This equation has infinitely many solutions.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Here, we have
Given: 3x+4y = -10...(1),
y = -3/4x - 5/2....(2)
We solve this linear equation and we get
We multiply equation (2) by 4 and we get
4y + 3x = -5(2)
4y + 3x = -10
Hence, this equation has infinitely many solutions.
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North A North 110% B
Answer:
Step-by-step explanation:
I do not know bro. If I was a robot i'd know. I don't. I'm different.
The equation $x^2 + 6x + y^2 + 6y = 18$ represents a circle. What is its center?
Answer:
Center = (-3, -3)
Step-by-step explanation:
[tex](x-h)^2+(y-k)^2=r^2\\\\Center=(h,k)[/tex]
[tex]x^2+6x+y^2+6y=18\\(x^2+6x \,\,\,\,\,\,\,) + (y^2+6y\,\,\,\,\,\,\,)=18\\\\\frac{6}{2} =(3)^2=9\,\,\,\,\,\,\,\,\,\,\,\,\,\, \frac{6}{2}=(3)^2 =9\\\\(x^2+6x+9)+(y^2+6y+9)=18+9+9\\(x+3)^2+(y+3)^2=36\\\\Center=(-3,-3)[/tex]
please help me answer this :((
a. The number of pizzas the pizzeria must sell today for employees to receive the bonus will be 78 pizza.
b. The percent decrease in the number of pizzas sold today compared to yesterday is 7.69%.
How to calculate the valuea) To determine the number of pizzas the pizzeria must sell today for employees to receive the bonus, we need to calculate 20% of the 65 pizzas sold yesterday. 20% of 65 pizzas is 0.20 * 65 = 13. So, the pizzeria must sell 65 + 13 = 78 pizzas today for employees to receive the bonus.
b) To calculate the percent increase or decrease in the number of pizzas sold today compared to yesterday, we need to divide the difference between the two days' sales by the number of pizzas sold yesterday and multiply by 100.
((60 - 65) / 65) * 100
= (-5 / 65) * 100
= -7.69%
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Which expression is equivalent to x2 + 10x + 24?
A-(x + 12)(x - 2)
B-(x + 8)(x + 2)
C-(x + 6)(x + 4)
D-(x + 8)(x + 3)
Answer: the answer is C just did it
PLEASE HELP THANK YOUU
Find the compound interest and future value. Round your answers to the nearest cent.
Principal Rate Compounded Time
4.29% Weekly 34 years
$116,000
The compound interest is $348,966.97 and the future value is $464,966.97.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We can use the formula for compound interest to calculate the future value of the investment:
[tex]FV=P(a1+r/n)^{nt}[/tex]
where:
P = the principal amount (the initial investment)$116,000
r = the annual interest rate (as a decimal)=0.0429
n = the number of times the interest is compounded per year=52
t = the number of years=34
Plugging in these values, we get:
FV = $116,000(1 + 0.0429/52)¹⁷⁶⁸
FV = $464,966.97
So the future value of the investment after 34 years is $464,966.97.
Compound interest = $464,966.97 - $116,000 = $348,966.97
Therefore, the compound interest is $348,966.97 and the future value is $464,966.97.
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Help, Solve the system of linear equations by Elmination.
Answer:
See the explanation below
Solve 2x − 1 = 5.
A . x = 1
B . x = 2
C . x = 3
D . x = 4
C
The answer to the question is C
Answer:
D is the answer cuz 2x-1=5
2x=5-1
2x=4
X=2
We divide both side by two
After putting the expression 4x² + x4 -8 -5 into Standard Form, what would be the leading
coefficient?
The leading coefficient of the expression is 1
How to determine the leading coefficient of the expressionFrom the question, we have the following parameters that can be used in our computation:
4x² + x4 -8 -5
When written in standard form, we have
x^4 + 4x^2 - 8 - 5
Evaluate the like terms
x^4 + 4x^2 - 13
The leading coeffiicient is the coefficient of the term with highest power
In this case, it is
Coefficient = 1
Hence, the value is 1
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4x
Store A $25 for a 45 minute lesson
Store B. $30 for a 1 hour lesson
Store C $45 for a 1.5 hour lesson
Store D. $80 for three 1 hour lessons
Julle wants to purchase swim lessons for her son. There are four different stores that offer swim lessons. Based on the lowest cost per minute, which store has the BEST dea
4x A
4x B
x
C
4x D
Store B
Store A
Store D
Store C
The store with the best deal is given as follows:
Store D.
