For z varies jointly with x and y. When x=5 and y=4, z=12.
a. Equation that models the relationship is z=(3/5)xy.
b. When x=15 and y=2 then z=18.
As given,
a. Equation that models relationship z varies jointly with x and y is:
z is directly proportional to product of x and y
⇒z∝ xy
⇒z=k xy
where k is symbol of proportionality.
When x=5 and y=4, z=12
12=k(5× 4)
⇒k=12/(5× 4)
⇒k=3 /5
Hence, z=(3/5)xy
b. When x=15 and y=2
z=(3/5)×15×2
=18
Therefore, for z varies jointly with x and y, when x=5 and y=4, z=12.
a. Equation that models relationship is z=(3/5)xy.
b. When x=15 and y=2 then z=18.
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in a set of 3 randomly selected people, what is the probability that at least two people were born on the same day of the week? round your answer to three decimal places.
19/49 = 0.388
Probability at least two were born on the same day of the week = 1 - probability of all three people were born on different days of the week
Probability of three random people born on different days of the week = 7/7 x 6/7 x 5/7 = 30/49
Probability that at least two were born on the same day of the week = 1 - 30/49 = 19/49 = 0.388
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Tom jarred 12 liters of jam after 2 days. How many days does Tom need to spend making jam if he wants to jar 24 liters of jam in all? Solve using unit rates.
PLS HELP
Answer:
4 days
Step-by-step explanation:
→ Find how much in 1 day
12 ÷ 2 = 6 litres in 1 day
→ Divide by 24
24 ÷ 6 = 4 days
What is 18(54)+72(929)?
EXPLANATION
Given the operation 18(54)+72(929), by applying the distributive property:
= 972 + 66,888
Adding numbers:
= 67,860
The solution is 67,860
Nicky is making cookies. She needs to add 1 1/2 teaspoons of baking soda, but she can only fined 1/4 teaspoons measuring spoon. How many 1/4 teaspoons measures should she use.
Answer:
6
Step-by-step explanation:
1 and 1/2 is equal to 1 and 2/4, or 6/4. This means that it would take 6 teaspoons to add 1 1/2 teaspoons of baking soda. hope this helps!
Which sequences of transformations could map rectangle A
onto rectangle B? Select all that apply.
A A 90° clockwise rotation around the origin, followed by a
translation to the left
B A dilation with a center of dilation at the origin, followed
by a translation down and a translation to the left
C A reflection across the x-axis, followed by a dilation with a
center of dilation at the origin and a translation to the left
B
-2
D A reflection across the y-axis, followed by a translation down and a dilation
with a center of dilation at the origin
E A 180° rotation around the origin, followed by a dilation with a center of
dilation at the origin, a translation down, and a translation to the left
The sequence of transformations of rectangle A onto rectangle B is
B) A dilation with a center of dilation at the origin, followed by a translation down and a translation to the left.
What is transformation in graphs?The graph's curve "moves to the left/right/up/down," "it expands or compresses," or "it reflects" when a function is transformed. For instance, simply advancing the graph of the function g(x) = x2 by 3 units will yield the graph of f(x) = x2 + 3. Function transformations are very useful for graphing the functions by simply moving, expanding, compressing, or reflecting the curve, as opposed to having to start from scratch with the graphing.
A function transformation "moves," "resizes," or "reflects" the parent function's graph, depending on the case. Function transformations can be broadly divided into three categories:
TranslationDilationReflectionLearn more about transformation
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The customers at the bank would like to withdraw money from the automated teller machine. Help them enter their personal ID numbers by completing the numeric patterns.
0, 1, 3, 6, 10, 15, 21,
We see here, from the first number to the second number, we add 1.
From the second number to the third number, we add 2.
From the third number to the fourth number, we add 3, so on and so on.
Therefore, the pattern is : From the second gap moving on, the addition moves up 1.
So, we can continue the pattern by adding 7,8,9,10,etc.
-> 0,1,3,6,10,15,21,28,36,45,55,66,78,91,...
Find the value of x
2x + 6
18
Answer: X = 6
Step-by-step explanation:
If 2 x 6 = 12 then you add 6, then it adds up to 18
4n — 6(3 — n) + _ = 10n —15
Answer:
n • (2n - 5)
——————————————————————
5 • (n - 5) • (3n - 1)
Step-by-step explanation:
4.3 Factoring 3n2 - 16n + 5
The first term is, 3n2 its coefficient is 3 .
The middle term is, -16n its coefficient is -16 .
