Steps to solve:
2(n + 3) = 2n + 3
~Distribute left side
2n + 6 = 2n + 3
~Subtract 6 to both sides
2n = 2n - 3
~Subtract 2n to both sides
n = -3
Best of Luck!
Adam built a tree house with a rectangular base. The length of the base is 7 inches more than its width.
Ifw represents the width of the tree house, which inequality could be used to determine what lengths would make the area of the base
of the tree house greater than 293 square Inches?
W + 7 > 293
202 + 286 > 2,051
w2 + 7w > 293
12 + 293 > 293
Submit
w²+7w>293 is the inequality which we use to determine what lengths would make the area of the base of the tree house greater than 293 square Inches
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that Adam built a tree house with a rectangular base.
The length of the base is 7 inches more than its width.
Length=W+7
W is the width
The area of the base of the tree house greater than 293
We need to find the inequality to represent the area of the base of tree
Area of rectangle=Length×width
293=(w+7)w
293=w²+7w
As area is greater we have
w²+7w>293
Hence, w²+7w>293 is the inequality which we use to determine what lengths would make the area of the base of the tree house greater than 293 square Inches
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how does "money breeds money" apply to simple interest
Answer:
The saying money breeds money means that with money, you have the possibility to create more money. Simple interest is the idea that you have something, and you obtain a percentage of that every designated time period. That being said, simple interest = money breeds money
You spin the spinner twice what is the probability of landing on 6 and then landing on 6 again
1/8 since 4*2=8 and there is one spot you can land on with 6.
Answer:
2/8
Step-by-step explanation:
If you are spinning it twice and there is 4 places that is where you get the 8 The 2 comes from how many times you are spinning
What function do you know from calculus is such that its first derivative is itself?The above function is a solution of which of the following differential equations?a. y = ey.b. y = 1.c. y = y.d. y = y2.e. y = 2y.What function do you know from calculus is such that its first derivative is a constant multiple k of itself? The above function is a solution of which of the following differential equations?a. y = ky.b. y = yk.c. y = eky.d. y = k.e. y = y + k.
Answer:
a. y= e raise to power y
c. y = e^ky
Step-by-step explanation:
The first derivative is obtained by making the exponent the coefficient and decreasing the exponent by 1 . In simple form the first derivative of
x³ would be 2x³-² or 2x².
But when we take the first derivative of y= e raise to power y
we get y= e raise to power y. This is because the derivative of e raise to power is equal to e raise to power y.
On simplification
y= e^y
Applying ln to both sides
lny= ln (e^y)
lny= 1
Now we can apply chain rule to solve ln of y
lny = 1
1/y y~= 1
y`= y
therefore
derivative of e^y = e^y
The chain rule states that when we have a function having one variable and one exponent then we first take the derivative w.r.t to the exponent and then with respect to the function.
Similarly when we take the first derivative of y= e raise to power ky
we get y=k multiplied with e raise to power ky. This is because the derivative of e raise to a constant and power is equal to constant multiplied with e raise to power y.
On simplification
y= k e^ky
Applying ln to both sides
lny=k ln (e^y)
lny=ln k
Now we can apply chain rule to solve ln of y ( ln of constant would give a constant)
lny = ln k
1/y y~= k
y`=k y
therefore
derivative of e^ky = ke^ky
what Is the area of the trapezoid
18m
Step-by-step explanation:
5x3=15 +3 =18
Please answer I will make you Brainliest if it's right How do I do this step by step??
Answer:
[tex] \sqrt{2 \times 2 \times 2 \times 3 } = \sqrt{24} = \sqrt{4 \times 6} = 2 \sqrt{6} [/tex]
Answer:
Step-by-step explanation:
a medical transcriptionist has a four drawer cabinet. one drawer is 4/5 full and one is 1/2 full and one drawer is 3/4 full. can the contents be combined into 3 drawers why or why not
Answer:
Yes, provided they are all the same size.
Step-by-step explanation:
4/5=0.8
1/2=0.5
3/4=0.75
0.8+0.5+0.75=n
8+5=13
0.8+0.5=1.3
1.3+0.75=2.05
Write a rule to describe each transformation.
11. P (3,4), Q (3,5), R (4,5), S (5,0)
to
P’ (0,3), Q’ (0,4), R’ (1,4), S’ (2,-1) 12.
F (-4,1), E (-4,3), D (-1,3) to
F’ (1,4), E’ (3,4), D’ (3,1)
B (-3, -5), C (-2,-2), D (-1,-2) to
B’ (3,-5), C’ (2,-2), D’ (1,-2)
Suppose f has absolute minimum value m and absolute maximum value M. Between what two values must 7 f(x) dx 4 lie?Which property of integrals allows you to make your conclusion?
