Final answer:
To find the equation of the line passing through two given points, we can use the slope-intercept form of a line. The equation of the line passing through (-5,2) and (9,0) is y = -1/7x + 9/7.
Explanation:
To find the equation of the line that passes through the points (-5,2) and (9,0), we can use the slope-intercept form of a line, y = mx + b. First, we need to find the slope (m) of the line. The slope is given by the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Plugging in the values, m = (0 - 2)/(9 - (-5)) = -2/14 = -1/7.
Next, we can choose one of the points and plug in its coordinates along with the slope into the equation y = mx + b to solve for b. Let's choose the point (-5,2): 2 = (-1/7)(-5) + b. Simplifying the equation, 2 = 5/7 + b. Subtracting 5/7 from both sides, 2 - 5/7 = b. Getting a common denominator, 14/7 - 5/7 = b. So, b = 9/7.
Finally, we can substitute the values of m and b into the equation y = mx + b to get the equation of the line: y = -1/7x + 9/7.
Taylor Breen took out a $100,000, 5-year term policy at age 48. The premium per $1,000 was $4.70. He will be 53 years old next year when the premium per $1,000 will be $6.40. What is the amount of the increase?
Select one:
a. $133
b. $136
c. $173
d. $170
To find the amount of the increase, calculate the difference in premiums per $1,000 between when Taylor Breen took out the policy at age 48 and when he will be 53 years old next year. The amount of the increase is $170.
Explanation:To find the amount of the increase, we need to calculate the difference in premiums per $1,000 between when Taylor Breen took out the policy at age 48 and when he will be 53 years old next year.
First, let's calculate the initial premium per $1,000 at age 48:
$100,000 / $1,000 = 100 (number of units)
$100,000 * $4.70 = $470,000 (initial premium)
Next, let's calculate the premium per $1,000 when Taylor Breen will be 53 years old:
$100,000 / $1,000 = 100 (number of units)
$100,000 * $6.40 = $640,000 (premium at age 53)
The amount of the increase is:
$640,000 - $470,000 = $170,000
Therefore, the amount of the increase is $170.
Jackie cut a piece of paper along its diagonal, as shown below, forming two triangles.
A rectangle is cut diagonally to form 2 equal triangles.
How do the height and base length of the two triangles compare to the height and base length of the original piece of paper?
The two dimensions are the same in the triangles as they were in the rectangle.
The two heights are the same in the triangles as they were in the rectangle, but the bases of the triangles are half the length of the base of the rectangle.
The two bases of the triangles have the same length as the base of the rectangle, but the triangles have heights equal to half the height of the rectangle.
The two dimensions of the triangles are each half what they were in the rectangle.
Answer:
B. The two dimensions are the same in the triangles as they were in the rectangle.
Step-by-step explanation:
Given
Initial Shape: Rectangle (Before cut)
Final Shape: Triangles (After cut)
Note that this can be explained properly with the use of attachments
See attachment 1 for Before Cut
Before Cut represent the full rectangle before Jackie cut the piece of paper.
Let H and B represent the height and base of the triangle
Given that the rectangle is cut diagonally, this means that the cutting starts and ends at the opposite edges of the rectangle
See attachment 2 for After Cut
After Cut represent the two triangles after cutting the rectangle
From the attachment, you'll observe that the dimension of the two triangles (Triangle 1 and Triangle 2) are the same as it is with the rectangle;
In other words, the two triangle have their heights as H and their bases as B.
Hence, it can concluded that the two dimensions are the same in the triangles as they were in the rectangle.
Answer:
c is the correct answer
Step-by-step explanation:
Laney builds a tower with wooden cubes. The bottom cubes edges are 8 centimeters long. The middle cubes edges are 2 centimeters shorter than the bottom cube. The top cubes edges are 2 centimeters shorter than the middle cube. What is the total volume of the cubes in the tower?
