Simplify
Let's simplify step-by-step.
x(5)−3(x−4)
Distribute:
=x(5)+(−3)(x)+(−3)(−4)
=5x+−3x+12
Combine Like Terms:
=5x+−3x+12
=(5x+−3x)+(12)
=2x+12
Answer:
=2x+12
(19x^2+12x+12)+(7x^2+10x+13)
Answer:
[tex]26x^2+22x+25[/tex]
Step-by-step explanation:
We remove the brackets, getting [tex]19x^2+12x+12+7x^2+10x+13[/tex].
We then combine like terms, getting [tex](19+7)x^2+(12+10)x+(12+13)[/tex].
As a result, we get [tex]26x^2+22x+25[/tex].
Answer:
[tex] \boxed{ \huge{ \boxed{ \bold{ \sf{26 {x}^{2} + 22x + 25}}}}}[/tex]Step-by-step explanation:
[tex] \sf{(19 {x}^{2} + 12x + 12) + ( {7x}^{2} + 10x + 13)}[/tex]
Remove the unnecessary Parentheses
⇒[tex] \sf{19 {x}^{2} + 12x + 12 + (7 {x}^{2} + 10x + 13)}[/tex]
When there is a ( + ) in front of an expression in parentheses , the expression remains the same
⇒[tex] \sf{19 {x}^{2} + 12x + 12 + 7 {x}^{2} + 10x + 13} [/tex]
Collect like terms
⇒[tex] \sf{26 {x}^{2} + 22x + 12 + 13}[/tex]
Add the numbers
⇒[tex] \sf{26 {x}^{2} + 22x + 25}[/tex]
Hope I helped!
Best regards!
Ethan made goodie bags for his birthday party guests. He put the same amount of goodies in each bag. He had 48 pieces of candy, 8 yoyos, 16 toy cars, and a box of 24 pencils with silly erasers. Eight guests came to Ethan's party. The party was three hours long. Ethan and his guests spent the first half of the party playing games. Then they had cake and ice cream. After that, Ethan opened his presents. Then they all ran around like little monsters until it was time for the guests to go home at 4:30 pm .How many pieces of candy did each guest get?
Answer:
6 candies
Step-by-step explanation:
The sentences "Ethan and his guests spent the first half...time for the guests to go home at 4:30 pm" are extra information because they don't relate to the problem, therefore, we can ignore them. We know that Ethan had 48 pieces of candy and that 8 guests came to his party. Since each guest got an equal amount of candy, to find the answer, we can do 48 / 8 = 6 candies.
A number is called perfect if it is the sum of its factors
other than itself. For example, 28 is a perfect number,
since 14 + 7 + 4 + 2 + 1 = 28.
I
The second, third, fourth, and fifth perfect numbers are 28;
496; 8,128; and 33,550,336.
What is the first perfect number?
Answer: 6
Step-by-step explanation:
The factors of 6 are 1, 2, and 3.
1 + 2 + 3 = 6
If (x+4): (3x+1) is the duplicate ratio of 3:4 find the value of x.
Step-by-step explanation:
According to the question:
(x+4) : = 3:4
or, (x+4) / (3x+1) = 3 / 4
or, (x+4) * 4 = (3x+1) * 3
or, 4x + 16 = 9x + 3
or, 16 - 3 = 9x - 4x
or, 13 = 5x
or, 13/5 = x
•
• • x = 2.6
Answer:
x = [tex]\frac{13}{5}[/tex]
Step-by-step explanation:
Express the ratios as equivalent fractions, that is
[tex]\frac{x+4}{3x+1}[/tex] = [tex]\frac{3}{4}[/tex] ( cross- multiply )
3(3x + 1) = 4(x + 4) ← distribute parenthesis on both sides
9x + 3 = 4x + 16 ( subtract 4x from both sides )
5x + 3 = 16 ( subtract 3 from both sides )
5x = 13 ( divide both sides by 5 )
x = [tex]\frac{13}{5}[/tex]
5.67 km are equal to _____________ meters * A. 5670 B. 56700 C. 567000 D. 56.7
Answer:
A
Step-by-step explanation:
Your answer is 5670 m
1km=1000m
5.67km=5.67×1000
=5670m
hope this helps
Answer:
5670
Step-by-step explanation:
can someone please help me.
