Answer:
n=-18
Step-by-step explanation:
Steps:
multiply 3 by both sides of the equation
2. cross out the 3 from [tex]3(\frac{2}{3} )[/tex] and you will get 2 and then do -12 x 3 and you will get -36.
3. you now have 2n=-36
4. divide both sides by 2 to isolate n by itself.
[tex]\frac{2n}{2} =\frac{-36}{2}[/tex]
5. divide by crossing out 2 and 2 on the right and then do -36 ÷ 2 which will give you n= -18
Hope this helps :) if you have any questions let me know.
Hi!
To find the value of n in the given equation, multiply both sides by 3.
That way, you'll clear the fractions and solving for n will be easier.
[tex]\implies\boldsymbol{\displaystyle\frac{2}{3} n\times3=-12\times3}[/tex]
Watch what happens:
[tex]\implies\boldsymbol{\displaystyle\frac{2}{\not3} n\times\not3=-36}[/tex]
On the LHS, the 3's cancel out, and we're left with 2n:
[tex]\implies\boldsymbol{2n=-36}[/tex]
Now, divide both sides by 2:
[tex]\implies\boldsymbol{n=-18.}[/tex]
Voila! There's our solution.
Have a nice day!
I hope this helps.
-stargazing
Patrick leaned a 30-foot ladder against the side of a building. The
base of the ladder is 17 feet from the base of the building. The top of
the ladder is 11 feet from the top of the building. How tall is the
building? Provide an answer accurate to the nearest tenth of a foot.
The distance between the bottom of the ladder and the ground's surface is 24.7 feet.
Given that a is the ground, b is the building, and c is the ladder.
Also the ground is perpendicular to the building, the ladder, the building, and the ground form a right triangle.
Therefore, the Pythagorean theorem can be applied as follows:
c² = a² + b²
According to the information in the problem, c is 30 feet, b is 17 feet, and we solve for a as follows:
(30 ft)² = a² + (17 ft)²
900 ft² = a² ₊ 289 ft²
900 ft² ₋ 289 ft² = a²
611 ft² = a²
a² = 611 ft²
a = √611 ft²
a = 24.71
rounding off to nearest tenth, so a = 24.7
Hence the bottom of the ladder is 24.7 feet far away from the base of the ground.
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Your question is incomplete. Please find the missing content here.
A 23-foot ladder is placed against a building. If the top of the ladder will lean against the building 17-feet high, how far away from the base of the building is the bottom of the ladder located?
five less than twelve times a number
Answer:
Five less than twelve times a number is represented by 12n - 5
Expressing word problems as Equations
Let the unknown nmber be represented as n
Such that twelve times the number will be represented as 12 n
There fore Five less than twelve times the number becomes 12n - 5
Lisa's father is paying for a $20 meal. He has a 15% off coupon for the meal.
After the discount, a 7% sales tax is applied. What does Lisa's father pay for
the meal?
Plssss answer fast
If a = 3 sqrt(3) in the right triangle shown, what is the value of b?
Note: Consider the below figure attached with this question.
Given:
[tex]a=3\sqrt{3}[/tex]
To find:
The value of b.
Solution:
In a right angled triangle,
[tex]\tan \theta = \dfrac{Perpendicular}{Base}[/tex]
For the given right angled triangle,
[tex]\tan \theta = \dfrac{a}{b}[/tex]
[tex]\tan (30^\circ) = \dfrac{3\sqrt{3}}{b}[/tex]
[tex]\dfrac{1}{\sqrt{3}} = \dfrac{3\sqrt{3}}{b}[/tex]
On cross multiplication, we get
[tex]1\times b=3\sqrt{3}\times \sqrt{3}[/tex]
[tex]b=3(3)[/tex]
[tex]b=9[/tex]
Therefore, the value of b is 9.
1. Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated with
the origin as the center of dilation using the rule (x, y) - (x, y) to create pentagon
M'N'P'Q'R'. Which statement is true?
Answer:
B
Step-by-step explanation:
if its less than 1 it shrinks
The correct statement is; Pentagon M’N’P’Q’R is smaller than pentagon MNPQR because the scale factor is smaller than 1.
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
If a polygon is dilated by a scale factor = k
Rule to be followed as;
(x, y) → (kx, ky)
Here, k = Scale factor
If 0 < k < 1, size of the image will be reduced.
