To solve the system by substitution, substitute the value of z in the equations and solve them simultaneously.
Explanation:To solve the system by substitution, we need to substitute the value of z in the other equations. Given that z=5, we can substitute this value in the first and third equations:
2x - y + 5 = -4
-2x + 3y - 5 = 10
Now, we can solve these two equations simultaneously to find the values of x and y.
To solve a system of equations by substitution, express one variable in terms of the other and substitute it into the other equations to eliminate that variable before solving for the remaining variables.
Explanation:To solve this system of equations by substitution:
Start by expressing one variable in terms of the other variable from one of the equations. In this case, we can express z as 5 since it is given.Substitute the value of z into the other two equations to eliminate the variable z.Solve the resulting system of equations for the remaining two variables.By following these steps, you can find the values of x, y, and z that satisfy the system of equations.
The length of each edge of a cube is 22 inches. The area of each face of the cube is square inches. The surface area of the cube is square inches.
Answer: Each face would have an area of 22 * 22 = 484 square inches.
Since a cube has 6 faces, then the total area = 6 * 484 = 2,904 square inches.
Step-by-step explanation:
A birthday cake was cut into equal pieces, and five pieces were eaten. The fraction 2/7 shows how many pieces are left. According to the fraction, how many pieces were not eaten
A.2
B.7
C.12
D.5
Find the area under the standard normal distribution curve for each.
a. between z 0 and z 1.95
b. between z 0 and z 0.37
c. between z 1.32 and z 1.82
d. between z 1.05 and z 2.05
e. between z 0.03 and z 0.53 2. find
To find the area under the normal distribution curve for a range of z-values, you refer to a z-table and possibly subtract two areas to find the area between two z-values. The areas above were calculated as examples.
Explanation:The subject in question involves finding the area under the standard normal distribution curve for various z-values. This is a concept in statistics that evaluates the probability which a particular range of values under the normal distribution curve might occur.
For z between 0 and 1.95, we refer to the z-table and find the area under the curve as 0.975.For z between 0 and 0.37, using the z-table, the area under the curve is 0.644.For z between 1.32 and 1.82, we find the areas corresponding to each value on the z-table and subtract them. This is 0.9664 - 0.9066 = 0.0598.For z between 1.05 and 2.05, again we find the areas corresponding to each value and subtract them, which gives us 0.975 - 0.8543 = 0.1207.For z between 0.03 and 0.53, we find the corresponding areas and subtract, resulting in 0.7054 - 0.5120 = 0.1934.Learn more about standard normal distribution here:https://brainly.com/question/29509087
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A board is 4.6 feet long. How many meters long is the board?
Find the slope write into slope intercept form (19,-16),(-7,-15)
Answer: [tex]m= -\frac{1}{26}[/tex]
(19,-16) = (x1,y1)
(-7-15) = (x2,y2)
Slope= [tex]\frac{y2-y1}{x2-x1}[/tex]
= [tex]\frac{-15-(-16)}{-7-19}[/tex]
= [tex]\frac{-15+16}{-7-19}[/tex]
= [tex]\frac{-15+16}{-26}[/tex]
= [tex]-\frac{1}{26}[/tex]
Marcello is constructing the perpendicular bisector of AB¯¯¯¯¯. He has already constructed arcs as shown.
What should Marcello do for his next step?
a) Place the point of the compass on point X and draw an arc, using AY as the width for the opening of the compass.
b) Use the straightedge to draw a line through points X and Y.
c) Use the straightedge to draw AX←→ and AY←→.
d) Place the point of the compass on point X and draw an arc, using AX as the width for the opening of the compass.
Answer: "Use the straightedge to draw a line through points X and Y." is the right answer.
Step-by-step explanation:
To perpendicular bisector of line segment AB. There are following steps:
1) Draw arcs from points A and B on the both sides of AB.
2) Name the intersection points as X and Y.
3) Use the straightedge to draw a line through points X and Y.
4) Name the point as O
hence we have construct perpendicular bisector XY of AB which bisects at O.
Lorrae swims at a constant speed, s, for 2 hours. Create a formula for the distance she swims, d.
The formula for the distance Lorrae swims at a constant speed for 2 hours is d = 2s, where d is distance and s is her speed.
Explanation:The question is asking for a formula to calculate the distance that Lorrae swims. Since distance (d) is equal to speed (s) multiplied by time (t), and we know that Lorrae swims at a constant speed, s, for 2 hours, a formula for her distance would be d = s * t.
In this case, the time, t, is 2 hours. So, we can substitute t with 2 in our formula. Hence, the formula for the distance Lorrae swims is d = s * 2 or d = 2s. This is the equation you can use to compute the distance Lorrae swims for any given speed at a constant period of 2 hours.
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Austin is watching a football game. His team loses 9 yards and then gains 5 yards. He doesn’t watch the next play, but afterwards he sees that his team now has a total loss of 1 yard. How many yards did the team gain or lose on the play Austin missed? Show your work.
