Answer with explanation:
For any system of linear equations, we can use a method called substitution method for solving the equations.
We make one variable, from either of the equations, the subject of that equation and substitute it in the other equation.
This way, we get to find the value of the remaining variable and next we substitute this value in one of the equations to get the value of the variable left.
Final answer:
To solve linear equations using substitution, identify the unknowns, isolate a variable in one equation, substitute into the other to solve for one variable, then back-substitute to find the other variable and check the solutions for accuracy.
Explanation:
Solving Systems of Linear Equations Using Substitution
To solve a system of linear equations using the substitution method, one must follow a series of steps. Step one is to identify what needs to be determined, which in this case, is the values for the variables, known as the unknowns. In step two, find an equation in the system where one variable can be easily isolated. Next, in step three, express this isolated variable in terms of the other variable.
Once you have this expression, you move to step four, where you substitute this expression into the other equation in the system. This allows you to solve for the one remaining variable, eliminating the need for the original substituted variable. After finding this value, you proceed to step five and substitute it back into the expression from step three to find the value of the other variable.
Step six is an important verification step - checking the solutions. Substitute the values found for both variables back into the original equations to ensure that they satisfy both equations. If they do, you have found the solution to the system. If not, you need to review your steps to find any possible mistakes.
Systems of equations:
3x-5y=8
2x+5y=22
3x-5y=8 2x+5y=22
Solve second equation for x; first subtract 5y from each side.
2x=-5y+22 (Divide by 2)
x=-5/2y+11 (Substitute into x into the first equation)
3 (-5/2y+11)-5y=8 (Simplify )
-15/2y +33-5y=8 (Combine like terms)
-25/2y+ 33=8 -25/2y=-25 (Divide each side by -25)
1/2y=1 y=2 Therefore 3x-5(2)=8 3x-10=8 3x=18 x=6
x=6, y=2
- Hope this helps!
Danielle xo
A gym container holds 50 balls of two sizes and two colors. Twenty-two balls are large and red, 12 balls
are small, and 25 balls are green. How many of the balls are small and green.
Since only 12 balls are small, each color has 25, 22 red balls are large - that leaves 3 red balls that are small. 12 small balls total less the 3 red small balls - that leaves 9 green small balls.
Find the inner product for (7,-2,4).(3,8,1) and state whether the vectors are perpendicular.
Answer:
(7, -2.4). (3,8,1) = 9
The vectors are not perpendicular
Step-by-step explanation:
The inner product between two vectors A = {a, b, c} and B = {d, e, h} is:
[tex]A * B = a * d + b * e + c * h[/tex]
In this case the vectors are (7, -2,4) and (3,8,1). Then the product point is:
[tex](7, -2,4). (3,8,1) = 7 * 3 + (- 2) * 8 + 4 * 1\\\\(7, -2.4). (3,8,1) = 9[/tex]
The dot product between two vectors is equal to zero only if the vectors are perpendicular to each other.
In this case the dot product is nonzero, therefore the vectors are not perpendicular
What is the measure of angle B? Give answer in degrees, round to nearest tenth.
Answer: 48.6 degrees
Step-by-step explanation:
Here we use the sin(-1) which is opp/ hypt. We get the ratio of 3/4 and put in our calculator .75 sin(-1) and get the output 48.59, which is rounded to 48.6.
100% with 8 equal parts
Are you asking what the 8 equal parts are ? If so 100/8=12.5
Dividing 100% into 8 equal parts means each part is 12.5% of the whole, showcasing a basic division of percentages.
The question "100% with 8 equal parts" involves dividing a whole into equal portions, which is a fundamental concept in mathematics. When we talk about 100% as being the whole, dividing it into 8 equal parts means we are essentially finding what 1/8th of this whole is, percentage-wise.
To calculate, we understand that 100% divided by 8 equals 12.5%. Therefore, each part of the 8 equal divisions of the whole is 12.5% of that whole. This is a simple percentage division problem and is relevant in understanding fractions, percentages, and their practical implications in everyday scenarios.
