Answers:
Domain = {-1, 2, 1, 8, 9}
Range = {2, 51, 3, 22}
==================================
Explanation:
The domain is the set of allowed inputs of a function. So it's the set of possible x values. We simply list the x coordinates of each point to form the domain.
The range is the set of possible y values or y outputs. So we simply list the y coordinates of the points. We toss out any duplicates. Since order doesn't matter in a set, we can have the values listed any way we want.
Side notes:
This is a function since we don't have any repeated x values between any of the points. This graph passes the vertical line test.This function is not one-to-one because we have y = 51 correspond to multiple x values (x = 2 and x = 9 simultaneously). This graph fails the horizontal line test.PLZ help fast thank you
Answer:
Step-by-step explanation:
An isosceles triangle is one that has 2 sides that are the same length, like ours here. Because of the Isosceles Triangle Theorem, if 2 side lengths are congruent, then the angles opposite those sides are congruent, as well. That means that both base angles are 53 degrees. However, we are looking for the altitude, or height, of the triangle. That changes everything. Drawing in the height serves to cut the triangle in half, splitting both the vertex angle (the angle at the top of the triangle) and the base exactly in half. Now we have 2 right triangles which are mirror images of each other. We only need concentrate on one of these triangles. What the triangle looks like now:
One base angle is 90 degrees and the other is 53 degrees. By the Triangle Angle-Sum Theorem, the third angle has to be a degree measure which ensures that all the angles add up to 180. Therefore, the third angle measures 180 - 90 - 53 = 37. Even still, besides knowing all the angle measures, we really don't need any besides the 53 degree one.
As far as side lengths go, the base is 12 (because the height cut it in half). To find a missing side in a right triangle you either use Pythagorean's Theorem or right triangle trig, depending upon the info you're given. We only have enough to use right triangle trig.
We have the base angle of 53, which is our reference angle, the side next to, or adjacent to, the reference angle, and we are looking for the side length opposite the reference angle. This is the tan ratio where
[tex]tan\theta=\frac{opp}{adj}[/tex] where tangent of the reference angle is equal to the side opposite the reference angle over the side adjacent to the reference angle. Filling in that ratio:
[tex]tan53=\frac{opp}{12}[/tex] and multiply both sides by 12 to get
12tan53 = opp and do this on your calculator to get that
opp = 15.9 inches
in need help
Relationships in Triangles
Answer: x = 17
Step-by-step explanation: Since ray SQ bisects <TSR, we know
that the m<TSQ ≅ m<QSR by the definition of an angle bisector.
So we can setup the equation (3x - 9) + (3x - 9) = 84
using the angle addition postulate.
Simplifying on the left gives us 6x - 18 = 84.
Now add 18 to both sides to get 6x = 102.
Now divide both sides by 6 so x = 17.
(g) (2 sin 60°)(3 kos 60°) + 3 tan 30°
Answer:
[tex](2 \ sin 60)(3\ cos 60) +3\ tan 30\ =\ \frac{5\sqrt3}{2}[/tex]
Step-by-step explanation:
[tex](2 \ sin 60)(3 \ cos 60) + 3\ tan 30\\\\= (2 \times \frac {\sqrt3}{2}) (3 \times \frac{1}{2})+ (3 \times \frac{1}{\sqrt3})\\\\=(\sqrt{3}\ \times \frac{3}{2})+ \frac{3}{\sqrt3}\\\\=\frac{3\sqrt3}{2}+\frac{3}{\sqrt3}\\\\=(\frac{3\sqrt3}{2} \times \frac{\sqrt3}{\sqrt3})+(\frac{3}{\sqrt3} \times \frac{2}{2})\\\\=\frac{3\times (\sqrt3)^2}{2\sqrt3}\ + \ \frac{6}{2 \sqrt3}\\\\=\frac{3 \times 3}{2 \sqrt3} +\frac{6}{2 \sqrt3}\\\\=\frac{9+6}{2\sqrt3}\\\\=\frac{15}{2\sqrt3} \times \frac{\sqrt3}{\sqrt3}\\\\[/tex]
[tex]=\frac{15 \sqrt3}{2 \times (\sqrt{3})^2}\\\\=\frac{15 \sqrt 3}{2 \times 3}\\\\=\frac{5\sqrt3}{2}[/tex]
Which equation does the graph above represent?
A. y = 2x
B. y = 1/2x
C. y = 1/2
D. y = 2 + x
Answer:
y=2x
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0).
1) Determine the slope (m)
The slope is the rate of change, or the number of units the line moves up divided by the number of units the line moves to the right.
Looking at the graph, we can see that for every 1 space the line travels to the right, the line travels 2 spaces up. This makes the slope of the line 2. Plug this into [tex]y=mx+b[/tex]:
[tex]y=2x+b[/tex]
2) Determine the y-intercept (b)
When x=0 on the graph, y=0. Therefore, the y-intercept is 0. Plug this into [tex]y=2x+b[/tex]:
[tex]y=2x+0\\y=2x[/tex]
I hope this helps!
Is (18,-4) a solution to the equation y = -6x - -87? yes no
Replace x with 18, solve the equation. If it equals -4 it’s a solution.
Y = -6(18) - -87
Y = -108 + 87
Y = -21
-21 does not equal -4 so (18,-4) is not a solution.
What is the value of x?
Enter your answer in the box.
Answer:
solution
Step-by-step explanation:
ADC = Sum of triangle
AD+ AC = 2.25+3 =5.25
Step 2:
BCD = Sum of acute angled triangle = a+b+
c
BCD= 2.25+4+3
BCD = 9.25
The value of x =ADC+BCD
= 5.25+ 9.25
= 14.5
Solve the inequality.
k + 4 – 2(k – 12) > 0
k > 28
k > –20
k < –20
k < 28
k<28
Step 1: Simplify both sides of the inequality.
−k+28>0
Step 2: Subtract 28 from both sides.
−k+28−28>0−28
−k>−28
Step 3: Divide both sides by -1.
−k /−1 > −28 /−1
k<28
Answer:
k < 28
Step-by-step explanation:
Given inequality :-
k + 4 - 2( k - 12 ) > 0 k + 4 - 2k + 24 > 0-k + 28 > 0 28 > k k < 28Last Option is correct .
A girl cycled a total of 15 kilometers by making 5 trips to work. How many trips will she have to make to cover a total of 24 kilometers
Answer:
8 trips
Step-by-step explanation:
You can solve this by unitary method.
15 kilometers in 5 trips means 1 trip consist of 3 kilometers
Therefore, 24/3 = 8
So the required answer is 8 trips.
Thank you!!
A concert hall has 25,350 seats. There are 78 rows of seats in the hall each row has the same number of seats how many seats are in each row?
Answer:
There are 325 seats in each row
Step-by-step explanation:
78 × 325 = 25,350
with steps please
A student uses a clinometer to measure the angle of elevation of a sign that marks the point on a tower that is 45 m above the ground. The angle of elevation is 32° and the student holds the clinometer 1.3 m above the ground. He then measures the angle of elevation of the top of the tower as 47º. Sketch and label a diagram to represent the information in the problem. Determine the height of the tower to the nearest tenth of a metre
Answer: [tex]75\ m[/tex]
Step-by-step explanation:
Given
The tower is 45 m high and Clinometer is set at 1.3 m above the ground
From the figure, we can write
[tex]\Rightarrow \tan 32^{\circ}=\dfrac{43.7}{x}\\\\\Rightarrow x=\dfrac{43.7}{\tan 32^{\circ}}\\\\\Rightarrow x=69.93\ m[/tex]
Similarly, for [tex]\triangle ACD[/tex]
[tex]\Rightarrow \tan 47^{\circ}=\dfrac{43.7+y}{x}\\\\\Rightarrow 69.93\times \tan 47^{\circ}=43.7+y\\\\\Rightarrow 74.99=43.7+y\\\Rightarrow y=31.29\ m[/tex]
Height of the tower is [tex]43.7+31.29\approx 75\ m[/tex]
so I have 40 dollars and i am buying 10$ gift card so how many 10$ gifts cards can I buy?
Answer:
4 gift card
Step-by-step explanation:
40 dollar /gift card price 10
=4
Answer:
4 dollar gift card
Step-by-step explanation:
40÷10=4
4 dollar gift card
Simplify the expression below.
50 - 2(32 + 1)
Answer:
[tex] = { \tt{50 - 2(32 + 1)}}[/tex]
Solve the bracket:
[tex] = { \tt{50 - 2(33)}}[/tex]
Open the bracket:
[tex]{ \tt{ = 50 - 66}}[/tex]
Subtract the expression:
[tex]{ \bf{ = - 16}}[/tex]
Step-by-step explanation:
Multiply 2 by 32 and 1
50-64-2
-14-2
-16 Answer
If a = ba and b = 2a, what is the value of a + b?
a = ba
1 = b
Since b = 1,
b = 2a
1 = 2a
a = 0.5
Therefore,
a + b = 0.5 + 1
a + b = 1.5
What is the next term in the sequence below?
24, 12, 6, 3, . . .
A. 0.5
B. 1.5
C. 1.75
D. 2.5
Answer:
1.5(B)
Step-by-step explanation:
This is a geometric sequence where each number is 1/2 times the last. So 3/2 is 1.5.
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
x ≈ 52.1°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{KL}{LM}[/tex] = [tex]\frac{36}{28}[/tex] , then
x = [tex]tan^{-1}[/tex] ([tex]\frac{36}{28}[/tex] ) ≈ 52.1° () to the nearest tenth )
If trstan has a pickup truck that could carry 7/4 cord of firewood, FInd the number trips needed to cary 63 cords of wood
Answer:
36
Step-by-step explanation:
63/(7/4) 63 divided by 7/4
63* 4/7 63 multiplied by 4/7
=36 answer is 36
What is the value of y, if the standard deviation of 8, 8, 8, 8, y, 8 is 0?
Answer:
y = 8
Step-by-step explanation:
First, we know that the equation for standard deviation is
σ = √((1/N)∑(xₐ-μ)²), with σ being the standard deviation, N being the count of numbers, xₐ being individual values, and μ being the mean. Working backwards, we have
0 = √((1/N)∑(xₐ-μ)²)
Squaring both sides, we get
0 = (1/N)∑(xₐ-μ)²
Since 1/N cannot be 0, we know that
0 = ∑(xₐ-μ)²
Since (xₐ-μ)² can only be ≥0, this means that each value of xₐ-μ must be equal to 0, so
0 = xₐ-μ for each a
xₐ = μ
This leads to the conclusion that each value is equal to the mean, so the mean must be 8.
The mean is equal to the sum / amount of numbers. There are 6 numbers, and the sum is (40+y). The mean is
8 = (40+y)/6
multiply both sides by 6
6*8 = 40+y
48 = 40 + y
This means that
y = 8
plz help me out with the answer and explaination
Answer:
7500 m
Step-by-step explanation:
5500 is the initial height. It increased by 1500, so 5500 + 1500 = 7000. Then it went down 2000 meters, so 7000 - 2000 = 5000. It went up 2500 again. 5000 + 2500 = 7500
Help,anyone can help me do quetion,I will mark brainlest.
Answer:
c) 25 cm^2
d) 52.5 cm^2
Step-by-step explanation:
5*2 = 1
10/2 = 5
40/2 = 20
20+5 = 25
This is just scratch work^
What is the scale factor from ABC to DEF?
Answer:
0 so D
Step-by-step explanation:
The shape didnt change at all. All the sides are 5 for both triangles.
-3 raised to the power 0=
Given:
The statement is "-3 raised to the power 0".
To find:
The value of the given expression.
Solution:
We know that [tex]a[/tex] raised to the power [tex]b[/tex] can be written as [tex]a^b[/tex].
Any non zero number raised to the power 0 is always 1. It means,
[tex]a^0=1[/tex], where [tex]a\neq 0[/tex].
-3 raised to the power 0 [tex]=(-3)^0[/tex]
[tex]=1[/tex]
Therefore, the value of the given statement is 1.
2.
B. Melody had $25 and withdrew $300 from his bank account. She bought a pair of trousers for $30.00, 2 shirts for
$19.00 each, and 2 pairs of shoes for $40.00 each. Give the final expression, and determine how much money Mel had
at the end of the shopping day.
Answer:
25 + 300 = 325
trousers: spent 30 (a pair of trousers = one unity of trousers)
shirts: spent 19 x 2 = 38
shoes: spent 40 x 2 = 80
80 + 38 + 30 = 148
325 - 148 = 177
She had $177,00 left.
hope it helps.
Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.
Write the equation of the line parallel to 4y - x = -20 that passes through the point (8,3).
Answer:
y= ¼x +1
Step-by-step explanation:
Rewriting the equation into the slope-intercept form (y= mx +c, where m is the gradient and c is the y- intercept):
4y -x= -20
4y= x -20 (+x on both sides)
y= ¼x -5 (÷4 throughout)
Thus, slope of given line is ¼.
Parallel lines have the same gradient.
Gradient of line= ¼
y= ¼x +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= 8, y= 3,
3= ¼(8) +c
3= 2 +c
c= 3 -2
c= 1
Hence the equation of the line is y= ¼x +1.
Of the 144 animals in the pet store, 56 are cats. The rest are dogs. What fraction of the pets are dogs?
Answer:
11/18
Step-by-step explanation:
56/144 = cats.
144 - 56 = 88
88/144 are dogs.
Simplified: 11/18
The function f(t) = 4t2 − 8t + 7 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, and interpret the vertex of f(t).
Answer:
Vertex form is f(t) = 4 [tex](t-1)^{2}[/tex] +3 and vertex is (1, 3).
Step-by-step explanation:
It is given that f(t)= 4 [tex]t^{2}[/tex] -8 t+7
Let's use completing square method to rewrite it in vertex form.
Subtract both sides 7
f(t)-7 = 4 [tex]t^{2}[/tex] -8t
Factor the 4 on the right side.
f(t) -7 = 4( [tex]t^{2}[/tex] - 2 t)
Now, let's find the third term using formula [tex](\frac{b}{2} )^{2}[/tex]
Where 'b' is coefficient of 't' term here.
So, b=-2
Find third term using the formula,
[tex](\frac{-2}{2} )^{2}[/tex] which is equal to 1.
So, add 1 within the parentheses. It is same as adding 4 because we have '4' outside the ( ). So, add 4 on the left side of the equation.
So, we get
f(t) -7 +4 = 4( [tex]t^{2}[/tex] -2 t +1)
We can factor the right side as,
f(t) -3 = 4 [tex](t-1)^{2}[/tex]
Add both sides 3.
f(t) = 4[tex](t-1)^{2}[/tex] +3
This is the vertex form.
So, vertex is (1, 3)
plzz help me out i really need help
Find x
Help me please
Answer:
x=31.2
Step-by-step explanation:
Since angle C is 4x-10 and angle A is 2x+3
then the two angles combined should equal 180 (based off of the inscribed quadrilateral theorem)
4x-10+2x+3=180
6x-7=180
6x=187
x=31.166...
if you round it to the nearest tenth it would be 31.2
What is the next step for this construction?
Connect points A' to C.
A. Connect points A’C
B. Draw another arc
C. Erase BC
D. Connect points C’ and B’
HELP ASAP 10 POINTS AND BRAINLIST AND 5 STAR AND THANKS BUT IF CORRECT
Step-by-step explanation:
hope it helps you..........
Answer:
[tex](\frac{2}{5} )^{3}[/tex] = [tex]\frac{8}{125}[/tex] [tex]cm^{3}[/tex]
Step-by-step explanation:
What is the solution of ?
Answer:
x=12 is the answer
Step-by-step explanation:
[tex] \frac{5}{2} x - 7 = \frac{3}{4} x + 14[/tex]
[tex] \frac{5}{2} x - \frac{3}{4} x = 14 + 7[/tex]
[tex] \frac{10}{4} x - \frac{3}{4} x = 21[/tex]
[tex] \frac{7}{4} x = 21[/tex]
[tex]x = 21 \div \frac{7}{4} [/tex]
[tex]x = 21 \times \frac{4}{7} [/tex]
[tex]x = 3 \times 4[/tex]
[tex]x = 12[/tex]