Answer:
Width is 2 feet and the length is 6 feet.
Step-by-step explanation:
The area of a rectangle is A = l*w. Here the length is 4 feet more than the width or 4 + w and the width is w. So the area is A = w(4+w) = 4w + w²
If the dimensions are changed then the expressions will change. The width is increased by 3 feet. This means the width w becomes w + 3. The length is increased by 3 feet. This means the length becomes 4 + w + 3 = 7 + w. So the area of the new triangle is A = (w+3)(7+w) = w² + 10w + 21.
The new area is 33 feet longer. We can add 33 to the original area then set them equal to each other and solve for w.
w² + 10w + 21 = 33+4w + w² Subtract w² from both sides.
10w + 21 = 33+4w Subtract 4w from both sides.
6w + 21 = 33 Subtract 21 from both sides.
6w = 12 Divide by 6.
w = 2 feet
The original width w is 2 feet. This means the original length which was 4 + w = 4 + 2 = 6 feet.
To solve the problem, set up two equations based on the given information, substituting the first equation into the second to solve for 'w' (width) and 'l' (length) - the original dimensions of the rectangle.
Explanation:To solve this problem, we'll first set up two equations based on the information provided in the question. Let's use 'w' to represent the width of the original rectangle and 'l' to represent its length. According to the problem, we know that:
The length of the rectangle is 4ft greater than its width. So, l = w + 4. If each dimension is increased by 3, the new area (length times width) is 33 square feet. So, (w+3) * (l+3) = 33.
Substitute the first equation (l = w + 4) into the second to find w and then l. This is the system of equations needed to find the original dimensions of the rectangle.
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Write and equation of the translated or rotated graph in general form (picture below)
Answer:
The answer is ellipse; 3x² + y² + 6x - 6y + 3 = 0
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
* 3x² + y² = 9
∵ A = 3 , B = 0 , C = 1
∴ B² - 4 AC = (0)² - 4(3)(1) = -12
∴ B² - 4AC < 0
∴ The graph is ellipse or circle
* If A and C are nonzero, have the same sign, and are not
equal to each other, then the graph is an ellipse.
* If A and C are equal and nonzero and have the same
sign, then the graph is a circle.
∵ A and C have same signs with different values
∴ It is an ellipse
* Now lets study T(-1 , 3), that means the graph will translate
1 unit to the left and 3 units up
∴ x will be (x - -1) = (x + 1) and y will be (y - 3)
* Lets substitute the x by ( x + 1) and y by (y - 3) in the equation
∴ 3(x + 1)² + (y - 3)² = 9
* Use the foil method
∴ 3(x² + 2x + 1) + (y² - 6y + 9) = 9
* Open the brackets
∴ 3x² + 6x + 3 + y² - 6y + 9 = 9
* Collect the like terms
∴ 3x² + y² + 6x - 6y + 12 = 9
∴ 3x² + y² + 6x - 6y + 12 - 9 = 0
∴ 3x² + y² + 6x - 6y + 3 = 0
* The answer is ellipse of equation 3x² + y² + 6x - 6y + 3 = 0
I f(x)= square root x-3 which inequality can be used to find the domain of f(x)
Answer:
[tex]x\ge3[/tex]
Step-by-step explanation:
The given function is [tex]f(x)=\sqrt{x-3}[/tex].
The domain of this function refers to all values of x, for which the function is defined.
This square root function is defined when the expression under the radical sign is greater or equal to zero.
That is; the domain of the function is [tex]x-3\ge0[/tex]
This implies that [tex]x\ge3[/tex]
Kylie and her two sisters each have 1/4 cup of chopped pineapple . How much do they have in all
you want to take 3×1/4 which would equal 0.75. but if you want to change it into a fraction it would be 3/4
The subway sold 439 tickets in one day. It wants to sell that amount each day over the next 13 days. How many tickets does the subway need to sell over the next 13 days?
Answer:
5707 tickets
Step-by-step explanation:
We want to sell 439 tickets each day for the next 13 days
439 * 13 =5707
We need to sell a total of 5707 tickets
A box of granola is 3 inches wide 4 inches long and 6 inches high . The box is half empty.What is the volume of granola bar left in the box
Answer:
[tex]36\ in^{3}[/tex]
Step-by-step explanation:
we know that
If the box is half empty, then the box is half full
therefore
Find the volume of the box and then divide by two to calculate the volume of granola bar left in the box
The volume of the box is
[tex]V=(3)(4)(6)=72\ in^{3}[/tex]
The volume of granola bar left in the box is
[tex]72/2=36\ in^{3}[/tex]
Let's illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. The given population is the scores of ten female students in a class. Student 0 1 2 3 4 5 6 7 8 9 Weight 136 99 118 129 125 170 130 128 120 147 The parameter of interest is the mean weight in pounds ???? in this population. The sample is an SRS of size ????=4 drawn from the population. Because the students are labeled zero to nine, a single random digit from Table A chooses one student for the sample. (a) Find the mean of the ten weights in the population. This is the population mean ???? . (Enter your answer rounded to one decimal place.)
