Answer:
B = 34.77°
Step-by-step explanation:
For this problem you are given all three side lengths and asked to find an angle. To do this you can use the law of cosines which is written:
[tex]b^{2} =a^{2} +c^{2} -2ac Cos(B)[/tex]
This can be rearranged to find the angle B:
[tex]b^{2} -a^{2} -c^{2} /-2ac = Cos(B)[/tex]
With lowercase letters being sides and uppercase being angles.
We simply plug in the sides and solve:
[tex]4^{2} -6^{2} -7^{2}/-2*6*7= Cos(B)[/tex]
0.8214 = Cos (B)
Then you use inverse cosine to get angle B alone.
B = 34.77°
find the 9th and 15th terms of the following geometric sequence 2, -4, 8, -16
Step-by-step explanation:
given the geometric sequence 2, -4, 8, -16, ...
a1 = 2
r = -4/2 = -2
find : a9 and a15
solutions:
an = a1. r^(n-1)
=> a9 = 2. (-2)^(9-1)
= 2. (-2)^8
= 2. 2^8
= 2^9
= 512.
=> a15 = 2. (-2)^(15-1)
= 2. (-2)^14
= 2. 2^14
= 2^15
= 32,768
Step-by-step explanation:
Hey there!
The given geometric sequence is: 2, -4, 8, -16.
The;
a1 = 2
Common ratio (r) = T2/T1
= -4/2
= -2
Now;
Use general formula of geometric sequence;
[tex]tn = {a1.r}^{n - 1} [/tex]
Where, "a1" is first term, "n" is no.of terms and "r" is common ratio.
Then;
[tex]t9 = 2 \times { (- 2)}^{9 - 1} [/tex]
or, t9 = 2*256
Therefore, t9 = 512.
Again;
[tex]t15 = 2. { (- 2)}^{15 - 1} [/tex]
or, t15= 2*16384
Therefore, t15 = 32768.
Hope it helps!
A triangle ABC is right angled at A, AL is perpendicular to BC. Prove that angle BAL= angle BCA.
Step-by-step explanation:
triangle BCA=BAL bcoz Angle BCA= Angle BAL
Circle w has a radius of 20 in and central right angle. VWX find the length of VX. Leave answer in terms of pi
The arc length is 10 Pi
(I don't know for sure, but its what I got)
A heel travels 850 miles in 28 gallons of gas. How many miles does it travel in one gallon of gas
Answer:
850/28=30 miles a gallon
Step-by-step explanation:
mark as brainlist
PLEASE HELP SUMMER SCHOOL!!!!
Ed is 7 years older than Ted. Ed’s age is also times Ted’s age. How old are Ed and Ted?
A.
Ted is 15 years old, and Ed is 22 years old.
B.
Ted is 14 years old, and Ed is 21 years old.
C.
Ted is 13 years old, and Ed is 20 years old.
D.
Ted is 12 years old, and Ed is 19 years old.
Answer:
EXPLAINED ON THE ATTACHED
How would the one-step equation x/5 = 5 be solved?
Multiply both sides by 1/5
Multiply both sides by the reciprocal of 1/5
Divide 5 by both sides
Divide one side by 5
Answer:
2nd option
Step-by-step explanation:
Given
[tex]\frac{x}{5}[/tex] = 5 ( multiply both sides by 5, the reciprocal of [tex]\frac{1}{5}[/tex] to clear the fraction )
x = 25
Choose the graph of y = -3 sin x.
Step-by-step explanation:
the graph should look something like this
AABC has vertices at A(5,1), B(-3,1), and C(-2,5).
Point D is located on the intersection of the altitude and AB, in such a way that D has coordinates at
(-2,1).
Find the values of x and y.
Answer:
since y is across from 60 so
y=60
and on the bottom it is 15 so
x+3=15
x=12
Hope This Helps!!!
How many solutions does the equation 5X +10 equals 5X - 8 have
A: zero
B: one
C:Two
D: infinity many
Answer:
zero
Step-by-step explanation:
5x+10 = 5x-8
5x-5x = -8-10
0 = -18
so zero
Find the 66th term of the arithmetic sequence 25, 10, -5, ...
Answer:
1000
Step-by-step explanation:
Given data
we have the sequence
25, 10, -5, ...
we want to find the 66th term, let us apply the formula
an = a + (n – 1)d
a= 25
n= 66
d= 15
substitute
a66= 25+(66-1)15
a66= 25+(65)*15
a66= 25+975
a66= 1000
Hence the 66th term is 1000
the sum of all the exponents on all the variables of a term
plsss answer
Answer:
Answer: for polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial
Work out the area of the shaded shape.
Hi there!
[tex]\large\boxed{77m^2}}[/tex]
We can divide the figure into 3 rectangles.
Area of top rectangle:
5 × 5 = 25m²
Long rectangle:
14 × 3 = 42m²
Bottom rectangle:
2 × 5 = 10m²
Add up the areas:
10 + 42 + 25 = 77m²
Your vacation cabin on the lake has three rooms. The bathroom is 12' X 6', the bedroom is 14' X 18' and the great room is 20' X 30'. The ceiling height is 10'. What is the total volume of your cabin? Group of answer choices 9420 Cubic Feet 9240 Cubic Feet 9240 Square Feet 9420 Square Feet
Answer: [tex]9240\ ft^3[/tex]
Step-by-step explanation:
Given
Dimension of the bathroom is [tex]12'\times 16'[/tex]
Dimension of the bedroom is [tex]14'\times 18[/tex]
Dimension of the great room is [tex]20'\times 30'[/tex]
Height of the ceiling is [tex]h=10'[/tex]
Total area of the cabin
[tex]\Rightarrow A=12\times6+14\times 18+20\times 30\\\Rightarrow A=72+252+600\\\Rightarrow A=924\ ft^2[/tex]
Volume of the cabin is [tex]V=A\times h[/tex]
[tex]\Rightarrow V=924\times 10\\\Rightarrow V=9240\ ft^3[/tex]
Why does it say your phone is being attacked and then said something with 26 when I go on a website is it lying or do I have a virus?
Answer:
If you go to a website that has a red (or orange) triangle with an exclamation mark next to the link, it's an untrusted site. The things you list (your phone is being attacked and then said something with 26..) are likely to be scam ads (probably viruses). Therefore, I do not recommend you to click the ads or enter that site again.
The question is in the photo
Answer:
Step-by-step explanation:
This is a right triangle because angle V is 90. Draw out a right triangle and put V at the 90 degree angle. It doesn't matter where you put U or T; you get the same cos value for T regardless of how you place your other 2 angles. The things you need to know are that UT is the hypotenuse of the triangle, side VU is across from angle T, and side TV is across from angle U.
The cos ratio is side adjacent to the reference angle over the hypotenuse.
Our reference angle is T, so we are looking for the side next to T that is NOT the hypotenuse. This side measures 33; the hypotenuse measures 65, so the tangent ratio of T is
[tex]tanT=\frac{33}{65}[/tex]
For each function below, identify and enter the percent rate of change per unit, t. Round to the nearest tenth of a percent.
Then use the drop-down menus to classify each as exponential growth or decay
The percentage rate of change of the given functions is given by the
derivative of their natural logarithm.
Responses:
[tex]f(t) = 1.18^t[/tex]
16.6%, exponential growth[tex]g(t) = 2^{-2 \cdot t}[/tex]
-138.6%, exponential decay[tex]h(t) = 1.19^{\frac{t}{10} }[/tex]
1.7%, exponential growth[tex]k(t) = 0.13^t[/tex]
-204%, exponential decayWhich method is used to determine the percentage rate of change?The percentage rate of change can be presented as follows;
[tex]Percentage \ rate \ of \ change = \mathbf{100 \times \dfrac{d}{dt} ln \left(f(t)\right)}[/tex]
[tex]f(t) = \mathbf{ 1.18^t} \ gives;[/tex]
[tex]100 \times \dfrac{d}{dt} \left( ln \left(1.18^t\right) \right) = \mathbf{ 100 \times ln(1.18)} \approx \underline{16.6\%}[/tex], exponential growth[tex]g(t) = \mathbf{2^{-2 \cdot t} }\ gives;[/tex]
[tex]100 \times \dfrac{d}{dt} \left( ln \left(2^{-2 \cdot t}\right) \right) = \mathbf{ 100 \times -2 \times ln(2)} \approx \underline{ -138.6 \%}[/tex] , exponential decay
[tex]h(t) = \mathbf{1.19^{\frac{t}{10} } }\ gives;[/tex]
[tex]100 \times \dfrac{d}{dt} \left( ln \left(1.19^{\frac{t}{10} }\right) \right) = \mathbf{ 100 \times \dfrac{10 \cdot ln(1.19)}{100}} \approx 1.7 \%[/tex], exponential growth
[tex]k(t) = \mathbf{ 0.13^t} \ gives;[/tex]
[tex]100 \times \dfrac{d}{dt} \left( ln \left(0.13^t }\right) \right) = \mathbf{100 \times ln(0.13)}\approx -204 \%[/tex], exponential decay
Learn more about exponential functions here:
https://brainly.com/question/14325265
What is the sum and classification of StartFraction 3 Over 20 EndFraction + StartRoot 10 EndRoot?
