if 5a+b=14 then a = what
explain how you got it pls
Answer:
[tex]a = \frac{14 - b}{5}[/tex]
Step-by-step explanation:
The rule to know and follow is:
You can add, subtract, multiply or divide by anything so long as the same thing is done to both sides of the equals sign;
5a + b = 14
If we want to get: "a = ...", then we use the rule to isolate the variable a on one side of the equation;
Firstly, we subtract b from both sides:
5a + b - b = 14 - b
5a = 14 - b
Then, divide both sides by 5:
[tex]\frac{5a}{5} = \frac{14 - b}{5} \\\\ a = \frac{14 - b}{5}[/tex]
Three polygons have been divided
into triangles by drawing a
segment from one vertex to all nonadjacent vertices. If n is the
number of sides in the polygon, which expression shows the
number of triangles created by each polygon?
A.n
B.(n + 2)
C.(n - 2)
D.3n, 4n, 8n
The relationship between the sides of the polygon and the triangle follows an arithmetic sequence
The expression that represents the number of triangles is (c) n - 2
From the diagrams, we have:
Sides Triangles
5 3
6 4
8 6
The above can be represented as functions as follows:
[tex]f(5) = 3[/tex]
[tex]f(6) = 4[/tex]
[tex]f(8) = 6[/tex]
Express 6 as 8 - 2
[tex]f(8) = 8 - 2[/tex]
Express 8 as n
[tex]f(n) = n - 2[/tex]
So, the expression that represents the number of triangles is (c) n - 2
Read more about sequence and patterns at:
https://brainly.com/question/24050043
If a = − 3 and b=−i, then find the value of a^ 3b in fully simplified form.
Answer:
27i.
Step-by-step explanation:
a^3b = (-3)^3 * -i
= -27 * -i
= 27i.
charles had a sheet cake for his birthday when 9/12 remained charles took 1/3 of the remaining cake to wrap and save for later what fraction of the original cake did he wrap
Answer:
He wrapped 3/4 of the cake.
Step-by-step explanation:
1/3 of 9/12 is 0.25 and 0.25 converted into a fraction is 3/4
- Hope this helps!
A price was decreased by 12%. Then it was increased by an additional 5%. What is the percent of the total decrease?
Answer:
7.6%
Step-by-step explanation:
First the decrease
(100-12)%=88%
then the increase
(88)(1.05)=92.4%
The total decrease
(100-92.4)% = 7.6%
Hope this helps
Hemp bell bell help math
Answer:
This is indeed a function!
Step-by-step explanation:
Find the slope of the line on the graph. Write your answer as a fraction or whole number, but a mixed number or decimal.
Answer:
-1/4
Step-by-step explanation:
Rise over run
Rises -1 runs 4
slope = -1/4
2, 1, 2, 4, 5, 4
What is the mean
[tex] \sf \: mean = \frac{Sum \: \: of \: \: Observation} {Total \: \: number \: \: of \: \: Observations} \\ \sf = \frac{2 + 1 + 2 + 4 + 5 + 4}{6} \\ = \sf \frac{18}{6} = 3[/tex]
Answer:
3
Hope you could get an idea from here.
Doubt clarification - use comment section.
I want a way to solve this question
Answer:
Step-by-step explanation:
[tex]cos~L=\frac{m^2+n^2-l^2}{2mn} \\=\frac{5^2+8^2-7^2}{2*5*8} \\=\frac{25+64-49}{80} \\=\frac{40}{80} \\=\frac{1}{2} \\=cos 60\\[/tex]
∠L=60°
Latex paint sells for $21 per gallon and will cost you $210 to paint your room. If each gallon will cover 300 square feet, how many square feet of wall space do you have in your room?
square feet
Answer: 3000 square feet
Step-by-step explanation: 21x10=210 . 300x10=3000
Angle wxz is congruent to angle zxy. Find the value of X
Answer:
x = 18
Step-by-step explanation:
Congruent angles have equal measures.
