The slope of the line is 2/3.
What is a line?
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.
Given coordinates of the points are A(1,-9) and (4,-7).
The formula of slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
Here x₁ = 1, y₁ = -9, x₂ = 4, and y₂ = -7
m = (-7 - (-9))/(4 - 1)
m = 2/3
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Twice w is at most 30
Answer:
2w [tex]\leq[/tex] 30
Step-by-step explanation:
Two times the value of w must be less than or equal to 30
Answer: w < = 15
Step-by-step explanation:
Our equation is
2w < = 30
Divided by 2 both sides
w < = 15
An engineer makes different-size samples of a new material. The table shows volumes and the related masses. What would be the mass of 100 cubic centimeters of the material? Of 500 cubic centimeters of the material? Use pencil and paper. Explain how you can use mental math to find the answer.
The mass of 100 cubic centimeters of the material would be [answer] enter your response here grams.
Answer:
The mass of 100 cubic cm = 1,000 grams.
The mass of 500 cubic cm = 5,000 grams.
Step-by-step explanation:
90/10=9
140/10=14
250/10=25
100x10=1000
500x10=5000
Can someone help me with Question 2b of this assignment? I'd deeply appreciate it! :)
Answer:
x=-6
Step-by-step explanation:
[tex]\frac{1}{2} x[/tex]-6=2x+3
∴2×( [tex]\frac{1}{2} x[/tex]-6)=2×(2x+3)
∴x-12=4x+6
∴3x=-18
∴x=-6
Please answer the question in the photo.
Answer:
m it's equal to 6 because division its equal subtract the power
Step-by-step explanation:
A* to the power 9 divided by A* to the power 3 its equal to 9-3 = A* to the power its a
A^6
Points A, B, and C are collinear. What is the slope of AB in simplest form?
The slope of the line AB in simplest form is 3/2.
What is slope?The slope is the rate of change of the y-axis with respect to the x-axis.
The equation of a line in slope-intercept form is y = mx + b, where
slope = m and y-intercept = b.
We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.
We also know that the slope is rise over run, rise represents the y-axis and run represents the x-axis.
From B to C rise is 3 and from B to C run is 2.
Therefore, the slope of the line AB is 3/2.
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If Hugo has 4 times as many quarters as nickels and they have a combined value of 840 cents, how many of each coin does he have?
Let Q be the number of quarters and N be the number of nickels that Hugo has. We are given that Hugo has 4 * N quarters and that the total number of quarters and nickels is worth 840 cents. Since each quarter is worth 25 cents and each nickel is worth 5 cents, the total number of quarters is worth 25 * Q cents and the total number of nickels is worth 5 * N cents. Therefore, the total number of quarters and nickels is worth 25 * Q + 5 * N cents. Since the total number of quarters and nickels is worth 840 cents, we can set up the following equation to represent this information:
25 * Q + 5 * N = 840
We are also given that Hugo has 4 * N quarters, so we can set up the following equation to represent this information:
Q = 4 * N
We can solve this system of equations to find the number of quarters and nickels that Hugo has. Substituting the value of Q in the second equation into the first equation, we get the following:
25 * (4 * N) + 5 * N = 840
Distributing the 25 on the left side of the equation, we get the following:
100 * N + 5 * N = 840
Combining like terms, we get the following:
105 * N = 840
Dividing both sides of the equation by 105, we get the following:
N = 8
Substituting the value of N into the second equation, we get the following:
Q = 4 * 8
Solving for Q, we get the following:
Q = 32
Therefore, Hugo has 8 nickels and 32 quarters.
Answer:
32 quarters
8 nickels
Step-by-step explanation:
Information:
1 quarter = 25 cents1 nickel = 5 centsDefine the variables:
Let x be the number of quarters.Let y be the number of nickels.If Hugo has 4 times as many quarters as nickels:
[tex]\implies x=4y[/tex]
If the combined value of quarters and nickels is 840 cents:
[tex]\implies 25x+5y=840[/tex]
Substitute the first equation into the second equation and solve for y:
[tex]\implies 25(4y)+5y=840[/tex]
[tex]\implies100y+5y=840[/tex]
[tex]\implies 105y=840[/tex]
[tex]\implies y=8[/tex]
Substitute the found value of y into the first equation and solve for x:
[tex]\implies x=4(8)[/tex]
[tex]\implies x=32[/tex]
Therefore, Hugo has:
32 quarters8 nickelsfor a normal distribution, assume the 'population' standard deviation is 7.7. what is the maximal margin of error associated with a 90% confidence interval for the true population mean if n
for a normal distribution, assume the 'population' standard deviation is 7.7. .645 * 7.7 / √(n) is the maximal margin of error associated with a 90% confidence interval for the true population mean if n
The margin of error is calculated as
Margin of Error = Critical Value * Standard Deviation / √(Sample Size)
= 1.645 * 7.7 / √(n)
= 1.645 * 7.7 / √(n)
The margin of error is a measure of the accuracy of an estimate based on a sample from a population. It is calculated by taking the critical value (1.645, for a 90% confidence interval) multiplied by the population standard deviation (7.7), divided by the square root of the sample size (n). The higher the sample size, the smaller the margin of error. This means that a larger sample size gives a more accurate estimate of the true population mean.
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What are the types of triangles based on their sides and angles? How do you classify a triangle as equilateral, isosceles, scalene, acute, right, or obtuse? Give an example of each.
Based on their sides, the 3 triangles are classified as equilateral triangles, isosceles triangles, and scalene triangles.
A triangle is scalene if all of its three sides and angles are differentScalene-Triangle-1
In the figure, all three symbols that are given on each side are different, which denotes that all three sides are unequal.
If two of its sides are equal, a triangle is called an isosceles.One example of the angles of an isosceles acute triangle is 50°, 50°, and 80°.
A triangle with all three equal sides is called equilateral.The sum of all three angles of an equilateral triangle is equal to 180 degrees. 60° + 60° + 60° = 180°
Acute angles measure less than 90 degrees.the examples of acute angles are 25°, 36°, 47°, 64°, 55°, 72°, 80° and so on
Right angles measure 90 degrees.Examples of right angles are all around us. We can see right angles in the corners of a room, book, cube, windows, and at several other places.
Obtuse angles measure more than 90 degreesExamples of obtuse angles include 166°, 121°, 110°, 117°, and 91°.
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Given that is it ever possible to have
Explain.
The answer is yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands.
What are square roots?A square root of a number is a value that, when multiplied by itself, gives the number.
Given that, is it possible √a+√b = √a+b
Yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands.
If either a or b equals zero, then the sums would be the same.
Since the square root of 0 is ±0, adding it to a given radical would not change the radical. Also, adding zero to the radicand would not change its value.
Hence, it is possible to have the sum of square roots equal the square root of the sum of the radicands.
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how should the decimal point in 52.48be m
Answer:
5 spaces right
hope this helps
Write the standard form equation for a hyperbola with center at the origin, vertices at (1, 0) and (-1, 0), and
foci at (5, 0) and (-5, 0).
Answer:
The answer is the standard form equation for a hyperbola with center at the origin, vertices at (1, 0) and (-1, 0), and foci at (5, 0) and (-5, 0), which is:
x^2 - \frac{y^2}{5} = 1
This equation describes the shape of the hyperbola and allows you to determine the location and size of the hyperbola on a coordinate plane.
Step-by-step explanation:
The standard form equation for a hyperbola with center at the origin, vertices at (1, 0) and (-1, 0), and foci at (5, 0) and (-5, 0) is given by:
$$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$
where $a$ and $b$ are the lengths of the semi-major and semi-minor axes, respectively. In this case, the distance between the vertices is 2, so the semi-major axis is 1 and the semi-minor axis is $\sqrt{5}$. Therefore, the equation of the hyperbola is:
$$\frac{x^2}{1^2} - \frac{y^2}{\sqrt{5}^2} = 1$$
which simplifies to:
x^2 - \frac{y^2}{5} = 1
Work out the circumference of this circle. Give your answer in terms of pi.
Answer:
[tex]12\pi[/tex]
Step-by-step explanation:
Circumference Formula: [tex]2\pi r[/tex]
Our radius is 6, plug that in.
[tex]2\pi 6[/tex]
12[tex]\pi[/tex]
Leave in terms of pi, so do not simplify further.
The distance between (-7, a) and
(5, 1) is 13 units.
Find two possible values for a.
Answer:
1
Step-by-step explanation:
you will be required to find a magnitude of the two points that is (5,1) -(-7,a) =(12,1-a)
then find square root using the formula √x^2+y^2
thus (√12^2+a^2)=13 thus 12+a= 13 hence a=13-12
a=1
if two sides of a triangle are 22 in and 13 in, what is the smallest whole number value for the 3rd side?
If two sides of a triangle are 22 in and 13 in, then is the smallest whole number value for the 3rd side will be 10
According to the rule of triangle the sum of first angle and second angle should be greater than the third angle.
first angle+ second angle > third angle
Here
22-13 = 9
so to became a triangle the minimum value of the third side will be 10(9+1).
Therefore, If two sides of a triangle are 22 in and 13 in, then is the smallest whole number value for the 3rd side will be 10
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Let's solve. 3x a) 3X 8 10. d) { + 14/= 1/1/2 ¼ 4 / = 7 3 8) ²³² + ³ = 5 X
Answer: hmmmm who knows?
Step-by-step explanation: but you got it good luck!
jay designed 4 t-shirts. sal designed 5 times as many t-shirts. which equation shows how many more t-shirts sal designed?
The equation which shows that how many more t- shirts sal designed is x^{y} .....
If jay designed 4 t-shirts and sal designed 5 times as many t-shirts. So the equation which shows how more t- shirts sal designed is....
Firstly we make the data to simplify the peoblem:
Suppose:
T-shirts designed by jay = x
T-shirts designed by sal = y
As t-shirts designed by jay are 4 so
x=4
and t-shirts designed by sal are 5 times as many t- shirts so
y= 5times = 4×4×4×4×4 = 1,024
So the equation which shows how many more t-shirts sal designed will be:
Required equation = x^{y}
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The scale factor of two triangles is 2:5. If the smaller triangle has side length of 30, what would be the length of the corresponding side on the bigger triangle?
Answer:
75
Step-by-step explanation:
From the way you've typed the question, it would appear that the ratio of the size of the smaller side to the ratio of the size of the larger side is 2:5.
Therefore, if the smaller side is 30, you can use the ratio the find the larger side:
[tex]S:L\\2:5\\\\[/tex]
(×15 to make the smaller side 30)
[tex]30:75[/tex]
Therefore, the bigger triangle would have side length 75.
Which interval contains 11 states? Check all that apply. 0 to 3 3 to 6 6 to 9 9 to 12 12 to 15 15 to 18 18 to 21
The intervals that contain 11 states, are given as follows:
3 to 6.6 to 9.What is shown by the bar graph?The bar graph presented by the image shown at the end of the answer shows the number of states present in each interval.
The features of the graph are given as follows:
Horizontal axis: interval.Vertical axis: number of states in each interval.Then the number of states for each interval are given as follows:
0 to 3: 16 states.3 to 6: 11 states.6 to 9: 11 states.9 to 12: 3 states.12 to 15: 3 states.15 to 18: 3 states.18 to 21: 4 states.Hence the intervals 3 to 6 and 6 to 9 are the intervals that contain 11 states, being the correct answers to this problem.
Missing InformationThe bar graph is given by the image shown at the end of the answer.
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The sum of two numbers is 46. The larger number is 16 more than the smaller number.
Answer:
Smaller number: 15 Larger number: 31
Step-by-step explanation:
Let's call the smaller number x
So, the larger number will be x+16 (it's 16 more)
Then, write an equation:
x (smaller number) + (x+16) (larger number) = 46 (sum)
x+x+16=46
2x+16=46
2x=30
x=15
So, the smaller number is 15
The larger number is x+16, so plug in x:
x+16 = 15+16 = 31
The smaller number is 15, and the larger number is 31
[tex]y = 15 \\ x = 31[/tex]
Step-by-step explanation:
[tex]y + 16 + y = 46 \\ 2y = 30 \\ y = 15 \\ \\ x = 15 + 16 \\ x = 31[/tex]
You might need:
Nizhoni adds water at a constant rate to a 2 L reservoir in a water filtering pitcher until it is full.
At the same time, water goes through the filter and out of the reservoir, into the pitcher. It takes
5/11 minutes to fill the reservoir, then another 3 minutes for the reservoir to empty.
3 1/3 minutes for it to empty. at what rate does nizhoni add water to the reservoir?
At the rate of 4 2/5 L of water is added into the reservoir per minute.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
As It takes 5/11 minutes to fill the reservoir.
So, the rate at which Nizhoni adds water to the reservoir.
Rate= Volume/ Time taken
Rate = 2 L/ (5/ 11)
= 2 x 11/5
= 22/5 L/ min
= 4 2/5 L/ min.
Hence, at the rate of 4 2/5 L of water is added into the reservoir in one minute.
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Answer: 5
Step-by-step explanation: I answered this question.
What are the first two steps when finding the value of the expression below?
65 (30-24 divided 6× 2)
Use the drop-down menus to explain the first two steps.
The first step us to find the value of ____
The second step is to find the value of ___
Answer:
The first step is 24 divided by 6 ..... (4)
The second step is 4 x 2 ...... (8)
Step-by-step explanation:
65(30-24 divided by 6 x 2)
65(30- 4 x 2)
65(30 - 8)
65(22)
1,430
if x,10,2x-4, and 12 are in proportion find the value of x
Answer:
x=5
Step-by-step explanation:
To find the value of x, we need to first set up the proportion using the given information. Since the given values are in proportion, we can set up the proportion as follows:
x / 10 = (2x - 4) / 12
Next, we can cross-multiply to solve for the value of x:
12x = 10(2x - 4)
12x = 20x - 40
-8x = -40
x = 5
Thus, the value of x is 5. This means that the other values in the proportion are also 5, 10, 10, and 12, respectively.
Write an equation of the line that passes through (4, 8) and is perpendicular to the line y = x-5.
