By solving a quadratic equation, we will see that the width of the walkway is 3ft.
How to get the width of the walkway?Remember that for a rectangle of length L and width W, the area is:
A = W*L
Now, we know that for our garden we have:
W = 8ft
L = 12ft
If we add a walkway of width x around the garden, then the new measures are:
W' = 8ft + 2x
L' = 12ft + 2x
So the area is:
A' = ( 8ft + 2x)*( 12ft + 2x)
And we know that it is equal to 192 ft^2, then:
192 ft^2 = ( 8ft + 2x)*( 12ft + 2x)
Now we can solve this for x.
192ft^2 = 96ft^2 + 4x^2 + 20ft*x
0 = 96ft^2 - 192ft^2 + 20ft*x + 4x^2
0 = -96ft^2 + 20ft*x + 4x^2
This is a quadratic equation, and the solutions are given by the Bhaskara's formula:
[tex]x = \frac{-20ft \pm \sqrt{(20ft)^2 - 4*4*(-96ft^2)} }{2*4} \\\\x = \frac{-20ft \pm 44ft}{8}[/tex]
We only take the positive solution, so we get:
x = (-20ft + 44ft)/8 = 3ft
So the width of the walkway is 3ft.
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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:
Which value of b will cause the quadratic equation x2 bx 5 = 0 to have two real number solutions?
A value in the interval (-∞,-2√5] ∪[2√5,∞) will give the two real number solutions.
Given quadratic equation is:
[tex]x^{2} +bx+5=0[/tex]
What is a quadratic equation?Any equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where a≠0.
To have two real number solutions the discriminant of a quadratic equation should be greater than or equal to zero.
[tex]b^{2} -4(1)(5)\geq 0[/tex]
[tex]b^{2} -20\geq 0[/tex]
[tex]b^{2} -(2\sqrt{5} )^2\geq 0[/tex]
[tex](b+2\sqrt{5} )(b-2\sqrt{5} )\geq 0[/tex]
[tex]b\in(-\infty,-2\sqrt{5} ]\cup [2\sqrt{5} ,\infty)[/tex]
Hence, a value in the interval (-∞,-2√5] ∪[2√5,∞) will give the two real number solutions.
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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.
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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
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.
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#SPJ2
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:
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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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
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.
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
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
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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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.
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Answer:
b,c
Step-by-step explanation:
trust
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.
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
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
A credit card is like a loan.
Select the three statements that explain why.
Answer:
The top right is the only incorrect one
Step-by-step explanation:
When money comes directly out of your bank account that is considered debit, not credit.
Does anybody know the answer to this?
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 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
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]
The box-and-whisker plot below shows the age distribution of people at a family reunion. a box-and-whisker plot is shown. the number line goes from 8 to 72 in increments of 8. the whiskers range from 8 to 71, and the box ranges from 23 to 47. a line divides the box at 38. the stem-and-leaf plot below shows the same data. a stem and leaf plot is shown. the stems from top to bottom are 0, 1, 2, 3, 4, 5, 6, 7. the first column of leaves is 8, 0, 3, 1, 0, 0, 0. the second column of leaves is 9, 1, 3, 6, 1, 2, 1. the third column of leaves is blank, 4, 5, 6, 2, 3, blank. the fourth column of leaves is blank, 5, 6, 8, 4, 6, blank. the fifth column of leaves is blank, blank, 6, 9, 6, blank, blank. the sixth column of leaves is blank, blank, blank, 9, blank, blank, blank. the seventh column of leaves is blank, blank, blank, 9, blank, blank, blank. which of the following best explains why one graph appears skewed and one graph appears symmetrical? the scale of the box-and-whisker plot does not start at zero. the interval of the box-and-whisker plot is too large. the interval of the stem-and-leaf plot is not consistent. the scale of the stem-and-leaf plot is too small for the set of data.
One graph appears skewed, and one graph appears symmetrical because the interval 2 stem and leaf plots is not consistent, statement third is correct.
What is a histogram?It is defined as the numerical data representation in the graph with the help of a bar without space. The histogram gives an idea about the data's approximate distribution.
The number line goes from 8 to 72 in incremental of 8, such as:
8, 16, 24, 32, 40, 48, 56, 64, 72
The whiskers range is from 8 to 71 and
Box ranges from 23 to 47.
The line divides the box at 38.
The mid-point of the line plot is at 40 and at first inspection, the stem and leaf plot appears to be accurate. In the stems, however, 5 is omitted entirely, giving the pattern a symmetrical rather than skewed appearance.
Thus, one graph appears skewed, and one graph appears symmetrical because the interval 2 stem and leaf plots is not consistent, statement third is correct.
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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
If the radius of a circle is 2 inches, what is the area of the circle? Use 3.14 for pi
Answer:
12.56 in squared
Step-by-step explanation:
the formula for area is radius x radius x pi
So you do 2x2x3.14
(I would just do 4x3.14)
And then you get 12.56
help me pleaseeeeeeeeee
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
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)Which shows one way to determine the factors of x3 4x2 5x 20 by grouping? x(x2 4) 5(x2 4) x2(x 4) 5(x 4) x2(x 5) 4(x 5) x(x2 5) 4x(x2 5)
The equation which shows one way to determine the factors of x3 4x2 5x 20 by grouping is x²(x + 4) + 5(x + 4).
How to find factor of polynomial?The factor of a polynomial is the terms in linear form, which are, when multiplied together, give the original polynomial equation as a result.
The polynomial equation given in the problem is,
[tex]x^3 +4x^2 +5x+ 20[/tex]
Take out the greatest common factor from the first two term which is x^2 and from the last two terms which is 5 as,
[tex]x^2(x +4)+5(x+ 4)\\[/tex]
Simplify it further,
[tex](x+4)(x^2+5)[/tex]
Thus, the equation which shows one way to determine the factors of x3 4x2 5x 20 by grouping is x²(x + 4) + 5(x + 4).
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