Answer:
20
Step-by-step explanation:
8x - 27 = 7x - 4
8x-7x = 24-4
x = 20
I hope im right!!
A type of new car loses 20% of its value in its first year.
It loses 15% per year in every year after the first. Graham buys one of these new cars.
Work out the percentage of its value that it has lost after five years.
Give your answer to the nearest whole number.
Answer:63%
Step-by-step explanation:
if 2years=25%loss
Then 5years=5/2×25%
=62.5%~63%
Answer:
After a year, your car's value decreases to 81% of the initial value. After two years, your car's value decreases to 69% of the initial value. After 3 years, your car's value decreases to 58% of the initial value.
5. What is the name of the segment inside the large triangle?
Which statement is true about the graphed function
Find the GCF of each pair of monomials.
1. 20, 45x
2. 15r, 25
3. 8xy, 14x
4. 16mn, 24m
5. 25f, 60g
6. 33c, 55cd
Which of the following represents the series? –13 + (–7) + (–1) + 5 + 11
Answer:
Adding +6 in turn
Step-by-step explanation:
-13+6=(-7)
(-7)+6=(-1)
(-1)+6=5
5+6=11
11+6=17
17+6=23
23+6=29
29+6=35
........... And so on
if it helped uh please mark me a brainliest :))How many buttons did Anne sew?
Rate: 8 buttons per minute Time: 7 minutes
Answer:
42 buttons
Step-by-step explanation:
8 x 7 = 42
42 buttons
Hope that helped have a nice day
Can I have brainliest btw?
help me kasama po yung sa baba na 1 and 2 question
Answer:
"it's in your notes"
Step-by-step explanation:
I I bet that's what your teacher told you that or you're just not capable of doing it yourself
Which transformation would take Figure A to Figure B?
Answer:.......................
A 2020-inch candle burns down in 10 hours. At what rate does the candle burn, in inches per hour?
Answer:
202 inches per hour
Step-by-step explanation:
2020 ÷ 10 = 202
Hope this helps..
Answer:
202
Step-by-step explanation:
2020/10=202
A remote interior angle is equal to exterior angles. True or false?
Answer:
No, but they add up to 180 degrees.
Step-by-step explanation:
Take one of the angles, interior or exterior and subtract it from 180 and you should have your other angle.
If Sarah love math what problem should she slove? 78 / 56 or 890 x 12.
Answer:
890 x 12
Step-by-step explanation:
you have savings of $100. you plan to save another $100 at the beginning of each year for 5 years. The account pays annual intrest of 8 percent, coumpounded quarterly. the ending balance (pincipal plus interest) will be $ at the end of 5 years?
Answer:
$638.10
Step-by-step explanation:
= $100 (1 + 2/100)^4
= $100 (1 + 0.02)^4
= $100* 1.0824
= $108.24
For the second year = $100+ $108.24= $208.24
= $ 208.24 * 1.0824
= $225.41
For the third year = $100 + $ 225.41 = $325.41
= $325.41 * 1.0824
= $352.23
For the fourth year = $100 + $ $352.23 = $452.23
= $452.23 * 1.0824
= $ 489.51
For the fifth year = $100+ $489.51 = $589.51
= $589.51 * 1.0824
= $ 638.10
The functions f(x) = −(x − 1^)2 + 5 and g(x) = (x + 2)^2 − 3 have been rewritten using the completing-the-square method. Apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.
If we write a quadratic in vertex form:
\(y=a(x-h)^2+k\)
Then:
\(\bold{a}\) \(\longrightarrow\) is the coefficient of \(x^2\)
\(\bold{h}\) \(\longrightarrow\) is the axis of symmetry.
\(\bold{k}\) \(\longrightarrow\) is the max/min value of the function.
Also:
If \(a > 0\) then the parabola will be of the form \(\cup\) and will have a minimum value.
\(a < 0\) then the parabola will be of the form \(\cap\) and will have a minimum value.
