Answer:
The area of the rectangle is 168 ft².
Step-by-step explanation:
Formula: A = lw
where l and w are the length and width of the rectangle respectively.
We're given with the length and the width as
a = 12 ft
b = 14 ft
Let's solve for the area using the formula above.
A = lw
A = 12ft(14ft)
A = 168 ft²
Given the number pattern: 20; 18: 14; 8;
a) Determine the nth term of this number pattern.
b) Determine the value of T12 in this number pattern.
c) Which term in this number pattern will have a value of - 36?
A quadratic number pattern has a second term equal to 1, a third term equal to -6 and a fifth term equal to - 14.
a) Calculate the second difference of this quadratic number pattern.
b) Hence, or otherwise, calculate the first term of this number pattern.
Answer:
tn = -n² +n +20; t12 = -112; t8 = -362; 10Step-by-step explanation:
You have two problems involving quadratic sequences. For the sequence that starts 20, 18, 14, 8, ..., you want the n-th term, the 12-th term, and the term number of -36. For the sequence with terms 2, 3, and 5 having values 1, -6, and -14, you want the second difference and the first term.
1. 20, 18, 14, 8The first attachment shows the first and second differences of this sequence each begin with -2. The first of differences at level n can be put into a formula for the n-th term:
∆0 +(n -1)(∆1 +(n -2)/2(∆2 + ...))
We have (∆0, ∆1, ∆2) = (20, -2, -2), so the expression for the n-th term is ...
tn = 20 +(n -1)(-2 +(n -2)/2(-2))
(a) tn = -n² +n +20
Listing the first 12 terms, we find the 12th term is ...
(b) t12 = -112
Locating the term -36 in the list, we find ...
(c) -36 is term 8
2. x, 1, -6, y, -14For a quadratic sequence the third differences are zero. The second attachment shows us the third differences for this sequence are ...
-3(y +11) = 0 ⇒ y = -11
y -x +21 = 0 ⇒ x = 10
That attachment also shows us the second differences are x-8 (or y+13):
x -8 = 10 -8 = 2
(a) The second difference is 2.
(b) The first term is 10.
__
Additional comment
The ability of this free calculator app to perform arithmetic symbolically and to find differences of successive list elements is very helpful for solving questions related to sequences. The linear and quadratic regression capabilities can also be useful for some questions. It pays to know your tools.
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Answer:
∠ 1 and ∠ 3 = 180°
Step-by-step explanation:
∠ 1 and ∠ 3 are same- side interior angles and sum to 180° , that is
∠ 1 + ∠ 3 = 180
of x. i) Let f: R-R be defined by f(x) = mx + c, x = R. If f(0) = 5 and f(1) = 6, find the values. of m and c. Also, find the function f(x).
The values of m and c are m = 1 and c = 5.
The function f(x) is given by: f(x) = x + 5
How to solve the functionTo find the values of m and c in the function f(x) = mx + c, we can use the given information that f(0) = 5 and f(1) = 6.
Let's substitute x = 0 into the function:
f(0) = m(0) + c = 0 + c = c
We know that f(0) = 5, so c = 5.
Now let's substitute x = 1 into the function:
f(1) = m(1) + c = m + c = m + 5 = 6
Subtracting 5 from both sides, we have:
m + 5 - 5 = 6 - 5
m = 1
Therefore, the values of m and c are m = 1 and c = 5.
The function f(x) is given by:
f(x) = mx + c
f(x) = 1x + 5
f(x) = x + 5
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Use table values to graph the Quadratic function.
y = x^2 - 2x + 4
Given the following Mayan Number, write the equivalent Base-10 number in the Answer Box. Each
row (place value) is separated with white space.
> Next Question
Your Answer:
:|| :||- €
The Mayan number || :||- € is equivalent to the base-10 number 1021.
How to find Mayan number?To convert a Mayan number to base-10, use the following steps:
Read the number from bottom to top, starting with the ones place.Assign a value to each digit, based on its position.Multiply each digit by its place value.Add the products together to get the final value.In this case, the values of the digits are as follows:
Ones: 1
Twentys: 0
Four-hundreds: 2
Eight-thousands: 1
The place values are as follows:
Ones: 1
Twentys: 20
Four-hundreds: 400
Eight-thousands: 8000
The final value is calculated as follows:
1 × 1 + 0 × 20 + 2 × 400 + 1 × 8000 = 1021
Therefore, the Mayan number || :||- € is equivalent to the base-10 number 1021.
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Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.
65
-3
2
8
4
K
The x- and y-intercepts of the graph are:
x-intercept: -7y-intercept: 14Finding the x- and y-intercepts of the graphFrom the question, we have the following parameters that can be used in our computation:
-4x + 2y = 28.
For the x-intercepts, we set y to 0
So, we have
-4x = 28
Evaluate
x = -7
For the y-intercepts, we set x to 0
So, we have
2y = 28
Evaluate
y = 14
Hence, the x- and y-intercepts of the graph are -7 and 14, respectively
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Question
Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.
-4x + 2y = 28.
A surveyor is standing 30 feet from the base of a tall building. The surveyor measures the angle of elevation from the ground to the top of the building to be 65 degrees. Find the height of the building to the nearest foot
Answer:
Height = 64 feet
Step-by-step explanation:
(***It's very important to model these kinds of problems. I attached a picture modeling the problem so show how modeling makes it easier to solve the problem)
We know that the building is vertical, and the ground is horizontal. Thus, the ground and the building make a right angle.
Therefore, the top of the building, the base of the building, and the surveyor form a right triangle, where
The distance between the surveyor and the building is a leg of the triangle,The height, h of the building (aka distance between the top of the building and the base) is another leg of the triangle,and the distance between the top of the building and the surveyor is the hypotenuse.Because we're working with a right triangle, we can now find h, the heigh of the building using one of the trigonometric ratios.
We know that the angle of elevation is made by the ground and the distance between the surveyor and top of the building.
When the 65° (angle of elevation) is our reference angle, the height of the building is the opposite side and the distance between the base of the building and the surveyor is the adjacent side.
Thus, we can use the tangent ratio, which is: tan (θ) = opposite / adjacent:
We can now plug in 65 for θ and 30 for the adjacent side. This will allow us to find the opposite side, which is the heigh of the building:
tan (65) = h / 30
30 * tan(65) = h
64.33520762
64 = h
Thus, the height of the building to the nearest foot is 64 feet.
Consider the relationship 9r+8t=9
Given the relationship, 9r + 8t = 9, the relationship as a function r = f(t) will be (9 - 8t) / 9.
The relationship 9r + 8t = 9 as a function r = f(t), one is needed to isolate the variable r first on one side of the equation.
Taking with the original equation:
9r + 8t = 9
Subtract 8t from both sides in order to isolate the term with r:
9r = 9 - 8t
Divide both sides by 9 in order to solve for r:
r = (9 - 8t) / 9
Therefore, the relationship 9r + 8t = 9 can be written as the function:
r = (9 - 8t) / 9.
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Your question seems incomplete, the probable complete question is:
Consider the relationship 9r + 8t = 9. a. Write the relationship as a function r = f(t).
y=-2x-1; y=-2x+6; is this parallel, perpendicular, or neither
Answer:
Step-by-step explanation:
first, to find if they are perpendicular, we would have to determine their slopes.
y=-2x-1, we know that the slope is -2 (due to y=mx+b, where m is the slope)
y=-2x+6, we also know that the slope is -2.
since the slope is equal, it would be parallel.
However, if the slopes were negative reciprocals, (e.g. 1/2 & -2) they would be perpendicular.
If the slopes were neither negative reciprocals or equal, it would be neither.
100 Points! Geometry question. Photo attached. Find x and y. Please show as much work as possible. Thank you!
The values of given x and y is,
x = 6 and y = 13/2
Since we know that,
Basic proportionality theorem,
The basic proportionality theory was developed by Thales, a great Greek mathematician; hence, it is also known as the Thales theorem. According to the great mathematician, the ratio of any two matching sides of any two equiangular triangles is always the same. The basic proportionality theorem (BPT) was suggested based on this premise.
Since we know that,
In the figure we that,
⇒ 2x + 1 = x +7
⇒ x = 6
Similarly
⇒ 3y - 8 = y +5
⇒ y = 13/2
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cos(a+b)= cosa.cosb.-Sina SinB to Find the Formula of Sin (a-B]
The formula for sin(a - b) is sin(a)cos(b) - cos(a)sin(b).
To find the formula for sin(a - b), we can use the identity for cosine of a sum of angles, which states that:
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
We can rearrange this equation to solve for sin(a - b):
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
cos(a + b) = cos(a)cos(b) + (-1)(sin(a)sin(b)) [multiplying sin(b) by -1]
cos(a + b) = cos(a)cos(b) + sin(a)(-sin(b)) [rearranging terms]
cos(a + b) = cos(a)cos(b) - sin(a)sin(b) [sin(b) can be replaced by -sin(b)]
Comparing this equation with the given identity, we can see that:
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)
Therefore, the formula for sin(a - b) is sin(a)cos(b) - cos(a)sin(b).
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Jckson plans to make an open box with the dimensions shown as a prop for the school play. the dimensions are 5 3.75 and 2.5
Based on the assumption mentioned above, the dimensions of the open box would be:
Length: 5 units
Width: 3.75 units
Height: 2.5 units.
To create an open box as a prop for the school play, Jackson will need three dimensions: length, width, and height. The given dimensions provided are 5, 3.75, and 2.5, but it is not specified which dimension corresponds to which measurement.
To determine which dimension represents which measurement (length, width, or height), we need additional information or clarification. Typically, the length refers to the longest side of the box, the width is the shorter side, and the height is the vertical dimension.
If we assume that 5 represents the length, 3.75 represents the width, and 2.5 represents the height, we can proceed with those dimensions. However, it's important to note that without confirmation or further context, this assumption may not be accurate.
Therefore, based on the assumption mentioned above, the dimensions of the open box would be:
Length: 5 units
Width: 3.75 units
Height: 2.5 units.
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4 - 32 x (-0.25)-12/ 1/3
Answer:
8x is your answer.
Step-by-step explanation:
The photo shows how it's solved.
find the perimeter of a rectangle where the width is 2x^2 + 5x-4 and the length is 3x+2
Answer:
The perimeter of the rectangle is P = 4x^2 + 16x - 4.
Step-by-step explanation:
1. L = 3x + 2, W = 2x^2 + 5x - 4
2. P = 2(L + W)
3. P = 2((3x + 2) + (2x^2 + 5x - 4))
4. P = 2(2x^2 + 8x - 2)
5. P = 4x^2 + 16x - 4
Which of the following graphs represent a function? Check all that apply.
A curve that rises from left to right, graphed in a coordinate plane
A graph in a coordinate plane. The graph starts as a line that ascends from left to right. Then it becomes a vertical line going up.
A graph in a coordinate plane. The graph begins at 0, 0 and curves up and down, creating peaks and valleys. As the graph moves to the right, the peaks and valleys get smaller and closer together.
Three-quarters of a circle, graphed in a coordinate plane
A graph in a coordinate plane. The graph curves up and down, creating peaks and valleys, but there is no pattern to these peaks and valleys.
A graph in a coordinate plane. The graph curves back and forth, from left to right.
If s(x) = 2x² and f(x) = 3x, which value is equivalent to (s-f)(-7)?
O-439
O-141
O 153
O 443
The value of expression (s - f) (- 7) would be,
⇒ (s - f) (- 7) = 119
We have to given that,
Functions are defined as,
⇒ s (x) = 2x²
⇒ f (x) = 3x
Now, We can find the value of (s - f) (- 7) is,
⇒ (s - f) (- 7)
⇒ s (- 7) - f (- 7)
⇒ 2 (- 7)² - (3 × - 7)
⇒ 2×49 + 21
⇒ 98 + 21
⇒ 119
Therefore, The value of expression (s - f) (- 7) would be,
⇒ (s - f) (- 7) = 119
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A number cube is rolled 500 times. Here are the results: Outcome Rolled 1 2 3 4 5 6 Calculate the following probabilities to the nearest thousandth. The theoretical probability of rolling a 5 or 6 The experimental probability of rolling a 5 or 6 [Choose ] Number of Rolls 81 95 79 89 80 76 [Choose]
Answer:
The theoretical probability of rolling a 5 or 6 can be calculated by finding the sum of the probabilities of rolling a 5 and rolling a 6. Since the number cube has 6 equally likely outcomes, the probability of rolling a 5 or 6 is:
Theoretical probability = (probability of rolling a 5) + (probability of rolling a 6)
= 1/6 + 1/6
= 2/6
= 1/3
The experimental probability of rolling a 5 or 6 can be calculated by dividing the number of times a 5 or 6 was rolled by the total number of rolls. From the given data, the number of rolls for each outcome is:
Outcome | Number of Rolls
1 | 81
2 | 95
3 | 79
4 | 89
5 | 80
6 | 76
Experimental probability = (number of times a 5 or 6 was rolled) / (total number of rolls)
= (number of times a 5 was rolled + number of times a 6 was rolled) / 500
= (80 + 76) / 500
= 156 / 500
= 0.312
Therefore, the theoretical probability of rolling a 5 or 6 is 1/3, and the experimental probability is approximately 0.312.
Step-by-step explanation:
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The cost for an eighth-grade party is $450 for room rental, entertainment, and decorations, plus $20 per person for food. Tickets for the party are sold for $25. What is the break-even point
A-45 TICKETS
B-90 TICKETS
C-18 TICKETS
D-23 TICKETS
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Answer:
B. 90 tickets
Step-by-step explanation:
For t tickets sold, we want the revenue equal to the cost.
25t = 450 +20t
5t = 450 . . . subtract 20t
t = 90 . . . . . divide by 5
90 tickets is the break-even point.
___
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Which statement correctly explains the association of the scatter plot? Since the Y values increase as the X values increase the Scatter plot shows a positive association. Sense to Weibo use decrease as the X values increase the scatter plot shows a positive association.
The statement "Since the y-values decrease as the x-values increase, the scatter plot shows a negative association" correctly explains the association of the scatter plot.
From the plot, we see that:
Any time the Y value decreases, it will be a negative valueAny time the X value decreases, it will be a negative valueA scatter pIot is a type of graph that shows the reIationship between two variables. The variabIes are plotted on the x-axis and y-axis, and each data point is represented by a dot. The pattern of the dots can be used to infer the reIationship between the variables.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
A. 1.78cm².
B. 331.34 square meters.
Step-by-step explanation:
The area of the shaded region in a circle if the radius and central angle is given can be calculated using the following formula:
Area of shaded region = (θ/360) * πr²
Where:
θ is the central angle in degrees. r is the radius of the circle. π is the mathematical constant pi, approximately equal to 3.14.A.
If the radius is 2 meters and the central angle is 51 degrees, then the area of the shaded region is:
Area of shaded region = (51/360)*π*2² = 0.357π m²
≈ 1.78 square meters
Therefore, the area of the shaded region is approximately 1.78square meters.
Therefore, the area of the shaded region is 1.78cm².
B.
If the radius is 12.5 meters and the central angle is 243 degrees, then the area of the shaded region is:
Area of shaded region = (243/360)*π*12.5² = 105.47π m²
≈ 105.47π square meters
Therefore, the area of the shaded region is approximately 331.34 square meters.
Graph the line with y-intercept 4 and slope 2.
Answer is in the file atttached.
What is the range of g(x) = |x + 3| + 2? A. [-3, ∞) B. (-∞, 2] C. [2, ∞) D. (-∞, ∞)
Answer:
C. [2, + ∞)-----------------
Given function:
g(x) = | x + 3| + 2We know that absolute value is non-negative, hence |x + 3| has a minimum value of 0 when x = - 3. Then the function has a minimum value of 2.
The range is the set of output values. As we see given function has a minimum value of 2 and no maximum value.
It can be shown as:
g ∈ [2, + ∞)The matching choice is C.
Question 8 (2 points)
What is the area of this figure?
6 yd
4 yd
4 yd
4 yd
4 yd
Answer: The figure you are describing seems to be a rectangle with a length of 6 yards and a width of 4 yards. The area of a rectangle is calculated by multiplying its length by its width. So, the area of this rectangle would be 6 yd * 4 yd = 24 square yards.
Answer: Total Area = 36yd
Step-by-step explanation:
You have to find the area of both square and triangle.
Area Triangle = .5x5x8= 20yd
Area Square = 4x4 = 16yd
Triangle + Square - 20yd+16yd = 36yd
Plant cells and animal cells were observed under a microscope. The characteristics of two cells are listed below.
Cell X: Has chloroplast
Cell Y: Does not have a cell wall
Which statement about the two cells is correct?
Cell X has a cell membrane.
Cell X has a small vacuole.
Cell Y has a large vacuole.
Cell Y has chloroplast.
PLEASE HELP!!!
The correct statement about the two cells is:Cell Y has a large vacuole.
Cell X is described as having chloroplast, which is an organelle found in plant cells and is responsible for photosynthesis. This indicates that Cell X is a plant cell. Since the presence of chloroplast is mentioned specifically for Cell X and not for Cell Y, it implies that Cell Y is an animal cell, as animal cells do not contain chloroplasts.
Cell X having a cell membrane is not stated explicitly, and it is a characteristic shared by both plant and animal cells. Therefore, we cannot conclude whether Cell X has a cell membrane or not based on the given information.
The statement Cell X has a small vacuole is not mentioned in the provided characteristics, so we cannot determine the size of the vacuole in Cell X.
On the other hand, Cell Y not having a cell wall is mentioned, which is a characteristic specific to animal cells.Cell Y does not have a cell wall.
The correct statement based on the given information is that Cell Y has a large vacuole, while the other statements cannot be determined from the provided characteristics.
The correct statement about the two cells is: Cell Y has a large vacuole.
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Answer:
Angles 3 and 5 are consecutive interior angles.
What is 7385.35 multiplied by 527.35
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Answer:
D. Alternate Interior Angles Converse
Edplanation:
13 ~= 12
13 altenated angle to nr.10
13 is parpendicular to nr.15 and 15 is alternate to 12
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
area of A = πr² = π7² = 153.9 m²
area of B = πr² = π9² = 254.5 m²
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer: A = 83.75
Step-by-step explanation:
A=a+b
2h=12.5+21
2·5=83.75
Janis wants to carpet her living room. Which means 15 feet by 12 feet. She picked out a nice style that Cost $2 per square foot How much will it cost.
Pls help