A triangular plot of land has sides of lengths 420 feet, 330 feet, and 180 feet. Approximate the smallest angle between the sides. The choices are rounded to the nearest degree.
A. 30 degree
B. 27 degree
C. 22 degree
D. 24 degree
Answer:
D. 24 degree
Step-by-step explanation:
Sides of the triangle are
a = 330 ft
b = 180 ft
c = 420 ft
From cosine rule we have
[tex]\angle A=\cos^{-1}(\dfrac{b^2+c^2-a^2}{2bc})\\ =\cos^{-1}(\dfrac{180^2+420^2-330^2}{2\times180\times 420})\\ =48.65^{\circ}[/tex]
[tex]\angle B=\cos^{-1}(\dfrac{a^2+c^2-b^2}{2ac})\\ =\cos^{-1}(\dfrac{330^2+420^2-180^2}{2\times 330\times 420})\\ =24.17^{\circ}[/tex]
[tex]\angle C=\cos^{-1}(\dfrac{a^2+b^2-c^2}{2ab})\\ =\cos^{-1}(\dfrac{330^2+180^2-420^2}{2\times 330\times 180})\\ =107.19^{\circ}[/tex]
The smallest angle in the triangle is [tex]\angle B=24.17^{\circ}[/tex].
What restriction should be applied to y = tanx for y = arctanx to be defined?
Answer:
restrict the domain to (-pi/2, pi/2)
Step-by-step explanation:
edge 2020
Answer: c. restrict the domain to (-pi/2, pi/2)
Step-by-step explanation:
Edge :)
answer the following
Step-by-step explanation:
–(11/4) = 11 : (–4) = –11/4 = 11/-4
what is the estimate of 29 x 688
Answer:
19952 :)
Step-by-step explanation:
Step-by-step explanation:
29 turns to 30
688 turns to 700
30×700=21000
Joe collects Pokemon cards. He already has 100 and buys a dozen more each week when he goes to the store. Jessica also collects Pokemon cards. She has 130 cards, and buys 6 more each week at the store.After how many weeks would the two kids have the same amount of cards?
Answer:
5 weeks
Step-by-step explanation:
To find the answer to this question we have to write an equation for both situation and put them equal to each other.
Let's write an equation for Joe:
12x + 100
Now, for Jessica
6x + 130
Next, put them equal to each other:
12x + 100 = 6x + 130
Solve:
12x + 100 = 6x + 130
6x + 100 = 130
6x = 30
x = 5
Therefore, it will take 5 weeks for Joe and Jessica to have the same amount of cards.
Check:
12(5) + 100 = 6(5) + 130
60 + 100 = 30 + 130
160 = 160
I hope this helps!!
- Kay :)
Suppose that the functions q and r are defined as follows.
q (x)=–2x+1
r(x) = 2x²+2
Find the following.
(r og)(-1) = 0
0/6
Х
(q or)(-1) = 0
5
?
Answer:
(r o q)(-1) = 20
(q o r)(-1) = -11
Step-by-step explanation:
Given
[tex]q(x) = -2x + 1[/tex]
[tex]r(x) = 2x^2 + 2[/tex]
Solving (a): (r o q)(-1)
In function:
(r o q)(x) = r(q(x))
So, first we calculate q(-1)
[tex]q(x) = -2x + 1[/tex]
[tex]q(-1) = -2(-1) + 1[/tex]
[tex]q(-1) = 2 + 1[/tex]
[tex]q(-1) = 3[/tex]
Next, we calculate r(q(-1))
Substitute 3 for q(-1)in r(q(-1))
r(q(-1)) = r(3)
This gives:
[tex]r(x) = 2x^2 + 2[/tex]
[tex]r(3) = 2(3)^2 + 2[/tex]
[tex]r(-1) = 2*9 + 2[/tex]
[tex]r(-1) = 20[/tex]
Hence:
(r o q)(-1) = 20
Solving (b): (q o r)(-1)
So, first we calculate r(-1)
[tex]r(x) = 2x^2 + 2[/tex]
[tex]r(-1) = 2(-1)^2 + 2[/tex]
[tex]r(-1) = 2*1 + 2[/tex]
[tex]r(-1) = 6\\[/tex]
Next, we calculate r(q(-1))
Substitute 6 for r(-1)in q(r(-1))
q(r(-1)) = q(6)
[tex]q(x) = -2x + 1[/tex]
[tex]q(6) = -2(6) + 1[/tex]
[tex]q(6) =- 12 + 1[/tex]
[tex]q(6) = -11[/tex]
Hence:
(q o r)(-1) = -11
Which graph represents the function fx) =|x–4?
The image below shows the graph f(x) = |x| – 4
Hope this helps! :)
a) Solve by determinant method: x - y = 2, 2x + 3y = 4
Answer:
x = 2
y = 0
Step-by-step explanation:
x - y = 2
2x + 3y = 4
Using creamers rule of determinants, we have;
D =
|1 1|
|2 3|
Thus; D = (1 × 3) - (1 × 2)
D = 1
Dx =
|2 1|
|4 3|
Dx = (2 × 3) - (1 × 4)
Dx = 2
Dy =
|1 2|
|2 4|
Dy = (1 × 4) - (2 × 2)
Dy = 0
Thus;
x = Dx/D = 2/1
x = 2
y = Dy/D = 0/1
y = 0
Write the given linear system without the use of matrices. Assume X = x y z . X' = 7 6 −9 5 1 1 0 −3 4 X + 0 3 1 e6t − 8 0 4 e−3t
Answer:
X= 3
Step-by-step explanation:
Tommy was trying to solve the system of a linear equation and a quadratic equation shown below. 2x – y = –1 x2 – 5x – y = –7 Tommy had completed the following steps in his algebraic solution process but could not factor the resulting quadratic, x2 – 7x – 1, to complete the problem. Step I: y = 2x + 1 Step II: x2 – 5x – (2x + 1) = –7 Step III: x2 – 5x – 2x – 1 = –7 Step IV: x2 – 7x – 1 = –7 Determine the step in which Tommy made his mistake and justify your reasoning.
Answer:
Step IV; Tommy must set the quadratic expression equal to 0 before factoring.
plz give brainlyest
It is found that in Step IV; Tommy must set the quadratic equations equal to 0 before factoring and then solving.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given that the system of a linear equation and a quadratic equation.
2x – y = –1
x² – 5x – y = –7
Now Tommy had completed the following steps in his algebraic solution process but could not factor the resulting quadratic equation as;
x² – 7x – 1,
Step I: y = 2x + 1
Step II: x² – 5x – (2x + 1) = –7
Step III: x² – 5x – 2x – 1 = –7
Step IV: x² – 7x – 1 = –7
Therefore, we conclude that in Step IV; Tommy must set the quadratic equations equal to 0 before factoring and then solving.
Learn more about quadratic equations;
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(11/18-4/9)+1/6 pemdas fraction
Answer:
1/3
Step-by-step explanation:
11/18 - 4/9 + 1/6
= 1/6 + 1/6
= 1/3
The value of the fraction is 1/3.
What is PEMDAS Rule?PEMDAS rule is the same as BODMAS rule.
PEMDAS is the abbreviation for Parenthesis, Exponents, Multiplication, Division, Addition and Subtraction.
Given fraction is : (11/18 - 4/9) + 1/6
We have a parenthesis (brackets) in the given expression. First solve the operations inside the bracket.
And multiply the fraction 4/9 with 2 on both numerator and denominator.
(11/18 - 4/9) + 1/6 = (11/18 - 8/18) + 1/6
= 3/18 + 1/6
There is only an operation of addition left.
Multiplying both numerator and denominator of 1/6 with 3,
(11/18 - 4/9) + 1/6 = 3/18 + 3/18
= 6/18
= 1/3
Hence the value of the fractional expression given is 1/3.
Learn more about PEMDAS here :
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Show that f '(x) = g'(x) for all x in their domains. Can we conclude from the corollary below that f − g is constant? If f '(x) = g'(x) for all x in an interval (a, b), then f − g is constant on (a, b); that is, f(x) = g(x) + c where c is a constant.
Answer:
Answer: 15 cm
Step-by-step explanation:
The derivative of a function at a point can be defined as its slope at that point. For f'(x) = g'(x) in the interval (a,b), it is proved that f - g is constant in (a,b).
What is a Derivative?A derivative of a function is its rate change of increase or decrease in a given interval with respect to its variable. Derivative of a constant function is always zero.
Given that, f'(x) = g'(x) for all x.
Taking integral on both sides
f(x) + C₁ = g(x) + C₂
=> f(x) - g(x) = C₂ - C₁
=> f(x) - g(x) = C
Thus, f(x) - g(x) is constant is proved.
Similarly for interval an interval (a,b),
f(x) - g(x) = C
=> f(x)= g(x) + C
Hence, it is proved that in an interval (a,b), if f'(x) = g'(x) then f(x)= g(x) + C.
To know more about Derivative click on the following link
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Which graph represents an even function?
Answer:
one that looks like triangle
Step-by-step explanation:
What error did Wanda make?
None. Wanda’s work is correct.
Wanda converted the percent to a decimal incorrectly. It should be 0.073.
Wanda converted the percent to a decimal incorrectly. It should be 0.73.
Wanda has the wrong label. It should be hours, not dollars.
Answer:
C
Step-by-step explanation:
the guy above sucks
None. Wanda’s work is correct.
Wanda converted the percent to a decimal incorrectly. It should be 0.073.
Wanda converted the percent to a decimal incorrectly. It should be 0.73.
Wanda has the wrong label. It should be hours, not dollars.
Step-by-step explanation:
Help me out here real quick please
Answer:
25
Step-by-step explanation:
10÷1/4=25
Together, teammates Pedro and Ricky got 2678 base hits last season. Pedro had 282 more hits than Ricky. How many hits did each player have?
Answer:
pedro- 1621
ricky- 1057
Step-by-step explanation:
tan 3( ) tan 3 lim
h
xh x
® h
Answer:
27
Step-by-step explanation:
know that
h = 3
h × h × h
3 × 3 × 3
= 27
If the father's age in 3 years will be twice the son's age 4 years ago, and if the sum of their ages now is 106, how old is the father now?
Answer:
The father is 67 and the son is 38
Step-by-step explanation:
TRUST ME Bois and Girls
82,77,72,67 find the sequince
Answer:
Subtract 5 as you go along the pattern.
82-5=77-5=72-5=67...
Step-by-step explanation:
1. A recipe calls for lb of flour for 1 batch. How many batches can be made with each of the following amounts? a. 1 lb b. lb c. lb
Find an equation of the line that passes through the pair of points (-5, -9) and (2,-7)
Answer:
y=0.3x - 7.6
Step-by-step explanation:
line: y=ax+b
a= Δy ÷ Δx
a= (-9 + 7) ÷ (-5 - 2)
a= -2 ÷ -7 = approximately 0.3
y=0.3x + b
Now you can fill in one of the points to find b (or both to make sure you got the answer right).
0.3 × 2 + b = -7
0.6 + b = -7
b = -7 - 0.6 = approximately -7.6
So: an equation of the line that passes through this pair of points is y=0.3x - 7.6
On a test, i would write as many decimals as possible if not said not to, to get the most exact answer. Also remember to keep calculating with the number on your calculator and not to round them off for the most exact answer.
Look at my picture, what’s the missing statement in step 4?
Answer:
Step-by-step explanation:
∠ACE=∠ BCD (reflexive property )
It is common to both the angles or both the angles represent the same angle.
We have to prove two triangles are similar.
Here we show two angles of different triangles are equal.
Hence similar by AA
Answer:
m<CBD is congruent to m<DBC
Step-by-step explanation:
Reflexive property states that any real number, for example a, is equal to itself. < cbd is congruent to < dbc :)
IF THE RATIO IN A VALENTINE'S
DAY CANDY BOX OF MILK TO DARK
CHOCOLATES IS 23. HOW MANY
DARK CHOCOLATES ARE THERE IF
THERE ARE 8 MILK CHOCOLATES?
Answer:
12 dark chocolates
Step-by-step explanation:
Let there are 2x milk chocolates and 3x dark chocolates.
Total no of milk chocolates = 8
ATQ,
2x = 8
x = 4
Dark chocolates = 3x
= 3(4)
= 12
Hence, there are 12 dark chocolates.
(PLEASE HELP) You buy your dream house and want to redesign the front of the house. The budget for the
front of the house is $1,800. You spent $90 of the budget on fresh flowers. What percent of the
budget did you spend on fresh flowers?
budget did you spend on fresh flowers?
Answer:
Step-by-step explanation:
1620.
Answer:
5%
Step-by-step explanation:
90/1800 = x/100
0.05 = x/100
0.05 * 100 = x
5 = x
1.800 * 5% = 90
Graph the solution set for the inequalíty
y> 2x-5 by following these steps:
Step 1: ldentify the slope and y-intercept.
slope = y-intercept =
Please help me
Answer:
Slope= 2
Y-intercept= -5
Step-by-step explanation:
This inequality is in slope-intercept form which means we can get both striaght from the inequaltiy. Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. In this inequality m would be 2 and b would be -5, so those are your answers.
the length of a rectangle is 8 centimeters. what is the width?
Answer:
This is a very vague question. We can't find out the width if it doesn't tell us the area. Comment on my answer the area and I can help.
What angle would you use to represent 40 red cars out of 90 cars in total on a pie chart?
. 40 degree
. 4 degree
. 160 degree
90 degree
Answer:
4
Step-by-step explanation:
i just know I took the test and I choose 90 and got it wrong
please HURRY IM ON A QUIZ
if 2 is substituted for x, which expression will NOT equal 5?
Answer:
It will be 2x -1
If x=2
2*2 - 1 = 4 - 1 = 3
Step-by-step explanation:
7 - x If x=2
7 - 2 = 5
11 - 3x If x=2
11 - 3*2 = 11 - 6 = 5
2x -1 If x=2
2*2 - 1 = 4 - 1 = 3
4x - 3 If x=2
4*2 - 3 = 8 - 3 = 5
How would you write the number displayed on the calculator screen in standard form
Answer:
E is short for 10^x. The number that comes after the E is the power of 10.
So its 7.6*10^12
now that scientifically notation
For standard your gonna need to simplify that
so we know 10^12 is 1000000000000
Multiply the 7.6
7600000000000
hope I helped :)
What is the product of 14/5
Answer:
2.8
Step-by-step explanation:
Just divide and get the answer