Answer:
x = [tex]\frac{2}{3}[/tex] , x = 1
Step-by-step explanation:
(x - [tex]\frac{5}{6}[/tex] )² = [tex]\frac{1}{36}[/tex] ( take square root of both sides )
x - [tex]\frac{5}{6}[/tex] = ± [tex]\sqrt{\frac{1}{36} }[/tex] = ± [tex]\frac{1}{6}[/tex] ( add [tex]\frac{5}{6}[/tex] to both sides )
x = [tex]\frac{5}{6}[/tex] ± [tex]\frac{1}{6}[/tex] , then
x = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
x = [tex]\frac{5}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{6}{6}[/tex] = 1
HELP
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world and mathematical problems in two and three dimensions
You did not provide any question. I will give general advice.
Pythagorean Theorem: a² + b² = c²
If you know two sides, you know ll three sides.
A house sits in the shade.
The house is 18 feet tall. The shadow is 24 feet long. What is the hypotenuse of this triangle?
We know a and b here! a=18, b=24.
18 * 18 = 324.
24 * 24 = 576.
324+576 = 900
The square root of 900 is what will be your answer:
18*18 + 24*24 = 30*30.
I hope this helps!
Help me please given ABcd is a parallelogram
What is the standard form of y=2x-2
Answer:
A standard form of a linear equation would look like this Ax+ By = C A x + B y = C
Step-by-step explanation:
3x+5y = 15 find the slope of a line perpendicular to each given line
Answer:
Slope = 5/3
Step-by-step explanation:
See attached image
Help plsss i dont get it
Part A
The pattern of squares is 1, 4, 9, ... which is the set of perfect squares
1 = 1^24 = 2^29 = 3^2and so on
The 7th figure will have 49 squares because 7^2 = 49
Answer: 49==============================================================
Part B
Each pattern has one circle per corner (4 circles so far). In addition, there's one circle per unit side to form the perimeter.
Pattern 1 has 4+4(1) = 8 circlesPattern 2 has 4+4(2) = 12 circlesPattern 3 has 4+4(3) = 16 circlesThe nth term will have 4+4n circles. The first '4' is the number of circles at the corners. The 4n is the circles along the perimeter. If you wanted, 4+4n factors to 4(1+n).
Plug in n = 20 to find the 20th figure has 4+4n = 4+4(20) = 84 circles
Answer: 84==============================================================
Part C
Pattern 1 has 1 square + 8 circles = 9 items totalPattern 2 has 4 squares + 12 circles = 16 items totalPattern 3 has 9 squares + 16 circles = 25 items totalThis seems to suggest if the pattern number is odd, then we need an odd number of tiles (square + circular).
Let n be the pattern number. Pattern n needs n^2 square tiles and 4+4n = 4n+4 circular tiles. Overall, n^2+4n+4 tiles are needed.
It turns out that if n is odd, then n^2+4n+4 is always odd. The proof is shown below.
Side note: n^2+4n+4 factors to (n+2)^2
Answer: B) will always be oddPlease help me with this
Answer:
1 and 4
Step-by-step explanation:
(x²+1)(x²-4) = x^4 -3x²-4
The green blank is 1 and the blue/purple is 4.
Hope this helped and brainliest please
A job applicant estimates that his chance of passing a qualifying examination is , and his chance of being appointed if he does pass is . what is the probability that he will receive the job?
The probability that he will receive the job will be 1 / 6
The complete question is given below:-
A job applicant estimates that his chance of passing a qualifying examination is 2/3, and his chance of being appointed if he does pass is 1/4. What is the probability that he will receive the job?
What is probability?
Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
It is given that:
The chance of passing a qualifying examination is 2/3=P
and chance of being appointed, if he does pass, is 1/4=P'
Now, we are asked to find the probability that he will receive the job.
We are asked to find the probability that he will receive the job.
The probability is calculated as The probability that he qualify the exam×Probability that he is being appointed.
=P×P'
=(2/3)×(1/4)
=1/6
Therefore the probability that he will receive the job will be 1 / 6
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Can you guys help me with this math questions
Answer:
2) $40 per shirt
3) 80/9 m = 8.9 m (nearest tenth)
Step-by-step explanation:
The first question has been answered here: https://brainly.com/question/27846862
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Question 2
Given information:
Previous sales = 300 shirts at $20 eachFor every $1 increase in price, the number of sales diminishes by 5Let [tex]x[/tex] = number of $1 increases
Let [tex]y[/tex] = total revenue (in dollars)
From the given information:
Price change of shirt: [tex](20 + x)[/tex]Number of sales change: [tex](300 - 5x)[/tex]Therefore, we can create a quadratic equation with the given information:
[tex]\implies y = (20+x)(300-5x)[/tex]
As we need to find the maximum amount of revenue, we need to find the vertex of [tex]y[/tex]. As the equation is already factored, the quickest way to do this is to the find the mid-point of the zeros (since a quadratic curve is symmetrical).
