The y-intercept of the function g(x) is y-intercept = 5 and the vertex is (3, -4)
The x-intercept and y-interceptSet g(x) = 0 for the x-intercept
So, we have
(x - 1)(x - 5) = 0
Evaluate
x-intercept = 1 and 5
For the y-intercept,
Substitute 0 for x in g(0)
So, we have
g(0) = (0 - 1)(0 - 5)
Evaluate
g(0) = 5
The vertex of the functionWe have
g(x) = (x - 1)(x - 5)
Express in vertex form
g(x) = (x - 3)² - 4
From g(x) = (x - 3)² - 4, the vertex is
Vertex = (3, -4)
The increasing and the decreasing intervalsThe function increases on the interval x > 3The function increases on the interval x < -1The function is positive on the interval x < -1Read more about quadratic functions at
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Possible question
The function f(x)=-1/2x+3 and g has a lesser y-intercept than f;
The function g(x) is g(x) = (x - 1)(x - 5)
The increasing and decreasing intervals
Find the vertex and y-intercept of g.
What is the meaning of Mode?
"Mode"
can have a LOT of different meanings. However, because you put this question under "mathematics", Im assuming you want to know more about the mode related to statistics.
Mode is defined as the number that repeats itself the most times in a data set!
Lets say you have a data set [1,2,3,4,5,6,7,8,9]
That data set has no mode, as every number presents itself the same number of times, in this case being 1.
Take this data set: [1,1,2,3,4,5,6,7,8,9]
That data set has a mode of 1. The number "1" presents itself twice in the data set, while every other number presents itself once.
Take this data set [1,1,2,3,4,5,5,6,7,8,9]
That data set has a mode of 1 AND 5. They BOTH repeat themselves TWICE, which every other number only ocurrs once.
If you have any other questions, comment below this answer.
~~~Harsha~~~
Mary can be 24 cookies one dozen per sheet in her oven in 12 minutes how long would it take her to bake 60 cookies
Maureen earned $5,232.50 commission when she sold a $45,500 car. What was the rate (in %) of commission?
Answer:
11.5%
Step-by-step explanation:
[tex]45,500*x=5232.5\\x=11.5%[/tex]
Slope of a line with points (-4,2)(0,-4)
It is an exercise of the equation of the line, related to the subject of the slope of a line is a fundamental measurement in analytical geometry and mathematics in general. It is a measure that indicates the inclination of a line, that is, how much the y coordinate changes for each unit that the x coordinate changes. The slope is represented by the letter m and is defined as the quotient between the variation of the y coordinates, divided by the variation of the x coordinates.
The importance of slope extends beyond analytic geometry, and it is used in many other areas of mathematics and science. For example, in physics, slope is used to calculate the velocity and acceleration of a moving object. In statistics and econometrics, slope is used to interpret data and make predictions from it.
Also, slope is used in solving analytic geometry problems. For example, slope can be used to find the equation of a line from two known points, or to determine whether two lines are parallel or perpendicular.
We calculate the slope:
To calculate the slope of the line, we apply the following formula:
m = (y₂ - y₁)/(x₂ - x₁)
Now we find the points of x and y.
x₁ = -4 , y₁ = 2
x₂ = 0 , y₂ = -4
We substitute our data in the slope formula and solve, then
m = (y₂ - y₁)/(x₂ - x₁)
m = (-4 - 2)/(0 - (-4))
m = (-6)/(4)
m = - 1.5
The slope between the points (-4,2) and (0,-4) is -1.5.
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You sit down to take a true-or-false test with 6 questions. If you randomly
guess on all questions, how many possible outcomes are there for the
6-question test?
OA. 36
B. 12
O C. 6
OD. 64
SURMIT
Answer:
Please mark me the brainliest.
Step-by-step explanation:
For each question, there are two possible outcomes: true or false. Therefore, the total number of possible outcomes for a 6-question true-or-false test is 2 x 2 x 2 x 2 x 2 x 2, which is equal to 2^6. Using a calculator, we can find that 2^6 is equal to 64.
Therefore, the answer is option D: 64.
A pyramid has a square base with a side length of 7 centimeters. If the volume of the pyramid is 196 cubic centimeters, what is its height in centimeters? 4 cm 12 cm 8 cm 7cm 21 cm
Answer:
The formula for the volume of a pyramid is:
V = (1/3) × base area × height
We know that the base of the pyramid is a square with a side length of 7 centimeters. So, the base area is:
base area = side length squared = 7² = 49 square centimeters
We also know that the volume of the pyramid is 196 cubic centimeters. Plugging these values into the formula above and solving for the height:
196 = (1/3) × 49 × height
588 = 49 × height
height = 588/49
height = 12
Therefore, the height of the pyramid is 12 centimeters.
help me with this please
The perimeter of the given triangle is: P = √10 + 4√2 + √26
What is the perimeter of the triangle?The formula for the distance between two coordinates is expressed as:
d = √[(y₂ - y₁)² + (x₂ - x₁)²]
Thus:
RS = √[(1 - 2)² + (1 + 2)²]
RS = √10
Similarly, we can say that:
ST = √[(-3 - 1)² + (-3 - 1)²]
ST = √32 = 4√2
RT = √[(-3 - 2)² + (-3 + 2)²]
RT = √26
Thus, perimeter of triangle is:
P = √10 + 4√2 + √26
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HELP SOLVE MY MATH pls
The corresponding answers to each expression are;
1. 5x x (3+5) / 12 - 2 x 2 = 5
2. (11 + 3²) ÷ 4 - 2 = 3
3. (48 - 12 ÷ 2 / 7 - 1) + 1 = 8
4. (25 - (4 - 1)² / 2³ - 4) + 2 = 6
5. (3² - 4) x (7 + 5) / -12 ÷ -3 = 15
How do you solve for each expression?
1. 5 x (3+5) / 12 - 2 x 2 =
5 x 8/ 12 - 4=
40/8 = 5
2. (11 + 3²) ÷ 4 - 2 =
11 + 9 ÷ 4 - 2=
20 ÷ 4 - 2
5 - 2 = 3
3. (48 - 12 ÷ 2 / 7 - 1) + 1 =
(48 - 6/ 6) + 1 =
42/6) + 1 =
7 + 1 = 8
4. (25 - (4 - 1)² / 2³ - 4) + 2 =
25 - 9/ 4) + 2 =
16/4 + 2 =
4 + 2 = 6
5. (3² - 4) x (7 + 5) / -12 ÷ -3 =
9-4 x 12/ 4 =
5 x 12/ 4=
60/4 = 15
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Jaeger the goat will be tied by a 15-meter chain to the outside of a 10-meter by 16-meter
rectangular shed that is surrounded by grass. Try three different places to attach the chain to the shed. For each, determine the area of grass that Jaeger could eat. Which of your
locations gives Jaeger the most to eat? (Note: Jaeger cannot walk through the shed.)
a. Sketch each of the solutions of the three different places you happen to pick to attach
the chain to the shed. Accuracy counts. What conclusions can you draw based on
your three test points? Do you see any patterns?
In general, your solution(s) need to have evidence which both supports and helps explain your solution(s). Evidence can include but is not limited to words, pictures, diagrams, tables,
The second location result in the largest area of grass that Jaeger can eat, which is approximately 353.57 square meters.
We may infer from the facts provided that Jaeger the goat will be confined to a 10- by-16-meter rectangular shelter by means of a 15-meter chain. All of the grass along the chain may be consumed by Jaeger. At three separate points in the shed, we are instructed to locate the patch of grass that Jaeger can eat.
Let's consider the three different locations as follows:
Attach the chain to a corner of the shed.
Jaeger can only eat as much grass as is contained inside a quarter-circle with a radius of 15 meters (the length of the chain) if the chain is fastened to a shed corner. This quarter-circle's area is:
Area = (1/4) x π x (15 meters)²
Area = 176.71 square meters (approx)
Affix the chain to the middle of one of the shed's longer sides.
This semicircle's area is:
Area = (1/2) x π x (15 meters)²
Area = 353. 57 square meters (approx)
To the center of one of the shed's shorter sides, fasten the chain.
This circular sector's area will be as follows:
Area = (90/360) x π x (15 meters)²
Area = 176.71 square meters (approx)
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Which equation is represented in the graph shown? parabola going down from the left and passing through the point negative 2 comma 0 and then going to a minimum of 1 comma negative 9 and then going up to the right through the point 4 comma 0 a y = x2 − 2x − 8 b y = x2 − 2x + 8 c y = x2 + 2x − 8 d y = x2 + 2x + 8
The equation represented in the graph shown is,
⇒ y = x² - 2x - 8.
Now, We know that the parabola goes down from the left and passes through the point (-2,0),
then goes to a minimum of (1,-9), and then goes up to the right through the point (4,0).
Hence, We can use this information to determine the equation of the parabola in vertex form, which is,
⇒ y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
Step 1: Finding the vertex We already know the vertex of the parabola is (1,-9) because it is given in the problem.
Therefore, h = 1 and k = -9.
Step 2: Finding the value of "a" To find the value of "a", we can use one of the points on the parabola (either (-2,0) or (4,0)).
Let's use the point (-2,0).
When x = -2, y = 0.
Therefore, we can substitute these values into the vertex form equation and solve for "a":
0 = a(-2 - 1)² - 9
0 = a(-3)² - 9
0 = 9a - 9
9 = 9a
a = 1
Therefore, the value of "a" is 1.
Step 3: Writing the equation in vertex form Now that we know the vertex (h, k) and the value of "a", we can write the equation in vertex form:
y = 1(x - 1)² - 9
Simplifying this equation gives us:
y = x² - 2x - 8
Therefore, the equation represented in the graph shown is option (a) y = x² - 2x - 8.
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I need help with this problem if do thank you a lot
The value of x is equal to 17 degrees.
What is the central angle property?In Mathematics and Geometry, the central angle property states that an inscribed angle is equal to one-half the measure of a central angle that is subtended by the same arc.
Based on the information provided about circle C, the central angle of circle P is represented by m∠C and the inscribed angle is represented by (x + 4)°.
This ultimately implies that, the measure of the central angle is twice (double) the measure of the inscribed angle;
m∠C = 2(x + 4)°.
3x - 9 = 2(x + 4)°.
3x - 9 = 2x + 8
3x - 2x = 8 + 9
x = 17
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Need help now with this problem please! If your not going to help, kindly don’t comment.
The value of θ for the given equation is θ = 54.74°.
What is inverse cosine function?The inverse cosine function (arccos) has a range of 0 to arccos(x), where x is a real number in the range of -1 to 1. An angle in radians between 0 and, which measures the angle between the x-axis and the terminal side of a unit circle that crosses the line between the origin and the point (x, y), is the result of the inverse cosine function. To put it another way, the inverse cosine function returns the angle whose cosine is equal to a specified value x.
The given equation is 4sec(θ) - 7 = 0:
Now, isolating the value of sec(θ) we have:
4sec(θ) = 7
sec(θ) = 7/4
Now, converting into cos we have:
cos(θ) = 4/7
θ = arccos(4/7)
θ = 54.74°
Hence, the value of theta for the given equation is θ = 54.74°.
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Find the probability of an event when the odds against the event are 3:7.
When the odds against an event are given as "a:b", the probability of the event can be found by using the formula:
Probability of the event = b / (a + b)
In this case, the odds against the event are 3:7, which means that the probability of the event not occurring is 3/(3+7) or 3/10. Therefore, the probability of the event occurring is:
1 - 3/10 = 7/10
So the probability of the event is 7/10 or 0.7 (70%) when the odds against the event are 3:7.
Which of the following represents the equation of a line that is parallel to the line represented by the equation y=12x+6 ?
Hint: Use the formula sheet to determine the formula(s) needed to solve the problem.
The equation of a line that is parallel to y = 12x + 6 is of the form:
y = 12x + b
What is equation of line?The relationship between the coordinates of each point (x, y) on a line is represented by the equation of a line, which is linear in the variables x and y. All of the points on the line satisfy the equation, in other words.
A line is parallel to the line y = 12x + 6 if and only if it has the same slope as the given line.
The slope-intercept form of the equation of a line is:
y = mx + b
where m is the slope of the line and b is the y-intercept.
Since the given line y = 12x + 6 has a slope of 12, any line that is parallel to it must also have a slope of 12. Therefore, the equation of a line that is parallel to y = 12x + 6 is of the form:
y = 12x + b
where b is any constant.
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Determine the 12th term in the following geometric sequence
7, 14, 28, 56, 112...
d
14,336
28,672
7,168
29
Answer:
14336
Step-by-step explanation:
the general term is:
s(n) = 7*(2)^(n-1)
you can check it by plugging in some number:
s(3) = 7*2^(3-1) = 7*4 = 28
s(4) = 7*2^(4-1) = 7*8 = 56
The 12th term is:
s(12) = 7*2^(12-1) = 7*2^11 = 7*2048 = 14336
How much paint is needed to cover silo with radius of 3 and
Which fraction would you find marked on a ruler ?
1/9 inch
1 4/8 inch
1 1/2 inch
1 3/8 inch
7/8 inch
The fraction that can be found on a ruler would be = 1½ inch. That is option C.
What is a fraction?Fraction is defined as the expression of a number in the form of numerator and denominator.
The meter rule is the device that is used in the measurement length of an object.