Similarly, k > 1, size of the image will be enlarged.
We are given that Pentagon MNPQR is dilated with the origin as the center of dilation to form an image M'N'P'Q'R'.
Rule used for the transformation,
(x, y) → (1/4x, 1/4y)
Here, the scale factor through which MNPQR has been dilated is 1/4.
Since, scale factor is between zero and 1/4, size of M'N'P'Q'R' will be reduced.
Therefore, the size of pentagon M'N'P'Q'R' will be 1/4 smaller than pentagon MNPQR.
Option (2) is the answer.
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Will mark brainliest for whoever answers
53 decreased by twice Mai's score
Answer:
This expression can be written as 53-2m
Step-by-step explanation:
Sometimes it can help to reword the sentence...
2 times Mai's score is being subtracted from 53.
Use 'M' for Mai's score:
53-2m
6x square +11x-10
Factories
Answer:
(2x+5)(3x-2)
Step-by-step explanation:
6x²+11x-10
6x²+15x-4x-10
3x(2x+5)-2(2x+5)
(2x+5)(3x-2)
The youth group at the church decided to plant geraniums and
daisies around the church grounds as a group project. Geraniums
in 6" pots cost $4 each and daisy plants cost $6 each. The youth
group spent $410 on 80 plants. How many geraniums and how many
daisy plants did the group buy?
Answer:
The youth group bought 35 geraniums and 45 daisy plants.
Step-by-step explanation:
We can solve this using a system of equations:
x + y = 80
4x + 6y = 410
X = Geraniums
Y = Daisies
First, let's solve for a variable in the first equation. I am going to solve for y in the first equation:
x + y = 80
y = -x + 80
Now that we have solved for y we can plug that back in to the 2nd equation:
4x + 6(-x + 80) = 410
4x - 6x + 480 = 410
-2x + 480 = 410
-2x = -70
x = 35
Now that we have found the amount of geraniums we can plug it back into the first equation and solve for y:
35 + y = 80
y = 45
Therefore the youth group bought 35 geraniums and 45 daisy plants.
Check:
(35) + (45) = 80
80 = 80
4(35) + 6(45) = 410
140 + 270 = 410
410 = 410
I hope this helps!!
- Kay :)
PLEASE HELP ME IM IN DESPERATE NEED> ill give brainliest ;\
Answer:
C. n^3 - 16 = 48
You invest $1,000 in a fund. You check your statement at the end of April and you have lost 13%. When the statement for May comes, you see you have gained 13% in May. What is the value of your account? Round to the nearest dollar.
Answer:
You still would have $1,000
Step-by-step explanation:
In April, you lost 13% of your fund. So we will subtract it.
In May, you gain 13% back. The rate of change was 0%.
Therefore, you still have $1,000 dollars.
Answer: The answer is that you have $983.
Step-by-step explanation:
I'll give brainly pls help
Answer:
I think the second one!
Step-by-step explanation:
The phone you want to purchase is $200. You have a coupon for 30% off the purchase price. How much will you pay for the phone after the discount?
Answer:
$140
Step-by-step explanation:
Orignal Price: $200
200 x 0.3
= 60
200 - 60
= 140
Answer:the phone will cost 140
Step-by-step explanation:
Y = .75x = .75(16)=
Can someone plz help me out
Terry has an investment account which compounds interest continuously at a rate of 1.4%. He puts $1600 in the account initially. After 3 years, how much money is in the account?
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1600\\ r=rate\to 1.4\%\to \frac{1.4}{100}\dotfill &0.014\\ t=years\dotfill &3 \end{cases} \\\\\\ A=1600e^{0.014\cdot 3} \implies A \approx 1668.63[/tex]
Select the two descriptions that match the dilation
Write a linear function f with the values f(-1)=-3 and f(2)=6.
Answer:
y = 3x
Step-by-step explanation:
Equation of a Line
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The point-slope form of the equation of a line is:
y - k = m ( x - h )
Where m is the slope and (h,k) is a point through which the line passes.
We are given the following values of the function: f(-1)=-3 and f(2)=6. The points are (-1,-3) and (2,6). The slope is:
[tex]\displaystyle m=\frac{6+3}{2+1}=\frac{9}{3}=3[/tex]
Now find the equation of the line using the second point:
y - 6 = 3 ( x - 2 )
Operating:
y - 6 = 3x - 6
Simplifying:
y = 3x
PLEASE HELP!!! WILL GIVE BRAIN I PROMISE!!!!
