2x-y=7
x+y=5
Use elimination
Answers
In other words, x = 4 and y = 1
==============================================
Explanation:
Add the equations straight down.
The x terms add to 3x because 2x+x = 3xThe y terms go away when you add them since -y+y = 0y = 0The terms on the right hand sides add to 7+5 = 12After those three sets of adding terms, we end up with 3x = 12. This solves to x = 4 when you divide both sides by 3.
Use this x value to find y.
2x-y = 7
2(4)-y = 7
8-y = 7
-y = 7-8
-y = -1
y = 1
or
x+y = 5
4+y = 5
y = 5-4
y = 1
Your best best is probably to use the second equation, but it doesn't hurt to have practice with both equations. Getting the same y value helps confirm we have the correct x value.
Therefore, the solution is the ordered pair (x,y) = (4,1). Meaning that x = 4 and y = 1 pair up together.
Visual confirmation can be done by using a graphing tool like Desmos. The two lines intersect at (4, 1). See below.
Related Questions
Alice weighs 20 dogs and 20 cats. The mean weight for the dogs is 32kg and the mean weight for cats is 4kg. The range in weight for dogs is 45kg and the range in weight for cats is 0.5kg. State two conclusions you can draw from this information.
Answers
With the mean and range, we can estimate the weights of the smallest and largest animals in each group.
For cats the interval is [ 3.75kg, 4.25kg] and for dogs is [9.5kg, 54.5kg]
Which conclusions can be made with the given information?
We know that the mean weight for cats is 4kg, and the range (difference between the largest value and smallest value) is 0.5kg.
From that, we can conclude with some confidence (but not exactly), that the largest cat weights 4kg + 0.5kg/2 = 4.25kgAnd the smallest cat weights 4kg - 0.5kg/2 = 3.75kg(Assuming a normal distribution).
Similar for the dogs, the mean weight is 32kg and the range is 45kg, then:
The largest dog weights 32kg + 45kg/2 = 54.5kgThe smallest dog weights 32kg - 45kg/2 = 9.5kg(again, assuming a normal distribution).
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find the value of y when x=3
y=10-3x
Answers
Answer:
y=1
Step-by-step explanation:
In order to solve this problem, you have to substitute 3 in for x. Then you would multiply 3 by 3, which equals 9. Subtract 9 from 10, equals 1.
I included a picture so you can see the work.
Hope this helped!
Step-by-Step Explanation:
y = 10-3x , x = 3
=> y = 10 - 3x
= y = 10 - 3(3)
= y = 10 - 9
=> y = 1
Therefore, y = 1
Simplify as far as possible without a calculator.
3√7(2√2+4√7)
Answers
Answer:
[tex]6 \sqrt{14} + 84[/tex]
Step-by-step explanation:
distribute 3√7 by multiplying to each term In parenthesis
3√7×2√2+3√7×4√7
6√14+12√49
6√14+12(7)
6√14+84
6√14 + 84
or
106.449944321
Step-by-step explanation:
have √7 behave like a variable like x
have √4 behave like a variable like y
3√7(2√2+4√7)
(3√7*2√2)+ (3√7*4√7)
6√14 + (12*7)
6√14 + (84)
6√14 + (6 * 14)
An isosceles trapezoid has base lengths of 12 in and 18 in. If the area of the larger shaded triangle is 72 square inches, find the area of the smaller shaded triangle.
Answers
Answer:
32 in²
Step-by-step explanation:
length ratio = [tex]\frac{12}{18}[/tex] = [tex]\frac{2}{3}[/tex]
area ratio = ([tex]\frac{2}{3}[/tex] )² = [tex]\frac{4}{9}[/tex]
smaller area = 72 × [tex]\frac{4}{9}[/tex] = 8 × 4 = 32 in²
The area of the smaller shaded triangle is approximately 31.98 square inches.
The area of a triangle is given by the formula: A = 1/2 * base * height. In an isosceles trapezoid, the two parallel sides are equal in length. In this case, the base lengths of the trapezoid are 12 inches and 18 inches.
To find the area of the larger shaded triangle, we need to determine its base and height.
The base of the larger shaded triangle is the same as the length of the larger base of the trapezoid, which is 18 inches.
