Answer:
y = 0 and z = 5
Step-by-step explanation:
the denominator of the expression cannot equal zero as this would make the expression undefined Equating the denominator to zero and solving gives the values that y and z cannot be
solve y(z - 5) = 0
equate each factor to zero and solve
y = 0 ← excluded value
z - 5 = 0 ⇒ z = 5 ← excluded value
Tom, Sally, Bob, and Jill ran a race. Toms time was 12.03 seconds, Sally's was 12.284 seconds, Bobs was 12.62 seconds, and Jills was 12.9 seconds. In what order did they finish? who won?
Answer:
1.Tom
2.Sally
3.Bob
4.Jills
Debbie cut cord to sixths she is five of the pieces to make necklaces she used equal length of the remaining cord for each of four bracelets what fraction of the original cord did Debbie use for each bracelet
Answer:
¹/₂₄
Step-by-step explanation:
Debbie used ⅚ of the cord for necklaces.
That left ⅙ of the cord for four bracelets.
Each bracelet used:
Fraction of cord = ⅙ ×¼ = ¹/₂₄
Debbie used ¹/₂₄ of the cord for each bracelet.
I need help with this question show steps! Quickly please!
Answer:
y+9 =-5(x-2) point slope form
y = -5x-1 slope intercept form
Step-by-step explanation:
If we have a slope and a point, we can use the point slope form of a line
y-y1 = m(x-x1)
y--9 = -5(x-2)
y+9 =-5(x-2)
If you want to write it in slope intercept form, distribute the -5
y+9 = -5x+10
Subtract 9 from each side
y+9-9 = -5x+10-9
y = -5x-1
How do i graph the equation -x + 2y = 2
Step-by-step explanation:
Firstly, set the x value as 0:
-0 + 2y = 2
2y = 2
y = 1
So when x = 0, y = 1
Now set y to 0:
-x + 2(0) = 2
-x = 2
x = -2
So when y = 0, x = -2
Simply plot the two following points:
(0 , 1) and (-2 , 0)
And don't forget to join these two points up!
Attatched is an image of this graph.
Find the slope of the line that passes through the pair of points.
(-40.86,5.6) and (0.86,4.2)
simplify
Answer:
-.033557047
Step-by-step explanation:
Slope = (y2-y1)/ (x2-x1)
= (4.2 - 5.6)/(.86- 40.86)
= -1.4/ (.86 + 40.86)
= -1.4/41.72
-.033557047
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-40.86, 5.6) and (0.86, 4.2). Substitute:
[tex]m=\dfrac{4.2-5.6}{0.86-(-40.86)}=\dfrac{-1.4}{0.86+40.86}=-\dfrac{1.4}{41.72}=-\dfrac{140}{4172}\\\\=-\dfrac{140:4}{4172:4}=-\dfrac{35}{1043}=-\dfrac{35:7}{1043:7}=-\dfrac{5}{149}[/tex]
Answer: The slope = - 5/149What is the range of AB?
a, b, c - sides of a triangle
Therefore:
a + b > c
a + c > b
b + c > a
---------------------------------
We have a = AB, b = 140mi, c = 100mi.
(1) a + b > c
AB + 140 > 100 subtract 140 from both sides
AB > -40 → AB > 0
----------
(2) a + c > b
AB + 100 > 140 subtract 100 from both sides
AB > 40
-----------
(3) b + c > a → a < b + c
AB < 140 + 100
AB < 240
Answer: 40 < AB < 240Which expression is equivalent to (5 × 6)×(3 × 2)?
A) (5 + 6) + (3 + 2)
B) (5 + 6)×(3 + 2)
C) (5 × 6) + (3 × 2)
D) (3 × 2)×(5 × 6)
Answer:
The original equation contains 3 multiplications.
When multiplying numbers, the order that they are in doesn't matter so 3 *2 is the same as 2 * 3.
This would make D, the same.
D) (3 × 2)×(5 × 6)
A line has a slope of -1/2 and a y-intercept of –2.
What is the x-intercept of the line?
a.–4
b.–1
c.1
d.4
Answer:
a.-4
Step-by-step explanation:
I pictured it as a graph and since the slope is negative, the line goes down and to the right. Since the slope is -1/2, for every 2 you move horizontally, you move one vertically. You have to move two up and unless the y intercept is 0, when the line intercepts y, you have 0 as x. You move two up and 4 backwards so the x intercept is -4
after 8% discount from the list price, the sale price price of a poster was $17.48. what was the list price of poster.
Final answer:
To find the list price of the poster after an 8% discount, subtract 8% of the list price from the list price and set it equal to the sale price.
Explanation:
To find the list price of the poster, we need to first calculate the original price before the discount. Let's assume the list price is 'x' dollars. After an 8% discount, the sale price of the poster is $17.48.
We can set up an equation to solve for the list price: x - 8% of x = $17.48. To calculate 8% of x, we multiply x by 0.08.
So the equation becomes: x - 0.08x = $17.48. Combining like terms, we get 0.92x = $17.48. Dividing both sides by 0.92, we find that x = $19.
Blue's Berry Farm charges Percy a total of $24.75 for entrance and 2.5 kilograms of strawberries. The entrance fee is $6, and the price for each kilogram of strawberries is constant. The total cost C for picking strawberries is a function of x, the kilograms of strawberries picked. Write the functions formula. C=
Answer:
C = 6 + 7.5 x
Step-by-step explanation:
Given,
The amount is $24.75 for entrance and 2.5 kilograms of strawberries.
⇒ Entrance fee + 2.5 kilograms of strawberries = $24.75
Since, Entrance fee = $ 6,
And, the price for each kilogram of strawberries is constant.
⇒ $ 6 + 2.5 × 1 kilograms of strawberries = $24.75
⇒ 2.5 × 1 kilograms of strawberries = 18.75
⇒ 1 kilograms of strawberries = $ 7.5.
Thus, the cost of x strawberries = 7.5 x
Also, the total charge for x strawberries = Entrance fee + the cost of x strawberries
= 6 + 7.5 x
⇒ C = 6 + 7.5 x
Which is the required function formula.
HELPP!!!
Find m angle 1 and m angle 3 in the kite.
Answers:
Angle 1 is 40 degrees
Angle 2 is 90 degrees
Angle 3 is 50 degrees
===========================================
Explanations:
Triangle ABC is a reflection of triangle ADC over the line AC. Doing this reflection forms the kite ABCD. Or you can think of it as gluing two congruent triangles together (ABC and ADC). We can prove the two triangles ABC and ADC congruent by the SSS congruence property. Then we use CPCTC (corresponding parts of congruent triangles are congruent) to prove that angle 1 is 40.
Let E be the intersection of the two diagonals. Through similar reasoning as earlier, we can prove that triangle AEB is congruent to triangle AED, so that leads to angle 2 being 90 degrees because this angle adds to its counterpart to get 180. Both unknown angles are x each meaning x+x = 180 leads to x = 90. One property of kites is that the diagonals are perpendicular.
Triangle AED is a right triangle as discussed above. Therefore, the angle 3 and the 40 degree angle are complementary. If angle 3 is y, then y+40 = 90 giving y = 90-40 = 50, which is why angle 3 is 50 degrees.
Using angle theorems, the value of the angles m1 and m3 are 40° and 50° respectively.
Taking the midpoint of DB as O ;
Angle OAD and Angle OAB are equal
OAD = 40° ; OAB = 40°
A right angle is formed at O ;
Hence,
(O + D + A) = 180°
90° + D + 40° = 180° (Sum of interior angles of a triangle)
D = 180 - 130
D = 50°
Hence, m∠3 = 50°.
Therefore, the value of the angles m1 and m3 are 40° and 50° respectively.
what is a equivalent expression for 2(c+c+c)
Answer: 2(C^3) or 2(C to the third power)
Step-by-step explanation: C^3 is the same thing a c+c+c
Hope this helps!
54d.
Change the following expression into a single fraction:
5b − 2/b
Larue score 10 points less than three times the number of points that Ross scored Livia scored 11 points how many points did Ross score?
can some one explain how to do these problems
Answer:
the slope is 0.
