well, this is an OCTAgon, OCTA = 8.
[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\ \cline{1-1} a=30\\ p=\stackrel{8\times 12}{96} \end{cases}\implies A=\cfrac{1}{2}(30)(96)\implies A=1440[/tex]
Jessica is 5 years older than her sister Jenna. Jenna tells her sister that in 5 years, she will be as old as Jessica was 5 years ago.
If Jenna’s age is x, which equation represents the situation? How many solutions does the equation have? (Only 1 choice of answer)
A.
x + 5 = (5 − x) − 5, which has one solution
B.
x + 5 = (x + 5) − 5, which has infinitely many solutions
C.
x + 5 = (x + 5) − 5, which has no solution
D.
x + 5 = (5 − x) − 5, which has infinitely many solutions
E.
(x + 5) + 5 = (x + 5) + 5, which has infinitely many solutions
Answer:
x + 5 = (x + 5) - 5, which has no solution ⇒ answer C
Step-by-step explanation:
* Lets study the situation in the problem
- Jessica is 5 years older than her sister Jenna
- After five years Jenna's age will be as old as Jessica was five years ago
- Jenna's age now is x
* Lets change all information above to equation
∵ Janna's age now is x
∵ Jessica is 5 years old than Janna
∴ The age of Jessica now is x + 5
- After 5 years Janna's age will be add by 5 years
∵ Her age now is x
∴ Her age after 5 years will be x + 5
- From 5 years ago Jessica's age was her age now mins 5 years
∵ Her age now is x + 5
∴ Her age from 5 years ago is (x + 5) - 5
∵ Janna's age after 5 years = Jessica age from 5 years ago
∴ x + 5 = (x + 5) - 5
- Lets solve the equation to know how many solution
∵ x + 5 = x + 5 - 5 ⇒ add the like terms
∴ x + 5 = x ⇒ subtract x from both sides
∴ 5 = 0
- But 5 ≠ 0, the two sides of the equation not equal each other
∴ There is no solution for this equation
* The equation is x + 5 = (x + 5) - 5, which has no solution
Answer:
C x + 5 =(5 - x) - 5
Step-by-step explanation:
If f(x) = -4x+3 and g(x) = 3x^2+2x-4 find (f+g)(x).
Answer:
(f+g)(x)= 3x^2 -2x-1
Step-by-step explanation:
f(x) = -4x+3
g(x) = 3x^2+2x-4
(f+g)(x)= -4x+3 +3x^2+2x-4
Combine like terms
(f+g)(x)= 3x^2 -2x-1
the slope pf a line is -8/7. Write a point slope equation of the line useing the coordinates of the labeled point (4,4)
Answer:
[tex]\large\boxed{y-4=-\dfrac{8}{7}(x-4)}[/tex]
Step-by-step explanation:
The point-slope equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have the slope m = -8/7, and the point (4, 4). Substitute:
[tex]y-4=-\dfrac{8}{7}(x-4)[/tex]
What is the midpoint of the segment below?
(2, 3)
(-3.-2)
The formula for finding the midpoint of a line segment is[tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]. Plug in and solve:
[tex](\frac{2-3}{2} , \frac{3-2}{2})[/tex]
(-1/2, 1/2)
(-0.5, 0.5)
Hope this helps!!
The midpoint of the segment is (-0.5, 0.5)
What is midpoint of the segment?The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.
Given points: (2, 3) and (-3.-2).
The formula for midpoint is
(x1+x2/2, y1+y2/2)
= (2-3/2, 3-2/2)
=(-1/2, 1/2)
= (-0.5, 0.5)
Hence, the midpoints of the segment is (-0.5, 0.5).
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Matti built a greenhouse in his backyard as shown below
well, Matti's house is a triangular prism, and to get the volume of it, we simply get the area of the triangle upfront and multiply by its length of 15.
[tex]\bf \stackrel{\stackrel{\textit{area of }}{\textit{triangular front}}}{\cfrac{1}{2}(7)(7)}\times \stackrel{\textit{length}}{15}\implies \cfrac{49}{2}\cdot 15\implies 367.5~ft^3[/tex]
Answer:
Option B.
