Given:
In a set of 3 numbers the first is a positive integer, the second is 3 more than the first and the 3rd is a square of the second.
To find:
The equation for the given situation if the sum of the numbers is 77.
Solution:
a. Let the first number in the set is x.
The second is 3 more than the first. So, the second number is [tex](x+3)[/tex].
The 3rd number is a square of the second. So, the third number is [tex](x+3)^2[/tex].
Therefore, the first, second and third numbers are [tex]x,(x+3),(x+3)^2[/tex] respectively.
b. The sum of the numbers is 77.
First number + Second number + Third number = 77
c. So, the equation in terms of x is:
[tex]x+(x+3)+(x+3)^2=77[/tex]
Therefore, the required equation is [tex]x+(x+3)+(x+3)^2=77[/tex].
d. On simplification, we get
[tex]x+x+3+x^2+6x+9=77[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
[tex]x^2+(6x+x+x)+(3+9)=77[/tex]
[tex]x^2+8x+12=77[/tex]
Subtract 77 from both sides.
[tex]x^2+8x+12-77=77-77[/tex]
[tex]x^2+8x-65=0[/tex]
Therefore, the simplified form of the required equation is [tex]x^2+8x-65=0[/tex].
16:32:12
Which linear inequality is represented by the graph?
O x < 2 x + 3
Oy> x+3
O y>x+3
O y<{x+3
-3 -2 -1
The linear inequality that represents the graph is y > (2/3)x + 3.
Option C is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
y < (2/3)x + 3
y > (3/2)x + 3
y > (2/3)x + 3
y < (3/2)x + 3
The graph is on the positive side of the y-coordinate so,
We can consider:
y > (3/2)x + 3
y > (2/3)x + 3
Now,
Plotting in a graph we see that,
We need to have the y-intercept at y = 3 and the x-intercept at x = 4.5.
So,
y > (2/3)x + 3 satisfied.
Thus,
y > (2/3)x + 3 represents the graph.
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ7
What is the slope of a line that is perpendicular to the line: -4x + 6y = -1 ?
A. -3/2
B. -2/3
C. 1/4
D. 3/2
8. A juice container shaped like a cylinder has a base area of 100 cm2 and can hold 1500 cm3 of juice. The height of the juice container is
The height of a juice cylinder container with base area of 100 cm² and volume of 1500 cm³ is 15 cm
Base area of a cylinderBase area = πr²
base area = 100 cm²
100 = π × r²
r² = 100 / π
r = √100 / π
Volume of a cylindervolume = πr²h
1500 = π (√100 / π)² × h
1500 = π(100 / π) × h
1500 = 100h
divide both sides by 100
h = 1500 / 100
h = 15 cm
learn more on cylinder here: https://brainly.com/question/27342403
Dave has been running every day to get
in shape for the track season. He wants
to determine his average rate.
Dave learned the following formula in his
science class:
d = r.t
where
d = distance
r = rate
t = time
Answer:
r = d/t
Step-by-step explanation:
Given:
d = r * t
where,
d = distance
r = rate
t = time
Rewrite the equation to determine Dave's rate
d = r * t
d = rt
Divide both sides by the
d / t = rt / t
d / t = r
r = d/t
Average rate, r = d/t
9. Choose the equation that represents the graph below:
Answer:
y= -4/3 x + 4
Step-by-step explanation:
i guess
2. The parameter "b": Compare the graphs of several different exponential growth functions in
Mathematica to discover the significance of the parameter "b". Explain in detail what the
parameter "b" tells you about the graph of an exponential growth function.
Answer:
See explanation
Step-by-step explanation:
Required
The significance of "b" in exponential function
An exponential function is represented as:
[tex]y = ab^x[/tex]
In the above equation, parameter "b" is the rate of the function
In other words, the constant multiplier of the function.
Take for instance;
[tex]y = 2*4^x[/tex]
By comparison:
[tex]b = 4[/tex]
Another instance is:
[tex]y = 2(-4)^x[/tex]
By comparison
[tex]b = -4[/tex]
Other significance of parameter b are:
If [tex]b > 0[/tex] then b represents a growth factor
If [tex]b < 0[/tex] the b represents the factor of decay
[tex]b \ne 0[/tex] i.e. b is never 0
Complete the equations below. 1.86 \div 2 =1.86÷2=1, point, 86, divided by, 2, equals \text{ hundredths}\div 2 hundredths÷2start text, space, h, u, n, d, r, e, d, t, h, s, end text, divided by, 2 1.86 \div 2 =1.86÷2=1, point, 86, divided by, 2, equals \text{ hundredths} hundredths start text, space, h, u, n, d, r, e, d, t, h, s, end text 1.86 \div 2 =1.86÷2=1, point, 86, divided by, 2, equals
Answer:
[tex]1.86 \div 2 = 0.93[/tex]
Step-by-step explanation:
The correct form of the question is:
Complete the equations below.
[tex]1.86 \div 2 =[/tex]
Required
Solve
Start from left to right
[tex]1 \div 2 = ??[/tex] --- this will give a fraction.
So, we append the next digit
[tex]1.8 \div 2 = 0.9[/tex]
Next:
[tex]0.06 \div 2 = 0.03[/tex]
Bring the results together:
[tex]1.86 \div 2 = 0.9+ 0.03[/tex]
[tex]1.86 \div 2 = 0.93[/tex]
What should be done first to evaluate the expression?
4 + 8 ÷ 4 - 2 × 5
Add 4 and 8.
Divide 8 by 4.
Subtract 2 from 4.
Multiply 2 by 5.
Divide 8 by 4
Because is PEDMAS, division comes first.
Answer:
divide 8 by 4
Step-by-step explanation:
PEMDAS or BODMAS
HELP QUICK ILL GIVE BRAINLIEST
Answer:
A=35 degrees, B=55 degrees, C=110 degrees
Step-by-step explanation:
The 35 degree given angle is vertical angles with A, so they are congruent
The sum of angles in a triangle is 180, and we already have 2 angles (35 and 90) so subtract those and you get 55
angle c and the other given angle (70 degrees) are supplementary so subract 70 from 180
50 POINTS!!!! If you were on a rocket ship for a month that sat in between the moon and earth, how might moon phases be different? (need quickly!!!) also at least 2-4 sentences
Answer:I would sayif the planet earth was making a shadown on it. when u on other side
Step-by-step explanation:
That is the best i got
Answer:
Different times
Step-by-step explanation:
The closer you could get to the moon, the faster the phases will move. If you are about half way it should cut the time it takes to get through a season. Since you get closer to the object.
Find the missing side length
Answer:
35
Step-by-step explanation:
Since the triangles are similar, we can write a ratio
25 ?
---- = -----
5 7
Using cross products
25*7 = 5 ?
Divide each side by 5
25*7/5 = 5?/5
35 = ?
Can someone help me with this math homework please!
Evaluate 4x-2 when x = 5.
A. 18
B. 12
C. 43
O D. 22
Answer:
A: 18
Step-by-step explanation:
1. 4(5) - 2
2. 20 - 2
3. 18
Mr. Serpe started with $200. He has a hole in his pocket and he lost $2 every day for a week. He then found $150. How much money does he have?
Answer:
336
Step-by-step explanation:
2x7=14, so 200-14=186, then 186+150=336
Solve for the triangle: ABC
A: 90 degrees
B: 6 feet
C: 10 feet
Literally what is this lol
Answer:
i think the first one- bc it should be 11x5pi but it would still end up as 55pi
Step-by-step explanation:
sorry if that doesnt help
Patricia has $34,000 to invest. She invests some at 17% and the balance at 20%. Her total annual interest income is $6245. Find the amount invested at each rate
Answer:
she invest $18,500 at the 17% rate and $15,500 at the 20% rate.
Step-by-step explanation:
Suppose that you invest some quantity A to an invest rate of x%
At the end, the amount you will have is given by:
Amount = A + A*(x%/100%)
Where:
A*(x%/100%) is the interest income
So, here she initially has $34,000
And she invest some quantity X to a 17% and a quantity Y to 20%
Then we have:
X + Y = $34,000
And we know that her total anual income is $6245
X*(17%/100%) + Y*(20%/100%) = $6245
Then we have a system of two equations:
X + Y = $34,000
X*(17%/100%) + Y*(20%/100%) = $6245
First we can rewrite the second one to a more simpler form:
X*(0.17) + Y*(0.20) = $6245
Now we can isolate one of the variables in the first equation to get:
X = $34,000 - Y
Now we can replace that in the other equation to get:
( $34,000 - Y)*0.17 + Y*0.20 = $6245
Now we can solve this for Y:
$34,000*0.17 + Y*(0.20 - 0.17) = $6245
$5,780+ Y*0.03 = $6245
Y*0.03 = $6245 - $5,780 = $465
Y = $465/0.03 = $15,500
And X = $34,000 - Y = $34,000 - $15,500 = $18,500
So she invest $18,500 at the 17% rate and $15,500 at the 20% rate.
There are 25 rows of seats in the high school auditorium with 20 seats in the first row, 21 seats in the second
row, 22 seats in the third row, and so on. How many total seats are in the auditorium?
OA) 800 seats
OB) 860 seats
Answer:
A) 800 seats
Step-by-step explanation:
Notice that an arithmetic sequence is formed with the number of seats. Since we're adding one seat each row, the last (25th) row will have 44 seats since the first row has 20 seats.
The sum of an arithmetic sequence is given by:
[tex]S_n=n\left(\frac{a_1+a_n}{2}\right)[/tex], where [tex]n[/tex] is the number of terms, [tex]a_1[/tex] is the first term, and [tex]a_n[/tex] is the last term
Therefore, substituting [tex]a_1=20[/tex], [tex]a_n=44[/tex], and [tex]n=25[/tex], we get:
[tex]S_n=25(\frac{20+44}{2}),\\s_n=25\cdot 32=\boxed{800}[/tex]
Write an equation of the line that passes through the point (6, -9) with the given slope m = 3.