Step-by-step explanation:
You can use the slope equation
[tex]\frac{y-y}{x-x}[/tex]
and plug in your points
[tex]\frac{10-10}{4-1}[/tex]
[tex]\frac{0}{3}[/tex]
slope = 0
Triangle CDE and triangle CFG are similar right triangles. Which proportion can be used to show that the slope of CE is equal to the slope of CG?
A) 2 − 3
2 − 0
= 3 − 1
4 −0
B) 3 − 2
2 − 0
= 3 − 1
4 − 0
C) 2 − 3
0 − 2
= 3 − 1
0 − 4
D) 3 − 2
0 − 2
= 3 − 1
0 − 4
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points E(2, 2), C(0, 3) and G(4, 1), C(0, 3).
Substitute:
[tex]\dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}\to\boxed{D}[/tex]
Answer: The correct option is (D) [tex]\dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}.[/tex]
Step-by-step explanation: Given that ΔCDE and ΔCFG are similar right triangles.
We are to select the correct proportion that can be used to show that the slope of CE is equal to the slope of CG.
We know that the slope of a line passing through two points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
From the given figure, we note that the co-ordinates of the points C, E and G are
C(0, 3), E(2, 2) and G(4, 1).
So, the slope of line CE is given by
[tex]m_1=\dfrac{2-3}{2-0},[/tex]
and the slope of line CG is given by
[tex]m_2=\dfrac{1-3}{4-0}.[/tex]
Since the lines CE and CG are same, they must be parallel and hence they have equal slopes.
Therefore,
[tex]m_1=m_2\\\\\\\Rightarrow\dfrac{2-3}{2-0}=\dfrac{1-3}{4-0}\\\\\\\Rightarrow \dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}.[/tex]
Thus, (D) is the correct option.
Year 1 number sold 725
Year 2 number sold 579
Year 3 number sold in year 4 the store sold 112% of the total number of scooters sold during the previous three years combined determine the number of scooter sold in year 4
Answer:
2, 240
Step-by-step explanation:
In the table, the values should be
Year 1 725
Year 2 579
Year 3 696
Since Year 4 sold 112% of the previous 3 years combined, we add 725+579+696=2000. We can find 112% by writing a proportion.
[tex]\frac{112}{100} =\frac{x}{2000}[/tex]
We solve through cross multiplication of numerator and denominator of the opposite fraction.
[tex]112(2000)=100(x)\\224000=100x\\2,240=x[/tex]
Brainliest + Points!
Please show work!
A target is made of a blue square inside of a red square. The blue square has an area of 64 square units, and the red square has an area of 196 square units.
Assuming it hits the target, what is the probability that a dart will land in the red region?
A.
0.25
B.
0.33
C.
0.67
D.
0.75
Answer:
C
Step-by-step explanation:
The target area is shown in the attached picture.
We want to figure out probability of hitting red region.
The area of the figure is the area of the red square, which is 196.
Area of red region is area of whole square (196) minus area of blue square (64). So we have:
Area of red region = 196 - 64 = 132
Probability of hitting red region is 132 divided by total, which is 196.
[tex]\frac{132}{196}=0.67[/tex]
Answer choice C is right.
what kind of decimal is an irrational number give an example
Answer:
An irrational decimal is a decimal that cannot be written in fraction form
Ex: Pi or any decimal that keeps going and doesn't repeat
Step-by-step explanation:
I would give you more examples but they are all really long numbers and go on forever.
Answer:
Pi!
Step-by-step explanation:
I know it might sound silly but Pi and it's digits are part of the irrational decimal family! It's irrational because the digits of Pi seem like they never end, right? Hope this helped!
twice the difference of a number and 6 equals 8
translate sentence into equation
Answer:
2*(n-6) = 8
Step-by-step explanation:
Twice the difference of a number and 6 equals 8
Equals means =
Difference means subtract
2*(n-6) = 8
Margo has a coin collection. She was given 1 coin as a gift, and she adds 3 coins per year. Which of the graphs below represents Margo's coin collection?
graph of line going through 1, 2 and 3, 4
graph of line going through 1, 1 and 3, 3
graph of line going through 1, 4 and 3, 10
graph of line going through 1, 2 and 2, 5
The graph that represents Margo's coin collection is:
Graph of line going through (1, 4) and (3, 10).
Step-by-step explanation:It is given that:
She was given 1 coin as a gift, and she adds 3 coins per year.
Let a_n denote the amount of Money Margo had in the end of the "nth" year.
According to the given information we have:
[tex]a_1=1+3=4[/tex]
[tex]a_2=4+3=7\\\\a_2=a_1+3[/tex]
[tex]a_3=10\\\\a_3=a_2+3\\\\\\a_3=a_1+3\times 2[/tex]
and so on.
Hence, we get:
[tex]a_n=a_1+3(n-1)[/tex]
Hence, we get a Arithmetic progression.
with first term as 4 and common difference as 3.
Hence, the graph is:
Graph of line going through (1, 4) and (3, 10).
( Since at n=1 we have: [tex]a_n=4[/tex]
and at n=3 we have: [tex]a_3=10[/tex] )
in my house, the ratio of dogs to fish is 1:10. the ratio of fish to cats is 6:1. What is the ratio of dogs to cats?
Answer:
The ratio of dogs to cats is 3 dogs to 5 cats
Step-by-step explanation:
dogs to fish: 1:10
fish to cats : 6:1
dogs to cats: 3:5
FISH:
llllllllll (10) llllllllll (10) llllllllll(10) (30 fish)
DOGS: 1 dog per 10 fish
D D D 3 dogs
CATS: 1 cat per 6 fish
C C C C C
Ratio represents partial data as some multiplies from numerator and denominator are lost due to simplification. You can assume them to be variables.
The ratio of dogs to cats is 3:5
How to get real quantity of ratio of first quantity to second quantity = a:b?We actually cannot get real quantities but we can use variables to partially get the information of how much their quantities were.
I said 'partially' since we don't get real values but with variables only.
Since the ratio is a:b, thus let the cancelled multiple during simplification was x.
Then we have:
First quantity = ax
Second quantity = bx
How to calculate the ratio of dogs to cats?It is given that:
Ratio of dogs to fish = 1:10
Then let number of dogs = 1x = x and number of fishes = 10x
Similarly,
Ratio of fish to cats = 6:1
Then let the multiple was y, then
Number of fishes = 6y,
Number of cats = 1y = y
But we have number of fishes = 10x and 6y both
Since number of fishes is constant, thus, they are equal. Or
[tex]10x = 6y\\\dfrac{x}{y} = \dfrac{6}{10} = \dfrac{3}{5}\\[/tex]
The ratio of dogs to cats = [tex]\dfrac{\text{Numbers of dogs}}{\text{Number of cats}} = \dfrac{x}{y} = \dfrac{3}{5}[/tex]
Thus, the ratio of dogs to cats is 3:5
Learn more about ratio here:
https://brainly.com/question/13513438
Which graph shows the solution set for 4x+3>-9
[tex]4x+3>-9\qquad\text{subtract 3 from both sides}\\\\4x>-12\qquad\text{divide both sides by 4}\\\\\boxed{x>-3}[/tex]
Given 4x =
a + b/8c
, rearrange the equation for a, in terms of b, c, and x
To rearrange the equation for a, subtract b/8c from both sides: a = 4x - b/8c.
Explanation:To rearrange the equation for a, we start with the given equation 4x = a + b/8c. First, we isolate a by subtracting b/8c from both sides, giving 4x - b/8c = a. Therefore, the equation for a in terms of b, c, and x is a = 4x - b/8c.
Which tool(s) are needed to construct a perpendicular bisector of a line segment?
Answer: compass and straightedge or ruler
Perpendicular bisector of a line segment
Geometry construction using a compass and straightedge
compass and straightedge or ruler
Step-by-step explanation:
Answer:
You need a straight edge and a compass.
Step-by-step explanation:
The straight edge should not be marked in any way. You are not allowed to put a mark on the straight edge at all. The only property it has is that it has no curvature in any direction.
The compass must be flexible and at the same time it must be able to stay at one radius unless changed by the owner. It's only property is that it can draw a perfect circle once the radius of the circle has been chosen,
What is the supplement of a 47 angle?
Answer:
133° angle
Step-by-step explanation:
Note that "supplement" means 180°.
To find the supplement of the angle given (47°), subtract the given measurement with the total supplementary measurement.
180 - 47 = 133
The supplement of a 47° angle is 133°.
~
I spent 3/4 of my money and then I spent 1/5 of what was left.
a) What part of all my money did I spend?
b) What part of all my money do I have left?
Answers:
a) 4/5
b) 1/5
================================================
Let's say you start off with $100. If you spend 3/4 of that, then you spend 75 dollars (because 75/100 = 3/4). Think of it like 75 cents = 3 quarters. If you spend 75 dollars out of 100 total, then you have 100-75 = 25 dollars left after the first round of spending.
If you spend 1/5th of what is left, then you spend $5 on the second round leaving 25-5 = 20 dollars left at the end of the day.
Total up what you spend for both rounds: 75+5 = 80, which divides over the original amount 100 to get 80/100 = 8/10 = 4/5
If you had 20 dollars at he end of the day, out of 100 initially, then 20/100 = 2/10 = 1/5 is the fraction of what you have left.
note how 4/5 and 1/5 add to 5/5 = 1.00 = 100%. This is because the amount you spend and the amount you have left over must add to 100% of all the money you started with
how would you graph the following systems of equations ?
y= -3x -7
x- 2y=-14
Deena decides to mark down prices at her jewelry store 20% for a clearance sale. She must add 6% to the sale price for state sales tax. Suppose an item was originally priced at x dollars. Which expression does not represent the total sale price, including sales tax, of the item?
The expression that does not represent the total sale price, including sales tax, of the item is x * (1 - 0.20 + 0.06). Hence the correct option is c.
1. Calculate the sale price after the markdown:
Original price: x dollars
Markdown rate: 20%
Sale price after markdown: x * (1 - 0.20) = 0.8x dollars
2. Calculate the amount of sales tax:
Sales tax rate: 6%
Sales tax amount: 0.06 * 0.8x = 0.048x dollars
3. Calculate the correct total sale price:
Sale price after markdown + Sales tax amount = 0.8x + 0.048x = 0.848x dollars
4. Analyze the given expressions:
x * (1 - 0.20) + 0.06x: This expression correctly calculates the discount and adds the sales tax to the original price, so it represents the total sale price.
x * (1 - 0.20) + 0.06 * 0.8x: This expression also correctly calculates the discount and adds the sales tax to the discounted price, so it represents the total sale price.
x * (1 - 0.20 + 0.06): This expression combines the discount and sales tax into a single percentage (14%), but it applies this percentage to the original price (x) instead of the discounted price (0.8x). This leads to an overestimation of the final sale price, so it does not represent the correct total price.
0.8x + 0.048x: This expression correctly calculates the sum of the discounted price and the sales tax amount, so it represents the total sale price.
Therefore, the expression that does not represent the total sale price, including sales tax, of the item is x * (1 - 0.20 + 0.06). Hence the correct option is c.
Complete question:
Deena decides to mark down prices at her jewelry store 20% for a clearance sale. She must add 6% to the sale price for state sales tax. Suppose an item was originally priced at x dollars. Which expression does not represent the total sale price, including sales tax, of the item?
x * (1 - 0.20) + 0.06x
x * (1 - 0.20) + 0.06 * 0.8x
x * (1 - 0.20 + 0.06)
0.8x + 0.048x
if an equilateral triangle has an angle of 3 X what is the value of X
Answer:
x = 20
Step-by-step explanation:
In an equilateral triangle, everything is the same; line length and angles. Each angle in an equilateral triangle is:
180 ÷ 3 = 60
So 3x = 60
Divide both sides by 3 to get x:
x = 20