What is the area of triangle ABC if a = 10 (degrees), B = 22 (degrees), and C = 70 (degrees) please help me.
A. 454.32 Sq Units
B. 103.37 Sq Units
C. 1.76 Sq Units
D. 17.61 Sq Units
Answer:
D. 17.61 square units
Step-by-step explanation:
To find the area of the ∆ABC, we can apply the formula below:
Area of ∆ABC = ½×a×c×sin(B)
a = 10
c = ??
B = 22°
Let's find c using Sine Rule:
Thus:
[tex] \frac{a}{sin(A)} = \frac{c}{sin(C)} [/tex]
Where,
a = 10
c = ??
A = 180 - (22 + 70) = 88°
C = 70°
Plug in the values
[tex] \frac{10}{sin(88)} = \frac{c}{sin(70)} [/tex]
Multiply both sides by sin(70)
[tex] \frac{10}{sin(88)} \times sin(70) = \frac{c}{sin(70)} \times sin(70) [/tex]
[tex] \frac{10 \times sin(70)}{sin(88)} = c [/tex]
[tex] 9.4 = c [/tex] (nearest tenth)
✔️Area of ∆ABC = ½×a×c×sin(B)
Plug in the values
Area of ∆ABC = ½ × 10 × 9.4 × sin(22)
Area = 17.61 square units (nearest tenth)
Determine whether the relationship is a function. Complete the explanation.
(0, 4), (8, 8), (3, 2), (9, 1), (8, 7)
Answer:
the relationship is not a function
Step-by-step explanation:
it's not a function because two of the domains are the same.
The relationship represented by these ordered pairs is not a function.
We have,
To determine whether the relationship is a function, we need to check if each input (x-value) is associated with exactly one output (y-value).
If there is any x-value that is associated with multiple y-values, then the relationship is not a function.
Let's analyze the given set of ordered pairs:
(0, 4), (8, 8), (3, 2), (9, 1), (8, 7)
Here, we can see that the x-value 8 is associated with both y-values 8 and 7.
Therefore, the relationship is not a function because one input (x-value) is mapped to multiple outputs (y-values).
In a function, each input must have a unique output, but in this case, the x-value 8 is associated with both 8 and 7 as the corresponding y-values.
Thus,
The relationship represented by these ordered pairs is not a function.
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Use the following function rule to find f(-7).
f(x) = 9x - 7
O 70
O-56
0 -70
56
What is the factorization of the trinomial below?
x^2- 5x+4
Answer:A
Step-by-step explanation:
FOIL
The factors of the quadratic equation x²- 5x + 4 are (x - 4)(x - 1) option (A) is correct.
What is a quadratic equation ?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
We have a quadratic equation:
= x²- 5x + 4
= x² -x - 4x + 4
= x(x - 1) - 4(x - 1)
= (x - 4)(x - 1)
Thus, the factors of the quadratic equation x²- 5x + 4 are (x - 4)(x - 1) option (A) is correct.
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Which of the numbers shown in the box below is the largest? 19/3, 31/5, 13/2, 25/4 pls help urgent
Answer: i think they are all the exact same 6 with a remainder of 1
Step-by-step explanation:
Simplify 8 - (14) please help
Answer:
The answer is - 6 hope this helped
A block of ice has a square top and bottom and rectangular sides. At a certain point in
time, the square top and bottom each have a length of 30 cm, which are decreasing at a
rate of 2 cm/h. At the same time, the height of the ice block is 20 cm and decreasing at
3 cm/h. How fast is the ice melting?
Answer:
[tex]\frac{dV}{dt} = 360 \ cm^3/h[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Geometry
Volume of a Rectangular Prism: V = lwhCalculus
Derivatives
Derivative Notation
Differentiating with respect to time
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
[tex]l = 30 \ cm\\w = l\\\frac{dl}{dt} = 2 \ cm/h\\h = 20 \ cm\\\frac{dh}{dt} = 3 \ cm/h[/tex]
Step 2: Differentiate
Rewrite [VRP]: [tex]V = l^2h[/tex]Differentiate [Basic Power Rule]: [tex]\frac{dV}{dt} = 2l\frac{dl}{dt} \frac{dh}{dt}[/tex]Step 3: Solve for Rate
Substitute: [tex]\frac{dV}{dt} = 2(30 \ cm)(2 \ cm/h)(3 \ cm/h)[/tex]Multiply: [tex]\frac{dV}{dt} = 360 \ cm^3/h[/tex]Here this tells us that our volume is decreasing (ice melting) at a rate of 360 cm³ per hour.