Answer:
3m ≤ ∫ f(x) dx ≤ 3M, at limit of b, a
Step-by-step explanation:
Like the question asked, which property of integral was used.
Property 8 of integrals was the basis upon which the question was solved.
The property of the integral is used to solve the problem. The function is given below.
[tex]3m & \leq \int_a^b f(x)dx \leq 3M \end{aligned}[/tex]
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
Suppose f has absolute minimum value m and absolute maximum value M.
We know that the property of the integral can be used.
If m ≤ f(x) ≤ M ∀ a ≤ x ≤ b. Then we have
[tex]m (b-a) \leq \int_a^b f(x) dx \leq M(b-a)\\[/tex]
Then we have
[tex]m \leq f(x) \leq M \ \ and \ \ 4 \leq x \leq 7[/tex]
This means that
[tex]\begin{aligned} m(7-4) & \leq \int_a^b f(x)dx \leq M(7-4)\\\\3m & \leq \int_a^b f(x)dx \leq 3M \end{aligned}[/tex]
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17. Write a quadratic equation to find two consecutive odd natural numbers whose
product is 63. Then find the numbers
Answer:
7 and 9
Step-by-step explanation:
So we want two consecutive odd numbers whose product is 63.
Let's write an equation.
Let's let n be a random integer: doesn't matter what it is. Therefore, the first integer must be 2n+1.
This is because we're letting n be whatever it wants to be. If we multiply that whatever number by 2, then it will turn even. If we add 1 to an even number, it becomes odd.
Therefore, our first odd number is (2n+1). Our second, then, must be (2n+3).
Multiply them together. They equal 63. Thus:
[tex](2n+1)(2n+3)=63[/tex]
Expand:
[tex]4n^2+6n+2n+3=63[/tex]
Combine like terms:
[tex]4n^2+8n+3=63[/tex]
Subtract 63 from both sides:
[tex]4n^2+8n-60=0[/tex]
Divide both sides by 4:
[tex]n^2+2n-15=0[/tex]
And now, factor:
[tex](n+5)(n-3)=0[/tex]
Zero Product Property:
[tex]n+5=0\text{ or } x-3=0[/tex]
Find n:
[tex]n=-5\text{ or } n=3[/tex]
So, we've found n.
Then the first integer is either:
[tex]2(-5)+1 \text{ or } 2(3)+1[/tex]
Evaluate:
[tex]-9 \text{ or } 7[/tex]
However, we want two consecutive odd natural numbers. So, ignore the -9.
Therefore, our first odd integer is 7.
And our second one would be 9.
So, our answer is 7 and 9.
And we're done!
Choose the function to match the graph.
Answer:
your pics a little blurry but if i am reading it right
the first one
f(x)=log x+5
Write the following words as an algebraic expression. The sum of the quotient of a number x and 5 and the product of 6 and a number y
Answer:
[tex]\frac{x}{5} + 6y[/tex]
Step-by-step explanation:
6) 6a + 34 = -3(-2a + 8)
step 1: open up the brackets ( rmb to flip the signs )
step 2: bring 'a' to one side and the numbers to the other
6a + 34 = -3(-2a + 8)
6a + 34 = 6a - 24
6a - 6a = -24 - 34
0 = - 58
the final ans is kind of weird but here's my solution :))
laws of Sines. Find each measurement indicated. Round your answers to nearest tenth. Part 1
Answer:
1) 19.0km
2) 23.9mi
3) 53.9yd
4) 30.0mi
(all answers rounded off to the nearest tenth)
Step-by-step explanation:
Please see the attached pictures for full solution.
Polygon QQQ is a scaled copy of Polygon PPP using a scale factor of \dfrac1221start fraction, 1, divided by, 2, end fraction. Polygon QQQ's area is what fraction of Polygon PPP's area?
Answer: Area of Polygon Q is [tex]\dfrac14[/tex] of Area of Polygon
Step-by-step explanation:
Given: Polygon Q is a scaled copy of Polygon P using a scale factor of [tex]\dfrac12[/tex] .
According to the property of scale factor ,
Area of the image = (scale factor )²x (Area of the original figure)
So, Area of Polygon Q = [tex](\dfrac12)^2[/tex] x (Area of Polygon P)
⇒ Area of Polygon Q = [tex]\dfrac14[/tex] x (Area of Polygon P)
Hence, Area of Polygon Q is [tex]\dfrac14[/tex] of Area of Polygon P.
Answer:
1/4
I did on khan
Step-by-step explanation:
Suppose we are estimating a population proportion by its sample equivalent.