-280=-7(6a-8)
Answer:
a=8
Step-by-step explanation:
-280=-7(6a-8)
Distribute
-280=-7*6a-7+-8
-280=-42a+56
Subtract 56 from both sides
-336=-42a
Divide both sides by -42.
a=8
PLEASE HELP!!!! Rearrange the equation so n is the independent variable. m + 1 = -2(n+6)
Answer:
m+13/-2 = n (m plus 13, divided by negative 2 equals n)
Step-by-step explanation:
m+1 = -2(n+6)
distribute -2
m+1 = -2n-12
add 12 to both sides
m+1 = -2n-12
+12 +12
with that you get
m+13 = -2n
next you divide -2 from both sides
m+13
-------- = n
-2
Consider the difference of cubes identity: a3 − b3 = (a − b)(a2 + ab + b2). For the polynomial x3 − 64, a = and b =
Answer:
a= x, b= 4
Step-by-step explanation:
a³ − b³ = (a − b)(a² + ab + b²)x³ - 64Comparing polynomials:
a³= x³ ⇒ a = xb³= 64 ⇒ b³ = 4³ ⇒ b= 4Applying same formula:
x³ - 64 = (x- 4)(x² + 4x + 16)The question is in the photo. Determine an equation for the pictured graph. Please help!!
Explanation:
It's probably not obvious, but the squiggly portion through the x intercept x = -1 is a triple root. This is because this portion resembles a cubic graph. If instead it was a more straightish line through this root, then we'd have a single root.
So because x = -1 is a triple root, this means the factor (x+1) has the exponent 3. We have the factor (x+1)^3
The other factor is (x-2) from x = 2 being the other root.
All together we have (x+1)^3*(x-2) as the complete factorization. The leading coefficient is 1 to have this graph open upward. Or put another way, since the end behavior is going to positive infinity for both endpoints, the leading coefficient must be positive.
Han wants to convert his Canadian dollars to euros for his trip to France. He has 427 Canadian dollars. the current exchange rate is 1.28 Canadian dollars per euro. how many euros will he have.
Answer:
He will have 334 Euros
Step-by-step explanation:
Hello.
Here is a currency conversion problem.
The man in this question seeks to convert his Canadian dollars to Euro as he is in France for a trip.
The exchange rate is given as;
1.28 canadian dollar = 1 euro
He has 427 CAD , and we want to know the amount in euro.
let the equivalent amount in Euro be x
Thus;
if
1.28 CAD = 1 EUR
427 CAD = X EUR
By cross multiplying, we have
1.28 * x = 427 * 1
x = 427/1.28
x = 333.59 Euros which is approximately 334 Euros
Find the value of 14+5•3-3^2. Then change two operation signs so that the value of the expression is 8
Answer:
Step-by-step explanation:
14+5*3-3²=14+15-9=29-9=20
14-5*3+3^2=14-15+9=23-15=8
For every 1000 it makes £2 from ad revenue.
How many are required to make £25?
Answer:
12,500= £25
Step-by-step explanation:
Because every 1000 it makes £2 from ad venue, we must: (we can do two methods)
1.Divide £25 by £2 then multiply it by 1000. By doing this, we will know how many times 1000 are made when there is £25.
1000= £2
? = £25
So:
£25 ÷ £2= 12.5
12.5 × 1000= 12,500
2. Find how much it made for £1 by dividing 1000 by £2, then multiplying it by £25.
So:
1000 ÷ £2= 500
500 × £25= 12,500
I hope this helps! I'm sorry if it's wrong and too complicated.
(b) A distance is related to time according to the expression x = A sin(2πft), where A and f are constants. Find the dimensions of A. Again, "L" is the length dimension and "T" is the time dimension. [Hint: A trigonometric function appearing in an equation must be dimensionless.]
Answer:
A is in length dimensions
Step-by-step explanation:
The expression:
x = A sin (2πft)
has in the second member two factors A and sin (2πft); a sine is a relation between two sides with the same dimension that means a sine is a number ( with minimum and maximum values of 0 for zero degrees and 1 for 90 degrees ). As t is in units of time ( seconds, minutes or hours) frequency "f", which is the number of cycles per unit of time ( seconds, minutes or hours), t and f should be both in the same unit, in order to get just a number for sin2πf.
Therefore A should be in units of length and x will get its units from A
For instance
x = A sin(2πft)
t in seconds f in 1/seconds A in meters
By substitution, we can see that
x[ m ] = A [m] * sin[ 2π*sec* 1/sec ]
x[ m ] = A [m] * number
Which of the following is an example of the difference of two squares? x2−9x2−9 (x−9)2 x3−9x3−9 (x+9)2
Answer: x²−9
Step-by-step explanation:
A square number is obtained ehen we multiply a number to itself.
For example: 5 × 5 = 5² = 25 [It is a square number]
We can do this in expression too, For example: z×z =z²
From all the given options, only x²−9 has both terms as square.
∵ x² = x × x
and 9 = 3×3= 3²
So that, x²−9 =(x)²-(3)²
Hence, the correct option is x²−9.
HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!! Two functions represent the composite function h(x) = (x – 1)³ + 10 so that h(x) = (g compose f)(x). Given f(x) = x + a and g(x) = x³ + b, what values of a and b would make the composition true?
Answer:
A= -1 B=10
Step-by-step explanation:
Answer:
a: -1
b: 10
edge 2020
What is the multiplicative inverse of 4
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
The multiplicative inverse of 4 is 1/4.
Answer:
1/4
Step-by-step explanation:
Multiplicative inverse is another meaning for reciprocal. The reciprocal of 4 is 1/4
The percentage of nickel in a U.S. dime is 8.33%. What is 8.33% rounded to the nearest tenth of a percent? pls help meh ASAP
Answer:
Hi! You already have the percentage of the nickel to the nearest hundredth, you just need to move to the left once to get to the tenth. That would mean the answer is 8.3%! Easy as that.
Answer:
8.3%
I just took the test
Granny has taken up deep-sea fishing! Last week, she caught a fish so big that she had to cut it into 3 pieces (head, body and tail) in order to weigh it. The tail weighed 9kg and the head weighed the same as the tail plus one third of the body. The body weighed as much as the head and tail together. How much did the whole fish weigh?
Answer:
54kg
Step-by-step explanation:
Body weight = B
Tail weight = T
Head weight = H
Total weight = F
Use equation = B + T + H = F
We are told that T = 9kg, H = T + (1/3) x B, B = H + T
We have 3 equations and 3 unknowns, solve the system of equations to find W.
B = H + 9
H = 9 + 1/3 x (H+9)=9+H/3+3 --> 2/3 x H = 12 --> H = 18
B = 18 + 9 = 27
F = 18 + 27 + 9 = 54kg
Steve took his remote controlled submarine to the pond. His submarine sank 19 out of 25 boats. What percentage of the boats were still afloat?
Answer:
24%
Step-by-step explanation:
1) 25-19=6
2) 6/25 x 100 = 24%
Combine the like terms to create an equivalent expression: 5n+6+(-7n)
Answer:
-2n + 6
Step-by-step explanation:
To combine this expression, we simply put the like terms, the coefficient with the same variables, and constants together.
5n + 6 + (-7n)
So we can reorganize this:
(5n + -7n) + 6
==> (-2n) + 6
==> -2n + 6
So that is the equivalent expression with the combination of like terms.
Cheers.
Answer:
-2n +6
Step-by-step explanation:
The expression we are given is:
5n + 6 + (-7n)
We want to combine like terms. First, let's analyze each term.
5n ⇒ has a variable, "n"
5 ⇒ does not have a variable
-7n ⇒ also has a variable, "n"
The like terms in this case are 5n and -7n, since they both include a variable. Let's combine the like terms.
5n + 6 + (-7n)
(5n - 7n) +6
Subtract 7n from 5n.
(5-7) *n +6
(-2)*n +6
(-2n)+6
-2n + 6
There are no more like terms, so this is simplified as much as possible.
The expression 5n+6+(-7n) after combining the like terms is -2n+6.
What is the area of a rectangle with 5cm height and 77cm length?
Answer:
area = 385 cm²
Step-by-step explanation:
area = 5cm * 77cm
area = 385 cm²
A ball is thrown starting at a time of 0 and a height of 2 meters. The height of the ball follows the function H(t)=−4.9t2+25t+2. What is the height of the ball at each second from 0 to 5?
