Final answer:
The solution to the given system of equations is x=3 and x=-7. To find the solution, set the expressions for y equal to each other, combine like terms, and solve for x. Substitute the values of x back into one of the original equations to find the corresponding y value.
Explanation:
The solution to the given system of equations is x = 3 and x = -7.
To find the solution, we can set the expressions for y equal to each other:
2x + 3 = -3x + 3
Combine like terms:
5x = 0
Divide both sides by 5:
x = 0/5
x = 0
Substitute x = 0 back into either of the original equations to find the corresponding y value:
y = 2(0) + 3
y = 0 + 3
y = 3
The solution to the system of equations is (0, 3).
what is the relationship between angle 1 and angle 5
Answer:
○ b Corresponding Angles
Step-by-step explanation:
These two angles are a mirror, so they correspond.
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Angle 1 and angle 5 are alternate interior angles with the same measure.
Explanation:Angle 1 and angle 5 are alternate interior angles formed by a transversal line intersecting two parallel lines. Alternate interior angles are equal in measure, which means that angle 1 and angle 5 have the same measure. This relationship holds true regardless of the specific measurements of angle 1 and angle 5.
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Which ordered pair is a solution of the equation? X+7y=17
Answer:
Both (10,1) and (-4,3)
Step-by-step explanation:
No need but hope it helps:D
Answer:
C
Step-by-step explanation:
if it is on khan this answer is right
The product of 8, and a number increased by 6, is 104. What is the number?
Answer:
Step-by-step explanation:
Its 56/8 or 7
The value of the number is 7 . There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
What is meant by equation?Two expressions joined by the equals symbol ("=") form an equation. [2] The "left hand side" and "right hand side" of the equation are the expressions on either side of the equals sign. The right side of an equation is frequently considered to be zero. Providing the generality is not diminished, this can be achieved by deducting the right-hand side from both sides.
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Given ,
product =8
increased number =6
8(x+6)=104
8x+48= 104
8x = 104 - 48 =56
x = 56/8
= 7
Therefore The value of the number is 7.
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The planet Mars has two moons – Phobos and Deimos. Phobos has a mass of 10.8 × 1015 kilograms, and Deimos has a mass of 2.0 × 1015 kilograms. How much greater is the mass of Phobos than the mass of Deimos?
A) 8.8 × 1015 kilograms
B) 8.8 × 1016 kilograms
C) 9.2 × 1014 kilograms
Eliminate
D) 9.2 × 1015 kilograms
A) 8.8 × 10^15 kilograms is the right answer
Step-by-step explanation:
Given
Mass of Phobos = [tex]10.8 * 10^{15}\ kg[/tex]
Mass of Deimos = [tex]2.0 * 10^{15}\ kg[/tex]
In order to find how greater is the mass of Phobos from Deimos, the smaller mass will be subtracted from the larger mass
So,
[tex]= 10.8*10^{15} - (2.0*10^{15})[/tex]
As the exponents are same, the numbers can be subtracted directly
[tex]=(10.8-2.0) * 10^{15}\\= 8.8*10^{15}\ kg[/tex]
Hence,
A) 8.8 × 10^15 kilograms is the right answer
Keywords: Exponents, Addition
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Victoria had $200 in her account at the end of one year. At the first of each subsequent year she deposits $15 into the account
and earns 2% interest on the new balance, compounded annually. Which recursive formula represents the total amount of
money in Victoria's account at the end of the nth year?
a, - 1.02( a -1 +15), aq - 215
an - 15+1.02a -1, 2, - 215
2,- 1.02(an-1 +15); a, - 200
an = 15+1.02am-11 an - 200
Answer:
The amount of money in Victoria's account at the end of n-th year will be,
$ [tex] (965 \times (1.02)^{(n -1)} - 765)[/tex]
Step-by-step explanation:
The amount of money in Victoria's account at the end of n-th year will be,
$ [tex](200\times (1.02)^{(n-1)} + 15 \times ((1.02)^{(n-1)} + (1.02)^{(n -2)} + (1.02)^{(n-3)} + ........ + (1.02)))[/tex]
= $ [tex](200 \times (1.02)^{(n -1)} + 15 \times \frac{1.02 \times ((1.02)^{(n-1)} - 1)}{0.02})[/tex]
= $ [tex](200 \times (1.02)^{(n -1)} + 15 \times 51 \times ((1.02)^{(n-1)} - 1))[/tex]
= $ [tex] (965 \times (1.02)^{(n -1)} - 765)[/tex]
Since, the interest is compounded over that $ 200 (which was there in the account at the end of 1st year) for (n-1) years and for (n-1) years, (n-2) years, (n -3) years, ...... 1 year respectively over those $ 15 which are deposited in the account at the end of 1 , 2, 3, ...... (n-1) years.
Answer:
[tex]a_{n}=\left [ a\left ( n-1 \right )+15 \right ]*1.02\\[/tex]
Step-by-step explanation:
1) A Recursive formula always makes reference to the previous term, written as a function.
2) From $200 to $215 there was a 7.5% growth, so since the question states that from the beginning of the second year there will be a regular growth.
3) Since it is 2% of interest compounded annually q=1+ 0.02.
[tex]A=215(1+\frac{0.02}{1})^{1}\\A=219.3[/tex]
Or simply
215*1.02=219.3
4) We can write a Recursive formula this way:
[tex]a(n)=215[/tex]
[tex]a(n)=a(n-1)(1.02)[/tex]
5) But since we have a pattern, She will deposit $15 yearly then we must make a little adjustment then add $15. to that. Considering the first term to be 200
[tex]a_{n}=\left [ a\left ( n-1 \right )+15 \right ]*1.02\\a_{1}=200[/tex]
Write the equation in function form
6y - 4x = 24
Answer:
f(x) = (2/3)x + 4
Step-by-step explanation:
An equation in function is found by isolating y, and changing "y" to "f(x)".
Isolate y by moving everything else to the other side
What is done to one side must be done to the other
6y - 4x = 24
6y - 4x + 4x = 24 + 4x (add 4x to both sides. -4x +4x cancels out)
6y = 24 + 4x
6y/6 = 24/6 + 4x/6 (divide both sides by 6)
y = 4 + (2/3)x (simplify)
y = (2/3)x + 4 (rearrange to a familiar format "y=mx+b")
f(x) = (2/3)x + 4 (replace y with f(x))
a buyer spend $164 for two loads of mulch at $22.50 per load $35 worth of flowers and 42 landscaping blocks. fine the cost per block
Answer:
The cost per block was about 45$
Step-by-step explanation:
I think so, but dont believe it... I may be wrong. Please mark me brainliest
The buyer spent $2 per landscaping block.
Explanation:Firstly, we need to find out how much money was spent on the landscaping blocks. Given that the buyer spent $164 for two loads of mulch at $22.50 per load and $35 worth of flowers, subtract the total cost of the mulch and flowers from the total amount spent. This gives us:
($22.50 x 2) + $35 =$80 spent on mulch and flowers. Therefore, $164 - $80 = $84 spent on landscaping blocks.
Finally, find the cost per block, by dividing the total amount spent on blocks by the number of blocks. So, $84 / 42 blocks = $2 per block.
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Danielle walked from her house to several locations in her town. The graph represents her distance from home after x hours.
a.How far from home was Danielle after 1/2 hour?
b.What was Danielle's speed between 0 and 1 hour?
c.What was Danielle's speed between 1 and 2 hours?
d.What is the domain when the function is increasing?
e.What is the domain when the function is decreasing?
f.What is the domain when the function is constant?
Graph down below
PLEASE HELP ASAP!!!
Answer:
The answer for A. Would be 1 mile B. 2mph C. 4mph and the rest Im still working on
Step-by-step explanation:
Answer:
a. How far from home was Danielle after 1/2 hour?According to the graph, after half hour, Danielle was 1 mile far from home.
b. What was Danielle's speed between 0 and 1 hour?To find the speed we have to apply the formula:
[tex]s=\frac{\Delta d}{\Delta t}[/tex]
From [tex]t=0[/tex] and [tex]t=1[/tex], Danielle went from [tex]d=0[/tex] to [tex]d=2[/tex]. Replacing this values, we calculate the speed:
[tex]s=\frac{\Delta d}{\Delta t}\\s=\frac{2-0}{1-0}=2[/tex]
Therefore, the speed between 0 and 1 hour is 2 miles per hour.
c. What was Danielle's speed between 1 and 2 hours?The Danielle's speed between 1 and 2 hours is zero ([tex]s=0[/tex]). Because, according to the graph, during this time, Danielle didn't move, and without move, there's no speed.
d. What is the domain when the function is increasing?The domain when the function is increasing refers to the increasing x intervals.
