what is the value of z, rounded to the nearest tenth? use the law of sines to find the answer.
A) 2.7 units
B) 3.2 units
C) 4.5 units
D) 5.3 units
Answers
[tex]\sf\dfrac{sin(X)}{x}=\dfrac{sin(Y)}{y}=\dfrac{sin(Z)}{z}[/tex]
We know what angle Y is and what side y is, so let's use that along with angle Z and side z:
[tex]\sf\dfrac{sin(Y)}{y}=\dfrac{sin(Z)}{z}[/tex]
Plug in what we know:
[tex]\sf\dfrac{sin(51)}{2.6}=\dfrac{sin(76)}{z}[/tex]
Multiply 'z' to both sides:
[tex]\sf\dfrac{sin(51)}{2.6}z=sin(76)[/tex]
Divide sin(51)/2.6 to both sides:
[tex]\sf z=\dfrac{sin(76)(2.6)}{sin(51)}[/tex]
Plug it into your calculator.
[tex]\boxed{\sf z\approx 3.2}[/tex]
The value of z is 3.2 units.
What is the law of sines?
The law of sine or the sine law states that the proportion of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides. It is additionally known as the sine rule.
For a triangle ABC the law of sine will be,
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
In triangle XYZ given here,
The law of sine can be written as,
[tex]\frac{x}{sinX} =\frac{y}{sinY} =\frac{z}{sinZ}[/tex]
here ∠Y and ∠Z is given so we write
[tex]\frac{y}{sinY} =\frac{z}{sinZ}[/tex]
y=2.6
∠Y=51°
∠Z=76°
sin51°≈0.78
sin76°≈0.97
[tex]\frac{y}{sinY} =\frac{z}{sinZ}[/tex]
[tex]2.6/0.78=z/0.97[/tex]
[tex]z=3.2 units[/tex]
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Related Questions
simplify 1-2 (-3+x) +x
Answers
1 -2(x - 3) + x
Step 2. Expand
1 - 2x + 6 + x
Step 3. Collect like terms
(1 + 6) + (-2x + x)
Step 4. Simplify
-2x + 7
In one city, 3,546 people attended a concert but in another city, 9,238 people attended the same band's concert. Estimate how many more people attended the concert in the second city by rounding to the nearest hundred and then subtracting.
Answers
Approximately 5,700 more people attended the concert in the second city.
To estimate how many more people attended the concert in the second city, we can round the attendance numbers to the nearest hundred and then subtract the smaller number from the larger one. For the first city, 3,546 people rounds off to 3,500 people, and for the second city, 9,238 people rounds off to 9,200 people. Now we subtract the rounded number of the first city from the rounded number of the second city.
So, 9,200 (rounded attendance in the second city) minus 3,500 (rounded attendance in the first city) equals 5,700.
Therefore, approximately 5,700 more people attended the concert in the second city.
Sabrina makes a pan pizza for the party she cuts the pizza into10 equal pieces after the party there was 5/10 of the pan pizza left write the fraction 5/10 as a product of a whole number and a unit fraction.
Answers
Number of pieces Pizza is cut is given as 10.After the party some pizza is left and some consumed .
Amount if pizza consumed in fractions is given as [tex] \frac{5}{10} [/tex]
The fraction can be reduced to simplest or lowest form by finding the common factor of numerator and denominator .Numerator is 5 and denominator is 10.
Both 5 and 10 can be divided by the common factor 5.
We have [tex] \frac{5}{10} =\frac{1}{2} [/tex]
The fraction can be written as [tex] \frac{1}{2} [/tex] in its lowest form or thei equals 0.5 in decimal .
emma drives 1/4 of the way to work and uses 1/9 gallon of gas what fraction of the distance can she drive to work which one gallon of gas?
Answers
Emma can drive 1/4 of the distance to work with one gallon of gas.
Explanation:To find out what fraction of the distance Emma can drive to work with one gallon of gas, we need to find the fraction of the distance she can drive with 1/9 gallon of gas and then multiply it by the number of gallons in one gallon.
Emma drives 1/4 of the way to work and uses 1/9 gallon of gas. So, she can drive 1/4 * 1/9 = 1/36 of the distance to work with 1/9 gallon of gas.
To find the fraction of the distance she can drive with one gallon of gas, we multiply 1/36 by the number of gallons in one gallon: 1/36 * 9/1 = 9/36 = 1/4.
