Answer:
The possible lengths of the shortest side, 'y', are 0 cm < y < (1 + √3) cm
Step-by-step explanation:
The given parameters of the right triangle are;
The length of one of the perpendicular sides = 2 cm longer than the other
The length of the hypotenuse side > 2 × The length of the shortest side
Let 'x' represent the length of one of the perpendicular sides, let 'y', represent the length of the shortest perpendicular side, and let 'h', represent the hypotenuse side, we have;
x = 2 + y...(1)
h > 2·y...(2)
From equation (1), we get;
y = x - 2
By Pythagoras theorem, the hypotenuse side, 'h', is given as follows;
h = √(x² + y²) > 2 × y
Simplifying the above equation by plugging in x = y + 2, gives
h = √((y + 2)² + y²) > 2 × y
h² = 2·y² + 4·y + 4 > 4·y²
∴ 2·y² - 4·y - 4 < 0
2·(y - 1 + √3)·(y - (1 + √3)) < 0
y < 1 - √3 < 0, or y < 1 + √3
Therefore, the possible lengths of the shortest side of the right triangle, y are;
0 cm < y < (1 + √3) cm.
Find the volume of the triangular prism.
_____ cubic centimeters
Explanation:
The hint pretty much gives away the entire answer. You just need to compute [tex]\frac{4 \times 6}{2} \times 8[/tex] and you should get 96 cm^3
The portion [tex]\frac{4 \times 6}{2}[/tex] represents the area of the triangular face (it has base = 6 and height = 4). Recall that base*height/2 is the area of any triangle. The area of the triangle is (4*6)/2 = 24/2 = 12 cm^2.
Once you know the base face area, you multiply that by the depth of the prism which is 8 cm. So we get 12*8 = 96 cm^3
A reindeer runs 2014 miles in 3 hours. At that rate, how many miles does it run in 1 hour?
Answer:
about 671 miles
Step-by-step explanation:
2014m=3h
2014/3= about 671 miles an hour
Answer:
671.33 repeating
Step-by-step explanation:
2014/3=671.33
Which option shows the expression correctly combined? 8 - 3(4 -9x) *
20-45x
23x
27x-4
Answer:
27x-4
Step-by-step explanation:
pls help me ASAP CUS WHY NOT?
Answer:
Complementary angles
Step-by-step explanation:
When the sum of two angles which adds up to 90° it's called a complementary angle.
You can tell this because <a and <b both form an right angle
I need help with number 1
Answer:
Likely is the answer.
:))))
how do you convert 3.45 pounds to grams
What is x - 1 = -1? Please help
Answer:
x = 0
Step-by-step explanation:
x - 1 = -1
Add 1 to each side
x-1+1 = -1+1
x = 0
Answer:
x = 0
Step-by-step explanation:
x - 1 = - 1
x - 1 + 1 = - 1 + 1
x = 0
You borrow $200. The simple interest rate is 12%. You pay off the loan after 2 years. How much doe you pay for the lone
Answer:
224
Step-by-step explanation:
200*0.12=24
200+24=224
The amount to be paid for the loan is $248.
What is simple interest?'Simple interest is the interest amount for a particular principal amount of money at some rate of interest.
According to the given problem,
Principal amount (P) = $200
Rate of interest (r) = 12%
Time period (t) = 2 years
We know,
Final amount to be paid with interest (A) = P( 1 + rt )
= 200{ 1 + ( 0.12 × 2 )
= 200( 1 + 0.24 )
= 200 × 1.24
= $248
Hence, we can conclude, we have to pay $248 for the loan.
Learn more about simple interest here: https://brainly.com/question/22621039
#SPJ2
PLEASE HELP ASAP!! THANK YOU
EXPLANATION = BRAINLIEST & 5 STARS
From the library, one car heads north, and another heads east. Some time later, the northbound car has traveled 17 miles, and the eastbound train has traveled 144 miles. The two cars, measured in a straight line, are ___ miles apart.
Question on image. part(2)
will report answers out of question. Thank you
Answer:
67°
Step-by-step explanation:
< EFB = ½× (163-29) = ½×(134) = 67°
with a diameter of about 64 inches. What is the circumference of this large front wheel?
60 ÷ 6 = (36 ÷ 6) + (24 ÷ __)
I don't know this
Answer:
6
Step-by-step explanation:
60÷6 = 10
so we know the right side of the equal sign must equal 10
36÷6 = 6
now we know that (24÷n) must equal 10-6
we can write and equation like this:
24/n = 4
cross-multiply to get:
4n = 24
n = 24/4
n = 6
Answer:
60 ÷ 6 = ( 36 ÷ 6) + (24 ÷ ___)
10 = 6 + (24÷6)
10 = 6 + 4
10 = 10
The graph below represents which system of inequalities?
Answer:
Graphing Systems of Linear Inequalities
To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. ...
If the inequality is strict ( < or > ), graph a dashed line. ...
Finally, pick one point that is not on either line ( (0,0) is usually the easiest) and decide whether these coordinates satisfy the inequality or not.
Write a decimal -1.2--- as a mixed number
Answer:
-1 1/5
Step-by-step explanation:
Rewrite the decimal number as a fraction with 1 in the denominator
Multiply to remove 1 decimal places. Here, you multiply top and bottom by 101 = 10
Find the Greatest Common Factor (GCF) of 12 and 10, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 2,
Simplify the improper fraction
-1 1/5
write 6x-2y=-12 in slope intercept form
Answer:
y = 3x +6
Step-by-step explanation:
6x-2y=-12
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
Subtract 6x from each side
6x-6x-2y=-6x-12
-2y = -6x-12
Divide each side by -2
-2y/-2 = -6x/-2 -12/-2
y = 3x +6
Find the sum of the first 36 terms of the following series, to the nearest integer. 13, 19,25,...
Answer:
223?
Step-by-step explanation:
6n +7 (nth term)
(6*36)+7 = 223
Does anyone know how to do this?
Answer:
sorry ma g dont know this but my boy aaron yeager is smart he can help u 839
Step-by-step explanation:
Evaluate the expression when n=5.
4n²
Answer:
100.
Step-by-step explanation:
4(5)^2
= 4 * 15 = 100.
Math help please show work
Answer:
You can measure the area of the yard but measuring the length and width and then multiplying. Then you can divide by the amount of sod that is used to cover to see how many bags that need to be bought.
Step-by-step explanation:
This should be good :)
pls mark brainliest:)
A coordinate plane with a line passing through (negative 4, 3), (0, 1), and (2, 0). What are the slope and y-intercept of the linear function graphed to the left?
Answer:
0,1
Hope it helps!
if your talking about edge
slope: -½
y-intercept: 1
Step-by-step explanation:
B
4
Which represents the value of Point D on the number line?
д
B
с
D
-2.
0
2
-4
-(-3)
оооо
-3
-(4)
Answer:
-3 maybe, sorry if wrong im doing a pretest on this on edge
Step-by-step explanation:
Which of the following are point-slope equations of the line going through (-3, 4) and (2, 1)? Check all that apply. A. y-1 = g(x-2) B. y-4 = (x+3) O C. y-4 = -(x+3) D. Y+ 2 = (x-1 E. Y+3 = (x-4) OF. y-1 = -(x-2)
The point slope equation of the line going through (-3,4) and (2,1) is
[tex]y - 1 = - 3 \frac{(x - 2)}{5} [/tex]
or,
[tex]y - 4 = - 3 \frac{(x + 3)}{5} [/tex]
Answered by GAUTHMATH
Please help!!!! I'll give brainlist
Answer:
Hello! answer: y = 122
Step-by-step explanation:
360 - 116 = 244 244 ÷ 2 = 122 therefore y = 122
Hope that helps!
Answer:
x= z (vertically opposite angles)
x+z= 116
x+x = 116
2x= 116
x=116/2
x= 58
x+y= 180°(straight angle)
58°+y= 180°
y= 180°-58°
y = 122°
The ratio of boys to girls in a school is 9 : 10 whats does this ratio mean
Answer:
The ratio means that for every 9 boys there are 10 girls
Step-by-step explanation:
if ∠7=95 what is the measure of angle 6
Answer: If angle 7 is 95 degrees measurement then angle 6 would be85?
Step-by-step explanation:
Section 1 - Question 1
Stanley attempted to simplify the expression below.
4. (2.5x - 1.25) – 3x
His work, step by step, Is shown below.
Step 1: -4. {(2.5x + (-1.25)} – 32
Step 2: - 10x + (-5) - 3:0
Step 3:- 10.2 - 3x + (-5)
Step 4: - 13x - 5
In which step did he make his first error simplifying the expression?
A
Step 1
B
Step 2
Answer:
a and bwhich step did he make his first error simplifying the expression?
A
Step
Ive done a I just need b :)
Answer:
Step-by-step explanation:
Simon needs 1000 ML of milk
Craig needs 60 G of butter
Answer:
Craig needs 7.5g of butter to make 12 pancakes.
Step-by-step explanation:
To calculate how many times you need to multiply 8 by to make 12, simply divide 12 by 8. This gives you 1.5.
1.5*5 =7.5
So Craig needs 7.5g of butter to make 12 pancakes.
The figure below is a square pyramid.
What is the surface area of the figure?
Answer:
120
Step-by-step explanation:
Answer:
surface area of the square pyramid
(6×6)+(2×6×5)
36+60
96 square meters
answer is option 4
What is the value of y in the solution to the system of equations?
1/3X + 1/4Y = 1
2X - 3Y = -30
A. -8
B. -3
C. 3
D. 8
Answer: y = 8
Step-by-step explanation:
Solve for a. 2.4a + 8 = 27.2
Answer:
Hello! answer: a = 8
Step-by-step explanation:
2.4 × 8 = 19.2
19.2 + 8 = 27.2 therefore a = 8 hope that helps!
Answer:
a = 8
Step-by-step explanation:
2.4a + 8 = 27.2
2.4a + 8 - 8 = 27.2 - 8
2.4a = 19.2
2.4a ÷ 2.4 = 19.2 ÷ 2.4
a = 8