Answer:
x = 5
Step-by-step explanation:
x + 4 = 3(x - 2) ← distribute parenthesis by 3
x + 4 = 3x - 6 ( subtract 3x from both sides )
- 2x + 4 = - 6 ( subtract 4 from both sides )
- 2x = - 10 ( divide both sides by - 2 )
x = 5
Answer:
Solution of equation is 5Step-by-step explanation:
In the question we have given an equation that is x + 4 = 3 ( x - 2 ) . And we are asked to solve the question that means we have to find the value of x .
Solution : -
[tex] \longrightarrow \quad \: x + 4 = 3(x - 2)[/tex]
Step 1 : Solving parenthesis on right side :
[tex] \longrightarrow \quad \: x + 4 = 3x - 6[/tex]
Step 2 : Subtracting 4 on both sides :
[tex] \longrightarrow \quad \: x + \cancel{4} - \cancel{ 4 }= 3x - 6 - 4[/tex]
On further calculations we get :
[tex] \longrightarrow \quad \: x = 3x - 10[/tex]
Step 3 : Subtracting 3x on both sides :
[tex] \longrightarrow \quad \: x - 3x = \cancel{3x } - \cancel{3x}- 10[/tex]
On further calculations we get :
[tex]\longrightarrow \quad \: - 2x = - 10[/tex]
Step 4 : Dividing both sides by -2 :
[tex]\longrightarrow \quad \: \dfrac{ \cancel{ - 2}x}{ \cancel{ - 2} } = \cancel{\dfrac{ - 10}{ - 2} }[/tex]
On further calculations we get :
[tex]\longrightarrow \quad \: \red{\underline\red{\boxed{ \frak{ x = 5}}}}[/tex]
Therefore , value of x is 5 .Verifying : -
We are verifying our answer by substituting value of x in given equation. So ,
x + 4 = 3 ( x - 2 )5 + 4 = 3 ( 5 - 2 )9 = 3 ( 3 )9 = 9L.H.S = R.H.S Hence, Verified.Therefore, our answer is correct .
#Keep LearningWhat is the area of figure
There is no figure pic above
Step-by-step explanation:
PLS HELP! Select all the correct locations on the image. Select functions f and g such that the ratio of function f to function g is equal to function h.
The functions f(x), g(x) and h(x) are related as a result of composite functions
The values of the functions are f(x) = x³ - 5x² + 2x + 8 and g(x) = x² - x - 2
How to determine the functions f(x) and g(x)?From the question, we have the following equation
h(x) = f(x)/g(x)
This gives
f(x) = g(x) * h(x)
The function h(x) is given as:
h(x) = x - 4
So, we have:
f(x) = g(x) * (x - 4)
The function g(x) cannot be x³ - 3x² - 6x + 8 because the leading coefficients of function f(x) are 3 and 2
Next, we assume that:
g(x) = x² - x - 2
So, we have:
f(x) = (x² - x - 2) * (x - 4)
Expand
f(x) = (x³ - x² - 2x - 4x² + 4x + 8)
Evaluate like terms
f(x) = x³ - 5x² + 2x + 8
The above function exists in the given table.
Hence, the values of the functions are f(x) = x³ - 5x² + 2x + 8 and g(x) = x² - x - 2
Read more about composite functions at:
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Can someone help me please!!
Answer:
D
Step-by-step explanation:
[tex](40 - 10)x - 12000 \geqslant 980[/tex]
[tex]30x - 12000 \geqslant 980[/tex]
Yoko deposited $4000 into an account with 5.8% interest, compounded semiannually. Assuming that no withdrawals are made, how much will she have in the account after 8 years?
Do not round any intermediate computations, and round your answer to the nearest cent.
If no withdrawls were made, the total amount of money Yoko would have in her account in 8 years is $6,319.84.
What is the value of the account after 8 years?When an account is compounded semiannually, it means both the amount deposited and the interest accrued increases in value twice yearly.
The formula that can be used to determine the value of the account in 8 years is:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate = 5.8/2 = 2.9%m = number of compounding = 2N = number of years$4000 x (1.029)^(2x8) = $6,319.84
To learn more about future value, please check: https://brainly.com/question/18760477
What kind of transformation converts the graph of f(x)=2x–2 into the graph of g(x)=2x+2?
Answer:
A transformation of (0,4), in order words, adding 4 to all your y-values.
