add similar elements: 2.5x-x+3.8x+0.7x= 6x
divide both sides by 6
x=0.09
Answer:
x=0.09
Step-by-step explanation:
2.5x−x+3.8x+0.7x=0.54
(2.5 -1 +3.8+0.7)x =0.54
6x=0.54
x=0.54/6
x=0.09
Write and simplify a rational expression for the ratio of the perimeter to the area of rectangle if the width is 4x and the length is x+6
Answer:
5x + 6 : 2x² + 12x
Step-by-step explanation:
Width = 4x
Length = x + 6
Perimeter
= 2(4x + x + 6)
= 2(5x + 6)
Area
= 4x(x + 6)
Ratio of perimeter to area:
= 2(5x + 6) : 4x(x + 6)
= (5x + 6) : 2x(x + 6)
= 5x + 6 : 2x² + 12x
Answer:
(5x + 6) : (2x² + 12x)
Step-by-step explanation:
Perimeter = 2(length + width)
= 2[4x + x + 6]
= 2(5x + 6)
Area = length × width
4x × (x + 6)
4x(x + 6)
Perimeter : Area
2(5x + 6) : 4x(x + 6)
(5x + 6) : (2x² + 12x)
If a 40 foot tree cast a 12 foot shadow find the length of the shadow cast by a 27 foot tree
Answer:
8.1 ft
Step-by-step explanation:
We can use proportions to solve. Put the height over the shadow
40 ft 27 ft
---------- = -----------
12 ft x ft
Using cross products
40x = 12*27
40x =324
Divide each side by 40
40x/40 = 327/40
x = 8.1
The shadow is 8.1 ft
URGENT PLEASE HELP!!!!!
A plant is 13 inches tall and grows 2 inches a week. How many weeks will it take for the plant to be 23 inches tall?
Answer:
5 weeks
Step-by-step explanation:
So if the plant is 13 inches tall in the beginning every week adds 2 inches.
0 weeks = 13 inch
1st week = 15 inch
2nd week = 17 inch
3rd week = 19 inch
4th week = 21 inch
5th week = 23 inch
So it would take 5 weeks to grow 23 inches
Answer:
5 weeks for the plant to be 23 inches long
Step-by-step explanation:
You could take the size the plant is supposed to be, which is 23 inches long then subtract how tall the plant is which is 13 inches long then divide by 2 because the plant grows 2 inches each week. Or you could use a chart to help you, until you get to 23 inches. please give me the brainliest answer?
1weeks= 13 inches + 2 inches = 15 inches
2weeks= 15 inches + 2 inches = 17 inches
3weeks= 17 inches + 2 inches = 19 inches
4weeks= 19 inches + 2 inches = 21 inches
5weeks= 21 inches + 2 inches = 23 inches
:) Hope this helped!!! Have a good day!!! <3
Find the value of n .
6/n = 24/28
y = ___.
Answer:
[tex]n=7[/tex]
Step-by-step explanation:
Cross multiply, isolate the variable, and divide by the coefficient to solve.
[tex]\frac{6}{n}=\frac{24}{28} \\ \\ 24n=168 \\ \\ n=7[/tex]
Plug back in to check.
[tex]\frac{6}{7}=0.857142857 \\ \\ \frac{24}{28} =0.857142857[/tex]
Answer:
7
Step-by-step explanation:
I did it and it was correct! Please make me brainliest!
Hope this helpd! :)
Triangle ABC was dilated using the rule Do.4. Triangle
A'B'C' is the result of the dilation
what is OB'?
1.5 units
3 units
4.5 units
6 units
Answer:
The correct option is B. The length of OB' is 3 units.
Step-by-step explanation:
The rule of dilation is D₀,₄. It means dilation by scale factor 4 with center of dilation is origin.
[tex]\text{Scale factor}=\frac{\text{Distance between center and any point of the image}}{\text{Distance between center and corresponding point of the Preimage}}[/tex]
[tex]\text{Scale factor}=\frac{OB'}{OB}[/tex]
[tex]4=\frac{OB'}{\frac{3}{4}}[/tex]
[tex]4\times \frac{3}{4}=OB'[/tex]
[tex]3=OB'[/tex]
The length of OB' is 3 units. Therefore the correct option is option is B.
Answer:
B on edge
Step-by-step explanation:
what is the cube root of 8x^27?
Answer:
2x^9
Step-by-step explanation:
∛8x^27
=∛(2x^9)^3
= 2x^9
Cube root of 8x^27 = 512.
How the cube root of 8x^27 is 512?In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers, have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots.
∛8x^27
=∛(2x^9)^3
= 2x^9
= 512.
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Vanessa practices the piano for 60 minutes each day. So far, she has practiced 42 minutes today. What percent of her practice time does she have left to complete?
Answer:
30%
Step-by-step explanation:
1) Find the amount of time left to complete
60 minutes total - 42 minutes already played = 18 minutes left
2) Divide the amount of minutes left by the total minutes
18 minutes left ÷ 60 minutes total = 0.3
3) Multiply that value by 100 to turn the decimal into a percent
0.3 * 100 = 30%
Answer:
30%
Step-by-step explanation:
The answer is thirty percent. One way to solve this problem is to start by finding what percent of Vanessa’s practice time forty-two minutes represents.
Let p represent the unknown percent, and set up a proportion that compares the like ratios of parts to wholes.
Divide out the like minutes and cross multiply.
Divide both sides by sixty to solve for the percent of time Vanessa has already practiced.
Subtract seventy percent from one hundred percent to determine the percent of time she has left to practice.
Vanessa still has thirty percent of her practice time to complete.
Examine today’s stock listing for Parchar Special Effects, shown below. 52 wk High 52 wk Low Symbol Div. Close Net Change 160.44 81.91 PCR 7.55 114.36 -4.89 Based on this information, what was yesterday’s price for Parchar Special Effects? a. $114.36 b. $109.47 c. $106.81 d. $119.25
Answer:
D
Step-by-step explanation:
I just took the test on E2020
Answer:
Option D. $119.25
Step-by-step explanation:
Today's stock listing for Parchar Special Effects shown below.
52 wk high = 160.44
52 wk low = 81.91
Symbol = PCR
Div. = 7.55
Close = 114.36
Net change = -4.89
Based on this information today's close is $114.36 and Net change is -4.89. It means the value of yesterday was 4.89 more than today's close.
Therefore, yesterday's price = 114.36 + 4.89 = $119.25
Yesterday's price was $119.25.
If you create a box-and-whisker plot for the data set, which expression correctly calculates the third quartile, Q3, of the data set?
{4.3, 5.1, 3.9, 4.5, 4.4, 4.9, 5.0, 4.6, 4.1, 4.6, 4.4, 4.3, 4.8, 4.4, 4.2, 4.5, 4.4}
A)
(4.6 + 4.9)
2
B)
(4.5 + 5.1)
2
C)
(4.6 + 4.8)
2
D)
(4.4 + 4.8)
2
Answer:
D or "(4.4 + 4.8)
_______
2
Step-by-step explanation: I got it right on USA Test Prep
solve log8 12=x-2. Round your answer to four decimal places.
Answer:
[tex]\large\boxed{x\approx3.1950}[/tex]
Step-by-step explanation:
[tex]\log_ab=c\iff a^c=b\\\\\log_812=x-2\iff8^{x-2}=12\\\\(2^3)^{x-2}=4\cdot3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{3(x-2)}=2^2\cdot3\qquad\text{use the distributive property}\\\\2^{3x-6}=2^2\cdot3\qquad\text{divide both sides by}\ 2^2\\\\\dfrac{2^{3x-6}}{2^2}=3\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\2^{3x-6-2}=3\\\\2^{3x-8}=3\qquad\text{logarithm of both sides}\\\\\log_22^{3x-8}=\log_23\qquad\text{use}\ \log_aa^n=n\\\\3x-8=\log_23\qquad\text{add 8 to both sides}[/tex]
[tex]3x=\log_23+8\qquad\text{divide both sides by 3}\\\\x=\dfrac{\log_23+8}{3}\\\\\log_23\approx1.5849625\\\\x\approx\dfrac{1.5849625+8}{3}\approx3.1950[/tex]
Answer:
B
Step-by-step explanation:
edge 2020
find the component form of -u - v given that u=(-3,5) and v =(6,-3)
ANSWER
B.
