The diagram shows an isosceles right
triangle. Follow these steps to explore the
relationship between side lengths.
m2 ABC = 45°
MZ ACB = 45°
1. Measure the length of each leg and
the hypotenuse:
AB =
units
AC =
units
BC =
units
B
C
A
III
IIIIIIIIIIIIIIIII
Answers
Answer:1. 1.0 1.0 1.4
Step-by-step explanation:
The length of the sides are given by the 45°–45°–90° triangle theorem.
Correct responses:
AB = 1AC = 1BC = √2 Methods used to find the lengthsThe 45°–45°–90° triangle theorem states that the ratio of the lengths of
the sides of triangles having interior angles of 45°, 45°, 90° is 1 : 1 : √2
The lengths of the legs of an isosceles triangle are equal.
The legs of the given isosceles right triangle are AB and AC
Therefore;
AB = AC
Taking the lengths of AB as 1 unit, we have;
AB = 1 = AC
According to Pythagorean theorem, we have;
[tex]\overline{BC}^2 = \mathbf{\overline{AB}^2 + \overline{AC}^2}[/tex]
Which gives;
[tex]\overline{BC}^2 = 1^2 + 1^2 = \mathbf{ 2}[/tex]
Therefore;
BC = √2
Therefore, by setting the length of AB = AC = 1, we have;
AB = 1AC = 1BC = √2 ≈ 1.414The above values are in the ratio 1 : 1 : √2, which corresponds with the
45°-45°-90° triangle theorem.
Learn more about Pythagorean theorem here:
https://brainly.com/question/66231
Related Questions
Write each of these ratios in their
simplest form.
A) 3:9 B) 12:36 C) 13:39 D) 71:213 E) 142:213 F) 38:57 G) 33:44 H) 31:42
Answers
Answer:
A) 3:9 => 1:3
B) 12:36 => 1:3
C) 13:39 => 1:3
D) 71:213 => 1:3
E) 142:213 => 2:3
F) 38:57 => 2:3
G) 33:44 => 3:4
H) 31:42 => 31:42 or 21:42 => 1:2
Step-by-step explanation:
The simplest form of the ratios are as follows:
A) 3:9
Dividing the ratio by 3
1:3
B) 12:36
Dividing the ratio by 12
1:3
C)13:39
Dividing the ratio by 13
1:3
D) 71:213
Dividing the ratio by 71
1:3
E) 142:213
Dividing the ratio by 71
2:3
F) 38:57
Dividing the ratio by 19
2:3
G) 33:44
Dividing the ratio by 11
3:4
H) 31:42
The ratio is already in simplest form as 31 and 42 don't have a common multiple.
Or it might be mistakenly typed 31 instead of 21
Then the simplest form will be:
21:42
1:2
Hence,
A) 3:9 => 1:2
B) 12:36 => 1:3
C) 13:39 => 1:3
D) 71:213 => 1:3
E) 142:213 => 2:3
F) 38:57 => 2:3
G) 33:44 => 3:4
H) 31:42 => 31:42 or 21:42 => 1:2
Solve this one step equation.
5x = 13
help please
Answers
Express 10 : 12 as a decimal.
(Round to the nearest hundrerdth)
Answers
Answer:
pretty sure it's .833
Step-by-step explanation:
Find an equation of the line perpendicular to the graph of 14x-7y=8 passing through the point at (-2,5)
Answers
Answer:
Equation of line perpendicular to given graph is:
[tex]y = -\frac{1}{2}x+4[/tex]
Step-by-step explanation:
Given equation of line is:
14x-7y=8
First of all, we have to convert the given equation into slope-intercept form to find the slope of the line
The slope-intercept form is:
[tex]y = mx+b[/tex]
Now
[tex]14x-7y=8\\14x-8 = 7y\\\frac{7y}{7} = \frac{14x-8}{7}\\y = \frac{14}{7}x - \frac{8}{7}\\y = 2x - \frac{8}{7}[/tex]
The co-efficient of x is 2 so the slope of given line is 2
Let m1 be the slope of line perpendicular to given line
The product of slopes of two perpendicular lines is -1
[tex]m.m_1 = -1\\2.m_1 = -1\\m_1 = -\frac{1}{2}[/tex]
The equation for line perpendicular line to given line will be:
[tex]y = m_1x+b\\y = -\frac{1}{2}x+b[/tex]
To find the value of b, putting (-2,5) in the equation
[tex]5 = -\frac{1}{2}(-2) + b\\5 = 1+b\\b = 5-1\\b = 4[/tex]
The final equation is:
[tex]y = -\frac{1}{2}x+4[/tex]
Hence,
Equation of line perpendicular to given graph is:
[tex]y = -\frac{1}{2}x+4[/tex]
Ryan drinks liters of water every of an hour at a constant rate.
How many liters of water does he drink in 3 hours?
Answers
Over a one week period in the summer, the price of a gallon of gas increased from $2.35 to $2.82. By what percent did the price of gas increase over that week?
What is it
Answers
Answer:
$0.47
Step-by-step explanation:
2.82 - 2.35
if the product of two number is 10 and the sum is 7 ,then the longest of the two number is
Answers
Answer:
5 units
Step-by-step explanation:
Step one:
Given data
Le the first number be x
and the second number be y
So
x*y= 10-----------------1
and
x+y= 7-----------------2
from eqn 1
x= 10/y
put x= 10/y in eqn 2
[tex]10/y+y= 7\\\\10/y= 7-y[/tex]
cross multiply we have
[tex]10=y(7-y)\\\\10=7y-y^2[/tex]
rearrange
[tex]y^2-7y+10=0[/tex]
the factors of the quadratic expression are
-5 and -2
[tex]y^2-5y-2y+10= 0\\\\y(y-5)-2(y-5) =0\\\\y-2=0\\\\y= 2\\\\y-5= 0\\\\y=5\\\\[/tex]
The longest side is 5 units
The local lighting company found that 2 out of every 10 lightbulbs was defective. If
there are a total of 120 bulbs in a box, how many can they predict will be defective?
Answers
Answer:
24
Step-by-step explanation:
2/10
120 ÷ 10 = 12
2 x 12 = 24
10 x 12 = 120
24/120
Answer:
24
Step-by-step explanation:
120 % 10 = 12
2 x 12 = 24
The top running speed of a giraffe is 250% of the top speed of a squirrel. If a squirrel’s top running speed is 12 miles per hour, find the speed of a giraffe.
Answers
Answer:
30
Step-by-step explanation: First take the fastest speed of the squirrel, and then you multiply it by the percentage (250%). You can this by moving on decimal point to the left from the zero (250% = 2.50). Then multply the speed of the squirrel by said percentage of the girrafe,
12 x 2.5 = 30
Marking brainlesssss!!
Answers
Answer:
A 22 inches
Step-by-step explanation:
Pls just trust me lol
please help me with triangle angles. due today !
Answers
Answer:
12
Step-by-step explanation:
8x-1+3x+4+3x+9=180
14x+12=180
14x=180-12
x=168/14
x=12
Answer:
8x-1+3x+9+3x+4=180
8x+3x+3x=180+1-9-4
14x=168
x=12
Step-by-step explanation:
2 3/8 x 3 3/4 divided by 2 2/3
Answers
Answer:
57/32
Step-by-step explanation:
171/32 divided by 2 2/3
Hello can someone help me with this question please!
Answers
Answer: 66.10
Step-by-step explanation:
Sin^-1(32/35)
whats 43.6 rouded to the nest tenth
Answers
Answer:
43.6
Rounded to the nearest 0.1 or
the Tenths Place.
Can somebody help me. Will mark brainliest.
Answers
2.both are the same because both point the same direction along with being worth the same
3. They equal horizontal lines
4. Doesn’t have one
Brainliest please
Probability.
It has been estimated that about 30% of frozen chickens contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have more than 6 contaminated chickens.
Answers
Answer: 0.0386
Step-by-step explanation:
Given: The probability hat the frozen chickens contain enough salmonella bacteria to cause illness if improperly cooked : p= 0.30
Sample size : n = 12
Let x = Number of contaminated chickens
Here , two outcomes for any chicken (either contaminated or not) , so it follows binomial distribution.
Binomial probability formula:
[tex]P(X=x) = \ ^nC_x p^x(1-p)^{n-x}[/tex]
The probability that the consumer will have more than 6 contaminated chickens :-
[tex]P(X>6)=P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)+P(X=12)\\\\=^{12}C_6(0.3)^6(0.7)^6+^{12}C_7(0.3)^7(0.7)^5+^{12}C_8(0.3)^8(0.7)^4+^{12}C_9(0.3)^9(0.7)^3+^{12}C_{10}(0.3)^{10}(0.7)^2+^{12}C_{11}(0.3)^{11}(0.7)^1+^{12}C_0(0.3)^{12}(0.7)^0[/tex]
[tex]=0.03860084306\approx0.0386[/tex] (simplified)
Hence, the required probability = 0.0386
what is (12x+5)+(-10x-3)
Answers
Answer:
2+2
Step-by-step explanation:
There ya go
a shop is having a sale all items are reduced by 30% work out the sale price of an item normally priced at £110
Answers
Answer:
77 us dollar
Step-by-step explanation:
because I used a calculator
Answer:
77
Step-by-step explanation:
I don’t know how to do this can someone help?
Answers
Answer:
i think its B cause 4 was the radius
Step-by-step explanation:
It’s an inequality I need the work for it ik the answer
Answers
Answer:
Solving the inequality [tex]1<\frac{a+7}{-2}[/tex] we get the value of a: [tex]\mathbf{a<-9}[/tex]
Step-by-step explanation:
We need to solve the inequality: [tex]1<\frac{a+7}{-2}[/tex]
We need to solve the inequality, to find the value of a.
Solving the inequality:
[tex]1<\frac{a+7}{-2}[/tex]
First step is Switching both sides (the inequality will be reversed)
[tex]\frac{a+7}{-2}>1[/tex]
The next step is to multiply both sides by -2 and reverse the inequality
[tex]\frac{a+7}{-2}*-2<1*-2\\a+7<-2[/tex]
Now, subtracting 7 on both sides
[tex]a+7-7<-2-7\\a<-9[/tex]
So, solving the inequality [tex]1<\frac{a+7}{-2}[/tex] we get the value of a: [tex]\mathbf{a<-9}[/tex]
what is 89999999+ 3099999999999=??????
Answers
3.100089999. This is is the answer
Answer:
3,100,089,999,998
Step-by-step explanation:
Hope this helped
What is the range of the cluster in the scatter plot?
A: Between 4 and 8 years of experience
B: Between 6 and 12 years of experience
C: Between $10,000 and $60,000
D: Between $40,000 and $60,000
Answers
Answer:
b
Step-by-step explanation:
b
hope this helped
Which of the following equations have infinitely many solutions?
Answers
Answer:
A
Step-by-step explanation:
The only one with nothing else in front of the X, which means you can't divide, which means it stays the same.
3(x-2)+1=
I have to turn this in, in 10 minutes. Help.
Answers
Answer:
3x-6+1
Step-by-step explanation:
I know algebraaaaaa
you deposit $500 in an account that pays 5% annual interest compound continuously what is the balance after 3 years
Answers
Answer:
So I= p x r/100 x t
= 500 x 5/100 x 3
= 25 x 3
$75 interest
Balnce will be $575
I need some help please and thank you
Answers
Simplify the expression 5 to the power of 3 x 5 to the power of -5.
Answers
Answer:
5^-2
Step-by-step explanation:
5^3 * 5^-5
~Use exponent rule [ x^y * x^z = x^y+z ]
5^3+(-5)
~Simplify
5^-2
Best of Luck!
PLEASE HELP!! I’ve got a car with an internal volume of 12,000 L. If I drive my car into the river and it implodes, what will be the volume of the gas when the pressure goes from 760 mmHg to 141.82 kPa?
Answers
Answer:
V2 = 8571.43L
Step-by-step explanation:
To solve for the V2, We can use V2 = P1V1 / P2
= 1.0 atm × 12,000 L / 1.4 atm
= 12,000 L / 1.4 atm
= 8571.43 L
Shannon and Bob are members of a cross-country team. Bob runs at a rate of 8 kilometers per hour and Shannon runs at a rate of 10 kilometers per hour. If the distance around the team's practice course is 1.7 kilometers, how much longer does it take Bob to complete one trip around the course than Shannon, to the nearest tenth of a minute?
Answers
Answer:
2.6 minutes
Step-by-step explanation:
Speed of Bob = 8 km/hr
Speed of Shannon = 10 km/hr
Distance of practice course = 1.7 km
As time = (distance)/(speed), so
Time taken by Bob to cover the distance, t1 = 1.7/8=0.2125 hours
Time taken by Shannon to cover the distance, t2 = 1.7/10= 0.17 hours
As t1 > t2, so, Bob takes more time than Shannon to complete the course.
t1-t2= 0.2125-0.17 = 0.0425 hours = 0.0425 x 60 minutes= 2.55 minutes.
On rounding up to tenth digit, t1-t2 = 2.6 minutes.
Hence, It takes 2.6 minutes more time for Bob to complete one trip around the course than Shannon
answers for both boxes please
Answers
Step 1: Multiply each equation by a suitable number so that the two equations have the same leading coefficient. ...
Step 2: Subtract the second equation from the first.
Step 3: Solve this new equation for y.
Step 4: Substitute y = 2 into either Equation 1 or Equation 2 above and solve for x.
variable equation. It is relatively difficult to determine the values of x and y without manipulating the equations. If one adds the two equations together, the x s cancel out; the x is eliminated from the problem. Hence it is called the "elimination method”.