Answer:
x=29 and y=53
Step-by-step explanation:
let y=3x-34 be the first equation (1) and y=2x-5 be the second equation (2)
Using the elimation method, (1)-(2): 0=x-29
-x=-29
x=29
Substitute x=29 into (2),
y=2(29)-5
y=58-5
y=53
So, x=29 and y=53
What is the slope of the line shown below?
Answer: -3/2
yeah use rise over run
Answer:
-2/3
Step-by-step explanation:
slope = rise/run
First find the y-intercept (point of crossing on the y-axis (the vertical one)), then find the next point that intercepts a box PERFECTLY, this next point is (4, -2)
Looking at the y-intercept's coordinates (0,1), count how many blocks down it takes to get to to 4 (2 blocks which is the RISE) and now count how many blocks to the right it takes to get to -2 (3 blocks)
Therefore it is 2/3 but it is also negative because it is going DOWN from left to right which is a negative decine
"x/3" is division
x/3 - 4 = -6
what does x equal?
Answer:
x = -6
Step-by-step explanation:
-6/3-4= -6
(8x + 6) - (x + 4).
Pls help with this and explain why it is wrong
The simplified form in base 3 for ln(3) + ln(9) is 3ln(3)
What is logarithm?logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if b^x = n, in which case one writes x = logb n.
In(9) can be written as ln3^2
which according law of logarithm is 2ln(3)
Expression becomes
ln(3) + 2ln(3) which is 3ln(3)
In conclusion, the simplified form of the expression in base 3 is 3ln(3)
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Solve for all values of x by factoring x2-53=-4
The values of x in the given equation, x² - 5x = -4, are x = 4 and x = 1
Solving Quadratic equations: Determining the values of xFrom the question, we are to solve the given equation by factoring
The given equation is
x² - 5x = -4
To solve the equation by factoring, transfer the constant to the other side of the equation
x² - 5x + 4 = 0
Factorize the left hand side expression
x² -x -4x + 4 = 0
x(x - 1) -4(x -1) = 0
(x - 4)(x - 1) = 0
x - 4 = 0 OR x - 1 = 0
x = 4 OR x = 1
Hence, the values of x are 4 and 1
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Kevin and Randy Muise have a jar containing 83 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $12.95. How many of each type of coin do they have?
The amounts of each type of coin that they have is given as follows:
Quarters: 44.Nickels: 39.How to obtain the amounts?The amounts of each type of coin are obtained using a system of equations, in which the variables are given as follows:
Variable x: amount of quarters.Variable y: amount of nickels.Kevin and Randy Muise have a jar containing 83 coins, hence:
x + y = 83.
The value of a nickel is of $0.05, while the value of a quarter is of $0.25. The total value of the coins in the jar is $12.95, hence:
0.25x + 0.05y = 12.95.
From the first equation, we have that:
y = 83 - x.
Replacing on the second equation, the amount of quarters is given as follows:
0.25x + 0.05(83 - x) = 12.95
0.2x = 8.8
x = 8.8/0.2
x = 44.
Then the amount of nickels is given as follows:
y = 83 - x = 83 - 44 = 39.
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How much must you deposit now in order to have $25,000 in 4 years in an account getting 5% interest compounded daily
There are $20468.55 must you deposit now in order to have $25,000 in 4 years in an account getting 5% interest compounded daily.
What is compound interest?
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Given:
A = Final amount = $25000
P = Initial principle balance
r = interest rate = 5% = 0.05
t = Number of time of years
n = number of times interest applied per time period = 365
Since, the formula for compound interest,
[tex]A = P(1+\frac{r}{n})^n^t[/tex]
Plug the values of A, r, n and t in the above formula
[tex]25000 = P(1 + \frac{0.05}{365})^3^6^5^*^4 \\25000 = P(1.0001369863)^1^4^6^0\\25000 = P(1.2213860258)\\P = 20,468.549231702[/tex]
P ≈ 20,468.55
Hence, there are $20468.55 must you deposit now in order to have $25,000 in 4 years in an account getting 5% interest compounded daily.
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1. The population of a town was 7420 in 2010. The population grows at a rate of 2.3% annually. (a) Use the exponential growth model to write an equation that estimates the population t years after 2010. (b) Estimate the population of the town in 2022. Show your work.
Hello,
I hope you and your family are doing well!
(a) The exponential growth model is given by the equation P(t) = P0 * r^t, where P(t) is the population t years after 2010, P0 is the population in 2010 (7420), and r is the annual growth rate (2.3%).
Substituting the given values into the equation gives us:
P(t) = 7420 * 1.023^t
This is the equation that estimates the population t years after 2010.
(b) To estimate the population of the town in 2022, we can substitute t = 12 into the equation:
P(12) = 7420 * 1.023^12
Calculating this gives us:
P(12) = 7420 * 1.023^12 = 7420 * 1.291891 = 9593.45
So the estimated population of the town in 2022 is approximately 9593
Happy to help!
bowl o rama charges 2.50 a game plus 2 for shoe rental, and bowling pinz charges 2 a game plus 4 for shoe rental. how many games must be played for the cost to be the same at both places? Define variables and solve the system of equations
The number of games that must be played for the cost to be the same at both places is 4.
How to solve system of equations?Bowl o rama charges 2.50 a game plus 2 for shoe rental, and bowling pinz charges 2 a game plus 4 for shoe rental.
The number of games that must be played for the cost to be the same at both places is as follows:
Using system of equation,
let
x = number of games
Hence,
2.50x + 2 = 2x + 4
2.50x - 2x = 4 - 2
0.5x = 2
divide both sides by 0.5
x = 2 / 0.5
x = 4
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Which lines are perpendicular to 3x – y = 10? Select all that apply.
A. y = 3x + 5
B. y = –13x + 17
C. x + 3y = 27
D. y – 2 = 13(3x + 36)
C. x + 3y = 27 lines are perpendicular to 3x – y = 10
What is the lines?A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. In a two-dimensional plane, it is specified by two points. The term "collinear points" refers to two points that are on the same line.
As we know,
When two lines are perpendicular then the product of their slope is -1.
The slope is given by: y = mx+c
where, m is the slope.
Thus, the given equation:
3x – y = 10
y = 3x - 10
Comparing this equation with y = mx+c, we get
m₁ = 3
So, the slope of the given equation (m₁) = 3
Now find slope of others lines:
A) y = 3x + 5, Comparing this equation with y = mx+c, we get -
m₂ = 3
When two lines are perpendicular then the product of their slope is -1.
Here, product of the slope is:
= m₁ × m₂
= 3×3 (putting the values we get)
= 9 ≠ -1
So, this line is not perpendicular to given line.
B) y = –13x + 17, Comparing this equation with y = mx+c, we get -
m₃ = -13
When two lines are perpendicular then the product of their slope is -1.
Here, product of the slope is:
= m₁ × m₃
= 3× (-13) (putting the values we get)
= -39 ≠ -1
So, this line is not perpendicular to given line.
C) x + 3y = 27
3y = 27 - x
y = 9 - x/3, Comparing this equation with y = mx+c, we get -
m₄ = -1/3
When two lines are perpendicular then the product of their slope is -1.
Here, product of the slope is:
= m₁ × m₄
= 3× (-1/3) (putting the values we get)
= - 1
So, this line is perpendicular to given line.
D) y – 2 = 13(3x + 36)
y = 39x +470, Comparing this equation with y = mx+c, we get -
So, m₅ = 39
When two lines are perpendicular then the product of their slope is -1.
Here, product of the slope is:
= m₁ × m₅
= 3× (39) (putting the values we get)
= 117 ≠ -1
So, this line is not perpendicular to given line.
Therefore, option C is correct.
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Find tanθ + sinθ for the angle θ shown in the right triangle?
12.6
Step-by-step explanation:
We need to find the hypotenuse
hyp² = opp² + adj²
hyp²= 2² + 3²
hyp²= 4 + 9
hyp²= 13
hyp=√13
hyp=3.6
sinθ=opp/hyp
sinθ=2/3.6
sinθ=5.6
cosθ=adj/hyp
cosθ=3/3.6
cosθ= 0.8
tan θ=sinθ/cosθ
tanθ= 5.6/0.8
tanθ=7
tan θ+sinθ
=7+5.6
=12.6
find the total surface area of this triangular prism
The total surface area of this triangular prism = 976
What is surface area?Surface area is the amount of space covering the outside of a three-dimensional shape.
