Answer:
Infinitely many solutions. The value of x can be any real number.
Step-by-step explanation:
6 times 1/3x = 2x
6 times 1/2 = 3
6 times (1/3x + 1/2) = 2x+3
The left side of the original equation becomes 2x+3. The right side is also 2x+3. Both sides are the same, so we get infinitely many solutions.
We have,
[tex]6(\frac{1}{3}x+\frac{1}{2})=2x+3[/tex]
First distribute 6 through parentheses
[tex]2x+3=2x+3[/tex]
We can see both sides are equal hence for all x the equation will result with tautology (undeniable equality).
The answer is [tex]x \in \mathbb{R}[/tex].
Hope this helps.
Which of the following is the correct representation of the polynomial
F(x) = x4 - 2x3 + 2x - 1 as a product of linear factors?
A. F(x) = (x+1)(x - 1)(x - 1)(x+1)
B. F(x) = (x - 1)(x - 1)(x - 1)(x + 1)
C. F(x) = (x-1)(x-1)(x - 1)(x - 1)
D. F(x) = (x + 1)(x + 1)(x+1)(x + 1)
Answer:
Your answer is B: F(x)=(x-1)(x-1)(x-1)(x+1)
The population of Collin County, which follows the exponential growth model, increased from 491,675 in 2000 to 782,341 in 2010. Find the exponential growth rate, k.
Answer:
p=ak^t
p1=491272*k^0
p2=782341*k^10
782341/491272 = k^10
k=1.047629
growth rate is 4.7629%
2012: predicted population is 491272*1.047629^12=858,642 people
1245863=491272*1.047629^t
1.047629^k=2.5363599
ln both sides is k ln 1.0476=ln 2.5363
t=20.000 years.
Rule of 72 would say 72/4.76 or 15.12 years for doubling
14.90 years
2017 predicted is 491272*1.0476^17 or 1083552, or more than actual, so the rate of growth is slowing down.
The required exponential growth rate, k is 4.7629%
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
The exponential function will be as
p=a[tex]k^t[/tex]
p₁=491272*k⁰
p₂=782341*k¹⁰
782341/491272 = k¹⁰
k = 1.047629
So, the growth rate is 4.7629%
2012: the predicted population is 491272 × 1.047629¹² =858,642 people
1245863=491272 × [tex]1.047629^t[/tex]
[tex]1.047629^k[/tex] = 2.5363599
ln both sides is k ln 1.0476 = ln 2.5363
t = 20.000 years.
Rule of 72 would say 72/4.76 or 15.12 years for doubling
14.90 years
2017 predicted is 491272 × 1.0476¹⁷ or 1083552, or greater than the real rate of increase, hence the rate of growth is decreasing.
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which numbers the additive inverse of -41/4
Answer:
The answer is 41/4.
Step-by-step explanation:
Given:
-41/4 to get the additive inverse.
Now, the additive inverse of any number is a number that, when added to the number the result is zero.
Here, 41/4 is the additive inverse.
Because when it is added to -41/4 the result is 0.
Therefore, the answer is 41/4.
Write an equation in point slope form line passing through (-4,3), (3,-4)
SHOW WORK
Answer:
[tex]\large\boxed{y-3=-(x+4)}\\or\\\boxed{y+4=-(x-3)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points (-4, 3) and (3, -4).
Substitute:
[tex]m=\dfrac{-4-3}{3-(-4)}=\dfrac{-7}{7}=-1[/tex]
Put the value of a slope and the coordiantes of the point (-4, 3) or (3, -4) to the equation of a line:
for (-4, 3)
[tex]y-3=-1(x-(-4))\\\\y-3=-(x+4)[/tex]
for (3, -4)
[tex]y-(-4)=-1(x-3)\\\\y+4=-(x-3)[/tex]
Multiply. Type your answer in the box. Do not use any spaces.
(–27) x (+8) =
Answer:
-216
Step-by-step explanation:
Negative times positive is negative.
27 * 8 = 216
Answer is negative, so
-27 * 8 = -216
Answer:
-216
Step-by-step explanation:
Write the problem as a mathematical expression. ( − 27 ) ⋅ ( 8 )
multiply -27 by 8
Solve for y. Then find the values of y that correspond
to the given values of x for the linear function.
y + 8x = -2 for x = 0, 1, 2
Choosing a number from 1 to 10 what is the probability of choosing a number less than 3?
About 2% chance.
There are ten numbers and you want to choose a number less than three. There are only two numbers less than three; 1 & 2. Because there are only 2 numbers less than three and 10 to choose from, it becomes a 2% chance.
Answer: 20%
Step-by-step explanation:
Which of the following fractions give a decimal answer whose non-zero digits repeat infinitely many times? Select all that apply.
A) 6/4
B) 4/11
C) 9/8
D) 5/7
E) 8/9
F) 7/8
Answer:
B and E repeat infinitely.
Step-by-step explanation:
A) 6/4 = 1.5 (ends)
B) 4/11 ≈ 0.36363636... (repeats 36 forever)
C) 9/8 = 1.125 (ends)
D) 5/7 ≈ 0.7143 (does not repeat)
E) 8/9 ≈ 0.88888888... (repeats 8 forever)
F) 7/8 = 0.875 (ends)
The number of games in the first round of a chess tournament is equal to 2×2×2×2×2×2. Write the number of games using an exponent.
Answer:
2^6
Step-by-step explanation:
2 is being multiplied 6 times meaning it would be 2 to the 6th power.
To solve for y in the equation 2 x + y = 5, subtract 2 from both sides of the equation.
True False
Answer:
False.
Step-by-step explanation:
Because we have to isolate y and subtracting 2 will not put y alone on one side.
We have to subtract 2x in order to solve for y.
Answer:
False
Step-by-step explanation:
To solve this equation 2x + y = 5, you need another pair equation with the same variables, or one of the variables (x or y) need to be known to solve this equation.
Or you need to subtract 2x from both side to make y subject of formula.
What is the surface area of a cone that has a radius of 8 feet and a slant height of 12 feet? (Use 3.14 for π.)
301.44 ft 2
502.4 ft 2
200.96 ft 2
803.84 ft 2
Answer:
[tex]SA=502.4\ ft^2[/tex]
Step-by-step explanation:
we know that
The surface area of a cone is equal to
[tex]SA=\pi r^{2}+\pi rl[/tex]
we have
[tex]r=8\ ft\\l=12\ ft\\\pi=3.14[/tex]
substitute the given values
[tex]SA=(3.14)(8^{2})+(3.14)(8)(12)[/tex]
[tex]SA=200.96+301.44=502.4\ ft^2[/tex]
what is 8/9 times 5/7 times 1/8 as a fraction in simplest form
Answer:
5/63
Step-by-step explanation:
8/9(5/7)(1/8)=
8/9(5/7)=
40/63(1/8)=
5/63
by the way 8/9 x 5/7 x 1/8
is also the same as (8/9)(5/7)(1/8)
To find the product of 8/9, 5/7, and 1/8, multiply the numerators and denominators to get 40/504 and simplify it to 5/63.
Explanation:To solve the multiplication of fractions, we need to multiply the numerators together and the denominators together. For the expression 8/9 times 5/7 times 1/8, we multiply the numerators 8, 5, and 1 to get 40, and the denominators 9, 7, and 8 to get 504. Simplifying the fraction 40/504 involves finding the greatest common divisor, which is 8 for both numerator and denominator, and dividing them by this number.
Doing so, we get 40 ÷ 8 = 5 and 504 ÷ 8 = 63. Hence, the solution simplified is 5/63.
simplify
(6 + 3i)(6 − 3i)
Answer:
45
Step-by-step explanation:
(6 + 3i)(6 − 3i) =6 (6 − 3i)+ 3i(6 − 3i)
= 36 -18i +18i-9[tex]i^{2}[/tex]
if [tex]i^{2} =-1[/tex]
36 -18i +18i-9[tex]i^{2}[/tex] = 36-9(-1)
=36+9
=45
=36-9i^2
=6^2 - (3i)^2
Answer:
[tex]\displaystyle 45[/tex]
Step-by-step explanation:
[tex]\displaystyle (6 + 3i)(6 - 3i) = 36 - 9i^2 = 36 - 9[-1] = 36 + 9 = 45[/tex]
Extended Information on the Complex Number System
[tex]\displaystyle \sqrt{-1} = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = 4\:[Any\:multiple\:of\:four][/tex]
I am joyous to assist you anytime.
what is the square root of 10
Answer:
3.1622776 OR √ 10
Step-by-step explanation:
The result can be shown in multiple forms.
Exact Form:
√ 10
Decimal Form:
3.16227766
3.1622776
Step-by-step explanation:
[tex]\sqrt{10}-\text{it's an irrational number}\\\\\text{You can only have an approximation}\ \sqrt{10}\approx3.1623[/tex]
(29)
4. During the morning commute
96 cars and 24 trucks passed
through the intersection. What is
the ratio of cars to trucks?
Answer:
Step-by-step explanation:
96:24
96 divide by 24 = 4
so it would be 4 cars to 1 truck
so 4:1
Answer:
4:1 Explanation: because of how when you divide the two its 4 and there's one truck left
5. Which statement is NOT true?
If x = 1, then x2 = 1.
If x2 = 1, then x = 1.
If x= -1, then x2 = 1.
x2 = 1 if and only if x = 1 or x = -1.
Answer:
[tex]x^{2} =1, then\ x=1[/tex] is NOT true.
Step-by-step explanation:
1.
[tex]If\ x=1, then\ x^{2} =1[/tex] ......True
( 1 )² = 1
2.
If [tex]x^{2} =1, then\ x=1[/tex] ........ NOT True
∴ x =± 1 .........this is correct
3.
[tex]If\ x=-1, then\ x^{2} =1[/tex] ......True
( -1 )² = 1
4.
x2 = 1 if and only if x = 1 or x = -1. .........True
( 1 )² = 1
( -1 )² = 1
How old will Bill be in 10 years if he is x + 2 years old now? Which expression represents this? (x + 2) + 10 10(x + 2) (x + 2) - 10
Answer: 10(x+2)
Step-by-step explanation:
Answer:
(x+2) + 10
Step-by-step explanation:
(x+2) is his current age, then you add the 10 years to get your answer.
The product of 8 and 12
[tex]\text{Hey there!}[/tex]
[tex]\text{The \bf{product}}\text{ of 8 and 12 is [blank]}[/tex]
[tex]\text{Whenever you see the word \bf{product}}\text{ in mathematics, it usually means}\\\text{multiply}[/tex]
[tex]\text{\bf{The PRODUCT of 8 and 12 is 96 because 8 times 12 equal 96}}[/tex]
[tex]\boxed{\boxed{\huge{\text{\bf{Answer: 96}}}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Step-by-step explanation:
Hello!
Product means to multiply.
Which means it’s x added by itself y times.
For this problem it means 8 added by itself 12 times.
You can do:
8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8, which equals 96.
Or, 8 x 12.
Which is 96.
It still represents 8 + 8, etc.
But your doing it faster.
Therefore, your Product is 96.
The table shows the cost,c, of buying each number of boxes,b,of cookies. Write an equation that models this situation.
A. b=3c
B. c=3b
C. b=8c
D. c=8b
Answer:
B
Step-by-step explanation:
Each box of cookies is $3 since 4 x 3 =12, 6 x 3 = 18, and 9 x 3 = 27. So we want to multiply the number of boxes, b, by 3 to get the cost, c. The correct equation is c = 3b.
An equation that models this situation is c = 3b. The correct option is B.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given the data is,
b c
4 12
6 16
9 27
c = kb
12 = k x 4
k = 12 / 4 = 3
c = 3b
Therefore, the equation that models this situation is c = 3b. The correct option is B.
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Let's say you opened your laptop and positioned the
screen so it's exactly at 90° - a right angle - from your
keyboard. Now, let's say you could take the screen and
push it all the way down beyond 90°, until the back of the
screen is flat against your desk. It looks as if the angle
disappeared but hasn't. What is the angle called, and
what is the measurement?
A. Straight angle at 180°
B. Linear angle at 90°
C. Collinear angle at 120°
D. Horizontal angle at 180°
it will surely look like an angle on a straight line. which adds up.to 180,so the answer is horizontal angle at 180degrees
Final answer:
The correct answer is A. Straight angle at 180°, describing the angle formed when a laptop screen is moved from a 90° position to lying flat against the desk.
Explanation:
The question asks about the angle formed when a laptop screen is opened from a right angle (90°) to lying flat against the desk, covering a full range from vertical to horizontal. This describes a straight angle, which measures 180°. Initially, the laptop screen at a 90° angle to the keyboard represents a right angle. Pushing the screen down to lie flat transitions this to a straight angle, where the angle between the keyboard and the back of the screen spans a flat, straight line. Therefore, the correct answer is A. Straight angle at 180°.
F(x)=x^2-8x+12 find the roots by graphing
Answer:
x² - 8x + 12 = 0
(x - 6)(x - 2) = 0
x = 2, 6
f(4) = -4
Plot (0, 12), (2, 0), (4, -4), (6, 0), and (8, 12) on the graph. Then draw a smooth curve that goes through these points.
Which expression is equal to 4^5x 4^-7 divided by 4^-2
Answer:
4^5x-5
Step-by-step explanation:
4^5x-7/4^-2
=4^5x-5
The expression 4⁵ × 4⁻⁷ divided by 4⁻² simplifies to 1 by using the properties of exponents. First, add the exponents in the numerator, then subtract the exponents for division, resulting in 4⁰, which equals 1.
We need to simplify the expression:
4⁵ times 4⁻₇ ext{ divided by } 4⁻²
To simplify, let's first combine the powers of 4 in the numerator:
Using the property that when multiplying like bases, we add the exponents:= 4⁵ times 4⁻⁷
= 4⁽⁵⁺⁽⁻⁷⁾⁾
= 4⁻²
Next, address the division with a like base, which subtracts the exponents:= 4⁻² ext{ divided by } 4⁻²
= 4⁽⁻²⁻⁽⁻²⁾⁾
= 4⁽⁻²⁺²⁾
= 4⁰
Any number raised to the power of 0 is 1:4⁰ = 1
Therefore, the given expression simplifies to 1.
blake buys paperback from the used bookstore for $5 each. Natalie purchased an annual membership to the same bookstore for $35
so she can buy paperbacks at a discounted price of $2.50 each. How many books would Natalie and Blake have to buy this year for their spending at the bookstore to be the same? What would their total cost be?
Answer: 2
Step-by-step explanation:
Answer:
I am not sure but i think 2
Find the points at which the graph of the equation -4y=15-5x crossed the x- axis and the y - axis.
Answer:
see explanation
Step-by-step explanation:
Where the graph crosses the x- axis the y- coordinate is zero.
Let y = 0 in the equation and solve for x
- 4(0) = 15 - 5x, that is
15 - 5x = 0 ( subtract 15 from both sides )
- 5x = - 15 ( divide both sides by - 5 )
x = 3 ← x- intercept ⇒ (3, 0 )
Where the graph crosses the y- axis the x- coordinate is zero.
Let x = 0 in the equation and solve for y
- 4y = 15 - 5(0), that is
- 4y = 15 ( divide both sides by - 4 )
y = - [tex]\frac{15}{4}[/tex] ← y- intercept ⇒ (0, - [tex]\frac{15}{4}[/tex])
1. Solve for x.
x + 11 = 3
-11
-11
x=- 8
2. Solve for x.
x + 5 = 11
25-5
*=6)
3. Solve for z.
2-33 = 40
+33 +33
(2
=
–
7
4. Solve for x.
- 8x = 56
Answer:
for #4 x=-7
Step-by-step explanation:
a negative times a negative is a positive and 8 times 7 = 56
Solve
394.029 + 5.38
Answer:
399.409
Step-by-step explanation:
Add both numbers to get your answer.
Answer:
The answer is
399. 409
unit rate for 8:12 “$8 for 12 cans of pasta sauce”
Ratio:
Unit rate:
Answer:
1.5
Step-by-step explanation:
12 divided by 8 = 1.5
1.5 x 8 = 12
Help answer this question
Answer:
a = 108° and b = 144°
Step-by-step explanation:
The opposite angles of a rhombus are the same and the sum of all the angles of the rhombus is 360°.
So, from the given diagram of the rhombus we can write
2b + 2× 36 = 360
⇒ 2b = 360 - 72 = 288
⇒ b = 144° (Answer)
Again, the each angles of a pentagon is given to be a.
Hence, we can write 3a + 36 = 360
⇒ 3a = 324
⇒ a = 108° (Answer)
The sine ratio of an angle is the opposite side over the adjacent side.
always
never
sometimes
Answer:
never
Step-by-step explanation:
In a right triangle, every angle has an opposite side and an adjacent side. And there's always a hypotenuse.
The sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.
The tangent ratio of an angle is the opposite side over adjacent side, it is not the sine ratio of a triangle.
For example, ABC is a right angled triangle having length of the sides are a,b,c.
So
[tex]sine\ C=\frac{a}{c}[/tex]
The sine ratio of an angle sometimes is the opposite side over the adjacent side.
The question pertains to the definition of the sine ratio in trigonometry. The sine ratio of an angle is not defined as the opposite side over the adjacent side; rather, it is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse of a right-angled triangle.
Therefore, the correct statement is the sine ratio of an angle sometimes is the opposite side over the adjacent side, specifically in the case of a 45°-45°-90° triangle where the sides are equal, but this is not generally true for all angles in trigonometry.
Which graph represents the solution set for the inequality 8z≤ 16?
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]8z\leq 16[/tex]
Solve for z
Divide by 8 both sides
[tex]z\leq 16/8[/tex]
[tex]z\leq 2[/tex]
The solution for z is the interval ----> (-∞,2]
All real numbers less than or equal to 2
In a number line the solution is the shaded area at left of z=2 (closed circle)
using a graphing tool
see the attached figure