Write the point-slope form of the equation of the line that passes through the origin and has a slope of 2. include your work in your final answer. type your answer in the box provided or use the upload option to submit your solution.
Hey I need geometry help asap (please Help) and you get some points
the answer is A x=15 and y =12
Philip has 2,000 and spends $23.75 on supplies.he divides the remaining amount equally among his 8 employees how much does each employee receive?
What is the best first step in solving the equation 3 + = 5? Subtract 3 from both sides. Find the cube of . Cube both sides of the equation. Subtract 5 from both sides.
How do I find the value of the variable?
the three inside angels need to equal 180, so first find the missing inside angle:
86.5 + 41.4 = 127.9
180-127.9 = 52.1
now that angle and y need to equal 180 degrees
so 180 - 52.1 = 127.9
y = 127.9 degrees
Complete the point-slope equation of the line through (1,3) and (5,1)
The point-slope equation of the line through (1,3) and (5,1) is y - 3 = -0.5(x - 1), where the slope m= -0.5 was calculated using the formula m = (y2 - y1) / (x2 - x1).
Explanation:To complete the point-slope equation of the line through points (1,3) and (5,1), we first need to find the slope of the line, which can be calculated using the formula: m = (y2 - y1) / (x2 - x1), here (x1,y1) and (x2,y2) are the coordinates of two points on the line.
Substituting in the given coordinate values gives us m = (1 - 3) / (5 - 1), which simplifies to m = -0.5, indicating a downward slope.
The point-slope form of the equation of a line is y - y1 = m(x - x1). So, substituting one of the given points (1, 3) and the calculated slope into the point-slope form gives us y - 3 = -0.5(x - 1).
Therefore, the point-slope equation of the line through (1,3) and (5,1) is y - 3 = -0.5(x - 1).
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The length of a rectangle is 5 in. more than 3 times its width. the area of the rectangle is 50in.2. a quadratic function represents the dimensions of the rectangle. what is the domain of the function?
How to I work out the answer?
What is
Write
52 over 6
as a mixed number.
Give your answer in its simplest form.
If one side of a square notebook measures 20 cm, what is the area of the front cover of the notebook?
The area of the front cover of the square notebook is A = 400 cm²
What is the area of a square?A square is a four sided quadrilateral with all of the side having equal lengths. The total internal angle of a square is 360° with each side perpendicular to each other.
A square is a 4 sided polygon where all the sides are of equal length.
The area of the square is the square of any one of its side
Let a be the side of the square
Area of the square = a²
Given data ,
Let the area of the square be represented as A
Now , the side length of the notebook a = 20 cm
And , the area of the front cover of the notebook = area of square
On simplifying , we get
The area of front cover A = a²
The area of the front cover of the notebook A = 20 x 20
The area of the front cover of the notebook A = 400 cm²
Hence , the area of the square notebook is 400 cm²
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The spelling contest awards four prizes Tim,Sam,Jen, and Kate all made it to the final round. In how many ways can first, second, third, and fourth place be assigned
In 24 ways the first, second, third, and fourth place be assigned
What is Permutation?A permutation is an arrangement of objects in a definite order. .
Given that, for a spelling contest awards four prizes Tim, Sam, Jen, and Kate all made it to the final round.
We need to find in how many ways can first, second, third, and fourth place be assigned.
This can be arranged in 4! ways.
4!=4×3×2×1
4!=24
Hence in 24 ways the first, second, third, and fourth place be assigned.
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for every five baseball cards that Mickey has Mike has 3 baseball cards if Mike has 72 baseball cards how many cards does Mickey have?
Mickey has 3 cards.
Explanation:To determine how many cards Mickey has, we can set up a proportion using the information given. We know that for every five cards Mickey has, Mike has 3 cards. So the proportion would be: (Mickey's cards) / 5 = 3 / (Mike's cards).
Given that Mike has 72 cards, we can plug that into the proportion: (Mickey's cards) / 5 = 3 / 72.
To solve for Mickey's cards, we can cross multiply: (Mickey's cards) = (3 / 72) * 5.
After simplifying, we find that Mickey has 3.125 cards. However, since we can't have a fraction of a card, we know that Mickey has 3 cards.
Kelly reads x hours a week. tim reads two times more than kelly and jim reads five hours more than tim. which expression represents the amount of time jim reads?
Answer:
2x+ 5 expression represents the amount of time jim reads
Step-by-step explanation:
As per the statement:
Kelly reads x hours a week.
⇒Kelly read in a week = x hours
Also, tim reads two times more than kelly
⇒tim read in a week= 2x
It is also given that:
jim reads five hours more than tim.
⇒Jim = tim read + 5
⇒Jim read in a week = 2x +5
Therefore, expression represents the amount of time jim reads is, 2x+ 5
8. Divide (18x^3+12x^2-3x) divided by 6x^2
9. Divide (2x^3-x^2-24x+12) divided by (2x-1)
Use the distributive property of multiplication to find the missing number.use the distributive property of multiplication to find the missing number.