Laney builds a tower with wooden cubes The bottom cubes edges are 8 cm long The middle cubes edges are 2 cm shorter than the bottom cube The top cubes edges are 2 cm shorter than the middle cube what is the total volume of the cubes in the tower
What is 20 5/10 + 9 3/10
Answer:
Exact Form:
149 /5
Decimal Form:
29.8
Mixed Number Form:
29 4 /5
Step-by-step explanation:
If this helped, please mark brainiest, thanks
Answer:
29 8/10
Step-by-step explanation:
because since the denominaters are the same you can just add the fractions.
5+3=8 and 20+9=29
12y=24x
6x=3y+5
Which statement best describes the relationship between the lines?
Answer: i think is A they are parallel
Step-by-step explanation: is not perpendicular NOT-B
The relationship between the lines represented by the equations 12y = 24x and 6x = 3y + 5 is that they are parallel lines. This conclusion is drawn from the fact that they have the same slope (2) but different y-intercepts (0 for the first line and -5/3 for the second line).
Explanation:To determine the relationship between the lines represented by these equations, we must first put them in slope-intercept form (y = mx + b), where m represents the slope of the line, and b indicates the y-intercept.
For the first equation, 12y = 24x, we can divide both sides of the equation by 12 to get y = 2x.
For the second equation, 6x = 3y + 5, we re-arrange the equation by subtracting 5 from both sides and then dividing by 3. This gives us y = 2x - 5/3.
From the equations y = 2x and y = 2x - 5/3, we can see that the slopes of both lines are the same which is 2. This indicates that the lines are parallel to each other. However, since the y-intercepts are different (0 for the first line and -5/3 for the second line), we can conclude that they are different parallel lines, not the same line.
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Line l is a straight line.
Which statements are true about the angles in the figure? Select two options
Answer:
The first and second are correct
Step-by-step explanation:
∠X and ∠Y and ∠W and ∠Z are linear angles and supplementary angles, and ∠Y and ∠Z are complementary angles. Then the correct options are A, B, and E.
What is an angle?Angle is the space between the line or the surface that meets. And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.
∠X and ∠Y are linear angles and supplementary angles.
∠W and ∠Z are linear angles and supplementary angles.
∠Y and ∠Z are complementary angles.
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Ms. Hatcher bought the pencil decoration shown below for her bulletin board.
If a = 11 in and b = 25 in, what is the area of the pencil?
Answer:
335.5 in^2
Step-by-step explanation:
The area is a rectangle and a triangle
The area of the rectangle is
A = a*b where a is 11 and b is 25
A = 11*25 =275
The area of the triangle is
A = 1/2 b*h where b is 11 and h is 11
A = 1/2 (11) * 11
A = 60.5
The total area is 275+60.5=335.5
Sooo..... can anybody help.....
What is the quotient?
StartFraction 7 Superscript negative 4 Over 7 Superscript negative 9 EndFraction
StartFraction 1 Over 7 Superscript 13 EndFraction
StartFraction 1 Over 7 Superscript 5 EndFraction
7 Superscript 5
7 Superscript 13
Answer:
A
Step-by-step explanation:
The required quotient is [tex]7^5[/tex].
To simplify [tex]7^{-4}/7^{-9}[/tex]
What is quotient?The quotient is the outcome value obtained when a particular value divided by a value.
Here,
Simplification,
[tex]=7^{-4}/7^{-9}\\=7^{-4}*7^{9}\\=7^{-4+9}\\=7^5[/tex]
Thus, the required quotient is [tex]7^5[/tex].
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Sara has a stack of 8 plates each plate is 0.5 inches and she is trying to wrap them as a gift the largest plate has a diameter of 10 inches and each plate has a diameter of 1 inch smaller than the previous plate. She has a cylindrical box with a radius of 5 in that can hold 150 cubic inches will her plates fit in the box
Answer: No her plates will not fit in the box
Step-by-step explanation: Each plate is 0.5 inches tall; therefore, the stack of 8 plates will have a height of .
