Hello there. To solve this question, we'll need to isolate a variable, substitute its expression into the other equation and find both values.
4x + 4y = 12
x = -2y + 8
Plug x = -2y + 8 in the first equation. Before doing so, divide both sides of the first equation by a factor of 4
x + y = 3
-2y + 8 + y = 3
Subtract 8 on both sides of the equation and add the values
-2y + y = 3 - 8
-y = -5
Multiply both sides of the equation by a factor of (-1)
y = 5
Plug this value into the expression for x
x = -2 * 5 + 8
Multiply the values
x = -10 + 8
Add the values
x = -2
These are the values we're looking for.
The solution for this system of equation is given by:
S = {(x, y) in R² | (x, y) = (-2, 5)}
Answer:
x = -2
y = 5
Step-by-step explanation:
Solving system of linear equations by substitution method:4x + 4y = 12
Divide the entire equation by 4,
x + y = 3 -------------(I)
x = -2y + 8 ------------(II)
Substitute x = -2y + 8 in equation (I)
-2y + 8 + y = 3
-2y + y + 8 = 3
Combine like terms,
-y + 8 = 3
Subtract 8 from both sides,
-y = 3 - 8
-y = - 5
Multiply the entire equation by (-1)
[tex]\sf \boxed{\bf y = 5}[/tex]
Substitute y= 5 in equation (II),
x = -2*5 + 8
= - 10 + 8
[tex]\sf \boxed{\bf x = -2}[/tex]
What is the slope of the line given by the following equation? 13x + 4y = 52
Given the linear equation;
[tex]13x+4y=52-----1[/tex]We can find the slope by comparing the above equation with the general equation of a line. This can be seen below.
[tex]y=mx+c------2[/tex]Where m is the slope of the equation
We then make y the subject of the formula in equation one
[tex]\begin{gathered} 13x+4y=52 \\ \text{subtract 13x from both sides} \\ 13x-13x+4y=52-13x \\ 4y=52-13x \\ \text{Divide both sides by 4} \\ \frac{4y}{4}=\frac{52}{4}-\frac{13x}{4} \\ y=13-\frac{13x}{4} \end{gathered}[/tex]By comparison,
[tex]m=-\frac{13}{4}[/tex]Answer: The slope of the equation is
[tex]\text{slope}=-\frac{13}{4}[/tex]If point (x, y) is rotated 270 degrees about the origin, the resulting point is (y, -x).TrueFalse
When we perform a clockwise rotation of 270° about the origin of a point (x, y) the resulting point is (-y, x), then the answer is false. But if the rotation is counterclockwise, the resulting point is (y, -x), so the answer is true
11.y +9=-3(x-2)14.y- 6= 4( x+3)17.y-2 =-1/2(x-4)
Three linear equations , write in standard form
y +9= 3*(x+2)
y = 3x + 3 -9 = 3x -6
y-6= 4(x + 3)
y = 4x +12 -6= 4x + 6
y - 2 = -1/2(x-4)
y = (-1/2)x +2 +2= (-1/2)x +4
The citizens of a certain community were asked to choose their favorite pet. The pie chart below shows the distribution of the citizens answers. If there are 90,000 citizens in the community, how many chose hamsters, fish, snakes?
ANSWER :
27000
EXPLANATION :
From the problem, 7% chose hamsters, 15% chose Fish and 8% chose Snakes.
A total of 7 + 15 + 8 = 30%
Multiply this percentage by the population (90,000) to get the number of people who chose these pets.
