Answer:
2[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{12}[/tex]
= [tex]\sqrt{4(3)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]
= 2[tex]\sqrt{3}[/tex]
The function f(x) is shown on the graph.
What is f(0)?
0 only
-6 only
-2,-1,1, and 3 only
-6,-2,-1,1,and 3 only
Answer: -6 only (choice B)
This is because the point (0,-6) is on the blue line. This is the y intercept.
Choice C would be true if you wanted to solve f(x) = 0, instead of f(0) itself.
Answer:
-6
Step-by-step explanation:
f(0) means what is the output when the input is 0
x=0 y= -6
!PLEASE HELP!
In angle ABC, AB = 2 and AC = 11. Find m
A.38
B.10
C.22
Answer:
10 digress when converted to nearest digree
Find the products using suitable identity:
a) (t –2)(t –2)
b) (3y –2z) (3y + 2z)
c) 105 × 98
Hello!
a) (t - 2)(t - 2) = (t - 2)² = t² - 4t + 4
b) (3y - 2z)(3y + 2z) = (3y)² - (2z)² = 9y² - 4z²
c) 105 × 98 = 10290
Good luck! :)
Answer:
Step-by-step explanation:
a) Identity : (a- b)² = a²- 2ab + b²
(t - 2)(t -2) = (t-2)² {a = t & b =2}
= t² -2*t*2 + 2²
= t² - 4t + 4
b) (a + b)(a - b) = a² - b²
a = 3y & y = 2z
(3y - 2z) (3y +2z) = (3y)² - (2z)²
= 3²y² - 2²z²
= 9y² - 4z²
c) (x + a)(x + b) =x² + (a+b)x + ab
105 * 98 = (100 + 5) (100 - 2) {here, x = 100 ; a = 5 ; b = -2}
= 100² + (5 +(-2) ) *100 + (5)*(-2)
= 10000 + (3)*100 - 10
= 10000 + 300 - 10
= 10290
bob swarm 4/9 killometers to an island .then he swam 2/9 killometers to a boat how far did he swim in all
Answer:
2/3 kilometers
Step-by-step explanation:
Add the two distances together
4/9 + 2/9 = 6/9
Simplify the fraction by dividing the top and bottom by 3
2/3
Answer:
Step-by-step explanation:
(4/9) + (2/9) = 6/9 = 2/3
I want to know what is the slope of the height of the cone and how to find it . please
Use the height of the cone and the radius of the base to form a right triangle. Then, use the Pythagorean theorem to find the slant height.
Sipho buys a bread on Monday and eats a third of it. On Tuesday he eats half of what is left over. If the bread is cut in 21 slice how many slice are left for Wednesday?
Answer:
7 slices
Step-by-step explanation:
1/3 of the bread would be seven slices (21/3), and he would be left with 2/3, half of which is 1/3; another seven slices were eaten. On Wednesday, he will have 7 slices left over.
The following geometric sequences represent the populations of two
bacterial cultures at the 1-hour mark, the 2-hour mark, the 3-hour mark, and so
on. Culture A starts with more bacteria, but culture B has a ratio of increase
that is larger. Which culture will have the greater population at the 18-hour
mark?
Culture A: 400, 600, 900, 1350,...
Culture B: 5, 10, 20, 40,...
A. Culture A
B. Culture B
HEELLLPPPPPP what’s the answer????????????????????????? HEELLLLLLLPPPPPPPPPPPPPP
Answer:
(-2,-2)
Step-by-step explanation:
x^2 + y^2 = 9
A circle has an equation of the form
(x-h)^2 + (y-k)^2 = r^2
where the center is at ( h,k) and the radius is r
The circle is centered at (0,0) and has a radius 3
The only point entirely within the circle must have points less than 3
(-2,-2)
What is the range of g ( x ) = 3x − 2, if the domain is { − 1, 0, 1, 2 }?
Answer:
range{-5,4)
Step-by-step explanation:
3(-1)-2= -5
3(2)-2=4
DB is a diagonal of parallelogram ABCD
What is the measurement of
Please help ASAP
Answer:
m∠DAB+m∠ADC=180
115+ 29 + m∠ADB=180
m∠ADB=180 - 115 -29
= 36°
Ella has two 8-ft. long boards. She
needs to cut pieces that are 15 inches
long. How many 15-inch pieces can
she cut from the two boards?