Therefore, Emma can drive 1/4 of the distance to work with one gallon of gas.
If c=3k+4 and d=7+9k^2, what is d in terms of c?
Answers
Answer:
d = (c -4)² +7 = c² -8c +23
Step-by-step explanation:
Both 'c' and 'd' are expressed in terms of the variable k. In general, that variable is eliminated by writing k in terms of 'c' or 'd', then substituting for k in the other equation.
Eliminating kWe recognize that the 9k² term in the expression for 'd' is the square of the 3k term in the expression for 'c'. That means we don't have to solve for k; we only need to solve for 3k. The equation for 'c' gives an easy way to do that.
c = 3k +4
c -4 = 3k . . . . . . . subtract 4 to get an expression for 3k
Substituting into the equation for 'd', we have ...
d =7 +9k²
d = 7 +(3k)² . . . . . writing 9k² in terms of 3k
d = 7 +(c -4)² . . . . substituting for 3k. This is d in terms of c.
This can be simplified to ...
d = c² -8c +23 . . . . another form of d in terms of c.
To express 'd' in terms of 'c', solve the first equation for 'k' and substitute this value into the second equation. This yields: d=7+((c-4)^2)/3.
Explanation:To express d in terms of c, we first need to make k the subject of c=3k+4. We do this by subtracting 4 from both sides, getting c-4=3k, and then dividing both sides by 3, which gives us k=(c-4)/3. Next, we substitute this value of k into the second equation: d=7+9k^2. Substituting, we get d=7+9*((c-4)/3)^2, which, when simplified, gives the result d=7+((c-4)^2)/3. This is the expression for d in terms of c.
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Use a strategy for the following problem(and I seriously need help!!):
In a sequence of numbers, each number in the sequence is called a term. In the sequence 1, 3, 5, 7, 9, the first term is 1, the second term is 3, the third term is 5, the fourth term is 7 and the fifth term is 9. In another sequence, the first term is 26. If a term in the sequence is even, then the next term will be half the value of that term. If a term in the sequence is odd, then the next term in the sequence is one more than three times that term. By following these rules, the first three terms of this sequence are 26, 13 and 40. Is the twenty-sixth term of the sequence odd or even. Justify your answer.
Answers
The best way to solve this problem is just create the list of terms that goes up to the 26th place. Don't worry, you will soon see a patter.
Remember the rules: If it's even, cut it in half. If it's odd, multiply by 3 and add 1.
So here is our list: 26 13 40 20 10 5 16 8 4 2 1 4 2 1 4 2 1 ...
Once you get to this point, the pattern will just continue with 4 2 1
And in the 26th place, you will see a 1.
find the diameter of a circle with an area of 226.98
Answers
[tex]V = \pi * r^{2} [/tex]
SO given that
V = 226.98
and [tex] \pi = 3.14[/tex]
Plug in a chug
226.98 = 3.14 * [tex] r^{2} [/tex]
[tex] r^{2}= 72.287[/tex]
r = 8.50
Remember that d = 2 * r
d = 2 * 8.5 = 17
Theodore works for Mr. Jones. Mr. Jones agreed to start Theodore at $.01 the first day, $.02 the second day, $.04 the third day, $.08 the fourth day, and so on.
`
a. How much does Theodore earn in fifteen days?
b. Suppose Theodore can start at $10 the first day, $10.75 the second day, $11.50 the third day, $12.25 the fourth day, and so on. Would he earn more in fifteen days than he does in part(a)? Explain.
Answers
So just multiply by 2 until day 15
Day 4: 0.8
0.8 x 2 = 0.16
Day 5: 0.16
0.16 x 2 = 0.32
Day 6: 0.32
From here you should know what to do and I'll skip the long math
Day 15: 163.84
============================================================
Part B
The difference in change for these number is about x1.07 so multiply by 1.07 till day 15.
Again I'll avoid the extra long math
Day 15: 25.78
He would not earn more in 15 days than part a
Mike owns two hardware stores. The scatter plots show the number of items sold at a specific price for each store for one week. Which store has more sales revenue ($$)?
A) Store #1
B) Store #2
C) The stores bring in the same amount of sales.
D) This cannot be determined from the scatter plots.
Answers
answer A
with the help of scatter plot we can calculate the revenue collection of the two stores
for store 1, revenue collection is 35100
for store 2, revenue collection is 29800
so, store 1 has more revenue collection than store 2
Which of the following statements are equivalent to the statement "price increased by 100%"?