[tex]\begin{aligned}y & =0\\\implies (20+x)(300-5x) & =0\\\implies (20+x) & =0 \implies x=-20\\\implies (300-5x) & = 0 \implies x=60\end{aligned}[/tex]
[tex]\textsf{Midpoint}=\dfrac{-20+60}{2}=20[/tex]
Therefore, Sammy should have 20 $1 increases to maximize the revenue, so the new price will be:
[tex]\implies \$20 + 20 \times \$1 = \$40\: \sf per\:shirt[/tex]
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Question 3
Given information:
Bridge is modeled as a parabolaWidth of bridge = 30 mMax height of bridge = 10 m high (in the middle)As the bridge is modeled as a parabola, and we have been given the width and height, we can create a quadratic equation using the vertex form.
Vertex form: [tex]y=a(x-h)^2+k[/tex]
where:
x is the horizontal distance of the bridgey is the height of the bridge(h, k) is the vertexa is some constantMiddle of the bridge = 30 m ÷ 2 = 15 m
Max height of the bridge = 10 m
Therefore, the vertex of the parabola is (15, 10)
[tex]\implies y=a(x-15)^2+10[/tex]
We know that when [tex]x = 0, y = 0[/tex]. Therefore, substitute these values into the equation and solve for a:
[tex]\implies 0=a(0-15)^2+10[/tex]
[tex]\implies 0=225a+10[/tex]
[tex]\implies 225a=-10[/tex]
[tex]\implies a=-\dfrac{10}{225}[/tex]
[tex]\implies a=-\dfrac{2}{45}[/tex]
Therefore, the equation of the parabola is:
[tex]\implies y=-\dfrac{2}{45}(x-15)^2+10 \quad \quad \textsf{for }0\leq x\leq 30[/tex]
The horizontal distance at 5 m right of the middle is:
[tex]\implies \dfrac{30}{2}+5=20\:\sf m[/tex]
Therefore, to find the height at this point, input [tex]x=20[/tex] into the equation and solve for y:
[tex]\implies -\dfrac{2}{45}(20-15)^2+10=\dfrac{80}{9}\:\sf m[/tex]
Therefore, the height of the bridge at 5 m to the right of the middle is:
[tex]\dfrac{80}{9}\:=8.9\: \sf m\:(nearest\:tenth)[/tex]
Mr. Franco's class wants to raise at least $750 for a fundraiser. Let r be the amount of money, in dollars, the class raised.help ASAP..
Answer:
>
Step-by-step explanation:
Cause 750 was the least they could raise
Answer:
>=
Step-by-step explanation:
>= because the teacher wants AT LEAST 750. at least meaning you can raise 750 or MORE
5.) The price of gas last year was $1.75 per gallon. The price went up by 5%,
what is the new price for a gallon of gas?
Answer: 1.75•5%=0.0875
1.75+0.0875=$1.84
I’m pretty sure this is correct
Answer:
5% of 1.75 is 0.085.
So 1.75 + 0.085 is 1.8375.
Write the equation of the trigonometric graph
The equation for the trigonometric graph given above is:
y = 4sin(2x + (π/2))
y = 4 cos 2x
It is to be noted that the domain value of θ is displayed on the horizontal x-axis and the range value is depicted on the vertical y-axis in the graphs of trigonometric functions.
What is the step-by-step solution to the question?Note that
y = A Sin (Bx - C) + D
The vertical shift → D
Horizontal [Phase] shift → C/B
Wavelength [Period] → (2/B) π
Amplitude → | A |
Vertical Shift → 0
Horizontal | Phase | Shift → C/B → [- (π/4)] → (-π/2/2)
Wavelength | Period | → (2/B)π → π → (2/2)π
Amplitude → 4
Hence, working the above further we get:
y = 4sin(2x + (π/2))
y = 4 cos 2x
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Answer(s):
[tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}) \\ y = -4cos\:(2x \pm \pi) \\ y = 4cos\:2x[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4sin\:2x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-1\frac{1}{4}\pi, 0],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{4}, 0],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
40% of the students in a class are girls and the number of boys is 24 find the total number of students and the number of girls
Answer:
Girls = 16
Total students = 40
Step-by-step explanation:
40% of the students are girls, this means 60% of the students are boys.
To find the number of girls, setup a proportion using the percentages and actual number of students in the class. I am going to make the numerator the numbers that go with the girls and the denominator will be the numbers that go with the boys.
Also let's convert the percentages to decimals by moving the decimal two places left.
40% = 0.4 and 60% = 0.6
[tex]\frac{.4}{.6} =\frac{g}{24} \\.6g=9.6\\\frac{.6g}{.6} =\frac{9.6}{.6} \\g=16[/tex]
Now let's find the total number of students by adding the number of girls to the number of boys.
16 + 24 = 40
Which triangles are similar please help lol
Answer:
triangles A and B are similar
Step-by-step explanation:
A circle has an area of 144pie square feet what is the diameter of the circle
Answer:
13
Step-by-step explanation:
144 = pie radio square
144 divided by pie = 45.83662361
45.83662361 square root = 6.770275003
6.770275003 multiply by 2 = 13.54055001
13.54055001 = diameter
After 3 hours,
Amelie has biked
15 miles
A professional
cyclist finished a
100-mile race in 4
hours
it took Emma
3 hours to bike 27
miles up to the top
of Mt. Evans
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3 of 12
acer
20 miles/hour
5 miles/hour
25 miles/hour
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X
a
12:19
Calcula el valor de la expresion
m + (m – 3), si m = –5
Answer: -13
Step-by-step explanation:
m = -5
-5 + (-5-3)
-5 -8
-13
Answer:
-13
Step-by-step explanation:
dado m= -5
m+(m-3) = -5+(-5-3) = -5 + (-8) = -5-8 = -13
What is the period of f(x) = sin (8x)?
X/8
X/4
4
8
Answer: B- x/4
Step-by-step explanation:
The period is the horizontal distance needed for the values to repeat themselves.
Which table represents a linear function?
Describe how to determine the average rate of change between x = 3 and x = 5 for the function f(x) = 3x3 + 2. include the average rate of change in your answer.
Answer:
147
Step-by-step explanation:
[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\ \\\frac{f(5)-f(3)}{5-3}\\ \\\frac{(3(5)^3+2)-(3(3)^3+2)}{2}\\ \\\frac{(3(125)+2)-(3(27)+2)}{2}\\ \\\frac{(375+2)-(81+2)}{2}\\ \\\frac{377-83}{2}\\ \\\frac{294}{2}\\ \\147[/tex]
Recall that if a function [tex]f[/tex] is continuous over the interval [tex][a,b][/tex], then its average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex].
how to simplify 8x-6x
subtracting 6x from 8x. It's quite simple to deal with small two-part numbers like these. After subtracting 6x from 8x, you will get the answer 2x.
Quick Answer:
You simply 8x-6x by subtracting 6x from 8x, and then you will get the answer 2x
HAVE A NICE DAY
One number is 4 times another. Their difference is 27. How to get the other two numbers?
Answer:
x = 36; y = 9
Step-by-step explanation:
To solve this problem you need to set up two equations. The first equation comes from the first sentence "One number is 4 times another." This equation can be written as x = 4*y where x and y are the two numbers. The second equation comes from the second sentence "Their difference is 27." This equation can be written as x-y = 27. To find the numbers you need to rearrange one equation and plug it into the other.
Step 1: write equations
x = 4*y
x-y = 27
Step 2: rearrange
Not necessary here
Step 3: substitute in
x - y = 27
4y -y = 27
3y = 27
y = 9
Step 4: solve for x
x = 4*y
x = 4*9
x = 36
[tex]x[/tex] - one number
[tex]4x[/tex] - the other number
[tex]4x-x=27\\3x=27\\x=9\\\\4x=4\cdot9=36[/tex]
These numbers are 9 and 36.
The quadratic function
d=-9x² + 40 models a
skateboarder's distance, in
feet, from the bottom of a hill
x seconds after the skateboarder
starts moving down the hill.
After how many seconds is the
skateboarder 4 ft from the
bottom of the hill?
A) 3s B) 4s C) 2s D) 3.5s
Please help!! Also if you could explain that would be great! Tysm!
