The length of the diagonal of a Rectangle is 14cm,and it forms a 30 degree angle in one corner of the rectangle.What is the area of the rectangle.(A=LxW)Just number 20
Answers
Explanation
Step 1
draw the rectangle
here we have a rigth triangle,then
Let
[tex]\begin{gathered} hypotenuse=14 \\ agle=30\text{ \degree} \\ \text{adjacent side= length= l} \end{gathered}[/tex]so, we need a function that relates those values
[tex]\cos \Theta=\frac{adjacent\text{ side}}{\text{hypotenuse}}[/tex]replace and solve for length
[tex]\begin{gathered} \cos \Theta=\frac{adjacent\text{ side}}{\text{hypotenuse}} \\ \text{hypotenuse}\cdot\cos \Theta=adjacent\text{ side} \\ 14\text{ cm }\cdot\cos 30=l \\ 12.12435\text{ cm=l} \end{gathered}[/tex]Step 2
width
similarity, we need a function that relates
[tex]\sin \text{ }\Theta=\frac{opposite\text{ side}}{\text{hypotenuse}}[/tex]let
[tex]\text{opposite side= width=w}[/tex]replace and solve for w
[tex]\begin{gathered} \sin \text{ }\Theta=\frac{opposite\text{ side}}{\text{hypotenuse}} \\ \text{hypotenuse}\cdot\sin \Theta=opposite\text{ side} \\ 14\text{ cm }\cdot\sin \text{ 30=w} \\ 7cm=w \end{gathered}[/tex]Step 3
finally, the area of a rectangle is given by
[tex]\begin{gathered} \text{Area}=\text{ length }\cdot width \\ \text{replacing} \\ \text{Area}=(12.12\cdot7)(cm^2) \\ \text{Area}=84.87(cm^2) \end{gathered}[/tex]therefore, the answer is
[tex]\text{Area}=84.87(cm^2)[/tex]I hope this helps you
Related Questions
A car rental company’s standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function S = 15.75+0.50 M, where M is the number of miles driven. The company also offers an option to ensure the car against damage. The insurance charge I in dollars is given by the function I = 5.70+0.15 M. Let C be the total cost in dollars for a rental that includes insurance. Write an equation relating C to M.
Answers
Answer:
[tex]C\text{ = 0.65 M + 21.45}[/tex]Explanation:
Here, we want to write an equation that relates C to M
From the given question, we have to add the insurance to the standard charge to get the total cost
Mathematically:
[tex]C\text{ = S + I}[/tex]Now, we substitute the values for both S and I
That would be:
[tex]\begin{gathered} C\text{ = 15.75 + 0.50M + 5.70 + 0.15 M} \\ C\text{ = 0.65M + 21.45} \end{gathered}[/tex]Sally has a mass of 70 kg and dave weighs 170 pounds what is Sally weight as a percentage of Dave’s weight
Answers
The percentage is 91% approx.
We have to find percentage here.
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
To find percentage, we need to have both the terms in the same unit.
So, we will convert kg into pounds
1 kg = 2.205 pounds
70 kg = 2.205 * 70 = 154.35 pounds
Sally's weight = 154.35 pounds
Dave's weight = 170 pounds
Percentage = Sally's weight/ Dave's weight * 100
= 154.35/170 * 100
= 90.794%
= 91% approx.
The percentage is 91% approx.
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find two vectors each of norm 1 that I perpendicular to vector A={3,2}
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(2√13/13 , 3√13/13) and (-2√13/13 , -3√13/13) are two vectors of norm 1 that are perpendicular to A = (3 , 2) .
What is perpendicular vectors ?In Cartesian coordinates, the given vector can be represented by the line y = -2x/3. The vector is the line segment that connects (0,0) and (3,-2).y = 3x/2 can be used to represent the normal.
If the vector is represented by a line connecting (0,0) to a point (p,q), then,p2 + q2 = 1 because the normal is one length, and q = 3p/2.
As a result,p² + 9p²/4 = 1, 13p²/4 = 1, p = ±√(4/13) = ±2/√13, q = ±3/√13.
After rationalization, one normal vector is (2√13/13 , 3√13/13) and the other is (-2√13/13 , -3√13/13).The two vectors of norm 1 perpendicular to A = (3 , 2) is :
(2√13/13 , 3√13/13) and (-2√13/13 , -3√13/13).
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John owes $25.20 to his mom. He borrowed $27.60 from his dad. Howmuch does he owe in all? Write your answer as a rational number *
Answers
John owes to his Mom and Dad.
From Mom = 25.20
From Dad = 27.60
The total amount he owes is the sum of both. We just add both the amounts.
Total: 25.20 + 27.60 = $52.80
A parabola opening up or
equation in vertex form.
down has vertex (-1, 4) and passes through (-2, 17). Write its equation in vertex form.
Answers
Equation of parabola in vertex form is 13x² + 26x + 17
Define Parabola
A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile traveling under the pull of gravity will travel along a curve similar to this one.
Given,
vertex (h,k) = (-1, 4)
points (x,y) = (-2, 17)
We know, The equation in vertex form is
y = a(x - h)² + k
put the (h,k) values,
y = a(x - (-1))² + 4
y = a(x + 1)² + 4 --------- eq(i)
Next, find the value of 'a' by plug in the points of (x, y) in eq(i)
y = a(x + 1)² + 4
⇒17 = a(-2 + 1)² + 4
⇒17 = a(-1)² + 4
⇒17 = a + 4
⇒a = 13
Now, substitute 'a' value in eq(i) to find the equation of parabola
y = a(x + 1)² + 4
⇒ y = 13(x + 1)² + 4
⇒ y = 13(x² + 1 + 2x) + 4
⇒ y = 13x² + 13 + 26x + 4
⇒ y = 13x² + 26x + 17
Therefore, equation of parabola in vertex form is 13x² + 26x + 17
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Which one of the following angle measurements is the largest?
Answers
We have
[tex]\pi\approx3.14\text{ radians}[/tex]and
[tex]\pi=180^0[/tex]From these,
[tex]2\text{ radians<3 radians<}\pi<200^o[/tex]The largest measurement is 200 degrees. Thus, option B is correct.
Hi I need help with this thank you! Previous question that may help answer this one : Line of best fit: ^y1=−0.02 x+4.68 ● Curve of best fit: ^y2=−0.09 x2+1.09 x+2.83 Section 2 Question 1 Using a curve to make a prediction of the y value for an x value between two existing x values in your data set is called interpolation. Suppose the year is 2005, where x = 5 years: (a) Use the equation for the line of best fit to predict the number of cell phones sold during that year. Round answers to one decimal place and be sure to include the appropriate units. Your Answer: we have the linear equation: y1=-0.02x+4.68Where x is the number of years since the year 2000, y1 ----> is the number of cell phones sold. So for the year 2005, x=2005-2000=5 years.substitute:y1=-0.02(5)+4.68y1=4.58Therefore, the answer is 4.6 cell phones sold.(b) Use the equation for the non-linear curve of best fit to predict the number of cell phones sold during that year. Round answers to one decimal place and be sure to include the appropriate units. Your Answer: We have the equation y2=-0.09x^2+1.09x+2.83For x=5 yearssubstitute:y2=-0.09(5)^2+1.09(5)+2.83y2=6.03Therefore, the answer is 6.0 cell phones sold.
Answers
From the information provided we will have that the predictions will be:
*Line of best fit:
[tex]y_1=0.02(13)+4.68\Rightarrow y_1=4.94\Rightarrow y_1\approx4.9[/tex]So, the extrapolation from the line of best fit is 4.9 sold.
*Curve of best fit:
[tex]y_2=0.09(13)^2+1.09(13)+2.83\Rightarrow y_2=32.21\Rightarrow y_2\approx32.2[/tex]So, the extrapolation for the curve of best fit is 32.2 sold.
3(4x+1)^2-5=25 using square root property
Answers
Answer:
[tex]x=\frac{-1+\sqrt{10}}{4}\text{ or }x=\frac{-1-\sqrt{10}}{4}[/tex]Explanation:
Given the equation:
[tex]3\left(4x+1\right)^2-5=25[/tex]To solve an equation using the square root property, begin by isolating the term that contains the square.