Step-by-step explanation:
If you were to plot f(x) and g(x), you'd notice that all the y-values have been moved up by 4. To prove this to yourself, lets take the y-intercept.
Let x = 0, then g(0) = 2 and f(0) = -2, as you can see the y-value of the intersect has been shifted upwards by 4. Therefore, it can be said that f(x) has been shifted by (0,4), so f(x) +4 = g(x).
if the vertex of a quadratic functions is on the x-axis, what must be true about the number of x-intercepts? How do you know?
Answer:
x-intercepts are points at which the curve intercepts the x-axis, so when y = 0.
If the vertex of a quadratic function is on the x-axis, there will be only one x-intercept since the parabola will intersect the x-axis at one point only.
If the vertex of the function touches the x-axis, the zero at this point will have a multiplicity of two. For example, if the vertex is at (4, 0), and therefore the zero is at x = 4, then the function will be [tex]y=a(x - 4)^2[/tex] (where a is some constant).
Vertex form of parabola
y=a(x-h)²+kWhere
vertex=(h,k)So
if vertex is on x axis k is 0 and the parabola has only 1 x intercept
The form will be
y=a(x-h)²2/3(x-6)=6 solve for x
Answer:
18
Step-by-step explanation:
2/3 = 66%
66% of 18 =
12-6=
6
When a business seeks a certain profit, it uses a factor to adjust its price. The factor is called a ____.
A.credit discount
B.Inventory adjustment
C. markup
D.quantity discount
Answer:
a
Step-by-step explanation: bc i just did it
Which expression is equivalent to
[tex]2 \sqrt[3]{ {x}^{2} } - \sqrt{16x} [/tex]
if x > 0?
[tex]2\sqrt[3]{x^2}\cdot \sqrt{16x}\\\\=2\sqrt[3]{x^2} \cdot 4\sqrt x\\\\=8x^{\tfrac 23} \cdot x^{\tfrac 12}\\\\=8\cdot x^{\tfrac 23 + \tfrac 12}\\\\=8\cdot x^{\tfrac 76}\\\\=8\sqrt[6]{x^7}\\\\=8\sqrt[6]{x^6 \cdot x}\\\\=8x\sqrt[6]{x}[/tex]
[tex]\text{Hence the answer is A}[/tex]
Answer:
[tex] \sf \: Option \: A \: \sf \ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8x \sqrt[6]{ {x}}[/tex]
Step-by-step explanation:
[tex] \sf \: if \: x > 0 \\ \sf \: 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 2 \sqrt[3]{ {x}^{2} } \cdot \: 4 \sqrt{x} \\ \sf \ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 {x}^{ \frac{2}{3} } \cdot \: {x}^{ \frac{1}{2} } \\ \sf \ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} =8 {x}^{ \frac{2}{3} + \frac{1}{2} } \\ \sf\ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 {x}^{ \frac{4 + 3}{3 \times 2} } \\ \sf\ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 {x}^{ \frac{7}{6} } \\ \sf 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 \sqrt[6]{ {x}^{7} } \\ \sf\ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 \sqrt[6]{ {x}^{6} + x } \\ \sf \ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8x \sqrt[6]{ {x}}[/tex]
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my bro needs help again whyy
Answer:
0.42
Step-by-step explanation:
when your multiplying decimals that small, it usually doesnt go into the whole number range
Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
Answer:
The slope should be -2
You should go down 2 and go over 1.
Slope Intercept Form: y= -2x+3
Step-by-step explanation:
First, you need to identify the slope: (meaning whether it is a postive or negative.)
In this case, You have a negative slope.
This means instead of rising you're decreasing down.
When you "run" or move horizontally you MUST move right even if it's a negative slope.
Now, you need to identify your Y-Intercept.
Your Y-Intercept should be (0,3)
Next, you have to find your slope:
In order to find your slope, you need to find where the line is crossing the coordinate.
Start at (-1,5) and go down and over to (0,3)
Your answer should be that you went down 2 and over 1.
The slope can't be 2 because if it were to be 2, then that would be a positive slope which isn't our occasion.
The slope is -2.
In Slope Intercept Form: y= -2x+3
In ΔHIJ, h = 38 inches, i = 45 inches and j=61 inches. Find the measure of ∠H to the nearest degree.
Answer:
h=97
Step-by-step explanation:
38+45=83
180-83=97
find the measure of angle WYU
Check the picture below.
HELP ASAP
6 divided by 200+ 40=
a possible verbal description for this function relation y=5x+10
Answer:
See below.
Step-by-step explanation:
The rate of a taxi is a $5 per mile and there is a service charge of $10. Represent the total cost, y, as a function of number of miles, x.
factor the following using the difference of squares method
a) x^2 - 16 b) 9y^2 - 25
Answer:
a)
[tex] {x}^{2} - 16 \\ = {x}^{2} - {4}^{2} \\ = (x + 4)(x - 4)[/tex]
b)
[tex] {9y}^{2} - 25 \\ = {(3y)}^{2} - {5}^{2} \\ = (3y + 5)(3y - 5) [/tex]
here is the answer hope that will help you
Fran is putting up a tent. Each triangular end of the tent has sides of length 6 ft. What is the approximate height of the tent, rounded
Answer:
5 ft
Step-by-step explanation:
The height will divide the base of the triangle in two parts of 3 ft, making two smaller right triangles.
Then, to find the height, we can use the Pythagoras' theorem in one of these triangles:
6^2 = 3^2 + height^2
36 = 9 - height^2
height^2 = 27
height = 5.19 ft
Rounding to the nearest foot, we have height = 5 ft
Answer:
5.20 ft (nearest hundredth)
Step-by-step explanation:
[tex]\textsf{Height of an equilateral triangle}=\dfrac12(\sqrt{3}x)\quad \textsf{(where}\:x\:\textsf{is the side length)}[/tex]
Given:
[tex]x[/tex] = 6 ft[tex]\begin{aligned}\implies \textsf{Height} & =\dfrac12(6\sqrt{3})\\ & =3\sqrt{3}\\ & =5.20\: \sf ft \: \textsf{(nearest hundredth)}\end{aligned}[/tex]
Hello! Pls help me! I dont get this!
Jaleel did the sides by eachother.
Since it's 3d, it also wants them/us to count the sides that are not shown. He did one side by the length and then another by the height, then doubled it. Finally he added it all together
LOCKS IN 15 MIN! WILL GIVE BRAINLEST! In a right triangle, the side opposite angle φ has a length of 29.0 meters, the side adjacent to angle φ has a length of 49.5 meters, and the hypotenuse has a length of 57.4 meters. What is the value of cot(φ)?
1.979
1.707
0.586
1.160
Answer:
option (b) 1.707
Step-by-step explanation:
1.707 is your required answer
Factor the polynomial by its greatest common monomial factor.
20
y
6
−
15
y
4
+
40
y
2
=
20y
6
−15y
4
+40y
2
Answer:
5y^2(4y^4 - 3y^2 +8
Step-by-step explanation:
20y^6 - 15y^4 + 40y^2
What is the inverse of the function below?
f(x) = x/3 -2
O A. f(x) = 3(x + 2)
O B. f(x) = 3(x - 2)
O c. f'(X) = 2(x - 3)
O D. f '(x) = 2(x + 3)
Answer:
A
Step-by-step explanation:
let f(x) = y and rearrange making x the subject
y = [tex]\frac{x}{3}[/tex] - 2 ( add 2 to both sides )
y + 2 = [tex]\frac{x}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
3(y + 2) = x
change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then inverse function is
[tex]f^{-1}[/tex] (x) = 3(x + 2)
The two figures have a ratio of similarity of 3:4. If the area of the larger is 100 square units, what is the area of the smaller?
Answer:
75 square units
Step-by-step explanation:
set up a proportion first.
[tex] \frac{3}{4} = \frac{x}{100} [/tex]
(x is on top because it asks for the smaller area, so it is on the same side of the 3)
after, cross multiply to find x
4x = 300
divide by 4
x= 75
Francesca wants to buy a package of balloons. She has $35.42 and each package costs $8.36. About how many packages of balloons can Francesca buy? (Round to the nearest dollar.)
Answer:
Francesca can buy 4 packages of balloons for $34.
Step-by-step explanation:
35.42 x 100 = 3542 ÷2 = 1771
8.36 x 100 = 836 ÷2 = 418
1771 ÷ 418 = 4.236842105263158 (We will round it to 4.23)
If we round it to 5, it will exceed Francesca's budget, so we will make 4.23 4.
4 x 8.36 = $33.44
We cannot cut the 44 cents so we will round it to $34.
