Final answer:
To solve the system of equations y = x - 10 and y = 2x + 5, we equate both expressions for y, solve for x, and find x = -15. Substituting x back into either equation gives y = -25, making the solution (x, y) = (-15, -25).
Explanation:
The question seeks the solution of the system of equations given by y = x - 10 and y = 2x + 5.
To find the solution, one can use the substitution method, where the expression for y in one equation is substituted into the other equation.
This gives us two equations stated to have the same value of y, which means they can be set equal to each other: x - 10 = 2x + 5.
Solving this equation for x involves moving x terms to one side and constants to the other, yielding x = -15. Substituting x back into either original equation (e.g., y = x - 10), we find y = -25.
Thus, the solution to the system of equations is x = -15 and y = -25.
Solve: 25x^2 - 36 = 0
A.) x = 6, 5
B.) x = -6, -5
C.) x = 36/25, x = -36/25
D.) x = 6/5, x = -6/5
Answer: 6/5 and -6/5
Step-by-step explanation: In order to solve this problem, we want to get the variable on one side. In order to do that, we must do the following:
Add 36 on Both Sides:
[tex]25x^2 - 36+36 = 0+36[/tex]
Divide 25 on Both Sides:
[tex]\frac{25x^2}{25}= \frac{36}{25}[/tex]
Take the square root of Both Sides:
[tex]\sqrt{x^2} = \sqrt{\frac{36}{25} }[/tex]
That means your answer is:
[tex]x = \frac {6}{5}[/tex], or [tex] -\frac {6}{5} [/tex]
What are the coordinates of the midpoint of the segment whose endpoints are J(3, -1) and K(9, 5)?
A. (1, 2)
B. (3, 2)
C. (3, 3)
D. (6, 2)
Answer:
Option D. (6, 2)
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute
[tex]M(\frac{3+9}{2},\frac{-1+5}{2})[/tex]
[tex]M(\frac{12}{2},\frac{4}{2})[/tex]
[tex]M(6,2)[/tex]
Determine the value of base b if (152)b = 0x6A. Please show all steps.
Assuming 0x6A is given in base 16, first convert [tex]152_b[/tex] and [tex]6A_{16}[/tex] to a common base, say base 10:
[tex]152_b=1\cdot b^2+5\cdot b^1+2\cdot b^0=(b^2+5b+2)_{10}[/tex]
[tex]6A_{16}=6\cdot16^1+10\cdot16^0=106_{10}[/tex]
Then
[tex]b^2+5b+2=106[/tex]
[tex]b^2+5b-104=(b-13)(b+8)=0[/tex]
[tex]\implies b=13[/tex]
Answer:
The value of b is, 8
Step-by-step explanation:
Determine the value of b;
Given:
[tex](152)_b = 0x6A[/tex] ....[1]
Since, 0x6A represents the hexadecimal form.
First convert this hexadecimal form into decimal form:
[tex](6A) = (6 \times 16^1)+(A \times 16^0) = (96)+(10 \times 1) = 96+10 = 106[/tex]
⇒[tex]0x6A = 106[/tex] (decimal form)
Now we have to convert this decimal form into octal
8 | 106
8 | 13 | 2
| 1 | 5
1
Then, the octal form we get, [tex](152)_8[/tex]
Substitute these in [1] we have;
[tex](152)_b=(152)_8[/tex]
On comparing both sides we get;
b = 8
Therefore, the value of b is, 8
Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit. The following table below shows the continents on her trip and how many cities she can choose from for each continent. Continent Number of cities Europe 10 Asia 888 Africa 4 Australia 3 How many different combinations of cities does Elyse have to choose from?
Answer:
960
Step-by-step explanation:
10 x 8 x 4 x 3
Hope This Helped
Regards Jaygtgajm11
Disclaimer: The number of cities in Asia will be 8 and not 888.
Elyse can choose from 960 different combinations of cities.
What are permutations and combinations?The different ways in which objects from a set can be picked, often without replacement, to produce subsets are known as permutations and combinations. When the order of selection is a factor, this selection of subsets is termed a permutation; when order is not a factor, it is called a combination.