Choose all correct answers.
(A) The price doubled
(B) The price is 150% of the price before
(C) The price was reduced by a quarter
(D) The price became a half of what it was before
(E) The price is now 1.5 of what it was before
(F) The price now is 66 2/3% of what it was before
(G) The price now is 200% of what it was before
(H) The price is 75% of what it was before
Plssss help me!!
Answers
(A) The price doubled
(G) The price now is 200% of what it was before
Explanation:
Assume that the original price of the product is x. Therefore, x represents 100% of the original price.
Now, we are given that:
The price increased by 100%
This means that:
new price = old price + 100% of old price
new price = x + 100% (x)
new price = 2x
Thus, we can note that the price is doubled
We know that x represents 100% of the price of the product.
Therefore:
new price = x + x = 100% + 100% = 200%
This means that the new price is 200% of the old price
Notes:
Options C,D, F and H are incorrect because they represent a decrease in the price while we know that the price increased
Options B and E are incorrect because they represent an increase of 50% in the price while we know that the increase is 100%
Hope this helps :)
Answer:
A G
Step-by-step explanation:
because when the price is doubled that means it increases by 100%
and when the price is 200% of what it was befor means it is also doubled
Which statement correctly shows the relationship found in Euler's formula?
Answers
Answer:
V + F = E + 2
The statement correctly shows the relationship found in Euler's formula is F + V - E = 2.
What is euler's formula?For any real value θ, we have:
[tex]e^{i\theta} = \cos(\theta) + i\sin(\theta)[/tex]
where 'e' is the base of the natural logarithm, and 'i' is iota, the imaginary unit.
We are given that;
Euler's formula states that for any convex polyhedron (a 3-dimensional solid with flat faces and straight edges), the number of faces (F), vertices (V), and edges (E) are related by the formula:
F + V - E = 2
One possible statement that correctly shows the relationship found in Euler's formula is:
"The number of faces, vertices, and edges in a convex polyhedron are related by Euler's formula, which states that F + V - E = 2."
Therefore by euler's formula the answer will be F + V - E = 2.
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solve for K. I TRIED MANY TIMES TO GET IT RIGHT BUT I STILL GET STUCK WHEN I AM CLOSE TO FINDING THE ANSWER!!!!
m=1/k+n
Answers
This is how you would solve for k.
m(k + n) = 1
k + n =[tex] \frac{1}{m} [/tex]
k = [tex] \frac{1}{m} [/tex] - n
[tex]m=\frac{1}{k}+n[/tex]
We need to solve for k.
In order to solve for k, we need to isolate k, meaning
1. subtract n on both sides in order to isolate k, simplify
[tex]m=\frac{1}{k}+n[/tex]
[tex]m-n=\frac{1}{k}+n-n[/tex]
[tex]m-n=\frac{1}{k}[/tex]
2. multiply k on both sides, do not forget the parentheses,
[tex]k(m-n)=1[/tex]
3. divide by (m-n) (do not forget the parentheses), simplify
[tex]k(m-n)/(m-n)=\frac{1}{(m-n}[/tex]
[tex]k=\frac{1}{(m-n)}[/tex]
So the final answer is
k=1/(m-n) do not forget the parentheses.
Enter the values for a and b that complete
the sum:
A-
b-
Answers
a = 3
b = 5
Answer:
[tex]a=3[/tex] and [tex]b=5[/tex]
Step-by-step explanation:
We have been given an equation [tex]\frac{3}{x}+\frac{5}{x^2}=\frac{ax+b}{x^2}[/tex]. We are asked to find the value of 'a' and 'b'.
Let us make a common denominator:
[tex]\frac{3*x}{x*x}+\frac{5}{x^2}=\frac{ax+b}{x^2}[/tex]
[tex]\frac{3x}{x^2}+\frac{5}{x^2}=\frac{ax+b}{x^2}[/tex]
Add numerators:
[tex]\frac{3x+5}{x^2}=\frac{ax+b}{x^2}[/tex]
Therefore, [tex]a=3[/tex] and [tex]b=5[/tex] for the given equation.
the triangle in the diagram are similar. how long will the footbridge be
Answers
[tex] \frac{80}{24} = \frac{d}{30} [/tex]
24d = 2400
d = 100
The footbridge will be 100m long.
