Answers
Given:
a.) The width of the rectangle is 0.7 meters less than the length.
b.) The perimeter of a rectangle is 44.6 meters.
First, let's draw the rectangle to better understand the problem.
Recall: The formula in getting the perimeter of the rectangle.
[tex]\text{ Perimeter = 2Length + 2Width}[/tex]But it stated that the width of the rectangle is 0.7 meters less than the length.
Thus,
Width = Length - 0.7
Let's now find its Length,
[tex]\begin{gathered} \text{ Perimeter = 2Length + 2Width} \\ \text{ 44.6 = 2Length + 2(Length - 0.7)} \\ \text{ 44.6 = 2Length + 2Length - 1.4} \\ \text{ 44.6 + 1.4 = 4Length} \\ \text{ 46 = 4Length} \\ \text{ 4Length = 46} \\ \text{ }\frac{\text{4Length}}{\text{ 4}}\text{ = }\frac{\text{ 46}}{\text{ 4}} \\ \text{ Length = }11.5\text{ meters} \end{gathered}[/tex]Therefore, the length of the rectangle is 11.5 meters.
Let's now determine the width,
Width = Length - 0.7
= 11.5 - 0.7
Width = 10.8 meters
Therefore, the width of the rectangle is 10.8 meters.
Related Questions
I’m having trouble finding the angles for Q,R, and S.
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Given
Find
Explanation
Final Answer
Answer:
See below
Step-by-step explanation:
RSP arc = 137 + 41 = 178 Inscribed angle Q is 1/2 of this = 89°
so arc RQP = 182 degees S is 1/2 of this = 91 °
the interior andles of the polygon sum to ( 4-2)*180 = 360°
then R = 360 - 89 - 91 - 57 = 123°
Help me answer question 8 and write in more detail, thank you.
Answers
2. 205 randomly selected students from a certain community college were asked a question "Withwhom do you find it easier to make friends?” Possible responses were 'opposite sex', 'samesex''no difference'. The students were also categorized as male or female. The followingtable records the data collected.Opposite Sex Same Sex No Difference TotalFemale 582070 148Male 241340 77Total 8233110 225a) What is the probability that a randomly selected student would say that it is easier to makefriends with the same sex or male?b. What proportion of female students answered that it is easier to make friends with the samesex?c. What probability that a male student said it easier to make friends with opposite sex?
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The sample contains 225 students, where there are 148 females and 77 males.
The probability of an event A occurring can be calculated as
[tex]P(A)=\frac{\text{Number of times A occured}}{Number\text{ of total events}}[/tex]QUESTION A:
Number of students that say that it will be easier to make friends with the same sex is 33.
The probability of this event is calculated as
[tex]P(S)=\frac{33}{225}[/tex]The students who will say it is easier to make friends with males are the females that make friends with the opposite sex and the males that make friends with the same sex. The sum will be
[tex]n(M)=58+13=71[/tex]The probability of this can be calculated by
[tex]P(M)=\frac{71}{225}[/tex]The probability of both events occurring is calculated as
[tex]P=P(S)+P(M)-P(S\cap M)[/tex]The intersection of S and M is simply the number of people that say same-sex and males. This number is 13, the number of males that say same sex.
The probability is calculated as
[tex]P(S\cap M)=\frac{13}{225}[/tex]Therefore, the general probability is given to be
[tex]\begin{gathered} P=\frac{33}{225}+\frac{71}{225}-\frac{13}{225} \\ P=\frac{91}{225} \end{gathered}[/tex]QUESTION B:
The number of females that answered that it is easier to make friends with the same sex is 20.
There are 148 females in total.
Therefore, the proportion of females that answered that it is easier to make friends with the same sex can be calculated as
[tex]\frac{20}{148}=\frac{5}{37}[/tex]QUESTION C:
The number of male students that said it is easier to make friends with the opposite sex is 24.
The probability is given as
[tex]P(S_M)=\frac{24}{225}=\frac{8}{75}_{}[/tex]describe the transformation.
[tex]y = x {}^{2} \: to \: y = - (x - 5) {}^{2} - 6[/tex]
Answers
1. Reflect over the x-axis.
2. Shift right 5 units.
3. Shift down 6 units.
In an input/output table, each output is larger than the corresponding input. Which operations could be used in the function rule? Select all that apply.options:subtractiondivisionadditionmultiplication
Answers
Solution:
In an input/output table, each output is larger than the corresponding input.
The operations which could be used are addition and multiplication.
Hence, the answer is addition and multiplication
I need to convert 35° into radian pls help.
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Answer:
[tex]35\cdot\frac{\pi}{180}=\frac{7}{36}\pi\approx0.611[/tex]Step-by-step explanation:
To convert degrees to radians, we can use the following formula:
[tex]\text{degrees}\cdot\frac{\pi}{180}=\text{radians}[/tex]Then, for 35 degrees:
[tex]35\cdot\frac{\pi}{180}=\frac{7}{36}\pi\approx0.611[/tex]Find the area of the figure. (Dimensions are in m)
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We are given a figure and we are asked to determine its area. We notice that he figure is formed by 4 right triangles and the area of a triangle is given by:
[tex]A=\frac{bh}{2}[/tex]Where "b" is the base and "h" is the height.
Since the figure is formed by 4 triangles each with the same base and the same height we will multiply the formula for the area by 4:
[tex]A=\frac{4bh}{2}=2bh[/tex]Now, we substitute the values of base and height. We have that each triangle has a base of 6 meters and a height of 5 meters. Substituting we get:
[tex]A=2(6m)(5m)[/tex]Solving the operations:
[tex]A=60m^2[/tex]Therefore, the area is 60 square meters.
In Pleasantburg, 2,850 people pay taxes. Of these taxpayers, 1/6 pay between $10,000 and $20,000 in taxes per year, inclusive. How many taxpayers pay either more than $20,000 or less than $10,000 in taxes per year?
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We know that
• There are 2,850 people that pay taxes.
,• 1/6 pay between $10,000 and $20,000.
Note that the problem is asking for the number of taxpayers that pay either more than $20,000 or less than $10,000. In other words, they are asking for the complement fraction of 1/6. Remember that the complement fraction can be found by subtracting the fraction from 1.
[tex]1-\frac{1}{6}=\frac{6-1}{6}=\frac{5}{6}[/tex]This means 5/6 of the taxpayers pay more than $20,000 or less than $10,000. Now let's multiply this fraction by the number of people.
[tex]\frac{5}{6}\cdot2,850=2,375[/tex]Therefore, 2,375 people pay taxes more than $20,000 or less than $10,000.Sasha wrote four statements about the graph shown. She wrote
two incorrect statements. Identify the two statements and write
the correct description or label.
a. Since a > 0, the graph opens upward.
b. Since lal > 1, the shape of the parabola is wider
than the quadratic parent function.
c. The vertex of the parabola is (0, 0).
d. The axis of symmetry is the line y = 0.
Tot
Sign
Answers
The incorrect statements are b and d, and the correct statements would be:
b: "Since lal > 1, the shape of the parabola is narrower"
d: "The axis of symmetry is the line x = 0"
Which are the two incorrect statements?We don't have the graph here, but is easy to identify the two incorrect statements.
The first incorrect statement is:
" Since lal > 1, the shape of the parabola is wider"
As larger is the value of a, faster the function goes upwards, then as we increase the value of the leading coefficient, the parabola becomes narrower.
The second incorrect statement is:
"The axis of symmetry is the line y = 0."
If the parabola opens upwards, the axis of symmetry would be x = 0, not y = 0.
Learn more about parabolas:
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The registration fee for a used car is 0.8% of the sale price of $5,800. How much is the fee?
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The registration fee for a used car is 0.8 percent of sale price price os $5800 is $46.4.
Given the registration fees is the 0.8 percentage of the sale price then the registration fees is :
fees = 0.8% of $5,800,
fees = 5800 * 0.8/100,
fees = 58*0.8,
fees = $46.4
To know more about percentage https://brainly.com/question/2802862
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Seriously cannot figure this out please help now
Answers
Answer:
x = 4 ; a = 15 ; b= -2
Step-by-step explanation:
i know you doy+18 + y+48 + y+18 = 180 but i always get things wrong.
Answers
The external angle of the triangle is equals to the sum of the 2 opposite angles. Therefore,
[tex]\begin{gathered} y+48=y+18+y+18 \\ y+48=2y+36 \\ \text{combine like terms} \\ 48-36=2y-y \\ y=12 \end{gathered}[/tex]Estimate. use rounding or compatible numbers. show how you estimate304 divided by 6 =
Answers
Okay, here we have this:
Considering the provided division, we are going to perform it, so we obtain the following:
[tex]\begin{gathered} \frac{304}{6} \\ =50.6666666667 \end{gathered}[/tex]Then, to round to the hundredths, as the thousandths digit is greater than 6, we will increase the hundredths digit by one, therefore we have:
[tex]\begin{gathered} =\frac{304}{6} \\ \approx50.67 \end{gathered}[/tex]Finally we obtain that 304 divided by 6 is approximately 50.67.
4 1/4 ÷ 3/4a. 5 2/3b. 5 1/3c. 5 5/3
Answers
4 1/4 ÷ 3/4 is the same as 4 1/4 x 4/3
To solve this, first you have to transform the mixed number into a fraction, as follows:
[tex]4\frac{1}{4}=\frac{4\cdot4+1}{4}=\frac{17}{4}[/tex]then:
[tex]4\frac{1}{4}\cdot\frac{4}{3}=\frac{17}{4}\cdot\frac{4}{3}=\frac{17}{3}=\frac{15+2}{3}=\frac{15}{3}+\frac{2}{3}=5\frac{2}{3}[/tex]Two angles in a triangle measures 20° and 90° what is the measure of the third triangle
Answers
Answer:
Step-by-step explanation:
The measure of the third triangle is 59°
Quadrilateral PQRS is rotated 90° clockwise about the origin to form quadrilateralP'Q'R'S'. What is the y-coordinate of point PlpQPSType the answer in the box
Answers
Find the inverse of A=
Find the Matrix equation of AX=b for X
Answers
Answer:
[tex]\textbf{A}^{-1} =\left[ \begin{array}{cc}-30&71\\-11&26\end{array}\right][/tex]
[tex]\textbf{X}=\left[\begin{array}{c}-4\\7\end{array}\right][/tex]
Step-by-step explanation:
The inverse of a matrix M is the matrix M⁻¹.
[tex]\textsf{If}\; \textbf{M} = \left[ \begin{array}{cc}a&b\\c&d\end{array}\right] \; \textsf{then} \; \textbf{M}^{-1}=\dfrac{1}{\text{det} \;\textbf{M}}\left[ \begin{array}{cc}d&-b\\-c&a\end{array}\right][/tex]
[tex]\textsf{For a $2 \times 2$ matrix} \; \textbf{M}=\left[\begin{array}{cc}a&b\\c&d\end{array}\right], \; \textsf{the determinant of} \; \textbf{M} \; \textsf{is $ad-bc$}.[/tex]
Given matrix:
[tex]\textbf{A}=\left[\begin{array}{cc}26&-71\\11&-30\end{array}\right][/tex]
Therefore:
[tex]a=26, \quad b=-71, \quad c=11, \quad d=-30[/tex]
Calculate the determinant of matrix A:
[tex]\begin{aligned}\implies \text{det}\; \textbf{A}&=26 \cdot (-30) - (-71) \cdot 11\\&=-780+781\\&=1\end{aligned}[/tex]
Therefore, the inverse of matrix A is:
[tex]\begin{aligned}\implies \textbf{A}^{-1} & =\dfrac{1}{1}\left[ \begin{array}{cc}-30&71\\-11&26\end{array}\right]\\\\&=\left[ \begin{array}{cc}-30&71\\-11&26\end{array}\right]\end{aligned}[/tex]
------------------------------------------------------------------------------------------
Given matrices:
[tex]\textbf{A}=\left[\begin{array}{cc}26&-71\\11&-30\end{array}\right], \quad \textbf{B}=\left[\begin{array}{c}-49\\-132\end{array}\right][/tex]
[tex]\textsf{Let}\;\textbf{X}=\left[\begin{array}{c}p\\q\end{array}\right][/tex]
If AX = B then:
[tex]\implies\left[\begin{array}{cc}26&-71\\11&-30\end{array}\right]\left[\begin{array}{c}p\\q\end{array}\right]=\left[\begin{array}{c}-49\\-132\end{array}\right][/tex]
[tex]\implies\left[\begin{array}{c}7p+(-3)q\\19p+(-8)q\end{array}\right]=\left[\begin{array}{c}-49\\-132\end{array}\right][/tex]
Therefore:
[tex]7p-3q=-49[/tex][tex]19p-8q=-132[/tex]Solving simultaneously:
[tex]p=-4[/tex][tex]q=7[/tex]Therefore:
[tex]\implies \textbf{X}=\left[\begin{array}{c}-4\\7\end{array}\right][/tex]
please use the answer in the attached picture to write down the co-ordinate of the turning point of x^2-5x+4
Answers
Solution
By general rule w ehave this property:
[tex](x-a)^2=x^2-2ax+a^2[/tex]Using this expression we can do the following:
[tex](x-\frac{5}{2})^2-\frac{9}{4}=(x\cdot x^{}-2\cdot x\cdot\frac{5}{2}+\frac{5}{2}\cdot\frac{5}{2})-\frac{9}{4}=x^2-5x+\frac{25}{4}-\frac{9}{4}=x^2-5x+\frac{16}{4}=x^2-5x+4=(x-1)(x-4)[/tex]Then the final simplfied form is:
(x-1)(x-4)
Then we can find the turning point like this:
[tex]x=-\frac{b}{2a}=-\frac{-5}{2\cdot1}=\frac{5}{2}[/tex]And the corresponding y coordinate is:
[tex](\frac{5}{2}-\frac{5}{2})^2-\frac{9}{4}=-\frac{9}{4}[/tex]Final answer:
[tex](\frac{5}{2},-\frac{9}{4})[/tex]2) Ralph ate 1/2 of a piebefore dinner. After dinnerhe ate 1/3 of what was left.What fraction of the pie didhe eat after dinner?'
Answers
In order to find the fraction of the pie Ralph eat after dinner, you take into account that after dinner He ate 1/3 of the pie he leaft before dinner.
You can write that the pie before dinner is variable x, then, before dinner Ralph ate 1/2 of such a pie, that is, Ralph ate 1/2x, hence, He leaft x - 1/2x=1/2x before dinner.
He ate 1/3 of the Pie he leaft before dinner, that is He ate 1/3(1/2x) = 1/6x
Hence, Ralph ate 1/6 of the pie after dinner.
Question 2A deli sells meal by the pound. The Expression 7.99m+5.99c represents the total cost of m pounds of meat and c pound of cheese . Select all true statements.
Answers
Answer:
The expression is given below as
[tex]7.99m+5.99c[/tex]Where,
The total pounds of meat is
[tex]=m[/tex]The total pounds of cheese is
[tex]=c[/tex]from the relation above,
[tex]\begin{gathered} m\text{ pounds of meat cost = 7.99m} \\ 1\text{ pound of meat will cost=x} \\ \frac{m\times x}{m}=\frac{7.99m}{m} \\ x=7.99 \end{gathered}[/tex]From the relation above,
[tex]\begin{gathered} c\text{ pounds of ch}eese\text{ cost = 5.99c} \\ 1\text{ pound of chesse will cost = y} \\ \frac{c\times y}{c}=\frac{5.99c\times1}{c} \\ y=5.99 \end{gathered}[/tex]To figure out the cost of 2 pounds of meat and 3 pounds of cheese, we will substitute the values below
[tex]\begin{gathered} m=2,c=3 \\ 7.99m+5.99c \\ 7.99(2)+5.99(3) \\ =15.98+17.97 \\ =33.95 \end{gathered}[/tex]Hence,
The options that are TRUE are OPTION A, OPTION B, and OPTION E
What is the description of <2 as it relates to the situation shown?
Answers
Consider the following example.
IN here, we have angles 1 and 2 measured with respect the horizontal line that passes through point A. Note that angle 2 is related to points A and C. In this case, angle is under the horizontal line that passes through A. Then, angle 2 is the angle of depression from point A to point C. Every angle that is under the horizontal line would receive the name of angle of depression. In the same manner, since angle 1 is above the horizontal line, then it is an elevation angle from point A to point C. In fact, every angle that is above the horizontal line, would receive the name of elevation angle.
Coming back to our problem, we can see that angle 2 is formed by the horizontal line that passes through the radar and the line that connects the plane to the radar. This angle would be above the horizontal line of the radar. Then, according to our previous explanation, this means that angle 2 is an elevation angle from the radar to the plane.
log 8Rewrite using properties of logarithms.5OA. logSOB. log 58OC. logOD. log V8Reset Selection
Answers
Given:
[tex]\frac{log8}{5}[/tex]Find: alternate form of the given expression.
Explanation:
[tex]\begin{gathered} log\sqrt[5]{8} \\ =log(8)^{\frac{1}{5}} \\ =\frac{1}{5}log(8) \\ =\frac{log8}{5} \end{gathered}[/tex]Final answer: the required expression will be
[tex]log\sqrt[5]{8}[/tex]Find the x- and y- intercepts of the line represented by the equation 2x-7y=28X=?, y=?
Answers
EXPLANATION:
The first thing we have to do is find the value of Y,To find the y-intercept when x equals zero,Then we find the x-intercept by setting Y equal to zero
[tex]\begin{gathered} 2x-7y=28 \\ -7y=-2x+28;\text{here we must multiply }by\text{ minis 1 }so\text{ that Y is positive} \\ 7y=2x-28 \\ y=\frac{2x}{7}-\frac{28}{7} \\ y=\frac{2x}{7}-4 \\ \textcolor{#FF7968}{m=\frac{2x}{7}} \\ \text{\textcolor{#FF7968}{Now Y AXIS intercepts}}\textcolor{#FF7968}{\colon} \\ x=0\text{ y}=-4\text{ }\textcolor{#FF7968}{(0,-4)} \\ \textcolor{#FF7968}{X}\text{\textcolor{#FF7968}{ intercepts:}} \\ y=0\text{ ; then 0}=\frac{2x}{7}-4 \\ 4=\frac{2x}{7} \\ 4(7)=\frac{2x}{7} \\ 28=2x \\ \frac{28}{2}=x \\ 14=x \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ intercepts (}}\textcolor{#FF7968}{14,0)} \end{gathered}[/tex]10 Find the area of the circle pictured above. Round your answer to the nearest tenth
Answers
The radius, r give in the problem is 10 units
Substituting it to solve for the area;
[tex]A=(3.1416)(10)^2=314.16sq.units[/tex]Rounding that off to the nearest tenths will give us 314.2 sq. units
Answer : 314.2 sq. units
Solve the equation: 4x - 5 = 8 + 4x *13-130all real numbersno solution
Answers
To solve the equation you can first subtract 4x from both sides. Then,
[tex]\begin{gathered} 4x-5=8+4x\rightarrow\text{original equation} \\ 4x-4x-5=8+4x-4x \\ 0-5=8+0 \\ -5=8 \end{gathered}[/tex]Since you arrive at something false, -5 is not equal to negative 8, so the equation has no solution.
Find the size of angle ABC, giving the answer in degrees to 1 decimal place.
Answers
ANSWER:
27.9°
STEP-BY-STEP EXPLANATION:
We can calculate the angle ABC, by means of the law of sine, which is the following:
[tex]\frac{\sin a}{A}=\frac{\sin b}{B}=\frac{\sin c}{C}[/tex]We apply in this case and we have the following equation:
[tex]\frac{\sin(\text{CAB)}}{CB}=\frac{\sin (\text{ABC)}}{AC}[/tex]We replace and calculate for ABC:
[tex]\begin{gathered} \frac{\sin125}{14}=\frac{\sin (\text{ABC)}}{8} \\ \sin (\text{ABC)}=\frac{8\cdot\sin 125}{14} \\ \text{ABC}=\sin ^{-1}(0.468) \\ \text{ABC}=27.9\text{\degree} \end{gathered}[/tex]The angle ABC is 27.9°
I don’t know what to do or how to do this
Answers
Best Fit Line
Given a series of points that represent some measures in the real world, for example, the heights vs the age of a group of children, when we plot it on a rectangular grid, we get a scatter plot, not necessarily aligned as to form a specific graph.
Sometimes is vital to have a known function that best represents the whole dataset, so we can make predictions.
The best fit line is widely used to do that. We can recognize the best fit line because it usually goes through the maximum number of points and the sum of the distances to each one of them is minimum.
From the three graphs given in the question, it's evident the first line is totally outside the set of points, so it does not do a good job representing the dataset.
The second graph approximates much better to a best-fit line but we can still see the trend of the line does not follow the trend of the dotted path.
Finally, the third graph looks very adequate to represent the scattered points because it keeps always close to them and follows their trend.
Select all the measures of variability or spreadA. meanB. IQRC. MADD. MedianE. Range
Answers
Solution
From then options given,
Mean and median are measures of central tendency.
Interquartile range (IQR), mean absolute deviation (MAD) and range are measures of variability or spread.
Hence, the answers are , MAD an and Range (B, C and E)
The approximate length of side XY is a: 3b: 3.16c: 4d: 4.24 units.
Answers
Solution
Given a triangle XYZ on the graph
The coordinates of points X, Y and Z are
[tex]\begin{gathered} X\Rightarrow(-3,-1) \\ Y\Rightarrow(-2,-4) \\ Z\Rightarrow(-6,-4) \end{gathered}[/tex]To find the approximate length of the sides, we apply the formula to find the distance, d, between two points which is
[tex]d=\sqrt{(x_2-x_2)^2+(y_2-y_1)^2}[/tex]To find the approximate length of side XY, substitute the coordinates of points X and Y into the formula to find the distance, d, between two points
[tex]\begin{gathered} XY=\sqrt{(-3-(-2))^2+(-4-(-1))^2} \\ XY=\sqrt{(-1)^2+(-3)^2} \\ XY=\sqrt{1+9}=\sqrt{10}=3.16\text{ units} \\ XY=3.16\text{ units} \end{gathered}[/tex]Hence, the approximate length of side XY is 3.16 units (option b)
the annual property tax on a house valued at $126,500 is 1007.32. what is the property tax per $100? (round 3 decimal places)
Answers
EXPLANATION
Let's consider the facts:
Property value= $126,500
Annual tax= $1007.32
Dividing the annual tax by the property value give us the unit value:
Annual tax/Property Value = 1007.32/126,500 = 0.00796300395
Multiplying this number by 100(the house-value factor) give us the desired number:
0.00796x100= $0.79tax/$100house
Rounding to three decimal places:
Answer= 0.796