How do we solve the given question?We are given 4 continents, with a number of cities to choose from for Elyse to visit.
The table is like this:
Continent Number of cities
Europe 10
Asia 8
Africa 4
Australia 3
We use permutations and combinations to find the number of combinations Elyse will have to choose from.
We can say that for every 10 cities in Europe, she can choose any of the 8 cities in Asia. Similarly, for every 8 cities in Asia, she can choose any of the 4 cities in Africa. And similar is the case for Africa and Australia.
∴ Elyse can choose from a combination of 10*8*4*3 cities,
or, Elyse can choose from a combination of 960 cities.
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What is the median of the following data values? 98, 102, 53, 80, 22.
Answer:
53
Step-by-step explanation:
median is right in the middle of the other numbers.
Answer:
The median is 80
Step-by-step explanation:
To find the median we should arrange the given data set in ascending or descending order. If there are even number of items in the given data set we have to take the average of central terms.
To find the median
It is given a data set,
98, 102, 53, 80, 22
Arrange them in ascending order
22, 53, 80, 98, 102
To find the middle term, From the set of data we get median is 80
22, 53, 80, 98, 102
Find the unknown measure
The two little lines through the two sides of the triangle mean that they are the same length.
When two sides of a triangle are the same, the two lower inside angles are also the same.
Angle A is given as 50 degrees, so angle C is also 50 degrees.
The sum of the three inside angles need to equal 180 degrees, so angle B would equal 180 - 50 - 50 = 80 degrees.
Angle B = 80
Angle C = 50
solve for y 2x- 3y= 3
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷ 2x-3y=3
First:
Add -2y to both sides
-3y=-2x+3
Next:
Divide both sides by -3
y= 2/3x - 1
The answer
y= 2/3x - 1
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
TROLLER
If CDEF ≅ MNPQ, then ∠N ≅ _____
∠E.
∠D.
∠F.
∠C.
Answer: ∠D.
Step-by-step explanation:
because they are in the same position (2nd letter placement)
If quadrilaterals CDEF ≅ MNPQ, then it follows that ∠N ≅ ∠D.
Hence ∠D is correct.
If CDEF and MNPQ are congruent,
Then it means they have the same shape and size.
In other words, all of their corresponding angles and sides are equal.
Therefore, if ∠C is congruent to ∠M,
∠D is congruent to ∠N,
∠E is congruent to ∠P, and
∠F is congruent to ∠Q.
This is because congruence is a relation of equality between two geometric figures.
So, if two triangles (or any other polygons) are congruent,
Then all of their corresponding angles and sides are equal.
Therefore, if CDEF ≅ MNPQ, then it follows that ∠N ≅ ∠D.
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An auditorium has 100 seats for every 10 rows. Each row has the same number of seats. If s represents the number of seats and r represents the number of rows, which equation represents this proportional relationship?
A.s = 10r
B.s=1/2r
C.100s = r
D.100s = 10r
I think the answer is C because the question says in one row there are 100 seats so with a total of 100 seats there is a row.
Answer:
D
Step-by-step explanation:
The answer is D because 100 divided by 10 = 10. Hope this helps! ☺
The volume is a rectangle prism is ( x^4+4x^3+8x+4) and the area of its base is (x^3+3x^2+8) if the volume of a rectangle prism is the product of its base area and height what is the height of the of the prism
Answer:
[tex]h=(x^{4}+4x^{3}+8x+4)/(x^{3}+3x^{2}+8)[/tex]
Step-by-step explanation:
Let
h------> the height of the prism
we know that
The volume of the prism is equal to
[tex]V=Bh[/tex]
where
B is the area of the base
h is the height of the prism
In this problem we have
[tex]V=x^{4}+4x^{3}+8x+4[/tex]
[tex]B=x^{3}+3x^{2}+8[/tex]
substitute and solve for h
[tex]x^{4}+4x^{3}+8x+4=(x^{3}+3x^{2}+8)h[/tex]
[tex]h=(x^{4}+4x^{3}+8x+4)/(x^{3}+3x^{2}+8)[/tex]
I need help please????