Using the triangles shown below, explain how the ASA congruence criteria follows from the definition of congruence in terms of rigid motions.
Answer:
I have this question too
Step-by-step explanation:
All i know is that the ASA shows that even when they are rotated or translated due to rigid motions, they are still congruent because it shows that the angles and sides are equal.
Which equation describes the function whose y-intercept is 6 and whose
graph has slope 2?
HELPP
Answer:
y=2x+6
slope intercept form: y=mx+y-intercept
m=slope
Find the value of x in each figure. B 9. - 15 2x A C
How do you write 22over5 in this
Answer:
00004.40 if you need to fill in every box. If not, 4 in front of the decimal, and a 4 after.
Show distributive property steps to evaluate 9 · 67 ?
603
Step-by-step explanation:We are given the expression:
9*67
Evaluating the expression:
We can write 67 as (60+7). So, we can rewrite the given expression as:
9*(60+7)
Using the distributive property:
(9*60) + (9*7)
540 + 63
603
What is the partial fraction decomposition of 11x-38/(2x-5)(x-4)
Answer:
D
Step-by-step explanation:
7/2x-5+2/x-4 is the partial fraction decomposition of 11x-38/(2x-5)(x-4)
What is Fraction?A fraction represents a part of a whole.
We need to write the partial fraction decomposition of 11x-38/(2x-5)(x-4)
(11x-38)/(2x-5)(x-4)=A/2x-5+B/x-4
11x-38=A(x-4)+B(2x-5)
11x-38=Ax-4A+2Bx-5B
We need to find the values of A and B
Compare the coefficients of x
11=A+2B
A=11-2B
Compare the constants
-38=-4A-5B
-38=-4(11-2B)-5B
-38=-44+8B-5B
-38=-44+3B
-38+44=3B
6=3B
Divide both sides by 3
B=2
Now A=11-2(2)=7
Hence, 7/2x-5+2/x-4 is the partial fraction decomposition of 11x-38/(2x-5)(x-4)
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centra
Jonah drives his car to and from work. The total length of the trip to and from work is 19.8 miles. In
August, Jonah worked 26 days.
How many miles in all did Jonah drive to and from work that month? Complete the explanation.
19.8
26
Jonah drove
miles in August
Plz
514.8 your welcome
All you have to do is multiply 19.8 x 26
Corinna is taking a test in which short-answer questions are worth 10 points each and essay questions are worth 15 points each. She estimates that it takes 3 min to answer each short- answer question and 6 min to answer each essay question. The total time allowed is 60 min, and no more than 16 questions can be answered. Assuming that all her answers are correct, how many questions of each type should Corinna answer in order to get the best score?
11) It takes you 15 minutes to frost a 2 layer cake. You and a friend have 100 1 point
cakes to frost for the church bake sale. How many hours will it take the two
of you to frost all of the cakes if you work at the same time rate? Hint: It
takes you 15 minutes to frost one cake, you can frost 4 cakes in 1 hr. *
B. 8 hours
O c. 12.5 hours
Answer:
12.5 hours
Step-by-step explanation:
100/4=25
25/2=12.5
Plz help with question
Answer:
x=25 and c=75
Step-by-step explanation:
(x+5)+(3x)+c=180
x+5+3x+c=180
x+3x+c=175
4x+c=175
c=-4x+175
c=3x
-4x+175=3x
175=7x
x=25
c=3x
c=3(25)
c=75
a store buys shirts for $12 each and marks up the price by %25. what is the price for a shirt at this store??
Answer:
Step-by-step explanation:
The price of the shirt at the store is $16
12 x .25 = 4
4 + 12 = 16
A school janitor has mopped
1/3 of a classroom in 5 minutes. At what rate is he mopping?
Answer:
1/3 of the school in 5 minutes or in 15 minutes he will mop the whole entire school.
Step-by-step explanation:
=================================================
Work Shown:
1/3 of a classroom = 5 minutes
3*(1/3 of a classroom) = 3*5 minutes
1 classroom = 15 minutes
It takes the janitor 15 minutes to mop a full classroom.
The rate is expressed in units of classrooms per minute. This means we'll need to divide both sides by 15 to get
1 classroom = 15 minutes
1/15 classroom = 15/15 minutes
1/15 of a classroom = 1 minute
The janitor's rate is 1/15 of a classroom per minute.
Which set of fractions is ordered from least to greatest?
A
five over eight, eight over twelve, three over four
B
eight over twelve, five over eight, three over four
C
three over four, five over eight, eight over twelve
D
five over eight, three over four, eight over twelve
Answer:
get the best i can and get you a good friend of yours to go with the other side and the first thing I think you have a lot
What is the solution set for 2x – (x + 5) < 3x – 9 ?
Answer:
x > 2
Step-by-step explanation:
x - 5 < 3x - 9
x - 5 + 5 < 3x - 9 + 5
x < 3x - 4
x - 3x < 3x - 4 - 3x
-2x < -4
(-2x)(-1) > (-4)(-1)
2x > 4
2x/2 > 4/2
x > 2
Answer:
x > 2.
The solution in interval notation is (2, ∞).
Step-by-step explanation:
2x - (x + 5) < 3x - 9
2x - x - 5 < 3x - 9
2x - x - 3x < -9 + 5
-2x < -4
Divide both sides by -2
x > 2 (Note that the sign flips because we are dividing by a negative)
Write the data from greatest to least: 0.8, 0.79, 0.08, 0.81, 0.09, 0.9, 0.89
Answer:
0.9, 0.89, 0.81, 0.8, 0.79, 0.09, 0.08
Step-by-step explanation:
Answer: 0.09 , 0.89 , 0.81, 0.08, 0.79 , 0.9, 0.8
Step-by-step explanation:
First find the greatest
0.09, 0.89,0.81, 0.08, 0,79
Then the least
0.9 .0.8
Now put it all together
0.09, 0.89. 0.81 , 0.08, 0.79 , 0.9, and lastly 0.8
if f = 3, g = -4 and h = -5
[3-h]+13
Write a number that when rounded to the nearest TENTHS is 382.9
Answer:
380
Step-by-step explanation:
If its a number 4-1 than it stays in the same tenths place if it a number 5- and up than it goes to a new number.
What is the rule for the function shown in the table?
Input x -2 -1 0 1/2
Output y -8-5-2 1 4
O y=2x-2
Oy= x-6
O y= 4x
O y = 3x - 2
PLS HELP LOL
Answer:
2nd
Step-by-step explanation:
what is the least common denominator for 2/5 and 3/2
Answer:
4/10
Step-by-step explanation:
⅖ = 4/10
3/2 = 15/10
The common denominator is 10.
The answer to the question is 10.
The least common denominator (LCD) is the most smallest number that can be a shared factor for a set of numerals. We see here the LCD is 10 because both fractions have a denominator of 10.
Find the missing side ?
Answer:
37
Step-by-step explanation:
which expession is equivalent to negative 2 1/4 over nagative 2/3
Answer:
Ahhhhhjhhhjhhhh
Step-by-step explanation:
How that helps ;)
In equilateral triangle ABC above, y =
(A) 40
(B) 60
(C) 70
(D) 75
(E) 80
Answer:
60°
Step-by-step explanation:
In an equilateral triangle all sides are equal so as all angles are same,
3 sided fig. 180÷3= 60°
Since the Boston marathon began in 1897, the finish time has been incrementally decreasing. The mean finish time to date is 231 minutes with a standard deviation of 40 minutes. Based on this information, what would allow us to use a Z-score in order to construct a confidence interval to estimate the mean finishing time of the most recent Boston Marathon with a sample size of 40 participants. Choose all that apply.
Answer:
hello your question lacks the required options but i will provide a general answer to your question
answer : The mean value and the standard deviation would allow us use a Z-score
Step-by-step explanation:
mean value = 231 minutes
standard deviation ( std ) = 40 minutes
sample size = 40
The parameters that would be applicable while use Z-score are : The given mean value and the standard deviation
This is because the value of a z-score gives us an information on how far we are from the mean score i.e. number of standard deviations
+Zscore means that the score is above the average value
-Zscore means that the score is below the average value