Answers
Answer:
1. Triangle: B = 47.0° , C = 103.05° , c = 2.53 cm
2. Lake: c = 1105.31 ft
Step-by-step explanation:
Law of Sine Formula:[tex]\frac{sin(A)}{A} = \frac{sin(B)}{B} = \frac{sin(C)}{C}[/tex]
Given: A = 30° , a = 1.3 cm , b = 1.9 cm
[tex]\frac{sin(30)}{1.3} = \frac{sin(B)}{1.9} = \frac{sin(C)}{C}[/tex]
Solving for sin(B). Cross Multiply.
[tex]\frac{sin(30)}{1.3} = \frac{sin(B)}{1.9}\\1.3*sin(B)=1.9*sin(30)\\sin(B)=\frac{1.9*sin(30)}{1.3} \\[/tex]
B = sin^-1( [tex]\frac{1.9*sin(30)}{1.3}[/tex] )
B ≈ 46.9509202
B = 47.0°
Solve for C°
A° + B° + C° = 180°
30° + 46.95° + C° = 180°
C° = 180° - 30° - 46.95°
C° = 103.05°
Solve for sin(C)
[tex]\frac{sin(30)}{1.3} = \frac{sin(103.05)}{C}\\[/tex]
Cross Multiply
[tex]C*sin(30)=1.3*sin(103.05)\\C=\frac{1.3*sin(103.05)}{sin(30)}[/tex]
C ≈ 2.532850806
C = 2.53 cm
Law of Cosine Formula: [tex]c^2=a^2+b^2-2*a*b*cos(C)[/tex]
Given: a = 850 ft , b = 960 ft , C=75°
Solve for c.
[tex]c^2=a^2+b^2-2*a*b*cos(C)\\c^2=(850ft)^2+(960ft)^2-2*(850ft)*(960ft)*cos(75)\\\\c=\sqrt{(850ft)^2+(960ft)^2-2*(850ft)*(960ft)*cos(75)\\} \\[/tex]
c ≈ 1105.308698
c = 1105.31 ft
Related Questions
Solve the equation 9(k-2)=- 6. ( slove for k
Answers
Answer:
k=4/3
Step-by-step explanation:
9(k-2)=-6
-expand the bracket
9k-18=-6
-keep "k" on one side
9k=12
-divide both sides by 9 to get k
k=4/3
For each value of w, determine whether it is a solution to -8+5w >32.
Answers
Answer:
• no
• no
• no
• yes
Step-by-step explanation:
Let's start by solving the inequality.
-8 +5w >32
5w> 32 +8
5w> 40
Divide both sides by 5:
w> 8
This means that the value of w should be greater than 8.
Since w is not ≥8, the value of w does not include 8. -6 and -5 are smaller than 8 and are thus not the value of w either.
9, being greater than 8, is a solution to the inequality.
Solve by factoring:
a² = 25
Answers
Answer:
[tex]a=[/tex] ±[tex]5[/tex]
Step-by-step explanation:
[tex]a^{2} =25[/tex]
equal to zero
[tex]a^{2} -25=0[/tex]
factor: difference of squares
[tex](a+5)(a-5)=0[/tex]
first factor:
[tex]a+5=0\\a_{1} =-5[/tex]
second factor:
[tex]a-5=0\\a_{2} =5[/tex]
Hope this helps
Find the smallest whole number by which 2268 should be multiplied so as to
get a perfect square number. Also find the square root of the square number
so obtained.
Answers
Answer:
Correct option is B)
252=
2×2
×
3×3
×7
The prime factor 7 does not appear in pairs. To make 252 a perfect square we need one more 7.
Hence, the smallest number by which 252 must be multiplied so that
the product is a perfect square is 7.
And, 252×7=
2×2
×
3×3
×
7×7
252×7
=
2×2
×
3×3
×
7×7
=2×3×7=42
Step-by-step explanation:
To find the smallest whole number by which 2268 should be multiplied to get a perfect square, we need to factorize 2268 into its prime factors. Then, we can determine which prime factors are needed to make the number a perfect square.
The prime factorization of 2268 is:
2268 = 2^2 * 3^2 * 7 * 9
To make it a perfect square, we need to include the missing factors. In this case, we are missing a factor of 2 and a factor of 3. Therefore, we need to multiply 2268 by 2 * 3 = 6.
2268 * 6 = 13608
Now, we have a perfect square number, 13608.
To find the square root of 13608, we can take the square root of each of its prime factors:
√(2^2 * 3^2 * 7 * 9)
= √2^2 * √3^2 * √7 * √9
= 2 * 3 * √7 * 3
= 6 * √7
So, the square root of the square number 13608 is 6√7.
what is 3/8 - 1/4 = in simplest form
Answers
Answer:
1/8
Step-by-step explanation:
The lowest common multiple of 4 and 8 is 8.
1/4 = 2/8
3/8 - 1/4 = 3/8 - 2/8 = (3 - 2)/8 = 1/8
1/8 cannot be simplified further.
50 POINTSSS AND WILL GIVE BRAIN
Look at the graph attached
What is the domain?
–6 ≤ x ≤ 4
–6 ≤ x ≤ 4, x ≠ –6, 2
–12 ≤ x ≤ 10
–12 ≤ x ≤ 10, x ≠ –6, 6
Answers
Domain: All possible x-values
Starting at the left side, the smallest value of the domain is -12. There is a break at x = -6, but there is still a closed circle, which means that there IS a value for -6. The same occurs at x = 6. The largest x-value of this graph is 10.
Therefore, the domain is -12 <= x <= 10
Hope this helps!
Write the equation in slope-intercept form, and detemine the slope and y-intercept. Write the y- intercept as an ordered pair.
−x + 5y = −5
The slope is .
The y-intercept is .
The equation written in slope-intercept form is ____________ .
Answers
Answer:
slope= 0.2; intercept=-1; slope-interception form: y=0.2x-1.
Step-by-step explanation:
1) if to re-write the given equation, then
[tex]y=\frac{1}{5}x-1;[/tex]
or y=0.2x-1;
this equation is slope-interception form;
2) according to the new view of the equation,
the required slope is 1/5;
the required y-intercept is -1.
If a number cube is rolled, how many times would we expect to get a number less than four out of 200 trials? Answer is 100
100
25
50
75
Answers
The expected outcomes less than 4 is the average of the outcomes
We would expect to get a number less than four out of 200 trials 100 times
How to determine the expected number of rolls?The sample space of a number cube is:
S = {1,2,3,4,5,6}
There are 3 outcomes less than 4.
So, the probability of obtaining a number less than 4 is:
p = 3/6
This gives
p = 0.5
In a roll of 200, the expected outcomes less than 4 is:
E(x) = 0.5 * 200
This gives
E(x) = 100
Hence, we would expect to get a number less than four out of 200 trials 100 times
Read more about expected values at:
https://brainly.com/question/15858152
Answer:
100
Step-by-step explanation:
Consider the following null and alternative hypotheses.
H zero: m < 67
Ha: m > 67
These hypotheses _______________.
Select one:
a. are established incorrectly
b. indicate a two-tailed test
c. indicate a one-tailed test with a rejection area in the right tail
d. indicate a one-tailed test with a rejection area in the left tail
Answers
Help 111111111111111
Answers
Answer:
6/11
Step-by-step explanation:
[tex]p(number \: less \: than \: 4) = \frac{3}{11} [/tex]
[tex]p(odd \: number) = \frac{5}{11} [/tex]
[tex]p(number \: \: less \: than \: 4 \: and \: odd) = \frac{2}{11} [/tex]
Now we know that
[tex]p(aUb) = p(a) + p(b) - p(anb)[/tex]
[tex]p(getting \: number \: less \: than\: 4 \: or \: odd \: number) = [/tex]
[tex] = \frac{3}{11} + \frac{5}{11} - \frac{2}{11} [/tex]
[tex] = \frac{6}{11} [/tex]
I hope it helped you
Which expression is equivalent to 4x+2y-8x
a) 2(3y-2x)
b) 2 (4y-2x)
c) 2(2y+3x)
d) 2(3x-2y)
Answers
Simplify 2x-- yfor x = 3 and y=-2.
•20
•14
•16
•10
Answers
Answer:
8 (none of the above)
Step-by-step explanation:
Given that,
→ x = 3
→ y = -2
Let's solve the equation,
→ 2x - y
→ 2(3) -(-2)
→ 6 + 2
→ 8 is the answer.
Juana and Andy completed 10 math problems total. Juana completed 6 of the problems. Write an equation to determine the number of math problems that Andy completed, then solve the equation. How many of the math problems did Andy complete?
Answers
Step-by-step explanation:
let the number of questions solved by Andy=x
this implies that 6+x=10
making x the subject of the equation
x=10-6
x=4
therefore Andy solved 4 questions
solve this sum plsss
Answers
Step-by-step explanation:
the answer is in the attachment.
hope this helps you.
