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What is the trigonometric ratio for sin C ?
Enter your answer, as a simplified fraction, in the boxes.
Answers
=root of 324=18
therfore altitude =18cm,hypotenuse =82
sinC=Opposite/hypotenuse=18/82=9/41
Answer:
The trigonometric ratio for [tex]\sin C[/tex] is [tex]\frac{9}{41}[/tex]
Step-by-step explanation:
Given : A right triangle ABC with ∠B = 90° and AC = 82 and BC = 80
We have to find the value of [tex]\sin C[/tex]
Since, Sine is defined as the ratio of perpendicular to its hypotenuse.
Mathematically written as [tex]\sin\theta=\frac{Perpendicular}{Hypotenuse}[/tex]
For the given triangle ABC, we have
Using Pythagoras theorem, For a right angled triangle, sum of square of base and perpendicular is equal to the square to its hypotenuse.
[tex](AC)^2=(AB)^2+(BC)^2[/tex]
Substitute, we get,
[tex](82)^2-(80)^2=(AB)^2\\\\ 6724-6400=(AB)^2\\\\ 324=(AB)^2\\\\ \Rightarrow AB =18[/tex]
[tex]\theta=C[/tex]
So, perpendicular = AB and Hypotenuse = AC
[tex]\sin C=\frac{AB}{AC}[/tex]
[tex]\sin C=\frac{18}{82}=\frac{9}{41}[/tex]
Thus, The trigonometric ratio for [tex]\sin C[/tex] is [tex]\frac{9}{41}[/tex]
A standard coffee mug has a capacity of 16 fluid ounces. If Annie needs to fill 12 mugs mugs with coffee, how many quarts of coffee does she need?
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16 is half of 32 so 1 quart fills 2 mugs meaning that she needs 6 quarts of coffee
the fish tank in Paul's bedroom has a pump that will recirculate 75 gallons of water in 1/4 of an hour. Find the unit rate in gallons per hour.
a. 5 gallons per hour
b. 18.75 gallons per hour
c. 300 gallons per hour
d. 187.5 gallons per hour
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(1/4) hour---------> 0.25 hour
if the pump recirculate 75 gallons of water in -------------> 0.25 hour
X gallons of water in-----------------------------------------> 1 hour
X=75/0.25----------> x=300 gallons /hour
the answer is 300 gallons /hour
If there is a 30% increase in the operation charge for using a service,$82.70 remains to be paid.how much is the original bill ?
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a jope rope is 9 feet long how long is the jump rope in yards
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find the difference (-ab+9a-1)-(5ab-3)
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Hope this helps!! ;))
Have a grat day!! <3
Picture is attached need help fast thanks
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[tex] \sqrt[3]{ 8^{x} } [/tex]
Verbally we can say we are taking cube root of [tex] 8^{x} [/tex]. Cube root is equivalent to raising the power to [tex] \frac{1}{3} [/tex].
So, we can say we raising [tex] 8^{x} [/tex] to the power [tex] \frac{1}{3} [/tex].
In expression form, this will be:
[tex] ( 8^{x} )^{ \frac{1}{3} } \\ \\ = 8^{ \frac{x}{3} } [/tex]
Therefore, third option is the correct answer
-4x-15y=-17
-x+5y=-13
[tex] - 4x - 15y = - 17 \\ - x + 5y = - 13[/tex]
Answers
we are given the following system of equations
[tex] - 4x - 15y = - 17[/tex]
[tex] - x + 5y = - 13[/tex]
if you look at the x variables in both equations you can see that we can easily eliminate them by multiplying the bottom equation by -4 as so
[tex] - 4x - 15y = - 17[/tex]
[tex] - 4( - x + 5y = - 13)[/tex]
simplify and we get
[tex] - 4x - 15y = - 17[/tex]
[tex]4x - 20y = 52[/tex]
now we can combine like terms on each side with the x's cancelling and get
[tex] - 35y = 35[/tex]
now divide off -35
[tex]y = - 1[/tex]
great now we can go back to our original system and pick a equation and substitute y back in to find x lets use
[tex] - x + 5y = 13[/tex]
so now we substitute y and get
[tex] - x + 5( - 1) = 13[/tex]
[tex] - x - 5 = 13[/tex]
[tex] - x = 17[/tex]
[tex]x = - 17[/tex]
now we put x and y into one coordinate (x,y)
so now our FINAL ANSWER IS
(-17,-1)
Find the discriminant of the quadratic $3x^2 - 7x + 6.$
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3 x^2 - 7 x + 6 = 0
Divide both sides by 3:
x^2 - (7 x)/3 + 2 = 0
Subtract 2 from both sides:
x^2 - (7 x)/3 = -2
Add 49/36 to both sides:
x^2 - (7 x)/3 + 49/36 = -23/36
Write the left hand side as a square:
(x - 7/6)^2 = -23/36
Take the square root of both sides:
x - 7/6 = (i sqrt(23))/6 or x - 7/6 = -(i sqrt(23))/6
Add 7/6 to both sides:
x = 7/6 + (i sqrt(23))/6 or x - 7/6 = -(i sqrt(23))/6
Add 7/6 to both sides:
Answer: x = 7/6 + (i sqrt(23))/6 or x = 7/6 - (i sqrt(23))/6
Answer:
Discriminant of the quadratic is-23
Step-by-step explanation:
The given quadratic function is [tex]3x^2-7x+6[/tex]
Comparing with the expression [tex]ax^2+bx+c[/tex]
a = 3, b = -7, c = 6
The discriminant of the quadratic is given by [tex]D=b^2-4ac[/tex]
Substituting the known values, discriminant of the quadratic is
[tex]D=(-7)^2-4(3)(6)\\\\D=49-72\\\\D=-23[/tex]
Therefore, discriminant of the quadratic is-23
If f=6 and g=8, what does h equal
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The value of h in this given alphabetical series is 10.