An equation of the perpendicular line is
The slope of a line that is perpendicular to the line y = x - 5 is the negative reciprocal of the slope of y = x - 5. The slope of y = x - 5 is 1, so the slope of the line that passes through (4, 8) and is perpendicular to y = x - 5 is -1.
We can use the point-slope form of a line to write the equation of the line that passes through (4, 8) and has a slope of -1. The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, (x1, y1) is (4, 8) and m is -1, so the equation of the line is y - 8 = -1(x - 4). Simplifying this equation, we get y - 8 = -x + 4. Adding 8 to both sides of the equation, we get y = -x + 12. This is the equation of the line that passes through (4, 8) and is perpendicular to y = x - 5.
(v³ + 2v² - 21v +21) ÷ (v + 6)
Answer:
v3+2v2−21v+21/v+6
Step-by-step explanation:
There are no solutions to this equation
cual es la respuesta
The verdict on each of the given scenarios are as follows;
1. Yes, enough information is given to conclude that the triangles are congruent by the side-side-side SSS congruence theorem.2. No, the information conveyed through the triangles is not enough to conclude that the triangles are congruent.3. Yes, the two triangles given are congruent by virtue of the HL Congruence theorem.Which congruence theorems render the triangles congruent?By observation:
1. Since the two Triangles represented in 1. share a side and also, the two corresponding sides are congruent; it can be concluded that the two triangles are congruent.
2. By observation, although two sides are said to be congruent in the triangles; it cannot be concluded that the triangles are congruent neither by HL nor SSS congruence theorem.
3. The two Triangles share the diagonal which serves as the hypothenuse of both triangles; in addition, one of the other side lengths of the triangles are congruent; Therefore, the triangles are congruent by the HL congruence theorem.
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Stephan borrowed $125 to buy an electric scooter. The function f(x) = 125 - 12.5x
can be used to represent the amount of money Stephan owes on the loan, where X is the number of weeks that Stephan pays towards the loan.
The amount that Stephen owed after 2 weeks is $100.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, Stephan borrowed $125 to buy an electric scooter and the function f(x) = 125 - 12.5x
can be used to represent the amount of money Stephan owes on the loan, where X is the number of weeks that Stephan pays towards the loan.
The amount after 2 weeks will be:
f(x) = 125 - 12.5x
= 125 - 12.5(2)
= 125 - 25
= $100
The amount is $100.
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Complete question
Stephan borrowed $125 to buy an electric scooter. The function f(x) = 125 - 12.5x
can be used to represent the amount of money Stephan owes on the loan, where X is the number of weeks that Stephan pays towards the loan. What is the amount owed after 2 weeks?
Ethan buy a video game on ale. If the video game ueully cot $39. 99 and it wa on ale for 20% off how much did ethan pay?
Answer:
$31.99
Step-by-step explanation:
I have no idea what to put here
At Sparky' Candy World, Mile pent a total of $13. 75 on gummy bear and jelly bean. He bought 2. 5 pound of gummy bear at $3. 40 per pound. If jelly bean cot $1. 50 per pound, how many pound of jelly bean did he buy?
By solving this question of algebra we can calculate that Mile bought 3.5 pounds of jelly bean.
What is algebra?Algebra is the study of using variables to denote some quantity, and then solving equations to calculate the value of the quantity based on some conditions given.
How to solve questions of algebra?Let x be the amount of gummy bear bought and y be the amount of jelly bean bought. Then, 3.40x + 1.5y = 13.75 (total amount of money)
x = 2.5 (given in question)
then,
3.40 (2.5) + 1.5y = 13.75
y = 3.5 pounds
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Which equation has infinitely many solutions? 5(2x 4) = 10x – 12 5(2x 4) = 10(x 2) 5(2x 4) = 12x 5(2x 10) = 20(x 1)
The equation that has infinitely many solutions is 5(2x + 4) = 10(x + 2).
An equation can have infinitely many solutions when both sides of the equation satisfy the same conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line. For the given equations it can determine if the equation has infinitely many solutions by simplifying the equation and see if both sides are equal. Hence,
5(2x + 4) = 10x – 12
10x + 20 ≠ 10x - 12
5(2x + 4) = 10(x + 2)
10x + 20 = 10x + 20
5(2x + 4) = 12x
10x + 20 ≠ 12x
5(2x + 10) = 20(x + 1)
10x + 50 ≠ 20x + 20
Hence, 5(2x + 4) = 10(x + 2) has infinitely many solutions.
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A certain arcade game gives players tickets. The table below shows the number of tickets a player gets for the number of points.
Answer: Each point appears to give the same number of tickets
9 points give 54 tickets
Step-by-step explanation:
Each point appears to give the same number of tickets
To find the number of tickets, a point gives
divide the number of tickets by the number of points.
18/3 = 6
you get six tickets per point
find the number of points that give 54 tickets by dividing 54 by 6
54/6=9
9 points give 54 tickets