Answer: 57.14 km/hr
Step-by-step explanation: if an hour is divided into quarters it will be in increments of 15 minutes, since one hour is 60 minutes. 60 minutes divided by 5 is 15 minutes.
So 1 hour and 38 minutes is rounded off to 1 hour and 45 minutes.
this is 1 hour + 3/4 hour = 1 3/4 hour. This is same as 1.75 hour
3/4 is .75
speed divided by the time will give the average speed.
100km/1.75hours = 57.14 km/per hour
Answer:
(a) 1 hour 45 min
(b) 57.1 km/h (nearest tenth)
Step-by-step explanation:
Given information:
Distance = 100 kmTime = 1 h 38 min 45 sec[tex]\large\boxed{\sf Speed=\dfrac{Distance}{Time}}[/tex]
Part (a)[tex]\begin{aligned}\sf \dfrac{1}{4}\;hour &= \sf 1 \; hour \div 4 \\& = \sf 60 \;mins \div 4\\& = \sf 15 \; mins\end{aligned}[/tex]
Therefore, the nearest ¹/₄ hours either side of the given time is:
1 hour 30 min1 hour 45 min1 h 38 min 45 sec is 8 min 45 sec more than 1 hour 30 min.
1 h 38 min 45 sec is 6 min 15 sec less than 1 hour 45 min.
Therefore, the nearest ¹/₄ hour to the given time is:
1 hour 45 min.Part (b)1 hour 45 min = 1.75 min (in decimal form)
Substitute the given distance and the rounded time (in decimal form) into the formula and solve for speed:
[tex]\begin{aligned} \implies \sf Speed & =\sf \dfrac{Distance}{Time}\\\\& = \sf \dfrac{100}{1.75}\\\\& = \sf 57.1\;km/h\;(nearest\;tenth)\end{aligned}[/tex]
triangle DEF and triangle CBD are similar right triangles which statement is slopes is DF and CDs true
We can calculate the slope of a line segment by using the formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1,y1) and (x2,y2) are two points of the line.
In this case the side DF goes from the point D(-2,-2) to the point F(1,7), then its slope is:
[tex]m=\frac{7-(-2)}{1-(-2)}=\frac{7+2}{1+2}=\frac{9}{3}=3[/tex]For the side, CD, it goes from D(-2,-2) to C(0,4), then its slope is:
[tex]undefined[/tex]please help me solve this
Answer:
a: undefined
b: -15
c: 20
d: 25
Step-by-step explanation:
a: look at x -3 on graph, the left hand limit and right hand limits are different so it's undefined
b: look at x 0 on graph, there is open dot at -15 meaning the limit is there
c: look at x -7 on graph, there is open dot at 20 meaning the limit is there
d: look at x 5 on graph, the y is at 25 meaning the limit is there (it's normal here)
DEEPER The scales shown are used to compare the weights of apples, tangerines, grapefruits, and bananas. How many tangerines
will balance one apple?
Justify your answer using a linear system. Let the weights of apples, tangerines, grapefruits, and bananas be represented by a, t,
g, and b respectively.
Equation for first picture:
Equation for second picture:
Equation for third picture:
4 Tangerines will balance 1 apple.
Given that
Weight of Apple is represented by: a
Weight of tangerine is represented by: t
Weight of Grapefruit is represented by: g
Weight of Banana is represented by: b
Consider 1st picture:
1 apple and 1 tangerine balance 1 grapefruit.
⇒ a+t = g ...(1)
Consider 2nd picture:
1 banana and 1 tangerine balance 1 apple.
⇒ b+t = a ...(2)
Consider 3rd picture:
2 grapefruits balance 3 bananas.
⇒ 2g = 3b
g = 1.5b ...(3)
The system of equations are:
First balance: a+t = g
Second balance: b+t = a
Third balance: g = 1.5b
Putting the value of g from equation (3) to equation (1), we get
a+t = 1.5b ...(4)
Now, putting the value of b from equation (2) to equation (4), we get
a+t = 1.5(a-t)
1.5a - 1.5t = a+t
0.5a = 2t
a = 4t
Hence, one apple is balanced by 4 tangerines.
