Answer:
Perimeter = 32.3
Area = 95.24
Step-by-step explanation:
Given:
△ABC, m∠A=60°
m∠C=45°, AB = 9
To find:
Perimeter of △ABC
Area of △ABC
Solution:
Using angle sum property in a triangle:
m∠A + m∠B + m∠C = 180°
m∠B = 180° - 45° - 60° = 75°
As per Sine Rule:
[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]
Where
[tex]a[/tex] is the side opposite to [tex]\angle A[/tex]
[tex]b[/tex] is the side opposite to [tex]\angle B[/tex]
[tex]c[/tex] is the side opposite to [tex]\angle C[/tex]
[tex]\dfrac{BC}{sin60^\circ} = \dfrac{AC}{sin 75^\circ} = \dfrac{AB}{sin 45^\circ} \\\Rightarrow \dfrac{BC}{\frac{\sqrt3}{2}} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow BC = 12.73\times 0.87 \\\Rightarrow BC = 11.08[/tex]
[tex]\Rightarrow \dfrac{AC}{0.96} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow AC = 12.73\times 0.96 \\\Rightarrow AC = 12.22[/tex]
Perimeter of △ABC = AB + BC + AC = 9 + 11.08 + 12.22 = 32.3
Area of a triangle is given as:
[tex]\dfrac{1}2\times ab sin(angle\ between\ a\ and\ b)[/tex]
[tex]\Rightarrow \dfrac{1}{2}\times AB\times AC\times sinA\\\Rightarrow 9\times 12.22\times sin 60\\\Rightarrow \bold{95.24}[/tex]
ABC is similar to XYZ. The lengths of two sides of each triangle are given in the figure. Find the length of side x.
Answer:
x=7/3
Step-by-step explanation:
AB/XY=BC/YZ
The length of {x} is equivalent to 7/3 units.
What is scale factor? How it is used in Dilating sides?Scale factor tells us by how much one quantity is greater than the other. It is denoted by K. Mathematically -
K = a/b.
Rewriting, we get -
a = Kb
If a side length [a] of any 2 - D figure is dilated by a scale factor of [k], then the length of new side will be [Ka].
Given is that ABC is similar to XYZ.
Since, the two triangles are similar, than their corresponding sides will be proportional to each other. This means that the ratio of corresponding sides will be equal. Mathematically -
BC/YZ = AB/XY = AC/YZ = K [scale factor]
We can write -
8/(2[tex]\frac{2}{3}[/tex]) = 7/x
8/(8/3) = 7/x
8 x 3/8 = 7/x
3 = 7/x
x = 7/3
Therefore, the length of {x} is equivalent to 7/3 units.
To solve more questions on dilation, visit the link below-
brainly.com/question/13439872
#SPJ2
5x-3(x-2)-x
Helppppp I just need you to simplify and show your work plz =)
Answer:
x+6
Step-by-step explanation:
5x-3(x-2)-x
5x-3x+6-x
x+6
2
Security Participants
You are screen sharing
New Share
Pause Share
Annotate
More
Stop Share
CHAPTER 22
Statistics and Central Tendencies
results are shown in the table below.
Number of visits
Number of people
1
6
2 3
119
5
7.
8
6
S
7.
4
(a) Find the median number of visits per person.
(b) Calculate the mean number of visits per person.
[ Jan., paper 1, No. 21
ling between two cities, 3/8 of the passengers ar
Fifty people visiting a museum were asked how many times they had visited the museum
Answer:
p
Step-by-step explanation:
A password contains eight digits. How many different passwords can be formed?
Now lets assume you use a stronger password with a mix of lowercase and uppercase characters, such as "blUeFisH", then the character set is 52. In this case, there are 52^8 possible combinations of 8 character passwords. So, to break an 8 character password, it will take (1.7*10^-6 * 52^8) seconds / 2, or 1.44 years.
What is the answer I’m dumb
Answer:
9units
Step-by-step explanation:
V = 4 + at, solve for A
Answer:
a=v-4
Step-by-step explanation:
Instead of having a cake, Ruben wants to make ice cream sundaes at his next birthday party.
He thinks each person will eat 2 cups of ice cream, and there will be 24 people at his party.
