Answers
A picture and a frame are given with dimensions. It is required to find the area of the frame.
To find the area of the frame, subtract the area of the picture from the total area (frame + picture).
Recall the area of a rectangle with a length l and a width w:
[tex]A=l\cdot w[/tex]Substitute l=22 and w=20 into the formula to find the area of the picture:
[tex]A=22\cdot20=440[/tex]Notice that the total length of the picture and frame is l=22+x+x=22+2x, while the total width is w=20+x+x=20+2x.
Substitute these dimensions into the area formula:
[tex]\begin{gathered} A=(22+2x)\cdot(20+2x) \\ A=4x^2+40x+44x+440 \\ \Rightarrow A=4x^2+84x+440 \end{gathered}[/tex]Subtract the areas to find the area of the entire frame:
[tex]\text{ Area of frame}=4x^2+84x+440-440=4x^2+84x+0[/tex]The area of the entire frame is 4x²+84x+0.
First-term is 4x², the second term is 84x, and the third term is 0.
To find the area when x=2, substitute x=2 into the expression for the area:
[tex]4(2)^2+84(2)+0=4(4)+168+0=16+168=184[/tex]The area of the frame when x=2 inches is 184 inches squared.
The perimeter is the sum of the side lengths of the frame given as:
[tex]P=2(l+w)[/tex]Substitute l=22+2x and w=20+2x into the formula:
[tex]P=2(22+2x+20+2x)=2(4x+42)=8x+84[/tex]Substitute x=10 to find the perimeter when x=10:
[tex]P=8(10)+84=80+84=164[/tex]The perimeter is 164 inches.
Answers:
The area of the entire frame is 4x²+84x+0.
First-term is 4x², the second term is 84x, and the third term is 0.
The area of the frame when x=2 inches is 184 inches squared.
The perimeter when x=10 is 164 inches.
Related Questions
I don’t understand the question its asking for the depth at 4 weeks and 9 weeks
Answers
Answer
Lake depth after 4 weeks: 343.6 ft
Lake depth after 9 weeks: 340.6 ft
Step-by-step explanation
The relation between time and lake depth is linear. Using the x-variable to represent time and the y-variable to represent the lake depth, we can use the next equation to relate these variables:
[tex]y=mx+b[/tex]where m is the slope and (0, b) is the y-intercept of the line.
The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the table, this line passes through (0, 346) and (2, 344.8), then its slope is:
[tex]m=\frac{344.8-346}{2-0}=\frac{-1.2}{2}=-0.6[/tex]From the table, this line passes through (0, 346), then parameter b is 346.
Substituting m = -0.6 and b = 346, the equation of the line is:
[tex]y=-0.6x+346[/tex]Evaluating this line at x = 4, that is, when time = 4 weeks, we get the next depth:
[tex]\begin{gathered} y=-0.6(4)+346 \\ y=-2.4+346 \\ y=343.6\text{ ft} \end{gathered}[/tex]Evaluating the equation of the line at x = 9, that is, when time = 9 weeks, we get the next depth:
[tex]\begin{gathered} y=-0.6(9)+346 \\ y=-5.4+346 \\ y=340.6\text{ ft} \end{gathered}[/tex]The side walls of a regular quadrilateral pyramid are equilateral triangles with sides equal to 8 cm. Calculate the pyramid:1) the sum of the lengths of all the sides;2) the area of the base;3) the length of the height of the side wall;4) the area of the side wall.
Answers
a) 64cm
b) 64 square cm
c) 4√3 cm
d) 16√3 square cm
Explanations:A regular quadrilateral pyramid with equilateral triangles is as shown below;
1) The pyramid has 8 side lengths, hence the sum of the length of all the sides is given as:
[tex]\begin{gathered} Sum\text{ of side lengths}=8\times8cm \\ Sum\text{ of side lengths}=64cm \end{gathered}[/tex]2) Since the triangular sides are equilateral, the base of the pyramid will be a square with side length of 8cm. The area of the base is expressed as:
[tex]\begin{gathered} A=length\times length \\ A=8cm\times8cm \\ A=64cm^2 \end{gathered}[/tex]3) Since one side wall is an equilateral triangle, the height will be perpendicular to the base as shown:
In order to determine the height, we will use the Pythagorean theorem as shown:
[tex]\begin{gathered} 8^2=h^2+4^2 \\ h^2=8^2-4^2 \\ h^2=64-16 \\ h^2=48 \\ h=\sqrt{48}=4\sqrt{3}cm \\ \end{gathered}[/tex]4) The area of the side wall is equivalent to the area of the triangle expressed as:
[tex]\begin{gathered} Area\text{ of side wall}=\frac{1}{2}\times base\times height \\ Area\text{ of side wall}=\frac{1}{2}\times8cm\times4\sqrt{3} \\ Area\text{ of side wall}=16\sqrt{3}cm^2 \end{gathered}[/tex]A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compareover the interval -2
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To check the decay rate, we need to check the variation in y-axis.
Since our interval is
[tex]-2We need to evaluate both function at those limits.At x = -2, we have a value of 4 for both of them, at x = 0 we have 1 for the exponential function and 0 to the quadratic function. Let's call the exponential f(x), and the quadratic g(x).
[tex]\begin{gathered} f(-2)=g(-2)=4 \\ f(0)=1 \\ g(0)=0 \end{gathered}[/tex]To compare the decay rates we need to check the variation on the y-axis of both functions.
[tex]\begin{gathered} \Delta y_1=f(-2)-f(0)=4-1=3 \\ \Delta y_2=g(-2)-g(0)=4-0=4 \end{gathered}[/tex]Now, we calculate their ratio to find how they compare:
[tex]\frac{\Delta y_1}{\Delta y_2}=\frac{3}{4}[/tex]This tell us that the exponential function decays at three-fourths the rate of the quadratic function.
And this is the fourth option.
question will be in picture
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given:
[tex]-7\le x[/tex]so, the line that represents the given inequality will be: b
Question 1 of 10 The graphs below have the same shape. What is the equation of the red graph? w GE? F%= 3 - 74 G(X)
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The equation of the red graph (Parabola) is g(x) = 1 – x².
The given graph is the graph of the parabolas.
We are given;
The equation of the blue graph (Parabola) is f(x) = 4 – x².
We need to find the equation of the red graph g(x).
Let's observe the graph;
All of the lines in the blue graph pass through point 4 on the graph. The same is true for the red line, except that they all pass through 1. As a result, we should alter the 4 in the blue line equation to a 1 to represent the red line.
The equation of the blue graph is:
f(x) = 4 – x²
Substitute 4 by 1;
p(x) = 1 – x² = g(x)
This is our required equation.
Thus, the equation of the red graph (Parabola) is g(x) = 1 – x².
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4. The triangles below lie on the same line. Find thehorizontal distance of the smaller triangle.25DA10Distance:pe here to searchN
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Thus the horizontal distance of the smaller triangle is 2.
S/14 = 14 a. -196 b. 196 C. 28 d. 0
Answers
In the given equation, the value of S is divided by 14, so to calculate the value of S you have to invert the operation, that is, multiply it by 14 so that both operations cancel each other.
And, for the equality to be valid, all operations made in one side of the = sign must be done on the other side as well. So, multiply both sides of the equation by 14:
[tex]\begin{gathered} \frac{14S}{14}=14\cdot14 \\ S=196 \end{gathered}[/tex]S=196 the correct choise is b.
A club that has 20 members is selecting a 5 representatives to send to a national conference. How many different groups of 5 can there be?
Answers
There can be a total of 15504 groups of selection
How to determine the groups of selection?From the question, we have
Total number of persons, n = 20
Numbers to selection, r = 5 i.e. the committee members
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 20 and r = 5
Substitute the known values in the above equation
Total = ²⁰C₅
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 20!/15!5!
Evaluate
Total = 15504
Hence, the number of ways is 15504
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Answer:
There can be 4 groups of 5.
> Next question Get a similar question You can retry this 8 3 Volume = Surface Area = Lateral Surface Area = Enter an interer or decimal number (more..] Submit Question
Answers
From the question, r = 8 cm, h =3 cm
Volume of a cylinder = pi x r^2x h = 22/7 x 8 x8 x 3 = 4224/7 = 603.43 cm^3
surface area of a cylinder= 2 x pi x r x h = 2 x 22/7 x 8 x 3 = 1056/7 =
150.86 cm^2
The bakery you choose cost $1000 per month to rent. The bakery that you almost rented was one fourth for the cost but was too small how much was the other bakery per month PLEASE HELPthis would be for a fifth grader and they have to show how they come up with the answer he would have to use the same scenario on multiple questions like this
Answers
The bakery you choose cost $1000 per month.
The bakery that you almost rented was one fourth for the cost: 1/4 of $1000.
When you have a fraction of a quantity you have to multiply the fraction by the value. Doing so, we have:
[tex]\begin{gathered} \frac{1}{4}\cdot1000 \\ \frac{1}{4}\cdot\frac{1000}{1}\text{ (Converting 1000 to a fraction)} \\ \frac{1000}{4}\text{ (Multiplying the numerators and then the denominators)} \\ 250\text{ (Dividing)} \\ \text{The answer is \$250} \end{gathered}[/tex]5 lb of apples cost $8.20. How much is it for 1 lb?
Answers
6. Write a regression equation for the data above. (MD1)Answer of 5. is C.
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Looking at the graph of item C in question 5, we can see that it is a straight line, so it is represented by a linear equation of the form:
[tex]y=mx+b[/tex]We can also see that, when the value of x increases, the value of y also increases, which means the slope of the line is positive (m > 0).
With this information and looking at the options, we can conclude that the correct option is B.
A piece of wire 5/4 m long is to be cut into 20 pieces of the same length. What is the length of each piece?Each piece is ____ m long.(Simplify your answer. Type an integer or a fraction.)
Answers
When we divide a fraction by a number, that's equivalent to multiplying the first fraction by the inverse of that number.
In this problem, we need to divide the fraction 5/4 by 20. So we obtain:
[tex]\frac{5}{4}\colon20=\frac{5}{4}\cdot\frac{1}{20}[/tex]Now, we need to multiply the numerator of the first fraction by the numerator of the second one, and the denominator of the first fraction by the denominators of the second one:
[tex]\frac{5}{4}\cdot\frac{1}{20}=\frac{5\cdot1}{4\cdot20}=\frac{5}{80}[/tex]Now, we need to simplify the answer. To do so, we can divide both the numerator and the denominator by 5:
[tex]\frac{5\colon5}{80\colon5}=\frac{1}{16}[/tex]Therefore:
Each piece is 1/16 m long.
Please only solve for angle 1 and ignore the question above.
Answers
Answer:
[tex]m\angle1\text{ = 115}\degree[/tex]Explanation:
Here, we want to get the value of the angle marked 1
From what we have, the bigger arc measures 236°
Now, we need to get the value of the arc ML
We have that as:
[tex]236-70-60\text{ = 106}\degree[/tex]Finally, we use one of the angle theorems to get the value
In using it, we have to consider the value of the smaller arc JK which is 124°
Now, we have its value as:
[tex]\frac{106\text{ + 124}}{2}\text{ = 115}\degree[/tex]We add the value of the arc ML and the value of the smaller arc JK and divide by 2
The graphs shows the number of hours that Tammy spends typing for work, x, and the amount of pay that she earns, y. What is the slope of the line?
A: 1/4
B: 8/17
C: 4
D: 6
HELP PLS
Answers
Answer: the answer is 6
Step-by-step explanation:
i did it step by step
• if the area of a square is 100cm ^2, what is the perimeter? • if the perimeter of a square is 116cm, what is it's area?
Answers
1) Given data:
Area of square = 100 cm square
[tex]A=a^2[/tex][tex]\begin{gathered} a^2=100 \\ a=10\operatorname{cm} \end{gathered}[/tex]The perimeter of square is,
[tex]\begin{gathered} P=4a \\ P=4\times10 \\ P=40\operatorname{cm} \end{gathered}[/tex]2) Given data:
Perimeter of square = 116 cm
[tex]P=4a[/tex][tex]\begin{gathered} 4a=116 \\ a=29 \end{gathered}[/tex]The area os square is,
[tex]\begin{gathered} A=a^2 \\ A=29\times29 \\ A=841\operatorname{cm}\text{ square} \end{gathered}[/tex]What is the equation of the line that passes through the point (4, 9) with a slope of - 5/8 Write the equation in point-slope form.
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the slope of the line is -5/8 and it is passing through (4, 9)
the equation of a line is
[tex]y-9=m(x-4)[/tex]put m = -5/8
[tex]\begin{gathered} y-9=-\frac{5}{8}(x-4) \\ y-9=-\frac{5}{8}x+\frac{1}{2} \end{gathered}[/tex]so the equation of line is
y = -5/8 x + (1/2) + 9
y = -5/8 x + 19/2
i forgot how i solved this, what im getting is 4x -24 which is wrong
Answers
Answer:
[tex](4x^2+22x-12)cm^2[/tex]Explanation:
From the given figure:
• The base of the triangle, b = (4x-2) cm
,• The perpendicular height, h = (2x+12) cm
The area of a triangle is calculated using the formula:
[tex]A=\frac{1}{2}bh[/tex]Substitute the given expressions:
[tex]\begin{gathered} A=\frac{1}{2}(4x-2)(2x+12) \\ Factor\text{ }4x-2\implies4x-2=2(2x-1) \\ A=\frac{1}{2}\times2(2x-1)(2x+12) \\ A=(2x-1)(2x+12) \end{gathered}[/tex]Next, open the brackets:
[tex]\begin{gathered} A=2x(2x+12)-1(2x+12) \\ =4x^2+24x-2x-12 \\ =(4x^2+22x-12)cm^2 \end{gathered}[/tex]The area of the triangle is:
[tex](4x^2+22x-12)cm^2[/tex]The pH of a fruit juice is 5.3 Find the hydronium ion concentration [H3O+] of the juice. Use the formula pH = -log[H30+]
Answers
Answer:
[tex]\lbrack H_3O^+\rbrack\text{ = }5.0\text{ }\times10^{-6\text{ }}moles\text{ per liter}[/tex]Explanation:
By definition, the pH of a solution is the negative logarithm to base 10 of the concentration of Hydroxonium or oxonium ion
Mathematically, we have this as:
[tex]pH=-log\lbrack H_3O^+\rbrack_{}[/tex]We can change the formula subject so we would have hydroxonium ion on the left
Mathematically, we have this as:
[tex]\lbrack H_3O^+\rbrack\text{ = ANTILOG (-pH)}[/tex]Finally, we have the calculation as follows:
[tex]\lbrack H_3O^+\rbrack\text{ = antilog(-5.3) = }0.000005011872[/tex]In the scientific form,we have this as:
[tex]5.0\text{ }\times10^{-6\text{ }}moles\text{ per liter}[/tex]
In an octagon, five of the angles are equal and each of the other three angles is 24° greater than each of the five other ones. Determine the angles of the octagon anto
Answers
Given:
5 angles are equal: x
Each of the other angles is 24 greater than the other 5 angles: x+24
An octagon has 8 angles; the sum of the interior angles of an octaogn is 1080º
[tex]5x+3(x+24)=1080º[/tex]Use the equation above to solve x:
[tex]\begin{gathered} 5x+3x+72=1080 \\ 8x+72=1080 \\ 8x=1080-72 \\ 8x=1008 \\ x=\frac{1008}{8} \\ \\ x=126 \end{gathered}[/tex]The 5 angles that are equal measure 126º
The other 3 angles measure:
[tex]x+24=126+24=150º[/tex]Then, the angles of the octagon are: 126º,126º,126º,126º,126º,150º,150º,150ºSolve for y. d = 5x + 5y 0 y = 5x-d 5 d-5.2 O Y = y = 5(d - 5x) o y Y d-5x 5
Answers
Given the equation:
[tex]d=5x+5y[/tex]Solve for y , which mean make y alone on the left side.
So,
[tex]5y=d-5x[/tex]Divide the equation by 5
[tex]y=\frac{d-5x}{5}[/tex]The answer is the last option
What is the relationship between the pair of angles ABC and LMN shownin the diagram below?
Answers
Solution:
From the given figure
Where
[tex][/tex]In circle C with m BCD= 48°, find the angle measure of minor arc BD.DB
Answers
Notice that angle BCD is a central angle, therefore, the measure of its arc will be the same as the measure of the angle, therefore, the measure of the minor arc BD is 48 degrees
Instructions: Write the function in slope-intercept form that represents the given. The roasting guide for a turkey suggests cooking for 100 minutes plus an additional 8 minutes per pound (x). Write the equation for total cooking time in terms of pounds of turkey.
Answers
Answer:
y = 8x + 100
Explanation:
Let us call the total cooking time y and the x the number of pounds of turkey, then we know that the roasing guid
A 33-ft ladder leans against a building so that the angle between the ground and the ladder is 85°.how high does the ladder reach on the building ?
Answers
We have the next situation:
Now, we need to label the sides:
- The largest side is always the hypotenuse
- The adjacent side is between the right angle and the given angle.
- The opposite side is opposite to the given angle.
Hence,
Hypotenuse = 33 ftt
Opposite side = h
Then, we need to find h:
We need to use a trigonometric function that involves the side that we know and the missing side:
So,
sinθ = opposite side / hypotenuse
Replacing:
Sin85 = 33ft / h
Solve for h:
h= 33ft¨*sin 85
h= 32.87
The answer is 32.87
Lucille wrote three numbers between 0.75 and 0.76 what numbers could she have written?
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As an answer to this question, any decimal between 0.75 and 0.76 will do.
So let us choose the three numbers at random.
0.751 , 0.754, and 0.756 will do.
Marked angle 3 different ways
Answers
Answer:
where are question I don't understand this question
Hello looking for someone to help me out on this question
Answers
Answer
The value of x = 14
m∠T = 65°
m∠S = 30°
m∠R = 85°
Explanation
From the given ΔRST,
m∠T + m∠S + m∠R = 180° (Sum of angles in a triangle)
m∠T = (4x + 9)°, m∠S = (2x + 2)° and m∠R = (7x - 13)°
⇒(4x + 9)° + (2x + 2)° + (7x - 13)° = 180°
Grouping the terms, we have
4x + 2x + 7x + 9 + 2 - 13 = 180°
13x - 2 = 180°
13x = 180 + 2
13x = 182
Divide both sides by 13
13x/13 = 182/13
x = 14
Therefore,
m∠T = (4x + 9)° = (4(14) + 9)° = (56 + 9)° = 65°
m∠S = (2x + 2)° = (2(14) + 2)° = (28 + 2)° = 30°
m∠R = (7x - 13)° = (7(14) - 13)° = (98 - 13)° = 85°
Help !!!! Please asap
Answers
Looking at the graph, the domain is:
[3, ♾️)
This is the case because the graph begins at 3, hence it is a defined starting point, and so brackets are used to indicate this.
Looking at the graph, the range is:
(-♾️, ♾️)
This is the case because the graph rises towards infinity as the x-coordinates become greater than 3. At the x-coordinate x=3, the graph extends infinitely downwards, and thus the graph extends upwards and downwards towards positive and negative infinity. Also note that infinity is a concept, not a defined point, so we use parentheses to indicate this.
The radius of a circle is 2 meters. What is the circle's circumference?r=2 mUse 3.14 for л.meters
Answers
To solve this problem, we will use the following formula for the circumference of a circle:
[tex]C=2\pi r,[/tex]where r is the radius of the circle.
Substituting
[tex]\begin{gathered} r=\text{ 2 m, } \\ \pi=3.14 \end{gathered}[/tex]in the above formula, we get:
[tex]C=2\times3.14\times2m.[/tex]Simplifying the above result, we get:
[tex]C=12.56m.[/tex]Answer: [tex]\begin{equation*} 12.56m. \end{equation*}[/tex]