That will be :
[tex]90000(0.30)=27000[/tex]Hugo is serving fruit sorbet at his party He has 1 gallon of fruit sorbet to serve to 32 friends. If each person receives the same amount, how many cups of fruit sorbet will each person get? A. 1/4 cupB.1/2 cupC. 3/4 cupD. 1 cup
Since 1 gallon is equal to 16 cups, each person will get
[tex]\begin{gathered} \frac{16}{32}\text{ cup} \\ \frac{16}{32}=\frac{1}{2} \\ \\ \text{ each person will get } \\ \frac{1}{2}\text{ cup} \end{gathered}[/tex]Meiling has 1/ 1 4 liter of orange juice. She drinks 1/3 liter how much orange juice does she have left
Litres left can be solve as shown below
[tex]\begin{gathered} 1\frac{1}{4}\text{ - }\frac{1}{3} \\ using\text{ the LCM, we have} \\ \frac{5}{4}-\frac{1}{3} \\ \frac{15\text{ - 4 }}{12}=\frac{11}{12} \end{gathered}[/tex]r(x)=−x−7 when x=−2,0, and 5
Given,
The expression of the function,
[tex]r(x)=-x-7[/tex]The value of r(x) at x = -2 is,
[tex]r(-2)=-(-2)-7=2-7=-5[/tex]The value of r(x) at x = 0 is,
[tex]r(0)=-(0)-7=0-7=-7[/tex]The value of r(x) at x = 5 is,
[tex]r(5)=-(5)-7=-5-7=-12[/tex]Hence, the value of r(x) is -2, -7 and -12.
A person wants to increase a (5 in. x 7 in.) photo to an (8 in. x 10 in.) but since the aspect ratios are not the same some of the picture will get chopped off. ti 8" original picture blown-up picture with frame shown What percentage of the picture can be used in the (8 in. x 10 in.) frame?
Using the properties of aspect ratio we calculate that approximately 89.3% of the picture will be used in the new frame.
The original picture has the dimension 5 × 7 inches .
The new dimension is 8 by 10.
Now let us consider that the height is 8 inches but the width will be x for the increased size picture.
Now we will us ratio to find the width.
original / new = 5/8 = 7 / x
or, x = 11.2 inches.
Area of the new picture = 11.2 × 8 = 89.6 square inches.
Area of the picture frame = 8 × 10 = 80 square inches.
Percentage of picture used
= 80 /89.6 × 100 %
= 89.268...
≈ 89.3%
Therefore using the properties of aspect ratio we calculate that approximately 89.3% of the picture will be used in the new frame.
to learn more about aspect ratio visit:
https://brainly.com/question/18492629
#SPJ9
if pa =1/3 and pb =2/5 and p(ab) = 3/5 what is p(ab)
Given:
[tex]P(A)=\frac{1}{3}\text{ ; P(B)=}\frac{2}{5}\text{ ; P(A}\cup B)=\frac{3}{5}[/tex][tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex][tex]\begin{gathered} \frac{3}{5}=\frac{1}{3}+\frac{2}{5}-P(A\cap B) \\ P(A\cap B)=\frac{1}{3}+\frac{2}{5}-\frac{3}{5} \\ P(A\cap B)=\frac{5+6-9}{15} \\ P(A\cap B)=\frac{2}{15} \end{gathered}[/tex]Option D is the final answer.
I'm not sure how to start this problemApproximate (b) to nearest 10th
ai) y = 3.32673x + 86.32673
ii) r = 0.944502376
b) 179.5 cm
Explanation:Regression equation model is in the form:
[tex]\begin{gathered} y\text{ = ax + b} \\ a\text{ = slope} \\ b\text{ = y-intercept} \end{gathered}[/tex]To get the model that shows the relationship between x and y, we will use a regression calculator:
[tex]\begin{gathered} \text{The model is given by:} \\ y=3.32673x+86.32673 \end{gathered}[/tex]ai) a = slope, b = y-intercept of the function
[tex]\begin{gathered} \text{from the model we got:} \\ m\text{ = }3.32673 \\ \text{slope = }3.32673 \\ b\text{ = y-intercept} \\ b\text{ = }86.32673 \end{gathered}[/tex][tex]\begin{gathered} aii)\text{ r = correlation coefficient} \\ r\text{ = }\frac{S_{xy}}{\sqrt[]{S_{x\times\text{ }\times}S_{yy}}} \\ \\ \text{From the model, r = }0.944502376 \end{gathered}[/tex]b) when feet = 28 cm long, height = ?
x = 28, y = ?