[tex] < \: - 3, -2 \: > [/tex]
EXPLANATION
The given vectors are:
[tex]u = < \: - 3,5 \: > [/tex]
and
[tex]v= < \: 6, - 3\: > [/tex]
[tex] - u - v = - 1< \: - 3,5 \: > -1 < \: 6, - 3\: > [/tex]
Use the scalar to multiply and obtain;
[tex] - u - v = < \: 3, - 5 \: > + < \: - 6, 3\: > [/tex]
Simplify to get:
[tex]- u - v = < \: 3 - 6, - 5 + 3 \: > [/tex]
[tex]- u - v = < \: - 3, -2 \: > [/tex]
To find the component form of -u - v, subtract the x-components and y-components separately. The x-component is 3, and the y-component is -2.
Explanation:The component form of -u - v can be found by subtracting the x-components and the y-components of u and v separately. Given that u=(-3,5) and v =(6,-3), the x-component of -u - v is -(-3) - 6 = -3 + 6 = 3, and the y-component is -(5) - (-3) = -5 + 3 = -2.
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What is the slope of the line between points A(-3,4) and B(2,-7)?
Answer:
I made the problem in a photo so you could do it for the next
look at the picture and plzz give me the correct answer
Answer: C
Step-by-step explanation:
The initial amount of trees planted is 1,500, so answers B and D are out. The number that is raised to years (t) is 1.02, and since 1.02 is greater than 1, the number of trees planter per year is growing, and the .02 means that it is growing at 2% because 0.02 * 100 = 2%
Answer:
Step-by-step explanation:
C is correct. The initial number (of trees) was 1500, and that 2% translates into 1.02 inside the parentheses.
please help me! this question is worth 30 points!
Answer:
1/k^4
Step-by-step explanation:
NEED HELP ASAP!! Find the indicated side of the trinagle
Answer:
b = 8sqrt(3)
Step-by-step explanation:
The triangle has a 30-deg angle and a right angle, so the third angle measures 60 degrees making this a 30-60-90 degree right triangle.
You don't mention which method to use to solve the problem.
You can use trigonometry ratios or the ratios of the lenghts of the sides of a 30-60-90 triangle
I'll use the second method.
In a 30-60-90 triangle, the lengths of the sides are in the ratio:
1 : sqrt(3) : 2
The long leg measures 12 and corresponds to sqrt(3) in the ratio, so we can find the length of the short leg by dividing 12 by sqrt(3).
12/sqrt(3) = [4 * sqrt(3) * sqrt(3)]/sqrt(3) = 4sqrt(3)
The hypotenuse is twice the length of the short leg.
b = 2 * 4sqrt(3) = 8sqrt(3)
The value of b is 8√3 because cos is the ratio of side adjacent to the angle to side opposite to the angle.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
We have a right angle triangle shown in the picture.
From the cos ratio:
cos30 = 12/b
b = 12/cos30
b = 12/(√3/2)
After factorization:
b = (24√3)/3
b = 8√3
Thus, the value of b is 8√3 because cos is the ratio of side adjacent to the angle to side opposite to the angle.
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Rise is the change between the y-coordinates of any two points along a line in the xy-plane. True or False
Rise is the change between the y-coordinates of any two points along a line in the xy-plane. True or False
The rise is the change between the y-coordinates of any two points along a line in the xy-plane is true.
What are rise and run?In a graph, the terms "rise" and "run" refer to the vertical and horizontal changes between two points on a line, respectively.
Here,
The rise of a line in the xy-plane is the vertical change between two points on the line, which is measured as the difference between their y-coordinates. The rise is sometimes also called the vertical distance or the vertical change.
Thus, the rise is the change between the y-coordinates of any two points along a line in the xy-plane is true.
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Explain why the triangles are similar, then find the value of x.
Answer:
ANSWER: D AA, x = 5 1/3
Calculation:
x/8 = 10/15
x = (10/15)(8)
x = 5 1/3
Step-by-step explanation:
Answer: AA postulate
Step-by-step explanation:
What is Brenda z-score
The z-score formula is:
x - mean / standard deviation
x = her height.
Z-score = (50 - 49) / 2
z-score = 1/2 = 0.5
The circle below is centered at the point (-3,4) and has a radius of length 3.
What is its equation?
A. (x+ 3)^2 + (x-4)^2 = 9
B. (x-3)^2 + (x+4)^2=9.
c. (x+4)^2 + (x-3)2 =3^2
D. (x-4)^2 + (x+3)^2 =3^2
Answer:
(x + 3)^2 + (y - 4)^2 = 3^2 = 9 This matches Answer A.
Step-by-step explanation:
Start with the standard equation of a circle with center at (h, k) and radius r:
(x - h)^2 + (y - k)^2 = r^2
Here the given point (h, k) is (-3, 4) and the radius is 3.
Substituting these values into the above equation, we get:
(x + 3)^2 + (y - 4)^2 = 3^2 = 9 This matches Answer A.
Answer: (x-3)2 + (y+4)2 =9
Step-by-step explanation:
Based on the tree diagram below, what is the probability that a student doesn't have lice, given that the student tested negative? Round your answer to the nearest tenth of a percent.
A. 97.6%
B. 99.4%
C. 96.4%
D. 98.6%
Answer:
Option D (APEX)
Step-by-step explanation:
L= Student has lice
NL= Student has no lice
PT=Test Shows positive
NT=Test Shows negative
P([tex]\frac{NT}{NL}[/tex]) =0.7708 (Probability that a student has no lice and the test shows negative)
P([tex]\frac{NT}{L}[/tex]) = 0.0108 ( Probability that a student has lice and the test shows negative)
[tex]P\frac{NT}{NL}[/tex] = [tex]\frac{P\frac{NT}{NL} }{P\frac{NT}{NL} +P\frac{NT}{L} }[/tex][tex]\frac{0.7708}{0.7708+00108}[/tex][tex]\frac{0.7708}{0.7816}[/tex]0.98618219 (Simplify)Terms Of Percentages
0.98618219 × 100
=98.6
Therefore your answer is 98.6% (Option D)
APEX
The probability that the student doesn't have lice, given that the student tested negative is P ( A ) = 98.6 %
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability that the student doesn't have lice, given that the student tested negative be P ( A )
Now , the equation will be
The probability that a student has no lice and the test shows negative is given by P ( NL ) = 0.7708
The probability that a student has lice and the test shows negative is given by P ( L ) = 0.0108
And , The probability that the student doesn't have lice, given that the student tested negative P ( A ) = P ( NL ) / [ P ( NL ) + P ( L ) ]
On simplifying , we get
P ( A ) = P ( NL ) / [ P ( NL ) + P ( L ) ]
P ( A ) = ( 0.7708 ) / [ 0.7708 + 0.0108 ]
P ( A ) = 0.98618
P ( A ) = 98.6 %
Hence , the probability is 98.6 %
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what is 9!
the exclamation point is supposed to be there
Answer:
362880
Step-by-step explanation:
9! is read as 9 factorial.
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
9! = 362880
Answer:
362,880
9! is also know as 9x all the numbers lower then it, so it would be 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.
If you multiply all of those digits together, your result would be 362,880.
area of circle
area
inscribed polygon
polygon
perimeter
equilateral
length
octagon
trapezoid
apothem
legs
hexagon
circle
composite figure
regular polygon
Answer:
1. area
2. circle
3. equilateral
4. length
5. perimeter
6. polygon
7. regular polygon
8. trapezoid
9. legs
10. area of a circle
11. hexagon
12. octagon
13. inscribed polygon
14. apothem
15. composite figure
Step-by-step explanation:
Express 18^1/2 in simplest radical form
The simplified form of 18^1/2 is 3√2
Radical expressions and indicesGiven the exponential expression
18^1/2
According to power law of Indices:
a½ = \sqrt{a}
Applying this law to the given expression;
This can also be written as:
[tex]18^{1/2} =\sqrt{18}[/tex]
Simplify the radical to have:
[tex]\sqrt{18} = \sqrt{9 \times 2} \\\sqrt{18} = 3\sqrt{2}[/tex]
Hence the simplified form of 18^1/2 is 3√2
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What type of triangle has exactly two acute angles?
right
obtuse
equilateral
acute
Answer:
right and obtuse
Step-by-step explanation:
a right triangle has one right angle and two acute angles, and an obtuse triangle has one obtuse angle and two acute ones
i hope that this helps :)
Solve for y: 6x-3y=24
Answer:
[tex]y=2x-8[/tex]
Step-by-step explanation:
Isolate the variable and divide by the coefficient to solve for a variable.
