Describe three ways to determine the measure of segment YZ.
Triangle X Y Z is shown. Angle X Y Z is a right angle and angle Z X Y is 30 degrees. The length of hypotenuse X Z is 50 meters.
Answers
Step-by-step explanation:
tan 30 degre = perpendicular /base
I wrote the rule than you can easily find hope this help you
Using 3 different methods, we can find that YZ = 25m
The complete image of a triangle is attached with the answer below.
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
For a given triangle rectangle with a known angle θ and a hypotenuse H, we can write the trigonometric relations
sin(θ) = (opposite cathetus)/H
cos(θ) =(adjacent cathetus)/H
tan(θ) =(opposite cathetus)/(adjacent cathetus)
Now, in the given image we can see that:
θ = 30°
H = 50m
XY = adjacent cathetus
YZ = opposite cathetus.
We want to find YZ, so with the known things, we can use the first relation:
Sin 30 = YZ / 50
YZ = 50 x Sin30 = 25 meters
Now let's try another way.
We know that the sum of the internal angles of a triangle is always equal to 180°
In a triangle rectangle, we always have an angle equal to 90°.
Then the missing angle for our triangle can be computed from:
Z + 90° + 30° = 180°
Z = 180° - 90° - 30° = 60°
From this angle, the side YZ is the adjacent cathetus, then we can use the second trigonometric relation:
Cos 60 = YZ / 50
YZ = 50 x Cos 60 = 25 meters
Third way.
Whit the same angle we could find the side XY, the opposite cathetus, with:
Sin 60 = XY / 50
XY = 50Sin 60 = 43.3 meters
Now that we know one of the catheti, we can use the last trigonometric relation
tan 60 = XZ / YZ = 43.3 / YZ
YZ = 43.3 / tan 60 = 25 meters
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Related Questions
cotpheta•sin2pheta=
1+cos2pheta
1+cospheta
1+sin2pheta
Answers
Answer:
Step-by-step explanation:
Did you mean.
[tex] = \cot( \theta) . \sin(2 \theta) [/tex]
[tex] = \frac{ \cos( \theta) }{ \sin( \theta) } .(2 \sin( \theta) \cos( \theta) )[/tex]
[tex] = \frac{2 \sin( \theta) \cos {}^{2} ( \theta) }{ \sin( \theta) } [/tex]
[tex] = 2 \cos {}^{2} ( \theta) [/tex]
[tex] = 2.(1 - \sin {}^{2} ( \theta) )[/tex]
[tex] = 2 - 2 \sin {}^{2} ( \theta) [/tex]
No option Solution.
Which of the following appear in the diagram below?
Answers
Answer:
Step-by-step explanation:
Comment
The one you can pick out that is true is D. The others you have to be careful with. C is a line and it has two arrowheads in the symbol above the two letters which makes it correct as well. A is not correctly marked, so it is not there the way it is marked. One would think ZX is a ray the way it is marked.
Answer: C and D
what is the answr to -5(b + 1) = 8
Answers
[tex] - 5(b + 1) = 8 \\ - 5b - 5 = 8 \\ - 5b = 8 + 5 \\ - 5b = 13 \\ b = \frac{ - 13}{5} [/tex]
PLEASE GIVE BRAINLIEST
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[tex]\Rsh[/tex] Hey! [tex]\Lsh[/tex][tex]\Rsh[/tex]Let's solve this! We can do this! [tex]\Lsh[/tex]
>>> First, let's multiply -5 by b and 1. Then we obtain
[tex]\pmb{-5b-5=8}[/tex].
>>> Now we add 5 to both sides.
[tex]\pmb{-5b=13}[/tex]
>>> And then, divide both sides by -5.
[tex]\pmb{b=-\dfrac{13}{5}}[/tex]
>>> That is the value of b.
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Hope the answer - and explanation - assisted you!
Happy studies! :)
A response variable, Price, is defined as the selling price of a used car. Three predictor variables include, Age, the age of the car in years, Mileage, the mileage of the car in thousands of miles, and Cylinders, the number of engine cylinders. The estimated regression equation is: Price
Answers
The estimated regression equation is Price = bo +b1Age+ b2Mileage + b3Cylinders
How to determine the regression equation?We have:
Predictor variables = 3Variable 1 = AgeVariable 2 = MileageVariable 3 = CylindersThe regression equation is estimated using:
Price = bo +b1 * Variable 1+ b2 * Variable 2 + b3 * Variable 3
Substitute the variable parameters
Price = bo +b1Age+ b2Mileage + b3Cylinders
Hence, the estimated regression equation is Price = bo +b1Age+ b2Mileage + b3Cylinders
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A sum of money is divided among three girls, Rheanna, Kerisha and Anne, in the ratio 2:3:7, respectively. If Anne gets $15
more than Kerisha, what is the value of the total sum that was shared?
Answers
Using proportions, it is found that the value of the total sum that was shared was of $45.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the rates, Anne's and Kerisha's proportions, out of the total value N, are given by:
[tex]A = \frac{7}{2 + 3 + 7}N = \frac{7N}{12}[/tex][tex]K = \frac{3}{2 + 3 + 7}N = \frac{3N}{12}[/tex]The difference is of $15, hence:
[tex]A - K = 15[/tex]
[tex]\frac{7N}{12} - \frac{3N}{12} = 15[/tex]
[tex]\frac{4N}{12} = 15[/tex]
[tex]\frac{N}{3} = 15[/tex]
N = 15 x 3 = 45
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John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width.
Which equation could John solve to find w, the greatest width in centimeters he can use for the mosaic?
w(w – 2) = 48
w(w + 2) = 48
2w(w – 2) = 48
2w(w + 2) = 48
Answers
The equation that could John solve to find w, the greatest width in centimeters he can use for the mosaic is option B: w(w + 2) = 48.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The mosaic to be formed is rectangular in shape.
Area of a rectangle = length x width
The length is longer than the width by 2,
So, length = w+2
Area of a rectangle = (w+2) x w
The correct equation is B: w(w + 2) = 48
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Answer: B
Step-by-step explanation:
f(x) = 4x² + 7x-3
g(x) = 6x³ – 7x² - 5
-
Find (f + g)(x).
Answers
Answer:
(f + g)(x) = 6x³ - 3x² + 7x - 8
Step-by-step explanation:
Another way of writing (f + g)(x) is f(x) + g(x). So, this question is asking you to combine both of the functions.
f(x) + g(x)
(4x² + 7x - 3) + (6x³ - 7x² - 5) <----- Insert functions
-3x² + 7x - 3 + 6x³ - 5 <----- Combine 4x² and -7x²
-3x² + 7x - 8 + 6x³ <----- Combine -3 and -5
6x³ - 3x² + 7x - 8 <----- Rearrange
Identify the method that will be used to solve for x for each equation.
4x = 20
x 119
5x + 6x = 22
5(x - 2) = 30
Answers
The solution of the equation 4x = 20, x – 11 = 9, 5x + 6x = 22, and 5(x – 2) = 30 will be 5, 20, 2, and 8.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equations are given below.
4x = 20
x = 5
x – 11 = 9
x = 20
5x + 6x = 22
11x = 22
x = 2
5(x – 2) = 30
x – 2 = 6
x = 8
The complete question is attached below.
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Given parallelogram ABCD and AB || CD, if mAB = -5 then mCD must be:
A)-5
B)
- 1
——
5
C) 5
D) 1
—
5
Answers
The slope of CD, which is parallel to AB must be: A. -5.
What is the Slope of Parallel Segments?If two line segments are parallel to each other, their slope value (m) would be equal to each other.
Side AB and CD in the parallelogram are parallel segments, therefore, their slope (m) would be the same.
Slope (m) of AB = -5, therefore, the slope of CD must be: A. -5.
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5(b)
Joe has a bucket containing 1370cm³ of water measured to the nearest 10 cm³.
Joe Says
"If I tip my bucket of water in the cuboid container, it will never overflow"
Is Joe correct?
You must explain your answer
Answers
If the side length is greater than 11.11 cm then it will not overflow.
Otherwise, it will overflow.
If Joe tips the bucket of water in a cuboid container and the water is not overflowing then the cuboid container must be of volume greater than 1370 cm³.
We find the cube root of 1370 cm³.
[tex]\sqrt[3]{1370} \approx11.11[/tex]
Then the cuboid container should have a side of length greater than 11.11 cm.
Here the statement "If I tip my bucket of water in the cuboid container, it will never overflow" is correct or wrong based on the information that the container has a side length lesser or greater than 11.11 cm.
If the side length is greater than 11.11 cm then it will not overflow.
Otherwise, it will overflow.
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the area of square ABCD is 10cm2 show that x^2+6x=a where a is a constant to be found
Answers
The value of a is 1 if the area of square ABCD is 10 cm² showing that x²+6x=a where a is a constant.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
The question is incomplete.
The question is:
The area of square ABCD is 10 cm² showing that x²+6x=a where a is a constant to be found.
The missing figure is attached; please refer to the picture.
As we can see in the figure we have given a rectangle.
Area of rectangle = (3 + x)(3 + x)
10 = (3 + x)(3 + x)
or
10 = (3 + x)²
10 = 9 + 6x + x²
After rearranging:
x² + 6x = 1
We have equation:
x² + 6x = a
After comparing:
a = 1
Thus, the value of a is 1 if the area of square ABCD is 10 cm² showing that x²+6x=a where a is a constant.
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If = 12 –3 a,find the value ofxwhen a= 8
Answers
Answer:
-12
Step-by-step explanation:
x = 12-3a
When a=8:
x = 12-3(8)
x = 12 - 24
x = -12
I need help please :3
Answers
Answer:
32ounces
Step-by-step explanation:
24/3=8pounds
8pounds=8x16=128ounces
but each 8 pounds is split into quarters so
8/4=2pounds=32ounces
24 divided by 3 is 8,
8 divided by 4 is 2,
So 2 times 16 is 32 ounces
the number of sides of regular polygon if the measure of its interior angle is 150 degree
Answers
Answer:
12 sides
Explanation:
[tex]\sf interior \ angle = \dfrac{(n-2) \times 180}{n} \quad (where \ n \ denotes\ number \ of \ sides)[/tex]
Solving Steps:
[tex]\sf \dfrac{(n-2) \times 180}{n} = 150[/tex]
[tex]\sf (n-2) \times 180} = 150n[/tex]
[tex]\sf 180n-360 = 150n[/tex]
[tex]\sf 180n-150n = 360[/tex]
[tex]\sf 30n = 360[/tex]
[tex]\sf n = 12[/tex]
suppose your household income increased to $2,000.00 and your energy bill came from $180.00 how many percent of your household income is being spent on electricity?
Answers
hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა
⊱┈────────────────────────┈⊰
[tex]\large \bold {ANSWER}[/tex]
[tex]\implies \boxed{\underline{\huge{\tt{\orange{\: \: 9\% \: \: }}}}}[/tex]9% of the family income is being spent to pay the energy bill.
[tex]\large \bold {SOLUTION}[/tex]
HOW TO FIND OUT THE PERCENTAGE?If your income is now $2,000.00 and you have withdrawn $180.00 from the value, then we say that the $2,000.00 is equivalent to 100% of the value, that is, the total amount. And the amount that was withdrawn will be X because we still don't know how much percent is equivalent to $ 180.00 of this value.
To solve, we will use the simple rule of three like this:
[tex]\frac{2000}{180} = \frac{100}{x}[/tex]With this we will multiply the denominator of one with the numerator of the other, being:
2000 * X and 180 * 100Where: 2000 * x is equal to 2000xAnd 180 * 100 is equal to 18,000Knowing this, we will solve it this way:
2000x = 18,000To start we will isolate the unknown(x) from the values taking the 2000 to the other side of the equality turning it into the denominator of 18,000.
[tex]x = \frac{18000}{2000}[/tex]And to finish, we cut the 3 zeros of the numerator with the d 3 zeros of the denominator getting 18 / 2. Now it's just dividing.
[tex]\begin{gathered}x = \frac{18}{2} \\ \\ x = 9\end{gathered}[/tex]We can conclude that the amount spent to pay the energy bill is equivalent to 9% of the family income.
Please help!!!!
A triangular patch of grass in a park is bordered by walking paths. The longest path bordering the patch of grass measures 135 feet. The smallest path bordering the patch of grass measures 60 feet. The smallest angle formed by the paths measures 26°. What is the measure of the largest angle of the triangular patch of grass? Round your answer to the nearest degree. Show all your work.
Answers
The measure of the largest angle of the triangular patch of grass is 81 degrees
Application of sine ruleIn order to determine the measure of the largest angle, we will use the expression below;
[tex]\frac{60}{sin26^0} =\frac{135}{sinx^0}[/tex]
Cross multiply
135sin26 = 60sinx
sinx = 135sin26/60
sinx = 59.18/60
sinx = 0.986
x = 80.5 degrees
Hence the measure of the largest angle of the triangular patch of grass is 81 degrees
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La siguiente operación 147.3 = 441 es una:
División b- Sustracción c- Multiplicación
plis necesito la respuesta ahora dare estrellas lo juro
Answers
La operación que representa 147.3 = 441 es dada por una multiplicación, por eso opción c es correcta.
¿Qué operación está representada por 147 . 3 = 441?El resultado del producto entre 147 y 3 es de 441, por lo que se hace una operación de multiplicación.
Así, hay que la opción c es correcta.
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Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard form, given that the point-slope form is y+1=3/3(x-8)
Answers
The equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.
The given coordinate are (8, -1) and (2, -5).
What is the slope of an equation?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
The slope of the equation is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].
The standard form of an equation is Ax + By = C.
The given the point-slope form is [tex]y+1=\frac{2}{3} (x-8)[/tex].
Multiply each term by 3 of the equation.
[tex](y+1) \times3=\frac{2}{3} (x-8) \times3[/tex]
⇒3y + 3 = 2x - 16
Subtract 2x from both sides of a equation.
That is, -2x + 3y + 3 = - 16
Subtract 3 from both sides of a equation.
That is, -2x + 3y = - 19
Multiply each term by - 1 from both sides of an equation.
That is, 2x - 3y = 19
Therefore, the equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.
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Zippy company manufactured 10,000 units in december with a total product cost of $22,900 they had zero finished goods inventory at the start of december. in december zippy sold 7,796 units at a unit price of $5.54. period expenses were $4,723. what is the amount of zippy's gross profit (otherwise know as gross margin).? round any intermediate calculations to four decimal places
Answers
The amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.
Gross profitSales revenue $43,189.84
(7,796 units × $5.54)
Less Cost of goods sold $17,852.84
[($22,900/10,000)×7,796]
Gross profit $25,337
( $43,189.84-$17,852.84)
Therefore the amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.
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(This is an Edge question)
Question:
Which expression is equivalent to negative 3 minus 3 times a number minus 1 plus a number.
[tex] - 3 - 3x - 1 + x[/tex]
Answer Choices:
A.
[tex]2x - 4[/tex]
B.
[tex] - 2x + 4[/tex]
C.
[tex] - 2x - 4[/tex]
D.
[tex]4 - 2x[/tex]
I will verify the answer and give Brainlyest for fastest and most accurate answer and 15 pts.
Answers
Answer:
The answer is C. -2x -4
Step-by-step explanation:
Your given information.
-3 - 3x - 1 + x
Combine and simplify common numbers/variables.
(-3x + x) + (-3 - 1)
-2x - 4
The table below shows the earnings, in thousands of dollars, for three different commissioned employees.
Who had the largest dollar amount in sales for the month of December?
a.
The salary plus commission employee.
b.
The straight commission employee.
c.
The graduated commission employee.
d.
They each had the same dollar amount in sales.
Answers
The answer to the person with the largest dollar sales in December is d. They each had the same dollar amount in sales.
What were the sales amounts in December?The sales of the salary + commission employee is:
= (4,400 - 2,000) / 3%
= $80,000
The sales of the straight commission employee is:
= 5,600 / 7%
= $80,000
The sales of the graduated commission employee is:
The amount earned on the first $40,000 is:
= 5% x 40,000
= $2,000
The rest of the sales is therefore:
= (5,200 - 2,000) / 8%
= $40,000
The total sales for this employee is:
= 40,000 for 5% commission + 40,000 for 8%
= $80,000
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_______________ is the value of the best alternative given up when a choice is made.
Answers
Please hit the thanks button :)
3.)3 * (2x - 6)
4.)2x * (5x + 11)
Answers
3) [tex]3(2x-6)=\boxed{6x-18}[/tex]
4) [tex]2x(5x+11)=10x^{2}+22x[/tex]
N
O O
What is the slope of the line represented by the equation y = --- 5x?
0-5
4 ~/m ~/m
+
O 5
O
Answers
red was rotated to form blue
describe the rotation
Answers
Red was rotated to form blue as the figure was turned in different directions.
What is rotation?
A rotation simply means a transformation that turns a figure about a fixed point called the center of rotation.
An object and its rotation are simply the same shape and size, but the figures may be turned in different directions. In this case, red was rotated to form blue.
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Raphael is ordering a scoop of ice cream. For the flavor, he is given the option of chocolate, strawberry, vanilla, cookies ‘n cream, or peanut butter. For the size, he is given the option of small, medium, or large. For the cone, he is given the option of a sugar cone, waffle cone, or cup. How many possible order combinations are there?
Answers
Answer: 165
Step-by-step explanation: If you calculate the 3 different choices and the total of 11 different objects, you get 165 total combinations.
Answer:
45 possible combinations
Step-by-step explanation:
since there are 5 options of flavour (chocolate, strawberry, vanilla, cookies 'n' cream, and peanut butter) then you must multiply your flavours by your next option.
the size options come in 3 options (small, medium, and large) therefore we multiply the flavours (5) by sizes (3)
5 * 3 = 15
then multiply the result (15) by the cup options (3)
15 * 3 = 45
your answer is 45
hope this helps:)
Which inequality represents all the solutions of
9(4x-8) < 4(6x + 9)?
Answers
Answer:
x < 9
Step-by-step explanation:
Our original inequality:
[tex]9(4x-8) < 4(6x+9)[/tex]
Firstly, let's expand the brackets on both sides:
[tex]36x - 72 < 24x + 36[/tex]
Now, we add the 72 over to isolate the [tex]x[/tex]:
[tex]36x < 24x + 108[/tex]
Next, we take away the [tex]24x[/tex] to isolate the [tex]x[/tex]:
[tex]12x < 108[/tex]
Finally, we divide both sides by 12 to convert the [tex]12x[/tex] to [tex]x[/tex]:
[tex]x < 9[/tex]
This means our final answer is [tex]x < 9[/tex].
What is the point-slope form of a line that has a slope of 3 and passes through point (1, 4)?
Answers
Answer:
(A). y - 4 = 3 ( x - 1 )
Step-by-step explanation:
Slope "m" and ( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) ⇒
Slope-point form of linear equation is y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~
m = 3 and point with coordinates ( 1 , 4 )
y - 4 = 3 ( x - 1 )
If f(x) = -3 and g(x) = 4x² + x − 4, find (ƒ+ g)(x).
Answers
Answer:
4x² + x - 7
Step-by-step explanation:
Given f(x) = -3 and g(x) = 4x² + x - 4, solve for (f + g)(x).
Step 1: Replace the function designators with the actual functions in f(x) and g(x); that gives us 4x² + x - 4 - 3.
Step 2: Simplify; that gives us the answer 4x² + x - 7.
Please mark me as Brainliest! Thanks :)Find the vertex and focus of the
parabola:
x² + 14x-8y + 65 = 0
I can’t figure this out!!!
Answers
Answer:
[tex]\boxed {Vertex = (-7, 2)}\\\boxed {Focus = (0, \frac{49}{8})}[/tex]
Step-by-step explanation:
Completing the square :
x² + 14x - 8y + 65 = 0
x² + 14x + 49 - 49 - 8y + 65 = 0
(x + 7)² - 8y + 16
(x + 7)² = 8y - 16
⇒ x = -7, y = 2 (Vertex)
Finding a :
⇒ x² = 4ay
⇒ (-7)² = 4(2)a
⇒ a = 49/8
Finding the focus :
⇒ (0, a)
⇒ (0, 49/8) (Focus)
