Find the area of triangle DFG.
A. 5.3 square units
B. 34.3 square units
C. 420.0 square units
D. 424.2 square units
Answers
Answer:
34.3 square unit.
Step-by-step explanation:
[tex]calculate \: df \: using \: pythagoras \\ theorem \\ df {}^{2} = 8 {}^{2} + 6 {}^{2} \\ df {}^{2} = 64 + 36 \\ df {}^{2} = 100 \\ df = \sqrt{100} \\ df = 10 \\ calculating \: for \: the \: area \: of \: \\ angle \: \: dfg \\ using \: heros \: formular \\ \\ area = \sqrt{s(s - a)(s - b)(s - c)} \\ s = \frac{a + b + c}{2} \\ s = \frac{10 + 11 + 7}{2} = \frac{28}{2} = 14 \\ area = \sqrt{14(14 - 10)(14 - 11)14(14 - 7)} \\ area = \sqrt{14(4)(3)(7)} = \sqrt{14 \times 84} \\ area = \sqrt{1176} = 34.2928564 \\ to \: the \: nearest \: tenth \: = 34.3[/tex]
Here it is stated that, side DE = 8 units, side EF = 6 units, side FG = 7 units and side GD = 11 units. We have to find area of ∆DFG, here we will use heron's formula which is given by:
Area of ∆ = √[s(s – a) (s – b) (s – c)]
Here a, b, and c are sides of ∆. We have;
b = FG = 7 unitsc = GD = 11 unitsa = DF = ?s = semi - perimeter = ?So firstly lets calculate a i.e DF by using Pythagoras theorem on ∆DEF:
➸ DF² = 8² + 6²
➸ DF² = (8 × 8) + (6 × 6)
➸ DF² = 64 + 36
➸ DF² = 100
➸ DF = √(100)
➸ DF = √(10 × 10)
➸ DF = 10 units
Now, lets calculate s i.e semi - perimeter:
s = (a + b + c)/2s = (10 + 7 + 11)/2s = 28/2s = 14 unitsNow, using heron's formula on ∆DFG to calculate its area:
➸ Area(∆DFG) = √[14(14 – 10) (14 – 7) (14 – 11)]
➸ Area(∆DFG) = √[14(4) (7) (3)
➸ Area(∆DFG) = √(14 × 4 × 7 × 3)
We can write it as;
➸ Area(∆DFG) = √(2 × 2 × 2 × 7 × 7 × 3)
➸ Area(∆DFG) = 2 × 7√(2 × 3)
➸ Area(∆DFG) = 14√(6)
➸ Area(∆DFG) = 14 × 2.449
➸ Area(∆DFG) = 34.28
➸ Area(∆DFG) = 34.3 square units (approx)
Hence, area of ∆DFG is option B. 34.3 square units.Related Questions
Can I take a picture of the problem and upload for you to see?
Answers
Based on a poll conducted by the Centers for Disease Control, 862 of 1013 randomly selected adults said that they always wear seat belts. Construct and interpret a 95% confidence interval for the proportion of adults who always wear seat belts.
Answers
The confidence interval is 0.028, 0.872
Given862 of 1013 randomly selected adults wear seat belts.
The 95% confidence interval for the proportion of adults who always wear seat belts.
What is confidence interval?A Confidence Interval is defined as a range of values we are sure our true value lies within it.
What is 95% confidence interval?A 95% confidence interval is defined as that if we take 100 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value.
= 862/1013 = 0.85
At a 95% confidence interval ,the critical value is [tex]z_{0.025} = 1.96[/tex]
The 95% confidence interval for proportion is
[tex]\widehat p +/- z0.025 * sqrt(\widehat p * (1 - \widehat p)/n)[/tex]
[tex]= 0.85 +/- 1.96 * sqrt(0.85 * (1 - 0.85)/1013)[/tex]
[tex]= 0.85 +/- 0.022[/tex]
= 0.028, 0.872
The sample should use at least 10 successes and 10 failures.
[tex]n * \widehat p = 1013 * 0.85 = 861 > 10[/tex]
[tex]n * (1 - \widehat p) = 1013 * 0.15 = 152 > 10[/tex]
As the sample size is larger, we can use an approximate formula for the standard error.
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Does this graph represent a function? why or why not ?
Answers
Answer:
C- Yes, because it pases the vertical line test.
Step-by-step explanation:
It passes through one point exactly.
The length of a rectangle is 3 yd longer than its width. if the perimeter of the rectangle is 58 yd, find its length and width.
Answers
Answer:
Length = 16 yds
Width = 13 yds
Step-by-step explanation:
P = 2w + 2l
l = w + 3
58 = (2w + 2(w + 3))
58 = 4w + 6
52 = 4w
w = 13
L = w + 3
= 13 + 3
= 16
The length and width of the rectangle are 16,13yd.
The Length and Width of the rectangle can be found as:
Given:The length of the rectangle is 3yds longer than the width which means length = w+3
and the perimeter is given by 58yd
Let W be the width and L be the length
We know that the perimeter of a rectangle is 2(L+w)
The perimeter of a rectangle is defined as the sum of all the sides of a rectangle
By simplifying we get2(w+w+3)=58
2(2w+3)=58
2w=29-3
w=13
then the length of the rectangle will be w+3
13+3 = 16
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white shapes and black shapes are used in a game. some shapes are circles. all the other shapes are squares. the ratio of white shapes to the number of black shapes is 7:3 the ratio of white circles to white squares is 2:7 the ratio of black circles to the number of black squares is 1:2 work out what fraction fo all shapes are circles give your answer as a fraction in its simplest form
Answers
[tex]\mathbf{\frac{23}{90}}[/tex] fraction of all shapes are circles.
Given that the ratio of the number of white shapes to black shapes is 7:3
Let the number of white shapes be [tex]7n[/tex]
Then the number of black shapes be [tex]3n[/tex]
So total number of shapes [tex]=7n+3n=10n[/tex]
Now ratio of white circles to white squares is 2:7
So the fraction of circles to all white shapes [tex]=\frac{2}{2+7}=\frac{2}{9}[/tex]
Hence the number of white circles [tex]=\frac{2}{9}\times7n=\frac{14n}{9}[/tex]
Again given that the ratio of black circles to the number of black sqaures is 1:2
So the fraction of circles in all black shapes [tex]=\frac{1}{1+2}=\frac{1}{3}[/tex]
The number of black circles [tex]=\frac{1}{3}\times3n=n[/tex]
Total number of circles [tex]=\frac{14n}{9}+n=\frac{14n+9n}{9}=\frac{23n}{9}[/tex]
The fraction of all shapes are circle is [tex]=\frac{\frac{23n}{9}}{10n}=\frac{23n}{90n}=\frac{23}{90}[/tex]
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Class A has 10 pupils and class B has 18 pupils. Both classes sit the same maths test. The mean score for class A is 34. The mean score for both classes is 55. What is the mean score (rounded to 2 DP) in the maths test for class B?
Answers
Answer:
Mean score for the class B is 66.66
Step-by-step explanation:
Mean : It is the sum (total) of all the values in a set of data, such as numbers or measurements, divided by the number of values on the list.
Mean = sum of all numbers/ total numbers
Given,
mean score of class A = 34.
mean score of both the classes = 55
mean score of class a = sum of marks/total strength of class
34 = sum of marks/10
340 = sum of marks of class A
similarly, Mean score of both classes
= ( sum of marks of class A and class B)/(total students in both classes)
= (340 + sum of marks of class B)/ 28
55 = (340 + sum of marks of class B)/ 28
55 × 28 = (340 + sum of marks of class B)
1540 - 340 = sum of marks of students of class B
1200 = sum of marks of students of class B
now to find Mean score of class B
sum of marks of students of class B / total students in class B
1200/18 = 66.66 answer
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Im bad at composite figures || please hurry
Answers
The figure is the combination of trapezoid and square. Then the area of the figure will be 39 square meters.
The complete question is attached below.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The figure is the combination of trapezoid and square.
Then the area of the geometry will be
Area = Area of trapezoid + Area of square
Area = 1/2 x (3 + 9) x 5 + 3 x 3
Area = 30 + 9
Area = 39 square meters
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Please Simplify 3√7 / 5√7
Answers
Step-by-step explanation:
please mark me as brainlest
Step-by-Step Explanation:
= 3√7/5√7
= (7)^1/3 / (7)^1/5
= 7^(1/3 - 1/5)
=> 7^2/15
What reason allows the following statement to be true?
Given Ð1 & Ð2 are a linear pair, then mÐ1 + mÐ2 = 180
Answers
Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
When two lines cross at a single point, a linear pair of angles is generated. If the angles are next to each other after the two lines intersect, they are considered to be linear pairs. The total of the angles of a linear pair is always 180°. These angles are also referred to as supplementary angles.
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Shape R is reflected in
a) What are the coordinates of C'?
Then R' is translated by (-3)
-6
R
=
-5 -4 -3 -2 -1
b) What are the coordinates of C"?
Y
5+
4-
3-
2+
1
- 1 to give R'.
-1-
-2-
--3-
-4-
--5+
1
to give R".
2
3 4
sit
5
X
Answers
The new coordinates of C is (-5,2), (-5,5) (-7,3) (-7,5)
The correct question is
Shape R is reflected in x axis and is translated by (-3, 0) , What will be the coordinates of the new figure
The figure is attached with the answer.
What happens when a figure is reflected on an axis ?When a figure is reflected along any axis , the coordinate of the axis on which it is reflected remains the same while the other coordinate vis the additive inverse of the given coordinate
It is given that the coordinate point of R
(-2 ,-2) , (-2,-5) (-4,-3) (-4,-5)
When it is reflected along x axis the new coordinates are
(-2 , 2), (-2,5) (-4,3) (-4,5)
and when translated by -3,0
(-5,2), (-5,5) (-7,3) (-7,5)
Therefore the new coordinates of C is (-5,2), (-5,5) (-7,3) (-7,5)
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2
3
4
5
Which distance measures 7 units?
L
M
N
-8-7-6-5-4-3-2-1012
3
the distance between points L and M
the distance between points L and N
the distance between points M and N
the distance between points M and P
5 6 7 8
TIME REMAINING
56:41
Answers
Answer:
the distance between points M and P
Step-by-step explanation:
i did it
If tan 0 = 4/3 and 0 lies in the third quadrant, which is the correct ratio for cos 0?
4/5
-3/5
-4/5
3/5
Answers
[tex] \frac{ - 3}{5} \\ [/tex]
because , in the third quadrant , the value of cos is negative. Moreover , we can find the third side of the triangle using Pythagoras theorem.
then ,
[tex] \cos(\theta) = \frac{base}{hypotenuse} \\ \\ \dashrightarrow \: \cos(\theta) = \frac{ - 3}{5} [/tex]
hope helpful.
The answer is cos 0 = -3/5
To calculate the answer:Given :
tan 0 = 4/3 and is in the 3rd quadrant
this implies that both the perpendicular and base are negative.
Perpendicular = -4
Base = -3
Hypotenuse = [tex]\sqrt{(perpendicular)^{2} + (base)^{2} }[/tex]
Hypotenuse = [tex]\sqrt{(-4)^{2} + (-3)^{2} }[/tex]
Hypotenuse = [tex]\sqrt{25} = 5[/tex]
cos 0 = [tex]\frac{Base}{Hypotenuse}[/tex]
cos 0 = -3/5
Therefore, cos 0 = -3/5
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ABD and DBC are complementary angles 43 what is the measure of x
Answers
The value of x is 60
How to determine the value of x?The complete question is added as an image
From the image, we have:
ABD = 30
DBC = x
The sum of complementary angles is 90.
So, we have:
30 + x = 90
Subtract 30 from both sides
x = 60
Hence, the value of x is 60
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Is there an end to prime numbers?
Answers
[tex]\huge\purple{Hi!}[/tex]
Except for 2 and 5, all prime numbers end in the digit 1, 3, 7 or 9.
Electricity bills: According to a government energy agency, the mean monthly household electricity bill in the United States in was . Assume the amounts are normally distributed with standard deviation . Use the TI-84 Plus calculator to answer the following. (a) Find the th percentile of the bill amounts. (b) Find the rd percentile of the bill amounts. (c) Find the median of the bill amounts. Round the answers to at least two decimal places
Answers
The 9th percentile of the bill amounts is 81.0634.
How to calculate the percentile?
Population mean, µ = 110.56
Population standard deviation, σ = 22
a) p = 0.09
Z score at p = 0.09 using excel = NORM.S.INV(0.09) = -1.3408
Value of X = µ + z*σ = 110.56 + (-1.3408)*22 = 81.0634
9th percentile = 81.0634
b) p = 0.66
Z score at p = 0.66 using excel = NORM.S.INV(0.66) = 0.4125
Value of X = µ + z*σ = 110.56 + (0.4125)*22 = 119.6342
66th percentile = 119.6342
c) Median = 0.50
Z score at p = 0.5 using excel = NORM.S.INV(0.5) = 0
Value of X = µ + z*σ = 110.56 + (0)*22 = 110.56
Median = 110.56
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A certain species of virulent bacteria is being grown in a culture. It is observed that the rate of growth of the bacterial population is proportional to the number present. If there were 1000 bacteria in the initial polulation and the number doubled after the first 30 minutes, how many bacteria will be present after 4 hours
Answers
Answer:
256,000
Step-by-step explanation:
If the culture doubles in size every 30 minutes, it doubles 2 times per hour. In 4 hours it will have doubled 2×4 = 8 times. Each doubling multiplies the number by 2, so 8 doublings will multiply the number by 2^8.
The population will be ...
1000×2^8 = 256,000 . . . bacteria present after 4 hours
tGive the values of a, b, and c from the standard form of the equation (2x + 1)(x - 2) = 0.
Answers
Answer:
a = 2
b = -3
c = -2
Step-by-step explanation:
The standard form of a quadratic equation:
ax² + bx + c = 0
…………………………
in order to determine the equation
in standard form ,we have to expand the given expression :
(2x + 1)(x - 2) = 2x² - 4x + x - 2
= 2x² - (4x - x) - 2
= 2x² - 3x - 2
Then the standard form is :
2x² - 3x - 2
Here's a graph of a linear function. Write the
equation that describes that function.
bad
Express it in slope-intercept form.
Answers
The equation of the line in slope-intercept form is y = (1/2)x + 3 and the slope is 1/2.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]
As we can see in the graph the line goes from (-6, 0) and (0, 3)
Finding the slope:
[tex]\rm m =\dfrac{3-0}{0-(-6)}\\[/tex]
m = 3/6 = 1/2
y = mx + c
y = (1/2)x + c
c is the y-intercept
c = 3
The equation:
y = (1/2)x + 3
Thus, the equation of the line in slope-intercept form is y = (1/2)x + 3 and the slope is 1/2.
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For which graph is the parent function y=x^2
On a coordinate plane, a parabola opens up and has a vertex at (negative 1, negative 2).
On a coordinate plane, a straight line has a positive slope.
On a coordinate plane, a cubic root function is shown.
On a coordinate plane, an absolute value function is shown.
Answers
y = x² is the parent function of a parabola opens up and has a vertex at (negative 1, negative 2)
What is the standard equation of a parabola ?The standard equation of a parabola is given by
y =a(x-h)² +k
Vertex at h , k
It is given that It has to be chosen from the options that whose parent function is
y = x²
As the plot of the first option is done , which is shown in the figure ,
The parabola is given by
y = (x +1)² +2
and the parent function is y = x²
Therefore the Option 1 is the answer.
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If the divisor is a decimal then you must multiply by a power of 10 to make it a whole number. Why is it important to multiply the dividend and the divisor by the same power of 10?
Answers
It is important to multiply the dividend and the divisor by the same power of 10 to remove the decimal point.
Division of whole numbers
When the numerator and denominator of improper fractions are in whole number form, it makes the division a lot easier.
For example;
what is the simplest form of 0.1/0.2?
To obtain the simplest form of the above function, we multiple the numerator and denominator by 10.
= (0.1 x 10)/(10 x 0.2)
= 1/2
Note: introducing factor of 10 to both numerator and denominator has not changed the function.
Thus, it is important to multiply the dividend and the divisor by the same power of 10 to remove the decimal point.
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Select the correct answer from each drop-down menu. one person working alone will take 30 days to paint an apartment. if d represents the number of days taken to complete the work and p represents the number of people working, the equation that represents this situation is . if 10 people work on this job, they take days to complete it.
Answers
It took 3 days to complete a work by 10 people.
What is Efficiency?
The efficiency is the output of the work which we divide by the work input and then express it in a percentage form.
Here, Efficiency of 1 person to complete a piece of work in 30 days is 1/30.
The number of days to complete the work = n days
Number of person to complete the work = p.
Now, according to question
Number of days to complete the work by 10 people = 30 / 10
= 3 days.
Thus, it took 3 days to complete a work by 10 people.
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Which of the following values can be found by using the formula √1+cos^2 0?
Answers
Let's check
Remove root over and simplify 1+cot²Ø
1+cos²theta/sin²thetasin²Ø+cos²Ø/sin²Ø1/sin²Øcosec²ØPutting root over
cscØSin can be found also along with csc
write 5 rational numbers between 1 and 2
Answers
Answer:
1.1, 1.2, 1.3, 1.4, 1.5 or 11/10, 12/10, 13/10, 14/10, 15/10
Explanation:
Rational numbers can be expressed as fractions (p/q), decimals, whole numbers, natural numbers, integers.
Some rational numbers between 1 and 2 are: -
1.05, 1.1, 1.15, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.95, 1.97
Five rational numbers are
1.5=15/101.05=105/1001.007=10007/10001.3=13/101.03=103/100Bailey and julie go running during their lunch break. bailey ran x miles while julie ran 3x miles. what information can we gather about the relationship between the number of miles bailey and julie ran?
Answers
The information we can see from the given data is that the speed of Julie is three times the speed of Bailey.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
Given that:-
Bailey and Julie go running during their lunch break. bailey ran x miles while Julie ran 3x miles.The speed of Bailey = x miles
The speed of the Julie = 3x miles
The ratio of the speeds will be given as:-
J / B = 3x / x
J / B = 3
J = 3 B
Therefore information we can see from the given data is that the speed of Julie is three times the speed of Bailey.
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What is the length of a 90 degree arc of a circle with the radius of 11 cm
Answers
Step-by-Step Explanation:
Angle (θ) = 90 degree
Radius (r) = 11 cm
Length of Arc = θ/360 * 2πr
Therefore,
= θ/360 * 2πr
= 90/360 * 2 * 22/7 * 11
= 1/4 * 2 * 22/7 * 11
= 1/2 * 22/7 * 11
= 11/7 * 11
= 121/7
=> 17.28
Length of Arc = 17.28 cm
What is the range of the translated function? {y|y < 0} {y|y ≥ 0} {y|y is a natural number} {y|y is a real number}
Answers
The Range of the function is {y|y is a real number} , Option D is the correct answer
What is Range ?Range of a function is all the value a function can obtain.
From the figure it can be seen that the graph is moving slowly in either direction.
It extends from -∞ to +∞ ,
Therefore , {y|y is a real number} , Option D is the correct answer.
The complete question is
The graph shows a vertical translation of y = ³√x
What is the range of the translated function?
{y|y < 0}
{y|y ≥ 0}
{y|y is a natural number}
{y|y is a real number}
The image of the translated function is attached.
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HELP !
Which of the following best describes the slope of the line below?
• A. Negative
O B. Zero
• C. Positive
D. Undefined
Answers
1. A bus traveled for 4 hours and 30 minutes to travel 183 miles. What was it's average speed?
A. 42.56 mph
B. 40.67 mph
C. 32.09 mph
D. 30.67 mph
Answers
Answer:
B or 40.67mph
Step-by-step explanation:
To solve we will use formula distance over total time, so are distance is 183miles and are time is 4 hours and 30 minutes. If we put that in hours we get 4.5 hours. Now we simply divide 183/4.5 to get about 40.67 .
Which of the following is not a good conductor of heat?
Answers
What are the minor arcs of O?
Answers
Answer:
3rd answer
Step-by-step explanation:
Pay attention to the arcs, minor arcs are less than 180 degrees