20 points and brainliest if correct
Which function grows at the fastest rate for increasing values of x?
g(x)=2.5x
h(x)=9.5x2
f(x)=8.5x+3
Answers
martin climbs 3 1/3 meters in the first 1/6 hour alexia climbs 17 1/2 meters in the first 5/6hour what is the rate martin and alexia climbed show workkk
Answers
rate=(distance )/(time)
Martin's rate will be:
(3 1/3)/(1/6)
=(10/3)/(1/6)
=20 meters per hour
Alexia's rate is:
(17 1/2)/(5/6)
=(35/2)/(5/6)
=21 meters per hour
2x+3(x-4)=8
Solve the equation
Answers
5x = 20
x = 4
2x + 3x - 12 = 8
5x = 20
x = 4
Brandon is baking cookies for a school bake sale. If he can make 2 dozen cookies in 23 minutes which is a reasonable estimate of the amount of time it will take him to make 12 dozen cookies? A) between 4 and 5 hours B) between 3 and 4 hours C) between 2 and 3 hours D) between 1 and 2 hours
Answers
Answer:
The answer would be C.
Step-by-step explanation:
what is 9.03×10^2 in standard form
Answers
9.03 * 100 =
903
The value of the exponent number in standard from is A = 903
What is Exponential Form?The exponential form is an easier way of writing repeated multiplication involving base and exponents. It has a base and a power
The exponential form of a number is a way of representing a number using exponents, where the base is typically a number greater than 1.
It is often used in mathematics and science to represent large or small numbers more efficiently. It can also be used to simplify certain mathematical operations, such as multiplication and division, by using the properties of exponents.
Given data ,
Let the exponential form of the number be A
Now , the value of A = 9.03×10²
To convert 9.03×10² to standard form, we need to multiply the number by the appropriate power of 10 so that it is expressed as a number between 1 and 10.
Starting with 9.03×10² , we can move the decimal point two places to the right to get:
9.03×10^2 = 903
So the standard form of 9.03×10² is simply 903
Hence , the standard form is A = 903
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There are 20 children at a library. Six of the children have an average age of 5 years. The remaining children have an average age of 8 years. What is the average age of the children at the library? Enter your answer in the box. WILL GIVE BARINLIYEST
Answers
This problem is an example of when we need to take a weighted average. We simply can't just find the average of 5 and 8, because there are different children of each each.
To start, lets multiply the total number of children by their individual ages.
6 x 5 = 30 years
14 x 8 = 112 years
There are 142 years among the 20 years, so divide 142 by 20. This gives us an average age of 7.1 years.
What Happened To The Guy Who Fell Into an Upholstery Machine
Answers
The question is about what happened to someone who fell into an upholstery machine. Physics principles such as Newton's laws of motion can explain the outcome of the incident.
Explanation:The question is about an incident where someone fell into an upholstery machine. Since it involves a physical event, the subject of this question is Physics, specifically related to forces and motion.
In this case, we can use the principles of Newton's laws of motion to explain what happened to the person who fell into the upholstery machine. The person's motion and the forces acting upon them would determine the outcome of the incident.
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The line plot and the bar graph show the same test scores. Where should you look to find the least common test score?
Answers
The shortest column of the line plot
The least common test score from the graphs is 70.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A line plot shows the frequency of data, in short it shows how many times something has occurred or the number of times data occurs in a group of data.
The number of data is represented by markers or in this case "x"s. The more x's along the column, the more times it occurred.
The bar graph there does not show the frequency of the different scores. This shows the relationship between the test number and the percentage of the scores obtained. It does not tell you the individual scores obtained.
The least common test score is 70
Hence, the least common test score from the graphs is 70.
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a function FX is described by the ordered pairs X Y if if the given function is translated 2 units to the right and then reflected across the x axis what are the ordered pairs that describe the transformed function
Answers
[tex] \left \{ {{ x_{1} = x - n} \atop {y_{1} = y}} \right. [/tex]
A reflection over the x-axis will follow the rule:
[tex] \left \{ {{x_{2} = x } \atop { y_{2} = - y}} \right. [/tex]
Applying the two rules at the same time, we have:
[tex] \left \{ {{x' = x - n} \atop {y' = - y}} \right. [/tex]
Therefore, in your case:
x' = X - 2
y' = - Y
I need the answer for B! whoever answers first will get a brainliest, a thanks, and 50 points! also plz tell me how you got the answer
Answers
_____
A graphing calculator is helpful.