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x/25.75=sin47.5 degrees
The value of x in the equation is 18. 98
What are trigonometric identities?Trigonometric identities are defined as mathematical equations relating to several trigonometric functions, holding true for all the values in the domain of the functions.
The several types of trigonometric identities includes;
sinecosinetangentcotangentsecantcosecantIt is important to note that the trigonometric ratios for major identities are;
sine = opposite/hypotenuse
tangent = opposite/adjacent
cosine = adjacent/hypotenuse
Given the equation;
x/25.75=sin47.5 degrees
Take the following steps to determine the value of 'x'
We have;
cross multiply
x = sin47.5 × 25. 75
Find the value of sin 47. 5 and substitute the value
x = 0. 7373 × 25. 75
multiply through
x = 18. 98
Hence, the value of x is 18. 98
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The complete question:
x/25.75=sin47.5 degrees
Find the value of x
A bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag.
The number of different samples possible when the shopper selects a sample of 4 apples from the bag is 126.
How to calculate the combinations?Combinations are a method of calculating the overall results of an event where the order of the results is irrelevant. From the information, the bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag.
It should be noted that the question has to do with a combination. The number of different samples that are possible will be:
Number of apples = 9
Number to be selected = 4
= ⁹C₄
= 9! / (9 - 4)! 4!
= 9 × 8 × 7 × 6 / 4 × 3 × 2
= 126
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A bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag. How many different samples are possible?
Jared lost a total of $56.00 on his investment over 7 months. He lost an equal amount of money each month. Jared used this equation to figure out how much money he lost each money. -56.00/7=-8.00 what does -56.00/7=-8.00 tell us?
Answer:
I'm not so very sure but I really need points
Maggie has space in her yard for a garden. A scale drawing of the garden is shown below. The scale of the drawing is 1 cm - 2.5 ft.6 cm!616 cmWhat is the area of Maggie's actual garden?
Units change translation from cm to feets
1 cm is equivalent to 2.5 feets
triangle is a rectangular triangle suported with the bigger side
this means the height of triangle is 6cm
the base is 16 cm
the area is (base x height)/2
so then area= 16x 6/2= 48cm ^2
BUT because 1cm is equivalent to 2.5 feets then
multiply 48 x 2.5 x 2.5 = 48 x 6.25 = 300 ft^2
On a blueprint, a guest bedroom has dimensions 3 cm
by 5 cm. If the blueprint is drawn using the scale of
½ cm = 2 ft, what is the actual AREA of the guest
bedroom?
A. 12 square ft
B. 20 square ft
C. 240 square ft
D. 15 square ft
The actual area of the guest bedroom is 240 square ft, if on a blueprint, a guest bedroom has dimensions 3 cm by 5 cm and the blueprint is drawn using the scale of ½ cm = 2 ft.
What is dimension?The minimal amount of coordinates required to specify any point within a mathematical space (or object) is known as the dimension in physics and mathematics. As a result, a line has one dimension (1D), since only one coordinate is required to specify a point on it, such as the point at 5 on a number line.
A surface, like the perimeter of a cylinder or sphere, has two dimensions (2D) because two coordinates are necessary to specify a point on it. For instance, both a latitude and a longitude are necessary to pinpoint a point on the surface of a sphere.
The dimensions are 3cm by 5 cm meaning length = 5cm and breadth = 3cm
Given that ½ cm = 2 ft, that is
1 cm = 4 ft
Using the conversion method
3 cm = 3 × 4
= 12 ft
5 cm = 5 × 4
= 20 ft
Actual area = 20 × 12 ft
= 240 square ft
Thus, the actual area of the guest bedroom is 240 square ft, if on a blueprint, a guest bedroom has dimensions 3 cm by 5 cm and the blueprint is drawn using the scale of ½ cm = 2 ft.
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When 3x² + 7x - 6 + 2x³ is written in
standard form, the leading coefficient is
(1) 7
(2) 2
(3) 3
(4) -6
Answer:
Your leading coefficient is 2
the formula for finding the area of a rectangle is A=LWSolve this formula for LL=______if the length of a rectangle is 18 feet qnd the width is 9 inches. what is the area of the rectangle in units of square feet? _______ ft^2
1) Dividing the given formula by W we get:
[tex]\begin{gathered} \frac{A}{W}=\frac{LW}{W}, \\ \frac{A}{W}=L. \end{gathered}[/tex]2) We know that:
[tex]1in=\frac{1}{12}ft.[/tex]Therefore:
[tex]9in=9*\frac{1}{12}ft=\frac{3}{4}ft.[/tex]Then:
[tex]W=\frac{3}{4}ft.[/tex]Substituting W=3/4ft and L=18ft in the given formula we get:
[tex]A=(18ft)(\frac{3}{4}ft)=13.5ft^2[/tex]Answer:
1)
[tex]L=\frac{A}{W}.[/tex]2)
[tex]13.5ft^2.[/tex]I need to find the c intercept and write the equation
The C-intercept is the point at which the function crosses the C-axis, then it is at t=0.
As we know two points on the line: (-20, 200) and (30,0), and we found previously the slope m=-4.
We can use the slope-intercept form of the equation of a line to find the C-intercept as follows:
[tex]C=m\cdot t+b[/tex]Where (t,C) is any point on the line, m is the slope and b is the C-intercept.
By replacing the know values we can solve for b:
[tex]\begin{gathered} 0=-4\cdot30+b \\ 0=-120+b \\ \text{Add 120 to both sides} \\ 0+120=-120+b+120 \\ 120=b \end{gathered}[/tex]Therefore,
I will give brainliest, like and rating if u solve this right
which of the following is not true?
As per the given matrix [tex]A= \left[\begin{array}{ccc}2&2\\-1&1\end{array}\right][/tex], Option (C) is not true.
Matrix:
The matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
Given,
[tex]A= \left[\begin{array}{ccc}2&2\\-1&1\end{array}\right][/tex]
Here we need to find which of the option is not true.
To find the incorrect options first we have to calculate the |A| and A⁻¹.
And we have also check whether is matrix has inverse or skew symmetric matrix.
First, we have to calculate the value of |A|,
|A| = (2 x 1) - (-1 x 2)
|A| = 2 - (-2)
|A| = 2 + 2 = 4
Therefore, option (A) is true.
Now we have to check this matrix has inverse,
It can be calculated using the formula,
[tex]A^{-1} =\frac{1}{|A|} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right][/tex]
So, the inverse of the matrix is,
[tex]A^{-1} =\frac{1}{4} \left[\begin{array}{ccc}1&-2\\-(-1)&2\end{array}\right][/tex]
Which is equal to,
[tex]A^{-1} =\left[\begin{array}{ccc}1/4&-2/4\\1/4&2/4\end{array}\right][/tex]
When we simplify it then we get,
[tex]A^{-1} =\left[\begin{array}{ccc}1/4&-1/2\\1/4&1/2\end{array}\right][/tex]
Through this we have conclude that Option (B) and (D) are true.
We know that,
In the skew-symmetric matrix, a matrix whose transpose is equal to its negative.
So, the transpose of the given matrix is,
[tex]A^{T}=\left[\begin{array}{ccc}2&-1\\2&1\end{array}\right][/tex]
So, the given matrix is not a skew-symmetric matrix.
Therefore, the incorrect option is (c).
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4(5x - 2) = 2(9x + 3)
Answer: x = 7
Explanation - 4(5x-2)=2(9x+3)
20x-8=18x+6
20x-18x=6+8
2x=14
x=14÷2
x=7
Hello there!
Here we need to solve for x.
The first thing that we're going to do is this:
Expand both sides by using the distributive property.[tex]\implies\boldsymbol{4(5x-2)=2(9x+3)}[/tex]
[tex]\implies\boldsymbol{20x-8=18x+6}[/tex]
Next, add 8 to both sides.[tex]\implies\boldsymbol{20x=18x+14}[/tex]
Then, subtract 18 from both sides.[tex]\implies\boldsymbol{20x-18x=14}[/tex]
[tex]\implies\boldsymbol{2x=14}[/tex]
Lastly, divide both sides by 2.[tex]\implies\boldsymbol{x=7}[/tex]
Therefore x=7. I hope this helps you, feel free to comment if you have any queries :)
Identify the Vertex. Let g be a translation 2 units up, followed by a reflection in the x-axis and a vertical stretch by a factor of 4 of the graph of. (Show Work)
The g graph exhibits a four-fold vertical stretch.
The graph of f (x)=[tex]x^{2}[/tex] is translated up to two units, then reflected in the X-axis.
The rule for g.
Identify the vertex
The g graph exhibits a four-fold vertical stretch.
=> g = 4f(x) (x)
an X-axis reflection
=> g = - 4f(x) (x)
(X-axis reflection of (X, Y) is (x , - y)
a conversion two units higher
=> g = -4f(x) + 2
f(x) = x²
=> g = - 4x² + 2
Vertex is at ( 2, 0)
What is a vertical stretch?
When a base graph is multiplied by a particular factor larger than 1, vertical stretch happens. As a consequence, the graph is stretched outward while keeping the input values (or x). We anticipate that the y values in a function's graph will be further away from the x-axis when it is vertically extended.
How to vertically stretch a function?
When given a function’s graph, we can vertically stretch it by pulling the curve outwards based on the given scale factor. Here are some things to remember when we vertically stretch functions:
Ensure that the values for x remain the same, so the base of the curve will not change.
This means that when applying vertical stretches on a base graph, its x-intercepts will remain the same.
Take note of the new critical points, such as the new maximum point of the graph.
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Answer asap what’s the correct answer answer now for brainlis5?
Answer: Smooth muscle contractions
Let A={1,2,3},B={7,8,9,10}andf={(1,7),(2,9),(3,8)} what type of function is this? Give reason
It is observed that f is a subset of A×B
What is subset ?A subset is a subset (another set or the same set). It is expressed as A⊆ B in the set notation to indicate that set A is a subset of set B.Set 1 is a subset of Set 2 if all of its components are included in Set 2. A set, as far as we are aware, is a clearly defined grouping of letters, objects, numbers, or anything else. Set 1 is a subset of Set 2 if Set 1 = A, B, C, and Set 2 = A, B, C, D, E, and F. This is because all the items in Set 1 are also present in Set 2.
Given that :A={1,2,3},B={7,8,9,10}andf={(1,7),(2,9),(3,8)}
A={1,2,3}
B={7,8,9,10}
A×B ={(1,7)(1,8)(1,9)(1,10)(2,7)(2,8)(2,9)(2,10)(3,7)(3,8)(3,9)(3,10)}
f={(1,7),(2,9),(3,8)}
A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A×B
It is observed that f is a subset of A×B
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Write the equation of a Circle with the given information.Center: (-4,7) Point on the Circle: (8,-4)
Given:
Center of circle: (-4, 7)
Endpoint on the circle: (8, -4)
Let's write the equation of the circle with the given information.
Apply the equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where:
Center of circle: (h, k) ==> (-4, 7)
Radius = r
Substitute the values of (h, k) in the equation:
[tex]\begin{gathered} (x-(-4))^2+(y-7)^2=r^2 \\ \\ (x+4)^2+(y-7)^2=r^2 \end{gathered}[/tex]To find the radius, let's find the distance between the points (-4, 7) and (8, -4).
Apply the distance formula:
[tex]d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}[/tex]Given:
(x1, y1) ==> (-4, 7)
(x2, y2) ==> (8, -4)
Thus, we have:
[tex]\begin{gathered} d=\sqrt[]{(-4-7)^2+(8-(-4))^2} \\ \\ d=\sqrt[]{(-4-7)^2+(8+4)^2} \\ \\ d=\sqrt[]{(11)^2+(12)^2} \\ \\ d=\sqrt[]{121+144} \\ \\ d=\sqrt[]{265} \\ \\ d=16.3 \end{gathered}[/tex]Therefore, the radius is 16.3
Therefore, we have the equation of the circle as:
[tex](x+4)^2+(y-7)^2=16.3^2[/tex]ANSWER:
[tex](x+4)^2+(y-7)^2=16.3^2[/tex]What is the probability of theft occurring in a room if it is left unlocked if 0.75 of dorm rooms are left unlocked, 3% of dorm rooms are affected by theft, and 84.2% of thefts occur in unlocked rooms
The probability that a theft can happen in a room that is left unlocked based on the statistics of dorm rooms affected by theft, is 1.89%
How to find the probability?To find the probability that a room will be subjected to theft if it is left unlocked, the formula is:
= Probability that dorm room is left unlocked x Probability of dorm room being affected by theft x Probability that a theft occurs in a unlocked room
The probability of an unlocked room being robbed is therefore:
= 0.75 x 0.03 x 0.842
= 0.0225 x 0.842
= 0.018945
= 1.89%
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Use a linear approximation to estimate 3√28 write your exact answer with fractions
The estimated value of 3√28 using linear approximation is 82/27 which is answered in form of fraction.
What is linear approximation?A general function can be approximated using a linear function in mathematics using the term "linear approximation" (more precisely, an affine function). They are frequently utilised in the finite difference method to create first order approaches for resolving or approximating solutions to equations.
We need to find the approximate value of ∛28 using linear approximation
Let f(a) = ∛a
then F(27) = ∛27 = 3
We compute the derivative of f(a) as being
[tex]f(a)=a^{\frac{1}{3}}[/tex] ⇒ [tex]f'(a)=\frac{1}{3}a^{-\frac{2}{3}}[/tex]
Hence,
[tex]f'(a)=\frac{1}{3}a^{-\frac{2}{3}}[/tex] = [tex]\frac{1}{3}(3)^{-2}=\frac{1}{3}(\frac{1}{9})=\frac{1}{27}[/tex]
Recall the equation of a line is given by
⇒ y - b = m(x - a)
⇒ [tex]y-3=\frac{1}{27}(x-27)[/tex]
⇒ [tex]y=\frac{1}{27}x-1+3[/tex]
⇒ [tex]y=\frac{1}{27}x+2[/tex]
So the approximation at x= 27.5 would be
⇒ [tex]y=\frac{1}{27}(28)+2[/tex]
⇒ y = 82/27
⇒ y = 3.037
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The following table summarizes the percent of U.S. who have diabetes and the accuracy of the current medical tests used to detect the disease.
Test positive Test negative Total
Have diabetes 36.1% 1.9% 38%
Do not have diabetes 5.2% 56.8% 62%
What percent of those who do not have diabetes test negative for the disease?
A 10.9%
B 56.8%
C 91.6%
D 96.8%
If the following table summarizes the percent of U.S. who have diabetes and the accuracy of the current medical tests used to detect the disease. The percent of those who do not have diabetes test negative for the disease is: B. 56.8%.
ProbabilityProbability can be defined as the tendency or likelihood that something will happen.
Hence,
Percentage of people do not have diabetes and test positive is 5.2%
Percentage of people do not have diabetes and test negative is 56.8%
Total percentage of people who tested positive and negative is 62%
Based on the above analysis for people who does not have a diabetes we can see that the Percentage of people do not have diabetes and test negative is 56.8%.
Therefore the correct option is B.
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What is the value of −5 + (−18) + 32? −45 −19 9 55
Answer:
9
Step-by-step explanation:
[tex]-5+(-18)+32 \\ \\ =-5-18+32 \\ \\ =-23+32 \\ \\ =9[/tex]
please show all work
Domain and Range of Functions
Given a function y = f(x), the domain of f is
The range of f is the
We are given the function:
[tex]f(x)=\frac{1}{2x}-3[/tex]It's required to find the domain and range of the inverse function.
We must recall that, if the inverse function exists, its domain is the range of f, and its range is the domain of f.
Since f(x) is a rational function, it may not exist for the values of x where the denominator is 0.
Concretely, for x=0, the denominator is 0 and the function does not exist, thus the domain of f consists of every real number except x=0.
This can be written as (-∞,0) U (0,∞). This is also the range of the inverse function.
Now let's find the inverse function. We must solve for x the equation:
[tex]y=\frac{1}{2x}-3[/tex]Adding 3:
[tex]y+3=\frac{1}{2x}[/tex]Multiplying by x and dividing by y+3:
[tex]x=\frac{1}{2(y+3)}[/tex]Swapping letters:
[tex]y=\frac{1}{2(x+3)}[/tex]This is the inverse function of f.
Thus the domain of the inverse is:
-3-3
And the range:
Answer: Choice d
A herd of 52 horses has 12 appaloosas and the rest are mustang and its most simplified form. What is the ratio of appaloosa to mustang horses?
The ratio of appaloosa to mustang horses is 12:40
The total number of horses is given as 52.
Number of white horses =12
Let the number of black horses be x
This means that ratio of white: black horses is 12 : x
Using the ratio above, we can find the number of black horses as follows:
[tex]\frac{x}{12+x} of 52 = x[/tex]
[tex]\frac{52x}{12+x} = x[/tex]
52x = x(12 + x)
[tex](12x + x^{2} ) = 52x[/tex]
[tex]x^{2}[/tex] + 12x - 52x = 0
[tex]x^{2}[/tex] - 40x = 0
Taking out the common factor x from equation we have:
x(x - 40) = 0
This gives us with two solution:
x = 0 and x = 40
Since the question said there are some black horses, the x=0 value can be ignored. So we have x = 40
Hence, The ratio of appaloosa to mustang horses is 12:40
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and Relative Change
The value of a car dropped from $23,800 to $22,300 over the last year. Determine the absolute
and relative change in this sitation.
Absolute Change: This car's value decreased by $
Round your answer to the nearest dollar.
Relative Change: This car's value decreased by
Round your answer to the nearest tenth of a percent.
last year.
% last year.
The absolute change or the car's value decreased by $1500.
The relative change: The value of the car decreased by 6.302 %.
The car's value dropped from $23,800 to $22,300 over the last year.
So, the initial price of the car is I = $23,800, and the final value of the car after a year is F = $22,300.
Therefore,
The Absolute change will be:
= I - F
= $23,800 - $22,300
= $1500
Hence, the car's value decreases by $1500.
Now, the relative change is the percentage by which the price decreased over the year.
So,
As the price decreased by $1500.
Let x be the relative change.
Then,
$ 23,800 × x/100 = $1500
238x = 1500
x = 6.302
Hence, the car's value decreased by 6.302% last year.
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Factor each of the following completely:
y² + 7y +6
I
y² - 7y + 6
Answer: 31y2 + 6
Step-by-step explanation:
61 y2 + 1 y2 = 62 y2
7y + -7y = 0
6+6 =12
62y2 + 12 then divide by 2 and it's 31y2 + 6
A real estate agent working in a large city believes that, for three-bedroom houses, the selling price of the house decreases by approximately $2,000 for every mile increase in the distance of the house from the city center. To investigate the belief, the agent obtained a random sample of 20 three-bedroom houses that sold in the last year. The selling price, in thousands of dollars, and the distance from the city center, in miles, for each of the 20 houses are shown in the scatterplot. The table shows computer output from a regression analysis of the data.
(a) Describe the relationship between distance from city center and selling price.
(b) Find the linear regression equation. Interpret the slope and y-intercept in context.
) One house that was 11 miles from city center had a residual of -2.962. What was the actual selling price of the home?
The description of the relationship is a linear relationship, the equation is y = 301.7 - 2.158x and the actual selling price of the home is $275
How to determine the relationship?The given parameter is in the attached figure
Also from the question, we have:
House price decreases by approximately every mile
The above implies that the relationship is an approximately linear relationship
How to find the linear regression equation.From the table, we have
Coefficient constant = 301.7
Coefficient distance = -2.158
This means that
y-intercept = 301.7
Slope = -2.158
So, the equation is
y = y-intercept + slope * x
This gives
y = 301.7 - 2.158x
The interpretation of the slope and y-intercept in context are:
Slope implies that the house price decreases by 2.158 miles, and the y-intercept implies that the initial house price is 301.7
The actual selling price of the homeHere, we have
Residual = -2.962
Miles = 11
This means that
Predicted price = 301.7 - 2.158 * 11
Evaluate
Predicted price = 277.96
So, we have
residual = actual - predicted
This gives
actual = residual + predicted
So, we have
actual = -2.962 + 277.96
Evaluate
actual = 275
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A square swimming pool is surrounded by a cement walkway with a uniform width. The swimming poa
has a side length of (x - 5) feet. The side length of the entire square area including the pool and the
walkway is (x+4) feet.
Enter an expression for the area of the walkway. Then find the area of the cement walkway when
x = 8 feet.
The area of the walkway is
ft².
When x = 8 feet, the area of the cement walkway
The expression of the square walkway is (x + 4)² - (x - 5)² and the area of the square cement walkway is 135ft².
Area of square:
The area of a square is refers the place covered by the square.
The formula to calculate the area of square is,
Area = s²,
where, 's' refers the side of the square.
Given,
A square swimming pool is covered by a cement walkway with a uniform width.
Length of swimming pool = (x-5) feet.
Length of square walkway including the swimming pool = (x+4) feet
Here we need to find the area of the cement walkway and when the value of x is 8 then the value of the cement walkway.
1) Here we have to write an expression for the area of the entire square minus area of the pool.
Remember the equation for the area of a square is , where
A = area of square and
s = side value of the square.
We are given that the side of the entire square including walkway and pool is s = (x+4)ft.
Apply the value of the side into the formula for the area of the square, then we get,
A = s²
A = (x + 4)² --------------(1)
We are also given that the side length of the swimming pool is s = (x-5)ft. Apply that into the equation for the area of a square to get the expression for the area of the pool:
A = s²
A = (x - 5)² --------------(2)
Now subtract the area of the pool (x - 5)² from the area of the entire square (x + 4)² to get your expression for the area of the walkway.
Expression for the area of the walkway:
=> (x + 4)² - (x - 5)²
2) Since you know that x = 8ft, you can solve your expression for the area of the walkway. Plug x into your expression:
=> (8 + 4)² - (8 - 5)²
=> (12)² - (3)²
=> 144 - 9
=> 135
The area of your walkway is 135ft².
To know more about the Area of the Square here.
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K
Solve.
(8v+5)(3v-9) = 0
why is 25 a compiste number
Answer: 25 is divisible by 5, so it is composite
Step-by-step explanation:
Answer both questions if possible or just the main questions if that's all you can do,
ASAP
Step-by-step explanation:
domain = width
range = height
closed point (filled in) means the number is included and we use ()'s.
set builder nation format: (x,y)
domain: (-5, -1)
range: (3,3)
f(1) means what does y equal when x equals 1:
locate on the graph where y is when x = 1:
f(1) = 2