Answers
Answer:
x = 67° (nearest whole degree)
Step-by-step explanation:
Sine Rule
[tex]\sf \dfrac{sin(A)}{a}= \dfrac{sin(B)}{b}= \dfrac{sin(C)}{c}[/tex]
where A, B and C are the angles, and a, b and c are the sides opposite the angles
Given information
From inspection of the triangle:
A = 38°a = 12B = x°b = 18Finding x:
Substitute given values into the formula and solve for x:
[tex]\sf \implies \dfrac{sin(38)}{12}= \dfrac{sin(x)}{18}[/tex]
[tex]\sf \implies 18\cdot\dfrac{sin(38)}{12}= sin(x)[/tex]
[tex]\sf \implies sin(x)=\dfrac32sin(38)[/tex]
[tex]\sf \implies x=sin^{-1}\left(\dfrac32sin(38)\right)[/tex]
[tex]\sf \implies x=67.44208077...[/tex]
Final Solution
x = 67° (nearest whole degree)
Answer:
∠x = 67°
Step-by-step explanation:
From the Law of Sines,
we know that :
sin(A) / a = sin(B) / aHere we have :
a = 12b = 18∠A = 38°∠B = x°On substituting,
sin38° / 12 = sinx° / 18sinx° = 3/2 x sin38°x = 3/2sin38° x sin⁻¹∠x = 67°Related Questions
∠C and ∠D are complementary.
Let m∠C=(5x)° and m∠D=(7x−6)°.
What is the value of x?
Enter your answer in the box. 10 points!!
Answers
Answer:
x = 8
Step-by-step explanation:
The sum of the measures of two complementary angles is 90°.
m<C + m<D = 90°
5x + 7x - 6 = 90
12x = 96
x = 8
3x + y = 4 6x + 4y = 6 equivalent equation and solution
Answers
Answer:
x = 5/3 , y = -1
Step-by-step explanation:
Given:
[tex]\begin{bmatrix}3x+y=4\\ 6x+4y=6\end{bmatrix}[/tex]
Solve:
[tex]\mathrm{Substitute\:}x=\frac{4-y}{3}[/tex]
[tex]\begin{bmatrix}6\cdot \frac{4-y}{3}+4y=6\end{bmatrix}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\begin{bmatrix}2y+8=6\end{bmatrix}[/tex]
[tex]\mathrm{For\:}x=\frac{4-y}{3}[/tex]
[tex]\mathrm{Substitute\:}y=-1[/tex]
[tex]x=\frac{4-\left(-1\right)}{3}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x=\frac{5}{3}[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=\frac{5}{3},\:y=-1[/tex]
3(5/3) + -1
5-1 = 4
True
6(5/3) + 4(-1)
10 -4 = 6
True
~lenvy~
WILL GIVE BRAINLIEST, THANKS AND 5 STARS! PLEASE HELP! LOTS OF POINTS
Sam kicks a ball off of a rooftop. After t seconds, its height, h (in feet), is given by the formula
h (t) = -16t2 + 64t + 80.
*NOTE: Complete this without using graphing features on your calculator, and show all work for credit. You may type out your work or upload it in the next question.
a. What is the maximum height reached by the ball?
b. When did the ball reach its maximum height?
c. When will the ball hit the ground? (Do algebraically)
d. What is the height of the ball after 1 second?
(THIS IS A 4 PART QUESTION, PLEASE DO ALL PARTS!!!) PLEASE GIVE INDEPTH EXPLANATION FOR ALL PARTS!
