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]
!!!!!!!!!!!!!!!plz help asap. 50 POINTS!!!!
Answer:
its c. 1,155.00
Step-by-step explanation:
Help please by slope and y- intercept
Answer:
Slope = -3/4Y - intercept = -3Step-by-step explanation:
y = mx + b
mx = slope
b = intercept
1. Simplify the equation
4y = -3x - 12
2. Divide both sides by 4
y = -3/4 x - 3
3. Make a graph
First start at the y-intercept, (0, -3)*
Then, use the pattern -3/4
It is called rise over run.
But, when the slope is negative you have to go down instead of up. So you have to go down 3 and 4 to the right.
Continue that pattern until you get your result.
But when you have to go to the upper part of the graph go up 3 and over 4 to the left.
Continue this pattern.
This also applies to other graphs.
* = remember a y-intercept always has a 0 as the x - coordinate.
Hope this helped,
Kavitha
Jessica found a coupon in the Sunday paper for $0.50 off each jar of
Ragu spaghetti sauce if you purchase 3 or more jars. Krogers is
selling the sauce for $4.75 a jar and Jessica purchased 4 jars. What
was the final price?
please help it’s timed
Find the slope of the line
Answer:
WE{OFGiuhu argoih
Step-by-step explanation:
Answer:-3
Step-by-step explanation:
y2-y1/x2-x1=m
-3-3/6-4=-6/2=-3
AACB = ADCE
ZA = 3x-10, ZC = 45°, ZD = 2x+10
Step-by-step explanation:
< A = < D
3x_10 = 2X+10
X=20
you invest $4500 into an interest earning account that compounds daily at 5%.How much will you have in 6 years.How much interest will you earn
Answer:
4500*1.05^(365*6) = 1.1422929e+50
The ratio of boys and girls in Mrs specks s class is 2 of 3 There is 18 girls what is the total number of students in Mrs.specks class HELP PLZ I WILL GIVE YOU THE BBRAINLYEST
Answer: 30 students in total
Step-by-step explanation: 2x+ 3x is 5x right. The 18 girls are the 3x. That means the 6 people is 1x. If there are 5 x people in total that means that there are 30 students
6x^2-19x+3=0
Find both of the x
4. Verify that the functions fand g are inverses of each other by showing that
f(g(x)) = x and g(f(x)) = x.
F(x)=2x-3/x+4
g(x) = 3+4x/2-x
Answer and step-by-step explanation:
We just have to apply one function in the other one. See:
→ f(g(x)):
[tex]f(x) = \dfrac{2x-3}{x+4}\\\\f(g(x)) = \dfrac{2g(x)-3}{g(x)+4} = \dfrac{2\cdot\dfrac{3+4x}{2-x}-3}{\dfrac{3+4x}{2-x}+4}\\\\f(g(x)) = \dfrac{\dfrac{6+8x}{2-x}-3}{\dfrac{3+4x}{2-x}+4}\\\\f(g(x)) = \dfrac{\dfrac{(6+8x)-3(2-x)}{2-x}}{\,\,\,\dfrac{(3+4x)+4(2-x)}{2-x}\,\,\,}=\dfrac{(6+8x)-3(2-x)}{(3+4x)+4(2-x)}\\\\f(g(x)) =\dfrac{6+8x-6+3x}{3+4x+8-4x}=\dfrac{11x}{11}\\\\\\\boxed{f(g(x)) = x}[/tex]
→ g(f(x)):
[tex]g(x) = \dfrac{3+4x}{2-x}\\\\g(f(x)) = \dfrac{3+4f(x)}{2-f(x)} = \dfrac{3+4\dfrac{2x-3}{x+4}}{2-\dfrac{2x-3}{x+4}}\\\\g(f(x)) = \dfrac{3+\dfrac{8x-12}{x+4}}{2-\dfrac{2x-3}{x+4}}\\\\g(f(x)) = \dfrac{\dfrac{3(x+4)+(8x-12)}{x+4}}{\,\,\,\dfrac{2(x+4)-(2x-3)}{x+4}\,\,\,}=\dfrac{3(x+4)+(8x-12)}{2(x+4)-(2x-3)}\\\\g(f(x)) =\dfrac{3x+12+8x-12}{2x+8-2x+3}=\dfrac{11x}{11}\\\\\\\boxed{g(f(x)) = x}[/tex]
What verifies that f and g are inverses of each other.
Q.E.D.
I have $100 and I want to buy tshirt that cost $10 and sweatshirts that cost $20 how many tshirts and sweatshirts can I buy
Answer:
10 tshirts or 5 sweatshirts
Step-by-step explanation:
One t-shirt + one sweatshirt = $30.
