50 points! Solve the following systems of equations.
Let -4x - 15y = 17 be known as equation 1 and -x + y = -13 as equation 2.
To solve the system of equations, we need to determine the value of the "x" and "y" variables. Let us start by determining the value of the y variable.
Note: Since the second equation looks easier to solve for y (in my opinion), I will determine the value of y in the second equation.
This can be done by isolating y on one side of the equation.
Equation 2: [tex]\bold{-x + y = -13}[/tex]
Add "x" on both sides of the equation:
[tex]\implies -x + y = -13[/tex]
[tex]\implies -x + y + x = -13 + x[/tex]
[tex]\implies y = -13 + x[/tex]
Therefore, the value of y is -13 + x. Let us substitute the value of y, obtained from equation 2, into equation 1 to determine the value of x.
Equation 1: [tex]\bold{-4x - 15y = 17}[/tex]
Substitute the value of y in the equation:
[tex]\implies 4x - 15y = 17[/tex]
[tex]\implies -4x - 15(-13 + x) = 17[/tex]
Simplify the distributive property:
[tex]\implies -4x - 15(-13 + x) = 17[/tex]
[tex]\implies -4x + (195 - 15x) = 17[/tex]
[tex]\implies -4x + 195 - 15x = 17[/tex]
Combine like terms on both sides:
[tex]\implies -4x + 195 - 15x = 17[/tex]
[tex]\implies -19x + 195 = 17[/tex]
Subtract 195 on both sides of the equation:
[tex]\implies -19x + 195 = 17[/tex]
[tex]\implies -19x + 195 - 195 = 17 - 195[/tex]
[tex]\implies -19x = -178[/tex]
Divide -19 on both sides of the equation:
[tex]\implies -19x = -178[/tex]
[tex]\implies \dfrac{-19x}{-19} = \dfrac{-178}{-19}[/tex]
[tex]\implies \bold{x = \dfrac{178}{19} }[/tex]
Now, substitute the value of x in -13 + x to determine the value of y. Once determined, we can put the solution in (x, y) form.
[tex]\implies y = -13 + x[/tex]
[tex]\implies y = -13 + \dfrac{178}{19}[/tex]
[tex]\implies y = \dfrac{-247}{19} + \dfrac{178}{19}[/tex]
[tex]\implies \bold{y = \dfrac{-69}{19} }[/tex]
∴ Solution ⇒ (x, y) ⇒ (178/19, -69/19)
Therefore, the solution to the following system of equations is (178/19, -69/19)
Learn more about system of equations: https://brainly.com/question/13024262
Which of the following is a better buy?
7 tickets for $22.75
10 tickets for $31.50
Answer:
10 tickets for $31.50
Step-by-step explanation:
So If we divide 22.75 by 7 it gives you 3 dollars and 25 cents per ticket
If you divide 31.50 by 10 it gives you 3 dollars and 15 cents.
So In conclusion 10 tickets for $31.50 dollars is the better buy
Answer:
10 Tickets Is The Better Deal
Step-by-step explanation:
So What You Do Is You Will Divide 22.75 By 7
You Will Get 3.25! That Means Its 3.25 Each For 7 Tickets
For The Next One You Do The Same Thing
You Want To Divide 31.50 By 10
You Will Get 3.15! That Means Its 3.15 Each For 10 Tickets
So 3.15 Is 10 Cheaper Than 3.25 So Getting 10 Tickets Is A Better Deal
Hope This Help
DOH! My Brain Hurts
There are 82 chairs at a birthday party. The chairs need to be lined up in equal-sized rows. How many possible ways can the chairs be lined up?
Explain your answer using complete sentences.
Answer:
2 rows of 41
Step-by-step explanation:
....... i think
I have the same question, and I have nothing in my brain....-_-''
3n+14=-4 =?
Please do this this right (my grade depends on it)
Answer:
Step-by-step explanation:
-6
A table of values of a linear function is shown below.
I don't ever understand this !
A farmer takes 1 week to fill 5 bins of squash. At this rate, how long will it take to fill 350 bins?
Answer:
490 days or 70 weeks
Step-by-step explanation:
Time needed for the farmer to fill 1 bin of squash:
7 days (1 week) divided by 5 = 7/5 days
Time needed to fill 350 bins:
350 x 7/5 days = 490 days or 70 weeks
In 2012, Indonesia experienced an intense earthquake with a magnitude of 8.6 on the Richter scale. In 1952, Uganda experienced an earthquake that measured 6.5 on the Richter scale. Compare the intensities of the two earthquakes. Use a logarithmic model to solve. Round to the nearest whole number.
Answer:
The intensity of the 2012 earthquake was about 126 times the intensity of the 1952 earthquake.
Step-by-step explanation:
To compare the intensities, we first need to convert the magnitudes to intensities using the log formula. Then we will set up a ratio to compare the intensities.
Convert the magnitudes to intensities and convert to exponential form.
R=logI
2012 earthquake:
8.6I=logI=108.6
1952 earthquake:
6.5I=logI=106.5
Form a ratio of the intensities.
intensity for 2012intensity for 1952
Substitute in the values and divide by subtracting the exponents to find
108.6106.5102.1≈126.
The intensity of the 2012 earthquake was about 126 times the intensity of the 1952 earthquake.
Your answer:
The intensity of the 1952 earthquake was about 110 times the intensity of the 2012 earthquake.
Answer:
The intensity of the 2012 earthquake was about 126 times the intensity of the 1952 earthquake.
Step-by-step explanation:
To compare the intensities, we first need to convert the magnitudes to intensities using the log formula. Then we will set up a ratio to compare the intensities.
Convert the magnitudes to intensities and convert to exponential form.
R=logI
2012 earthquake:
8.6I=logI=108.6
1952 earthquake:
6.5I=logI=106.5
Form a ratio of the intensities.
intensity for 2012intensity for 1952
Substitute in the values and divide by subtracting the exponents to find
108.6106.5102.1≈126.
The intensity of the 2012 earthquake was about 126 times the intensity of the 1952 earthquake.
Summer used of her ground beef to make burgers. If she used pounds of beef, how much beef did she have at first?
Do not include units (pounds) in your answer.
Your packaging orders at green market food suppliers.each crate holds four large bottles one in each quadrant identify the mixed fraction in simplified form of bottles in the tow crates in the drawing
Answer: 1/2
Step-by-step explanation:
Answer:
1 and 1/2
Step-by-step explanation:
$28.35 bill; 6.25% tax;
20% tip (before tax)
please help!!!!!
How do I find slope and y-intercept??? Please help me!!
The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.
Which is true about the data shown in the scatter plot
Answer:
d
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Got it right in use test prep
A local little league has a total of 65 players, of whom 20% are right-handed. How many
right-handed players are there?
Answer:
13
Step-by-step explanation:
convert percent to decimal: .20
.20 x 65
13
PLEASE HELP!!!!!!!!!!There are 12 boys and 8 girls in a class.
If 2 more girls join the class, what is
the new ratio for the number of boys to
the number of girls in the class?
Answer:
12:10 or 6:5
Step-by-step explanation:
If 2 more girls join, the ratio will be 12:10 or 6:5.
what is the maximum value of the function? explain what the maximum value of this represents in this situation. make sure to include information about the x-value and y-value in your explanation
wowwwww he just roasted youuuuuuuuuu!!!!!
easy points but please answer with correct answer:)
Answer:
C
Step-by-step explanation:
I need help with math homework algebra #4
Answer:
A. (-5, 0) and (1, -3)
B. Slope (m) = -½
C. y + 3 = -½(x - 1)
D. y = -½x - ⁵/2
E. ½x + y = ⁵/2
Step-by-step explanation:
A. Two points on the line from the graph are: (-5, 0) and (1, -3)
B. The slope can be calculated using two points,(-5, 0) and (1, -3):
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - 0}{1 -(-5)} = \frac{-3}{6} = -\frac{1}{2} [/tex]
Slope (m) = -½
C. Equation in point-slope form is represented as y - b = m(x - a). Where,
(a, b) = any point on the graph.
m = slope.
Substitute (a, b) = (1, -3), and m = -½ into the point-slope equation, y - b = m(x - a).
Thus:
y - (-3) = -½(x - 1)
y + 3 = -½(x - 1)
D. Equation in slope-intercept form, can be written as y = mx + b.
Thus, using the equation in (C), rewrite to get the equation in slope-intercept form.
y + 3 = -½(x - 1)
2(y + 3) = -1(x - 1)
2y + 6 = -x + 1
2y = -x + 1 - 6
2y = -x - 5
y = -x/2 - ⁵/2
y = -½x - ⁵/2
E. Convert the equation in (D) to standard form:
y = -½x - ⁵/2
½x + y = ⁵/2
Help asap i will do brainlist and everything
Answer:
the picture isnt showing
A cruise ship traveling at a constant rate of speed was 192 miles from port after 8 hours and 600 miles from port after 25 hours.
i need to know. i have an f in math and i need to bring my grade up ASAP!!!
Answer:
THE IS ANSWER IN THE ATTACHMENT
You deposit $600 in a account earning 5% interest compounded annually. How much will you have in the account in 15 years?
Answer:
$1050 in total including the interest.
Step-by-step explanation:
The answer is 1050 because 5% of 600 is 30 and 30 multiplied by 15 is 450, and 600 plus 450 is 1050
Eric wishes to triple the recipe how much of each ingredient does
Answer:
wait what? sorry ,,,,,,,
Answer:
multiply
Step-by-step explanation:
it depends on how much eric has currently
Ex: eric has 3 teaspoons of water and 4 cups of flour
3x3=9
so he has 9 teaspoons intead of 3
4x3=12 so he needs 12 cups of flour
Medicare Hospital Insurance The average yearly Medicare Hospital Insurance benefit per person was $4064 in a recent year. Suppose the benefits are normally distributed with a standard deviation of $460. Round the final answers to at least four decimal places and intermediate z-value calculations to two decimal places.
Answer:
The answer is "0.0764"
Step-by-step explanation:
Please find the complete question in the attached file.
[tex]\to \mu = \$ \ 4064\\\\\to \sigma = \$ \ 460 \\\\\to \sigma \bar{x} = \frac{\sigma}{\sqrt{n}}\\\\[/tex]
[tex]= \frac{460}{\sqrt{21}}\\\\ = \frac{460}{4.58257569}\\\\=100.3802[/tex]
[tex]\to P(\bar{x}< \$ \ 3920) = \frac{P((\bar{x} - \mu \bar{x})}{\frac{\sigma \bar{x}<(3920 - 4064)}{100.3802)}}[/tex]
[tex]\to P(z < -1.43) = 0.0764 \\\\\to P(\bar{x}< \$ \ 3920) = 0.0764\\\\[/tex]
determine which equation below have x =15 as a solution
Answer:
x-30=-15
Step-by-step explanation:
x-30=-15
subtact 30 from both sides
255.6 grams to ounces
Answer:
9.016025oz
Step-by-step explanation:
Answer: 9.016
Step-by-step explanation:
for an approximate result, divide the mass value by 28.35
The distance between the points (3,y1) and (11,11) is 17. What is a possible value of y1?
A.
4
B.
-2
C.
-4
D.
-3
The temperature fell from 0 Degrees Fahrenheit to 15 and one-half Degrees Fahrenheit below 0 in 5 and three-fourths hours. Wen tried to find the change in temperature per hour. Her work is shown below. Negative 15 and one-half divided by 5 and three-fourths = negative StartFraction 31 over 2 EndFraction divided by StartFraction 23 over 4 EndFraction = negative StartFraction 31 over 2 EndFraction times StartFraction 23 over 4 EndFraction = Negative StartFraction 713 over 8 EndFraction When she checked the answer by estimating, it did not make sense. What error did Wen make? Wen incorrectly converted a mixed number to an improper fraction. Wen added the numerators and denominators instead of multiplying. Wen did not take the reciprocal of the divisor. Wen did not change the division problem to multiplication.
Answer:
a
Step-by-step explanation:
you should Mark me brainliest;)
What is the equation of this line?
Please Help
Y=4x
Y=-1/4x
Y=-4x
Y=1/4x
Answer: Y=-1/4x
Step-by-step explanation:
A good way to find an equation of a line is to look for the slope. An obvious spot on this line would be when it crosses (0,0), and another one to the right would be when it crosses at (4,-1).
The slope is rise over run, or if we use the two points we found, "rise" would be -1, because it's dropping 1 unit when going from (0,0) to (4,-1), and the "run" would be 4, because it moves to the right 4 from (0,0) to (4,-1).
Putting these two values together we get:
m (slope) = rise / run
m = -1 / 4
Out of all the equations we're given, we can look for the one with a slope of -1/4, which is given to us:
y = (-1/4)x
Can someone please help me with this question this is due today
Answer:
Jamie is 56 years old and savannah is 24 years old
Step-by-step explanation:
60 split in half 30, then savannah is 16 years younger than jamie so u subtract 16 from 30 and u get 14, then u add the 16 to the other 30 and get 46. Then you add 10 to each of those numbers.
What is 2345+ (27457+96584)6- 1/2 divided by 2
Answer:
746590.75
You can alos just type it into a calculator.
(PLEASE HELP I WILL MARK YOU AS BRAINLIEST!)
Dessie can type twice as many words per minute as Jasmine.
Define a variable:
Jasmine:
Dessie:
Answer:
jasmine: x
dessie: 2x
hope it helps
please mark me brainliest
The variables as per the given statement for jasmine and Dessie will be x and 2x.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the instructions provided in the question,
Dessie can type twice as compared to Jasmine per minute.
Let's assume that Jasmine can type x words per minute.
Then,
Twice Jasmine will be equal to 2x.
Then, the words typed by Dessie will be 2x per minute.
To know more about the expression:
https://brainly.com/question/14083225
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