A meter rule can be marked as in centimeter or in inches.
The best fraction that can be seen on a meter rule is 1½in = 1.05in.
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a rectangler prism has a length of 2.5 yards and a width of 1.5 yards and a height of 1.5 yards use cubes with fractional edge lengths of 1/2 yard to find the volume how many cubes are there for the length, width and heigth of the prism and then what is the volume of the prism.
There are 96 cubes are there for each of the length, width, and height of the prism.
The volume of a rectangular prism is 12 yd³.
Given that;
A rectangular prism has a length of 2.5 yd, a width of 1.5 yd, and a height of 1.5 yd.
Hence, length 2.5 and 1/2 yd = 2 1/2 + (1/2) yd = 5/2 + 1/2 = 6/2= 3 yd
Width 1.5 and half yd = 1 1/2 + (1/2) yd = 3/2 + 1/2 = (4/2) = 2 yd
Height 1.5 and half yd = 1 1/2 + (1/2) yd = 3/2 + 1/2 = (4/2) = 2 yd
Hence, Cubes of edge length (1/3) yd are used to fill the rectangular prism.
The length would contain (3) ÷ (1/2) = 6
The width would contain (2) ÷ (1/2) = 4
The height would contain (2) ÷ (1/2) = 4
Hence, Number of cubes are there for each of the length, width, and height of the prism
6 × 4 × 4 = 96 cubes
Thus, There are 96 cubes are there for each of the length, width, and height of the prism.
And,.
The volume of rectangular prism = 3 × 2 × 2 = 12
The volume of a rectangular prism is 12 yd³.
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Which expressions are equivalent to -8x + 4? Mark all that
apply.
A. -4 (2x - 1)
B. 4(2x - 1)
C. 4x (2 - 1)
D. 4x (2x + 1)
E. 4(-2x + 1)
F. 4(2x + 1)
Answer:
A and E
Step-by-step explanation:
A. -4 (2x - 1) = -8x + 4
B. 4 (2x - 1) = 8x - 4
C. 4x (2 - 1) = 8x - 4
D. 4x (2x + 1) = 8x² + 4x
E. 4 (-2x + 1) = -8x +4
F. 4 (2x + 1) = 8x + 4
Given the following triangle, if c = 25 and angle A = 20 degrees, find a
The length of the side a is 8.55 units.
Given is a right triangle, the side c which the hypotenuse is 25 units, and an acute angle A is 20°,
We need to find the length of the side a,
Considering the angle, A as reference angle, we have,
Sin A = a / c
Sin 20° = a / 25
a = Sin 20° × 25
a = 8.55
Hence, the length of the side a is 8.55 units.
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I'LL GIVE THE BRAINLIEST IF YOU ANSWER!
Data Set 1 has a mean of 54 and a MAD of 4. Data Set 2 has a mean of 60 and a MAD of 2.
What can be concluded about the two distributions?
Select each correct answer.
A} The distributions are similar.
B} The distributions are somewhat similar.
C} The means-to-MAD ratio is 3.
D} The means-to-MAD ratio is 1.5.
The two distributions can be concluded as:
The distributions are similar.
The means-to-MAD ratio is 3.
Options A and C are the correct answer.
The MAD (Mean Absolute Deviation) is a measure of variability similar to standard deviation, but it measures the average absolute difference between each value and the mean, regardless of the direction of the deviation.
The means-to-MAD ratio is a measure of how spread out the data is, relative to the mean.
Since the means-to-MAD ratio for Data Set 1 is 3 and the means-to-MAD ratio for Data Set 2 is 30, Data Set 1 is more spread out than Data Set 2.
However, since the ratio is not extremely different (i.e., not greater than 10), the two distributions can still be considered similar.
Thus,
The two distributions can be concluded as:
The distributions are similar.
The means-to-MAD ratio is 3.
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The digits circled in the numbers below are replaced by 9 which number increases the most?
Please Open The Picture
among the available choices is 9456.
What are place values?
Place values describe a digit's location within a number and the value that digit represents based on that location. Each digit in a number is given a place value in our decimal number system according to where it is from the rightmost side. The first position to the right is known as the one's place, followed by the tens place, hundreds place, thousands place, and so on, with each position to the left denoting ten times the value of the position to its immediate right.
The new set of numbers is produced by substituting the number 9 for the previous ones:
7989, 9456, 4592, 3972
We can see that 9 is the greatest digit by comparing the leftmost digit of each integer to itself. Due to the absence of a 9 in the leftmost digit, we can rule out alternatives 7989 and 3972.