(a) We have a sample of n = 10 units and we find the proportion is p = .4. If the true proportion is p= .3 find PC Ô-p|>.2)
(b) Consider the same problem as in part (a) but now, our sample size is n = 400. Find P( P-p> .001)
Answer:
(a) 0.16759
(b) 0.9649
Step-by-step explanation:
Given that:
n = 10 , p = 0.3 and [tex]\hat p = 0.4[/tex]
[tex]P(|\hat p - p| > 0.2 ) = 1 - P ( |\hat p -p| \leq 0.2)[/tex]
= [tex]1 - P(-0.2 \leq \hat p-p \leq 0.2)[/tex]
= [tex]1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{\dfrac{pq}{n}}} \leq \dfrac{\hat p -p}{\sqrt{\dfrac{pq}{n}}} \leq \dfrac{0.2}{\sqrt{\dfrac{pq}{n}}} \end {pmatrix}[/tex]
[tex]=1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{\dfrac{(0.3)(1-0.3)}{10}}} \leq Z \leq \dfrac{0.2}{\sqrt{\dfrac{(0.3)(1-0.3)}{10}}} \end {pmatrix}[/tex]
[tex]=1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{\dfrac{(0.3)(0.7)}{10}}} \leq Z \leq \dfrac{0.2}{\sqrt{\dfrac{(0.3)(0.7)}{10}}} \end {pmatrix}[/tex]
[tex]=1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{0.021}} \leq Z \leq \dfrac{0.2}{\sqrt{0.021}} \end {pmatrix}[/tex]
[tex]=1 - P \begin {pmatrix} -1.380 \leq Z \leq 1.380 \end {pmatrix}[/tex]
= 1 - P( Z ≤ 1.380) - P(-1.380)
= 1 - ( 0.91620 - 0.08379 )
= 1 - 0.83241
= 0.16759
b) when n = 400; p =0.3 , q = 1 - p = 1 - 0.3 = 0.7
[tex]P( |\hat p - p | > 0.001) = 1- P ( |\hat p - p | < 0.001 )[/tex]
[tex]= 1- P ( -0.001 < \hat p - p < 0.001 )[/tex]
[tex]= 1- P ( \dfrac{-0.001}{\sqrt{\dfrac{pq}{n}}} < \dfrac{ \hat p - p}{\dfrac{pq}{n}} < \dfrac{0.001}{\sqrt{\dfrac{pq}{n}}} )[/tex]
[tex]= 1- P ( \dfrac{-0.001}{\sqrt{\dfrac{0.3\times 0.7}{400}}} < Z < \dfrac{0.001}{\sqrt{\dfrac{0.3 \times 0.7}{400}}} )[/tex]
[tex]= 1- P ( \dfrac{-0.001}{\sqrt{5.25 \times 10^{-4}}} < Z < \dfrac{0.001}{\sqrt{5.25 \times 10^{-4}}} )[/tex]
[tex]= 1- P ( -0.0436< Z < 0.0436)[/tex]
= 1 - P ( Z < 0.0436) - P ( -0.0436)
= 1 - (0.5176 - 0.4825)
= 1 - 0.0351
= 0.9649
The length of a toucan is about two thirds the length of a macaw. Toucans are about 24 in. long. What is the length of macaw
Answer:
12, 12 and 12 so 36
Step-by-step explanation:
Write 40/64 in simplest
-1
The distance AB
rounded to the
nearest tenth = [?]
Help Resources
-2
-1
0
Skip
B
Hint: Use the distance formula:
d = (x2 – X1)2 + (y2 - yı)?
Enter
Answer:
AB = 4.5
Step-by-step explanation:
Distance between A(-1, 2) and B(1, -2):
[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] A(-1, 2) = (x_1, y_1) [/tex]
[tex] B(1, -2) = (x_2, y_2) [/tex]
[tex] AB = \sqrt{(1 - (-1))^2 + (-2 - 2)^2} [/tex]
[tex] AB = \sqrt{(2)^2 + (-4)^2} [/tex]
[tex] AB = \sqrt{4 + 16} = \sqrt{20} [/tex]
[tex] AB = 4.5 [/tex] (nearest tenth)
At noon, the temperature in Ebonsville, Texas was 29℉. By midnight, the temperature had fallen to −10℉. What was the change in temperature over the 12-hour period?
