The domain of the function is possible values of independant varaible such that function is defined or have real values.
So the expression
[tex]\frac{(x+2)(x-3)}{(x-1)(x+6)}[/tex]is not defined for x = -6 and for x = 1, as expression becomes undefined for this values of x (Denominator becomes 0).
So answer is,
[tex]\frac{(x+2)(x-3)}{(x-1)(x+6)}[/tex]Option B is correct.
I am needing help. I do not understand these types of problems.
For angle 45 degree, hypotenuse side is 15 and base side is x.
Determine the measure of side x by using trigonometry.
[tex]\begin{gathered} \cos 45=\frac{x}{15} \\ 0.707=\frac{x}{15} \\ x=15\cdot0.707 \\ =10.605 \end{gathered}[/tex]Thus value of x is 10.605 m.
Answer: x = 10.605 m
You are performing a left-tailed test with test statistic z = -2.329, find the p-value accurate to 4
decimal places.
p-value =
The p-value is 0.00993
What is critical value ?
The distribution's critical values are the points that have the same probability as your test statistic and are equal to the significance level. It is considered that these values are at least as extreme as those essential values.
The points with the property that the area under the density curve of the test statistic from those points to the tails is equal to can be readily represented as critical values:
Left-tailed test: The critical value to the left of the area under the density curve is equal to ;
Right-tailed test: The density curve's area under the right side of the critical value equals ; and
Two-tailed test: The total area is equal to since the area under the density curve from the left critical value to the left is equal to ∝/2 and the area under the curve from the right critical value to the right is equal to ∝/2 as well.
When z = -2.329
After left-tailed test the p-value from the graph is 0.00993
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Lynn is tracking the progress of her plant's growth. The plant is already 8 centimeters high. The plant grows 1.5 centimeters per day. Which function shows this relationship? y=8x+1.5y=1.5x+8y=9.5x
Given the information, we know that the plant is already 8 centimeters, therefore that would be our intercept with the y-axis (i.e. b = 8). Now, to find the slope, we have that on the first day the plant grows 1.5 centimeters, therefore for day 1, the plant is 9.5 centimeters high. With this observations we have the following:
[tex]\begin{gathered} \text{Given (0,8) and (1,9.5)} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{9.5-8}{1-0}=1.5 \\ m=1.5 \end{gathered}[/tex]Using the formula y=mx+b, we obtain the desired function:
[tex]\begin{gathered} y=mx+b \\ \Rightarrow y=1.5x+8 \end{gathered}[/tex]Therefore, the function that shows the relationship is y=1.5x+8
2. Solve the system of equations: *S 2x – 4y = 201x=4x = 4=
EXPLANATION
Since we have the system of equations:
(1) 2x - 4y = 20
(2) x = 4
Plugging in x=4 into (1):
2*4 - 4y = 20
Multiplying numbers:
8 - 4y = 20
Subtracting -8 to both sides:
-4y = 20 -8
Subtracting numbers:
-4y = 12
Dividing both sides by -4:
y = 12 / -4
Simplifying:
y = -3
The solution to the system of equations is (x,y) = (4,-3)
write an equation in slope intercept form for the line that passes through the given point and is perpendicular to the graph of the equation. (-4,2); y= -1/2x + 6
First of all we are going to find the slope perpendicular to the equation y = -1/2 x +6.
We need to remember that two slopes are perpendicular if its product is equal to -1. Like this:
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ m_1=-\frac{1}{2}_{} \\ m_2=-\frac{1}{m_1}=-\frac{1}{-\frac{1}{2}}=2 \\ m_2=2 \end{gathered}[/tex]Now, we find the equation of the line using the general form:
[tex](y-y_1)=m(x-x_1);\text{ }[/tex]m - slope
[tex](x_1,y1)=(-4,2)_{}[/tex]That was a point of the line, now:
[tex]\begin{gathered} (y-2)=2(x-(-4)) \\ y-2=2x+8 \\ y=2x+10 \end{gathered}[/tex]Finally, the equation of the line that passes through (-4,2) and is perpendicular to the equation y = -1/2x+6 is
y=2x+10
function notations For the function below for which values of x does f (x)=4?
Answers:
x = 3
x = 5
Explanation:
In the function, the first set represents the x and the second set represents f(x), so to find for which values of x does f(x) = 4, we need to identify the beginning of the arrows that end in the number 4.
Therefore, these numbers are 3 and 5. It means that x = 3 and x = 5 make f(x) equal to 4.
So, the answers are x = 3 and x = 5.
Equation A and Equation B are Equivalent Equations.Equation A: 3/5x + 4/5 = 2Equation B: 3x + 4 = 10Explain what was done to both sides of equation A to create equation B?
You have the following equations:
3/5 x + 4/5 = 2
3x + 4 = 10
In order to show that the previous equations are equivalent equations, multiply the first equation by 5, to eliminate the denominators of the fractions:
(3/5 x + 4/5 = 2)(5)
3x + 4 = 10
Hence, it was necessary to multiply by 5 the first equation to obtain the second one
Sondra Anderson was looking at a winter coat that regularly sells for $179.99. On the rack was a sign that read 25% off all winter coats. What will the sale price be of the coat that Sondra wants to buy?
Given:
The regular price of the coat = $179.99
Percent-off the regular price = 25%
To find:
The sales price of the coat
To determine the sales price of the cot, we need to first find the amount of discount
[tex]\begin{gathered} Discount\text{ = 179.99 }\times\text{ 25\%} \\ Discount\text{ = 179.99 }\times\text{ 0.25} \\ Discount\text{ = 44.9975} \end{gathered}[/tex]The sales price = Original price - discount
[tex]\begin{gathered} The\text{ sales price = 179.99 - 44.9975} \\ \\ The\text{ sales price = 134.9925} \\ \\ The\text{ sales price of the coat Sandra want to buy = \$134.99} \end{gathered}[/tex]What is the perimeter of triangle XYZ? A. 17.1 cmB. 15.1 cmC. 13.1 cmD. 11.1 cm
The perimeter of the triangle XYZ is 15.1 cm.
The two given triangles are ΔUVW and ΔXYZ are similar.
In ΔUVW ∠U=36°
In ΔXYZ ∠Y = 72° and ∠Z = 72° , ∴ ∠X = 180° - (72+72)° = 36°
Hence in the two triangles we can assume that they are similar by AAA axiom of similarity
So the sides of the triangle XYZ will be
XY = 5.7 cm
YZ = 5.7 cm
ZX = 3.7 cm
Hence the perimeter = XY+YZ+ZX = 5.7 + 5. 7+ 3.7 = 15.1 cm
A perimeter is a closed path that encompasses, encircles, or delineates a one-dimensional length or a two-dimensional shape. The circumference of a circle or an ellipse is referred to as its perimeter.
Perimeter calculations have many practical applications. The perimeter is the width of the fence required to completely enclose a yard or garden. The circumference, or perimeter, of a wheel or circle determines how far it will travel in one rotation.
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A basket of fruits contains 50 mangoes and 30 orange. what percentage of the fruits are oranges?
The percentage of oranges is the basket of fruits is 37.5%.
According to the question,
We have the following information:
A basket of fruits contains 50 mangoes and 30 orange.
Now, we can easily find the number of oranges in this basket by following the given steps.
Total number of fruits in the basket = number of mangoes + number of oranges
Total number of fruits = 50+30
Total number of fruits = 80
Percentage of oranges in the basket = Number of oranges in the basket*100/total number of fruits in the basket
Percentage = (30*100)/80
Percentage = 37.5%
Hence, the percentage of oranges is the basket of fruits is 37.5%.
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A ladder, 510 cm long, leans against a building. If the angle between the ground and the ladder is 57 degrees, how far from the wall is the bottom of the ladder? Round to the nearest tenth
Let's use cosine function to find the distance between the wall and the bottom of the ladder:
[tex]\begin{gathered} \cos (\theta)=\frac{adjacent}{hypotenuse} \\ \cos (57)=\frac{x}{510} \\ solve_{\text{ }}for_{\text{ }}x\colon \\ x=510\cdot\cos (57) \\ x=277.8\operatorname{cm} \end{gathered}[/tex]7. Write an equation that results when f(x) = 5^xhas been transformed by:a. Shifted to the left 2 and up 3b. Shifted right 3 and down 1
The given function is:
[tex]undefined[/tex]Under her cell phone plan, Ella pays a flat cost of $58.50 per month and $3 per gigabyte, or part of a gigabyte. (For example, if she used 2.3 gigabytes, she would have to pay for 3 whole gigabytes.) She wants to keep her bill under $65 per month. What is the maximum whole number of gigabytes of data she can use while staying within her budget?
The maximum number of gigabytes of data she can use while staying within her budget is 2 gigabytes.
Given that Ella pays a flat cost of $58.50, and per gigabyte used have to pay $3. If she uses g gigabytes she has to pay $3xg.
Now we have to find the maximum whole number of gigabytes data, she can use within her budget.
Her budget is less than $65.
We can create a inequality expression for this, as follows.
58.50+3g< 65
Calculating further, we get
3g<65-58.50
3g<6.5
g<6.5/3
g<2.163.
Therefore, the maximum whole of gigabytes, she should use to keep the expense within budget is 2 gigabytes.
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A person riding a ferris wheel takes 10 minutes to make one complete trip around thewheel. A function in the form y = A cos (Bt) + C can be used to model thissituation. Based on the information given, determine the values of B.
ANSWER
[tex]\frac{\pi}{300}[/tex]EXPLANATION
The function given is a cosine function:
[tex]A\cos (Bt)+C[/tex]From the function, B can be found as:
[tex]B=\frac{2\pi}{P}[/tex]where P represents the period of the function.
The period is given as 10 minutes (600 seconds), which means that we can find B:
[tex]\begin{gathered} B=\frac{2\pi}{600} \\ B=\frac{\pi}{300} \end{gathered}[/tex]That is the value of B.
a Density is the ratio of mass to volume. An object with a volume of 25 cubic centimeters (cm?) has a mass of 125 grams (g). What is the density, in g/cm", of the object? A 5 B. 25 C. 100 D. 3125
The density is a ratio, defined as
[tex]\rho=\frac{m}{v}[/tex]replace in the ratio of density
[tex]\rho=\frac{125g}{25\operatorname{cm}3}[/tex]the density will be
[tex]\rho=\frac{5g}{\operatorname{cm}3}[/tex]The table below shows the cost of a pizza based on the number of toppings. Defend your choice.
Answer: This problem can be modelled using the linear function, which is as follows:
[tex]y(x)=mx+b[/tex]Based on the information provided, the function can be constructed as follows:
[tex]C(n)=1.5(n-1)+12[/tex]Therefore the answer is Option (A).
twice a number is 24a. 2- n = 24b. 2 + n = 24c. 2 / n = 24 d. 2n = 24
Answer:
d. 2n = 24
Explanation:
Let the number be n
Twice the number = 2 x n
The word 'is" is the equality sign.
Therefore, the expression twice a number is 24 in mathematical symbol is:
[tex]2n=24[/tex]Please help will mark Brainly
Answer:
y = 4x + 3
Step-by-step explanation:
if you try plugging in the x on the table to the x in the equation you should get the answer under the column y to match up
If h is the function given by h(x) = (f • g)(x) where f(x) = squareroot of x and g(x) =(sqrtx)^3, then h(x) =
Given;
[tex]\begin{gathered} f(x)=\sqrt[]{x} \\ g(x)=(\sqrt[]{x)}^3=x^{\frac{3}{2}} \\ (f\circ g)(x)=\sqrt[]{x^{\frac{3}{2}}} \\ h(x)=(f\circ g)(x)=x^{\frac{3}{4}} \end{gathered}[/tex]CORRECT OPTION: D
Kim typed a 36-word paragraph in 2/3 minute. What is his typing speed, in words per minute?
ANSWER
54 words per minute
EXPLANATION
We want to know how much words he can write in 1 minute, so we have to find the ratio of words to minutes by dividing the number of words he wrot
a Ford is traveling 20 miles per hour slower than a Buick. the Buick is traveling at a rate of 65 miles per hour.Let F = the speed of the Ford which formula would correctly calculate the speed of the ford?
The answer is: F - 20mph = 65mph
x + y =5x + y =5one solution no solutions infinity many solutions
We have the same equation twice, then there are infinity many solutions
A painter charges $20 for every hour that he paints. Let h equal the number of hours he paints and e represent his earnings.Select TWO equations that represent the situation.A. e= 20hB. h=20+eC. 20=h+eD. 20=hxeE. e/h=20
The form of the linear equation is
[tex]y=mx+b[/tex]m is the rate of change
b is the initial amount
Since The painter charges $20 every hour, then
The rate is 20
m = 20
Since there is no initial amount of payment, then
b = 0
Since the number of hours is h, then
x = h
Since the earning is e, then
y = e
The equation is
[tex]e=20h[/tex]Then the first equation is A
Divide both sides by h
[tex]\begin{gathered} \frac{e}{h}=\frac{20h}{h} \\ \frac{e}{h}=20 \end{gathered}[/tex]The 2nd equation is E
How high is the top of the ladder from the ground?
We will use the Pythagorean theorem in order to find the missing value that is the height of the top ladder from the ground
[tex]c^2=a^2+b^2[/tex]In our case
c=10
a=5
b=?
We isolate the b
[tex]b=\sqrt[]{c^2-a^2}[/tex]We substitute the values
[tex]b=\sqrt[]{10^2-5^2}[/tex][tex]b=5\sqrt[]{3}[/tex][tex]b=8.66\approx8.7[/tex]round to the nearest tenth the answer is 8.7 ft
Oh no! You have just discovered Superhero C is actually a villain! He plans toactivate an underwater volcano that is 50 miles away. Superhero A is goingto try to stop him.Suppose getting to the underwater volcano requires a combination ofrunning, flying, and swimming.Using the rates from Table 1, make a plan for how far each Superheroshould run, fly, and swim to make sure that Superhero A gets to the volcanobefore Superhero C and can save the world.Note: You must use all three modes of travel.
SOLUTION:
First, let's calculate for superhero C the villian.
Using the three modes of travelling,
He needs to cover a distance of 50 miles
If he:
i. Runs
1 mile in 2 minutes, Hence
50 miles will be in 100 minutes
ii) Flys
2 miles in 2 minutes, Hence
50 miles will be in 50 minutes
iii) Swims
4 miles in 3 minutes, Hence
50 miles will be in 37.5 minutes
Next, let's calculate for superhero A.
Using the three modes of traveling,
He needs to cover a distance of 50 miles
If he:
i. Runs
4 miles in 1 minute, Hence
50 miles will be in 12.5 minutes
ii) Flys
4 miles in 4 minutes, Hence
50 miles will be in 50 minutes
iii) Swims
3 miles in 1 minute, Hence
50 miles will be in 16.67 minutes.
Finally, let's calculate for superhero B.
Using the three modes of traveling,
He needs to cover a distance of 50 miles
If he:
i. Runs
5 miles in 1 minute, Hence
50 miles will be in 10 minutes
ii) Flys
7 miles in 2 minutes, Hence
50 miles will be in 14.29 minutes
iii) Swims
10 miles in 3 minutes, Hence
50 miles will be in 15 minutes.
5. It is an angle formed above the horizontal is called A. Depression B. Elevation C. Right D. Acute
Given
It is an angle formed above the horizontal is called ---
Find
Complete the sentence
Explanation
as we know that the angle of elevation is the angle formed by the line of sight with horizontal .
so , here the correct option is Elevation
Final Answer
Therefore , an angle formed above the horizontal is called Elevation
in a class of 36 students, 6 are in the drama club and 12 are in the art club. if a student is selected at random, what is the probability that the selected student is in the drama club?
Total number of students = 36
Students in drama club = 6
Divide the number of students that are in the drama club (6) by the total number of students (36)
P = 6 /36 = 0.16666666 or 1/6 (fraction form)
5 books weight a total of 6 2/5 pounds. If each book weighs the same amount, how much does each book weigh? Show your work
Hello there. To solve this question, we'll have to remember some properties about mixed fractions.
5 book weight a total of 6 2/5 pounds. If each book weighs the same amount, how much does each book weigh?
We start by converting the fraction from the mixed fraction notation to the normal notation:
Therefore we have:
Now, suppose each book weigh x pounds. 5 books weight will be equal to 5x.
If 5 books weigh 32/5, then we have the following equation:
Divide both sides of the equation by a factor of 5
To find the value of this fraction, the trick is to multiply it by 4/4 (when the denominator is 25):
Each book weighs 1.28 pounds.
If the scale is 1 in: 4 yards, what’s the area of the actual right triangle?
To answer this question, first, we transform the base and the height from inches to yards.
Since the scale is 1 in : 4 yards, then:
[tex]\begin{gathered} 9\text{ in=36 yards,} \\ 6\text{ in=24 yards.} \end{gathered}[/tex]Substituting the above values in the formula for the area of a triangle, we get:
[tex]A=\frac{36\text{yards}\cdot24\text{yards}}{2}\text{.}[/tex]Simplifying the above result, we get:
[tex]A=\frac{864}{2}squareyards=432\text{ square yards.}[/tex]Answer:
[tex]A=432\text{ square yards.}[/tex]Problem: Solve the following equations for the given variable: 1. P = 2L + 2W for W. 2. 2x + 3y = -10 for y.
EXPLANATION
Given the equations:
1. P = 2L + 2W for W. (Subtracting 2L to both sides)
P - 2L = 2l + 2W - 2l (Dividing both sides by 2)
P/2 -2L/2 = W (Simplifying and switching)
W = P/2 - L
2. 2x + 3y = -10 for y. (Subtracting 2x to both sides)
2x - 2x + 3y = -10 -2x (Simplifying)
3y = -2x - 10 (Dividing both sides by 3)
y = -2x/3 - 10/3