How many 1-gallon tubs of ice cream should he buy?
tubs
Answer:
he should buy 3 gallons
Step-by-step explanation:
There are 16 cups in a gallon, and if each person will eat 2 cups, and there are 24 ppl, multiply 24 by 2 to get the number of cups.
24 x 2 = 48.
Then, divide that by 16 (the number of cups in a gallon) to t how many gallons.
48 ÷ 16 = 3
so, he needs 3 gallons
hope this helped!
Write a different expression that has the same quotient as -3/8 and 3/8.
Answer:
x = -3/8
Step-by-step explanation:
HELP PLEASE!! NUMBER 6!!
You will get the brainiest if you can tell me how you did it, so I can finish doing them myself lol. If It comes back right, I will give it you instantly. Thank you very much.
Answer:
hey it's not clear....
Estimate the area of the inregular shape. Explain your method and show your work.
Please help 100 points and brainliest
Answer:
30
Step-by-step explanation:
Since we are estimating. We know that it is about 5 units on top and about 6 units on the side. Therefore, you would multiply them
5*6=30
That is why the area of this irregular shape is 30 units.
Answer in Slope form
Answer:
y=1/4x+3
Step-by-step explanation:
How to change a fraction to a decimal
Answer:
just divide the numerator by the denominator
Step-by-step explanation:
an example is ⅔ as a decimal is about .666 or .7
What is 31.99 divided by 5.99 in long division? Explain & I will mark as brainliest
Answer:
Its 5.3405 I think:>
Step-by-step explanation:
QUESTION 16 Which of the numbers below are related in the same way as 3259 and 2? A. 5789 and 29 B. 3174 and 6 C. 2749 and 4 D. 9047 and 12
Answer:
Option (B)
Step-by-step explanation:
Relation between two numbers 3259 and 2,
3259 → 3 × 2 + 5 - 9 = 2
Now we will check the relation in the given options,
Option (A).
5789 → 5 × 7 + 8 - 9 = 34
Option (B).
3174 → 3 × 1 + 7 - 4 = 6
Option (C).
2749 → 2 × 7 + 4 - 9 = 9
Option (D).
9047 → 9 × 0 + 4 - 7 = -3
Therefore, Option (B) shows the same relation.
PLEASE HELP ME SIMPLIFY THIS PLEASE SHOW WORK TO! THANK YOU 5.3x - 9 + 7.6x
Answer:
12.9x - 9
your welcome
Need help will mark Brainliest
Answer:
40
Step-by-step explanation:
You know that angle m<SRT is 40, because it's a supplementary angle with 140. 180 - 140 = 40.
Next, you also know that the interior angles of a triangle add up to 180, so you would now make an equation adding all three angles and setting them equal to 180.
40 + 3x + 4 + 8x + 4 = 180
You would now add like terms.
11x + 48 = 180
You would now subtract 48 from both sides.
11x = 132
You would now divide both sides by 11.
x = 12
You would now plug x into m<RST, 3x + 4.
3(12) + 4 = m<RST
36 + 4 = m<RST
40 = m<RST
Can you Explain how to do this plz
Find the slope of the line passing through the points (-4,7) and (2,-8)
Answer:
[tex]m=\frac{-5}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-4, 7)
Point (2, -8)
Step 2: Find slope m
Substitute: [tex]m=\frac{-8-7}{2+4}[/tex]Subtract/Add: [tex]m=\frac{-15}{6}[/tex]Simplify: [tex]m=\frac{-5}{2}[/tex]which is the right andwer?????????? please help me
Answer:
The first one
What number group is 45/5 in
Answer:
Its in rational
Step-by-step explanation:
Answer:
45/5 is a rational number
Step-by-step explanation:
45/5 is equal to 9.
9 is a rational number.
son
Undaunted co
American re
Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form?
Answer:
Slope = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Let's take two points on the line graphed for a function.
Slope of this linear function = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
Between two points chosen,
Rise = Vertical distance on y-axis (Increase or decrease) from one point to the second
Run = Horizontal distance on x-axis from one point to second
Let the points on the graph are (-8, 0) and (0, 4).
Rise = 4
Run = 8
Therefore, slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex] = [tex]\frac{4}{8}[/tex]
Slope = [tex]\frac{1}{2}[/tex]
A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 2 pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 35 minutes.