Step-by-step explanation:
Volume of a green house in the backyard which in the shape of triangular prism V = (Area of base)×(Height)
In the figure attached,
Height of the triangular base = 7 ft
Base = 7 ft
Area of the triangle = [tex]\frac{1}{2}(7)(7)[/tex]
Area = [tex]\frac{49}{2}=24.5[/tex] ft²
Therefore, volume of the prism = 24.5 × 15
= 367.5 ft²
Option B. is the correct option.
What type of triangle has side lengths 2, √12, and √19?
Answer:
Is an scalene obtuse triangle
Step-by-step explanation:
step 1
Find the type of triangle by the measure of the interior angles
we know that
If applying the Pythagoras Theorem
[tex]c^{2}=a^{2}+b^{2}[/tex] ----> we have a right triangle
[tex]c^{2} > a^{2}+b^{2}[/tex] ----> we have an obtuse triangle
[tex]c^{2}< a^{2}+b^{2}[/tex] ----> we have an acute triangle
where
c is the greater side
we have
[tex]c=\sqrt{19}\ units[/tex]
[tex]a=2\ units[/tex]
[tex]b=\sqrt{12}\ units[/tex]
substitute
[tex]c^{2}=(\sqrt{19})^{2}=19[/tex]
[tex]a^{2}+b^{2}=(2)^{2}+(\sqrt{12})^{2}=16[/tex]
so
[tex]19 > 16[/tex] -----> [tex]c^{2} > a^{2}+b^{2}[/tex]
we have an obtuse triangle
step 2
Find the type of triangle by the measure of the sides
we have that
The measure of its three sides is different
therefore
Is an scalene triangle
Which of the following transformations will result in an image that maps onto
itself?
A. rotate 90 degrees counterclockwise and then reflect across the y
axis
B. reflect across the x-axis and then reflect across the y-axis
c. rotate 90 degrees counterclockwise and then translate 4 units up
D. reflect across the x-axis and then reflect again across the x-axis
I agree. It reflects A G A I N
"Reflect across the x-axis and then reflect across the y-axis" will result in an image that maps onto itself. The correct option is B.
What is transformations?Transformations in mathematics refer to the process of changing the position, size, or shape of a geometric figure in a coordinate plane.
When a figure is reflected across the x-axis, the y-coordinate of each point on the figure is multiplied by -1, while the x-coordinate remains unchanged.
Similarly, when a figure is reflected across the y-axis, the x-coordinate of each point on the figure is multiplied by -1, while the y-coordinate remains unchanged.
When we reflect a figure across the x-axis and then across the y-axis, we essentially multiply the x-coordinate of each point by -1 and then the y-coordinate by -1.
This corresponds to a 180-degree rotation around the origin. Because a 180-degree rotation maps a figure onto itself, this transformation will produce an image that also maps onto itself.
Thus, the correct option is B.
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Shania is making a scale diagram of the badminton court at the community center. She uses a scale of 1 centimeter to 0.5 meter to draw the scale diagram. If the scale length of the badminton court is 26.8 centimeters and the scale width is 12.2 centimeters, what is the actual area of the court?
Answer: 13.4 meters by 6.1 meters
Step-by-step explanation: Applying the scale to the given measurements gives us: 13.4 meters long and 6.1 meters wide
A string of decorative lights is 24 feet long. The first light on the string is 16 inches from the plug. The lights on the string are spaced 4 inches apart.
How many lights are there on the string?
In older series light strings, if a bulb burns out, the string goes dark as the circuit is broken, with each bulb operating at 3 V normally. In modern strings with short-circuiting bulbs, the rest of the lights remain lit and each bulb would then operate at approximately 3.08 V if one burns out.
When strings of holiday lights are wired in series, the entire circuit is affected if one bulb fails. In older versions, if a bulb burns out, it acts like an open switch, causing the entire string of lights to go out as the electrical circuit is broken. Each of the 40 identical bulbs in a string operating on 120 V would have a normal operating voltage of 120 V / 40 = 3 V per bulb.
In newer versions of holiday lights, where bulbs short circuit when they burn out, the string continues to operate even when one bulb fails. However, the total voltage of the string remains the same, so the voltage gets redistributed among the remaining bulbs. If one bulb out of 40 burns out, you then have 39 bulbs through which the 120 V is distributed, giving an operating voltage of 120 V / 39 ≈ 3.08 V per bulb.
In a city, the distance between the library and the police station is 3 miles less than twice the distance between the police
station and the fire station. The distance between the library and the police station is 5 miles. How far apart are the police
station and the fire station?
miles
Answer:
Tthe distance between the police station and the fire station is 4 miles
Step-by-step explanation:
Let's call x the distance between the library and the police station
Let's call z the distance between the police station and the fire station
We know that:
[tex]x = 5[/tex] miles
The distance (x) between the library and the police station is 3 miles less than twice the distance (z) between the police station and the fire station
This is:
[tex]x = 2z-3[/tex]
We wish to find the distance z.
Then we equate both equations and solve for the variable z
[tex]5 = 2z -3\\\\2z = 5+3\\\\2z = 8\\\\z =\frac{8}{2}\\\\z = 4\ miles[/tex]
Answer:
c) 4 miles
Step-by-step explanation:
When rolling two dice , there are blank different ways to roll at least one 4.
Answer:
[tex]3[/tex]
Step-by-step explanation:
These [tex]3[/tex] ways are:
The first die showing a 4 and the second die showing a different numberThe second die showing a 4 and the first die showing a different numberBoth dice showing 4sAnswer:
11
Step-by-step explanation:
At least one means 1 being 4 or 2 of them being 4 this in case.
You could set a table:
1| 1 2 3 4 5 6
2| 1 2 3 4 5 6
3| 1 2 3 4 5 6
4| 1 2 3 4 5 6
5| 1 2 3 4 5 6
6| 1 2 3 4 5 6
There are 11 different ways to get at least one 4.
See this:
(first dice, second dice)
(1,4)
(2,4)
(3,4)
(4,4)
(4,5)
(4,6)
But there is also
(4,1)
(4,2)
(4,3)
(4,4) already counted earlier so don't count this one again
(4,5)
(4,6)
Kelli started keeping a reading log. the first night, she read 77 pages. Every day she reads 35 pages more. If this pattern continue, how many pages will she have read by days 53?
Final answer:
To find out how many pages Kelli will have read by day 53, we need to calculate how many pages she reads each day and add them up.
Explanation:
To find out how many pages Kelli will have read by day 53, we need to calculate how many pages she reads each day and add them up. On the first night, Kelli read 77 pages. Every day after that, she reads 35 pages more than the previous day. So each day, the number of pages she reads is increasing by 35. To find out how many pages she will have read by day 53, we can use the formula:
Total Pages Read = (First Night's Pages) + (35 * (Total Number of Days - 1))
Plugging in the values, we have:
Total Pages Read = 77 + (35 * (53 - 1))
Total Pages Read = 77 + (35 * 52)
Total Pages Read = 77 + 1820
Total Pages Read = 1897
Marlena has 3 straws. Two straws have the lengths
shown. She does not know the length of the shortest
straw, but when she forms a triangle with all three, the
triangle is obtuse. Which are possible lengths of the
shortest straw? Check all that apply.
5 inches
6 inches
7 inches
8 inches
9 inches
Answer:
5 6 7 is the correct answer
Step-by-step explanation:
The possible lengths of the shortest straw are 5 inches, 6 inches, 7 inches and 8 inches
How to determine the possible lengths of the strawThe lengths of the two straws are given as: 9 inches and 12 inches
Represent the length of the shortest straw with x.
So, we have the following inequality
[tex]x + 9 > 12[/tex]
Subtract 9 from both sides
[tex]x > 3[/tex]
This means the length of the shortest straw is greater than 3 inches
Hence, the possible lengths are 5 inches, 6 inches, 7 inches and 8 inches
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16 is 64% of what number
Answer:
25
Step-by-step explanation:
Is means equals and of means multiply
16 = 64% * W
Change to decimal form
16 = .64 * W
Divide each side by .64
16/.64 = .64W/.64
25 = W
Answer:
25
Step-by-step explanation:
We can model this question with:
16 = 0.64x
x represents "what number."
0.64x = 16
Divide 0.64 from both sides
0.64x ÷ 0.64 = 16 ÷ 0.64
16 ÷ 0.64 = 25.
Therefore, 16 is 64% of 25.
Two ships leave port at the same time, Ship X is heading due north and Ship Y is heading due east. Thirteen hours later they are
650 miles apart. If the Ship X had travels 520 miles from the port, how many miles will Ship Y travel?
A. 520 miles
OB. 325 miles
C. 455 miles
D. 390 miles
If x =1/2 and y =-x which of the following is equal to x-y
Answer:
x=-1/2
y=-1/2
-1/2-(-1/2)
0
Step-by-step explanation:
Maya is mailing packages. Each small package costs her $2.90 to send . Each larded package costs her $4.50. How much will it cost her to send 6 small packages and 4 large packages
Answer:$35.40
Step-by-step explanation:
1. $4.50 multiplied by 4 is $18
2. $2.90 multiplied by 6 is $17.4
3. $18+$17.4=$35.40
Write an equation of the line given the two points below (Write your equation in slope-intercept form, y=mx+b): (-4, 4) and (6, -4)
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-4-4}{6-(-4)}\implies \cfrac{-8}{6+4}\implies \cfrac{-8}{10}\implies -\cfrac{4}{5}[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=-\cfrac{4}{5}[x-(-4)]\implies y-4=-\cfrac{4}{5}(x+4) \\\\\\ y-4=-\cfrac{4}{5}x-\cfrac{16}{5}\implies y=-\cfrac{4}{5}x-\cfrac{16}{5}+4\implies y=-\cfrac{4}{5}x+\cfrac{4}{5}[/tex]
Archie can buy 5 buckets of popcorn and 2 drinks for $16.25. Terry can buy 3 buckets of popcorn and 1 drinks for $9.50. Assume that all buckets of popcorn are the same price and all drinks are the same price.
Answer:
The cost of one bucket of popcorn is $2.75
The cost of one drink is $1.25
Step-by-step explanation:
Let
x ----> the cost of one bucket of popcorn
y ----> the cost of one drink
we know that
5x+2y=16.25 -----> equation A
3x+y=9.50
y=9.50-3x ----> equation B
Solve the system of equations by substitution
Substitute equation B in equation A and solve for x
5x+2(9.50-3x)=16.25
5x+19-6x=16.25
6x-5x=19-16.25
x=$2.75
Find the value of y
y=9.50-3x
y=9.50-3(2.75)=$1.25
therefore
The cost of one bucket of popcorn is $2.75
The cost of one drink is $1.25
Which statement is true about f(x)=-6x+5-2
Not enough information (attach the statements).
There are 25 students in a class. Sixteen of those students are boys. What percent of the class are girls?
The percent of girls in the class is %
Hello There!
WHAT WE KNOW 25 students in a class and 16 out of the 25 students in the class are girls. There are 9 boys in the class because "25-9=16"
HOW TO SOLVE If we know that 9 out of the 25 students in the class are girls, we can represent it as the fraction [tex]\frac{9}{25}[/tex]. Next, we divide 35 by 9 to get a quotient of 0.36 and then multiply by 100 to get our percent of girls in the class which is 36%
HAVE A GREAT DAY!
To find the percentage amount of girls in the class, we need to first find the amount of girls in the class.
Since 16 of the 25 students are boys, the rest must be girls. Subtract 16 from 25 to find the amount of girls in class.
25-16=9
Now, to find out what percent of 25 9 is, divide 9 by 25.
9/25= .36
The percentage of girls in the class was 36%.
Hope this helps!
what is the factorization of the trinomial below -x^2-2x+48
Answer:
Step-by-step explanation:
In some fashion or another, the two factors are 6 and 8. But how are they put together?
-(x^2 + 2x - 48)
The 8 will be plus. That would make 2x plus. It should factor like this.
-(x + 8)(x - 6)
To check it, we should find the roots and post the graph. The graph will be upside down. That's what the minus outside the brackets does.
x + 8= 0
x = - 8
=======
x - 6 = 0
x - 6 + 6 = 6
x = 6
50 POINTS!!! pls help ASAP!!! 12. Building codes regulate the steepness of stairs. Homes must have steps that are at least 13 inches wide for each 8 inches that they rise. a. Discuss how to find the slope of the stairs. b. Describe how changing the width or height affects the steepness of the stairs.
Answer:
Slope tells you about the steepness of a line. It can is the ration of vertical change to horizontal change and you can solve this by using the slope formula:
[tex]m=\dfrac{\triangle y}{\triangle x}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
a. So in your case, starting from the bottom, the slope is:
[tex]m=\dfrac{8}{13}[/tex]
If you want to use coordinates, you can think of the first point (bottom of the stairs} would be at the point of origin (0,0). The next point would be at the top of the first stair 13 inches wide (horizontal or x) and 8 inches high (vertical or y)
So the coordinates of the two points would be:
(0,0) and (13, 8)
Using the formula we would have:
[tex]m=\dfrac{\triangle y}{\triangle x}=\dfrac{y_2-y_1}{x_2-x_1}\\\\m=\dfrac{8-0}{13-0}=\dfrac{8}{13}[/tex]
b. Looking at the answer above, you can see that the slope with increase if the vertical change is greater, so if you increase the height of the stairs, the stair would be steeper. The opposite is true if you would increase the width.
However, if you proportionally increase the width and the height, then the slope will remain the same.
Attached is how the graph of this would look like.
6. A circle has an area of 78.5 square inches.
What is the radius of the circle?
Answer:
The radius is equal to 5 inches or 12.7 cm
Step-by-step explanation:
Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=12
Y=7 when x=3
. Show that square of any positive integer can not be of form 7q + 3 or 7q+5or 7q + 6, for any integer q
Step-by-step explanation:
7q + 3 or 7q+5 or 7q + 6
solve for q
7q + 3 =
7q + 3 -3 =-3
7q = -3
7q/7 = -3/7
q = -3/7
7q + 3 =
7q + 6 -6 =-6
7q = -6
7q/7 = -6/7
q = -6/7
Point E is the midpoint of AB and point F is the midpoint of CD .
Which statements about the figure must be true? Check all that apply.
AB is bisected by . CD
CD is bisected by . AB
AE = 1/2 AB
EF = 1/2 ED
FD= EB
CE + EF = FD
Answer:
# AB is bisected by CD
# AE = 1/2 AB
# CE + EF = FD
Step-by-step explanation:
* Lets talk about the mid point
- The mid-point of a segment is divided the segment into two
equal parts
- The figure has line segment AB
- E is the mid-point of AB
∴ E divides the line segment AB into two equal parts
∴ AE = EB
∴ AE = 1/2 AB ⇒ (1)
- Any line passes through the point E will bisects the line segment AB
∴ AB is bisected by CD ⇒ (2)
∵ F is the mid-point of CD
∴ F divides the line segment CD into two equal parts
∴ CF = FD
∵ Point E lies on CF
∴ CE + EF = CF
∵ CF = FD
∴ CE + EF = FD ⇒ (3)
* There are three statements must be true (1) , (2) , (3)
# AB is bisected by CD
# AE = 1/2 AB
# CE + EF = FD
Answer:1,3,5
Step-by-step explanation:
Please Help Finial Test tomorrow Thank you!
Answer:
The area is 522.935 square inches.
Step-by-step explanation:
A trapezoid's area is calculated as follows: h(b1+b2)/2
Plugging numbers in gives 34.3+12.6=46.9
so now all that's left is to multiply 22.3 and 46.9, and divide by 2.
This gives 522.935
Hope this helps!
Answer:
522.935 square inches
Step-by-step explanation:
OPTION 1:
First, the area of the rectangle in the center is 12.6*22.3 (w*l or b*h), or 280.92
Second, the area of the two triangles on the side are right triangles since we made a rectangle in the center, so the area of that is (base2 - base1)*h*1/2, or (34.3-12.6)*22.3*1/2=21.7*22.3*1/2=483.91*1/2=241.955
Therefore, the area is 280.98+241.955 or 522.935 square inches
OPTION 2:
Using the formula to find the area of a trapezoid, you would do ((base1 + base2)/2)*h, or ((12.6+34.3)/2)*22.3 which is 522.935 square inches
Write the expression in complete factored
form.
5n_(c - 3) - n(C - 3) =
Answer:
(c-3) (4n)
Step-by-step explanation:
5n(c - 3) - n(C - 3) =
Factor out (c-3) from each term
(c-3) (5n-n)
Simplify the 2nd term
(c-3) (4n)
if you run for 4 hours at 8 miles and walk 8 hours at 2 miles how far will you have gone at the end of 12 hours?
Answer:
4 times 8 is 32 then 8 times 2 is 16 then add them together
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer:
48 miles
Step-by-step explanation:
4 times 8 equals 32 plus 8 times 2 equals 16 add them up equals 48