Answer:
1/a+ 1/b = 1/2
Adding the fractions we get
b+a/ab=1/2
cross Multiplying the denominator we get,
b+a=ab/2
a= ab/2 -b
Answer:
a = 1/(1/2 + 1/b)
Step-by-step explanation:
1/a + 1/b = 1/2
1/a = 1/2 - 1/b
1 = a(1/2 - 1/b)
1/(1/2 + 1/b) = a
Please state the equation of the line in standard form
Answer:
See below
Step-by-step explanation:
Slope = rise / run
from 0,-1 to 1.5 , 0
this is 1 / 1.5 = 2/3
y xis intercept = -1
y = 2/3 x -1 Slope intercept form
2/3 x - y = 1 another form
2x - 3y = 3 Standard form (I think this is 'standard form' ....yah?)
I will give BRAINLIEST! ANSWER QUESTION! I NEED IT ASAP
Out of a sample of 500 high school students, 376 said they would prefer to have computers in every classroom. Construct a 95% confidence interval for the population mean of high school students who would prefer to have computers in every classroom.
CI = (71.41%, 78.99%)
CI = (71.98%, 79.45%)
CI = (70.23%, 80.17%)
CI = (72.02%, 78.38%)
The correct answer is CI = (71.415%, 78.915%)
The correct option is (A)
What is Confidence level?A confidence interval is the mean of your estimate plus and minus the variation in that estimate.
Given:
x = 376
Sample = 500 students
CI= [(376/500-1.96 √((376/500)*(124/500)/500) , (376/500-1.96
√((376/500)*(124/500)/500)]
CI = (71.415%, 78.915%)
Hence, CI = (71.415%, 78.915%)
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Which of the following statements are true?
A. Both graphs have exactly one asymptote.
B. Both graphs have been shifted and flipped.
c. Both graphs are logarithmic functions.
D. Both graphs are exponential functions.
Which statement describes how the y-intercept of the graph of f(x) = |2x − 1| compares to the y-intercept of the graph of g(x) = |2x − 5|? A. The y-intercept of g is 4 units above the y-intercept of f. B. The y-intercept of g is 4 units below the y-intercept of f. C. The y-intercept of g is 4 units to the right of the y-intercept of f. D. The y-intercept of g is 4 units to the left of the y-intercept of f.
The statement "the y-intercept of g is 4 units above the y-intercept of f'' is true option first is correct.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have two functions:
f(x) = |2x - 1| and
g(x) = |2x - 5|
After plotting on a coordinate plane.
The y-intercept of f(x) is 1
The y-intercept of g(X) is 5
Or plug x = 0 to find the y-intercept.
The y-intercept of g is 4 units above the y-intercept of f
Thus, the statement "the y-intercept of g is 4 units above the y-intercept of f'' is true option first is correct.
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MATH: Inverse function, 10 pts for your help!
The inverse of g(5) and the inverse of h(x) are 2 and [tex]h^{-1}=\frac{-x-13}{4}[/tex] respectively
Inverse of a function
Given the following coordinates and function
g = {(-6, -5), (2, 5), (5,6), (6,9)}
The inverse of "g" is determined by switching the coordinates to have:
g^-1(x) = {(-5, -6), (5, 2), (6, 5), (9,6)}
Since the value of the y-coordinate when x = 5 is 2, hence g^-1(5) = 2
Given the function expressed as:
h(x) = -4x - 13
y = -4x - 13
Replace y with x
x = -4y - 13
4y = -x - 13
y = (-x-13)/4
[tex]h^{-1}=\frac{-x-13}{4}[/tex]
Determine the composite function [tex](hoh^{-1})(-1)[/tex]
h(h(x)) = h(-4x-13)
h(h(x)) =[tex]\frac{-(-4x-13)-13}{4} \\[/tex]
[tex]h(h(x))=\frac{4x}{4} \\h(h(x)) = x\\h(h(-1)) = -1[/tex]
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On a walk through the woods, Mr. Finley saw 16 blue jays and 25 purple finches. Write the ratio of finches to blue jays three different ways.
Answer:
25:16
50:32
100:64
Step-by-step explanation:
What is the probability if a penny lands on heads 30 times after being tossed 50 times?
The probability will be equal to 60%.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The best thing to do here is to put it into a fraction. as 30 landed heads up, 20 (50-30) must be tails.
You can then put this into a fraction, which becomes 20/50.