Answer:
The correct one is b nice you chose the right one!
Step-by-step explanation:
Olivia is cutting 1 1/2 m by 3/4 m pieces of rectangular paper in the two pieces along its diagonal What is the area of each of the pieces
Answer: 2 1/4
Step-by-step explanation:
Convert both to same denominators and mixed numbers
1 1/2 = 1 2/4 = 6/4
3/4 = 3/4
3/4*6/4 = 18/16
Simplify: 9/4 = 2 1/4
A height is labeled on the triangle below. Which line segment shows the base that corresponds to the given height of the triangle?
Answer:
Option A
Step-by-step explanation:
We are given that a height is labeled on the triangle in given figure.
We have to find the that segment which shows the base that correspond to the given height of the triangle
We know that base is that side of triangle on which height is perpendicular.
In the given figure, Height is perpendicular to side A.
Therefore, side A represent the base of triangle.
Hence, line segments A shows base that corresponds to the given height of the triangle.
Option A is true.
jadzia finished 8 of the 10 problems she had for homework what percent of her homework did jadzia finish?
Answer:
Jadzia finished 80% of her homework.
What best describes the expression y/3 ? (5 points)
3 more than some number
Some number times 3
Some number divided by 3
3 less than some number
What is the constant term in the expression 8xy − 9x2 y − 5x + 6? (5 points)
−9
−5
6
8
Answer:
Step-by-step explanation:
"y/3" is the symbolic representation of "an unknown number, y, divided by 3."
Note that all terms in 8xy − 9x2 y − 5x + 6, except for the 6, involve a variable, either x or y. 6 is the constant term.
Write the following coordinates where they belong in the line segments below. Consider the graph below. Which of the following coordinates belong in the box?
A.(4 3/4,-3 3/4)
B.(4 5/8,-2 3/4)
C.(4 1/4,-5 1/2)
D.(4 1/8,-2 3/5)
Answer:
The option B (4 5/8,-2 3/4) = (4.6 , -2.75) will be the coordinates belonging in the box.
Step-by-step explanation:
A.(4 3/4,-3 3/4) = (4.75,-3.75)
B.(4 5/8,-2 3/4) = (4.6 , -2.75)
C.(4 1/4,-5 1/2) = (4.25, -5.5)
D.(4 1/8,-2 3/5) = (4.125, -2.6)
The first point of line segment is: (5.5, -4.25)
second will be (4.75,-3.75)
third will be (4.6 , -2.75)
fourth will be (4.125, -2.6)
and fifth is (3.75,-1.25)
The option C is not correct i.e not included in line segment.
The option B will be the coordinates belonging in the box.
Please help I need help with this ASAP please
please i really need help
Answer:
D
Step-by-step explanation:
Two events are independent if the intersection of the two events is the same as multiplying each events probability.
P (Texas) = 125/ 275 = 0.45
P (Brand A) = 176/275 = 0.64
0.45 * 0.64 = 0.29
P (Texas ∩ Brand A) = 0.29
So to find P (Texas | Brand A) = 0.29 / 0.64 = 0.45
Answer choice D makes the best choice.
HELP ASFAST AS POSSIBLE. What ratio is equivalent to 40%.
A. 1 to 4
B. 4 to 1
C. 2 to 5
D. 5 to 2
Divide the first number by the second number for each ratio:
A. 1 to 4 = 1/4 = 0.25 = 25%
B. 4 to 1 = 4/1 = 4 = 400%
C. 2 to 5 = 2/5 = 0.4 = 40%
The answer is C.
An equivalent ratio to 40% is 2 to 5, which is option C. The percentage is simplified by dividing it by the greatest common divisor to find its simplest ratio form.
Explanation:To find a ratio equivalent to 40%, we first understand that percentages are a way of expressing a ratio where the second term is 100. Therefore, 40% is the same as saying 40 out of 100 or 40/100.