Answers
Answer:
(a) 144 ft
(b) 2 s
(c) 5 s
(d) 128 ft
Step-by-step explanation:
[tex]h(t) = -16t^2 + 64t + 80[/tex]
Part (a)
To find the turning point of the parabola:
1. differentiate the function:
[tex]\implies h'(t) = -32t + 64[/tex]
2. Set it to zero and solve for t:
[tex]\implies h'(t) =0[/tex]
[tex]\implies -32t + 64=0[/tex]
[tex]\implies 32t = 64[/tex]
[tex]\implies t=2[/tex]
3. Input found value of t back into the function and solve for h:
[tex]\implies h(2) = -16(2)^2 + 64(2) + 80=144[/tex]
Therefore, the maximum height reached by the ball is 144 ft
Part (b)
As found in part (a), the maximum height is reached when t = 2, so the ball reached its maximum height at 2 seconds.
Part (c)
The ball will hit the ground when h(t) = 0
1. Set the function to zero
[tex]\implies h(t)=0[/tex]
[tex]\implies -16t^2 + 64t + 80=0[/tex]
2. Solve for t:
Divide both sides by 16
[tex]\implies -t^2 + 4t + 5=0[/tex]
[tex]\implies t^2 - 4t - 5=0[/tex]
Factor:
[tex]\implies t^2 +t-5t - 5=0[/tex]
[tex]\implies t(t+1)-5(t+1)=0[/tex]
[tex]\implies (t+1)(t-5)=0[/tex]
Therefore:
[tex](t+1)=0 \implies t=-1[/tex]
[tex](t-5)=0 \implies t=5[/tex]
As time is positive, t = 5
So the ball will hit the ground at 5 seconds.
Part (d)
To find the height of the ball after 1 second, input t = 1 into the function and solve for h:
[tex]\implies h(1) = -16(1)^2 + 64(1) + 80=128[/tex]
Therefore, the height of the ball after 1 second is 128 ft
--------------------------------------------------------------------------------------
Parts (a) & (b) - alternative method
Rewrite the function in vertex form by completing the square.
Set the function to zero:
[tex]\implies-16t^2 + 64t + 80=0[/tex]
Subtract 144 from both sides:
[tex]\implies -16t^2+64t-64=-144[/tex]
Factor out -16:
[tex]\implies -16(t^2 - 4t +4)=-144[/tex]
Factor expression in brackets:
[tex]\implies -16(t-2)^2=-144[/tex]
Add 144 to both sides:
[tex]\implies -16(t-2)^2+144=0[/tex]
Therefore:
[tex]\implies h(t)=-16(t-2)^2+144[/tex]
The maximum height is the y-value of the vertex.
The vertex is (2, 144) so the maximum height is 144 ft.
The time the ball reached the max height is the x-value of vertex.
So the time then the ball reached the maximum height is 2 s
Jake is saving for a new tablet. It costs $250, and he has $100. He earns $5 per week for doing chores. Jake wants to figure out how many weeks it will take for him to have at least enough money to buy a new tablet. Write an inequality and solve it to determine the number of weeks it will take.
Answers
Answer: 250 ≤ 100+5x
150≤5x divide by 5
30≤x
It will take 30 weeks to earn enough.
Step-by-step explanation:
hurry please im running out of time
ill give brainliest
Answers
Answer:
Step-by-step explanation:
16 ticks, the pointer is on 12. there fore it is the second answer.
2 3/4 lb
A 70kg person jumps off a staircase. They are going 5 m/s just before they hit the ground. How high up where they.
Answers
Answer:
0.02 seconds
Step-by-step explanation: A 70kg man jumps 1.00 meters down onto a concrete walkway. His downward motion stops in 0.02 seconds.
Answer:
1.25m
Step-by-step explanation:
v=u+gt
5=0+10t
5=10t
t=0.5s
s=ut+1/2gt^2
=0+(0.5×10×(0.5)^2)
=1.25m
find the value of x in the triangle shown below
Answers
Answer:
D
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of thesquares on the other two sides, that is
x² + 8² = 9²
x² + 64 = 81 ( subtract 64 from both sides )
x² = 17 ( take square root of both sides )
x = [tex]\sqrt{17}[/tex]
Answer:
√17 (Option D)⠀
Step-by-step explanation:
This is Right Angled Triangle.⠀
We'll solve this using the Pythagorean Theorem.