For the given functions:
\(a < 0\)
\(f(x)=-(x-1)^2+5\) this has a maximum value of \(\bold{5}\)
\(a > 0\)
\(f(x)=(x+2)^2-3\) this has a minimum value of \(\bold{-3}\)
Use the function f(x) to answer the questions:
F(x)=2x²-x-10
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show
work. (3 points)
Part C: What are the steps you would use to graph fx)? Justify that you can use the answers obtained in Part A and Part B to draw the graph (5 point
Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:
2x² - x - 10 = 0
This equation can be factored as:
(2x + 5)(x - 2) = 0
Setting each factor equal to zero, we get:
2x + 5 = 0 => 2x = -5 => x = -5/2
x - 2 = 0 => x = 2
Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.
Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).
In this case, a = 2 and b = -1. Plugging these values into the formula, we have:
x = -(-1) / (2 * 2) = 1/4
To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point
Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).
Part C: To graph f(x), we can follow these steps:
Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.
Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).
Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.
Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.
Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.
The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.
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The x-intercepts from the graph attached are
(-2, 0) (2.5, 0)The vertex from the graph attached is
(0.25, -10.125)How to find the required parametersPart A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:
2x² - x - 10 = 0
x = (-b ± √(b² - 4ac)) / (2a)
a = 2, b = -1, c = -10
Plugging these values into the quadratic formula:
x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)
x = (1 ± √(1 + 80)) / 4
x = (1 ± √81) / 4
x = (1 ± 9) / 4
x₁ = (1 + 9) / 4 = 10 / 4 = 2.5
x₂ = (1 - 9) / 4 = -8 / 4 = -2
Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.
Part B
To find the coordinates of the vertex, we can use the formula:
x = -b / (2a)
x = -(-1) / (2 * 2) = 1 / 4 = 0.25
we substitute this value back into the original function:
f(0.25) = 2(0.25)² - 0.25 - 10
f(0.25) = 0.125 - 0.25 - 10
f(0.25) = -10.125
Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).
Part C: The steps to graph f(x) include:
Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.
Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.
Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.
Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.
By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)
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factorise x³-4x²+x+6
The binomial factors of x³- 4x²+x+6 are (x+2), (x+3), and (x-1).
Using the splitting and grouping the terms:
x³ + 4x² + x - 6
= x³ + 2x² + 2x² + x - 6 [Splitting 4x² = 2x² + 2x²]
= (x³ + 2x²) + (2x² + x - 6)
= x² (x + 2) + (2x² + 4x - 3x - 6)
= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]
= x² (x + 2) + (x + 2) (2x - 3)
= (x + 2) ( x² + 2x - 3)
= (x + 2) ( x² + 3x - x - 3)
= (x + 2) [x (x + 3) - 1 (x + 3)]
= (x + 2) (x + 3) (x - 1)
Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)
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While reviewing the previous day’s arrest report, a police sergeant notices that five suspects were arrested, all of whom had either one or two previous arrests. Including yesterday’s arrests, there were 12 total arrests among them. How many suspects had less than two prior arrests?
The number of suspects had less than two prior arrests are 3.
Given that, While reviewing the previous day’s arrest report.
Let x be the number of suspects have been arrested once before and y be the number of suspects arrested twice before.
Here, x+y=5 -----(i)
2x+3y=12 -----(ii)
From equation (i), x=5-y in equation (ii), we get
2(5-y)+3y=12
10-2y+3y=12
10+y=12
y=2
Substitute y=2 in equation (i), we get
x+2=5
x=3
Therefore, the number of suspects had less than two prior arrests are 3.
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Find the inequality represented by the graph.
A = 2x + 6xz Solve for X
Answer:
x= a/6z+2
Step-by-step explanation:
Step 1: Flip the equation.
Step 2: Factor out variable X
Step 3: Divide both side by 6z+2
math math math math math math math
The angle m∠JIX is 90 degrees.
How to find angles in line intersection?IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.
IG bisect CIJ. Hence,
m∠CIG ≅ m∠GIJ
Therefore,
m∠CIX = 150 degrees
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
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The measure of angle m∠JIX is estimated to be 90⁰.
How to find the angles?You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.
IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.
Frim the given parameters,
IG⊥CIJ.
But; m∠CIG ≅ m∠GIJ
⇒ m∠CIX = 150⁰
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
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The function f(x)=x(200-x) models the area of a pasture, in square yards, as a function of its length. Which are possible lengths of the pasture? 125 yards 200 yards 170 yards 225 yards 210 yards
Answer:
(a): x = 125 yards.
