Answer:
Let's solve the equation \( x - 1 = 5x + 2 \) to find the solutions:
1. **Subtract \(5x\) from both sides**:
\[
x - 5x - 1 = 2
\]
2. **Combine like terms**:
\[
-4x - 1 = 2
\]
3. **Add 1 to both sides**:
\[
-4x = 3
\]
4. **Divide both sides by -4**:
\[
x = -\frac{3}{4}
\]
So, the solution to the equation is \( x = -\frac{3}{4} \).
Now, let's check which of the options are solutions:
A. \( x \): Yes, \( x = -\frac{3}{4} \) is a solution.
B. \( x = \): No, this is not a valid format for a solution.
C. \( x = 2 \): No, \( x = -\frac{3}{4} \neq 2 \).
D. \( x - \): No, this is not a valid format for a solution.
Therefore, the correct answer is **A. \( x \)**.
The correct options are [tex]\frac{-3}{4}[/tex].
To find the solutions to the equation [tex]\( x - 1 = 5x + 2 \)[/tex], we first need to solve for [tex]\( x \)[/tex]. Let's do that step by step:
Start with the given equation:
[tex]\[ x - 1 = 5x + 2 \][/tex]
Move all terms involving [tex]\( x \)[/tex] to one side of the equation and constants to the other side. To do this, subtract [tex]\( x \)[/tex] from both sides and subtract [tex]\( 2 \)[/tex] from both sides:
[tex]\[ x - 1 - x - 2 = 5x + 2 - x - 2 \][/tex]
[tex]\[ -1 - 2 = 4x \][/tex]
[tex]\[ -3 = 4x \][/tex]
Now, divide both sides by [tex]\( 4 \)[/tex] to isolate [tex]\( x \)[/tex]:
[tex]\[ \frac{-3}{4} = \frac{4x}{4} \][/tex]
[tex]\[ -\frac{3}{4} = x \][/tex]
(a) Find the GCF of 18 and 8
(b) use the GCF to factor 18-8
18 - 8 = blank x (blank - blank)
The Greatest Common Factor (GCF) of 18 and 8 is 2. Using this GCF, 18 - 8 can be factored as 2 × (9 - 4).
(a) To find the GCF (Greatest Common Factor), we need to determine the largest number that divides both 18 and 8 without leaving a remainder.
Prime factors of 18: 2 × 3 × 3
Prime factors of 8: 2 × 2 × 2
The only common prime factor is 2.
So, the GCF of 18 and 8 is 2.
(b) We know that 18 - 8 = 10. To factor this expression using the GCF, we rewrite 10 as a product involving the GCF.
Factor out the GCF (2) from 18 - 8:
10 = 2 × (9 - 4)
So, 18 - 8 = 2 × (9 - 4).
Which fraction has the greatest value 1/3 2/3 2/9 2/9
Answer:
2/3
Step-by-step explanation:
Sarah is taking a test. The test is designed to produce an overall mean score of 85 with a standard deviation of 5 for all test takers.
Suppose Sarah scored a 90 on the test. Given that the data is approximately normal, standardize the test score and find the area
under the normal curve below the standardized test score
A.
The area below the standardized test score is 0.504
B.
The area below the standardized test score is 0.1587
C.
The area below the standardized test score is 1
D.
The area below the standardized test score is 0.8413
Answer:
Option D)
The area below the standardized test score is 0.8413
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 85
Standard Deviation, σ = 5
We are given that the distribution of score is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(score is below 90)
[tex]P( x < 90) = P( z < \displaystyle\frac{90 - 85}{5}) = P(z < 1)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 90) =0.8413 = 84.13\%[/tex]
Thus, the correct answer is
Option D)
The area below the standardized test score is 0.8413
Please help me with the following question.
I am pretty sure x is 9 because if you divide 14 by 2 you get 7. 18 divided by 2 is 9.
Answer:
x=9
Step-by-step explanation:
the word similar means the same shape but different sizes. That means that you can think of this problem as ratios. The ratio for the first triangle would be 14:14:18. Since the second ones ratio is 7:7:x we know that the seven was found by dividing 14 by two so we do that with the rest of the of the number to find x you divide 18 by two and get 9. So x=9.
What is the factor pair for the multiplication sentence below?
11 x 9 = 99
A. 9,99
B. 11.99
c. 11,9
In a company, 65% of the workers are men. If 1,155 women work for the company, how many workers are there in all?