⠀
Let,
x be BC, where BC is the Perpendicular.8 be AB, where AB is the Base.9 be AC, where AC is the Hypotenuse.⠀
We know that,
[tex]{ \longrightarrow \pmb{\qquad \: (AB) {}^{2} +( BC) {}^{2} = (AC) {}^{2} }}[/tex]
[tex]{ \longrightarrow \sf \qquad \: (8) {}^{2} +( x) {}^{2} = (9) {}^{2} } [/tex]
[tex]{ \longrightarrow \sf \qquad \: ( x) {}^{2} = (9) {}^{2} - (8) {}^{2}} [/tex]
[tex]{ \longrightarrow \sf \qquad \: ( x) {}^{2} = 81 - 64} [/tex]
[tex]{ \longrightarrow \sf \qquad \: ( x) {}^{2} = 17} [/tex]
[tex]{ \longrightarrow \it \qquad \pmb {x = \sqrt{17 \: \: } } }[/tex]
⠀
Therefore,
The value of x is √17 .Henry begins a savings account with $500. The savings account accumulates 2.5% annual interest based on the
equation Vh= 500(1.025), where Vh is the value of the account after t years. Andres begins a savings account three
years later with the same initial amount of money at the same interest rate. Which equations represent the value of
Andres's account after t years?
A.
B.
C.
D.
Answers
Andre's account after t years is [tex]V_h=538.45(1.025)^t[/tex] since is option C.
Amount at the year endThe Amount accumulated at the end of a interest year is the sum of the principla amount and the interest gained on the principal amount.
How to find amount at the end of interest year?As Andres start the savings account after 3 years so, the equation representing the value of Andre's account after t years is-[tex]v_h=500(1.025)^{t-3}[/tex].
Also, the amount accumulated in the mean 3 years will be-
[tex]A=500(1.025)^3[/tex]
=$538.45
Hence, another way of writing the equation representing the value of Andre's account after t years is-[tex]V_h=538.45(1.025)^t[/tex]
As a result, option C is the correct answer.
Learn more about interest here: https://brainly.com/question/25545513
#SPJ2
will give brainliest, pls help ASAP!
Answers
Step-by-step explanation:
2 × 10⁸ - 7 × 10⁷
= 200,000,000 - 70,000,000
=130,000,000
= 1.3 × 10⁸
Answer:
130 million
Step-by-step explanation:
200 million in N
70 million in F
200-70 = 130 million
Hope this helps have a great day
Question 4: there are 7 frosted donuts and 43 not frosted. what is the
ratio of frosted to total donuts?
a) 7 to 43
b) 50 to 7
c) 43 to 7
d) 7 to 50
Answers
Answer:
answer is a
Step-by-step explanation:
ur welcome
Help me someone please
Answers
Answer:
150
Step-by-step explanation:
since a circle is 360 degrees, add up all of the other degrees and then subtract from 360
Let f(x)=4x^2-3 and g(x)=-x^2+2.Find f+g and state the domain. Then evaluate the sum when x=2
Answers
Answer:
f+g = 3x^2-1. domain = all real numbers. then plug in two wherever there is an x.
f(x)=4*2^2-3, which equals 13
g(x)= -2^2+2, which equals -2
add
f+g when x=2 is 11
Step-by-step explanation:
i really need
help on this work it is really difficult help plsss
Answers
Answer: 105 square feet
Step-by-step explanation: The answer is 105 square feet because find the area of the pool by multiplying 12 and 20 to get 240. You then want to find the area of the total space. Add 3 to 12 and add 3 to 20. Then multiply 23 by 15 to get 345. You then want to subtract 345 - 240 to get rid of the extra space to get your answer of 105.
solve pls brainliest
Answers
Answer:
No, No, Yes, Yes, Yes.
Step-by-step explanation:
A integer is a whole number. 1, 2, 3, etc.
Answer:
Only -46 is an integer number and others are not.
