W'(-2 , 6), X'(-2 , 2), Y'(-6 , 2), Z'(-6 , 5).
This is the vertices after the 270° counterclockwise rotation.
What does counterclockwise rotation mean ?Counterclockwise is a turn to the left, opposite the direction of the hands on a clock.Given vertices,
W(-6,-2), X(-2,-2), Y(-2,-6), and Z(-5, -6).
Here we have to rotate 270°.
We know that,
Rotating a point 90° counterclockwise: (x, y) → (-y, x).
Rotating a point 180° counterclockwise: (x, y) → (-x, -y).
Rotating a point 270° counterclockwise: (x, y) → (y, -x).
So here we are rotating the figure 270°,
W(-6,-2)→ W'(-2 , 6)
X(-2,-2)→ X'(-2 , 2)
Y(-2,-6)→ Y'(-6 , 2)
Z(-5, -6)→ Z'(-6 , 5)
The vertices after rotating 270° counterclockwise about origin is:
W'(-2 , 6), X'(-2 , 2), Y'(-6 , 2), Z'(-6 , 5).
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PLS ANSWER FAST!!! A triangle has coordinates R(2,−1),S(3,3), and T(4,6). The triangle is dilated by a scale factor of 1.5 with the origin as the center of dilation. What is the x-coordinate of R′ in the dilated triangle?
The x-coordinate of point R′ after dilation is 3
How to determine the x-coordinate of R′ after dilation?The given parameters are:
R(2,−1),S(3,3), and T(4,6).
The scale factor of dilation is given as
Scale factor = 1.5
Mathematically, this transformation can be represented as
(x, y) = 1.5(x, y)
When represented as a function, we have
Image = 1.5 * Point
For point R, we have
R = (2, -1)
Substitute the equation Point = (2, -1) in the equation Image = 1.5 * Point
So, we have the following equation
R' = 1.5 * (2, -1)
Evaluate the product
R' = (3, -1.5)
Remove the y-coordinate
R'x = 3
Hence, the image of the x cooridnates is 3
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solve the following problems by writing a proportion. a) what is 70% of 4b) 5 is what percent of 20?
We have in a) that
[tex]\begin{gathered} 70\cdot\text{ }\frac{4}{100}\text{ = }\frac{\text{70 }\cdot\text{ 4}}{100} \\ =\text{ 2.8} \end{gathered}[/tex]So the answer for a) is 2.8
Now in b) we have that
[tex]5\cdot\text{ }\frac{100}{20}\text{ = 25}[/tex]So the answer for b) is 25%.
Paula measured the auditorium and made a scale drawing. The stage, which is 56 feet long in real life, is 84 inches long in the drawing. What scale did Paula use?
3 inches= blank feet
Based on the number of inches in the drawing and the number of feet in real life, the scale that Paula used was 3 inches = 2 feet
What scale did Paula use?The scale that Paula used was such that the stage was 56 feet long in real life but 84 inches long on the drawing.
The scale can therefore be shown by the ratio:
56 feet : 84 inches
If the number of inches is 3 then the number of feet in the scale would be:
56 feet : 84 inches
x feet : 3 inches
Cross-multiplying gives:
84x = 168
x = 168 / 84
x = 2 feet
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Hello I'm trying to figure out this math problem can anyone help me
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
Earnings:
January = $2350
February = january + $500
March = twice as much (february)
Step 02:
March's earnings:
February = $2350 + $500 = $2850
March = 2 * $2850 = $5700
The answer is:
She earned $5700 in March
Which answer is equivalent to
OA.
B. √
(4
OB.
C.
16
49
D.
16
49
3/16
349
√16
(49
?
A value that, when multiplied by itself, yields the number is the square root of a number.
The expression which is equivalent to [tex]$\frac{\sqrt{16}}{\sqrt{49}}$[/tex] is 16/49.
What is meant by square root?A radical symbol is used to represent a square root; the number or expression included within the radical symbol, designated by the letter a below, is known as the radicand.
