What are the solutions to the following system of equations?
2x − y = 6
y = x2 − 9
Answer:
(3, 0) and (-1, -8)
Step-by-step explanation:
Equation 1
2x - y = 6Rearrange it so that it is equal to 'y'-y = 6 - 2xy = 2x - 6Substituting the value of y in Equation 2
y = x² - 9⇒ 2x - 6 = x² - 9⇒ x² - 2x - 3 = 0⇒ x² + x - 3x - 3 = 0⇒ x(x + 1) - 3(x + 1) = 0⇒ (x - 3)(x + 1) = 0⇒ x = 3, -1Taking x = 3
y = 2(3) - 6y = 0Solution 1 = (3, 0)Taking x = -1
y = 2(-1) - 6y = -2 - 6y = -8Solution 2 = (-1, -8)Solutions
(3, 0) and (-1, -8)Pls help
I don’t understand
Answer:
700ft^2
Step-by-step explanation:
What's there not to understand?
The rectangle on top has area of 23 × 14 = 322ft^2
The rectangle on bottom has area of 23 × 12 = 276ft^2
Two triangles make 1 rectnagle with area 17 × 12 = 102ft^2
Add them all up 700 ft^2
I need help NOW !!!!!!!!
Answer:
[tex]x=1~ \text{and}~ x = -6~ \text{but}~ -6 ~\text{is extraneous.}[/tex]
Step by step explanation:
[tex]2-x = 3-\sqrt{7-3x}\\\\\implies \sqrt{7-3x} = 3-2+x\\\\\implies \sqrt{7-3x} = 1+x\\\\\implies 7-3x = (1+x)^2\\\\\implies 7-3x=1+2x+x^2\\\\\implies x^2+3x+2x+1-7=0\\\\\implies x^2+5x -6 =0\\\\\implies x^2+ 6x-x -6=0\\\\\implies x(x+6)-(x+6)=0\\\\\implies (x-1)(x+6)=0\\\\\implies x =1~~, x = -6[/tex]
[tex]x=-6~ \text{Doesn't satisfy the original equation, so it is an extraneous solution.}[/tex]
Pls help…
A rectangular prism has volume 1,392 cubic feet, length 24 feet, and
height 29 feet. Find its width, in feet.
Answer:How to Find the Height of a Rectangular Prism when the Volume of a Rectangular Prism is given? The height of a rectangular prism can be calculated if the volume of the prism is given using the same formula, Volume (V) = base area × height of the prism.
Step-by-step explanation:
state the probability and odds for each event: think about rolling a die.
P(4) _____ _____
P(1 or 3) ______ ______
Answer: 1/18
Step-by-step explanation:
the probability that you roll a 4 on a standard die is 1/6 because there is 6 sides then the probability of rolling a 1 or a 3 is 2/6 or one third. then multiply 1/3 by 1/6 and you get the final answer of 1/18 :)
To either side kneel two high-court functionaries, dressed very like the oba, but with plainer headdresses and fewer neck-rings. they wear belts hung with small crocodile heads, the emblem of those authorized to conduct business with europeans – and the heads and shoulders of two tiny europeans can be seen floating in the background. the europeans are portuguese, who from the 1470s were sailing down the west coast of africa in their galleons on their way to the indies, but who were also seriously interested in west african pepper, ivory and gold. –a history of the world in 100 objects, neil macgregor which details from the passage help readers visualize the plaque? check all that apply. "plainer headdresses and fewer neck-rings" "belts hung with small crocodile heads" "the heads and shoulders of two tiny europeans" "sailing down the west coast of africa" "west african pepper, ivory and gold"
Answer:
A - B - C
Step-by-step explanation:
edge
The subtleties which are obvious in both the selection and the picture are:
Ceremonial jewelleryGovernment leadersEuropean tradersWhat is the context of the Bennin plaque?Picture result for Benin plaque metal plaques helps metal plaques that were used to embellish the Oba's castle are among the most notable of the multitude of regal specialities of Benin.
Albeit habitually portrayed as Benin Bronzes most plaques are made of leaded metal in different organizations. It is broadly acknowledged that they date to the sixteenth seventeenth hundred of years.
For more information about Benin plaque, refer to the following link:
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PLS HELP PLS HELP
If x = -4 and y = 3x – 1, then y
equals what number?
I NEED TO FINISH THIS <3
Answer:
y=-13
Step-by-step explanation:
if x=-4 and y=3x-1,
plug the value for x into the y= equation:
y=3(-4)-1
multiply through distributing 3
y=-12-1
y=-13
hope this helps <3
The probability of winning a prize in the drawing is one in a million. What is the probability if not winning a prize in the drawing?
Answer: Its 999,999
Step-by-step explanation:
You just take your chance of losing and minus your chance of winning to it.
help me pleaseeeeeeeeee
Does anybody know the answer to this?
write P if the following represents a plane and SP if Space figure.
1. one face of a rectangular box
2. shoe box
3. a pyramid
4. a sheet of plywood
5. an aquarium
6. box
7. ball
8. dice
9. ice cream
10. globe
Which statements are true? check all that apply. the data is best represented by an exponential model. the data is best represented by a quadratic model. if the price is $5 per unit, the expected profit is approximately $4,686. if the price is $80 per unit, the expected profit is negative. as the price per unit increases, the profit increases indefinitely.
The statements true are B)The data is best represented by a quadratic model. and C) If the price is $5 per unit, the expected profit is approximately $4,686.
We have the Information regarding the data is given below
What is the meaning of expected profit?Expected profit is the probability of receiving a certain profit times the profit, and the expected cost is the probability that a certain cost will be incurred times the cost.
The data should be best presented by the quadractic model.
In the case when the price should be $5 per unit so the profit should be $4,686.
Therefore,option B and option C these two options are correct.
Theefore the true statements are,The data is best represented by a quadratic model. and If the price is $5 per unit, the expected profit is approximately $4,686.
To learn more about the expected profit visit:
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Answer:
b,c
Step-by-step explanation:
trust
Rick was given a 15% tip waiting on a table of customers who ordered $60. 00 in food and drinks. How much did Rick earn in tips for waiting on this table?
Answer:
$9.00
Step-by-step explanation:
Multiply $60.00 by 15% or 0.15 to get 15% of $60.00
Solve for x. Round to the nearest tenth, if necessary.
X=???
Answer:
160
Step-by-step explanation:
[tex]the \: value \: in \: angle \: e = 180 - (90 + 60) \\ = 180 - 150 = 30degrees \: \\ using \: sinerule \: to \: find \: x \\ \frac{sin(90)}{x} = \frac{sin(30)}{80} \\ making \: x \: subject \: \\ x = \frac{sin90 \times 80}{sin30} \\ x = \frac{1 \times 80}{0.5} \\ x = \frac{80}{0.5} \\ x = 160[/tex]
Answer: x=160
Step-by-step explanation:
how do you graph the linear equation -4x-y=-4
Answer:
y=4x-4
Step-by-step explanation:
Y>-1/2x+2
Y<1/3x-1
Which graph represents the system of inequalities?
Answer:
the correct answer is option B
Answer: D
Step-by-step explanation:
Can be graphed like a regular equation. Then use the </> symbols to shade.
> above the line
< below the line
Tip: Use Desmos graphing calculator if you can.
Your parents have been paying your car insurance with the understanding that you willget a part-time job and begin to take over the payments.You have recently startedworking at a local grocery store for 20 hours a week.Your part-time pay rate is $9.00per hour.You will not be able to work any overtime
Answer:
You will earn $180 a week or $25.71 a day.
If your car is $16000 - $20000 then you will pay off the car in 622.32 days or 88 weeks or 1.68767 years.
Step-by-step explanation:
Patrick is five years younger than Ben. In two years Ben will be twice as old as Patrick. Calculate their ages
Answer:
Patrick: 5
Ben: 8
Step-by-step explanation:
Check the attachment.
Identify the a, b, and c-values for this equation:
y=-2x²+x-5
–
1. a= 2, b= 1, c= -5
2. a= -2, b=1, C = -5
3. a= -2, b = 0, c= -5
3. a= -2, b=1, c= 5
Answer:
option 2
Step-by-step explanation:
the standard form of a quadratic is
y = ax² + bx + c ( a ≠ 0 )
y = - 2x² + x - 5 ← is in standard form
with a = - 2, b = 1, c = - 5
What is the area of this i'll give brainliest if its right
Answer:
40
Step-by-step explanation:
The way you find the area is 1/2 *base*height
In this situation, it would be 1/2 *10*8
When we solve, a half of 10 is 5, and then we multiply 5*8
5*8=40
40
Find the value of x.
Answer:
8
Step-by-step explanation:
see in the attached picture...
What is the two different values of the digit 8 in the number 428. 87?
Answer:
8 and .8 or 8/10
Step-by-step explanation:
The 1st 8 is in the ones place, so it's value is 8.
The 2nd 8 is in the tenths place, so it's value is .8 or 8/10
How many lines of symmetry does this triangle have? 10 ОА. о OB. 1 O c. 2 OD. 3 O E 4
Answer: D
Step-by-step explanation: to know symmetry you must draw line from vertices of the figure ad the triangle has 3 vertices so you will draw 3 lines
The figure below is a rectangle with the dimensions given. If the perimeter of the rectangle is 48 cm, what are the
dimensions of the rectangle?
Х
3x
Answer:
6 cm and 18 cm.
Step-by-step explanation:
We are given that:
Dimensions of rectangle: x and 3xPerimeter of rectangle: 48 cmThe perimeter of any rectangle is:
L + W + L + WTo determine the dimensions of the rectangle, we need to determine the value of "x". The word "dimensions" are the length and the width of the rectangle. Since the question has not stated the length and width, we can consider the length as x and the width as 3x.
⇒ (x) + (3x) + (x) + (3x)It is also given that the perimeter of the rectangle is 48 cm. Thus, the formula with the length and the width substituted is equivalent to 48 cm.
⇒ (x) + (3x) + (x) + (3x) = 48 cmIt is required for the expression on the left hand side to be simplified. This can be done by combining like terms.
⇒ x(1 + 3 + 1 + 3) = 48 cm⇒ x(8) = 48 cmThen, we can divide 8 both sides to isolate the coefficient from "x". Once the coefficient of "x" is isolated, we will obtain the value of "x".
⇒ x(8)/8 = 48/8⇒ x = 6Finally, substitute the value of "x" into the length and the width. We considered the length to be "x" and the width to be "3x". Therefore,
⇒ Length = x cm = 6 cm⇒ Width = 3x cm = 3(6) cm = 18 cmThus, the dimensions of the rectangle are 6 cm and 18 cm.
Now
2(L+B)=482(x+3x)=482(4x)=488x=48x=6B=6
L=3(6)=18
Please help I will give brainliest.
Answer:
Options: 1, 4 & 6
Step-by-step explanation:
Yes:
1. [tex]-1(x-1)^{2} +9=-1(x^{2} -2x+1)+9=-x^{2} +2x-1+9=-x^{2} +2x+8[/tex]
4. [tex]-x^{2} +2x+8[/tex]
6. [tex](x+2)(4-x)=2x-x^{2} +8=-x^{2} +2x+8[/tex]
No:
2. [tex]-(x-9)^{2} +1=-(x^{2} -18x+81)+1=-x^{2} +18x+81+1=-x^{2} +18x+82[/tex]
3. [tex]x^{2} +2x-8[/tex]
5. [tex](x+2)(x-4)=x^{2} -2x-8[/tex]
Hope this helps
heyyy pretty pls help im lsot rn i dont understand
Answer:
52ft
Step-by-step explanation:
You divide the box in 2 pieces and multiply the numbers by the separate boxes that you made, then you add them.
5x2= 10
8-2= 6 -----> 7x6= 42
10 + 42 = 52
Answer: The first box is 56 The second box is 4 and the last is 52
Step-by-step explanation: The total area of the full rectangle is 8×7=56
The area of the small cut out portion is 2×2=4
The area of the remaining figure is 56-4=52
Explain for me functions in mathematics
Step-by-step explanation:
You can say that a function take input and outputs something back. for example, let's y = X + 3. You may think this is a equation.Yeah it is but it is also a function. The original function notation is for example f(X) = X+3.But we set y = f(X) so it turn out to be y=X+3.Basically these two have the same meaning.X is a input in the function above.If you set X= 5,the input is now 5 and you will get a kinda output of 5+3 =8.so y= 8 or f(5) = 8.That's all.You can check out more on the internet.
While introducing two-digit addition to a second-grade class, the teacher first models adding a problem with Unifix cubes to demonstrate the relationship between tens and ones. The next day, the teacher models adding a problem with base ten blocks and has the students draw and write the problem in their math notebooks. On day three, the teacher moves to a more abstract approach to adding two-digit numbers. What would be the next step for the teacher in this lesson series?
The next step for the teacher in this lesson series is to give them questions on addition to show the knowledge regarding the addition.
How to illustrate the addition?From the information, the teacher is introducing two-digit addition to a second-grade class.
In this case, the teacher first models adding a problem with unifix cubes to demonstrate the relationship between tens and ones and also models adding a problem with base ten blocks and has the students draw and write the problem in their math notebooks.
Therefore, it can be deduced that the teacher has taught them the necessary things to know regarding the topic. Hence, it's important to give them questions on addition to show the knowledge regarding the topic.
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Luke is cutting a board to make a trapezoid for a project. What is the angle measure of the piece left over after Cut A?
The angle measure of the piece is the amount of space left between the vertices
The angle of the piece left over after cut A is 35 degrees
How to determine the angle measure of cut A?In cut A, we have the following expression
x + 55 = 90
Subtract 55 from both sides to determine the measure of angle left
x = 35
Hence, the angle of the piece left over after cut A is 35 degrees
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*50 POINTS*
Select each function that has an inverse that is also a function for all values of x.
A. F(x) = 2x^2 + 4x - 3
B. F(x) = 2x + 3
C. F(x) = 3/2(x) + 2
D. F(x) = 2x^3 + 2
E. F(x) = 2x^4 + 3x^2 - x + 1
Considering the condition for an inverse function, it is found that the functions that also have an inverse for all values of x are given by:
B. F(x) = 2x + 3
C. F(x) = 3/2(x) + 2
D. F(x) = 2x^3 + 2
What is the condition for an inverse function?A function f(x) has an inverse if it does not have any horizontally aligned points, that is, if f(a) = f(b), then a = b.
Polynomial functions of even degrees have horizontally aligned points, hence functions A and E do not have inverses.
The other polynomial functions, with odd degrees, have inverses.
More can be learned about inverse functions at https://brainly.com/question/8824268