The last term, "the constant", is +5
Step-1 : Multiply the coefficient of the first term by the constant 3 • 5 = 15
Step-2 : Find two factors of 15 whose sum equals the coefficient of the middle term, which is -16 .
-15 + -1 = -16 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and -1
3n2 - 15n - 1n - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
3n • (n-5)
Add up the last 2 terms, pulling out common factors :
1 • (n-5)
Step-5 : Add up the four terms of step 4 :
(3n-1) • (n-5)
Which is the desired factorization
Answer:
n • (2n - 5)
——————————————————————
5 • (n - 5) • (3n - 1)
Step-by-step explanation:
Will give brainliest
A school ordered 3 large boxes of board markers. After giving 15 markers to each of 3 teachers, there were 90 markers left. The diagram represents the situation. How many markers were originally in each box?
Answer:
45
Step-by-step explanation:
90/3=x-15
30=x-15
45=x
check
45-15=30
30*3=90
Answer:
45
Step-by-step explanation:
I need help on algebra 1 rewriting expression with radicals !
It is required to combine the radicals which can be done as follows:
[tex]\begin{gathered} 5\sqrt[]{27}-17\sqrt[]{3}=5\sqrt[]{3\times3\times3}-17\sqrt[]{3} \\ =5\times3\sqrt[]{3}-17\sqrt[]{3} \\ =15\sqrt[]{3}-17\sqrt[]{3} \\ =(15-17)\sqrt[]{3} \\ =-2\sqrt[]{3} \end{gathered}[/tex]Option D is correct.
Please help thank you
Answer:y=-9x+3
Step-by-step explanation:
In a y=mx+b equation (slope intercept form) like this one m is the slope and b is the y intercept.
The total body surface area, or BSA, of a human is difficult to calculate. There are various models that estimate BSA based on a person's weight and height. One simpler model isBSA = sqrt (wh/3600)where w= weight in kg and h= height in cm. a. Using this model, estimate the height of a person who weighs 72 kg and whose BSA is 1.9.
CaTansposing The modeled function is given as,
[tex]B.S.A\text{ = }\sqrt{\frac{wh}{3600}}[/tex]For w = 72 kg and B.S.A = 1.9, height is calculated as follows,
[tex]1.9=\text{ }\sqrt{\frac{72\times h}{3600}}[/tex]Disposing root in L.H.S,
[tex]\begin{gathered} 1.9^2\text{ = }\frac{72\times h}{3600} \\ 3.61\text{ }\times\text{ 3600 = 72 }\times\text{ h} \end{gathered}[/tex]Calculating the value of h,
[tex]\begin{gathered} h\text{ = }\frac{3.61\times3600}{72} \\ h\text{ = }\frac{12996}{72} \\ h\text{ = 180.5} \end{gathered}[/tex]Thus the required value of height is 180.5 cm.
Your friend uses the order of operations to findthe value of 11(39-3). How could you usethe Distributive Property to show that eithermethod gives the same answer? Explainshowing both methods.
ANSWER AND EXPLANATION:
Given:
[tex]11(39-3)[/tex]Note that the acronym PEMDAS describes the order of operations and each letter stands for;
P - Parentheses
E - Exponents
M/D- Multiplication/Division (from left to right)
A/S - Addition/Subtraction (from left to right)
Following the above order of operations, we can go ahead and solve the expression as seen below;
[tex]\begin{gathered} 11(39-3) \\ =11(36) \\ =396 \end{gathered}[/tex]Using the Distributive Property, we can go ahead and solve the expression as seen below;
[tex]\begin{gathered} 11(39-3) \\ =11*39-11*3 \\ =429-33 \\ =396 \end{gathered}[/tex]We can see from the above that both methods give the same answer.
Mr Arnold bought 10 boxes of oranges for $480 Each box had a dozen oranges He later sold the oranges and made a total profit of $120 What was the selling price of one orange? (giving 30 points for this!!
Answer:
5$
Step-by-step explanation:
480$+120$=600$ 600÷120=5
Evaluate.
10 4/5+(8 3/4−6 1/2)
Enter your answer as a mixed number in simplest form by filling in the boxes.
Step-by-step explanation:
Two state parks, Elm Grove and Cathedral Rock, each recorded the number of visitors to the park each day for 15 days. The parks made line plots from the data recorded.
For given two state parks Elm Grove and Cathedral Rock, the range of visitors per day to Elm Grove Park is equal to the range of visitors per day to Cathedral Rock Park.
Also, the maximum number of visitors to Elm Grove Park is less than the minimum number of visitors to Cathedral Rock Park.