Angelica says the tangent is the ratio of the length of the leg opposite angle A ∠ A over the length of the leg adjacent to angle A This means B C must have a length of 3 3 units A C must have a length of: 4 4 units. They can find the length of Latex A B using the Pythagorean Theorem and then use it to find the sine and cosine ratios. Graciella says that they cannot find the length of any side of the triangle and, therefore, cannot find the ratios for sine and cosine. Both students have errors in their reasoning. Identify the mistake Angelica made in her reasoning. Provide an example that shows why she is incorrect. Identify the mistake that Graciella made in her reasoning. Explain why she is incorrect. Find the ratios for the sine and cosine of angle A Explain your process.
Answers
Based on the trigonometry ratios and the Pythagorean theorem both of them were incorrect.
Cos A = 4/5; Sin A = 3/5
What is the Trigonometry Ratios?The Trigonometry ratios relates the length of the sides of a right triangles. They are given as:
Sine ratio, sin ∅ = opp/hypCosine ratio, cos ∅ = adj/hypTangent ratio, tan ∅ = opp/adj.What is the Pythagroean Theorem?If two sides of a right triangle are known the third side can be determined using the Pythagorean theorem, which is given as, c² = a² + b², where and b are legs, and c is the hypotenuse of the right triangle.
1. Given that tan A = 3/4, it is not necessarily true that BC MUST have a length of 3 units, and AC MUST have a length of 4 units, because:
If BC = 9 units and AC = 12 units, the it will give us the same tangent ratio as:
tan A = 9/12 = 3/4.
Therefore, Angelica's mistake is stating that BC MUST be 3 units, and AC MUST be 4 units.
2. Knowing two length of the sides of a right triangle is enough information needed to find the length of the third side using the Pythagorean theorem, so Graceilla is incorrect.
3. Find AC using the Pythagorean theorem:
AB = √(3² + 4²)
AB = 5 units.
Cos A = adj/hyp = AC/AB
Cos A = 4/5
Sin A = opp/hyp = BC/AB
Sin A = 3/5
Learn more about the trigonometry ratios on:
https://brainly.com/question/10417664
After several days of camping and long-distance bicycle riding, you decide to right straight home, riding at a constant rate. After 2 hours of riding you
kilometers from home and after 4 hours of riding youare 5 kilometers from home. Once you begin to ride home, how many hours will it take you to arrive at home?
Answers
Answer:
I just need points.
Step-by-step explanation:
x/9 times 15-47=28
help pls
Answers
Answer:
x=45
Step-by-step explanation:
Then,
x/5(15)-47=28
Step 1: Simplify the equation on both sides
x/9(15)-47=28
5/3x-47=28
Step 2: Add 47 to both sides
5/3x-47+47=28+47
5/3x=75
Step 3: Multiply both sides by 3/5
(3/5)*(5/3x)=(3/5)*(75)
x=45
Which choice is equivalent to the expression below?
7x2 - 42 + x2
O A. 3x12
O5x22
O C. 8x^2 - 4-15
O D. 6x1/2 -3-2
Answers
Answer:
the answer to your problem is c
Answer:
Did you copy C correctly?
If not, then C should equal 8x^2 - 16
Step-by-step explanation:
Simplify 7x^2 - 4^2 + x^2
I hope this helps!
could someone help me super super quick?
Answers
Answer:
Vertex form of a quadratic equation is y=a(x-h)2+k, where (h,k) is the vertex of the parabola
The vertex of a parabola is the point at the top or bottom of the parabola
Step-by-step explanation:
Different textbooks have different interpretations of the reference "standard form" of a quadratic function. Some say f (x) = ax2 + bx + c is "standard form", while others say that f (x) = a(x - h)2 + k is "standard form". To avoid confusion, this site will not refer to either as "standard form", but will reference f (x) = a(x - h)2 + k as "vertex form" and will reference f(x) = ax2 + bx + c by its full statement.
#1
y=a(x-h)²+ky=a(x²)+3Put (2,-5)
-5=2²a+3-5=4a+34a=-8a=-2Equation
y=-2(x-0)²+3#2
y=a(x-2)²Put (5,9)
9=a(5-2)²3²a=99=9a=1Equation
y=(x-2)²+0#3
y=a(x+3)²+2put (-1,14)
14=a(2)²+214=4a+24a=12a=3Equation
y=3(x+3)²+2#4
y=a(x-5)²-3Put (1,-8)
-8=a(-4)²-3-8=16a-316a=-5a=-5/16Equation
y=-5/16(x-5)²-3
Explanation and answer please
Answers
Answer:
$41.96
Step-by-step explanation:
30% of 59.95 is 17.99 (rounding to the nearest hundredth place since it was 17.985)
subtract 17.99 since it is the sale (30%)
59.95 - 17.99 = 41.96
the cd is worth $41.96 on sale for 30% off.
