Find the solution of the system of equations. -2x-y=6 over -2x+8y=-39
The solution of the system of equations. -2x-y=6 over -2x+8y=-39 is the ordered pair (-0.5, -5).
How to graphically solve this system of equations?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
-2x-y=6 ......equation 1.
-2x+8y=-39 ......equation 2.
In this exercise, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.
Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which is given by the ordered pair (-0.5, -5).
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can you find the probability of one thing happening before another based on their expected time until occurance
Yes, we can determine the probability of one thing happening before another based on their expected time to occur.
A coin has two sides: one side ("heads") is side A and the other ("tails") is side B. A coin is tossed into the air and the question is what are the chances, the "probability" if you want it to land on side A. The probability of an event occurring describes the number of chances that the event occurred. The total probability of hitting A before B is the sum: P(A before B) = p + rp + r² + r³p + r⁴p + … = p[1 + r + r² + r³ + r⁴ + … ] and this determines the result. Thus, it is possible to determine the probability of one thing happening before another, based on their expected time to occur.
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Which equation matches the table?
An equation that matches the table include the following: y = x + 5.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (6 - 5)/(1 - 0)
Slope (m) = 1/1
Slope (m) = 1.
At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = 1(x - 0)
y - 5 = x
y = x + 5
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Ted jumped 1,300 times. He did 100 more jumps than Mario. How many jumps did Mario do?
Answer: 1,200
Step-by-step explanation: 1,300 - 100 = 1,200
Help Please I need this answer soon
The solution for the value of x is 55.
How to solve for the value of x?Since the segments of the secant segment and the tangent segment share an endpoint outside of the circle.
According to Tangent-Secant Theorem, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment. That is:
x² = 5 * (5 + 6)
x = 5 * 11
x = 55
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find the product of (3-2x)(2x+1)(x-5)
Answer:
the product of (3-2x)(2x+1)(x-5) is -4x^3 + 26x^2 - 19x - 75.
Step-by-step explanation:
To find the product, we need to multiply these three expressions:
(3 - 2x)(2x + 1)(x - 5)
Let's start by multiplying the first two expressions using the distributive property:
(3 - 2x)(2x + 1) = 6x - 4x^2 + 3 - 2x
Now we can multiply this result by the third expression using the distributive property again:
(6x - 4x^2 + 3 - 2x)(x - 5) = 6x^2 - 34x + 15x - 75 - 4x^3 + 20x^2
Simplifying this expression by combining like terms, we get:
-4x^3 + 26x^2 - 19x - 75
Therefore, the product of (3-2x)(2x+1)(x-5) is -4x^3 + 26x^2 - 19x - 75.
Find the quotient. Assume that no denominator has a value of 0.
(6x-24)÷x^2-16/6x
The quotient of the expression (6x-24)÷x^2-16/6x is 36x/(x + 4)
Finding the quotient of the expressionFrom the question, we have the following parameters that can be used in our computation:
(6x-24)÷x^2-16/6x
Assume that no denominator has a value of 0, we have
(6x-24)÷x^2-16/6x = 6(x - 4) ÷ (x - 4)(x + 4)/6x
Express as products
So, we have the following representation
(6x-24)÷x^2-16/6x = 6(x - 4) * 6x/(x - 4)(x + 4)
When the factors are evaluated, we have
(6x-24)÷x^2-16/6x = 36x/(x + 4)
Hence, the solution is 36x/(x + 4)
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Put these numbers in order starting with the smallest
Answer: -1.12, -1^(1/2), 1^(1/8), 1^(1/2), 1^(2/3), 1.12
Step-by-step explanation:
Starting with the smallest:
-1.12
-1^(1/2) (which is equal to -1)
1^(1/8) (which is equal to 1)
1^(1/2) (which is equal to 1)
1^(2/3) (which is equal to 1)
1.12
Therefore, the numbers in order from smallest to largest are: -1.12, -1, 1, 1.12.
Sam started the week with a balance of -$10 in his checking account. Then he deposited some money into the account. The ending balance was $70. How much did sam deposit?
Answer:
Sam balance was -10 and the ending balance was $70
=80+(-10)
=$70
Questions are Below!!!
Answer:
Step-by-step explanation:
Question 1 :
The statement that best describes the solutions of a two-variable equation is (1) The ordered pairs must lie on the graphed equation. This means that any ordered pair (x,y) that satisfies the equation will corresponds to a point on the graph of the equation. In other words, if we plot all the points (x,y) that make the equation true, we will obtain the graph of the equation. Any points that do not lie on the graph is not a solution to the equation. Therefore, when solving a two-variable equation, we need to find the values of x and y that make the equation true and plot those points on the graph to visualize the solutions.
Question 2 :
To use the arithmetic sequence formula, we need to know the first term (a1), the common difference (d), and the desired term (an). In this case, we are given the first term as 4 and the common difference as 3 (since each term is increasing by 3). To find the 10th term, we would replace the variable "n" with 10 in the formula. Therefore, to determine the 10th term of this sequence, we would use the formula:
a10 = a1 + (n-1)d
a10 = 4 + (10-1)*3
a10 = 4 + 27
a10 = 31
Thus, the 10th term of the given sequence is 31.
Question 3 :
The formula an = al + (n-1)d is used to determine the nth term in an arithmetic sequence, where "a" represents the first term in the sequence, "n" represents the term number being solved for, and "d" is the common difference between terms. The formula essentially states that to find any term in an arithmetic sequence, one must add the common difference between terms multiplied by the number of terms-1 to the value of the first term. This formula can be applied to various situations, such as determining the total cost of goods sold in a business with a constant markup percentage, or calculating the number of days it will take to save a given amount of money with a fixed monthly contribution. By understanding the principles behind the formula, individuals can successfully solve problems involving arithmetic sequences in a variety of contexts.
URGENT - Will also give brainliest to simple answer
Step-by-step explanation:
Radius = 70 cm then diameter = 140 cm
Circumference = rope length = pi * diameter
= 140 * pi = 439.8 cm long (round as needed)
Natalie saved $9,750 at 5.5%
simple interest per year. After 3
years, what is the earned
interest?
the earned interest after 3 years is $1,608.75.
What is simple interest?
Before delving further into the concept of simple interest, it is worth noting that it is a straightforward method for calculating interest on money, whereby interest is added at a constant rate for each time period and always to the initial principal amount. When we deposit our money into a bank, we can earn interest on our investment. Simple interest is one type of interest that banks may offer.
The formula for simple interest is:
I = P * r * t
where:
I = interest earned
P = principal (initial amount)
r = interest rate per year (as a decimal)
t = time (in years)
Substituting the given values, we have:
P = $9,750
r = 0.055 (since the interest rate is 5.5%)
t = 3
I = $9,750 * 0.055 * 3
I = $1,608.75
Therefore, the earned interest after 3 years is $1,608.75.
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17. Corina makes $27 for every 2 hours that she works. If she worked 36
hours this week, how much money did she make?
If she worked 36 hours this week, then Corina made $486 this week.
From the question, we have the following parameters that can be used in our computation:
Corina makes $27 for every 2 hours that she works.
So she makes:
27/2 = $13.50 per hour
If she worked 36 hours this week, she would make:
36 hours x $13.50 per hour = $486
Therefore, Corina made $486 this week.
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Help me calculate this integral!
Answer:
Step-by-step explan 456
If you needed only 1cup of milk, what is your best choice at the grocery store-a quart container, a pint container or a 1/2 gallon container?
Since 1 gallon = 4 quarts → (1/2) gallons = 2 quarts
1 gallon = 8 pints → (1/2) gallons = 4 pints
1 gallon = 16 cups → (1/2) gallons = 8 cups
Therefore from the given relation with gallons we can describe the relation between the cups, quarts and pints.
(1/2) Gallon > quarts > pints > cups
If we need 1 cup of milk then a pint container will be the best choice at a grocery store.
Answer: 1 pint would because a quart has 4 cups and 1/2 a gallon would be way to much. and a pint would be 2.
Step-by-step explanation:
1 pint would be because a quart has 4 cups and 1/2 a gallon would be way to much. and a pint would 1 cup more than you need so 1 pint is right
In a circle ABCD, OB = 10 cm. Find the measure of AC.
The measure of AC, in circle ABCD can be found to be 20 cm.
How to find the measure?In Circle ABCD, O is the midpoint of the circle which means that OB is the radius.
As A and C are on opposite sides of the circle, it means that the value of the measure of AC would be the diameter of the circle which can be found if we have the radius.
The diameter which is AC would then be:
= Radius x 2
= OB x 2
= 10 x 2
= 20 cm
In conclusion, the measure of AC is 20 cm.
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A 35 foot ladder is set against the side of a house so that it reaches up 21 feet. If Elijah grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 17 ft.) Round to the nearest tenth of a foot.
The side of the house which the ladder will reach now is equal to 14.2 feet.
What is Pythagorean theorem?In Mathematics and Geometry, Pythagorean's theorem is represented or modeled by the following mathematical equation:
x² + y² = z²
Where:
x, y, and z represents the length of sides or side lengths of any right-angled triangle.
In order to determine how far up the side of the house will the ladder reach, we would have to apply Pythagorean's theorem as follows;
21² + y² = 35²
y² = 1,225 - 441
y² = 784
y = √784
y = 28 feet.
Since Elijah grabs the ladder at its base and pulls it 4 feet farther from the house, we have:
New Length = 28 + 4 = 32 feet.
Therefore, the required length is given by;
Distance = √(35² - 32²)
Distance = 14.2 feet.
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Need in deed classrooms participate in great service learning projects! One classroom took 254 photos of their Saving Honeybees project. Another classroom took 15 times as many pictures of their Advocacy Project for Homeless Pets. How many photos did the Advocacy Project for Homeless Pets classroom take? Show or explain your work
Answer:
To solve the problem, we can use multiplication. We know that one classroom took 254 photos and the other classroom took 15 times as many pictures. So, we can write an equation to represent the situation:
Number of photos taken by Advocacy Project for Homeless Pets classroom = 254 x 15
We can then solve this equation using multiplication.
254 x 15 = 3810
Therefore, the Advocacy Project for Homeless Pets classroom took 3,810 photos.
5) Danielle goes shopping for yoga pants. The promotion at the
store is if you buy 8 pairs for $98. How much would Danielle pay
if she bought 5 pairs with the same promotion?
determine if (4,1) is a solution for the system of equations
y=-1x+5
y=2x-7
Answer: The point (4, 1) is a solution to this system of equations.
Step-by-step explanation:
To determine if (4, 1) is a solution to this system, you must plug it in to both of the equations. It is in the form of (x, y); so x = 4, and y = 1
Equation #1: y = -x + 5
1 = -(4) + 5
1 = 1 <————— This is part of the solution to this equation.
Equation #2: y = 2x - 7
1 = 2(4) - 7
1 = 8 - 7
1 = 1 <———- This is part of the solution to this equation.
The point (4, 1) is a solution to this system of equations.
What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation?
-3x^2-298=60x-1
Thus, the intermediate step in the form (x+a)² = b as a result of completing the square for the given equation is - (x + 10)² = 1 /3.
Define the term "completing the square":A quadratic equation can be made together into perfect square trinomial simply adding or removing elements from both sides, a technique known as "completing the square."
You can use the square's completion as another mathematical tool to solve a variety of problems:
Make algebraic statements simplersolve quadratic problemsTransform expressions between different forms.Quadratic functions' minimum and maximum values should be determined.Given expression:
-3x² - 298 = 60x - 1
isolating the x values:
-3x² - 60x = 298 - 1
-3x² - 60x = 299
Taking -3 common from the left hand side:
-3(x² + 20x) = 299
x² + 20x = - 299/3
This, can be written as:
x² + 2*10x = - 299/3
add both side by 100
x² + 2*10x + 100 = - 299/3 + 100
On simplification:
(x + 10)² = (-299 + 300) /3
(x + 10)² = 1 /3
Comparing obtained expression with the given form: (x+a)²=b
a = 10 and b = 1/3
Thus, the intermediate step in the form (x+a)² = b as a result of completing the square for the given equation is - (x + 10)² = 1 /3.
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A scoop from a bin of assorted jelly beans contained a mix of flavors. root beer 5 licorice 22 cinnamon 6 What is the experimental probability that the next jelly bean scooped from the bin will be a cinnamon jelly bean? Write your answer as a fraction or whole number. P(cinnamon)=
Answer: The experimental probability of an event happening is defined as the number of times the event occurs divided by the total number of trials.
In this case, the number of cinnamon jelly beans in the scoop is 6. The total number of jelly beans in the scoop is 5+22+6=33.
Therefore, the experimental probability of scooping a cinnamon jelly bean from the bin is:
P(cinnamon) = number of cinnamon jelly beans / total number of jelly beans
P(cinnamon) = 6 / 33
P(cinnamon) = 2 / 11
So the experimental probability of scooping a cinnamon jelly bean from the bin is 2/11, which can be written as a fraction.
Step-by-step explanation:
please help
The terms of a geometric sequence are −4, [tex]\frac{4}{3}[/tex], [tex]-\frac{4}{9}[/tex], [tex]\frac{4}{27}[/tex]. Please write the formula for the nth term an.
The common ratio is -1/3 and the initial term is -4, then the formula is:
A(n) = -4*(-1/3)^(n - 1)
How to find the formula for the nth term?Remember that in a geometric sequence, to get the next term we need to multiply the previous term by the common ratio.
To get the common ratio, take the quotient between two consecutive terms.
We will get:
(4/3)/(-4) = -1/3
Then the n-th term of the geometric sequence is:
A(n) = -4*(-1/3)^(n - 1)
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Answer:
[tex](-4)\left(\frac{1}{3}\right)^{n-1}[/tex]
Step-by-step explanation:
The common ratio between any two terms in a geometric sequence is constant. Let this ratio be denoted by r. Then, we have:
[tex]r = \frac{\frac{4}{3}}{-4} = \frac{-\frac{4}{9}}{\frac{4}{3}} = \frac{\frac{4}{27}}{-\frac{4}{9}} = \frac{1}{3}[/tex]
Using this value of r, we can write the formula for the nth term an as:
[tex]an=[/tex][tex](-4)\left(\frac{1}{3}\right)^{n-1}[/tex]
the cunninghams are moving across the country. mr. cunningham leaves 4 hours before mrs. cunningham. if he averages 46mph and she averages 62mph , how long will it take mrs. cunningham to overtake mr. cunningham?
Answer: Let's call the time it takes for Mrs. Cunningham to overtake Mr. Cunningham "t".
In that time, Mr. Cunningham will have traveled for 4 more hours than Mrs. Cunningham, so he will have traveled 4 + t hours.
We can set up an equation to represent the distance each person traveled:
distance = rate x time
For Mr. Cunningham:
distance = 46 mph x (4 + t) hours
For Mrs. Cunningham:
distance = 62 mph x t hours
Since they end up at the same place, their distances must be equal:
46 mph x (4 + t) = 62 mph x t
Simplifying this equation:
184 + 46t = 62t
16t = 184
t = 11.5
Therefore, it will take Mrs. Cunningham 11.5 hours to overtake Mr. Cunningham.
Step-by-step explanation:
What is the ¨length of a soccer field¨ unit of measurement
A - Square meters
B - Yards
C - Cubic inches
D - Cubic feet
E - Square centimeters
The unit of measurement "length of a soccer field" is in yards
What is the ¨length of a soccer field¨ unit of measurementThe unit of measurement "length of a soccer field" is typically measured in yards, which is option B.
A standard soccer field is rectangular, with a length ranging from 100 to 130 yards and a width ranging from 50 to 100 yards.
The measurement of the length of a soccer field is based on the distance between the goal lines, which is equivalent to the length of the field.
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The quotient of 30y³ + 50y2 - 35y divided by 5y is:____.a. 6y +10y² - 7. b. 6y² +10y + 7. c. 6y2+10y - 7. d. 6y³ +10y² - 7.
The quotient of 30y³ + 50y² - 35y divided by 5y is: 6y² +10y - 7
Hence option c is the correct answer.
Applying long division rule to find quotient,
Dividend is 30y³ + 50y² - 35y and divisor is 5y
Dividing 30y³ + 50y² - 35y by 5y step by step we get ( +) 30y^3 is divisible by 5y as the remainder is zero and the quotient is (+) 6y^2.
Then at second step we get (+) 50y^2 is divisible 5y as the remainder is zero and the quotient is (+) 10y.
And at the last step we get (-) 35y is divisible by 5y as the remainder is zero and the quotient is (-) 7.
Thus adding up the quotients found at each step of division of 30y³ + 50y² - 35y by 5y is 6y² +10y - 7.
Hence option c is the correct answer.
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50 POINTS
A study was conducted to investigate whether local car mechanics charge women more than men for a transmission repair. The researcher selected randomly one man and one woman from everyone who had used the same mechanic for the same transmission repair. The process was repeated for a total of seven selected randomly cars. The repair prices and the differences are shown in the table.
Car 1 Car 2 Car 3 Car 4 Car 5 Car 6 Car 7
Women $3,550 $3,200 $1,850 $2,000 $3,000 $1,950 $2,250
Men n $3,285 $3,100 $1,975 $2,150 $2,850 $1,750 $2,175
Difference$265 $100 −$125 −$150 $150 $200 $75
Mean Standard Deviation
Women $2,542.86 $691.27
Men $2,469.29 $599.77
Difference $73.57 $157.37
Dotplots of the data and the differences are shown.
(image)
Do the data provide convincing statistical evidence that women pay more than men for the same transmission repair?
we do not have convincing statistical evidence that women pay more than men for the same transmission repair
How to determine if data provide convincing statistical evidence that women pay more than men for the same transmission repairTo determine whether the data provide convincing statistical evidence that women pay more than men we do not have convincing statistical evidence that women pay more than men for the same transmission repair for the same transmission repair, we can perform a hypothesis test.
Null hypothesis: The mean repair cost for women is the same as the mean repair cost for men.
Alternative hypothesis: The mean repair cost for women is greater than the mean repair cost for men.
We can use a two-sample t-test for the difference in means, assuming equal variances.
The test statistic is given by:
t = (xbar1 - xbar2) / (s_p * sqrt(1/n1 + 1/n2))
where xbar1 and xbar2 are the sample means, s_p is the pooled standard deviation, and n1 and n2 are the sample sizes.
The degrees of freedom is given by:
df = n1 + n2 - 2
Using the data given, we have:
xbar = 2542.86, xbar2 = 2469.29
s1 = 691.27, s2 = 599.77
n1 = n2 = 7
First, we can calculate the pooled standard deviation:
s_p = sqrt(((n1-1)*s1^2 + (n2-1)*s2^2) / (n1 + n2 - 2))
s_p = sqrt(((6)*691.27^2 + (6)*599.77^2) / (7 + 7 - 2))
s_p = 644.47
Then, we can calculate the t-statistic:
t = (xbar 1 1 - xbar2) / (s_p * sqrt(1/n1 + 1/n2))
t = (2542.86 - 2469.29) / (644.47 * sqrt(1/7 + 1/7))
t = 0.97
Using a t-distribution table with df = 12 and a significance level of 0.05, the critical value for a one-tailed test is 1.7823. Since our t-statistic is less than the critical value, we fail to reject the null hypothesis.
Therefore, we do not have convincing statistical evidence that women pay more than men for the same transmission repair
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Geometry Work
It's due today please help asap
The correct volume of the solid shape given above would be = 3726.1in³.
How to calculate the volume of the solid shape?To calculate the volume of the solid shape, the volume of the cylinder and a cone shoe be subtracted form the Vol of the inner cylinder within the solid shape.
The formula for volume of a cylinder = πr²h
where r = 8in, h = 18in,π= 3.14
vol of cylinder = 3.14× 64×18
= 3617.28in³
volume of cone =⅓πr²h
where hb= 5in
vol = 1/3×3.14×64×5
= 1004.8/3 = 334.9in³
Total volume of shape = 3617.28in³+334.9in³ = 3952.18in³
Vol of inner cylinder = πr²h
where r = 2in
vol = 3.14×4× 18 = 226.08in³
The volume of the shape = 3952.18- 226.08 = 3726.1
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PLEASE HELP ME ITS URGENT MY GRADE NEEDS HELP! THIS IS MULTIPLE CHOICE QUESTION!
Which ordered pairs are solutions to the inequality 2x+3y≥−1?
Select each correct answer.
Responses
(0, −1)
begin ordered pair 5 comma negative 1 end ordered pair
(−2, 1)
begin ordered pair negative 2 comma 1 end ordered pair
(0, 1)
begin ordered pair 0 comma 1 end ordered pair
(−6, 0)
begin ordered pair negative 6 comma 0 end ordered pair
(2, −1)
Answer:
b, c, d, f
Step-by-step explanation:
Which ordered pairs are solutions to the inequality?
2x+3y≥−1?
a≥b means that A must be equal to or greater than B.
Let's do this the long, but easy way, by plugging it in!
(x,y)
a. (0,-1) -> -3≥-1 -> false
b. (5,-1)-> 7≥-1 -> true
c. (-2,1) -> -1≥-1 -> true
d. (0,1) -> 3≥-1 -> true
e. (-6,0) -> -12≥-1 - > false
f. (2,-1) -> 1≥-1 -> true
Let me know if it is incorrect!
- a friendly 8th grader :)
Time plots are special scatterplots where the explanatory variable, x, is a measure of time
The statement " Time plots are special scatterplots where the explanatory variable, x, is a measure of time" is true because time plots are scatterplots where the x-axis represents time, and they are commonly used to visualize trends and patterns in time series data.
A time plot is a type of scatterplot where the x-axis represents time and the y-axis represents a response variable. Time plots are useful for displaying data that change over time and can reveal trends, patterns, and seasonality in the data. They are commonly used in fields such as economics, finance, and social sciences to analyze time series data.
By visualizing data over time, time plots can help to identify relationships, outliers, and potential forecasting models. Overall, time plots are a powerful tool for analyzing and understanding trends and patterns in time series data.
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The given question is incomplete, the complete question is:
Time plots are special scatterplots where the explanatory variable, x, is a measure of time. True or false