Given:
The system of equations is:
[tex]x+3y=-13[/tex]
[tex]4x+4y=-12[/tex]
To find:
The solution for the given system of equations.
Solution:
We have,
[tex]x+3y=-13[/tex] ..(i)
[tex]4x+4y=-12[/tex] ...(ii)
Multiply equation (i) by 4, to make common coefficient of x.
[tex]4x+12y=-52[/tex] ..(iii)
Subtract (ii) from (iii).
[tex]4x+12y-4x-4y=-52-(-12)[/tex]
[tex]8y=-40[/tex]
[tex]y=\dfrac{-40}{8}[/tex]
[tex]y=-5[/tex]
Putting [tex]y=-5[/tex] in (i), we get
[tex]x+3(-5)=-13[/tex]
[tex]x-15=-13[/tex]
[tex]x=-13+15[/tex]
[tex]x=2[/tex]
Therefore, the solution of the given system of equations is [tex]x=2,y=-5[/tex].
Place a check mark in the box next to each irrational number
combine like terms for 2x + 4 + 6x - 3
Answer:
8+1
Step-by-step explanation:
2+4+6−3
2+1+6
Element X decays radioactively with a half life of 8 minutes. If there are 480 grams of
Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 14 grams?
y=a(.5)
Answer:
40.8 minutes
Step-by-step explanation:
Element X decays radioactively with a half life of 8 minutes. If there are 480 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 14 grams?
The formula to find how long it would take which is the time elapsed is given as:
t = t½ × In(Nt/No)/-In2
t = ?
t½ = 8 minutes
Nt = Amount after the time of decay = 14 grams
No = Original Amount of substances = 480 grams
t = 8 × In(14/480)/-In2
t = 40.796285388407 minutes
Approximately to the nearest tenth = 40.8 minutes
Therefore, it would take the element X, 40.8 minutes to decay to 14 grams
Betsy borrowed $525 for a new foot stool. She made 6 monthly payments to repay the loan. She paid $35 interest. What is her simple interest rate?
35%
13.3%
6.7%
40%
20%
The simple interest rate of the loan is 13.3%.
What is simple interest rate?A simple interest rate is a type of rate that is paid only on the amount borrowed and not on both the amount borrowed and the interest already accrued as it is in a compound interest.
Simple interest rate = interest / (time x principal)
$35 / (6/12 x 525)
= 13.3%
To learn more about interest, please check: https://brainly.com/question/26164549
PLEASE HELP ME!!!! I'M GIVING 10 POINTS
1. A landscaping company charges $100 for its services plus $15 per hour. Another company charges $40 per hour. Find the number of hours for which the two companies would charge the same amount.
2. Refer to the previous problem. What would that charge amount be?
Answer: 4 hours, $160
Step-by-step explanation:
100+15x= 40x
100= 25x
4=x
4 Hours
4*40 = 160
or 100 + 15*4= 160
What is the equation of the axis of symmetry
Answer:
x=3
Step-by-step explanation:
Item 4
Write the word sentence as an inequality.
A number b is at least −3.
Answer: b≥-3
Step-by-step explanation:
at least means that it's great or equal than -3.
b≥-3
Trapezoid
Area= 1/2 (6+14)8
A=80
Now i know what the equals but i don’t know how to find the m2
Please help :)
bb
Step-by-step explanation:
honda is the lowest price on the market and the price of the following lines are not anybody else so expect to have a good time and be able to make a few things that are good
Chandra and her friends bought three tubs of popcorn at the movies for t dollars each and some candy that cost $7.00. If the girls spent less than $28, what is the most a tub of popcorn could cost? Write an inequality to represent the situation.
Answer:
3t+ 7 < 28
Step-by-step explanation:
The inequality function as follows;
Given that the cost is $7
There are three tubs of popcorn i.e. t
And, if the girl spend lower than $28 so the inequality function is
3t + 7<28
Hence, the above represent the answer
A canister holds 3 blue pens, 4 black pens, 2 red pens, and 6 pencils. The simplified ratio of ALL the pens to pencils is
Answer:
The simplified ratio of ALL the pens to pencils is
= 3:2
Step-by-step explanation:
A canister holds 3 blue pens, 4 black pens, 2 red pens, and 6 pencils.
Step 1
Sum of all the pens is:
Blue pens + Black pens + Red pens
= 3 + 4 + 2
= 9 pens
Number of pencils = 6 pencils
Step 2
The simplified ratio of ALL the pens to pencils is
Pens : Pencils
= 9 : 6
= 3:2
A grocery store offers a service where customers can place an order and have their groceries delivered to their home for a additional fee. The equation y=1.5x can be used to find y, the total cost in dollars for x, the grocery cost In dollars. Ian has groceries delivered for a total cost of &125.90. He says his grocery cost must be $118.90. Is Ian correct? Explain your reasoning
Answer:
The answer is below
Step-by-step explanation:
A linear function graph can be represented by:
y = mx + b; where m is the slope and b is the y intercept, x is the independent variable and y is the dependent variable.
Given that y represents the total cost, x represent the grocery cost and the equation is given as:
y = 1.5x
The groceries where delivered for a total cost of $125.90, The grocery cot can be gotten by substituting y = 125.9 and calculating x. Hence:
125.9 = 1.5x
x = 125.9/1,5
x = $83.93
Therefore saying that the grocery cost must be $118.90 is incorrect.
Can someone please help me?
9514 1404 393
Answer:
see below for a graphone possible solution: (12, 5)Step-by-step explanation:
I like a graphing calculator for creating graphs. Here, each inequality is in "slope-intercept" form, so the y-intercepts are easily located (+8 and -4).
The slope (x-coefficient) is the "rise" divided by the "run". The boundary line of the first inequality has a rise of -1 for each run of 3 to the right. The second rises 5 units for each 3 to the right. Starting from the y-intercept, additional points to plot are easily found.
Of course, the boundary line is solid for y ≥ ( ), and is dashed for y < ( ). The shading will be above the line (for higher y-values) for the first inequality, and below the line (for lower y-values) for the second inequality. That puts the double-shaded solution area in the right-side quadrant of the X where the lines cross.
There are an infinite number of solution points to choose from. One of them is (12, 5). Points with an x-value that is a multiple of 3 will be easiest to substitute into the inequalities to check.
5 ≥ (-1/3)(12) +8 ⇒ 5 ≥ 4 . . . true
5 < (5/3)(12) -4 ⇒ 5 < 16 . . . true
If a triangle has a leg with a length of 6 units and a hypotenuse with a length of 10 units, find the length of the other leg.
Answer: 8 units
Step-by-step explanation:
This can be solved using the Pythagorean Theorem:
c² = a² + b²
c is the hypotenuse
a and b are the sides
Solving for the length:
10² = 6² + b²
100 = 36 + b²
b² = 100 - 36
b² = 64
b = √64
b = 8 units
The missing side is 8 units.
write an equation of the line that passes through the given points (3,1) (0,10)
Answer:
y = -3x + 10
Step-by-step explanation:
10-1/0-3 = -3
y = -3x + b
1 = -3(3) + b
1 = -9 + b
10 = b
check your answer:
10 = -3(0) + 10
10 = 10
b should be 10
Can someone please help me on this??
the plane of a room is shown in the picture. the scale is 2 inches: 6 feet. what is the actual length of the room?
what is the actual width of the room? what is the actual area of the room?
Since 2 inches = 6 ft and length of room in the place = 7 inches,
(2x3.5) inches = 6x3.5 ft
7 inches = 21ft
Actual Length of Room = 21 ft.
Width of Room in plane = 3 inches
(2x1.5) inches = 6 x 1.5 ft
= 9 ft
Actual Length of Rook = 9 ft.
Actual Area of Room = Actual Length of Room x Actual Width of Room = 21 x 9 = 189 ft^2
GEOMETRY HELP WILL MARK BRAINLIEST!!!!
Answer:
PT = 11
Step-by-step explanation:
In a parallelogram, the diagonals bisect each other. So, QS cuts PR in half so that PT = TR
PT + TR = PR = 22
2 * PT = 22
PT = 11
Answer:
PT = 11
Step-by-step explanation:
Theorem: The diagonals of a parallelogram bisect each other.
So, if PR = 22, then PT = 11
See how easy that is if you know the theorem.
Will a pair of 6 feet 11 inch long skis fit in a wardrobe that is 3 feet long, 2 feet wide and 6 feet high?
Answer:
Step-by-step explanation:
Length of a pair of skis = 6 feet 11 inches
Maximum length of a the skis that can be fitted in a wardrobe is along the diagonal of the wardrobe.
