Answer:
The mode is the number that occurred the most often. The range is the difference between the highest and lowest values.
Step-by-step explanation:
Answer:
Mode:The number whose repetaed the most is the set (there can be multiple)
Range: The largest number minus the smallest = The range
n the diagram below, points $A,$ $E,$ and $F$ lie on the same line. If $ABCDE$ is a regular pentagon, and $\angle EFD=90^\circ$, then how many degrees are in the measure of $\angle FDE$?
[asy]
size(5.5cm);
pair cis(real magni, real argu) { return (magni*cos(argu*pi/180),magni*sin(argu*pi/180)); }
pair a=cis(1,144); pair b=cis(1,72); pair c=cis(1,0); pair d=cis(1,288); pair e=cis(1,216);
pair f=e-(0,2*sin(pi/5)*sin(pi/10));
dot(a); dot(b); dot(c); dot(d); dot(e); dot(f);
label("$A$",a,WNW);
label("$B$",b,ENE);
label("$C$",c,E);
label("$D$",d,ESE);
label("$E$",e,W);
label("$F$",f,WSW);
draw(d--f--a--b--c--d--e);
draw(f+(0,0.1)--f+(0.1,0.1)--f+(0.1,0));
[/asy]
Answer:
18
Step-by-step explanation:
Each interior angle of a regular pentagon is 108 degrees. So Angle AED is 108 degrees. Since Angle AEF is a straight line (180 degrees), Angle FED is 72. This is because 180-108 = 72. Now, since a triangle has a total of 180 degrees, we add 72 and 90, because those are the 2 degrees we have calculated. This gives us a total of 162. Now, we subtract 162 from 180 to find out the degree of Angle FDE. This is 18. So our final answer is 18.
Sidenote: I hope this answer helps!
The properties of a pentagon and the given right triangle formed by
segments EF and FD give the measure of ∠FDE.
Response:
∠FDE = 18°Which properties of a pentagon can be used to find ∠FDE?The given parameters are;
A, E, F are points on the same line.
ABCDE is a regular pentagon
∠EFD = 90°
Required:
The measure of ∠FDE
Solution:
The points A and E are adjacent points in the pentagon, ABCDE
Therefore;
line AEF is an extension of line side AE to F
Which gives;
∠DEF is an exterior angle of the regular pentagon = [tex]\frac{360 ^{\circ}}{5}[/tex] = 72°∠EFD = 90°, therefore, ΔEFD is a right triangle, from which we have;
The sum of the acute angles of a right triangle = 90°
Therefore;
∠DEF + ∠FDE = 90°
Which gives;
72° + ∠FDE = 90°
∠FDE = 90° - 72° = 18°
∠FDE = 18°
Learn more about the properties of a pentagon here:
https://brainly.com/question/15392368
Help me please
I’m having so much trouble
Answer:
Step-by-step explanation:
5 * 45 = 225
225+75=300
300/500=0.6
The tank will be 60% full.
If this helped, make sure to mark it as brainliest :D
Answer:
C.60%
Step-by-step explanation:
45 x 5 = 225 225 + 75 = 300
300 / 500 = 0.6 = 60%
17. Mary bought 10 quarts of juice at the
grocery. How many gallons of juice did
she buy?
A 1.4 gal
C 3.5 gal
B 2.5 gal
D 4.5 gal
Pls help
Answer:
B 2.5 Gal
Step-by-step explanation:
Answer:
I think the correct answer may be B.
Step-by-step explanation:
2.) Evaluate 6a² if a = 4
Answer:
96
Step-by-step explanation:
We simply need to plug in a = 4 so 6a² = 6 * 4² = 6 * 16 = 96.
7 3/8 + (-4 1/2) ÷ (-5 2/3) Please Explain
Answer:
7 3/8 + (-4 1/2) ÷ (-5 2/3) = 8 23/136
Step-by-step explanation:
1) First I turned all the mix numbers into improper fractions:
7 3/8 ----> ( 7(8)+3/8) = 59/8, 4 1/2 ----> (4(2)+1/2) = 9/2, 5 2/3 ----> (5(3)+2/3) = 17/3
So now it should look like this: 59/8 + (-9/2)÷(-17/3)
2) Now our goal is to divide both of the improper fractions (-9/2)÷(-17/3),
- We first apply our fraction rule: -a/-b = a/b (when we have two negatives they cancel out each other and make a positive)
Our Case, From this:-9/2 ÷ -17/3 = To This: 9/2 ÷ 17/3
3) Now we can divide the fractions using this rule: a/b ÷ c/d = a times d / b times
Our Case, From This: 9/2 ÷ 17/3 To This: 9(3)/2(17) Which Gives Us: 27/34
(9 x 3 = 27, 2 x 17= 34)
So now it looks like this: 59/8 +27/34
4) Our look goal is to have the same denominator (which is the bottom part of the fraction) which are 8 and 34
To find it we find the LCM or Least Common Multiple of 8 and 34
(The LCM of a, b is the smallest positive number that is divisible by both a and b) which in this case a and b are 8 and 34
LCM is 136
5) We adjust our two fractions based on the LCM,
(Multiply each numerator ( top part of the fraction) by the same amount of needed to multiply its corresponding denominator to turn it to the LCM 136.
From This: 59/8 and 27/34 To This: 1003/136 and 108/36 ( 59(17)/8 (17) = 1003/136, 27(4)/34(4) = 108/306
6) Finally we can add the numerator (1003 and 108) together: 1003+108= 1111 and now we are left with 1111/136
Then we turn our improper fraction back into a mix number: 1111/138= 8 23/136
Answer:
[tex]\frac{1111}{136} = 8 \frac{23}{136}[/tex]
Step-by-step explanation:
We want to simplify:
[tex]7 \frac{3}{8} + \frac{ -4 \frac{1}{2} }{ -5 \frac{2}{3} }[/tex]
First, convert all the fractions to improper fractions:
[tex]\frac{59}{8} + \frac{ - \frac{9}{2} }{ - \frac{17}{3} } \\\\= \frac{59}{8} + \frac{27}{34}[/tex]
Find the LCM of the denominators:
[tex]\frac{(17 * 59) + (4 * 27)}{136} \\\\ = \frac{1003 + 108}{136}\\ \\= \frac{1111}{136} \\\\= 8 \frac{23}{136}[/tex]
Andrew's bicycle has tires with a radius of 7 inches. What is the area of one of the bicycle tires, in terms of π?
Answer:
49π
Step-by-step explanation:
The formula for the area of a circle is,
[tex]\pi r^2[/tex]
If the radius is 7 inches we need to plug that in for r in the formula.
π(7)^2
7*7 = 49
Thus,
the area in terms of pi is 49π.
Hope this helps :)
Answer:
49πStep-by-step explanation:
[tex]r = 7\\A = ?\\A =\pi r^2\\A =\pi7^2\\A = 49\pi[/tex]
Drag a statement or reason to each box to complete this proof.
If -5(x + 8) = -25, then x =
-3
The principal feature of the redesigned checks is a series of printed instructions that the company hopes will help merchants confirm a check’s authenticity, which includes reminders to watch the endorsement, compare signatures, and view the watermark while holding the check to the light.
(A) which includes reminders to watch the endorsement, compare signatures, and view
(B) which include reminders for watching the endorsement, to compare signatures and view
(C) by including reminders for watching the endorsement, comparing signatures, and viewing
(D) including reminders to watch the endorsement, comparing signatures and viewing
(E) including reminders to watch the endorsement, compare signatures, and view
Answer:
(E) including reminders to watch the endorsement, compare signatures, and view
Step-by-step explanation:
The principle features that will help the company to confirms checks authenticity. It include endorsements and compare the signatures with the designated signatories. If the signatures are matched correctly with the assigned signatories the check is hold in light to view the watermark on it.
Bob and Dan earned a total of $72
shoveling snow. If Bob earned 3 times as
much as Dan, how much did each boy
earn?
Answer:
see explanation
Step-by-step explanation:
If Dan earns $x then Bob earns $3x ( 3 times as much as Dan ), then
x + 3x = 72 , that is
4x = 72 ( divide both sides by 4 )
x = 18
Thus
Dan earns $18 and Bob earns 3 × $18 = $54
The earning of Bob will be 54 dollars and the earning of Dan will be 18 dollars.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Let the earning by Bob be x and the earning by Dan be y.
Bob and Dan earned a total of $72 shoveling snow. Then the equation will be
x + y = 72 ...1
If Bob earned 3 times as much as Dan. Then the equation will be
x = 3y ...2
Substitute the value of x in equation 1, then the equation will be
3y + y = 72
4y = 72
y = $18
Then the money earned by Bob will be
x = 3y
x = 3(18)
x = $54
Thus, the earning of Bob will be 54 dollars and the earning of Dan will be 18 dollars.
More about the linear system link is given below.
https://brainly.com/question/20379472
#SPJ2
What is the value of discontinuity of x^2+8x+4/x^2-x-6? Choices:
Answer:
-2
Step-by-step explanation:
Hello,
First of all, let's check the denominator.
[tex]x^2-x-6 \ \ \text{ *** How to factorise it ...? ***}\\\\\text{*** The product of the roots is -6=-2*3 and their sum is 1 ***}\\\\x^2-x-6=x^2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)[/tex]
Now, let's see the numerator.
[tex]x^2+8x+4 \ \text{ *** -2 is not a zero as ***}\\\\(-2)^2+8*(-2)+4=4-16+8=-4\\\\\text{*** 3 is not a zero as ***}\\\\3^2+8*3+4=9+24+4=37\\[/tex]
So we cannot factorise the numerator with (x+2) or (x-3)
Then, -2 and 3 are the the discontinuities of the expression.
There is only -2 in the list, this is the correct answer.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number. Which equations can be used to model the situation? Check all that apply. x = one-half y minus 3 2 x minus y = negative 6 2 x minus y = negative 3 x = one-half (y minus 3) y = 10 (x minus 1)
Answer: x=one-half y minus
Step-by-step explanation:
Answer:
x=1/2 y-3
Step-by-step explanation:
Drew likes to take the long way to school each morning. He walks 3 blocks west and then 3 blocks north to arrive at the school. Today he is running late and decides go directly to school to save time. (Assume there is nothing obstructing his path.) If one block is 310 feet, how many feet will he travel if he goes directly to school? Round to the nearest tenth of a foot.
Answer:
Distance travel by Drew = 1,315.21 feet (Approx)
Step-by-step explanation:
Given:
Total block in north = 3
Total block in west = 3
1 block = 310 feet
Find:
Distance travel by Drew
Computation:
Total distance in north = 3 × 310 = 930 feet
Total distance in west = 3 × 310 = 930 feet
Distance travel by Drew = √Total distance in north² + Total distance in west²
Distance travel by Drew = √930² + 930²
Distance travel by Drew = √864,900 + 864,900
Distance travel by Drew = √1,729,800
Distance travel by Drew = 1,315.21 feet (Approx)
A circle with center A and radius three inches is tangent at C to a circle with center B, as shown. If point B is on the small circle, what is the area of the shaded region? Express your answer in terms of \pi.
Answer:
27π Sq in.
Step-by-step explanation:
Circle A is equal to 9π sq inches. (Radius squared times Pi), Segment BC is a radii of Circle B and the diameter of Circle A. Meaning Circle B's radius is 6 inches. The area of circle B would be 36π sq inches. Now we subtract Circle A's area from Circle B's area(36π sq in. - 9π sq in.), the area of the shaded region is 27π sq in.
Write 4x2 + 16x - 9 in vertex form. Write 5x2 - 10x + 4 in vertex form.
Hi king,
Write [tex]4x^{2} + 16x - 9[/tex] in vertex form:
f(x)=[tex]4x^{2} + 16x - 9[/tex]
f(x)=[tex]4(x+2)^{2} -25[/tex]
Write [tex]5x^{2} - 10x + 4[/tex] in vertex form:
g(x)=[tex]5x^{2} - 10x + 4[/tex]
g(x)=[tex]5(x-1)^{2} -1[/tex]
Have a great day.
In a local ice sculpture contest, one group sculpted a block into a rectangular based pyramid. The dimensions of the base were 3 m by 5 m, and the pyramid was 3.6 m high. Calculate the amount of ice needed for this sculpture.
Answer:
18m square
Step-by-step explanation:
Formula for rectangular- based pyramid is L x W x H divided by 3
= 3 x 5 x 3.6 divided by 3 = 18
So you would need 18 m square for the sculpture
Find the volume in cubic meters, of the 3-Dimensional composite
figure.
8m
5m
Answer:
890 m^3 to the nearest whole number.
Step-by-step explanation:
Volume = volume of the cylinder + volume of the hemisphere:
= π r^2 h + 1/2 * 4/3 π r^3
= π*5^2 * 8 + 1/2 * 4/3 π 5^3
= 890.12
Two choises! Pick the right one!
Answer:
The function has a maximum value of 3 that occurs at x = 1.
Step-by-step explanation:
First, note that the leading coefficient is negative. This means that the parabola will curve downwards. Because of this, the function has a maximum. The maximum value will simply be the vertex.
The formula for the x-coordinate of the vertex is -b/2a.
a=-3, b=6, c=0
Plug in the numbers:
x=-(6)/2(-3)
=-6/-6=1
Now, plug 1 back into the original function:
-3x^2+6x
-3(1)^2+6(1)
=-3(1)+6
=-3+6
=3
What is the slope of the line shown below? (-2,3) (-4,-9)
Answer:
6Step-by-step explanation:
Let the points be A and B
A ( - 2 , 3 ) -------> ( x1 , x2 )
B ( -4 , -9 ) -------> ( x2 , y2 )
Now, finding the slope:
[tex]slope \: (m) = \frac{y2 - y1}{x2 - x1} [/tex]
Plug the values
[tex] = \frac{ - 9 - 3}{ - 4 - ( - 2)} [/tex]
Calculate
[tex] = \frac{ - 12}{ - 4 - ( - 2)} [/tex]
When there is a (-) in front of an expression in parentheses , change the sign of each term in expression
[tex] = \frac{ - 12}{ - 4 + 2} [/tex]
Calculate
[tex] = \frac{ - 12}{ - 2} [/tex]
Reduce the fraction with -2
[tex] = 6[/tex]
Hope this helps..
Best regards!!
My state's lottery has 30 white balls numbered from 1 through 30 and 20 red balls numbered from 1 through 20. In each lottery drawing, 3 of the white balls and 2 of the red balls are drawn. To win, you must match all 3 white balls and both red balls, without regard to the order in which they were drawn. How many possible different combinations may be drawn?
Answer:
I dont give you the answer right away so you will read what i write and fully understand :D
Step-by-step explanation:
We are picking 3 balls from 30 balls, so its C(30,3) because the order of picking the balls doesnt matter. We also need to pick 2 balls from 20 balls, which is C(20,2). So the answer is C(30,3) * C(20,2).
What is the value of x
Answer:
4
Step-by-step explanation:
For the first triangle which is triangle <KJL
Hypotenuse= 8✓2
Angle=30°
Opposite = ?
Therefore we will use Sine formula
Sin30° = Y/8✓2
Y=4✓2
For the second triangle which is triangle <JML
Hypotenuse= 4✓2
Opposite=X
Angle=45°
Therefore we will use Sine formula again
Sin45°=X/4✓2
X=4
Answer:
x = 4Step-by-step explanation:
ΔJKL is half of equilateral triangle and ΔJML is half of square.
We can use properties of these triangles (picture):
m∠KJL=90° and m∠JKL = 30° ⇒ JL = 0.5KL = 0.5•8√2 = 4√2
m∠JML=90° and m∠MJL = 45° ⇒ JL = ML√2
4√2 = x√2
x = 4
What is the approximate angle between two position vectors if their terminal points are (5, -2) and (7, 3)?
Hi,
Answer:
[tex]Angle=\frac{pi}{4}[/tex] = π/4 = 45°
Have a good day.
Find the center and radius of x^2 – 18x + y^2 -10y = -6. part two write x2 – 18x + y2 -10y = -6 in standard form
Answer:
see explanation
Step-by-step explanation:
I will begin with part two, first.
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius.
Given
x² - 18x + y² - 10y = - 6
Using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 9)x + 81 + y² + 2(- 5)y + 25 = - 6 + 81 + 25, that is
(x - 9)² + (y - 5)² = 100 ← in standard form
with centre = (9, 5 ) and r = [tex]\sqrt{100}[/tex] = 10
Natasha and her two dogs were walking on a perfectly straight road when her two dogs ran away from her in opposite directions. Her beagle is now \dfrac{25}{4} 4 25 start fraction, 25, divided by, 4, end fraction meters directly to her right, and her labrador is \dfrac{51}{20} 20 51 start fraction, 51, divided by, 20, end fraction meters directly to her left. Which of the following expressions represents how far apart the two dogs are?
Answer:
[tex]\dfrac{74}{20}=3.7 meters[/tex]
Step-by-step explanation:
Hello!
1) Since no other data has been given. Suppose Natasha is in the center and the beagle is to the right.
[tex]\dfrac{25}{4} \:meters[/tex]
2) The labrador is [tex]\dfrac{51}{20}\: to\: the\: left.[/tex]
[tex]\dfrac{25}{4} -\dfrac{51}{20} =\dfrac{(5*25)-51}{20} \\\dfrac{(125-51}{20} =\dfrac{74}{20}[/tex]
Answer:
The answer is B :D hope this helps
Step-by-step explanation:
Look at picture to see question
The number of people contacted at each level of a phone tree can be represented by f(x) = 3^x where x represents the level.
What is x when f(x) = 27?
A. X = 2; At level 2, 27 people will be contacted.
B. x = 24; At level 24, 27 people will be contacted.
C. x = 3; At level 3, 27 people will be contacted.
D. x = 9; At level 9,27 people will be contacted.
Answer:
3
Step-by-step explanation:
Answer:
c is the correct answer
Step-by-step explanation:
8 7 12 7 11
10 7 12
Find:
a)the median
b) the range
c)the mode
Answer:
a) Median: 9
b) Range: 5
c) Mode: 7
Step-by-step explanation:
The median is the number in the middle.
First, you put the numbers in order: 7, 7, 7, 8, 10, 11, 12, 12
The middle of this is 8 and 10, so you plus them and divide by to 2, then it gives 9, so the median is 9.
To find the range, you minus the highest number and the lowest number, 12-7=5.
Mode is the most occurring and repetitive number, in this case, 7, because it is written 3 times.
Hope this helps!!!
Answer:
[tex]\boxed{\mathrm {Median = 9}}[/tex]
[tex]\boxed{\mathrm{Range = 5}}[/tex]
[tex]\boxed{\mathrm{Mode = 7}}[/tex]
Step-by-step explanation:
The observations are:
8,7,12,7,11,10,7,12
In ascending order:
=> 7,7,7,8,10,11,12,12
A) Median => Middlemost no.
Median = 8,10
=> [tex]\frac{8+10}{2}[/tex]
=> [tex]\frac{18}{2}[/tex]
Median = 9
B) Range = Highest No. = Lowest No.
RANGE = 12-7
Range = 5
C) Mode => frequently occurring number
Mode = 7
Instructions: Find the missing side. Round your answer to the
nearest tenth
Answer:
x = 64Step-by-step explanation:
To find x we use tan
tan∅ = opposite / adjacent
From the question
The adjacent is x
The opposite is 30
So we have
tan 25° = 30/x
x tan 25 = 30
Divide both sides by tan 25
x = 30/tan 25
x = 64.34
x = 64 to the nearest tenth
Hope this helps you
What is 5,000 - 245( 30/2))?
Answer:
1,325
Step-by-step explanation:
30 /2
= 155,000 - 245(15)
= 5,000 - 3,675
= 1,325
Answer:
1,325
Step-by-step explanation:
How many real solutions In this problem
Answer:
D
Step-by-step explanation:
Given
y = x² + 1
y = x
Equating gives
x² + 1 = x ( subtract x from both sides )
x² - x + 1 = 0
Consider the discriminant Δ = b² - 4ac
with a = 1, b = - 1 and c = 1
b² - 4ac = (- 1)² - (4 × 1 × 1) = 1 - 4 = - 3
Since b² - 4ac < 0 then there are no real solutions
Which equation represents a line that is perpendicular to line FG? A. y=-1/2x+5 B. y=1/2x+2 C. y=-2x-3 D. y=2x-6
The equation of line which is perpendicular to the line FG is
y = -2x -3.
What is equation of line?
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.
Formula for finding the equation of line from two points [tex](x_{1} ,y_{1} ) and (x_{2}, y_{2} )[/tex][tex](y -y_{1}) = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } (x-x_{1} )[/tex]
What is the slope of two perpendicular lines?If [tex]m_{1}[/tex] be the slope of one line, then the slope of the perpendicular line is [tex]\frac{-1}{m_{1} }[/tex].
What is the slope intercept form of a line ?The slope intercept form of the line is given by y = mx + b
Where, m is the slope of a line.
According to the given question
We have a line FG and the coordinates of points F and G are (-5,1) and (9,8) respectively.
Therefore, the slope of the line FG = [tex]\frac{8-1}{9+5}=\frac{7}{14} =\frac{1}{2}[/tex]
⇒ The slope of the line which is parallel to line FG is -2
Now, from the given option of the equation of line , y = -2x -3 has a slope of -2 .
Hence, the equation of line which is perpendicular to the line FG is
y = -2x -3.
Learn more about the equation of a perpendicular line here:
https://brainly.com/question/20712656
#SPJ2