Step-by-step explanation:
An integer is a whole number but not a fractional number that can be positive, negative, or zero.
In this chart -46 is an integer cause it is a whole number and -1/2, 57.68, 24/6, 9/3 are not integers cause they are a fraction.
Solve the following equation for x 13x2 - 5 =0
Answers
Step-by-step explanation:
if its x13^2-5=0 then 5/169
but if its x13*2-5=0 then 1.07
The numbers in this sequence increase by 40 each time 30, 70, 110, 150. The sequence is continued with the same rule. Which number in the sequence will be closest to 300?
Answers
The value in the sequence closest to 300 is 310
Arithmetic SequenceArithmetic sequence is a sequence where each term increases or decreases by addition or subtraction of a constant term
the first term a = 30
common difference, d = 40
which term is closest to 300 we solve like this
300 / 40 = 7.5 say 7
the 7th term, T7 is solved by
T7 = a + ( n - 1 ) d
T7 = 30 + ( 7 - 1 ) 40
T7 = 30 + 240
T7 = 270
checking for the 8th term to confirm the nearest
T8 = T7 + d = T7 + 40
T8 = 270 + 40
T8 = 310
therefore the 8th term is closest and the value is 310
Read more on Arithmetic sequence here:
https://brainly.com/question/7882626
https://brainly.com/question/6561461
Given five vertices, how many different graphs can be made? will give BRAINLIEST
Answers
Answer:
Where is the question?
Step-by-step explanation:
I don't see the graphs.
please help i am confused.
Answers
Answer:
87.5 percent
Step-by-step explanation:
80 passed the first, 70 passed the second. 7/8 passed both. 7/8 as a percentage is 87.5.
Answer:
C. 87.5%
Step-by-step explanation:
[tex]P(A|B)[/tex]
this is what you are trying to find.
P(A | B) can be found by dividing the percentage who passed both, by the percentage who passed the first.
70/80 = 0.875
multiply by 100 to get percentage instead of decimal
87.5
Pls help i will give 5 starts and brainliest question is down below 9:22
Answers
Answer:
C) 390
Step-by-step explanation:
Area of Blue:
18 × 25 = 450 in
Area of White:
6 × 10 = 60 in
450 - 60 = 390
Therefore, 390 sq in is the correct answer.
pleaseeee check picture its about finding area of triangle.
Answers
Answer:
13.75 is your answer
Step-by-step explanation:
find area of whole triangle 5.5*7*1/2=19.25
Find area of blank spot 5.5*2*1/2=5.5
Subtract 19.25-5.5=13.75
Gabby is working on reducing traffic in her town. Last week, she tracked how many cars
drove down Main Street each hour. This box plot shows the results.
Cars per hour
20
60
100
140
180
120
1) What percent of the time did Main Street have 100 or more cars per hour?
Answers
The box plot represents the rate of cars in the Main Street per hour
25 percent of the time, the Main Street have 100 or more cars per hour
How to determine the proportion of the boxplot?From the box plot, we have the following parameter:
The upper quartile of the boxplot is 100
This means that:
Q3 = 100
The upper quartile is the 75% dataset
The actual percentage is then calculated as:
Actual = 100% - 75%
This gives
Actual = 25%
Hence, 25 percent of the time, the Main Street have 100 or more cars per hour
Read more about boxplots at:
https://brainly.com/question/14277132
can some one answer this question please show work
Answers
When you reflect across the Y axis, the Y value remains the same and the x value becomes opposite.
Answer: (5,-3)
Can someone help me out with this?
What is the value of x?
Enter your answer in the box.
Answers
Answer:
x = 4Step-by-step explanation:
x has the same value as RT since they are equal sides of the isosceles triangle.
RT is also the hypotenuse of ΔRST - 30°×60°×90° right triangle.