74° = (4x +2)°
72 = 4x . . . . . . divide by °, subtract 2
18 = x . . . . . . . divide by 4
A spherical solid, centered at the origin, has radius 4 and mass density(x,y,z)=6-(x^2+y^2+z^2). Set up the triple integral and find its mass.
I've attached a photo of the question.
There's something very off about this question.
In spherical coordinates,
x² + y² + z² = ρ²
so that
f(x, y, z) = 6 - (x² + y² + z²)
transforms to
g(ρ, θ, φ) = 6 - ρ²
When transforming to spherical coordinates, we also introduce the Jacobian determinant, so that
dV = dx dy dz = ρ² sin(φ) dρ dθ dφ
Since we integrate over a sphere with radius 4, the domain of integration is the set
E = {(ρ, θ, φ) : 0 ≤ ρ ≤ 4 and 0 ≤ θ ≤ 2π and 0 ≤ φ ≤ π}
so that the integral is
[tex]\displaystyle \int_{\phi=0}^{\phi=\pi} \int_{\theta=0}^{\theta=2\pi} \int_{\rho=0}^{\rho=4} (6 - \rho^2) \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi[/tex]
Computing the integral is simple enough.
[tex]\displaystyle = \int_{\phi=0}^{\phi=\pi} \int_{\theta=0}^{\theta=2\pi} \int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \sin(\phi) \, d\rho \, d\theta \, d\phi[/tex]
[tex]\displaystyle = 2\pi \int_{\phi=0}^{\phi=\pi} \int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \sin(\phi) \, d\rho \, d\phi[/tex]
[tex]\displaystyle = 2\pi \left(\int_{\phi=0}^{\phi=\pi} \sin(\phi) \, d\phi\right) \left(\int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \, d\rho\right)[/tex]
[tex]\displaystyle = 2\pi \cdot 2 \cdot \left(-\frac{384}5\right) = \boxed{-\frac{1536\pi}5}[/tex]
but the mass can't be negative...
Chances are good that this question was recycled without carefully changing all the parameters. Going through the same steps as above, the mass of a spherical body with radius R and mass density given by
[tex]\delta(x, y, z) = k - (x^2 + y^2 + z^2)[/tex]
for some positive number k is
[tex]\dfrac{4\pi r^3}{15} \left(5k - 3r^2\right)[/tex]
so in order for the mass to be positive, we must have
5k - 3r² ≥ 0 ⇒ k ≥ 3r²/5
In this case, k = 6 and r = 4, but 3•4²/5 = 9.6.
In a recent survey, it was found that 133 out of 631 randomly selected Knott's Berry Farm attendees consider Silver Bullet their favorite ride at Knott's. It was also found that 23 out of 121 randomly selected Knott's Berry Farm employees consider Silver Bullet their favorite ride. Test the hypothesis that the percentage of attendees who consider Silver Bullet their favorite ride is different than the percentage of Knott's Berry Farm employees who consider Silver Bullet their favorite ride. Use the a=.05 level of significance.
The P-value is __________, rounded to the nearest ten-thousandth (4 decimal places).
Using the z-distribution, it is found that the p-value is of 0.5975.
At the null hypothesis, it is tested if the proportions are equal, that is, their subtraction is 0, hence:
[tex]H_0: p_1 - p_2 = 0[/tex]
At the alternative hypothesis, it is tested if they are different, that is, their subtraction is not 0, hence:
[tex]H_1: p_1 - p_2 \neq 0[/tex]
The sample sizes and proportions are given by:
[tex]n_1 = 631, p_1 = \frac{133}{631} = 0.2108[/tex]
[tex]n_2 = 121, p_2 = \frac{23}{121} = 0.1901[/tex]
The standard errors are given by:
[tex]s_1 = \sqrt{\frac{0.2108(0.7892)}{631}} = 0.0162[/tex]
[tex]s_2 = \sqrt{\frac{0.1908(0.8092)}{121}} = 0.0357[/tex]
For the distribution of differences, the estimate and the standard error are:
[tex]\overline{p} = p_1 - p_2 = 0.2108 - 0.1901 = 0.0207[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0162^2 + 0.0357^2} = 0.0392[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
In which [tex]p = 0[/tex] is the value tested at the null hypothesis.