A triangle would be divided in half, but since there are two, the ratio would remain the same.
14 x 24 = 336
10 x 25 = 250[ because there are two of them, multiply by 2.]
10 x 14 = 140
The total surface area of this triangular prism = 336 + 250 + 140
= 976
Therefore, the total surface area of this triangular prism = 976
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t a student government fundraiser, a notebook costs $7 and a t-shirt costs $12. If the total received for 60 items was $540, how many notebooks were sold?
The number of notebook is 36.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the notebook be n.
Let the t shirt be t.
The equation will be:
n + t = 60 ..... i
7n + 12t = 540 ..... ii
From I n = 60 - t ..... iii
Put equation III into ii
7n + + 12t = 540 .
7(60 - t) + 12t = 540
420 - 7t + 12t = 540
5t = 540 - 420
5t = 120
Divide
t = 120 / 5
t = 24
Notebook will be:
= 60 - 24
= 36
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help meeeeeeeeeee pleaseee
The number of acres owned for which the average intake is 2200 calories per day is 2 acres obtained by the algebraic expression that relates the acres of land and the calories per day.
What is an algebraic expression?An algebraic expression is formed by variables, constants, and arithmetic operations.An algebraic expression provides the relation between the input and output variables i.e., x and f(x) respectively.Calculation:It is given that, the number of calories consumed daily by a person owing x acres of land is given by the algebraic expression,
C(x) = 270 ln(x+1) + 1900
The average intake of calories consumed per day is given by C(x) = 2200
Here x is the number of acres of land. Then, the required number of acres of land is
C(x) = 270 ln(x+1) + 1900
⇒ 2200 = 270 ln(x+1) + 1900
⇒ 270 ln(x+1) = 2200 - 1900
⇒ 270 ln(x+1) = 300
⇒ ln(x+1) = 300/270 = 10/9
Applying base 'e' on both sides, we get
⇒ (x+1) = [tex]e^\frac{10}{9}[/tex]
⇒ x+1 = 3.0377
⇒ x = 3.0377 - 1 = 2.0377
When rounding the final answer to the nearest tenths, we get x = 2 acres.
When rounding the final answer to the nearest thousand, we get x = 2.038 acres.
Thus, for an average intake of 2200 calories per day, the number of acres of land owned is approximately 2 acres.
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If $300 is invested at an interest rate of 2.5% per year, find the amount of the investment at the end of 10 years for the
following compounding methods. (Round your answers to the nearest cent.)
(a) Annually
$
(b) Semiannually
$
(c) Quarterly
$
(d) Continuously
Parking Spaces múltipl
5. My sister and I wanted to go to the circus. A ticket was 10% less on a Tuesday than it was on a Saturday. We paid $27 each to attend Tuesday's show. What would our total cost have been had we attended the circus on Saturday?
Hello,
I hope you and your family are doing well!
If a ticket to the circus was 10% less on a Tuesday than it was on a Saturday, then it was 90% of the Saturday ticket price. If you paid $27 each to attend Tuesday's show, then the Saturday ticket price was $27 / 0.9 = $30.
Since you bought two tickets, the total cost of attending the circus on Saturday would have been 2 * $30 =60
Therefore, your total cost would have been $60 had you attended the circus on Saturday.
Please rate this answer 5 stars and brainliest if you find it helpful.
Happy Holidays and New Year!
Which compound inequality has no solution? x ≤ –2 and 2x ≥ 6 x ≤ –1 and 5x ≤ 5 x ≤ –1 and 3x ≥ –3 x ≤ –2 and 4x ≤ –8
The correct inequality which has no solution will be;
⇒ x ≤ –2 and 2x ≥ 6
⇒ x ≤ –1 and 5x ≤ 5
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
There are some inequality is shown.
Now,
Find the inequality which has no solution as;
a) x ≤ –2 and 2x ≥ 6
⇒ x ≤ - 2
⇒ 2x ≥ 6 = x ≥ 6/2 = x ≥ 3
We get;
⇒ x ≤ - 2 and x ≥ 3
Which is not possible.