Second from the left is then put up for comparison. The number is four in both 9456 and 4592. The 5 in 9456, on the other hand, is greater than the 5 in 4592 and is the next digit to the right in the number. As a result, option 4592 can be disregarded.
And that leaves 9456 and 7989 for us to work with. 9 in the number 9456 is the leftmost digit, which is greater than 7 in the number 7989. In both 9456 and 7989, the second digit is 4, making them the same. 9456's third digit, however, is 5, which is larger than 7989's eighth digit, which is 8. The biggest number,
therefore, among the available choices is 9456.
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NEED HELP WILL GIVE BRAINLIEST AND 5 STARS I HAVE 20 MINUTES PLEASE HELP!
For this rational function, using proper notation, describe the end behavior of m(x)
Answer:
Step-by-step explanation:
the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches ) and to the left end of the x-axis (as x approaches
Match each point of intersection with the system of equations whose solution is at that point
The Match of each point of intersection with the system of equations whose solution is at that point are
y = -2x − 3 / y = 2x − 1 --> Z y = x + 4 / y = -x + 2 --> X y = -2x − 3 / y = x + 4 --> Wy = 2x − 1 / y = -x + 2 --> YWhat is the point of intersection?For the 1st system is:
y = -2x - 3 ------- (1)
y = 2x - 1 (2)
So one need to equate (1) and that of (2) so it will be:
2x - 1 = -2x - 3
Add 2x to both sides
4x - 1 = - 3
Add 1 to both sides
4x = -2
Divide both sides by 4
x = -1/2
- Substitute the value of x in equation (1) or (2)
y = 2( ) - 1
y = -1 - 1
y = -2
Therefore, the point of intersection of the two equations is found to be (-1/2, -2), and it is shown by the letter Z.
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What is the probability that a person orders a sandwich with cheddar cheese?
Answer:
50%
Step-by-step explanation:
Add 13.2 and 0.9,and then divide by 0.6.
Answer:
23.5
Step-by-step explanation:
13.2 + 0.9 = 14.1
14.1 / 0.6 = 23.5
The graph y=x² is shown in red. Then x² +5 is shown
in blue and x²-3 is shown in green. Record your
observations of what happened.
1. Adding different constant terms to
The translations to each graph are described as follows:
y = x² + 5 -> translation of the parent function y = x² up by 5 units.y = x² - 3 -> translation of the parent function y = x² down by 3 units.What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.Hence the meaning of each operation is given as follows:
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Please help. 8th grade math homework
Completing the table using the rounded values showing the relative frequencies is as follows:
Column Relative Frequency Table
Men Women Total
January - June 25% 25% 25%
July - December 75% 75% 75%
Total 100% 100% 100%
What is the relative frequency?Relative frequency shows the quotient between the number of events and the total number of possible events occurring.
The quotient of relative frequency is expressed over 100 to show the result in percentage terms.
Frequency Table
Men Women Total
January - June 21 19 40
July - December 62 58 120
Total 83 77 160
Column Relative Frequency Table
Men Women Total
January - June 25% (21/83) 25% (19/77) 25% (40/160 x 100)
July - December 75% (62/83) 75% (58/77) 75% (120/160 x 100)
Total 100% 100% 100% (160/160 x 100)
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This figure shows the dimensions for a package to be shipped. Enter the minimum amount of wrapping paper, in square inches, needed to cover the package. Round your answer to the nearest whole inch.
The minimum amount of wrapping paper, needed to cover the package surface area is 174 square inches.
From the given three dimensional figure,
Total surface area = Area of 2 similar trapeziums + Area of rectangles of 4 different rectangles
We know that, area of a triangle = 1/2 ×Base×Height and area of a rectangle is Length×Breadth.
= 2×1/2(7+3)×3+8×5+8×3+8×3+8×7
= 30+40+24+24+56
= 174 square inches
Therefore, the minimum amount of wrapping paper, needed to cover the package surface area is 174 square inches.
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Solve for x.
35⁰
15 cm
X
x = [?] cm
Round to the nearest hundredth.
Enter
The value of the side x = 26. 316cm
How to determine the valueWe need to know the different trigonometric identities. These identities includes;
sinetangentcotangentsecantcosecantcosineTheir different ratios are given as;
sin θ = opposite/hypotenuse
tan θ = opposite/adjacent
cos θ = adjacent/hypotenuse
From the information given, we have that;
Angle , θ = 35 degrees
Opposite side = 15
Hypotenuse side =
Substitute the values
sin 35 = 15/x
cross multiply
x = 26. 316cm
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