How to obtain the store with the best deal?The store with the best deal is obtained applying the proportions in the context of the problem.
The best deal is the store with the lowest cost per hour, and the cost per hour is obtained dividing the total cost by the number of hours.
Hence the hourly cost for each store is obtained as follows:
Store A: 25/0.75 = $33.3 per hour. (45 minutes = 45/60 hour = 0.75 hour).Store B: $30/1 = $30 per hour.Store C: $45/1.5 = $30 per hour.Store D: $80/3 = $26.7 per hour -> best deal.More can be learned about proportions at https://brainly.com/question/24372153
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Find the probability.
10) A die is rolled 20 times and the number of twos that come up is tallied. Find the
probability of getting exactly two twos. Round to the nearest thousandth when necessary.
The probability of getting two twos is 0.003
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
probability = sample space/total outcome
probability of getting two = 1/6
probability of getting two twos = 1/36
getting two two can only 10times = 1/36 ÷ 10
= 10/36 = 0.003 (nearest thousandth)
therefore the probability of getting two twos in 20 rolls is 0.003( nearest thousandth)
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What is the result when the number 45 is increased by 57%?
Answer: The result when the number 45 is increased by 57% is approximately 70.65.
Step-by-step explanation:
To find the result when the number 45 is increased by 57%, we need to calculate 45 * (1 + 0.57), where 0.57 represents 57% as a decimal.
Performing the calculation, we get:
45 * (1 + 0.57) = 45 * 1.57 = 70.65
So, the result when the number 45 is increased by 57% is approximately 70.65.
Answer:
70.65
Step-by-step explanation:
The new value =
45 + The value of the percentage increase =
45 + (57% × 45) =
45 + 57% × 45 =
(1 + 57%) × 45 =
(100% + 57%) × 45 =
157% × 45 =
157 ÷ 100 × 45 =
157 × 45 ÷ 100 =
7,065 ÷ 100 =
70.65
a. Draw a tree diagram for the results from tossing a fair two-sided coin (H, T) four times
b. How many stages are there in the tree diagram?
c. List all the possible outcomes (the sample space).
d. How many outcomes are there in the sample space?
▪ You must show ALL of your work in order to receive full credit.
Answer:
Step-by-step explanation:
a) The tree diagram for the results of tossing a fair two-sided coin four times would look like this:
(1)
/ \
(H) (T)
/ \ / \
(2-H) (2-T) (2-H) (2-T)
/ \ / \ /
(3-HH) (3-HT) (3-TH) (3-TT)
b) There are four stages in the tree diagram.
c) The possible outcomes (the sample space) would be all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times. The possible outcomes are:
HHHHH
HHHTT
HHTHT
HHTTH
HTTHH
HTHHT
HTHTH
THHHH
THHTT
THTHT
TTHHT
TTHTH
TTTTT
d) There are 2^4 = 16 outcomes in the sample space.
ALSO:
a) Draw the Tree Diagram
Start with a root node labeled with the first toss (toss 1)
From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.
Repeat this process for each of the next tosses (toss 2, 3, and 4)
Continue until all the possible outcomes of the four tosses have been represented.
Here is an example of the tree diagram:
(1)
/
(H) (T)
/ \ /
(2-H) (2-T) (2-H) (2-T)
/ \ / \ /
(3-HH) (3-HT) (3-TH) (3-TT)
/ \ / \ /
(4-HHH) (4-HHT) (4-THH) (4-TTT)
b) Number of Stages in the Tree Diagram
There are four stages in the tree diagram, one for each toss of the coin.
c) Possible Outcomes (Sample Space)
The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.
There are 16 possible outcomes in the sample space, as shown below:
HHHHH
HHHTT
HHTHT
HHTTH
HTTHH
HTHHT
HTHTH
THHHH
THHTT
THTHT
TTHHT
TTHTH
TTTHH
TTTTH
TTTTT
d) Number of Outcomes in the Sample Space
There are 2^4 = 16 outcomes in the sample space.
This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.
ALSO:
a) Draw the Tree Diagram
Start with a root node labeled with the first toss (toss 1).
From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.