Hence, it has no solution.
b) x ≤ –1 and 5x ≤ 5
⇒ x ≤ - 1
⇒ 5x ≤ 5 = x ≤ 1
We get;
⇒ x ≤ - 1 and x ≤ 1
Which is not possible.
Hence, it has no solution.
c) x ≤ –1 and 3x ≥ –3
⇒ x ≤ - 1
⇒ 3x ≥ - 3 = x ≥ - 1
We get;
⇒ x ≤ - 1 and x ≥ - 1 ⇒ x = - 1
Thus, It has solution.
d) x ≤ –2 and 4x ≤ –8
⇒ x ≤ –2 and
⇒ 4x ≤ - 8 = x ≤ - 2
Thus, It has solution.
Therefore, The correct inequality which has no solution will be;
⇒ x ≤ –2 and 2x ≥ 6
⇒ x ≤ –1 and 5x ≤ 5
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I need help please!!
Answer:
it is 3/5
Step-by-step explanation:
cos is the adjuacent devided by hypotenuse so it is 27/45 and that is 3/5
Select the correct answer from each drop-down menu
-Each participant tastes snack A and snack B and then chooses their favorite. Some participants have eaten snack A before and some have not. The results
of the test are shown in a table. Using the data in a table, the company that makes snack A calculates probabilities related to a random selected person
Prefers Snack A
Prefers Snack B
Total
Has Eaten Snack
A before
144
92
Has Not Eaten
108
228
Snack A before
Total
252
320
Complete the conclusions based on the data in the table.
236
336
572
Given a person who has eaten snack A before, the customer will
Given a person who has not eaten snack A before, the customer will want to eat snack
The probability of the customer wants to take snack B is 144/320 as they have already taken snack A
and the probability of the customer who has not taken snack A before
wants to take snack A =108/252
What is probability?
It is the ratio of favorable outcome to total possible outcome of an event.
How can we determine the probability in this question?based on given data, we calculated the number of customers who has taken snack A before may want to take snack B. The customers have not taken snack A yet may want to snack A.
hence, probability to take snack B = 144/320
probability to take A =108/252
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a) The probability a person who has eaten snack A before is 59/143.
b) The probability a person who has eaten snack A before is 84/143
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Given that the total number of people that are taken for the event is 572.
The number of people who have eaten snack A before is 236.
The number of people who have not eaten snack A before is 336.
Probability = The number of outcomes of favorable event/ Total number of outcomes
The probability getting a person who has eaten snack A before is
= 236/ 572
= 59/143 [Divide denominator and numerator by 4]
The probability getting a person who has not eaten snack A before is
= 336/ 572
= 84/143 [Divide denominator and numerator by 4]
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Graph the inequality on the axes below.
-x + 2y > 4
Answer:
Check out the image shown above/below
Using the matrix solve the following simultaneous equations
2x+5y=18
x-3y=-2
2x+5y=18 equ(1)
x-3y=-2 equ(2)
from equ (2) make x the subject of the formula
x=-2+3y
substitute x=2+3y in equ (1)
2+(-2+3y)+5y=18
-4+6y+5y=18
6y+5y=18+4
11y/11=22/11
y=2
substitute y=2 in equ(2)
x+3(2)=-2
x-6=-2
x=-2+6
x=4
x=4 and y=2
Help Which number line shows the solution set to this inequality?
-20 + 9
Answer:
A
Step-by-step explanation:
-2x + 9 < x - 9
-2x - x < -9 - 9
-3x < -18
x > -18/-3
x > 6
10+((6-4)*4) equal what
Answer:
18
Step-by-step explanation:
6-4=2
2x4=8
10+8=18
Geometry Support 4. Given: 6x-4 = 3x + 8. Prove: x = 4
Answer:
6(4)-4=3(4)+8
24-4=12+8
20=20
Step-by-step explanation:
To prove x=4, substitute four into the equation
6(4)-4=3(4)+8
24-4=12+8
20=20
Therefore x=4 is proved
Answer:
(Answer in Image)
Step-by-step explanation:
6x-4=3x+8
6x-4-3x=3x+8-3x subtract -3x on both sides
3x-4=8
3x-4+4=8+4 add four on both sides
3x=12 simplify
3/3x=12/3 divide both sides by 3
x=4
Hurry please I will give brainly need this in about 15 mins help me help meee
Answer:
x = -2
Step-by-step explanation:
The first thing we can notice about this figure is that the two small outer triangles are congruent because of the given side congruence markings as well as the fact that the large triangle ABC is isosceles, thus angle A is congruent to angle C.
