Answer: The solution of the system of the equation is, (8,-1)
Step-by-step explanation:
Using substitution method
[tex]2x+4y=12[/tex] .......... (1)
[tex]y=\frac{1}{4}x-3[/tex] ......... (2)
Now we are putting equation (2) into equation (1), we get the value of 'x'
[tex]2x+4(\frac{1}{4}x-3)=12[/tex]
[tex]2x+\frac{4}{4}x-4\times 3=12[/tex]
[tex]2x-x=12+12[/tex]
[tex]3x=24[/tex]
[tex]x=8[/tex]
Now put the value of 'x' in equation (2), we get the value of 'y'
[tex]y=\frac{1}{4}x-3[/tex]
[tex]y=\frac{1}{4}\times 8-3[/tex]
[tex]y=2-3[/tex]
[tex]y=-1[/tex]
Hence, the correct option is, (8,-1)
The solution to the system of equations is (-1, 8).
Explanation:The given system of equations is:
2x + 4y = 12
y = ⅓x - 3
To find the solution to the system, we can solve it by substitution or elimination method:
Substitution Method:
From the second equation, we have y = ⅓x - 3.Substitute this value of y in the first equation.Replace y with ⅓x - 3 in the first equation: 2x + 4(⅓x - 3) = 12.Distribute 4 to both terms inside the parentheses: 2x + ⅓*4x - 12 = 12.Combine like terms: 2x + ⅓*4x = 12 + 12.Combine like terms: 2x + ⅓*4x = 24.Simplify: 2x + 4/4*x = 24.Simplify: 2x + x = 24.Combine like terms: 3x = 24.Divide both sides by 3 to solve for x: x = 8.Substitute the value of x in the second equation to find y: y = ⅓(8) - 3 = 2 - 3 = -1.Therefore, the solution to the system of equations is (-1, 8).
if 4 cans of tomato sauce cost $2, what is the unit price for 1 can of tomato sauce? show your work.
Which expression represents the distance between −14.6 and −5.2 on the number line?
Drag and drop the correct expression
For this case we have that the distance between the points will be given by the absolute value of the difference of both:
[tex]d = | -14.6 - (- 5.2) | = | -14.6 + 5.2 | = | -9.4 | = 9.4[/tex]
This is equivalent to:
[tex]d = | -5.2 - (- 14.6) | = | -5.2 + 14.6 | = | 9.4 | = 9.4[/tex]
Asnwer:
[tex]| -14.6 - (- 5.2) | = | -5.2 - (- 14.6) | = 9.4[/tex]
What is the value of b in -3b+5=13
Solve for x. The triangles in each pair are similar. Triangle CBA is similar to Triangle VUT.
You earned $43.70. You would like to buy some new T-shirts. Estimate the number of T-shirts you can buy if each one costs $5.45. 9 T-shirts 10 T-shirts 8 T-shirts 7 T-shirts
A box contains 10 cups of pancake mix. You use 2/3 cup each time you make pancakes. How many times can you make pancakes?
Please help what is the area of a square that is 12.4 cm on each side
Two factors are multiplied and their product it 34.44. One factor is a whole number. What is the least number of decimal places in the other factor. Explain.
The number of decimal places is the count of numbers after the decimal point in a decimal number. The least number of decimal places of the decimal factor is 2.
Let the factors be x and y; where:
[tex]x \to[/tex] whole number
[tex]y \to[/tex] number with decimal
The possible products that give 34.44 are represented as:
[tex]x \times y = 34.44[/tex]
So, we have:
[tex]2 \times 17.22 = 34.44[/tex]
[tex]3 \times 11.48 = 34.44[/tex]
[tex]4 \times 8.61 = 34.44[/tex]
[tex]5 \times 6.888 = 34.44[/tex]
[tex]6 \times 5.74 = 34.44[/tex]
And so on....
From the above computation, we have the decimal places of factors that represent y to be:
2 decimal places; i.e. numbers like 17.22, 11.483 decimal places; i.e. numbers like 6.888By comparing the decimal places of these two factors, we can conclude that the least number of decimal places is 2.
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You need to haul a load of patio bricks to a job site. Each brick weighs 4 pounds 14 ounces. Your truck can carry a 3/4-ton load. How many bricks can your truck carry in a full load?
A square pond is to be built in a park. The pond is 50 meters long and 50 meters wide. There should be a tile sidewalk 5 meters wide all around the pond. The tile is sold in crates of 45 square meters of tile. What will the tile cost if the cost of each box of tile is $74?
area of the pond is 50*50 = 2500 square meters
the walkway is 5 meters wide so the outside dimensions would be 60 meters by 60 meters
area of that is 60 *60 = 3600 meters
area of walkway is 3600 - 2500 = 1100 square feet
number of crates needed: 1100 / 45 = 24.44, round up to 25 crates
25 crates x $74 each = $1,850 total
Do you simplify first or after you divide a fraction to a decimal
2n+8n=-60
help Noelie please help babes show work
What is true about triangle LMN? Check all that apply.
Triangle is defined as the joining of three non-collinear points. The triangles based on their properties can be isosceles, scalene, equilateral, and right-angled triangles.
In the given image, the correct statements for the triangle LMN are:
A. LM ⊥ MN
D. The triangle is isosceles.
E. The triangle is a right-angled triangle.
In the given image, a right-angled triangle can be an isosceles triangle, which has its two sides equal. The right-angled triangle is defined as the triangle having one of the angles at 90-degrees.
In the given image, LM is perpendicular to the MN.
Also, the triangle is isosceles, such that LM and MN are equal because the angles MLN and LNM will be 45-degrees.
Thus, the triangle is isosceles.
The triangle is right-angled because the line segment LM is perpendicular to the MN.
Therefore, triangle LMN is an isosceles and right-angled triangle.
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The triangle is a right triangle.
Explanation of properties of triangle LMN including perpendicular segments, scalene triangle, and being a right triangle.
LM ⊥ MN: This statement indicates that segment LM is perpendicular to segment MN in triangle LMN.
The triangle is scalene: A scalene triangle has all sides of different lengths, indicating that the triangle is not equilateral or isosceles.
The triangle is a right triangle: Since LM is perpendicular to MN, this implies the triangle is a right triangle.
Complete question-
What is true about triangle LMN? Check all that apply.
LM ⊥ MN.
The triangle is scalene.
The triangle is equilateral.
The triangle is isosceles.
The triangle is a right triangle.
The monthly finance charge on a charge account is 1.5% on the unpaid amount up to $500, and 1% on the unpaid amount over $500. What is the charge on an unpaid amount of $750?
Answer:10
Step-by-step explanation:
How much cake will each person get if 3 people share 1 2 of a cake equally?
A) 1 6 B) 1 3 C) 2 3 D) 3 4
Shirley has to travel 1600 meters to get to school. How many dekameters does she have to travel?
Jacob is making spaghetti for the Anderson family reunion. He will use 14 boxes of spaghetti, with a total weight of 168 ounces. What is the rate of boxes of spaghetti to number of ounces?
Step-by-step explanation:
There are 14 boxes to 168 ounces.
Answer:
There are 14
✔ boxes to 168 ounces
Step-by-step explanation:
write 47/21 as a decimal rounded to the nearest tenth
47/21 can be written as decimal rounded to the nearest tenth as 2.2.
What is Decimals numbers?Decimal numbers are numbers which has basically a whole number part and a fractional or decimal part after a point called decimal point.
Decimal number system describes the base 10 number system.
The given number is 47/21
This is in the fractional form.
We have to make it in the decimal form.
The actual quotient got when we divide 47 by 21 is,
47/21 = 2.238095
But we need it in the rounded form which is rounded to the nearest tenth.
The tenth place value digit is 2.
The next digit is 3 which is less than 5.
So rounded to the nearest tenth is 2.2.
Hence 47/21 can be written as decimal rounded to the nearest tenth as 2.2.
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1 and 20 are alternate exterior angles true or false
a babysitter earns $9 for 1 h and $36 for 4 h
Ethan's taxable income is $87,525. Use this tax schedule to calculate the total amount he owes in taxes. $10,425.75 $18,617.75 $26,123.75
Answer:
$18,617.75
Step-by-step explanation:
$87,525-$77,100=$10,425 (the amount over $77,100)
$10,425 x .28=$2,919 (the 28% taxed amount over $77,100)
$2,919+$15,698.75 (the already taxed amount in the chart)=$18,617.75
Write 2 addition word problems using 3-digit numbers and solve them using any strategy
The speed limit is 35 MPH. What is the translation?
I NEED IT NOW
GO GO GO GO
The speed limit of 35 mph translates to approximately 56.327 km/hr.
The translation of the car's speed from kilometers per hour to miles per hour is as follows:
12 hours ago: 1 km/hr = 0.621371 miles/hour
4 hours ago: 30 km/hr = 18.6411 miles/hour
1 hour ago: 100 km/hr = 62.1371 miles/hour
15 minutes ago: 350 km/hr = 217.479 miles/hour
6 minutes ago: 1000 km/hr = 621.371 miles/hour
3 minutes ago: 3000 km/hr = 1864.11 miles/hour
Now: 20,000 km/hr = 12427.4 miles/hour
The speed limit of 35 mph translates to approximately 56.327 km/hr. The car is currently exceeding the speed limit.
Graph the line for y − 6 = −4(x+2) on the coordinate plane.
What are the points I would graph???
y=2x+4
The y-intercept is 4.
The x-intercept is -2.
The slope is 2.
The point (2,-6) runs through the line.
Freida friendly works for a local car dealer ship. She noticed that 3/4 of the cars are sedans and that half of them are white. What fraction of the dealership cars are white sedans?
Mr. Rao buus a computer, a printer and a scanner for $2543. The computer costs $1502 more than the printer. The printer costs $123 more than the scanner. How much does Mrs. Rao pay for the computer?
The marker cost 1/3 as much as the pen.the pen cost 1/3 as much as the book.the book cost 1/3 as much as the game.the price of the marker is what fraction of the price of the game??
for each equation, find the ordered pair whose x-coordinate is -4.
1. y=18-5x 2. 2x + 3y=4 3. -7 + 6y=10
To find the ordered pairs with an x-coordinate of -4 for the given equations, substitute -4 for x in the first two equations and solve for y. The resulting ordered pairs are (-4, 38) and (-4, 4). The third equation does not contain x, so no ordered pair can be found for it.
Explanation:To find the ordered pair whose x-coordinate is -4 for each given equation, we will substitute x with -4 and solve for y.
Equation 1: y = 18 - 5x
Substitute x with -4:
y = 18 - 5(-4) = 18 + 20 = 38
The ordered pair is (-4, 38).
Equation 2: 2x + 3y = 4
Substitute x with -4:
2(-4) + 3y = 4
-8 + 3y = 4
3y = 4 + 8
3y = 12
y = 12 / 3
y = 4
The ordered pair is (-4, 4).
Equation 3: -7 + 6y = 10
This equation does not contain x, therefore we cannot find an ordered pair with x-coordinate -4.
The ordered pairs with an x-coordinate of -4 for each equation are: (-4, 38) for y=18-5x, (-4, 4) for 2x+3y=4, and there is no ordered pair possible for -7+6y=10, as the equation does not contain an x-variable.
Explanation:To find the ordered pair whose x-coordinate is -4 for each given equation, we substitute x with -4 and solve for y:
For y = 18 - 5x, when x = -4:
y = 18 - 5(-4)
y = 18 + 20
y = 38
The ordered pair is (-4, 38).
For 2x + 3y = 4, when x = -4:
2(-4) + 3y = 4
-8 + 3y = 4
3y = 4 + 8
3y = 12
y = 12 / 3
y = 4
The ordered pair is (-4, 4).
For -7 + 6y = 10, we do not need to substitute x here because it is not present in the equation and no x-coordinate is needed to solve for y. This equation can be solved directly for y by isolating it:
-7 + 6y = 10
6y = 10 + 7
6y = 17
y = 17 / 6
y ≈ 2.83
The value of y is approximately 2.83, but since no x-coordinate is provided we cannot create an ordered pair.
You talk to a friend who lives in a different state. She tells you that today it is 12° below zero where she lives. You tell her it is 54° where you live. What is the difference in temperatures?
Suppose the pattern 8, 16, 24, 32, ... is continued forever. Will the number 174 appear in the pattern? Why or why not?
174 will not appear in the pattern 8, 16, 24, 32,
The given pattern 8, 16, 24, 32, ... is an arithmetic sequence where the first term (a) is 8 and the common difference (d) is 8.
We can use the formula for the nth term of an arithmetic sequence, which is:
an = a + (n-1)d
To find out if 174 is in the sequence, we set an to 174 and solve for n:
174 = 8 + (n-1)8
174 = 8 + 8n - 8
174 = 8n
n = 174 / 8
n = 21.75
Since n must be an integer for 174 to appear in the sequence, and 21.75 is not an integer, 174 will not appear in the pattern.