We know that $100 ÷ $30 = 3 times with $10 left over.
This leads to the conclusion that you can buy 4 t-shirts and 3 sweatshirts.
A. 0.75s+0.4t=980
B. 0.75s-0.4t=980
C. 0.75s+0.04t=980
D. 0.75s-0.04t=980
5. Juliet has swimming lessons every 5th day and dance lessons every 3rd day. If she
had a swimming lesson and a dance lesson on October 1, when will be the next
date on which she has both swimming and dance lessons?
A. October 5
B. October 10 C. October 15 D. October 18
Hope this helps!
C. October 15
Consider the following hypothesis test:
H0: µ = 20
Ha: µ < 20
A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.
a. Compute the value of the test statistic (to 2 decimals).
b. What is the p-value (to 3 decimals)?
c. Using a = .05, can it be concluded that the population mean is less than 20?
d. Using a = .05, what is the critical value for the test statistic?
e. State the rejection rule: Reject H0 if z is the critical value.
f. Using a = .05, can it be concluded that the population mean is less than 20?
Answer:
a
[tex]z = - 2.12[/tex]
b
[tex]p- value = 0.017003[/tex]
c
There is sufficient evidence to show that the population mean is less than 20
d
[tex]z_{0.05} =- 1.645[/tex]
e
The decision rule is
Reject the null hypothesis
f
The conclusion is
There is sufficient evidence to show that the population mean is less than 20.
Step-by-step explanation:
From the question we are told that
The null hypothesis is [tex]H_o: \mu = 20[/tex]
The alternative hypothesis is Ha: µ < 20
The sample size is n = 50
The sample mean is [tex]\= x = 19.4[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The population standard deviation is [tex]\sigma = 2[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }[/tex]
=> [tex]z = \frac{19.4 - 20 }{ \frac{2}{ \sqrt{50 } } }[/tex]
=> [tex]z = - 2.12[/tex]
From the z table the area under the normal curve to the left corresponding to -2.12 is
[tex](P< -2.12) = 0.017003[/tex]
Generally the p-value is
[tex]p- value = 0.017003[/tex]
From values obtained we see that [tex]p-value < \alpha[/tex] hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to show that the population mean is less than 20.
Generally form the normal distribution table the critical value at a level of significance of [tex]\alpha = 0.05[/tex] is
[tex]z_{0.05} =- 1.645[/tex]
Generally given that [tex]z < z_{0.05}[/tex]
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to show that the population mean is less than 20.
What is the solution to x^6 – 6x ^5 + 15x ^4 – 20x ^3 + 15x^ 2 – 6x + 1 ≥ 0? x = 0 x = 1 all real numbers all real numbers except zero
Answer:
Answer: C all real numbers
Answer: All real numbers
Step-by-step explanation: Edge 2022
Write the fraction 5/8 as a percent and as a decimal.
Answer:
0.625
62.5%
Step-by-step explanation:
5/8 is 0.625 as a decimal and
0.625*100 is 62.5 as a percent
There are 31 guests at your home for a dinner party. In how many ways could the guests arrange themselves on a four person couch?
Answer:
7.75
Step-by-step explanation:
The total number of ways could the guests be arranged on a four person couch is 31465.
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is that there are 31 guests at your home for a dinner party.
The total number of ways could the guests be arranged on a four person couch is -
C{31, 4} = 31!/{(31 - 4)!4!}
C{31, 4} = (31 x 30 x 29 x 28 x 27!/27! x 4!) = (31 x 30 x 29 x 28)/24 = 31465
C{31, 4} = 31465
Therefore, the total number of ways could the guests be arranged on a four person couch is 31465.
To solve more questions on equations, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ5
Simplify each term. please help!! 30 points + brainliest :)
1. -(-3y)³
2. (2c)⁵
3. (-2m)⁴
4. (4g)³
5. (7j)²
6. (-5z)⁵
Answer:
1. 27y^3
2. 32c^5
3. 16m^4
4. 64g^3
5. 49j^2
6. -3125z^5
Step-by-step explanation:
Can you help answer my question too, please?
hvfygcicgdigcigcicticigcdbgvbug
Answer:
This is a hw site pls dont post this, if you dont need help. I dont want your account to be deleted. :) Hope u have a great day tho, but in the future dont post this.
Step-by-step explanation:
need helppp on this question!!
In the table, please select the product (s), by name, that has the higher percentage of being ordered.
There are 12 more apples than oranges in the basket of 36 apples and oranges. How
many apples are there in the basket?