Next, we simplify this fraction to its lowest terms. Dividing both numerator and denominator by their greatest common divisor, which is 20 in this case, gives us 2/5. Thus, the ratio equivalent to 40% in its simplest form is 2 to 5, which corresponds to option C.
If we were to check the other options given, A (1 to 4) and B (4 to 1) are equivalent to 25% and 400% respectively, while D (5 to 2) is equivalent to 250%. Hence, these are not correct.
To illustrate the concept, let's consider an example. If the scale dimension is 4 cm, then to find the actual dimension using the proportion 1:2=4:x, we would cross-multiply to find x, which would be 8 cm, showing how ratios can be used to find corresponding values.
At a sporting event, the price of 3 cheeseburgers and 2 cups of lemonade is $14 and the price for 2 cheeseburgers and 4 cups of lemonade is $12. How much does it cost for 1 cheeseburger and 2 cups lemonade?
Show Work Please Please Help Imediatly
Answer: $2
Step-by-step explanation: this is only if everything is the same price.
Which complex number has a distance of (squareroot) of 17)) from the origin on the complex plane?
2 + 15i
17 + i
20 – 3i
4 – i
Answer:
[tex]4-i[/tex]
Step-by-step explanation:
The distance of a complex number
[tex]z=a+bi[/tex]
from the origin is given by:
[tex]|z|=\sqrt{(a-0)^2+(b-0)^2}[/tex]
[tex]|z|=\sqrt{a^2+b^2}[/tex]
The length of [tex]2+15i[/tex] is;
[tex]=\sqrt{2^2+15^2}[/tex]
[tex]=\sqrt{4+225}[/tex]
[tex]=\sqrt{229}[/tex]
The length of [tex]17+i[/tex] is;
[tex]=\sqrt{17^2+1^2}[/tex]
[tex]=\sqrt{289+1}[/tex]
[tex]=\sqrt{290}[/tex]
The length of [tex]20-3i[/tex] is;
[tex]=\sqrt{20^2+3^2}[/tex]
[tex]=\sqrt{400+9}[/tex]
[tex]=\sqrt{409}[/tex]
The length of [tex]4-i[/tex] is;
[tex]=\sqrt{4^2+1^2}[/tex]
[tex]=\sqrt{16+1}[/tex]
[tex]=\sqrt{17}[/tex]
The correct choice is D
how i solve that please
Answer:
i cant see the picture
Step-by-step explanation:
what is 21ax + 10by - 35ay - 6bx?
Answer:
Your question is the answer
Step-by-step explanation:
None of the terms can be simplified further
what does x in this equation
2x-3=6
Answer:
x=4.5
Step-by-step explanation:
Answer:
[tex]x = 4.5[/tex]
Step-by-step explanation:
[tex]2x - 3 = 6 \\ 2x = 6 + 3 \\ 2x = 9 \\ \frac{2x}{2} = \frac{9}{2} \\ x = 4.5[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
[tex]xy + x + y = 11 \\ x {}^{2}y + xy {}^{2} = 30[/tex]
find x & y
I think the answer is 2 and 3.
x=1,2,3,5
y=5,3,2,1
Step-by-step explanation:see the image
In a sample of 32 city residence, 24 reported that they take vitamin C supplement daily. There are 46,480 residence in the city. Which estimate represents the number of city residents who take vitamin C supplement daily?
Answer:
34,860
Step-by-step explanation:
In a sample of 32 residence, 24 take Vitamin C. From here we can get the proportion of residents who take Vitamin C, which is 24/32 = 3/4 = 0.75
0.75 in percentage is 75%. This means 75% of the residents in sample take Vitamin C.
We can expect the same percentage of people in entire population to take Vitamin C.
Total population of city = 46480
Expected number of residents who take vitamin C in the city = 75% of 46480
= 0.75 x 46480
= 34860
This means, 34860 is an estimate of number of city residents who take Vitamin C supplement daily.
Based on the sample study and assuming its representativeness of the general population, it is estimated that approximately 34,860 residents of the city take a vitamin C supplement daily.
