Answer:
The point of intersection of the system of equations is:
(x, y) = (-2, 1)
The correct system of equations intersect at point A in this graph will be:
[tex]\begin{bmatrix}y=4x+9\\ y=-3x-5\end{bmatrix}[/tex]
Thus, the second option is correct.
Step-by-step explanation:
Given the point
A (-2, 1)Let us check the system of equations to determine whether it intersect at point A in this graph.
Given the system of equations
[tex]\begin{bmatrix}y=4x+9\\ y=-3x-5\end{bmatrix}[/tex]
Arrange equation variable for elimination
[tex]\begin{bmatrix}y-4x=9\\ y+3x=-5\end{bmatrix}[/tex]
so
[tex]y+3x=-5[/tex]
[tex]-[/tex]
[tex]\underline{y-4x=9}[/tex]
[tex]7x=-14[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}y-4x=9\\ 7x=-14\end{bmatrix}[/tex]
Solve 7x = -14 for x
[tex]7x=-14[/tex]
Divide both sides by 7
[tex]\frac{7x}{7}=\frac{-14}{7}[/tex]
Simplify
[tex]x = -2[/tex]
For y - 4x = 9 plug in x = 2
[tex]y-4\left(-2\right)=9[/tex]
[tex]y+4\cdot \:2=9[/tex]
[tex]y+8=9[/tex]
Subtract 8 from both sides
[tex]y+8-8=9-8[/tex]
Simplify
y = 1
Thus, the solution to the system of equations is:
(x, y) = (-2, 1)
From the attached graph, it is also clear that the system of equations intersects at point x = -2, and y = 1.
In other words, the point of intersection of the system of equations is:
(x, y) = (-2, 1)
Therefore, the correct system of equations intersect at point A in this graph will be:
[tex]\begin{bmatrix}y=4x+9\\ y=-3x-5\end{bmatrix}[/tex]
Thus, the second option is correct.
Find the coordinates of the vertex of the following parabola algebraically.
Write your answer as an (x, y) point.
y = x2
Answer:
I have no idea what it is sorry
PLEASE HELP
ill raise points if needed
Describe the possible lengths of the third side of the triangle if the lengths of the other two sides are 11 feet and 18 feet.
Answer: [tex]6ft < x < 30ft[/tex]
6ft is less then x and x is less then 30ft
Step-by-step explanation:
The possible length of the third side is 7 < x < 29.
What is a Triangle?Polygon which has three sides and three vertices are called a triangle.
The sum of all the angles of the triangle is 180°.
Given:
The lengths of the other two sides of a triangle are 11 feet and 18 feet.
Let the third side's length is x feet.
The sum of the two sides of the triangle is always greater than the length of the third side of the triangle.
That means,
18 + 11 > x.
And 11 + x > 18.
So, we have a possible choice,
11 + 18 < x
Simplifying,
29 < x.
Arranging in better terms,
x > 29.
Another possible choice,
18 -11 < x
7 < x
Combining both inequalities,
we get,
7 < x < 29.
Therefore, 7 < x < 29.
To learn more about the triangle;
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Nina is selling three types of energy bars at a market stall. She bought 50 Enerbars at 30p per bar and 150 Grainbars at 50p per bar from her normal supplier. She was also given 50 Amazebars as a promotion from a new supplier. Nina sells the bars for £2.20 and manages to sell all the Enerbars and Grainbars but only some Amazebars. She makes a profit of £402.80. How many Amazebars did she sell?
Answer:
24
Step-by-step explanation:
Given that:
Cost of each Enerbar = 30p
Number of Enerbars = 50
Cost of each grain bar = 50p
Number of grain bars = 150
Number of Amazebars = 50
Cost of each Amazebar = 0p (Because it was given as promotion)
Sales price of each bar = £2.20
Total profit earned = £402.80
All other bars were sold but Amazebars.
To find:
How many Amazebars were sold?
Solution:
First of all, let us have a look at the profit earned by selling each type of bar.
Profit is nothing but the difference between sales price and cost price.
Profit at selling each Enerbar = £2.20 - 30p = £1.90
Profit at selling 50 Enerbars = £1.90 [tex]\times[/tex] 50 = £95
Profit at selling each grain bar = £2.20 - 50p = £1.70
Profit at selling 50 grain bars = £1.70 [tex]\times[/tex] 150 = £255
Profit by selling Enerbars and grain bars = £95 + £255 = £350
Profit by Amazebars = £402.80 - £350 = £52.8
Number of Amazebars sold = Profit by Amazebars divided by Profit by selling one Amazebar
[tex]\Rightarrow \dfrac{\£52.80}{\£2.2}\\\Rightarrow \bold{24}[/tex]
Triangle JKL is formed by plotting three points, as shown below. What is the length of side
JK?
Answer:
5
Step-by-step explanation:
9-4=5
given
[tex] log_{2}(x) = \frac{3}{ log_{xy}(2) } [/tex]
express y in terms of x
Answer:
[tex]\displaystyle y = x^{-\frac{2}{3}}[/tex]
Step-by-step explanation:
Logarithms
Some properties of logarithms will be useful to solve this problem:
1. [tex]\log(pq)=\log p+\log q[/tex]
2. [tex]\displaystyle \log_pq=\frac{1}{\log_qp}[/tex]
3. [tex]\displaystyle \log p^q=q\log p[/tex]
We are given the equation:
[tex]\displaystyle \log_{2}(x) = \frac{3}{ \log_{xy}(2) }[/tex]
Applying the second property:
[tex]\displaystyle \log_{xy}(2)=\frac{1}{ \log_{2}(xy)}[/tex]
Substituting:
[tex]\displaystyle \log_{2}(x) = 3\log_{2}(xy)[/tex]
Applying the first property:
[tex]\displaystyle \log_{2}(x) = 3(\log_{2}(x)+\log_{2}(y))[/tex]
Operating:
[tex]\displaystyle \log_{2}(x) = 3\log_{2}(x)+3\log_{2}(y)[/tex]
Rearranging:
[tex]\displaystyle \log_{2}(x) - 3\log_{2}(x)=3\log_{2}(y)[/tex]
Simplifying:
[tex]\displaystyle -2\log_{2}(x) =3\log_{2}(y)[/tex]
Dividing by 3:
[tex]\displaystyle \log_{2}(y)=\frac{-2\log_{2}(x)}{3}[/tex]
Applying the third property:
[tex]\displaystyle \log_{2}(y)=\log_{2}\left(x^{-\frac{2}{3}}\right)[/tex]
Applying inverse logs:
[tex]\boxed{y = x^{-\frac{2}{3}}}[/tex]
help mee plzz will give brainliest
Answer:
Answer: X=12
Explanation: 180-72= 108. 108/9 = 12
Step-by-step explanation:
i am in middle school
Answer:
1.25 per pound
Step-by-step explanation:
A perfect score in the game is 300 points You get a perfect score if you knock down 120 pins
Find what percent 120 is of 300 then express the percent oa a decimal
1.) You decide to order strands of LED lights for a party. Amazon charges
a flat fee of $7.00 to ship this item, whether you order two strands or
fifty strands. If each strand costs $4.50, and your total came to $56.50,
how many strands did you order?
Quick answer please
Answer:
11
Step-by-step explanation:
56.50-7=49.50
49.50divided by 4.50=11
What is the volume of the rectangular prism? Type the answer in the boxes below. Icm cm?
Answer:
3 3/4 cm ^3
Step-by-step explanation:
The length is 2.5 the width is 1 and the height is 1.5 so 2.5x1x1.5
Hope it helps!
help pleaseeeeeeeeeeeeee
Luke bought a computer for $525 and two computer games for $34.99 each. The sales tax rate was 6.25%. How much sales tax was Luke charged?
Luke charged an amount of $37.18 in sales tax which is determined by the evaluation of 6.25% of 595.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Luke bought a computer for $525 and two computer games for $34.99 each. The sales tax rate was 6.25%.
⇒ 525 + 2×34.99 = 595
We have to determine the evaluation of 6.25% of 595.
⇒ 6.25% of 595
6.25% is expressed as 6.25/100 in fractional form
⇒ (6.25/100)(595)
6.25/100 is expressed as 0.0625 in decimal form
⇒ (0.0625 )(595)
Apply the multiplication operation, and we get
⇒ 37.18
Therefore, Luke charged an amount of $37.18 in sales tax.
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What is the common difference in the arithmetic sequence -3, -1, 1, 3, ...?
Answer:
2
Step-by-step explanation:
The common difference in an arithmetic sequence is the difference between any two terms
So, you could start by doing -3 + d = -1
-3 + d = -1
-3 + d +3 = -1 +3
d = 3 -1
d = 2
Now test it with other terms
-1 + d = 1
Substitute
-1 +2 = 1
2 -1 = 1
1 = 1
It works!!!
If you want you can try it with 1 and 3
1 + d = 3
1 + 2 = 3
3 = 3
I hope this helps!!!!
Pls help as soon as possible
Answer: 161.6 seconds
Step-by-step explanation:
1. 8.216 + 3.652 = 11.868 (add together, this is for one car)
2. 11.868 x 42 = 161.6
I will give brainliest!!!!
Answer: A, 3 B, 2 C, 6
Step-by-step explanation:
Sara went shopping. She bought six oranges at $0.25 each, two apples at $0.40 each, three plums at $0.18 each. She gave the cashier $5.00. How much change will Sara receive from the $5.00?
Answer:
$2.16
Step-by-step explanation:
Amount of change received
= $[5.00-0.25(6)-0.40(2)-0.18(3)]
= $(5.00-1.50-0.80-0.54)
= $2.16
Marie works in a garment factory that makes shirts. Marie’s job is sewing in sleeves. Marie receives .55 for each pair of sleeves she completes. During this pay period, she completed 1, 632 pairs of sleeves. What were Marie’s gross earnings?
Answer:
879.6
Step-by-step explanation:
I had a similar question that I solved which helped me here.
What is the sum of (-10)+(-7)=
Answer:
-17
Step-by-step explanation:
Answer:
-17
Step-by-step explanation:
[tex](-10)+(-7)= - 10 - 7 = - 17[/tex]
Which point represents 2?
Answer:
The answer is simple
Step-by-step explanation:
The answer is B, on a line graph the order goes from 0, 1, 2, 3 and so on without this order you can't use negative terms without a equation
A line passes through the points (6, 8) and (5,5). What is its equation in slope-intercept
form?
Answer:
y = 3x -10
Step-by-step explanation:
Use the method [tex]\frac{rise}{run}[/tex].
I took a screenshot of the graph below, as an example of the rise over run method.
3 ÷ 1 = 3
To find the y intercept, count down on the graph until you reach the point where the line crosses.
In this case, the line crossed at -10 on the y-axis.
(Look at the second image)
So plug the numbers into the equation, and then you get y = 3x -10.
40 is a rational number.
Answer: if its a true or false question then yes 40 is a rational number
Step-by-step explanation:
Answer:
40 is a rational number
Step-by-step explanation:
It can be expressed as a quotient of two factors
40/1
5
X
2
4
6
8
f(x)
7
11
15
19
Which of the following functions is represented
by the table above?
a. f(x) = 4x + 7
b. f(x) = 4x + 3
c. f(x) = 2x + 7
d. f(x) = 2x + 3
Answer:
d
Step-by-step explanation:
just substitute the numbers and if both sides equals, then its correct
HELP PLEASE I ONLY HAVE 10 MINUTES LEFT I WILL MARK BRAINLIEST ANSWER
Which equation results from adding the equations in this system?
11x-3y=-17
-4x+3y=-18
A -7x= -35
B -7x= 35
C 7x= -35
D 7x= 35
adding 11x and -4x makes it 7x
adding-3y and 3y cancels it out so your left with nothing
adding a negative and a negative keeps it a negative so its 18+17 making it -35
so the answer is C
Rewrite in simplest terms: 4(-6t – 3) - 10t
Step-by-step explanation:
4(-6t-3)-10t
-24t-12-10t
-12-24t-10t
-12-34t
Greg needs to buy plastic forks. Brand A has a box of 25 forks for $1.97. Brand B has a box of 48 forks for $2.98
Find the unit price for each brand. Then state which brand is the better buy based on the unit price.
Round your answers to the nearest cent.
Answer:
To find the price per spoon of brand A, divide the cost by the amount of spoons:
1.99 / 25 = 0.0796
Repeat this process for brand B:
3.89 / 42 = 0.0926
Brand A, at $0.08 a unit, is the better buy of brands A and B.
Hope this helps.
what is the area of the parallelogram shown?
please help!!!!
Answer
24 (x) 13= 312cm
Step-by-step explanation:
area of a parallelogram= area of a rectangle/ sqaure=
24 (x) 13= 312cm
(the 18 inches it there to confuse you some times)
The area of a circle will _____ be larger than the area of a polygon circumscribed about the circle.
always
often
sometimes
never
Which equation represents the vertical line passing through (7,-3)?
А.X=-3
B. y=-3
C. x=7
D. y=7
A geometry student named Cornell claims that the two triangles in the diagram below are similar to one another. He asserts that the LMN is similar to STU because the sides on the bigger triangle are spaced the same as the sides of the smaller triangle.
Explain why Cornell is mistaken in his conclusions about LMN and STU. In writing your response, be sure to explain the concept of proportionality. Also be sure to include important math vocabulary such as
similarity, corresponding sides, and ratios.
Jordan made a wooden square box. All sides of the wooden are 6 cm. If he wants to increase the length of all sides by 1.6 cm, what will be the perimeter and area of the new box
Answer:
Perimeter: 30.4 cm
Area:57.76
Step-by-step explanation:
6cm+1.6cm=7.6cm
Perimeter:7.6x4
Area:7.6x7.6