Then:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
[tex]z = \frac{0.0207 - 0}{0.0392}[/tex]
[tex]z = 0.528[/tex]
Using a z-distribution calculator, with a two-tailed test, as we are testing if the mean is different of a value, the p-value is of 0.5975.
A similar problem is given at https://brainly.com/question/25869410
help me with this math problem please
Answer:
BC ≅ EF
Step-by-step explanation:
Since the triangles are congruent then corresponding sides are congruent
ABC ≅ DEF
The corresponding sides are BC and EF
Suppose a 5-digit number is formed using the digits from 1 to 9 (without replacement). What is the probability that it will be an even number?
By finding the probability that the unit digit is even, we will see that the probability that the 5-digit number will be even is P = 4/9.
So we have a 5-digit number, let's say that it is:
abcde
Now, we have 5 "slots" where we can put numbers from 1 to 9 (without replacement).
We want to find the probability that the number will be even, so we only care for the last digit, e (it must be even).
Let's assume that the first digit at which we assign its value is this, e, the last one.
For this digit we have 9 options, {1, 2, 3, 4, 5, 6, 7, 8, 9}
4 of these options are even numbers.
So there are 4 out of 9 cases where the last digit is even, then the probability that the 5-digit number will be even is just:
P = 4/9
Now the other four digits can be anything (even or odd), so we only care for the probability above.
If you want to learn more about probability, you can read:
https://brainly.com/question/23044118
Getting trained and licensed as a truck driver involves a one-time cost of $450. Gas and insurance end up costing about $2 per mile. For the first delivery, you will get paid $350 plus $6 per mile that you drive. Write 2 equations and solve this system.
The question is an illustration of a system of linear equations.
The system of linear equations is: [tex]y=450 + 2x[/tex] and [tex]y = 350 + 6x[/tex]The solution to the equation is (25,500)Let the number of miles be x.
Getting trained and licensed
One time cost: $450Gas and Insurance: $2 per mileSo, the equation is:
[tex]y=450 + 2x[/tex]
Delivery
First delivery: $350Rate: $6 per mileSo, the equation is:
[tex]y = 350 + 6x[/tex]
Hence, the system of linear equations is:
[tex]y=450 + 2x[/tex] and [tex]y = 350 + 6x[/tex]
To solve the equation, we equate both, as follows:
[tex]450 + 2x = 350 + 6x[/tex]
Collect like terms
[tex]6x - 2x = 450 - 350[/tex]
[tex]4x = 100[/tex]
Divide both sides by 4
[tex]x = 25[/tex]
Substitute 25 for x in [tex]y=450 + 2x[/tex]
[tex]y = 450 + 2 \times 25[/tex]
[tex]y = 450 + 50[/tex]
[tex]y = 500[/tex]
Hence, the solution to the equation is (25,500)
Read more about linear equations at:
https://brainly.com/question/14323743
A taxi ride costs $3.50 plus $2.50 per mile driven. If Sasha has $37 in cash , what is the greatest whole number of miles she can ride in this taxi ? Happy Holiday ´ s...
Answer:13
Step-by-step explanation:
37-3.5=33.5
33.5/2.5=13.4
since it ask for the whole number, it will be 13
Solve two eighths times four fifths
Answer:
8/40 or 1/5
Step-by-step explanation:
2x4=8
8x5=40
That gives us the answer of 8/40 but if you need simplifying just divide 8/40 by 8/8 and you will get the final answer of 1/5
5cm
10cm
Q
Q2
Q3
Referring to the diagram above.
if Q1 = 9.0 uC, Q2 = -5.0 uC and Q3 = 32.0 uc,
what is the magnitude of the electric field at Q2, due to Q1 and Q3?