Explanation:In the sample study, the proportion of residents who take vitamin C supplements daily is calculated by dividing the number of individuals who reported taking the supplement (24) by the total number of individuals in the sample (32). This yields a proportion of 0.75, or 75%. Then, we can apply this proportion to the total population of the city to estimate the number of residents who take vitamin C daily. Therefore, the estimated number is 0.75 * 46,480 = 34,860.
In conclusion, assuming that the small sample is representative of the larger population, we would estimate that "approximately 34,860" city residents take a vitamin C supplement daily.
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if you subtract 8 from 7 times a certain number, you end up with 34. what is the number?
If we call the unknown number x, we have:
7 times a certain number is [tex]7x[/tex]If we subtract 8, we have [tex]7x-8[/tex]If this equals 34, we have
[tex]7x-8=34[/tex]
Add 8 to both sides:
[tex]7x=42[/tex]
Divide both sides by 7:
[tex]x=6[/tex]
Mario simplified the expression as shown.
Which statement explains Mario’s error?
Answer: Last option
Step-by-step explanation:
1. According to the properties of exponents, you have that:
[tex]a^{-n}=\frac{1}{a^n}\\\\(a^n)^m=a^{mn}[/tex]
2. Then, he must simplify the expression as following:
[tex](4z^8)^{-3}={4^{-3}z^{8(-3)}=\frac{1}{64z^{24}}[/tex]
3. Therefore, as you can see, should have also applied the negative exponent to 4 to get [tex](4z^8)^{-3}={4^{-3}z^{8(-3)}=\frac{1}{64z^{24}}[/tex]
Answer:
The correct answer option is He should have also applied the exponent -3 to 4 to get [tex]4^{-3}z^{8 \cdot(-3)} = 4^{-3}z^{-24} = \frac{1}{64z^{24}}[/tex].
Step-by-step explanation:
The following expression was to be simplified by Mario:
[tex] (4z^8)^-3 [/tex]
Given this expression, we need to apply this rule on it in order to simplify:
[tex] (a b)^m = a^m \cdot b^m [/tex]
So we would get:
[tex] (4z^8)^-3 [/tex]
[tex]4^{-3} \cdot (z^8)^{-3}[/tex]
[tex]\frac{1}{4^3} \cdot z^{-24}[/tex]
[tex]\frac{1}{64z^{24}}[/tex]
This would be the right simplification for the given expression but by looking at Mario's work shown, we can conclude that:
He should have also applied the exponent -3 to 4 to get [tex]4^{-3}z^{8 \cdot(-3)} = 4^{-3}z^{-24} = \frac{1}{64z^{24}}[/tex].
Which ordered pair is a solution of the linear equation shown in the graph above?
1. (-2, 0)
2. (1, 3)
3. (-1, 1)
4. (0, -1)
Which ordered pair is a solution of y=x-4?
1. (-1, -5)
2. (1, 3)
3. (-1, 1)
4. (0, -1)
I will award please help
First one is #2
Second one is #1
I'm positive about this
Point A is located at (-5, -8). After it is translated, point A' is located at (-5, -5). What was the translation?
3 units to the right
3 units to the left
3 units up
3 units down
The answer is 3 units up
An element has half life of about 20 days. How much of 3000 gram sample is left after 100 days?
t=100
p=3000
t 1/2 = 20
Try inserting the numbers in the half-life formula.
Answer:
93.75 gm.
Step-by-step explanation:
We have been given that an element has half life of about 20 days. We are asked to find the amount of 3000 gm sample left after 100 days.
We will use half-life formula to solve our given problem.
[tex]A=a\cdot (\frac{1}{2})^{\frac{t}{h}}[/tex], where,
A = Amount left after t units of time,
t = Time,
a = Initial amount,
h = Half-life.
Upon substituting our given values in above formula, we will get:
[tex]A=3000\cdot (\frac{1}{2})^{\frac{100}{20}}[/tex]
[tex]A=3000\cdot (0.5)^{5}[/tex]
[tex]A=3000\cdot 0.03125[/tex]
[tex]A=93.75[/tex]
Therefore, 93.75 gm of sample is left after 100 days.