Isabella is bouncing a rubber ball that has a density of 1.5 g/cm3 . The rubber ball has a volume of 113 cm³.
What is the mass of the rubber ball?
Answer:
The mass of the rubber ball is 169.5 g
Step-by-step explanation:
we know that
The density is equal to the ratio of the mass by the volume
D=m/V
Solve for m
m=D*V
In this problem we have
V=113 cm³
D=1.5 g/cm³
substitute
m=1.5*113=169.5 g
This data set represents the number of cups of coffee sold in a café between 8 a.m. and 10 a.m. every day for 14 days.
{10, 9, 6, 12, 4, 6, 7, 8, 15, 14, 12, 9, 10, 5}.
The difference of the values of the first and third quartiles of the data set is
.
Answer:
6
Step-by-step explanation:
The difference between the third quartile and first quartile is known as interquartile range.
The upper quartile is the median of upper half of the data.
The lower quartile is the median of lower half of the data.
Let's arrange in least to greatest:
4,5,6,6,7,8,9,9,10,10,12,12,14,15
The upper half of the data is 9,10,10,12,12,14,15
The median is the 4th number here, so 12. Thus, third quartile = 12
The lower half of the data is 4,5,6,6,7,8,9
The median is the 4th number here, so 6. Thus, first quartile = 6
Interquartile range (difference in third quartile and first quartile) = 12 - 6 = 6
Find the volume of the toy rocket shown. The rocket consists of a prism and a pyramid
Answer: [tex]8.66in^3[/tex]
Step-by-step explanation:
The oy rocket shown is formed by a rectangular prism and a regular pyramid whose base is a square.
The volume of the rectangular prism can be calculated with:
[tex]V_{rp}=l*w*h[/tex]
Where "l" is the length, "w" is the width and "h" is the height.
You can observe that:
[tex]l=8in\\w=1in\\h=1in[/tex]
Then, you can substitute values:
[tex]V_{rp}=(8in)(1in)(1in)=8in^3[/tex]
The volume of the regular square pyramid can be calculated with:
[tex]V_p=\frac{s^2*h}{3}[/tex]
Where "s" is the lenght of a side of the base and "h" is the height of the pyramid.
You can observe in the figure that:
[tex]s=1in\\h=2in[/tex]
Substitute into the formula. Then:
[tex]V_p=\frac{(1in)^2(2in)}{3}=\frac{2}{3}in^3[/tex]
The volume of the toy rocket is the sum of the volume of the rectangular prism and the volume of the regular square pyramid. Then:
[tex]V_{toy}=8in^3+\frac{2}{3}in^3=8.66in^3[/tex]
on the design of the new car the steering wheel has a diameter with endpoints at (4 9) and (12,3) what are the center and raduis of the wheel
Answer:
The center of the circle is point (8 , 6)
Step-by-step explanation:
* At first lets revise how to find the mid-point between two points
- If (x1 , y1) and (x2 , y2) are the end point of a segment
- If (x , y) is the mid-point of this segment
- To find x add x1 and x2, then divide the answer by 2
∴ x = (x1 + x2)/2
- Similar to find y add y1 and y2, then divide the answer by 2
∴ y = (y1 + y2)/2
∴ The mid-point (x , y) = [(x1 + x2)/2 , (y1 + y2)/2]
* Now lets solve the problem
- The center of the circle is the mid-point of the diameter
- Consider the center of the circle is (x , y)
- (x , y) is the mid-point of the diameter of the circle with endpoints
(4 , 9) and (12 , 3)
- Let (4 , 9) is (x1 , y1) and (12 , 3) is (x2 , y2)
∵ x1 = 4
∵ x2 = 12
∵ x = (x1 + x2)/2
∴ x = (4 + 12)/2 = 16/2 = 8
* Similar
∵ y1 = 9
∵ y2 = 3
∵ y = (y1 + y2)/2
∴ y = (9 + 3)/2 = 12/2 = 6
∴ (x , y) = (8 , 6)
* The center of the circle is point (8 , 6)
Answer:
The center is (8,6) and radius is 5 units of the wheel
Step-by-step explanation:
On the design of the new car the steering wheel has a diameter with endpoints at (4 9) and (12,3)
End point of diameter is (4 9) and (12,3)
As we know mid point of diameter is center of circle.