From the picture attached,
BC² = 3² + 2² [By Pythagoras theorem]
BC = √(13)
By applying Pythagoras theorem in ΔABC,
AB² = AC² + BC²
AB² = 6² + (√13)²
= 36 + 13
AB = √49
Ab = 7 feet
Since, "diagonal length of the wardrobe is more than the length of skis,
skis can be fitted"
Q. What is the second step in solving the following equation?
-3x + 5 = 20
Nina mixes 200 mL of cranberry juice, 300 mL of grapefruit juice,and 700 mL of spring water to make fruit punch. What is the ratio of cranberry juice to grapefruit juice to spring water
8.4.PS-16
I NEED HELP ASAP
A student needed to find the measure of angle b. She incorrectly said
m2b = 127°. Find the correct measure of angle b. What mistake did she
likely make?
. .
b
53°
(The figure is not shown to scale.)
mZb=IN
H
1
0
va
Va
.
(1,1)
More
Enter your answer in the answer box and then click Check Answer.
1 part
remaining
Clear All
Check Answer
Answer:
your answer will be m<b=37
Step-by-step explanation:
hope it helps
Answer:
37°
She likely thought that angle b and 53° added up to 180 instead of 90
Step-by-step explanation:
b and 53° make a right angle
b + 53° = 90°
90° - 53° = 37°
She likely thought that angle b and 53° added up to 180 when it actually adds up to 90
Please help ASAP will give brainilest to best answer
Answer: 100
Step-by-step explanation:
1 cubic inch would just be 100 because each cube is 1 cubic inch. So 100(number of cubes)/1(cubic inch)=100 I hope I'm right :)
The beachfront path was 5,942 feet long.
A tropical storm caused waves that washed away 2,916
feet from the end. How long was the path after the storm?
A 3,016 feet
B 3,026 feet
C 8,858 feet
D 3,036 feet
B) 3,026 feet
Cause 5,942 - 2,916 = 3,026 feet
you can view the question below.
How much more does 2.6 need to get to 4.07?
Answer:
The answer is 1.47
Step-by-step explanation:
You would want to subtract 4.07 by 2.6
Like this: 4.07
- 2.60 <------- You can add a zero if it's easier for you to subtract.
1.47
To check your answer you can add the numbers.
2.60
+ 1.47
4.07
Which of the following is the reference angle for an angle that measures 222 degrees ?
1.22
2.48
3.64
4.42
Mr Thompson please help with my new HW
Answers:
C) x = plus/minus 11B) No real solutionsC) Two solutionsA) One solutionThe value 18 goes in the first blank. The value 17 goes in the second blank.========================================================
Explanations:
Note how (11)^2 = (11)*(11) = 121 and also (-11)^2 = (-11)*(-11) = 121. The two negatives multiply to a positive. So that's why the solution is x = plus/minus 11. The plus minus breaks down into the two equations x = 11 or x = -11.There are no real solutions here because the left hand side can never be negative, no matter what real number you pick for x. As mentioned in problem 1, squaring -11 leads to a positive number 121. The same idea applies here as well.The two solutions are x = 0 and x = -2. We set each factor equal to zero through the zero product property. Then we solve each equation for x. The x+2 = 0 leads to x = -2.We use the zero product property here as well. We have a repeated factor, so we're only solving one equation and that is x-3 = 0 which leads to x = 3. The only root is x = 3.Apply the FOIL rule on (x+1)(x+17) to end up with x^2+17x+1x+17 which simplifies fully to x^2+18x+17. The middle x coefficient is 18, while the constant term is 17.Katherine has 4 red pens, 6 blue pens, and 11 black pens in her book bag. If she randomly pulls out one pen, what is the probability that it will be black?
Answer: 52.38%
Step-by-step explanation:
11 out of 21
11/21
.5238
52.38%
The area of a rectangle is 192 in ^2. The ratio of the length to the width is 4:3. Find the length and the width.
The length of the rectangle is ___ in.
The width of the rectangle is___.
Answer:
Length = 16 in
Width = 12 in
Step-by-step explanation:
Given:
Area of a rectangle = 192 in²
Ratio(length to width) = 4:3
Find:
Length and the width
Computation:
Ratio(length to width) = 4:3
So,
Length = 4a
Width = 3a
Area of a rectangle = Length x Width
192 = 4a x 3a
192 = 12a²
a² = 16
a = 4
Length = 4a = 4 x 4 = 16 in
Width = 3a = 3 x 4 = 12 in
What is the value of the expression shown?
24 - 5^2
Answer:
-1 is the value
Step-by-step explanation:
24 - 5² = 24 - 25
= -1