From the graph, this increasing interval is from 0 to 1 hours only, it's the only period of time when Danielle was increasing her position.
e. What is the domain when the function is decreasing?The parts of the decreasing domain are:
From 2 to 3 hours.From 3 and a half to 4 hours.In the graph, you can see these decreasing intervals, which are characterized by a downwards direction of the line.
f. What is the domain when the function is constant?The parts where the function is constant:
From 1 to 2 hours.From 3 to 3 and a half hours.Constant intervals, means no increase, no decrease, just an horizontal line.
Need help with geometric sequences quick
30 points!!!!!!!!
Answer:
Step-by-step explanation:
2.5 \dfrac{\text{g}}{\text{cm}^3}2.5 cm 3 g 2, point, 5, start fraction, start text, g, end text, divided by, start text, c, m, end text, cubed, end fraction.
Answer:
bojdsvj
Step-by-step explanation:dvsDV
I sorry lol i need points :/
Order the integers from least to greatest 11 , 0, -8, 9, 3
Answer:
The answer is -8, 0, 3, 9, 11
Answer:
-8, 0, 3, 9, 11
Step-by-step explanation:
Round 67,492,384 to the nearest million
The next higher million is 68 million.
The next lower million is 67 million.
67,492,384 is closer to 67 million than to 68 million.
So the nearest million is 67,000,000 .
To round 67,492,384 to the nearest million, round the millions place up by 1 because the digit to its right is 7.
To round 67,492,384 to the nearest million, we need to consider the digits in the millions place and the digit to its right. In this case, the digit in the millions place is 6, and the digit to its right is 7. Since 7 is greater than or equal to 5, we round the millions place up by 1. Therefore, 67,492,384 rounded to the nearest million is 68,000,000.
Please help me and please use substitution
4x - y = 18
-8x – 2y = 4
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2. What elevation is Point E on Map 1? *
10 feet
30 feet
50 feet
70 feet
3. What elevation is Point F on Map 1? *
10 feet
30 feet
50 feet
70 feet
Answer:
2. 30 ft
3. 50 ft.
Step-by-step explanation:
2. The contour map of a place is shown in the diagram.
The point E is placed near to the 30 ft contour line.
Therefore, the elevation of the point E on the map is 30 ft. (Answer)
3. From the same contour map shown in the diagram, it is clear that,
The point F is placed near to the 50 ft contour line.
Therefore, the elevation of the point F on the map is 50 ft. (Answer)
Amanda wants to know if the teenagers in her town like a new Friday night bowling event.
Answer:
C
Step-by-step explanation:
Answer choice A and B are biased towards No answers because they point out flaws with the event. Choice D is not biased because it doesn't discuss good or bad aspects of the event.
As per the question the teenagers in Amanda's town like to watch the bowling event every new Friday night.
This can be known by sentence C that states that you like the new Friday night bowling event with free snacks and lives music. As this response is most likely to trigger a yes.Hence the option C is correct.
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Question 5
Which set of coordinates represents a function?
(x, y)
(-2, 4)
(-1, 1)
(0,0)
(-1,-1)
(-2,-4)
(x, y)
(0,5)
(1, 10)
(2, 15)
(3, 20)
(4, 25)
(x, y)
(0,0)
(3, 3)
(3,-3)
(5,5)
(5, -5)
(x, y)
(1, 1)
(1,2)
(1, 3)
(1,4)
(1,5)
Answer:
Im guessing every time (x,y) comes, it starts a new set
Step-by-step explanation:
In that case,
(x, y)
(0,5)
(1, 10)
(2, 15)
(3, 20)
(4, 25)
is the correct set
4. What is the largest number of identical cubes whose volumes are whole numbers (1,2,3,...) that would fit in a cube
whose volume is 1080 cm3? Show all your work.
Answer:
The largest number of identical cubes whose volumes are whole numbers that would fit in a cube of volume 1080 [tex]cm^{3}[/tex] is 10.
Step-by-step explanation:
Given that volume of larger cube is 1080[tex]cm^{3}[/tex]
To find number of smaller cube with volume as whole numbers can fit the larger cube:
Imagine Rubik's cube of 3x3 as larger volume and one piece of Rubik's cube is smaller cube. On one edge, three smaller cube with volume
In the same way,
Assuming one edge has 'x' number of cube with volume as whole numbers
Since, It is cube. Number of cube in other edges will be 'x' too
For smaller cube,
Take one side of smaller cube as x
Therefore, One side of larger cube will be nx
For cube, length = height = breath =nx
The volume of larger cube : [tex](nx)^{3} =1080[/tex]
nx=10.2598cm
we need to find the "largest" number of cube( i.e n )
Therefore, Side x will be smallest and n will be largest.
