Given:
Right triangle XYZ has right angle Z.
[tex]\sin(x)=\dfrac{12}{13}[/tex]
To find:
The value of [tex]\cos x[/tex].
Solution:
We know that,
[tex]\sin^2(x)+\cos^2(x)=1[/tex]
[tex]\cos^2(x)=1-\sin^2(x)[/tex]
[tex]\cos(x)=\pm\sqrt{1-\sin^2x}[/tex]
For a triangle, all trigonometric ratios are positive. So,
[tex]\cos(x)=\sqrt{1-\sin^2x}[/tex]
It is given that [tex]\sin(x)=\dfrac{12}{13}[/tex]. After substituting this value in the above equation, we get
[tex]\cos(x)=\sqrt{1-(\dfrac{12}{13})^2}[/tex]
[tex]\cos(x)=\sqrt{1-\dfrac{144}{169}}[/tex]
[tex]\cos(x)=\sqrt{\dfrac{169-144}{169}}[/tex]
[tex]\cos(x)=\sqrt{\dfrac{25}{169}}[/tex]
On further simplification, we get
[tex]\cos(x)=\dfrac{\sqrt{25}}{\sqrt{169}}[/tex]
[tex]\cos(x)=\dfrac{5}{13}[/tex]
Therefore, the required value is [tex]\cos(x)=\dfrac{5}{13}[/tex].
There were 14 dogs adopted from the animal shelter last week. This week, 8 dogs were adopted .There are 5 dogs left. How many dogs, d, did the shelter have for adoption?
Answer:
d=27
Step-by-step explanation:
A total of 14+8=22 dogs were adopted. Since there are 5 left, there were 22+5=27 dogs up for adoption.
Kelli buys a new backpack for $35. There is a 20% discount and a 7% tax. What will be the final cost of the backpack?
Answer:
29.96
Step-by-step explanation:
First find the discount
35 * 20 %
35*.2
7
Subtract the discount from the price
35-7
28
Now find the tax on the new price
28* 7%
28 *.07
1.96
Add the tax to the new price
28+1.96
29.96
The graph of a quadratic equation has x-intercepts at (−5, 0) and (1, 0). Which of the following could be the equation described?
Answer:
Step-by-step explanation:
Find \sin(\beta)sin(β)sine, left parenthesis, beta, right parenthesis in the triangle.
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
\dfrac{15}{8}
8
15
start fraction, 15, divided by, 8, end fraction
(Choice B)
B
\dfrac{8}{17}
17
8
start fraction, 8, divided by, 17, end fraction
(Choice C)
C
\dfrac{8}{15}
15
8
start fraction, 8, divided by, 15, end fraction
(Choice D)
D
\dfrac{15}{17}
17
15
start fraction, 15, divided by, 17, end fraction
Answer:
Its 15/17
Step-by-step explanation:
I did it on Khan
Based on the sine ratio, sin (β) in the right triangle is: D. 15/17.
How to Apply the Sine Ratio?Where the hypotenuse and opposite side lengths are known, the sine ratio is expressed as, sine β = opposite/hypotenuse.
Given the following:
Opposite side = 15Hypotenuse = 17Applying the sine ratio, we have:
sin β = 15/17
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The number of hours worked at a factory and the money earned is proportional. If an employee works 40 hours, they will earn $2500. How many hours does the employee work if earn $1500, Explain your reasoning
Mr Kent sells calculators for $35 each. If an order is placed from a business account, there is a $50 shipping fee, and no fewer than 100 calculators can be purchased. Which is a reasonable amount of money that a business would spend when ordering calculators?
Answer:
The reasonable amount is $3550 or greater
Step-by-step explanation:
Given
[tex]c=\$50[/tex] ---- shipping fee
[tex]r =\$35[/tex] --- unit selling price
[tex]n \to[/tex] number of orders
[tex]n \ge 100[/tex] ---- domain of order
Required
The reasonable ordering amount
The function for n calculator can be represented as:
[tex]f(n) = r * n + c[/tex]
This gives:
[tex]f(n)=35 * n + 50[/tex]
[tex]f(n)=35n + 50[/tex]
Recall that the domain is: [tex]n \ge 100[/tex]
So, we have:
[tex]f(n)=35n + 50[/tex] [tex]n \ge 100[/tex]
The reasonable amount of order implies that we calculate the range of the function
[tex]n \ge 100[/tex] implies that the minimum is 100
So:
Substitute 100 for n in [tex]f(n)=35n + 50[/tex]
[tex]f(100) = 35 * 100+50[/tex]
[tex]f(100) = 3500+50[/tex]
[tex]f(100) = 3550[/tex]
So, the range of the function is:
[tex]3550 \le f(n) < \infty[/tex]
Find the interior angle sum for each polygon. Round your answer to the nearest tenth if needed
(#4 and #3 are solve for x)
Answer:
1) 720
2) 540
3) x = -1
4) x = 10
Step-by-step explanation:
The formula for finding the sum of interior angles in a polygon is the following,
[tex]S=180(n-2)[/tex]
Where (S) represents the sum of interior angles, and (n) represents the number of sides.
1)
The given polygon is a hexagon, meaning it has (6) sides. Substitute the number of sides into the formula and solve for the sum of interior angles.
[tex]S=180(n-2)[/tex]
[tex]S=180(6-2)\\\\S=180(4)\\\\S = 720[/tex]
2)
This polygon is a pentagon, meaning it has (5) sides. Substitute the number of sides into the formula and solve for the sum of interior angles.
[tex]S=180(n-2)[/tex]
[tex]S=180(5-2)\\\\S=180(3)\\\\S=540[/tex]
3)
The sum of interior angles in a triangle is (180) degrees. One can see that one of the measures of an angle is (90) degrees (indicated by the box around the angle). One can form an equation by adding up the expressions for the angle measures and setting it equal to (180) degrees.
(55) + (x + 36) + (90) = 180
Simplify,
181 + x = 180
Inverse operations,
181 + x = 180
x = -1
4)
The remote angles theorem states that when one extends one of the sides of a triangle, the angle formed between the side and the extension is equal to the sum of the two non-adjacent interior angles in the triangle. Based on this theorem, one can form an equation and solve for the unknown.
<F + <G = <FEZ
Substitute,
(4x) + (-5 + 7x) = 105
Simplify,
4x - 5 + 7x = 105
11x - 5 = 105
Inverse operations,
11x - 5 = 105
11x = 110
x = 10
If -10x – 9y = -7 is a true equation, what would be the value of
-30x – 27y?
Answer:
-30x-27y = -21
Step-by-step explanation:
We know that;
-30x-27y = 3(-10x-9y)
Recall, -10x-9y = -7
Thus; -30x-27y = 3(-7) = -21
I've been learning this but I don't remember how to find x?
Answer:56 degrees
Step-by-step explanation: Using Base Angles Theorem, we can conclude that angle x is 180-62*2, which is 180-124, which is 56 degrees.
Answer:
the answer is x = 56 degrees
and your not finding the side lengths
Step-by-step explanation:
there is 2 62 degrees,
meaning the TOP RIGHT ANGLE OF THE TRIANGLE IS 62 DEGREES if you can't find it in my answer and X IS EQUAL TO THE ANGLE OF 56 DEGREES if you can't read that either
so x = 56
by rounding to 1 significant figure estimate 8.31÷1.87
Answer:
4
Step-by-step explanation:
put into calculator
The required rounding of the number 8.31 ÷ 1.87 is 4.4.
Given that,
To find the simplified value for 8.31÷1.87.
A recurring Decimal is defined as also named repeating decimal, is a decimal number that only consists of repeating digits after a certain interval after the decimal. For example, 94.642642642..., 213.569569... etc.
Here,
8.31÷1.87 = 4.444
Where 4 is a repeating decimal so the round to 1 decimal point is 4.4
Thus, the required rounding of the number 8.31 ÷ 1.87 is 4.4.
For more information about recurring decimals check it out here:
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A rectangular prism with a volume of 222 cubic units is filled with cubes with side lengths of \dfrac14
4
1
start fraction, 1, divided by, 4, end fraction unit.
How many \dfrac14
4
1
start fraction, 1, divided by, 4, end fraction unit cubes does it take to fill the prism?
Answer: 128 cubes
Step-by-step explanation:The dimension of the rectangular prism is not given, assumed not important.
Find the volume of 1 cube:
Volume = 1/4 x 1/4 x 1/4
Volume = 1/64 units³
Find the number of cubes that can go into the prism:
Number of cubes = 2 ÷ 1/64
Number of cubes = 128
The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price. Some of the expressions shown below represent the sale price, in dollars,of the item.Expression A: Expression B: Expression C: Expression D: Expression E: Which two expressions each represent the sale price of the item?AExpression A and Expression EBExpression B and Expression CCExpression B and Expression DDExpression C and Expression D
Answer:
Expression B: 0.8p
Expression D: p - 0.2p
Step-by-step explanation:
The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price. Some of the expressions shown below represent the sale price, in dollars, of the item.
Expression A: 0.2p
Expression B: 0.8p
Expression C:1 - 0.2p
Expression D: p - 0.2p
Expression E: p - 0.8p
Which two expressions each represent the sale price of the item?
Regular price of the item = $p
Sale price = 20% off regular price
Sale price = $p - 20% of p
= p - 20/100 * p
= p - 0.2 * p
= p - 0.2p
= p(1 - 0.2)
= p(0.8)
= 0.8p
The sale price is represented by the following expressions
Expression B: 0.8p
Expression D: p - 0.2p
please help me solve
please show how you got the answer
Answer:
Step-by-step explanation:
The total amount paid by a member according to this table is
Total Amount Paid = fee + monthly fee(# of months)
Since the fee is the same regardless of how many months one signs up for, it should come out the same for each row in our table.
Row 1:
TAP = fee + 15(#months)
135 = fee + 15(4) and
135 = fee + 60 so
fee = $75
Row 2:
165 = fee + 15(6) and
165 = fee + 90 so
fee = $75
Row 3:
255 = fee + 15(12) and
255 = fee + 180 so
fee = $75
Apparently, the fee is $75.
Use a graph to tell whether the ordered pairs represent a linear function, an exponential
function, or a quadratic function.
(-2, 2), (-1, 5), (0, 3), (1, 1) (2, 3)
Answer: exponential function
Step-by-step explanation:
Graph it.
You will see that the ordered pairs make the shape of a sideways "S."
Linear functions are straight lines and quadratic functions are "U" or upside-down "U" shaped curves. Exponential functions can have multiple curves like including a sideways "S" shape, so it is exponential.
Which is a better estimate for the length of an almond?
a. 3 meters b. 3 centimeters
Answer:
3 centimeters
Step-by-step explanation:
nope
Answer:
[tex]B[/tex]
Step-by-step explanation:
What is the reference angle for 5pi over 3?
a. pi over 6
b. pi over 3
c. 2pi over 3
Answer:
b. pi over 3 ig~~~~~~~~~~~~~~~
Answer:
(b) pi over 3 is correct
Step-by-step explanation:
EDGE 2022
1. Romero's Gas-n-Go buys their gas for $1.50 per gollon and marks it up 80%
What is the sale price of Romero's Gas
Answer:
The answer is $2.7
Step-by-step explanation:
A triangle has side lengths of (5.5x + 6.2y) cm, (4.3x + 8.3z) cm, and (1.6z - 5.1y) cm. Which expression represents the perimeter, in centimeters, of the triangle?
Answer:
9.8x+1.1y+9.9z
Step-by-step explanation:
Hi there!
Perimeter = Sum of all sides
[tex]P=(5.5x + 6.2y)+(4.3x + 8.3z)+(1.6z - 5.1y)[/tex]
Open up the parentheses
[tex]P=5.5x+6.2y+4.3x+8.3z+1.6z-5.1y[/tex]
Combine like terms
[tex]P=5.5x+4.3x+6.2y-5.1y+8.3z+1.6z\\P=9.8x+1.1y+9.9z[/tex]
Therefore, the expression 9.8x+1.1y+9.9z (cm) best represents the perimeter of the triangle.
I hope this helps!
Answer:
answer is c
Step-by-step explanation:
A rectangle and a vertical line are shown. If the rectangle is revolved about the vertical line, what is the resulting object?
a rectangle with one side against a vertical line
solid cylinder
hollow cylinder
hollow cone with truncated top
solid cone
Answer:
Preetyy sure its D
Step-by-step explanation:
Its not a hollow cylinder
The resulting object will be a solid cylinder. Then the correct option is A.
What is a solid revolution?When a figure is revolved around some fixed axis, the whole three-dimensional solid formed from the area that it swaps out is called a solid of revolution.
A rectangle and a vertical line are shown. If the rectangle is revolved around the vertical line.
Then the resulting object will be
If the rectangle is rotated about the vertical axis then the resulting shape will be a solid cylinder.
The diagram is shown below.
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i need all the questions and where is says to explain I need you to explain, it's pythagorean theorem, plsssss help me
Answer:
Step-by-step explanation:
sams house=6 miles east and 9 mies south
let the distance towards east be a and distance towards south be b
so we have to find straight line distance from sams house to amys house .let it be c(or hypotenuse)
according to the pythagors theorem
a^2 + b^2 =c^2
6^2 + 9^2 =c^2
36 + 91 =c^2
117 =c^2
[tex]\sqrt{117[/tex] =c
10.8=c
the two coordinate points are
(4,12)=(x1 , y1)
(6,2)=(x2 , y2)
distance formula = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
=[tex]\sqrt{(6-4)^2 + (2-12)^2}[/tex]
=[tex]\sqrt{2^2 + (-10)^2}[/tex]
=[tex]\sqrt{4 + 100}[/tex]
=[tex]\sqrt{104}[/tex]
=2[tex]\sqrt{26}[/tex]
=10.1 units
fairy travels=10.1 * 2
=20.2 miles
three sides are 17,8,15
according to the pythagoras theorem
to be right angles triangle square of hypotenuse(longest side) must equal to the sum of square of two other smaller sides
so here 17 is longest and 8 and 15 are two other smaller sides of a triangle
17^2=8^2 + 15^2
289=64 + 225
289=289
since both sides are equal it can be concluded that they form a right angled triangle.
Hope this helps u!!
Answer:
1. option b : 10.8 miles
2. Distance = 10.2 units
Distance in miles = 20.4 miles
3. Paulie is correct because the measurements satisfies Pythagoras theorem.
Step-by-step explanation:
1. option b
Let straight line length be x
x² = 6² + 9²
= 36 + 81
= 117
x = 10.8 miles
2.
Current location ( 4 , 12 )
Destination ( 6, 2 )
a)
[tex]Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \\\\[/tex]
[tex]= \sqrt{(4 - 6)^2 + (12 - 2)^2} \\\\= \sqrt{2^2 + 10^2}\\\\=\sqrt{104}\\\\=10.2 \ units[/tex]
b)
Grid (units) Distance( miles)
1 2
10.2 x
[tex]\frac{1}{10.2} = \frac{2}{x}\\\\x = 2 \times 10.2\\x = 20.4 \ miles[/tex]
3.
a)
Square of Longer side = sum of squares of other sides
[tex]17^2 = 8 ^2 + 15^2 \\289 = 64 + 225\\289 = 289 \\[/tex]
Yes, Paulie is Correct.
b)
Paulie is correct because the measurements of the sides of triangle satisfies Pythagoras theorem.
Pythagoras' theorem states that for all right-angled triangles, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
Eugene has to buy cupcakes for a picnic. He needs to make sure that there are more than 8 cupcakes so each of his friends gets at least one cupcake. If Eugene buys y boxes that each contain 4 cupcakes, which inequality represents this situation?
A.
y < 8
B.
y > 8
C.
4y > 8
D.
4y < 8
Answer:
C
Step-by-step explanation:
4xy=4y
since each friend must get at least a cupcake, 4y must be larger than 8
2. What is the equation of the line that passes
through the point (4. – 5) and has slope
Answer:
D. y = 1/2x - 7
Step-by-step explanation:
y = 1/2x + b
-5 = 1/2(4) + b
-5 = 2 + b
-7 = b
What process allows your body to cool off on a hot day?
A. insulation
B. evaporation
C. convection
(Ik I put the subject as math it's cuz biology hardly gets any answers)
Answer:
I believe the Answer is B
Answer:
B. evaporation
Step-by-step explanation:
8 1/3% as a common fraction.
Answer:
[tex]\frac{27}{100}[/tex]
Step-by-step explanation:
Given data:
[tex]\frac{81}{3}%[/tex]%
Now
It can be written as:
[tex]\frac{81}{3}[/tex]%=[tex]27[/tex]%
27%=[tex]\frac{27}{100}[/tex]
Therefore, common fraction will be [tex]\frac{27}{100}[/tex]
Answer:
2500/3
Step-by-step explanation:
[tex]8\frac{1}{3}[/tex] %
=(8*3+1/3) %
=25/3 %
=25/3 / 100
=25/3 *100/1
=2500/3
What is the range of the given function?
Answer:
you have it on the correct answer
Step-by-step explanation:
range is the y values, and its the lowest negetive to the highest positive
Can someone help me? It's urgent and thank you!
Answer:
d = 6
Step-by-step explanation:
Since the line is horizontal then the distance from B to C is the distance between the x- coordinates.
d = | - 3 - 3 | = | - 6 | = | 6 | = 6
Answer:
option C
Step-by-step explanation:
[tex]distance, d = \sqrt{(x_B- x_C)^2 + (y_B - y_C)^2}[/tex]
[tex]=\sqrt{(-3 -3)^2 + (6 - 6)^2 }\\\\=\sqrt{(-6)^2 + 0 }\\\\=\sqrt{36}\\\\= 6[/tex]
round to the nearest ten i dont get it
Answer:
130
Step-by-step explanation:
instead of 132 round to the nearest 10 so its 130
Answer:
130
Step-by-step explanation:
algebra
huh still difficult and will always be.
Someone just...…..
please help me to figure out this
Answer:
[tex]z = 6[/tex]
Step-by-step explanation:
Let's solve:
[tex]5(z+1)=3(z+2)+11[/tex]
Step 1: Simplify both sides of the equation.
[tex]5(z+1)=3(z+2)+11 \\ (5)(z)+(5)(1)=(3)(z)+(3)(2)+11(Distribute) \\
5z+5=3z+6+11 \\
5z+5=(3z)+(6+11)(Combine Like Terms) \\
5z+5=3z+17 \\
5z+5=3z+17[/tex]
Step 2: Subtract 3z from both sides.
[tex]5z+5−3z=3z+17−3z \\ 2z+5=17[/tex]
Step 3: Subtract 5 from both sides.
[tex]2z+5−5=17−5 \\ 2z=12[/tex]
Step 4: Divide both sides by 2.
[tex] \frac{2z}{2} = \frac{12}{2} \\ z = 6[/tex]
If a = 22 ft, b = 34 ft, and c = 36 ft, what is the area of the backyard?
Answer:
363
Step-by-step explanation:
The Chang family is on their way home from a cross-country road trip. During the trip, the function D(t)=3260−55t can be used to model their distance, in miles, from home after t hours of driving. find D(12) and interpret the meaning in the context of the problem.
Answer:
D(12) = 2,600 miles
It means a distance of 2,600 miles is already traveled from home after 12 hours
Step-by-step explanation:
To find D(12); all we have to do is to substitute the value of 12 for D
We have this as;
D(12) = 3260-55(12)
D(12) = 2,600
In the context of this problem, what this mean is that the distance away from home is 2,600 miles after traveling 12 hours
