Answer:
11.6
Step-by-step explanation:
The length of f of the triangle is f = 11.7 cm
What is Law of Cosines?The Law of Cosines is a mathematical formula used to find an unknown side or angle of a triangle, given the lengths of the other two sides and the angle opposite the unknown side. It is also known as the Cosine Rule.
The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite side c, the following equation is true:
c² = a² + b² - 2ab cos(C)
where cos(C) is the cosine of angle C. This formula can be rearranged to solve for any of the variables, depending on which values are known.
Given data ,
Let the triangle be represented as ΔEFG
And , the measures of the sides of the triangle are
g = 4.3 cm
e = 9.1 cm
And , measure of angle ∠F = 116°
where c² = a² + b² - 2ab cos(C)
On simplifying , we get
a² = c² - b² + 2abcos ( C )
78.26 ( cos 116° ) - 4.3² - 9.1² = f²
f² = 135.7344
Taking square roots on both sides , we get
f = 11.7 cm
Hence , the length is f = 11.7 cm
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Please ASAP.
The rectangle on the right is a scaled copy of the rectangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
Scale factor is [tex]\frac{14}{21}[/tex].
What is a scale factor?A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.
Given
The rectangle on the right is a scaled copy of the rectangle on the left.
[tex]\frac{42}{63}[/tex] and 15 ÷ [tex]\frac{45}{2}[/tex]
[tex]\frac{42}{63}[/tex]
Rationalizing [tex]\frac{42}{63}[/tex] by 45
= [tex]\frac{42(45)}{63(45)}[/tex]
= [tex]\frac{1890}{2835}[/tex]
15 ÷ [tex]\frac{45}{2}[/tex]
Rationalizing 15 ÷ [tex]\frac{45}{2}[/tex] by 63
= [tex]\frac{30(63)}{45(63)}[/tex]
= [tex]\frac{1890}{2835}[/tex]
If we want to find the scale factor we have to equal the proportions of two rectangles.
∴ Scale factor = [tex]\frac{1890}{2835}[/tex] = [tex]\frac{14}{21}[/tex]
Hence, scale factor is [tex]\frac{14}{21}[/tex].
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There are 32 students in the class. Of the class 3/8 of the students bring their own lunch. How many students bring their own lunch?
David’s salary used to be £19,500 before he received a 8% pay rise. Work out how much David is now paid?
Answer:
21060
Step-by-step explanation:
19500÷100=195
195×8=1560
1560+19500=21060
It’s PreCal I just need a method to solve it
Answer:
see explanation
Step-by-step explanation:
Using the identities
tanx = [tex]\frac{sinx}{cosx}[/tex] , cotx = [tex]\frac{cosx}{sinx}[/tex]
Consider the left side
[tex]\frac{tanx}{tanx+cotx}[/tex]
= [tex]\frac{\frac{sinx}{cosx} }{\frac{sinx}{cosx}+\frac{cosx}{sinx} }[/tex]
= [tex]\frac{\frac{sinx}{cosx} }{\frac{sin^2x+cos^2x}{cosxsinx} }[/tex]
= [tex]\frac{\frac{sinx}{cosx} }{\frac{1}{cosxsinx} }[/tex]
= [tex]\frac{sinx}{cosx}[/tex] × [tex]\frac{cosxsinx}{1}[/tex] ← cancel cosx on numerator/ denominator
= sin²x
= right side
what is the mathematical sentence of "A number increasd by 7 is 15?
A n - 7 = 15
B n + 7 = 15
C 7n = 15
D. n/7 = 5
Answer:
B
Step-by-step explanation:
A number increased by 7 means, 7 was added to the number and the result is 15
If f(x) = -2x + 5 and g(x) = 5x - 5, what is the value of f(g(-4))?
Answer:
55
Step-by-step explanation:
g(-4)=-20-5 or -25
f(g(4)=-2(-25)+5 or 50+5
what is 44 > 7+s + 26
Answer:
s<11
Step-by-step explanation:
44>7+s+26
Switch sides:
7+s+26<44
Group like terms:
s+7+26<44
Add the numbers:7+26=33
s+33<44
Subtract 33 from both sides:
s+33-33<44-33
Simplify:
s<11
In a bag there are blue sweets, red sweets and yellow sweets. The number of blue sweets is four times the number of yellow sweets. The number of red sweets is half the number of yellow sweets. Find the percentage of sweets in the bag that are yellow.