Repeat this process for each of the next tosses (toss 2, 3, and 4).
Continue until all the possible outcomes of the four tosses have been represented.
Here is an example of the tree diagram:
(1)
/
(H) (T)
/ \ /
(2-H) (2-T) (2-H) (2-T)
/ \ / \ /
(3-HH) (3-HT) (3-TH) (3-TT)
/ \ / \ /
(4-HHH) (4-HHT) (4-THH) (4-TTT)
b) Number of Stages in the Tree Diagram
There are four stages in the tree diagram, one for each toss of the coin.
c) Possible Outcomes (Sample Space)
The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.
There are 16 possible outcomes in the sample space, as shown below:
HHHHH
HHHTT
HHTHT
HHTTH
HTTHH
HTHHT
HTHTH
THHHH
THHTT
THTHT
TTHHT
TTHTH
TTTHH
TTTTH
TTTTT
d) Number of Outcomes in the Sample Space
There are 2^4 = 16 outcomes in the sample space.
This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.
I hope this step-by-step explanation with the diagram helps! Let me know if you need further clarification.
someone pls help with this question
a² y² - 2aby + b²
Find the slope of the line on the graph. Reduce all fractional answers to lowest terms.
-4
-1
-2
The slope of the line on the graph will be a negative one. Then the correct option is A.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
From the graph, the two points are (-2, 2) and (2, -2). Then the slope is given as,
m = (- 2 - 2) / (2 + 2)
m = - 4 / 4
m = - 1
The slope of the line on the graph will be a negative one. Then the correct option is A.
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The complete question is attached below.
Find the perimeter of the trapezoid round to the nearest tenth
The perimeter of the trapezoid is 49.4.
What is trapezium?A trapezium is a quadrilateral with four sides where two sides are parallel to each other.
We have,
From the graph,
Height = 12 units
Parallel sides = 9 units and 15 units
Now,
Another side = x
Using Pythagorean theorem.
x² = 6² + 12²
x² = 36 + 144
x² = 180
x = √180
x = 13.42
Now,
The perimeter of the trapezoid.
= 12 + 13.42 + 9 + 15
= 49.42
= 49.4
Thus,
49.4 is the perimeter of the trapezoid.
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write a formula for f(x)=1x1 shifted up one unit and right 3 units
Y = (1/x-3) has been moved 3 units to the right and up one unit. If it is moved to the right, it should look like this: (x-3). It should show up as (x+3) if it were moved to the left. If the result were moved ahead, the outcome would be (1/x-3).
How is the calculation for switching functions done?The original function f is horizontally shifted into the new function g(x)=f(xh), where h is a constant. Given a function f. The graph will shift to the right in a positive h situation. If h is negative, the graph will slide to the left.
How is a function moved to the left and right?To move a function left in function notation, add within the function's argument: f(x + b) moves f(x) b units left. In the same way, shifting to the right moves f(x) b units to the right.
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If the diameter of the pie is ten inches, the approximate arc length of one slice of pie is.
Answer:
It depends on the amount of slices.
Step-by-step explanation:
The diameter of the pie is 10 inches. Multiply this by π and we get approximately 31.4. Basically just divide it by the number of slices. For example, if there were six slices, 31.4/6=5.23, so that's the arc length of one slice.
Triangle XYZ is shown on the coordinate plane.
A triangle on the coordinate plane with vertices X at 0 comma 5, Y at 10 comma 3, and Z at 4 comma negative 1.
If triangle XYZ is translated using the rule (x, y) → (x + 2, y + 3) and then reflected across the x-axis to create triangle X″Y″Z″, what is the location of Z″?
(2, −8)
(6, −2)
(8, −2)
(12, −6)
The transformation of triangle XYZ vertices at X(0, 5), Y(10, 3), and Z(4, -1), indicates that the coordinate of the point Z'' following a composite transformation of a translation of (x, y) → (x + 2, y + 3), and a reflection across the x-axis, is located at the point (6, -2). The correct option is therefore;
(6, -2)What is a reflection transformation?A reflection transformation is a transformation that produces a mirror image of a geometric figure across a line of reflection.
