[tex]\left(\dfrac{g}{f}\right)(x)=\dfrac{x^2-6}{3x+1}[/tex]
What is the value of y?
The sum of all the angles of a triangle is 180 degrees. To solve for y you can make a formula of the sum of the angles equal to 180 like so...
y + y + 60 = 180
Now you must combine like terms. This means that first numbers with the same variables (y) must be combined...
y + y + 60 = 180
y + y = 2y
2y + 60 = 180
Now bring 60 to the left side by subtracting 60 to both sides (what you do on one side you must do to the other). Since 60 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.
2y + 60 - 60 = 180 - 60
2y + 0 = 120
2y = 120
Next divide 2 to both sides to finish isolating y. Since 2 is being multiplied by y, division (the opposite of multiplication) will cancel 2 out (in this case it will make 2 one) from the left side and bring it over to the right side.
2y / 2 = 120 / 2
y = 60
C. 60
Hope this helped!
~Just a girl in love with Shawn Mendes
please multiply (4x + 7)^2
Answer:
16x² + 56x + 49
Step-by-step explanation:
First, expand:
(4x + 7)² = (4x + 7)(4x + 7)
Follow the FOIL method. FOIL = First, Outside, Inside, Last.
(4x)(4x) = 16x²
(4x)(7) = 28x
(7)(4x) = 28x
(7)(7) = 49
16x² + 28x + 28x + 49
Combine like terms:
16x² + (28x + 28x) + 49
16x² + (56x) + 49
16x² + 56x + 49 is your answer.
~
Transversal t cuts parallel lines r and s. Which angles must be congruent to 2?
Answer:
A.) ∠3, ∠6, and∠7
If you have a protractor, that would help you alot :) but I hope this help you!
Answer:
A. ∠3, ∠6 and ∠7.
Step-by-step explanation:
Given,
r ║ s
Also, t is the common transversal of parallel lines r and s,
By the given diagram,
∠2 and ∠3 are vertical angles,
By vertically opposite angle theorem,
∠2 ≅ ∠3,
∠2 and ∠6 are corresponding angle,
By the corresponding angle theorem,
∠2 ≅ ∠6,
∠2 and ∠7 are alternate exterior angles,
By the alternate exterior angle theorem,
∠2 ≅ ∠7
Hence, Option 'A' is correct.
Consider the two exponential equations shown. Identify the attributes for each equation to complete the table.
Answer:
[tex] y = 2 5 0 ( 0 . 8 9 ) ^ x [/tex]
Initial value: 250
Decay
Decay rate: 11%
[tex] y = 4 0 ( 1.11 ) ^ x [/tex]
Initial value: 40
Growth
Growth rate: 11%
Step-by-step explanation:
The function we have on the left of the table is:
[tex] y = 2 5 0 ( 0 . 8 9 ) ^ x [/tex]
Initial value (when x = 0): [tex] y = 2 5 0 ( 0 . 8 9 ) ^ 0 [/tex]
y = 250 (initial value)
Growth or Decay: 0.89 < 1 so decay
Decay rate: (1 - 0.89) * 100 = 11%
Function on right side:
[tex] y = 4 0 ( 1.11 ) ^ x [/tex]
Initial value (when x = 0): [tex] y = 4 0 ( 1 . 1 1 ) ^ 0 [/tex]
y = 40 (initial value)
Growth or decay: 1.11 > 1 so growth
Growth rate: (1.11 - 1) * 100 = 11%
i took the test 100%
A point has coordinates (-3,-3). Where is it located in the coordinate plane?
C quadrant 3 because negative x value and negative y value
ABC is dilated by a scale factor of 0.5 with the origin as the center of dilation resulting in the image ABC. If a equals (2, 2), b equals (4, 3), and c equals (6, 3), what is the length of BC?
Answer:
BC should be 1 unit
Step-by-step explanation:
Answer:
1 unit is your answer
what is the greatest common factor of the following monomials: 12g^5h^4 g^5h^2
Answer:
g^5h^2
Step-by-step explanation:
12g^5h^4, g^5h^2
This is one way of doing it. Break down every number and every variable into a product of the simplest factors. Then see how many of each factor appear in both monomials.
12g^5h^4 = 2 * 2 * 3 * g * g * g * g * g * h * h * h * h
g^5h^2 = g * g * g * g * g * h * h
So far you see every single prime factor of each monomial.
Now I will mark the ones that are present in both. Those are the common factors.
12g^5h^4 = 2 * 2 * 3 * g * g * g * g * g * h * h * h * h
g^5h^2 = g * g * g * g * g * h * h
The greatest common factor is the product of all the factors that appear in both monomials.
