The sides of a triangle are 7, 4, n. If n is an integer, state the largest and smallest possible values of n.
smallest value-
largest value-
plz help
Smallest value and largest value of n is [tex]11 , 3[/tex].
The third side of a triangle has a range,
[tex]Sum\; of \;two\; other\; sides\geq n\geq Difference\; of\; the\; sides[/tex]
[tex]7+4\geq n \geq7-4[/tex]
[tex]11\geq n \geq 3[/tex]
Therefore
Largest[tex]=11[/tex]
Smallest[tex]=3[/tex]
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What is the Median Q1 ,Q3 and IQR of 80,90,95,85,70
Answer:
17.5
Step-by-step explanation:
70, 80, 85, 90, 95
Median: 85
Lower quartile: 75
Upper quartile: 92.5
Interquartile range: 92.5 - 75 = 17.5
Is it necessary to use the formulas for special products of binomials to multiply these binomials?
Final answer:
While it's not necessary to use the binomial theorem to multiply binomials, it can greatly simplify the process. This theorem is handy for higher powers and in cases where technology tools are not available.
Explanation:
The formulas for special products, like the binomial theorem, are not always necessary for multiplying binomials, but they can simplify the process significantly, especially for higher powers. When multiplying binomials without these formulas, one would have to apply the distributive property multiple times, which can be tedious and prone to error. The binomial theorem provides a direct way to expand binomials raised to a power in a series expansion: (a + b)n = an + n*an-1*b + ... + bn. Utilizing this formula can speed up calculations and help avoid mistakes.
In understanding series expansions, working with exponents, and creating formulas based on logical sense and unit consistency, students can sometimes simplify problems without needing to memorize formulas. However, for complex problems or when working with large exponents, knowing and applying the binomial theorem can be much more efficient.
Moreover, technologies like calculators and computer software often have functions that apply these theorems or carry out the multiplications of binomials, which can make manual calculations unnecessary, provided you have access to these tools. But understanding the underlying principles is important for a strong mathematical foundation.
If 14 over 3 equals x over y to the second power than 14 over x equals
What is the measure of ∠DEG?
A) 133°
B) 103°
C) 77°
D) 67°
How would six billion, nine hundred thirty-six thousand, fourteen be written in standard form? A.693,614B.6,936,014C.6,000,936,014D.6,936,000,014
Can anyone help me on this
A right rectangular prism has a length of 6 cm, a width of 8 cm, and a height of 4 cm. The dimensions of the prism are halved.
What is the volume of the reduced prism?
Enter your answer in the box.
_cm³
There are 36 students in the chess club , 40 students in the drama club , and 24 students in the film club. Which ratio is equivalent to 5:3
Jack is sharing 3 bananas with 3 Friends. Which expression represents the amount each one will get if they share them equally?
If L
is 30
units long and W
is 10
units long, how long is the diagonal to the nearest tenth?
Answer:
Step-by-step explanation:
Noah bought 1/2 pound of candy to share with his friends.They ate 3/8 pound of the candy.How much candy does Noah have left?
Total pound of candy with Noah = [tex] \frac{1}{2} [/tex]
Total pound of candy eaten by his friends = [tex] \frac{3}{8} [/tex] of [tex] \frac{1}{2} [/tex]
= [tex] \frac{3}{8} \times \frac{1}{2} [/tex]
= [tex] \frac{3}{16} [/tex]
Pound of candy left with Noah = [tex] \frac{1}{2} - \frac{3}{16} [/tex]
= [tex] \frac{8-3}{16} [/tex]
= [tex] \frac{5}{16} [/tex] pound
Therefore, [tex] \frac{5}{16} [/tex] pound of candy is left with Noah.
Emma created the poster shown below: A rectangle is shown. The length of the rectangle is labeled as length equal to 36 cm, and the width is labeled as width equal to 24 cm. What would be the dimensions of the poster at fraction 1 over 4 times its current size? Length = 32 cm, width = 20 cm Length = 40 cm, width = 28 cm Length = 144 cm, width = 96 cm Length = 9 cm, width = 6 cm
Answer:
Length = 9 cm, width = 6 cm
Step-by-step explanation:
If the length of the rectangle is labeled as length equal to 36 cm, and the width is labeled as width equal to 24 cm.
Length = 36cm
Width = 24cm
One fourth the current size of the rectangle will be;
New length= 1/4×36 = 9cm
New width = 1/4 × 24 = 6cm
The new dimension of the poster is therefore 9cm×6cm
Length = 9cm
Width = 6cm
a car is travelling at x kilometres per hour find the cars speed, in terms of x in metres per second give your answer in its simplest form
To convert a car's speed from kilometers per hour (x km/h) to meters per second, divide x by 3.6. This is because there are 1,000 meters in a kilometer and 3,600 seconds in an hour, leading to the simple formula: x / 3.6 m/s.
Explanation:To find the car's speed in meters per second (m/s) when it is traveling at x kilometers per hour (km/h), we need to convert km/h to m/s. There are 1,000 meters in a kilometer and 3,600 seconds in an hour. So, to convert from km/h to m/s, we use the conversion factor 1 km = 1,000 m and 1 hour = 3,600 seconds.
The formula to convert x km/h to m/s is: x \(\times\) 1,000 m / 3,600 s. Simplifying this, we get:
x \(\times\) 1,000 / 3,600 = x / 3.6 m/s.
Therefore, if a car is traveling at x kilometers per hour, its speed in meters per second is x / 3.6 m/s in its simplest form.
I’m not sure if I’m doing this right :/
how to slove this more complex negative exponent problem?
When an expression or a number is raised to the negative exponent, you have to reciprocate the expression or the number.
In this problem, the expression is raised to the power of -2
Therefore, the expression would become like this after reciprocating:
1/ (3x^2) ^2
Simplifying the expression:
1/ 9x^4
Find the unit rate.
625 revolutions in 223 seconds
The unit rate is ___
revolutions per second.
Step-by-step explanation:
a line's y-intercept is 0, and its slope is 6/5. what is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
what is (x-5)(x-3)=10 as a quadratic equation
how do you find the ratio of 40:28
Is the sum of 3√2 and 4 √2 rational or irrational? Explain your answer.
Sum of 3√2 and 4√2 is an irrational number.
What are irrational numbers?" Irrational numbers are those numbers which cannot be written in fraction or rational form."
According to the question,
Suppose 3√2 + 4√2 be a rational number.
which can be expressed in form of (p / q) form such that 'q' does not divides 'p'
3√2 + 4√2 = (p / q)
⇒ 7√2 = ( p / q)
Squaring both the sides we get,
49 × 2 = ( p² / q² )
⇒ 2 ×(49q²) = p²
⇒ p is an even number
⇒p = 2k , k≠0
Therefore,
2 × ( 49q²) = (2k)²
⇒2×(49q²) = 4k²
⇒q² = (2k² / 49)
Both p and q are even which implies 'q' divides 'p'.
It is contradictory to our supposition,
Therefore, 3√2 + 4√2 is an irrational number.
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Solve – 4y – 3 + 3y = 8 – 2y – 15 interpret the results
Candy is at the balloon shop and sees that 10 balloons cost 0.15 he needs 50 balloons to decorate his room how much will 50 balloons cost?
Alyssa works as a sales representative in an electronics store. She earns a fixed daily wage plus a commission on the sales she makes. The table shows her earnings based on the amount of sales she makes in a day.
Total Sales ($) Daily Earnings ($)
0 80
200 110
500 155
800 200
1,200 260
The equation that gives Alyssa's daily earnings based on her total sales is_____ .
When this data is plotted on a graph with a line connecting all the points, the y-intercept of the line represents _______ and the slope of the equation represents .
In this scenario, the y-intercept is________ .
fill in the blanks
here are the answer choices for the 1st one y=1.5x+80
y=0.
Answer: the same as the other person is righti
Step-by-step explanation:
Just #10 please!! Due soon too!!
Find the value of x.
A) x = 60
B) x = 59
C) x = 121
D) x = 177
What should be added to 3 to make the sum of 0?
Two similar parallelograms have areas of 18 in2 and 32 in2. Find the ratio of their perimeters.
Mark and Jill each have a $6500 loan with a loan term of 4 years. The interest rate on Mark’s loan is 3% and the interest rate on Jill’s loan is 4%. Mark’s monthly payment is $144 and Jill’s monthly payment is $147. How much more in interest will Jill pay than Mark?
A.
$144
B.
$412
C.
$556
D.
$968
A rectangle has a perimeter of 24 feet‚ the width of the rectangle is 3ft. what is the length
(4x)^-2 (4x)^3(4x)^9= (4x)
The answer is 4x to the 10th power