What is an arithmetic sequence?The difference between every two successive terms in an arithmetic series is always the same. The number "a" is the first term, and "d" is the common difference between the. sequence. The nth term of an arithmetic sequence is given by. aₙ = a + (n – 1)d
Given, f=6 and g=8
Since, there is no additional data is given I will assume this is the question of Alphabetic sequence.
In Alphabet Series section, a string of alphabets, either in a single file or in combination form a sequence. This sequence comes together following a definite rule. The candidate is expected to detect this rule and answer the questions at the end.
So,
the value of f = 6 and g = 8
Since, Alphabetic order after f and g is h, i ,j, k, l, .....
And common factor is 2
Thus,
The value of h = 8+2 = 10
The value of i = 10+2 = 12
The value of j = 12 +2 =14
And so on
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2 - 4x = 14 A) -4 B) -3 C) 0 D) 3 Eliminate
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Hope this helps
subtract 2 from both sides
-4x = 12
divide both sides by -4
x= -3
ANSWER: B) -3
Hope this helps! :)
What is the volume of a cube with an edge length of 3.2 meters? Enter your answer, as a decimal, in the box.
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A circle is increased to have a circumference that is 4 times larger than the original. Which of the following options best describes the change in the radius of the original circle? increased by a factor of 8 increased by a factor of 4 increased by a factor of 16 increased by a factor of 12
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Answer:
Increased by a factor of 4
Step-by-step explanation:
Carlos and Maria drove a total of 233 miles in 4.4 hours. Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 50 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary.
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Equation 1: x + y = 4.4
x = 4.4 - y
Equation 2: 55x + 50y = 233
55(4.4 - y) + 50y = 233
242 - 55y + 50y = 233
-5y = 233-242
-5y = -9
y=9/5 or 1.8 hours Maria drove
To find time Carlos drove:
x=4.4 - 1.8
x = 2.6 hours
Answer:
Time of driving of Maria = 1.8 hours
Step-by-step explanation:
Let a be time drove by Carlos and b be the time drove by Maria.
Carlos and Maria drove a total of 233 miles in 4.4 hours.
Total time = 4.4 hours
a + b = 4.4 ------------------eqn 1
Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 50 miles per hour.
Speed of Carlos = 55 miles per hour
Speed of Maria = 50 miles per hour
Total distance = 233 miles
That is
55 a + 50 b = 233----------------------eqn 2
eqn 1 x 50
50 a + 50 b = 220---------------------------eqn 3
eqn 3 - eqn 2
55 a + 50 b - 50 a - 50 b = 233 - 220
5a = 13
a = 2.6
Substituting in eqn 1
2.6 + b = 4.4
b = 1.8
Time of driving of Maria = 1.8 hours
Mike says that 3/3 of his fraction model is shaded blue. Ryan says that 6/6 of the same model is shaded blue. Are the two fractions equivalent?
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Hope this helped!
which expression is equivalent to 20-4x/4
a. 5-x
b. 5-4x
c. 20-x
d. 80-16x
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The expression (20-4x)/4 equals 5 - x.
Given is an expression (20-4x)/4 we need to find an equivalent expression to it,
A mathematical expression or equation that is equivalent to another expression or equation is one that has the same value or meaning.