Which is an advantage of using a credit card?
A. You can make purchases when you don’t have cash
B. You don’t indulge in impulse buying
C. You don’t have to pay interest
factorise
18p+6
please im so bad
A rectangle has a length of x + 7 and a width of x-2. Which equation below describes the perimeter, P, of
the rectangle in terms of x?
Answer:
P = 4x + 10
Step-by-step explanation:
perimeter of a rectangle = 2( width + length )
P = 2 ( x - 2 + x + 7 )
P = 2 ( x + x + 7 - 2 )
P = 2 ( 2x + 5 )
P = 4x + 10
Joyce drives from Louisville to St. Louis which is 260 miles in 4 hours. How many miles can she drive in 10 hours
Answer:
260 miles in 4 hours equals (260 / 4) = 65 miles per hour
In 10 hours she can drive 650 miles
Step-by-step explanation:
I need help on my homework.
Answer:
[tex] \frac{3}{4} > \frac{ - 2 + 2x}{4} \\ \\ (4 \times) \frac{3}{4} > \frac{ - 2 + 2x}{4} ( \times 4) \\ \\ 3 > - 2 + 2x \\ \\ 3 + 2 > - 2 + 2 + 2x \\ \\ 5 > 2x \\ \\ 5 \div 2 > 2x \div 2 \\ \\ \frac{5}{2} > x \\ \\ x < \frac{5}{2} [/tex]
I hope I helped you^_^
Learning Task 1: Write the fraction of each shaded figure. Find the sum. Write your answer in your notebook.
Please is anyone can help me please
1. 3. 3. 1.
4. 2
2. 5. 4. 6.
9. 13
5. 3. 6. 7.
5. 9
Step by step explanation:
hopefully that's help
2m>30
what is the answer to this
Answer:
m>15
Step-by-step explanation:
Divide both sides by 2
Hello there! :-)
This is a one-step inequality, which means we can solve it in one step.
The goal is to find m.
To isolate m, we divide both sides by 2:
m>15
Remember to divide both sides by 2.
Therefore, m>15 (this means m is greater than 15)
Hope it helps. Use the comment section to clarify your doubts.
Answered by
~A felicitous teen who helps others :-)
Good luck with your studies. :)
Jeremiah buys 6 tacos and 8 enchiladas for 60 dollars. Kennedy buys 3 tacos and 2 enchiladas for 18 dollars.
Answer:
What's the question lol
How to find the derivative???
[tex]e^{2x} = \ln(y^3)\\\\\implies e^{2x} = 3 \ln y\\\\\implies \dfrac{d}{dx} e^{2x} = 3\dfrac{d}{dx}( \ln y)\\\\\implies 2e^{2x} = 3 \cdot \dfrac 1y \cdot \dfrac{dy}{dx}\\\\\implies 3\dfrac{dy}{dx} = 2ye^{2x}\\\\\implies \dfrac{dy}{dx} = \dfrac{2y}3 e^{2x}[/tex]
Solve for x, y, and z
Step-by-step explanation:
[tex]x = 46.16 \\ y = 23.00 \\ z = 55.7[/tex]
Use the drawing tools to form the correct answer on the graph.
What is the inverse of the function shown?
Click on a tool to begin drawing.
Delote
Undo
Reset
Drawing Tools
Select
iz
Point
10
Line Segment
8
6
4
2
x
6
-10
-8
-6
-4
-2
2
6
8
10
2
Answer:
i need to know this one fast i cant get past this mastery test
Step-by-step explanation:
The inverse of a function is the opposite of the function
From the graph, we have the following ordered pairs
(5,0), (8,3) and (2,-3)When the (x,y) coordinates are rewritten as (y,x), we have the following ordered pairs
(0,5), (3,8) and (-3,2)This means that the inverse of the function passes through the above points
See attachment for the graph of the inverse function
Read more about inverse function at:
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