Answer:
C
Step-by-step explanation:
equate d to 4 and solve for t , that is
- 9x² + 40 = 4 ( subtract 40 from both sides )
- 9x² = - 36 ( divide both sides by - 9 )
x² = 4 ( take square root of both sides )
x = [tex]\sqrt{4}[/tex] = 2
It takes 2 seconds for the skateboarder to be 4m from bottom of hill
Consider the given quadratic equations. Equations function it defines. Equation A y= 3x² - 6x + 21 Equation B y=3x² - 6x + 18 Equation C y= 3(x-1)2 +18 Equation Dy=3(x-1)² +21 Complete the following statement. equation. are equivalent , and of those, equation. is in the form most useful for identifying the extreme value of the function it define
Equation A and equation C are equivalent , and of those, equation C is in the form most useful for identifying the extreme value of the function it defines.
Evaluation of the quadratic expressions
The quadratic expressions can be simplified as follows;
Equation A: y = 3x² - 6x + 21Equation C: y = 3(x - 1)² + 18Equation C is simplified as follows;
y = 3(x - 1)² + 18
y = 3(x² - 2x + 1) + 18
y = 3x² - 6x + 3 + 18
y = 3x² - 6x + 21
Thus, equation A and equation C are equivalent , and of those, equation C is in the form most useful for identifying the extreme value of the function it defines.
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A certain television is advertised as a 95-inch tv (the diagonal length). if the width of the tv is 77 inches, how tall is the tv? round to the nearest tenth of an inch.
The height of the television given the length of its diagonal and its width is 55.6 inches
What the height of the tv?The height of the television can be determined using Pythagoras Theorem.
The Pythagoras theorem: a² + b² = c²
where a = length
b = base
c = hypotenuse
√95² - 77² = 55.6 inches
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Answer: 55.6
Step-by-step explanation: 55.6 that's what I put in and got it right
pls pls pls pls pls help me assap.
The quadrilaterals and their corresponding properties as shown in the given table are explained below.
How to Identify properties of Quadrilaterals?Property 1; All sides are Congruent means all sides are equal and only Square and Rhombus have this property.
Property 2; All angles are congruent means all angles are equal. Only Rectangle and Square have this property.
Property 3; Diagonals are perpendicular to each other. Only Square and rhombus have this property.
Property 4; Diagonals are congruent. This means the diagonals are equal and only Square and Rectangle have this property.
Property 5; Exactly One pair of parallel sides is given by Only Trapezoid.
Property 6; Two pairs of opposite sides are congruent. Only Parallelogram, Rectangle, Rhombus and Square have this property.
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i NEED HELP ASAP
A(n) sampling method is one that is representative of the population, selected at random, and large enough to provide accurate data.
A sample is one that is representative of the population, selected at random, and large enough to provide accurate data.
What is a sample?A sample is a smaller group that is representative of the population. A sample is sometimes necessary because it might not be feasible or cost effective to access the whole population.
For example, if a researcher is studying the impact of inflation on US families. It is not feasible to reach the whole of the families in the US. So, the researcher would use a representative group of US families. This is known as a sample.
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i need help grades are do today sorry for the trouble
Answer:
13
Step-by-step explanation:
[tex]Sin = \frac{opp}{hyp} \\cos= \frac{adj}{hyp} \\tan = \frac{opp}{adj}[/tex]
=> get the length of the diag on bottom
[tex]tan x = \frac{3}{4} x = 36.87[/tex] degree
[tex]sin(36.87)=\frac{3}{y}[/tex]
y is about 5
=> calculate max length of stick
[tex]tan\left(x\right)\:=\frac{5}{12}, x= 22.62degree[/tex]
[tex]sin\left(22.62\right)\:=\:\frac{5}{x}[/tex]
which is 13
The measure of an angle is 44.8°. What is the measure of its supplementary angle?
Answer:
Step-by-step explanation:
MATHH!!! find the surface area of the prism. pleaseee answer correctly and tell me how you got your answer.
Answer:232 inch^2
Step-by-step explanation:to solve, add the surface area of each side. Remember, there are 3 pairs of sides and the pairs have equal area. Area =length x length. So we have 2x(8x2)+2x(2x10)+2x(10x8) in square inches.
An 8in x 11in photo is enlatged by 200% what are the Dimensions of the enlargement?
Answer:
16in x 22in
Step-by-step explanation:
8in = 100%
x = 200%
(200*8) / 100 = 16
11in = 100%
X = 200%
(200*11) / 200 = 22
The trick is to cross multiply (without multiplying the X) and then divide by the number that was not multiplied :)
Answer:
16 in by 22 in
Step-by-step explanation:
Each dimension is multiplied by the scale factor when a photo is enlarged or reduced.
__
The enlarged photo will have dimensions ...
(200% × 8 in) by (200% × 11 in) = 16 in by 22 in
_____
Additional comment
The factor 200% is equal to 200/100 = 2. (% and /100 are interchangeable)