Answer:
16 edges.
Step-by-step explanation:
We will use Euler's polyhedron formula to solve for the edges of our convex polyhedron.
Euler's polyhedron formula is: [tex]V+F-E=2[/tex], where,
V= Vertices of polyhedron,
F= Faces of polyhedron,
E= Edges of polyhedron.
Let us substitute V=6 and F=12 in Euler's formula to find number of edges of our polyhedron.
[tex]6+12-E=2[/tex]
[tex]18-E=2[/tex]
Let us subtract 18 from both sides of our equation.
[tex]18-E-18=2-18[/tex]
[tex]-E=2-18[/tex]
[tex]-E=-16[/tex]
[tex]E=16[/tex]
Therefore, our convex polyhedron will have 16 edges.
Categorize the following polygon by the number of sides
heptagon
decagon
dodecagon
hexagon
Answer:
heptagon
Step-by-step explanation:
This polygon has 7 sides
heptagon is a seven sided polygon
decagon is a ten sided polygon
dodecagon is a 12 sided polygon
hexagon is a six sided polygon
Please help on this one ?
Answer:
C. (-3.6, 17)
Step-by-step explanation:
The relative maximum occurs at an x coordinate between -3 and -4. The relative maximum is between 15 and 20. The best approximation is
C. (-3.6, 17)
Answer:
c. (-3.6, 17)
Step-by-step explanation:
The relative maximum is the maximum in a region. The maximum between -6 and is found and x=-3.6 and the value is 17. So x=-3.6 and y=17
True or False??
In the following number, the 8 is in the hundreds place.
15,829
Answer:
your answer is true.
Step-by-step explanation:
As 8 is in the hundredth place.
Answer:
The answer is True.
Step-by-step explanation:
9 is in the "ones place", 2 is in the "tens place, 8 is in the "hundreds place", and so on...
Given: Parallelogram KLMN
Prove: ∠N≅∠L and ∠M≅∠K
Statement Reason
Parallelogram KLMN Given
KL¯¯¯¯¯∥NM¯¯¯¯¯¯¯ and KN¯¯¯¯¯¯∥LM¯¯¯¯¯¯
m∠K+m∠N=180°
m∠L+m∠M=180°
m∠K+m∠L=180°
Same-Side Interior Angles Theorem
m∠K+m∠N=m∠K+m∠L
m∠L+m∠M=m∠K+m∠L
m∠N=m∠L
m∠M=m∠K
∠N≅∠L and ∠M≅∠K Angle Congruence Postulate
Substitution Property of EqualityTransitive Property of CongruenceSubtraction Property of EqualityDefinition of parallel linesDefinition of parallelogram
Answer:
Since, KLMN is a parallelogram, then by the property of parallelogram that opposite angles of a parallelogram is equal, therefore ∠N=∠L and ∠M=∠K.
Step-by-step explanation:
Answer:
It is followed by properties of parallelogram and the proof is explained in step-by-step solution.
Step-by-step explanation:
Given a parallelogram KLMN
Parallelogram is a quadrilateral with parallel opposite sides.
To Prove: ∠N≅∠L and ∠M≅∠K
In Parallelogram KLMN the opposite sides are parallel therefore, the opposite angles are vertical angles. And the vertical angles are always equal and congruent. Hence,
∠N≅∠L and ∠M≅∠K
For any quadrilateral sum of all angles equal to 360°
m∠K + m∠L + m∠M + m∠N = 360°
Now given quadrilateral is parallelogram therefore opposite angles are equal. So, we can write m∠L = m∠N, m∠M = m∠K
⇒ m∠K + m∠N + m∠K + m∠N = 360°
2 m∠K + 2 m∠N = 360°
m∠K + m∠N = 180°
For the same parallelogram, because opposite sides are equal therefore use m∠K = m∠L, m∠N = m∠M using above equation, we get
m∠L + m∠M = 180°
Because m∠M = m∠K
m∠K + m∠L = 180°
Same Side Interior Angles Theorem states that if the two parallel lines intersect or cut by a transversal then the interior angles on the same side are supplementary that means their sum is equal to 180°
Hence, by above theorem m∠K + m∠N = 180°
& m∠K + m∠L = 180°
By above two equations, we get
m∠K + m∠N = m∠K + m∠L
because m∠K = m∠M & ∠N = ∠L
⇒ m∠L + m∠M = m∠K + m∠L
Because opposite angles of a parallelogram are alternate angles therefore are equal. hence,
m∠N = m∠L
m∠M = m∠K
Angle congruency postulate
Opposite angles of parallelogram are vertical angles and the vertical angles are congruent as well as equal.
∠N≅∠L and ∠M≅∠K
Substitution Property of equality states that if one angle is equal to another angle the one can be substituted in the place of another that means if ∠M=∠K then we can substituted ∠K in place of ∠M
Transitive property of congruence states that if if the two angles or segments or triangles are congruent to third then they are congruent to each other.
Subtraction Property of Equality states that if if two sides of any equation are equal then subtraction of same value from both sides results in equality of equation.
Parallel lines are those lines which do not intersect or cut each other at the end.
Parallelogram is a quadrilateral have opposite sides equal and parallel.
:
Find (g - f)(x). f(x) = 1/x g(x) = x2 + 2x -5
A. 1/2-x^2-2x+5
B. 1/x+x^2+2x-5
C. x^2+2x-5-1/x
D. 1/x +x^2-5
Answer:
C) [tex]g(x)-f(x)=x^2 + 2x -5-\frac{1}{x}[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{1}{x} \ g(x) = x^2 + 2x -5[/tex]
To find (g-f)(x) , we need to calculate g(x) - f(x)
WE know f(x) = 1/x and g(x) = x^2 + 2x -5
Plug in g(x) and f(x) and then subtract
[tex]g(x)-f(x)=x^2 + 2x -5- (\frac{1}{x})[/tex]
All are unlike terms so we cannot combine like terms
[tex]g(x)-f(x)=x^2 + 2x -5-\frac{1}{x}[/tex]
In order to find (g - f)(x), you need to subtract f(x) from g(x). The correct subtraction results in the expression x^2+2x-5-1/x, corresponding with answer choice C.
Explanation:The question asks you to calculate (g - f)(x) where f(x) = 1/x and g(x) = x^2 + 2x -5. This entails finding the difference between g(x) and f(x).
Firstly, write out g(x) and f(x):
g(x) = x^2 + 2x - 5f(x) = 1/xSecondly, subtract f(x) from g(x):
g(x) - f(x) = (x^2 + 2x - 5) - (1/x)
This simplifies to: g(x) - f(x) = x^2 + 2x - 5 - 1/x
Therefore, the correct answer is C. x^2+2x-5-1/x
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What is the value of x?
Answer:
15
Step-by-step explanation:
The fact angle G and F are equal means the triangle is isosceles triangle. And an isosceles triangle has two equal sides on the opposite sides of the equal angles. Which means x equals HF which is 15.
Question
What is the value of x?
Answer:
15Step-by-step explanation:
this is an isosceles triangle, 2 equal sides and 2 equal angles, so
FH = GH
15 = 15
there are 3 literature books, 4 algebra books, and 2 biology on a shelf. if a book is randomly selected, what is the probability of selecting a literature book or an algebra book?
Answer:
[tex]\frac{7}{9}[/tex]
Step-by-step explanation:
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
so
Let
x------> size of the event space
y-----> size of the sample space
so
[tex]P=\frac{x}{y}[/tex]
step 1
Find the probability of selecting a literature book
we have
[tex]x=3[/tex]
[tex]y=3+4+2=9[/tex]
substitute
[tex]P=\frac{3}{9}[/tex]
step 2
Find the probability of selecting an algebra book
we have
[tex]x=4[/tex]
[tex]y=3+4+2=9[/tex]
substitute
[tex]P=\frac{4}{9}[/tex]
step 3
Find the probability of selecting a literature book or an algebra book
Adds the probability of selecting a literature book plus the probability of selecting an algebra book
[tex]P=\frac{3}{9}+\frac{4}{9}=\frac{7}{9}[/tex]
Answer:
Step-by-step explanation:
Is it mutually exclusive?
Look at the triangle:
A right angle triangle is shown with hypotenuse equal to 17 centimeters. An acute angle of the triangle is labeled as x degrees
What is the value of cos x°? (1 point)
Select one:
a. 8 ÷ 17
b. 17 ÷ 8
c. 15 ÷ 17
d. 8 ÷ 15
In reference to the image below, the trigonometric ratio cos [tex]\alpha[/tex]° is calculated by dividing the base by the hypotenuse, thus making part c) 15 ÷ 17 the correct option.
The trigonometric ratios are six different proportions of the three sides of right angled triangle, namely, hypotenuse, perpendicular and base. The trigonometric ratios are sine, cosine, tan, sec, cosec and cot.
In the given question, the trigonometric ratio cos is given by dividing the base of the triangle to the hypotenuse.
In any question,
hypotenuse = side opposite of the right angle = 17
base = side adjacent to the acute angled marked = 15
Thus giving the value of cos [tex]\alpha[/tex]° as 15 ÷ 17.
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The complete question is given below:
A right angle triangle is shown with hypotenuse equal to 17 centimeters. An acute angle of the triangle is labeled as [tex]\alpha[/tex] degrees.
What is the value of cos [tex]\alpha[/tex]°?
a. 8 ÷ 17
b. 17 ÷ 8
c. 15 ÷ 17
d. 8 ÷ 15
The figure of triangle is given below:
In the triangle below, what is cos B?
Answer:
[tex]\text{cos}(B)=\frac{c}{a}[/tex]
Step-by-step explanation:
We have been given a triangle. We are asked to find [tex]\text{cos}(B)[/tex].
We know that cosine relates adjacent side of a right triangle to its hypotenuse.
[tex]\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]
We can see that side AB is adjacent side and CB is hypotenuse of our given right triangle.
[tex]\text{cos}(B)=\frac{AB}{CB}[/tex]
[tex]\text{cos}(B)=\frac{c}{a}[/tex]
Therefore, our required value is [tex]\text{cos}(B)=\frac{c}{a}[/tex]
The population of a town increased by 15% in 2016, and decreased by 5% in 2017. If the population of the town was 60,000 in the beginning of 2016, then what was it at the end of 2017?
Answer:
65,550.
Step-by-step explanation:
We have been given that the population of a town increased by 15% in 2016, and decreased by 5% in 2017.
Since an exponential is in form: [tex]a*b^x[/tex].
For growth b=(1+r), where r in rate in decimal form.
For decrease b=(1-r), where r in rate in decimal form.
[tex]15\text{ percent}=\frac{15}{100}=0.15[/tex]
Let us find the population increase in 2015.
[tex]\text{Population at the end of year 2016}= 60,000*(1+0.15)^1[/tex]
[tex]\text{Population at the end of year 2016}= 60,000*(1.15)[/tex]
[tex]\text{Population at the end of year 2016}= 69,000[/tex]
Therefore, the population at the end of year 2016 will be 69,000.
Now let us find population decrease of 5% in year 2017.
[tex]15\text{ percent}=\frac{5}{100}=0.05[/tex]
[tex]\text{Population at the end of year 2017}= 60,000*(1-0.05)^1[/tex]
[tex]\text{Population at the end of year 2017}= 60,000*(0.95)[/tex]
[tex]\text{Population at the end of year 2017}= 65,550[/tex]
Therefore, the population at the end of year 2017 will be 65,550.
The amount of money Alan earns as a plumber after x hours is modeled by the equations y=25x + 50 what is the meaning of 25 in this models
Answer:
25 represents how much he makes per hour
Step-by-step explanation:
What is the asymptote of the graph of g(x)=3^x+6 ?
y=3
y=4
y=5
y=6
Answer:
y=6
Step-by-step explanation:
I took the test and got 100%
Please help!!! I only have three questions left!!!
A general proof for this would be that since Angle A + Angle F + Angle E = 180°, and each of these angles is congruent to some angle inside of Triangle CGH; that CGH would equal 180°.
Interior angles of triangles = 180°, which is common knowledge; unfortunately this isn't an answer choice - so we use the above proof.
F ~= C
A ~= H
E ~= G
So, Angles A and H are congruent would be the correct solution.
He surface area for a rectangular prism with a square base is SA=2s2+4sh. What is the surface area if s=2 and h=4?
Answer:
40 units²
Step-by-step explanation:
substitute the given values for s and h into the formula
SA = ( 2 × 2² ) + (4 × 2 × 4 ) = 8 + 32 = 40
Answer:
40 units²
Step-by-step explanation:
Given that the surface area for a rectangular prism with a square base is SA=2s2+4sh.
Where the values of the variables in the equation which are s and h are known, the area can be computed by the substitution of the known variables into the equation.
Hence where s = 2 and h = 4
SA = 2(2)² + 4(2)(4)
= 8 + 32
= 40 units²
20. What is the determinant of B? {-18 3} {4 1}
Answer:
-30
Step-by-step explanation:
-18x1 - 4x3 = -18-12= -30
Arrange the systems of equations that have a single solution in increasing order of x-values in their solutions. 2x+y=10
x-3y=-2
2x + y= 10
-6x -3y=-2
x+2y= 5
2x + y = 4
5x+ y= 33
x=18-4y
Y=13 -2x
8x + 4y =52
x+ 3y =5
6x-y=11
Y=10 + x
2x + 3y =45
Answer:
(III), (VI),(VII), (I), (IV)
Step-by-step explanation:
Solving the system of equations one by one by elimination method
(I) 2x+y=10
x-3y= -2 ( multiply by 2)
we have unique solution
x=4, y=2
(II) 2x+y=10 (multiply by -3)
-6x-3y= -2
No solution.
(III) x+2y=5 (multiply by 2)
2x+y=4
Unique solution
x=1, y=2
(IV) 5x+ y= 33
x=18-4y ---> x+4y=18 (multiply by 5)
Unique solution
x=6, y=3
(V) Y=13 -2x ----> 2x+y=13 ( multiply by 4)
8x + 4y =52
No solution
(VI) x+ 3y =5
6x-y=11 (multiply by 3)
Unique solution
x=2, y=1
(VII) Y=10 + x ----> -x+y=10 (multiply by 2)
2x + 3y =45
Unique solution
x=3 , y=13
Values of x in increasing order= (III), (VI),(VII), (I), (IV)
Could 1 2 . 2 cm , 6 . 0 cm , 12.2 cm,6.0 cm, and 4 . 2 cm 4.2 cm be the side lengths of a triangle?
Answer:
Yes they can be
A knitting machine used a total of 457,500 meters of yarn to make 100 cardigans and 200 pullovers yesterday. The machine takes the same length of yarn to make 21 pullovers as to make 20 cardigans.
What length of yarn does the machine use to make cardigans and pullovers?
The machine uses ______meters of yarn per cardigan and uses ______
meters per pullover.
Answer:
The machine uses 1575 meters of yarn per cardigan and uses 1500 meters per pullover.
Step-by-step explanation:
Let P be yarn needed by machine for each pullover and C be yarn needed by machine for each Cardigan.
We are told that the machine takes the same length of yarn to make 21 pullovers as to make 20 cardigans. We can represent this information as:
[tex]20C=21P...(1)[/tex]
The machine used a total of 457,500 meters of yarn to make 100 cardigans and 200 pullovers. We can represent this information as:
[tex]200P+100C=457,500...(2)[/tex]
Let us solve our system of equations using substitution method.
From equation (1) we will get,
[tex]C=\frac{21P}{20}[/tex]
Upon substituting this value in equation (2) we will get,
[tex]200P+100(\frac{21P}{20})=457,500[/tex]
[tex]200P+5*21P=457,500[/tex]
[tex]200P+105P=457,500[/tex]
[tex]305P=457,500[/tex]
[tex]P=\frac{457,500}{305}[/tex]
[tex]P=1500[/tex]
Therefore, the machine uses 1500 meters of yarn per pullover.
Upon substituting P=1500 in equation (1) we will get,
[tex]20C=21*1500[/tex]
[tex]20C=31,500[/tex]
[tex]C=\frac{31,500}{20}[/tex]
[tex]C=1575[/tex]
Therefore, machine uses 1575 meters of yarn per cardigan.
Answer:
1575 meters of yarn per cardigan
1500 meters per pullover
Step-by-step explanation:
Long division (4b^3+10b^2-32b+15) divided by (4b-6)
Answer:
4b^3 + 10b^2 - 32b + 15
___________________
2(2b - 3)
Step-by-step explanation:
Take out the greatest common factor of (4b - 6) which is 2 and 3.
Two friends ordered a restaurant special in which they each recived a meal and shared a desert. The final bill with tax and tip was $21.86.How much should each friend pay
Suppose we want a 90% confidence interval for the average amount spent on
entertainment (movies, concerts, dates, etc.) by Freshman in their first semester at a
large university. The interval is to have a margin of error of $2, and the amount spent
has a normal distribution with a standard deviation s = $30. The number of
observations required is closest to
A) 25.
B) 30.
C) 609.
D) 865.
Your mom asked you to turn the oven down to 325 degrees. This is 75 degrees less than it was. What was the original temperature?
math help.......... will be marking brainly
Answer:
B.) 28%
Step-by-step explanation:
There are 50 total spins so far and 28% of them have been 4's. So that is the probability.
AAHHH PLZ I HAVE 5 MIN LEFT!!!!
The sum of the measures of two angles of a scalene triangle is calculated, and the result is the same as the measure of one of the external angles of a triangle. Which pair of angle measures was calculated?
the remote interior angles
the adjacent interior angles
the adjacent interior angle and the larger remote interior angle
the adjacent interior angle and the smaller remote interior angle
There are 8 blue marbles and 7 red marbles in a bag. Julie pulls two marbles at random from the bag first. What is the probability that she first pulls a blue marble and then a red marble?
Answer:
either a ratio 8;7. or a percentage of 53% for picking the blue marble first i think and a 50/50 chance if you keep that blue marble out.
Step-by-step explanation:
Answer: [tex]\frac{4}{15}[/tex]
Step-by-step explanation:
Given: Number of blue marbles = 8
Number of red marbles = 7
Total number of marbles = 8+7=15
Now, the probability that she first pulls a blue marble is given by :-
[tex]P(B)=\frac{\text{blue marbles}}{\text{Total marbles}}\\\\=\frac{8}{15}[/tex]
Now, total marbles left in bag = 15-1=14
Now, the probability that she second pulls a red marble is given by :-
[tex]P(B)=\frac{\text{red marbles}}{\text{Total marbles left}}\\\\=\frac{7}{14}=\frac{1}{2}[/tex]
Thus, the probability that she first pulls a blue marble and then a red marble is given by :-
[tex]P(B)\timesP(R)=\frac{8}{15}\times\frac{1}{2}=\frac{4}{15}[/tex]
What is an equation of the line, in point slope for, that passes though the given point and has the given slope? point:(7,3);slope:4/7
Answer:
The equation of this line is y - 3 = 4/7(x - 7)
Step-by-step explanation:
To find this, start with the base form of point-slope form.
y - y1 = m(x - x1)
Now put the slope in for m and the two coordinates in for (x1, y1).
y - 3 = 4/7(x - 7)
Y=7 and x= 6, perpendicular , parallel or neither?
Answer:
I think the answer is neither. Hope this helps.
Step-by-step explanation:
WILL MARK BRAINLEST PLS HELP
Which equation represents this ellipsis
A (x-2)^2 / 6^2 + (y-4)^2 /3^2 = 1
B(x-2)^2 / 12^2 + (y-4)^2 /6^2 = 1
C)(x-4)^2 / 6^2 + (y-2)^2 /3^2 = 1
D) (x-4)^2 / 12^2 + (y-2)^2 /6^2=1
Answer:
None
Step-by-step explanation:
The center of the ellipse is at (2, 4)
The length of the x axis is a= (8-2) =6
The length of the y axis is b=(16-4) = 12
The formula for an ellipse is
(x-h) ^2 (y-k)^2
----------- + -------------- = 1^2
a^2 b^2
where (h,k) is the center
and a and b are the lengths of the major and minor axes
(x-2) ^2 (y-4)^2
----------- + -------------- = 1
6^2 12^2
none of your choices have b>a and for the ellipse to be vertical b>a
Omar has a new credit card. He earns 300 reward points for every 100 dollars he spends. If Omar earned 1800 reward points, how much money did he spend?
Answer:
He earned 1800 reward points for 600 dollars
Step-by-step explanation:
Given the statement: Omar has a new credit card. He earns 300 reward points for every 100 dollars he spends. If Omar earned 1800 reward points.
Unit rate are expressed as a quantity of 1, such as 3 feet per second or 4 miles per hour, they are called unit rates.
Earn 300 reward point for every 100 dollars.
⇒ unit rate per reward = [tex]\frac{100}{300}[/tex] dollars
we have to find how many dollars he earned for 1800 points.
[tex]Number of dollars = unit rate \times 1800[/tex]
= [tex]\frac{100}{300} \times 1800 = 600[/tex]
Therefore, he earned 1800 reward points for 600 dollars
Answer:
$600 money Omar spends .
Step-by-step explanation:
As given
Omar has a new credit card.
He earns 300 reward points for every 100 dollars he spends.
i.e
300 reward points for every 100 dollars .
Let us assume that the Omar earned 1800 reward points when he spends x money.
Than the equation becomes
[tex]x = \frac{1800\times 100}{300}[/tex]
[tex]x = \frac{1800}{3}[/tex]
x = $600
Therefore $600 money Omar spends .
At a horse show, ribbons are awarded for first, second, third, and fourth places. There are 16 horses in the show. How many different arrangements of four horses are possible?
Answer:
43680 different arrangements are possible.
Step-by-step explanation:
The total number of horses are :16
We have to find different arrangement of four horses
Since, we have to find arrangements means we will use permutation
So, the required arrangement will be:
[tex]^{16}P_4[/tex]
Now, using: [tex]^{n}P_r=\frac{n!}{(n-r)!}[/tex]
Here, n= 16 and r=4 on substituting the values we get:
[tex]^{16}P_4=\frac{16!}{(16-4)!}[/tex]
[tex]\Rightarrow \frac{16!}{12!}[/tex]
[tex]\Rightarrow \frac{16\cdot 15\cdot 14\cdot 13\cdot 12!}{12!}[/tex]
Cancel out the common term that is 12! we get:
[tex]16\cdot 15\cdot 14\cdot 13[/tex]
After simplification we get: 43680
Hence, 43680 different arrangements are possible.