(c): x = 170 yards.
Step-by-step explanation:
Given
\(f(x) = x(200 - x)\)
\(x = length\\\\\)
\(f(x) = area\)
Required
Determine the possible length
For a length to be possible or usable, the calculated area must be greater than 0.
(a): x = 125 yards.
\(f(x) = x(200 - x)\)
Substitute 125 for x
\(f(125) = 125 * (200 - 125)\)
\(f(125) = 125 * 75\)
\(f(125) = 9375\)
(b): x = 200 yards.
\(f(x) = x(200 - x)\)
Substitute 200 for x
\(f(200) = 200 * (200 - 200)\)
\(f(200) = 200 * 0\)
\(f(200) = 0\)
(c): x = 170 yards.
\(f(x) = x(200 - x)\)
Substitute 170 for x
\(f(170) = 200 * (200 - 170)\)
\(f(170) = 200 * 30\)
\(f(170) = 6000\)
(d): x = 225 yards.
\(f(x) = x(200 - x)\)
Substitute 225 for x
\(f(225) = 200 * (200 - 225)\)
\(f(225) = 200 * (- 25)\)
\(f(225) = -5000\)
(e): x = 210 yards.
\(f(x) = x(200 - x)\)
Substitute 210 for x
\(f(220) = 200 * (200 - 210)\)
\(f(220) = 200 * (- 10)\)
\(f(220) = -2000\)
From the above calculations, only values of x that are 125 and 170 makes the function true
solve the system of two linear inequalities graphically.
y≤−5x−10
y>x+2
y≤−5x−10 and y>x+2 The shaded region satisfies both inequalities and represents the solution to the system of linear inequalities.
To graphically solve this system of linear inequalities, we can start by graphing each inequality on the same coordinate system:
First, let's graph the inequality y ≤ -5x - 10. We can start by graphing the line y = -5x - 10, which is the boundary line of the inequality. We can plot two points on this line, say (-2,0) and (0,-10), and draw a straight line passing through them.
Next, we need to determine which side of the line satisfies the inequality y ≤ -5x - 10. We can choose any point on one side of the line, say (0,0), and test it in the inequality. If y ≤ -5x - 10 is true for (0,0), then that side of the line satisfies the inequality. Otherwise, the other side satisfies the inequality. Testing (0,0), we have:
0 ≤ -5(0) - 10
0 ≤ -10
This is false, so the side of the line containing the origin does not satisfy the inequality. The other side of the line does.
Now, let's graph the inequality y > x + 2. We can start by graphing the line y = x + 2, which is the boundary line of the inequality. We can plot two points on this line, say (-2,0) and (0,2), and draw a straight line passing through them.
Next, we need to determine which side of the line satisfies the inequality y > x + 2. We can choose any point on one side of the line, say (0,0), and test it in the inequality. If y > x + 2 is true for (0,0), then that side of the line satisfies the inequality. Otherwise, the other side satisfies the inequality. Testing (0,0), we have:
0 > 0 + 2
This is false, so the side of the line containing the origin does not satisfy the inequality. The other side of the line does.
Now, we can shade the region that satisfies both inequalities. The shaded region is the region that is below the line y = -5x - 10 (including the line itself) and above the line y = x + 2 (excluding the line itself).
The shaded region is shown below:
Graph of y≤−5x−10 and y>x+2
The shaded region satisfies both inequalities and represents the solution to the system of linear inequalities.
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Twice the difference of a number and 3 is 8. Use the variable for the unknown number.
Answer:
2(x-3) = 8
Step-by-step explanation:
first it says 'difference of a number and 3' so that equals to (x-3), we use 'x' for the variable for the unknown number
next it says 'twice', so two times which equals 2(x-3)
last it says 'is 8', which means 'equals' so "2(x-3) = 8"
the volume of a cylinder is 196x in. 3 and the hight of the cylinder is 1 in. what is the radius of the cylinder
The radius of the cylinder is 7. 9 in
How to determine the radiusFirst, we need to know the formula for volume of a cylinder
The formula for calculating the volume of a cylinder is expressed as;
V = πr²h
Such that the parameters of the formula are expressed as;
V is the volume of the cylinderr is the radius of the cylinder h is the height of the cylinderFrom the information given, we have that;
Substitute the values
196 = 3.14 × 1 × r²
Divide both sides by the values
r² = 62. 42
Find the square root of both sides
r = 7. 9 in
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How to solve this problem?