Answer:
height = 2m at t = 0s
height = 22.1m at t = 1s
height = 32.4m at t = 2s
height = 32.9m at t = 3s
height = 23.6m at t = 4s
height = 4.5m at t = 5s
Step-by-step explanation:
Given equation:
H(t) = -4.9t² + 25t + 2 ----------------(i)
The height of the ball is a function of time. Therefore;
(i) At the 0th second. i.e t = 0, we get the height by substituting the value of t = 0 into equation (i). i.e
H(0) = -4.9(0)² + 25(0) + 2
H(0) = 2
∴ At t = 0, the height is 2 meters. This is also obvious in the first statement of the question.
(ii) 1st second. i.e t = 1, we get the height by substituting the value of t = 1 into equation (i). i.e
H(1) = -4.9(1)² + 25(1) + 2
H(1) = 22.1
∴ At t = 1, the height is 22.1 meters.
(iii) 2nd second. i.e t = 2, we get the height by substituting the value of t = 2 into equation (i). i.e
H(2) = -4.9(2)² + 25(2) + 2
H(2) = 32.4
∴ At t = 2, the height is 32.4 meters.
(iv) 3rd second. i.e t = 3, we get the height by substituting the value of t = 3 into equation (i). i.e
H(3) = -4.9(3)² + 25(3) + 2
H(3) = 32.9
∴ At t = 3, the height is 32.9 meters.
(v) 4th second. i.e t = 4, we get the height by substituting the value of t = 4 into equation (i). i.e
H(4) = -4.9(4)² + 25(4) + 2
H(4) = 23.6
∴ At t = 4, the height is 23.6 meters.
(vi) 5th second. i.e t = 5, we get the height by substituting the value of t = 5 into equation (i). i.e
H(5) = -4.9(5)² + 25(5) + 2
H(5) = 4.5
∴ At t = 5, the height is 4.5 meters.
Answer:
the answer is (0,2) ball thrown from an initial height of two feet Jeremys change jar that started with a 2$ deposit
Step-by-step explanation:
what is 4n- 3n someone plase help :(
Answer:
n
Step-by-step explanation:
4n-3n=1n
1n=n
Solve the equation
(If possible please show work)
Answer:
[tex]n=-4[/tex]
Step-by-step explanation:
So we have the equation:
[tex]2+4(2-3n)=58[/tex]
First, distribute the second term:
[tex]2+4(2)-4(3n)=58\\2+8-12n=58[/tex]
Add the left side:
[tex]10-12n=58[/tex]
Subtract both sides by 10. The left side cancels:
[tex](10-12n)-10=(58)-10\\-12n=48[/tex]
Divide both sides by -12. The left side cancels:
[tex](-12n)/-12=(48)/-12\\n=-4[/tex]
Therefore, the value of n is -4.
⇒2 + 4(2 - 3n) = 58
⇒4(2 - 3n) = 58 - 2
⇒2*4 - 3n*4 = 56
⇒8 - 12n = 56
⇒-12n = 56 - 8
⇒-12n = 48
⇒-n = 48/12
⇒-n = 4
⇒n = - 4
Hence, value of n is - 4
Dewayne is throwing a birthday party for his friend. He wants to serve each guest one cupcake and one can of soda. At the store, soda is
sold 6 to a pack, and cupcakes are sold 4 to a pack. What is the fewest number of cupcakes and sodas Dewayne must buy so that he has
the same number of each?
Answer:
3
Step-by-step explanation:
so if he buys 2 packs of soda and three packs of cupcakes they will be even
cause it's gonna be 12-12
Find the inverse of the relation. Use proper notation. {(8,−1),(−8,−1),(−2,−8),(2,8)} please help!!
Answer: The inverse relation is { (-1, -8), (-1, -8), (-8, -2), (8, 2) }
The inverse is effectively the opposite of the original relation. It undoes what the original relation does. So we'll swap the x and y values for each given point in the form (x,y). Something like (8,-1) becomes (-1,8). The other points follow the same pattern as well.
If n and t are positive integers, what is the greatest prime factor of the product nt ? (1) The greatest common factor of n and t is 5. (2) The least common multiple of n and t is 105.
Answer:
Greatest prime factor of [tex]nt[/tex] is 7.
Step-by-step explanation:
Given that
Two positive integers are [tex]n[/tex] and [tex]t[/tex].
(1) Greatest Common Factor or HCF of [tex]n[/tex] and [tex]t[/tex] is 5.
(2) Least Common Multiple or LCM of [tex]n[/tex] and [tex]t[/tex] is 105.
To find:
The greatest prime factor of the product [tex]nt[/tex] = ?
Solution:
First of all, let us learn about a property of HCF and LCM of two numbers.
The product of two numbers [tex]p[/tex] and [tex]q[/tex] is equal to the product of their HCF and LCM.
[tex]p \times q =LCM\times HCF[/tex]
Using this property for the given numbers:
[tex]n\times t =5\times 105\\OR\\nt =5\times105[/tex]
Now, let us make prime factors of [tex]5 \times 105[/tex] to find the greatest of the prime factors.
[tex]5\times 105 = 5\times 5 \times 21 =5\times 5 \times 3 \times \bold{7}[/tex]
So, the prime factors of [tex]5 \times 105[/tex] are 5, 5, 3 and 7.
Greatest prime factor of [tex]nt[/tex] is 7.
See attachment for question (I will report you if you are only doing it for the points)
Answer:
x => y
-6 => 9
3 => 5
15 => -3
-12 => 15
Step-by-step explanation:
Given the domain function, {-12, -6, 3, 15}, and the equation of the function, [tex] y = -\frac{2}{3}x + 7 [/tex], we can complete the given table by simply plugging in the value of either x to find y, or y to find x in the table given. The domain values are all x-values you have in the table.
Find y when x = -6:
[tex] y = -\frac{2}{3}(-6) + 7 [/tex]
[tex] y = -\frac{2}{1}(-2) + 7 [/tex]
[tex] y = 2 + 7 [/tex]
[tex] y = 9 [/tex]
Find x when y = 5:
[tex] 5 = -\frac{2}{3}x + 7 [/tex]
[tex] 5 - 7 = -\frac{2}{3}x + 7 - 7 [/tex]
[tex] -2 = -\frac{2}{3}x [/tex]
[tex] -2 = \frac{-2x}{3} [/tex]
[tex] -2*3 = \frac{-2x}{3}*3 [/tex]
[tex] -6 = -2x [/tex]
[tex] \frac{-6}{-2} = \frac{-2x}{-2} [/tex]
[tex] 3 = x [/tex]
[tex] x = 3 [/tex]
Find y when x = 15:
[tex] y = -\frac{2}{3}(15) + 7 [/tex]
[tex] y = -\frac{2}{1}(5) + 7 [/tex]
[tex] y = -10 + 7 [/tex]
[tex] y = -3 [/tex]
Find x when y = 15:
[tex] 15 = -\frac{2}{3}x + 7 [/tex]
[tex] 15 - 7 = -\frac{2}{3}x + 7 - 7 [/tex]
[tex] 8 = -\frac{2}{3}x [/tex]
[tex] 8 = \frac{-2x}{3} [/tex]
[tex] 8*3 = \frac{-2x}{3}*3 [/tex]
[tex] 24 = -2x [/tex]
[tex] \frac{24}{-2} = \frac{-2x}{-2} [/tex]
[tex] -12 = x [/tex]
[tex] x = -12 [/tex]
what is the slope of the following 12x - 6y = 30
Answer:
[tex]slope = m = 2[/tex]
Answer:
2
Step-by-step explanation:
The slope intercept form is
y = mx+b where m is the slope
Solve for y
12x - 6y = 30
Subtract 12x from each side
-6y =-12x+30
Divide by -6
y = -12x/-6 +30/-6
y = 2x -5
The slope is 2
I dont know how to do this and need help.
Answer:
The correct option is;
The variable x has a coefficient
Step-by-step explanation:
The given vertex form of a quadratic function and the quadratic function can be written as follows;
Vertex form of a quadratic function, f(x) = (3·x + 1/3)² + 8/9
The quadratic function, f(x) = 9·x² + 2·x + 1
The vertex form of a quadratic function f(x) = a·x² + b·x + c is f(x) = a·(x - h)² + k
Where;
h = -b/(2·a) = -2/(2×9) = -1/9
k = f(h) = f(-1/9) = 9 × (-1/9)² + 2 × (-1/9) + 1 = 8/9
Which gives the vertex form a s f(x) = 9·(x - (-1/9))² + 8/9
f(x) = 9·(x + 1/9)² + 8/9
Therefore, f(x) = (3·x + 1/3)² + 8/9 is not the vertex form of f(x) = 9·x² + 2·x + 1 because the variable x has a coefficient.