Answer:
x = -8
Step-by-step explanation:
We are given the following expression which we are to solve for [tex]x[/tex]:
[tex] 2 7 ^ x = 9 ^ { x - 4 } [/tex]
For this expression, we will make the bases same on both sides of the equation and then equate the exponents equal to each other.
[tex](3^3)^x = (3^2)^{x-4}[/tex]
Multiplying the exponents and equating them to get:
[tex] 3 x = 2 ( x - 4 ) [/tex]
[tex] 3 x = 2 x - 8 [/tex]
[tex] 3 x - 2 x = - 8 [/tex]
x = -8
For this case we must solve the following equation:
[tex]27 ^ x = 9 ^ {x-4}[/tex]
We rewrite:
[tex]27 = 3 * 3 * 3 = 3 ^ 3\\9 = 3 * 3 = 3 ^ 2[/tex]
So:
[tex]3^{3(x)}=3^{2(x-4)}[/tex]
Since the bases are the same, the two expressions are only equal if the exponents are also equal. So, we have:
[tex]3 (x) = 2 (x-4)\\3x = 2x-8[/tex]
Subtracting 2x on both sides:
[tex]3x-2x = -8\\x = -8[/tex]
Answer:
[tex]x = -8[/tex]
reduce the fraction: x-y/x^2-1 times x-1/x^2-y^2
Answer:
l
Step-by-step explanation:
Answer: [tex]\frac{1}{(x+1)(x+y)}[/tex]
Step-by-step explanation:
Given the expression:
[tex](\frac{x-y}{x^2-1})(\frac{x-1}{x^2-y^2})[/tex]
The first step is to multiply the numerator of the first fraction by the numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction. Then:
[tex]=\frac{(x-y)(x-1)}{(x^2-1)(x^2-y^2)}[/tex]
Since [tex](x^2-1)[/tex] and [tex](x^2-y^2)[/tex] are perfect squares, you can factorize them in the form:
[tex]a^2-b^2=(a+b)(a-b)[/tex]
Then:
[tex]=\frac{(x-y)(x-1)}{(x+1)(x-1)(x+y)(x-y)}[/tex]
Simplifying, you get:
[tex]=\frac{1}{(x+1)(x+y)}[/tex]
If 4x = 12, then 12x= what
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.
Determine the height of each triangle. Round to the nearest foot.
a. 7 ft
c. 8 ft
b. 5 ft
d. 4ft
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]
For which intervals is the function positive?
Select each correct answer
(−1.5,−1)
(4,∞)
(−2, 0)
(2,2.5)
(−∞,−2)
(0,4)
Answer: -2,0 0,4
Step-by-step explanation:
let me know if you need help still UwU
Answer:
The function is positive from (-∞,-2) and (0,4).
Explanation:
To find the intervals where the function is positive, note where the line of the graph is above the x-axis.
As the functions goes toward negative infinity, the arrow of the graph is pointed up, so the function is positive starting from -∞ until x = -2, where it becomes negative.
The function once again goes above the x-axis at x = 0 and stays positive until x = 4. After this point, the function decreases forever, so (-∞,-2) and (0,4) are the only intervals where the function is positive.
write y=x^2-2x-3 in vertex form
Answer: [tex]y=(x-1)^2-4[/tex]
Step-by-step explanation:
The vertex form of the equation of a parabola is:
[tex]y=a(x-h)^2+k[/tex]
Where (h,k) is the vertex.
To obtain this form, we need to complete the square:
Move the 3 to the other side of the equation:
[tex]y+3=x^2-2x[/tex]
Add this value to both sides of the equation: [tex](\frac{-2}{2})^2=1[/tex]
[tex]y+3+1=x^2-2x+1[/tex]
[tex]y+4=x^2-2x+1[/tex]
Then, rewriting:
[tex]y+4=(x-1)^2[/tex]
Finally, we must solve for "y", getting the equation of the parabola in vertex form:
[tex]y=(x-1)^2-4[/tex]
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!
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
The vertex of the parabola below is at the point (3,2) and the point (4,6) is on the parabola. What is the equation of the parabola?
Answer:
[tex]\large\boxed{y=4(x-3)^2+2\ \bold{vertex\ form}}\\\boxed{y=4x^2-24x+38\ \bold{standard\ form}}[/tex]
Step-by-step explanation:
The vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - vertex
We have the vertex at (3, 2) → h = 3 and k = 2.
Substitute:
[tex]y=a(x-3)^2+2[/tex]
The point (4, 6) is on athe parabola. Put the coordinates of this point to the equation:
[tex]6=a(4-3)^2+2[/tex] subtract 2 from both sides
[tex]6-2=a(1)^2+2-2[/tex]
[tex]4=a\to a=4[/tex]
Finally:
[tex]y=4(x-3)^2+2[/tex] vertex form
use (a - b)² = a² - 2ab + b²
[tex]y=4(x^2-6x+9)+2[/tex] use the distributive property
[tex]y=4x^2-24x+36+2[/tex]
[tex]y=4x^2-24x+38[/tex] standard form
Answer:
y=4(x-3)^2+2
Step-by-step explanation:
Hopefully this helps :)
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.
~
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.
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.
-2x-2=14 ....how to you solve this equation... plz include the process
Answer:
x = -8
Step-by-step explanation:
-2x-2=14
We want to solve for x
Add 2 to each side
-2x-2+2 = 14+2
-2x=16
Divide each side by -2
-2x/-2 =16/-2
x = -8
Which of the following is the correct factorization of the polynomial below? x^3-12
Answer:
This question is not complete.