In other words, if two phrases yield the same result or depict the same mathematical relationship, they are deemed equal.
So,
By multiplying each word in the brackets by 4, it is possible to simplify the formula (20-4x)/4.
This results in:
(20/4) - (4x/4)
Simplifying even more
5 - x
Therefore, the expression (20-4x)/4 equals 5 - x.
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Greyson's mom used 4 out of 12 eggs to make pancakes. Then she used 3 out of 12 eggs to make cupcakes. What fraction of a dozen eggs did she used in all? ( Hint: 1 dozen = 12)
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NBDHBbhjnsjkbhBSDBWjcd
Well . . .
4 out of 12 eggs makes the fraction 4/12 for pancakes.
3 out of 12 eggs makes the fraction 3/12 for cupcakes.
4/12 + 3/12 + 7/12
If you don’t know how to do it here you go judging by how easy the question is -
Only add the numerator (top) and keep the denominator (bottom) the same.
Hope this helps :)
The table shows data for a random sample of 20 students out of middle school. Use the sample to draw an inference about each measure. Explain your reasoning.
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please help! determine whether the number is closest to 0, or 1. explain why. (a. 10/9) (b. 9/16) (c. 2/15) theyre not answer choices.
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A number greater than 1 is closer to 1 than to 0.
A number between 0 and half is closer to 0 than to 1.
A number between half and 1 is closer to 1 than to 0.
Now we need to see if the given numbers are less than 0, greater than 1, between 0 and half, or between half and 1.
a. 10/9 is greater than 1, so it is closer to 1 than to 0.
b. 9/16 is between half and 1, so it is closer to 1.
c. 2/15 is between 0 and half, so it is closer to 0.
1) Given that lines L and M are parallel, which of the statements is true? A) ∠ DEF ≅ ∠ EBC B) ∠ ABC ≅ ∠ DEF C) ∠ ABC ≅ ∠ EBC D) ∠ BEF ≅ ∠ ABC
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A candy wrapping robot can wrap 434 pieces of candy in five minutes. How many pieces of candy can it wrap in any number of minutes
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y=86.8x (y is total candies wrapped, x is the number of minutes)
What is the answer to 3(t-7)=6t
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3(t) = 3t
3(-7) = -21
3t -21 = 6t
isolate the -21 by subtracting 3t from both sides
-21 + 3t = 6t
-21 + 3t (-3t) = 6t (-3t)
-21 = 3t
divide 3 from both sides to isolate the t
3t = -21
3t/3 = -21/3
t = -21/3
t = -7
t = -7 is your answer
hope this helps
I need to know the answer
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PLEASE HELP. WILL OFFER 50 POINTS AND BRAINLIEST FOR CORRECT ANSWER!
Graph the two lines
2x + 3y = 18
3x -4y > 16.
Give the Domain and Range, Slope, and Y-intercept for each line. Graph each equation above on the graph below and show all work. Give the Domain and Range, Slope, and Y-intercept for each line. Explain in detail how you got each answer.
2x + 3y = 18 3x -4y > 16
Slope-Intercept Form: Slope-Intercept Form:
Domain: Domain:
Range: Range:
Slope: Slope:
Y-intercept: Y-intercept:
Answers
Answer:
For Equation 1:
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\displaystyleP-\frac{2}{3}}[/tex]Y-intercept: 6For Equation 2:
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\frac{3}{4}[/tex]Y-intercept: -4Step-by-step explanation:
We are given two lines - one is an equation and one is an inequality.
Neither are in slope-intercept form (y = mx + b), so we need to make these adjustments.
Slope-intercept form has two key parts to the equation: m, which is the slope of the line and b, which is the y-intercept of the line.
Equation 1
[tex]\displaystyle2x+3y=18\\\\3y = -2x + 18\\\\y = -\frac{2}{3}x+6[/tex]
With this, we can now determine the domain, range, slope, and y-intercepts for this line.
For Equation 1, because our equation is in slope-intercept form, we can find the slope and the y-intercept.
Our equation is [tex]y=-\frac{2}{3}x+6[/tex]. Therefore, our m is [tex]-\frac{2}{3}[/tex] and our b is 6.
Because the equation is linear, there is no instance in which the line will not meet an x- or y-value. Therefore, our domain and range is all real numbers, or [tex]\mathbb{R}[/tex].
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\displaystyleP-\frac{2}{3}}[/tex]Y-intercept: 6Equation 2
[tex]\displaystyle3x-4y>16\\\\-4y>-3x+16\\\\y < \frac{3}{4}x-4[/tex]
Now that we have solved the inequality, we can determine our slope, the domain, and the range of the function.