Answer:
18.18%
Step-by-step explanation:
The percentage of sweets in the bag that are yellow is as follows:
Let us assume the number of yellow sweets be x
So for number of blue sweets be 4x
And, the number of red sweets be 0.5x
So it could be written as
Blue Red Yellow
4 0.5 1
8 1 2
So for yellow, the percentage is
= 2 ÷ (8 + 1 + 2)
= 2 ÷ 11
= 18.18%
Another chance for brainliest if it correct ! Please help
Answer:
A B and C are true
Step-by-step explanation:
A variable needs to be eliminated to solve the system of equations below.
Choose the correct first step.
-10x + y = 64
-10x + 5y = 40
Answer:
-10x + y = 64
Step-by-step explanation:
hope it helps
17.) An ostrich can run 174 feet in 3 seconds. What is the slope of the line and what does it
represent?
What is the Scale Factor?
Point B was dilated using C as the center of dilation
What is the scale factor?
Explain your thinking.
9514 1404 393
Answer:
5the length of the expanded segment is 5 times the original lengthStep-by-step explanation:
We have to assume that the image of B is the large dot at upper right. We further have to assume that the distance between dots on the line segment is equal to CB.
The scale factor multiplies the distance from C. That distance has been multiplied by 5, so the scale factor is 5.
Solve the system of equations 3x – 3y = 30 and 2x + y = 11 by
combining the equations.
slope = 2/3 ; y-intercept = -1
• Write the linear equation in slope intercept form!
helppppp !!
Answer:
y=2/3x-1
Step-by-step explanation:
slope intercept form is y=mx+b
where m is the slope and b is the y-intercept
You already know that the slope is 2/3 and the intercept is -1 so all you have to do is plug it in
y=2/3x-1
Sam had 225 grams of raisins. After buying another two bags of raisins he then had
175 grams of raisins
He writes this equation where r represents number of bags of raisins to describe how
225r+2=1475
Is he correct? Explain your answer.
How many grams of raisins were in one bag?
Answer: No, he is not correct, the correct equation is:
225 + 2*r = 1475
Solving that, we can find that each bag of raisins has 625 grams of raisins.
Step-by-step explanation:
I suppose that the problem is as follows:
"Sam had 225 grams of raisins. After buying another two bags of raisins he then had 1475 grams of raisins"
Then, if each bag of raisings has r grams of raisings, two bags will have two times that, or:
2*r grams of raisings.
Then if we take what he had at the beginning, and we add these 2*r grams, we should get the 1475 grams that he has at the end:
225 + 2*r = 1475
This is what he should get.
and we can solve it for r, to get:
2*r = 1475 - 225 = 1250
r = 1250/2 = 625
r = 625
This means that each bag of raisins has 625 grams of raisins.
But instead, he got:
225*r + 2 = 1475
In this case, he multiplied his previous amount of raisings by the amount that each bag has, so his equation is wrong.
Middle school students were asked how they got to school each morning. There were 375 students who said they rode the bus. This number represents 60% of the school enrollment. How many students are enrolled?
Answer:
625 students
Step-by-step explanation:
What would the area be for a circle with the diameter of 7
Answer:
The answer is 38.48
Step-by-step explanation:
Picture with explanation provided below.
HELP!!! What mistake did I make? And what would u suggest to help me???