[tex]\begin{gathered} \text{substitute for x in the model:} \\ y=3.32673x+86.32673 \\ y=3.32673(28)+86.32673 \\ y=\text{ }179.47517 \end{gathered}[/tex]To the nearest tenth number, the height 179.5 cm
Swimming pool A is 20 yards long and 10 yards wide. Swimming pool B is 40 yardslong and 20 yards wide.Pool A20 ydsPool B20 deIn terms of area, how many times bigger is Pool B in relation to Pool A?The area of Pool B is ten times the area of Pool A.The area of Pool B is 50 percent larger of Pool A.The area of Pool B is four times the area of Pool A.The area of Pool B is twice the area of Pool A.Both pools have the same area
Data
Swimming pool A Swimming pool B
20 yards long 40 yards long
10 yards width 20 yards width
Area of a rectangle
Area = length x width
Substitution
Area A = 20 x 10 Area B = 40 x 20
Simplification
Area A = 200 yards 2 Area B = 800 yards 2
Proportion
Area B/A = 800 / 200
Result
Area B/A = 4
The area of Pool B is four times the area of Pool A.
A researcher randomly purchased several different kits of a popular building toy. The following table shows the number of pierces in each kit in the sample. Find the mode of the data
The modes of the data are 62, 282, and 367
Explanation:The mode of a distibution is the number with the highest frequency. That is, the number with the highest number of appearances.
By considering the data in the table shown:
62 appears twice
282 appears twice
367 appears twice
The other numbers appear only one time each
This means that the distribution is multimodal
The modes of the data are 62, 282, and 367
The cost of 42 grams of a nitric acid is $14.40. Type 1 nitric acid costs 45€ a gramtype 2 nitric acid costs 30¢ a gram. How many grams of each nitric acid were usecform the compound?
Solution:
Given:
Let the amount of Type 1 nitric acid used be represented by a
Let the amount of Type 2 nitric acid used be represented by b
Hence, the system of equations is;
[tex]\begin{gathered} Total\text{ }grams\text{ used is 42g} \\ a+b=42.................(1) \\ \\ \\ Cost\text{ of type 1 nitric acid is }0.45a \\ Cost\text{ of type 2 nitric acid is 0.30b} \\ Total\text{ cost of 42g used is \$14.40} \\ Hence, \\ 0.45a+0.30b=14.40...............(2) \end{gathered}[/tex]Thus, solving the system of equations simultaneously,
From equation (1),
[tex]\begin{gathered} a=42-b \\ \\ Substitute\text{ into equation \lparen2\rparen} \\ 0.45(42-b)+0.3b=14.4 \\ 18.9-0.45b+0.3b=14.4 \\ 18.9-0.15b=14.4 \\ 18.9-14.4=0.15b \\ 4.5=0.15b \\ \\ Hence, \\ \frac{4.5}{0.15}=b \\ b=30 \end{gathered}[/tex]Solving for a,
[tex]\begin{gathered} a=42-b \\ a=42-30 \\ a=12 \end{gathered}[/tex]Therefore, the answer is;
12 grams of Type 1 and 30 grams of Type 2
I NEED THIS ASAP!!!
The Helping Hands Student Club set a goal to raise $2,000 by the end of the school year for a project. After 3 months, it reaches 37% of its goal. How much was raised during the first 3 months?
Answer:
$740
Step-by-step explanation:
You want to know the amount that is 37% of $2000.
AmountThe amount can be found by multiplying the fraction by the total:
0.37 × $2000 = $740
During the first 3 months, $740 was raised.
<95141404393>
Use a system of linear equations with two variables and two equations to solve.
A number is 11 more than another number. Twice the sum of the two numbers is 14. Find the two numbers. (Enter your answers as a comma-separated list)
In order to solve linear equations in two variables two equations are needed. The solution of the equations 2(x + y) = 14 and y = 11 + x is x = -2 and y = 9.
What is a system of linear equations?A system of linear equations is a group of equations having same number of variables and degree.
For the n number of variables n number of equations are required.
On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.
Given that,
One of the number is 11 more than the other,
And, twice the sum of two numbers = 14.
Suppose one of the number be x.
And, the other number is y.
Then as per the question the pair of equations can be formed as,
2(x + y) = 14 (1)
y = 11 + x (2)
In order to solve these equations, multiply equation (2) by 2 and then substract it from equation (1) as,
2(x + y) - 2y = 14 - 2(11 + x)
=> 2x = 14 - 22 - 2x
=> 2x + 2x = -8
=> 4x = -8
=> x = -2
Substitute x = -2 in equation (2) to obtain y as,
y = 11 - 2
y = 9.
Hence, the equations for the given case are 2(x + y) = 14 and y = 11 + x and their solution is x = -2 and y = 9.
To know more about system of equations click on,
brainly.com/question/24065247
#SPJ1
-x+2y=-158x-2y=-20After performing your first step in Elimination, what is the resulting equation?Then solve for x
Let:
[tex]\begin{gathered} -x+2y=-15_{\text{ }}(1) \\ 8x-2y=-20_{\text{ }}(2) \end{gathered}[/tex]Using elimination:
[tex]\begin{gathered} (1)+(2) \\ -x+8x+2y-2y=-15-20 \\ 7x=-35 \end{gathered}[/tex]Solve for x:
Divide both sides by 7:
[tex]\begin{gathered} \frac{7x}{7}=-\frac{35}{7} \\ x=-5 \end{gathered}[/tex]Replace the value of x into (1):
[tex]\begin{gathered} 5+2y=-15 \\ 2y=-20 \\ y=-\frac{20}{2} \\ y=-10 \end{gathered}[/tex]What is the slope of a line that is perpendicular to y = 2x - 6?a.2b.-1/2c.-2d.1/2
When two lines are perpendicular to each other, their slope are inverted. This means that if the slope of a line is "m", then the one that is perpendicular to it should be "-1/m". The slope-intercept equation of a line is given by:
[tex]y=mx+b[/tex]Where "m" is the slope. The line from this problem has the slope equal to 2, therefore the slope of the line that is perpendicular to it is:
[tex]m_2\text{ = }\frac{1}{m}=-\frac{1}{2}[/tex]Consider the equation V = 4h where V is the volume (in cubic centimeters) of a box with a variable height h in centimeters and a fixed base of area 4 cm².
complete the table below to satisfy
Using linear function given, the value of v when h is 2, 6, 7 and 9 are 8cm³, 24cm³, 28cm³ and 36cm³ respectively
Linear FunctionA linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with y, this function can be written as y = 3x - 2.
In the relation, V = 4h. All we need to do is substitute the value of h into the formula and find v for that value of h.
When h = 2
v = 4h
v = 4 * 2 = 8cm³
When h = 6
v = 4 * 6 = 24cm³
when h = 7
v = 4 * 7 = 28cm³
when h = 9
v = 4 * 9 = 36cm³
Learn more on linear function here;
https://brainly.com/question/4025726
#SPJ1
Solve the following equation for and y - 3 - 7i + 6x = 19 + 2i + 13yi
Okay, here we have this:
Considering the provided equation, we are going to solve it, so we obtain the following:
[tex]\begin{gathered} -3-7i+6x=19+2i+13yi \\ (-3+6x)-7i=19+(2+13y)i \end{gathered}[/tex]So let's remember that a set of complex numbers can only be equal if their real and imaginary parts are equal. According to this we have:
-3+6x=19, -7=2+13y
6x=19+3, -7-2=13y
6x=22, -9=13y
x=22/6, y=-9/13
x=11/3, y=-9/13
Finally we obtain the following set: x=11/3, y=-9/13.
Solve for x. Round to the nearest tenth, if necessary.V4.1U43°W
For the angle 43 degree, perpendicular side is 4.1 and base side is x.
Determine the length of side x by using trigonometry.
[tex]\begin{gathered} \tan 43=\frac{4.1}{x} \\ x=\frac{4.1}{\tan 43} \\ =4.396 \\ \approx4.4 \end{gathered}[/tex]So value of x is 4.4
The sales tax rate is 10%. If Lindsey buys a fountain priced at $125.40, how much tax will she Inay? $
We have to calculate the sales tax over a purchase of $125.40.
The sales tax rate is 10%, so we can calculate:
[tex]\text{Sales tax}=\frac{10}{100}\cdot125.40=0.1\cdot125.40=12.54[/tex]Answer: the sales tax on this purchase is $12.54,
a single lily pad lies on the surface of a pond. Each day the number of lily pads doubles until the entire pond is covered on day 30. make a table that shows the number of lily pads at each day rfom day 1 to day 5. let x be the day number and y be the number of lily ad on that day
Given:
A single lily pad lies on the surface of a pond.
The number of lily pads doubles each day until the entire pond is covered on day 30.
To make a table that shows the number of lily pads on each day from day 1 to day 5:
Let x be the day number and y be the number of lily ads on that day.
On the first day, the number of lilies is 1.
On the second day, the number of Lillies is 2.
On the third day, the number of Lillies is 4.
And so on.
So, the table is,
# 8-13 classifying the polygon the number of sides.Tell weather the polygon is equilateral,equilangular,or regular. Explain your answer
EXPLANATION:
8..This is an octagon and it is a regular polygon because its sides and interior angles are equal or measure the same.
9.This is a pentagon and it is a regular polygon because its sides and interior angles are equal or mesure the same.
10.This is an equilateral triangle that means that its three sides are equal, and its three internal angles are also equal.
11.This triangle has two equal sides and one unequal, which is why it is an obtuse triangle;that is, it is equiangular, it only has two equal sides.
12.This is a regular square because all four sides are equal.
13.This is an equiangular polygon is a type of polygon whose vertex angles are equal. they are equiangular polygons because they alternate sides of two lengths.
The accompanying table shows the value of a car over time that was purchased for 13700 dollars, where x is years and y is the value of the car in dollars Write an exponential regression equation for this set of data, rounding all coefficients to the nearest thousandth . Using this equation , determine the value of the car, to the nearest cent , after 12 years ,
ANSWER
[tex]y=13700(0.919)^x[/tex]Value of the car after 12 year: $4971.72
EXPLANATION
The exponential regression equation is
[tex]y=ab^x[/tex]Using the values of the table we can find both a and b. Note that a is the value of y when x = 0, so a = 13700.
For b replace a, and x and y with the next values of the table:
[tex]\begin{gathered} 12590=13700b^1 \\ b=\frac{12590}{13700} \\ b\approx0.919 \end{gathered}[/tex]The equation is
[tex]y=13700(0.919)^x[/tex]To find the value of the car after 12 years, replace x = 12:
[tex]y=13700(0.919)^{12}\approx4971.72[/tex]Find a linear inequality for the graph.y ≥ 3y > 3x ≤ 3x < 3
Given:
A graph is given
Required:
To tell whose inequality is this.
Explanation:
[tex]\begin{gathered} This\text{ graph shows the inequality of } \\ y\ge3 \end{gathered}[/tex]Required answer:
Option A is correct.
16. An empty jar has a volume of8x2 + 2x - 4 cubic inches. Josh pours4x2 – 3x +2 cubic inches of waterinto the jar. How many more cubicinches of water could the jar stillhold?
