3. Consider the following diagram.
Find the values of m and n that prove the two triangles are congruent by the
HL Theorem.
Answer:
m = 3, n = 6
Step-by-step explanation:
The hypotenuse leg (HL) theorem states that two triangles are said to be similar if one leg and the hypotenuse of the triangles are congruent.
From the diagram, comparing the hypotenuse of the triangles;
4m + 1 = 13
4m = 13 - 1
= 12
m = [tex]\frac{12}{4}[/tex]
= 3
m = 3
Also, comparing the sides;
2m + n = 8m - 2n
substitute the value of m to have,
6 + n = 24 - 2n
collect like terms,
n + 2n = 24 - 6
3n = 18
n = [tex]\frac{18}{3}[/tex]
= 6
n = 6
m = 3, n = 6
To solve the problem we must know about HL theorem.
What is the HL theorem?According to the HL theorem, If the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. therefore, the hypotenuse will be congruent to each other, and the corresponding sides will be congruent to each other.
The value of m and n are 3 and 6, respectively.
Given to us
The hypotenuse of the first triangle = 13One leg of the first triangle = 2m+nThe hypotenuse of the second triangle = 4m+1One leg of the second triangle = 8m - 2nAccording to the HL theoremIf the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. therefore,
the hypotenuse will be congruent to each other, and the corresponding sides will be congruent to each other.
Hypotenuse Congruent[tex]4m + 1 =13\\\\4m=13-1\\\\m=\dfrac{12}{4}\\\\m=3[/tex]
Corresponding Congruent sides[tex]2m+n = 8m-2n\\[/tex]
Substitute the value of m,
[tex]2(3)+n = 8(3)-2n\\\\6+n = 24-2n\\\\6-24 = -2n-n\\\\-18 = -3n\\\\n=\dfrac{-18}{-3}\\\\n = 6[/tex]
Hence, the value of m and n are 3 and 6, respectively.
Learn more about HL theorem:
https://brainly.com/question/11804042
write in word form 329.080 in word formwrite in word form 329.080 in word form
Answer:
Three Hundred Twenty-nine and Eighty Thousandths.
The rational number -21/28 in standard form is
a) -3/4
b) 3/4
c) 3/7
d)-3/7
What is 30-20-65+10+4=
Answer:
-41
Step-by-step explanation:
THIS IS EASY!!! (PLEASE HELP... ILL GIVE BRAINLIST)
Answer:
-7(9) < -56
Step-by-step explanation:
-7(9) is -63 which is less than -56 so anything above that is less than 56-
Answer:
x=8
Step-by-step explanation:
Hope,it helps it wasn’t that easy (:
The length of a rectangle is 5 more than the side of a square, and the width of the rectangle is 5 less than the side of the square. If the area of he square is 45, what is the area of the rectangle
Answer:
20
Step-by-step explanation:
Given :
Length = l
Width = w
Area of square = 45
Let side of square = x
Area of square = x²
45 = x²
√45 = x
l of rectangle = x + 5 = √45 + 5
w of rectangle = x -5 = √45 -5
Area of rectangle= l * w
Area = (√45 + 5) * (√45 - 5)
Area = 45 - 5√45 + 5√45 -25
Area = 45 -25
Area of rectangle = 20
Sid has £5 to buy apples and bananas.
He uses his money like this:
He buys 18 apples.
Then he buys as many bananas as possible.
With his change he buys more apples.
How many apples and bananas does he buy?
(Apples=6p Each)
(Bananas= 40p Each)
Step-by-step explanation:
cost of 18 apples= 18x6p= 108p
£5-108p= x (will let it be x since i do not know the conversion)
maximum number of banana he can buy= x divide by 40p (rounded down to smallest whole number)= b
The change he have= x-(40×b) = y
apples bought with change= y divide by 6p= a
do the working above to find value for a and b, add a to the 18 apples bought initially and b is number of banana
A woman has a ladder that is 10 feet long. If she sets the base of the ladder on level ground 8 feet from the side of a house, how many feet above the ground will the top of the ladder be when it rests against the house?
1. 2
2. 5
3. 8
4. 6
Answer:
2 feet extra
Step-by-step explanation:
so if you do common subtraction 8-10is 2 so here is 2 feet over her house
Can someone please answer these there due today in math
1.)3c + 8= 29
2.)12/c - 6=78
3.) -20 = -4x - 6x
4.) -4 (3 + 4K) = 52
5.) -45 = -3(4x - 1)
heeeeeeeeeeeeeeeeeeeeeellllllllllllllllllllllllp
C=
5
9
(F−32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5
9
degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
ANSWER EXPLANATION: Think of the equation as an equation for a line
y=mx+b
where in this case
C=
5
9
(F−32)
or
C=
5
9
F−
5
9
(32)
You can see the slope of the graph is
5
9
, which means that for an increase of 1 degree Fahrenheit, the increase is
5
9
of 1 degree Celsius.
C=
5
9
(F)
C=
5
9
(1)=
5
9
Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of
9
5
degrees Fahrenheit.
C=
5
9
(F)
1=
5
9
(F)
(F)=
9
5
Since
9
5
= 1.8, statement II is true.
The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of
5
9
degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true:
C=
5
9
(F)
C=
5
9
(
5
9
)
C=
25
81
(whichis≠1)
An increase of
5
9
degree Fahrenheit leads to an increase of
25
81
, not 1 degree, Celsius, and so Statement III is not true.
Answer:
final answer is D
UwU
D okakkakakakakkakakakkakakakaka
Is the equation a function?
Answer:
I do so believe the equation is a function
Step-by-step explanation:
if im wrong im so sorry
Can you please help
Answer:
The answer to the question provided is
[tex] \frac{9}{5} [/tex]
Step-by-step explanation:
T
given logx 2=p and logx 7=q , express log7 4x² in terms of p and q
Answer:
[2(p + 1)]/q
Step-by-step explanation:
logx 2 = p
logx 7 = q
log7 4x² = log7 (2x)²
= (logx (2x)²)/(logx 7)
= (2 logx 2x)/(logx 7)
= (2 logx 2 + 2 logx x)/(logx 7)
= (2p + 2)/q
= [2(p + 1)]/q
Albert makes 20 kg of sweets in 5 weeks. If he continued to make sweets, how much would he have after 10 weeks?
Answer:
he will have 40 kg
Step-by-step explanation:
10:5=2
20 x 2 = 40
Write the equation of the line that passes through the point (-9,10) and is parallel to the y axis
Answer:
y = 10Step-by-step explanation:
The equation of any line parallel to the y axis is y = y₀
where y₀ is the y-coordinate of any point from the line
(and the y-intercept of the line)
1. Which ratio is equivalent to 3:9?
24.54
18:54
36.81
Both 9/3 and 54/18 come out to 3, so your answer is:
18:54
Answer:
18:54
Step-by-step explanation:
We have to simplify these ratios.
If the most simplified form of the ratios are equal, they are equivalent
3:9
24:54
18:54
Same ratio as 3:9, so 18:54 is equivalent to 3:9
36:81
Which equation is true for this triangle?
Answer:
c
Step-by-step explanation:
makes most sense
Answer:
c
Step-by-step explanation:
its a guess sorryyyjsjsjsssksk
Point Q with coordinates (4, –7) is rotated 270° clockwise about (5, 1) . What are the coordinates of its image?
Answer:
The coordinates of the image are [tex]Q'(x,y) = (13,0)[/tex].
Step-by-step explanation:
The rotation of point Q around a given point of reference is defined by:
[tex]Q'(x,y) = O(x,y) + r_{OQ}\cdot (\cos (\theta_{OQ}\pm \theta_{R}),\sin (\theta_{OQ}\pm \theta_{R}))[/tex] (1)
Where:
[tex]O(x,y)[/tex] - Point of reference.
[tex]r_{OQ}[/tex] - Magnitude of line segment OP.
[tex]\theta_{OQ}[/tex] - Direction of the point Q with respect to the point of reference, measured in sexagesimal degrees.
[tex]\theta_{R}[/tex] - Rotation angle, measured in sexagesimal degrees.
[tex]Q'(x,y)[/tex] - Rotated point.
Please notice that positive sign means counterclockwise rotation, whereas the negative sign represents clockwise rotation.
The magnitude and direction of the line segment are defined by the following expressions:
Magnitude
[tex]r_{OQ} = \sqrt{(x_{Q}-x_{O})^{2}+(y_{Q}-y_{O})^{2}}[/tex] (2)
Direction
[tex]\theta_{OQ} = \tan^{-1}\left(\frac{y_{Q}-y_{O}}{x_{Q}-x_{O}} \right)[/tex] (4)
Where:
[tex]x_{O}[/tex], [tex]y_{O}[/tex] - Coordinates of point of reference.
[tex]x_{Q}[/tex], [tex]y_{Q}[/tex] - Coordinates of the point Q.
If we know that [tex]x_{O} = 5[/tex], [tex]y_{O} = 1[/tex], [tex]x_{Q} = 4[/tex], [tex]y_{Q} = -7[/tex], then the magnitude and direction of the segment OQ are, respectively:
[tex]r_{OQ} = \sqrt{(4-5)^{2}+(-7-1)^{2}}[/tex]
[tex]r_{OQ} \approx 8.062[/tex]
[tex]\theta_{OQ} = \tan^{-1}\left(\frac{-7-1}{4-5} \right)[/tex]
[tex]\theta_{OQ} = \tan^{-1}\left(\frac{-8}{-1} \right)[/tex] (Which means that line segment OQ belongs to third quadrant)
[tex]\theta_{OQ} \approx 262.875^{\circ}[/tex]
If we know that rotation is clockwise, [tex]x_{O} = 5[/tex], [tex]y_{O} = 1[/tex], [tex]r_{OQ} \approx 8.062[/tex] and [tex]\theta_{OQ} \approx 262.875^{\circ}[/tex], then the rotated point is:
[tex]Q'(x,y) = (5,1) + (8.062\cdot \cos (262.875^{\circ}-270^{\circ}),8.062\cdot \sin (262.875^{\circ}-270^{\circ}))[/tex]
[tex]Q'(x,y) = (5,1) + (8, -1)[/tex]
[tex]Q'(x,y) = (13, 0)[/tex]
The coordinates of the image are [tex]Q'(x,y) = (13,0)[/tex].
During a field trip, 60 students are put into equal-sized groups. Describe two ways to interpret 60÷5 60 ÷ 5 in this context. Find the quotient. Explain what the quotient would mean in each of the two interpretations you described. Consider the division expression 712÷2 7 1 2 ÷ 2 . Select all multiplication equations that correspond to this division expression. 2⋅?=712 2 ⋅ ? = 7 1 2 712⋅?=2 7 1 2 ⋅ ? = 2 2⋅712=? 2 ⋅ 7 1 2 = ? ?⋅712=2 ? ⋅ 7 1 2 = 2 ?⋅2=712
The second question:
Consider the division expression [tex]7\frac{1}{2} / 2[/tex]. Select all multiplication equations that correspond to this division expression.
[tex]2 * ? = 7\frac{1}{2}[/tex] [tex]7\frac{1}{2} * ?= 2[/tex] [tex]? * 2 = 7\frac{1}{2}[/tex]
[tex]2* 7\frac{1}{2} = ?[/tex] [tex]? * 7\frac{1}{2} = 2[/tex]
Answer:
1. See Explanation
2. [tex]2 * ? = 7\frac{1}{2}[/tex] and [tex]? * 2 = 7\frac{1}{2}[/tex]
Step-by-step explanation:
Solving (a):
Given
[tex]Students = 60[/tex]
[tex]Group = Equal\ Sized[/tex]
Required
Interpret [tex]\frac{60}{5}[/tex] in 2 ways
Interpretation 1: Number of groups if there are 5 students in each
Interpretation 2: Number of students in each group if there are 5 groups
Solving the quotient
[tex]Quotient = \frac{60}{5}[/tex]
[tex]Quotient = 12[/tex]
For Interpretation 1:
The quotient means: 12 groups
For Interpretation 2:
The quotient means: 12 students
Solving (b):
Given
[tex]7\frac{1}{2} / 2[/tex]
Required
Select all equivalent multiplication equations
Let ? be the quotient of t [tex]7\frac{1}{2} / 2[/tex]
So, we have:
[tex]7\frac{1}{2}/2 = ?[/tex]
Multiply through by 2
[tex]2 * 7\frac{1}{2}/2 = ? * 2[/tex]
[tex]7\frac{1}{2} = ? * 2[/tex]
Rewrite as:
[tex]? * 2 = 7\frac{1}{2}[/tex] --- This is 1 equivalent expression
Apply commutative law of addition:
[tex]2 * ? = 7\frac{1}{2}[/tex] --- This is another equivalent expression
PLEASE HELP 30 POINTS
Solve the equation.
60% of 45 =
25% of 80 =
16% of 40 =
Answer:
60% of 45 = 0.6 × 45 = 27
25% of 80 = 0.25 × 80 = 20
16% of 40 = 0.16 × 40 = 6.4
The area of a rectangular field is 5695 m².
If the width of the field is 67 m, what is its length?
Answer:
85 m
Step-by-step explanation:
5696/67=85
what is Inequality Notation
Answer:
There are four inequality notations. They are. > means greater than. ≥ means greater than or equal to. < means less than.
Step-by-step explanation:
Billy bought 2 sweatshirts and 3 t-shirts. His friend Jordan bout 3 sweatshirts and 3 t-shirts. Billy's bill was $35 and Jordan's bill was $45. What is the price of one t-shirt and what is the price of one sweatshirt?
A married couple makes a combined $100,000 a year. This means their income will be taxed about 25%. How much money will they be left with after taxes are taken out of their paychecks?
Group of answer choices
$25,000
$50,000
$75,000
Answer:
$75,000
Step-by-step explanation:
$100,000 x 0.25 = $25,000
$100,000 - $25,000 = $75,000
A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she descended 41.6 feet. How many feet had she been below sea level, if she was 102 feet below sea level after she descended?
Answer:
143.6 below sea level
Step-by-step explanation:
Given that:
Initial altitude of the submarine = 102 feet below sea level
Distance descended over the next 10 minutes = 41.6 minutes
To find:
The altitude below sea level after she descended ?
Solution:
To find the resultant altitude below sea level, we need to subtract the altitude descended in the next ten minutes from the initial altitude.
We are doing so because scientist has further descended i.e. gone below the water.
Initial altitude is also in negative sign because of the fact that it is below sea level.
Therefore, the answer can be found as:
-102 - 41.6 = - 143.6
OR
143.6 below sea level is the answer.
If a scale factor of One-fifth is used to make a reduction, what is the base of the original triangle?
Original triangle
Reduced triangle
Height
3
Base
5
1
10
15
25
Answer: the answer is d
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
ASAP PLS Joselyn expects her new software company to increase its sales next year 2 3/4 the present value. Write this increase as a percent.
Answer:
175% i think
Step-by-step explanation:
What is the value of KL
Answer:
40.5
Step-by-step explanation:
Since the centroid (the point of concurrency of the sides of a triangle) divides the 3 medians into the ratios from the point to the centroid to the centroid to the side into the ratio of 2:1. To find PK divide 27 by 2
27/2=13.5
Then add 27 and 13.5 to get KL
27+13.5=40.5
function or not a function?
Answer:
Not a function
Step-by-step explanation:
You draw lines going down the graph and if any of those lines have more than one point then it is not a function.