Step-by-step explanation:
Required Answer:-Total number of fruits=36Let
the number of oranges =x
The number of apples=x+12
ATQ[tex]{:}\leadsto [/tex][tex]\sf x+x+12=36 [/tex]
[tex]{:}\leadsto [/tex][tex]\sf 2x+12=36 [/tex]
[tex]{:}\leadsto [/tex][tex]\sf 2x=36-12 [/tex]
[tex]{:}\leadsto [/tex][tex]\sf 2x=24 [/tex]
[tex]{:}\leadsto [/tex][tex]\sf x={\dfrac {24}{2}}[/tex]
[tex]{:}\leadsto [/tex][tex]\sf x=12 [/tex]
Number of Apples =12+12=24Answer:
24 apples
Step-by-step explanation:
apples = x
oranges = y
y+12 = x
x+y = 36
y+y+12 = 36
2y = 24
y = 12
x = 24
PLS GIVE BRAINLIEST
picture attached please help!
PLZ HELP I BEG U!!!!!! ILL MARK U BRAINLIEST
Create a story using the inequality symbols , ≤,≥,≠ . the story must be creative, detailed, coherent, and written clearly. it does not have to be solely math related.
Answer:
T_T said to 个_个: Hallo, I am so happee!!!
Step-by-step explanation:
Plz mark as Brainliest!
Every 125 pages that Raul reads during his summer reading challenge, he will collect 5 book points to use at his local library. Which graph models a relationship with the same unit rate?
Answer:
The answer is "[tex]\frac{1}{25}[/tex]"
Step-by-step explanation:
They might claim that perhaps the ratio to Raul would've been:[tex]\frac{y}{x} = \frac{5}{125} = \frac{1}{25}[/tex] per each 125(x) page, which he reviewed throughout a summer competition.
Raul's cost per unit for each paragraph reads is [tex]\frac{1}{25}[/tex] page points, that's why the model a link with the same unit rate. please find the graph in the attached file.
Cuánto le falta a 3/5para llegar a 9/10
Answer:
3/10
Step-by-step explanation:
3/5 se puede convertir en 6/10
(3x2)/(5x2).
9/10 - 6/10 = 3/10
le falta 3/10 para llegar a 9/10.
Queue really good summer time happy feeling good memories music
Answer:
u want recommendations?
Step-by-step explanation:
Answer:
Watermelon Sugar
2.1.2 Linear Tables and Graphs (Algebra 1)
The question is on the image below
Answer:
Step-by-step explanation:
1). Let the equation of a line is,
y = mx + b
Here, m = slope of the line
b = y-intercept
From the graph attached,
Slope = [tex]\frac{\text{Rise}}{\text{Run}}[/tex] = [tex]\frac{1}{4}[/tex]
y-intercept = -2
Equation → y = [tex]\frac{1}{4}x-2[/tex]
2). Slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}=\frac{3}{4}[/tex]
y-intercept 'b' = -3
Equation → y = [tex]\frac{3}{4}x-4[/tex]
3). Slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}=\frac{-5}{0.75}[/tex]
= [tex]-\frac{20}{3}[/tex]
y-intercept = 5
Equation → y = [tex]-\frac{20}{3}+5[/tex]
4). Slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}=\frac{-2}{4}=-\frac{1}{2}[/tex]
y-intercept = 4
Equation → y = [tex]-\frac{1}{2}x+4[/tex]
5). Since, line is passing through origin (0, 0)
y-intercept = 0
Slope = [tex]\frac{\text{Rise}}{\text{Run}}=\frac{1}{1}[/tex]
Equation → y = x
6). Slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}=\frac{1}{4}[/tex]
y-intercept = -4
Equation → y = [tex]\frac{1}{4}x-4[/tex]
can someone please help me thank you
Answer:
Neither of the students are correct.
Step-by-step explanation:
Sarah:
P = 3x + x +7 + 3x + x +7 ..... this first step is correct
= 6x + 14 .... this step is incorrect, Sarah forgot to add the other 2 xs
John:
P = 2(x + 7) + 2(3x)
= 2x + 7 + 6x .... this step is incorrect, John forgot to distribute the 2 to the 7
= 8x + 7 .... incorrect because of the previous step
The answer should've been 8x + 14.
How many ?!!!!
?!!!
?!!
15
hope this helps you alot☺✌❤
22. (01.05)
A function is created to represent the amount of money you save or spend each day of the week. What
restrictions would be made to the range? (1 point)
The range would only include integers.
The range would only include positive integers.
The range would only include negative integers.
The range would include all real numbers.
Answer:
Step-by-step explanation:
The range would only include positive integers.