Volume of empty jar 8x² + 2x - 4
Volume of water poured = 4x² - 3x + 2
More number of cubic inches that the jar can still hold= (8x² +2x - 4) -(4x²- 3x+2)
= 8x² + 2x - 4 - 4x² + 3x - 2
Rearrange
=8x² - 4x² + 2x + 3x - 4 - 2
=4x² + 5x - 6
Hence, the more number of cubic inches that the jar can still hold is
4x² + 5x - 6
Clearly and neatly show all work for each problem. Round all final answers to thenearest dollar. Do not round intermediate work.Fitzwilliam is buying a new car. The sticker price for the base model is $10,000,but the options he wants will cost him an extra 15%. He then talks the dealer intogiving him 10% off. Fitzwilliam has also decided to put down a 25% downpayment on the car.Find Fitzwilliam's down payment on the car.Find the balance that Fitzwilliam needs to finance.
Given:
Sticker price of car = $10,000
His options will cost him extra 15% = 0.15
Percentage discount = 10% = 0.10
Down payment = 25% = 0.25
Let's solve for the following:
• (a). Find Fitzwilliam's down payment on the car.
Given that his options will cost him extra 15% and he got a percentage discount of 10%, the total amount he will pay for the car will be:
[tex]\begin{gathered} T=10000(1+(0.15-0.10)) \\ \\ T=10000(1+0.05) \\ \\ T=10000(1.05) \\ \\ T=10500 \end{gathered}[/tex]The total cost of the car will be $10,500
Now, to find the down payment, we have:
Down payment = 25% of Tottl cost
Down payment = 0.25 x 10500
Down payment =2625
Therefore, his down payment s $2625
• (,b). Find the balance that Fitzwilliam needs to finance.
To find the amount he needs t balance, apply the formula:
Balance = Total cost - down payment
Balance = 10500 - 2625
Balance = 7875
Therefore, the balance he will need to finance is $7875
ANSWER:
(a). $2625
(b). $7875
A trap for insects is in the shape of a triangular prism. The area of the base is 4.5 in2 and the height of the prism is 3 in. What is the volume of this trap? The volume of the trap is in3
Answer:
[tex]\text{Volume}=13.5in^3[/tex]Step-by-step explanation:
The area of the volume is represented by the multiplication of the area of the base by the height:
[tex]\text{Volume}=\text{Area}\cdot\text{height}[/tex]Then, the volume of the trap is:
[tex]\begin{gathered} \text{Volume}=4.5\cdot3 \\ \text{Volume}=13.5in^3 \end{gathered}[/tex]Question Help 7.4.PS-12 Juan is designing an exercise room in his house. How many square feet of rubber flooring will he need to cover the floor? The product is sold in whole square yards. How many square yards should he buy? Explain. 10 ft 3 ft 9 ft 13 ft TUJIU . une lola alea O Te exeICISE TOUNT IS THIS IS also the lurar ammouTCOI Tuppen Houming mat Juan must have. (Type a whole number.) The number of square yards equivalent to this totallarea is 11.4 square yards. (Round to the nearest tenth as needed.) Since rubber flooring is sold in whole sq. yards, Juan must purchase exactly square yards. (Round up to the nearest square yard.) Enter your answer in the answer box and then click Check Answer. Check Answer Clear All All parts showing Review progress Next → Question Back of 10 6
The figure can be divided into a 2 shape. It can be divided into 2 rectangle. Let us find the individual areas and sum to get the area of the entire figure.
Area of first rectangle
[tex]\begin{gathered} \text{area}=lw \\ \text{area}=3\times4=12ft^2 \end{gathered}[/tex]Area of the second rectangle
[tex]undefined[/tex]BD bisects ABC. Ifm ABD - 3x +27 andm2DBC = 8x-33, what ism2 DBC?
because the line BC bisects the angle ABC we can do the next equality
the angles DBC and ABD are equals
angle ABD = angle DBC
the value of ABD = 3x+37
the value of DBC = 8x-33
then we can do the next equality with the values
3x+27=8x-33
we need to clear x, so the terms of x will go to the right side and the terms without x will go to the left side
27+33=8x-3x
60=5x
we can change the sides in order to have x
5x=60
x=60/5
x=12
angle DBC=8(12)-33=63
the angle DBC is 63°