Mid point formula:
[tex](x,y)\rightarrow (\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
Mid point of (4 9) and (12,3)
[tex]Centre: (\dfrac{4+12}{2},\dfrac{9+3}{2}[/tex]
Center: (8,6)
Radius is distance between center and any one end point of diameter.
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
[tex]R=\sqrt{(8-4)^2+(6-9)^2[/tex]
[tex]R=\sqrt{16+9}=\sqrt{25}[/tex]
Radius = 5
Hence, The center is (8,6) and radius is 5 units of the wheel
which of the following represents the graph of f(x)=1/2^x+2
Answer:
Hi! Next time attach all possible answers in media form. Check attachment for the answer. Please mark brainliest I'm trying to get to next rank, have a good day. Message me if you ever need more help.
which statement correctly describes the inverse of the following function
Answer:
Option a
Step-by-step explanation:
A function is a relationship between two sets called domain and co domain where there is one output for every input. If you have more than one output for a particular input, i.e. if the mapping of elements of A to B are not unique, then the quantities represent a relation. A graph of a relationship can be shown to be a function using the vertical line test, which says that at any point if a vertical line makes two intercepts of the curve, the curve cannot be a function.
Given are two sets with {1,2,3,4,5,6} and {2,3,4,5,6,7} where there is a mapping.
We find that while 1,3 have unique mappings 2 does not have an image at all while 4 and 5 have the same image.
Since there is an element in the I set which does not have an image, this cannot be a function.
Option a
3 bags of crisps cost the same as 1 pack of biscuits. Tom paid
the shopkeeper £3 for a pack of biscuits and got 39p change.
What is the cost in pence of 1 bag of crisps?
Show
your
working
Answer:
0.87
Step-by-step explanation:
3 - 0.39 = 2.61
2.61 : 3 = 0.87
To find the cost of one bag of crisps, subtract the change from the amount paid for the biscuits to find the cost of the biscuits in pence, then divide by three since three bags of crisps cost the same as one pack of biscuits. The cost of one bag of crisps is 87 pence.
The student is asking for the cost of one bag of crisps in pence, given that three bags cost the same as one pack of biscuits. Tom paid the shopkeeper £3 for a pack of biscuits and received 39p as change.
First, we calculate the actual cost of the biscuits:
£3 paid - £0.39 change = £2.61 or 261p (since 1 pound equals 100 pence)
Next, we know that this cost is equal to three bags of crisps, so:
261p / 3 bags = 87p per bag
Therefore, the cost of one bag of crisps is 87 pence.
Can someone convert this from hexadecimal??? 8425095
Answer:
[tex]\large\boxed{8425095_{10}=808E87_{16}}[/tex]
Step-by-step explanation:
You divide the given number by 16. Write the result underneath, and the rest of the division on the right.
The number in the hexadecimal system is wrote from the bottom.
10 = A, 11 = B, 12 = C, 13 = D, 14 = E, 15 = F
[tex]\begin{array}{c|c}8425095&7\\526568&8\\32910&14=E\\2056&8\\128&0\\8&8\\0\end{array}\\\\8425095_{10}=808E87_{16}[/tex]
I minimized the steps in the second part. Hope you understand
The graph of which function does not have a y-intercept of (0, 1)?
Answer:
For example, the function [tex]y=x^{2}[/tex] does not have a y-intercept of (0, 1). To prove this, let's make x=0, and if the value of 'y' is different from 1, then, the graph does nt have a y-intercept of (0,1):
[tex]y=x^{2}[/tex] ⇒ [tex]y=(0)^{2}[/tex] ⇒ [tex]y=0[/tex]
Therefore, the y-intercept is at (0, 0) not (0, 1).
Find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of
z0 = 1 + 2i.
a.