The correct statements are statement 1 and statement 2
Here, we have been given two state parks Elm Grove and Cathedral Rock. Each recorded the number of visitors to the park each day for 15 days.
We were given line graphs of this data.
We have to choose the correct statements about the two plots.
For Elm Grove Park,
Maximum number of visitors: 350
Minimum number of visitors: 50
Range of visitors per day,
350-50 = 300
And in case of Cathedral Rock Park,
Maximum number of visitors 600
At least 300 visitors and the range of visitors per day is 600-300 = 300
This means that the range of visitors per day to Elm Grove Park is equal to the range of visitors per day to Cathedral Rock Park.
Also, the maximum number of visitors to Elm Grove Park is less than the minimum number of visitors to Cathedral Rock Park.
The correct statements are statement 1 and statement 2
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Which describes the range of the parent absolute value function?
{yly} is a real number}
{yly} is an integer}
{yly ≥ 0}
{yly ≤ 0}
Answer:
{ y l y ≥ 0 }
Step-by-step explanation:
The absolute value parent function is:
[tex]f(x) =|x|[/tex]
The absolute value of a number means how far the number is from zero on a number line. Therefore, the absolute value of a number is its positive numerical value.
This means that regardless of the value of x, the value of the absolute value parent function (y-value) will always be positive or zero.
The range of a function is the set of all possible output values (y-values).
Therefore, the set notation that describes the range of the parent absolute value function is:
{ y l y ≥ 0 }Given f(x) = x² - 10x + k, and the remainder when f(x) is divided by x + 2 is
32, then what is the value of k?
The value of k is [tex]8[/tex]
Given that f(x) = [tex]x^{2} -10x+k[/tex] and when it is divided by [tex]x+2[/tex] it gives us the remainder as [tex]32[/tex]
now we know that Divident=Divisor*quotient+remainder...(1)
Now since the quotient is [tex]x+2[/tex]remainder [tex]32[/tex] and we don't know the divisor while the divident is [tex]x^{2} - 10x + k[/tex]
hence putting the values of divident, divisor, quotient, and the remainder in (1)
we get
[tex]x^{2} - 10x + k=divisor*(x+2)+32[/tex]
using the remainder theorem put [tex]x+2=0[/tex] which gives us the value of x as [tex]-2[/tex]
Now put [tex]x=-2[/tex] in f(x) that is find the value of f(x) at [tex]x=-2[/tex] that is find[tex]f(-2)[/tex]and put that value equal to the remainder which is [tex]32[/tex] in our case
Hence according to the remainder theorem;
[tex]f(-2)=(-2)^2-10(-2)+k=32[/tex]
[tex]4+20+k=32[/tex]
[tex]24+k=32[/tex]
on solving we get a value of k as [tex]8[/tex]
Hence the value of k is [tex]8[/tex]
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How many times smaller is 1.9 × 10^3 than 4.085 × 10^5?
it's 215 times smaller
Step-by-step explanation:
I JUST SIMPLIFIED THIS
3. You can paint 14 feet in 4 minutes and your friend can paint 18 feet in 6
minutes. How many feet total can you and your friend paint in 22 minutes?
Answer:
You and your friend can paint 143 feet in 22 minutes.
Step-by-step explanation:
14/4 to find the unit rate. The unit rate is 3.5.
Multiply 3.5 by 22 to get 77.
18/6 to find the unit rate. The unit rate of this is 3.
Multiply 3 by 22 to get 66.
Add the two amounts together to get the total amount.
143.
Please mark Brainliest!
Answer:
143
Step-by-step explanation:
in an examination room, seating is available for 34 students, which is 85% of the required seating. how many more seats should be added if all students must be seated?
6 more seats should be added if all students must be seated.
As per the question statement, in an examination room, seating is available for 34 students, which is 85% of the required seating.
We are required to calculate the number of seats to be added to accommodate the seating of all the candidates.
To solve this question, first let us assume that the total number of candidates appearing for the exam is "x", i.e., the room needs "x" seats to accommodate the seating of all the appearing candidates.
And as per the question statement, 85% of x is 34.
We will need to form a linear equation in one variable "x", based on our above-mentioned assumptions and the conditions mentioned in the question statement, and solving this equation, we will obtain our desired answer, i.e.,
(85% of x) = 34
Or, [{(85/100) * x} = 34]
Or, [x = {34 * (100/85)}]
Or, [x = {2 * (100/5)}]
Or, [x = (2 * 20)]
Or, [x = 40]
That is, the total number of candidates appearing for the exam is 40, and hence, the room needs allover 40 seats to accommodate the seating of all the appearing candidates. Therefore, [(40 - 34) = 6] seats need to be added to accommodate the seating of all the candidates.
