Answers
Since it is a right triangle, we can use the trigonometric ratio cos(θ) to find the length c.
[tex]\cos(\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}}[/tex]So, we have:
[tex]\begin{gathered} \cos(\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}} \\ \cos(45°)=\frac{c}{7} \\ \text{ Multiply by 7 from both sides} \\ \cos(45\degree)\cdot7=\frac{c}{7}\cdot7 \\ 7\cos(45\degree)=c \\ \frac{7\sqrt{2}}{2}=c \end{gathered}[/tex]Second triangleSince it is a right triangle, we can use the trigonometric ratio cos(θ) to find the length a.
So, we have:
[tex]\begin{gathered} \cos(\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}} \\ \cos(60°)=\frac{a}{2} \\ \text{ Multiply by 2 from both sides} \\ \cos(60°)\cdot2=\frac{a}{2}\cdot2 \\ 2\cos(60\degree)=a \\ 2\cdot\frac{1}{2}=a \\ 1=a \end{gathered}[/tex]Answer[tex]\begin{gathered} c=\frac{7\sqrt{2}}{2} \\ a=1 \end{gathered}[/tex]
Related Questions
a regular octagon has an area of 49 m 2 . find the scale factor of this octagon to a similar octagon with an area of 100 m 2
Answers
Given,
The area of the regular octagon is 49 square metre.
The area of the another regular octagon is 100 square metre.
[tex]\begin{gathered} \text{Scaling factor=}\frac{\sqrt{\text{area of regular polygon}}}{\sqrt[]{\text{area of another regular plogon}}\text{ }} \\ \text{Scaling factor=}\frac{\sqrt[]{\text{4}9}}{\sqrt[]{\text{1}00}\text{ }} \\ \text{Scaling factor=}\frac{7}{10\text{ }} \end{gathered}[/tex]Here, the scaling factor of the regualar octagon is 7:10
Hence, the scaling factor is 7:10.
F(x)=1/x g (x)=x-4 can you evaluate (golf)(0)? Explain why or why not.
Answers
If f(x) = 1/x and g(x) = x-4 , then (gof)(0) cannot be evaluated as the function becomes not defined .
In the question
it is given that the functions
f(x) = 1/x
and g(x) = x-4
to find g=(gof)(x) ,
(gof)(x) = g(f(x))
= g(1/x) ... because f(x) = 1/x
= 1/x - 4 ....because g(x) = x-4
On simplifying further , we get
= (1-4x)/4x
On substituting x=0 , we get
gof(0) = (1-0)/4(0)
= 1/0
which is not defined , hence cannot be evaluated.
Therefore , if f(x) = 1/x and g(x) = x-4 , then (gof)(0) cannot be evaluated as the function becomes not defined .
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Find the distance between:(4,-9) and(-8,0)Round your answer to the nearest hundredth.
Answers
The distance between 2 points (x1, y1) and (x2, y2) is calculated as:
[tex]\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]So, if we replace (x1, y1) by (4, -9) and (x2, y2) by (-8,0), we get:
[tex]\begin{gathered} \text{distance}=\sqrt{(-8-4)^2+(0-(-9))^2} \\ \text{distance}=\sqrt{(-12)^2+(9)^2} \\ \text{distance}=\sqrt{144+81} \\ \text{distance}=\sqrt{225} \\ \text{distance}=15 \end{gathered}[/tex]Answer: the distance is 15
400 meters to 350 meters increase or decrease
Answers
In this case we have a negative change, therefore decrease
answer: decrease
A bookstore sells a college algebra book for $90. If the bookstore makes a profit of 25% on each sale,what does the bookstore pay the publisher for each book?
Answers
Okay, here we have this:
Considering the provided information, we obtain that:
The total price = Commission of the bookstore + Payment to the publisher
Replacing:
$90=$90(0.25)+Payment to the publisher
Payment to the publisher=$90-$90(0.25)
Payment to the publisher=$90-$22.5
Payment to the publisher=$67.5
Finally we obtain that the bookstore pay $67.5 to the publisher for each book.
Your cousin is building a Sandbox for his daughter how much sand will he need to fill the Box? Explain. How much paint will he need to paint all six surface of the sandbox? Explain. 1ft 4ft 6ft not answer choices
Answers
Since the image is a rectangular prism
The volume of the box can be obtained by using the formula:
Volume = l x b x h
The box has a dimension of 1ft x 4ft x 6ft
The volume of the box = 1 x 4 x 6 = 24 cubic feet
Therefore, the volume of sand needed to fill the box will be = 24 cubic feet of sand
The surface area of the box can be obtained using the formula:
2(lb + lh + bh)
= 2(1x4 + 1x6 + 4x6)
=2(4 + 6 + 24)
=2 (34)
= 68 square feet
Therefore a total surface area of 68 square feet needs to be painted
Hello, I had a question on how to find the leading coefficient and the degree.
Answers
Given:
given polynomial is
[tex]23v^5-2v+4v^8-18v^4[/tex]Find:
we have to find the leading coefficient and degree of the polynomial.
Explanation:
The lewading coefficient is the coefficient of highest power term of the polynomial.
Highest power of v is 8 and its coefficient is 4.
Therfore, leading coefficient is 4.
and the degree of the polynomial is equal to the highest power of v in the polynomial, which is 8.
Therefore, the leading coefficient of polynomial is 4 and degree is 8.
The endpoints of diameter in a circle form an angle with point C. What is the measure of angle BCD?
Answers
Answer:
90 degrees
Explanation:
Please note that whenever a triangle is inscribed in a circle and one side of the triangle is a diameter of the circle as in the given figure, then the angle that is opposite the diameter of the circle is a right angle;
[tex]\therefore\angle BCD=90^{\circ}[/tex]Martha's video game rental plan costs $18 per month. Which tableshows the sum of the amounts that Martha will pay for her video gamerental plan over the next 5 months?
Answers
Let's complete a table with the amounts of cost per month:
Month Sum od cost
1 18
2 2 * 18 = 36
3 3 * 18 = 54
4 4 * 18 = 72
5 5 * 18 = 90
So, please select the table that is correct
1. ¿Qué expresiones a continuación se pueden usar para encontrar el área del prisma rectangular de abajo? ¡ELIJA TODOS LOS QUE SE APLIQUEN! Nota: Puede probarlos todos para asegurarse de que sean iguales. * 15 (5x2x3) + (2x3x3) (5x2) + (5x2) + (5x2) + (5x2) 5x2x2 2 (5x2) + 2 (5x2) + 2 (2x2)
Answers
We need to find the area of the prism given in the following image:
You need to add the surfaces of ALL rectangles in the image (recall that the area of a rectangle is : Base x Height)
So for this prism we have:
FOUR rectangles that measure 5 x 2
and also TWO small squares of area 2 x 2
So we need to select all the formulas they give you that read like the addition of the two above:
(5x2) + (5x2) + (5x2) + (5x2) + (2x2) + (2x2)
It can also be written as:
2 (5x2) + 2 (5x2) + 2 (2x2)
the ratio of the length to the width of a rectangular hall is 5:3. if the width is 1500cm, find the lenght.
Answers
Step-by-step explanation:
The ratio of the length to the width that is- length:width = 5:3
Take x as a common value,
5x= length
3x= width
Width of the rectangle= 1500 cm
3x= 1500 cm
x= 1500/3
x= 500 cm
Length of the rectangle= 5x
x=500 cm
Length= 5*500
=2500 cm
Length of the rectangle= 2500 cm
For the following set of data, find the number of data within 2 population standard deviations of the mean.28, 65, 114, 74, 68, 75, 70, 69, 64
Answers
To determine the data that is within 2 population standard deviations of the mean, let's calculate the mean first.
To determine the mean, let's add all the data and divide the result by the total number of data.
[tex]28+65+114+74+68+75+70+69+64=627[/tex][tex]627\div9=69.66667[/tex]The mean is 69.66667.
Let's now calculate the standard deviation. Here are the steps:
1. Subtract the mean from each data, then square the result.
[tex]\begin{gathered} 28-69.66667=(-41.66667)^2=1,736.1114 \\ 65-69.66667=(-4.66667)^2=21.7778 \end{gathered}[/tex][tex]\begin{gathered} 114-69.66667=(44.33333)^2=1,965.4441 \\ 74-69.66667=(4.33333)^2=18.7777 \end{gathered}[/tex][tex]\begin{gathered} 68-69.66667=(-1.66667)^2=2.7778 \\ 75-69.66667=(5.33333)^2=28.4444 \end{gathered}[/tex][tex]\begin{gathered} 70-69.66667=(0.33333)^2=0.1111 \\ 69-69.66667=(-0.66667)^2=0.4444 \\ 64-69.66667=(-5.66667)^2=32.1111 \end{gathered}[/tex]2. Add the results in step 1.
[tex]1,736.1114+21.7778+1,965.4441+18.7777+2.7778=3,744.8888[/tex][tex]28.4444+0.1111+0.4444+32.1111=61.111[/tex][tex]3,744.8888+61.111=3,805.9998[/tex]The sum is 3, 805.9998.
3. Divide the sum by the total number of data.
[tex]3,805.9998\div9=422.8889[/tex]4. Square root the result in step 3.
[tex]\sqrt{422.8889}\approx20.56[/tex]The standard deviation is approximately 20.56.
So, the data that are within 2 population standard deviations of the mean are between:
[tex]\begin{gathered} 69.67-(2)(20.56)=28.55\approx29 \\ 69.67+(2)(20.56)=110.79\approx111 \end{gathered}[/tex]The data that are within 2 population standard deviations of the mean are between 29 and 111. Based on the given data, the data that are between 29 and 111 are the following: 64, 65, 68, 69, 70, 74, and 75. There are 7 data that are within 2 population standard deviations of the mean.
Fiona is making a banner in the shape of a triangle for a school project. She graphs the banner on a coordinate plane with vertices at P(0, 4) , Q(2, 8) , and R(−3, 6) . She wants to reflect the banner over the line x=1. Identify the image of the banner reflected in the line x=1.
Answers
The coordinates of the banner after the reflection across x = 1 is P'(2, 4), Q'(0, 8), and R'(5, 6)
How to determine the coordinates of the banner after the reflection?From the question, the coordinates are given as
P(0, 4), Q(2, 8), and R(−3, 6)
The line of reflection is given as
x = 1
The rule of reflection across the line x = 1 is represented as
(x, y) = (-x + 2, y)
When the above rule is applied, we have
P'(2, 4), Q'(0, 8), and R'(5, 6)
This means that the coordinate of the image are P'(2, 4), Q'(0, 8), and R'(5, 6)
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40% of what number is 26? Please show work!
Answers
65
1) To find that, we need to write an equation:
[tex]x(0.4)=26[/tex]Note that we rewrote that 40% as 0.4.
2) Now, let's solve it
[tex]\begin{gathered} x0.4=26 \\ \frac{0.4x}{0.4}=\frac{26}{0.4} \\ x=65 \end{gathered}[/tex]3) So the 26 is 40% of 65
Can I Plss get some help I got stuck I don’t know how to find x
Answers
Using Sine of angles to evaluate for x
The formula is,
[tex]sin\theta=\frac{Opposite}{Hypotenuse}[/tex]Given:
[tex]\begin{gathered} Opposite=x \\ Hypotenuse=19 \\ \theta=21^0 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} sin21^0=\frac{x}{19} \\ \therefore x=19\times sin21^0 \end{gathered}[/tex]Simplify
[tex]x=6.80899\approx6.81\text{ \lparen2 decimal places\rparen}[/tex]Hence,
[tex]x=6.81[/tex]The standard normal curve is grafted below. Shade the region under the standard normal curve to the left of x=1.00Use the table to find the area under the standard normal curve to the left of x=1.00
Answers
Explanation
Part A
The shaded area under the standard normal curve to the left of z=1.00 can be seen below.
Part B
Using the z table, the area under the standard normal curve to the left of z.=1.00 is
Answer: 0.8413
What is the value of x? 20/72=x/360
Answers
The value of x = 100
Which equation is equivalent to: 3r=78+14 ?A. −3r=−78+14B. 3r−14=78C. 3r=78−14D. −3r=78−14
Answers
How would these look graphed ? Look at image attached .
Answers
These are two lines intersected ,in one point
One is positive inclined, the other negative.
Then now GRAPH
THEN BOTH LINES INTERSECT AT
From the diagram below, given the side lengths marked, and if we know that < C is congruent to < F, we can say that ___
Answers
SAS Similarity Theorem: If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
AC is proportional to DE while BC is proportional to FE, but F is not the included angle between those sides, therefore, those triangles are not similar by SAS.
The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. Since we have information only about one of the angles, ASA also doesn't apply.
For two triangles to be congruent, all of their measures must be congruent, which is not the case of our triangles.
The answer is option d. The two cannot be proven to be similar.
Solve the missing elements for each problem. Use 3.14 for π. Area = πr^2; C=π D
Answers
Given,
Diameter = 32 cm
Radius
We know the radius is half of the diameter. Thus,
[tex]\begin{gathered} r=\frac{32}{2} \\ r=16 \end{gathered}[/tex]Radius 16 cm
Circumference
The formula is:
[tex]C=\pi D[/tex]Where
D is the diameter
So,
[tex]\begin{gathered} C=\pi D \\ C=(3.14)(32) \\ C=100.48 \end{gathered}[/tex]Circumference = 100.48 cm
Area
The formula is:
[tex]A=\pi r^2[/tex]Where
r is the radius
So,
[tex]\begin{gathered} A=\pi r^2 \\ A=(3.14)(16)^2 \\ A=(3.14)(256) \\ A=803.84 \end{gathered}[/tex]Area = 803.84 sq. cm.
in order to clean her aquarium Stephanie much remove half of the water the garden measures 30 inches long 16 inches wide and 12 inches deep the aquarium is currently completely full with volume of water in cubic inches must Stephanie remove?
Answers
Hello!
30in long (length)
16in wide (width)
12in deep (height)
First, we have to calculate the volume when the aquarium is full of water, using the formula:
[tex]undefined[/tex]Paulina bought a used car as she was entering college and planned to trade it in when she graduated four years later. She had learned in her high school financial algebra class that the average used car depreciated at an annual rate of 15%. If she had paid $13,900 for her car, how much can she expect to get when it is time for her to trade it in for a new car?
Answers
1st year
depreciable value: $13900
annual depreciation: $13900*15% = $2085
2nd year
depreciable value: $13900 - $2085 = $11815
annual depreciation: $11815*15% = $1772.25
3rd year
depreciable value: $11815 - $1772.25 = $10042.75
annual depreciation: $10042.75*15% = $1506.41
4th year
depreciable value: $10042.75 - $1506.41 = $8536.34
annual depreciation: $8536.34*15% = $1280.45
Final value: $8536.34 - $1280.45 = $7255.89
4. A teacher can only make 3000 copies in a month. If a teacher-has-made 2700 copies so far this month, what percentage of her copies has she used?
Answers
In order to determine the percentage, let x as the percentage. Then, you can write:
[tex]\frac{x}{100}\cdot3000=2700[/tex]factor x/100 is the percentage in decimal form. The product of this factor and 3000 equals 2700.
Solve for x and simplify:
[tex]x=\frac{2700}{3000}\cdot100=90[/tex]Hence, teacher has used 90% of the copies.
can you help me solve this in expanded form. 156 X 687 = ?
Answers
Given data:
The given expression is 156x687.
The given expression can be written as,
[tex]\begin{gathered} (100+50+6)(600+80+7)=60000+8000+700+30000+4000+350+3600+480+42 \\ =107172 \end{gathered}[/tex]Thus, the value of the given expression is 107172.
Find all X values where the tangent line to the graph of the function…
Answers
Consider the function,
[tex]f(x)=6\sin x+\frac{9}{8}[/tex]The first derivative gives the slope (m) of the tangent of the curve,
[tex]\begin{gathered} m=f^{\prime}(x) \\ m=\frac{d}{dx}(6\sin x+\frac{9}{8}) \\ m=6\cos x+0 \\ m=6\cos x \end{gathered}[/tex]The equation of the line is given as,
[tex]y-3\sqrt[]{3}x=\frac{7}{3}[/tex]This can be written as,
[tex]y=3\sqrt[]{3}x+\frac{7}{3}[/tex]Comparing with the slope-intercept form of the equation of a line, it can be concluded that the given line has a slope,
[tex]m^{\prime}=3\sqrt[]{3}[/tex]Given that the tangent to the curve is parallel to this line, so their slopes must also be equal,
[tex]\begin{gathered} m=m^{\prime} \\ 6\cos x=3\sqrt[]{3} \\ \cos x=\frac{\sqrt[]{3}}{2} \\ \cos x=\cos (\frac{\pi}{6}) \end{gathered}[/tex]Consider the formula,
[tex]\cos A=\cos B\Rightarrow A=2k\pi\pm B[/tex]Applying the formula,
[tex]x=2k\pi\pm\frac{\pi}{6}[/tex]Thus, the required values of 'x' are,
[tex]x=2k\pi\pm\frac{\pi}{6}[/tex]Therefore, options 1st and 2nd are the correct choices.
Triangle KLM has KL = 28, KM = 28, and LM = 21. What is the area of the triangle?The area of AKLM is about(Simplify your answer. Round to one decimal place as needed.)
Answers
Area = (b * h)/2, b = 21 bu we don't know h, s we have to calculate it
To calculate the height "h" we can use pythagoras with a triangle rectangle with base = 21/2 = 10.5 and hypothenuse = 28, so the height "h" is:
28² = h² + 10.5² ==> h² = 28² - 10.5² = 784 - 110.25 = 673.75
h² = 673.75
h = 25.96
Now that we have the height, the Area of the triangle = (b * h)/2 = (21 * 25.96)/2 = 272.5
Answer:
272.5
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The general form of an ellipse is 15x2+4y2+30x−16y−29=0.
What is the standard form of the ellipse?
Answers
The equation of ellipse in standard form is (x + 1)² / 4 + (y - 2)² / 15 = 1.
How to determine the standard form of the ellipseIn this problem we find the equation of an ellipse in general form, whose standard form can be found by algebra properties. The general form of the equation of an ellipse centered at (h, k) is introduced below:
(x - h)² / a² + (y - k)² / b² = 1
Where:
a, b - Lengths of the semiaxes.(h, k) - Coordinates of the center.The complete procedure is now presented:
15 · x² + 4 · y² + 30 · x - 16 · y - 29 = 0
(15 · x² + 30 · x) + (4 · y² - 16 · y) = 29
15 · (x² + 2 · x) + 4 · (y² - 4 · y) = 29
15 · (x² + 2 · x + 1) + 4 · (y² - 4 · y + 4) = 29 + 15 · 1 + 4 · 4
15 · (x + 1)² + 4 · (y - 2)² = 29 + 15 + 16
15 · (x + 1)² + 4 · (y - 2)² = 60
(x + 1)² / 4 + (y - 2)² / 15 = 1
The equation of ellipse is (x + 1)² / 4 + (y - 2)² / 15 = 1.
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Find the distance between the points (5,5) and (-3,7). Round your answer to the nearest tenth, if necessary.8.2 units11.8 units3.2 units12.2 units
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The formula for the distance between two points in the plane is:
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]So:
[tex]\begin{gathered} (x_1,y_1)=(5,5) \\ (x_2,y_2)=(-3,7) \\ d=\sqrt[]{(5-(-3))^2+(5-7)^2} \\ d=\sqrt[]{(8)^2+(-2)^2} \\ d=\sqrt[]{64+4} \\ d=\sqrt[]{68} \\ d=8.2462\ldots\approx8.2 \end{gathered}[/tex]So, the distance is approximately 8.2 units.
need help asap look at attachmen
Answers
The rectangle has a width of 7 yards and a length of 42 yards.
How to find the length and width?For a rectangle of length L and width W, the perimeter is:
P = 2*(L + W)
Here we know that:
L = 6*W
P = 98yd = 2*(L + W)
Then we have the system of equations:
L = 6*W
98yd = 2*(L + W)
If we substitute the first equation into the second one, we get:
98yd = 2*(6*W + W)
98yd = 14*W
98yd/14 = W = 7yd
So the width is 7 yards, and the length is 6 times that, so:
L = 6*7yd = 42yd
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