Point A is the midpoint of side XZ and point B is the midpoint of side YZ. Triangle X Y Z is cut by line segment A B. Point A is the midpoint of side X Z and point B is the midpoint of side Y Z. The length of X Y is 5 x minus 7, the length of A B is x + 1, and the lengths of X A and Z A are 2 x minus 2. The lengths of Y B and B Z are congruent. What is AX? 2 units 4 units 6 units 8 units
Answers
Answer:
B. 4unitsStep-by-step explanation:
Find the diagram attached. The diagram is a similar triangle.
From the diagram, XZ/XY = CA/AB
Given XZ = 2x-2+2x-2 = 4x-4
XY =5x-7
CA = 2x-2
AB= x+1
On substituting this parameters into the formula to get x first
4x-4/5x-7 = 2x-2/x+1
cross multiply
(4x-4)(x+1) = 5x-7(2x-2)
open the parenthesis
4x²+4x-4x-4 = 10x²-10x-14x+14
4x²-4 = 10x²-24x+14
10x²-4x²-24x+14+4 = 0
6x²-24x+18 = 0
x²-4x+3 = 0
x²-3x-x+3 = 0
x(x-3)-1(x-3) =0
(x-3)(x-1) = 0
x = 3 and 1
Next is to get length AX.
Given AX = 2x-2
Substitute x = 3 into the expression
AX = 2(3)-2
AX = 6-2
AX = 4 units
Hence the measure of length AX is 4 units
Answer:
4
Step-by-step explanation:
4
Related Questions
v=1/3 pi r squared h what is h?
Answers
Step-by-step explanation:
V = 1/3 pi r^2 h
root(V ÷ 1/3 pi) = h
An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. If x engines are made, then the unit cost is given by the function C(x)=0.5x^2-330x+65,738. How many engines must be made to minimize the unit cost? Do not round your answer
Answers
Answer:
330 enginesStep-by-step explanation:
If the unit cost is given by the function C(x)=0.5x^2-330x+65,738 where x is the amount of engines made while C(x) is the unit cost. In order to know the amount of engine needed to minimize the cost;
we will first find dC/dx and equate the resulting function to zero to get x.
dC/dx = 2(0.5)x - 330
dC/dx = x - 330
since dC/dx = 0
x - 330 = 0
x = 330 (critical point)
Then find the second derivative to check if it is greater than zero.
d²C/dx² = 1
Since d²C/dx² > 0, then the cost will be at the minimum when x = 330
Substitute x = 330 into the modeled function;
C(330)=0.5(330)^2-330(330)+65,738.
C(330)= 54,450-108,900+65,738.
C(330)= -54,450+65,738.
C(330)= 11,288
Hence the amount of engines that must be made to minimize the unit cost is 330 engines and the unit cost at the minimum price is 11,288
1. Identify the slope and the y-intercept in
the following equation:
y = x +7
Answers
Answer:
Step-by-step explanation:
slope is 1
y intercept is 7
ASAP!!!!
how do i write the intercept form equation
y=a(x-p)(x-q)
when i know a=-16
p=-0.12
q=1.12
Answers
Answer:
y = -15x - 3.04
Step-by-step explanation:
1) First place down what you are given.
Y = a(x - p) (x - q)
2) Then Substitute.
a = -16
p = -0.12
q = 1.12
y = (-16)(x - (-0.12))(x - (1.12)
3) Do order of operations (PEMDAS)
y = (-16)(x + 0.12)(x - 1.12)
Now distribute
y = − 16 x − 1.92 + (x - 1.12)
y = -16x - 1.92 + x - 1.12
y = -16x + x - 1.92 - 1.12
y = -15x - 3.04
4)
You answer is:
y = -15x - 3.04
what property is y(x+5)
Answers
Retake:will give brainliest
Answers
Answer:
Step-by-step explanation:
The graph should start with an y-intercept of 100 because even if zero people attend, it costs $100 for the DJ. Then, the line should have a slope of 20 because for each additional person it costs another $20. when you reach the point (10,200) the line will plateau where every y value after that will be 200
please help. im bad at math.
Find the exact value of the following.
-3(1.2) ^2 =
Answers
Problem: In good weather, tomato seeds can grow into plants and bear ripe fruit in as few as 19 weeks. Lorna planted her seeds 11 weeks ago. How long must she wait before her tomatoes are ready to be picked?
Solution: The variable in question is the number of weeks until the tomatoes are ready. Call this variable w.
Answers
Answer:
the answer is w=19-11=8
Step-by-step explanation:
19-11=8
HELP!!!!!BRAINLIEST
PLEASE SHOW YOUR WORK ON A PAPER BRAINLIEST!!!!!!!!!!!!!!!!!!
Answers
Answer: Noah's mixture would be more flavorful and fizzy because his ratio of water and fizz powder aren't to off (not a large ratio gap). Andre's orange fizz would be a little more watered down making it less fizzy and less flavorful because 8 cups were added instead of 6 or 7 cups of water. Also Noah would have less drink made them Andre because he only used 6 cups of water.
Step-by-step explanation:
What is the average rate of change from x = −4 to x = 1
Answers
Answer:
+5
Step-by-step explanation:
the average rate of change is adding 5
Janae is buying food for a party. She is buying a cheese tray for $4.50 and a few pounds of fruit for $1.99 each. Write the equation to represent the situation
Answers
Answer:
$6.49
Step-by-step explanation:
Fruit=$1.99
Cheese tray=$4.50
1.99
+4.50
=$6.49
Look at the picture please
Answers
Answer:
15 words per minute.
Step-by-step explanation:
We can look at the line graph, and look at the "1" at the bottom, then go up to where the line is. It's at the point "15". The unit rate is 15 words per minute.
PLZ HELP ME! I WILL GIVE BRAINLIEST!!! PLZ ONLY ANSWER IF YOU KNOW!!!
Answers
Answer:
Yes they are the same (equivalent)
Step-by-step explanation:
replace y with 2
There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon. For each question, explain or show reasoning.
1. How many milliliters are in 3 gallons?
2. How many milliliters are in 1 quart?
(Note) Please keep reasonings simple
Answers
Answer:
There are 11,355 milliliters in 3 gallons, and 946.25 milliliters in 1 quart.
Step-by-step explanation:
If there are 3,785 milliliters in 1 gallon, multiply each side by 3 because you want the product to equal 3 gallons.3,785 times 3 is equal to 11,355, and 1 times 3 is 3. So, 3 gallons are equal to 11,355 milliliters. If there are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon, that means that there are 3,785 milliliters in 4 quarts. Now, you want to find the amount of milliliters in 1 quart so you should divide both the 3,785 and the 4 by 4. So, there are 946.25 milliliters in 1 quart.
Find the equation of a line when y-intercept is 2, and gradient is -2/3
Answers
y=-2/3x+2
Explanation:
When we need to find the equation of a line and the question gives us the slope/gradient and y-intercept, we organize our answer in slope-intercept form.
Slope intercept form: y=mx+b
Here’s what the variables mean:
Y=the y coordinate
M=the slope/gradient
X=the x coordinate
B=the y-intercept (the point on the line that intercepts the y-axis)
Now, all we have to do is plug in the given information. The m variable is the slope of the line so we plug in -2/3 as m.
y=mx+b
y=-2/3x+b
And the b variable is the y intercept so we plug in 2 as b.
y=-2/3x+2
I hope this helps! Please comment if you have any questions.
12 divided by 3/ 4 !
Answers
Answer:
16
Step-by-step explanation:
what is 4 1/5 divided by 2/3
Answers
Answer:
6 3/10
Step-by-step explanation:
What is the range of the given function?
Answers
Answer:
the answer is D
[tex] - 7 < y \leqslant 5[/tex]
Identify whether each equation has one solution, infinitely many solutions, or no solution.
2(x - 5) = 2(x - 5)
One Solution
Infinitely Many Solutions
No Solution
5(x + 4) = 5(x-6)
5(x + 4) = 3(x-6)
4(x - 2) = 4(x + 2)
x + 2(x - 5) = 3(x - 2) - 4
Answers
Answer:
1. 2(x - 5) = 2(x - 5) has infinitely many solutions
2. 5(x + 4) = 5(x-6) has no solution
3. 5(x + 4) = 3(x-6) has one solution
4. 4(x - 2) = 4(x + 2) has no solution
5. x + 2(x - 5) = 3(x - 2) - 4 has infinitely many solutions
Step-by-step explanation:
I did the assignment and I got it correct edge2020
1. 2(x-5)= 2(x-5) = Infinitely many solutions.
2. 5(x+4) = 5(x-6) = No solution
3. 5(x+4) = 3(x-6) = One solution
4. 4(x-2) = 4(x+2) = No solution
5. x+2(x-5) = 3(x-2) - 4 = Infinitely many solution
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now,
The given equations is;
1. 2(x-5) = 2(x-5)
2x-10 = 2x-10
0=0
Hence, This equation has infinitely many solution
2. 5(x+4) = 5(x-6)
5x+20 = 5x-30
20 ≠ (-30)
Thus, This equation has no solution
3. 5(x+4) = 3(x-6)
5x+20 = 3x -18
5x-3x = -20-18
2x = -38
x=-19
Thus ,this equation has one solution
4. 4(x-2) = 4(x+2)
4x-8 = 4x+8
-8 = 8
Thus, this equation has no solution
5- x+2(x-5) = 3(x-2) -4
x+2x-10 = 3x-6-4
3x-10 = 3x-10
0=0
Thus, this equation has infinitely many solution
Learn more about the mathematical expression visit:
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I need to know how to write 1.08 × 10⁴ in standard form
Answers
Answer:
1.08 • 10⁴ = 10,800
Step-by-step explanation:
1 0 8 0 0 1 2 3 4Tyler is having a party at a local recreational center. The normal price to rent the space is $10.00 per adult and $5.50 per child and $15 per hour. The center agrees to rent the space for half the normal price because Tyler's father works at the center. A total of 4 adults and 16 children are going to the party. The party is planned to last 5 hours. What is the total price to rent the space for the party?
