help me please. Find the values of x and y that make these triangles congruent by the HL Theorum.
A. x=2, y=1
B. x=3, y=2
C. x=1, y=2
D. x=2, y=3
Answers
well it means that 3y = x + 3, and that y + 1 = x, when does that happen anyway? let's see,
[tex]\bf \begin{cases} 3y=x+3\\ y+1=\boxed{x} \end{cases}\implies 3y=\boxed{y+1}+3\implies 3y=y+4 \\\\\\ 2y=4\implies y=\cfrac{4}{2}\implies y=2\\\\ -------------------------------\\\\ \textit{and since we know that }y+1 =x\implies (2)+1=x\implies 3=x[/tex]
Related Questions
If 2a+3b=12 and ab=6 find the value of 8a^3+27b^3
Answers
((4a^2 - 6ab + 9b^2) + 18ab) = 144
4a^2 - 6ab + 9b^2 = 144 - 18 ab
8a^3 + 27b^3 = (2a + 3b)(4a^2 - 6ab + 9b^2)
8a^3 + 27b^3 = (2a + 3b)*(144 - 18ab)
8a^3 + 27b^3 = 12 * (144 - 18ab)
= 12 * ( 144 - 18*6) since ab = 6
= 12 * (144 - 108)
= 12 * (36)
= 432 <<<<==== answer
Find the slope of a parallel line to 5x+2y=6
Answers
Answer: [tex]\dfrac{-5}{2}[/tex]
Step-by-step explanation:
We know that equation in intercept form is given by :-
[tex]y=mx+c[/tex] , where m is the slope of the line {Coefficient of x}
The given equation of a line : [tex]5x+2y=6[/tex]
First rewrite the given equation in intercept form , we get
[tex]2y=6-5x\\\\\Rightarrow\ y=\dfrac{1}{2}(6-5x)\\\\\Rightarrow\ y=\dfrac{-5}{2}x+\dfrac{6}{2}\\\\\Rightarrow\ y=\dfrac{-5}{2}x+3[/tex]
Comparing to the general intercept form , we have , the slope of the line = [tex]\dfrac{-5}{2}[/tex]
Since the slopes of two parallel lines is equal.
Therefore, the slope of a parallel line to [tex]5x+2y=6[/tex] : [tex]\dfrac{-5}{2}[/tex]
Find the missing value to the nearest hundredth cos___= 7/18
Answers
cos x=7/18
x=arc cos (7/18)-----> using a calculator-------> x=67.11°-----> x=1.17 radians
the answer is
x=67.11° or x=1.17 radians
The missing value to the nearest hundredth using inverse trigonometric function is 67.11°
Let us say
Cos x = 7/18
x will be the inverse of cosine of (7/18)
What is an inverse trigonometric function?The inverse trigonometric functions are the inverse functions of the trigonometric functions and are used to obtain an angle from any of the angle's trigonometric ratios.
x = cos⁻¹ (7/18)
x = 67.11°
Hence, the missing value to the nearest hundredth is 67.11°.
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peter makes $6 per hour doing yard work plus $10 every house if pter does yard work for 6 houses and receives a paycheck for $210 how many hours did he work
Answers
The answer is 25 hours.
After calculating Peter's earnings from working on 6 houses, the remaining amount from his total paycheck indicates that he worked for 25 hours at his hourly wage of $6.
To determine how many hours Peter worked when he received a paycheck for $210, we need to consider his earnings per house and his hourly wage. Peter makes $6 per hour for doing yard work plus $10 for every house he does work on.
First, we calculate the total earnings from the houses he worked on. Since he did yard work for 6 houses, we multiply 6 houses by $10 per house:
6 houses times $10 per house = $60
Now, subtract the total earnings from houses from his total paycheck to find out how much he earned from hourly wages:
$210 (total paycheck) - $60 (earnings from houses) = $150 (earnings from hourly wage)
$150 / $6 per hour = 25 hours
So, Peter worked 25 hours doing yard work.
Brainliest + 15 points. Help please? Who's up for the challenge?
Answers
x - y = -3 2x + y = 14
Solve using substitution.
First, isolate one variable.
x + y = 5
x = 5 - y
Then, plug its expression into the other equation and solve.
x - y = -3
5 - y - y = -3
5 - 2y = -3
-2y = -8
y = 4
Next, plug your new value into one of the original equations to solve for the second variable.
x + y = 5
x + 4 = 5
x = 1
Finally, check work with substitution.
x + y = 5 => 1 + 4 = 5 <--True
x - y = -3 => 1 - 4 = -3 <--True
Next.
y = 3x - 1
2x + y = 14
2x + y = 14
2x + (3x - 1) = 14
2x + 3x - 1 = 14
5x - 1 = 14
5x = 15
x = 3
y = 3x - 1
y = 3(3) - 1
y = 9 -1
y = 8
y = 3x - 1 => 8 = 3(3) - 1 => 8 = 9 - 1 <--True
2x + y = 14 => 2(3) + 8 = 14 => 6 + 8 = 14 <--True
Answer:
4.
x = 1
y = 4
5.
x = 3
y = 8
I have a math Brainliest reward
Answers
2. is gonna be D. a special endorsement is when someone has insufficient funds but it isn't there fault and will lead into giving there money BACK that was lost( this is one of the reasons the country is in dept.
3. is gonna be A. When you take the amount of money you have in your account and you go over that limit then you will be 1.Charged for overdrawing and 2. Your card will be frozen.
4. is gonna be D. You will have the right to change how much you can spend a day. (minimum balance)
Check my answer?
Given the proportion a/b = 8/15, which ratio completes the equivalent proportion a/8 = ?
My answer: 15/b
@KirbyLegs
Answers
When you solve a proportion, you cross multiply. You can have the same proportion just by interchanging 8 and b
a/8 = b / 15 When you cross multiply, you get
15a = 8b Try the given proportion to see what happens
1a 2a 3b 4d 5b
Which of the following statements best describes the graph of x + y = 4?
It is a line which intersects the x-axis at (4, 4).
It is a line which intersects the y-axis at (4, 4).
It is a line joining the points whose x- and y-coordinates add up to 8.
It is a line joining the points whose x- and y-coordinates add up to 4.
Answers
For the first one the y intercept is when x = 0. The point would be 0,4
The second one gives a point of (4,0)
The third one is nonsense. (4,4) is not on this line.
Which expressions are polynomials?
Select each correct answer.
x – 1
5x²-√x
6+p
8x-z³
Answers
A square root is the same as a (1/2) power. The variables in a polynomial must all have powers that are positive integers.
Answer:
5x²-√x
Step-by-step explanation:
1)6 +p
2) x-1
3) 8x-z3
4) 5x²-√x --> has a root so it is not a polynomial
Someone please help me with this, i'm a little confused :(
A guy-wire is attached to a pole for support. If the angle of elevation to the pole is 67 and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the length of the guy wire (round to 2 decimal places)?
A) 58.15 feet
B) 143.40 feet
C) 148.83 feet
D) 350.62 feet
Answers
If lines l and m are parallel, then ∠2 and ∠3 are _______ angles.
alternate interior
corresponding
alternate exterior
same-side-interior
Answers
Answer:
B) Corresponding
Step-by-step explanation:
Hello! The answer to this question is that <2 and <3 are corresponding angles. If you know the definition of corresponding angles and how they appear on a figure such as this, you should have no problem answering these problems in the future. Hope this comes to your help!