[tex]6x-3y=24 \\ \\ -3y=-6x+24 \\ \\ y=2x-8[/tex]
Answer:
y = 2x - 8
Step-by-step explanation:
=> 6x - 3y = 24
=> -3y = 24 - 6x
=> 3y = 6x - 24
=> y = 2x - 8
4y+3y+8-5 simplify Plz help meh!
7y+3
combine like terms.
Hey there!
4y + 3y + 8 - 5
COMBINE the LIKE TERMS
= (4y + 3y) + (8 - 5)
= 4y + 3y + 8 - 5
= 7y + 3
Therefore, your answer is: 7y + 3
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Use angle ABD shown below to answer the question that follows:
Which of the following is a step towards proving the similarity of triangles ABC and DBA?
Answer:
They have the same measure.
Step-by-step explanation:
M<ABD and M<DBA have the same measure.
Answer:
segment BC is a hypotenuse
Step-by-step explanation:
the longest side of a right triangle, opposite the right angle.
Please help i don't have alot time
Answer:
[tex]g\left(x\right)=-\sqrt{x+3}+8[/tex]
Step-by-step explanation:
Given function is [tex]f\left(x\right)=-2\sqrt{x-3}+8[/tex].
Now let's find it's range.
we know that square root function always gives positive output then:
[tex]\sqrt{x-3}\ge0[/tex]
[tex]-2\sqrt{x-3}\le-2\left(0\right)[/tex]
[tex]-2\sqrt{x-3}\le0[/tex]
[tex]-2\sqrt{x-3}+8\le0+8[/tex]
[tex]-2\sqrt{x-3}+8\le 8[/tex]
[tex]f(x) \le 8[/tex]
Hence range of the function is [tex](-\infty,8][/tex].
we can repeat same process to find the range of all the given choices.
we will find that only 3rd choice has same range.
Hence final answer is [tex]g\left(x\right)=-\sqrt{x+3}+8[/tex]
Over 2 years, how much more does $2000 in a savings account with an APR
of 4.6% compounded semiannually earn in interest than the same amount in
a savings account with an APR of 4.4% compounded quarterly?
Answer:
Final answer is $7.52.
Step-by-step explanation:
Given that initial amount P = $2000
Interest rate r = 4.6% = 0.046
Number of compounding periods per year = n = 2 {semiannually}
Time = 2 years
Then future value is given by :
[tex]A=P\left(1+\frac{r}{n}\right)^{n\left(t\right)}[/tex]
[tex]A=2000\left(1+\frac{0.046}{2}\right)^{2\left(2\right)}=2190.45[/tex]
Similarly calculate future value for 2nd case:
Given that initial amount P = $2000
Interest rate r = 4.4% = 0.044
Number of compounding periods per year = n = 4 {quarterly}
Time = 2 years
Then future value is given by :
[tex]A=P\left(1+\frac{r}{n}\right)^{n\left(t\right)}[/tex]
[tex]A=2000\left(1+\frac{0.044}{4}\right)^{4\left(2\right)}=2182.93[/tex]
then difference = 2190.45 - 2182.93 = 7.52
Hence final answer is $7.52.
Answer:
$7.52
Step-by-step explanation:
look at the picture and plzzz help
the answer to the problem would be c
ANSWER
The correct choice is C.
EXPLANATION
We know that:
[tex] \sqrt[3]{7} = {7}^{ \frac{1}{3} } [/tex]
We want to simplify:
[tex]( { {7}^{ \frac{1}{3} } )}^{3} [/tex]
The exponent here is 3. This means that the base must multiply itself 3 times.
[tex] ( { {7}^{ \frac{1}{3} } )}^{3} = {7}^{ \frac{1}{3} } \times {7}^{ \frac{1}{3} } \times {7}^{ \frac{1}{3} } [/tex]
Recall that:
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
This implies that,
[tex] ( { {7}^{ \frac{1}{3} } )}^{3} = {7}^{ \frac{1}{3} + \frac{1}{3} + \frac{1}{3} } [/tex]
Simplify:
[tex] ( { {7}^{ \frac{1}{3} } )}^{3} = {7}^{ \frac{3}{3}} [/tex]
[tex]( { {7}^{ \frac{1}{3} } )}^{3} = {7}^{ 1} = 7[/tex]
The correct choice is C