Answer: 6i
Step-by-step explanation:
20 POINTS! Please help! Solve using a system of equations, elimination or substitution method. Show all work please :) thank you! No spam answers please.
x + y + z = 7200
0.04x + 0.11y + 0.14z = 805
z = x + y + 200
Using the system of equations x+y+z=7200, 0.04x+0.11y+0.14z=805 and z=x+y+200, the value of x=1400,y=2100 and z=3700
Given,
The equations
x+y+z=7200
0.04x+0.11y+0.14z=805
z=x+y+200
Substitute the value of z in the first and second equations
x+y+x+y+200=7200
2x+2y+200=7200
2x+2y=7000
x+y=3500 (1)
Similarly
0.04x+0.11y+0.14(x+y+200)=805
0.04x+0.11y+0.14x+0.14y+28=805
0.18x+0.25y=777
Multiply the equation by 4
0.72x+y=3108 (2)
We have to use elimination method here
Subtract the equation (1) from (2)
x-0.72x=3500-3108
0.28x=392
x=1400
Then,
x+y=3500
1400+y=3500
y=2100
z= x+y+200
z=1400+2100+200
z=3700
Hence, using the system of equations x+y+z=7200, 0.04x+0.11y+0.14z=805 and z=x+y+200, the value of x=1400,y=2100 and z=3700
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Morgan throws a ball up into the air. The height of the ball above the ground, in feet, is modeled by the function h(t) = −16t 2 + 24t, where t represents the time, in seconds, since the ball was thrown. What is the appropriate domain for this situation?
Answer:
I will give you the link below to a PDF that one of my young friends made for someone who had this exact question.
Step-by-step explanation:
The appropriate domain for this situation is [tex]\{t : 0 \leq t \leq 1.5\ \& \: t \in \mathbb R \}[/tex] (that means t can be any real number and between 0 and 1.5 (both endpoints included)
What is domain and range of a function?Domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
For this case, we have only those values of 't' as appropriate value, which are from t = 0 till the time when ball hits the ground, since after that the height will be constantly 0, but the height function will give negative values which doesn't model the situation correctly.
Thus, those values of t for which the equation [tex]h(t) = -16t^2 + 24t[/tex] correctly models the real world situation are said to be appropriate values of domain of this function.
The time when the ball will reach the ground will be when the height will be 0, thus,:
[tex]0 = -16t^2 + 24t\\2t^2 - 3t = 0\\(2t-3)(t) = 0\\t = 0, t = 3/2 = 1.5 \: \rm sec[/tex]
The height is 0 when ball starts going up(t=0), and when t = 1.5 the ball reaches ground.
Thus, the appropriate domain for modelling the situation is values of t in the interval [0, 1.5] (both endpoints are inclusive, as shown by big bracket).
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5th grade math. Correct answer will be marked brainliest.
Answer:
17,070
Step-by-step explanation:
Continue to move the decimal point to the right, and it adds a zero when the decimal places are all taken.
Answer:
10,070
Step-by-step explanation:
so 10 to the power of three is 1 with three 0s
so 1000
remember 10 cubed is 10 times 10 times 10 that equals 1000
then 1000 times 17.07 is 17070
this is a 2 step equation
Evaluate (Solve) the expression. 6+b when b=7
Answer:
13
Step-by-step explanation:
Substitute 7 for b
6 + 7 = 13
Answer:
It's 13.
Step-by-step explanation:
6+7=13
Which is the mode of this data?
12, 19, 22, 17, 15, 18, 15, 14, 16
Answer:
Sry but i hope u have great christmas and get all the gifts you wnated.
Step-by-step explanation:
c) tan^2A - cot^2A = sec^2A (1 - cot^2A)
plzz help me...tomorrow there is opt math test in my school...If I fail then i have to leave opt classes and go to eco....our teacher only taught trigonometry and I was absent 2 3 days due to sickness...plzz help me
Answer:
The steps are :
[tex] {tan}^{2} θ - {cot}^{2} θ = {sec}^{2} θ(1 - {cot}^{2} θ)[/tex]
[tex]RHS = {sec}^{2} θ(1 - {cot}^{2} θ)[/tex]
[tex]RHS = (1 + {tan}^{2} θ)(1 - \frac{1}{ {tan}^{2} θ} )[/tex]
[tex]RHS = (1 + {tan}^{2} θ)( \frac{ {tan}^{2}θ - 1}{ {tan}^{2} θ} )[/tex]
[tex]RHS = - \frac{(1 + {tan}^{2}θ)(1 - {tan}^{2} θ)}{ {tan}^{2} θ}[/tex]
[tex]RHS = - \frac{(1 - {tan}^{4} θ)}{ {tan}^{2} θ} [/tex]
[tex]RHS = \frac{ {tan}^{4} θ - 1}{ {tan}^{2}θ } [/tex]
[tex]RHS = {tan}^{2} θ - \frac{1}{ {tan}^{2}θ } [/tex]
[tex]RHS = {tan}^{2} θ - {cot}^{2} θ[/tex]
[tex]RHS = LHS (proven)[/tex]
Find the value of
(4/25) -1/2
[tex]\textsf{Hey there!}[/tex]
[tex]\mathsf{\dfrac{4}{25} - \dfrac{-1}{2}}[/tex]
[tex]\textsf{Cross\ multiply and you should see what the result comes}[/tex]
[tex]\mathsf{New\ equation: \dfrac{8}{50} + \dfrac{-25}{50}}[/tex]
SOLVE ABOVE/ BREAK IT DOWN TO MAKE IT EASIER TO SOLVE! [tex]\mathsf{\dfrac{8 + (-25)}{50}}[/tex][tex]\mathsf{8 - 25 = -17\leftarrow \text{\bf{{NUMERATOR}}}}[/tex]
[tex]\mathsf{50 + 0 = 50\leftarrow \text{\bf{DENOMINATOR}}}[/tex]
[tex]\boxed{\boxed{{\boxed{\textsf{Therefore, your answer is most likely: \boxed{\boxed{{\huge{\mathsf{\bf{\dfrac{-17}{50}}}}}}}}}}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]
Algebra 2
S varies inversely as G. If S is 8 when G is 3.5, find S when G is 7.
a) Write the variation.
b) Find S when G is 7.
Answer:
a) S varies inversely as G
[tex]S\propto\frac{1}{G}[/tex]
or [tex]S=\frac{K}{G}[/tex]
b) S=4 when G=7
Step-by-step explanation:
a) Write the variation.
S varies inversely as G
[tex]S\propto\frac{1}{G}[/tex]
So, We can write: [tex]S=\frac{K}{G}[/tex]
Where k is constant of proportionality
b) Find S when G is 7.
Now, if S=8, G = 3.5 we will find K
[tex]S=\frac{K}{G}\\K=SG\\K=8\times 3.5\\K=28[/tex]
So, value of K= 28
Now, find S when G is 7
[tex]S=\frac{K}{G}\\S=\frac{28}{7}\\S=4[/tex]
So, S=4 when G=7
Use the equation y=3x+1 to complete the table and solve for the missing y values. Identify the ordered pairs from the table. Select all that apply.
(-2, -7)
(-1, -2)
(0, 1)
(1, 3)
(2, 7)
Answer:
(-2, -5)
(-1, -2)
(0, 1)
(1, 4)
(2, 7)
Step-by-step explanation:
Substitute x with each number and solve equation.
complete the table of values y = 2x + 3
Answer:
x=0 y =3x=1 y= 5x=2 y= 7Step-by-step explanation:
for first,
1. let's take x = 0then solving this we get
y=32. take x=1 then y = 53. take x= 2 then y=7What's 6804 rounded to the nearest hundred
Answer:
6800
Step-by-step explanation:
Im not the brightest, because this is easy, I just overthink stuff :]
What does "how many times greater" mean in math? Like do you subtract, multiply, add, divide? Are there steps, I have to follow? Help lol
Answer:
multiplication
Step-by-step explanation:
cuz it says "times greater"
Answer:
It means how may times can the other variable fit into that variable, so you would divide.
- For example: Bob has 6 flowers in his basket, but Sally has only 2 flowers in her basket.
Q: How many times greater is Bob's basket of flowers than Sally's?
A: Bob's basket is 3 times greater than Sally's (bc 6/2 = 3, or 2 can fit into 6 three times)
**please mark brainliest!!