Answers
Answer: The triangles are congruent by the HL theorem
HL = hypotenuse leg
======================================================
Explanation:
Through the segment addition postulate, we can say:
WZ = WT+TZ
YT = TZ+ZY
Notice how both WZ and YT have TZ as part of their segments.
Since WZ and YT are the same length, we can then say,
WZ = YT
WT+TZ = TZ+ZY
WT = ZY
I used substitution for the second step.
The last step is where I subtracted TZ from both sides, and they canceled out.
---------------------
We have the following info:
WT = ZY (just found)AT = UZ (given)angle AWT = angle UYZ (given)Normally, the conclusion from here would be "not enough info" because this is a SSA case. Note how the angles are not between the congruent sides. So we wouldn't use SAS.
However, despite us having SSA, it doesn't mean we can't keep going. The reason why is because we have two right triangles. So we can use the HL theorem instead. Statement 1 above refers to the L of HL, while statement 2 is the H.
HL = hypotenuse leg
Again, HL only works for right triangles. It's the only time we can use SSA to prove right triangles are congruent; otherwise, SSA is not a valid congruence theorem.
Related Questions
Find the equation of the line parallel to y = 2/3x-7
passing through A(6,-1).
Answers
Answer:
y = 2/3x - 5
Step-by-step explanation:
If two lines are parallel, they have the same slope. This means the line we are looking for has a slope of 2/3. Since we are also given a point, we can start by writing the equation in point-slope form which is represented by
[tex]y-y_{1} =m(x-x_{1} )[/tex]
Where m is the slope and (x1, y1) is a point. We have both, so we can substitute the values and simplify:
y + 1 = 2/3 (x - 6)
y + 1 = 2/3x - 4
y = 2/3x - 5
1. Write as a mathematical equation.
The sum of a number and 5 times the number is 42.
(n + 5). n = 42
n + 5n = 42
(n + 5). n
n + 5n
Answers
Answer:
2nd option: n + 5n = 42
Step-by-step explanation:
what is the volume of a cylinder in cubic in with a height of 11in and a base diameter of 6in
Answers
Answer:
311.01 in^3
Step-by-step explanation:
Volume of cylinder = pi*r^2*h
Volume of cylinder = pi*9*11=311.01 in^3
PLEASE HELP! NO SPAMMING! SHOW WORK!
The ratio of the dimensions of the model to the dimensions of the Great Pyramid is about 1 to 38. The surface area of the real pyramid is about how many times the surface area of the model.
Dimensions: a pyramid with a square base.
base sides: 6m
height: 4m
Answers
========================================================
Explanation:
Consider a square on paper that is 3 inches by 3 inches. It's area would be 3*3 = 9 square inches.
The ratio 1 to 38 means that 1 inch on paper corresponds to 38 inches in real life (assuming the "1 to 38" doesn't have any verbal units attached to it; if so, then refer to the note below). So a 3 by 3 square corresponds to a 114 by 114 square because 3*38 = 114.
The area of the second larger square is 114*114 = 12,996 square inches.
Now divide the two areas: (12,996)/(9) = 1444
It's probably not entirely obvious, but through a bit of playing around with various numbers, you should find that 38^2 = 1444. It's not a coincidence that this happens. The linear scale factor is 38 which means the area scale factor is 38^2 = 1444.
In short, the larger square in real life has area that is 1444 times that of its scaled down counterpart.
Or put another way:
large area = 1444*(small area)
------------------
Side note: This all assumes that the numbers in "1 to 38" are both the same unit. If we had a mixed ratio of units like "1 inch to 38 feet", then the answer would be different. You would need to convert from feet to inches, and then follow the steps above to get a different answer.
What is the area of a figure with the measurements of 3,6, and 5?
Answers
Answer:
I think it is 181m.
Step-by-step explanation:
[tex]by \: imagination \: you \: separate \: all \: the \: shapes[/tex]
you also name it .
I name the triangle area A
I name the rectangle area B
it is a triangle because it has different measurements on its sides.
I name the semi- circle area C.
[tex]area \: of \: a \: triangle \: = \\ \frac{1}{2} \times b \times h \\ \frac{1}{2} \times 5 \times 3 \\ \frac{1}{ 2} \times 15 \\ 7.5[/tex]
[tex]aea \: of \: a \: rectangle \: = l \times b \\ 5 \times 6 = \\ 30[/tex]
[tex]area \: of \: a \: semi \: circle \: = \frac{1}{2 } \times \pi \times {r}^{2} \\ \frac{1}{2} \times 3.14 \times 3 \times 3 \\ \frac{1}{2} \times 3.14 \times 9 \\ \frac{1}{2} \times \frac{314}{10} \times 9 \\ [/tex]
[tex]you \: then \: cancle \: 134 \: by \: 2[/tex]
[tex] = \frac{154}{10} \times 9[/tex]
[tex] = \frac{1431}{10} \\ 143.1[/tex]
[tex]you \: now \: add \: all \: the \: ares \: to \: get \: your \: full \: area \\ 7.5 + 30 + 143.1 \\ = 180.6 \\ to \: the \: nearest \: hundred \: will \: be \: 181m[/tex]
PLEASE HELP ME!!! THANK YOU i really need it
The radius of a circle is 6 inches. What is the area of a sector bounded by a 102° arc?
give exact answer in simplest form
explaining your answer = brainliest/ five stars
Answers
Answer:
10 1/5 pi
Step-by-step explanation:
First find the area of the circle
A = pi r^2 = pi *6^2 = 36 pi
Then find the fraction of the circle that is shaded
A circle is 360 degrees
102/360 =17/60
Multiply the fraction by the area
17/60 * 36 pi
51/5 pi
10 1/5 pi
Answer:
32.04
Step-by-step explanation:
firstly area of a sector is angle/360 multiplied by pi *r squared
so in this case it is going to be 102/360 *pi *6^2
6 squared is 36 all multiplied by pi and 106/360
it is advisable that you enter them all at once in your calculator
the final answer will be32.0444507
which is rounded to 32.04
please help! I dont understand how to answer. i got x^2-9x+20=0 as my answer. am i incorrect?
Answers
Answer:
x² - 9x + 20
You are correct.
None of the listed choices are correct.
-----------------------------
I think the question originally had 5 and -4 as the solutions
https://www.jmap.org/Worksheets/A.APR.B.3.ZerosofPolynomialsPR1.pdf
x = {-4, 5}
(x + 4)(x - 5) = 0
x² - 5x + 4x - 20 = 0
x² - x - 20 = 0 Answer E
Step-by-step explanation:
x = {4, 5}
y = (x - 4)(x - 5)
y = x² - 5x - 4x + 20
y = x² - 9x + 20
5.
Which of the quadratic functions has the narrowest graph?
A. [tex]y=-2x^2[/tex]
B. [tex]y=\frac{1}{2} x^2[/tex]
C. [tex]y=\frac{1}{7} x^2[/tex]
D. [tex]y=-4x^2[/tex]
Answers
Answer:
C. y= 1/7x2
Step-by-step explanation:
The equation with the highest leading coefficient (the number before the x^2 term) will have the narrowest graph. Here, we have to choose between -1, 1/6, 2, and 1/8. The highest number out of all of those numbers is 2, so y = 2x^2 will have the narrowest graph.
Type the correct answer in the box. Use numerals instead of words. What value of x satisfies this equation? log2 (6x – 8) – log2 8 = 1 The value of x is
Answers
Answer:
Espero te sirva
Step-by-step explanation:
Suerte ******'**
You can use two important properties of log to find out the solution of the given equation.
The value of x that satisfies the given equation is 4
What is logarithm and some of its useful properties?When you raise a number with an exponent, there comes a result.
Lets say you get
[tex]a^b = c[/tex]
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
[tex]b= log_a(c)[/tex] , here 'a' is called base of logarithm.
Some properties of logarithm are:
[tex]log_a(b) = log_a(c) \implies b = c\\\\\log_a(b) + log_a(c) = log_a(b \times c)\\\\log_a(b) - log_a(c) = log_a(\frac{b}{c})\\\\log_a(a) = 1[/tex]
(take special attention over that base "a" in all of the above property as you might mix them with other base logarithms which is not allowed)
How to find the solution to the given equation?We can use the fourth, property and then can use third and first property as follows:
[tex]log_2(6x-8) - log_2(8) = 1\\\\log_2(\frac{6x-8}{8}) = log_2(2)\\\\\dfrac{6x-8}{8} = 2\\\\6x-8 = 2 \times 8\\6x-8 = 16\\6x = 16 + 8\\6x = 24\\\\x = \dfrac{24}{6} = 4\\\\x= 4[/tex]
Thus, the value of x for the given condition is obtained as 4.
Learn more about logarithms here:
https://brainly.com/question/20835449
Simplify using the distributive property: 5(2x + 7). Show all of your work.
Answers
Answer:
10x + 35
Step-by-step explanation:
Given
5(2x + 7) ← multiply each term in the parenthesis by 5
= 5(2x) + 5(7)
= 10x + 35
Answer:
10x+35
Step-by-step explanation:
5×2x=10x
5×7=35
=10x+35
Find the missing side
Answers
Answer:
12.94811641 =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj/ hyp
cos 44 = x /18
18 cos 44 =x
12.94811641 =x
Answer:
12.9
Step-by-step explanation:
cos(44) = x/18
x = cos(44) * 18
x = 12.9
Jane and Tannic split the cost of buying a video game. The game costs$25, and the sales is 6% markup. How much do they each pay?
Answers
Answer:
$13.25
Step-by-step explanation:
Given data
Cost of game = $25
Markup= 6%
Let us find the total cost of the game
First, the markup cost
=6/100*25
=0.06*25
=$1.5
Now the total cost is
=25+1.5
=$26.5
So, each is expected to pay
=26.5/2
=$13.25
Dois triângulos semelhantes possuem razão entre suas áreas igual a 9. Se o perímetro de um deles é 10, o perímetro do outro deve ser:
Answers
Answer:
O perímetro do outro triângulo deve ser ou de 30 unidades de comprimento, ou de 3.33 unidades de comprimento.
Step-by-step explanation:
Dois triângulos semelhantes possuem razão entre suas áreas igual a 9.
O perímetro tem grau um, enquanto a área tem grau 2. Isto implica que a razão entre os perímetros é a raiz quadrada da razão entre as áreas, então a razão entre os perímetros é de 3.
Se o perímetro de um deles é 10, o perímetro do outro deve ser:
Ou 10*3 = 30, ou [tex]\frac{10}{3} = 3.33[/tex]
O perímetro do outro triângulo deve ser ou de 30 unidades de comprimento, ou de 3.33 unidades de comprimento.
I will mark you brainliest if you solve this
show your working as well
4) (4x2– x – 7) + (2x3+ 6x2– 11)
5)(2x3– x + 4) + (5x2– 6x – 5)
6)(3x2+ 2x + 1) – (x2– 3x + 4)
7)(2x2– 3x + 7) – (5x2+ 3x + 6)
Answers
Answer:
4) 2x3 + 10x2−x−18
5) 2x3+5x2−7x−1
6) 2x2+5x−3
7) −3x2−6x+1
Step-by-step explanation:
4) (4x2 - x - 7) + (2x3+ 6x2– 11)
Combine Like Terms:
=4x2+−x+−7+2x3+6x2+−11
=(2x3)+(4x2+6x2)+(−x)+(−7+−11)
=2x3+10x2+−x+−18
5) (2x3– x + 4) + (5x2– 6x – 5)
Combine Like Terms:
=2x3+−x+4+5x2+−6x+−5
=(2x3)+(5x2)+(−x+−6x)+(4+−5)
=2x3+5x2+−7x+−1
6) (3x2+ 2x + 1) – (x2– 3x + 4)
Distribute the Negative Sign:
=3x2+2x+1+−1(x2−3x+4)
=3x2+2x+1+−1x2+−1(−3x)+(−1)(4)
=3x2+2x+1+−x2+3x+−4
Combine Like Terms:
=3x2+2x+1+−x2+3x+−4
=(3x2+−x2)+(2x+3x)+(1+−4)
=2x2+5x+−3
7)(2x2– 3x + 7) – (5x2+ 3x + 6)
Combine Like Terms:
= (2x2 −5x2 )+(−3x−3x)+(7−6)
Solve for O pls and thank you
Answers
Answer:
a) 67.4°
Step-by-step explanation:
since this is a right triangle you can use the sine trigonometric ratio of opposite/hypotenuse
sin⁻¹(Ф) = 12/13 which equals 67.4°
From the given figure,write the corresponding angle of puv
Answers
Answer: RVN
Step-by-step explanation:
Corresponding angles are angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
By that - the bottom angle RVN can be an example of corresponding angles.
Please give brainliest!
Answer:
∠ RVN
Step-by-step explanation:
∠ PUV and ∠ RVN are corresponding angles.
Each is in the same position (lower left hand corner ) in its group of 4 angles.
Gloria set aside $100 to buy school lunches for the year. Each school lunch cost $2. The inequality 100 – 2x < 20 can be used to find the number of school lunches Gloria can buy before she has less than $20 left. What is the solution to this inequality?
Answers
Answer:
she would be able to buy 40 lunches
Step-by-step explanation:
Subtract 100 from both sides of the inequality
Divide each term by −2 and simplify.
The solution to the inequality 100 – 2x < 20 is x > 40
How to find solution to an inequality?
She set aside $100 to buy school lunches for the year. Each school lunch cost $2.
Therefore, the inequality can be used to find the number of school lunches Gloria can buy before she has less than $20 left.
100 – 2x < 20
The solution of the inequality is as follows;
100 – 2x < 20
subtract 100 from both sides
100 - 100 - 2x < 20 - 100
-2x < - 80
divide both sides by -2
x > 40
learn more on inequality here: https://brainly.com/question/11872626
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Context: You and your friends go to the state fair. It costs $6 to get into the fair and $2 each time you go on a ride. Where do you see the y-intercept in the table and in the equation?
Answers
Answer:
see below
Step-by-step explanation:
The y intercept is when x =0
The equation is y =2x+6
The equation is in the form y = mx+b. It is the constant added to the equation.
In the table it is the y value when x =0
Which type of angle is related to supplementary angles?
Reflex
Straight
Acute
Obtuse
Answers
straight angle because the supplementary angle and straight angle is same.
Figure VWYX is a kite.
3
(18x-2)
V
Y
(12x+2)
х
Answers
Answer:
18X-2+12X+2=360-180
30X=180
X=6
The value of the variable x is 6, in the given rhombus.
What are the properties of the rhombus?A quadrilateral having the following characteristics is called a rhombus:
The lengths of the four sides are equal.Parallel sides are situated next to one another.Angles that are opposite each other are equal (i.e., they have the same measure).The diagonals form a right angle split across one another.Each diagonal is the same length.From the properties of a rhombus,
The sum of all angles is 360°.
Thus, in the given case,
18x-2+12x+2+ 90° +90° = 360°
18x- 2 + 12x +2 = 180°
30x = 180
x = 6
Therefore, the value of the x is 6.
Learn more about Rhombus here:
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Each number in the sequence is 8 less than the previous number which list of number can be described by the following rule
A.69,60,53
B.53,61,69
C.53,60,69
D.69,61,53
Answers
Answer: a
Step-by-step explanation:
for freshman year Nick had 3.5 for a gpa. what gpa does Nick needs for sophomore, junior, senior year to get the average of at least 4.0?
Answers
Answer:4.0
Step-by-step explanation:
Helpppp does anyone know
Answers
======================================================
Explanation:
We can apply the remote interior angle theorem. Some math books or teachers may refer to this as the "exterior angle theorem". They're the same idea just with different names.
According to that theorem, the interior angles x and 53 add up to the exterior angle 158
x+53 = 158
x = 158-53
x = 105
This theorem only works if neither interior angle is adjacent to the exterior angle. Hence the "remote" part.
----------
If you wanted a slightly longer approach, then let y be the missing angle that isn't marked in the diagram. Angle y is adjacent to the 158 degree angle.
We can find y by noting how 158 and y are supplementary
158+y = 180
y = 180-158
y = 22
Then we use the fact that adding three angles of any triangle always gets us 180 degrees
x+y+53 = 180
x+22+53 = 180
x+75 = 180
x = 180-75
x = 105
Effectively, this example helps reinforce why the remote interior angle theorem is true.
Simplify the expression
3(5x+8)
Answers
Answer:
Solution given:
3(5x+8)
distribute
15x+8*3
15x+24 is a required answer.
Answer:
15x + 24
Step-by-step explanation:
Apply the Distributive Property of Multiplication. Multiply each of the two terms inside parentheses by 3:
3(5x + 8) = 15x + 24
WILL MARK BRAINLIEST
solve for x: m(2m-x)=3(x+6) if m≠3
Answers
Answer:
x=2m−6
Step-by-step explanation:
x = 4 and y = 2, what is the value of x^2 + y^3 ?
Answers
Answer:
14
Step-by-step explanation:
x * 2 = 8
y * 3 = 6
6 + 8 = 14
A set of parents started a savings account for their newborn child. After 7 years, the
child's account had 900 dollars. The balance in the account continues to grow by a
factor of 5 in value every 7 years. Let n be the number of 7-year periods since the
account was started.
Which function, f(n), represents the value of the savings account?
Answers
Answer:
hsshshshwwbwbbs29oooo
PLZ HELP ITS URGENT
Answers
it is blurry so take it again
Given that
a
= 7 cm and
b
= 8 cm, work out the area of the triangle.
Answers
Answer:
28
Step-by-step explanation:
1/2 x base x height = Area
a = base
b = height
1/2 x 7 x 8 = 28
Answer:
28
Step-by-step explanation:
1/2x 7 x 8
answer is 28
Bye
:-)
What is the measure of ZWX?
Answers
Step-by-step explanation:
180°+63°
=243°
holp it help