Why is the standard deviation preferable to the range as a measure of variation? select the correct answer below.
a. the standard deviation is preferable to the range as a measure of variation because the standard deviation takes into account all of the observations, whereas the range considers only the largest and smallest ones.
b. the standard deviation is preferable to the range as a measure of variation because the standard deviation is resistant to outliers, whereas the range is not.
c. the standard deviation is preferable to the range as a measure of variation because it is optimal when the median is used as the center of measure.
d. the standard deviation is preferable to the range as a measure of variation because the standard deviation is always smaller than the range?
Answers
Answer:
Option a is right.
Step-by-step explanation:
Both standard deviation and range are used as measures of dispersion. These show the deviations of the data within.
While range is maximum -minimum, the std deviation is the square root of variance and variance is the average of the sum of squares of each entry from the mean.
While range depends only on max and min the std deviation depends on each entry of the sample. Hence std deviation is a better measure.
a. the standard deviation is preferable to the range as a measure of variation because the standard deviation takes into account all of the observations, whereas the range considers only the largest and smallest ones.
Would be glad if you answer my question!
Answers
With negative exponents, you make them into fractions to get rid of the negative.
[tex] 3^{-2} = \frac{1}{3^2} [/tex]
Now, just square the bottom.
[tex] \frac{1}{9} = \frac{1}{3^2} [/tex]
Next one.
[tex] 2^{-2} = \frac{1}{2^2} [/tex]
Now, square the bottom.
[tex] \frac{1}{4} = \frac{1}{2^2} [/tex]
Now, we have:
[tex] \frac{1}{9} + \frac{1}{4} [/tex]
Make a combine denominator of 36.
[tex] \frac{1}{9} = \frac{4}{36} \\\\\frac{1}{4} = \frac{9}{36} [/tex]
Now, add them together.
[tex] =\frac{13}{36} [/tex]
I hope this helps!
~kaikers
2. Given the equation 2x – 3y + 4z =12, find the three intercepts for this plane and graph it below. Show your work. Please view the video “how to submit a part 2” for help on how to graph. (2 point for each intercept, 3 for the graph.) Answer:
Answers
x-intercept:
To get x-intercept we let y=0 and z=0. The substitute these values in our equations follows:
2x+3(0)+4(0)=12
2x=12
hence:
x=12/2
x=6
therefore the x-intercept will be at point (6,0,0)
y-intercept:
To calculate for y-intercept we let x=0 and z=0 and substitute the values in the equation, here we shall have:
2(0)-3y+4(0)=12
solving for y we get:
-3y=12
hence:
y=12/(-3)
y=-4
therefore the y-intercept is at point (0,-4,0)
z-intercept:
To get the z-intercept we let x=0 and y=0, the we substitute the values in the equation as follows:
2(0)-3(0)+4z=12
solving for z we get:
4z=12
z=12/4
z=3
hence the z-intercept is at (0,0,3)
HELP FAST PLEASE!!
Martin simplified the composed function f(x)=sin(arctan x). His work is shown below. Step 1: f(x)=sinA, where A=arctan x and x = tanA
Step 2: tanA= opp/adj=x/1
Step 3: hypotenuse= square root of 1^2-x^2= square root of 1-x^2
Step 4: sinA=opp/hyp=x/squareroot 1-x^2
In which step did Martin make is first error?
Answers
Step 1:
f (x) = sinA,
where
A = arctan x
and
x = tanA
step 1 it's OK
Step 2:
tanA = opp / adj = x / 1
step 2 it's OK
Step 3:
hypotenuse = square root of 1 ^ 2-x ^ 2 = square root of 1-x ^ 2
step 3 it's NOT OK
The correct form in this case is:
hypotenuse = square root of 1 ^ 2 + x ^ 2 = square root of 1 + x ^ 2
Answer:
Martin did make his first mistake in Step 3.
The largest doll is 12 inches tall. The height of each of the other dolls is
7
10
710
the height of the next larger doll. Write an expression involving a power for the height of the smallest doll. Then evaluate the expression to find the height of the smallest doll to the nearest tenth of an inch.
Answers
To get the next smallest doll (the second) we multiply 12 by 7/10.
To get the one after that (the third) we multiply 12 by 7/10 by 7/10
To get the one after that (the fourth) we multiply 12 by 7/10 by 7/10 by 7/10
and so on...
The height of each doll after the first will be multiplied by (7/10) raised to a power. Let's call n the number of the doll (first, second, third, ...). It might be easier to determine the power if we write it like this:
First Doll -> n =1 -> height = 12
Second Doll -> n=2 -> height = [tex](12)( \frac{7}{10}) ^{1} [/tex]
Third Doll -> n = 3 -> height = [tex](12)( \frac{7}{10}) ^{2} [/tex]
Fourth Doll -> n=4 -> height = [tex](12)( \frac{7}{10}) ^{3} [/tex]
Notice that the exponent of the fraction (7/10) is always one less than the value of n. This even works for the first doll. It's height is [tex](12)( \frac{7}{10}) ^{0} [/tex]
Thus, we have an expression for the height of the nth doll and it is [tex](12)( \frac{7}{10}) ^{n-1} [/tex]
The height of any doll can be found using this formula. Whatever the smallest doll is (the 10th, 27th, 99th, etc.) just use that number for n. Since we arrive at each height by multiplying the prior by (7/10) the heights form a geometric sequence.
Answer: with the problem you can see that
Smallest is 4.1 inches
Expression is 12 multiply by (7/10) to the power of 3
Answer:
Smallest is 4.1 inches
Expression is 12 multiply by (7/10) to the power of
Carol payed 271$ to rent a car for 4 days. What was the rate, r, per day to rent the car
Answers
15 points and brainliest for CORRECT answer.
Given: ABCD is a trapezoid,
AD = 10, BC = 8,
CK - altitude
Area of ∆ACD = 30.
Find: Area of ABCD
Answers
30=1/2(10)h
30=5h
Divide each side by 5:
30/5=5h/5
6=h
The height of the triangle is also the height of the trapezoid. We can now find the area of the trapezoid. The formula we need is A=1/2(B+b)h. Substituting our numbers in, we have:
A=1/2(10+8)(6)=1/2(18)(6)=54
The area of the trapezoid is 54.
What is the recursive rule for the sequence? −7.4, −21.2, −35, −48.8, −62.6
Answers
Answer:
[tex]a_n = a_{n-1}-13.8[/tex]
Step-by-step explanation:
The recursive rule for the arithmetic sequence is given by:
[tex]a_n = a_{n-1}+d[/tex] .....[1]
where, d is the common difference of two consecutive terms.
Given the sequence:
−7.4, −21.2, −35, −48.8, −62.6
This is an arithmetic sequence
Here, first term[tex](a_1)[/tex] = -7.4 and d = -13.8
Since,
-21.2+7.4 = -13.8,
-35+21.2 = -13.8 ans so on...
Substitute the given value in [1] we have;
[tex]a_n = a_{n-1}+(-13.8)[/tex]
⇒[tex]a_n = a_{n-1}-13.8[/tex]
Therefore, the recursive rule for the sequence is, [tex]a_n = a_{n-1}-13.8[/tex] and [tex]a_1[/tex]= -7.4
The recursive rule for the sequence is [tex]\rm a_{n} = a_{n-1} -13.8[/tex] and [tex]\rm a_{1}[/tex] = -7.4.
What is the recursive rule?The recursive rule refers to the first term of the sequence and describe
the relation to the preceding term with the recursive equation.
The recursive formula for the arithmetic sequence is as follows
[tex]\rm a_{n} = a_{n-1} + d[/tex]
where [tex]\rm a_{n}[/tex] is the nth term and d is a common difference
The arithmetic sequence is given as
−7.4, −21.2, −35, −48.8, −62.6
[tex]\rm a_{1}[/tex] = -7.4 (first term)
d = -21.2+7.4 = -13.8,
d = -35+21.2 = -13.8
Substitute the given value, we get
[tex]\rm a_{n} = a_{n-1} + d[/tex]
[tex]\rm a_{n} = a_{n-1} -13.8[/tex]
Hence, the recursive rule for the sequence is [tex]\rm a_{n} = a_{n-1} -13.8[/tex] and [tex]\rm a_{1}[/tex] = -7.4.
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Di sediakan angka 4,5,6,7,8 dan huruf e,s,
f. Bila tidak boleh ada angka dan huruf yg sama, maka banyaknya.plat nomer yg dapat dibuat adalah
Answers
PLEASE HELPPPPPP
Photo necessities produces camera cases. They have found that the cost , c (x) of making x camera cases is a quadratic function in terms of x.
The company also discovered that it cost $45 to produce 3 camera cases $257 to produce 7 camera cases and $792 to produce 12 camera cases.
Find the total cost producing 1 camera case
Answers
In this case the points will be:
(3. 4. 5)
(7, 257)
(12, 792)
The equation of the quadratic function in this case will be:
c (x) = 6x ^ 2 - 7x + 12
Therefore for x = 1 we have:
c (1) = 6 * (1) ^ 2 - 7 * (1) + 12
c (1) = 11 $
Answer:
Total cost producing 1 camera case is:
c (1) = 11 $
The total cost producing 1 camera case is:
$ 11
Step-by-step explanation:Let the quadratic function be:
[tex]c(x)=ax^2+bx+c[/tex]
Now, c(3)=45
This means:
[tex]9a+3b+c=45------------(1)[/tex]
c(7)=257
This means that:
[tex]49a+7b+c=257----------------(2)[/tex]
and c(12)=792
This imply:
[tex]144a+12b+c=792-------------------(3)[/tex]
On subtracting first equation from second we get:
[tex]40a+4b=212------------(4)[/tex]
and on subtracting second equation from third we get:
[tex]95a+5b=535-----------(5)[/tex]
Now on multiplying equation (4) by 5 and equation (5) by 4 and subtracting both equation we get:
a=6
Putting value of a in equation (4) we get:
b= -7
and putting the value of a and b in equation (1) we get:
c=12
Hence, the cost function is:
[tex]c(x)=6x^2-7x+12[/tex]
Now, the cost of producing 1 camera will be the value of c(x) when x=1
i.e.
[tex]c(1)=6-7+12\\\\\\c(1)=11[/tex]
Hence, the answer is:
$ 11
The radius of a sphere is 6 inches. Find the length of a chord connecting two perpendicular radii
Answers
6 sqrt 2
Answer:
Hence, the length of the chord joining two perpendicular radii is:
6√2 inches.
Step-by-step explanation:
Let r denote the radius of circle.
i.e. r=6 inches.
Let AB be the chord that connects two perpendicular radii i.e. OA and OB whose lengths are given to be 6 inches.
We can apply pythagorean theorem to find the length of the chord.
[tex]AB^2=OA^2+OB^2\\\\AB^2=6^2+6^2\\\\AB^2=36+36\\\\AB^2=72\\\\AB=\sqrt{72}\\\\AB=6\sqrt{2}[/tex].
Hence, the length of a chord connecting two perpendicular radii is:
6√2 inches.
Elizabeth has two gardens in her yard. The first garden is 8 feet long and 6 feet wide. The second garden is half the length of the first garden. the area of the second garden is twice the area of the first garden. What is the area of the second garden?
Answers
Answer:
the answer is B: 128 divided by 8 equals 16
Step-by-step explanation:I know this becasue to check ur answer after doing multiplication you must do division
multiplication-->division
division-->multiplication
subtraction-->addition
addition-->subtraction
maya has 15 stickers . she places them on a page in rows of 5 . there are 2 flowers and 3 hearts in each row . how many hearts are on the page ? Draw to solve the problem . Write how many hearts are on the page
Answers
Before you make any payments to the organization handling your DMP (debt management plan) what should you do?
Answers
Answer:
" A DMP allows you to deposit a set amount of money with a credit counseling organization each month, which is then strategically dispersed to your various creditors "
" DMPs are designed to help consumers work off their debt as quickly as possible by leaving these decisions largely to credit counseling professionals "
Before sending monthly payments to the organization handling your DMP, confirm with your creditors that they have in fact accepted the plan.
Before you make any payments to the organization handling your DMP (debt management plan) you should confirm with your creditors that they have accepted the plan.
What is Debt Management Plan?A Debt Management Plan is a laid-out framework for settling debts that is coordinated by a credit counseling organization. A certain amount of money is deposited with these organizations that help the debtor to offset his bills in a strategic manner.
So, before making any payments to the organization handling your DMP (debt management plan) you should confirm with your creditors that the plan for repayment is acceptable by them.
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A rugby player passes the ball 7.75 m across the field, where it is caught at the same height as it left his hand. At what angle was the ball thrown if its initial speed was 12.0 m/s, assuming that the smaller of the two possible angles was used?
Answers
(a)(b)range x=V²sin (2θ)/g
7.75m=(12 m/s)sin (2θ)/ 9.8m/s²
sin (2θ)=0.5274
hence:
2θ=arcsin 0.5274=31.83°
or 2θ=180-31.83=148.17°
hence the smaller angle will be:
31.83/2=15.915~15.92°
and the larger angle will be:
148.17/2=74.085°
The smaller of the two possible angles used is;
θ = 15.92°.
We are given;
Range of pass; R = 7.75 m
Speed; u = 12 m/s
Formula for range is;
R = [u²sin (2θ)]/g
Where; θ is the angle at which the ball was thrown.
Thus;
7.75 = 12² × (sin(2θ))/9.8
(sin(2θ)) = (7.75 × 9.8)/12²
(sin(2θ)) = 0.5274
2θ = sin^(0.5274)
2θ = 31.83
θ = 31.83/2
θ = 15.92°
Now, if we assume that this angle is to the vertical, it means the angle to the horizontal is;
90 - 15.92 = 74.08°
In conclusion, the two possible angles are 15.92° and 74.08°.
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Tyler has a rectangular garden that measures 10 m wide by 13 m long. he wants to increase the area to 208 m2 by increasing the width and length by the same amount. what will be the length (longer dimension) of the new garden?
a. 14 m wide
b. 15 m wide
c. 16 m wide
d. 17 m wide
Answers
(10+3)(13+3)=13*16=208
The length of the new garden is the 13+3 which is 16.
So c should be the right answer.
1. Sketch and/or explain the evidence you created for the Pythagorean Theorem. Be sure to explain how each part related to the Pythagorean Theorem.
Answers
Answer:
u see the formula for the Pythagorean theorem is a^2 + b^2 = c^2 i hope this helps please mark as brainliest have a good day!!! :D Bye
Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Use the domain {, 1, 2, 4, 8, 16} and plot the points on the graph that would best satisfy the equation y = log2x.
Answers
I will use these properties:
log base m of m^n = n,
Which written with the math editor is:
[tex]log_{m}m^n=n[/tex]
1) x = 1
1 = 2^0 =>
[tex]log_{2}1=log_{2}2^0=0[/tex]
2) x = 2
2 = 2^1 =>
[tex]log_{2}2 = log_{2}2^1=1[/tex]
3) x = 4
4 = 2^2 =>
[tex]log_{2}4=log_22^2=2[/tex]
4) x = 8
8 = 2^3 =>
[tex]log_28=log_22^3=3[/tex]
5) x = 12
16 = 2^4 =>
[tex]log_216=log_22^4=4[/tex]
6) Now you can plot the points on the graph. The points that you have to plot are:
(1,0)
(2,1)
(4,2)
(8,3)
(16,4)
What is the area of a square with sides that are 3 2/5 in long?