Answers
Answer:
n = {9, 10}Step-by-step explanation:
Let the equation be:
n² - 19n + 91 = k²Multiply both sides by 4 and complete the square:
4n² - 76n + 364 = 4k²(2n)² - 2(2n)(19) + 19² + 3 = 4k²(2n - 19)² - 4k² = - 3(2n + 2k - 19)(2n - 2k - 19) = -3Since -3 = 1(-3) = (-1)*3, we have following options:
1)
2n + 2k - 19 = 12n - 2k - 19 = -3Eliminate k by adding up equations:
4n - 38 = -24n = 36n = 92)
2n + 2k - 19 = -12n - 2k - 19 = 3Eliminate k by adding up equations:
4n - 38 = 24n = 40n = 10Related Questions
What is 3.7 as a mixed number
Answers
Answer:
3 7/10
Step-by-step explanation:
37/10 = 3 7/10
applications of rational numbers
Answers
Step-by-step explanation:
Rational numbers are real numbers which can be written in the form of p/q where p,q are integers and q ≠ 0. We use taxes in the form of fractions. When you share a pizza or anything. Interest rates on loans and mortgages.
Hope it helps you
Mark my answer as brainlist
have a nice day
If carina can ride her bike at a speed of 7 mph, it will take her 3 hours to travel 21 miles. True or false?
Answers
Answer:
True
Step-by-step explanation:
We know that distance = rate * time
21 miles = 7 miles per hours * 3 hours
21 miles = 21 miles
True
(1/1+sintheta)=sec^2theta-secthetatantheta pls help me verify this
Answers
Answer:
See Below.
Step-by-step explanation:
We want to verify the equation:
[tex]\displaystyle \frac{1}{1+\sin\theta} = \sec^2\theta - \sec\theta \tan\theta[/tex]
To start, we can multiply the fraction by (1 - sin(θ)). This yields:
[tex]\displaystyle \frac{1}{1+\sin\theta}\left(\frac{1-\sin\theta}{1-\sin\theta}\right) = \sec^2\theta - \sec\theta \tan\theta[/tex]
Simplify. The denominator uses the difference of two squares pattern:
[tex]\displaystyle \frac{1-\sin\theta}{\underbrace{1-\sin^2\theta}_{(a+b)(a-b)=a^2-b^2}} = \sec^2\theta - \sec\theta \tan\theta[/tex]
Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:
[tex]\displaystyle \displaystyle \frac{1-\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta \tan\theta[/tex]
Split into two separate fractions:
[tex]\displaystyle \frac{1}{\cos^2\theta} -\frac{\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta\tan\theta[/tex]
Rewrite the two fractions:
[tex]\displaystyle \left(\frac{1}{\cos\theta}\right)^2-\frac{\sin\theta}{\cos\theta}\cdot \frac{1}{\cos\theta}=\sec^2\theta - \sec\theta \tan\theta[/tex]
By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:
[tex]\displaystyle \sec^2\theta - \sec\theta\tan\theta \stackrel{\checkmark}{=} \sec^2\theta - \sec\theta\tan\theta[/tex]
Hence verified.
Which of the following numbers has exactly two significant digits? OA) 3.40 OB) 2.125 OC) 1.0475 OD) 0.00050
Answers
Answer:
Here, option (d) has significant digits. hence , option (d) ✓ is correct.Geometry, please answer question ASAP
Answers
Answer:
C
Step-by-step explanation:
Using the tangent ratio in the right triangle
tanC = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{c}{a}[/tex] , then
C = [tex]tan^{-1}[/tex] ([tex]\frac{c}{a}[/tex] )
what fraction of these houses have seven rooms
Answers
Answer:
9/50
Step-by-step explanation:
18 % have 7 rooms
18 % means 18 out of 100
18/100
Divide top and bottom by 2
9/50
i would like if someone helped me with this.
Answers
Answer:
the answer is to the question is b
Answer:
(-1.5,9)
Step-by-step explanation:
In second quadrant the x- component is negative where as y- component is positive
. Tập nghiệm của bất phương trình
1 5
1 1
x x
x x
là:
Answers
Answer:
pnj hnu n
126
11
yes ......
....
.
..
x u g
Find the indicated side of the
right triangle.
45°
y
6
45°
Answers
Answer:
6
Step-by-step explanation:
tan 45 = 6 / x
1 = 6 / x
x = 6
Note :
Tan 45 value = 1
Answer:
x=6
Step-by-step explanation:
Since this is an isosceles triangle, the sides must be equal next to the base angles that are equal
x=6
May somebody help do this please??
Answers
Answer:
a. 1 yard:3 feet
b. 3 feet:1 yard
c. Sean ran exactly a mile
Step-by-step explanation:
For a and b there are 3 feet in a yard
For c a mile is exactly 5280 feet
Answer:
A: 3 : 1
B: 1 : 3
C: less
Step-by-step explanation:
A: There are 3 feet in a yard, so feet: yard would be 3:1
For example, 21 feet equals 7 yards, 21:7 is equal to 3:1B: For every yard, there are 3 feet, so th ratio would be 1:3
For example, 4 yards equals 12 feet, 4:12 is equal to 1:3C: Sean ran 1,600 yards. To convert this into feet, multiply by 3. He ran 4,800 feet. Since 4,800 < 5,280, he ran less than a mile
URGENT. Geometric Probability.
Answers
Answer:
Hello,
Step-by-step explanation:
heigth of the equilateral triangle:
[tex]h=3*\dfrac{\sqrt{3}}{2}[/tex]
Area of the triangle:
[tex]A=\dfrac{6*3\sqrt{3} }{2*2} =\dfrac{9\sqrt{3} }{2} \\\\[/tex]
Area of the disk:
[tex]S=\pi*4^2=16\pi\\\\[/tex]
Probability:
[tex]p=\dfrac{9\sqrt{3} }{2*16*\pi}=0.15506125....\approx{15.5\%}[/tex]
Answer:
Step-by-step explanation:
The height of the triangle is given as 6.5, the base is given as 6, therefore, the area of the triangle is:
[tex]A=\frac{1}{2}(6)(6.5)\\A=19.5[/tex]
The area of the circle is:
[tex]A=\pi(4)^2\\A=16\pi\\A=50.26548[/tex]
Divide the area of the triangle by the area of the circle:
[tex]\frac{19.5}{50.2654}*100=38.8[/tex]%
whats the area in square inches
Answers
Answer:
Area of triangle =1/2b×h
1/2×10×8.7
=44 square inches
Answer:
44
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
where b is the base and h is the height
A = 1/2 (10) (8.7)
A= 43.5
Rounding to the nearest whole number
A = 44
If m = 8 and n = 5, then man + 3) – n+1-
Answers
Answer:
P (−1)n(n+1)(n+2) (n+1)3 converges
Step-by-step explanation:
Which correlation best describes the data below.
Answers
Answer:
weak positive
Step-by-step explanation:
weak because the line of best fit (the line passes through all points and used to express the relationship between them) doesn't pass through all ponts here.
positive because the values of data points are rising throughout the graph.
For the given functions f and g , find the indicated composition. F(x) = -5x + 4, g(x) = 4x + 6 (g∘f)(x)
Answers
Answer:
(g∘f)(x) = -20x + 22
Step-by-step explanation:
(g∘f)(x) simply means g(f(x))
We are given;
f(x) = -5x + 4
g(x) = 4x + 6
Thus;
(g∘f)(x) = 4(-5x + 4) + 6
(g∘f)(x) = -20x + 16 + 6
(g∘f)(x) = -20x + 22
Find the value of m if x + m is a factor of x^2 - 5mx + 3
Answers
Answer:
+or- sqrt(3/4)
Step-by-step explanation:
If x + m is a factor, that means that when x = -m the equation equals 0. Sub -m into x
0 = (-m)^2 - 5m(-m) + 3
0 = m^2 - 5m^2 + 3
0 = -4m^2 + 3
Factorise
0 = -4(m^2 - 3/4)
0 = -4(m + sqrt(3/4))(m - sqrt(3/4))
:. m = +or- sqrt(3/4)
2p+8p>-20 help please ☺️
Answers
Answer:
p > -2
Step-by-step explanation:
2p + 8p > -20
10p > -20
10/10p > -20/10
p > -2
p is greater than -2
How to find the unknown angles
Answers
Answer:
How do you find the unknown angle of a triangle? To determine to measure of the unknown angle, be sure to use the total sum of 180°. If two angles are given, add them together and then subtract from 180°. If two angles are the same and unknown, subtract the known angle from 180° and then divide by 2.
Step-by-step explanation:
y+1=3/4(x+3) in general form pls??
Answers
Answer:
Step-by-step explanation:
y+1 =(3/4)x+9/4
y=(3/4)x+1/4
Answer:
3x - 4y + 5 = 0
Step-by-step explanation:
The equation of a line in general form is
Ax + By + C = 0 ( A, B, and C are integers )
Given
y + 1 = [tex]\frac{3}{4}[/tex] (x + 3) ← multiply through by 4 to clear the fraction
4y + 4 = 3(x + 3)
4y + 4 = 3x + 9 ( subtract 4y + 4 from both sides )
0 = 3x - 4y + 5 , that is
3x - 4y + 5 = 0 ← in general form
prove sin^2 π/6 + cos^2 π/3 - tan^2 π/4 = -1/2
Answers
=(
2
1
)
2
+(
2
1
)
2
−1
2
=
2
−1
Therefore, L.H.S = R.H.S
x423-2
Which expression is equivalent to log12
-?
(x+1)
O 410g,2x+ 2logi z(x2 – 2)- 5logiz(x: 1)
O 410912x+ žlog12. - 5log,2x+log421
o (x2
log124x+10912(x - 2)-510912(x)+1
4109,2x+ 3 109126x - 2)- 5log12(x + 1)
Answers
Answer:
D
Step-by-step explanation:
log(x^4*sqrt(x^3-2)/(x+1)^5)=log(x^4)+log(sqrt(x^3-2))-log((x+1)^5)
=> 4log(x)+(1/2)*log(x^3-2)-5log(x+1)
U= a/k, for a. I really don’t get this whole topic an in depth explanation would be great thanks!
Answers
Answer:
ku=a
Step-by-step explanation:
We are given
[tex]u = \frac{a}{k} [/tex]
and we need to solve for a. First let multiply k by both sides to isolate a.
[tex]ku = a[/tex]
Two linear functions are described below.
Function f(x) has the equation f(x)=3x−4.
Function g(x) has the table of values shown below.
x g(x)
0 4
3 5
6 6
9 7
Which statement is true regarding the functions f(x) and g(x)?
A
The slopes of the two functions are the same.
B
The slopes of the two functions are opposites.
C
The y-intercepts of the two functions are the same.
D
The y-intercepts of the two functions are opposites.
Answers
Answer:
D
The y-intercepts of the two functions are opposites.
Step-by-step explanation:
f(x) = 3x-4 which has a slope of 3 and a y intercept of -4
g(x)
m = (5-4)/(3-0) = 1/3
g(x) = 1/3 x +4
g(x) has a slope of 1/3 and a y intercept of 4
Please Help!!!!!
Prove that polynomials are not closed under division.
Answers
Solve the simultaneous equation, will give out brainliest answer
a=bcd
a+b=cd
a+b+c=d
a+b+c+d=1
Answers
Answer:
a = 1/42, b = 1/7, c = 1/3 and d = 1/2
Step-by-step explanation:
a = bcd (1)
a + b = cd (2)
a + b + c = d (3)
a + b + c + d = 1 (4)
Substituting equation (3) into equation (4), we have
a + b + c = d (3)
a + b + c + d = 1 (4)
(a + b + c) + d = 1 (4)
d + d = 1 (5)
2d = 1
dividing through by 2, we have
d = 1/2
Taking equation (2) and equation (3), we have
a + b = cd (2)
a + b + c = d (3)
substituting equation (2) into equation (3), we have
a + b = cd (2)
(a + b) + c = d (3)
cd + c = d
Factorizing, we have
c(d + 1) = d
dividing through by d + 1, we have
c = d/(d + 1)
substituting d = 1/2 into the equation, we have
c = d/(d + 1)
c = 1/2 ÷ (1/2 + 1)
c = 1/2 ÷ 3/2
c = 1/2 × 2/3
c = 1/3
Taking equations (1) and (2), we have
a = bcd (1)
a + b = cd (2)
Substituting equation (1) into (2), we have
a = bcd (1)
a + b = cd (2)
bcd + b = cd (2)
Factorizing, we have
b(cd + 1) = cd
dividing through by (cd + 1), we have
b = cd/(cd + 1)
substituting the values of c and d into the equation,, we have
b = cd/(cd + 1)
b = 1/3 × 1/2/(1/3 × 1/2 + 1)
b = 1/6/(1/6 + 1)
b = 1/6 ÷ 7/6
b = 1/6 × 6/7
b = 1/7
Since a = bcd, substituting the values of b,c and d into the equation, we have
a = bcd
a = 1/7 × 1/3 × 1/2
a = 1/42
So, a = 1/42, b = 1/7, c = 1/3 and d = 1/2
The length of a rectangle is 2 Inches less than three times its width, and its perimeter is 36 Inches. Find the width of the
rectangle
Answers
Answer: Width = 5 inches
Concept:
Here, we need to know the idea of the perimeter.
A perimeter is a path that encompasses/surrounds/outlines a shape.
Perimeter of rectangle = 2 (w + l)
w = width
l = length
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
w = w
l = 3w - 2
P = 36 inches
Given formula
P = 2 (w + l)
Substitute the value into the formula
36 = 2 (w + 3w - 2)
Simplify values in the parentheses
36 = 2 (4w -2)
Divide 2 on both sides
36 / 2 = 2 (4w - 2) / 2
18 = 4w - 2
Add 2 on both sides
18 + 2 = 4w - 2 + 2
20 = 4w
Divide 4 on both sides
20 / 4 = 4w / 4
w = 5
Hope this helps!! :)
Please let me know if you have any questions
Find the measure of one exterior angle for the following regular polygon that’s for both questions
Answers
Answer:
Step-by-step explanation:
=
-x- 2x + 1 on the interval from
What is the average rate of change of the function g(x)
X = 2 to x = 6?
Pleaseeeee help
Answers
Answer:
X = 2 is your answer
hope this will help you
Answer:
x=2
Step-by-step explanation:
P =5000 T =2year R =7%find simple intreset
Answers
Answer:
5070
Step-by-step explanation:
Total = P(1+rt) =5000(1+0.007*2) =5070
If the question is asking about the amount of interest earnt, its 70