5 + 2i, 13 + 2i, 29 + 2i
c.
5 - 2i, 13 - 2i, 29 - 2i
b.
3 + 2i, 17 + 2i, 23 + 2i
d.
3 - 2i, 17 - 2i, 23 - 2i
Please select the best answer from the choices provided
A
B
C
D
Answer:
a. 5 + 2i, 13 + 2i, 29 + 2i
Step-by-step explanation:
We'll use the formula f(z) = 2z + (3 - 2i) for each iteration. The output of the first iteration will be come the input of the second iteration, and so on.
So, we start with z0 = 1 + 2i and we plug that into the base equation:
z0 = 1 + 2i ==> f(z) = 2(1 + 2i) + 3 - 2i = 2 + 4i + 3 - 2i = 5 + 2i
z1 = 5 + 2i ==> f(z) = 2(5 + 2i) + 3 - 2i = 10 + 4i + 3 - 2i = 13 + 2i
z2 = 13 + 2i ==> f(z) = 2(13 + 2i) + 3 - 2i = 26 + 4i + 3 - 2i = 29 + 2i
z3 = 29 + 2i
Answer:a
Step-by-step explanation:
Systematic random sampling is used to interveiw residents in 25% of 80 apartments in a building. The sampling interval would be
A.) 4
B.)20
C.)5
D.)16
The answer is A, A is the answer
The sampling interval would be 20, the correct option is B.
What is a Random Sampling?It is a type of sampling technique in which each sample has an equal probability of being chosen.
The total number of residents in the building is 80.
Random sampling is done and the residents are interviewed.
The percentage of the residents that are being interviewed is 25%.
The sampling interval has to be calculated.
The sampling interval is given by = 25 % of 80
= 25 * 80 / 100
= 20
The number of residents that were interviewed is 20.
The sampling interval is 20 people.
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(1) The Yearling is one of my favorite novels.(2) It is by Marjorie Kinnan Rawlings. (3) It is about a yearling, which is a young deer, or fawn. (4) It takes place in Florida during the 1870s. (5) It has an interesting plot. (6) A boy named Jody finds the yearling during a hunting trip. (7) Jody’s father, Penny, had shot the fawn’s mother without realizing that it had a baby. (8) Jody feels sorry for the orphan and brings it to the family farm. (9) Jody loves his pet, but his parents start to hate it after it begins eating the family’s crops. (10) Penny finally orders Jody to get rid of the deer because it is destructive, but Jody refuses to obey his father.
Which is the most effective way to vary the sentences in the passage?
Start sentences with different parts of speech.
Lengthen sentence 10 by adding detail to it.
Combine sentences 8 and 9.
Yea u have to do that the most effective is the 10 bc penny is right
The Yearling, a novel by Marjorie Kinnan Rawlings, tells of Jody's bond with a deer despite family conflict over crop damage.
Combining sentences 8 and 9:
(8/9) Jody feels sorry for the orphan and brings it to the family farm, but his parents start to hate it after it begins eating the family’s crops.
Starting sentences with different parts of speech:
(1) One of my favorite novels is The Yearling.
(2) By Marjorie Kinnan Rawlings, it captures my imagination.
(3) About a yearling, which is a young deer or fawn, it unfolds.
(4) Taking place in Florida during the 1870s, it immerses readers in its setting.
(5) An interesting plot it possesses.
(6) During a hunting trip, a boy named Jody finds the yearling.
(7) Jody’s father, Penny, had shot the fawn’s mother without realizing that it had a baby.
(8/9) Jody feels sorry for the orphan and brings it to the family farm, but his parents start to hate it after it begins eating the family’s crops.
(10) Finally, Penny orders Jody to get rid of the deer because it is destructive, but Jody refuses to obey his father.
Lengthening sentence 10 by adding detail:
(10) Finally, Penny, frustrated by the relentless destruction wreaked by the deer on their precious crops, sternly orders Jody to get rid of the deer, demanding obedience from his son. However, defying his father's command, Jody adamantly refuses to part ways with his beloved companion.
how to find the volume
Answer: 226200 ft
Step-by-step explanation:
Length=100 ft
Width=58 ft
Height=78 ft
(78x58x100)/2=226200 ft
I know it sounds crazy, but I'm pretty sure that's the answer.