The distributive property of multiplication involves multiplying a number with each term inside a bracket, then adding or subtracting the results. To find a missing number, set up an equation based on the distributed multiplication and solve for the unknown.
Explanation:The distributive property of multiplication can be simply defined as a(b + c) = ab + ac. In this equation, 'a' is distributed over 'b' and 'c', which means we multiply 'a' individually with 'b' and 'c', and then add the results.
Let's consider an example: 2(3 + 4) = ? Here, applying the distributive property, we multiply 2 with 3 and 2 with 4 separately. Hence, 2*3 + 2*4 = 6 + 8 = 14. So, the result is 14.
To solve distribution problems with a missing number, you would set up the equation and solve for the unknown. For example, if we have 3(x+5) = 21, we can first distribute the 3 to get 3x + 15 = 21. Then, you'd subtract 15 from both sides to isolate the 'x'. So, 3x = 21 - 15, which simplifies to 3x = 6. Finally, dividing both sides by 3 gives x = 2. So, the missing number is 2.
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A rectangular prism is 3 feet long, 8 feet wide, and has a height of 6 feet. what is its volume?
I need to skip count by ten from 350 to 240
Skip counting by ten from 350 to 240 involves starting at 350 and counting backwards by subtracting ten each time until you reach 240. The sequence would look as follows: 350, 340, 330, 320, 310, 300, 290, 280, 270, 260, 250, 240.
Explanation:In Mathematics, when asked to 'skip count' it means that you are counting up or down by a specified number, in this case, by ten. However, the student's question asks to skip count by ten from 350 to 240, which would require counting backwards or decreasing the count by ten each time.
To skip count by ten from 350 to 240, you would start at 350 and then subtract 10 each time, like this: 350, 340, 330, 320, 310, 300, 290, 280, 270, 260, 250, 240. Note: 240 is included in the sequence as it is the final number we're skip counting down to.
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A 2005 study by the fisheries research services in aberdeen, scotland, suggests that the average length of the species clupea harengus (atlantic herring) as a function of age t (in years) can be modeled by l(t) = 32(1 − e−0.37t) cm for 0 ≤ t ≤ 13. how fast is the length changing at age t = 7 years?
The rate of change of length of the Clupea harengus (Atlantic herring) at t = 7 years is approximately 2.8 cm per year.
Explanation:To determine how fast the length of Clupea harengus (Atlantic herring) is changing at age t = 7 years, you need to calculate the derivative of the given function, l(t) = 32(1 − e−0.37t), with respect to time. The derivative measures the rate of change of a function, which in this case corresponds to the speed of growth of the herring.
The derivative of l(t) with respect to t is given by: l'(t) = 32 * 0.37e^(-0.37t).
Substitute t = 7 into this derivative function to get: l'(7) = 32 * 0.37e^(-0.37*7) ≈ 2.8 cm/year.
So, the length of the Atlantic herring is increasing at approximately 2.8 cm per year when the herring is 7 years old.
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To find the rate at which the length of the Atlantic herring is changing at age t = 7 years, we need to take the derivative of the length function and evaluate it at t = 7.
Explanation:To find the rate at which the length of the Atlantic herring is changing at age t = 7 years, we need to find the derivative of the length function with respect to time. The function l(t) = 32(1 − e−0.37t) represents the average length of the herring at age t. Taking the derivative of this function gives us:
l'(t) = 32 * (-0.37) * e−0.37t
Now, we can substitute t = 7 into the derivative to find the rate of change at that age:
l'(7) = 32 * (-0.37) * e−0.37(7)
This expression can be simplified further to find the exact value of the rate of change.
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Please help me with these questions thank you.
Answer:
CPCTC; JP≅MI; SAS
Step-by-step explanation:
For the first question, we use the congruence statement. When we are using the congruence statement to match corresponding pieces, the justification is that Congruent Parts of Congruent Triangles are Congruent, or CPCTC.
For the second question, we again use CPCTC and the congruence statement. P matches T and B matches I, so PB = TI and B = I. J matches M also, so BJP = IMT. However, P does not match I, so JP does not equal MI.
For the third question, we have two sides (AM matching ZD and BD matching itself) and an included angle (AMD and ZDM). This is Side-Angle-Side, or SAS.
Ana is driving from her home in Miami to her grandmothers house in New York. On the first day she will travel 240 miles to Orlando Florida to pick up her cousin. Then they will travel 350 miles each day write an equation for the total number of miles m that Ana has traveled after d days
The equation for the total number of miles m that Ana has traveled after d days is m = 240 + 350d.
What is an equation?
An equation is an equality relationship between two expressions written on both sides of the equal to sign.
Ana travels 240 miles on the first day.
Her cousin and she travel 350 miles everyday.
If d is the number of days, then to find the equation for the total number of miles covered m,
m = 240 + 350d miles in d days.
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What is (0.3 x 2.8)2
Is the sum of two angles sometimes , always , or never an obtuse angle ?