The coordinates of the vertices of the triangle are;
X(0, 5), Y(10, 3), Z(4, -1)
The transformation rule that is used to translate the triangle ΔXYZ (to get ΔX'Y'Z'), can be presented as follows;
(x, y) → (x + 2, y + 3)The reflection of the translated figure of the triangle (ΔX'Y'Z'), to get ΔX''Y''Z'', is a reflection across the x-axis, therefore, we get;
The coordinates of the point (x, y) following a reflection across the x-axis is the point (x, -y)Therefore, we get the coordinate of the point (x, y) following the composite transformation is the point (x + 2, -(y + 3))
(x, -y) → (x + 2, -(y + 3))The coordinates of the point Y(4, -1) following the composite transformation is therefore;
Y(4, -1) → (4 + 2, -(-1 + 3)) = (6, -2)
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A group of friends wants to go to the amusement park. They have no more than $295
to spend on parking and admission. Parking is $11.50, and tickets cost $39
person, including tax. Which inequality can be used to determine x, the maximum
number of people who can go to the amusement park?
Answer:
295>_ 39x+11.50
Step-by-step explanation:
the >_ means less than or equal to.
Help !! I can’t find the answer for this question
Answer:
41 inches
Step-by-step explanation:
to find the perimeter of any shape, add the length of all the sides together
why is it important to understand the concept of interest
It is important to understand the concept of interest beacause it is a part of our life and it hels us to understand the economic situation of ourselves.
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
We have.
There are two types of interest commonly studied.
1)
Simple interest
2)
Compound interest
Now,
Simple interest is the interest calculated only on the principal year after year.
Whereas compound interest is the interest calculated on the principal as well as the interest after the first year.
Example:
Principal = $100
Rate = 10%
Time = 2 years
Simple interest after two years.
= 2 x (10% of 100)
= 2 x (1/10 x 100)
= 2 x 10
= $20
Compound interest after two years.
Ist year:
= (10% of 100)
= (1/10 x 100)
= $10
2nd year:
= 10% of (100 + 10)
= 1/10 x 110
= $11
So,
= 10 + 11
= $21
Thus,
The concept of interest is given above.
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Determine the number of monthly payments of $611.09 that would be required to pay off the loan of $128,000 at 4% interest.
The number of monthly payments required to pay off the loan of $128,000 at 4% interest is 232.48 which is equivalent to approximately 232 payments.
How do we determine the number of monthly payments for the loan?To determine the number of monthly payments required to pay off a loan, you can use the formula for loan amortization: n = (-log(1 - B/A * r)) / log(1 + r)
Where: n = number of monthly payments, A = loan amount ($128,000), B = monthly payment ($611.09), r = monthly interest rate (4% / 12 months = 0.0033)
The number of monthly payments for the loan is plugged and computed as:
n = (-log(1 - $128,000/$611.09 * 0.0033)) / log(1 + 0.0033)
n = (-log(1 - 0.0208)) / log(1.0033)
n = (-log(0.9792)) / log(1.0033)
n = 21.8068 / 0.093984
n = 232.48 payment.
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Two gliders collide on an air track. Glider 1 has a mass of 7. 0 kg, and glider 2 has a mass of 4. 0 kg. Before the collision, glider 1 had a velocity of 2. 0 m/s, and glider 2 had a velocity of -5. 0 m/s. If the collision is perfectly elastic, what is the total kinetic energy of both gliders after the collision?
A. -36. 0 J
B. 36. 0 J
C. 64. 0 J
D. 128. 0 J
For the information provided, the total kinetic energy of both gliders after collision is 13.5 J. In an elastic collision, both momentum and kinetic energy are conserved.
The momentum conservation principle states that the total momentum of the system before the collision is equal to the total momentum after the collision. Mathematically, we can write this as:
m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f
where m₁ and v₁i are the mass and initial velocity of glider 1, m₂ and v₂i are the mass and initial velocity of glider 2, and v₁f and v₂f are their velocities after the collision.
Using this equation and the given values, we can solve for the final velocities:
(7.0 kg)(2.0 m/s) + (4.0 kg)(-5.0 m/s) = (7.0 kg)v₁f + (4.0 kg)v₂f
14.0 kg·m/s - 20.0 kg·m/s = 7.0 kg·v₁f + 4.0 kg·v₂f
-6.0 kg·m/s = 7.0 kg·v₁f + 4.0 kg·v₂f ---(1)
The kinetic energy of an object is given by the equation:
KE = 1/2 mv²
Therefore, the total kinetic energy of both gliders after the collision can be calculated as:
KE_total = 1/2 m₁ v₁f² + 1/2 m₂ v₂f²
Substituting the values of m₁, m₂, v₁f, and v₂f from equation (1) into this equation, we get:
KE_total = 1/2 (7.0 kg) (0.86 m/s²) + 1/2 (4.0 kg) (5.14 m/s²)
KE_total = 13.5 J
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Figure 1 and figure 2 are right triangles.
two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 7 units long
What scale factor was used to produce Figure 2 from Figure 1?