Answer:
[tex]\large\boxed{V=226,200\ ft^3}[/tex]
Step-by-step explanation:
The formula of a volume of a prism:
[tex]V=BH[/tex]
B - area of a base
H - height
We have the triangle in the Base. The fomula of an area of a triangle:
[tex]A_\triangle=\dfrac{bh}{2}[/tex]
b - base
h - height
We have b = 58ft and h = 78ft. Substitute:
[tex]B=\dfrac{(58)(78)}{2}=(29)(78)=2,262\ ft^2[/tex]
The volume:
B = 2,262 ft², H = 100 ft. Substitute:
[tex]V=(2,262)(100)=226,200\ ft^3[/tex]
Fill in the blank: in e^3=____
[tex]\(e^3\)=2.71828[/tex]
In [tex]\(e^3\)[/tex], "e" represents Euler's number, an irrational mathematical constant approximately equal to 2.71828. When raised to the power of 3, [tex]\(e^3\)[/tex] signifies the exponential growth of "e" compounded three times. This can be interpreted as the result of continuously compounding interest or growth at a rate of "e" over three time periods. The expression [tex]\(e^3\)[/tex] calculates the value after three such compounding intervals, showcasing the inherent rapid and self-reinforcing nature of exponential growth. In practical terms, [tex]\(e^3\)[/tex] can represent scenarios where a quantity increases or decreases exponentially, such as population growth, financial investments, or decay processes. Understanding [tex]\(e^3\)[/tex] involves recognizing the profound impact of continuous compounding, making it a fundamental concept in various scientific and mathematical applications.
Need Help For This Question
Answer:
The Answer is B
Step-by-step explanation:
+7 at the end means up 7
The - 4 in the middle represents right 4
These are found using basic rules of translating equations
For this case we have to define function transformation that:
Let k> 0:
To graph [tex]y = f (x) + k,[/tex] the graph is displayed k units up.
To graph[tex]y = f (x) -k[/tex], the graph is displayed k units units down.
Let h> 0:
To graph[tex]y = f (x-h)[/tex], the graph moves units to the right.
To graph [tex]y = f (x + h)[/tex], the graph moves h units to the left.
We have [tex]y = - \sqrt [3] {x}[/tex]
It moves 7 units up and 4 to the right.
So we have to:
[tex]h = 4\\k = 7[/tex]
The shifted graphic is:
[tex]y = - \sqrt [3] {x-4} +7[/tex]
ANswer:
[tex]y = - \sqrt [3] {x-4} +7[/tex]
What is 271,403 rounded to the nearest hundred thousand?
Answer:
300,000
Step-by-step explanation:
Answer:
300,000 is the nearest **hundred thousand.
Step-by-step explanation:
Read as nearest thousand lol.
Mary and Mia are assembling floor lamps. Mary can assemble 10 lamps per hour. Mia can complete 12 lamps per hour. Together, they assemble 600 lamps. Let x = hours worked by Mia and y = hours worked by Mary. If Mia works for 25 hours, how many hours did Mary work?
Answer:
12
Step-by-step explanation:
Mary worked for 30 hours. This is calculated by first determining how many lamps Mia assembled, then subtracting this from the total to find out how many lamps Mary assembled. Finally, we divide the number of lamps assembled by Mary by her rate to find out how many hours she worked.
Explanation:The question requires us to find out how many hours Mary worked if we know that together, Mary and Mia assembled 600 lamps, Mary assembles 10 lamps per hour, Mia assembles 12 lamps per hour, and Mia worked for 25 hours.
First, we can determine how many lamps Mia assembled by multiplying her working hours by her rate, resulting in 300 lamps (12 lamps per hour * 25 hours).
Next, we subtract the number of lamps assembled by Mia from the total to find how many lamps Mary assembled, resulting in 300 lamps (600 lamps total - 300 lamps assembled by Mia).
Finally, we can calculate how many hours Mary worked by dividing the number of lamps she assembled by her rate, resulting in 30 hours (300 lamps / 10 lamps per hour).
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Which is a true statement about any two cords that are the same distance from the center of a circle
Answer:
Probably that they are both the same length!
Answer:
they are congruent
Step-by-step explanation:
please help ASAP! will give brainlist.
What is the value of X line A is parallel to line B and is cut by a transversal?
A. X = 35.
B. X cannot be determined from the information given.
C. X = 19.
D. X = 27.25.
I would personally choose B.
what mixed number is equivalent to 19/6
Answer:
[tex]3 ^{1}/_{6}[/tex]
Step-by-step explanation:
6 goes into 19 3 times with a remainder of 1.
So your base number is going to be 3 with your remainder of 1 going into your numerator over the denominator of six.
ANSWER
[tex]3 \frac{1}{6} [/tex]
EXPLANATION
The given expression is :
[tex] \frac{19}{6} [/tex]
This is an improper fraction because the numerator is greater than the denominator.
To express this as a mixed number find the number of times the denominator will divide the numerator exactly and express the remainder over the denominator in simplest form.
[tex] \frac{19}{6} = 3 \frac{1}{6} [/tex]
15/2g-7=3/5 what is g
[tex] \frac{15}{2} g - 7 = \frac{3}{5} \\ \\ \\ 1. \: \frac{15g}{2} - 7 = \frac{3}{5} \\ 2. \: \frac{15g}{2} = \frac{3}{5} + 7 \\ 3. \: \frac{15g}{2} = \frac{38}{5} \\ 4. \: 15g = \frac{38}{5} \times 2 \\ 5. \: 15g = \frac{76}{5} \\ 6. \: g = \frac{ \frac{76}{5} }{15} \\ 7. \: g = \frac{76}{5 \times 15} \\ 8. \: g = \frac{76}{75} [/tex]
Select ALL the correct answers.
Select all of the equations with a solution of x = 3.
Answer:
A.
C.
D.
Step-by-step explanation:
Answer:
the first, third, and the 4th
Step-by-step explanation:
What is the value of x?
Answer:
15
Step-by-step explanation:
The angle in total is 90* because its a right angle.
The equation is 4x+30=90
subtract 30 from both sides
4x=60
divide 4 from both sides
x=15
hope this helped!
Answer:
15
Step-by-step explanation: 90-30=60 60÷4=15
Kevin is making a set of candles to give as a gift. The first candle is a triangular prism with a height of 17 centimeters. The base is a triangle with two angles measuring 90 degrees and 65 degrees. What is the measure of the third angle? Show work
Answer:
The measure of the third angle is 25°
Step-by-step explanation:
we know that
The sum of the internal angles of a triangle must be equal to 180 degrees
so
Let
x----> the measure of the third angle
90°+65°+x=180°
Solve for x
155°+x=180°
x=180°-155°
x=25°
There are 10 dogs at the dog park on a busy Saturday. 2 of them are pugs.
What is the probability that a randomly selected dog is a pug?
Simplify your answer and write it as a fraction or whole number.
P(pug) =
Answer:
1/5
Step-by-step explanation:
2/10 chance that a pug would be selected
2/10 is simplified to 1/5
The probability that a randomly selected dog is a pug is 1/5.
What is a Probability?It is a ratio of number of required outcomes to the total outcomes.It is usually used to predict the outcome of any event.It is very useful in solving mathematical problems.Given:
There are 10 dogs at the dog park.
2 dogs are pugs.
We have to find the probability that a randomly selected dog is a pug.
We know, probability is given by:
⇒ Probability = Total number of dogs which are pug / Total number of dogs at the park
⇒ Total number of dogs which are pug = 2
⇒ Total number of dogs at the park = 10
⇒ P(pug) = 2/10
⇒ P(pug) = 1/5
Therefore, the probability that a randomly selected dog is a pug is 1/5.
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