Answer:
[tex]\dfrac{x}{2 \cdot x + 14} + \dfrac{x - 4}{6} = \dfrac{3}{x^2} + 2\cdot x - 35; Domain \ restriction \ x \neq 0 \ or \ -7[/tex]
Step-by-step explanation:
The given rational equation is presented here as follows;
[tex]\dfrac{x}{2 \cdot x + 14} + \dfrac{x - 4}{6} = \dfrac{3}{x^2} + 2\cdot x - 35[/tex]
A domain restriction are the limits to the ranges of input values (x-values) of a function
The three main types of domain restrictions are the reciprocal function, the log function, and the root function
The form of restriction in the given rational are reciprocal form, which are;
[tex]\dfrac{x}{2 \cdot x + 14}[/tex], and [tex]\dfrac{3}{x^2}[/tex], from which the function is undefined when;
2·x + 14 = 0, therefore when x = -7, or x² = 0, when x = 0
Therefore, the domain restrictions are that the function is defines for all x, except x = -7 and x = 0
The domain restrictions are x ≠ -7 and x ≠ 0.
Answer:
it's -7 and 5
Step-by-step explanation:
used his and got it wrong
The area of Ray’s rectangular living room, in square feet, can be found by using the expression 4(3x+3y). Use the distributive property to write an equivalent expression for the area of Ray’s living room. Equivalent Expression Use your equivalent expression to find the area of Ray’s living room, in square feet, if x = 2 and y = 4. Write answer here: square feet Show work
Answer:
Area = 72 square feet
Step-by-step explanation:
[tex]4(3x+3y)[/tex]
Multiply the four to the values inside the parentheses to find the "equivalent expression"
[tex]12x +12y[/tex]
Using the "equivalent expression" we found above, we now want to find the area of Ray's living room, in square feet if [tex]x=2[/tex] and [tex]y = 4[/tex]
[tex]12(2) + 12(4)[/tex]
[tex]= 24 +48[/tex]
[tex]= 72[/tex]
Help me pls look at this PHTOo Bc I don’t know how to explain
Answer:
42.1
Step-by-step explanation:
15.2% = 0.152
277 * 0.152 = 42.104
42.1 megabytes have been downloaded.
Hope this is helpful.
Answer:
42.1
Step-by-step explanation:
thanks for the pts
✌️❤️✌️
Graph 8x-2y=1 and 4x+y=3
Answer:
no thanks i dont feel like doing all that work to help u. i apologize my dear friend bahahahahahahahahahahhahaha
Step-by-step explanation:
need help with this Q&A 3
Answer:
the second option
yes, because they are similar triangles
Step-by-step explanation:
the scaling factor is 3
3×3 = 9
3×7 = 21
so, the ratios of the sides remain the same, and the 90 degree angle remains the same. therefore, just one triangle is larger than the other, but the relative attributes and even the orientation are the same, so yes, since we don't know the absolute coordinates of the corners, indeed, the Hypotenuse of both triangles could be on the same line.
solutia reala a ecuatiei 4x la a doua = 6 intregi si 1/4 (dau coroana)
Answer:
x = + 5/4 or x = - 5/4
Step-by-step explanation:
[tex]4 x^2 = 6\frac{1}{4}\\\\4 x^2 = \frac{25}{4}\\\\x^2 =\frac{25}{16}\\\\x = \pm \frac{5}{4}[/tex]
Which of the following is NOT an example of a contract?
lease
credit card
borrowing lunch money
rental
A squash ball is thrown from the top of a building and falls to the ground below. The height of the ball above the ground is approximated by the relation h=-6t^2+24t + 30, where h is the height above the ground in metres and t is the elapsed time in seconds. Determine the maximum height that is reached by the ball. Show all your work.
Step-by-step explanation:
the answer is 6 ft and all my workings are in the image above
use the diagram to find the value of x
Answer:
4
Step-by-step explanation:
18x = 12(x+2)
18x = 12x+24
18x-12x = 24
6x = 24
x = 4
Alaina has $28 in her account .she wants to purchase a pair of shoes that costs $45 .if alaina makes the purchase which integer will represent the amount of money in alaina account?
--Answer--
negative integer
--Explanation--
28 - 45 = -17; the number subtracting is greater than the original number.
Find the exact value of x.
Answer:
24
Step-by-step explanation:
4 times 4
8 times 8
Subtract the 2 #'s
Then divide your answer by 2.
Step-by-step explanation:
use Pythagoras theorem
hypotenuse² = base² + height²
8²=base²+4²
64-16=B²
√48=B
√2×3×2×2×2=B
2×2√3
4√3 = B
hope it helps
The product of two integers is 84. If one
integer is (-12), find the other.
Answer:
-7
Step-by-step explanation:
-12x = 84
/-12 /-12
x = -7
Answer:
The other integer is - 7.
Step-by-step explanation:
Let the 2 integers be x and y
Given:
one of the integer is -12, Let x = - 12
Product of two integers is 84,
that is,
x × y = 84
- 12 × y = 84 [ given one of the integer is -12 ]
[tex]\frac{-12 \times y }{-12} = \frac{84 }{-12}[/tex] [ divide both sides by -12 ]
[tex]y = - 7[/tex]
PLEASE HELP LOL
what type of angles are <4 and <8
Answer:
C. Corresponding angles
Step-by-step explanation:
Visualize the two points of intersection and the four angles around each of them being separated. If you put the on top of each other, you can see that angle 4 corresponds with angle 8.
Answer: corresponding :)
Step-by-step explanation:
corresponding angles are angles that are in the same position relative to lines intersected by a transversal
basically theyre equal and on the same side of the transversal
hope this helps :)
A hat contains slips of paper with the names of the 26 other students in Eduardo’s class on them, 10 of whom are boys. To determine his partners for the group project, Eduardo has to pull two names out of the hat without replacing them.
What is the probability that both of Eduardo’s partners for the group project will not be boys?
StartFraction 9 Over 65 EndFraction
StartFraction 24 Over 65 EndFraction
StartFraction 64 Over 169 EndFraction
StartFraction 128 Over 325 EndFraction
Answer:
24/65
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
edge 2023
What is the equation of the following line written in general form? (The y-intercept is 7.)
y
(-2.1)
Answer:
[tex]{ \tt{slope = \frac{7 - 1}{0 - ( - 2)} = 3 }} \\ \\ { \tt{y = mx + c}} \\ { \boxed{ \bf{y = 3x + 7}}}[/tex]
help asap please thanks
-pi/4 is the same thing as 7pi/4.
The sine function will get us the y-value we need.
Keep in mind that our y-value will be negative (based on the position of the line), and pi/4 and 3pi/4 will both have positive y-values.
Therefore, the correct expression is sin(7pi/4).
Hope this helps!! :)
Justin was asked to write equations based on the triangle below. So far he has come up with the following equations: Which of the following would be another correct equation?
Answer:
C: tan 60 = √3
Step-by-step explanation:
Let the adjacent part of the triangle be x and let the opposite side be y.
Thus, from trigonometric ratios;
x/10 = cos 60
We are given cos 60 = ½
Thus;
x/10 = ½
x = ½ × 10
x = 5
Similarly;
y/10 = sin 60
Now,from trigonometric relationship we know that; sin 60 = cos 30. Thus;
y/10 = cos 30
We are given cos 30 = (√3)/2
Thus;
y/10 = (√3)/2
y = 10 × (√3)/2
y = 5√3
Since it is a right angle triangle with one angle being 60°, it means the other one is 30° since sum of angles in a triangle is 180°.
Thus;
5/(5√3) = tan 30°
1/√3 = tan 30
Similarly;
5/10 = sin 60°
sin 60° = ½
Also;
tan 60 = (5√3)/5
tan 60 = √3
Also;
sin 30 = 5/10
sin 30 = ½
Looking at the options, the only correct one is Option C
The equation x ^ 2 - 2x + y ^ 2 - 4y = 20 defines a circle in the xy-coordinate plane What is the radius of the circle?
Answer:
I'll set up the problem and you can do the calculation
Step-by-step explanation:
we need to complete the squares to get the equation in the general form:
[tex] {(x - h)}^{2} + {(y - k) }^{2} = {r}^{2} [/tex]
where h = the x coordinate of the center
k = the y coordinate of the center
r = the radius
so looking at
[tex] {x}^{2} - 2x[/tex]
we can see that if use -1 as the constant we have
[tex] {(x - 1)}^{2} = {x}^{2} - 2x + 1[/tex]
doing the same for y
[tex] {y}^{2} - 4y[/tex]
we can use -2 as the constant (basically you that the s
quare of the y coefficient )
[tex] {(y - 2)}^{2} = {y}^{2} - 4y + 4[/tex]
so now we have to add or subtract the constant on the RHS to see what the square of the radius is according to the general form of the equation at the top
20 +1+4=25
Take the square root and you have the radius
A roll of nickels is worth $2.00. Write and
solve an equation to determine the number
of nickels in a roll.
Answer: 20 nickels to make $2.00
Step-by-step explanation:
Answer:
5x = 200
x=40
Step-by-step explanation:
state wether the product of √3 and √9 is rational or irrational. explain your answer
√9 is rational and √3 irrational number
Please, I am begging. I don't understand inverses.
Answer:
0
9
-2
-23
Step-by-step explanation:
a function f(x) defines a y-value for any valid x-value.
that's why it is often written as y = f(x).
the inverse function of an original function just turns the question upside down.
now we want to see for a given y-value of the original function, what was the original x-value to get this y.
therefore we try to transform the original equation that calculates y out of x into one that calculates x out of y.
so, in our example
f(x) = y = -4x - 3
4x + y = -3
4x = -y - 3
x = (-y - 3) / 4
in order to keep the usual terminology with functions also for inverse functions, which are in the end nothing else than functions again, we then name the input variable "x" again, and the result "y".
so, the inverse function is therefore as a function of x
y = (-x - 3) / 4
for x = -3, y = (--3 - 3) / 4 = (3-3) / 4 = 0
when we have y for the inverse function looking for its corresponding x value, then we are investing the inverse function and come back to the original function.
so, for y=-3 of the inverse function that means x=-3 for the inverse inverse (or original) function looking for the y, which is then the x of the inverse function.
f(-3) = -4×-3 - 3 = 12 - 3 = 9 = x of the inverse function.
for x=5 of the inverse function, y = (-5-3)/4 = -8/4 = -2
for y=5 of the inverse function that means x=5 for the inverse inverse (or original) function looking for the y, which is then the x of the inverse function.
f(5) = -4×5 - 3 = -20 - 3 = -23 = x of the inverse function.
Maria rode her bicycle at an average speed of 18 mph on level roads and then slowed down to 10mph on the hilly roads of the trip. The entire trip covered 98 miles. How long did the entire trip take if traveling the level roads took the same time as traveling the hilly roads? {Remember, d = r·t }
Let the time = X
Distance = Rate times time
Level roads = 18x
Hills = 10x
Total is 98 miles
18x+10x = 98
Add:
28x = 98
Divide both sides by 28:
x = 3.5
She spent 3.5 hours on each part
Total time = 3.5 + 3.5 = 7 hours
What is the average rate of change of f
over the interval (-5,0]?
Give an exact number.
Answer:
Average rate of change = 0.6
Step-by-step explanation:
Average rate of change of a function between x = a and x = b is given by,
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
From the graph attached,
f(-5) = 0
f(0) = 3
Average rate of change of the graph between x = -5 and x = 0,
Average rate of change = [tex]\frac{3-0}{0-(-5)}[/tex]
= [tex]\frac{3}{5}[/tex]
= 0.6
Therefore, average rate of change of the given function between x = -5 and x = 0 is 0.6.
2. What is the mode for the data set 13, 11, 10, 12, 14, 9,
11, 8, 11?
A.10
B. 11
C. 12
D. none of the above
Answer:
11
Step-by-step explanation:
mode is the number that is most frequent
11
Answer:
11
Step-by-step explanation:
Mode means the highest repeated observation in the data set,
Therefore Mode = 11, as 11 has repeated 3 times, the most in the data set
1. Convert the quinary number 42 into binary number.
Answer:
42 in binary number is 101010.
if( 1 ,2 )and( 3 - 2)
are the two end point of a diameter of circle find the coordinates of the centre
Answer:
(2,0)
x-value: [1+3]/2 = 4/2 = 2
y-value: [2+-2]/2 = 0/2 = 0
Step-by-step explanation:
What is the first step in solving quadratic equations by finding square roots? a. give the positive and negative answer c. square root both sides to isolate x b. isolate the x squared by using inverse operations d. none of these Please select the best answer from the choices provided A B C D
Answer:
C: isolate the x squared by using inverse operations
Step-by-step explanation:
This method of solving quadratic equation is used when there is only x² term and no x term. Thus;
For example, we have a quadratic equation;
x² - 1 = 80
To solve this by square root method, the first step we have to take is to isolate the x² term by inverse operation which is by addition of 1 to both sides to get rid of the -1 on the left side so that x² can be isolated.
Which number is the EXPONENT? 4^2 = 16 *
Answer: 4
Step-by-step explanation:
The exponent in the given number [tex]4^{2}=16[/tex] is 2.
What is exponent?
An exponent refers to the number of times a number is multiplied by itself.
For example, [tex]3^{4}[/tex] means we are multiplying 3 four times. Here the base is 3 and exponent is 4.
According to the question
We have a number
[tex]4^{2} =16[/tex]
Here, we are multiplying 4 two times. So, the base is 4 and the exponent is 2.
Hence, the exponent in the given number [tex]4^{2}=16[/tex] is 2.
Learn more about the exponent here:
https://brainly.com/question/5497425
#SPJ2
I was doing my khan and i got stuck
6=2(y+2)
Answer:
[tex]y=1[/tex]
Step-by-step explanation:
Given:
[tex]6=2(y+2)[/tex]
Distribute the parenthesis
[tex]6=2y+4[/tex]
Subtract both sides by 4
[tex]2=2y[/tex]
Divide both sides by 2 to get [tex]y[/tex] alone
[tex]1=y[/tex]
Hope this is helpful
1. Which two points fail the VLT here in this graph?
PLEASE HELP!!!!
10 normal six sided dice are thrown.Find the probability of obtaining at least 8 failuresif a success is 5 or 6.
Answer:
0.2992 = 29.92% probability of obtaining at least 8 failures.
Step-by-step explanation:
For each dice, there are only two possible outcomes. Either a failure is obtained, or a success is obtained. Trials are independent, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A success is 5 or 6.
A dice has 6 sides, numbered 1 to 6. Since a success is 5 or 6, the other 4 numbers are failures, and the probability of failure is:
[tex]p = \frac{4}{6} = 0.6667[/tex]
10 normal six sided dice are thrown.
This means that [tex]n = 10[/tex]
Find the probability of obtaining at least 8 failures.
This is:
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{10,8}.(0.6667)^{8}.(0.3333)^{2} = 0.1951[/tex]
[tex]P(X = 9) = C_{10,9}.(0.6667)^{9}.(0.3333)^{1} = 0.0867[/tex]
[tex]P(X = 10) = C_{10,10}.(0.6667)^{10}.(0.3333)^{0} = 0.0174[/tex]
Then
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1951 + 0.0867 + 0.0174 = 0.2992[/tex]
0.2992 = 29.92% probability of obtaining at least 8 failures.