In the figure below, find x. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth.
Answers
Check the picture below.
A ball has a mass of 3g and a volume of 6 cm3. It's density is what
and will it float or sink
in water.
Answers
Answer:
float
Step-by-step explanation:
density = mass/voume
3g/6c.m. ^3
0.5g/c.m.^3 = 0.5g/mL^3
Since the density of water is about 1g/mL^3 and 0.5g/mL^3 is less than that, it will float
pls view the calculations section of this ans for more details.
Calculations ↓[tex]\boxed{\\\begin{minipage}{3cm}\xrightarrow{density}\\$\displaystyle\frac{mass}{volume} \\ \end{minipage}}[/tex]
Mass = 3g
Volume = 6
3/6
1/2 <----- density
So the density is 1/2 mL³It will float because it's density is less than the density of waterhope helpful ~
A circle has a radius of 11.4 cm
What is the exact length of an arc formed by a central angle measuring 120°?
Enter your answer in the box. Express your answer using .
NEED HELP QUICK!!!
Answers
Answer:
7.6pie
Step-by-step explanation:
120°/360°=X/11.4×2 pie
1/3×22.8 pie =X
X= 7.6 pie
Please help me I need help asap
Answers
Answer:
AB = 23 , BC = 13
Step-by-step explanation:
Isosceles mean two side angle is equal to each other.
AB and AC are the same. So we can solve for x.
[tex]AB=AC\\5x-7=23\\5x=30\\x=6\\\\AB = 5x-7\\AB = 5*6-7\\AB=30-7\\AB = 23\\\\BC = 3x-5\\BC = 3*6-5 = 18 - 5 = 13\\BC = 13[/tex]
Answer:
Step-by-step explanation:
Because they tell us it's an isosceles triangle we know two sides are the same length. since AB and AC look like they are similar we can assume that those sides are the exact same length. Since we know , now, that AB and AC are equal in length, set them equal
AB = AC
now plug in given info
5x-7 = 23
nice, now use your super hero algebra skillz to solve for X. My calculus prof. always says that students are bad at algebra, i'll help you do the algebra.
5x-7=23 ( add 7 to both sides)
5x=23+7 (add 7 to 23 )
5x=30 (divide both sides by 5 )
x=6
yay, we have X now.
we know AB =23 , because of the isosceles triangle thing.
BC = 3x-5
plug in for X :)
3*6-5=BC
18-5=BC
13=BC
Yay, all the answers, and way to get the answers are above :P
A system of equations is given below. To solve this system using substitution, which of the following equations could be used?
A. 2x-4x-6=8
B. 2x- (4x-6)=8
C. 2x+3(4x-6)=8
D. 2x-3(4x-6)=8
Answers
What is value of 5 in 2 500.7
Answers
Answer:
500
Step-by-step explanation:
Since the 5 is in the hundreds place in the number 2500.7, its value is 5 * 100 = 500.
Answer:
hundreds
Step-by-step explanation:
1 dozen roses for $29.75 how much does one rose cost
Answers
Answer:
$2.48
Step-by-step explanation:
29.75/12 =2.479
chase deposits $7440.93 into a savings account that pays a simple annual interest rate of 1.23%
Answers
Answer:
To find how much money Chase will get in a certain amount of years, set up the following equation:
(7440.93*0.0123)*x = y
Plug in x. "x" stands for how many years Chase keeps the money in his account while earning interest.
Keep "y" unknown, as that stands for what you are trying to solve for, which is how much interest money Chase will make.
what is the quotient of 4 ÷ 1/4?
Answers
Answer:
16
Step-by-step explanation:
4 divided by 1/4 =
4/.25
16
Find the area of this figure. Round your
answer to the nearest hundredth. Use
3.14 to approximate 7.
12.2 ft.
10 ft.
6 ft.
14 ft.
A = [?] ft.2
Notice that only half of the circle is included in the figure!
Enter
Answers
Answer:
209.25 ft²
Step-by-step explanation:
The area of the composite figure is the sum of the areas of its parts. Those parts are a triangle, rectangle, and semicircle.
__
triangleThe area formula is ...
A = 1/2bh
A = 1/2(6 ft)(10 ft) = 30 ft²
rectangleThe area formula is ...
A = bh
A = (14 ft)(10 ft) = 140 ft²
semicircleThe area formula is ...
A = 1/2πr² . . . . where radius r is half the diameter
A = 1/2(3.14)(5 ft)² = 39.25 ft²
total areaThe sum of the areas of the parts is ...
total area = (30 +140 +39.25) ft² = 209.25 ft²