Using the above information, we can construct the equation:
3x + 2 = 2x
and solve it for x.
x = -2
The equation we constructed simply equates the corresponding sides of the two small outer triangles, as they are congruent by the CPCTC theorem.
Round to the nearest degree
The measure of angle A of the triangle is 50°.
How to find angles of the triangle?
Eight angles are created when a transversal intersects two parallel lines. The pair of non-adjacent interior angles that are on the same side of the transversal are known as the same side internal angles.Two angles that are inside (between) the two lines, more especially on the same side of the transversal, are referred to as same side inside angles.Similar side interior angles therefore:
have unique vertices or no shared verticesstraddle two lineswas developed on the same transverse side of theCo-interior angles are another name for "same side interior angles."So, ∠C = ∠A
∠A = 50°
Hence, the measure of angle A of the triangle is 50°.
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Look at HIJ. Which of the triangles below can be proven similar to HIJ based only on the given information? Select all that apply.
The tringles ΔKLM, ΔXYZ, and ΔUVW are similar to the ΔHIJ.
What is the similarity of the triangles?
When it comes to Euclidean geometry, two things are said to be comparable if they have the same shape or the same shape as each other's mirror image. One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.
We have,
In ΔHIJ
∠HIJ = 64°
∠JHI = 96°
and the side are
HI = 2 unit
IJ = 5.5 unit
HJ = 5 unit
So, the third angle will according to the sum of the angles of a triangle:
∠IJH = 20°
the triangles similar to ΔHIJ are:
A) It is similar to ΔHIJ cause,
∠HIJ ≅ ∠KLM
∠IJH ≅ ∠LMK
so, the third also will be equal:
∠JHI ≅ ∠LKM
D) It is similar to ΔHIJ cause,
∠IJH ≅ ∠XZY
HI/YX = 2/4 = 1/2
HJ/YZ = 5/10 = 1/2
C) It is similar to ΔHIJ cause,
HI/UV = 2/4 = 1/2
HJ/UW = 5/10 = 1/2
IJ/VW = 5.5/11 = 1/2
Hence, the tringles ΔKLM, ΔXYZ, and ΔUVW are similar to the ΔHIJ.
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Stock in a certain company sold for $2.50 per share in June. The price of the stock increased $4.75 after one month. It then decreased $1.25 and $2.45 over the next two months. What was the price of the stock after these changes?
Responses
Answer: $3.55
Step-by-step explanation:
Started at 2.50 increased 4.75 which means the stock is 7.25 then decreased 1.25 making it 6 then another decrease of 2.45 making it $3.55
- Roll a die twice and consider the events A = {first roll gives at
least 4}, B = {second roll gives at most 4} and C = {the sum of the
rolls is 10}.
(a) Find P(A), P(B),P(C), and P(A ∩ B ∩ C).
(b) Are A, B, and C independent?
Part a: P(A) = 1/2; P(B) = 2/3; P(C) = 1/12; P(A ∩ B ∩ C) = 1/36.
Part b: Part b: A, B, and C independent events.
What is meant by the term sample space?All potential results make up the sample space of the a random experiment. A subset of a sample space is an event connected to a random experiment. Any outcome's probability is a value between 0 and 1. The sum of all the outcomes' probabilities is one.Rolling a dice twice has 36 possible results, hence the following is the sample space:
S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
For the stated question-
A = {first roll gives at least 4}, B = {second roll gives at most 4} and C = {the sum of the rolls is 10}.Part a: P(A), P(B),P(C), and P(A ∩ B ∩ C).
P(A) = 18/36 = 1/2
P(B) = 24/36 = 2/3
P(C) = 3/36 = 1/12
P(A ∩ B ∩ C) = 1/36
Part b: A, B, and C independent or not.
For the events to be independent,
P(A ∩ B ∩ C) = P(A).P(B).P(C)
P(A).P(B).P(C) = 1/2*2/3*1/12 = 1/36
As, P(A ∩ B ∩ C) = P(A).P(B).P(C).
Thus, the events are independent.
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