[tex]\begin{gathered} 3(4x+1)^{2}-5=25 \\ \text{ Add 5 to both sides of the equation} \\ 3(4x+1)^2-5+5=25+5 \\ 3(4x+1)^2=30 \\ \text{ Divide both sides by 3} \\ \frac{3(4x+1)^2}{3}=\frac{30}{3} \\ (4x+1)^2=10 \end{gathered}[/tex]After isolating the variable that contains the square, take the square root of both sides and solve for the variable.
[tex]\begin{gathered} \sqrt{(4x+1)^2}=\pm\sqrt{10} \\ 4x+1=\pm\sqrt{10} \\ \text{ Subtract 1 from both sides} \\ 4x=-1\pm\sqrt{10} \\ \text{ Divide both sides by 4} \\ \frac{4x}{4}=\frac{-1\pm\sqrt{10}}{4} \\ x=\frac{-1\pm\sqrt{10}}{4} \end{gathered}[/tex]Therefore, the solutions to the equation are:
[tex]x=\frac{-1+\sqrt{10}}{4}\text{ or }x=\frac{-1-\sqrt{10}}{4}[/tex]
i am supposed to find the volume of this pyramid
Answers
For this type of problems we use the formula for the volume of a pyramid:
[tex]\begin{gathered} V=\text{ }\frac{1}{3}A_bh \\ A_b\text{ is the area of the base} \\ h\text{ is the height of the pyramid} \end{gathered}[/tex]Substituting h=12 yd and knowing that the area of a square is side*side we get that:
[tex]\begin{gathered} A_b=\text{ 10yd }\cdot10yd=100yd^2 \\ V=\frac{1}{3}100yd^212yd=100yd^24yd=400yd^3 \end{gathered}[/tex]Find the equation line parallel y=(-4/5)x+12 passing through (-6,2)
Answers
So we want to find the equation of a line parallel to
[tex]y=-\frac{4}{5}x+12[/tex]Passing through the point (-6,2).
First, remember that a line is parallel to other if their slopes are the same.
Then, the slope of our parallel line will be also -4/5.
Remember that a line has the following equation:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Now, we know that the parallel line has slope = -4/5 and passes through the point (x,y) = (-6,2), so we could replace in our previous equation as follows:
[tex]\begin{gathered} 2=-\frac{4}{5}(-6)+b \\ 2=\frac{24}{5}+b \\ b=2-\frac{24}{5} \\ b=-\frac{14}{5} \end{gathered}[/tex]Therefore, the equation of the parallel line to y=(-4/5)x+12 passing through (-6,2) is:
[tex]y=-\frac{4}{5}x-\frac{14}{5}[/tex]
find the greatest common factor for 8n^3 6n^3
Answers
We determine the greatest common factor as follows:
[tex]8n^3+6n^3[/tex]So, we factor:
[tex]2n^3(4+3)[/tex]So, the greatest common factor is 2n^3.
6-Find the measure of ∠AEB.A. 122°B. 132°C. 142°D. 152°7-Find the measure of ∠BEC.A. 58 °B. 48°C. 38°D. 28°8-Find the measure of ∠CED.A. 52 °B. 48 °C. 42 °D. 32°9-Find the measure of ∠FEB.A. 142°B. 180°C. 90°D. 0°10-Find the measure of ∠FED.A. 0°B. 180°C. 45°D. 90°
Answers
The answer for 6 is C. 142°
Explanation
∠AEB = 180 - ∠AEF (Sum of angle on a straight line)
∠AEB = 180 - 38 = 142°
Find an equation of the tangent line to the graph of y = B(x) at x = 25 if B(25) = −1 and B ′(25) = − 1 5 .
Answers
The most appropriate choice for tangent to a curve will be given by-
[tex]3x + 2y = 73[/tex] is the required equation of tangent.
What is tangent to a curve?
Tangent to a curve at a point is the straight line that just touches the curve at that point.
Equation of tangent to a curve at a point [tex](x_1, y_1)[/tex] is given by
[tex]y - y_1 = \frac{dy}{dx}|_{(x_1,y_1)} (x - x_1)[/tex]
Here,
y = B(x), B(25) = -1, B'(25) = -1.5
Equation of tangent =
[tex](y - (-1)) = -1.5(x - 25)[/tex]
[tex]y + 1=-1.5x +37.5\\y + 1 = -\frac{3}{2}x + 37.5\\2y + 2 = -3x + 75\\3x+2y = 75-2\\3x+2y=73[/tex]
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why are integers rational numbers? give an example
Answers
Integers are rational numbers because it consists of zero, positive and negative numbers till infinity only.
What is Rational number?This is referred to as a number which can be expressed as the quotient p/q of two integers such that q ≠ 0 and they are present till infinity due to the large numbers and examples include 2000, 25 etc.
Integers are rational numbers because they contain zero, positive and negative numbers. Decimals and fractions are not included in this context and an example is 12, 100 etc which is why the aforementioned above was chosen as the correct choice.
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A veterinarian is visited by many pets and their owners each day. Before the doctor attends to each pet, an assistant records information including the type, age, weight, and height of each pet. What are the individuals in the data set?
Answers
Since all the information in the study, such as the type, the age and the weight are related to the pet, individuals in each data-set are the pets.
Who are the individuals on a data-set or on a study?The individual of a data-set is the object which is being analyzed in the study, the object that has it's characteristics analyzed.
In the context of this problem, these following information are analyzed, at the register when the doctor attends each pet and registers the information.
Type of the pet.Age of the pet.Weight of the pet.Height of the pet.All these information belong to the pet that visits the veterinary, hence the individuals in each data-set are the pets.
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Use the drawing tool(s) to form the correct answer on the provided graph, The function fx) is shown on the provided graph. Graph the result of the following transformation on f(X). f(x) + 6
Answers
We have that the line passes by the points (0, -2) & (1, 2). Using this we determine the slope (m) and then the function. After that we transformate the function. We proceed as follows:
[tex]m=\frac{2-(-2)}{1-0}\Rightarrow m=4[/tex]Now, using one of the points [In our case we will use (0, -2), but we can use any point of the line] and the slope, we replace in:
[tex]y-y_1=m(x-x_1)[/tex]Then:
[tex]y-(-2)=4(x-0)[/tex]Now, we solve for y:
[tex]\Rightarrow y+2=4x\Rightarrow y=4x-2[/tex]And we apply the transformation to our line, that is f(x) -> f(x) + 6:
[tex]y=4x-2+6\Rightarrow y=4x+4[/tex]Therefore our final line (After the transformation) is y = 4x + 4, and graphed that is:
A glassblower makes vases. To prevent them from breaking,each vase's thickness should be 6 millimeters and candeviate by no more than 1 millimeter.Write an inequality to represent this situation, where t is thethickness in millimeters, and solve for the maximumthickness.
Answers
Since each vase should be 6 millimeters and can only deviate by no more than 1 millimeter, the inequality for the thickness would be:
[tex]6\ge t\leq7[/tex]And the maximum thickness would be 7 millimeters.
urgently need help with question 30, it’s Venn diagram, is it valid or not valid & is the argument sound or not?
Answers
For statement 30:
Premise: All fruits are foods with sugar;
Premise: Chocolate bars contain sugar;
Conclusion: Chocolate bars are fruit.
Since the conclusion does not necessarily follow from the premises, this is an invalid argument, regardless of whether chocolate is fruit.
Consider the line segment porque shown. For which of the following transformations would the image porque be contained entirely in Quadrant II?
Answers
We will have the following:
In order to have PQ entirely in the quadrant II, the transformation must be:
*Translate PQ up 4 units and to the left 3 units. [Option K]
Riley has $955 in a savings account that earns 15% interest, compounded annually.To the nearest cent, how much interest will she earn in 2 years?
Answers
In order to calculate the interest generated in 2 years, we can use the formula below:
[tex]I=P((1+r)^t-1)[/tex]Where I is the interest generated after t years, P is the principal (initial amount) and r is the interest rate.
So, for P = 955, r = 0.15 and t = 2, we have:
[tex]\begin{gathered} I=955((1+0.15)^2-1) \\ I=955(1.15^2-1) \\ I=955(1.3225-1) \\ I=955\cdot0.3225 \\ I=307.99 \end{gathered}[/tex]Therefore the interest generated is $307.99.
What kind of polyhedron can be assembled from this net?
Answers
It could be assembled a rectangular prism
and
given that f(x)=3x-6, determine f(8)
Answers
According to the given data we have the following function:
f(x)=3x-6
To determine f(8) we would have to plug in into the equation the 8 and then proceed to calculate it, so:
If f(x)=3x-6
Then, f(8)=3(8)-6
f(8)=24-6
f(8)=18
CD is the midsegment of trapezoid WXYZ. you must show your work to all the parts below
Answers
Given that CD is the midsegment of the trapezoid WXYZ
From the properties of Midsegment of trapezoid we have :
0. The midsegment of a trapezoid is parallel to each base.
,1. The length of the midsegment of a trapezoid is equal to half the sum of the lengths of its bases.
[tex]\text{length of mid segment =}\frac{a+b}{2}[/tex]In the given figur, the mid segement CD= 22
length of parallel side is WZ=x+3
and the length of another side XY = 4x+1
so apply the mid segment length formula :
[tex]\begin{gathered} CD=\frac{WZ+XY}{2} \\ 22=\frac{x+3+4x+1}{2} \\ 5x+4=44 \\ 5x=40 \\ x=8 \end{gathered}[/tex]x=8,
For, XY :
Substitute x=8 into the given length expression of XY
XY =4x+1
XY=4(8)+1
XY=33
For, WZ :
Substitute x=8 into the given expression length of WZ
WZ=x+3
WZ=8+3
WZ=11
Answer :
a). x = 8
b). XY = 33
c). WZ = 11
Evaluate the expression (4x^3y^-2)(3x^-2y^4) for x = –2 and y = –1.
Answers
Answer:
3x−2y)(4x+3y)
It can be written as =3x(4x+3y)−2y(4x+3y)
By further calculation =12x
2
+9xy−8xy−6y
2
So we get =12x
2
+xy−6y
2
Two numbers sum to 61. Twice the first subtracted from the second is 1. Find the numbers.
Answers
x + y = 61
y - 2x = 1
y = 2x + 1
x + (2x + 1) = 61
3x + 1 = 61
3x = 60
x = 20
y = 61 - 20 = 41
Topic 8.2: Solving Using Linear/HELP RN!!!!!Area Scale Factor3. Examine the two similar shapes below. What is the linear scale factor? What is the area scalefactor? What is the area of the smaller shape?3a. Linear scale factor =3b. Area scale factor =Area =99 un.2=3c. Area of small shape =
Answers
Solution
Question 3:
- Let the dimension of a shape be x and the dimension of its enlarged or reduced image be y.
- The linear scale factor will be:
[tex]sf_L=\frac{y}{x}[/tex]- If the area of the original shape is Ax and the Area of the enlarged or reduced image is Ay, then, the Area scale factor is:
[tex]sf_A=\frac{A_y}{A_x}=\frac{y^2}{x^2}[/tex]- We have been given the area of the big shape to be 99un² and the dimensions of the big and small shapes are 6 and 2 respectively.
- Based on the explanation given above, we can conclude that:
[tex]\begin{gathered} \text{ If we choose }x\text{ to be 6, then }y\text{ will be 2. And if we choose }x\text{ to be 2, then }y\text{ will be 6} \\ \text{ So we can choose any one.} \\ \\ \text{ For this solution, we will use }x=6,y=2 \end{gathered}[/tex]- Now, solve the question as follows:
[tex]\begin{gathered} \text{ Linear Scale factor:} \\ sf_L=\frac{y}{x}=\frac{2}{6}=\frac{1}{3} \\ \\ \text{ Area Scale factor:} \\ sf_A=\frac{y^2}{x^2}=\frac{2^2}{6^2}=\frac{1}{9} \\ \\ \text{ Also, we know that:} \\ sf_A=\frac{A_y}{A_x}=\frac{y^2}{x^2} \\ \\ \text{ We already know that }\frac{y^2}{x^2}=\frac{1}{9} \\ \\ \therefore\frac{A_y}{A_x}=\frac{1}{9} \\ \\ A_x=99 \\ \\ \frac{A_y}{99}=\frac{1}{9} \\ \\ \therefore A_y=\frac{99}{9} \\ \\ A_y=11un^2 \end{gathered}[/tex]Final Answer
The answers are:
[tex]\begin{gathered} \text{ Linear Scale Factor:} \\ \frac{1}{3} \\ \\ \text{ Area Scale Factor:} \\ \frac{1}{9} \\ \\ \text{ Area of smaller shape:} \\ 11un^2 \end{gathered}[/tex]Solve the inequality and how do i graph ?
Answers
The most appropriate choice for linear inequation will be given by-
[tex]m > \frac{1}{2}[/tex] is the correct solution
What is linear inequation?
At first it is important to know about algebraic expressions.
Algebraic expressions consists of variables and numbers connected with addition, subtraction, multiplication and division.
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by > , < , [tex]\geq, \leq[/tex]
A one degree inequation is known as linear inequation.
Here,
The given inequation is [tex]\frac{1}{2} - \frac{m}{4} < \frac{3}{8}[/tex]
Now,
[tex]\frac{1}{2} - \frac{m}{4} < \frac{3}{8}\\\\\frac{m}{4} > \frac{1}{2} - \frac{3}{8}\\\\\frac{m}{4} > \frac{4 - 3}{8}\\\\\frac{m}{4} > \frac{1}{8}\\\\m > \frac{1}{8} \times 4\\m > \frac{1}{2}[/tex]
The number line has been attached here.
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I have already found X . I need help finding m<2
Answers
Given:
[tex]m\angle1=8x-102\text{ and }m\angle4=2x+6[/tex]Required:
[tex]\text{ Find the measure of }\angle2.[/tex]Explanation:
Step 1:
[tex]m\angle1=m\angle4[/tex]Step 2:
[tex]\begin{gathered} 8x-102=2x+6 \\ 6x=108 \\ x=18 \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} m\angle1=8(18)-102 \\ m\angle1=144-102 \\ m\angle1=42 \\ Now, \\ m\angle1+m\angle2=180 \\ 42+m\angle2=180 \\ m\angle2=180-42 \\ m\angle2=138 \end{gathered}[/tex]Answer:
Measure of angle 2 equals 138.
Solve each system of the equation by elimination. y=-4x+14y=10x-28
Answers
Explanation:
The elimination method consists in substracting one equation from the other, so you eliminate one of the variables and you have only one equation to solve for one variable.
In this case, y has the same coefficient in both equations, so this is the variable we will eliminate.
Substract the first equation from the second:
[tex]\begin{gathered} y=10x-28 \\ - \\ y=-4x+14 \\ \text{ ---------------------} \\ y-y=10x+4x-28-14 \\ 0=14x-42 \end{gathered}[/tex]And solve for x:
[tex]\begin{gathered} 14x=42 \\ x=\frac{42}{14} \\ x=3 \end{gathered}[/tex]Now, we replace x = 3 into one of the equations and solve for y:
[tex]y=-4\cdot3+14=-12+14=2[/tex]Answer:
• x = 3
,• y = 2
which of these is a formula that can be used to determine the nth term of the arithmetic sequence 15,27,39,51,....?
Answers
For an arithmetric progression, we need to find the common difference in the sequence
common difference = d = 2nd term - 1st term = 3rd term - 2nd term = 4th term - 3rd term
2nd term - 1st term = 27 -15 = 12
3rd term - 2nd term = 39-27 = 12
The result are the same.
Hence, d = 12
The first trm = 15
The formula for arithmetric sequence:
The nth term = 1st term + d(n - 1)
Replacing with the values we got above:
The nth term = 15 + 12(n - 1)
Since none of the options have the above, we would expand the parenthesis.
The nth term = 15 + 12×n - 12×1
The nth term = 15 + 12n - 12
= 15 -12 + 12n
The nth term = 3 + 12n = 12n + 3
From the options:
The nth term = 12n + 3 (option B)
[tex]a_n=\text{ }12n+3\text{ (}optionB)[/tex]