Answers
Answer:
203
Step-by-step explanation:
10x + 5.5y + 15h
x= 4
y= 16
h= 5
10(4) + 5.5(16) + 15(5)
40 + 88 + 75
203
Answer:
$93.50
Step-by-step explanation:
Ok so divide $10.00 by 2 which is $5.00 and divide $5.50 by 2 which is $2.25 and divide $15 by 2 which is 7.50. Since there was 4 adults so it cost $20.00 because 5.00X4=20.00. Since there was 16 kids going it cost $36.00 because $2.25X16=36. Since they were there for 5 hours it cost $37.50 because $7.50x5=$37.50. Add all of those up and you will get $93.50.
HOPE THIS HELPS
HELP PLZZZZZZZZ!!!!!!!!!!!!!!!!
Answers
Answer:
c
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The answer to this question plz
Answers
The greenhouse club is purchasing seed for the lawn in the school courtyard. The club needs to determine how much to buy. Unfortunately, the club meets after school, and students are unable to find a custodian to unlock the door. Anthony suggests they just use his school map to calculate the area that will need to be covered in seed. He measures the rectangular area on the map and finds the length to be 10 inches and the width to be 6 inches. The map notes the scale of 1 inch representing 7 feet in the actual courtyard. What is the actual area in square feet?
Answers
Answer:
The answer is 2940ft^2
Step-by-step explanation
First convert length and width to feet using the value given (7ft=1inch).
[tex]10*7= 70[/tex]
[tex]6*7= 42[/tex]
Multiply these values for the actual area.
[tex]42*70= 2940[/tex]
The actual area of the lawn is 2940ft^2
Find the inverse: y = 0.3ˣ
If you could explain the steps too that would be really helpful! :)
Answers
Answer:
y = 0.3x
Step-by-step explanation:
Simplifying
y = 0.3x
Solving
y = 0.3x
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Simplifying
y = 0.3x
The boiling point of water is 212∘F. In degrees Celsius, how much heat do I have to add to boil water that is already 194∘F? Use the formula C = 59(F − 32), where C represents the temperature in degrees Celsius and F represents the temperature in degrees Fahrenheit.
Answers
The amount of heat to add to boil the water is 42000J
What is specific heat capacity?The specific heat capacity of a substance is the energy required to raise the temperature of of the substance by 1°C or 1k. It is measured in J/kg/k
The amount of heat to raise temperature is given as
H= mck
where k is the temperature change.
converting 212°f to Celsius
C = 5/9( 212 -32) = 5/9 × 180
= 100°C
converting 194°f to Celsius
C = 5/9( 194 -32)
C = 5/9 × 162
C = 90°C
Therefore;
H = 4200 × 100-90
H = 42000J
Therefore, the amount of heat to boil the water is 42000J.
learn more about specific heat capacity from
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Hank has read 25 percent of his book. If Hank has read 150 pages, which equation can be used to find the total number of pages in the book?
Answers
Answer:
it would be first one, 150/600
Step-the by-step explanation:
Why, because 25% of 600 is 150
Answer:
first option
Step-by-step explanation:
What is the quotient of 4.29 x 10^5 and 9.75 x 10^2 expressed in scientific notation?
Answers
The quotient by dividing the given numbers is required.
The quotient is 0.44 x 10³.
DivisionThe given numbers are
4.29 x 10⁵
9.75 x 10²
Let us make the numbers into whole numbers
4.29 x 10² x 10³ = 429 x 10³
9.75 x 10² = 975
So,
(429 x 10³) ÷ 975 = (39 x 11 x 10³) ÷ (39 x 25)
= (11/25) x 10³
= 0.44 x 10³
Learn more about division:
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i need help PLZZZ ITS DUE TODAY IM SCARED IF I GET IT WRONG
Answers
Answer:
C.
Step-by-step explanation:
It's the only one that doesn't start exactly on the line of (1,5) but it's starts on (1,4.50) to show 4.50 per pound.
write the algebraic expression 5 more then the product of 4 and m
Answers
Answer:
4m + 5
Step-by-step explanation:
product of 4 and m: 4m
5 more than the product of 4 and m: 4m + 5
Answer: 4m + 5