Also, the diameter of the largest plate is 10 inches or has a radius of 5 inches, which matches the radius of the cylindrical box; therefore, we know that the stack of plates can fit into the base area of the cylindrical box.
What we want to figure out now is the height of the cylindrical box to see if it is greater than or equal to 4 inches—the height of the stack of plates.
The volume of a cylinder is , and since for our cylindrical box the volume is 150 cubic inches; therefore,
putting in and solving for height we get
,
which is not greater than 4 inches, which means the plates will not fit into the box since the height of the stack is greater than the height of the box.
What is the volume of the sphere, rounded to the nearest cubic foot?
Given:
Radius = 5 ft
To find:
The volume of the sphere
Solution:
Volume of the sphere:
[tex]$V=\frac{4}{3}\pi r^3[/tex]
[tex]$V=\frac{4}{3}\times 3.142 \times 5^3[/tex]
[tex]$V=523.66[/tex]
[tex]$V=524[/tex]
The volume of the sphere is 524 ft³.
Carol wanted to see how the data would change if she did not include the outlier in her study. The results are shown in the table with the outlier crossed out.
Find each listed value.
Range =
Median =
Lower quartile and upper quartile =
Interquartile range =
Which value was affected the most?
Answer:
range: 20
Median: 38
Lower quartile and upper quartile: 29 and 42.5
Interquartile: 13.5
Which value 2was affected the most: Range
Step-by-step explanation:
Factor completely 3x^2+33x+90=?
Answer:
3(x+5) (x+6)
Step-by-step explanation:
The factored form of 3x² + 33x + 90 is: 3(x + 6)(x + 5)
To factor completely the quadratic expression 3x² + 33x + 90, we can look for two binomial factors that multiply together to give us the original expression.
First, we can check if the expression can be factored by using the common factor 3:
3x²+ 33x + 90
We can factor out 3 from each term:
3(x^2 + 11x + 30)
Now, we need to find two binomial factors that multiply to give us x² + 11x + 30.
The factors can be determined by factoring the quadratic expression further:
x² + 11x + 30 = (x + 6)(x + 5)
Therefore, the completely factored form of 3x² + 33x + 90 is:
3(x + 6)(x + 5)
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Mich had $10.52 after he left the bookstore. If he bought a book for $6.39, and a magazine for $3.99, how much money did he have before he went to the book store? a.) $0.14 b.) $10.38 c.) $16.91 d.) $20.90
g(x) = “8x
What is the domain of g?
Answer: -1 is not in the domain and 0 and 2 are in the domain
Step-by-step explanation:
The domain of the function g(x) = “8x” is all real numbers, as there are no restrictions on the values that x can take.
The question seeks to find the domain of a function represented as g(x) = “8x. A function's domain refers to all the possible values that can be input into the function. In the case of g(x) = “8x, this is a linear function where x can take any real number value since there are no restrictions like square roots or denominators that could potentially exclude certain x values. Therefore, the domain of g is all real numbers, often represented as (-∞, +∞) or ℝ in set notation.
Give the equation of the line with a slope of 1/3 and a y-intercept of −6
Answer:
y=1/3x-6
Step-by-step explanation:
equation: y=mx+b
m=slope, b=y-intercept
equation: y=1/3x-6
What is the test that you can do to tell if a graph represents a function?
A. the horizontal line test
B. the vertical line test
C. the expression test
D. the litmus test
Answer:
I think it's gonna be c
Step-by-step explanation:
C The expression test
Brianna surveyed a representative sample of students at her school to collect data about the numbers of Internet-compatible devices they own. Estimate about how many of the 250 students who attend Brianna’s school own exactly two Internet-compatible devices.
Answer:
125 students
Step-by-step explanation:
The following table is missing:
Number of Devices Number of Students
1 18
2 25
3 or more 7
Total 50
From the sample, we can estimate that 25/50 = 0.5 or 50% of the students have exactly two Internet-compatible devices. Then there are 0.5*250 = 125 students who have exactly two Internet-compatible devices in Brianna’s school.