Answer:
1,715
Step-by-step explanation:
100-65=35
x*(.65)=1,115
1,715
y=−7x+8 y=−7x−8 Choose 1 answer: Choose 1 answer: (Choice A) A Exactly one solution (Choice B) B No solutions (Choice C) C Infinitely many solutions
Answer:
I THINK ITS A ;-;
Step-by-step explanation:
Answer:
no solution
Step-by-step explanation:
the ordered pair is not a solution to the equation
A landscaper planted 10 cattails by a new pond. The number of cattails double each month over a period of time. Write a function f(x) to model the number of cattails in the pond after x months. f(x)=?
Answer:
[tex]\large \boxed{f(x) = 10(2)^{ x}}[/tex]
Step-by-step explanation:
Write a table giving the number of cattails for the first few months
[tex]\begin{array}{lr}\mathbf{x} & \mathbf{f(x)}\qquad \qquad\quad \\0 & 10 = 2^{0}(10) = 10(2)^{0}\\1 & 2(10) = 2^{1}(10)= 10(2)^{1} \\2 & 2\times2(10) = 2^{2}(10)= 10(2)^{2} \\3 & 2\times 2^{2}(10) = 2^{3}(10)= 10(2)^{3}\\4 & 2\times 2^{3}(10) = 2^{4}(10)= 10(2)^{4}\\\end{array}\\\text{The pattern appears to be $\large \boxed{\mathbf{f(x) = 10(2)^{\mathbf{x}}}}$}[/tex]
Hey please help with this problem I cannot get passed is Thank you.
Answer:
40
Step-by-step explanation:
Because these angles are the same, we can make an equation, 5x-5=3x+13.
2x - 18 = 2 • (x - 9)
Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solve : x-9 = 0
Add 9 to both sides of the equation :
x = 9
Replace x with 9 in this equation, 3(9) + 13
27+13
=40
Please help me ASAP i give brainliests and thanks :)
Answer:
Positive
Step-by-step explanation:
Since there are two x-intercepts, -2 and 2, there is a positive discriminant. If the parabola was below the x axis and opened downwards, the discriminant would be negative.
Answer:
positive
Step-by-step explanation:
Use the table to work out the values of
a
,
b
,
c
, and
d
.
x
y
=
x
2
+
2
x
−
4
−
3
−
1
−
2
a
−
1
b
0
−
4
1
−
1
2
c
3
d
a
=
b
=
c
=
d
=
By substituting the given x-values from the table into the equation y = x² + 2x - 4, we found that a=-4, b=-5, c=4, and d=11.
Explanation:The values of a, b, c, and d can be found by substituting the given x-values from the table into the formula y = x2 + 2x - 4.
For a, place -2 in the equation so we get y = (-2)2 + 2*(-2) - 4 = 4 - 4 - 4 = -4.
For b, place -1 in the equation, and it results y = (-1)2 + 2*(-1) - 4 = 1 - 2 - 4 = -5.
The third value, c, is computed by substituting 2 for x to obtain y = (2)2 + 2*2 - 4 = 4 + 4 - 4 = 4.
Lastly, for d, the y-value when x is equal to 3 is y = (3)2 + 2*3 - 4 = 9 + 6 - 4 = 11.
So, the solutions are a=-4, b=-5, c=4, and d=11.
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find the product d^j•d^k
Answer:
d^(j+k)
Step-by-step explanation:
d^j * d^k
We know that a^b * a^c = a^(b+c)
d^(j+k)
Kenny and Kylee's music players have the same capacity for music. Kenny's music player is full with 320 songs. His songs have an average length of four minutes. Kylee has fewer songs, but the average length of her songs is five minutes. Assuming both music players are at full capacity, how many songs does Kylee have?
224
200
128
256
Given that both players have the same capacity, we first calculate the total time in minutes for Kenny's music player by multiplying the number of Kenny's songs (320) by the average length per song (4 minutes). The result is 1280 minutes. We then take this number and divide by the average length of Kylee's songs (5 minutes) to find that Kylee's music player holds 256 songs.
Explanation:In this problem, we are given that Kenny and Kylee's music players have the same capacity, but Kylee's songs are longer on average. We are asked to find out how many songs Kylee has on her player assuming it is at full capacity. To do this correctly, we first need to understand that we're dealing with an issue of equal music player capacities, but the time a song occupies on each player is different.
Let's calculate the total capacity of the music player in minutes, we multiply the number of Kenny's songs (320) by the average length of each song (4 minutes), giving us 1280 minutes.