Answer:
i believe it's 39
Step-by-step explanation:
29 -39 = -10
Divide $70 in the ratio 1:2:4
Answer:
Here Ratio=1:2:4
total money =$70
Step-by-step explanation:
let the ratio number be 1x,2x and4x
Now,
1x+2x+4x =$70
or, 7x. =$70
or, x. =$70÷7=$10
again,
1x=1×$10=$10,
2x=2×$10=$20 and
4x=4×$10=$40
the perimeter of the isosceles triangle with base length y-2 and legs of length y
Answer:
3y-2
Step-by-step explanation:
y+y+y-2
3y-2
The perimeter of the isosceles triangle with base length y - 2 and length of legs y is 3y - 2. legs.
Here,
Base length of triangle is y - 2.
Length of legs of triangle is y.
What is Perimeter of triangle?
Perimeter of triangle is sum of all three sides of a triangle.
Now,
Base length of triangle is y - 2.
Length of legs of triangle is y.
Perimeter = y - 2 + y + y
= 3y - 2
Hence, The perimeter of the isosceles triangle with base length y - 2 and legs of length y is 3y - 2.
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What is the missing value A=3 b=5 c=?
Answer:
4
Step-by-step explanation:
(Question is on the picture)
Answer:
Step-by-step explanation:
5. (6.5 - 2)/(7 - 4) = 4.5/3 = 1.5
6. (8 - 8)/(-5 - 10)= 0/-15= 0
7. (-3 + .75)/(4 - 1) = -2.25/3 = -.75= -3/4
8. (2 + 7)/(18 - 18)= 9/0 = undefined
In a hockey game, Seth took 12 shots and scored 3 times.
Zak took 10 shots and scored twice. Who scored on a
greater fraction of his shots?
Answer:
Seth
Step-by-step explanation:
Seth:3/12 = 0.25
0.25*100 = 25%
Seth scored at 25%
Zak:2/10 = 0.2
0.2*100 = 0.2
0.2*100 = 20%
Zak scored at 20%
then:
25>20
then:
Seth scored on a greater fraction of his shots.
Zak scored on a greater fraction of his shots.
Given,
In a hockey game, Seth took 12 shots and scored 3 times.
Zak took 10 shots and scored twice.
We need to find who scored on a greater fraction of his shots.
How do we compare fractions?
We can compare fractions by finding their decimal values a nd comparing them.
Example: 1/2 and 2/5
1/2 = 0.5
2/5 = 0.4
0.5 is greater than 0.4.
Find the number of score Seth shots out of 12 shots.
= 3
We can write in fractions as:
3/12 _____(1)
Find the number of score Zak shots out of 10 shots.
= 2 x 3
= 6
We can write in fractions as:
6/10 _____(2)
Compare (1) and (2)
3/12 = 1/4 = 0.25
6/10 = 3/5 = 0.6
0.25 is less than 0.6
6/10 is a greater fraction than 3/12
Thus Zak scored on a greater fraction of his shots.
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Simplify the expression using
order of operations
12 (10-5) - 40 + (4+1)
ans is 25
Step-by-step explanation:
12(10-5)-40+(4+1)
=12 of 5 - 40 + 5
= 60 - 40 +5
=60 +5 - 40
=65-40
=25
Answer:
-25
Step-by-step explanation:
We start off by using PEMDAS. 10-5 then 4+1.
12(5)-40+5
we multiply, then add and subtract giving us -25
Veronica deposited $11 in a savings account that earns 1.9% simple interest. Which graph represents this scenario?
Answer:
Option C
Step-by-step explanation:
Initial balance= $11Interest rate = 1.9% PA simpleIt will be graphed as function:
y = 11 + 0.019xSince is has a very small slope of 0.019 it will be shown almost parallel to x axis.
Some points on the graph:
Amount in 1 year= 11*(1+0.019) = $11.21Amount in 2 years = 11*(1+2*0.019) = $11.42Amount in 6 years = 11*(1+6*0.019) = $12.25Amount in 10 years = 11*(1 + 10*0.019) = $13.09Correct graph is option C
1. The point A(-4,6) is rotated 90 degrees counterclockwise and then translated 3 units up.
What is the point A'?
A
(-6, -7)
B. (-6, -1)
C. (6.7)
D. (9.7)
Answer:
Step-by-step explanation:
-6mn + 5mn - 3x2 - 4x2
Help
Answer:
Step-by-step explanation:
3x^2 - 4x^2 - 6mn + 5mn
-x^2 - mn
ok so I need help on this question. How would you evaluate this expression, -8x + 5 -2x - 4 + 5x when x=2. How would you write the expression in simplest form?
Answer:
Here are the basic steps to follow to simplify an algebraic expression:
remove parentheses by multiplying factors.
use exponent rules to remove parentheses in terms with exponents.
combine like terms by adding coefficients.
combine the constants.
Step-by-step explanation: