The values of the dependent variable associated to corresponding linear equations are listed below:
x = - 12x = 13 / 2How to find the values associated to the results of a linear function
Herein we find two cases of linear equations in slope-intercept form, in which we need to clear the independent variable (x) associated to given values in the dependent variable (y). The equation of the line in slope-intercept form is described below:
y = m · x + b
Where:
m - Slopeb - InterceptBy algebra properties, the value of the independent variable can be defined by the following expression:
x = (y - b) / m
Now we proceed to determine the values of x:
Case 1: y = - x - 14, y = - 2
x = (- 2 + 14) / (- 1)
x = - 12
Case 2: y = - (3 / 2) · x - 9, y = - 48
x = (- 48 + 9) / (- 3 / 2)
x = - 39 / (- 3 / 2)
x = 13 / 2
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In a game, you pilot a spaceship and gain a point for every asteroid you
destroy. The game ends when your ship is hit by an asteroid. You already
have 94 points. Graph your possible final scores for the game.
Answer:
y = p+94
Step-by-step explanation:
If you already have 94 points you can't get lower than that.
p represents the amount of points you have, or the amount of asteroids you've destroyed.
What is the area of the smaller figure, in square centimeters?
04
08
O 20
O 40
Answer:
020
Step-by-step explanation:
I hope it will be helpful for u
Point p(3,0) partitions the line segment AB so that the ratio of AP to PB is 2:1 if point A is located at A (-3,-2) state the coordinates of B
The coordinates of B for the line segment AB where P divides it in the ratio 2: 1 is equal to (6 ,1).
Ratio that divides line segment AB is equal to,
AP : PB = 2 : 1
⇒ ( m : n ) = 2 : 1
Coordinates of point P (x ,y ) = ( 3 ,0 )
Coordinates of point A(x₁ , y₁ ) = ( -3, -2 )
Let us use the ratio of distances formula to find the coordinates of point B.
If point P divides the line segment AB in the ratio 2:1,
AP/PB = 2/1
Let the coordinates of point B be (x₂, y₂).
Use the midpoint formula to find the coordinates of the midpoint of the line segment AB.
which is also the coordinates of point P.
[ (mx₂ + nx₁ ) / (m + n) , (my₂ + ny₁ ) / (m + n) ] = ( x , y )
Substitute the values we have,
⇒ [ (2x₂ + (1)(-3) ) / (2 + 1) , (2y₂ + (1)(-2) ) / (2 + 1) ] = ( 3 , 0 )
Equate the corresponding values we get,
⇒ 2x₂ -3 / 3 = 3 and 2y₂ -2 / 3 = 0
⇒x₂ = 6 and y₂ = 1
Therefore, the coordinates of point B for the line segment AB are (6 ,1).
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The face of a fair sided cube are numbered 1-6 based on rhetorical probability if a number cube is rolled 60 times how many times should a 2 be rolled
Answer:
10
Step-by-step explanation:
P(2) = 1/6
1/6 = x/60
x = 10
1)
Given: m∠KAL = 100º
m∠L = 25°, OA = 21
Find: AK, AL, KL
2)
Given: ΔABC, m∠BAC = 77°, AD = 18
AD⊥CB, ∠ C = 18°,
Find: AC, AB, BC
AC = 18 + CB, AB = 18 + AD, BC = AB + AC - CB. The measures of the angles of the triangle are m∠BAC = 77°, ∠C = 18° and m∠A = 95°. The lengths of the sides of the triangle are AD = 18, AC = 18 + CB and AB = 18 + AD. The length of the side KL of the triangle KAL is KL = √(AK² + AL²).
AK = √(21² - (25)²) = 20
AL = √(21² - (20)²) = 25
KL = √(20² + 25²) = 29.7
AC = 18 + CB
AB = 18 + 18 = 36
BC = AB + AC - CB = 36 + 18 - CB = 54 - CB
The given information includes the measures of the angles of ΔABC, m∠BAC = 77°, ∠C = 18° and m∠A = 95°, and the length of the side AD = 18. We know that AD⊥CB, so we can use the Pythagorean Theorem to find the length of CB. We have CB = √(AD² - AC²) = √(18² - 18²) = 0. From this, we can calculate the lengths of the sides of the triangle. AC = 18 + CB = 18. AB = 18 + AD = 36. BC = AB + AC - CB = 54 - CB = 54.
The given information also includes the measure of m∠KAL = 100º and OA = 21. We can use the Pythagorean Theorem to find the lengths of the sides AK, AL, and KL of the triangle KAL. AK = √(OA² - AL²) = √(21² - (25)²) = 20. AL = √(OA² - AK²) = √(21² - (20)²) = 25. KL = √(AK² + AL²) = √(20² + 25²) = 29.7.
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You want to order a pizza for dinner. The pizza shop has a deal where you can buy a three-topping pizza for 11.99 . If the pizza shop has 30 different toppings that you can put on your pizza, how many different pizzas could you get for 11.99?
Answer:
10
Step-by-step explanation:
because each pizza is 11.99 and you can get three toppings, so 30 divided by 3 is 10, so you can get three different pizza.
Answer:
I think 10 pizzas.
Step-by-step explanation:
I WILL MARK
Q.5
HELP PLEASEEEE
How many solutions does the system of equations x − y = 7 and y equals the square root of the quantity 3 times x plus 3 end quantity minus 2 have?
A. 0
B. 1
C. 2
D.Infinitely many
Answer: A. 0
Step-by-step explanation: To determine the number of solutions for the system of equations x - y = 7 and y = sqrt(3x + 3) - 2, we can substitute y in the first equation with the expression for y in the second equation, giving us x - (sqrt(3x + 3) - 2) = 7. Simplifying this equation, we get sqrt(3x + 3) = -x + 9.
Since the square root of a number is always non-negative, we can conclude that there are no solutions to this system of equations. Therefore, the answer is A. 0.
- Lizzy ˚ʚ♡ɞ˚
What is the value of h?
We can see that h is the opposite angle of the angle which measures 47, as they are the angles that are directly opposite to each other where 2 lines/rays cross.
And since 2 opposite angles are equal to each other, h = 47.
Students may purchase Student may purchase ingredients from the camp store if they wish to make s'mores at the campfire. For every 15 students,the ingredients cost the camp store $31. 50 estimate the cost for 1 student
The estimated cost for one student to purchase the ingredients for s'mores at the camp store is $2.10.
To estimate the cost for one student, we can divide the total cost for 15 students by the number of students. Given that the ingredients cost $31.50 for 15 students, we can calculate the cost for one student as follows:
Cost for 1 student = Total cost for 15 students / Number of students
Cost for 1 student = $31.50 / 15
Cost for 1 student ≈ $2.10
Therefore, the estimated cost for one student to purchase the ingredients for s'mores at the camp store is approximately $2.10. This calculation assumes that the cost is evenly distributed among the students and that the quantity of ingredients per student remains constant.
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what is this answer.
Answer:
Step-by-step explanation:
is A
A person starts in Boulder, drives to Denver (50 km away) in 1 hour, stays in Denver 1 hour, then speeds back to Boulder in 30 minutes. What is the average speed of the round trip\
The person may have driven at different speeds during different parts of the trip (such as 50 km/hour on the way to Denver and 100 km/hour on the way back), the average speed over the entire trip is 40 km/hour.
The average speed for a round trip is calculated by dividing the total distance travelled by the total time taken.
In this case, the person travelled 50 km from Boulder to Denver and another 50 km back from Denver to Boulder, for a total of 100 km. The time taken for the round trip was 1 hour to drive from Boulder to Denver, 1 hour spent in Denver, and 0.5 hours to drive back from Denver to Boulder, for a total of 2.5 hours.
Using these values, we can calculate the average speed for the round trip as 40 km/hour. This means that on average, the person travelled at a speed of 40 kilometers per hour during the entire round trip. Although the person may have driven at different speeds during different parts of the trip (such as 50 km/hour on the way to Denver and 100 km/hour on the way back), the average speed over the entire trip is 40 km/hour.
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Every day, Kim practices volleyball and clarinet. Each day, she practices volleyball for 2.5 hours. If after 8 days she practiced both volleyball and clarinet for a total of 36 hours, how many hours per day did Kim practice clarinet?
Answer:
jhfjhfhfhkjfskjfshfskjjh
Step-by-step explanation:
Ju Chan solved the previous question by finding the expression 4(-15).
Which problem would give the same result? Select two options.
Answer:
-15(4) or -4(15) or 15(-4)
Step-by-step explanation:
As long as you stick with the same variables, you can change their position in the equation or change both of their signs. This should give you the same answer.
Let's say your equation was -2(6). This means you must multiply -2 and 6. This should give you -12. You could also phrase it as 2(-6) or -6(2) or 6(-2). They all give you -12 as a result.
Answer:
(-1)(15+15+15+15)
(-15)+ (-15)+ (-15)+ (-15)
Step-by-step explanation:
In 2000, 1500 rabbits live in a warren in a certain area. the number of rabbits increases exponentially at a discrete rate of 7% per year. predict population in 2008&2022
The predicted populations of rabbits in the warren in 2008 and 2022 are 2909 and 9933, respectively.
To predict the population of rabbits in the warren in 2008 and 2022, we can use the formula for exponential growth:
P(t) = P₀ (1 + r)ᵗ
Where P(t) is the population at time t, P₀ is the initial population, r is the growth rate, and t is the time elapsed.
For this problem, we know that P₀ = 1500, r = 0.07 (since the growth rate is 7%), and we want to find P(8) and P(22) (since we're predicting the population in 2008 and 2022, respectively).
Using the formula, we get:
\(P(8) = 1500( 1 + 0.07)^{8} = 2909\)
So we can predict that there will be about 2909 rabbits in the warren in 2008.
To find P(22), we simply plug in t = 22:
\(P(22) = 1500 (1 + 0.07)^{22} = 9933\)
So we can predict that there will be about 9933 rabbits in the warren in 2022.
Therefore, the predicted populations of rabbits in the warren in 2008 and 2022 are 2909 and 9933, respectively.
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a basketball player makes 65% of her free throws. if she attempts 10 free throws, what is the probability she will make exactly 7 of them?
The probability that the basketball player will make exactly 7 of her 10 free throws is approximately 0.226, or 22.6%.
How is probability determined?We may utilize the binomial probability formula to resolve this issue:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
where X is the number of made baskets from free throws, k is the number of made baskets we're looking for (k=7), n is the total number of attempts (n=10), p is the chance of success (p=0.65), and C(n,k) is the number of combinations of n things taken k at a time. (also known as the binomial coefficient).
When we enter the values, we obtain:
P(X=7) = C(10,7) * (0.65)⁷ * (1-0.65)³
We can calculate that C(10,7) = 120 using a calculator or a table. We thus have:
P(X=7) = 120 * (0.65)⁷ * (0.35)³
P(X=7) ≈ 0.226
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Write the equation of a line that is parallel to y = -1 and that passes through the point (8, -4)
Step-by-step explanation:
y = 0x - 1.
Slope of the line = 0.
A line that is parallel to the original line must have the same slope, which is 0.
y = 0x + c.
When x = 8, y = -4.
-4 = 0(8) + c. So c = -4.
Hence the equation of the parallel line is y = -4.
(HELP ILL GIVE BRAINLY PLEASE)
Answer:
4 is 2059
5 is 6xy^2
Step-by-step explanation:
The area of the figure is how many square units?
Answer:
hope it helped
have a nice day mate
Help this is the question pls help I need your help answer correctly
23 pts
Answer:
\(3/8* 16 \\3*2\\6\)
Step-by-step explanation:
Thus the mileage of water for this vehicle is 6 miles per gallon.
Find the product 8/6n - 4(9n^2 -4)
Answer:
- (27n^3 - 12n - 1) over 3n
Step-by-step explanation:
work out the area of a rectangle with base, b = 20mm and perimeter, p = 50mm.