Answer:
a: sample mean: 130.2 pounds
This is not the population mean
Step-by-step explanation:
To find the mean weight of the sample, add up all the values and divide by the total number of values entered. In this case, 10, so we have...
mean: (136 + 99 + 118 + 129 + 125 + 170 + 130 + 128 + 120 + 147)/10 =
1302/10 = 130.2
This is not the population mean. It is the mean of the sample. We would have to know more information to make a conjecture about the population mean.
Final answer:
The population mean of the students' weights is determined by summing all the weights and dividing by the number of students, resulting in 130.2 pounds.
Explanation:
To find the population mean (denoted as μ), we add up all the weights of the ten students in the population and divide it by the total number of students. Let's do the calculation:
The weights of the students are 136, 99, 118, 129, 125, 170, 130, 128, 120, and 147 pounds.
The sum of these weights is 136 + 99 + 118 + 129 + 125 + 170 + 130 + 128 + 120 + 147 = 1302 pounds.
Since there are 10 students in the population, we divide the total weight by 10 to find the mean:
μ = ΣX / N = 1302 / 10 = 130.2 pounds
Therefore, the population mean (μ) is 130.2 pounds.
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 5x − 6y = 3 10x − 12y = 6 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =
Final answer:
The system of equations has infinitely many solutions because they represent the same line. The solution can be written in terms of the parameter t as (x, y) = ((3 + 6t)/5, t).
Explanation:
The student's question involves determining the type of solution a system of two linear equations has and finding the solution if it exists. The given system of equations is:
5x - 6y = 3
10x - 12y = 6
Notice that the second equation is just the first equation multiplied by 2. This means the system has infinitely many solutions because the two equations are actually the same line. To find these solutions in terms of a parameter t, we can solve the first equation for x as follows:
Choose t to represent y (i.e., let y = t).
Substitute y = t into the first equation to get 5x - 6t = 3.
Solve for x to find x = (3 + 6t)/5.
Therefore, the solutions to the system can be expressed as (x, y) = ((3 + 6t)/5, t), where t is any real number.
Given csc x/cot x =square root 2, find a numerical value of on trigonometric function of x
Answer:
a. sec(x) = √2
Step-by-step explanation:
csc(x)/cot(x) = (1/sin(x))/(cos(x)/sin(x)) = 1/cos(x) = sec(x) = √2
Answer:
The correct answer is a) [tex] \sec(x) = \sqrt{2}[/tex].
Step-by-step explanation:
Here we need to use some trigonometric identities:
[tex] \csc(x) = \frac{1}{\sin(x)}[/tex],[tex] \cot(x) = \frac{\cos(x)}{\sin(x)} [/tex].Then, substituting the above identities in the given formula we have:
[tex] \frac{\csc(x)}{\cot(x)} = \frac{\frac{1}{\sin(x)}}{\frac{\cos(x)}{\sin(x)}} = \frac{1}{\sin(x)}\frac{\sin(x)}{\cos(x)} [/tex]
Notice that we can simplify the sinus in both fractions. Thus,
[tex]\frac{\csc(x)}{\cot(x)} = \frac{1}{\cos(x)} = \sec{x}[/tex].
From here, the solutions is pretty straightforward.
Im on a time limit! could someone help me with this?
Answer:
B is the answer because the other equations have real numbers
Step-by-step explanation:
Answer:
B is the correct answer
Step-by-step explanation:
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 0.3x − 0.4y = 0.2 −0.2x + 0.5y = 0.1 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =
Answer:
One solution. It is (2, 1)
Step-by-step explanation:
Clear out all fractions right away by multiplying all terms by 10. Then:
0.3x − 0.4y = 0.2
−0.2x + 0.5y = 0.1
becomes
3x - 4y = 2
-(2x + 5y = 1)
Multiply the first row by 2 and the second row by 3, which produces:
6x - 8y = 4
-6x +15y = 3
Combining like terms results in: 7y = 7. Then y = 1.
Now subst. 1 for y in the first equation, to calculate x:
3x - 4(1) = 2
3x = 2 + 4 = 6. Then x = 2.
The solution is (2, 1). There is ONLY ONE SOLUTION.
Which is log x+ 6 log(x+7) written as a single logarithm.
Answer: option d.
Step-by-step explanation:
To solve this problem you must keep on mind the properties of logarithms:
[tex]log(b)-log(a)=log(\frac{b}{a})\\\\log(b)+log(a)=log(ba)\\\\a*log(b)=log(b)^a[/tex]
Therefore, knowing the properties, you can write the expression gven in the problem as shown below:
[tex]5logx+6log(x+7)=logx^5+log(x+7)^6=logx^5(x+7)^6[/tex]
Then, the answer is the option d.
Answer:
D
Step-by-step explanation:
We can use 2 properties of logs to write this as single logarithm:
1. [tex]Log(A^B)=BLog A[/tex]
2. Log x + Log y = Log (x*y)
We can use property #1 to write this as:
[tex]5Logx+6Log(x+7)\\=Logx^{5}+Log(x+7)^{6}[/tex]
Now we can use property #2 to write this as:
[tex]Logx^{5}+Log(x+7)^{6}\\=Log((x^5)((x+7)^6)\\=Logx^{5}(x+7)^{6}[/tex]
We see that answer choice D is right.
Circle O has a circumference of 88 cm. What is the length of the radius of the circle?
Answer is 44cm
Step-by-step explanation:
Write an equation that represents a linear function that has a slope of 4/5 and a y intercept of -6
The equation is y =(4/5)x -6
Answer:
[tex]\large\boxed{y=\dfrac{4}{5}x-6}[/tex]
Step-by-step explanation:
The slope-intercept form of the equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the slope [tex]m=\dfrac{4}{5}[/tex] and the y-intercept [tex]b=-6[/tex].
Substitute:
[tex]y=\dfrac{4}{5}x-6[/tex]
Ben drove 350 miles in 6 1/2 hours Marcie drove 520 miles on 12 1/4 hours who drove faster
Answer:
Ben drove faster
Step-by-step explanation:
BEN:350 miles / 6.5 hours = 53.84 miles per hour
MARCIE:520 miles / 12.25 hours = 42.44 miles per hour
53.84 is faster than 42.44 therefore Ben is faster.
A roll of 40 quarters weighs 8 ounces. Which proportion can be used to find the weight in ounces, w, of 200 quarters?
Answer:
40oz
Step-by-step explanation:
just make it easy 20 quarters is 4 oz multiply that by 10 it would be 200 quarters and 40 oz
the weight of 200 quarters is 40 ounces.
The question asks to find the weight in ounces, w, of 200 quarters, given that a roll of 40 quarters weighs 8 ounces. To solve this problem, we can set up a proportion which is a statement that two ratios are equal. Since we know the weight of 40 quarters, we can compare this to the weight of 200 quarters. The proportion can be set up as follows:
40 quarters / 8 ounces = 200 quarters / w ounces
To find w, simply cross-multiply and divide:
(40)(w) = (8)(200)40w = 1600w = 1600 / 40w = 40 ouncesTherefore, the weight of 200 quarters is 40 ounces.
A division problem can be written out using repeated subtraction. Which division problem is solved below? 40 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4
Answer:
The problem that is getting solved is 40 divided by zero
Answer:
Step-by-step explanation:
This is a faulty way of showing it. What you are solving here is
40 - 10*4 which is 0. What is transcribed is not equivalent to any division that I can see.
Perhaps 0/40
If you have answers, please list them.
If you roll a number cube 22 times about how many times do you expect to roll a numeber Less than 4?
Answer:
About 7 times
Step-by-step explanation:
Which graph represents the solution set of the system of inequalities?
Answer:
your first Graph :D Hope this helps
The first equation is greater than or equal to, so the line would be solid.
The second equation is less than so the line would be dotted.
Greater than or equal to would be above the solid line, less than would be to the left of the dotted line.
The top left graph is correct.
Evaluate each log without a calculator
[tex]log_{4} \frac{1}{16}[/tex]
[tex]log_{2}\sqrt[5]{32}[/tex]
QUESTION 1
The given logarithmic expression is
[tex]\log_4(\frac{1}{16})[/tex]
We rewrite [tex]\frac{1}{16}[/tex] in the index form to base 4.
This implies that;
[tex]\log_4(\frac{1}{16})=\log_4(4^{-2})[/tex]
We now apply the power rule: [tex]\log_a(m^n)=n\log_a(m^n)[/tex].
[tex]\log_4(\frac{1}{16})=-2\log_4(4)[/tex]
Recall that logarithm of the base is 1.
[tex]\log_4(\frac{1}{16})=-2(1)[/tex]
[tex]\log_4(\frac{1}{16})=-2[/tex]
QUESTION 2
The given logarithm is;
[tex]\log_2(\sqrt[5]{32})[/tex]
[tex]\log_2(\sqrt[5]{2^5})[/tex]
This is the same as;
[tex]\log_2(2^{5\times \frac{1}{5}})[/tex]
[tex]\log_2(2^{1})[/tex]
[tex]\log_2(2)=1[/tex]
Write an expression to represent: Four less than the quotient of a number x and 5
The mathematical representation of the expression 'Four less than the quotient of a number x and 5' is 'x/5 - 4'. This involves division and subtraction of the number x.
Explanation:The subject of this question is Mathematics, particularly algebraic expressions. In this case, you are being asked to express the phrase 'Four less than the quotient of a number x and 5' as an algebraic expression. The 'quotient of a number x and 5' implies division of the number x by 5, which is represented as 'x/5'. 'Four less than' signifies a subtraction of four from the preceding expression. Therefore, the whole expression can be written as 'x/5 - 4'.
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True or false (Picture provided)
Answer:
The correct answer is F (false)
Step-by-step explanation:
Points to remember
Sin θ = Opposite side/Hypotenuse
Tan θ = Opposite side/Adjacent side
Sec θ = Hypotenuse/Adjacent side
To find Sin 45, Sec 45 and Tan 45
We have Sin 45 = 1/√2
Sec 45 = 1/Cos 45 = 1/(1/√2) = √2
Tan 45 = 1
To find Sec θ/Tan θ
Here θ = 45
Sec (45)/Tan (45) = √2/1 = √2 ≠ Sinθ
Therefore the correct answer is False(F)
(13 points) HELP PLEASEEE!
Subtract the equations
3x + 4y = 17
- (3x + 2y = 3)
Answer:
y = 7 x = -11/3
Step-by-step explanation:
3x + 4y = 17
- (3x + 2y = 3)
Distribute the minus sign and add together
3x + 4y = 17
- 3x - 2y = -3
------------------------
2y = 14
Divide by 2
2y/2 = 14/2
y = 7
Now find x
3x + 4y = 17
3x +4(7) = 17
3x +28 = 17
Subtract 28 from each side
3x+28 -28 = 17 -28
3x = -11
Divide each side by 3
3x/3 = -11/3
x = -11/3
Answer:
A.2y=14
Step-by-step explanation:
Apex
Hope this helps Have a nice day
Type the correct answer in each box. The length of a rectangle is 3 inches more than its width. The perimeter of the rectangle is 34 inches. The length of the rectangle is inches ?, and its width is ? Inches.
Answer:
The length is 10 inches and the width is 7 inches.
Step-by-step explanation:
A rectangle is shape with 4 sides where 2 pairs of sides are equal and form 4 perpendicular angles. 1 pair of sides is the width and is distance w. 1 pair of sides id the length and is 3 inches more than the width or 3 + w. The total distance around the shape is the perimeter. We know the perimeter is 34 inches. Add each side together and set it equal to 34. Then solve for w.
P = l + l + w + w
34 = 3 + w + 3 + w + w + w
34 = 6 + 4w
28 = 4w
7 = w
This means its length which is 3 inches longer is 7 + 3 = 10.
If 2/3x + 4 less than or equal to 14 what is the largest possible value of 7x - 2
⅔x+4≤14
⅔x≤10
2x≤30
x≤15
Max value of x is 15
7x-2≤?
7(15)-2=105-2=103
7x-2≤103
Greatest value for 7x-2 is 103
A rectangular piece of stained glass has the dimensions shown in the diagram. What is the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid?
Answer:
The correct option is D) [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Consider the provided figure.
We need to find the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid.
For this first find the total area as shown:
The given figure is a rectangle.
The area of rectangle is [tex]l\times b[/tex]
Where, l = 6 cm + 3 cm = 9 cm and b = 5cm
Therefore the area of the rectangle is;
Area of rectangle = [tex]9cm\times 5cm=45cm[/tex]
Now find the area of trapezoid.
The area of trapezoid is: [tex]\frac{a+b}{2}h[/tex]
Where h is the height and a and b are the parallel sides.
Area of trapezoid = [tex]\frac{9+3}{2}\times 5=30[/tex]
Thus, the area of trapezoid is 30 cm.
Therefore, the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid is:
[tex]Probability=\frac{\text{Area of trapezoid}}{\text{Area of rectangle}}[/tex]
[tex]Probability=\frac{30}{45}=\frac{2}{3}[/tex]
Hence, the correct option is D) [tex]\frac{2}{3}[/tex]
Answer:
2/3
Step-by-step explanation:
I got it right
If they are going 12 miles per 1/3 hour . What is the average speed per hour in miles
Answer:
12 miles per (1/3) hour equals
36 miles per hour
Step-by-step explanation:
The United States of House of Representatives has 35 members more than four times the number of members in the United States Senate Define a variable and write an expression to represent the number of members in the House of Representatives then find the number of members in the House of Representatives if there are 100 members in the Senate
Answer:
House of representatives=h
United states senate= u
h=4u+35
If u=100:
h=4(100)+35
h=400+35
h=435
Hope this helps :}
What is the recursive rule for this geometric sequence?
-64,-16,-4,-1, ...
Enter your answers in the boxes
An= __ •an-1
A1= __
Answer:
1/4
-64
Step-by-step explanation:
If f( x ) = x - 5, then match each of the following.
1 .
-6
2 .
-4
3 .
-5
4 .
3
5 .
0
6 .
-3
f(-1)
f(0)
f(1)
f(2)
f(5)
f(8)
Answer:
1. f(-1)
2.f(1)
3.f(0)
4.f(8)
5.f(5)
6.f(2)
Step-by-step explanation:
[tex]f(-1)-------------\ \ \ \ -6\\\\f(0)-------------\ \ \ \ \ \ \ -5\\\\f(1)-------------\ \ \ \ \ \ \ -4\\\\f(2)-------------\ \ \ \ \ \ \ -3\\\\f(5)-------------\ \ \ \ \ \ \ \ \ 0\\\\f(8)-------------\ \ \ \ \ \ \ \ \ 3[/tex]
Step-by-step explanation:We are given a function f(x) by:
[tex]f(x)=x-5[/tex]
It is a linear function with positive slope i.e. 1.
Also, now we will calculate the value of the function at different values of x and match the function to it's corresponding value.
a)
[tex]f(-1)[/tex]
[tex]f(-1)=-1-5\\\\i.e.\\\\f(-1)=-6[/tex]
b)
[tex]f(0)[/tex]
Now when x=0 we have:
[tex]f(0)=0-5\\\\i.e.\\\\f(0)=-5[/tex]
c)
[tex]f(1)[/tex]
when x=1
[tex]f(1)=1-5\\\\i.e.\\\\f(1)=-4[/tex]
d)
[tex]f(2)\\\\f(2)=2-5\\\\i.e.\\\\f(2)=-3[/tex]
e)
[tex]f(5)[/tex]
when x=5 we have:
[tex]f(5)=5-5\\\\i.e.\\\\f(5)=0[/tex]
f)
[tex]f(8)[/tex]
Put x=8
[tex]f(8)=8-5\\\\i.e.\\\\f(8)=3[/tex]
Colby is making a home video consisting of a 5-minute introduction followed by several short skits. Each skit is 6 minutes long. If Colby's video is 101 minutes long, how many skits are in his video?
The answer is: There are a total of 16 skits in the video.
Why?From the statement, we know that the total length of the video is 101 minutes and it contains a 5-minute introduction, the rest of the minutes are short skits (which are 6 minutes long each one).
So, we need to write the following equations:
First equation:
[tex]TotalDuration=Introduction+n*Skit[/tex]
Second equation:
[tex]Skit=6Minutes[/tex]
Where,
[tex]TotalDuration=101Minutes\\Introduction=5Minutes\\n=NumberOfSkits\\Skit=6Minutes[/tex]
So, replacing and substituting the second equation into the first equation we have:
[tex]101Minutes=5Minutes+n*6Minutes\\n*6Minutes=101Minutes-5Minutes\\n*6Minutes=96Minutes\\n=\frac{96Minutes}{6Minutes}=16[/tex]
So, there are a total of 16 skits in the video.
Let's prove it substituting "n" into the first equation:
[tex]101Minutes=5Minutes+16*6minutes\\101Minutes=5Minutes+96Minutes\\101Minutes=101Minutes[/tex]
Have a nice day!
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