The answer of the problem by the SAS similarity theorem sides is \(\frac{AC}{GI} = \frac{HI}{BC}\).
What is the SAS similarity theorem of triangle?
According to the SAS similarity theorem, two triangles are considered similar if their included angles are congruent and their two sides are proportionate to one other.
It is also known as Side-Angle-Side similarity of two triangles.
There is a common ratio of sides in the given problem figure, which is,
\(\frac{AC}{GI} = \frac{HI}{BC}\)
Additionally, these similar sides produce equal relative angles,
∠\(ACB =\) ∠\(GIH\)
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Find the x-intercepts and y-intercepts from the graph.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The x-intercept(s) is/are
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. The graph has no x-intercepts.
what is y
The x-intercepts and y-intercepts of the graph are x = 5 and y = 2
Finding the x-intercepts and y-intercepts from the graph.From the question, we have the following parameters that can be used in our computation:
The graph (see attachment)
The x-intercepts are when y = 0
In this case, it is
x = 5
The y-intercepts are when x = 0
In this case, it is
y = 2
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find the distance between the following pairs of points (-1,5)and(-7,-3)
The distance between the points (-1, 5) and (-7, -3) is 10 units.
What is the distance between the given points?The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
Point 1 (-1,5)
x₁ = -1y₁ = 5Point 2 (-7,-3)
x₂ = -7y₂ = -3Plug the given values into the distance formula and simplify.
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
D = √[(-7 - (-1))² + (-3 - 5)²]
D = √[(-7 + 1)² + (-3 - 5)²]
D = √[-6² + (-8)²]
D = √[36 + 64]
D = √100
D = 10
Therefore, the distance is 10 units.
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The two-way table represents data from a survey asking schoolchildren whether they are attending a summer camp, taking swimming lessons, or both.
A 4-column table with 3 rows. The first column has no label with entries swimming lessons, no swimming lessons, total. The second column is labeled camp with entries 42, 18, 60. The third column is labeled no camp with entries 32, 4, 36. The fourth column is labeled total with entries 74, 22, 96.
Which is the joint relative frequency for school children who plan to attend camp and have swimming lessons? Round the answer to the nearest percent.
4%
19%
33%
44%
The joint relative frequency for school children who plan to attend camp and have swimming lesson is 44%.
The correct option to the given question is option d.
We are required to find the joint relative frequency for school children who plan to attend camp and have swimming lessons, rounded to the nearest percent.
To find the joint relative frequency, we use the formula as follows:
Joint relative frequency = frequency of interest / total frequency
Joint relative frequency for school children who plan to attend camp and have swimming lessons = 42 / 96
(As we are looking for the students who plan to attend camp and have swimming lessons, we are interested in the first column of the table and the entry at the intersection of the first row and second column.)
Joint relative frequency for school children who plan to attend camp and have swimming lessons = 0.4375
Joint relative frequency for school children who plan to attend camp and have swimming lessons (rounded to the nearest percent) = 44%(option d).
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a computer that normally cost 500 dolars was on sale for 200 dollars. what is the percent decrease. please show work for brainlist
Answer:
(100/500) *200 =40%
Step-by-step explanation:
Melanie buys 6 basketballs and 2 volleyballs for 114. A volleyball cost her 3 less than a basketball. How much did each volleyball cost?
Help meeee!
Answer:
16 dollars
Step-by-step explanation:
114÷6=19-3 is 16
In one county, the farms had a mean harvested area of 103 acres with a standard deviation of 9 acres.
What will be the mean and standard deviation of the distribution of area in square kilometers?
1 acre approximately equals 0.004 square kilometers.
A) Mean: 0.412 square kilometers
Standard deviation: 0.036 square kilometers
B) Mean: 0.412 square kilometers
Standard deviation: 9 square kilometers
C) Mean: 103 square kilometers
Standard deviation: 0.036 square kilometers
D) Mean: 103 square kilometers
Standard deviation: 9 square kilometers
Answer: A)
Step-by-step explanation: khan academy