+8y\geq 250[/tex].
PLEASE HELP! I GIVE 20 POINTS
Answers
Answer: (C) 108
Step-by-step explanation:
The corresponding angle to x and (x - 36) form a linear pair, which means they are supplementary angles, hence their sum is 180°
(x) + (x - 36) = 180
2x - 36 = 180
2x = 216
x = 108
Answer:
The Answer is 108
Step-by-step explanation:
Few things to Note:
180 angles are linear (so two angles in straight line ADDS UP to makes 180 degree)
Corresponding angles equal each other (aka the two angles shown is corresponding..meaning BOTH are "x"; also, this problem tells you that)
Knowing this, x-36 and its adjacent(angle next to it) is x and they are on a 180 straight line, set equation (x-36)+x= 180 and solve
(x-36)+x= 180--->2x-36=180--->216/2=x
PLEASE HELP!!! How do you write 2x^2+12x-4 in vertex form?
Answers
Answer:
2(x + 3)^2 - 22
Step-by-step explanation:
2x^2 + 12x - 4
Start by making your "a" value equal to 1 by factoring the 2 from the first 2 terms in the standard form equation.
2(x^2 + 6x) - 4
Complete the square by using the formula (b/2)^2. Identify your "b" value, which is 6. Now you can complete the square.
((6)/2)^2 = 9
After completing the square, add 9 inside the parentheses and subtract 9 outside the parentheses. Since the 9 inside the parentheses is also being multiplied by 2, multiply the subtracted 9 by 2 as well.
2(x^2 + 6x + 9) - 4 - 9(2)
Factor the terms inside the parentheses by using the product/sum factoring method. This is where you find two of the same terms that multiply to "c" (9) and add to "b" (6).
In this case, positive 3 multiplies to 9 and adds to 6, so we will use the factors (x + 3)(x + 3), which is the same as (x + 3)^2.
2(x + 3)^2 - 4 - 9(2)
To finish off the problem, combine the like terms outside of the parentheses by multiplying 9 times 2 first and then subtracting -4 by 9(2).
[tex]\boxed{2(x + 3)^2 - 22 }[/tex]
A 2-pound box of spaghetti costs $2.50 philip says the unit cost is 2/2.50=0.80 per pound explain his error
Answers
Answer:
He did not calculate correctly.
Which input value produces the sane output value for the two functions on the gragh f(x)=-2/3x+1 g(x)=1/3x-2
Answers
Answer:
X=3
Step-by-step explanation:
We have two linear functions which intersect at a point. This point is shown in the attached graph. Linear functions are lines which are made of points that satisfy the function or relationship. This means at the intersection, this point (3,-1), both functions have the same values. An input of x=3 produces y=-1 in both functions.
Final answer:
To find the input value that yields the same output for both functions f(x) = -2/3x + 1 and g(x) = 1/3x - 2, we set the functions equal, combine like terms, and solve for x, getting the result x = 3.
Explanation:
The question asks which input value produces the same output value for the two functions f(x) = -2/3x + 1 and g(x) = 1/3x - 2. To find this value, we need to set the two functions equal to each other and solve for x.
Here are the steps to find the input value:
Set f(x) equal to g(x):
-2/3x + 1 = 1/3x - 2
Combine like terms:
-2/3x - 1/3x = -2 - 1
Combine the x coefficients on the left side and constants on the right side:
-1x = -3
Divide both sides by -1 to solve for x:
x = 3
Therefore, the input value that produces the same output value for both functions is x = 3.
What is the difference between a two point and a three point turn
Answers
Three-point Turns
Three-point turns are typically used to reverse direction on narrow, two-lane roads. They are tricky due to the narrowness of the road and the fact that your car completely blocks all traffic flow during part of the procedure.
Two-point turns (left side)*
If we’re going to get technical, then I must put a qualifier to these types of turns. Many driver’s ed professionals call these two-point turns and I have to agree albeit with an asterisk. Most professionals reserve three point turns for those turns which reverse direction on narrow streets without the aid of a side street. Therefore, any turn that reverses direction with the aid of a side street would be a two-point turn.
Suppose Marcy's rectangular laptop measures 12 inches by 9 inches. Find the diagonal measurement from corner A to corner B.
Answers
Answer:
the diagonal measurement from corner A to corner B=15 inches
Step-by-step explanation:
as we know that the loptop has the shape of a rectangle that means all it's angles are right angles. so we can use the pythogoras theorem to find out the diagonal of the rectangle.
let us denote the diagonal of rectangle by D and the sides of rectangle be denoted by X=12 and Y=9
so by using pythogoras theorem we have,
[tex]D^{2} =X^{2} +Y^{2}[/tex]
[tex]D^{2}[/tex]=225
D=15
Hence the diagonal measurement from corner A to corner B is 15 inches.
Answer:
The diagonal measures 15 inches
Step-by-step explanation:
The diagonal of the Marcy's rectangular laptop forms a right angle triangle with its width and length.
We can use the Pythagoras Theorem to write the following equation,
[tex]|AB|^2=12^2+9^2[/tex]
This implies that,
[tex]|AB|^2=144+81[/tex]
We simplify the right hand side to obtain,
[tex]|AB|^2=225[/tex]
We take the positive square root of both sides to obtain,
[tex]|AB|=\sqrt{225}[/tex]
[tex]|AB|=15inches[/tex]
Hence the diagonal of Marcy's laptop measures 15 inches.
Please help! Urgent!
Answer options:
-180°
-270°
-300°
-360°
Answers
Answer:
Step-by-step explanation: answer should be 360
The graph of the function f(x) is shown below. When f(x) = 0, determine x
PLEASE COMPLETE THIS PROBLEM WITH THE PICTURE BELOW :)
Answers
Answer:
x=-1.8
Step-by-step explanation:
When x = 0, we look at the graph and the point (0,5)
The value of the function at x=0 is 5, so we want to find the point (x,0)
Looking around the graph, we find it at (-1.8, 0)
The function f(x) is =0 at x= -1.8
Answer:
A:-1.8
Step-by-step explanation:
how because its me i'm always right