3.31227766..., irrational
3.31227766..., rational
18.16227766..., irrational
18.16227766..., rational
9514 1404 393
Answer:
3.31227766..., irrational
Step-by-step explanation:
3/20 +√10 = 0.15 + 3.16227766017...
The root of 10 is irrational, so adding that to a rational number will give an irrational sum.
The sum is about 3.31227766017..., an irrational number.
Answer:
A
Step-by-step explanation:
Jill has just moved to a new town and wants to share plates of baked goods with her neighbors. She has 20 cookies and 12 brownies to share, and wants to split them equally among the plates with no food left over. What is the greatest number of plates she can make to share?
Answer:
4
Step-by-step explanation:
The greatest number of plates Jill can split the 20 cookies and 12 brownies into can be determined by calculating the highest common factor and 20 and 12
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 20 = 1, 2,4, 5, 10, 20
Find the value of x that makes A || B
HELPPPPP
Answer:
x = 90
Step-by-step explanation:
If lines A and B were parallel , then
∠ 1 and ∠ 4 are corresponding angles and congruent, so
3x - 160 = x + 20 ( subtract x from both sides )
2x - 160 = 20 ( add 160 to both sides )
2x = 180 ( divide both sides by 2 )
x = 90
What is the distance between
(
−
5
,
−
5
)
(−5,−5)left parenthesis, minus, 5, comma, minus, 5, right parenthesis and
(
−
9
,
−
2
)
(−9,−2)left parenthesis, minus, 9, comma, minus, 2, right parenthesis?
Answer:
do you have a pic of the problem
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
the answer is the sqare rute of 25 which is 5
The line y = 2x + 6 cuts the x-axis at A and the y-axis at B. Find
(a) the length of AB,
(b) the shortest distance of O to AB, where O is the origin (0,0)
Answer:
(a)
[tex]3 \sqrt{5} [/tex]
(b)
[tex] \frac{6}{ \sqrt{5} } [/tex]
Step-by-step explanation:
A(-3,0)
B(0,6)
[tex]d = \sqrt{{( - 3 - 0)}^{2} + {(0 - 6)}^{2} } = \sqrt{9 + 36} = 3 \sqrt{5} [/tex]
[tex]d = \frac{ax0 + by0 + c}{ \sqrt{ {a}^{2} + {b}^{2} } } [/tex]
2x-y+6=0
a=2, b=-1, c=6
x0=0, y0=0
[tex]d = \frac{6}{ \sqrt{4 + 1} } = \frac{6}{ \sqrt{5} } [/tex]
Find the measure of the missing angle using the exterior angle sum theorm
Answer:
r = 30°
Step-by-step explanation:
According to the Exterior Angle Sum Theorem, the exterior angle, which is 90°, is equal to the 2 interior angles, which are 60° and r°. We know that the angle next to the exterior angle is 90°, and since all angle sums add up to 180°, r = 30°.
2x^2 - 4x + 5 x = -3
The graph of y=x^3+x^2-6x is shown....
hello,
" a turning point is defined as the point where a graph changes from either increasing to decreasing, or decreasing to increasing"
a)
[tex]y=x^3+x^2-6x\\\\y'=3x^2+2x-6=0\\x=\dfrac{-2-\sqrt{76} }{6} \approx{-1.786299647...}\\or\\x=\dfrac{-2+\sqrt{76} }{6} \approx{1.1196329...}\\[/tex]
b)
Zeros are -3,0,2.
Sol={-3,0,2}
The solution of the graph function y=x³+x²-6x are -3 , 0 and 2
What is graph?The link between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of certain points and the connecting lines. It doesn't matter how long the lines are or where the points are located. A node is the name for each element in a graph.
We have the function
y=x³+x²-6x
now, equating it to 0
x³+x²-6x = 0
x² + x - 6= 0
x² - 3x + 2x -6 =0
x(x -3) + 2(x -3)
x= 3 and -2
Now, ew can see from the that the equation is touching the x-axis at three points and it will represent three zeroes of the equation.
So, the solution of the graph are -3 , 0 and 2
Learn more about graph here:
https://brainly.com/question/17267403
#SPJ2
Evaluate the expression. 24.32
2^4×3^2 = 144
___________
Answer:
144 would be the answer.
Step-by-step explanation:
Question:- [tex]2^{4}[/tex] · [tex]3^{2}[/tex]
[tex]2^{4}[/tex] = 2 x 2 x 2 x 2
= 4 x 2 x 2
= 8 x 2
= 16
[tex]3^{2}[/tex] = 3 x 3
= 9
So, [tex]2^{4}[/tex] · [tex]3^{2}[/tex] = 16 x 19
= 144
a) Work out the value of 10
Step-by-step explanation:
√10= 1.414×2.236
= ±3.162
hope it is helpful to you ☺️
If a car is moving on a straight line with a velocity of 40 m/s and it changes its velocity to 60 m/s in 4 seconds, calculate its acceleration.
Answer:
5m/s²
Step-by-step explanation:
Given :-
Initial Velocity = 40m/s Final velocity = 60 m/sTime = 4sTo Find :-
The acceleration .Solution :-
We know that the rate of change of velocity is called acceleration. Therefore ,
[tex]\sf\implies a = v - u / t \\ [/tex]
[tex]\sf\implies a = 60m/s - 40m/s/ 4 \\ [/tex]
[tex]\sf\implies a = 20m/s \div 4 \\[/tex]
[tex]\bf\implies a = 5m/s^2[/tex]
Given that is a standard normal random variable, find for each situation (to 2 decimals). a. The area to the left of is . (Enter negative value as negative number.) b. The area between and is . c. The area between and is . d. The area to the left of is . e. The area to the right of is . (Enter negative value as negative number.)
Answer:
-0.80
1.66
0.26
2.56
-0.50
Step-by-step explanation:
The values are the probability values either to the right or left of a given z - value ;
The Z - values could be obtained using the standard normal distribution table or a calculator :
Using the Z probability calculator ;
Area to the left of z is 0.2119
1.)
P(z < z) = 0.2119
z = - 0.8
2.)
Area between - z and z = 0.9030
Area to the left of z = 0.9030 plus
Area to the right of z = (1 - 0.9030) / 2 = 0.097/2 = 0.0485
(0.9030 + 0.0485) = 0.9515
P(z < z) = 0.9515
z = 1.66
3.)
Area between - z and z = 0.2052
Area to the left of z = 0.2052 plus
Area to the right of z = (1 - 0.2052) / 2 = 0.7948/2 = 0.3974
(0.2052 + 0.3974) = 0.6026
P(z < z) = 0.6026
z = 0.26
D.)
The area to the left of z is .9948
P(Z < z) = 0.9948
z = 2.562
E.)
The area to the right of z is .6915.
P(Z < z) = 1 - 0.6915
P(Z < z) = 0.3085
z = - 0.5
Find the circumference of this circle
using 3 for TT.
C = ?
[tex]{ \bf{ \underbrace{Given}}}[/tex]:
Diameter of the circle "[tex]d[/tex]" = [tex]36[/tex]
Value of [tex]π[/tex] = [tex]3[/tex]
[tex]{ \bf{ \underbrace{To\:find}}}[/tex]:
The circumference "[tex]C[/tex]" of the circle.
[tex]{ \bf{ \underbrace{Solution }}}[/tex]:
[tex]\sf\pink{The\:circumference \:"C"\:of\:the\:circle\:is\:108.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:πd }[/tex]
[tex] = 3 \times 36[/tex]
[tex] = 108[/tex]
Therefore, the circumference of the circle is [tex]108[/tex].
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
Answer:
[tex]\Longrightarrow: \boxed{\sf{108}}[/tex]
Step-by-step explanation:
Apply the formula for the circle's circumference.
[tex]\text{Circumference circle formula:}[/tex]
[tex]\Longrightarrow: \sf{C=\pi d}[/tex]
[tex]\Longrightarrow:\sf{C=?}\\\\\Longrightarrow:\sf{\pi =3}\\\\\Longrightarrow:\sf{d=36}[/tex]
Multiply.
[tex]\sf{3*36=\boxed{\sf{108}}[/tex]
Therefore, the correct answer is 108.I hope this helps! Let me know if you have any questions.