Answer:
9units²
Step-by-step explanation:
A triangle has 3 sides. Let the length of the three sides be a, b, c.
If the perimeter of the triangle is 18, then;
P = a+b+c
a+b+c = 18... 1
If the sum of the squares of the three side lengths is 128, this means;
a²+b²+c² = 128... 2
Since the triangle is also right angled, according to Pythagoras theorem;
c² = a²+b²... 3 (taking c as the hypotenuse)
Substitute equation 3 into 2;
(a²+b²)+c² = 128
c²+c² = 128
2c² = 128
c² = 128/2
c² = 64
c = √64
c = 8
Substituting c = 8 into 1
a+b+c = 18
a+b+8=18
a+b = 10 ...... 3
Substituting c = 8 into 2
a²+b²+c² = 128
a²+b²+8² = 128
a²+b²+64 = 128
a²+b²= 64..... 4
Solve equation 3 and 4 simultaneously;
a+b = 10
a²+b²= 64
From 4; a = 10-b
Substitute a = 10-b into 4;
(10-b)²+b² = 64
100-20b+b²+b² = 64
2b²-20b+100-64 = 0
2b²-20b+36 = 0
Divide through by 2:
b²-10b+18 = 0
b = 10±√10²-4(18)/2
b = 10±√100-72/2
b =( 10±√28)/2
b =(10±√4×7)/2
b = (10±2√7)/2
b = 5±√7
Hence b = 5+√7
If a+ b = 10
a+(5+√7 ) = 10
a = 10-(5+√7)
a = 10-5-√7
a = 5-√7
Area of the triangle A = 1/2 ab
A = 1/2 × (5+√7) × (5-√7)
A = 1/2 × (25-5√7+5√7-7)
A = 1/2 × (25-7)
A = 1/2 × 18
A = 9
Hence the are of the triangle is 9units²
Five roses cost $25 how many Roses can you purchase for $75
Answer: 15
Step-by-step explanation: 5 roses are 25 dollars so what your going to do is multiply 5 by 3 to get 15 do the same with 25, 25 x 3 is 75 so you will get 15 roses for 75 dollars
2. Which of these graphs represents a function?
Answer:
I think the first one.
Step-by-step explanation:
Tanya is 6 times younger than her great-grandfather. If a zero is placed between the digits of her age, it will read as the age of her great-grandfather. How old is Tanya?
Answer:
Tanya is 18 years old.
Step-by-step explanation:
In order to determine this, we assume the following
x = tens digit of the age of Tanya, and also the hundreds digit of Tanya's great-grandfather age
y = units digit of the age of Tanya, and also the units digit of Tanya's great-grandfather age
Therefore, we have:
10x + y = (1 / 6) * (100x + y)
Multiply both sides by 6, we have:
[10x + y] * 6 = [(1 / 6) * (100x + y)] * 6
60x + 6y = 100x + y
Collect the like terms, we have:
6y - y = 100x - 60x
5y = 40x
Divide through by 5, we have:
y = 8x
That is,
8x = y
Note that x and y has to be single digits. This can only be obtained only when x = 1 and y = 8. And given how x and y is defined above, we have:
The age of Tanya = 18
This can be verified as follows:
18 = 108 / 6
18 * 6 = 108
108 = 108
Therefore, Tanya is 18 years old.
1. M=? J=? K=?
2. N=?
3. ( did not know how to crop, please ignore this question! )
Thank you so much!
Answer:
See Explanation
Step-by-step explanation:
m = 46° (vertical angles)
j = 92° (vertical angles)
j + k + 46° = 180° (staright line angles)
92° + k + 46° = 180°
138° + k = 180°
k = 180° - 138°
k = 42°
n = 37° + 44° = 81°
Can someone answer fast?
Which of the following rules describes the function graphed below?
I have no idea how to do this
Answer:
I would say c im not 100% sure sorry if i got it wrong
Step-by-step explanation:
A bag holds 12 red marbles, 11 green
marbles, 17 blue marbles, and 5 yellow
marbles. What is the probability that
you will NOT choose a blue marble?