PLZ HELP, GRAPH IT THEN FOR BRAINLIEST
graph the quadratic function f(x)=x^2−12x+27.
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answers
find Vertex (h, k)
x = h= -b/2a = -(-12)/2(1) = 6
k = f(h) = 36 - 12(6) + 27
k = -9
so vertex (6,-9)
y = a(x - h)^2 + k
so
y = (x - 6)^2 - 9
x intercept when y = 0
x^2−12x+27 = 0
(x - 9)(x - 3) = 0
x - 9 = 0; x = 9
x - 3 = 0; x = 3
so x-intercept (9,0); (3,0)
y intercept when x = 0 so y = 27 (0, 27)
OK now you can use these to graph the function
(6, -9) (9,0) and (3,0)
A triangular prism is 14.3 millimeters long. It has a triangular face with a height of 12 millimeters. The volume of the prism is 1,123.98 cubic millimeters. What is the base of its triangular face?
Answers
The formula for the volume of the prism is below. All we have to do is input the values we know and solve for the missing B.
Volume = BH/2 (Length)
1123.98= (12B/2) x (14.3)
78.6 = 12B/2
157.2 = 12B
13.1 = B
Answer
13.1 millimeters
Explanation
The volume of any regular object is found by;
Volume = base area × length.
In the question, the base is a triangle of height 12 millimeters and a base length L.
The length of the prism is 14.3 millimeters.
∴ Volume = base area × length.
1,123.98 = (1/2 × 12 × L) × 14.3
1,123.98 = 85.8 L
L = 1,123.98/85.8
= 13.1 millimeters
A spherical balloon is inflated until its diameter is 24 in. Air is then released from the balloon until its diameter is 18 in. Approximately many cubic inches of air were released from the balloon?
formula: V =4π(r^3)/3 **make sure you use the radius and not the diameter**
Answers
amount of air released = 4184.6 in³
Explanation:
We can get the volume of released air by calculating the difference between the volume of the balloon before and after the air was released. This difference will represent the amount of released air.
Initial volume of balloon:
V = [tex] \frac{4}{3} [/tex]πr³
We have diameter = 24 in
Therefore:
radius = 24/2 = 12 in
volume = [tex] \frac{4}{3} [/tex]π(12)³
initial volume = 2304π in³
Final volume of balloon:
V = [tex] \frac{4}{3} [/tex]πr³
We have diameter = 18 in
Therefore:
radius = 18/2 = 9 in
volume = [tex] \frac{4}{3} [/tex]π(9)³
final volume = 972π in³
Amount of air released:
amount of air released = initial volume - final volume
amount of air released = 2304π - 972π
amount of air released = 1332π = 4184.6 in³
Hope this helps :)
Answer:
4182 is ur answer
Step-by-step explanation:
Find the AREA of this triangle
Answers
________________________________________________________
Note:
________________________________________________________
The formula for the area, "A" of a triangle:
" A = (1/2) * b * h " ;
in which: "A = area" (for which we are to solve);
"b = base length" = 8 (given) ;
"h = perpendicular height = 5 (given) ;
A = (1/2) * b * h = (1/2) * 8 * 5 = 4 * 5 = 20 .
_________________________________________________________
Answer: The area of the triangle given is: " 20 units² " ;
or, write as: " 20 square units" .
_________________________________________________________
Edit: Another way to write the formula for the area, "A", of a triangle is:
" A = (b * h) / 2 " ;
and we can solve: " A = (b * h) / 2 = (8 * 5) / 2 = 40 / 2 = 20 .
_________________________________________________________
The answer is: " 20 square units " ; or, write as: " 20 units² " .
_________________________________________________________
The following points for a function are graphed in the coordinate plane: (0,4), (1,5), (2,6), and (3,7). What function is being graphed?
a. y=x
b. y=2x+3
c. y=x+4
d. 3x+4
Answers
Answer:
c
Step-by-step explanation:
The correct function is,
⇒ y = x + 4
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We have to given that;
The following points for a function are graphed in the coordinate plane: (0, 4), (1, 5), (2, 6), and (3, 7).
Now, We know that;
All the points are satisfy the function.
Hence, By options c;
y = x + 4
Put x = 0, y = 4
y = x + 4
4 = 0 + 4
4 = 4
Hence, The correct function is,
⇒ y = x + 4
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Which equation best represents a trend line for the scatter plot?
y=−3/7x+4
y=3/7x+4
y=−7/3x+4
y=7/3x+4