Let's denote the height of the larger shaded triangle as h1. Using the formula for the area of a triangle, we have: 72 = 1/2 * 18 * h1 To solve for h1, we can multiply both sides of the equation by 2 and divide by 18: 2 * 72 = h1 h1 = 144 / 18 h1 = 8 inches
So, the height of the larger shaded triangle is 8 inches. Now, let's find the area of the smaller shaded triangle. The base of the smaller shaded triangle is the same as the length of the smaller base of the trapezoid, which is 12 inches. Let's denote the height of the smaller shaded triangle as h2. Using the formula for the area of a triangle, we have: A = 1/2 * base * height A = 1/2 * 12 * h2
We don't know the value of h2, but we do know that the two shaded triangles are similar because they have equal angles. This means that the ratio of the heights of the two triangles is the same as the ratio of their bases. The ratio of the bases of the two triangles is 18/12 = 3/2.
So, the ratio of the heights of the two triangles is also 3/2.
To find the height of the smaller shaded triangle, we can set up a proportion: h2 / 8 = 2/3 Cross-multiplying, we have: 3 * h2 = 8 * 2 3 * h2 = 16 h2 = 16 / 3 h2 = 5.33 (rounded to two decimal places)
So, the height of the smaller shaded triangle is approximately 5.33 inches.
Now, we can find the area of the smaller shaded triangle using the formula: A = 1/2 * base * height A = 1/2 * 12 * 5.33 A = 31.98 square inches (rounded to two decimal places)
Therefore, the area of the smaller shaded triangle is approximately 31.98 square inches.
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I'm pretty sure it is, but it just seems so onesided so I wanted to make sure, is this correct?
Answers
Find the value of x in the given figure.
Answers
Sum measure of interior angles of traingle is 180° according to this rule ; sum measure of interior angles = (n-2)180 where n is the no. of sides
(3-2)180
=180°
So
[tex]72 + 65 + y= 180 \\ 137 + y= 180 \\ y= 180 - 137 \\ y = 43[/tex]
The sum of an interior and exterior angle equals to 180°
According to this
[tex]y + x = 180 \\ 43 + x = 180 \\ x = 180 - 43 \\ x = 137[/tex]
Hope it helps
Please give brainliest
What is m/D?
118°
B
87°
A
D
23/24-
A
12
Answers
Answer:
[tex]62^\circ[/tex]
Step-by-step explanation:
This is a cyclic quadrilateral (all points of the quadrilateral are on the circle), meaning opposite angles are supplementary (add up to [tex]180^\circ[/tex]).
[tex]\angle D[/tex] is opposite [tex]\angle B[/tex], which is equal to [tex]118^\circ[/tex]. This means [tex]\angle D[/tex] is equal to [tex]180^\circ - 118^\circ[/tex], which is [tex]\boxed{62^\circ}[/tex].
NEED ASAP PLS HELP
given: XZ WY, WXZ and YXZ are right triangles. Step 1: cos(W)=WZ/y; ycos(W)=Wz. Which step contains the first error in calculation
Answers
The sine ratio that was applied in step 2 is incorrect, therefore, the first error is in: B. step 2.
How to Apply the Sine Ratio?The sine ratio that is applied when we want to solve a right triangle is, sin ∅ = opposite length / hypotenuse length.
In step 2, the sine ratio applied is wrong because:
∅ = WOpposite length = XZHypotenuse length = yThus, we should have:
sin(W) = XZ/y
The first error is in: B. step 2.
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How do I solve for y on this?
Answers
(4x-6)° and (x+6y)° are both 90° because they are perpendicular, so:
4x-6= 90
4x= 96
x= 24
x+6y=90
24+6y=90
6y=66
y=11
Which of the following best describes the pattern in the diagram shown below? 2 3 O A. As you move from left to right, the number of points in the star decreases by 1. OB. As you move from left to right, the number of points in the star increases by 1. O C. As you move from right to left, the number of points in the star increases by 1. O D. As you move from left to right, the number of points in the star remains the same.
Answers
A quadrilateral is formed by the points a(1, -1), b(0, 3), c(5, 5), and d(6, 1). plot the points and use the distance formula to find the lengths of all 4 sides. what type of quadrilateral is this?
Answers
The type of quadrilateral is rectangle.
What is distance formula?
