Answer:
Step-by-step explanation:
To eliminate ambiguity please use parentheses when typing a function like this one. I'm going to assume that you meant
f(x) = 1 / (x + 3) - 2
Start with the graph of y = 1/x. Its vertical asymptote is the line x = 0. The graph never touches the x-axis.
Translating the entire graph 3 units to the left will give you the function
h(x) = 1 / (x + 3).
Translating the above graph 2 units down will give you the desired function g(x) = 1 / (x + 3) - 2.
Answer:
Graph B on Edge2022.
Have a great day.
Please help me I need to finish today!
Answer:
C
Step-by-step explanation:
For Youfang, the time spent running is equal to 15 times the week
which graph shows the solution to the system of linear inequalities x-4y< 4 y < x+1
Answer:
Third graph in the image attached
Step-by-step explanation:
Let's rewrite the first inequality:
x - 4y < 4
-4y < 4 - x
4y > x - 4
y > x/4 - 1
We can draw the line y = x/4 - 1, then all values above this line will be solution for this inequality (check first graph in the image attached)
Now, for the second inequality, we have:
y < x+1
We can draw the line y = x + 1, then all values below this line will be solution for this inequality (check second graph in the image attached)
Now, if we combine these solutions, we have the third graph in the image attached.
The crossing point can be found making the value of y from one line equal the value of y from the other line:
[tex]x/4 - 1 = x + 1[/tex]
[tex]x - x/4 = -2[/tex]
[tex]3x/4 = -2[/tex]
[tex]3x = -8[/tex]
[tex]x = -8/3[/tex]
[tex]y = x + 1 = -5/3[/tex]
The crossing point is (-8/3 , -5/3)
Answer:
its c
Step-by-step explanation:
edge
Which quantity does this number line represent?
A) less than 5
B) less than 4
C) less than 3
D) less than or equal to 4
Four college roommates rented an apartment together. When they
moved out, they were charged $1500 for damages to the carpet
and walls. The roommates agreed to equally share the cost.
What integer represents how much each person will have to pay?
Answer:
Step-by-step explanation:
What we do is to divide 1500 by 4 = $1500/4 = $375
Answer:375
Step-by-step explanation:
1500/4=375
HELP I will give brainliest to make the perfect shade of orange cake frosting, Mya needs 8 drops of yellow food coloring for every 12 drops of red food coloring. If she adds 32 drops of yellow food coloring to her frosting, how many drops of red food coloring should she add
Answer: 48 red drops
Step-by-step explanation:
ratio of yellow food drops to red food drops is 8:12
8:12 simplifies to 2:3
2:3 = 2/5:3/5
2x/5 = 32 = # of yellow drops (where x is the total # of drops)
2x/5 = 32
2x = 160
x = 80
Since there are 80 total drops and 32 yellow drops, there must be 48 red drops (80-32=48)
Part 2:
1. Make sure your answers and work is SHOWN please and steps are in order.
2. List all possible rational roots.
3. Use synthetic division to test possible rational roots
4. Identify complex roots, if possible.
5. Sketch a graph of the function, please show:
a. the end behavior correctly
b. the shape of the near x-intercepts
c. (if possible) anything you can learn by considering symmetry and transformations
2a. p(x)= x^4 + 4x^3 + 13x^2 + 36x + 36
Answer:
2. ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±36
3. see below for synthetic division
4. complex roots: ±3i
5. see the second attachment for a graph (has no symmetry)
Step-by-step explanation:
2. The Rational Root Theorem tells you possible rational roots are the form of ...
±(divisor of constant term) / (divisor of leading coefficient)
Here, we're lucky in that the leading coefficient is 1. The constant is 36, and its divisors are 1, 2, 3, 4, 6, 9, 12, 18, 36. Possible rational roots, according to the Rational Root Theorem are ...
±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±36
__
3. When actually searching for possible roots, it is useful to narrow down this list of 18 candidates. We can do this using Descarte's Rule of Signs and a couple of other simple tests. The rule of signs has us look at the signs of the coefficients. They are ...
+ + + + +
There are no sign changes, hence no positive real roots. This means we're looking at negative roots only.
We know that p(0) = 36, the constant term. We can evaluate p(-1) simply, by reversing the signs of the odd-degree coefficients and adding them up:
1 -4 +13 -36 +36 = 10
So p(0) = 36 and p(-1) = 10. The average rate of change is -26, so we expect p(-2) to be zero or less. That value (-2) may be a good first choice for a possible root.
The synthetic division for the root -2 is shown in the first attachment. It shows a remainder of 0, so -2 is a root. The polynomial with the corresponding factor divided out is ...
q(x) = x^3 +2x^2 +9x +18
__
We can apply the above steps to this polynomial. It will have no positive real roots. The value of q(0) is 18, and the value of q(-1) is -1 +2 -9 +18 = 10. The average rate of change between these points is (18 -10)/(0 -(-1)) = 8, so we expect the function to be zero or negative between x=-2 and x=-3.
Further, we observe that the ratio of the first two coefficients is 1 : 2, the same as the 9 : 18 ratio of the last two coefficients. This suggests we can factor this polynomial by "grouping."
q(x) = (x^3 +2x^2) +(9x +18) = x^2(x +2) +9(x +2) = (x^2 +9)(x +2)
So, without doing any more synthetic division, we have found a second root at x = -2. This means -2 is a double root.
Our factorization so far is ...
p(x) = (x +2)^2(x^2 +9)
__
4. The remaining polynomial factor (x^2 +9) has only complex roots:
x^2 +9 = 0
x^2 = -9
x = ±√(-9)
x = ±3i . . . . the complex roots
__
5. The graph is shown in the second attachment, along with the graph of the final quadratic factor.
The leading coefficient is positive and p(x) is of even degree, so it will have a general U shape, going to +∞ for large positive and negative values of x.
Since x = -2 is a double root, the graph touches the x-axis there, but does not cross it.
The graph of p(x) shows no symmetry.
______
Comment on the graph
With modern graphing calculator software it is entirely feasible to start by graphing the polynomial, then reading the (rational) roots from the graph. The same calculator can effectively divide out those roots. If the result is a quadratic, its vertex form equation can be read from the graph, making it easy to find any additional real or complex roots.
This graph shows ...
p(x) = (x +2)^2·q(x)
q(x) = x^2 +9
At the start of the week, Ladasha’s checking account had a balance of $34. She deposited $50 each day for three days. She made a $60 withdrawal on the fourth day. Ladasha also wrote a check for $22. Explain how you can write an expression to show the account balance at the end of the week.
Step-by-step explanation: The account started at $34. Three $50 credits were added. Indicate the withdrawal by subtracting $60 or adding –$60. The check is also represented by subtracting $22 or by taking the additive inverse and adding –$22.
Sample Response: The account started at $34. Three $50 credits were added. Indicate the withdrawal by subtracting $60 or adding –$60. The check is also represented by subtracting $22 or by taking the additive inverse and adding –$22.
What is the equation of a circle with center (-3,-1) that contains the point (1,
2)?
Answer:
(x+3)^2+(y+1)^2=25
Step-by-step explanation:
the distance of the center and the point is the radius of the circle
distance=(4^2+3^2)^(1/2)=5
(x+3)^2+(y+1)^2=25
Sammy wants to deposit into a 7% annual simple interest account she will also deposit twice as much in a certificate of deposit earning 5% annual simple interest to earn $390 of annual interest how much should she invest in each account?
Answer: $2294 should be invested in the simple interest account while $4588 should be invested in the certificate of deposit.
Step-by-step explanation:
Let x represent the amount that he would deposit in the simple interest account.
Let y represent the amount that he would deposit in the certificate of deposit.
she will deposit twice as much in the certificate of deposit. It means that
y = 2x
Interest from the simple interest account would be 7%. This mean that the interest would be 7/100 × x = $0.07x
Interest from the certificate of deposit account would be 5%. This mean that the interest would be 5/100 × y = $0.05y.
The total interest from both accounts would be $390. It means that
0.07x + 0.05y = 390- - - - - - - - - - 1
Substituting y = 2x into equation 1, it becomes
0.07x + 0.05 × 2x = 390
0.07x + 0.1x = 390
0.17x = 390
x = 390/0.17 = $2294
y = 2x = 2 × 2294
y = 4588
The units of the subway map at the right are in miles. Suppose the routes between stations are straight, find the distance you would travel between each the Elm and Symphony Stations. Round your answer to the nearest tenth of a mile. The distance between the Elm and Symphony Stations is how many miles?
Answer:
Distance between 2 stations= 8.94 miles
Step-by-step explanation:
The coordinates of Symphony Station is given by:
Symphony Station: (x₁ , y₁) : (1,2)
The coordinates of Elm station is given by:
Elm Station: (x₂ ,y₂) : (-3,-6)
We know that the distance formula can be used to find distance between these 2 points. Distance formula is given as
d= √((x₂ - x₁)² + (y₂ - y₁) ²)
Substitute values
d= √((-3 - 1)² + (-6 - 2) ²)
d= √((-4)²+(-8)²)
d= √(16+64)
d=√80
d= 8.94 miles
What is the quotient of 2,173 ÷ 53
Answer:
41
Step-by-step explanation:
A triangle has two sides that have a length of 4 cm.
Which answer choices list possible types of angles for this triangle? Select two that apply.
1 obtuse angle and 2 acute angles with different measures
3 obtuse angles with different measures
1 right angle and 2 acute angles with different measures
1 right angle and 2 acute angles with the same measure
1 obtuse angle and 2 acute angles with the same measure
3 acute angles with different measures
Answer:
3 acute angles with different measures and 1 right angle and 2 acute angles with same measures
A shirt originally cost $49.31, but it is on sale for $41.91. What is the percentage decrease of the price of the shirt? If necessary, round to the nearest percent.
Answer:
8%
Step-by-step explanation:
The Cost price is = 49.31
The Selling price is = 41.91
The profit is =-7.4
The percentage decrease of the price of the shirt is hence=
=41.31/49.31 * 100
= 8%
Hence, 8% is the percentage of the decrease of the price of the shirt.
Help! I need to know if 7√3+2√9 is rational or irrational
Answer:
Irrational
Step-by-step explanation:
[tex]7\sqrt{3}+2\sqrt{9}= \\\\7\sqrt{3}+2(3)= \\\\6+7\sqrt{3}[/tex]
Therefore, this is irrational. Hope this helps!
Solve the following inequality. Then place the correct answer in the box provided. Answer in terms of a mixed number.
2(P +1) + 3(P + 2 ) > 2
Answer: [tex]-1\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]2(P +1) + 3(P + 2 ) > 2[/tex]
Distribute 2 and 3
[tex]2P+2+3P+6>2[/tex]
Combine like terms;
[tex]5P+8>2[/tex]
Subtract 8
[tex]5P>2-8[/tex]
[tex]5P>-6[/tex]
Divide by 5
[tex]P>-\frac{6}{5}[/tex]
Convert to a mixed number by dividing. However, when we have the numerator greater than the denominator, we must find a way to make the numerator lower. We can achieve this by separating it into 2 fractions.
[tex]-\frac{6}{5}=-\frac{5}{5}-\frac{1}{5}[/tex]
When we do this, we can see that 5/5 = 1
[tex]-1-\frac{1}{5}=-1\frac{1}{5}[/tex]
The equation c=13t gives the cost c (in dollars) of t tickets for a play. Identify the independent and dependent variables.
help
Answer:
Independent variable is tickets.
Dependent variable is cost(dollars).
Step-by-step explanation:
Dependent variable depends on independent variable.
In this question, the total amount deoend on number of ticket bought. As number of tickets increases, the total cost will also increase.
What is the radius of this cone ? V=16cm3 and 12 cm
Answer:
1.13 cm
Step-by-step explanation:
V=1/3 * pi*r^2*h
h=12 cm (assuming, since that's what you gave)
V=16
r=1.13 cm
Question 1 (1 point)
Solve
- +13 > 10
(Blank 1 is <,>, S, or 2. Blank 2 the number)
Recall that < and > are on the keyboard. You can get S and respectively by doing Alt < and Alt > on the keyboard. You may also copy the
symbols from the instruction page or the Copy Symbol and Keyboard Shortcuts Page.
Blank 1:
Blank 2:
Jernel has to figure out the area of her square garage. she knows that one side of the garage is equal to the length of her rabbit pen. the dimensions of the rectangular rabbit pen are 14 by 10. what is the area of the garage?
Answer: 196
Step-by-step explanation:
Just answered this...
14x14=196
Draw a diagram for (x+2)(x+4)
Answer:
Download this mm file
Use the law of sines to find the value of y. Round to the nearest tenth.
Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction
1.4 units
1.6 units
2.5 units
2.6 units
Answer:
b) 1.6 units
y = 1.586 ≅ 1.6 units
Step-by-step explanation:
Explanation:-
step(i):-
The sine rule
[tex]\frac{a}{Sin A} = \frac{b}{Sin B} = \frac{c}{Sin C} = 2 R[/tex]
Given a = 2 and b = y
∠A = 75° and ∠ B = 50°
Step(ii):-
by sine rule
[tex]\frac{a}{Sin A} = \frac{b}{Sin B}[/tex]
[tex]\frac{2}{Sin 75} = \frac{y}{Sin 50}[/tex]
Cross multiplication , we get
2 × sin 50° = y sin 75°
2 × 0.766 = y × 0.9659
[tex]y = \frac{ 2 X 0.766}{0.9659} = 1. 586[/tex]
y = 1.586 ≅ 1.6 units
Answer:
Step-by-step explanation:
Which of these is an example of a literal equation?
A. 12 = 9 + 3x
B. 6 + 30 = 62
C. ax - by = k
D. 3x - 4y
How many solutions exist for the system of equations 3x+y=18 3x+y=16
Answer:
no solutions
Step-by-step explanation:
Subtract the two equations
3x+y=18
-(3x+y=16)
--------------------
0 + 0 = -2
0 does not equal negative 2
This is never true so there are no solutions
Answer:
The number of solutions is 0.
Step-by-step explanation:
The x and y terms are equal. The constants are different. The lines are parallel. No solution.
BRAINLIEST WILL BE MARKED(THAT MEANS- 3 EXTRA POINTS) HERE! GRAPHING HELP 101
The graph of f(x)=x2 is shown.
Use the parabola tool to graph the function g(x)=(1/5x)2.m
The 1/5 is a fraction.
The graph with the blue highlight is my answer. LET ME KNOW IF MY ANSWER IS RIGHT OR WRONG! ASAP PLEASE AND THANK YOU WILL MARK BRAINLIEST!
Answer:
I think its wrong. For g(5)=(5/5)^2=1 and in your graph is something close to 3. The correct graph for [tex]g(x)=(\frac{1}{5}x)^2[/tex] is
Answer:
False
Step-by-step explanation:
Took the test and this is what I got
if f(x)=x+3 g(x)=2x+6 find (f+g)(x)
Answer:
3x + 9
Step-by-step explanation:
For value of (f+g)(x) add two functions up
x + 3 + 2x + 6 = 3x + 9
Find the area of rhombus. Please help
Answer:
195
Step-by-step explanation:
The area of a rhombus is the product of the two diagonal lengths / 2. The two diagonals measure 15 and 26 respectively. Therefore, the rhombus' area is 390/2=195
when 7 is subtracted from 3 times a certain number , the result is 28. What is the number
7 multiply by three u get 21 then add it to the number 28 add u get the answer 49
I need help with this problem.
Answer:
D
Step-by-step explanation:
[tex]f(x)=3x+5 \\\\g(x)=x^2 \\\\(f-g)(x)=(3x+5)-(x^2)=-x^2+3x+5[/tex]
Therefore, the correct answer is choice D. Hope this helps!
any suggestions on how to solve this? thanks
Answer: x = 4
Step-by-step explanation:
You basically want to solve for the angle A. Do arcsin of 1/3, which is approximately 19.47 degrees. In this triangle, we are missing the adjacent and opposite, but we do have the angle luckily. Lets use SOH-CAH-TOA.
[tex]sin(theta) = \frac{opposite}{hypotenuse}[/tex]
We can see here that doing sine will give us the length of the opposite
[tex]sin19.47 = \frac{x}{12}[/tex]. Do sine of 19.47, then multiply by 12. I got 4
How many cubes with a side length of 1/2 unit would it take to fill a rectangular prism with a volume of 2 cubic units?
Answer:
16
Step-by-step explanation:
1/2*1/2*1/2 = 1/8 cubic units
2/(1/8) = 16
Answer:
16
Step-by-step explanation:
[tex](\frac{1}{2})^3 = \frac{1^3}{2^3} = \frac{1}{8}\\\frac{2}{\frac{1}{8}} = 2 \cdot 8 = 16[/tex]