5
A
45
(В)
11
45
12
© 45
28
45
Answer:
62.22%
Step-by-step explanation:
First, find how many total marbles there are:
12 + 11 + 17 + 5
= 45
Then, find how many marbles that are not blue:
12 + 11 + 5
= 28
Then, divide 28 by 45, and multiply by 100
(28/45) x 100
= 62.22% is the probability of not choosing a blue marble
how do i graph negative square roots on a number line
Answer:
see below
Step-by-step explanation:
On the real number line you can't
to graph them you have to make a Cartesian plane
with x= the real numbers
and y= the imaginary numbers
The temperature at 3:00 pm is 27 degrees. The temperature drops 4 degrees every hour for 8 hours. What is the temperature at 11:00 pm?
what is the value of the expression below when x=8? 9x-5
Answer:
67
Step-by-step explanation:
9x−5
x=8
9(8)−5
72−5
=67
The area of a trapezium is 360 cm² and its height is 18 cm. If one of the parallel sides is longer than the other by 6 cm, then the two parallel sides are.
Answer:
The two parallel sides a and b are 17 cm and 23 cm respectively
Step-by-step explanation:
Area of a trapezium = {(a+b)/2} h
Where
h = height = 18 cm
a = parallel side 1 = x
b = parallel side 2 = x + 6
Area of a trapezium = {(a+b)/2} h
360 = {(x + x + 6) / 2} 18
360 = { (2x + 6) / 2} 18
360 = (2x + 6) 9
360 = 18x + 54
Subtract 54 from both sides
360 - 54 = 18x
306 = 18x
Divide both sides by 18
x = 306 / 18
= 17
x = 17 cm
a = parallel side 1 = x
x = 17 cm
b = parallel side 2 = x + 6
x + 6
= 17 + 6
= 23 cm
If you give me the right answer i will give you the brainlyest!!!!!!
Answer:
the graphed points are in the picture attached
They intersect at (-8,1)
It passes through the x-axis at (-10,0)
It passes through the y-axis at (0,5)
Step-by-step explanation:
:)
Answer:
its a blue line from one ten to anothor
2x=y=6
X+2y=-2
Solving system of equations
Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest form. a1 = – 25 an = an–1–14 an=
Given :
[tex]a_1=-25[/tex] .
[tex]a_n=a_{n-1}-14[/tex] .
To Find :
The general equation of [tex]a_n[/tex] .
Solution :
We know , when difference between any two consecutive terms in an A.P is equal , then the series is in arithmetic progression .
Now , common difference ,
[tex]d=a_n-a_{n-1}\\\\d=-14[/tex]
Also , first term is -25 .
Now , general term of an A.P is given by :
[tex]a_n=a+(n-1)d\\\\a_n=-25+(n-1)(-14)\\\\a_n=-25-14n+14\\\\a_n= -11-14n[/tex]
Hence , this is the required solution .
Let b represent the hours Liz spends babysitting. Let t represent the number of hours she spends tutoring. Given that Liz can work at most 12 hours per week, write an inequality that models the number of hours she spends babysitting and tutoring in a week.
Answer:
b+t < 12 (< has a line under it)
Step-by-step explanation:
Liz can work at most 12 hours per week. So, add the number of hours she spends babysitting, b, and the number of hours she spends tutoring, t, in a week, and represent the sum as less than or equal to 12:
b + t < 12
Also I just got done doing this problem my self
Need help with this problem
Answer:
Step-by-step explanation:
2x + 1 + x + 23 = 180
3x + 24 = 180
3x = 156
x = 52
2(52) + 1 = 104 + 1 = 105
52 + 23 = 75
Write the Linear Equation in Point-Slope Form for a line that has a slope of
-10 and passes through the point (8,2). *
Answer:
y = -10x + 82
Step-by-step explanation:
Plug in the slope and point into y = mx + b to solve for b:
y = mx + b
2 = -10(8) + b
2 = -80 + b
82 = b
Then, plug b and the slope into y = mx + b
y = -10x + 82 is the equation in point slope form.
Max is thinking of a number, which he calls n. He adds 8 and then doubles the sum.
• Write an expression to represent Max's number.
Answer:
2(n+8)
sum is 30
Step-by-step explanation:
Answer:
2(n+8)
Step-by-step explanation: taking quiz right now
simplify 12-15÷3-3 pwease
Answer: -6
Step-by-step explanation: mark me as brainliest if i helped
The value of the expression is 4.
We have,
Expression:
12 - 15 ÷ 3 - 3
Now,
Apply PEMDAS.
Divide 15 by 3.
12 - 15/3 - 3
[ 3 x 5 = 15]
So,
12 - 5 - 3
12 - (5 + 3)
12 - 8
4
Thus,
The value of the expression is 4.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ6
i need help on this please
Answer:
[tex]\frac{3}{7}[/tex] × [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
Step 1. Turn the second fraction upside down (it becomes a reciprocal):
[tex]\frac{4}{5}[/tex] becomes [tex]\frac{5}{4}[/tex]
Step 2. Multiply the first fraction by that reciprocal:
[tex]\frac{3}{7}[/tex] × [tex]\frac{5}{4}[/tex] = ?
3 x 5 = 15
7 x 4 = 28
[tex]\frac{3}{7}[/tex] × [tex]\frac{5}{4}[/tex] = [tex]\frac{15}{28}[/tex]
Step 3. Simplify the fraction:
[tex]\frac{15}{28}[/tex] = [tex]\frac{15}{28}[/tex] You can't simplify this fraction
Answer:
15/28
Step-by-step explanation:
Solve for the length of BC
Answer:
BC= 9cm
Step-by-step explanation:
You'll need to use the Pythagorean theorem:a^2 + b^2 = c^2
12^2 + b^2 = 15^2The slanted side of the triangle is always going to be 'c' because it is the longest side of the triangle.
Now simplify: 144 + b^2 = 225I got these numbers because 12^2= 144 and 15^2= 225
Subtract. 225 - 144 = 81Now find the square root of 81. The answer is 9.The ratio of white cars in the parking lot to
black cars is is 5 to 7. The number of white
cars is 24 less than the number of black cary
How many black cars are there?
Answer:84
Step-by-step explanation:
you multiply each side by 12. That gets you 60 white cars and 84 black cars. 60 is 24 less than 85
A student runs 100 meters in 11 seconds. What is the speed of the student in miles?
Answer:
0.00565 miles / second
Step-by-step explanation:
1 mile = 1609.344 meters
100 meters = 100/1609.344 = 0.0621 miles (aprox)
100 meter/ 11 seconds = 0.0621miles / 11 seconds
= 0.00565 miles / second
Here is a list of numbers.
-45
-21
-16
12
33
40
Workout the sum of all numbers in this list
Answer:
3
Step-by-step explanation:
add all numbers
Answer:3
Step-by-step explanation:
Probability.
!!!!!!!!!!!!!!
will mark brainliest
Answer:
2/9ths hope this helps!
Please mark brainliest.
Step-by-step explanation:
Evaluate the expression when a=3.
a^2+12
[tex]3^{2} + 12 = 9 + 12 = 21[/tex]
The answer is 21.
Answer:
The correct answer is 21.
Step-by-step explanation:
To solve this problem, we simply substitute 3 for a in the expression.
Given the expression,
a^2 + 12
we should replace "a" with 3, as denoted by the problem, giving us:
(3)^2 + 12
Now, we simplify using the order of operations. PEMDAS tells us that we should simplify what is in the parentheses first because it has an exponent.
9 + 12
Now, we can just add the two remaining terms together, giving us:
21
Therefore, the answer is 21.
Hope this helps!
The scale is 1:500 the students cell model has a length of 15 Cm.
How many cm is the real cells length
A. 33cm
B. 0.002
C. 0.03
D. 7500 cm
Answer:
Option C - 0.03 cm
Step-by-step explanation:
The model has a length of 15 cm.
Now, we are told that the scale is 1:500. This means that 1 unit is represents 500 cm on the model.
Since the length on the model is 15 cm which is 15 units, then the true length would be;
15 × 1/500 = 0.03 cm
Therefore, the true length is 0.03 cm.
Option C is correct
Answer:
0.03 cm
Step-by-step explanation:
HELP ME!!! THIS IS THE LAST QUESTION ON MY HOMEWORK
The musical theme was first introduced by the
Answer:
entire orchestra I'm gonna say
what is 24-6x3+52-(12÷2)
Answer:
Step-by-step explanation:
524-6x3+52-(12÷2)
Multiplique los números
524-18+52- (12÷2) paso tres divida los números 524-18+52-6calcula la suma o resta 524-18+52-6=552solución= x = 552Someone please help me out with this question ASAP thank u
Answer:
Yes, it is AC.
Explanation:
There’s no other way of naming it.