Answer:
[tex]\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]
Step-by-step explanation:
NOTE :
[tex]x^2+ax=\left( x+\frac{a}{2} \right)^{2} -\left( \frac{a}{2} \right)^{2}[/tex]
………………………………………
f(x) = x² + x +1
[tex]=x^{2}+2\times \frac{x}{2} +1[/tex]
[tex]=\left( x+\frac{1}{2} \right)^{2} -\left( \frac{1}{2} \right)^{2} +1[/tex]
[tex]=\left( x+\frac{1}{2} \right)^{2} - \frac{1}{4}+1[/tex]
[tex]=\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]
The perimeter of a rectangle is 96 ft and the width is 22 ft what is the length of the rectangle
The length of the rectangle is 26ft.
What is the perimeter of a rectangle?
The sum of all sides of a rectangle is the perimeter of the rectangle.A rectangle has two equal lengths and two equal widths.Therefore, the perimeter 'P' of a rectangle is the sum of two equal lengths and two equal widths. That is, 'P=2l+2w' where 'l' is the length and 'w' is the width of the rectangle.What is the length of the rectangle with perimeter 96ft and the width 22ft?The perimeter of a rectangle is, P = 96 ft.
The width of the rectangle is, w = 22ft.
As we know the perimeter P of a rectangle is given by the formula, P=2l+2w
Therefore, substituting the values in the equation we get,
P = 2l + 2w
96 = 2l + 2*22
96 = 2l + 44
2l = 96 - 44
2l = 52
l = 52/2
l = 26
Hence, the length of the rectangle is 26ft.
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What is the midpoint of the segment shown below?
Answer:
The correct answer choice is D
If the value the discriminant is exactly O,
what is true about the graph of the
quadratic equation?
Jenna collects stamps. She puts the same number of stamps on each page and then inserts each page into one of her two stamp books. One of her stamp books has a total of 840 stamps. The other has 1008. What is the largest number of stamps that Jenna could be putting on each page
168 is the largest number of stamps that Jenna could be putting on each page
What is the Greatest Common Factor?
The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.
So the largest number of stamps that Jenna could be putting on each page
would be gcd of 1008 and 840.
840 = 2 x 2 x 2 x 3 x 5 x 7
1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7.
∴ The Gcd = 2 x 2 x 2 x 3 x 7 = 168.
Hence 168 is the largest number of stamps that Jenna could be putting on each page
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Copy DEF to the line so that S is the
vertex.
This task will be complete when you have
constructed an angle with vertex S that is
congruent to ZDEF.
Estimate the distance between points G and I with a compass and sketch an arc from point V which bisects the earlier arc U.
How to construct an angle with vertex?
To copy an angle we observe the subsequent steps,
1). Mark a working line with the help of a straightedge.
2). Now we set a point S as the vertex of the angle.
3). Create an arc with a radius 'r' (any length ) from vertex S which bisects the working line V.
4). With the exact radius we mark an arc from point E which bisects the line ED and EF at G and H respectively.
5). Mark an arc from point G which bisects line EF at I.
6). Estimate the distance between points G and I with a compass and sketch an arc from point V which bisects the earlier arc U.
7). Now join the points S and U.
Therefore we copy any angle.
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Circle O is shown. Line segments B O and O C are radii. Point A is on the circle and is not within angle B O C.
The measure of Arc B A C is 240. What is the ratio of the measure of the major arc to the measure of the minor arc?
3:1
1:3
2:1
1:2
The ratio of major to minor arc = 2 : 1
What is a Circle?
A circle is the locus of a point such that its distance from a fixed point (center) is always constant.
Calculation
The length of an arc (L) with center angle θ is given by:
L = (θ/360) * 2πr
where r is the radius.
Putting the values in the above formula.
For the major arc:
L = (240/360) * 2πr
For the major arc:
l = ((360-240)/360) * 2πr
l = (120/360) * 2πr
The ratio of major to minor arc = [(240/360) * 2πr] / [(120/360) *2πr] = 2 : 1
The ratio of major to minor arc = 2 : 1.
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Answer:c
Step-by-step explanation:
Find the volume of the sphere.
Answer:
268.08 (268)
Step-by-step explanation:
The volume of a sphere is 4/3*pie*r^3
Which graph represents the circle given by the equation x + y - 4x + 9y -7 = 0?