Percent: In Mathematics, Percentage is a number or a ratio which can be expressed as the numerator to a denominator of 100 in a fraction, and is denoted using the percent sign, "%"
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Find CE
Given sides are 6, x-5, 14, 2x+3
AB= 6
BC= x-5
CE= 14+2x+3
After conducting some mathematical operations we know that the length of the side CE is 49 units.
What do we mean by mathematical operations?In mathematics, an operation is a function that converts 0 or more input values into a clearly defined output value.The quantity of operands determines the arity of the operation.The order of operations refers to the rules that specify how to solve an expression that requires multiple operations.Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (or PEMDAS) (from left to right).So, the length of CE is:
According to the image, we know that AB + BC = CE. Then,
AB + BC = CE6 + x - 5 = 14 + 2x + 31 + x = 17 + 2x2x - x = 1 - 17x = -16Since length cannot be negative: So, x = 16
Substitute x = 16 in 14 + 2x + 3 to find CE as follows:
14 + 2x + 314 + 2(16) + 314 + 32 + 349Therefore, after conducting some mathematical operations we know that the length of the side CE is 49 units.
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step by step solution to 10x-7y=-8
The x and y-intercept of the linear equation 10x - 7y = -8 in an ordered pair form are ( -4/5, 0 ) and ( 0, 8/7 ) respectively.
How to determine the x and y-intercept of the linear equation?The intercept of a line on a graph is simply the point at which it intersects either the x-axis or y-axis.
Given the data in the question;
10x - 7y = -8x-intercept = ?y-intercept = ?To find the x-intercept, substitute in 0 for y and solve for x.
10x - 7y = -8
10x - 7(0) = -8
10x - 0 = -8
10x = -8
Divide both sides by 10
10x/10 = -8/10
x = -8/10
x = -4/5
Therefore, the x-intercept is ( -4/5, 0 ).
To find the y-intercept, substitute in 0 for x and solve for y.
10x - 7y = -8
10(0) - 7y = -8
0 - 7y = -8
-7y = -8
Divide both sides by the coefficient of y
-7y / -7 = -8 / -7
y = -8 / -7
y = 8/7
Therefore, the y-intercept is ( 0, 8/7 ).
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y=2x-5 I need help quick
Answer:
5/2
Step-by-step explanation:
13/19 as a decimal rounded to the nearest tenth.
Answer:
0.7
Step-by-step explanation:
13/19 as a decimal rounded to the nearest tenth.
13/19 = 0.68421...
rounded:
= 0.7
Answer:
0.684
Step-by-step explanation:
13/19
= 13 ÷ 19
= 0.68421052631579
=0.684
15. pls help will give brainliest
Answer:
Point-slope form: y - 120 = 2(x - 25)
Slope-intercept form: y = 2x + 70
The expression below shows a sum multiplied by a factor:
3(2+6D)
Which options are equivalent to the expression above?
Select ALL that apply.
A (3 x 2)+(3 x 6d)
B 6+6d
C 3+2+6d
D 2+ (3 x 6d)
E 6+18d
3(2+6d)
Answer:
A and E
Step-by-step explanation:
I see no other correct answer option.
3(2 + 6D) = 3×2 + 3×6D = 6 + 18D
= (3×2)+(3×6D)
with or without brackets this is the same thing as per the priorities of mathematical operations (first multiplications and divisions, and only then secondly additions and subtractions).
Help pls I need the answer fast and today
Answer:
B.
Step-by-step explanation:
0.264172 is how many gallons are in one liter soooo yeah, the estimation of that is 0.26/1 which is B
what is 9/10 divided by - 6/5
Answer:
answe is negative 3/4
Step-by-step explanation:
mark me as branlist
Answer:
-0.75 or -3/4
Step-by-step explanation:
9/10 • -5/6 = -45/60 = -3/4 = -0.75
4722x835
Canu show me the work for this i rlly need it
Answer: 3,942,870
Step-by-step explanation:
Answer:
3942870
Step-by-step explanation:
Numerical terms in this expression have been added.
(4722+835= 48557)
(48557) To factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).
(59x823 ) The number of times that each prime divides the original integer becomes its exponent in the final result.
In my example,
Prime number 59 to the power of 1 equals 59.
Prime number 823 to the power of 1 equals 823.
Hope this helps you!
