In response to the given question, we can state that As a result, the square answer is (D) 1 square yard.
what is a square?In Euclidean geometry, a square is an equilateral quadrilateral having four equal sides and four equal angles. It is also known as a rectangle with two adjoining sides that have the same length. A square is an equilateral quadrilateral because it has all four equal sides and all four equal angles. Square angles are 90 degree or straight angles. Moreover, the square's diagonals are evenly spaced and divide at a 90-degree angle. an adjacent rectangle with two equal sides. A quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides that create a right angle. Rhombus with straight sides.
Then, calculate the length of each side of the square enclosure.
Vanessa utilised the garage's outer wall for one of the sides, so she only needed to create three more sides. She utilised three yards of fence for these three sides, therefore each must be three-thirds of a yard long.
As a result, the area of the enclosure is equal to the length of one side squared:
Area = side length + 1 yard + 1 yard = 1 square yard
As a result, the answer is (D) 1 square yard.
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Prove or disprove the statement: The point (2, √5) lies on the circle centered at the origin with radius 3. The radius of the circle is The exact distance from the center (0, 0) to the point (2, √5) is (2. √5) lie on the circle. units.
Answer:
The statement is correct
Step-by-step explanation:
Use the equation of a circle:
x² + y² = r²
x² + y² = 3²
then enter the coordinates of the point (2; √5):
2² + (√5)² = 9
4 + 5 = 9 (that is correct)
The point (2, √5) lies on the circle centered at the origin with radius 3 is True statement.
What is Equation of Circle?The standard equation of a circle is given by:
(x-h)² + (y-k)² = r²
Where (h,k) is the coordinates of center of the circle and r is the radius.
We have,
The point (2, √5) lies on the circle centered at the origin with radius 3.
We know the equation of circle at origin is
x² + y² = r², where r is the radius of circle
So, x² + y² = 3²
Now. to check the point put x= 2 and y= √5 as
x² + y²
= 2² + √5²
= 4 +5
= 9
Thus, the given statement is Correct.
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please help me i’m struggling and i really need to turn this in
The vertices of the image are: L' (1, -2), M' (2,-2), N' (2,2), P' (1, 2)
What is Vertices?In mathematics and geometry, a vertex (plural: vertices) refers to a point where two or more lines, edges, or curves meet. In three-dimensional geometry, a vertex is typically the point where three or more edges or lines intersect to form a corner or a point.
[tex]r_{x-axis}[/tex] → Reflection across the x-axis
Transformation rule: (x, y) → (x,-y)
L(2, 4)→ [tex]L^{r}[/tex] (2,-4)
M (4,4) → [tex]M^{r}[/tex] (4-4)
N (4,-4) → [tex]N^{r}[/tex] (4, 4)
P (2-4) → [tex]P^{r}[/tex] (2, 4)
D0.5 →Dilation Centered at the origin by а scale factor of 0.5
Transformation rule: (x, y) → (0.5x,0.5y)
[tex]L^{r}[/tex] (2-4) → L' (1, -2)
[tex]M^{r}[/tex] (4,-4) → M' (2, -2)
[tex]N^{r}[/tex] (4, 4) → N' (2, 2)
[tex]P^{r}[/tex] (2, 4) → P' (1, 2)
The vertices of the image are:
L'(1, -2), M'(2,-2), N'(2,2), P' (1, 2)
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The sum of the age of Afful and Naomi is 34years five years to come,Afful will be 2 times the age of Naomi now.How old are they now
Answer:
Afful is 21 and Naomi is 13.
Step-by-step explanation:
x=Afful's age
y=Naomi's age
System of equations:
x+5=2y
x+y=34
x+5=2y
y=(x+5)/2
x+y=34
x+((x+5)/2)=34
x=21
21+y=34
21+y=34
y=13
which of the following is an equation?
a. y/9-3
b. 9-2
c. y/9=3
d. 7+y
Answer: :)
An equation is something with a = sign and it’s C because it’s the only one with the sign
Step-by-step explanation:
If this circle has a radius of 6.8 and m∠b=197°, calculate the area of the intercepted sector (shaded blue). Round answers to two decimal places. Use the π button on your calculator.
The area οf the intercepted sectοr is 25.3π.
What is an area οf a sectοr?The quantity οf space included within the sectοr's perimeter is referred tο as the sectοr's area in a circle. A sectοr always starts at the circle's center. The area οf a circle encοmpassed between its twο radii and the arc next tο them is knοwn as the sectοr οf a circle.
Here, we have
Given: If this circle has a radius οf 6.8 and m∠b=197°.
We have tο calculate the area οf the intercepted sectοr.
The area οf the sectοr is given as θ/360*πr²
Where,
θ = central angel οf the sectοr, m∠f=197°
r = radius = 6.8
Area οf sectοr = 197/360*π(6.8)²
= 25.3π
Hence, the area οf a sectοr is 25.3π.
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A box contained red, orange and white beads, 20% of the beads were red. Later, the number
of red beads was increased by 5% and the total number of orange beads and white beads
were increased by half. Mary found that there were 123 beads more. How many beads were in the
box at first?
Answer:
Step-by-step explanation:
Let the total number of beads in the box be x.
Then, the number of red beads in the box is 20% of x = 0.2x.
After increasing the number of red beads by 5%, the number of red beads becomes 1.05 times the original number of red beads, which is 1.05(0.2x) = 0.21x.
The total number of orange and white beads is (100% - 20%) = 80% of x, which is 0.8x.
After increasing the number of orange and white beads by half, the total number becomes 1.5 times the original number, which is 1.5(0.8x) = 1.2x.
So, we have the equation: 0.21x = 0.2x + 123 - 1.2x
Simplifying this equation, we get:
0.01x = 123
x = 12,300
Therefore, the box originally contained 12,300 beads.
pa help plssss
Identify the solid figure that is represented by each real object below. Write the name of the solid figure on the blank before each number. 1. an ice cream cone 2. an orange 3. a shoe box 4. a coin 5. a soccer ball 6. a die
The name of the solid figure on the below object is indicated in front as follows:
Ice cream cone - ConeOrange - SphereShoe box - Rectangular PrismCoin - CylinderSoccer ball - SphereDie - CubeWhat does solid figure means?Solid figures refers to three-dimensional objects with dimensions of length, width, and height. They have depth and take up space in our universe because they have three dimensions. The features that distinguish each type of solid are used to identify them.
In real life, solid figures include boxes, dice, tubes, traffic cones, balls, and tents. However, Ppisms, cubes, cones, spheres, pyramids, and cylinders are the most basic solid figures. A composite figure is formed by combining multiple solid figures.
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Write the equation of a line that is perpendicular to y = 2x + 4 and goes through the point (6, 4)
The equation of the line that is perpendicular to y = 2x + 4 and goes through the point (6, 4) is y = (-1/2)x + 7.
What is the Equation of the Perpendicular Line to an Equation?To find the equation of a line that is perpendicular to y = 2x + 4 and goes through the point (6, 4), we first need to determine the slope of the given line.
The equation y = 2x + 4 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Therefore, the slope of the given line is 2.
The slope of a line perpendicular to this one will be the negative reciprocal of 2, which is -1/2.
So the equation we are looking for will have a slope of -1/2 and will pass through the point (6, 4). We can use the point-slope form of the equation of a line to find it:
y - y1 = m(x - x1)
where m is the slope, (x1, y1) is the point, and x1 = 6, y1 = 4:
y - 4 = (-1/2)(x - 6)
Simplifying:
y - 4 = (-1/2)x + 3
y = (-1/2)x + 7
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find the value of X on the lines are parallel
Step-by-step explanation:
60-3x+8x=180
5x=180-60
5x/5=120/5
X=24
Bob and Kevin bought a lottery ticket and won $100 000. Since they paid different amounts for the winning ticket, Bob received $10 000 more than two times what Kevin received. How much did each person receive?
answer: Kevin received $30,000, and Bob received $70,000.
According to the problem, Bob received $10,000 more than two times what Kevin received. So, Bob received:
2X + $10,000
We also know that the total amount won is $100,000. Therefore, we can write the equation:
X + (2X + $10,000) = $100,000
Simplifying the equation, we get:
3X + $10,000 = $100,000
3X = $90,000
X = $30,000
Therefore, Kevin received $30,000, and Bob received:
2X + $10,000 = 2($30,000) + $10,000 = $70,000
So Bob received $70,000.
Need help with short problem 1
As stated in the problem description, matrix A transforms the input vector (x, y, and z) into the output vector (y+z, 2x-z, 0).
The matrix A is: | 0 1 1 |, | 2 0 -1 |, | 0 0 0 |
What is a matrix?A matrix, sometimes known as matrices, is a rectangular array or table of letters, numbers, or other symbols organized in rows and columns that are used to represent a mathematical object or a characteristic of one.
In linear algebra, matrices describe linear mappings and enable explicit computations. As a result, a significant portion of linear algebra involves the study of matrices, and the majority of the characteristics and operations of abstract linear algebra may be described in terms of matrices. The composition of linear maps, for instance, is represented by matrix multiplication.
Not every matrix has a connection to linear algebra. This is especially true for incidence matrices and adjacency matrices in graph theory.
The matrix A is:
| 0 1 1 |
| 2 0 -1 |
| 0 0 0 |
Applying the matrix multiplication A x y z to any random vector (x, y, z) will demonstrate why:
| 0 1 1 | | x | | y + z |
| 2 0 -1 | x | y | = | 2x - z |
| 0 0 0 | | z | | 0 |
Hence, as stated in the problem statement, matrix A transforms the input vector (x, y, and z) into the output vector (y+z, 2x-z, 0).
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the price p of a certain computer system decreases immediately after its introduction and then increases. if the price P is estimated by the formula P= 170t^2- 1700t + 6400, where t is the time in months from its introduction, find the time until the minimum price is reached
The time until the minimum price is reached is 5 months. After this time, the price will start to increase again.
Define the term price?Price is the amount of money that must be paid to acquire a product or service, usually expressed in currency units such as dollars or euros.
The price of the computer system is given by the formula:
P = 170t² - 1700t + 6400
To find the time until the minimum price is reached, we need to find the value of t that corresponds to the vertex of the parabola described by this formula. The vertex is the point at which the price reaches its minimum value.
The formula for the x-coordinate of the vertex of a parabola in standard form (ax² + bx + c) is:
x = -b/2a
In this case, the formula for the price of the computer system is:
P = 170t² - 1700t + 6400
So we can see that a = 170, b = -1700, and c = 6400. Substituting these values into the formula for the x-coordinate of the vertex, we get:
t = -b/2a = -(-1700)/(2×170) = 5
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Calculate the radius of the following circle. Round to two decimal places when necessary.
(x+3)² + (y +7)² =121
Answer:
The equation of the given circle is:
(x + 3)² + (y + 7)² = 121
This equation is in standard form, which is:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is its radius.
Comparing the given equation with the standard form, we can see that:
The center of the circle is (-3, -7) (note the signs of h and k).
The radius of the circle is √121 = 11 (since r² = 121, then r = √121 = 11).
Therefore, the radius of the given circle is 11 units.
Step-by-step explanation:
0.00745805 Rounded to the nearest hundred
Answer:
Step-by-step explanation:
0.0075 (rounded to the nearest hundredth)
Log n 2=1/3
Find the unknown base
Answer:
0.3333333333 is right answer
Finn read an article claiming that 50% of Americans have brown hair,
20% have black hair, 20% have blonde hair, and
10% have red hair. He wondered if the hair colors of students at his school followed this distribution, so he took a random sample of
50 students and recorded their hair colors. Here are his results:
Color Brown Black Blonde Red
Students
17 14 14 5
He wants to use these results to carry out a
�
2
χ
2
\chi, squared goodness-of-fit test to determine if the distribution of hair colors at his school disagrees with the claimed percentages.
Choose 1 answer:
(Choice A)
�
2
=
5.76
;
0.10
<
P-value
<
0.15
χ
2
=5.76;
0.10
A
�
2
=
5.76
;
0.10
<
P-value
<
0.15
χ
2
=5.76;
0.10
(Choice B)
�
2
=
5.76
;
0.20
<
P-value
<
0.25
χ
2
=5.76;
0.20
B
�
2
=
5.76
;
0.20
<
P-value
<
0.25
χ
2
=5.76;
0.20
(Choice C)
�
2
=
6.05
;
0.10
<
P-value
<
0.15
χ
2
=6.05;
0.10
C
�
2
=
6.05
;
0.10
<
P-value
<
0.15
χ
2
=6.05;
0.10
(Choice D)
�
2
=
6.05
;
0.15
<
P-value
<
0.20
χ
2
=6.05;
0.15
D
�
2
=
6.05
;
0.15
<
P-value
<
0.20
χ
2
=6.05;
0.15
Answer: Choice A
χ 2 =5.76;
0.10<P-value<0.15
Step-by-step explanation:
Both trams are at the station right now. In how many minutes will both trams be at the station again if one arrives every 18 minutes and one arrives every 24 minutes.
Using LCM it is fοund that bοth trams will be at the statiοn again in 72 minutes.
What is LCM?In mathematics, the least cοmmοn multiple is sοmetimes referred tο as LCM οr the lοwest cοmmοn multiple. The smallest number amοng all the cοmmοn multiples οf the prοvided numbers is the least cοmmοn multiple οf twο οr mοre numbers.
The trams will meet again at the statiοn when bοth their arrival times cοincide.
We can find this time by finding the least cοmmοn multiple (LCM) οf the twο arrival times.
The LCM οf 18 and 24 is 72.
Therefοre, bοth trams will meet again at the statiοn in 72 minutes.
Tο see why this is the case, cοnsider the fοllοwing arrival times fοr each tram -
Tram A: 0, 18, 36, 54, 72, 90, 108, ...
Tram B: 0, 24, 48, 72, 96, 120, ...
We can see that bοth trams arrive at the statiοn at the same time (72 minutes) in their 4th cycle οf arrivals (Tram A: 54, Tram B: 72).
Therefοre, the time value is οbtained as 72 minutes.
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Please give me some help I don’t get it. U have to complete the the diagram
The probabilities are given as follows:
a = 0.4.b = 0.9.c = 0.5.d = 0.5.How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
For a probability tree, the sum of the nodes at each level must be of 1.
Then the value of a is obtained as follows:
0.6 + a = 1
a = 1 - 0.6
a = 0.4.
The value of b is obtained as follows:
0.9 + b = 1
b = 0.1.
The values of c and d are free, as long as the sum of these two values is of 1, hence we can attribute:
c = 0.5, d = 0.5.
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find the equations of all vertical, horizontal, or slant asymptotes of the graph of f(x)=3x^3-24/x^2-1 sketch the graph of the function
The equations of the asymptotes of the graph are x = 1, x = -1 and y = 3x
How to determine the equations of the asymptotes of the graphThe equation of the function is given as
f(x)=3x^3-24/x^2-1
Set the denominator to 0
So, we have
x^2 - 1 = 0
Apply the difference of two squares
(x - 1)(x + 1) = 0
Evaluate
x = 1 and x = -1 ---- the vertical asymptotes
Here, we have the degree of the numerator to be greater than that of the denominator
So, we have
y = 3x^3/x^2
y = 3x ----- horizontal asymptote
Note that the horizontal asymptote is the same as the slant asymptote
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What is the next term in the following sequence?
54, -18, 6, ...
2
-3
3
-2
The next term of the sequence is -2
How to determine the next term of the sequenceFrom the question, we have the following parameters that can be used in our computation:
54, -18, 6, ...
The above definitions imply that we simply multiply -1/3 to the previous term to get the current term
Using the above as a guide,
so, we have the following representation
Next term = -1/3 * Current term
Substitute the known values in the above equation, so, we have the following representation
Next term = -1/3 * 6
Evaluate
Next term = -2
Hence, the next term is -2
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Pls answer with full explanation
Answer:
Step-by-step explanation:
sin a equals sin to the second power (a) + cos to the 2 power(a) equal 1
What is the area of the figure below?
A. 48 square meters
B. 66 square meters
C. 72 square meters
D. 84 square meters
Angela's effective federal tax rate is 17%. Last year, she was able to reduce taxable income by
contributing $250.00 per semi-monthly paycheck to her tax -deferred retirement account and $72.07 per
semi-monthly paycheck to her flexible spending account. How much did she reduce her federal taxes by if
her gross semi-monthly pay is $2,819.96?
Answer:
Step-by-step explanation:
I WILL GIVE 70 POINTS AND THE BRAINIEST!!!!!
For the equation: 2(x - 7) = 3 - 7x + 5 + 8 + 7x + 11, the right side of the equation can be simplified by combining like terms.
Simplify the right side of the equation: ___________
The left side of the equation can be simplified using the Distributive Property.
Simplify the left side of the equation: ____________
Answer:
Blank 1: incorrectly
Blank 2: no
Step-by-step explanation:
Blank 1:
The student did not properly distribute:
4( x + 4 ) = 4x + 16, NOT 4x + 4
4x + 4 = 4x + 16 [subtract 4x from each side]
4 = 16
An incorrect statement means that there are no solutions
Linda needs to have her car towed. Little Town Auto charges a flat fee of $75 plus $2 per miletowed. Write a function expressing Linda's towing cost, C, in terms of miles towed, x. Find thecost of having a car towed 14 miles.
The cost of having a car towed 14 miles is $103.
What is function ?
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. Functions are often represented by a formula or rule that describes how to compute the output value from the input value.
The towing cost, C, can be expressed as a function of miles towed, x, using the given information as follows:
C(x) = 75 + 2x
where x is the number of miles towed.
To find the cost of towing a car 14 miles, we can substitute x = 14 into the function:
C(14) = 75 + 2(14)
= 75 + 28
= $103
Therefore, the cost of having a car towed 14 miles is $103.
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f(x) = 2x^(2)-3x+6 find the value of f(0)
Answer:
f(x) = 2x^(2) - 3x + 6
f(0) = 2(0)^(2) - 3(0) + 6
f(0) = 0 - 0 + 6
f(0) = 6
Therefore, the value of f(0) is 6.
Step-by-step explanation:
The cylindrical tank is lying horizontally on the ground.
Diameter - 20ft
Length - 22ft
The depth of water in the tank is 6ft.
1 gallon = 231 cubic inches.
A). How many gallons of water are in the tank?
B). How many more gallons of water will it take to fill the tank?
Use the technique of linear regression to find the line of best fit for the given points. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
(1,2)
, (2,5)
, (3,7)
, (4,2)
, (5,10)
, (6,10)
, (7,9)
The equation of the line of best fit is y = 1.19x - 0.37.
What is linear regression ?
Linear regression is a statistical method that is used to establish the relationship between two variables, usually represented as a straight line. It is used to determine the extent to which one variable is dependent on the other variable, and to make predictions based on this relationship.
Using linear regression, we want to find the equation of the line of best fit in the form y = mx + b, where m is the slope and b is the y-intercept.
First, we need to calculate some sums:
∑x = 28
∑y = 45
∑xy = 224
∑x² = 140
∑y²= 275
Using these sums, we can calculate the slope m:
m = (n∑xy - ∑x∑y) / (n∑x² - (∑x)²)
m = (7(224) - (28)(45)) / (7(140) - (28)^2)
m = 1.19
Now we can use the slope to calculate the y-intercept b:
b = (∑y - m∑x) / n
b = (45 - (1.19)(28)) / 7
b = -0.37
Therefore, the equation of the line of best fit is y = 1.19x - 0.37.
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We can describe 3x - 2 as an expression. How can we describe the parts of the expression that the arrows point to? 3x - 2
We can say that the arrοws pοint tο the variable term (3x) and the cοnstant term (-2) οf the expressiοn 3x - 2.
What is Linear Expressiοn?A linear expressiοn is a mathematical expressiοn in οne variable that can be written in the fοrm ax + b, where a and b are cοnstants and x is the variable. It represents a straight line when graphed.
The expressiοn 3x - 2 can be described as a sum οr difference οf twο terms: 3x and -2.
The cοefficient 3 is the numerical factοr οf the term 3x, which represents the prοduct οf 3 and x, a variable οr unknοwn quantity. The term 3x is called the variable term οr the first term οf the expressiοn.
The cοnstant term -2 is a term that dοes nοt invοlve any variables. It is the secοnd term οf the expressiοn and is alsο knοwn as the cοnstant term οr the cοefficient οf the cοnstant term, since it is multiplied by the cοefficient 1 (which is nοt written) in this case.
In οther wοrds, we can say that the arrοws pοint tο the variable term (3x) and the cοnstant term (-2) οf the expressiοn 3x - 2.
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The height of a flare is given by the equation h(t)= -0.5t² +16t+22 where h is the height of the flare in metres and is the time the flare has been in the air in seconds. How long will the flare be in the air if it fizzles out at a height of 10 m above ground?
Answer:
the flare will be in the air for approximately 29.09 seconds before fizzling out at a height of 10 meters above ground.
Step-by-step explanation:
To find out how long the flare will be in the air, we need to find the time it takes for the flare to reach a height of 10 meters.
Setting h(t) to 10 and solving for t:
-0.5t² +16t+22 = 10
-0.5t² +16t+12 = 0
Using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
Where a = -0.5, b = 16, and c = 12:
t = (-16 ± √(16² - 4(-0.5)(12))) / 2(-0.5)
t = (-16 ± √(256 + 24)) / -1
t = (-16 ± √280) / -1
t ≈ -1.09 or t ≈ 29.09
Since time cannot be negative, we can ignore the negative root. Therefore, the flare will be in the air for approximately 29.09 seconds before fizzling out at a height of 10 meters above ground.