The graph of the circle equation is graph (d)
How to determine the circle?The equation is given as:
x^2 + y^2 - 4x + 9y -7 = 0
Rewrite as:
x^2 - 4x + y^2 + 9y = 7
Express (x^2 - 4x) and (y^2 + 9y) as perfect squares.
So, we have:
(x - 2)^2 + (y + 3)^2 = 7 + 4 + 20.25
Evaluate the sum
(x - 2)^2 + (y + 3)^2 = 31.25
A circle equation is represented as:
(x - h)^2 + (y - k)^2 = r^2
Where
Center = (h, k)
Radius = r
So, we have:
(h, k) = (2, -3)
r^2 = 31.25
r = 5.5
The circle that has a center of (2, -3) and a radius of 5.5 is graph d
Hence, the graph of the circle equation is graph (d)
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Joe needs to get to his house, which is 106 miles away in 2 hours. How fast does he need to drive? 48 mph 104 mph 0.019 mph 53 mph
Answer:
53 mph
Step-by-step explanation:
We need to give the answer in terms of miles per hour. This means that we need to find out how many miles Joe needs to travel in one hour. Therefore, this is a ratio problem.
We can set up a proportion where the unknown variable is the number of miles driven in one hour:
[tex]\frac{106}{2} =\frac{x}{1}[/tex]
x is just 106/2, or 53. Therefore, Joe needs to travel 53 mph
A recent survey at a local company showed that 300 employees, or 66⅔% of the company’s employees, carpool to work each day. How many employees work at this company?
I'm sorry for all this trouble just really need help I'm in summer school because I was gone most of the school year and its all online so i don't understand anything
Answer:
450 employees work at this company.
Step-by-step explanation:
300 = 2/3 of x
300 × 3 = 2x
900 = 2x
450 = x
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Answer:
Option D is correct
Step-by-step explanation:
there were no corn muffins sold.
Answer:
No corn muffins were sold at the bake sale :)
Step-by-step explanation:
Lets go thru each answer choice to see why it is incorrect/correct :)
A.
A is incorrect because more cookies were sold than muffins! that is why A is incorrect :)
B.
This calls for adding! lets do that now :)
Chocolate chip: 5
Oatmeal: 1
Peanut: 3
6 + 1 + 3 = 10
10 < 11
10 is not greater than 11 so B is incorrect!! :)
C.
We need to add again so lets do that now!
Corn: 0
Muffin: 2
2 + 0 = 2
2 < 3
2 is less than 3 so C is incorrect!! :)
D.
It is true that 0 corn muffins were sold at the bake sale so D is our answer!! :D
Have an amazing day!!
Please rate and mark brainliest!!
A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20, and a van containing 8 people is charged $32. 1. How much do you think a bus containing 30 people would be charged?
The charges of entrance fee for a bus containing 30 people is $98
Equationlet
Fixed charge = xAdditional charge per person = yNumber of person = mCharges For 2 people = mx + y
14 = 2x + y
Charges For 4 people = mx + y
20 = 4x + y
14 = 2x + y
20 = 4x + y
subtract both equation20 - 14 = 4x - 2x
6 = 2x
x = 6/2
x = 3
Substitute x = 3 into
14 = 2x + y
14 = 2(3) + y
14 = 6 + y
14 - 6 = y
8 = y
Charges For 8 people = mx + y
= 8(3) + 8
= 24 + 8
= $32
Therefore,
Charges For 30 people = mx + y
= 30(3) + y
= 90 + 8
= $98
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Solve to find the value for x in the linear equation: 3(−4x 5) = 12. 1. use the distributive property: 2. use the subtraction property of equality: 3. division property of equality: 3(−4x) 3(5) = 12 −12x 15 = 12 −12x 15 − 15 = 12 − 15 −12x = −3 x =
Answer:
1/4
Step-by-step explanation:
I think that you forgot the addition or the subtraction sign between -4x and 5. I will assume that it was an addition sign
3(-4x+5) = 12 Multiply everything in the parentheses by 3
-12x + 15 = 12 Subtract 15 from both sides
-12x = -3 Divide both sides by -12
x = -3/-12 = 3/12 =1/4
If a problem is 8(2x+4) = 2(1x+3) is the first step done of PEMDAS for THIS SPECIFIC PROBLEM parentheses or multiplication?
The first step is the parenthesis
How to determine the first step?The equation is given as:
8(2x+4) = 2(1x+3)
Using PEMDAS, the first step is to open the brackets by multiplication.
So, we have:
16x + 32 = 2x + 6
Hence, the first step is the parenthesis
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Which type of arc requires another entity to specify its start point?
Jasmine wants to buy a car marked at $5200 at a second hand car dealer. The deposit is two-fifth of the price of the car
for the next weck's delivery. Jasmine's father helped her in the deposit by paying 30% of the price. Will jasmine have
enough for her car deposit? If not, how much more does she need to add to get the deposit?
Jasmine will not have enough for the car. The amount more that she needs is $520.
Will Jasmine have enough for the car?
The first step is to convert the fraction that represents the amount needed as a deposit to percentage.
(2/5) x 100 = 40%
Difference in the deposit and the amount Jasmine's father deposited: 40% - 30% = 10%
Amount more that she needs : 10% x 5200 = $520
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To solve the equation 1. 75n = 7 for n, what operation must be applied to both sides in order to isolate the variable n?
I'LL GIVE YOU BRAINIEST!
1 1/5 · x/3 = 9/10 solve for x
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{1 \dfrac{1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]
[tex]\huge\textbf{Solve:}[/tex]
[tex]\mathbf{1 \dfrac{1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]
[tex]\mathbf{\rightarrow \dfrac{1\times5+1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]
[tex]\mathbf{\rightarrow \dfrac{5 + 1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]
[tex]\mathbf{\rightarrow \dfrac{6}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{\rightarrow \dfrac{2}{5}x = \dfrac{9}{10}}[/tex]
[tex]\huge\textbf{Multiply \boxed{\bf \dfrac{5}{2}} to both sides:}[/tex]
[tex]\mathbf{\rightarrow \dfrac{5}{2}\times \dfrac{2}{5}x = \dfrac{5}{2}\times \dfrac{9}{10}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{\rightarrow x = \dfrac{5}{2}\times \dfrac{9}{10}}[/tex]
[tex]\mathbf{\rightarrow x = \dfrac{5\times9}{2\times10}}[/tex]
[tex]\mathbf{\rightarrow x = \dfrac{45}{20}}[/tex]
[tex]\mathbf{\rightarrow x = \dfrac{45\div5}{20\div5}}[/tex]
[tex]\mathbf{\rightarrow x = \dfrac{9}{4}}[/tex]
[tex]\mathbf{x \approx 2 \dfrac{1}{4}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = }\frak{2 \dfrac{1}{4}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Question :
1 1/5 . x/3 = 9/10 Solve for xSolution :
>> (5 × 1 + 1 / 5) × (x / 3) = 9 / 10
>> (5 + 1 / 5) × (x / 3) = 9 / 10
>> (6 / 5) × (x / 3) = 9 / 10
>> 6 × x / 5 × 3 = 9 / 10
>> 6x / 15 = 9 / 10
>> 2x / 5 = 9 / 10
>> 2x × 10 = 5 × 9
>> 20x = 45
>> x = 45 / 20
>> x = 9 / 4
Therefore,
Value of x is 9 / 4 !!Which of the following ordered pairs is a solution of the system?
x + 3y = 12
y-x=12
Answer:
Step-by-step explanation:
√
A scientist measured the water pressure at different depths. She made a table showing her findings. The x-values
represent the depth, in meters. The y-values represent the pressure in atmospheres (atm).
0
15
30
0
3
6
Assuming there is a proportional relationship, which additional set of values could be included in the table?
(10,2)
(40,9)
(50,38)
(100, 76)
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The additional set of values which could be included in the table is; (10,2).
Which additional set of values can be included in the table?As evident in the task content, it follows that for a 15 unit increase in x, depth, there is a 3 unit increase in y, pressure.
On this note, it follows that with each 5 unit increase in x corresponds to 1 unit increase in y.
And ultimately, at x = 10, y = 2 × 1 = 2.
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Measure the length of AD & D B what is the ratio of AD to DB
Based on the calculations, the ratio of AD to DB is equal to 0.6.
What is a ratio?A ratio is a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
From the graph, we have:
Length of AD = 1.5
Length of DB = 2.5
Ratio = AD/DB
Ratio = 1.5/2.5
Ratio = 0.6.
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Identify the property being demonstrated for each expression.
3+ (5 + 7) = (3+5)+7
(3)[5(7)] = (3)[7(5)]
Intro
5+0=5
Dor
What is the range of the function shown on the graph
Answer:
[tex]y \geq - 6[/tex]
Step-by-step explanation:
the range is all the y values shown in the graph, so as you can see, the y values are all those greater than or equal to -6
What is the value of x? Show your work.
(Please hurry and see image for details.)
Answer:
7
Step-by-step explanation:
By the AA Postulate, triangles JKL and MNP are similar. Segment JK corresponds to segment MN, and segment JL corresponds to segment MP.
JK/MN = JL/MP
25/30 = 20/(4x-4)
25(4x-4) = 20*30
100x - 100 = 600
100x = 700
x = 7
During the month of May there were 130 births, of which 127 were full-term births and three were premature births. There were five newborn deaths. The newborn death rate is
During the month of May, there were 130 births, of which the newborn death rate is 38.4615.
According to the question,
There were 130 births, of which 127 were full-term births and three were premature births. There were five newborn deaths.
In order to find the newborn death rate we have the formula:
= [tex]\frac{number of death under 28 days of age }{Total live births in the same year}[/tex] × 1000
= [tex]\frac{5}{130}[/tex] × 1000
=[tex]\frac{5000}{130}[/tex]
=38.4615
Hence, the new born death rate is 38.4615.
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Identify the recursive formula for the sequence -3, 9, -27, 81, ....
Answer:
A
Step-by-step explanation:
there is a common ratio between consecutive terms , that is
9 ÷ - 3 = - 27 ÷ 9 = 81 ÷ - 27 = - 3
this indicates the sequence is geometric.
the recursive formula allows a term in the sequence to be found by multiplying the previous term by the common ratio r , that is
f(n) = - 3f(n - 1) if n > 1 : f(1) = - 3
Find the length of JN
The length of JN from the figure is 108
Measure of segment of a lineA line is the shortest distance between two points. Given the following parameters
Required
We need the length of JN
JN = JK + KN
JN = 59 + 49
JN = 108
Hence the length of JN from the figure is 108
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Can someone please help me on this problem and show work pleasee I’m having trouble doing this!!!
Let’s start by stating the formula for the area of a rectangle,
A=LW
the letter a represents area, l represents length, and w represents width.
Next let’s substitute known values.
A=x(x+10)
Next let’s use the distributive property
A=(x(x))+(10(x))
Now simplify.
A=x^2 + 10x
So the equation for the area of this rectangle is A=x^2+10x
I believe this is the most simplified answer, please tell me if I am wrong and I will redo my work.
An interior wall is made up of metal studs with 5/8 gypsum board on each side if the actual width of a stud is 3 5/8 what is the total thickness of the wall
Question 5 of 15
What would be the best first step in solving this system
x²-3x + 2y = -4
y = 3x + 2
Now you can equate it with second one to get x
Answer:
Substitute y = 3x + 2 into x² - 3x + 2y = -4
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}x^2-3x+2y=-4\\y=3x+2\end{cases}[/tex]
Since y is already isolated in the second equation, the best first step would be to substitute the second equation into the first equation, then solve for x.
Substitute equation 2 into equation 1:
[tex]\implies x^2-3x+2(3x+2)=-4[/tex]
Expand the brackets and simplify so that the equation equals zero:
[tex]\implies x^2-3x+6x+4=-4[/tex]
[tex]\implies x^2+3x+4+4=0[/tex]
[tex]\implies x^2+3x+8=0[/tex]
Now use the Quadratic Formula to solve for x.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Define the variables:
[tex]\implies a=1, \quad b=3, \quad c=8[/tex]
Substitute the values into the formula and solve for x:
[tex]\implies x=\dfrac{-3 \pm \sqrt{3^2-4(1)(8)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{-3 \pm \sqrt{-23}}{2}[/tex]
[tex]\implies x=\dfrac{-3 \pm \sqrt{-1 \cdot 23}}{2}[/tex]
[tex]\implies x=\dfrac{-3 \pm \sqrt{-1}\sqrt{23}}{2}[/tex]
Remember that [tex]i^2=-1[/tex]
[tex]\implies x=\dfrac{-3 \pm i\sqrt{23}}{2}[/tex]
Therefore, the solutions to the system of equations are:
[tex]x=\dfrac{-3 + i\sqrt{23}}{2}, \quad \dfrac{-3 - i\sqrt{23}}{2}[/tex]
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