Answer:
100
Step-by-step explanation:
If the base is 20, then 2 of the sides must have a length of 20. This means that the TOTAL length of the remaining sides is 10. (20*2) + (10) = 50. If we divide that in half, we get 5. That is the side length of the remaining 2 sides. This means that 20 * 5 will give us the area (b*h).
Given,
base, b = 20mm &
perimeter, p = 50mm.
the area of the rectangle : (50 – 20 × 2) ÷ 2 = 5. 5 × 20 = 100 \(mm^{2}\).
Perimeter and area are two important and basic mathematical subjects. They help quantify the physical space and also provide a more advanced foundation of mathematics in algebra, trigonometry, and calculus. Perimeter is a measure of the distance around a shape, and area indicates how much area the shape covers.
The perimeter of a 2D shape is the distance around the shape. You can imagine wrapping a string around a triangle. The length of this cord is around the triangle. Or, if you're traveling outside the park, take a route that goes around the edge of the park.
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Zane is washing cars to help pay for a school trip. He gets paid $8 for every car he washes and made a total of $64 on Saturday. Write an equation to show how many cars Zane washed on Saturday.
8 − x = 64
64x = 8
8 + x = 64
8x = 64
Answer:
I just to the test
It D: 8x=64
Answer:
D: 8x = 64
Step-by-step explanation:
($8) equals the amount he makes for washing 1 car
($64) is the total amount Zane has made from washing cars
(X) is equal to how many cars he has washed for the total to be $64
Now, all we have to do is write down an equation that shows how we can find how many cars have been washed for him to get his sum of $64.
8 times x (x is equal to the number of cars he's washed) so 8 times something (or x) gives you the amount of money Zane has made which would be the only viable answer to the question.
8 - x = 64 - Incorrect
You would not be subtracting the amount of cars Zane has washed by the amount of money he is making per car.
64x = 8 - incorrect
This would mean you're multiplying the total amount of money Zane has made, by how many cars he's washed, which then equals the amount he makes per car. Doesn't make sense ik.
8 + x = 64 - incorrect
While this could look like a viable answer to what they're asking, don't be tricked. You have to multiply the number of cars Zane has washed by the amount he makes per car, otherwise you would just be adding 8 plus the number of cars he washed which does not equal $64.
Hope this helped:)
What value of will make the triangles similar by the similarity theorem?
As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.
Similarity theorem:
In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.
Given,
Here we need to find the t value of will make the triangles similar by the similarity theorem.
For example, we are told that the 2 triangles are similar by SSS theorem.
Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem
Therefore, in the triangles ,applying the SSS postulate gives;
=> x/35 = 44/20
Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;
=> x = (44 * 35)/20
When we simplify this one then we get,
=> x = 77
Therefore, the value of x is 77.
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what is the grand objective function in terms of x1,x2, when w1 = 0.6, w2 = 0.4.
The grand objective function in terms of x1 and x2 with w1 = 0.6 and w2 = 0.4 is a mathematical equation that represents the overall objective of the system or problem being analyzed.
The grand objective function is a mathematical expression used to optimize a certain goal or outcome, considering multiple variables and their corresponding weights. In this case, you have two variables x1 and x2, with weights w1 (0.6) and w2 (0.4).
It is typically used in optimization problems to find the optimal values of x1 and x2 that will maximize or minimize the function. Without additional information or context, it is impossible to provide a specific equation for the grand objective function.
Your grand objective function can be written as:
G(x1, x2) = 0.6 * x1 + 0.4 * x2
This function represents the weighted sum of x1 and x2, and can be used to optimize a specific objective by finding the appropriate values for x1 and x2.
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The amount of cereal in a box is normally with a mean of 24 oz. And a standard deviation of 0.72 oz. If 17,500 boxes of cereal are packaged in one day,approximately how many would contain less than 23.1 oz? You must show your work to receive credit
The approximately 2,912 boxes of cereal would contain less than 23.1 oz.
Given data:The mean is 24 oz.The standard deviation is 0.72 oz.The number of cereal boxes packaged in one day is 17,500.