Answer:
Step-by-step explanation:
From the given information:
[tex]R_{in} = ( \dfrac{1}{2} \ lb/gal) (6)\ gal /min \\ \\R_{in} = 3 \ lb/min[/tex]
Given that the solution is pumped at a slower rate of 4gal/min
Then:
[tex]R_{out} = \dfrac{4A}{100+(6-4)t}[/tex]
[tex]R_{out}= \dfrac{2A}{50+t}[/tex]
The differential equation can be expressed as:
[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A = 3 \ \ \ ... (1)[/tex]
Integrating the linear differential equation; we have::
[tex]\int_c \dfrac{2}{50 +t}dt = e^{2In |50+t|[/tex]
[tex]\int_c \dfrac{2}{50 +t}dt = (50+t)^2[/tex]
multiplying above integrating factor fields; we have:
[tex](50 +t)^2 \dfrac{dA}{dt} + 2 (50 + t)A = 3 (50 +t)^2[/tex]
[tex]\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2[/tex]
[tex](50 + t)^2 A = (50 + t)^3+c[/tex]
A = (50 + t) + c(50 + t)²
Using the given conditions:
A(0) = 20
⇒ 20 = 50 + c (50)⁻²
-30 = c(50) ⁻²
c = -30 × 2500
c = -75000
A = (50+t) - 75000(50 + t)⁻²
The no. of pounds of salt in the tank after 35 minutes is:
A(35) = (50 + 35) - 75000(50 + 35)⁻²
A(35) = 85 - [tex]\dfrac{75000}{7225}[/tex]
A(35) =69.6193 pounds
A(35) [tex]\simeq[/tex] 70 pounds
Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.
A cake recipe called for using 6 ¼ cups of sugar before baking and another 5 ¾ cups after baking. What is the total amount of sugar needed in the recipe?
Answer:12 cups of sugar are needed in the recipe
Step-by-step explanation:
6 ¼ + 5 ¾ =11 4/4=12
The total amount of sugar needed for the cake recipe is 12 cups.
Given that, A cake recipe called for using 6¼ cups of sugar before baking and another 5¾ cups after baking.
What is addition of two fractions?To add fractions there are three simple steps:
Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators), put that answer over the denominator.
Step 3: Simplify the fraction (if possible)
Now, the total amount of sugar needed
6¼ + 5¾
= 25/4 + 23/4
= (25+23)/4
= 48/4
= 12
Hence, the total amount of sugar needed for the cake recipe is 12 cups.
To learn more about the addition of fractions visit:
https://brainly.com/question/17544795.
#SPJ2
Given (3x + 2) : (x - 2) = 7:5, what is the
value of x?
Answer:
(3x+2)/(x-2)=7/5
5(3x+2)=7(x-2)
15x+10=7x-14
15x-7x=-14-10
8x=-24
X=-24/8
X=-3
Which is the graph of y=3/4x-3
Answer:
need the graph, but go to desmos for answer to graphing questions
Step-by-step explanation:
The legs of a right triangle measure 8 inches and 12 inches. What is the area
of the triangle?
A. 192 sq. inches
B. 24 sq. inches
C. 48 sq. inches
D. 96 sq. inches
Answer:48 sq. Inches
Step-by-step explanation:
Find the value of X.
Answer:
x = 6
Step-by-step explanation:
Answer:
x=6
Step-by-step explanation:
32+4 is 36
90-36 is 54
9 times 6 is 54
54+4 is 58
58+32 is 90
pls mark me brainliest :)
Someone please help answer completely !
Answer:
the answer is [tex]T=\frac{VP}{8}[/tex]
Step-by-step explanation:
V=[tex]\frac{8T}{P}[/tex]
you need to make T the subject of the formula:
step1: multiply P for both sides.
V=[tex]\frac{8T}{P}[/tex]
VP=8T
step2: divide by 8 for both sides.
T=[tex]\frac{VP}{8}[/tex]
the answer is [tex]T=\frac{VP}{8}[/tex]
300/12.500000000000000000
Answer: 24
Step-by-step explanation: Hope this helps.
please help im stuck
Answer:
NOT a relation and NOT a function