[tex]\frac{1}{3}x-1=\frac{3}{5}\\ \\5x-15=9\\\\5x=9+15\\\\5x=24\\\\x=\frac{24}{5}\\ \\x=4\frac{4}{5}[/tex]
A rectangular turtle aquarium is 6 ft long by 4 ft wide. The aquarium is enlarged by increasing
the length and width by an equal amount in order to double its area. What are the dimensions of
the new aquarium?
Answer:
8ft x 6ft
Step-by-step explanation:
For this problem, we want to create measurements of length and width that double our current area. First we need to find the current area.
C_Length = 6 ft
C_Width = 4 ft
C_Area = C_Length * C_Width
C_Area = 6 ft * 4 ft = 24 ft^2
Now we want our new area to be double the old area.
N_Area = 2C_Area
N_Area = 2 * 24 ft^2
N_Area = 48 ft^2
Now we simply need to find the increase in width and length, distributed equally, that will create the new area.
N_Area = (C_Length + x) * (C_Width + x)
Where x is the amount that each variable is increased by to create the new area.
Now we simply solve for x.
N_Area = (C_Length + x) * (C_Width + x)
48 = (6 + x) * (4 + x)
48 = 24 + 10x + x^2
0 = -24 + 10x + x^2
Now we can either apply the quadratic formula or attempt to factor using the constant break down method.
(x + 12) (x - 2) = 0
x = -12; x = 2
Note that we will choose x = 2 since the other option would require us to have negative material, which is impossible.
Now we can check to validate our answer by plugging in the value of x.
48 ?= (6 + 2) * (4 + 2)
48 ?= (8) * (6)
48 == 48
Thus, we have found the dimensions of the new aquarium, 8ft x 6ft.
Cheers.
The arcs in the diagram are labeled with their measures in degrees. What is the measure of arc uv?
Answer:
10 steps
Step-by-step explanation:
The cost C of mailing a letter first class in the United States is $0,45 for the first ounce.
Each added ounce, or fraction of an ounce, o, costs an additional $0.20.
1. Write an equation to represent the total cost, C, to mail a first class letter that
weighs n ounces.
C=
Answer: C= 0.25 + 0.20n
Step-by-step explanation:
Let n be the number of ounces of the letters.
As per given,
Cost per ounce = $0.45
Additional cost per ounce = $0.20
So, the equation to represent the total cost, C, to mail a first class letter that weighs n ounces will be
C= 0.45 + (n-1)(0.20)
⇒ C= 0.45 + 0.20n-0.20
⇒ C= 0.25 + 0.20n
Hence, the required equation is C= 0.25 + 0.20n .
i need help................
Answer:
Hey there!
Three basic rules determine this:
Positive Numbers are always greater than Negative Numbers.
If both are positive, the number with the greater magnitude is larger.
If both are negative, the number with the smaller absolute value is larger.
Let me know if this helps :)
Answer:
23x15=23x(10+5) Method 1 and 5
=23x10+23x5
=230+115
23x15=(20+3)x15 Method 2
=20x15+3x15
=300+45
23x15=(20+3)x(10+5)
=20x10+20x5+3x10+3x5 Method 3 and 6
=200+100+30+15
Step-by-step explanation:
Which lines are parallel? Justify your answer.
Lines a and b are parallel because their corresponding angles are congruent.
Lines a and b are parallel because their same side exterior angles are congruent.
Lines e and f are parallel because their corresponding angles are congruent.
Lines e and f are parallel because their same side exterior angles are supplementary.
Answer:
Lines a and b are parallel because their corresponding angles are congruent
Step-by-step explanation:
The corresponding angle postulate states that Two lines are said to be parallel if when cut by a transversal, their corresponding angles are congruent.
Therefore given line a and line b which is cut by transversal e, both corresponding angles are equal to 110 (congruent), therefore according to the corresponding angle postulate, we can say that line a and line b are parallel to each other.
Answer: A
Step-by-step explanation:
(20 points)Solve the equation cos x = sin (x + 22)
Answer:
[tex]\bold{x = 34^\circ}[/tex]
Step-by-step explanation:
Given:
[tex]cos x = sin (x + 22^\circ)[/tex]
To solve:
The given equation.
Solution:
First of all, let us consider an important property of sine and cosine.
[tex]sin(90^\circ-\theta )=cos\theta[/tex]
OR
[tex]cos(90^\circ-\theta )=sin\theta[/tex]
We can apply above property to solve for [tex]x[/tex] as per given equation.
[tex]cos x = sin (x + 22^\circ)[/tex]
Changing [tex]cosx[/tex] to sine form:
[tex]cosx=sin(90^\circ-x)[/tex]
[tex]cosx=sin(90^\circ-x) = sin(x+22^\circ)[/tex]
[tex]\therefore 90^\circ-x=x+22^\circ\\\Rightarrow 90^\circ-22^\circ=x+x\\\Rightarrow 2x=68^\circ\\\Rightarrow \bold{x = 34^\circ}[/tex]
So, solution to the equation [tex]cos x = sin (x + 22^\circ)[/tex] is:
[tex]\bold{x = 34^\circ}[/tex]
1/3x+5=12 i do not understand this math equation
Answer: x = 21
Step-by-step explanation: First, isolate the x term by
subtracting 5 from both sides of the equation.
We get 1/3x = 7.
Next, multiply both sides of the equation by
the reciprocal of 1/3 which is 3/1 to get x by itself.
On the left, 3/1(1/3) cancels and on the
right when we multiply 7(3/1), we get 21.
So we have x = 21.
!HELP! What is the equation for the following absolute-value functions?
Answer:
f(x) = |x -1|
Step-by-step explanation:
The parent absolute value function f(x) = |x| is shifted one unit to the right. We know that replacing x with (x-h) will shift a function h units to the right. Here, we want h=1. The shifted function is ...
f(x) = |x -1|
Rewrite as a simplified fraction.
\large{0.\overline{8} = {?}}0.
8
=?0, point, start overline, 8, end overline, equals, question mark
Answer:
[tex]\bold{x = \dfrac{8}{9}}[/tex]
Step-by-step explanation:
We have to rewrite the below as simplified fraction.
[tex]\large{0.\overline{8} = {?}}[/tex]
Solution:
Let [tex]x =0.\overline 8[/tex] which means [tex]x =0.888888.......[/tex]
Here a bar over 8 means that there the given decimal value is non terminating and there are a large numbers of 8 present after the decimal.
To solve the given non terminating decimal as fractions, we will have to eliminate the bar term from the given value.
So, we can rewrite [tex]x[/tex] as:
[tex]x =0.8\overline8[/tex] ......(1)
Now, let us multiply the above with 10.
[tex]10x = 0.8\overline 8 \times 10\\\Rightarrow 10 x= 8.\overline8[/tex] ....... (2)
Now, let us subtract (1) from (2):
[tex]10x-x=8.\overline8 - 0.\overline8\\\Rightarrow 9x = 8\\\Rightarrow \bold{x = \dfrac{8}{9}}[/tex]
So, in simplified fractions:
[tex]\large{0.\overline{8} = \bold{\dfrac{8}{9}}}[/tex]
Answer:
There is no statements/info.
Step-by-step explanation:
find the difference 3 d and 7 d
Answer:
[tex]-4d[/tex]
Step-by-step explanation:
We can subtract a term from another if they have the same variable. Both [tex]3d[/tex] and [tex]7d[/tex] have the variable [tex]d[/tex], so we can subtract them.
When subtracting these terms, we subtract the coefficients and keep the variable.
So:
[tex]3d - 7d = 3-7(d) = -4d[/tex]
Hope this helped!
Answer:
-4d
Step-by-step explanation:
3d - 7d
=> 3 x D - 7 x D
=> (3 - 7)(D)
=> -4 x D
=> -4d
Determine which of the following correctly states the ratio of pens and pencils. Select yes or no for each.
(For each one, you can just number it and put yes or no besides it)
Answer:
6 : 8, 3/4, 3 to 4
Step-by-step explanation:
As counted on the picture, there are:
6 pens and 8 pencilsThe ratio pens to pencils is:
6 : 8 = 3 : 4 = 3 to 4So there are 3 correct choices
A business school event invites all of its graduate and undergraduate students to attend. Of the students who attend, male graduate students outnumber male undergraduates by a ratio of 7 to 2, and females constitute 70% of the group. If undergraduate students make up 1/6 of the group, which of the following CANNOT represent the number of female graduate students at the event?
a. 18
b. 27
c. 36
d. 72
e. 180
Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half?
Answer:
If the total scored was 123 and your team scored 67 in the first half then in the second half they will score 56 points.
Step-by-step explanation:
What is the turning point or vertex of the parabola???