To determine approximately how many boxes of cereal would contain less than 23.1 oz,
we need to calculate the z-score for 23.1 using the formula:z-score = (x - μ) / σ, where:x = 23.1 (the value we are interested in)μ = 24 (the mean)σ = 0.72 (the standard deviation)Plugging in the values,
we get:z-score = (23.1 - 24) / 0.72 = -0.97We can use a standard normal distribution table to find the area (probability) to the left of this z-score.
The area to the left of -0.97 is approximately 0.1664.This means that approximately 16.64% of boxes would contain less than 23.1 oz.
To find the actual number of boxes, we multiply this probability by the total number of boxes packaged in one day:0.1664 x 17,500 = 2912 (rounded to the nearest whole number)
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Urgent help needed!
Asap please:)
12. What is the value of x to the nearest tenth?
Answer:
x = 10.5
Step-by-step explanation:
If you draw a line from the center to either end of 18.8, this will make a right triangle with hypotenuse is x, one side is 4.7, the other side is 18.8/2 = 9.4
so the Pythagorean Theorem states that a^2 + b^2 = c^2
x^2 = 4.7^2 + 9.4^2 = 22.09 + 88.36 = 110.45
x = 10.5
A hall 110 feet in length is to be designed as a whispering gallery If the foci are located 30 feet from the center, how high will the ceiling be at the center? The ceiling will be about feet high (Type an integer or decimal rounded to one decimal place as needed)
The height of the ceiling at the center of the hall will be approximately 19.9 feet.
Why will be a hall 19.9 feet in length?To design a hall 110 feet in length as a whispering gallery, the height of the ceiling at the center should be 19.9 feet. This is calculated as follows:
Given that the hall has a length of 110 feet and is designed as a whispering gallery.
Also, the foci are located 30 feet from the center. We are to determine the height of the ceiling at the center.
To solve the problem, we will use the formula for a whispering gallery which is given as:
1 / b2 = 1 / a2 - 1 / c2where a, b, and c are the semi-axes of the ellipse and are related by the equation:
a2 = b2 + c2Using the given information, we can find the value of a as follows:
a = 55 feet (half the length of the hall) and
c = 30 feet (distance of the foci from the center of the hall)
Substituting these values in the equation for a above, we have:
b2 = a2 - c2= 55² - 30²= 3025 - 900= 2125 feet²Therefore, b = √2125 = 46.1
feetNow we can calculate the height of the ceiling at the center using the formula for the height of an ellipse at its center, which is given as:
height = b2 / a= (46.1)2 / 55= 19.9 feet (rounded to one decimal place)
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Solve the inequality. Graph the solution. 3x≤−54
\(x\leq -18\)
Graph Displayed Below
Hope this helps!
The solution to the given inequality \(3x \leq -54\) is \(x \leq \frac{-54}{3}\) .
Inequality is a fine statement that compares two values, showing if one is lower than, lesser than, or simply not equal to another value. Inequalities are frequently used to represent connections between amounts, similar to the relationship between the height and weight of a person, or the relationship between the speed and time of an object in stir.
We first divide the inequality \(3x \leq -54\) by 3 on both sides to obtain:
\(x \leq \frac{-54}{3}\) .
Then, we plot the line \(x = \frac{-54}{3}\) on the graph. The region left to the line thus obtained is the solution of the given question.
Thus, the line \(x \leq \frac{-54}{3}\) is plotted in the graph.
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Need help asap! thanks!
The opposite sides are parallel to each other because the opposite sides have the same slope value.
What is the Slope of Parallel Sides/Lines?When two sides or lines are parallel to each other, the value of their slope would be the same.
Slope of WZ = rise/run = -1/3
Slope of XY = rise/run = -1/3
Slope of XW = rise/run = 3/2
Slope of XW = rise/run = 3/2
Therefore, since the slopes of the opposite sides, then they are parallel to each other.
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The long side of a rectangle is 2b + 4 units, and its area is
4b2 + 12b + 8. Find the width
Answer:
3
Step-by-step explanation:
its 3