Given:
4/5 of a pie left after their family picnic.
Each slice of pie was 1/15 of the total pie.
To find:
The number of remaining slices of pie.
Solution:
Let x be the number of remaining slices of pie.
Part of total pie in one slice = [tex]\dfrac{1}{15}[/tex]
Remaining part of total pie in x slices = [tex]\dfrac{1}{15}x[/tex]
According to the question, 4/5 of a pie left after their family picnic.
[tex]\dfrac{1}{15}x=\dfrac{4}{5}[/tex]
Using cross multiplication, we get
[tex]5\times x=15\times 4[/tex]
[tex]5x=60[/tex]
Divide both sides by 5.
[tex]x=12[/tex]
Therefore, the remaining number of slices of pie is 12.
Prove the following statement: If the x- and y-intercepts of a line are identical nonzero numbers, the line must have a slope of -1.
What is the x-intercept you are using?
What is the y-intercept you are using?
Show what you did to prove the slope is -1
Answer:
Step-by-step explanation:
Proof:
If:
x intercept is at a number nonzero "a"
so the point where it intersects the x-axis is at (a,0)
y-intercept is at the same nonzeronumber "a"
so the point where it intersects the y-axis is at (0,a)
Then:
slope between point (a,0) and (0,a) is m= (y2-y1)/(x2-x1) = 0-a/a-0=-a/a= -1
x intercept is 2 (for example)
so the point where it intersects the x-axis is at (2,0)
y-intercept is 2
so the point where it intersects the y-axis is at (0,2)
slope between point (2,0) and (0,2) is m= (y2-y1)/(x2-x1) = 0-2/2-0=-2/2=-1
please be fast ill give brainliest How many solutions does the system have? y=1/2x-1 and y=-x+5
Answer:
(4, 1)
Step-by-step explanation:
since y=1/2x-1 in the first equation, you can substitute it into the second one:
1/2x - 1 = -x + 5
then add x to both sides:
3/2x - 1 = 5
then add 1 to both sides:
3/2x = 6
then divide both sides by the fraction to get:
x=4
then you substitute 4 into y=1/2x - 1
y = 1/2(4)-1
y = 1
so your answer is x=4 and y=1
CAN SOMEONE PLEASE HELP ME!! THANK YOU
Answer:
C
Step-by-step explanation:
I'm pretty sure it's C
Answer:
not sure but b or c because it says less than
Step-by-step explanation:
−2 1/6 divided by 1 1/4
100 points
Answer:
-1 11/15Step-by-step explanation:
−2 1/6 divided by 1 1/4:
-2 1/6 ÷ 1 1/4 = - 13/6 ÷ 5/4 = - 13/6 × 4/5 = - 26/15 =-1 11/151) to divide that mixed number we'll need to turn it into an improper fraction:
[tex] - 2\frac{1}{6} = - ( \frac{6 \times 2 + 1}{6} ) = - \frac{13}{6} \\ 1 \frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4} [/tex]
2) now let's divide it, reciprocating 1 1/4 and multiplying both fractions one by another:
[tex] - \frac{13}{6} \times \frac{4}{5} = - \frac{52}{30} = - \frac{26}{15} [/tex]
3) Hence the answer is -26/15
plssss i need help it’s due rn if u don’t know the answers pls don’t write random stuff plsssss
Answer:
1. y=3x+2
2. slope=3 It represents the rate of which the panda gained weight over the course of 4 weeks
3. 2 It represents the weight of the panda at the first week
Step-by-step explanation:
Determine whether the triangles are congruent using sas sas asa aas HL
Answer:
They are congruent bc they are the same size and shape
Answer:
Congruent by SAS
Step-by-step explanation:
As given by the diagram, we have two congruent sides already. From the set of parallel lines, we see that two angles are congruent because they are corresponding. Luckily, this angle falls between the two congruent sides, which gives you the proof of SAS.
which of these mappings is a function
Answer:
x
Step-by-step explit can only be a function if every input has its own output
Lisa, a researcher at the Centers for Disease Control and Prevention, is studying the growth of a bacteria. She starts her experiment with 77 bacteria that grow at a rate of 21% per hour. She will check on the bacteria every 11 hours. How many bacteria will she find in 11 hours? Round your answer to the nearest whole number.
Answer:
776
Step-by-step explanation:
Jamie borrows $2,000 to purchase a new living room furniture set. She will pay an 8% interest rate over 18 months. How much will Jamie pay in interest?
Answer: 2800 dollars in intrest
Step-by-step explanation:
Fill in the missing numbers to complete the pattern:
1.31, 1.81, _____ ,2.81, _____ ,3.81
Answer:
2.31 and 3.31
Step-by-step explanation:
since .81 is repeating, we can assume .31 does too
simplify 4 - 3(-2a + 2) please!