Answer:
y = 3x - 27
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 3 , then
y = 3x + c ← is the partial equation
To find c substitute (6, - 9) into the partial equation
- 9 = 18 + c ⇒ c = - 9 - 18 = - 27
y = 3x - 27 ← equation of line
Which r-value represents the weakest correlation?
–0.75
–0.27
0.11
0.54
Answer:
0.11
Step-by-step explanation:
Strongest correlation:
The strongest correlations happen for [tex]r = -1[/tex] and [tex]r = 1[/tex], that is, when r has the higher absolute value.
In this question:
The value of r with the lowest correlation is the one with the lowest absolute value(absolute value of -0.75 is 0.75 for example), so it is 0.11, which is the answer.
Answer:
it's C on edg
Step-by-step explanation:
.11
Today only, a desk is being sold at a 33% discount. The sale price is $268. What was the price yesterday?
Discount percent = 33%
Sale price = $268
Let the original price be $x.
So,
[tex]x - (33\% \: of \: x) = 268 \\ = > x - ( \frac{33}{100} \times x) = 268 \\ = > x - ( \frac{33x}{100}) = 268 \\ = > \frac{100x}{100} - \frac{33x}{100} = 268 \\ = > \frac{(100x - 33x)}{100} = 268 \\ = > \frac{67x}{100} = 268 \\ = > 67x = 268 \times 100 \\ = > 67x = 26800 \\ = > x = \frac{26800}{67} \\ = > x = 400[/tex]
So, yesterday the price was $400.
The midpoint of AB is M(1,1). If the coordinates of A are (3, 3), what are the coordinates of B?
Answer:
The answer in (-1,-1) because it goes down by x-2 and y-2
which expression is equivalent to (4 square root 5 to the power of 3) to the power of 1/2?
the answer is on the photo
For each function, state whether it is linear, quadratic, or exponential.
Answer:
Step-by-step explanation:
Table for function 1,
x y Difference 1 Difference 2
2 10 - -
3 1 1 - 10 = -9 -
4 10 10 - 1 = 9 9 - (-9) = 18
5 37 37 - 10 = 27 27 - 9 = 18
6 82 82 - 37 = 45 45 - 27 = 18
Since, difference 2 is common as 18,
Table will represent a quadratic function.
Table for function 2,
x y Difference 1 Difference 2
5 16 - -
6 19 19 - 16 = 3 -
7 28 28 - 19 = 9 9 - 3 = 6
8 43 43 - 28 = 15 15 - 9 = 6
9 64 64 - 43 = 21 21 - 15 = 6
Since, difference 2 is common as 6,
Table will represent a quadratic function.
Table for function 3,
x y Ratio
1 112 -
2 56 56 ÷ 112 = [tex]\frac{1}{2}[/tex]
3 28 28 ÷ 56 = [tex]\frac{1}{2}[/tex]
4 14 14 ÷ 28 = [tex]\frac{1}{2}[/tex]
5 7 7 ÷ 14 = [tex]\frac{1}{2}[/tex]
Since, ratio is common as [tex]\frac{1}{2}[/tex].
Table will represent an exponential function.
Find DC, given that line AD is the angle bisector of < CAB.
Answer:
8
Step-by-step explanation:
LINE DC =BD
because line AD is a bisector of CAB
Dividing line CAD into two equal half's
please help. i need this done today
Answer:
herlojffhgdxvjdxhyeb olis the tim view on the euros 2020 final
Will give brainliest to the first person who answers
Answer:
z =86
Step-by-step explanation:
The exterior angle of a triangle is the sum of the opposite interior angles
z + z-39 = z+47
2z-39 = z+47
Subtract z from each side
z-39 = 47
Add 39 from each side
z = 47+39
z =86
The given information is,
To find the required value of z.
Property we use,
The exterior angle of a triangle is the sum of the opposite interior angles.
Now we can get the value of z,
→ z + z-39 = z + 47
→ 2z-39 = z + 47
→ 2z -z = 47 + 39
→ z = 47 + 39
→ [z = 86]
Thus, the required value of z is 86.
How much less is 17km than 24.6km?
Answer:
[tex]7.4km[/tex]
Step-by-step explanation:
[tex]24.6km - 17km \\ = 7.4km[/tex]
hope this helps you.
Simplify. 1224√
THIS IS A KEYSTONE ALGEBRA THING LOL
Answer:
6[tex]\sqrt{34}[/tex]
Step-by-step explanation:
[tex]\sqrt{1224}\\[/tex] = [tex]\sqrt{36*34}[/tex] = 6[tex]\sqrt{34}[/tex]
x-(x-(x-y³)) use x=9, and y=1
Answer:
The answer: 8
Step-by-step explanation:
x-(x-(x-y³))
x=9 , y=1 —> 9 - (9-(9-1³)) —> 9 - (9-(8))—> 9 - ( 1) —> =8