Acoording to the property of such triangles, the ratio of sides is:
a : b : c = 1 : √3 : 2We have:
b = 2√3 and c = RTUse the ratio to find the lenght of RT
2√3 : RT = √3 : 2RT = 2*2√3/√3RT = 4So the value of x is 4 units
Find RT
sin60=2√3/RT√3/2=2√3/RTRT=4√3/√3RT=4Now
tan45=x/4x=410. To calculate the area of a rectangle, you multiply the length by the width. If the
length of a rectangle is (2x + 1) and the width is (x - 1), what is the area of the
) -
rectangle?
A. 3x
B. 3x2 - 1
C. 2x2 - x - 1
D. X - 1
Answers
Answer:
Multiply those side lengths using the F.O.I.L method (first-outer-inner-last). Write it longhand then simplify if that’s what is needed.
(x+5)(x-5) = x^2 -5x + 5x -25
the -5x and + 5x cancel each other so it simplifies to x^2 - 25 units squared.
PLEASE HELP AS I SAID I HAVE A F IN MATH AND I HAVE LIKE 6 OTHER SI TO DO PLEASE ANSWER ALL OF THEM
The prism below is made of cubes which measure of a foot on one side. What is the volume?
Note: Figure is not drawn to scale.
A.
B.
C.
D.
Answers
Answer: 32
Step-by-step explanation: count one row and then multiply that by 4 And then it equals 32
A cylindrical-shaped container is 8 in. tall with a diameter of 6 in. How much water could this container hold?
A 24pie cubic inches
B 72pie cubic inches
C 216pie cubic inches
D 288pie cubic inches
Answers
Answer:
72pi cubic inches.
Step-by-step explanation:
area = pi r²
r = d / 2
r = 3
3² = 9
9pi x 8 = 72pi.
their sum is -11 and difference is 41
Answers
Answer:
15 and -26.
Step-by-step explanation:
Answer:
15 and -26
Step-by-step explanation:
just bc
50 points, PLEASE HELP
i have a test in 2 hours i really need to know how to do this problem
25g^2 - 15gh - 28h^2
Answers
Answer:
the answer is (5g+4h)(5g-7h)
Step-by-step explanation:
25g^2-15gh-28h^2
=(25g^2+20gh)+(-35gh-28h^2)
=5g(5g+4h)-7h(5g+4h)
=(5g+4h)(5g-7h)
-
Find the equation of the line that
is perpendicular to y = -2x - 9 and
contains the point (8, -4).
Answers
Answer:
[tex]y=\frac{1}{2} x-8[/tex]
Step-by-step explanation:
The final answer is in the slope-intercept form, which is y=mx +c, where m is the slope and c is the y-intercept.
The slope of a perpendicular line is the negative reciprocal of the slope of the given line (the line it is perpendicular to). Thus, let's find the slope of the given line first.
Given line: y= -2x -9
The above equation is already in the slope-intercept from and thus, the slope is the coefficient of x.
Slope of given line= -2
The coefficient is the number that comes before a variable and it includes the positive or negative sign, which explains why the slope of the given line is -2 instead of 2.
Slope of perpendicular line= [tex]\frac{1}{2}[/tex]
Substitute the value of the slope into the equation:
[tex]y=\frac{1}{2} x+c[/tex]
To find the value of c, substitute a pair of coordiantes the line passes through.
When x= 8, y= -4,
[tex]-4=\frac{1}{2}(8)+c[/tex]
-4= 4 +c
c= -4 -4
c= -8
Thus, the equation of the perpendicular line is [tex]\bf{y=\frac{1}{2} x-8}[/tex].
What is reciprocal?
The reciprocal of a number is 1 divided by that numberFor example, the reciprocal of 2 is [tex]\frac{1}{2}[/tex]In this question, we are interested in negative reciprocal. This means that if the slope of the given line is m, the slope of the perpendicular line is [tex]-\frac{1}{m}[/tex].Cyrus' tennis match lasted two and a half hours. Everett's tennis match lasted four and a half hours. How much longer did Everett’s match last?
Answers
Answer:
2 hours
Step-by-step explanation:
4.5 - 2.5 = 2
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