The distance between coordinate P(x1 , y1) and coordinate Q(x2 , y2) is calculated using the distance formula: d = √[(x2 - x1)² + (y2 - y1)²]
Given coordinates: a(1, -1), b(0, 3), c(5, 5), and d(6, 1).
ab= √(0-1)² + (3+1)²
ab= √17
bc= √(5-0)² + (5-3)²
bc= √29
cd= √(6-5)² + (1-5)²
cd= √17
da=√(6-1)² + (1+1)²
da= √29
ac=√(5-1)² + (5+1)²
ac= √16+36
ac= √52
bd =√(6-0)² + (1-3)²
bd= √36+4
bd= √40
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Answer:
PARALLELOGRAM
Step-by-step explanation:
opposite sides are congruent, but it doesn't have 4 right angles or 4 congruent sides; this means it's a parallelogram (and not a rectangle or rhombus)
NoT YellInG ThIS IS JuSt TO AtTRaCT AtTeNTiOn 50 POiNtS PLeaSE ANswER I Am NoT WasTiNg PoInTS!!! Find the range of 1 1/4, 5/8, 3/4, 1/2, 1 1/2, and 1 3/4
Answers
Answer:
Range = 1 1/4
Step-by-step explanation:
Range = Maximum - Minimum
Arranging the data in ascending order :
1/2, 5/8, 3/4, 1 1/4, 1 1/2, 1 3/4Solving for range :
Range = 1 3/4 - 1/2Range = 1 3/4 - 2/4Range = 7/4 - 2/4Range = 5/4Range = 1 1/4Exact Form: 5/4
Decimal: 1.25
Explanation: Range is where you subtract the biggest number and the lowest number.
Biggest Number: 1 3/4
Lowest Number: 1/2
1 3/4 - 1/2 = 1 1/4
(8 x 10^5) x (8 x 10^5)
Find the product write your answer in scientific notation
Answers
Answer:
6.4 x 10¹¹
Step-by-step explanation:
(8 x 10⁵)(8 x 10⁵) = 6.4 x 10¹¹
______________ can hold multiple values within a single variable and is defined by having values between square brackets.
Answers
The term that completes the blank and fits the description is an array
How to complete the blank?From the question, we understand that:
The variable term holds multiple valuesIt uses square bracketsit is defined by a single variableThe term that fits the above highlights is array
Hence, the complete statement is:
array can hold multiple values within a single variable and is defined by having values between square brackets.
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Find the distance between the points with coordinates (0,-2,0), (3,0,-6).
Answers
Answer:
[tex]C)~ 7~ \text{units}.[/tex]
Step-by-step explanation:
[tex]\text{Given that,}~ (x_1,y_1,z_1) = (0,-2,0)~ \text{and}~ (x_2,y_2,z_2) = (3,0,-6)\\\\\text{Distance,}~ d = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\\\\~~~~~~~~~~~~~~~=\sqrt{(3-0)^2 + (0+2)^2 +(-6-0)^2}\\\\~~~~~~~~~~~~~~~=\sqrt{3^2 +2^2 +(-6)^2}\\\\~~~~~~~~~~~~~~~=\sqrt{9+4+36}\\\\~~~~~~~~~~~~~~~=\sqrt{49}\\\\~~~~~~~~~~~~~~~=7~ \text{units}.[/tex]
Determine the solution for the following equation: (8x-8) 3/2 = 64
x = 3
x = 5
x = 13
x = 65
Answers
The correct answer is option A which is x = 3.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The expression will be solved as:-
( 8x - 8 )[tex]^\dfrac{3}{2}[/tex] = 64
We can write 64 as [tex]16^{\dfrac{3}{2}}[/tex]
( 8x - 8 )[tex]^\dfrac{3}{2}[/tex] = [tex]16^{\dfrac{3}{2}}[/tex]
8x - 8 = 16
8x = 24
x = 3
Therefore the correct answer is option A which is x = 3.
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Answer:
A. x=3.
Step-by-step explanation:
Edge 2022.
Which graph represents the solution set for the system 2x + 5y ≤ 9 and 3x + 5y ≤ 9? A. graph A B. graph B C. graph C D. graph D
Answers
Answer:
c is the answer to the question
A student claims that tan^2 0+1 = sec^2 0 can be converted to sin^2 0 + cos^2 0 = 1. which sequence of steps supports this claim?
Answers
Students claim is correct. We can convert tan²θ + 1 = sec²θ to (sin²θ + cos²θ) = 1.
What is Trigonometry?Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles.
Here,
tan²θ + 1 = sec²θ
sin²θ/cos²θ + 1 = 1/cos²θ
By taking LCM, we get
(sin²θ + cos²θ)/cos²θ = 1/cos²θ
(sin²θ + cos²θ) = cos²θ/cos²θ
(sin²θ + cos²θ) = 1
Thus, Students claim is correct. We can convert tan²θ + 1 = sec²θ to (sin²θ + cos²θ) = 1.
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Please help with the Area
Answers
PLEASE HELP QUICK :(
Answers
Answer:
A
Step-by-step explanation:
Thats how the mean works lol
(5)(5)(5)(5)(5)(5) i do not understand what that means or what am i supposed to do
Answers
Answer:
Your supposed to multiply 5*5*5*5*5*5 so the answer is 15,625
Katy invests a total of $13,000 in two accounts paying 2% and 7% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $310.00.
Invested at 2%___?
Invested at 7%___?
Answers
Answer:
2 % amount = 12000 7% amount = 1000 dollars
Step-by-step explanation:
x = 2% amount
then 13 000 - x = 7% amount
.02x + .07 (13000-x) = 310
-.05x + 910 = 310
.05x = 600
x = 600/.05 = 12000 then the 7% amount is 1000
Annie choose a red shirt at random. what is the likelihood that the shirt's large, given that it's red?
Answers
The likelihood that the shirt is large given that it is red is 14.29%
What is the probability?Probability determines the likelihood that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The likelihood that the shirt is large given that it is red = number of large red shirts / total number of red shirts
5/35 = 14.29%
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Guys please can you help with this question i dont get it at all. 10 x (-8)
Answers
Answer:
80 maybe no ummm udk sorry I might
Step-by-step explanation:
I got you I think
Suppose the length and the width of the sandbox are doubled.
Answers
The percentage change in perimeter is 100%.
The percentage change in area is 300%
How to find perimeter and area?The perimeter of the sandbox = 2l + 2w
where
l = lengthw = widthTherefore,
perimeter = 2(10) + 2(6)
perimeter = 20 + 12 = 32 ft
The area of the sand box = lw
area = 10 × 6 = 60 ft²
If the length and width are doubled,
length = 2(10) = 20 ft
width = 2(6) = 12 ft
hence,
perimeter = 2(20) + 2(12) = 40 + 24 = 64 ft
area = 12 × 20 = 240 ft²
Therefore,
percentage change in perimeter = 64 - 32 / 32 × 100 = 100%
percentage change in area = 240 - 60 / 60 × 100 = 18000 / 60 = 300%
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PLEASE PLEASE HELP ILL LIKE AND ITS WORTH 20 POINTS !!
Answers
Answer:
Left one: 27.755 Right one: 3487.5
Step-by-step explanation:
You have to use sin of angle to find the area.
Find the equation of the line through the points (-2,4) and (3,-5) using point-slope form. Then rewrite the equation in slope-intercept form.
Answers
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-2)}}} \implies \cfrac{-5 -4}{3 +2}\implies \cfrac{-9}{5}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{9}{5}}(x-\stackrel{x_1}{(-2)})\implies y-4=-\cfrac{9}{5}(x+2) \\\\\\ y-4=-\cfrac{9}{5}x-\cfrac{18}{5}\implies y=-\cfrac{9}{5}x-\cfrac{18}{5}+4\implies y=-\cfrac{9}{5}x+\cfrac{2}{5}[/tex]
A Clothing shop sold 140 Jackets an d 60 rain coats during the winter sale . Find the ratio of the number of raincoats sold to the Jackets sold.
Answers
Answer:
3:7
Step-by-step explanation:
60 ratio 140
Divide both sides by 10
6 ratio 14
Divide both sides by 2
3 ratio 7
3:7 ✔️
If the mean annual wage of her career is $35,240.00, what will her lifetime earnings be when she retires at the age of 60?
Answers
Answer:
2,114,400
Step-by-step explanation:
35,250 x 60 = 2,114,400
help please! will give brainle giving 20 points love !
Answers
Answer:
D. 75%
Step-by-step explanation:
100% - 25% = 75%
Answer:
D. 75%
Step-by-step explanation:
If 25% get into an accident then how many teenagers don't? :
100% - 25% = 75%
Have a great day! :)