A value that, when multiplied by itself, yields the number is the square root of a number. The radical symbol for the number's root is "√" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number.
Therefore, the correct answer is option A. [tex]$\frac{16}{49}$[/tex]
The complete question is:
Which answer is equivalent to [tex]$\frac{\sqrt{16}}{\sqrt{49}}$[/tex]?
A. [tex]$\frac{16}{49}$[/tex]
B. [tex]$\frac{\sqrt{4}}{\sqrt{7}}$[/tex]
c. [tex]$\sqrt{\frac{16}{49}}$[/tex]
D. [tex]$\frac{\sqrt[3]{16}}{\sqrt[3]{49}}$[/tex]
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what is 5x squared if x is 10
Answer: 2500
Step-by-step explanation: 5x10 = 50. 50x50 = 2500
Answer:
2500
Step-by-step explanation:
Simplify. I^61
(I is invisible number)
PLEASE HELP
After simplifying i^61 we get the answer is i
Define Complex number
Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labelled i sometimes known as the imaginary unit, and satisfying the equation i² = 1.
We have the given expression : i ^ 61
Rewrite it,
i ^ 61 as (i^4)^15 * i
we know, i² = -1
so, i ^ 4 = i² * i² = -1 * -1 = 1
so, put i ^ 4 value,
⇒1^15 * i
power 1 to the 15 is 1,
⇒1 * i
⇒ i
Hence, the answer is ' i '
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Nick is splitting 4 quarts of ice cream with 9 members of the team. If the ice cream is split evenly, how many cups will each person get? Explain1 quart equals _ pints, which equals _ cups, so 4 quarts equals _ cups. Dividing the ice cream among _ people means each gets _ cup(s)
ANSWER
[tex]\text{1}\frac{7}{9}\text{ cups}[/tex]EXPLANATION
Nick has 4 quarts of ice and he wants to split it with 9 members of the team.
To solve this, we have to convert quarts to cups. We have that:
1 quart = 2 pints
and
1 pint = 2 cups
This means that:
1 quart = 2 * 2 cups
1 quart = 4 cups
So, 4 quarts will be:
4 quarts = 4 * 4 cups
4 quarts = 16 cups
Therefore, dividing the ice cream among 9 people would mean that we have to divide 16 cups by 9 people.
That is:
[tex]\begin{gathered} \frac{16}{9} \\ =\text{ 1}\frac{7}{9}\text{ cups} \end{gathered}[/tex]The complete statement is:
1 quart equals 2 pints, which equals 4 cups, so 4 quarts equals 16 cups. Dividing the ice cream among 9 people means each gets 1 7/9 cup(s)
in a research report by richard h. weindruch of the ucla medical school, it is suggested that mice with an average life span of 34 months will live longer when 30% of the calories in their food are replaced by vitamins and protein. what hypotheses should we use to test this claim?
A declaration of anticipation or prediction that will be put to the test through study is called a research hypothesis.
How do you calculate hypothesis example?
Different forms of hypothesis testing are used to establish whether or not the null hypothesis can be rejected depending on the type and quantity of the evidence supplied.The following list of significant test statistics includes the formula for testing hypotheses:z = ¯¯¯x−μσ√n x ¯ − μ σ n . We already know that the z-score is 1.645 and the level of significance is 0.05.Let's compare it to the Z-test now.Because 0.744 1.645, the null hypothesis is true.So, the assertion made by the firm that the average lifespan of their batteries is 2.1 years is validated. The null hypothesis is typically represented in statistics by the letter H with the subscript "0" (zero), creating the symbol H0.It is said with the sound "H-null," "H-zero," or "H-nought."The alternative hypothesis also describes the observations that were determined by the non-random cause.H1 or Ha are used to symbolize it.The assertion that will be put to the test is the alternative to the null hypothesis.It is designated as H1 and contains the parameter's value that we believe to be plausible.The test statistic, which is a number calculated from the sample data, is used to determine whether to accept or reject the null hypothesis. An example of a straightforward hypothesis is that daily consumption of sugary beverages causes obesity.An illustration of a null hypothesis is that all lilies have the same number of petals.A person will feel less worn out if they receive 7 hours of sleep as opposed to sleeping fewer.To learn more about hypotheses refer
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Question 2 of 6
A truck rental company charges $50 plus $10 per hour. Identify a function that represents the total
charge for renting a truck for a certain number of hours. What is the value of the function for an input
of 4, and what does it represent?
Of(h) 50h + 10
=
$210, which is the total charge in dollars for renting 4 trucks
Of(h) = 50 - 10h
$40, which is the total charge in dollars for renting a truck for 4 hours
f(h) = 50h - 10
$190, which is the total charge in dollars for renting 4 trucks
Of(h) = 50+ 10h;
$90, which is the total charge in dollars for renting a truck for 4 hours. PLEASE HELP
Questiobn Translate and solve: 46 less than y is at least-184. Give your answer in interval notation. Provide your answer below:
Questiobn Translate and solve: 46 less than y is at least-184. Give your answer in interval notation.
Algebraic expression is equal to
[tex]y-46\ge184[/tex]Solve for y
[tex]\begin{gathered} y-46\ge184 \\ y\ge184+46 \\ y\ge230 \end{gathered}[/tex]The solution for y is the interval {230, infinite)only fill in the missing ones pls
The input and output is follows,
4 4 * 20 + 40
17 18 * 20 + `70
t t+1 * 20 + (t * 10)
What is patterns in math?The arithmetic pattern is also known as the algebraic pattern.A numerical pattern is a sequence of numbers that has been created based on a formula or rule called a pattern rule.Pattern rules can use one or more mathematical operations to describe the relationship between consecutive numbers in the pattern.How to Recognize Patterns :
Actively Look for PatternsOrganize the PiecesQuestion the DataVisualize the DataImagine New PossibilitiesTherefore,
From given question the first no is just next number of input that is input +1i.e.. input number is 2 then the first number of output is 2+1 = 3
Second number of output is constant 20.Third number of output is input value * 10i.e. . input number is 2 then the third number of output is 2 * 10 = 20
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PLEASE HELP FASR ILL GIVE BRAINLIEST IF CORRECT!!!!
Victor sells candles. The graph shows the number of candles sold and the
income from the sales. It represents a linear function.
Which statement best describes Victor's income from selling these candles?
A. He sells 4 candles per dollar.
B. He sells 7.5 candles per dollar.
C. He gets $4 per candle.
D. He gets $7.50 per candle.
Answer:
D
Step-by-step explanation:
22.5÷3 is 7.5 and 52.5÷3 is 7.5 as well
Money is y axis (x,y) and candles is x axis (x,y)
Kylie has ten chocolate squares.
His friend Allison takes three of them.
What fraction of chocolate did Kylie give his friend?
3/10ths if im not wrong
Use the frequency polygon to work out an estimate for the mean rounded to 1 DP
Considering the given frequency polygon, the mean of the distribution is of:
E(X) = 57.1.
Frequency polygonThe frequency polygon works similarly to an histogram, giving the number of times that each observation happens, with the dot being placed at the center of each interval.
Considering the given polygon, the absolute frequencies are given as follows:
X = 40: 10.X = 52.5: 7.X = 65: 8.X = 77.5: 2.X = 90: 3.The sum of the absolute frequencies is given as follows:
10 + 7 + 8 + 2 + 3 = 30.
Hence the relative frequencies = probabilities are given as follows:
P(X = 40) = 10/30 = 1/3 = 0.3333.P(X = 52.5) = 7/30 = 0.2333.P(X = 65) = 8/30 = 0.2667.P(X = 77.5) = 2/30 = 0.0667.P(X = 90) = 3/30 = 0.1.The mean is given by the sum of each outcome multiplied by it's probability, hence:
E(X) = 40 x 0.3333 + 52.5 x 0.2333 + 65 x 0.2667 + 77.5 x 0.0667 + 90 x 0.1 = 57.1.
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Directions are with the pic below. Please help with question #1.
Solution:
Let each cubic block be represented with x
Let each spherical block be represented with y
Let each cylindrical block be represented with z
For A,
3x + y = 2y + z
For B,
3x = 5y
For c,
We want to find 3x + 3y
From
3x + y = 2y + z
3x +y -2y =z
3x-y = z-----------------------(m)
From B,
3x = 5y
Substitute 3x = 5y into (m) above
3x-y = z
5y-y = z
4y = z----------------------------------(b)
From C,
3x + 3y = 5y + 3y = 8y
3x + 3y = 2(4y)
3x + 3y = 2z
Recall, z = cylindrical block
The two blocks that will balance C is cylindrical block
A Large bag contains 7/12 pound of nails. How many 1/4 pound bags can be filled with this amount of nails?
The number of 1/4 pound bags that can be filled with this amount of nails is 2 1/3 bags.
How to calculate the fraction?The large bag contains 7/12 pound of nails.
We also want to fill them into 1/4 pounds of bags. The number of bags needed will be calculated through division. This will be:
= Amount in large bags / Smaller bags
= 7/12 ÷ 1/4
= 7/12 × 4/1
= 28/12
= 2 1/3
Therefore, 2 1/3 1/4 bags are required
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Points A(-1, 2) and B(5,8) are the endpoints of AB. What are the coordinates of point C on AB such that AC is 2/3 the length of AB
The coordinates of point C on AB such that AC is 2/3 the length of AB is (2,0)
What is Pythagoras' Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).
To find out how long AC is, we must first find the length of AB.
According to Pythagoras’ theorem,
[tex]a^2 + b^2 = c^2[/tex].
Thus [tex]4^2 + 6^2 = c^2[/tex].
[tex]16 + 36 = c^2[/tex].
The square root of this is;
c = √52.
AB is 7.21 units long.
2/3 of 7.21 is 4.8
The coordinate that fits this is (2,0).
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can you explain each step please for i can write it on a paper along with you
The two groups are given one is those who are studied and other is those who are not studied.
Studied - 88,100,94,79,92,100,95,83,89,99,100,91,89,95,100,93,96,84.
Arrange in order.
79, 83, 84, 88, 89, 89, 91, 92, 93, 94, 95, 95, 96, 99, 100, 100, 100, 100
The mean of this group is
[tex]\frac{88+100+94+79+92+100+95+83+89+99+100+91+89+95+100+93+96+84}{18}[/tex][tex]\frac{1667}{18}=92.6[/tex]The mean is 92.6.
The median of this group is
Use the median formula for even
[tex]m=\frac{(\frac{n}{2})^{th}+(\frac{n}{2}+1)^{th}^{}}{2}[/tex]Substitute the value of n =18
[tex]m=\frac{(\frac{18}{2})^{th}+(\frac{18}{2}+1)^{th}^{}}{2}=\frac{9^{th}+10^{th}^{}}{2}[/tex][tex]m=\frac{93+94}{2}=93.5[/tex]The median is 93.5.
The mode of this group is 100 as it is appears 3 times .
The another group is not studied group.
Not studied - 82,72,45,91,58,83,65,87,90,77,73,89.
Arrange in order-
45, 58, 65, 72, 73, 77, 82, 83, 87, 89, 90, 91
The mean is determined as
[tex]\frac{82+72+45+91+58+83+65+87+90+77+73+89}{12}=\frac{912}{12}=76[/tex]The median is determined as
[tex]m=\frac{(\frac{n}{2})^{th}+(\frac{n}{2}+1)^{th}}{2}[/tex]Substitute n=12.
[tex]m=\frac{(\frac{12}{2})^{th}+(\frac{12}{2}+1)^{th}^{}}{2}=\frac{6^{th}+7^{th}}{2}=\frac{77+82}{2}=79.5[/tex]There is no mode.
So, from the all the data given.
The mean of the group that studied is over 15 percent points higher than the mean of the group that did not studied.
[tex]92.61-76=16.61[/tex]The median of the group that did not studied is less than 80.
In general , those students that studied scored much higher than those students that did not study.
The correct options are a , c and e.
write the equation of a line through ( 3, 1), parallel to y = 2/3x + 1.
Answer:
y = 2/3 x - 1
Step-by-step explanation:
Parallel slopes are equal.
y = mx + b
m = 2/3
x = 3 Use the x and y given in the point (3,1)
y = 1
Solve for b the y-intercept
y = mx + b
1 = 2/3(3) + b
1 = 2 + b Subtract 2 from both sides
-1 = b
y= mx +b
y = 2/3x -1
The value of 4 + n when n = 17
Answer:
21Step-by-step explanation:
The value of 4 + n when n = 17
4 + n =
replace n with 174 + 17 = 21
15yards to 18 yard increase or decrease
Answer:
Increase
Step-by-step explanation:
You start at 15 yards then proceed to MOVE UP(Increase) 3 more yards getting you to 18.
Answer:
increase
Step-by-step explanation:
because your going 3 more yards on a number line you would travel right
Please help me write a 1 page story explaining the identified above.
Blaise Pascal and Pierre de Fermat, two eminent mathematicians, exchanged correspondence in the middle of the 17th century that provided the groundwork for probability and altered how scientists and mathematicians regarded uncertainty and risk.
Who established the odds for dice games in 1560?The issue with the Duke of Tuscany (1560)
The Duke of Tuscany was a constant competitor. He had noticed that number 10 frequently occurred over number 9 in a game where three dice are tossed and the points are added. De Duke, however, asserts that there are six different ways to generate both figures.
What dice game is the oldest?Pyramidal dice (four-sided), which date back to Summer in the third millennium bce, are just as old as cubical dice. These dice were discovered alongside the so-called Royal Game of Ur, one of the oldest complete board games ever uncovered.
In his book A Pocket Guide to Dice & Dice Games, Keith Souter develops the Sir Farkle theory and fixes Iceland as the setting and the year as 1492.
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This question has two parts. First, answer Part A. Then, answer Part B.
part B :
The length of the incline of the ramp will be [h] = 12.0415 ft. The estimated length of the incline would be - 12ft
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically, we can write -
h² = p² + b²
Given is the installation of wheelchair ramp such that the ramp should have a base of 12 ft and height of 1 ft long.
[A]
From the data given, we can consider the ramp construction as right angled triangle. We can write -
base [b] = 12 ft
height [p] = 1 ft
Using the Pythagoras theorem -
h² = (12 x 12) + (1 x 1)
h² = 144 + 1
h = √145
h = 12.0415
[B]
For estimating the length of the incline, we will round it off to the exact value. The rounding of length for zero digits after decimal will give the desired result as 12 ft
Therefore, the exact length of the incline of the ramp will be [h] = 12.0415 ft. The estimated length of the incline would be - 12ft
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[ This answer is the answer of part B of the question whose part A is attached with the answer.]
my tutors keep getting cut off due to connection and i need help!!
Let:
(x1,y1) = (0,4)
(x2,y2) = (4,0)
The slope m is:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1}=\frac{0-4}{4-0}=\frac{-4}{4}=-1 \\ \end{gathered}[/tex]Using the point slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-4=-1(x-0) \\ y=-x+4 \\ \text{ In standard form:} \\ x+y=4 \end{gathered}[/tex]Jim's backyard is a rectangular that is 15 5/6 yards long and 10 2/5 yards wide. Jim buys sod in pieces that are 1 1/3 yards long and 1 1/3 yards wide. How many pieces of sod will Jim need to but to cover his backyard with sod.
The number of pieces of sod will Jim need to cover his backyard with sod is 4 pieces.
What is termed as the unitary method?The unitary method is a process that determines the value of a single unit from the value of multiple units, as well as the value of multiple units from of the value of a single unit.For the given question;
The backyard of Jim is in the shape of the rectangle.
The dimension of the yards are in given in mixed fraction, convert that in improper fraction as;
Length : 15 5/6 yards = 95/6 yardsWidth : 10 2/5 yards = 52/5 yardsThe area of the rectangle yard is;
Area = length x width
Area = 95/6 x 52/5
Area = 76 sq. yd.
The dimension of the sod in pieces are -
Length : 1 1/3 yardsWidth : 1 1/3 yardsArea of each sod is -
Area = length x width
Area = 11/3 x 11/3
Area = 121/6 sq. yd.
Thus, the total umber of the sods required for the yard is;
Number = 76 sq. yd. / 121/6 sq. yd.
Number = 3.76 ≈ 4
Thus, the number of pieces of sod will Jim need to cover his backyard with sod is 4 pieces.
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what is 1656 divided by 16
Answer:
103.5
Step-by-step explanation:
Answer:
103.5
Step-by-step explanation:
The question is,
→ what is 1656 divided by 16?
Forming as problem,
→ 1656 ÷ 16
Let's solve the problem,
→ 1656 ÷ 16
→ 103.5
Thus, the answer is 103.5.
12. Troy made 5 out of 7 jumps on his dirt bike. What percentage ofjumps did he make?62%57%85%71%
Question: Troy made 5 out of 7 jumps on his dirt bike. What percentage of jumps did he make?
Answer:
Note that, the 7 jumps are 100 percent of the jumps. Therefore, we make a rule of three, that is:
that is equivalent to say the following equation:
percentage of jumps = (5x 100%) ÷ 7 = 500% ÷ 7 = 71.42 = 71,3
that is, approximately 71 %
HELP PLEASE!!!!! i'M GIVING 30 POINTS
The intensity of the dishwasher will be 44.44 times the maximum intensity.
What is intensity of sound?
Sound intensity, also known as acoustic intensity, is defined as the power carried by sound waves per unit area in a direction perpendicular to that area. Mathematically, we can write the intensity of sound as -
[tex]\mathrm {I} =2\pi ^{2}\nu ^{2}\delta ^{2}\rho c[/tex]
Given is the sound intensity as measured in decibels and its measurement for a dishwasher is 37 decibels.
The given formula is -
db = 10 log(I/I₀)
Substituting the values, we get -
37 = 10 log(I/I₀)
log(I/I₀) = (37/10)
log(I/I₀) = (37/10)
(I/I₀) = e ^ (37/10)
I/I₀ = 40.44
I = 40.44I₀
Therefore, the intensity of the dishwasher will be 44.44 times the maximum intensity.
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Please help me
I have a math HW that needs to be solved asap but I have lots of things on my hands right now. Thank you
For first, ∠J=55°, ∠L=55°, ∠K=70°. For second, ∠T=34°, ∠S=34°, ∠R=112°,
For third, AB=5, BC=10, AC=10. For fourth, XY=29, XZ=48, YZ=29
What is isosceles triangle?An isosceles triangle definition states it as a polygon that consists of two equal sides, two equal angles, three edges, three vertices and the sum of internal angles of a triangle equal to 180°.
For 1,
in ΔKJL,
KJ=KL
So,
∠J=∠L
∠J=180-125
∠J=55°
∠L=55°
∠K=180-(55+55)
∠K=70°
For 2,
in ΔRST,
RS=RT
So,
∠T=∠S=3x-2
3x-2+3x-2+9x+4=180°
15x=180°
x=12
∠T=3x-2=34°
∠S=3x-2=34°
∠R=9x+4=112°
For 3,
in ΔABC,
AC=BC
So,
3x+4=10
3x=6
x=2
AB=x+3=5
BC=10
AC=3x+4=10
For 4,
in ΔXYZ,
XY=YZ
So,
4x+1=29
4x=28
x=7
XY=4x+1=29
XZ=7x-1=48
YZ=29
For first, ∠J=55°, ∠L=55°, ∠K=70°.
For second, ∠T=34°, ∠S=34°, ∠R=112°,
For third, AB=5, BC=10, AC=10.
For fourth, XY=29, XZ=48, YZ=29
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