Answer:
6a - 2
Step-by-step explanation:
4 - 3(-2a + 2)
4 + 6a - 6
6a - 2
Write an equation for the n th term of the arithmetic sequence 56, 48, 40, 32, ....
Answer:
-8n+64
Step-by-step explanation:
what is the sum of the first five terms of the geometric sequence in which a1=5 and r=1/5
express your answer as an improper fraction.
Answer:
Sum of the first five terms of the geometric sequence in which a1=5 and r=1/5 is [tex]\mathbf{S_n=\frac{781}{125} }[/tex]
Step-by-step explanation:
We need to find sum of the first five terms of the geometric sequence in which a1=5 and r=1/5
The formula used to find sum of the geometric sequence is: [tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
Where a is the first term, r is the common ratio and n is the number of terms
Now finding sum of the first five terms of the geometric sequence
We have a=5, r=1/5 and n=5
Putting values in the formula:
[tex]S_n=\frac{a(r^n-1)}{r-1}\\S_n=\frac{5((\frac{1}{5}) ^5-1)}{\frac{1}{5}-1}\\S_n=\frac{5(\frac{1}{3125}-1)}{\frac{1-5}{5}}\\S_n=\frac{5(\frac{1-3125}{3125})}{\frac{-4}{5}}\\S_n=\frac{5(\frac{-3124}{3125})}{\frac{-4}{5}}\\S_n=5(\frac{-3124}{3125})}\times{\frac{-5}{4}}\\S_n=\frac{781}{125}[/tex]
So, sum of the first five terms of the geometric sequence in which a1=5 and r=1/5 is [tex]\mathbf{S_n=\frac{781}{125} }[/tex]
log16^*+log4^*+log2^*=7
Answer:
[tex]x = 16[/tex]
Step-by-step explanation:
Given
[tex]log_{16}(x) + log_4(x) + log_2(x) = 7[/tex]
Required
Solve for x
[tex]log_{16}(x) + log_4(x) + log_2(x) = 7[/tex]
Change base of 16 and base of 4 to base 2
[tex]\frac{log_2(x)}{log_2(16)} + \frac{log_2(x)}{log_2(4)} + log_2(x) = 7[/tex]
Express 16 and 4 as 2^4 and 2^2 respectively
[tex]\frac{log_2(x)}{log_2(2^4)} + \frac{log_2(x)}{log_2(2^2)} + log_2(x) = 7[/tex]
The above can be rewritten as:
[tex]\frac{log_2(x)}{4log_22} + \frac{log_2(x)}{2log_22} + log_2(x) = 7[/tex]
[tex]log_22 = 1[/tex]
So, we have:
[tex]\frac{log_2(x)}{4*1} + \frac{log_2(x)}{2*1} + log_2(x) = 7[/tex]
[tex]\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x) = 7[/tex]
Multiply through by 4
[tex]4(\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x)) = 7 * 4[/tex]
[tex]log_2(x) + 2}log_2(x) + 4log_2(x) = 28[/tex]
[tex]7log_2(x) = 28[/tex]
Divide through by 7
[tex]\frac{7log_2(x)}{7} = \frac{28}{7}[/tex]
[tex]log_2(x) = 4[/tex]
Apply the following law of logarithm:
If [tex]log_ab = c[/tex] Then [tex]b = a^c[/tex]
So, we have:
[tex]x = 2^4[/tex]
[tex]x = 16[/tex]
What is the difference of the fractions? Use the number line to help find the answer.
-
T0
Answer:
-7/10
Step-by-step explanation:
Answer:
you got you must be so Mad rn that I'm not helping you with your question Jiggle what you going to do with that big old behind
Step-by-step explanation:
Write 14/9
as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
Answer:
1.5 repeating
Step-by-step explanation:
Please help ASAP
What are the equations of the asymptotes of the hyperbola?
(y-1)^2/9-(x-2)^2/100=1
y-1= ±3/10(x-2)
Im not sure how to get this answer but my teacher gave it to me so i hope this helps!
The equation of the asymptote of the given hyperbola is; y - 1 = ±(3/10)(x - 2)
We are given the equation of the hyperbola as;
[(y - 1)²/9] - [(x - 2)²/100] = 1
We can rewrite this equation as;
[(y - 1)²/3²] - [(x - 2)²/10²] = 1
The general equation form of hyperbola is;
[(y - k)²/a²] - [(x - h)²/b²] = 1
Comparing this general form to our given equation we can see that;
k = 1
h = 2
a = 3
b = 10
Now the equation of the asymptote of a hyperbola follows the general formula;
y = ±[a(x - h)/b] + k
Plugging in the relevant values gives us;
y = ±(3/10)(x - 2) + 1
y - 1 = ±(3/10)(x - 2)
Read more about hyperbola asymptotes at;https://brainly.com/question/12919612
Thank you so very much will give branliest
Answer:
Slope = 7
Y intercept = 23
Step-by-step explanation:
(can I get brainliest now)
Based on the table, what is the unit rate for one gallon of gasoline?
Answer:
a.3.30
Step-by-step explanation:
Answer:
3.30
Step-by-step explanation:
Because I did le Quiz
If the value of y varies directly with x, which function represents the relationship between x and y when y = 16/5
and X=20
A. Y=25/4x
B. Y=116/5x
C. Y=4/25x
D. Y=64x
Answer:
C. Y=4/25x
Step-by-step explanation:
If y varies directly as x, tis is expressed as;
y ∝ x
y = kx
k is the constant of proportionality
Goven
y = 16/5 and x = 20
16/5 = 20k
16 = 100k
k = 16/100
k = 4/25
Substitute k = 4/25 into the original equation
y = kx
y = 4/25 x
Hence the required expression is y = 4/25 x
the pie chart shows about voters in an election. 2800 more women vote than men. work out the total number of voters.
Answer:
Can you show the pie chart please.
Step-by-step explanation:
Answer:
show pie chart
Step-by-step explanation:
9^x-6=729^3(x+2) solve the equation
Answer:
x= -730/363
Step-by-step explanation:
9x-6=729×3(x+2) multiply
9x-6=2187(x+2) remove the paranthesis
9x-6=2187x+4374 move the terms
9x-2187x=4374+6 collect like terms calculate
-2178x=4380 divide both sides
what is the GCF of 16s^3t, 40s^5, and 68t^2
Answer The Greatest Common Factor of 16, 40, 68 is 4. But the GCF of 16s^3t, 40s^5 and 68t^2 is 1, as there are no common terms for these given alphanumeric terms.
Step-by-step explanation:
Solve the equation ƒ - (-4) = 12.
ƒ = -8
ƒ = 8
ƒ = 16
ƒ = -9
???
What value(s) of b will cause 3x2 + bx + 3 = 0 to have one real solution? Select all that apply.
b = –6
B.b = –9
C.b = 6
D.b = 9
Answer: -6 and 6
Step-by-step explanation:
Possible factors that could produce 3x² + 6x +3 are (x + 1)(3x + 3)
the solution for values of x: x+1=0, x= -1 3x+3=0, 3x= -3 . x= -1 . Same.
Possible factors that could produce 3x² - 6x +3 are (x - 1)(3x - 3)
the solution for values of x: x-1=0, x= 1 3x-3=0, 3x= 3 . x= 1 . Same.
From the attached graph of the possible equations, you can see that 9 and -9 won't produce ONE real solution. They each have "zeros" at two points on the x-axis. That is two solutions that would make x = 0.
The equations with -6 and +6 each touch the x-axis at only one point each.
What number has the prime factorization 2^2*3*5^2 * 7? Show how you
found the number.
Answer:
3 • 74509
I this is right
Three concert tickets cost $27. At this rate, what is the cost per ticket?
Hello.
To find this, divide the cost per amount.
In this case, the cost of the tickets is $27, and the amount is 3.
Divide 27 by 3.
27 / 3 = 9
Each ticket costs $9.
Answer:
$9 per ticket
Step-by-step explanation:
all you do is divide 27 by 3 and get 9
When the number of units sold on November 21 is 36, the cost of merchandise sold on November 21 is $
Answer:
When The Number Of Units Sold On November 21 Is 36, The Ending Inventory On November 30 Is 3. When The Number Of Units Sold On November 21 Is 8, The Cost Of Merchandise Sold On November 21 Is 4.
Step-by-step explanation:
so 4
can i have brainliest
Dennis has less than 70 min. to spend on some homework questions. He spent 10 min. on the first two questions. The rest of the questions will take 52 min. each.
Which statement describes the solution to this inequality?
Drag and drop the answer into the box.
Answer:
A. Dennis can complete less than 24 questions.
Step-by-step explanation:
Let x represent the remaining number of questions to be completed. He can complete each of them in 5/2 minutes each; this gives us the expression 5/2x.
He has already spent 10 minutes; this gives us 5/2x+10.
He has less than 70 minutes to spend; this gives us the inequality
5/2x+10<70
Subtract 10 from each side:
5/2x+10-10 < 70-10
5/2x < 60
Divide both sides by 5/2:
5/2x÷5/2 < 60÷5/2
x < 60/1 ÷ 5/2
To divide fractions, flip the second one and multiply:
x < 60/1 × 2/5
x < 120/5
x < 24
Answer:
Dennis can complete fewer than 24 questions.
Step-by-step explanation:
Which equation could have been used to create this graph?