Answer:
[tex] x^2 + x = 42[/tex]
Step-by-step explanation:
Let the required number be x
Therefore, it's square = [tex] x^2 [/tex]
[tex] \therefore \: x + {x}^{2} = 42 \\ \huge \red{ \boxed{{x}^{2} + x = 42}}[/tex]
Answer:
the answer is a
Step-by-step explanation:
Solve the equation
(If possible please show work)
Answer:
3 is right answer
Step-by-step explanation:
see in attached picture
hope it helped you:)
If M is the midpoint of segment AB and AM=9x-5 and MB=15-x, what is the length of AB?
Answer:
AB = 8x+10Step-by-step explanation:
If M is the midpoint of the segment AB, then AM+MB = AB. Given the following parameters;
AM=9x-5 and MB=15-x
Required parameter
segemnt AB
Substituting the given parameters into the given formula to get AB we will have;
AB = AM+MB
AB = 9x-5+15-x
collect like terms
AB = 9x-x-5+15
AB = 8x+10
Hence the length of segment AB is 8x+10
write 0.18 repeating as a fraction in simplest form.
Answer:
180/1000 or 18/100 0.18
Step-by-step explanation:
The repeating decimal 0.18 to a fraction is 2/11
Converting the repeating decimal to a fraction.From the question, we have the following parameters that can be used in our computation:
Number = 0.18
Express as fraction
So, we have
Number = 18/100
Subtract 1 from the denominator
Number = 18/99
Simplify
Number = 2/11
Hence, the fraction is 2/11
Read more about fraction at
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A large negative number is added to a small positive number. Which of the following statements is correct about the sum?
Answer:
its negative :)
Step-by-step explanation:
..........
Answer:
The sum will be negative
Step-by-step explanation: Negative+Negative=Positive//Positive+Positive=Positive//Positive+Negative=Negative//Negative+Positive=Negative
Barun said says, "The number sqrt49 is an irrational number." Do you agree or disagree? Explain using the definition of rational and irrational numbers.
Here's why:
sqrt(49) = sqrt(7^2) = 7
We can write 7 as a ratio or fraction of two integers 7 = 7/1
This shows that 7 is rational, so that makes sqrt(49) rational as well.
An irrational number is one where we cannot write it as a fraction of two integers. An example of an irrational number would be pi. Another irrational number is sqrt(2).
Note: the denominator can never be zero.
A teacher is making a history test composed of the same number of multiple choice questions as short answer questions she estimates it will take students an average of two minutes to complete each multiple-choice questions and an average of 3.5 minutes to complete each short answer questions, n,quality to determine how many questions and the teacher can include if the test must take students less than 45 minutes to complete
Answer:
8 questions each for short answer questions and 8 questions of Multiple Choice Questions type.
A total of 16 questions.
Step-by-step explanation:
Given:
The number of multiple choice questions and number of short answer type questions are same.
Let it be equal to [tex]x[/tex].
Average Time taken to attempt multiple choice question = 2 minutes
Total time taken to attempt multiple choice question = 2[tex]\times x[/tex] minutes
Average Time taken to attempt short answer type question = 3.5 minutes
Total Time taken to attempt short answer type question = 3.5[tex]\times x[/tex]
Total time for test should be less than 45 minutes.
Therefore, the equation becomes:
[tex]2x+3.5x<45\\\Rightarrow 5.5x <45\\\Rightarrow x<8.18[/tex]
Hence, the value of [tex]\bold{x=8}[/tex]
Therefore, the answer is:
8 questions each for short answer questions and 8 questions of Multiple Choice Questions type.
A total of 16 questions.
Answer:
Step-by-step explanation:
2n+3.5n <45
Factoring for GCF. Help please and thanks!
Answer:
Since there are no common factors, the only common factor is 1
(●'◡'●)
NEED MATH HELP NOW. I WILL BRAINLIEST
Answer:
see below (I hope this helps!)
Step-by-step explanation:
To find the distance between two points, we can use the formula d = √(x₂ - x₁)² + (y₂ - y₁)² where d = distance and (x₁, y₁), (x₂, y₂) are the points. Therefore:
d = √(-6 - 2)² + (2 - (-6))²
= √(-4)² + (8)²
= √16 + 64
= √80 ≈ 8.944272
Solve for . Simplify your answer as much as possible. please help
Answer:
[tex]x=-6[/tex]
Step-by-step explanation:
So we have the equation:
[tex]-34=7(x+8)+8x[/tex]
First, distribute the 7 into the (x+8) and simplify:
[tex]-34=7(x)+7(8)+8x\\-34=7x+56+8x[/tex]
Combine the like terms 7x and 8x by adding them together:
[tex]-34=56+15x[/tex]
Subtract 56 from both sides to isolate the x:
[tex]-34-56=15x+56-56\\15x=-90[/tex]
Divide both sides by 15 to get x:
[tex]x=-90/15=-6[/tex]
Please solve Question 11 correctly..
Answer:
i) width = 3.75
length = 4.5
ii) 6.75m^2
iii) 78.75m^2
Step-by-step explanation:
11)
i) Bedroom 1
actual width = 2.5 × 1.5
= 3.75 m
actual length = 3 × 1.5
= 4.5m
ii) Kitchen
actual width = 1.5 × 1.5
= 2.25 m
actual length = 2 × 1.5
= 3 m
actual area = 2.25× 3
= 6 .75 m^2
iii) Apartment
actual width = 5 × 1.5
= 7.5 m
actual length = 7 × 1.5
= 10. 5 m
actual area = 7.5 * 10.5
= 78.75 m ^2
Harvey the wonder hamster can run 3\dfrac16 \text{ km}3 6 1 km3, start fraction, 1, divided by, 6, end fraction, start text, space, k, m, end text in \dfrac14 4 1 start fraction, 1, divided by, 4, end fraction hour. Harvey runs at a constant rate.
Answer:
[tex]2\frac{8}{15}[/tex]
Step-by-step explanation:
The calculation of average speed in kilometres per hour is shown below:-
As we know that
[tex]Speed = \frac{Distance}{Time}[/tex]
So, the average speed is
[tex]= 3\frac{1}{6} \div 1\frac{1}{4}[/tex]
Now we will convert into a mixed number i.e
[tex]3\frac{1}{6} = \frac{19}{6} \\\\ 1\frac{1}{4} = \frac{5}{4}\\\\ = \frac{19}{6} \div\frac{5}{4}\\\\ = \frac{19}{6} \times \frac{4}{5}[/tex]
Now the cross cancel common factor is 2
So,
[tex]= \frac{19}{2}\times \frac{2}{5} \\\\ = \frac{38}{15} \\\\ = 2\frac{8}{15}[/tex]
hence, the average speed is [tex]2\frac{8}{15}[/tex] in kilometers per hour
Therefore we simply applied the above formulas to determine the average speed that comes in kilometers per hour
George had $6,000 in a savings account earning simple interest at a rate of 5% per year. At the end of the year, George paid 25% in taxes on his interest. How much money did George earn in interest that year after paying taxes?
Answer:
$225
Step-by-step explanation:
Given that:
Principal = $6,000
Interest rate = 5%
Time = 1 year
Taxes paid = 25% on the interest earned
To find:
Money earned after paying taxes ?
Solution:
First of all, let us calculate the total interest earned:
Formula for Simple Interest is given as:
[tex]SI =\dfrac{PRT}{100}[/tex]
Where P is the principal
R is the rate of interest
T is the time taken
Putting the given values:
[tex]SI =\dfrac{6000 \times 5\times 1}{100} =\$300[/tex]
Now, it is given that 25% of the interest earned is given as taxes.
Taxes paid = 25% of $300
[tex]\Rightarrow \dfrac{25}{100} \times 300 =\$75[/tex]
Therefore, the money earned = Interest earned - Taxes paid
The money earned = $300 - $75 = $225
Write the equation of the line that passes through (1, 3) and has a slope of 2 in point-slope form
Answer:
y-3= 2(x-1)
Step-by-step explanation:
1. The equation of a line in point slope form is y-y1= m(x-x1)
2. m=slope and (x1,y1) is the point the line passes through
3. The point the line passes through is (1,3)
4, The slope is 2
5. Therefore the answer is y-3=2(x-1)
Answer:
y-3=2(x-1)
Step-by-step explanation:
Point slope form is y-y1=m(x-x1)
Now we just need to plug in what you have into this equation.
y-3=2(x-1) and this is the point slope form for this line.
8-2b = -2 find the solution to the equation
Answer: 5
Step-by-step explanation:
8-2b=-2
8-2b-8=-2-8
-2b=-10
-2b/-2=-10/-2
b=5
Find the area of triangle ABC. A. 14.45 units² B. 18.51 units² C. 13.76 units² D. 14.39 units²
Answer:
C. [tex] 13.76 units^2 [/tex]
Step-by-step explanation:
Given:
∆ABC,
m<A = 66.28°
m<B = 31.09°
AB = 7.6
BC = 7.01
Required:
Area of ∆ABC
SOLUTION:
Area = ½*AB*BC*sin(B)
[tex] Area = \frac{1}{2}*7.6*7.01*sin(31.09) [/tex]
[tex] Area = \frac{1}{2}*7.6*7.01*sin(31.09) [/tex]
[tex] Area = 13.76 units^2 [/tex]
please help me on this
Answer:
(-3,-2)
Step-by-step explanation:
well, you take the difference between the midpoint and given endpoint and add it on in the other direction
Given the points (–3,k)(–3,k) and (2,0)(2,0), for which values of k would the distance between the points be 34−−√34 ?
Answer:
The possible values of k are 3 and -3
Step-by-step explanation:
Given
Points: (-3,k) and (2,0)
Distance between them = √34
Required
Determine the value of k
The distance between two points is calculated as thus;
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Let
[tex](x_1,y_1) = (-3,k)[/tex]
[tex](x_2,y_2) = (2,0)[/tex]
Substitute these values in the given formula
[tex]Distance = \sqrt{(-3 - 2)^2 + (k - 0)^2}[/tex]
Evaluate the brackets
[tex]Distance = \sqrt{-5^2 + k^2}[/tex]
[tex]Distance = \sqrt{25 + k^2}[/tex]
Recall that Distance = √34
So; we have
[tex]\sqrt{34} = \sqrt{25 + k^2}[/tex]
Take square of both sides
[tex]34 = 25 + k^2[/tex]
Collect Like Terms
[tex]k^2 = 34 - 25[/tex]
[tex]k^2 = 9[/tex]
Take square root of both sides
[tex]k = \±3[/tex]
Hence, the possible values of k are 3 and -3
Solve for x. A. 24 B. 32 C. 22 D. 35
Answer:
B. 32
Step-by-step explanation:
The product of the lengths of segments to the near and far circle intercepts are the same, where the length is measured from the point where the secant and tangent meet. The tangent point counts as both circle intercepts, so we have ...
30×30 = 18×(18 +x)
900 = 324 +18x . . . . eliminate parentheses
576 = 18x . . . . . . . . . subtract 324; next, divide by 18
32 = x
The sum of the angle measures of any triangle is 180 degrees. Angle 2 is twice the measure of angle 1. Angle 3 is 15 degrees less than the measure of angle 2. What is the measure of each angle?
Answer:
Angle 1 = 39, Angle 2 = 78 , Angle 3 = 63
Step-by-step explanation:
78/2 = 39
(Angle 2/2 = Angle 1)
78 - 15 = 63
(Angle 2 - 15 = Angle 3)
39 + 78 + 63 = 180
(Angle 1 + Angle 2 + Angle 3 = 180)
Answer:
39°, 78°, 63°
Step-by-step explanation:
let ∠ 1 = x, then
∠ 2 = 2x ( twice the measure of ∠ 1 )
∠ 3 = 2x - 15 ( 15° less than ∠ 2 )
Sum the 3 angles and equate to 180
x + 2x + 2x - 15 = 180, that is
5x - 15 = 180 ( add 15 to both sides )
5x = 195 ( divide both sides by 5 )
x = 39
Thus
∠ 1 = 39°
∠ 2 = 2 × 39° = 78°
∠ 3 = 78° - 15 = 63°
A large ice chest holds 62 liters of water. A smaller chest holds 4/5 as much water. How many liters of water does the smaller chest hold?
Answer:
49.6 liters
Step-by-step explanation:
Let the number of water that the smaller chest be x liters. If the smaller chest can hold 4/5 of the water that the large chest can hold, then:
The amount of water held by small chest (x) = 4/5 × amount of water that can be held by large chest
x = 4/5 × 62 liters = 49.6 liters
This means that the small chest can hold up to 49.6 liters of water
Smaller chest can hold 49.6 liters.
The smaller chest holds 4/5 the amount of water that the larger chest can hold which is 62 liters.
The amount the smaller chest can hold is therefore:
= Amount of water large chest can hold x proportion of large chest that small chest can hold
= 62 x 4/5
= 248/5
= 49.6 liters
The smaller chest can therefore hold 49.6 liters.
Find out more at https://brainly.com/question/17474612.
How many different two digit numbers can be formed from the digits, 7,8, and 9 if the numbers must be even and no digit can be repeated?
Answer:
2
Step-by-step explanation:
If the number must be even, the units digit must be 8. That leaves 2 choices for the tens digit. The possible numbers are ...
78
98
There are 2 of them.
Answer: Only two: 78 and 98
Step-by-step explanation: 8 is the only even number available to put in the units place where even or odd is determined. With no repetition allowed, the only possibilities left are to switch positions of the 7 and 9 in the tens place.
Which of the following quadratics is a Perfect Square Trinomial?
Answer:
[tex] 16x^2 + 8x +1[/tex]
Step-by-step explanation:
[tex] 16x^2 + 8x +1 = (4x+1)^2 [/tex]
Jada wanted to construct a line perpendicular to line L through point C. The diagram shows her construction. What was her mistake?
Answer:
Perpendicular lines are 90 degrees on their central angle.
Step-by-step explanation:
1. Draw the line L with a meter-rule and a pencil.
2. extend the hand of the protractor beyond the radius of the line and bisect the line L, by placing the protractor pin on both ends of the line and marking up and down.
3. Join the points where the markings meet drawing a line through C which is the center of the line L.
If B is the midpoint of AC, AB = x + 6, and AC = 5x - 6, then what is BC?
BC =
HELP PLEASE
Answer:
bc= 12 :)
Step-by-step explanation:
which is the graph of y =-x +2
Answer:
A
Step-by-step explanation:
The - in front of -x tells us that the line has to go down (slope -1), and the +2 tells us it will pass through (0,2).
Then you can see that only graph A fits that description.
Hello!
Answer:
A
Step-by-step explanation:
if x=0 => y=2
if x=1 => y=1
This is A graph!
What is the range of the graph? A) (3, 5) B) [3, 5] C) (2, 5) D) [2, 5]
Answer:
B. [3, 5]
Step-by-step explanation:
The range of a graph are the y-values that are plotted on the vertical axis (y-axis). In order words, the range values, are the possible set of output values of that are plotted on the vertical axis on the graph.
"[ ]" is usually used to denote the possible set of values.
Therefore, the range of the given graph, as we can see from the y-axis, include values from 3 to 5. Therefore, the range of the graph is [3, 5].
Factor the following polynomial completely.
Hello, please consider the following.
[tex]\begin{aligned}1280x^{11}-405x^7&=5x^7(256x^4-81)\\\\&= 5x^7(16^2(x^2)^2-9^2)\\\\&=5x^7(16x^2-9)(16x^2+9)\\\\&=5x^7((4x)^2-3^2)(16x^2+9)\\\\&\large \boxed{=5x^7(4x-3)(4x+3)(16x^2+9)}\end{aligned}[/tex]
So, the last one is the correct answer.
Thank you.
Use the distributive property to multiply the polynomials.
-5x²(6x - 1)
Enter the simplified polynomial expression in the box.
Answer:
-30x^3+5x^2
Step-by-step explanation:
if the sides of a square measure 10 square root 6 units then find the length of the diagonal
Answer:
20[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The diagonal splits the square into 2 right triangles
Using Pythagoras' identity on one of the right triangles
With legs 10[tex]\sqrt{6}[/tex] and hypotenuse the diagonal d, then
d² = (10[tex]\sqrt{6}[/tex] )² + (10[tex]\sqrt{6}[/tex] )² = 600 + 600 = 1200 ( take square root of both sides )
d = [tex]\sqrt{1200}[/tex] = [tex]\sqrt{400(3)}[/tex] = [tex]\sqrt{400}[/tex] × [tex]\sqrt{3}[/tex] = 20[tex]\sqrt{3}[/tex]
how do you rewrite the formula to solve for r?
Answer:
The answer is C.
The steps are :
[tex] {T}^{2} = ( \frac{4 {\pi}^{2} }{GM} ) \times {r}^{3} [/tex]
[tex] {T}^{2} \div ( \frac{4 {\pi}^{2} }{GM}) = {r}^{3} [/tex]
[tex] {T}^{2} \times \frac{GM}{4 {\pi}^{2} } = {r}^{3} [/tex]
[tex] \frac{GM {T}^{2} }{4 {\pi}^{2} } = {r}^{3} [/tex]
[tex] \sqrt[3]{ \frac{GM {T}^{2} }{4 {\pi}^{2} } } = r[/tex]
[tex]r = \sqrt[3]{ \frac{GM {T}^{2} }{4 {\pi}^{2} } } [/tex]
Answer :
C
[tex]r = \sqrt[3]{ \frac{ {T}^{2}GM} {4 {\pi}^{2} } } [/tex]
Step-by-step-explanation :
[tex] {t}^{2} = ( \frac{4 {\pi}^{2} }{gm} ) {r}^{3} \\ {t}^{2} = \frac{4 {\pi}^{2} {r}^{3} }{gm} [/tex]
[tex] {t}^{2} gm = 4 {\pi}^{2} {r}^{3} \\ \frac{ {t}^{2} gm}{4 {\pi}^{2} } = \frac{4 {\pi}^{2} {r}^{3} }{4 {\pi}^{2} } [/tex]
[tex] {r}^{3} = \frac{ {t}^{2} gm}{4 {\pi}^{2} } [/tex]
[tex] \sqrt[3]{ \frac{ {t}^{2} gm}{4 {\pi}^{2} } } = \sqrt[3]{r} [/tex]
[tex]r = \sqrt[3]{ \frac{ {t}^{2} gm}{4 {\pi}^{2} } } [/tex]