Answer: 333.2ft
Step-by-step explanation:
We can draw a triangle rectangle, where the distance between the base of the building and the car is one cathetus (300ft)
The height of the building is the other cathetus.
Now, we know that the angle of depression from the top of the building to the car is 42°
This angle is measured from a perpendicular line in from the building, so the "top angle" of the triangle rectangle will be:
90° - 42° = 48°
if we steep on this angle, the 300ft cathetus is the opposite cathetus and the height of the building is the adjacent cathetus.
Here we can use the relation:
Tan(A) = Opposite cathetus/adjacent cathetus:
Then:
Tan(48°) = H/300ft
Tan(48°)*300ft = H = 333.2ft
Answer:
270 ft
Step-by-step explanation:
The angle of depression from the top of the building to the car = 42° and the distance from the car to the building is 300 ft.
This can be represented by a right triangle with:
Adjacent side to the angle = distance from the car to the building = 300 ft, opposite side to angle = height of building = x and angle (θ) = 42°
From trigonometry:
[tex]tan(\theta)=\frac{opposite}{adjacent} \\Therefore:\\tan(42)=\frac{x}{300}\\ x = 300*tan(42)= 300*0.9\\x=270ft[/tex]
The height of the building is 270 ft
What are the foci of the hyperbola represented by the equation (x^2)/64 - (y^2)/32 =1
Answer:
x = √2y^2 + 64 or x = √2y^2 + 64
Step-by-step explanation:
Solve for x.
x^2/64 - y^2/32 = 1
Step 1: Add 1/32 y^2 to both sides.
1/64 x^2 + -1/32 y^2 + 1/32 y^2 = 1 + 1/32 y^2
Step 2: Divide both sides by 1/64.
1/64 x^2/ 1/64 = 1/32 y^2 + 1/ 1/64
x^2 = 2y^2 + 64
Step 3:
x = √2y^2 + 64 or x = √2y^2 + 64
Answer:
x = √2y^2 + 64
Step-by-step explanation:
= 1/64 x^2 + -1/32 y^2 + 1/32 y^2 = 1 + 1/32 y^2
= 1/64 x^2/ 1/64 = 1/32 y^2 + 1/ 1/64
= x^2 = 2y^2 + 64
= x = √2y^2 + 64
Hope this helps!
Help I don't understand it.
Answer:
6/15 * 2/14 = 12/210
Step-by-step explanation:
This is compound probability. To calculate compound probability, you need to multiply the probabilities of each event happening together.
In this example, the events are selecting a pineapple cake, then a strawberry cake.
Let's find the probabilities!
There are 2 strawberry cakes, 6 pineapple cakes, and 7 chocolate cakes. This means that he has 15 cakes in total.
Therefore, the probability of selecting a pineapple cake is 6/15.
Now, if we assume that he has selected a pineapple cake already, there are now 14 cakes.
Next, the probability of selecting a strawberry cake is now 2/14. This is because he already took a pineapple cake, and now he has to pick a strawberry cake out of the remaining 14 cakes.
Multiply these two probabilities to find the compound probability: 12/210 ( this could be further simplified, but that's how they give it to you! )
Hope this helps! Please feel free to contact me if you have any further questions :)
Helpppppppp here plz
Answer:
x + x+12 + 3(x+12) = 123
x = 15
Step-by-step explanation:
Jamil : x
Kiera : x+12
Luther : 3 ( x+12)
x + x+12 + 3(x+12) = 123
Distribute
x + x+12 + 3x+36 = 123
Combine like terms
5x+ 48 = 123
Subtract 48 from each side
5x+48-48 = 123-48
5x =75
Divide by 5
5x/5 = 75/5
x = 15
Answer:
Equation:
123 = x + 12 + x + 3(12 + x)
Solution:
x = 15
Step-by-step explanation:
Jamil: x
Kiera: 12 + x
Luther: 3(12 + x)
Total: 123 badges
Equation:
123 = x + 12 + x + 3(12 + x)
Solve:
123 = x + 12 + x + 3(12 + x)
123 = x + 12 + x + 36 + 3x
123 = 5x + 48
-48 -48
75 = 5x
/5 /5
15 = x
Therefore, the value of x is 15.
Which expression is equivalent to (- 2c / d^2)^3
-8c^3/d^6 is equivalent to the expression
Answer:
-8c^3/d^6
You are correct!
find the derivatives of the following implicit function
Answer:
[tex]\frac{d}{dx}\left(y\right)=\frac{2-6x+6y}{-6x+2y+1}[/tex]
Step-by-step explanation:
[tex]3x^2-6xy+y^2=2x-y\\\mathrm{Treat\:}y\mathrm{\:as\:}y\left(x\right)\\\mathrm{Differentiate\:both\:sides\:of\:the\:equation\:with\:respect\:to\:}x\\\frac{d}{dx}\left(3x^2-6xy+y^2\right)=\frac{d}{dx}\left(2x-y\right)\\\frac{d}{dx}\left(3x^2-6xy+y^2\right)=6x-6\left(y+x\frac{d}{dx}\left(y\right)\right)+2y\frac{d}{dx}\left(y\right)\\\frac{d}{dx}\left(2x-y\right)=2-\frac{d}{dx}\left(y\right)\\6x-6\left(y+x\frac{d}{dx}\left(y\right)\right)+2y\frac{d}{dx}\left(y\right)=2-\frac{d}{dx}\left(y\right)[/tex]
[tex]\mathrm{For\:convenience,\:write\:}\frac{d}{dx}\left(y\right)\mathrm{\:as\:}y^{'\:}\\6x-6\left(y+xy^{'\:}\right)+2yy^{'\:}=2-y^{'\:}\\\mathrm{Isolate}\:y^{'\:}:\quad y^{'\:}=\frac{2-6x+6y}{-6x+2y+1}\\y^{'\:}=\frac{2-6x+6y}{-6x+2y+1}\\\mathrm{Write}\:y^{'\:}\:\mathrm{as}\:\frac{d}{dx}\left(y\right)\\\frac{d}{dx}\left(y\right)=\frac{2-6x+6y}{-6x+2y+1}[/tex]
∠A=8x−10 ∘
∠B=3x+90 ∘
PLEASE PLEASE HELP OR I WON'T PASS MY MATH CLASS AND I WILL HAVE TO TAKE ANOTHER YEAR OF MATH
Answer:
Step-by-step explanation:
if vertical angles (formed when two lines cross each other) or congruent angles (equal degree measure total)
8x-10=3x+90
5x=100
x=20
if complementary (together equal 90 degrees)
8x-10+3x+90=90
11x+80=90
11x=10
x=(10/11)
which in decimal form is about 0.90
if supplementary (together equal 180 degrees)
8x-10+3x+90=180
11x+80=180
11x=100
x=(100/11)
which in decimal form is about 9.09
Rename 1 3/4 as an improper fraction.
Answer:
7/4
Step-by-step explanation:
1 3/4=1 x 4=4 + 3=7/4
How is the graph of log (x – 2) + 1 translated from the graph of log x?
Answer:
See the two translations described below
Step-by-step explanation:
Start with the graph of y = log x. This graph passes through (1, 0) and exists only for x > 0. The line x = 0 is its vertical asymptote.
Translating this graph 2 units to the right results in h(x) = log (x - 2).
Translating the graph of h(x) = log (x - 2) upward by 1 unit results in the graph of log (x – 2) + 1.
HELP. ITS ABOUT FUNCTIONS! HELPPPPPPPPPPPPPP HELPPPPPPP
Answer:
B
Step-by-step explanation:
It cannot be C. The Y-intercept of Function W is 30, while the Y-intercept of Function Z is 15.8. Now, we are left with A, B, and D.
It cannot be D, because 30 is not less than 15.8. Now, we are left with options A and B.
Function Z as an equation is approximately y=-1/24x+15.8.
The slopes are NOT equal, so the answer cannot be A.
Explanation why it's B:
1/16 is bigger than 1/24, however, since the fractions are NEGATIVE, -1/16 is actually LESS THAN -1/24. The slopes of Function W is less than the slope of Function Z.
Answer:
B. the slope of function W is less than he slope of function Z
Step-by-step explanation:
Function W:
y= - 1/16x+30Function Z:
from the table we can see it is decreasing function with step change of -0.04
using the data from the table we can put the function in y= mx + b format:
x=0 ⇒ y= 15.8 ----- interceptx=1 ⇒ y= 15.7615.76- 15.8 = - 0.04= - 4/100 = -1/25 ----- slopeas per above, we get the the form of function Z
y= -1/25x+15.8we can now compare the slops and intercepts of functions W and Z
m - is the slope: -1/16 and - 1/25
-1/25>-1/16 ⇒ the slope of function W is less than Zb is the y-intercept: 30 and 15.8
30>15.8 ⇒ the y-intercept of function Z is lessAs per above the correct option is
B. the slope of function W is less than he slope of function ZWhich is true about the degree of the sum and difference of the polynomials
3x^5y - 2x^3y^4 - 7xy^3 and -8x^5y + 2x^3y^4 + xy^3 ?
Answers:
Both the sum and difference have a degree of 6
Both the sum and difference have a degree of 7
The sum has a degree of 6, but the difference has a degree of 7
The sum has a degree of 7, but the difference has a degree of 6
Answere is C
The sum has a degree of 6 but the difference haa a degree of 7
The true statement about the degree of the sum and difference of the polynomials 3x⁵y - 2x³y⁴-7xy³ and -8x⁵y +2x³y⁴ + xy³ is "the sum has a degree of 6, but the difference has a degree of 7."
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
There are two polynomials,
3x⁵y - 2x³y⁴-7xy³ and -8x⁵y +2x³y⁴ + xy³.
The sum of the polynomials,
= 3x⁵y - 2x³y⁴-7xy³ -8x⁵y +2x³y⁴ + xy³.
= 5x⁵y -6xy³.
And the degree is 6.
The difference of the polynomials,
= 3x⁵y - 2x³y⁴-7xy³ + 8x⁵y - 2x³y⁴ - xy³.
= 13x⁵y - 4x³y⁴-8xy³.
And the degree is 7.
Therefore, the sum has a degree of 6, but the difference has a degree of 7.
To learn more about the Polynomials;
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URGENT: At what annual rate of simple interest must $12,000 be invested to earn $135 in interest each quarter? (I will give brainliest)
Answer:
4.5%
Step-by-step explanation:
Firstly we should understand that a quarter is every three months.
So if $135 is earned each quarter, then 4 * 135 = $540 is earned per annnum
We use the simple interest formula to get the rate.
Mathematically;
I = PRT/100
where P is the amount deposited = 12,000
R is what we are looking for which is the rate
T is the time which is 1 year
I is the interest which is 540
We can rewrite the simple interest formula to be:
100I = PRT
R = 100I/PT
Thus substituting the values we have;
R = (100 * 540)/(12,000 * 1) = 4.5%
Answer:
4.5%Step-by-step explanation:
Using the simple interest formula to tackle this question.
[tex]SI = \frac{PRT}{100}[/tex]
P = principal = $12,000
R = rate (in %) = ?
T = Time(in years) = 1/4 years
135 = [tex]\frac{12000*R}{100*4}[/tex]
[tex]135 = \frac{12000R}{400}\\ 54000 = 12000R\\R = \frac{54000}{12000}\\ R = 4.5\ %[/tex]
The annual rate of simple interest is 4.5%
In the diagram, which two angles are corresponding angles with angle 12?
Angle 8 and Angle 16
Angle 6 and Angle 10
Angle 9 and Angle 11
Angle 5 and Angle 15
Answer:
It's 8 the answer is 8
Step-by-step explanation:
∠8 and ∠16 are corresponding angles with ∠12
What is corresponding angles ?the angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal
According to the question,
Given the diagram we have to find the angles which are corresponding angles with ∠12.
Those angles which are on the same side of traversal called corresponding angles.
By definition of corresponding angles the angles which are corresponding to ∠12 are ∠8 and ∠16. These angles lie on same side of traversal line.
Hence, ∠8 and ∠16 are corresponding angles with ∠12
Option 1 is correct.
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plz help me how would you solve 4x + 2y = 18, 3x - 5y =20 by elemination
Answer: x = 5, y = -1
Step-by-step explanation:
Equation 1: 4x + 2y = 18
Equation 2: 3x - 5y = 20
In order to eliminate one of the variables , find the LCM of either x or y.
I chose to eliminate y. The LCM of 2 & 5 is 10.
Multiply the entire equation so the coefficient of the variable equals the LCM.
Then add the equations and solve for the remaining variable.
5(4x + 2y = 18) --> 20x + 10y = 90
2(3x - 5y = 20) --> 6x - 10y = 40
26x = 130
÷26 ÷26
x = 5
Next, input x = 5 into either of the equations to solve for y.
Equation 1: 4x + 2y = 18
4(5) + 2y = 18
20 + 2y = 18
-20 -20
2y = -2
÷2 ÷2
y = -1
10x+9=4x -9 solve
please help
Answer:
x = -3
Step-by-step explanation:
To solve this, you need to isolate the variable x, this means only one side of the equation should have the variable x. To do this, you need to do the opposite operation from what's given (if it's addition, use subraction; if it's multiplication, use division; these work vise versa)
Subtract 9 from both sides of the equation. This gives you 10x = 4x - 18.Subtract 4x from both sides of the equation. This gives you 6x = -18.Divide both sides by 6. This gives you x = -3The final answer is x = -3
74.88 rounded to three significant figures?
Answer:
74.9
Step-by-step explanation:
Round to the tenths place.
Answer:
74.9
Step-by-step explanation:
When the question asks for something to be rounded to 3 significant figure,
then round in such a way that there are only 3 non-zero digits in the number.
Hope this helps.
Good Luck
You bought a magazine for $3 and two notepads. You spent a total of $13. How much did each notepad cost? *
Answer:
$5
Step-by-step explanation:
We want to find the cost of a notepad considering a magazine costs $3 and we buy 2 notepads and the total cost of the magazine and the 2 notepads is $13 so we can set up an equation to represent this situation. Let 'n' be notepads and that's the value we are solving for so,
⇒ Form the equation
→ 2n + 3 = 13
⇒ Minus 3 from both sides to isolate 2n
→ 2n = 10
⇒ Divide both sides by 2 to find the cost of one notepad
→ n = 5
The cost of one notepad is $5 considering that a magazine cost's $3 and two notepads and total is $13.
The hypotenuse, c, of right triangle ABC is 5.0 cm long. Give the trigonometry ratio cosA=0.50 for angle A, what is the area of the triangle to the nearest tenth of a cm?
Answer:
[tex]\frac{25\sqrt{3} }{8}[/tex]
Step-by-step explanation:
CosA = [tex]\frac{1}{2}[/tex] , so <A is 60º
Hypotenuse (c) is 5
Opposite is (b)
Adjascent is (a)
cos A = [tex]\frac{adjascent}{hypotenuse}[/tex] -----> [tex]\frac{1}{2} = \frac{a}{5}[/tex] ---------> a = [tex]\frac{5}{2}[/tex]
Pytagoras
[tex]5^{2} = (\frac{5}{2}) ^{2} + b^{2}\\ b^{2} = 25 - \frac{25}{4} \\b^{2} = \frac{75}{4} \\\\b = \frac{5\sqrt{3} }{2}[/tex]
A = b . a . 1/2
A = [tex]\frac{25\sqrt{3} }{8}[/tex]
CosA = , so <A is 60º
Hypotenuse (c) is 5
Opposite is (b)
Adjascent is (a)
cos A = -----> ---------> a =
Pytagoras
A = b . a . 1/2
A =
Step-by-step explanation:
Determine the value of x in this polygon.
Answer:
X24
Step-by-step explanation:
Write an expression for the situation described. Each person's share if 'p' people share 8 slices of pizza equally.
Answer:
The expression that represent each person's share is: [tex]y(p) = \frac{8}{p}[/tex]
Step-by-step explanation:
To divide a pizza, or anything else, equally among a certain number of people, we need to divide the total of pizza available by the number of people who will eat the pizza. In this case there are 8 slices and 'p' people, therefore:
[tex]y(p) = \frac{8}{p}[/tex]
In order to validate the expression, we can see that if 8 people eat the pizza, each gets one slice, because 8 divided by 8 is 1, while if 4 people eat the pizza each get 2 and so on.
The expression that represent each person's share is: [tex]y(p) = \frac{8}{p}[/tex]
Evaluate: 14/2 - 3 + 6/3
Answer:
Brainliest!!!
Step-by-step explanation:
see picture
Answer:
[tex]6[/tex]
[tex] \frac{14}{2?} - 3 + \frac{6}{3 ?} \\ 7 - 3 + \frac{6}{?3 } = 6 \\ 4 + \frac{6}{?3} = 6 \\ 4 + 2 = 6[/tex]
What is the value for f(x) = 32x+1 when x = 1/2
Answer:
9
Step-by-step explanation:
We can solve this by plugging x into the function:
3^(2(1/2) + 1)
=3^(1+1)
=3^2
= 9
Answer: The answer would be 9
Step-by-step explanation:
could i please get brainliest
evaluate -5+(-5r)+10
150 miles converted to kilometres?
Answer:
erm
Step-by-step explanation:
241.402
B is the midpoint of AC. Find AB, BC, and AC
Answer:
9, 9, 18
Step-by-step explanation:
3x=5x-65x-3x=62x=6x=3AB=3x=9
BC=AB=9
AC=2AB=18
B is mid point of AC
that means,
[tex]\frac{3x + 5x - 6 }{2} = b \\ \: \: \: \: \: \: \: \: \: \: \: \frac{8x - 6}{2}= b \\ \frac{2(4x - 3)}{2} = b \\ b = 4x - 3[/tex]
[tex]3x = 5x - 6 \\ 2x = - 6 \\ x = - 3[/tex]
[tex]ab = 3x = 3 \times - 3 = - 9 \\ ab = - 9[/tex]
[tex]bc = 5x - 6 = 5 \times - 3 (- 6) \\ \: \: \: \: \: = - 15 - 6 = - 21[/tex]
[tex]ac = 8x - 6 = 8 \times - 3( - 6) = - 24 - 6 = - 30[/tex]
[tex]hope \: it \: helped[/tex]
Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 18% each week. The following function represents the weekly weed growth: f(x) = 86(1.18)x. Rewrite the function to show how quickly the weeds grow each day. f(x) = 86(1.02)x; grows approximately at a rate of 0.2% daily f(x) = 86(1.18)7x; grows approximately at a rate of 1.8% daily f(x) = 86(1.02)7x; grows approximately at a rate of 2% daily f(x) = 86(1.187)x; grows approximately at a rate of 0.18% daily
Answer:
A.f(x) = 86(1.04)x; grows approximately at a rate of 0.4% daily
Step-by-step explanation:
i did this question already
hope this helps
Answer:
it's C
Step-by-step explanation:
Solve and graph. Thank you so much.
Answer:
Step-by-step explanation:
-9 + b/4 >= -4
b/4 >= 5
b >= 20
the solution is d
slope (-5,12)(-17,4)
So the right answer is 4/11
please see attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
[tex] = \frac{2}{3} [/tex]
Step-by-step explanation:
[tex]slope = \frac{y1 - y2}{x1 - x2} \\ = \frac{12 - 4}{ - 5 - ( - 17)} \\ = \frac{8}{ - 5 + 17} \\ = \frac{8}{12} \\ = \frac{2}{3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Solve The System Of Equations
Answer:
x=4, y=-7
Step-by-step explanation:
A) -8x - 3y = -11 .(-5) -----> A) 40x + 15y = 55
B) -7x - 5y = 7 . (3) ------> B) -21x -15y = 21
A) + B) ----> 19x = 76 --------> x = 4
-8 . 4 - 3y = -11
-32 - 3y = -11
32 + 3y = 11
3y = 11 - 32
3y = -21
y = -7
PLEASE HELP!! if sec x=5/3 what is the value of b? NL=20 LM=3b angle of L is x degrees.
a. b=4
b. b=5
c. b=6
d. b=7
Answer:
a. b=4
Step-by-step explanation:
[tex]\sec \theta =\dfrac{1}{\cos \theta} = \dfrac{Hypotenuse}{Adjacent}[/tex]
From the attached triangle drawn below:
NL=20, LM=3b, [tex]\angle L=x^\circ[/tex]
[tex]\sec x =\dfrac{20}{3b}[/tex]
Since we are told that:
[tex]\sec x =\dfrac{5}{3}\\$Then:\\\dfrac{20}{3b} =\dfrac{5}{3}\\$Cross multiply\\5 \times 3b =20 \times 3\\15b=60\\$Divide both sides by 15\\15b \div 15 =60 \div 15\\b=4[/tex]
The correct option is A.
Answer:
B= 4
Step-by-step explanation:
I got it right on the test
Which function has a negative discriminant value?
Answer:
i believe that the answer is a but if its not that then it must be d
Step-by-step explanation:
sorry if i'm wrong
Answer:
The guy above me is wrong. The answer is B
Step-by-step explanation:
edge