For smallest value of x,
It is also said that " volumes are whole numbers "
smallest whole number is 1
Thus,
nx=10.2598cm
n=10.2598
n is also whole number so that n=10
The largest number of identical cubes whose volumes are whole numbers that would fit in a cube of volume 1080 [tex]cm^{3}[/tex] is 10.
PLEASE PLEASE PLEASE ANSWER!!
Sarah wants to make a quilt that is 6 feet wide and 8 feet long. She is patching together 4- inch sided squares of fabric to make the quilt. How many patches of fabric will Sarah need?
A.) 120 patches
B.) 216 patches
C.) 432 patches
D.) 1,728 patches
Answer:
The answer is D brother
Step-by-step explanation:
First, convert the 6 by 8 into inches: 96 by 72 which equals 6912. Now take 6912 and divide it by 4 (for the individual squars) and you get: 1728
A = L x W
A= 8 x 6
A= 96 x 72
96 x 72 = 6912
6912 / 4" = 1728
If your teachers mean like mine, they make you write it out like this:)
Hope that clears it up:)
By taking the quotient between the area of the quilt and the area of a single patch, we will see that she needs 432 patches.
How many patches does she need?
To get this, we need to find the quotient between the surface area of the quilt and the area of a patch.
The quilt is 6ft by 8ft, then the area is:
A = 6ft*8ft = 48ft^2
Remember that:
1ft = 12 in
1ft^2 = (12 in)^2 = 144 in^2
Then the area in square inches is:
A = 48ft^2 = 48*(144 in^2) = 6,912 in^2
Now, the patches are squares of sidelength of 4 inches, then the area of each patch is:
a = (4 in)^2 = 16 in^2
The quotient between the areas gives:
A/a = (6,912 in^2)/(16 in^2) =432
This means that Sarah needs 432 patches, so the correct option is C.
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you run 10 miles in 1 hour and 15 mintues keeping the same pance how long would it take to run 15miles
Answer:
1 hour and 30 minutes
Step-by-step explanation:
because it took an hour for 10 mile so add another five miles and it would take 30 minutes
Answer:
it would take you 1 hour and 30 mins
Step-by-step explanation:
it would be that because 1 hour is 60 mins and it takes you 60 mins to run 1 mile add half a mil and then it would be 1 hr 30
How many cubes with side lengths of 1/2 cm does it take to fill the prism? Height: 3/2 cm Width:1 cm length: 2 cm
Answer:
24
Step-by-step explanation:
If we want to cover the base of the prism having dimensions 2 cm × 1 cm with [tex]\frac{1}{2}[/tex] cm length of cube, then there will be (4 × 2) = 8 cubes that can occupy the base.
Width is 1 cm, so there can fit 2 cubes of length [tex]\frac{1}{2}[/tex] cm and length is 2 cm, where 4 cubes of length [tex]\frac{1}{2}[/tex] cm can fit. So, in total (4 × 2) = 8 cubes of [tex]\frac{1}{2}[/tex] cm length.
Now, height of the prism is [tex]\frac{3}{2}[/tex] cm where 3 cubes of length [tex]\frac{1}{2}[/tex] cm can fit.
Therefore, in total there can be (8 × 3) = 24 cubes of [tex]\frac{1}{2}[/tex] cm length. (Answer)
Answer:
24 cubes
Step-by-step explanation:
Please see the pictures below:
(I hope this helped! :) )
John has $8 in his bank account when he gets a job. He begins making $80 a day. A student found that
the equation that represents this situation is y = 8x + 80.
What is wrong with the student's equation? Complete the explanation and correct the student's error.
Answer:
y = 8 + 80x
Step-by-step explanation:
Given,
The equation is, y = 8x + 80
It is the wrong equation. Because John has $8 in his bank when he gets a job. It means it is fixed. On the other hand, since he begins earning $80 per day. It becomes variable earnings for him. We know that variables (x, y, z) are multiplied by the variable number (If there is no value for variables). Therefore, the equation will be =
As $8 is fixed and $80 is a variable earnings,
y = 8 + 80x
Here, x represents the number of days John will work. If he works for 20 days, the value will be changed for the number of days he earns. The fixed amount will never be changed.
The inequality of the graph
Answer:
[tex]\displaystyle y > 4x - 2[/tex]
Step-by-step explanation:
Starting from the y-intercept of [tex]\displaystyle [0, -2],[/tex]you do [tex]\displaystyle \frac{rise}{run}[/tex]by either moving four blocks south over one block west or four blocks north over one block east [west and south are negatives]. Next, we have to determine the types of inequality symbols that are suitable for this graph, which will be less than and greater than since this is a dashed line graph. We then use the zero-interval test [test point (0, 0)] to ensure whether we shade the opposite portion [portion that does not contain the origin] or the portion that DOES contain the origin. At this step, we must verify the inequalities as false or true:
Greater than
[tex]\displaystyle 0 > 4[0] - 2 → 0 > -2[/tex]☑
Less than
[tex]\displaystyle 0 < 4[0] - 2 → 0 ≮ -2[/tex]
This graph is shaded in the portion of the origin, so you would choose the greater than inequality symbol to get this inequality:
[tex]\displaystyle y > 4x - 2[/tex]
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A collection of dimes and quarters is worth $10.45. There are 70 coins in all. Find how many of each there are
There are 47 dimes and 23 quarters.
Step-by-step explanation:
Total amount = $10.45 = 10.45*100 = 1045 cents
Total coins = 70
1 dime = 10 cents
1 quarter = 25 cents
Let,
Dimes = x
Quarters = y
According to given statement;
x+y=70 Eqn 1
10x+25y=1045 Eqn 2
Multiplying Eqn 1 by 10;
[tex]10(x+y=70)\\10x+10y=700\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](10x+25y)-(10x+10y)=1045-700\\10x+25y-10x-10y=345\\15y=345[/tex]
Dividing both sides by 15;
[tex]\frac{15y}{15}=\frac{345}{15}\\y=23[/tex]
Putting y=23 in Eqn 1
[tex]x+23=70\\x=70-23\\x=47[/tex]
There are 47 dimes and 23 quarters.
Keywords: linear equations, subtraction
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7x-3y = 10
-3x-8y= 5
ABCD is a trapezoid with mid-segment (E f). If Ad=5x-11, E f=3x+7, Bc=2x+7, how many units in length is (E f) i need equation, algebra procedures, value of x, and length of (E f)
Answer:
x = 18
Step-by-step explanation:
The length of the midsection is the sum of the two bases divided by 2. Remember that the bases of a trapezoid are the two parallel sides. So that means:
((5x - 11) + (2x + 7)) /2 = 3x + 7
Simplify ((5x - 11) + (2x + 7)) /2:
(5x - 11) + (2x + 7) /2 = (5x + 2x - 11 + 7) /2 = (7x - 4) /2
Therefore:
(7x - 4) /2 = 3x + 7
Now solve this simultaneous equation:
7x - 4 = 6x + 14
7x = 6x + 18
x = 18
Is (-3,2)(−3,2) a solution of -4x -10y < -9−4x−10y
Answer:
No
Step-by-step explanation:
-4(-3)-10(2)=-8
-9-4(-3)-10(2)=-17
-8>-17
Can someone check on this problem if I did it right this problem is about law of cosines just look at #1
Answer:
x = 5.57
Step-by-step explanation:
c² = a² + b² − 2ab cos C
x² = 10² + 6² − 2(10)(6) cos 29°
x = 5.57
Your answer and steps are correct.
Brian went shopping and spent $47 on jewelry. If he spent $67 total, what percentage did he spend on jewelry? Round your answer to the nearest percent.
Brian spent 70% of his money on jewelry.
Step-by-step explanation:
Given,
Amount spent on jewelry = $47
Total amount spent = $67
Percentage of jewelry = [tex]\frac{amount\ spent\ on\ jewelry}{total\amount\ spent}*100[/tex]
[tex]Percentage\ of\ jewelry=\frac{47}{67}*100\\\\ Percentage\ of\ jewelry=\frac{4700}{67}\\Percentage\ of\ jewelry= 70.14\%[/tex]
Rounding to nearest whole number.
Percentage of jewelry = 70%
Brian spent 70% of his money on jewelry.
Keywords: percentage, division
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(x2 - 4x + 3) + (3x2 – 3x - 5)
What’s the difference in standard form?
Answer:
the different is 96 * 56
Step-by-step explanation:
for example
4555/69 ///////54
Answer: (x-2)•(4x+1)
Step-by-step explanation:
2/5(10x+15)=26 solve for x
Answer:
x=5
Step-by-step explanation:
2/5(10x+15)=26
10x+15=26/(2/5)
10x+15=(26/1)(5/2)
10x+15=130/2
10x+15=65
10x=65-15
10x=50
x=50/10
x=5
Answer:
x=5
Step-by-step explanation: