Answer:
tan(A) = 12/5Step-by-step explanation:
Given a right angle triangle ABC.
If ∠BCA = 90°
the hypotenuse AB = 26
AC = 10 and BC = 24.
Using the SOH, CAH, TOA trigonometry identity, SInce we are to find tanA, we will use TOA. According to TOA;
Tan (A) = opp/adj
Taken BC as opposite side since it is facing angle A directly and AC as the adjacent;
tan(A) = BC/AC
tan(A) = 24/10
tan(A) = 12/5
Answer:
[tex]\ tan \ A = \dfrac{24}{10}[/tex]
Step-by-step explanation:
[tex]\sf Tan \ A = \dfrac{opposite \ side \ of \ angle \ A}{adjacent \ side \ of \ angle A}\\\\Tan \ A = \dfrac{BC}{AC}\\\\Tan \ A = \dfrac{24}{10}[/tex]
4. Use the formula to evaluate the series 3 + 6 + 12 + 24 +48 +96. Sn a₁(1 - r^) 1-r
Answer:
[tex]S_6=189[/tex]
Step-by-step explanation:
This is a geometric series with [tex]a_1=3[/tex] and common ratio [tex]r=2[/tex]. Using the formula [tex]\displaystyle S_n=\frac{a_1(1-r^n)}{1-r}[/tex] to find the sum of the first [tex]n=6[/tex] terms, we have:
[tex]\displaystyle S_n=\frac{a_1(1-r^n)}{1-r}\\\\S_6=\frac{3(1-2^6)}{1-2}\\\\S_6=\frac{3(1-64)}{-1}\\\\S_6=\frac{3(-63)}{-1}\\\\S_6=\frac{-189}{-1}\\\\S_6=189[/tex]
So, the given series works out to be [tex]S_6=189[/tex].
When the sun's angle of elevation is 76°, a tree casts an 18-foot shadow on the ground. Find the length of the tree to the nearest tenth of a foot.
Answer:
56.5 ft
Step-by-step explanation:
See the attached figure which represents the explanation of the problem.
We need to find the length of the tree to which is the length of AD
From the graph ∠BAC = 90° and ∠ABD = 76°, AB = 18 ft
At ΔABD:
∠BAD = ∠BAC - ∠DAC = 90° - 4° = 86°
∠ADB = 180° - ( ∠BAD + ∠ABD) = 180 - (86+76) = 180 - 162 = 18°
Apply the sine rule at ΔABD
∴[tex]\frac{AB}{SinD} =\frac{AD}{sinB}[/tex]
∴ 18/sin 18 = AD/sin 76
∴ AD = 18 * (sin 76)/(sin 18) ≈ 56.5 (to the nearest tenth of a foot)
So, The length of the tree = 56.5 ft.
The answer is 56.5 ft
The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The manufacturer also has fixed costs each month of $8000.
Find the revenue function R when x energy drinks are sold.
The graph below could be the graph of which exponential function?
A. F(x) = 3x
B. Fx) = 3 • (1.4)^x
O C. F(x) = 3•(0.4)^x
O D. F(x) = 3 • (-1.4)^x
Answer:
The correct option is B.
Step-by-step explanation:
The only given function that is an exponential decay function is;
B. Fx) = 3 • (1.4)^x
What is Exponential decay function?Now, the general formula for exponential decay function is;
f(x) = abˣ
where b is the decay factor.
here, we have,
we know that,
Now, the decay factor which we will call the base of the exponent must be greater than 1 .
and, we have,
Also, the exponent x must be negative to be called an exponential decay function.
so, from the given graph we get,
Looking at the given options, only Option B meets the criteria for an exponential decay function.
The only given function that is an exponential decay function is;
B. Fx) = 3 • (1.4)^x
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Calculate the diameter of the
circle.
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[tex]\diamond\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
[refer to attachment for question]
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
Remember, the radius is exactly one-half of the diameter, so if we need to find the diameter, we multiply the radius times 2:-
r=6.5m
d=13m
r=9.1 ft
d=18.2 ft
Good luck with your studies.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - -
Find the maximum accepted height for a basketball ring which must be positioned 3050 ± 6 mm above the floor.
__MM ??
Work Shown:
3050+6 = 3056
If you wanted the min height allowed, then you'd compute 3050-6
Note: 3050 mm = 10 feet approximately
(50 + brainiest if correct!)
From each square we can construct a second square, whose area is double that of the first square.
Construct from the square abcd below a second square, whose area is double the area of the square abcd.
Answer:
So the first thought would be to make the length and width twice the size of the original square but this would actually cause us to multiply the area by 4.
The second thought was to raise one of the sides to be twice the length or width and that would give us the correct answer since we are just multiplying it by 2. If side AB is the only one that can move then we would just extend that side twice the original length.
A packet of biscuits is shared between two people so that
one person gets three times as many as the other. Write
down the ratio involved. If there are 20 biscuits in the
packet, how many does each person get?
Answer:
Ratio 3 : 1
First person 5 biscuits
Second person 15 biscuits
Step-by-step explanation:
“one person gets three times as many as the other” means “the ratio is 3 to 1 or just 3 : 1”
………………………
Let x be the number of biscuits that the first person got then the second person should get 3x biscuits.
It’s clear that we have to solve this equation:
x + 3x = 20
Solving:
x + 3x = 20
⇔ 4x = 20
⇔ x = 20/4 = 5
Final answer:
First person: 5 biscuits
Second person: 3×5 = 15 biscuits
Find the mean and standard deviation for the data set
{6, 8, 7, 5, 10, 6, 9, 8, 4}
Please SHOW steps for everything
Answer:
See below
Step-by-step explanation:
The mean is simply adding up each data value and dividing your result by the number of data values:
[tex]\text{Mean}=\frac{6+8+7+5+10+6+9+8+4}{9}=\frac{63}{9}=7[/tex]
The standard deviation is calculated through finding the sum of the squared differences between the mean and each data point, and dividing that result by the number of data values, which we then take the square root of:
[tex]\text{Standard Deviation}=\sqrt{\frac{(6-7)^2+(8-7)^2+(7-7)^3+(5-7)^2+(10-7)^2+(6-7)^2+(9-7)^2+(8-7)^2+(4-7)^2}{9}}=\sqrt{\frac{10}{3}}\approx1.8257[/tex]
What this value means is that each data point is spread about 1.8257 apart from the mean. Standard deviation describes how dispersed the data is in relation to the mean.
whats the mean and median of 13, 1, 17, 6, 2, 111, 3?
Answer:
111
Step-by-step explanation:
To multiply 64 • 8.32, use the logarithmic equation:
1) log 72.32
2) log 64 + log 8.32
3) antilog 64 + antilog 8.32
4) (log 64)(log 8.32)
To multiply 64 • 8.32, use the logarithmic equation (2) log 64 + log 8.32
How to determine the equivalent equation?The product is given as:
64 * 8.32
As a general rule, the product of a and b can be calculated using:
a * b = antilog(log(a) +log(b))
This means that:
64 * 8.32 = antilog(log(64) +log(8.32))
Hence, we make use of the logarithmic equation (2) log 64 + log 8.32
Read more about logarithmic equation at:
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a ball has a diameter of 4 inches what is the volume
Answer:
268.08 cubic inches
Step-by-step explanation:
I'm sorry if this isn't helpful
please help me quick!
Answer:
transition 1 would be 5 to the right
transition 2 would be 1 down
Step-by-step explanation:
find the mode of the following data set.
help please
Answer:
Step-by-step explanation:
The most repeated number is 1,
Therefore, 1 is the anser
Need help asapppp plssss helppp meeee thanksss
Answer:
0.0000000673
Step-by-step explanation:
7.4*10^-8=0.000000074
6.7*10^-9=0.0000000067
0.000000074-0.0000000067
=0.0000000673=673*10^-10
Answer:
6.73 × [tex]10^{-8}[/tex]
Step-by-step explanation:
7.4 × [tex]10^{-8}[/tex]
6.7 × [tex]10^{-9}[/tex] = 0.67 × [tex]10^{-8}[/tex]
7.4 × [tex]10^{-8}[/tex] - 0.67 × [tex]10^{-8}[/tex] = ( 7.4 - 0.67 ) × [tex]10^{-8}[/tex] = 6.73 × [tex]10^{-8}[/tex]
When the temperature in London is 5 degrees celsius, the temperature in New York is - 7 degrees C. If the temperature in London falls by 6 degrees, what is the new lower temperature.
Answer:
the temperature in London would be -1 degrees as 5-6=-1
solve this question please
Answer:
Step-by-step explanation:
a) 1.8 kg in grams is 1800 g
b) If 6 toys weigh 1800g; then 1 toy weighs 300 g(6:1)
c) If 1 toy weighs 300 g, 4 toys weigh 1200 g and you convert in kg which is 1.2 kg
Please solve (15 points)
You’ll earn points just answer.. I know the answer already I’m just giving points
Answer:
10 inches
Step-by-step explanation:
2+2.25+2.25+2.25+2.5+2.75+2.75+3.25=10!!!!!!!!!
Answer:
thank youuu
Step-by-step explanation:
The sum of a number and its square is 6. Find the number
Answer: The sum of a number and its square is 6. Find the number
Step-by-step explanation:
n + n^2 = 6 n^2 + n - 6 = 0 factoring ___ (n + 3)(n - 2) = 0 n + 3 = 0 ___ n = -3 n - 2 = 0 ___ n = 2 two solutions
Answer:
n = -3, 2
Step-by-step explanation:
We're given:
The sum of a number and its square is 6Let the number be n.
The sum of a number and its square is 6⇒ [tex]n+n^2=6[/tex]
[tex]n+n^2=6[/tex]
⇒ Move everything to one side of the equation:
[tex]n+n^2-6=0[/tex]
⇒ Organize in [tex]ax^2+bx+c=0[/tex] form:
[tex]n^2+n-6=0[/tex]
⇒ Factor:
[tex]n^2-2n+3n-6=0\\n(n-2)+3(n-2)=0\\(n+3)(n-2)=0[/tex]
⇒ Use the zero-product property to find n:
[tex]n+3=0\\n=-3[/tex] or [tex]n-2=0\\n=2[/tex]
Solve 2(x + 1) = 2x + 2
Answer: ( −∞ , ∞)
Step-by-step explanation: Any value of x makes the equation true.
All real numbers
original equation
[tex]2(x+1)=2x+2[/tex]
distribute
[tex]2x+2=2x+2[/tex]
solve
[tex]2=2\\\\0=0[/tex]
the answer is 0.
Let the vector v have an initial point at (6,-7) and a terminal point at (4,-6). determine the components of vector v
The components of v are -2 and 1.
What are components of vector?
The components of a vector in two dimension coordinate system are usually considered to be x-component and y-component. It can be represented as, V = ([tex]v_x, v_y[/tex]), where V is the vector.
As, Vector v have an initial point at (6, -7) and a terminal point at (4, -6).
If initial point of vector [tex](x_1,y_1)[/tex] and terminal point is [tex](x_2,y_2)[/tex], then components of vector is
v= ([tex]x_2-x_1, y_2-y_1[/tex])
Initial point= (6,-7) and terminal point=(4,-6)
Then,
v= (4-6, -6-(-7))
v=(-2, 1)
Thus, the vector v=(-2, 1) have two components -2 and 1.
Learn more about vectors here:
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Calculus, complete the sentence below.
Answer:
If a= ⅓
Gradients are perpendicular if they are multipled they will equal to - 1
Need help fast thanks and god bless
Answer:
275.
Step-by-step explanation:
The gradient of the graph is 70/2 = 35 and it passes through the origin so we can write its equation as
y = 35x.
The gradient of the function represented by the the table is
(240-180) / (4-3) = 60
Ehen x = 3 y = 180 so when x = 0 y = 180 - 60 - 60 - 60 = 0 and the equation of this function is
y = 60x.
For the first equation when x = 11, y = 35*11 = 385.
For the second it is 60 * 11 = 660
So our answer is 660 - 385
= 275
1. Kayla and Heidi each buy a tiger. Kayla pays for her tiger using a $10 bill and two $1 bills. Heidi pays for her tiger using a $20 bill and a quarter. How much change does each girl receive? a tiger costs 11.23$
Answer:
Kayla gets $0.77 back, Heidi gets $9.02 back
Step-by-step explanation:
12 - 11.23 = 0.77 (how I got 12 is the $10 dollar bill and TWO $1 dollar bills)
20.25 - 11.23 = 9.02 (how I got 20.25 is the $20 dollar bill and the quarter which is worth $0.25)
A bakery sells vanilla cupcakes and chocolate cupcakes. It sold 276 vanilla cupcakes in a day. 8% of the cupcakes sold that day were chocolate. How many total cupcakes did the bakery sell that day?
ASSAP
Answer:
hello!!!
300 cupcakes
please read the explanation.. it always helps... trust me...
Step-by-step explanation:
alrighty here it goes...
okay.. so we start by reading the problem (duh) but also underlining the important numbers that we need. yes, it really is that simple, trust me....
okay so the percentage of chocoalte cupcakes was 8% and the amount of vanilla cupcakes was 276.
we start by taking 100% - 8% = 92% so the amount of vanilla cupcakes sold was 276 which is also 92% of the total amount of cupcakes.
so now we need to find out 92% of what number gets us 276.
the percentage formula (in this problem) should be as follows:
92/100 x (total amount of cupcakes) = 276
to solve for total amount of cupcakes you do 276 x 100 then you divide by 92 to get your answer (which is 300)
i hope this helps!!!
Answer:
300
Step-by-step explanation:
Q) Rewrite these newspaper headline in PERCENTAGE?
1.There was a one in two chance that the goldfish would swin to left.
Answer:
There was a 50% chance that the goldfish would swim to the left
Step-by-step explanation:
Percentage means "amount in one hundred".
[tex]\textsf{one in two}=\sf \dfrac{1}{2}=\sf \dfrac{1\times 50}{2 \times 50}=\dfrac{50}{100}=50\%[/tex]
Newspaper headline:
There was a 50% chance that the goldfish would swim to the left.
Is (-3, 1) a solution to this system of inequalities?
5x + 5y ≤ -19
10x 16y < 1
yes or no
Answer:
No
Step-by-step explanation:
5(-3)= -15
5(1)= 5
-15+5=-10
-10 is greater than -19 not less than or equal too.
Hope this helps!
PLS HELP ASAP
Solve the following system of equations.
x + y = 3
2x + 2y = 6
A) (1.5, 1.5)
B) (0, 3)
C) infinite number of solutions
D) no solution
Answer:
C.
Step-by-step explanation:
x + y = 3
2x + 2y = 6
Multiply the first equation by 2:
2x + 2y = 6
This is the same equation as the second one.
So there are an infinite number of solutions.
Read each item carerur 1. What is the rule of the sequence: 7, 13, 19, 25, 31? A. Add 6 B. Subtract 6 C. Multiply by 2 D. Multiply by 3
Answer:
A.
Step-by-step explanation:
it’s add 6 because, 6 + 7 = 13 and 13 + 6 = 19 and it keeps on continuing this is how I know I am correct.
Answer:
the answer is A) Add 6
Step-by-step explanation:
you add so 7 plus 6 is 13 and 13 plus 6 is 19 and so it continues
hope this helps!!