We can use the same tactic as before - m is our slope and b is our y-intercept. Therefore, [tex]\frac{3}{4}[/tex] is our slope and -4 is our y-intercept.
Because the inequality represents a line, our domain is all real numbers, or [tex]\mathbb{R}[/tex]. If we were to plug in any number for x, y would be true for that value. Therefore, our range is also all real numbers, or [tex]\mathbb{R}[/tex].
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\frac{3}{4}[/tex]Y-intercept: -4Evan's mother used 1/3 pound of beef, 1/2 pound of shrimp, and 3 pounds of pasta to make dinner for 4 people.
Use this information to answer ALL FOUR PARTS below.
Question:
Part A:
Each person will receive an equal share of beef with none left over. What is the amount, in pounds, of each serving of beef?
Part B:
Each person will receive an equal share of shrimp with none left over. What is the amount, in pounds, of each serving of shrimp?
Part C:
Each person will receive an equal share of pasta with none left over. What fraction represents the amount, in pounds, of each serving of pasta?
Part D:
Evan only ate 1/2 of the pasta that he received. What is the amount, in pounds, of pasta did Evan eat? Explain how you got this answer step-by-step using math vocabulary.
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Part B: 1/2 / 4 = 1/8. Each person gets 1/8 pound of shrimp.
Part C: 3 / 4 = 3/4. Each person gets 3/4 pound of pasta.
Part D: If we're talking about pasta, then Evan ate 3/8 pound of pasta. Half of 3/4 (the amount of pasta given to everyone) is 3/8, so if Evan ate 1/2 of his share (3/4), he ate 3/8 pounds of pasta.
Hope this helps! Have an awesome day :)
|-2x+6|=-8 absolute value equations
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The left side must be non-negative. (An absolute value is always 0 or positive.) The right side is negative. There can never be any point of intersection.
Gcf of 28x3 and 16x2y2
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The greatest common factor (GCF) of [tex]28x^{3}[/tex] and [tex]16x^{2} y^{2}[/tex] is the greatest common factor (GCF) of and [tex]16x^{2} y^{2}[/tex] is [tex]4x^{2}[/tex] .
To find the greatest common factor (GCF) of [tex]28x^{3}[/tex] and [tex]16x^{2} y^{2}[/tex]
, we need to identify the common factors between the two expressions.
The prime factorization of is [tex]2.2.7.x.x.x.[/tex]
The prime factorization of [tex]16x^{2} y^{2}[/tex] is [tex]2.2.2.2.x.x.y.y.[/tex]
Now, let's identify the common factors:
Both expressions have [tex]2.2.x.x[/tex] in common.
So, the greatest common factor (GCF) of and [tex]16x^{2} y^{2}[/tex] is [tex]4x^{2}[/tex] .
COMPLETE QUESTION:
Circle the GCF of [tex]28x^{3}[/tex] and [tex]16x^{2} y^{2}[/tex]
[tex]28x^{3}[/tex]: [tex]2.2.7[/tex].*•*•*
[tex]16x^{2} y^{2}[/tex]:[tex]2.2.2.2.x.x.y.y[/tex]
The area of a rectangle playgrond is 78 square meters. If the length of the playground is 13 meters, what is its width?
Answers
78 = length * 13
[tex] length = \frac{78}{13} [/tex] use a calculator to find out the answer then,
Answer:
6 meters.
Step-by-step explanation:
Let w represent width of the rectangle.
We have been given that the area of a rectangle playground is 78 square meters. The length of the playground is 13 meters.
We know that area of a rectangle is width times length of rectangle. We can represent our given information in an equation as:
[tex]\text{Area of rectangle}=\text{Length}\times \text{Width}[/tex]
[tex]78\text{ m}^2=13\text{ m}\times \text{Width}[/tex]
[tex]13\text{ m}\times \text{Width}=78\text{ m}^2[/tex]
[tex]\frac{13\text{ m}\times \text{Width}}{13\text{ m}}=\frac{78\text{ m}^2}{13\text{ m}}[/tex]
[tex]\text{Width}=6\text{ m}[/tex]
Therefore, the width of the rectangle is 6 meters.
a photograph measuring 4 inches wide and 5 inches long is enlarge to make a wall mural. If the mural is 120 inches wide, how long is the mural?
Answers
4x=120×5
x=600÷4
x=150 inches
A sports store donates basketballs and soccer balls to the boys and girls club. The ratio of basketballs to soccer balls is 7 : 6. The store donates 24 soccer balls. How many basketballs does the store donate
The store donates __ basketballs