The answer/ why it’s right
FOLLOW ME FOR CLEARING YOUR NEXT DOUBT
Answer:
The answer is option 2.
Step-by-step explanation:
It is given that the formula of the volume of rectangular prism is, V = length×width×height. Then you have to substitute the values into the formula to find the volume :
length = 3x
width = 7x
height = 15x
V = (3x) × (7x) × (15x)
= 315x³
Mr.O'Connor had $90 to spend at a football game. He spent 31/45 on his ticket. Then, he spent 3/7 of his remaining money at the concession stand. While walking back to his seat, he saw a new hat on sale for $18. Did Mr. O'Connor have enough money left to buy the hat?
I am not sure what to do.
Answer:
no
Step-by-step explanation:
he starts with 90 bucks to find what the fraction represents you can multiply it by 2 to get an equal denominator of 90 then subtract 90-62 that'll give you 28 then it says he spent 3/7 so you do the same thing get an equal denominator by multiplying by 4 and get 28 and as they say whatever you do to the denominator is done to the numerator so 3 times 4 is 12 then you do 28-12 and you gets 16 which isn't enough to buy the hat. :)
A footbridge is in the shape of an arc of a circle. The bridge is 7 ft tall and 29 ft wide. What is the radius of the circle that contains the bridge? Round your answer to the nearest tenth.
Answer:
18.5 ft (to the nearest tenth)
Step-by-step explanation:
The diameter of the circle passes through the center of the circle and divides the width of the circle into two equal parts.
We complete the circle and apply the Law of Intersecting Chords.
In the diagram, by this law:
AB X BC =DB X BE
7*x=14.5X14.5
x=14.5X14.5÷7
x=30.04
Therefore:
Length of the Diameter= 7+30.04 ft=37.04 ft
Radius =37.04/2= 18.5 ft
The radius of the circle should be 18.5 ft (to the nearest tenth).
Calculation of the radius:
Since there is the bridge is 7 ft tall and 29 ft wide.
Also,
here we apply the Law of Intersecting Chords.
So,
[tex]AB \times BC =DB \times BE\\\\7\times x=14.5\times 14.5\\\\x=14.5\times 14.5\div 7[/tex]
x=30.04
Now
Length of the Diameter= 7+30.04 ft=37.04 ft
So, Radius = 50% of 37.04 = 18.5 ft
Hence, The radius of the circle should be 18.5 ft (to the nearest tenth).
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PLS HELP IM DOING THIS NOW and IDU, Students from Williams Middle School are also recycling aluminum cans. The data for the numbers of cans brought in each school day for a month were divided by quartiles and summarized in the box plot. Use the drop-down menus to choose the median, interquartile range, and range.
>Median:
>Interquartile range:
>Range:
Given:
Students from Williams Middle School are also recycling aluminum cans. The data for the numbers of cans brought in each school day for a month were divided by quartiles and summarized in the box plot.
We need to determine the Median, Interquartile range and Range.
Median:
The median is the middle value of the given set of data.
From the box plot, it is obvious that the median line is at 18.
Thus, Median = 18
Hence, the value of the median is 18.
Interquartile range:
The interquartile range is can be determined by finding the difference between the ends of the box in the box plot.
From the box plot, we have;
Interquartile range = 20 -16
Interquartile range = 4
Hence, the value of the interquartile range is 4.
Range:
The range can be determined by subtracting the highest and the lowest value in the given set of data.
From the box plot, the range can be determined by subtracting the ends of the line.
Thus, we have;
Range = 28 - 10
Range = 18
Hence, the value of the range is 18.
Answer:
Median: 18
Interquartile range: 4
Range: 18
Step-by-step explanation:
I just did this on edgen so this is the correct answer.
Rocco received 5 new shirts and 2 new pairs of jeans for his birthday how many different ways can he wear his shirts with jeans?
2
5
7
10
None of these
Answer:
D
10
Step-by-step explanation:
The requried Rocco can wear his shirts with jeans in 10 different ways. The correct answer is 10.
To determine the number of different ways Rocco can wear his shirts with jeans, we need to multiply the number of options for shirts by the number of options for jeans. In this case, Rocco has 5 different shirts and 2 different pairs of jeans.
Since he can wear any shirt with any pair of jeans, the total number of different combinations is obtained by multiplying the number of shirts (5) by the number of jeans (2):
5 shirts * 2 pairs of jeans = 10 different ways
Therefore, Rocco can wear his shirts with jeans in 10 different ways. The correct answer is 10.
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4. Suppose Tyler sprayed around the house for ants. Which formula would be used to find the number of ants still alive after a certain time if the number of ants was changing exponentially?
A. exponential decay
B. exponential growth
C. compound interest
D. cannot be determined from given information
I’m giving as much points as I can please help I need this right now
Answer:
I think that the answer is A.
Step-by-step explanation:
Bailey has a jar of marbles. The bowl has 16 green, 20 red, and 14 yellow marbles. He reaches into the jar without looking and randomly grabs a marble.
What is the probability that he grabs either a green marble or a yellow marble?
Enter your answer as a fraction in simplest form.
Choose the formula and the probability?
Answer:
3/5
Step-by-step explanation:
16g
20r
14y
=50 marbles
16/50 = 3.5/10
20/50 = 4/10
14/50 = 3/10
= 16/50 + 14/50 = 30/50 = 3/5
How far, to the nearest foot, does a horse on a Merry-Go-Round travel in one revolution if he is 6.5 feet from the center? (Use 3.14 for π)
A) 26 feet
B) 39 feet
C) 41 feet
D) 56 feet
Answer:
c
Step-by-step explanation:
I'm pretty sure it's asking for the circumference. The formula for finding the circumferene is C=πd (d=diameter) First, you need to fiind the diameter. Thequestion gives you the radius, 6.5, which is half the diameter. multiply that by 2 and you get 13. The question says to use 3.14 as π, so just multiply 3.14 by 13 and you get 40.82, which rounds to 41.
The given figure is a square pyramid. The side length of the base of the pyramid is 6.6 feet. The height of the
pyramid is 12.672 feet. What is the volume of the pyramid?
Answer:
Step-by-step explanation:multiply then round
4x+9Y=-19
-4X-7=13
Solving systems of equations using any method
Final answer:
To solve the system of equations, use the method of elimination. Multiply the second equation by 4 to make the coefficients of 'x' in both equations opposite. Add the two equations together to eliminate 'x' and solve for 'y'. Substitute the value of 'y' into one of the original equations and solve for 'x'. The solution to the system of equations is x = -5/2 and y = -1.
Explanation:
To solve the system of equations:
4x + 9y = -19
-4x - 7y = 13
We can use the method of elimination. Multiply the second equation by 4 to make the coefficients of 'x' in both equations opposite:
16x + 28y = -52
Now, add the two equations together to eliminate 'x':
37y = -39
Divide both sides by 37:
y = -1
Substitute the value of 'y' into one of the original equations:
4x + 9(-1) = -19
4x - 9 = -19
Add 9 to both sides:
4x = -10
Divide both sides by 4:
x = -10/4 = -5/2
Therefore, the solution to the system of equations is x = -5/2 and y = -1.
What is the perimeter, to the nearest hundredth of a unit, of the the
following polygon with vertices (-3, 2), (1, 2), (3,-1),(0,-3), (-4, -3)?
Answer:
Step-by-step explanation:
equivalent expression with fewer terms to 5+2x+7+4x ??
Answer: 12+6x
Step-by-step explanation:
add like terms
Answer:
12+6x
Step-by-step explanation:
5+2=7
2x+4x=6x
Plug the two expressions together and you will have 12+6x