Step-by-step explanation:
Proof using Discrimant:
[tex]3 { x}^{2} - 2x + \frac{1}{3} = 0[/tex]
The discrimant is
[tex] \sqrt{ {b}^{2} - 4ac} [/tex]
B is -2, A is 3 and C is 1/3 so we get
[tex] \sqrt{ {2}^{2} - 4( 3)( \frac{1}{3}) } [/tex]
[tex] \sqrt{4 - 4} [/tex]
[tex] \sqrt{0 } = 0[/tex]
Since the discrimant equal zero, there is one real distinct zero.
This zero will also have a multiplicity of 2, so the zero is technically equal to each other.
To get better at solving, let solve for zero.
[tex]3 {x}^{2} - 2x + \frac{1}{3} = 0[/tex]
[tex]3( {x}^{2} - \frac{2}{3} x + \frac{1}{9} )[/tex]
[tex]3( x - \frac{1}{3} )(x - \frac{1}{3} )[/tex]
[tex]3(x - \frac{1}{3} ) {}^{2} = 0[/tex]
[tex]x = \frac{1}{3} [/tex]
That zero is 1/3,1/3
Ray's favorite activity is taking a leisurely bike ride through the park after work. If he 326 burns calories every hour, how many hours does he need to ride in order to burn off an extra doughnut and large frozen latte that he ate that afternoon? The doughnut had 320 approximately calories, and the latte had 820 calories.
Answer: 3.5 hours
Step-by-step explanation:
From the question, we are informed that Ray's burns 326 calories every hour. We are further told that he ate a doughnut that had 320 calories, and a latte had 820 calories. The total calories will be:
= 320 + 820
= 1140 calories
The number of hours needed to burn the calories will be the total calories divided by the amount of calories burnt in an hour. This will be:
= 1140/326
= 3.5 hours
Solve for x. Round to the nearest tenth of
a degree, if necessary.
с
7
8.1
A
B
3.9
Answer: 28.8
Step-by-step explanation:
Harry has a cable the cable has a length of 16 meters harry cuts the cable into two parts, part A and part B the length of part A is 5 meters the weight of part A is 8kg work out the weight of part B
Answer:
17.6 kg
Step-by-step explanation:
5 meters = 8 kg
8/5 = 1.6 kg per meter
16-5 = 11
11*1.6 = 17.6 kg
200% is equal to what fraction?
What is the approximate volume of the cone below?
Yep A.
419 cm3
B.
1,257 cm3
C.
2,094 cm3
D.
8,377 cm3
2,094 cm^3
==========================================================
Explanation:
The diameter of 20 cm divides in half to the radius r = 10 cm.
The height is h = 20 cm.
V = volume of the cone
V = (1/3)*pi*r^2*h
V = (1/3)*pi*10^2*20
V = 2,094.3951023932 is approximate
I used my calculator's stored version of pi when computing the volume
That value then rounds to 2,094 cm^3 when rounding to the nearest whole number.
Original price? The discount is 40% in the sale price is $18
Answer:
$10.80
Step-by-step explanation:
Final Price = Original Price - Discount
Final Price = 18 - 7.2
Final Price = $10.80
What is an equation of the line that passes through the point (-4,3) and is
perpendicular to the line 4x - 5y = 20?
Answer:
5x + 4y = - 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
4x - 5y = 20 ( subtract 4x from both sides )
- 5y = - 4x + 20 ( divide all terms by - 5 )
y = [tex]\frac{4}{5}[/tex] x - 4 ← in slope- intercept form
with slope m = [tex]\frac{4}{5}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{4}{5} }[/tex] = - [tex]\frac{5}{4}[/tex] , thus
y = - [tex]\frac{5}{4}[/tex] x + c ← is the partial equation
To find c substitute (- 4, 3) into the partial equation
3 = 5 + c ⇒ c = 3 - 5 = - 2
y = - [tex]\frac{5}{4}[/tex] x - 2 ← in slope- intercept form
Multiply through by 4
4y = - 5x - 8 ( add 5x to both sides )
5x + 4y = - 8 ← equation in standard form
Given 7x + 2 58, which number is not in the solution set
I need help ASAP.
Measure of Variabilty
Easy 30 points.
Answer:
The first one is 12.0, the second one is 12.9, and the third one is greater than or equal to I believe
Step-by-step explanation:
1. because it wants the average but the average is 12.9 so we use the median which is 12.0
2. because it is basically making it into a fraction so 12.9 is the total average
3. 2.4 is greater than or it can be equal to 1.5
what is the opposite of the opposite of -6
Answer:
-6
Step-by-step explanation:
Using additive inverse you will get the answer 6 because additive inverse is the opposite of a number on the number line. But you will reverse it again so it would be -6
Answer:
the opposite of -6 = 6
the opposite of the opposite of -6 = -6
Step-by-step explanation:
easy?
what will be the total number of pencils in 9 packages?
Answer:
9x
Step-by-step explanation:
9 packages and x pencils
9x
Cindy and her family went out to eat for dinner and had a bill of $65.90 before tax and tip. There is a 7.5% tax and Cindy wants to leave a tip of 18%.
Step 1: What is her tax amount? $
Step 2: What is her bill now with the tax added? $
Step 3: What is the tip amount from Step 2's amount $
Step 4: What is the total bill amount with Step 3's amount? $
Answer: 1. 0.075 (i think) , 2. $70.84, 3. 4.77$ , 4. 71.15$ ( i think this is true i don't know fs.)
Step-by-step explanation:
Henry wraps a gift box in the shape of a square pyramid. The figure below shows a net for the gift box.
The amount of wrapping paper needed for the square pyramid gift box is: 96.72 in.².
What is the Surface Area of a Square Pyramid?Surface area of a square pyramid = area of the square base + area of the 4 triangular faces = s² + 4(1/2bh).
We are asked to find the amount of wrapping paper that would be needed to wrap the gift box, which is the surface area of the gift box that has a square pyramid shape.
Given the following dimensions of the gift box:
s = 5.2 in.
b = 5.2 in.
h = 6.7 in.
Plug in the values into s² + 4(1/2bh):
Surface area of a square pyramid = 5.2² + 4(1/2 × 5.2 × 6.7).
Surface area of a square pyramid = 96.72 in.²
Therefore, the amount of wrapping paper needed for the square pyramid gift box is: 96.72 in.².
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Find the 64th term 2,−3,−8
[tex]2~~,~~\stackrel{2-5}{-3}~~,~~\stackrel{-3-5}{-8}~~,~~...~\hspace{10em}\stackrel{common~difference}{d = -5} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\stackrel{\textit{term position}}{64}\\ a_1=\stackrel{\textit{first term}}{2}\\ d=\stackrel{\textit{common difference}}{-5} \end{cases} \\\\\\ a_{64}=2+(64-1)(-5)\implies a_{64}=2+(-315)\implies a_{64}=-313[/tex]
Answer:
-313 is the 64th term
Step-by-step explanation:
you take the second term an minus the first term with the second one {2-(-3)}
{=5} then you take two an minus five
it gives you -3 then you press minus five again it gives you negative eight then you press (equals to)until you reach the term you looking for
A
45°
B
Reflex Angle B =
degrees.
Answer:
315
Step-by-step explanation:
360 - 45 = 315
since a full circle is 360 degrees that is why we take away the 45 degrees.
Match the equations of the lines with their graphs.
y = 2x + 3
y = -2x + 3
y = 2x − 3
y = -2x − 3
pictures are in order on the sheet ill label them 1,2,3,4 so now you can answer which goes where to that.
Answer:
Step-by-step explanation:
1. y=2x-3
2. y=2x+3
3. y=-2x+3
4. y=-2x-3
The equations of the lines which goes with their graphs.
1. y=2x-3
2. y=2x+3
3. y=-2x+3
4. y=-2x-3
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
Here, we have to points (1.5,0) and, (0,-3)
So, by using the formula of equation of straight line of two-point form, we get,
(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )
=>3x-1.5y=4.5
y=2x-3
Again,
Here, we have to points (-1.5,0) and, (0,-3)
So, by using the formula of equation of straight line of two-point form, we get,
(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )
=>3x+1.5y=-4.5
y=2x+3
Here, we have to points (1.5,0) and, (0,-3)
So, by using the formula of equation of straight line of two-point form, we get,
(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )
=>-3x+1.5y=4.5
y=-2x+3
Here, we have to points (-1.5,0) and, (0,3)
So, by using the formula of equation of straight line of two-point form, we get,
(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )
=>3x+1.5y=4.5
y=-2x-3
Hence, the required equations are,
1. y=2x-3
2. y=2x+3
3. y=-2x+3
4. y=-2x-3
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The product of 5 and a number x is 14. What is the value of x? x=1 9/4 x=1 2/0 x=5/4 x=4 3/4
Answer:
[see below]
Step-by-step explanation:
"The product of 5 and a number x is 14" would be:
[tex]5x=14[/tex]
[tex]5x=14\\\\\frac{5x=14}{5}\\\\ \boxed{x=2 \frac{4}{5}}[/tex] or 2.8
Hope this helps.
Tickets to Disney World are $100. The price is going to increase on January 1. What is
the percent of change if the cost increases to a $120?
Answer:
120%
Step-by-step explanation:
Re-write the equation 6x + 3y = 30 in slope-intercept form y=mx+b.
Slope=2
x−intercept= 2/10 =5
y−intercept= −10/-1 =−10.00000
Answer:
2x+y-10=0
Step-by-step explanation:
6x+3y=30 move the constant to the left and change its sign
6x+3y-30=0
6x+3y-30=0 divide both sides of the equation by 3
Find the value of x
Change these decimals to fractions. reduce completely 0.25=
Answer:
1/4
Step-by-step explanation:
0.25
25/100
25 ÷ 25 = 1
100 ÷ 25 = 4
1/4
select correct equation rule
Answer:
x/2
Step-by-step explanation:
2/2=1=y
4/2=2=y
6/2=3=y
Find the perimeter of the rectangle. The drawing is
not to scale.
47 ft
57 ft
Answer:
p=2l+2w
p=2(57)+2(47)
p=208 feet
The perimeter of rectangle is 208 ft.
What is perimeter of rectangle?The perimeter of a rectangle is the total length or distance of its boundary on all sides. The perimeter of a rectangle is a linear measure and is expressed in linear units of meters, feet, inches, or yards. Let us first understand the two main properties of a rectangle.
All four angles of a rectangle are 90°.The opposite sides of a rectangle are equal in measure.Therefore, the Perimeter of a rectangle = 2(l + w).
Given:
length = 47 ft
width = 57 ft
So, the perimeter of rectangle
= 2( l + w)
=2( 47 + 57)
= 2 x 104
= 208.
Hence, the perimeter of rectangle is 208 ft
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E is the midpoint of AB. If
AE = 4x +6 and EB = 10x - 12.
what is AB?
Answer:
AB = 36
Step-by-step explanation:
Since E is the midpoint of AB, then
AE = EB , substitute values
4x + 6 = 10x - 12 ( subtract 10x from both sides )
- 6x + 6 = - 12 ( subtract 6 from both sides )
- 6x = - 18 ( divide both sides by - 6 )
x = 3
Thus
AB = AE + EB = 4x + 6 + 10x - 12 = 14x - 6 = 14(3) - 6 = 42 - 6 = 36
In Mr. Martins math class there are 15 students out of which 4 will be selected to receive a special award. How many combinations of students can be selected
Answer:
1365 combinations
Step-by-step explanation:
This is 15C4
= 15!/ (4!11!
= 15*14*13*12 / 4*3*2*1
= 32760/24
= 1365.
The perimeter of a regular nonagon is 45 m. How long is each side?
Answer:
5 m
Step-by-step explanation:
A nonagon has 9 sides. You get individual side length by dividing the perimeter by amount of sides. 45 divided by 9 is 5.
ANSWER GETS 50 POINTS PLEASE HELP FAST
Which of the following is NOT a possible root of the function for f(x)=3x3+ 2x2+x +4
Answer: It must be A
Step-by-step explanation:
The reason is because it is the only that is a integer and a fraction
A club puts its members into 5 groups for an activity. After 10 students have to leave early ,there are only 15 students left to finish the activity. How many students were in
each group?
Answer:
First, we need to figure out the total amount of students:
+ 10 students(ten students leave)
+ 15 students(15 students left)
10 + 15
= 25 students.
x = will represent the total amount of students in each group, so:-
5 groups per x students.
5x = 25(total students before alteration)
÷5 ÷5
x = 5, there are 5 students in each group.
what is the area of this triangle
Answer:
Give the triangle area so we can solve it for you.
Step-by-step explanation:
½*base*height
Step-by-step explanation:
the triangle is not given so let us take its base=b,and height=h
by using the formula=½*base*height
½*b*h
PLEASEEE help me on these 2 questions
Answer:
See below.
Step-by-step explanation:
Given numbers :-
⇒ 176, 231, 247, 256, 272, 299, 325, 343, 366, 375
⇒ Median = 272 + 299 / 2 = 285.5
⇒ Mean = 2890/10 = 289
(a) median if 375 becomes 265
⇒ 176, 231, 247, 256, 265, 272, 299, 325, 343, 366
⇒ New median = 265 + 272 / 2 = 268.5
⇒ Decreases by 17
(b) mean if 375 becomes 265
⇒ New mean = 2890 - 110 / 10 = 2780/10 = 278
⇒ Decreases by 11