My sister needs help?
Answer:
Step-by-step explanation:
help asap! what does sinø=
Answer:
-3/5
Step-by-step explanation:
Pythagorean formula :
x^2 + y^2 = r^2
(-8)^2 + (-6)^2 = r^2
64 + 36 = 100
r^2 = 100
r= 10
sin is the y coordinate over the radius :
-6/10
-3/5
A ball is thrown into the air. The path it takes is modeled by the equation: -3t+24t = h, where t is the time in seconds and h is the height of the ball above the ground, measured in feet. Write an inequality to model when the height of the ball is at least 36 feet above the ground. For how long is the ball at or above 36 feet?
Given:
The given equation is:
[tex]-3t^2+24t=h[/tex]
Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.
To find:
The inequality to model when the height of the ball is at least 36 feet above the ground. Then find time taken by ball to reach at or above 36 feet.
Solution:
We have,
[tex]-3t^2+24t=h[/tex]
The height of the ball is at least 36 feet above the ground. It means [tex]h\geq 36[/tex].
[tex]-3t^2+24t\geq 36[/tex]
[tex]-3t^2+24t-36\geq 0[/tex]
[tex]-3(t^2-8t+12)\geq 0[/tex]
Splitting the middle term, we get
[tex]-3(t^2-6t-2t+12)\geq 0[/tex]
[tex]-3(t(t-6)-2(t-6))\geq 0[/tex]
[tex]-3(t-2)(t-6)\geq 0[/tex]
The critical points are:
[tex]-3(t-2)(t-6)=0[/tex]
[tex]t=2,6[/tex]
These two points divide the number line in 3 intervals [tex](-\infty,2),(2,6),(6,\infty)[/tex].
Intervals Check point [tex]-3(t-2)(t-6)\geq 0[/tex] Result
[tex](-\infty,2)[/tex] 0 [tex](-)(-)(-)=(-)<0[/tex] False
[tex](2,6)[/tex] 4 [tex](-)(+)(-)=+>0[/tex] True
[tex](6,\infty)[/tex] 8 [tex](-)(+)(+)=(-)<0[/tex] False
The inequality is true for (2,6) and the sign of inequality is [tex]\geq[/tex]. So, the ball is above 36 feet between 2 to 6 seconds.
[tex]6-2=4[/tex]
Therefore, the required inequality is [tex]-3t^2+24t\geq 36[/tex] and the ball is 36 feet above for 4 seconds.
Which statements are true about finding the difference of the expressions? Select three options
[tex]\frac{3p+1}{6p}[/tex] and [tex]\frac{2p-3}{2px^{2} }[/tex]
A. The common denominator is 6p.
B. The first fraction rewritten with the LCD is [tex]\frac{3px^{2} +p}{6px^{2} }[/tex]
C. The second fraction rewritten with the LCD is [tex]\frac{6p-9}{6p}[/tex]
D. The diffrence is [tex]\frac{3px^{2} -5p+9}{6px^{2} }[/tex]
E. The difference is a rational expression.
Answer:
CAUTION HERE !!!!!
if you suggested edits are accurate the solution would be...
[tex]\frac{3p^2 - 5p+9}{6p^2}[/tex]
that is not one of your choices, but is is almost identical to choice "D"
which is different by [tex]6px^2[/tex] vs [tex]6p^2[/tex]
which i think is your comment ????
Step-by-step explanation:
please evaluate P(7,1)
Answer:
7
Step-by-step explanation:
Using the definition
n[tex]P_{r}[/tex] = [tex]\frac{n!}{(n-r)!}[/tex]
where n! = n(n - 1)(n - 2)..... 3 × 2 × 1
Then
7[tex]P_{1}[/tex] = [tex]\frac{7!}{(7-1)!}[/tex] = [tex]\frac{7!}{6!}[/tex] ← cancel out the multiples 6 ×5 × 4 × 3 × 2 × 1 , then
7[tex]P_{1}[/tex] = 7
PLEASE HELP ME FAST!!!
QUESTION IN ATTACHMENTS
Answer:
b i think
Step-by-step explanation:
Answer:
Its A
Step-by-step explanation:
I'm very sure
A giant pie is created in an attempt to break a world record for baking. The pie is shown below:
A circle is shown with a central angle marked 45 degrees and the diameter marked 15 feet.
What is the area of the slice of pie that was cut, rounded to the nearest hundredth?
9514 1404 393
Answer:
22.09 ft²
Step-by-step explanation:
The area of a circle is given by the formula ...
A = πr² . . . . where r is the radius, half the diameter
The slice, at 45°, is 1/8 of the circle, so the area of the slice is ...
A = (1/8)π(15 ft/2)² = 225π/32 ft² ≈ 22.09 ft²
FIND THE EQUATION OF THE LINE SHOWN: QUICK I NEED TO SUMBIT MY HW
Answer:
y = -1/4x +2
Step-by-step explanation:
First find the slope using two point
(0,2) and (4,1)
m = (y2-y1)/(x2-x1)
= (1-2)/(4-0)
= -1/4
The y intercept is 2
The slope intercept form of a line is
y= mx+b where m is the slope and b is the y intercept
y = -1/4x +2
Answer:
the equation of the line is y = -1/4x +2
Step-by-step explanation:
The first step is to see where the line intercepts on the y-axis, which is 2. The next step is to see what the slope is so because it goes down 1 right 4, you find out that the slope of the line is -1/4.
Hope this helps!
Use the coordinates of the labeled point to find the point-slope equation of the line.
(12, -1)
Answer:
Choice C.
[tex]y + 1 = - 2(x - 2)[/tex]
Step-by-step explanation:
When converting to
[tex]y = mx + b[/tex]
We are left with:
[tex]y = - 2x + 3[/tex]
Which fits both the x-intercept and y-intercept.
Which of the following would best be solved using factoring by grouping?
3x^2 + 12x = 8 or x^2 + 3x - 10 = 0 or x^2 = 25 or x^3 + 5x^2 - 9x - 45 = 0
Answer:
the last one: x^3 + 5x^2 - 9x - 45 = 0
Step-by-step explanation:
You can solve all the other ones by simple factoring and/or calculator.
Since the last one has more than 3 terms, it's likely that you'll have to use group factoring to solve it.
if x=2+√5 find the value of x²-1/x²
Answer:
[tex]{ \tt{ {x}^{2} - \frac{1}{ {x}^{2} } }} \\ = { \tt{ {(2 + \sqrt{5} )}^{2} - \frac{1}{ {(2 + \sqrt{5}) }^{2} } }} \\ = { \tt{ \frac{(2 + \sqrt{5} ) {}^{4} - 1}{ {(2 + \sqrt{5} )}^{2} } }} \\ = { \tt{ \frac{(9 + 4 \sqrt{5}) {}^{2} }{ {(9 + 4\sqrt{5}) }}}} \\ = { \tt{9 + 4 \sqrt{5} }}[/tex]
Answer:
[tex]8\sqrt{5}[/tex]
Step-by-step explanation:
[tex]x = 2 + \sqrt{5}\\\\ x^{2} = (2+ \sqrt{5})^{2} \\\\ \ \ \ \ = 2^{2}+2* \sqrt{5}*2+( \sqrt{5})^{2}\\\\[/tex]
[tex]= 4 + 4 \sqrt{5}+5\\\\= 9+4 \sqrt{5}[/tex]
[tex]\frac{1}{x^{2}}=\frac{1}{9+4\sqrt{5}}\\\\=\frac{1*(9-4\sqrt{5}}{(9+4\sqrt{5})(9-4\sqrt{5})}\\\\=\frac{9-4\sqrt{5}}{9^{2}-(4\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-4^{2}(\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-16*5}\\\\=\frac{9-4\sqrt{5}}{81-80}\\\\=\frac{9-4\sqrt{5}}{1}\\\\=9-4\sqrt{5}[/tex]
[tex]x^{2}-\frac{1}{x^{2}}= 9 + 4\sqrt{5} -(9 - 4\sqrt{5})\\\\[/tex]
[tex]= 9 + 4\sqrt{5} - 9 + 4\sqrt{5}\\\\= 9 - 9 + 4\sqrt{5} + 4\sqrt{5}\\\\= 8\sqrt{5}[/tex]
Bagels cost 35p each how much is 6?
Answer:
1 = 35p
6 = 35p×6
= 240p
Therefore, 6 bagels cost 240 p
Which of the following are important properties of the arithmetic mean? Check all that apply. Multiple select question. The mean is always less than the median. All of the values in the data are used in calculating the mean. Σ(X-X)=0 i.e. the sum of the deviations is zero. There is only one mean for a set of data. The mean can be calculated for nominal data.
Answer:
All of the values in the data are used in calculating the mean.
The sum of the deviations is zero.
There is only one mean for a set of data.
Step-by-step explanation:
Required
True statement about arithmetic mean
(a) False
The mean can be equal to, greater than or less than the median
(b) True
The arithmetic mean is the summation of all data divided by the number of data; hence, all values are included.
(c) True
All mean literally represent the distance of each value from the average; so, when each value used in calculating the mean is subtracted from the calculated mean, then the end result is 0. i.e.[tex]\sum(x - \bar x) = 0[/tex]
(d) True
The mean value of a distribution is always 1 value. When more values are added to the existing values or some values are removed from the existing values, the mean value will change.
(e) False
Nominal data are not numerical or quantitative data; hence, the mean cannot be calculated.
Find BD, given that line AB is the angle bisector of < CAD.
Answer:
5
Step-by-step explanation:
because line AB divided the triangle into two equal halves
A line plot with the lengths of meteors is shown. Two more identical meteor measurements were added so that the total length of all meteors measured is 16 inches. What is the length of each new meteor?
A line plot with the title, length of meteors. The data is measurement in inches. The line plot goes from two eighths to one and seven eighths, with fourteen tick marks in all. The first tick mark is two eighths and has one data point. The second tick mark is three eighths and has three data points. The third tick mark is four eighths and has two data points. The fourth tick mark is five eighths and has no data points. The fifth tick mark is six eighths and has two data points. The sixth tick mark is seven eighths and has no data points. The seventh tick mark is one and has no data points. The eighth tick mark is one and one eighth and has no data points. The ninth tick mark is one and two eighths and has one data point. The tenth tick mark is one and three eighths and has two data points. The eleventh tick mark is one and four eighths and has no data points. The twelfth tick mark is one and five eighths and has no data points. The thirteenth tick mark is one and six eighths and has two data points. The fourteenth tick mark is one and seven eighths and has one data point.
1 inch
one and one eighth inches
one and two eighths inches
one and three eighths inches
Answer:The answer is 1 3/8 (D)
Step-by-step explanation:
If you added the amounts of each tick mark (which would be 13 2/8), and then subtracted it by 16, it would be 2 6/8. 2 6/8 divided by two (because we need to find the length of both of the indentical meteors) would be 1 3/8.
Now, to make sure it is 1 3/8: 13 2/8 + 1 3/8 + 1 3/8 = 16.
It is confirmed, 1 3/8 (Answer D) is the correct answer.
(Also, I took this test and got it correct :D)
Step-by-step explanation:
Which statement correctly compares Line segment AB Which statement correctly compares Line segment AB and Line segment FD? And Line segment FD?
Answer:
AB is longer FD
Step-by-step explanation:
Given
See attachment for triangles ABC and FDE
Required
Compare line segments AB and FD
From the attachment, we have:
[tex]AC = FE[/tex] --- equal line segments
The measure of angles will then be used to compare the line segments;
[tex]\angle C = 72^o[/tex]
[tex]\angle F = 65^o[/tex]
The longer the angle of depression, the shorter the required line segment
[tex]72 > 65[/tex] implies that AB is longer
Answer:
C 3dge
Step-by-step explanation:
4.Find the first five terms of the recursive sequence
Answer:
5, 12, 19, 26, 33
Step-by-step explanation:
Using the recursive rule and a₁ = 5 , then
a₂ = a₁ + 7 = 5 + 7 = 12
a₃ = a₂ + 7 = 12 + 7 = 19
a₄ = a₃ + 7 = 19 + 7 = 26
a₅ = a₄ + 7 = 26 + 7 = 33
The first 5 terms are 5, 12, 19, 26, 33
Which of the following rational functions is graphed below?
10
- 10
10
- 10+
O A. F(x) =
X-2
*(x+5)
B. F(x) =
(x + 5)(x-2)
C. F(x) =
(x+5)(- 2)
х
х
D. F(x) =
(x + 5)(x - 2)
The rational function is:
f(x) = x/ (x - 2)(x + 5).
The correct option is D.
What are the asymptotes?As the function approaches a certain value—typically infinity or negative infinity—as the input approaches positive or negative infinity, this is known as a horizontal asymptote.
When the vertical asymptotes are x = 2 and x = -5, this means that the denominator of the rational expression must contain the factors (x - 2) and (x + 5), but not (x - a) or (x + b) for any other values of a and b.
When the horizontal asymptote is x = 0, this means that the degree of the numerator and denominator must be the same, and the leading coefficients must be equal.
Let's start by setting up the denominator:
denominator = (x - 2)(x + 5)
To satisfy the horizontal asymptote at x = 0, the numerator must also have a factor of x, so we can write:
numerator = kx
where k is a constant to be determined.
To ensure that the rational expression has the desired vertical asymptotes, we need to add any necessary linear or quadratic factors to the numerator.
Since the denominator already has linear factors, we only need to add a quadratic factor.
We can choose any quadratic factor that doesn't affect the horizontal asymptote or the other vertical asymptote.
For example, we can choose:
numerator = kx(x + 7)
Putting it all together, the rational expression is:
f(x) = kx / (x - 2)(x + 5)
To determine the value of k, we can use the fact that the leading coefficients of the numerator and denominator must be equal. The leading term of the numerator is kx², and the leading term of the denominator is x².
Therefore:
k = 1
So the final rational expression is:
f(x) = x / (x - 2)(x + 5)
To learn more about the asymptotes;
https://brainly.com/question/4084552
#SPJ7
Lines AB and CD (if present in the picture) are straight lines. Find x. Give reasons to justify your solutions.
Answer:
180- 110= 70
70+x+90=180
160+x=180
180-160=x
20=x
4.
a. The total area of the model is 130 m2. Write an equation to find x. b. Solve the equation by completing the square.
A. (x + 2)(2x + 2) = 130; x = 5.12 m
B. (x + 2)(2x + 2) = 130; x = 6.70 m
C. (x + 2)(x + 2) = 130; x = 9.40 m
D. (x + 2)(2x + 2) = 130; x = 6.58 m
Answer:
(x+2)(2x+2) = 130
x=6.58m
Step-by-step explanation:
The shape of the whole figure is a triangle. Hence the area of the whole figure is expressed as:
Area = Length * Width
Given
Length = 2 + x + x = 2+2x
Width = 2 + x
Area = 130m²
Substitute the resultng values into the formula;
(2+2x)(2+x)= 130
(x+2)(2x+2) = 130
Expand the bracket:
[tex]2x^2+2x+4x+4=130\\2x^2+6x+4=130\\[/tex]
Divide through by 2
[tex]x^2+3x+2=65\\x^2+3x=65-2\\x^2+3x = 63[/tex]
Complete the square by adding the square of the half of the coefficient of x to both sides:
[tex](x^2+3x+(\frac{3}{2} )^2)=63+(\frac{3}{2} )^2[/tex]
[tex](x+\frac{3}{2} )^2=63 + \frac{9}{4} \\(x+\frac{3}{2} )^2=\frac{252+9}{4} \\(x+\frac{3}{2} )^2=\frac{261}{4}\\(x+\frac{3}{2} )^2=65.25[/tex]
Take the square root of both sides
[tex]\sqrt{(x+(\frac{3}{2} ))^2} = \sqrt{65.25}\\x+\frac{3}{2}= 8.078\\x=8.078-1.5\\x=6.58m[/tex]
Hence the value of x is 6.58m