Answer:
The answer
Step-by-step explanation:
Figure 1 figure
3/4
The graph of a function is shown below. Describe the relationship between the number of gallons of gas and the cost in dollars. Explanation too please
The relationship between the number of gallons of gas and the cost in dollars is: C. The cost of gas is $3.75 per gallon.
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x represent the number of gallons of gas.k is the constant of proportionality.y represent the cost of gas in dollars.Next, we would determine the constant of proportionality (k) for the relationship between the number of gallons of gas and the cost in dollars on this graph as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 7.5/2
Constant of proportionality, k = $3.75.
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5. Annette bought 8 dozen eggs from Mr. Joseph's Farm Store for $2,800.00. What was the price per dozen?
In a casee whereby Annette bought 8 dozen eggs from Mr. Joseph's Farm Store for $2,800.00 the price per dozen is $350 per dozen
How can the price per dozen be calculated?The concept that will be use here is division. Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
The total dozen = 8 dozen eggs
The total price of the 8 dozen eggs $2,800.00
The price per dozen = $2,800.00/ 8 dozen
=$350 per dozen
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The relationship between the amount of energy released by an earthquake and its magnitude is described by this formula. Here E is energy, in joules, and M is magnitude. Approximately how much energy is released by a magnitude 5 earthquake? Select the correct answer.logE=5.24+1.44M
Approximately 2.51 x 10¹² joules of energy is released by a magnitude 5 earthquake.
What is a logarithmic equation?A logarithmic equation is an equation that involves a logarithmic function. A logarithmic function is the inverse of an exponential function, and it represents the exponent to which a given base must be raised to obtain a given number.
The formula that relates the energy released by an earthquake to its magnitude is given by:
logE = 5.24 + 1.44M
To find the amount of energy released by a magnitude 5 earthquake, we can substitute M = 5 into the formula and solve for E.
logE = 5.24 + 1.44(5)
logE = 5.24 + 7.2
logE = 12.44
Now we need to convert this logarithmic value to a regular value of E. We can do this by taking the antilogarithm (or exponentiating) both sides of the equation.
10⁽ˡᵒᵍᴱ⁾ = 10⁽¹²ॱ⁴⁴⁾
E = 2.51 x 10¹² joules
Therefore, approximately 2.51 x 10¹² joules of energy is released by a magnitude 5 earthquake.
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3 1/2x - 5 1/3x , x = 2/5
The value of the expression is -11/15
How to determine the value of the expressionIt is important to note that algebraic expressions are expressions having factors, constants, variables, coefficients and terms.
From the information given, we have that;
3 1/2x - 5 1/3x
turn into improper fractions
7x/2 - 16x/3
Now, let's determine the value by substituting the value of x as 2/5 in the expression, we have;
7(2/5)/2 - 16(2/5)/3
Multiply the values
14/5/2 - 32/5 /3
Take inverse of the denominator
14/5 ×1/2 - 32/5 × 1/3
7/5 - 32/15
21 - 32/15
-11/5
Hence, the value is -11/15
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The iced tea can is made from a sheet of aluminum that weighs 0.01
ounce per square inch. You receive $0.40 per pound of aluminum that
you recycle. How much do you earn for recycling 24 iced tea cans?
You would earn $0.006 for recycling 24 iced tea cans.
How to find the earning for the recyclingTo determine the amount earned from recycling 24 iced tea cans, we need to find the total weight of the aluminum used in those cans and then convert that weight to pounds.
The total weight of the aluminum used in 24 cans as follows:
24 cans * 0.01 ounce per square inch = 0.24 ounces
Converting ounces to pounds, using a conversion factor of 1/16:
0.24 ounces / 16 ounces per pound = 0.015 pounds
The total amount earned:, since each pound is $0.40
0.015 pounds * $0.40 per pound = $0.006
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