GCF = g * g * g * g * g * h * h = g^5h^2
6x^3+(-3x^3y^2) when simplified is
Answer:
6x^3-3x^3y^2
Step-by-step explanation:
6x^3+\left(-3x^3y^2\right)
6x^3+\left(-3x^3y^2\right)=6x^3-3x^3y^2
=6x^3-3x^3y^2
the answer is 3x^3(2-y^2).
6x^3 + (-3x^3y^2) =
6x^3 - 3x^3y^2 =
3x^3(2-y^2)
You operate the cash register at diner. A customer gives you $20 bill to pay for his check, which totals$12.19. How much change should you give back?
Answer:
7.81 dollars
Step-by-step explanation:
20 which was given to
take away the cost of the bill of 12.19
which will give you how much change you will need to give back
Which graph shows a rate of change of 1/2
between -4 and 0 on the x-axis?
Answer:
Step-by-step explanation:
its the first one in edge
The graph which shows a rate of change of 1/2 is the linear graph shown in the image attached below.
What is the Rate of Change?Rate of change = change in y / change in x.
The two points between -4 and 0 on the x-axis as shown in the diagram attached are, (-4, 1) and (0, 3). It is also a linear graph.
Rate of change = (3 - 1)/(0 -(-4)) = 2/4 = 1/2
The graph that shows a rate of change is the linear graph attached below.
Learn more about the rate of change on:
https://brainly.com/question/25184007
#SPJ5
Evaluate a + 7b if a = 14 and b =12
Plug 14 in for a and 12 in for b like so...
14 + 7(12)
14 + 84
98
Hope this helped!
~Just a girl in love with Shawn Mendes
the cost of a service call to fix a washing machine can be expressed by the linear function y = 45x + 35, where y represents the total cost and x represents the number of hours it takes to fix the machine. what does the y-intercept represent?
The y-intercept is where it crosses the y-axis. That means the x-coordinate is zero there. So this point represents how much it cost before any hours are applied. This is also known as the initial cost.
Determine the height of each triangle. Round to the nearest foot.
a. 7 ft
c. 8 ft
b. 5 ft
d. 4ft
Which value is in the domain of f(x)?
Answer:
4
Step-by-step explanation:
[tex]f(x)=-2x+3, 0<x<=4[/tex]
Answer:
4
Step-by-step explanation:
The domain is the inputs (or the x values)
We start at -6 (but do not include it) and end at +4 (we include it)
-6 < x ≤4
The value that is included is 4
Can someone please help me out here ?
Answer:
4
Step-by-step explanation:
The median is the middle, since the amount of data is an even number we need to add up the third number and fourth number. These are 3 and 5 respectively. Adding these up gives up 8. Dividing this by 2 is 4.
If the variance of the ages of the people who attended a rock concert is 38, what is the standard deviation of the ages? Round your answer to two decimal places
Answer:
The standard deviation of the age is 6.16
Step-by-step explanation:
* Lets talk about the variance and the standard deviation
- The variance is the measure of how much values in a set of data are
likely to differ from the mean value of the same data
- The steps to find the variance are:
1- Find the mean of the data
2- Subtract the mean from each value and square the answer
3- Add all of these squared answer and divide the sum by the number
of the values
- The answer of the step 3 is The variance (σ²)
- The standard deviation (σ) is the square root of the variance
* Now lets solve the problem
∵ The variance of the ages of the people who attended a rock
concert is 38
∴ σ² = 38
∵ The standard deviation is the square root of the variance
∴ σ = √38 = 6.16
* The standard deviation of the age is 6.16
Answer:
[tex]\sigma=6.16[/tex]
Step-by-step explanation:
By definition, the variance V of a population is defined as:
[tex]V = \sigma^2[/tex]
Where [tex]\sigma[/tex] is the standard deviation
We know that [tex]V = 38[/tex], then we can solve the equation for the standard deviation [tex]\sigma[/tex]
[tex]38 = \sigma^2[/tex]
[tex]\sigma^2=38[/tex]
[tex]\sigma=\sqrt{38}[/tex]
[tex]\sigma=6.16[/tex]
Finally the standard deviation is: [tex]\sigma=6.16[/tex]
Write the expression 3x24 + 4x12 + 7 in quadratic form.
Answer:
3 m^2 + 4m +7
Step-by-step explanation:
3x^24 + 4x^12 + 7
Let m =x^12
m^2 = x^12 ^2 = x^24
Substitute this into the first equation
3 m^2 + 4m +7
Solve the inequality and graph its solution: x - 7>-20
A x>-13
-12
6
0
6
12
18
24
30
-30 -24 -18
B. x>-13
-6
0
6
12
18
24
30
-30 -24 -18 -12
cx<-27
6
0
6
12
18
24
30
-3024 -18 -12
X<-27
D.
+
+ +
--3026 -18
1
-12
6
0
6
12
18
24
30
The inequality x - 7 > -20 is solved by adding 7 to both sides, resulting in x > -13. The graph of this inequality has an open circle at -13 with shading to the right.
To solve the inequality x - 7 > -20, you want to isolate the variable x on one side. You can do this by adding 7 to both sides of the inequality:
x - 7 + 7 > -20 + 7
x > -13
So, the solution to the inequality is x > -13. To graph this solution on a number line, you would draw an open circle at -13 and shade to the right, indicating that x can be any value greater than -13 but not including -13 itself.
Find the area of an equilateral triangle (regular 3-gon) with the given measurement.
4-inch side
A = sq. in.
Using Heron's formula where s = 9 ...... and a = b = c = the side lengths .....we have......
A = √[s(s -a)^3] = √[4*3^3] = √[4*27] = √[4*9*3] = √[36*3) = 9√3 sq. in.
What is the solution to the equation
Answer:
x = -13
Step-by-step explanation:
Distribute:
8 - 6x + 10x - 15 = 20 - 5x
Combine like terms:
4x - 7 = 20 - 5x
Isolate Variable
-x = 13
-1(-x) = -1(13)
x = -13
Answer: [tex]x=3[/tex]
Step-by-step explanation:
You need to apply Distributive property on the left side of the equation:
[tex]2(4-3x)+5(2x-3)=20-5x\\\\8-6x+10x-15=20-5x[/tex]
Now you must add the like terms on the left side of the equation:
[tex]-7+4x=20-5x[/tex]
Add [tex]5x[/tex] to both sides:
[tex]-7+4x+5x=20-5x+5x\\\\-7+9x=20[/tex]
Add 7 to boht sides of the equation:
[tex]-7+9x+7=20+7\\\\9x=27[/tex]
And finally, divide both sides by 9:
[tex]\frac{9x}{9}=\frac{27}{9}\\\\x=3[/tex]
find the difference. 60 degrees-30 degrees, 50'-40', 40"-50"
Answer:
60 degrees-30 = 90
50'-40'= 10
40"-50"= 10
Please mark brainliest and have a great day!
Write an equation in point-slope form for the line through the given point that has the given slope (-2,-7);m=-3/2
For this case we have that the point-slope equation of a line is given by:
[tex](y-y_ {0}) = m (x-x_ {0})[/tex]
Where:
m: It's the slope
[tex](x_ {0}, y_ {0}):[/tex] It is a point
We have as data that:
[tex](x_ {0}, y_ {0}): (- 2, -7)\\m = - \frac {3} {2}[/tex]
We replace:
[tex](y - (- 7)) = - \frac {3} {2} (x - (- 2))\\(y + 7) = - \frac {3} {2} (x + 2)[/tex]
Answer:[tex](y + 7) = - \frac {3} {2} (x + 2)[/tex]
which of the numbers below are whole numbers A 0.328 B.678.79 C.159113 D.3809 E.757 F.0
Answer:
F
Step-by-step explanation:
F
zero
Anytime you have zero as a possible answer, you have to consider it carefully. Part of the whole number system is 0. They go up from there. No fraction is a whole number. No decimal is a whole number except those that are equal to a whole number.
The rest are all decimals so they are not whole numbers. Note I just noticed that the other numbers have periods after the choice. There are other whole numbers there if that is the case.
C D E and F are all whole numbers if that is a period after their choice letters.
How many ounces of trial mix are in a bag that weighs.908 kilograms?
Answer:
32028.8 ounces
Step-by-step explanation:
We are given that there are 908 kilograms of of trial mix are in a bag and we are to find the number of ounces of the same amout of mix in the bag.
For that, we will use the ratio method.
We know that, 1 kg = 35.274, so:
[tex] \frac { 1 k g }{908kg} =\frac{35.274 oz}{x}[/tex]
[tex]x=32028.8[/tex]
Therefore, there are 32028.8 ounces of mix in the bag.
Final answer:
To find the amount of trail mix in ounces from 0.908 kilograms, convert the weight to grams and then to ounces using the conversion of 1 oz = 28.35 g, resulting in approximately 32.012 ounces of trail mix.
Explanation:
To convert the weight of the trail mix from kilograms to ounces, we need to use the conversion factor: 1 oz is produced by a mass of 28.35 g. First, convert the kilograms to grams by multiplying by 1000, because there are 1000 grams in a kilogram. Then, once we have the weight in grams, we can convert grams to ounces using the provided conversion rate.
Here's the calculation step by step:
Convert kilograms to grams: 0.908 kg × 1000 = 908 grams.
Convert grams to ounces: 908 g ÷ 28.35 g/oz = 32.012 ounces (rounded to three decimal places).
Thus, a bag that weighs 0.908 kilograms contains approximately 32.012 ounces of trail mix.
what is the square root of 4/9?
please explain the steps.
Thank you!
Answer:
I just know it is 0.222222222222
Step-by-step explanation:
Answer:
± [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{\frac{4}{9} }[/tex]
= [tex]\frac{\sqrt{4} }{\sqrt{9} }[/tex] = ± [tex]\frac{2}{3}[/tex]
What are the solutions to the equation 4x2+3x=24-x
Answer:
x=2 x=-3
Step-by-step explanation:
4x2+3x=24-x
Subtract 24 from each side
4x^2 +3x -24 = 24-24 -x
4x^2 +3x -24 = -x
Add x to each side
4x^2 +3x+x -24 = -x+x
4x^2 +4x -24 = 0
Factor out a 4
4(x^2 +x -6) = 0
Divide by 4
x^2 +x -6 =0
Factor
What 2 numbers multiply to -6 and add to 1
-2*3 = -6
-2+3 =1
(x-2) (x+3) =0
Using the zero product property
x-2 =0 x+3 =0
x-2+2=0+2 x+3-3=0-3
x=2 x=-3
Answer:x=-3 , x = 2
Step-by-step explanation:
First move the expression ( 24-x) to the left.
This gives us 4x^2+3x+24-x.
Collect the like terms which gives us 4x^2+4x+24
4x^2+4x-24 = 0. Divide both sides by 4.
x^2 + x-6 = 0
Factorise the expression so you get (x+3)(x-2)=0
Solve the equations x+3 = 0 and x-2=0
The final solutions are x=-3 and x=2.
The equation of a linear function in point-slope form is y – y1 = m(x – x1). Harold correctly wrote the equation y = 3(x – 7) using a point and the slope. Which point did Harold use? When Harold wrote his equation, the point he used was (7, 3). When Harold wrote his equation, the point he used was (0, 7). When Harold wrote his equation, the point he used was (7, 0). When Harold wrote his equation, the point he used was (3, 7).
For this case we must find the point that Harold used to arrive at the following equation:
[tex]y = 3 (x-7)[/tex]
Starting from the fact that the equation of the point-slope form of a line is given by:
[tex](y-y_ {1}) = m (x-x_ {1})[/tex]
If we compare the standard equation with Harold's, we see that the slope of the line is [tex]m = 3.[/tex]
In addition, it is observed that [tex]x_ {1} = 7[/tex]and [tex]y_ {1} = 0.[/tex]
Then, the correct option is: Harold used the point (7,0)
ANswer:
When Harold wrote his equation, the point was used (7,0).
Find the LCM of each pair of numbers 8 and 9
Answer:
The LCM of 8 and 9 is 72.
Step-by-step explanation:
Please mark brainliest and have a great day!
The graph shows the weight of a jar (in grams) when it contains different numbers of pickles. When empty, the jar weighs 20 grams. What is the change in the weight of the jar for each pickle added? What is the slope of the line?
A) 2 grams; The slope is 2.
B) 2 grams; The slope is
1
2
.
C) 4 grams; The slope is 4.
D) 4 grams; The slope is
1
4
.
Answer: i think C
Step-by-step explanation:
4. A golf ball company called Great Drive is designing a new style of golf ball. The company uses rubber
for the core of the ball, and needs to determine what volume of rubber they need to use to fill each golf
ball. Assume the core of the ball is a sphere with a diameter of 1.68 inches. What's the volume of the
core of the ball? Round to the nearest hundredth of a cubic inch.
A. 2.48 in3
B. 2.99 in3
C. 2.21 in3
D. 1.65 in3
Final answer:
The volume of the core of the golf ball from Great Drive, with a diameter of 1.68 inches, is approximately 2.48 cubic inches. This is calculated using the formula for the volume of a sphere with the radius derived from the given diameter. The correct answer is 2.48 in³, which is option A.
Explanation:
The volume of a sphere is given by the formula V = (4/3) πr3, where π is pi (approximately 3.14159) and r is the sphere's radius. The diameter of the golf ball's core is given as 1.68 inches, so the radius is half of that, which is 0.84 inches. Plugging this into the formula gives us:
V = (4/3) π (0.84 inches)3 = (4/3) π (0.84 inches × 0.84 inches × 0.84 inches)
Doing the math, we find that:
V ≈ (4/3) π (0.592704 inches3) ≈ 2.48 in3
Therefore, the volume of the core of the ball rounded to the nearest hundredth is 2.48 cubic inches.
The correct answer is option A.