Need Help ASAP algebra 2
Answer:
a = √10
Step-by-step explanation:
a² + b² = c²
a² + 9² = (√91)²
a² + 81 = 91
a² = 10
a = √10
hope this helps :)
Answer:
square root of 10
Step-by-step explanation:
a^2 + b^2 = c^2
=> a^2 + 9^2 = square root of 91^2
=> a^2 + 81 = 91
=> a^2 = 91 - 81
=> a^2 = 10
=> a = square root of 10
How many solutions does the equation 3x − 7 = 4 + 6 + 4x have? Two Zero Infinitely many One
Answer:
one solution
Step-by-step explanation:
3x − 7 = 4 + 6 + 4x
Combine like terms
3x-7=4x+10
Subtract 3x from each side
-7=x+10
Subtract 10 from each side
-17 =x
There is one solution
How do i match the statements
Step-by-step explanation:
Michelle orders soup, or she orders salad goes with disjunction.
The fireworks were loud and colorful goes with conjunction.
If the watch is broken, then it it showing the wrong time goes with conditional.
Simplify -7x - (15y) + 3x - 2y
Answer:
Step-by-step explanation:
combine like terms
-7x + 3x - 15y - 2y
-4x - 17y
(Score for Question 1:
of 5 points)
1. Suzette ran and biked for a total of 80 miles in 9 hours. Her average running speed was 5 miles per hour
(mph) and her average biking speed was 12 mph,
Let x = total hours Suzette ran.
Let y = total hours Suzette biked.
Use substitution to solve for x and y. Show your work. Check your solution.
(a) How many hours did Suzette run? I
(b) How many hours did she bike?
Answer:
Answer:
A) 4 Hours (of running)
B) 5 Hours (of biking)
Step-by-step explanation:
So Suzette ran and biked for a total of 80 miles,
and she did all of that in 9 hours.
Let x equal the total hours of Suzette ran and let y equal the total hours of Suzette biked.
Therefore:
[tex]x+y=9[/tex]
This represents the total hours. We know that the hours she had ran and biked totals 9. Thus, x plus y must equal 9.
And also:
[tex]5x+12y=80[/tex]
The 5x represents the miles she had ran in x hours, while the 12x represents the miles she had biked in y hours. All together, they must equal 80 miles total.
Therefore, our system is:
[tex]x+y=9\\5x+12y=9[/tex]
We can solve this using substitution. First, subtract x from the top equation:
[tex]x+y=9\\y=9-x[/tex]
Now, substitute the y into the second equation:
[tex]5x+12y=80\\5x+12(9-x)=80[/tex]
Distribute:
[tex]5x+108-12x=80[/tex]
Combine like terms:
[tex]-7x+108=80[/tex]
Subtract 108 from both sides:
[tex](-7x+108)-108=(80)-108\\-7x=-28[/tex]
Divide both sides by -4:
[tex]x=4[/tex]
Therefore, Suzette ran for a total of 4 hours.
Since she biked and ran for a total of 9 hours, she must have biked for 9-4 or 5 hours.
Checking:
4 hours of running plus 5 hours of biking does indeed equal 9 hours total:
[tex]4(5)+5(12)=20+60=80[/tex]
So by running 5mph for 4 hours and by biking 12mph for 5 hours, she did indeed reach a total of 80 miles.
Liz is using the distributive property to evaluate the expression 27 (36) by using friendlier numbers. Her work is shown below. Liz’s Work 27(36) Step 1 27 (3 + 12) Step 2 27 (3) + 27 (12) Step 3 81 + 324 Step 4 405 What was the first error that Liz made? PLZ HELP ME I DONT UNDERSTAND HELP ME PLZ!!!!!
Answer:
In step 1
Step-by-step explanation:
She has [tex]27(36)=27(3+12)[/tex]
this mean that 36=3+12
that's her mistake
Answer:
step 1
Step-by-step explanation:
Which equation below represents the equivalent exponential equation for the equation of log6 256=x?(in picture)
Answer:
Here is my answer I hope this helps <(^w^)>
The correct expression is [tex]6^{x} = 256[/tex]
What is exponential equation?An exponential equation is an equation with exponents where the exponent a part of the exponent is a variable.
Given an exponential equation, [tex]log_{6} 256 = x[/tex]
Using formula :-
[tex]y = log_{a} x \\x = a^{y}[/tex]
[tex]log_{6} 256 = x[/tex]
[tex]6^{x} = 256[/tex]
Hence, the correct answer is [tex]6^{x} = 256[/tex]
For more references on exponential equation, click;
https://brainly.com/question/29506679
#SPJ2
ILL MARK YOU BRAINLIEST!!!!!! ∠A = 5x - 15.∠B = 2x + 21.Solve for x and then find the measure of ∠B.
Answer:
x=6 b=45
Step-by-step explanation:
45=5x-15. 45-15=30. 5x=30. x=6. b=45
during a basketball game, your team scored three times as many 2-point field goals than it did 3-point field goals, and scored a total of 90 points. How many field goals did your team score?
Answer:
40 field goals
Step-by-step explanation:
Represent 2-point with x and 3-point with y;
Given
[tex]x = 3y[/tex]
[tex]2x + 3y =90[/tex]
Required
Determine x and y
[tex]x = 3y[/tex]
[tex]2x + 3y =90[/tex]
Substitute 3y for x in [tex]2x + 3y =90[/tex]
[tex]2(3y) + 3y = 90[/tex]
[tex]6y + 3y = 90[/tex]
[tex]9y = 90[/tex]
Divide both sides by 9
[tex]y = 10[/tex]
Substitute 10 for y in [tex]x = 3y[/tex]
[tex]x = 3 * 10[/tex]
[tex]x =30[/tex]
The number of field goals = x + y
[tex]x + y = 30 + 10[/tex]
[tex]x + y = 40[/tex]
Hence, the number of field goals is 40
help me please!!!i rlly need it!
Answer:
7.5
Step-by-step explanation:
How long does it take a car to travel 1 mile if its average speed is 40 mph? The answer is 1/40 of an hour or 1.5 minutes. multiply this by 5
Answer:
0.1 hours to the nearest tenth (0.125 hours exact)
Step-by-step explanation:
For this problem, we simply need to do a conversion to find the length of time.
We are given the rate 40 miles per hour, and the distance of 5 miles. We simply need to know the amount of time.
5 miles * (1 hour per 40 miles) = 1 hour / 8
Note, the distance unit cancels out.
So, to travel 5 miles it will take 1/8 of an hour.
1/8 as a decimal is equal to 0.125. The answer rounded to the nearest tenth would be 0.1 hours, since the 2 rounds down.
Cheers.
rate of change x=3 x=5
Answer:
The average rate of change for g(x) is { g(x+h)-g(x) }/h
In our case,
{ log(5+1) - log(3+1) }/(5-3) = (.778-.602)/2 = .088
Compare it to the derivative of log(x+1) for the values: the derivative is D = (1/ln10)(1/(x+1))
at x = 3 D = .1086
at x = 4 D = .0869
at x = 5 D = .0724
Take the average of D over the interval and you get .0893 and very close to the midpoint of the x values
Step-by-step explanation:
Carlos spent 1 1/4 hours doing his math homework. He spent 1 1/4 as much time practicing piano. How many hours did Carlos spend practicing piano?
Answer:
7.6525 hours
Step-by-step explanation:
11 / 4 = 2.75 so he spent 2.75 h doing his HW.
and he spent (11/4) x 2.75 practicing piano
(11/4) x 2.75 = 7.6525
The number of hours Carlos spends practicing piano will be 7.6525 hours.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
It is given that 11 / 4 = 2.75 he spent 2.75 h doing his HW. and he spent (11/4) x 2.75 practicing piano.
The number of hours Carlos spends practicing piano will be calculated as below:-
(11/4) x 2.75 = 7.6525 hours
Therefore, the number of hours Carlos spends practicing piano will be 7.6525 hours.
To know more about expression follow
https://brainly.com/question/723406
#SPJ2
Write the number in standard notation. 9x 10^-4
Answer:
0.0009
Step-by-step explanation:
9*10⁻⁴ = 0.0009
Which religions were established during the Common Era (CE)? Check all that apply.
Answer:
Christianity and Islamic religion
Step-by-step explanation:
Based on the picture you provided It would be Christianity and Islamic religion.
Based on the Events of the Common Era (year 0) was the birth of Jesus of Nazareth. From Year 0 to year 29 Jesus of Nazareth expanded his faith. During the 29th year Jesus of Nazareth was crusified in Jeruselem.
Estimated around Year 570 Muhammad (the Prophet of Islam) was born and rose his religion to great heights. In 632 Muhammad died.
Hope this helps
Answer:
Christianity and Islam
Step-by-step explanation:
PLEASE HELO ASAP WILL MARK BRAINLIEST
The mass of the part of a metal rod that lies between its left end and a point x meters to the right is 3x^2 kg. Find the linear density when is 1 m, Where is the density the highest? The lowest?
Answer:
6 kg/m
Step-by-step explanation:
mass m = 3x^2.
rho ρ= dm/dx =6x
ρ(1) =6 Kg/m
linear density is the derivative of mass (m) with respect to position(x)
that is how fast is the mass changing at that position.