Hope this helped!
triangle that is reflected, rotated, then translated will result with the pre-image and the image being two congruent triangles? true or false
Yes the pre image and image are congruent inspite of reflection, rotation or translation
This happens because they are rotated or translated according to a constant factor called scale factor
k=y/xAlissa would like to make a deposit into her savings account. she filled out a deposit ticket and handed it to the teller at her bank. the teller apologizes to alissa and explains that she cannot accept the deposit ticket in its current form. determine what, if anything, alissa will have to change in order for her deposit ticket to be accepted. a deposit ticket. the amount deposited is 899 dollars and 86 cents and she is taking 260 dollars out as cash. the total on the slip is 629 dollars and 86 cents. a. the sub total is calculated incorrectly b. alissa forgot to sign the deposit ticket for less cash back c. the total is calculated incorrectly d. alissa forgot to date the deposit ticket please select the best answer from the choices provided a b c d
Alisa should either fill out a new ticket or write the correct amount and append her signature beside it.
What is a deposit ticket?A deposit ticket is a little paper where you are required to fill in the details of the deposit that you seek to make into your savings account. All information in the ticket ought to be filled accurately.
The teller may have declined to receive the ticket due to incorrect total amount filled on the ticket. Alisa should either fill out a new ticket or write the correct amount and append her signature beside it.
Learn more about savings account:
brainly.com/question/1446753
Answer:
a. the subtotal is calculated incorrectly
Step-by-step explanation:
I'm good at math ;)
A professor grades students on three tests, four quizzes, and a final examination. Each test counts as two quizzes and
the final examination counts as two tests. Sara has test scores of 65, 62, and 60. Sara's quiz scores are 61, 96, 80, and
89. Her final examination score is 65. Use the weighted mean formula to find Mara's average for the course. (Round
your answer to one decimal place. )
Using the weighed mean formula, it is found that Mara's average for the course was of 68.6.
What is the weighed mean?The weighed mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.
In this problem, the weights are as follows:
A quiz has a weight of 1.A test has a weight of 2.The final examination has a weight of 4.Hence, her weighed mean is given as follows:
[tex]M = \frac{2(65 + 62 + 60) + (61 + 96 + 80 + 89) + 4(65)}{6 + 4 + 4} = 68.6[/tex]
Mara's average for the course was of 68.6.
More can be learned about the weighed mean formula at https://brainly.com/question/24398353
Madison has a fish tank that is 12.8 inches wide, 36 inches long and 24`\frac{1}{2}`inches deep. The manager at the fish shop suggested that she fill the tank half way up with water because the fish will still have plenty of room to swim and they will not jump out. If Madison follows the manager's suggestion, how much water will it take to fill the tank half way up? Please hurry
Answer:
Step-by-step explanation:
First Multiply 12.8, 36, and 24 1/2 or 12.8 x 36 x 24.5 which equals 11289.6, and divide it by 2 which gives you 5644.8 inches of water.
At a local department store, slacks typically cost $45. However, due to a special, the slacks are reduced to $18. What. percent of the original price has the slacks been reduced to? Round your answer to the nearest whole number if necessary.
Answer:
40 Percent decrease
Step-by-step explanation:
We can use a simple formula to solve this problem.
Starting price * X/100 = Ending Price
We plug in our values to solve for X
45 * x/100 = 18
You simplify the equation and you should get X as 40, meaning there is a 40 Percent decrease in price.
what is the volume of the rectangular prism?
Answer:
4 inches x 8 inches x 3 inches = 96 inches³
Which table shows a function that is decreasing over the interval (−2, 0)? A 2-column table with 4 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 0, negative 5, 0, 5. A 2-column table with 4 rows. The first column is labeled x with entries negative 2, 0, 2, 4. The second column is labeled f of x with entries negative 15, negative 5, negative 20, negative 30 A 2-column table with 4 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0. The second column is labeled f of x with entries 2, 0, negative 10, negative 24. table shows a function that is decreasing over the interval (−2, 0)? A 2-column table with 4 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 0, negative 5, 0, 5. A 2-column table with 4 rows. The first column is labeled x with entries negative 2, 0, 2, 4. The second column is labeled f of x with entries negative 15, negative 5, negative 20, negative 30 A 2-column table with 4 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0. The second column is labeled f of x with entries 2, 0, negative 10, negative 24.
Answer: A 2-column table with 4 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0. The second column is labeled f of x with entries 2, 0, negative 10, negative 24.
Step-by-step explanation:
The table shown in the attachment has the function that is decreasing in the interval of interest."Decreasing" means that for increasing x-values, each f(x) value is less than the one before.