Answer: x=2y+3
Step-by-step explanation:
Switch around the 6y
3x-9=6y
Add 9 to both sides
3x-9+9=6y+9
3x=6y+9
Divide everything by 3
x=2y+3
Gavin has a points card for a movie theater. He receives 20 rewards points just for signing up. He earns 9.5 points for each visit to the movie theater. He needs 77 points for a free movie ticket. Which equation could be used to determine vv, the number of visits Gavin must make to earn a free movie ticket?
10 less than 7 times a number is the same as 3 times the number plus 18
Answer:
yes, it is the same
Step-by-step explanation:
7x - 10 = 3x + 18
7x-10+10 = 3x + 18 + 10
7x = 3x + 28
7x - 3x = 3x - 3x + 28
4x = 28
4x ÷ 4 = 28 ÷ 4
x=7
Plug x back in and check the answer.
7x-10 = 3x+18
7(7)-10 = 3(7)+18
49-10 = 21+18
39 = 39
So, YES they are the same.
What is the solution of the system of equations?
13x-6y=2
3x-4y=-10
(Write as ordered pair)
Step-by-step explanation:
let's multiply the first equation by 2 and the second equation by -3, and then we add them together :
26x - 12y = 4
-9x +12y = 30
-------------------------
17x 0 = 34
x = 2
and now we use one of the original equations to solve for y :
3×2 - 4y = -10
6 - 4y = -10
-4y = -16
y = 4
the solution is (2, 4).
2. An account is opened with $28000 earning12% interest compounded yearly. What is thebalance in the account after 4 years?
The principal is $28000 with rate 12% compounded yearly .
To determine the balance after 4 years,
[tex]SI=\frac{P\times R\times T}{100}[/tex][tex]SI=\frac{28000\times12\times4}{100}[/tex][tex]SI=13440[/tex]The balance in the account after 4 years is the sum of principal and simple interest.
[tex]A=\text{ 28000}+13440[/tex][tex]A=41440[/tex]Thus, the balance in the account after 4 years is 41440 dollar.
Write the equation of the line in fully simplified slope-intercept form.
plss help
Answer: y=2x-5
Step-by-step explanation:
what is the volume of the cone? use 3.14 for Pi and round to the nearest hundredth
The volume of the cone:
[tex]V\text{ = }50.24in^3[/tex]Explanations:The radius of the cone, r = 2 in
The height of the cone, h = 4 in
The volume, V, of a cone is given by the formula:
[tex]V\text{ = }\pi r^2h[/tex]Substituting r = 2, h = 4, and π = 3.14 into the formula for calculating the volume shown above:
[tex]\begin{gathered} V=3.14\text{ }\times2^2\text{ }\times\text{ 4} \\ V\text{ = 3.14 }\times\text{ 4 }\times\text{ 4} \\ V\text{ = }50.24in^3 \end{gathered}[/tex]What is -2(-x+5y-4) (simplify equation)
Using the distributed property, the simplified form of -2(-x+5y-4) is 2x-10y+8.
In the equation question,
The given expression is -2(-x+5y-4).
We have to simplify the given expression.
We simplify the given expression using the distributed method.
In the distributed method we have to multiply the number outside the bracket to all the terms that are inside the bracket.
As a(b+c) = ab+bc
In the given question there is -2 outside the bracket and -x+5y-4 is inside the bracket.
To simplify the given expression we multiply -2 to each term inside the bracket.
-2(-x+5y-4) = (-2)×(-x)+(-2)×5y-(-2)×4
Simplifying
-2(-x+5y-4) = 2x+(-10)y-(-8)
Simplifying the bracket
-2(-x+5y-4) = 2x-10y+8
Hence, the simplified form of -2(-x+5y-4) is 2x-10y+8.
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Learning Diagnostic Analytics Math Skill plans Recommendations Fifth grade > Z.11 Parts of a circle Q7N The radius of a circle is 12 feet. What is the circle's diameter? feet Submit
Given:
The radius of the circle = 12 feet
The circle diameter = two times of the radius
so, the diameter = 2 * 12 = 24 feet
So, the answer is 24 feet
Mr. Kilgore made a pot of gumbo with 72 ounces of okra and 2 lbs of shrimp. He made another pot
of gumbo with the same amount of okra, but three times as many lbs of shrimp. How many ounces
of okra did he use per lb of shrimp in the second pot of gumbo
Answer:
12
Step-by-step explanation:
72 / 2 =36
36 / 3 = 12
12, 24, 36, 48, 60, 72.
9. Charlie has 6 more quarters than dimes in a jar and a total of $9.20. Which system of
equations can be used to determine the number of each type of coin Charlie has if
q= the number of quarters and d = the number of dimes?
A. [q=d+6
10d + 25q = 920
B. [d=q+6
10d + 25q = 920
C. [d+q=6
10d + 25q = 920
D. q=d+920
10d + 25q = 6
In linear equation the number of dimes 10d + 25q = 920 .
What are examples of linear equations?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18. A linear equation is a first-order (linear) term and a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.if
q= the number of quarters and d = the number of dimes
d = q + 6
10d + 25q = 920
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The population P of Phoenix, Arizona (in thousands) from 1970 through 2000 can be modeled by the equation P = 590e ^ (0.027t) where r represents the year, with t = 0 corresponding to 1970. According to this model, when will the population reach 1.5 million.
The population of Phoenix , Arizona will reach 1.5 million in the year 2005 .
In the question ,
it is given that ,
the equation , modelling the the population P of Phoenix, Arizona (in thousands) from 1970 through 2000 is
P = 590[tex]e^{0.027\times t}[/tex]
where t represents the year corresponding to 1970 .
we need to find the time required for the population to reach 1.5 million.
since population is represented in thousands , so ,
1.5 million = 1500000 will be taken as 1500 .
Substituting P = 1500 in the equation ,
we get ,
1500 = 590[tex]e^{0.027\times t}[/tex]
1500/590 = [tex]e^{0.027\times t}[/tex]
2.5423 = [tex]e^{0.027\times t}[/tex]
taking ㏑ both the sides , we get
㏑(2.5423) = (0.027t)×㏑(e)
0.93306 = 0.027×t
t = 0.93306/0.027
t = 34.55 years
t ≈ 35 years
the year will be 1970 + 35 = 2005 .
Therefore , The population of Phoenix , Arizona will reach 1.5 million in the year 2005 .
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Julia ran 1,000 meters in 9 minutes. How many meters/minute did she run?
Answer:
111.11111111111111111
Step-by-step explanation:
find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval.
Remember that
If f is continuous over [a,b] and differentiable over (a,b), then there exists c∈(a,b) such that
[tex]f^{\prime}(c)=\frac{f(b)-f(a)}{b-a}[/tex]In this problem, we have the function
[tex]f(x)=\frac{9}{x^3}[/tex]over the interval [1,3]
so
f(a)=f(1)=9/(1)^3=9
f(b)=f(3)=9/(3)^3=1/3
substitute
[tex]f^{\prime}(c)=\frac{\frac{1}{3}-9}{3-1}=\frac{-\frac{26}{3}}{2}=-\frac{26}{6}=-\frac{13}{3}[/tex]Find out the first derivative f'(x)
[tex]f^{\prime}(x)=-\frac{27}{x^4}[/tex]Equate the first derivative to -13/3
[tex]\begin{gathered} -\frac{27}{x^4}=-\frac{13}{3} \\ \\ x^4=\frac{27*3}{13} \\ \\ x=1.58 \end{gathered}[/tex]therefore
The value of c is 1.58 (rounded to two decimal places)What is 3 to the 9th power times 3 to the 5th power
Answer:
3^14
Step-by-step explanation:
Multiplication of two values with same base and different exponent:
When we are multiplicating two values with the same base and different exponents, we keep the base and add the exponents. For example:
[tex]x^a\ast x^b=x^{a+b}[/tex]In this question:
[tex]3^9\ast3^5=3^{9+5}=3^{14}[/tex]Solve the equation 7x = 91 for x.
−98
84
−13
13
Your answer will be D 13
Identify all pairs of congruent corresponding parts.Then write another congruence statement for the polygons.AABC ~ADEF
1) Congruent parts possess the same length, or measure (if angles).
2) As we can see, by the marks on the angles notation within each triangle we can state the following:
[tex]\begin{gathered} AB\cong ED \\ AC\cong DF \\ BC\cong EF \end{gathered}[/tex]Note that was possible since we could base ourselves on the measure of those angles.
3) Thus, we can state that these triangles as we can see, fall under the case of:
SSS - Side Side Side Congruence
Given that those three sides are congruent to each other.
help meeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Simplify each expression. (–5x2y)(3x4)a. 15x6yb. –15x2yc. –15x6yd. –15x8y
The given expression is
[tex](-5x^2y)(3x^4)[/tex]We will multiply at first -5 by 3
[tex]-5\times3=-15[/tex]Then we will multiply x^2 by x^4 by adding their powers
[tex]x^2\times x^4=x^{2+4}=x^6^{}[/tex]And multiply y by 1 as there is no y in the second bracket, then
[tex](-5x^2y)(3x^4)=-15x^6y[/tex]The answer is C
After Batman brought the Joker to justice, the crime rate in Arkham City decreased by 12\%12%12, percent. Previously, the crime rate was ccc incidents per 100010001000 people.
0.88 is the new crime rate in Arkham City.
What is crime rate?The number of offenses reported to law enforcement authorities per 100,000 people in a population is referred to as the crime rate. By dividing the total number of reported offenses by the population, the crime rate is determined.
Given,
The crime rate in Arkham City decreased by 12% when Batman managed to capture the Joker.
In the past, there were c occurrences of crime per 1000 persons.
How can one create an expression that models the issue?
A drop in the percent of crime is subtracted from the prior crime rate, which was defined as incidences per 1000 persons.
c the number of recent crimes per 1,000 individuals;
New crime rate = previous crime rate - decrease in crime %.
New crime rate = c - 12%c
New crime rate = c - 0.12c
New crime rate = 0.88c
Hence, the new crime rate is 0.88c.
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The complete question is:
"After batman brought the joker to justice , the crime rate in arkham city decreased by 12%. Previously the crime rate was c incidents per 1000 people. Which of the following expressions could represent the crime rate in Arkham City after Batman brought the Joker to justice?
a. 22/25 c
b. 0.12c
c. -0.12
d. 0.88c
e. c/1.12"
if dyllan makes 7 out of 10 free throws on any given day what is the probability he will make his next free throw? ( write your answers as a precent.)
Answer:
70%
Explanation:
The probability can be calculated as the number of free throws that Dylan makes divided by the total number of free throws.
So, if Dylan makes 7 out of 10 free throws, the probability can be calculated as:
[tex]P=\frac{7}{10}=0.7[/tex]Then, to know the probability as a percent, we need to multiply 0.7 by 100% to get:
P = 0.7 x 100% = 70%
Therefore, the answer is 70%
What is the slope of the line passing through the points (1, -5) and (4, 1)?
Answer: 2
Step-by-step explanation: i used my brain
PLS HELP ASAP THIS IS DUE TODAY!!!!
line AD is parallel to line HE. Identify one pair of alternate interior angles.
The alternate interior angles : ∠4 and ∠5
∠3 and ∠6
In this question, we have been given line AD is parallel to line HE.
We need to identify one pair of alternate interior angles.
We know that the alternate interior angles are formed when a transversal intersects two lines which are coplanar. These angles, lie on the inner side of the parallel lines but on the opposite sides of the transversal.
For given figure alternate interior angles are:
∠4 and ∠5
∠3 and ∠6
Therefore, the alternate interior angles : ∠4 and ∠5
∠3 and ∠6
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2. A rock club's profit from booking local bands depends on the ticket price. Using past receipts, the owners find that
the profit p can be modeled by the function p = -15t² + 600t + 50, where t represents the ticket price in dollars.
a. What price yields the maximum profit?
b. What is the maximum profit?
Based on the given function,
a) The price that yields the maximum profit is $20.
b) The maximum profit is $6,050
Function
Function defines the relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
Given,
A rock club's profit from booking local bands depends on the ticket price. Using past receipts, the owners find that the profit p can be modeled by the function p = -15t² + 600t + 50, where t represents the ticket price in dollars.
Here we need to find the price that yields maximum profit and the amount of maximum profit.
In order to find the price that yield the maximum profit, we have to find the value of t, that can be obtained by using the formula,
t = -b/2a
According to the given function the values of a = -15 and the value of b = 600
Apply these values on the given function then we get,
t = -600/ 2(-15)
t = -600/-30
t = 20
Therefore, the price that yields the maximum profit is $20.
Now, we need to find the maximum profit, by apply the value of t as 20 in the given function then we get,
p = -15(20)² + 600(20) + 50
P = -15(400) + 12000 + 50
p = -6000 + 12000 + 50
p = 6000 + 50
Therefore, the maximum profit is $6,050.
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Find the equation of a line perpendicular to y = -3x + 5 that passes through the point (6,7)
789
Answer:
Step-by-step explanation:
a random sample of 2 measurements is taken from the following population of values: 1, 2, 4, 5, 8. what is the probability that the range of the sample is 7?
The probability of the sample required where the range is 7 is 0.1 .
The range of a sample is the difference of the maximum and minimum values.
The range of the sample to be 7, the maximum and minimum values should be 8 and 1.
The outcomes required are (8,1).
The total probability of the sample for 2 measured values:
P=[tex]C_{5,2}[/tex]
P=5!/(2!(5-2)!)
P=5!/(2![tex]\times[/tex]3!)
P=20/2
P=10
The probability of the outcome desired,
=(required outcomes)/(total outcomes)
=1/10
=0.1
The probability of the outcome required is 0.1 .
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please help! where it says “select” the options are 1997-2006
We can find the average rate of change of change using the following expression:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]for the period betwen 1999 and 2002, we have the following:
[tex]\begin{gathered} m=\frac{1483-1336}{2002-1999}=\frac{147}{3}=49 \\ \Rightarrow m=49 \end{gathered}[/tex]therefore, the average rate of change of population between 1999 and 2000 is 49.
Next, we do the same for the period between 2001 to 2005:
[tex]\begin{gathered} m=\frac{801-1591}{2005-2001}=-\frac{790}{4}=-197.5 \\ \Rightarrow m=-197.5 \end{gathered}[/tex]thus, the average rate of change of population between 2001 and 2005 is 197.5
Finally, notice that the population increased from 1997 to 2001, while it decreased from 2002, to 2006
What transformations map the figure onto itself? Select all that apply.
A.
Reflection over line y
B.
Reflection over point P
С.
Rotation 180 degrees
D.
Reflection over line m
E.
Rotation 270 degrees
Answer:
Step-by-step explanation:
C because its right
Which of the following expressions is equivalent to the one shown below?(-5.4)How do I solve this and what’s the answer ?
Option B
Using the law of indices
[tex]undefined[/tex]Samuel has 10 coins that add up to $3.80. Some are 50 cent and the rest are 20 cent coins. How many 50 cent coins does he have?
Answer:
6 coins of 50cent
Step-by-step explanation:
Information we have:
1. x number of 50cent and y number of 20cent added up to 380cent.
2. x and y is 10coins
eq1 : 50x + 20y = 380
eq2: x + y = 10
write eq2 to y in term of x
y = 10 - x -> eq3
replace eq3 into eq1
50x + 20(10 - x) = 380
50x + 200 - 20x = 380
50x -20x = 380 -200
30x = 180
x = 180/30 = 6
At any time t (in hours), there are 216(t +18) of Type A bacteria in a sample and 362t + 8 of Type B bacteria in a sample. After how many hours will the number of type A bacteria be less than the type B bacteria?
1. The given situation can be described in the following inequality:
[tex]216^{(t+18)}<36^{(2t+8)}[/tex]2. To solve the prevous inequality, proceedas follow:
write 216 as 6^3 and 36 as 6^2, then, apply log_6 both sides:
[tex]\begin{gathered} 6^{3(t+18)}<6^{2(2t+8)} \\ \log _66^{3(t+18)}<\log _66^{2(2t+8)} \\ 3(t+18)<2(2t+8) \end{gathered}[/tex]then, solve for t, as follow:
[tex]\begin{gathered} 3t+54<4t+16 \\ 3t-4t<16-54 \\ -t<-38 \\ t>38 \end{gathered}[/tex]Hence, from t = 38 hours the number of type A bacteria will be less than the type B bacteria
3. In a number line, you obtain: