Question
Gabrielle is
7
years older than Mikhail. The sum of their ages is
91
. What is Mikhail's age?
Answers
Answer:
42
Step-by-step explanation:
Since Gabrielle is 7 years older than Mikhail, we subtract 7 from 91. Then we divide it by 2. So 84/2=42. Since Gabrielle is 7 years older we add 7 to 42. She is 49 and Mikhail is 42 years old. To double check our answer we should add both of the ages we got to make sure they add up to 91, so 42+49 is 91.
Related Questions
Which point is a solution to the system of equations?
y = 2x + 2
Y = 3x
Answers
Answer:
(2,6)
Step-by-step explanation:
y = 2x + 2
Y = 3x
2x+2=3x
2x-3x+2=0
-x+2=0
-x=-2
x=2
y=3(2)=6
Add or write the fraction or mixed number in its simplest form
2/5 + 1/4 + 7/10
Answers
8/20 + 5/20 + 14/20
27/20 or 1 7/20
help i nedeed to pass the quizzzzzzzzzzzzzzz
Answers
The area of the figure is 108cm²
How to determine the value of the areaThe formula for calculating the area of a triangle is expressed as;
Area = 1/2 base × height
Substitute the values, we have;
Area = 1/2 ×8×3 = 12 cm²
The formula for calculating the area of a rectangle is expressed as;
Area = length × width
substitute the values, we have;
Area = 8 × 10
Area = 80 cm²
The formula for area of a trapezoid is expressed as;
Area = a + b/2 h
Substitute the values
Area = 4 + 4/2 (4)
Area = 16cm²
Total area = 16 + 12 + 80 = 108cm²
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What is the domain of h?y7h---7 6 5 4 3 276+5+4+3+21++ +++++1 2 3 4 5 6 72+-3+-4+-5 .-6+-7
Answers
The domain of a function is the set of all possible x-values.
In this case, the function h(x) is discrete, then the domain is the set of x-values where h(x) is defined, that is,
Domain: {-2, -1, 1, 5, 6}
What is the slope of the line
Answers
Step-by-step explanation:
Look at the points (0,-3) and ( 3,0)
slope, m = rise / run = 3 / 3 = 1
Answer:
1
Step-by-step explanation:
y=x+3
Find the vertices and foci of the ellipse.
Answers
Solution
- The question would like us to find the vertices and foci of the ellipse with the following equation:
\(\frac{x^2}{9}+\frac{y^2}{5}=1\)- Before we can solve, we need to write down the general equation of an ellipse and formulas for the foci and vertices.
- These are given below:
\(\begin{gathered} \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1 \\ \text{where,} \\ \text{Vertices are:} \\ (h+a,k),(h-a,k),(h,k+b),(h,k-b) \\ \\ \text{The foci are:} \\ (\pm c,0),\text{ where, }c^2=a^2-b^2\text{ (If the major axis is on the x-axis)} \\ \\ (\text{if }a>b\text{, then, the major axis is on the x)} \end{gathered}\)- Based on the formulas given above, we can proceed to solve as follows:
\(\begin{gathered} \text{ Compare the general equation of an ellipse to the equation given to us} \\ \frac{x^2}{9}+\frac{y^2}{5}=1 \\ \\ \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1 \\ \\ h=k=0 \\ a^2=9,b^2=5 \\ a=\pm3,b=\pm\sqrt[]{5} \\ \\ \text{ We can s}ee\text{ that } \\ a>b\implies3>\sqrt[]{5} \\ \text{Thus, the major axis is on the x} \\ \\ \text{Thus, the Vertices are:} \\ (h+a,k)=(0+3,0)=(3,0) \\ (h-a,k)=(0-3,0)=(-3,0) \\ (h,k+b)=(0,0+\sqrt[]{5})=(0,\sqrt[]{5)} \\ (h,k-b)=(0,0-\sqrt[]{5})=(0,-\sqrt[]{5}) \\ \\ \text{The foci is gotten as follows:} \\ a^2-b^2=c^2 \\ 9-5=c^2 \\ c^2=4 \\ c=\pm\sqrt[]{4} \\ c=\pm2 \\ \text{Thus, the foci are:} \\ (\pm2,0) \end{gathered}\)Final Answer
The answers are:
\(\begin{gathered} \text{Vertices are:} \\ (3,0),(-3,0),(0,\sqrt[]{5}),(0,-\sqrt[]{5}) \\ \\ \text{Foci are:} \\ (2,0),(-2,0) \end{gathered}\)3^3 times 3^3 divides by 3^4
3^0
3^1
3^2
3^4
Answers
Answer:
3^2
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c)
__
\(\dfrac{(3^3)(3^3)}{(3^4)}=3^{3+3-4}=\boxed{3^2}\)
Answer:
3^2
Step-by-step explanation:
For clarity rewritet 3^3 times 3^3 divides by 3^4 as follows:
3^3*3^3
-----------------
3^4
This, in turn, simplifies to
3^(3 + 3) 3^6
---------------- or ------------ = 3^2 (third answer choice)
3^4 3^4
There is a 1 in 8 chance of a player winning a game. Which value is equivalent to the chance
of the player winning a game?
F
100
125
G
125
10
H 1.25
J 0.125
Answers
The value which is equivalent to the 1 in 8 chance of the player winning a game is Choice J: 0.125.
The question statement implies that the probability of a player winning a game is 1 in 8.
We must know that the probability of an event occuring can be expressed as any choice of real numbers. However, the probability must ultimately not be more than 1 upon evaluation.
For choice F:
The expression 100/125 = 0.8 which is not equivalent to 1 in 8.For choice G:
The expression 125/10 = 12.5 which is not equivalent to 1 in 8.For choice H:
The expression 1.25 is more than 1, therefore, it is obviously not equivalent to 1 in 8.For Choice J:
The expression 0.125 is equivalent to 1 in 8 because 1/8 = 0.125.Read more:
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Find the length of the highlighted arc. Round your answer to the nearest tenth. *
Answers
Answer:
Approximately 23.6
Step-by-step explanation:
So first find the fraction of the whole circumference the arc is.
270 ÷ 360 = 0.75
The circumference is 10π
0.75 * 10π = 7.5π
7.5π = 23.5619449019 ≈ 23.6
Correct answer gets brainliest!!!!
Answers
Answer:
a) 5
Step-by-step explanation:
the question say how many zero-dimensional objects are labeled on the object. so, you would count how many blue dots you see on the object, as you can see their are four dots on the the bottom, and one dot at the top.
so, 4 dots + 1 dot = ?
5 blue dots
so your answer is 5.
hopefully this helps, let me know if it doesn't.
When a 3-D figure cut to create a cross-section parallel to the base which direction is the perpendicular vertical or horizontal 
Answers
Answer:
When a 3D figure is cut to create a cross-section parallel to the base, the direction of the perpendicular is vertical. This means that the cross-section will be perpendicular to the base and will have a vertical orientation.
Which method would you use to solve the problem substitution or graphing explain your answer (PART B)
Answers
Answer:
Based on the solution that is being on Part A, the method used is substitution.
Explanation:
The two equations in Part A were:
x = the number of weeks
Equation 1: Lyle's savings = 100 + 20x
Equation 2: Shaun's savings = 500 + 10x
Since we wanted to know when Lyle's and Shaun's savings will be equal, we substituted "Lyle's savings" in the equation with 500 + 10x. It made equation 1 become 500 + 10x = 100 + 20x.
Or, we substituted "Shaun's savings" in the equation with 100 + 20x. It made equation 2 become 100 + 20x = 500 + 10x.
From this, we were able to calculate that at week 40, both Lyle and Shaun will have the same amount in their savings account.
\(\begin{gathered} 500+10x=100+20x \\ 500-100=20x-10x \\ 400=10x \\ \frac{400}{10}=\frac{10x}{10} \\ 40=x \end{gathered}\)please help asap and please give real answers
Answers
Answer:
x = 2, x = - 5
Step-by-step explanation:
To factor it, you can split the middle term to get:
x² - 2x + 5x - 10 = 0
Then, you can factor the first two and the last two to get:
x (x - 2) + 5(x - 2) = 0
And if you divide both sides by (x - 2) you get:
(x - 2) (x + 5) = 0
Finally, this can be solved by the Zero Product Property which states that if x*y=0, then x and/or y has to be equal to 0. If you apply it to the eqaution you get:
x - 2 = 0, x + 5 = 0
which results in:
x = 2, x = - 5
Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options. 5(x2 + 4x + 4) = –7 + 20 x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot 5(x2 + 4x) = 7 5(x2 + 4x + 4) = 7 + 20 5(x2 + 4x) = –7
Answers
The steps Sergey could use to solve the quadratic equation by completing the square is 5(x2 + 4x) = –7
How to use the completing the square method?We should know that in completing the square method both sides of the equation are made perfect squares.
The given equation is 5x²+20x-7=0
Solving this equation by completing the square method we have
5(x²+4x+4)=-7
This means that (x+2)=±√27/5
Simplifying further we have
5(x²+4x)=7
Then expanding to make ²HS a perfect square we have
5(x²+4x+4)=7+20
This means that 5(x²+4x)=-7
Therefore the step he could use is 5(x²+4x)=-7\
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The graph shows the number of miles you and a friend run each week while training for a race. Your friend runs______ more miles than you each week.
Answers
Answer:
42
Step-by-step explanation:42
Answer:
4
Step-by-step explanation:
7x-4 =20 + 3x
x=???????
Answers
Answer:
x=6
Step-by-step explanation:
collect like terms
7x-3x=20+4
4x=24
x=
Answer:
\(x=6\)
Step-by-step explanation:
\(7x-4=20+3x\)
Add 4 to both sides.
\(7x-4+4 =20 + 3x+4\)\(7x=3x+24\)Subtract 3x from both sides.
\(7x-3x=24\)\(4x=24\)Divide both sides by 4.
\(\cfrac{4x}{4}=\cfrac{24}{4}\)\(x=6\)-Hope this helps!
let C be the curve y=5sqrtx for 1.1
Answers
We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
We have,
To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:
S = ∫(a to b) 2πy√(1 + (f'(x))²) dx
In this case,
f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).
Let's calculate the surface area:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx
Simplifying the expression inside the integral:
S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx
Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
To find the surface area of revolution about the x-axis of the function
f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx
Let's calculate the integral:
S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx
To simplify the calculation, let's simplify the expression inside the integral first:
S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx
Next, we can distribute the square root and simplify further:
S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx
Thus,
We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
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Answer two questions about Equations A and B:
A. 2x - 1 = 5x
B. - 1 = 3x
1) How can we get Equation B from Equation A?
Choose 1 answer:
A. Add/Subtract the same quantity to/from both sides
B. Add/Subtract a quantity to/from only one side
C. Rewrite one side (or both) by combining like terms
D. Rewrite one side (or both) using the distributive property
2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
Choose 1 answer:
A. Yes
B. No
Answers
1. Rewrite one side (or both) by combining like terms. Option C
2. Yes, the equations are equivalent. Option A
Reasons for the answers
1.
Equation A ; 2x -1 = 5x
Equation B ; -1 = 3x
To get equation B from equation A
2x - 1 = 5x
Collect like terms
-1 = 5x -2x
Subtract the like terms
-1 = 3x
Thus, rewrite one side (or both) by combining like terms. Option C
2. 2x - 1 = 5x ...... equation A
Solution ;
2x -5x = 1
-3x = 1
x = -1/3
-1 = 3x
Solution;
x = -1/3
Thus, the equations are equivalent. Option A
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The number of children's books at a library was 2/5 of the total number of books. After 298 children's books were added to the library, the number of children's books was 4/7 of the total number of books. How many books were there in the library at first?
Answers
Answer:
745
Step-by-step explanation:
You want the original number of books in the library if adding 298 children's books increased the fraction of children's books from 2/5 to 4/7.
RatioWe often like to work problems like this in terms of "ratio units." Here, we'll let x represent the number of books in a ratio unit. This means the number of children's books is originally 2x, and the total number of books is originally 5x. Then we have ...
(2x +298)/(5x +298) = 4//7
SolutionCross multiplying gives ...
7(2x +298) = 4(5x +298)
3(298) = 6x . . . . . . . . . . . . . subtract (14x+4(298))
149 = x
745 = 5x . . . . . . the original number of books in the library
There were 745 books in the library at first.
__
Additional comment
If we let x represent the original number of library books, then the arithmetic involves more fractions. You would have an equation like ...
2/5x +298 = 4/7(x +298)
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The table shows your test results for math class. What test score do you need on the last exam to earn 90% of the total points?
Answers
Answer:
262.6/300% for the first 3 test if you were to add another test it would be 400% total and you need 360% of test grades to have an average of 90% and so 360 - 262.6 = 97.4%
Step-by-step explanation:
mations to Determine Similarity
What steps would you take to determine if these
figures are similar? Check all that apply.
Use a scale factor of 2.
Multiply the vertices of polygon ABCD by
O Translate the intermediate image 4 units down.
Perform two different dilations.
Reflect the intermediate image.
Answers
The steps which you would take to determine if these figures are similar include the following:
2. Multiply the vertices of polygon ABCD by 1/2.
5. Reflect the intermediate image.
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.
Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.
By critically observing the graph representing polygon ABCD, we can logically deduce that a sequence of transformations that would polygon ABCD (pre-image) onto polygon A"B"C"D" (image) is a dilation by a scale factor of 1/2 and a reflection of intermediate image.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The circumference of a circle is 7xm.
What is the area of the circle?
A. 3.57x m²
B. 12.257x m2
C. 147xm2
D. 497xm2
Answers
Answer:
A = 3.57 m²
Step-by-step explanation:
Given that,
The circumference of a circle is 7xm.
The expression for the circumference of a circle is given by :
\(C=2\pi r\)
r is the radius of the circle
\(r=\dfrac{C}{2\pi}\\\\r=\dfrac{7}{2\times \dfrac{22}{7}}\\\\r=1.11\ m\)
The area of a circle is given by :
\(A=\pi r^2\\\\A=3.14\times (1.11)^2\\\\A=3.89\ m^2\)
Out of given option,
A = 3.57 m²
So, the area of the circle is 3.57 m².
dude what is this i dont understand
Answers
Answer:
g(1) = 1
Step-by-step explanation:
the absolute value function always gives a positive result, that is
| - a | = | a | = a
to evaluate g(1) substitute x = 1 into g(x)
g(1) = - 3| 1 - 2| + 4
= - 3| - 1| + 4
= - 3(1) + 4
= - 3 + 4
= 1
Option (c) p =10000 (1.04)-t . Given
To find the poulation, p of a town after t years is represented using the equation, p = .
Which of the following is an equivalent expression?
(a) p = 10000 (1/25)t
(b) p = 10000 (25/26)t
(c) p = 10000 ( 26/25)t
(d) p = 10000(25/1)t
Answers
The equivalent expression is p=10000(26/25)t
What is expression ?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.
Considering that the population, p, of a town after t years is represented using the equation p=10000(1.04)^-t
The equation is equivalent to
p=10000(26/25)t
26/25 = 1.04
Hence; p=10000(26/25)t
⇒ p=10000(1.04)^t
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Of 10 test scores, eight are less than or equal to 82. What is the percentile rank of a test score of 82?
Answers
Answer:
80%
Step-by-step explanation:
Percentile rank = (number of scores lower or equal to 82 / total number of scores) * 100%
Percentile = (8 / 10) * 100%
= 0.8 * 100%
= 80%
1x²- 16x = 20 is mg questions
Answers
The solutions to the equation 1x² - 16x = 20 are x = 8 + 2√21 and x = 8 - 2√21.
To solve the quadratic equation 1x² - 16x = 20, we need to rearrange it into the standard form ax² + bx + c = 0. Let's simplify the equation step by step:
1x² - 16x = 20
First, move all terms to one side of the equation:
1x² - 16x - 20 = 0
Now we have a quadratic equation in the standard form. To solve it, we can use factoring, completing the square, or the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
For our equation, a = 1, b = -16, and c = -20. Substituting these values into the quadratic formula:
x = (-(-16) ± √((-16)² - 4(1)(-20))) / (2(1))
Simplifying further:
x = (16 ± √(256 + 80)) / 2
x = (16 ± √336) / 2
x = (16 ± √(16 * 21)) / 2
x = (16 ± 4√21) / 2
Simplifying:
x = 8 ± 2√21
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Pat's income is 20 % more than Adam. How much percent is Adam's income less than Pat's?
Answers
Adam's income is 16.67% less than Pat's income.
Let's assume Adam's income is $100
Then Pat's income is 20% more than Adam's income, which means Pat's income is:
$100 + $20 = $120
Now, we need to find out how much percent Adam's income is less than Pat's income. We can use the following formula to calculate the percentage decrease:
Percentage decrease = (Decrease in value / Original value) x 100
Decrease in value is the difference between Pat's income and Adam's income, which is:
$120 - $100 = $20
The original value is Pat's income, which is $120
So, the percentage decrease in Adam's income compared to Pat's is:
(20 ÷ 120) × 100
= 0.16666 × 100
= 16.666%
= 16.67% (approx)
Therefore, Adam's income is 16.67% less than Pat's income.
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A train leaves Philadelphia at 2:00 PM. A second train leaves the same city in the same direction at 4:00 PM. The second train travels
52 mph faster than the first. If the second train overtakes the first at 6:00 PM, what is the speed of each of the two trains?
Answers
Answer: First train speed shall be 42 mi/hr
Second train speed shall be 84 mi/hr
Yes it is the valid answer, it gets annoying when almost everyone enters the wrong answer for a good laugh. Either way, hope this helps! Have a spectacular day.
Step-by-step explanation:
What is the 1st train's head start in miles?
Let +s+ = the speed of the 1st train in mi/hr
From 2PM to 4PM is 2 hrs
+d%5B1%5D+=+s%2A2+
---------------------
Let +d+ = distance the 2nd train travels until
it overtakes the 1st train
From 4PM to 6PM is 2 hrs
Start time when the 2nd train leaves
---------------------
Equation for 1st train:
(1) +d+-+2s+=+s%2A2+
Equation for 2nd train:
(2) +d+=+%28+s%2B42+%29%2A2+
--------------------
Substitute (2) into (1)
(1) +%28+s%2B42+%29%2A2+-+2s+=+s%2A2+
(1) +2s+%2B+84+-+2s+=+2s+
(1) +2s+=+84+
(1) +s+=+42+
and
+s%2B+42+=+42+%2B+42+
+s+%2B+42+=+84+
------------------
The 1st train's speed is 42 mi/hr
The 2nd train's speed is 84 mi/hr
---------------------------
check:
(2) +d+=+%28+s%2B42+%29%2A2+
(2) +d+=84%2A2+
(2) +d+=+168+
and
(1) +d+-+2s+=+s%2A2+
(1) +d+-+2%2A42+=+42%2A2+
(1) +d+=+84+%2B+84+
(1) +d+=+168+
What is 1.8 added 8 times? (IF YOU CAN PLS DO IT IN EXPLANATION) and this is about decimals and pls do it in grade five type, bc I won't be able to understand anything too big for me, example: (e^(4^(2)
Thank you
Answers
Answer:
14.4
Step-by-step explanation:
1.8 added 8 times = 1.8 * 8
1.8 * 8
use distributive property
1.8 = 1 + 0.8
1.8 * 8 = (1+0.8) * 8
= 1*8 + 0.8*8
anything multiplied by 1 equals itself
1*8 + 0.8*8 = 8 + 0.8 * 8
0.8 = 8/10
0.8 * 8 = (8/10) * 8
= 64/10
= 6.4
8 + 0.8 * 8 = 8 + 6.4 = 14.4 as our answer
Alisha kept track of the growth of a plant. at the beginning of one week, her plant was 1 7/8 inches tall. the next week, the plant was 2 3/4 inches tall. how many inches did Alisha's plant grow over the week?
Answers
Answer:
Alisha's plant grow over the week:
2 3/4=((4*2)+3)/4=11/4
1 7/8=((8*1)+7)/8=15/8
so
2 3/4 - 1 7/8=11/4-15/8=(2*11-15)/8=7/8
so Alisha's plant grow over the week 7/8 inches
The number of inches grown over the week is 7/8 inches.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Length of the plant in the first week = 1(7/8) inches.
Length of the plant the next week = 2(3/4) inches.
The length of plant grown over the week.
= 2(3/4) - 1(7/8)
= 11/4 - 15/8
= (22 - 15)/8
= 7/8 inches
Thus,
7/8 inches was grown over the week.
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