Because both players have the same capacity, Kylee's player can also hold 1280 minutes of music. However, since Kylee's songs are longer on average (5 minutes each), she will have fewer songs on her player. So, dividing the total capacity in minutes (1280) by the length of Kylee's songs (5 minutes) gives us 256 songs. That is the number of songs on Kylee's music player.
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Find the circumference of the circle.r=9in
56.52 inches
14.13 inches
63.59 inches
254.34 inches
28.26 inches
Answer:56.52
Step-by-step explanation: I just did it
What number would you add to the equation below to complete the square?
x2 + 5x = 0
A. 25/4
B. 4
C. 5/2
D. 25
Answer:
A. 25/4
Step-by-step explanation:
[tex](5/2)^{2}[/tex] = 25/4
In a scale drawing, the height of a tree is 3 inches. In real life, the height of the tree is 6 feet. What is the scale factor?
A. 1/24
B. 24
C. 3 in : 6 ft
D. 6 in : 3 ft
Answer:
The answer is A 1/24
How do you graph the equation f(x)=2•3x
Answer:
Step-by-step explanation:
slope=6
y-int=0
just plot this on a graph
Gavin is starting a running plan to train for a race. In the first week of his running plan, Gavin will run 5 miles. The plan calls for Gavin to increase his weekly milage by 3.5 miles every week. If Gavin sticks to the plan, how many miles would he be expected to run during his 11th week of the training plan? Round to the nearest tenth (if necessary).
Step-by-step explanation:
In the first week of his running plan,the number of miles covered = 5 miles
Weekly mileage will increase by 3.5 miles every week.
At the end of second week, the number of miles covered = 5 + 3.5 = 8.5
At the end of third week, the number of miles covered = 8.5 + 3.5 = 12
The series is 5, 8.5, 12, ...
Consider this as an AP, where a = 5, d = 3.5
By formula,
[tex]a_{n} = a + (n-1)d[/tex]
Substituting the values in the above equation, we get
[tex]a_{11} = 5 + (10-1) 3.5[/tex]
= 5 +(9)3.5
= 5 + 31.5
=36.5 miles.
Gavin would be expected to run during 36.5 miles during his 11th week of the training plan
Suppose ABCD is a rhombus such that the angle bisector of ∠ABD meets
AD at point K. Prove that m∠AKB = 3m∠ABK. Help meee!! What do I put in the box shown below??
Answer:
Step-by-step explanation:
As we know that:
BK is bisector of ∠ABD=> ∠ABK=∠KBD=x
=> ∠ABD=2x
Now AB=AD, two sides of rhombus ABCD=> ∠KDB=∠ABD=2x
∠AKB being exterior angle of ΔKBD, we have:∠AKB=∠KDB+∠KBD=2x+x=3x
Please have a look at the attached photo
Air Jordan’s are manufactured in China and reportedly cost Nike a bit more then $16 a pair in 2014. The Air Jordan 10s are listed on Amazon for $240. What is the percent increase for Air Jordan’s sold in the US to the nearest tenth?
Answer: That would be a massive 1500% increase from 16 to 240
Solve for an angle in right triangles help
Answer:
71.57
Step-by-step explanation:
Tangent = opposite over adjacent (sides)
TanA = ( 9/3 )
A = [tex]Tan^{-1}[/tex](3)
A = 71.57
If the sum of the interior angles of a polygon is 1800°, how many sides does it
have?
Answer: 12
Step-by-step explanation: (s-2)(180)=1800, s-2=10, s=12
Using the formula for the sum of the interior angles of a polygon, we can determine that a polygon with an interior angle sum of 1800 degrees has 12 sides.
To determine the number of sides a polygon has based on its interior angle sum, we can use the formula for the sum of the interior angles of a polygon, which is (n - 2) times 180 degrees, where n is the number of sides of the polygon. Given that the sum of the interior angles is 1800 degrees, we can set up the equation n - 2 = 1800 / 180, which simplifies to n - 2 = 10. Solving for n gives us n = 12, so the polygon must have 12 sides.
If m = 35 cm and n = 37 cm, what is the length of l?
A. 15 cm
B. 13 cm
C. 12 cm
D. 2 cm
So the right answer is 12cm.
Look at the attached picture ⤴
Hope it will help u..
Answer:
12
Step-by-step explanation:
Write an equation for the line in slope-intercept form
The slope of the line is 3. The y-intercept is (0,4)
Answer:
y - 4 = 3(x - 0)
y - 4 = 3x - 0
y = 3x + 4
Step-by-step explanation:
What’s the answer to the question
Answer:
Out of all four, your answer would be the second choice: Y=0.4X.