Step-by-step explanation:
Hi, The question is not complete but i think the question was this:
Which of the following is the correct factorization of the polynomial below?
x^3 - 12
A. (x + 3)(x - 4)
B. (x - 3)(x + 4)
C. (x + 3)(x^2 - 4x + 4)
D. The polynomial is irreducible.
in which case, the answer will be this:
D as this polynomial can't be reduced
Answer:
x³ - 12 = (x - ∛12)(x² + x∛12 + 12²/³)
Step-by-step explanation:
Question is incomplete (options are missing);
However, I'll factorize the polynomial using identity
Given
x³ - 12
This can be factorized using the following identity
a³ - b³ = (a - b)(a² + ab + b²)
By comparison,
a³ = x³ and b³ = 12
a = x and b = ∛12
Replace a with x and b with ∛12 in the above equation
a³ - b³ = (a - b)(a² + ab + b²) becomes
x³ - 12 = (x - ∛12)(x² + x∛12 + ∛12²)
x³ - 12 = (x - ∛12)(x² + x∛12 + 12²/³)
This is as far as it can be factorized
So, the factorization of x³ - 12 using identity is (x - ∛12)(x² + x∛12 + 12²/³)
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%
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.
You and your friends decide to camp for one night. Look at the diagram of your tent below. It is drawn on 1 cm squared paper. The scale is 1 cm : 0.25 m
What are the dimensions of the tent’s porch area in metres?
m multiplied by
m
The dimension of a sleeping bag and ground mat is 2 m x 1 m. Each sleeping bag and ground mat must be 0.25 metres away from the edge of the tent.
How many people can sleep in the tent?
people
Answer:
1.Area of Porch =2.5m²
2.Number of people =3 people
Step-by-step explanation:
The porch area from the diagram has a dimension of 4 units by 10 units
One units =1cm
Thus the porch is drawn with dimensions of 4cm by 10 cm
Taking length is 10 cm and width as 4 cm, convert these dimensions according to the scale.
The scale is 1cm=0.25m
The width will be= 0.25×4=1 m
The length will be=0.25×10= 2.5m
Area of the porch is given by the formula;
length×width because its has a shape of a rectangle
Area of porch will be
=1m ×2.5m =2.5m²
2.
Find the dimensions of the tent
14 units by 10 units
Applying the scale on the dimensions by multiplying by 0.25
14×0.25=3.5m
10×0.25=2.5m
Width=2.5m
length=3.5m
Subtract the edge distance on both the length and width
Length will be=3.5-(0.25×2)=3.0m
Width will be=2.5-(0.25×2)=2.0m
Find the area remaining to be covered by the people while sleeping
=3.0×2.0=6m²
Area covered by sleeping bag and a ground mat
2m×1m=2m²
Number of people that can sleep in the tent
6m²÷2m²=3 people
Answer: Area of porch in metres [tex]= 2.5 m^{2}[/tex]
No. of people that can sleep in the tent = 0 (according to the given conditions)
Step-by-step explanation:
In the given figure we have the scale of 1 cm : 0.25 m which denotes that we have 0.25 m length in actual for every 1 cm on the figure. Also, each square in the figure measures 1 cm on each side.
From the fig. the dimensions of tent porch area are:
Length = 10 cm = [tex]10 \times 0.25[/tex]
[tex]= 2.5 m[/tex] on ground
Breadth= 4 cm = [tex]4 \times 0.25[/tex]
[tex]= 1 m[/tex] on ground
∴ Area of porch in metres = [tex]1\times 2.5[/tex]
Area of porch in metres [tex]= 2.5 m^{2}[/tex]
From the attached image it is visible that we cannot place any mat and sleeping bag of the given dimensions inside the tent satisfying the given condition of keeping the ground mat 0.25 metres away from the edge of the tent.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
What is the length of the unknown leg in the right triangle ?
Answer: [tex]\sqrt{32}\text{ mi}[/tex]
Step-by-step explanation:
The Pythagoras theorem of right triangle says that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
From the given figure , the hypotenuse of the right triangle = [tex]\sqrt{113}\text{ mi}[/tex]
Then According to Pythagoras theorem , we have
[tex](\sqrt{113})^2=x^2+(9)^2\\\\\Rightarrow\ x^2=113-81\\\\\Rightarrow\ x^2=32\\\\\Rightarrow\ x=\sqrt{32}\text{ mi}[/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
Help needed! Due by 6/22/19
[tex]y=\dfrac{k}{x}[/tex]
1.
[tex]12=\dfrac{k}{13}\\\\k=156[/tex]
2.
[tex]y=\dfrac{156}{x}[/tex]
3.
[tex]y=\dfrac{156}{44}=\dfrac{39}{11}[/tex]
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:
A company uses two vans to transport
workers from a free parking lot to the
workplace between 7:00 and 9:00 a.m.
One van has 14 more seats than the
other. The smaller van makes two trips
every morning while the larger one
makes only one trip. The two vans can
transport 65 people, maximum.How many seats does the larger van have
Answer:
31 seats
Step-by-step explanation:
Let x be the smaller van, and y be the larger one.
We know that y = x + 14
We also know that 2x + y = 65
If we replace y by its value in the second equation we have:
2x + (x + 14) = 65, then we solve
2x + x + 14 = 65
3x + 14 = 65
3x = 51
x = 17
We now know the smaller van has 17 seats.
To find how many seats are in the big one, we take the first equation:
y = x + 14
y = 17 + 14
y = 31
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!
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).
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 help me please
Answer:
A and B are the solutions....
Step-by-step explanation:
7 and 12 are smaller than 17.
Answer:
A. [tex]x=7[/tex]
B. [tex]x=12[/tex]
Step-by-step explanation:
Check each option individually.
A. [tex]17>7[/tex] is true, so it is a correct choice.
B. [tex]17>12[/tex] is true, so it is a correct choice.
C. [tex]17>17[/tex] is false, so it is an incorrect choice.
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]
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.