Answer:
All the dots need to be on the line, and maybe dont add so many dots
Step-by-step explanation:
if the simple answer interest on 2,000 for 10 years is 1,600, then what is the interest rate
Answer:
8%
Step-by-step explanation:
Solving our equation
r = 1600 / ( 2000 × 10 ) = 0.08
r = 0.08
converting r decimal to a percentage
R = 0.08 * 100 = 8%/year
The interest rate required to
accumulate simple interest of $ 1,600.00
from a principal of $ 2,000.00
over 10 years is 8% per year.
please help me, I am so confused. Thanks
Answer:
c. 80
Step-by-step explanation:
cos x = sin(x-70)
cos x = cos [90-(x-70)]
cos x = cos (90-x +70)
cos x = cos 160 -x
x= 160-x
2x = 160
x =80
-7 2/3 + (5 1/2) + 8 3/4 = Need the answer asap
Answer:
answer is 7898tI don't know either thank very much for the points though
Please help!!
What is the measure of angels DEF and angles DEG?
2. Find the vector equations of the following lines:
a. A=(6,5,7),m=2i+5j–k
b. A=(8,6,2),B=(3,4,1)
Answer:
a) The vector equation
[tex]AB^{-} = -4i^{-} -0j^{-} -8k^{-}[/tex]
b) The vector equation
[tex]AB^{-} = -5i^{-} -2j^{-} -k^{-}[/tex]
Step-by-step explanation:
Step(i):-
a)
Given that the points are A( 6,5,7) and B = m = 2i+5j-k
OA = 6i+5j+7k and OB = 2i+5j-k
AB = OB-OA
= 2i+5j-k - (6i+5j+7k)
= 2i -6i +5j-5j-k-7k
= [tex]-4i^{-} -0j^{-} -8k^{-}[/tex]
b)
Given that the points are A( 8,6,2) and B = (3,4,1)
OA = 8i+6j+2k and OB = 3i+4j+k
AB = OB-OA
= 3i+4j+k -(8i+6j+2k)
= 3i -8i +4j-6j+k-2k
= [tex]-5i^{-} -2j^{-} -k^{-}[/tex]
Please help, thank you.
The question is in the picture
Answer:
D
Is the answer okkkkkkkkkkkkkkkk
Answer: A regular decagon has all sides of equal length and each internal angle will always be equal to 144°.
Step-by-step explanation:
PLEASE ANSWER ASAP... MANY THANKSSS <3
A straight line is parallel to Y=3x-1 and passes through (0,4)
What is the equation of the line??
9514 1404 393
Answer:
y = 3x + 4
Step-by-step explanation:
The given line is in the form ...
y = mx + b
where m is the slope (3) and b is the y-intercept (-1).
The parallel line will have the same slope. The given point (0, 4) is the y-intercept, so the desired equation is ...
y = 3x +4
Pls help fast !! Thanks
Simplify the expression 4f × 2g + 3h
A. 8fg + 3h
B. 24fgh
C. 9fgh
D. 6gf + h
Answer:
A. 8fg + 3h
Step-by-step explanation:
[tex]4f × 2g + 3h \\ \\ = 4 \times 2 \times f \times g + 3h \\ \\ = 8fg + 3h[/tex]
Step-by-step explanation:
[tex]4f \times 2g + 3h \\ = (4 \times 2)fg + 3h \\ = 8fg + 3h \\ [/tex]
HELP THIS IS DUE VERY SOONN
Answer:
A: 7
B: 84,035
Step-by-step explanation:
The population increases by 7 each time, so 12,005x7=84035.
(Side note: I'm not completely sure what the "exponential function" is but I think the answer is correct. Check over it yourself to be sure :)
Answer:
a. x plus 5 times 7
b. 84035
Step-by-step explanation:
.FIND THE DIFFERENCE OF 8,328 AND 459?
Answer:
7869
Step-by-step explanation:
8,328
- 459
________
7,869
Would it be better to have a higher interest rate on a loan or on an investment? Explain.
Answer:
When a company borrows money it is better to have a low interest rate. The lower the interest rate, the less amount of money the company has to pay back as interest on the loan.
Step-by-step explanation:
Is it better to have a higher interest rate when a company borrows money or to have a lower interest rate?
Viasat has a $100 setup fee and costs $65 per month. Geo Satellite has a setup fee of $30 and costs $70 per month. Write a system of equations to represent this situation. In how many months will both providers cost the same? What will that cost be?
Answer:
Step-by-step explanation:
I don’t know
Answ
i dont know
Step-by-step explanation: