Answer: 12
Step-by-step explanation:
Because a translation is a rigid motion, we know that YZ corresponds to GH (and they will have the same length).
Now, we can the fact that EFGH is a rectangle to obtain that EF=GH=12 (since opposite sides of a rectangle are congruent)
Hence, YZ=12.
Pat, Jo, Al, and Dan are finalists in a talent contest. How many different ways can Pat, Jo, Al, and Dan finish in first, second, third, and fourth place in the contest?
23 ways
10 ways
24 ways
12 ways
Answer:
24 ways!
Step-by-step
Pat, Jo, Al, Dan
Pat, Al, Dan, Jo
Pat, Dan, Jo, Al
Pat, Jo, Dan, Al
Pat, Al, Jo, Dan
Pat, Dan, Al, Jo List all permutations beginning with Pat.
Jo, Al, Dan, Pat
Jo, Dan, Pat, Al
Jo, Pat, Al, Dan
Jo, Al, Pat, Dan
Jo, Dan, Al, Pat
Jo, Pat, Dan, Al List all permutations beginning with Jo.
Al, Dan, Pat, Jo
Al, Pat, Jo, Dan
Al, Jo, Dan, Pat
Al, Pat, Dan, Jo
Al, Dan Jo, Pat
Al, Jo, Pat, Dan List all permutations beginning with Al.
Dan, Pat, Jo, Al
Dan, Jo, Al, Pat
Dan, Al, Pat, Jo
Dan, Jo, Pat, Al
Dan, Pat, Al, Jo
Dan, Al, Jo, Pat List all permutation beginning with Dan.
There are 24 ways for Pat, Jo, Al, and Dan to finish in first, second, third, and fourth place in the contest.
Using permutations, they are 24 different ways Pat, Jo, Al and Dan finish in first, second, third, and fourth place in the contest.
What is permutations?A permutations is "a mathematical calculations of the number of ways a particular data can be arranged".
According to the question,
Pat, Jo, Al and Dan finish in first, second, third, and fourth place in the contest.
Formula for Permutation [tex]nP[/tex]ₓ = [tex]\frac{n!}{(n-x)!}[/tex] where 'n' number of items set and 'x' is the item taken for Permutation.
In order to find number of ways first, second, third, and fourth place are arrangement or Permutation in the contest.
First, second, third and fourth are four places can be obtained by Pat, Jo, Al and Dan by four position
Formula for permutation P(n , n) = n!. Using this formula P(4,4) = 4!
= 1×2×3×4 =24 ways.
Hence, using permutations, they are 24 different ways Pat, Jo, Al and Dan finish in first, second, third, and fourth place in the contest.
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kindly answer this please
Answer:
See below ~
Step-by-step explanation:
13.
∠2 and ∠5 are adjacent as they lie right next to ∠1C. Angles 2 & 514.
∠5 will form a linear pair as they add up to 180°C. Angle 515.
∠2 = 180° - 70° - 50°∠2 = 60°B. 60°16.
A. ∠RVT and ∠RVUAnswer:
13. C. Angles 2 and 5, becuase adjacent means the angles are touching and right next to each other, and three is too far away and is not buffering up to angle 1.
14. That would be C. angle 5, because linear pair angles are angles that share a line and would add up to 180, in this case only angle 5 does that.
15. B. 60 degrees, to find out angle 2, you first need to know the information that a line=180 degrees, and all three angles share a single line being line TQ. so all you have to do, is add up the angles you know, so 70+50=120, and then subtract them by 180, giving you the remainder that is unkown, in this case being angle 2, so 180-120=60.
16. A. angles RVT and angle RVU, remember, ajacent angles are angles that share a side and buffer each other, in which angles RVT and RVU are the only ones that do that.
3Ix+5I=7
I= absoulute value symbol
Answer:
[tex]x = -\dfrac{8}3~~~~\text{or}~~~x = -\dfrac {22}3[/tex]
Step by step explanation:
[tex]~~~~~3|x+5|=7\\\\\implies |x+5| = \dfrac 73\\\\\implies x +5=\dfrac 73~~~\text{or}~~~x+5 = -\dfrac 73\\\\\implies x = \dfrac 73 -5~~~\text{or}~~~ x = -\dfrac 73 - 5\\\\\implies x = -\dfrac{8}3~~~~~~\text{or}~~~x = -\dfrac {22}3[/tex]
Marisa has 26 pokémon cards. Marisa claims that she will have 146 or more pokémon cards after she receives her shipment of 8 packs of cards. How many cards must be in each pack so that Marissa’s statement is true?
Answer:
26 + 8x.x = 15.Step-by-step explanation:
Marise has 26 pokemon cards. Marisa claims that he will have 146 or more cards after she receives her shipment of 8 packs of cards.
So, we have to make a unknown value on 8.
8x.Now, we have to find out that unknown value:
26 + 8x= 26 + 8(15)= 26 + 120= 146.x = 15.There will be 15 cards in Marisa's 8 boxes.
What is plancks constant?what is it used for and where is it used?
The photon's energy (E) is equal to its frequency (f) multiplied by the Planck constant (h).
What is Plancks constant?Planck's constant is the elementary quantum of action. Its unit is the metre-kilogram-second or Joule second. It is denoted by h and has a value of 6.62607015 × 10⁻³⁴ joule second.
The photon's energy (E) is equal to its frequency (f) multiplied by the Planck constant (h). It is given by:
E = hf
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Answer:
Planck's constant is used to relate the energy in one quantum of electromagnetic radiation to the frequency of that radiation.
Step-by-step explanation:
Have a great rest of your day
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From the top of a lighthouse 160 feet above sea level, the angle of depression to a boat
at
sea is 25 degrees. To the nearest foot, what is the horizontal distance from the boat to
the base of the lighthouse?
Answer:
75 feet
Step-by-step explanation:
The perpendicular height from the base of the lighthouse to the top is 160 feet. The angle of depression is the angle that is adjacent to this side. The opposite of this angle is the horizontal distance from the boat to the base of the lighthouse, so we need to use the tangent. tan 25°=x/160, tan 25° is 0.466 so when we multiplty by 160 to find x, we get x=74.56, which rounded up is 75.
write an approximate equation of the line of best fit, then predict the average temperature.
Answer:
[tex]\textsf{\sf(a)} \quad y=-\dfrac54x+\dfrac{205}{2}[/tex]
(b) $46.25
Step-by-step explanation:
When adding a line of best fit, ensure that the number of points above and below the line is about equal.
See attachment for line of best fit.
Part (a)From inspection of the graph, two points on the line are (10, 90) and (50, 40). Therefore,
[tex]\textsf{let}\:(x_1,y_1)=(10,90)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(50,40)[/tex]
Calculating the slope of the line:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{40-90}{50-10}=-\dfrac54[/tex]
Using the point-slope form of linear equation: [tex]y-y_1=m(x-x_1)[/tex]
(where m is the slope and (x₁, y₁) is a point on the line)
[tex]\implies y-90=-\dfrac54(x-10)[/tex]
[tex]\implies y-90=-\dfrac54x+\dfrac{25}{2}[/tex]
[tex]\implies y=-\dfrac54x+\dfrac{205}{2}[/tex]
(where x is the average monthly temperature in °F and y is the monthly heating costs in dollars)
Part (b)Substitute x = 45 into the equation found in part (a):
[tex]\implies -\dfrac54(45)+\dfrac{205}{2}=46.25[/tex]
Therefore, the monthly heating cost for a month with an average temperature of 45 °F is approximately $46.25
Phoebe works for a company that advertised an annual increase
of 5% to an employee's hourly pay. When Phoebe went to sign
her contract with the company, she noticed that her boss had
indicated that she would receive an annual increase of
$0.75 per hour. please help its for a test
Based on the annual percentage increase and the actual amount, the wage rate per hour at Phoebe's job is $15 per hour.
What is Phoebe paid per hour?The company gives an increase of 5% on the hourly wage per hour and this amount comes out to be $0.75.
The wage rate per hour is therefore:
= Actual increase amount / Percentage increase
Solving gives:
= 0.75 / 5%
= $15 per hour
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Help Meeee Please. I don’t understand
Which algebraic expressions are binomials? Check all that apply
Answer:
Of the ones listed, in the way they are written, the answers are x²y – 3x and 6y² – y.
Explanation:
A monomial is a constant, a variable, or the product of constants and variables. A binomial is the sum or difference of two monomials.
The first option, xy, is a monomial. There is only one, so it is not a binomial.
The second one, x²y-3x, is the difference of two monomials; this means it is a binomial.
The third one, 6y²-y, is the difference of two monomials; this means it is a binomial.
The last one, y²+4xy-x², is the sum and/or difference of at least three monomials (there is a plus at the end that makes me think there is more to it). This means it is a trinomial, not a binomial.
Answer: B, C, and E.
Step-by-step explanation:
Since all three show the characteristics found in a binomial then these three are your answers. Plus I just did it on Edge.
:)
What type of angle is shown below?
29°
O A. Obtuse
O B. Acute
O C. Right
O D. Straight
Help pls
Answer:
B. Acute
Step-by-step explanation:
Any angle less than 90 degrees is an acute angle. A 90-degree angle is a right angle, and is typically marked with a little box. Any angle more than 90 degrees and less than 180 degrees is an obtuse angle. A 180-degree angle is a straight angle and is basically just a line.
Since 29 degrees is less than 90 degrees, we know that the answer is B, an acute angle.
I hope this helps! Have a lovely day!! :)
(also, here is a picture of examples of the different angles)
100 POINTS!!!!!!!!!! PLEASE HELP NEED THIS DONE AS SOON AS POSSIBLE ASAP
Answer:
20.28
Step-by-step explanation:
Triangles; 4
Area of 1 Triangle; 2
Rectangles; 8
Semi Circle; 6.28
Area in total; 20.28
Hope This Helps! :)
Step-by-step explanation:
Area of the rectangle: 4×2=8
Area of the semicircle: πr² ÷ 2= 22/7×2² ÷2 = 12.57 ÷2 = 6.29
Area of one triangle: 1/2×2×2= 2
Area of total figure: 8+6.29+2+2= 18.29
Hope this helps =)
Which is true for
the vertex?
A. A vertex is any angle.
B. A vertex is the end point of a single line segment.
C. A vertex is a point that describes the corner or
intersection of an angle.
Answer:
C.
Step-by-step explanation:
It is the corner or a point where line segments meet.
Hi!
Your answer is C.
The vertex is the point where two different rays meet, forming an angle.
It can also simply be the point where 2 straight lines simply meet.
Option A is NOT correct because a vertex is not angle, it is a part of an angle.
Option B is NOT correct because, if there's only one segment, we cannot form a vertex.
See the image below for an example:
Saniya has 5 2/3 of fabric one fourth of fabric is green and 1/3 of remaining fabric is white how many feet of green fabric does she have how many feet of white fabric does she have
Find the sum of 6x^2+10x-16x 2 +10x−1 and -5x^2-2x+1−5x^2 −2x+1.
Answer:
-21x² + 8x + 2
Step-by-step explanation:
Addition of two polynomials:
Like terms have same variable with same power. Combine like terms.
(-16x² & -5x² are like terms ; 10x and (-2x) are like terms ; (1 and 1 are constants)
-16x² + 10x + 1 + (-5x² - 2x + 1) = -16x² + 10x + 1 -5x² - 2x + 1
= -16x² - 5x² + 10x - 2x + 1 + 1
= -21x² + 8x + 2
[tex](6x^2+10x-1) +(-5x^2-2x+1)\\\\=6x^2+10x-1-5x^2-2x+1\\\\=x^2+8x[/tex]
Which values of c will cause the quadratic equation -x^2+3x+c=0 to have no real number solutions? Check all that apply.
Taking into account the discriminant of a cuadratic function, values of c less than[tex]-\frac{9}{4}[/tex] cause the quadratic equation -x²+3x+c=0 to have no real number solutions.
Discriminant of a cuadratic functionThe function f(x) = ax² + bx + c with a, b, c real numbers and a ≠ 0, is a function quadratic expressed in its polynomial form (It is so called because the function is expressed by a polynomial).
The following expression is called discriminant:
Δ= b²- 4×a×c
The discriminant determines the amount of roots of the function. The roots are those values of x for which the expression is 0, so it graphically cuts the x-axis.
Then:
If Δ <0 the function has no real roots and its graph does not intersect the x-axis.If Δ> 0 the function has two real roots and its graph intersects the x-axis at two points .If Δ = 0 the function has a real root and its graph intersects the x-axis at a single point that coincides with its vertex. In this case the function is said to have a double root.Value of cIn this case, for the quadratic equation -x²+3x+c=0 you know:
a= -1b= 3c= cIf the function has no real roots, the discriminant is less than zero (Δ <0). This is: b²- 4×a×c < 0
Substituting the corresponding values, you get:
3²- 4×(-1)×c < 0
Solving:
9 + 4×c < 0
4×c < -9
c< (-9)÷4
c< [tex]-\frac{9}{4}[/tex]
Finally, values of c less than[tex]-\frac{9}{4}[/tex] cause the quadratic equation -x²+3x+c=0 to have no real number solutions.
Learn more about the discriminant of a cuadratic function:
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3*(2)=6+5 3*(2+5)
Please help
Answer:
6 = 413 is a not true statement
Step-by-step explanation:
I've attached my work below
Hope it helps, Let me know if you have any questions/concerns !
Have a nice rest of your day :)
Type the correct answer in the box. Write your answer as a fraction, using / for the fraction bar. A jar of alphabet tiles contains 10 unique consonant tiles and 5 unique vowel tiles. If 5 tiles are picked randomly, the probability that 3 are consonants and 2 are vowels is .
Answer:
its the only way to get the monkey out of the cage
Step-by-step explanation:
u gave to free the monkes
a grocery gave a 25 discount on all items. if harry bought 248.50 worth of stuff. how much did he pay?
Answer: 186. 375
Step-by-step explanation:
25/100 × 248.50 /1 = 62.125
He paid 248.50 - 62.125
please help
3a-10pts
3b-10pts
3c-10pts
answer
Solved 3a. (10 pts) fa? x2 arctan (3.c) dx = 3b. (10 pts)
Step-by-step explanation:
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Neil and his mom are volunteering at an emergency relief center. To help prepare in case of a flood, they pack emergency kits with food and water. Neil puts 3 water bottles into each kit they pack. In all, he packs 150 water bottles. Which equation can you use to find the number of emergency kits k Neil packs?
The number of emergency kits that Neil packed in total for the 150 bottles is gotten as; k = 50 kits.
How to create equations?We are told that Neil puts 3 water bottles into each emergency kit packed.
Now, let the number of emergency kits be k.
Thus;
3k = 150
Division property of equality, we have;
3k/3 = 150/3
k = 50
Thus, the number of emergency kits that Neil packed is gotten as k = 50 kits.
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Can anyone solve this correctly?
Answer:
J. x = 1
Step-by-step explanation:
Write an equation based on the image of the scales.
3x + 6 = 9
Subtract 6.
3x = 3
Divide by 3.
x = 1
If you haven't learned to solve equations yet, the same thought process can be used with the scale image. The scales are balanced. To keep them balanced, remove 6 of the pieces marked "1" from BOTH sides of the scale. Then the scale will have three x's on one side and three "1"'s on the other side. So each x has to be one "1".
Brian can't decide which of three shirts he should wear to a party he could closes eyes and randomly pick a shirt or he could put the three shirts in a bag and then remove one either way the selection is not random Brian may end up making a biased choice in this activity you will find the probability of event using a simulation. Can you use playing cards to simulate the situation? explain
Answer:
Do know sorry I can help but maby
can someone please help me with #1, -a-b pleaseee
Answer:
A - Isosceles
B - 9
Step-by-step explanation:
(20x - 10)
factor out the 10 so now it is
10(2x - 1)
simplify 20x - 10
Which equation represents a line which is parallel to the line x-
8y = 48?
Answer:
y = 1/8x
Step-by-step explanation:
REMEBER: When the slopes are two lines are equal, they're parallel.Given Equation:
x - 8y = 48 ---> This equation is in standard form.⇒ -8y = -1x + 48
⇒ y = 1/8x + 6
As a result, the equation of the parallal line to the given equation x - 8y = 48 is:
⇒ y = 1/8x
Given: f(x)=x²+1 and f(g(x)) = 4x² + 4x +2. Find g(x).
Answer:
g(x)=2x+1
Step-by-step explanation:
(2x+1)^2+1=4x^2+4x+2
What’s ur opinion on that manga rate it out of 10
need some help with this question in the image
Cheers
Step-by-step explanation:
a) 24.7×52.3=1291.81
On rounding off to 3 significant digits we get
1290
b)
[tex] \sqrt{ {42}^{2} - {28}^{2} } [/tex]
[tex] \sqrt{1764 -784 } = \sqrt{980} [/tex]
=31.304951
On rounding off to 5 significant figures we get
=31.305
c)
[tex] \sqrt[3]{78} = 4.27265[/tex]
On rounding off to 2 significant figures we get
=4.3
Hence required answers
a)1290
b)31.305
c)4.3
I hope it helped you
help asap please,i don’t get the question
Answer:
see below
Step-by-step explanation:
I do not know what the 'given expression' is, bu the three UN-highlighted expressions in each question 1 and 2 are equivalent
Only the highlighted one is not equiv to the other three
2. Find the sum of the geometric series.
Answer:
324
Step-by-step explanation:
** The attachment shows an arithmetic sequence **
Sum of Arithmetic Series formula
[tex]S_n=\dfrac12n(a+l)[/tex]
where:
a = initial terml = last term[tex]a_n=2n-1[/tex]
[tex]\implies a_1=2(1)-1=1[/tex]
[tex]\implies a_{18}=2(18)-1=35[/tex]
[tex]\implies S_{18}=\dfrac12(18)(1+35)=324[/tex]
[tex]\\ \rm\Rrightarrow \sum^{18}_{n=1}2n-1[/tex]
[tex]\\ \rm\Rrightarrow 2(1)-1+2(2)-1\dots+2(18)-1[/tex]
a=2-1=1a_18=l=36-1=35So
[tex]\\ \rm\Rrightarrow S_n=\dfrac{n(a+l)}{2}[/tex]
[tex]\\ \rm\Rrightarrow S_n=\dfrac{18(1+35)}{2}=9(36)=324[/tex]