Step-by-step explanation:
In order to get the answer, all you have to do this divide any y value you find on the line by the any x-value (as long as they're connected).
In this case, I decided to divide 2 by 5.
2/5 = 0.4.
You can also divide 4 by 10 and 6/15. You'll always get 0.4 as your answer.
P.S. I wish you good luck with the rest of your assignment!!
The points in the table lie on a line. What is the slope of the line?
To find the slope(m), use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] And plug in two points on the line. I will use
(-2, 1) = (x₁, y₁)
(4, -6) = (x₂, y₂)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{4-(-2)}{-6-1}[/tex] (two negative signs cancel each other out and become positive)
[tex]m=\frac{4+2}{-6-1}[/tex]
[tex]m=\frac{6}{-7}[/tex]
To calculate the slope of the line passing through the points (-8, -2) and (4, 10), use the formula m = (y2 - y1) / (x2 - x1), which gives a slope of 1.
The question pertains to finding the slope of a line that passes through certain points with given x and y coordinates. The slope of a line is the ratio of the change in y (the rise) to the change in x (the run). To calculate it, we can use any two points on the line. Let's use the points (-8, -2) and (4, 10) as an example.
We calculate the slope (m) using the formula:m = (y2 - y1) / (x2 - x1)
Substituting the values:m = (10 - (-2)) / (4 - (-8))
m = (12) / (12)
The slope m equals 1.This means for every increase of 1 on the horizontal axis, there is a rise of 1 on the vertical axis.
Would do anything for the answer to this question
Given:
The length of the entire rectangle is 10x + 7.
The width of the entire rectangle is 6x.
The length of the unshaded rectangle is 4x - 5.
The width of the unshaded rectangle is 2x.
We need to determine the area of the shaded region of the rectangle.
Area of the entire rectangle:
The area of the entire rectangle can be determined using the formula,
[tex]A=length \times width[/tex]
Substituting the values, we have;
[tex]A_1=(10x+7)(6x)[/tex]
[tex]A_1=60x^2+42x[/tex]
Thus, the area of the entire rectangle is 60x² + 42x
Area of the unshaded rectangle:
The area of the unshaded rectangle can be determined using the formula,
[tex]A=length \times width[/tex]
Substituting the values, we have;
[tex]A_2=(4x-5)(2x)[/tex]
[tex]A_2=8x^2-10x[/tex]
Thus, the area of the unshaded rectangle is 8x² - 10x
Area of the shaded region of the rectangle:
The area of the shaded region of the rectangle can be determined by subtracting the area of the entire rectangle by the area of the unshaded rectangle.
Thus, we have;
[tex]A=A_1-A_2[/tex]
Thus, we have;
[tex]A=60x^2+42x-(8x^2-10x)[/tex]
[tex]A=60x^2+42x-8x^2+10x[/tex]
[tex]A=52x^2+52x[/tex]
[tex]A=52x(x+1)[/tex]
Thus, the area of the shaded region of the rectangle is 52x(x + 1)
The graph below represents the path of a grasshopper as it jumps which type of function models the data on the graph
Answer:
Quadratic
Step-by-step explanation:
Given function is a quadratic function.
There are many key features in a quadratic graph such as the zeroes (x-intercepts, also known as the roots), y-intercept, axis of symmetry, and the vertex.
The graph of a quadratic function is a parabola, which has several important properties:
Vertex: The vertex is the point where the parabola changes direction. It is the highest or lowest point on the parabola, depending on whether the parabola opens upward or downward, respectively.
Axis of symmetry: The axis of symmetry is a vertical line that divides the parabola into two symmetrical halves. It passes through the vertex and is perpendicular to the directrix.
Directrix: The directrix is a horizontal line that is located at a distance equal to the distance between the vertex and the focus. It is perpendicular to the axis of symmetry and reflects the parabola onto itself.
Focus: The focus is a point on the axis of symmetry that is located at a distance equal.
As we can see that given graph has two roots and it is symmetric to the line parallel to the y-axis.
From the graph we know this is a quadratic function { a parabola with respect to symmetry and axis symmetry}
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The domain of F(x) is the set of all numbers greater than or equal to 0 and
less than or equal to 2.
A. True
B. False
Answer:
Frue
Step-by-step explanation:
Easy 50 points, one multi choice question
Answer:
A
Step-by-step explanation:
but it prob doesnt help tho
Answer:
B is the correct answer
Step-by-step explanation: