can you please help me
Answers
We have to calculate the area and perimeter of ABC.
Area:
We can calculate the area by substracting from the area of the big triangle ABD the area of the little triangle BCD. Both are right triangles.
The area of ABD is:
[tex]A_{\text{ABD}}=\frac{b\cdot h}{2}=\frac{(15+5)\cdot12}{2}=\frac{20\cdot12}{2}=\frac{240}{2}=120[/tex]The area of BCD is:
[tex]A_{\text{BCD}}=\frac{b\cdot h}{2}=\frac{5\cdot12}{2}=\frac{60}{2}=30[/tex]Then, the area of ABC is:
[tex]A_{\text{ABC}}=A_{\text{ABD}}-A_{\text{BCD}}=120-30=90[/tex]The area of ABC is 90 cm^2.
Perimeter:
We calculate the perimeter by adding the length of the three sides. We know only 2 of the sides, so we have to calculate the other one (BC).
The length of BC can be calculated using Pythagorean theorem for the triangle BCD, so we can write:
[tex]\begin{gathered} BC^2=CD^2+BD^2=5^2+12^2=25+144=169 \\ BC=\sqrt[]{169}=13 \end{gathered}[/tex]Now, we can calculate the perimeter as:
[tex]P_{\text{ABC}}=AB+BC+AC=25+13+15=53[/tex]The perimeter is 53 cm.
Related Questions
PLS HELP ASAP
!!!!!!
Answers
Orlando is getting balloons for his grandmother's birthday party. he wants each balloon string to be 6 feet long. at the party store, string is sold by the yard. if orlando wants to get 72 balloons, how many yards of string will he need?
Answers
144 yards of string will need to use balloons for the party.
Given,
The length of balloon string Orlando wanted = 6 feet
Number of balloons = 72
We have to find the total length of strings wanted for 72 balloons in yards.
1 yard = 3 feet
Now,
Total length of strings Orlando needs = length of one string x number of balloons = 6 x 72 = 432 feet
Now convert 432 feet into yard
That is,
432 / 3 = 144 yards
So,
144 yards of string will need to use balloons for the party.
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Find the possible outcomes for each event in rolling a number die. Then find the probability of each event as a fraction, decimal and percent.
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the formula for calculating probability
[tex]P(event)=\frac{number\text{ of favorable outcomes}}{number\text{ of possible outcomes}}[/tex]STEP 2: State the number of possible outcomes
[tex]\begin{gathered} A\text{ die has 6 faces numbered 1,2,3,4,5,6} \\ Therefore,\text{ the number of possible outcomes will be 6} \end{gathered}[/tex]STEP 3: Answer question A
Rolling a number less than 7
[tex]\begin{gathered} Numbers\text{ less than 7}\Rightarrow6,5,4,3,2,1 \\ n(numbers\text{ less than 7\rparen}\Rightarrow6 \\ \\ By\text{ substituting the values into the formula in step 1,} \\ P(Rolling\text{ a number less than 7\rparen}\Rightarrow\frac{6}{6}=1 \\ \\ Percentage\Rightarrow\frac{1}{1}\times100=100\% \end{gathered}[/tex]Hence,
Possible outcomes are 6,5,4,3,2,1
Probability = 1
Probability = 1.0 as decimal
Probability = 100% as percentage
STEP 4: Answer Question B
Rolling an 8
[tex]\begin{gathered} Possible\text{ outcomes}\Rightarrow8 \\ n(8)\Rightarrow0 \\ Probability=\frac{0}{8}=0 \\ Percentage=0\times100\%=0\% \end{gathered}[/tex]Hence,
Possible outcome is 0 since there is no face of the die having 8
Probability = 0
Probability = 0.0 as decimal
Probability = 0% as percentage
STEP 5: Answer Question C
Rolling a number greater than 4
[tex]\begin{gathered} Possible\text{ Outcomes}\Rightarrow5,6 \\ n(Possible\text{ outcomes\rparen}\Rightarrow2 \\ Probability=\frac{2}{6}=\frac{1}{3}\approx0.333 \\ Percentage=\frac{1}{3}\times100=\frac{100}{3}=33.33\% \end{gathered}[/tex]Hence,
Possible outcomes are 5,6
Probability = 1/3
Probability = 0.333 as decimal
Probability = 33.33% as percentage
STEP 6: Answer Question D
Rolling a number other than 6
[tex]\begin{gathered} Possible\text{ outcomes}\Rightarrow1,2,3,4,5 \\ n(Possible\text{ outcomes\rparen}\Rightarrow5 \\ Probability=\frac{5}{6}=0.8333 \\ Percentage=\frac{5}{6}\times100=83.33\% \end{gathered}[/tex]Hence,
Possible outcomes are 1,2,3,4,5
Probability = 5/6
Probability = 0.8333 as decimal
Probability = 83.33% as percentage
PLEASE HELP!!!!!
Which of the following equations represents the line that passes through the point (4, 3) and has a slope of 1/2?
A) 2x-3y=-18
B)2x-3y=17
C)3x-2y=-17
D)3x-2y-18
Answers
The equation of a line that passes through the point (4, 3) and has a slope of 1 / 2 is y = 1 / 2 x + 1.
How to find the equation of a line?The equation of a line that passes through a point can be describe as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line passes through (4, 3) and the slope is 1 / 2.
Hence, let's find the y-intercept using (4, 3)
y = 1 / 2 x + b
3 = 1 / 2 (4) + b
3 = 2 + b
b = 3 - 2
b = 1
Therefore, the equation of the line is y = 1 / 2 x + 1.
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can you help show me the steps to solve this?
Answers
Answer:69
Step-by-step explanation8966966969996^996969969969699696996996969699696969699696699696966969669669669669669669669669
what is 1/3 of 9 cookies and lollipops
Answers
∵ 1/3 of 9 means multiply it by 9
[tex]\begin{gathered} \because\frac{1}{3}\times9=\frac{1\times9}{3}=\frac{9}{3} \\ \therefore\frac{1}{3}\times9=3 \end{gathered}[/tex]3 is 1/3 of 9 cookies and lollipops
Answer:
1/3 of 9 is 3.
Step-by-step explanation:
Think of it like this: what number can be added to itself 3 times to get 9? The answer is 3! 3 + 3 + 3 = 9. So, 1/3 of nine is 3 because 9 split into 3 sections would be 1/3 + 1/3 + 1/3 = 1 and 3 + 3 + 3 = 9. So, 1/9 simplified is 1/3!
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Divide. Enter the correct answer.
17+2=
Answers
I need help understanding, how do I solve this?
3 – [–(–1)]
Answers
Answer:
3-[1]
3-1
2
Step-by-step explanation:
=//7777/))_+++++++4
2x + y = 2
Step 2 of 2: Determine the missing coordinate in the ordered pair (?, -3) so that it will satisfy the given equation.
Answers
Answer:
2.5
Step-by-step explanation:
Plug is -3 for y and solve for x
2x -3 = 2 Add 3 to both sides
2x = 5 Divide both sides by 2
x = [tex]\frac{5}{2}[/tex] o r 2[tex]\frac{1}2}[/tex] or 2.5
a jury pool has 22 men and 16 women, from which 12 jurors will be selected. assuming that each person is equally likely to be chosen and that the jury is selected at random, find the probability that the jury consists of
Answers
Determine the rate at which the sloth travels.
Justify your answer.
Distance (ft)
987654MN-
6.
3-
2
1
0
Speed of a Sloth
1 2
3 4
Time (min)
Answers
The rate at which the sloth travels as required in the task content is; -22ft/min.
Speed as a rate of distance with respect to time.It follows from the task content that the rate at which the sloth travels is to be determined.
Since the correct representation of the data is such that the distance and corresponding time pairs are as follows;
(98, 1) , (76, 2) , (54, 3), (32, 4).
Hence, the rate of distance change per time is the speed of the sloth and hence, the rate of distance change is;
Rate = ∆Distance/∆time.
Rate, R = (98 - 76)/(1 - 2)
Rate, R = 22/-1
R = -22 ft/min.
Ultimately, the rate at which the sloth travels is therefore; -22 ft/min.
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suppose that you need to build as many chairs as possible. each chair requires one seat, one back, and four legs. if you have 12 seats, 15 backs, and 44 legs, which of the chair components limits the number of chairs you can make? legs seats backs how many chairs can you make with the 12 seats, 15 backs, and 44 legs? what chair components will be leftover after making as many chairs as possible? seats and backs legs and backs seats and legs
Answers
The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.
What is meant by probability?The study of probabilities, which are determined by the ratio of favorable occurrences to probable cases, is known as probability.
The maximum number of chairs that can be made will be the minimum of the number of parts divided by the number of parts required for each chair, as calculated across the various types of parts required.
seats: 12 available, used 1 per chair: 12/1 = 12 chairs possible
backs: 15 available, used 1 per chair: 15/1 = 15 chairs possible
legs: 44 available, used 4 per chair: 44/4 = 11 chairs possible
The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.
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Here is a sketch of the unique triangles that can be
made with angle measures 80° and 20° and side
length 5.
PLEASE HELPPPP
ASAAAAPPPPP DUE AT END OF TODAY
Answers
Option (B) describes the correct unique possibilities of the given triangle.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. △ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane. A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same. Triangles can be divided into three types based on the lengths of their sides, and these are Scalene, Isosceles, and Equilateral.So, according to the given image:
We can easily observe that the triangle is an isosceles triangle with base angles being equal and the third angle being the smallest.Then, the correct option about the triangle will be an option (B).Therefore, option (B) describes the correct unique possibilities of the given triangle.
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Model car is a 1/40 scale model expressed as a ratio
Answers
Answer:1:40
Step-by-step explanation:
the answer should be 1:40
Find MN such that LN = 5.7.
Answers
Line LN is compounded by segments LM and MN. The lenght of segment LM is fixed (1.3), and we need to find how long should segment MN be so the whole segment LN has a length of 5.7.
The length of segment LN is the sum of lengths of segments LM and MN. Writing it as an equation:
[tex]LN=LM+MN[/tex]We an replace the values we know in the equation:
[tex]5.7=1.3+MN[/tex]Now, we just need to solve for MN:
[tex]\begin{gathered} MN=5.7-1.3 \\ \\ MN=4.4 \end{gathered}[/tex]Segment MN should have a length of 4.4 for the segment LN to be 5.7. Correct answer is option D.
-3a - 10 = 20
Solve the following equation
Answers
Answer:
a = -10
Step-by-step explanation:
-3a - 10 = 20
add 10 to both sides:
-3a - 10 + 10 = 20 + 10
-3a = 30
divide both sides by -3:
-3a/-3 = 30/-3
a = -10
Answer:
a=- 10
Step-by-step explanation:
-3a - 10 = 20
+10=+10
you end up with -3a=30
divide by -3 both side
a=-10
can you please answer work the math problem the easiest quick way please
Answers
Given: the three points are plotted on graph.
For the first point it is observed that,
For the x =3/2 the value is y=6/2
For second point ,
For x= 9/2 the y value is y=12/2
For the third point ,
For x= 15/2 the y value is y=18/2
According to obtained information it matched to option J)
Answer: Option J)
Paula measured the auditorium and made a scale drawing. The stage, which is 56 feet long in real life, is 84 inches long in the drawing. What scale did Paula use?
3 inches= ? feet
Answers
There are 2 feet in real life be 3 inches long in the scale drawing.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
The stage, which is 56 feet long in real life, is 84 inches long in the scale drawing.
Let the x feet in real life be 3 inches long in the drawing.
According to the given question, we can write a ratio as
56 feet : 84 inches = x feet : 3 inches
⇒ 56 / 84 = x / 3
Apply the cross-multiplication operation,
⇒ 56 × 3 = x × 84
⇒ 168 = 84x
⇒ 84x = 168
⇒ x = 168 / 84
⇒ x = 2
Therefore, there are 2 feet in real life be 3 inches long in the scale drawing.
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Write an inequality, in slope-intercept form, for the graph below. If necessary,use "<=" for sor">=" for >.5(-3,0)5(0, -3)
Answers
we need to find the line equation for the dashed line. Since we have 2 points of the line, its slope is
[tex]\begin{gathered} m=\frac{-3-0}{0-(-3)} \\ m=\frac{-3}{3} \\ m=-1 \end{gathered}[/tex]where we used the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then, our searched line has the form:
[tex]y=-x+b[/tex]where b is the y-intercept. We can finde b by substituting point (0,-3) into the last equation:
[tex]\begin{gathered} -3=-(0)+b \\ b=-3 \end{gathered}[/tex]then, the searched line in slope-intercept form is
[tex]y=-x-3[/tex]Therfore, the given area can be modeled as
[tex]y>-x-3[/tex]because when a line is dashed it doesn't belong to the given area.
professor horvat designs a study to assess the work satisfaction and home-life satisfaction of a group of graduate students. she administers the same measures of work and home-life satisfaction on two occasions, 1 year apart. she finds at both the first time point and the second time point there is a strong correlation between work satisfaction and home-life satisfaction. which type of correlations are these?
Answers
The type of correlation founded in the study by assessing the work and home life satisfaction measure identically at two occasions, a year apart, is a cross-sectional correlation.
Cross-sectional correlation is a non-experimental research design that uses data collected from a single time point. It is used to generate a static portrait of research variables. As opposed to serial correlation which is a correlation of one variable at different times, cross- sectional correlation is a correlation of two variables at the same time.
In the given study, professor measured the work satisfaction and home-life satisfaction at one time point and repeated it after a year at the second time point. She found a strong correlation between variable at both time points. Hence, it is cross-sectional correlation.
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what is the equation of the line perpendicular to y = 1/2x+1 that contains the point ( - 2 ,1)
Answers
The linear equation perpendicular to y = 1/2x+1 that contains the point ( - 2 ,1) is:
y = -2x - 3
How to get the equation of the perpendicular line?Let's say that:
y = m*x + b
Where m is the slope and b is the y-intercept.
Is the line we want to find.
Two lines are perpendicular if the product between the slopes is -1, so this line is perpendicular to:
y = (1/2)*x + 1
Only if:
m*(1/2) = -1
m = -1*2 = -2
So the linear equation is of the form:
y = -2*x + b
If this line passes through (-2, 1), then:
1 = -2*(-2) + b
1 = 4 + b
1 - 4 = b
-3 =b
The linear equation is y = -2x - 3
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Need help solving this problemNote for part A I got 4/22 and it was incorrect
Answers
First, we need to find the total frequency. This is given by adding all the given frequencies. That is,
[tex]\begin{gathered} f_{\text{total}}=4+6+7+5 \\ f_{\text{total}}=22 \end{gathered}[/tex]and the relative frequency is the division of the frequency of the corresponding interval by the total frequency,
[tex]f_{\text{rel}}=\frac{f_{\text{ interval}}}{f_{total}}[/tex]Therefore, the answers are:
a) 4/22 but written in simple form:
[tex]\frac{2}{11}[/tex]b)
[tex]\frac{5}{22}[/tex]
What are the coordinates of the midpoint of segment whose endpoints are A(-2,7) and B(4,-2)?
Answers
A tennis racket sells for $54.At the spring clearanceevent, the price is 30% lessthan the original. What isthe sale price?
Answers
We have
tennis racket price $54
Firs we need to obtain the 30 %
54*.30=16.2
then in order to know the sale price we need to substract the 30% of the original price
54-16.2=37.8
the sale price is $37.8
Graph, on a separate piece of paper, the equation of a line with a slope of −3 and a y-intercept of 2.
Select the points that appear on the graph.
Multiple select question.
cross out
A)
(0, 0)
cross out
B)
(0, 2)
cross out
C)
(1, 1)
cross out
D)
(1, −1)
cross out
E)
(2, 0)
Answers
Based on the slope of the line and the y-intercept, when graphed, the points that will appear on the graph will be:
B. (0, 2) D. (1, -1)How to graph the line?The equation of a line takes the form:
y = mx + b
m = slope
b = y - intercept
This line would therefore take the equation form:
y = - 3x + 2
When graphed, the graph would be as attached.
As shown by the graph, the points that will appear include:
(0 , 2) (1 , - 1)
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PLEASE HELP ME. SERIOUSLY. I HAVE 30 MINUTES LEFT.
Let D be the dilation with center O and scale factor r>0 so that Dilation (P) = P' and
Dilation (Q) = Q'.
233.8
If |OQ|= 10 units, 10Q'] = 15 units, and IP'Q'] = 11.2 units, determine |PQ|. Round your
answer to the tenths place, if necessary.
incase you cant see, he right side is P, and below it is P1
Answers
Dilation factor is 3/2.
Define dilation factor.Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. According to Math Bits Notebook, the scale factor is equal to the ratio of these distances.
Given,
OQ = 10
OQ' = 15
Let dilation factor be r
OQ ×r = OQ'
10× r = 15
r = 3/2
Dilation factor is 3/2.
Coordinates of P = (-4, -3)
Coordinates of P' = (-6, -4.5)
b) ΔOPQ ≅ ΔOP'Q'
Congruent,
[tex]\frac{OQ}{OQ'}[/tex] = [tex]\frac{PQ}{P'Q'}[/tex]
[tex]\frac{10}{15}[/tex] = [tex]\frac{PQ}{11.2}[/tex]
PQ = 7.46
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Rectangles DEFG with vertices D(1,0) E(7,2) F(8, -1) and G (2, -3)
A. Translations along the the rule (x, y) —> (x -8 y -3)
Answers
Part A
[tex]D(1,0) \longrightarrow D'(1-8, 0-3)=D'(-7, -3)\\\\E(7,2) \longrightarrow E'(7-8, 2-3)=E'(-1, -1)\\\\F(8,-1) \longrightarrow F'(8-8, -1-3)=F'(0, -4)\\\\G(2,-3) \longrightarrow G'(2-8, -3-3)=G'(-6, -6)[/tex]
Part B
Reflecting over the x axis means [tex](x, y) \longrightarrow (x, -y)[/tex].
[tex]D'(-7, -3) \longrightarrow D''(-7, 3)\\\\E'(-1, -1) \longrightarrow E''(-1, 1)\\\\F'(0, -4) \longrightarrow F''(0, 4)\\\\G'(-6, -6) \longrightarrow G''(-6, 6)[/tex]
the d score is a standardized measure of the degree to which the independent variable caused a change in the dependent variable. this is also known as the
Answers
The standardized measure of the degree to which the independent variable caused a change in the dependent variable is a standard change.
What is a dependent variable?A dependent variable is what is determined in an experiment or test and is the one that is influenced throughout the experiment. The dependent variable is affected by the independent variable.
In mathematical modeling, statistical modeling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are explored in an experiment under the assumption or requirement that they are dependent, by some law or rule, on the values of other variables.
In conclusion, the standard change illustrates the change.
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find the value of x in each case
Answers
Answer:
x=23
Step-by-step explanation:
The amount of degrees in a triangle is 180 degrees.
line AC and line DF are straight angles meaning that the opposite angles are equal to each other. That means that angle FBC is also equal to x. Because line AC and EF are parallel we know that FBC and BFE are equal. Therefore, BFE is equal to x. The sum of the values of each angle of the triangle should add up to 180. 5x+65=180
5x=115
x=23
Simplify 6 + 2(5 – 8)2 + 7
Answers
The answer is very simple. .
6 + 2 (5 - 8 ) ² + 7
Firstly we solve what is inside the parenthesis
[tex]6\text{ + 2}\cdot(-3)^2\text{ + 7}[/tex][tex]6\text{ + 2 (9) +7}[/tex]Then we solve the multiplications
[tex]6\text{ + 18 + 7 }[/tex]Finally we solve the sums.
[tex]\text{ 6 +18 + 7 = }31[/tex]That is the solution.