Answer:
[tex]x^2=10+\frac{18y^2}{5}[/tex]
Step-by-step explanation:
If you really want to get x^2 by itself the first step is to add 36y^2 on both sides giving you:
[tex]10x^2-36y^2=100[/tex]
[tex]10x^2-36y^2+36y^2=100+36y^2[/tex]
[tex]10x^2+0=100+36y^2[/tex]
[tex]10x^2=100+36y^2[/tex]
Now you divide both sides by 10:
[tex]x^2=\frac{100+36y^2}{10}[/tex]
You could separate the fraction:
[tex]x^2=\frac{100}{10}+\frac{36y^2}{10}[/tex]
You can reduce both fractions:
[tex]x^2=10+\frac{18y^2}{5}[/tex]
What fraction of an hour is 33 minuets in the simplest form
Ok.
So an hour contains 60 minutes.
The fraction is therefore,
[tex]\dfrac{33}{60}=\boxed{\dfrac{11}{20}}[/tex]
Hope this helps.
r3t40
Answer:
33 minutes is 11/20 of an hour.
Explanation:
So we know that 30 minutes is equal to half an hour. 30÷60 = 0.5
0.5 as a fraction is equal to 1/2.
Now let's use that same method for 33.
33÷60= 0.55.
0.55×100== 55.
55 as a fraction would be 55/100.
Let's convert that to its simplest form.
55÷5 = 11
100÷5 = 20
33 minutes is 11/20 of an hour.
1/2x+3 2/3x+1
What is the solution to the equation
Answer:
12
Step-by-step explanation:
Start by multiplying both sides by 2.
[tex]\frac{1}{2} x+3=\frac{2}{3} x+1\\x+6=\frac{4}{3} x+2[/tex]
Next, multiply both sides by 3.
[tex]x+6=\frac{4}{3} x+2\\3x+18=4x+6[/tex]
Combine like terms.
[tex]3x+18=4x+6\\18=x+6\\12=x[/tex]
In triangle ABC, BG = 24 mm. What is the length of segment
GE?
12 mm
24 mm
36 mm
48 mm
Answer:
A. 12 mm
Step-by-step explanation:
May I have brainliest please? :)
Answer: A: 12 mm
Step-by-step explanation:
^^
The graph shows the solution to a system of inequalities:
Which of the following inequalities is modeled by the graph?
A.
[tex]4x + 3y \leqslant 12;x \geqslant 0[/tex]
B.
[tex]4x + 3y \geqslant 12;x \geqslant 0[/tex]
C.
[tex]4x - 3y \leqslant 12;x \geqslant 0[/tex]
D.
[tex] - 4x - 3y \leqslant 12;x \geqslant 0[/tex]
Answer:
Option A. [tex]4x+3y\leq 12[/tex] and [tex]x\geq 0[/tex]
Step-by-step explanation:
we know that
The solution of the first inequality is the shaded area below the solid line [tex]4x+3y=12[/tex]
The solid line passes through the points (0,4) and (3,0) (the y and x intercepts)
therefore
The first inequality is
[tex]4x+3y\leq 12[/tex]
The solution of the second inequality is the shaded area to the right of the solid line x=0
therefore
The second inequality is
[tex]x\geq 0[/tex]
Describe an example of an augmented matrix.
Answer:
Step-by-step explanation:
When we join the columns of two or more matrices having the same number of rows it is known as augmented matrix.
Let A= [tex]\left[\begin{array}{ccc}1&6\\0&3\\\end{array}\right][/tex]
B= [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
Then the augmented matrix is(A|B)
Note that a vertical line is used to separate te columns of A from the columns of B
(A|B) [tex]\left[\begin{array}{ccc}1&6\\0&3\\\end{array}\right | \left\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
This is a simple example of augmented matrix....
Answer:
An augmented matrix refers to a matrix formed by appending the columns of two matrices.
The perfect example to show this is a linear systems of equations, because there we have a matrix formed by the coeffcients of the variables only, and we have a second matrix formed by the constant terms of the system.
If we have the system
[tex]2x+3y=5\\x-4y=9[/tex]
The two maxtrix involved here are
[tex]\left[\begin{array}{ccc}2&3\\1&-4\end{array}\right] \\\left[\begin{array}{ccc}5\\9\end{array}\right][/tex]
However, to solve the system using matrices, we have to formed an augmented matrix
[tex]\left[\begin{array}{ccc}2&3&5\\1&-4&9\end{array}\right][/tex]
So, as we defined it at the beginning, an augmented matrix is the appending of colums from two matrices to form one.
P is a prime number and q is a positive integers such that p + q = 1696 IF P and Q are co primes and their Lcm is 21879 Then find p and q
Answer:
P = 1 3
Q = 1 6 8 3
Step-by-step explanation:
through factorization of 21879
Instructions:Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). The native bird population in a city is decreasing at a rate of 10% per year due to industrialization of the area by humans. The population of native birds was 14,000 before the decrease began. Complete the recursively-defined function to describe this situation. f(1) = f(n) = f(n - 1) · , for n ≥ 2 After 3 years, birds will remain.
Answer:
The recursive function is;
f(n)=f(n-1)×0.9 for n≥2
After 3 years, 11340 birds will remain.
Step-by-step explanation:
First the native population was 14,000 before decreasing started, hence this is your f(1)
f(1)=14000
⇒A decrease of 10% is similar to multiplying the native value of birds with 90%
New number of birds = native value × 90% ⇒f(1)×0.9
For second year , you multiply the value you get after the first decrease by 0.9 to get the new number of birds;
f(2)=f(1)×0.9= 0.9f(1)=0.9×14000=12600
For the 3rd year, the value of the second year,f(2) is then reduced by 10%. This is similar to multiplying value of f(1) by 90%
f(3)=f(2)×0.9=12600×0.9=11340
Apply the same for the 4th year and above, hence for nth year;
f(n)=f(n-1)×0.9 for n≥2
four less than the quotient of a number cubed and seven, increased by three
Answer:
(a^3/7) - 4 + 3
Step-by-step explanation:
We need to translate the words into equations:
The quotient of a number cubed and seven: (a^3/7)
four less than the quotient of a number cubed and seven: (a^3/7) - 4
four less than the quotient of a number cubed and seven, increased by three:
(a^3/7) - 4 + 3
The celsius and Fahrenheit scales are related by the equation C=5/9(f-32). What temperature fahrenheit would give a temperature of 5C?
Answer:
41F
Step-by-step explanation:
41-32=9
9*5/9=5
Answer:
41 degrees F.
Step-by-step explanation:
C = 5/9(f - 32)
5 = 5/9 (f - 32) Multiply both sides by 9/5:
5 * 9/5 = f - 32
9 = f - 32
f = 9 + 32
= 41.
Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n 2 1?
2.5, 6.25, 15.625, 39.0625, ..
2.5, 5, 10, 20
-10,-7.5, -5, -2.5, ...
-10, -25, 62.5, 156.25
Answer:
Sequence 3
-10,-7.5,-5,-2.5,...
Step-by-step explanation:
So f(n+1)=f(n)+2.5 means a term can be found by adding it's previous term to 2.5. That means this is an arithmetic sequence with a common difference of 2.5.
f(n+1)=f(n)+d is the recursive form for an arithmetic sequence with common difference d.
So you are looking for a sequence of numbers that is going up by 2.5 each time.
Let's check sequence 1:
2.5+2.5=5 so not this one because we didn't get 6.25 next.
Let's check sequence 2:
2.5+2.5=5 is what we have for the 2nd term.
5+2.5=7.5 so not this one because we didn't get 10 next.
Let's check sequence 3:
-10+2.5=-7.5 is the 2nd term
-7.5+2.5=-5 is the 3rd term
-5+2.5=-2.5 is the 4th term
Sequence 3 is arithmetic with common difference 2.5 assuming the pattern continues.
Let's check sequence 4 for fun:
-10+2.5=-7.5 is not -25
So we are done. Sequence 3 is the only one that fits term=previous term+2.5 or f(n+1)=f(n)+2.5.
Find the tenth term of the
geometric sequence, given the
first term and common ratio.
a =4 and r=1/2
Answer:
[tex]\frac{1}{128}[/tex]
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a [tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio, hence
[tex]a_{10}[/tex] = 4 × [tex](\frac{1}{2}) ^{9}[/tex] = 4 × [tex]\frac{1}{512}[/tex] = [tex]\frac{1}{128}[/tex]
Final answer:
The tenth term of the geometric sequence with the first term 4 and the common ratio of 1/2 is calculated using the formula for the nth term. Substituting the given values into the formula and simplifying yields the tenth term as 1/128.
Explanation:
To find the tenth term of a geometric sequence, we use the formula for the nth term in a geometric sequence which is an = a1 x r(n-1), where a1 is the first term, r is the common ratio, and n is the term number.
In this case, the first term a1 is given as 4 and the common ratio r is 1/2. To find the tenth term, we substitute n with 10 in the formula:
a10 = 4 x (1/2)(10-1)
This simplifies to:
a10 = 4 x (1/2)9 = 4 x 1/512 = 4/512 = 1/128
Therefore, the tenth term of the geometric sequence is 1/128.
A 4cm cube is cut into 1 CM cubes. what is the percentage increase in the surface area after such cutting?
Answer:
400%.
Step-by-step explanation:
The surface area of a 4 cm cube = 6 * 4^2
= 96 cm^2.
The number of 1 cm cubes that can be cut from the larger cube is :
16 * 4 = 64.
The surface area of each of these smaller cubes is 6*1 = 6 cm^2.
The increase in surface area is a factor of (6*64) / 96
= 4 = 400%.
What is the 20th digit after the decimal point of the sum of the decimal equivalents for the fractions 1/7 and 1/3?
Use the elimination method to solve the system of equations. Choose the
correct ordered pair,
2y = x + 2
x - 3y = -5
Answer:
x = 4, y = 3 → (4, 3)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2y=x+2&\text{subtract x from both sides}\\x-3y=-5\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-x+2y=2\\x-3y=-5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-y=-3\qquad\text{change the signs}\\.\qquad\boxed{y=3}\\\\\text{put the value of y to the second equation:}\\\\x-3(3)=-5\\x-9=-5\qquad\text{add 9 to both sides}\\\boxed{x=4}[/tex]
If a = m 2 + 2, what is the value of a when m = -3? -7 -4 8 11
Given
a = m(2) + 2value of a when m = -3Substitute m with -3
a = -3*2 + 2
a = -6 + 2
a = -4
Answer
The value of a when m = -3 is -4
Answer:
=11
Step-by-step explanation:
The equation given is a=m²+2
To find a when m= -3 , we substitute for m in the equation.
a=(-3)²+2
=9+2
=11
Therefore a=11 when m is -3
I need the answer to a parts I-iii and the answer to b
Answer:
a)
i) Mean = 72
ii) Median = 72
iii) Mode = 72
b)
69, 70, 71, 72, 72, 72, 73, 74, 75
Step-by-step explanation:
a. To find mean, median and mode
It is given that all the 9 students get 72 marks.
Therefore the data set be,
72, 72, 72, 72, 72, 72, 72, 72 72
i) mean = (sum of data)/(total number of data)
= (9 * 72)/9 = 9
ii) Median - Central data in the data set when arranging ascending or descending order
72, 72, 72, 72, 72, 72, 72, 72 72
Median = 72
iii) Mode - Most repeating data in the data set
Here mode = 72
b). To find a data set
69, 70, 71, 72, 72, 72, 73, 74, 75
Here Mean, mode and median are all 72
Use the tables to determine which function will eventually exceed the other, and provide your reasoning.
x f(x)
−1 −5
0 −6
1 −5
2 −2
x g(x)
−1 0.166
0 1
1 6
2 36
f(x) will eventually exceed g(x) because f(x) is an exponential function.
f(x) will eventually exceed g(x) because f(x) has a higher rate of change.
g(x) will eventually exceed f(x) because g(x) is an exponential function.
g(x) will eventually exceed f(x) because g(x) has a higher rate of change.
Answer:
g(x) will eventually exceed f(x) because g(x) is an exponential function.
Step-by-step explanation:
From the first table we can observe the following patterns:
[tex]f( - 1) = {( - 1)}^{2} - 6 = - 5[/tex]
[tex]f(0) = {( 0)}^{2} - 6 = - 6[/tex]
[tex]f( 1) = {( -1)}^{2} - 6 = - 5[/tex]
[tex]f(2) = {( 2)}^{2} - 6 = - 2[/tex]
In general,
[tex]f(x) = {x}^{2} - 6 [/tex]
From the second table we can observe the following pattern:
[tex]g( - 1) = {6}^{ - 1} = \frac{1}{6} [/tex]
[tex]g(0) = {6}^{ 0} = 1[/tex]
[tex]g(1) = {6}^{1} = 6[/tex]
[tex]g(2) = {6}^{2} = 36[/tex]
In general,
[tex]g( x) = {6}^{ x} [/tex]
Conclusion:
Since the f(x) represents a quadratic function and g(x) represents an exponential function, g(x) will eventually overtake f(x).
The correct answer is C.
Answer: C.
Step-by-step explanation:
Go it right on my test
4. A student is chosen at random from the student body at a given high school. The probability that the
student selects Math as the favorite subject is 1/4. The probability that the student chosen is a junior is
116/459. If the probability that the student selected is a junior or that the student chooses Math as the
favorite subject is 47/108, what is the exact probability that the student selected is a junior whose
favorite subject is Math?
Answer:
The exact probability that the student selected is a junior whose favorite subject is Math is [tex]\frac{124}{459}[/tex].
Step-by-step explanation:
Let the following events represents by the alphabets A and B.
A: Student selects Math as the favorite subject
B: Student chosen is a junior
The probability that the student selects Math as the favorite subject is 1/4.
[tex]P(A)=\frac{1}{4}[/tex]
The probability that the student chosen is a junior is
[tex]P(B)=\frac{116}{459}[/tex]
The probability that the student selected is a junior or that the student chooses Math as the favorite subject is 47/108.
[tex]P(A\cup B)=\frac{47}{108}[/tex]
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
[tex]\frac{47}{108}=\frac{1}{4}+\frac{116}{459}-P(A\cap B)[/tex]
[tex]P(A\cap B)=\frac{1}{4}+\frac{116}{459}-\frac{47}{108}=\frac{31}{459}[/tex]
The exact probability that the student selected is a junior whose favorite subject is Math is
[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]P(\frac{B}{A})=\frac{\frac{31}{459}}{\frac{1}{4}}=\frac{124}{459}[/tex]
Therefore the exact probability that the student selected is a junior whose favorite subject is Math is [tex]\frac{124}{459}[/tex].
The exact probability that the student selected is a junior whose favourite subject is maths is 124/459
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
The probability that the student selects Maths the favourite subject:
P(A) = 1/4
The probability that the student chosen is a junior:
P(B) = 116/459
The probability that the student selected is a junior or that the student chooses maths the favourite subject:
P(A∪B) = 47/108
We know:
P(A∩B) = P(A) + P(B) _P(A∪B)
P(A∩B) = 1/4 + 116/459 - 47/108
P(A∩B) = 31/459
The exact probability that the student selected is a junior whose favourite subject is maths:
P(B|A) = P(A∩B) /P(A)
= (31/459)/(1/4)
= 124/459
Thus, the exact probability that the student selected is a junior whose favourite subject is maths is 124/459
Learn more about the probability here:
brainly.com/question/11234923
#SPJ2
You have$560 in an account which pays 4.8% compounded annually. If you invest your money for 8 years, then how many dollars of interest will you earn by the end of term
Answer:
$ 254.85
Step-by-step explanation:
Total amount invested = $ 560
Interest rate = r = 4.8% = 0.048
Time in years = t = 8 years
The formula for compound interest is:
[tex]A =P(1+\frac{r}{n})^{nt}[/tex]
Here,
A is the total amount accumulated after t years. P is the amount invested initially and n is the compounding periods per year. Since in this case compounding is done annually, n will be 1. Using the values in the above formula, we get:
[tex]A=560(1+\frac{0.048}{1})^{8} = \$ 814.85[/tex]
Thus, the total amount accumulated after 8 years will be $ 814.85
The amount of interest earned will be:
Interest = Amount Accumulated - Principal Amount
Interest = $ 814.85 - $ 560 = $ 254.85
By the end of 8 years, $ 254.85 would be earned in interest.
For a sequence an=3/n(n+1) what is the value of a 10
Answer:
[tex]\large\boxed{a_{10}=\dfrac{3}{110}}[/tex]
Step-by-step explanation:
Put n = 10 to the equation [tex]a_n=\dfrac{3}{n(n+1)}[/tex]
[tex]a_{10}=\dfrac{3}{10(10+1)}=\dfrac{3}{10(11)}=\dfrac{3}{110}[/tex]
For this case we have the following sequence:
[tex]a_ {n} = \frac {3} {n (n + 1)}[/tex]
We must find the value of[tex]a_ {10}[/tex], then, substituting [tex]n = 10[/tex] in the formula we have:
[tex]a_ {10} = \frac {3} {10 (10 + 1)}\\a_ {10} = \frac {3} {10 * 11}\\a_ {10} = \frac {3} {110}[/tex]
ANswer:
[tex]a_ {10} = \frac {3} {110}[/tex]
The perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width of the rectangle. Can the perimeter of the rectangle be 60 units when its width is 12 units and its length is 18 units?
A)No. If the rectangle has L = 18 and W = 12, P would not equal 60.
B) No. The rectangle cannot have P = 60 and L = 18 because L + W is less than 24.
C) Yes. The rectangle can have P = 60 and L = 18 because 60 = 24 + 18.
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60.
Answer:
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60
Step-by-step explanation:
The formula for the perimeter of a rectangle is [tex]P=2L+2W[/tex].
If the width is [tex]W=12\:units[/tex] and the length is [tex]L=18\:units[/tex], then the perimeter becomes:
[tex]P=2\times 12+2\times 18[/tex].
[tex]\implies P=24+36[/tex].
[tex]\implies P=60[/tex].
Therefore the answer is
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60
Answer:
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60
Step-by-step explanation:
The formula for the perimeter of a rectangle is .
If the width is and the length is , then the perimeter becomes:
.
.
.
Therefore the answer is
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60
If the Zeros of a quadratic equation are seven and -4 what would be the x intercepts
Answer:
7, -4
Step-by-step explanation:
The zeros are just another name for the x intercepts
7, -4
Write the equation of the line in slope-intercept form that has the following points: (2, -1)(5, -3) y = -2x + 1/3 y = -2/3x + 1 y = -2x + 1 y = -2/3x + 1/3
Answer:
[tex]\large\boxed{y=-\dfrac{2}{3}x+\dfrac{1}{3}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
===============================================
We have the points (2, -1) and (5, -3). Substitute:
[tex]m=\dfrac{-3-(-1)}{5-2}=\dfrac{-2}{3}=-\dfrac{2}{3}[/tex]
We have the equation:
[tex]y=-\dfrac{2}{3}x+b[/tex]
Put the coordinates of the point (2, -1):
[tex]-1=-\dfrac{2}{3}(2)+b[/tex]
[tex]-1=-\dfrac{4}{3}+b[/tex] add 4/3 to both sides
[tex]\dfrac{1}{3}=b\to b=\dfrac{1}{3}[/tex]
Finally:
[tex]y=-\dfrac{2}{3}x+\dfrac{1}{3}[/tex]
in triange ABC, AB=5 and AC=14. Find The measure of angle c to the nearest degree
Answer:
The answer is ∠C= 20 degree
Step-by-step explanation:
The answer is ∠C= 20 degree
We have given:
AB= 5
AC = 14
and we have to find ∠c to the nearest degree.
So,
We know that:
tan(C)= AB/AC
tan(C)= 5/14
tan(C)= 0.3571
C=20 degree
Thus the answer is ∠C = 20 degree ....
Consider the polynomial p(x)=x^3-9x^2+18x-25, which can be rewritten as p(x)=(x-7)(x^2-2x+4)+3 . The number _[blank 1]_ is the remainder whenp(x) is divided by x-7, and so _[blank 2]_ a factor of p(x)
What is blank 1 and 2?
options:
a)7
b)is
c)is not
d)0
e)3
Answer:
Blank 1: 3 is the remainder
Blank 2: not a factor
Step-by-step explanation:
If p(x)=(x-7)(x^2-2x+4)+3, then dividing both sides by (x-7) gives:
[tex]\frac{p(x)}{x-7}=(x^2-2x+4)+\frac{3}{x-7}[/tex].
The quotient is [tex](x^2-2x+4)[/tex].
The remainder is [tex]3[/tex].
The divisor is [tex](x-7)[/tex].
The dividend is [tex]p(x)=x^3-9x^2+18x-25[/tex].
It is just like with regular numbers.
[tex]\frac{11}{3}[/tex] as a whole number is [tex]3\frac{2}{3}[/tex].
[tex]3\frac{2}{3}=3+\frac{2}{3}[/tex] where 3 is the quotient and 2 is the remainder when 11 is divided by 3.
Here is the division just for reminding purposes:
3 <--quotient
----
divisor-> 3 | 11 <--dividend
-9
---
2 <---remainder
Anyways just for fun, I would like to verify the given equation of
p(x)=(x-7)(x^2-2x+4)+3.
I would like to do by dividing myself.
I could use long division, but I have a choice to use synthetic division since we are dividing by a linear factor.
Since we are dividing by x-7, 7 goes on the outside:
x^3-9x^2+18x -25
7 | 1 -9 18 -25
| 7 -14 28
-------------------------------
1 -2 4 3
We have confirmed what they wrote is totally correct.
The quotient is [tex]x^2-2x+4[/tex] while the remainder is 3.
If p/(x-7) gave a remainder of 0 then we would have said (x-7) was a factor of p.
It didn't so it isn't.
Just like with regular numbers. Is 3 a factor of 6? Yes, because the remainder of dividing 6 by 3 is 0.
PLEASE HELLPPPPPPPP
Answer:
6
Step-by-step explanation:
f(0) means let x=0
In the table when x=0 f(0) =6
Find an ordered pair to represent t in the equation t=1/2u+v if u=(-1,4) and v=(3,-2)
Answer:
t=(2.5,0)
Step-by-step explanation:
Given that
[tex]t=\frac{1}{2} u+v[/tex]
and
u=(-1,4)
v=(3,-2)
Then,substitute value of u and v in the equation
[tex]t=\frac{1}{2} (-1)+3=-\frac{1}{2}+ (3)=2.5\\\\\\\\t=\frac{1}{2} (4)+-2=2+-2=0\\\\\\t=(2.5,0)[/tex]
Answer:
The answer on edge is C
Step-by-step explanation:
Find the distance between the points (-3, 2) and (4, -5)
Answer:
[tex]\large\boxed{7\sqrt2}[/tex]
Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (-3, 2) and (4, -5). Substitute:
[tex]d=\sqrt{(4-(-3))^2+(-5-2)^2}=\sqrt{7^2+(-7)^2}=\sqrt{49+49}=\sqrt{(49)(2)}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{49}\cdot\sqrt2=7\sqrt2[/tex]
one line segment is 5 cm more than four times the length of another the difference in their lengths is 35cm how long are they
Answer:
Length of the segments will be 10 cm and 45 cm.
Step-by-step explanation:
Let the length of one segment is x.
Then by the statement of this question,
"one segment is 5 cm more than four times the length of another".
Length of other segment = 4x + 5
(4x + 5) - x = 35
4x + 5 - x = 35
3x + 5 = 35
3x = 35 - 5
3x = 30
x = 10 cm
Length of other segment = 4(10) + 5 = 45 cm
Therefore, two segments are of length 10 cm and 45 cm.
one positive integer is 7 less than another. The product of two integers is 44. what are the integers?
Answer:
4 and 11
Step-by-step explanation:
Lets call the smallest n
And the other one n+7
Then,
n.(n+7)=44
n²+7n=44
Subtract 44 from both sides.
n²+7n-44=44-44
n²+7n-44=0
Factorize the equation.
n²+11n-4n-44=0
n(n+11)-4(n+11)=0
(n+11)(n-4)=0
n+11=0 , n-4=0
n=-11 , n=4
n=4 is the only positive solution, so the numbers are:
4 and 11....
Answer:
The two integers are: 4 and 11.
Step-by-step explanation:
We are given that one positive integer is 7 less than another. Given that the product of two integers is 44, we are to find the integers.
Assuming [tex]x[/tex] to be one positive integer and [tex]y[/tex] to be the other, we can write it as:
[tex]x=y-7[/tex] --- (1)
[tex]x.y=44[/tex] --- (2)
Substituting x from (1) in (2):
[tex](y-7).y=44[/tex]
[tex]y^2-7y-44=0\\\\y^2-11y+4y-44=0\\\\y(y-11)+4(y-11)[/tex]
y = 11
Substituting y = 11 in (1) to find x:
[tex]x=11-7[/tex]
x = 4