To turn this into a decimal, you can then divide 1 by 50
1/50= 0.02
As you've got 22 lots of this, you then need to multiply 0.02 by 20.
0.2x20= 0.40
To find the percentage, you've then got to multiply the decimal by 100.
100x0.40= 40.
Therefore, 40% of the tosses would be tails
As you've found what one percentage is, you simply need to take this number away from 100 to find the other, rather than having to go through the process again.
100-40= 60
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2. (06.03)
What is the solution to the following system of equations? (2 points)
y = -x2 – 5x − 4
y = -x² + 9x - 18
O (-1,-10)
O (1,-10)
O (-1,10)
(1.10)
Answer: (1, -10)
Step-by-step explanation:
Since both of the equations are set equal to y, we can conclude that:
[tex]-x^2 -5x-4=-x^2 + 9x-18\\\\-5x-4=9x-18\\ \\ -14x-4=-18\\\\-14x=-14\\\\x=1[/tex]
If x=1, then [tex]y=-(1)^{2}+9(1)-18=-10[/tex]
Thus, the solution is (1, -10)
Dedi had a combination lock.To open the lock he started at 37.He made 3 half turns clockwise and 3 quarter turns anticlockwise
What number did he end up at?
PLEASE HELP ME!!!!!!!!!
Answer:
option 4 and option 3 are the answers respectively
Answer:
[tex] \sqrt{ {2}^{3} } \\ \sqrt{3} \\ .............[/tex]
0 1 3 6 10 what goes after 10?
Answer:
15
Step-by-step explanation:
0 + 1 = 1
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
Solve for all values of y
in simplest form.
∣y−12∣=16
Answer:
[tex]y=-4; y=28[/tex]
Step-by-step explanation:
The way I like to think about it, with absolute value meaning the distance is
"find which number are 16 apart from 12". Which means 28 (to the right) or -4 (to the left).
More formally, applying the definition of absolute value,
[tex]|y-12|=16 \leftrightarrow y-12=\pm16\\y-12=-16 \rightarrow y=-4\\y-12=+16 \rightarrow y=28[/tex]
Hi. how can i Find the *number* of terms of a finite geometric sequence?
r= .75
a= 40
sum= 280
We have to use the formula [tex]n = log_{r} (1+\frac{S_{n}(1-r) }{a})[/tex] to find the number of terms of a finite geometric sequence.
If a be the first term of a finite sequence, r be the common ratio between consecutive terms and n be the number of terms.
So, we have to use the formula of sum of sequence and then calculate it to reduce the equation to find the value of number of terms, that is n.
Then, Sum of the sequence (Sn) = [tex]\frac{a(1-r^{n}) }{1-r}[/tex]
Here, in the given problem,
Sum(Sn) = 280, First term of the sequence(a) = 40, Common ratio(r) = 0.75
So, Sn = [tex]\frac{a(1-r^{n}) }{1-r}[/tex]
⇒ [tex]1-r^{n} =\frac{S_{n}(1-r) }{a}[/tex]
⇒ [tex]r^{n} =1+\frac{S_{n}(1-r) }{a}[/tex]
⇒ [tex]n = log_{r} (1+\frac{S_{n}(1-r) }{a})[/tex]
Now you have to put the values and get the number of terms.
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Expand and simplify: (6a+2)(6a-5)-(7a-1)(a-2)
Answer:
29a² - 3a - 12
Step-by-step explanation:
Given expression:
(6a+2)(6a-5)-(7a-1)(a-2)
Solution:
Apply distributive property.
[tex] \rm=(6a)(6a)+(6a)(-5)+(2)(6a)+(2)(-5)-7a^2+15a-2[/tex]
[tex] \rm= 36a {}^{2} - 30a + 12a - 10 - 7a {}^{2} + 15a - 2[/tex]
Combine like terms:
[tex] \rm=(36a {}^{2} - 7a {}^{2} )+( - 30a+12a+15a)+( - 10 - 2)[/tex]
[tex] = \boxed{ \rm \: 29a {}^{2} - 3a - 12}[/tex]
Done!
Darrel divided 8,675 by 87. His work is shown below
Which answer choice correctly identifies the error Darrel made when dividing?
a b c or d?
2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
Step-by-step explanation:
2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
2x+4+5x+25=4x-32+2x-4
7x+29=6x-36
7x-6X=-36-29
X=-65
Answer:
x = -65
Step-by-step explanation:
2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
Distribute:
2(x + 2): 2x + 4
5(x + 5): 5x + 25
=
4(x - 8): 4x - 32
2(x - 2): 2x - 4
Combine like terms:
(2x + 4) + (5x + 25) = (4x - 32) + (2x - 4)
5x + 2x: 7x = 4x + 2x: 6x
4 + 25 = 29 = -32 - 4: -36
7x + 29 = 6x - 36
Now we want to separate like terms,
subtract 29 from both sides
subtract 6x from both sides
7x + 29 - 29 - 6x = 6x - 29 - 6x- 36
7x - 6x = - 29 - 36
x = -65
Express verbal statement in algebraic form.
The cost to rent a sailing boat at Catalina Island is $370 per day
plus $80 for every hour of use. What is the maximum number of
hours the sail boat can be rented for each day, if the rental cost is
not to exceed $1090 per day?
Answer:
370 + 80x ≤ 1090
Step-by-step explanation:
By using letter variables for the unknown numbers, we can break down the question into mathematical terms:
If the cost is $370 per day and the number of days is unknown, we can substitute the number of days with a placeholder. In this case, it'll be a variable such as x. So the cost can be represented by $370y.
If the cost is $80 per hour and the number of hours is unknown, we can substitute the number of hours with a placeholder. In this case, it'll be a variable such as y. So the cost can be represented by $80x.
The questions asks for the total cost not to exceed $1090 per day. This means that we know that the number of days is 1. We're trying to find the maximum number of hours, so our equation will combine the costs of both day costs and hour costs:
$370 (1 day) + $80 (x hours) ≤ $1090 per day
The symbol is the equal to or less than symbol, meaning the combined total costs is either equal to $1090 or less than it.
To simplify this, we can rewrite it as:
370 + 80x ≤ 1090
Determine the slope-intercept form of the equation of the line parallel to y = x + 11 that passes through the point (–6, 2).
Parallel lines have equivalent slopes, so as the slope of the given line is 1, the slope of the line we want to find is also 1.
Substituting into point-slope form and rearranging into slope-intercept form,
[tex]y-2=1(x+6)\\\\y-2=x+6\\\\\boxed{y=x+8}[/tex]
Find the volume of a cone that has a diameter of 7 and a height of 8.
98/3 Pi
448/3 Pi
131 Pi
24 Pi
Fig. R24 shows a flower vase whose circular base is parallel to its circular top.
Use the dimensions in the figure to calculate the curved surface area of the flower vase
Answer:
operant conditioning and schedules of reinforcement
what is next number in pattern 7, 11, 2, 18, -7
Answer:
the answer is -7+-25=-32
Can someone help me? I’ll give brainliest to whoever gets it right first
Answer:
72 Degrees
Step-by-step explanation:
We know that its 72 because of VAT, the vertical angle theorem.
What is the area of the polygon given below?
Answer:
340 i am pretty sure
Step-by-step explanation:
p + (-q) - 2 = ? When p = -3 and q = 5
Answer:
= -10
Step-by-step explanation:
p + (-q) - 2 = x
if:
p = -3
q = 5
then:
-3 + (-5) - 2 = x
we know that:
+(-) = -
then:
-3 +(-5) - 2 = -3 - 5 - 2 = x
x = -10
The value of the expression p + (-q) - 2 is -10 if the p = -3 and q = 5 the answer is -10.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have given an expression:
= P + (-q) - 2
Plug p = -3
q = 5
= -3 + (-5) - 2
= -3 - 5 - 2
= -10
Thus, the value of the expression p + (-q) - 2 is -10 if the p = -3 and q = 5 the answer is -10.
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Follow the steps to find the
area of the shaded region.
First, use the formula
below to find the area
of the whole sector.
Sector Area =
angle of sector
360
tor) πr²
Sector Area = [?] cm²
Round to four decimal places.
14 cm
46°
14 cm
The area of the shaded part is 8.1447cm²
Area of a sectorThe formula to calculate the area of the shaded region is expressed as:
Area of the shaded region = Area of sector - Area of triangle
Determine the area of the sector
Area of sector = r²β/2
Area of sector = 14²(46π/180)/2
Area of sector = 78.64 cm²
Determine the area of triangle
Area of triangle = 1/2r²sinβ
Area of triangle = 1/2(14²sin46)
Area of triangle = 140.99/2
Area of triangle = 70.49 cm²
Area of shaded part = 78.64 cm² - 70.49 cm²
Area of shaded part = 8.1447cm²
Hence the area of the shaded part is 8.1447cm²
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I keep putting in the formula but I keep getting the answer wrong
Answer:
314 in² (nearest whole number)
Step-by-step explanation:
Radius of a regular polygon: The distance from the center of the polygon to any vertex. The radius of a hexagon is equal to the length of one side.
Therefore, from inspection of the given diagram:
radius = 11 in ⇒ side length = 11 inTo find the area of a regular polygon, we first need to calculate the apothem. The apothem is the line drawn from the center of the polygon to the midpoint of one of its sides.
[tex]\textsf{Length of apothem (a)}=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}[/tex]
where:
s = length of one siden = number of sidesGiven:
s = 11 inn = 6Substitute the given values into the formula and solve for a:
[tex]\implies \textsf{a}=\dfrac{11}{2 \tan\left(\frac{180^{\circ}}{6}\right)}=\dfrac{11\sqrt{3}}{2}[/tex]
Area of a Regular Polygon
[tex]\textsf{A}=\dfrac{n\:s\:a}{2}[/tex]
where:
n = number of sidess = length of one sidea = apothemGiven:
n = 6s = 11[tex]\textsf{a}=\dfrac{11\sqrt{3}}{2}[/tex]Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=\dfrac{6 \cdot 11 \cdot \dfrac{11\sqrt{3}}{2}}{2}[/tex]
[tex]\implies \sf A=314.3672216...[/tex]
[tex]\implies \sf A=314\:\:in^2\:\:(nearest\:whole\:number)[/tex]
Which of the following transformations produce congruent figures?
i. Rotation
ii. Reflection
iii. Translation
iv. Dilation
i, ii, and iii
i and ii
iv only
iii and iv
x2y, for x = 3 and y = 6
Answer:
12
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{ASSUMING}[/tex]
[tex]\mathsf{x^{2y}}[/tex]
[tex]\huge\textbf{IF SO, FOLLOW THESE STEPS TO}\\\huge\textbf{SOLVE FOR YOUR RESULT}[/tex]
[tex]\mathsf{x^{2y}}\\\mathsf{= 3^{2(6)}}\\\mathsf{= 3^{2\times6}}\\\mathsf{= 3^{12}}\\\mathsf{= 3\times3\times3\times3\times3\times3\times3\times3\times3\times3\times3\times3}\\\mathsf{= 9\times9\times9\times9\times9\times9}\\\mathsf{= 81\times81\times81}\\\mathsf{= 6,561\times81}\\\mathsf{= 531,441}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{531,441}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]My friend has $672 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $17/yard on one side, and cheaper metal fencing which costs $7/yard for the other three sides.
What are the dimensions of the garden with the largest area she can enclose?
The dimensions of the garden with the largest area she can enclose are given by 24*14 square yards.
The area (A) of the rectangle with length L and Width W is given by,
A=L*W
The maximum of [tex]y=ax^2+bx[/tex] occurs at x = -b/2a
Let the length and width of the garden be L and W respectively.
Now let my friend use cedar fencing for one width and cheaper metal fencing for rest sides.
Rate of cedar fencing is $17/yard
Then she has to pay for cedar fencing = 17W
rate of cheaper metal fencing is $7/yard
Then she has to pay for metal fencing = 7W+7*2L = 7W+14L
Then according to condition,
17W+7W+14L = 672
24W+14L = 672
12W+7L = 336
7L = 336-12W
L = (336-12W)/7
Then the area of the rectangular garden is given by,
A = L*W
[tex]A=\frac{336-12W}{7}\times W\\A=-\frac{12}{7}W^2+48W[/tex]
So here a = -12/7 and b = 48
Then maximum of W occurs at,
W = -48/(2*(-12/7)) = (48*7)/(2*12) = 336/24 = 14
Then maximum width = 14 yards
then length (L) = (336-12*14)/7 = 168/7 = 24 yards
Hence the dimensions with the leargest area she can enclose is given by = 24 * 14 square yards.
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Show me 2 line up and down are they parallelside by side on a graph
Two (2) lines are considered to be parallel if their slopes are the same (equal) and they do not intersect.
The condition for two parallel lines.In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.
This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
In conclusion, two (2) parallel lines are shown in the image attached below for more understanding,
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