The number of days Super Sally and Lazy Petunia work are illustrations of simultaneous equations
(a) Super Sally and Lazy Petunia
Represent their earnings with the first letters.
So, we have:
[tex]\mathbf{L = \frac 12S}[/tex] -- number of days
[tex]\mathbf{20L + 57S= 7733}[/tex] --- the total earnings
Make S the subject in [tex]\mathbf{L = \frac 12S}[/tex]
[tex]\mathbf{S = 2L}[/tex]
Substitute 2L for S in [tex]\mathbf{20L + 57S = 7733}[/tex]
[tex]\mathbf{20L + 57 \times 2L = 7733}[/tex]
Expand
[tex]\mathbf{20L + 114L = 7733}[/tex]
Add
[tex]\mathbf{134L = 7733}[/tex]
Divide both sides by 134
[tex]\mathbf{L = 57.7}[/tex]
From the options, the closest to 57.7 is 60.
Hence, the number of days that Petunia worked is closest is 60
(b) 4 digit even numbers
The digits are given as: 0, 1, 5, 6, 7, 8 and 9
To create a 4-digit number, the first digit cannot be 0.
So, the first digit can be any of the remaining 6
Because, it is an even number, the number can only end with 0, 6 or 8
So, the last digit can be any of the 3
Since there is no repetition, the second and the third digits can be any of the remaining 5 and 4 digits, respectively.
So, the number of digits is:
[tex]\mathbf{n =6 \times 3 \times 5 \times 4}[/tex]
[tex]\mathbf{n =360}[/tex]
Hence, the number of digits is (d) 360
(c) The value of 28^983 x 98^984/14^2948
Rewrite the expression as:
[tex]\mathbf{\frac{28^{983} \times 98^{984}}{14^{2948}}}[/tex]
Express all number as a base of 14
[tex]\mathbf{\frac{14^{2 \times 983} \times 14^{7 \times 984}}{14^{2948}} }[/tex]
Apply law of indices
[tex]\mathbf{14^{2 \times 983+7 \times 984-2948}}[/tex]
Evaluate all products
[tex]\mathbf{14^{1966+6888-2948}}[/tex]
Evaluate the exponent
[tex]\mathbf{14^{5906}}[/tex]
Hence, the result of [tex]\mathbf{\frac{28^{983} \times 98^{984}}{14^{2948}}}[/tex] is [tex]\mathbf{14^{5906}}[/tex]
Learn more at:
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4 bells toll together at 9 am. They toll after 7, 8. 11 and 12 seconds respectively. How many times will they toll together again in the next 3 hours?
Answer:
5 times
Step-by-step explanation:
What we need to do here is to find the lowest common multiple of 7,8,11 and 12
This is;
1848
Now, let’s calculate the number of seconds in 3 hours
In 1 hour, we have 3600 seconds
In 3 hours, this will be;
3600 * 3 = 10,800 seconds
So, to find the number of times in which all 4 will toll together, we need to know the number of 1848 seconds in 10,800 seconds
Mathematically, that will be;
10,800/1848 = 5.844
Our answer will be 5 times however
This is because the sixth time they would have sounded together would be more than the 3 hours time frame
Sam had 48 stickers to put on the walls in his bedroom. He divided the stickers
evenly among the 4 walls of his room. How many stickers did he put on each wall?
32
24
16
12
Answer:
48/4
12 he divided the stickers
evenly among the 4 walls of his room
Joshua is driving to visit his friend who lives 165 miles away. He has driven 25 miles, and now he hopes to drive 40 miles per hour the rest of the way. How many more hours will it take Joshua to reach his friends house
Answer: akcbebvu9pewgrvw8ugvubeufhfhef89h8efhw9a9s
Answer:
top one is correct yessss
asap.?
anyone please
Please help me!!!!! I will give 15 points
Answer:
Step-by-step explanation:
all of them could be made into a difference of squares since they all have a minus sign in the expression, but maybe the question is if they can easily be made into a difference of squares.
with that said
[tex]y^{4}[/tex] -2 => [tex](y^{2}) ^{2}[/tex]- [tex](\sqrt{2}) ^{2}[/tex] could be a difference of squares but not easy
25[tex]m^{2}[/tex][tex]n^{4}[/tex] - 1 => (5m[tex]n^{2}[/tex])^2 - [tex]1^{2}[/tex] yes and pretty easy
[tex]p^{8}[/tex] - [tex]q^{4}[/tex] => [tex](p^{\sqrt{8} } )^2[/tex]-[tex](q^{2})^2[/tex] could be but not easy
16[tex]x^{2}[/tex] - 24 => [tex](4x)^{2}[/tex] -[tex](\sqrt{24}) ^{2}[/tex] could be but not easy
I need help with it i don’t know how to do it
Answer:
What do you mean? Like you need to specify your question...
Step-by-step explanation:
what do you mean by that?
simplify fully please
Answer:
8x² + 8
Step-by-step explanation:
Given
(x² + 3)² - (x² - 1)² ← expand both factors using FOIL
= [tex]x^{4}[/tex] + 6x² + 9 - ([tex]x^{4}[/tex] - 2x² + 1) ← distribute by - 1
= [tex]x^{4}[/tex] + 6x² + 9 - [tex]x^{4}[/tex] + 2x² - 1 ← collect like terms
= 8x² + 8
Answer:
-8(x^2 - 1)
Step-by-step explanation:
(x^2 + 3)^2 and (x^2 - 1)^2 are both squares of binomials. The first step here is to expand both:
-(x^2 + 3)^2 = -x^4 - 6x^2 - 9
(x^2 - 1)^2 = x^4 - 2x^2 + 1
Combine the two right-hand expressions, obtaining:
-8x^2 - 8 or -8(x^2 - 1)
This -8(x^2 - 1) is the simplest form of the given expression.
If desired, -8(x^2 - 1) can be factored: -8(x - 1)(x + 1)
In a bag of trail mix, the ratio of raisins to M & M's is 2,3. Which fraction represents the ratio of raisins to M & Ms.
Answer:
...you may want to check my explanation...
Step-by-step explanation:
If the ratio of raisins to M&Ms in a bag of trail mix was 2:3, that means that there are 2 raisins for every 3 M&Ms. This means that in a bag of 100 items, there would be 40 raisins and 60 M&Ms. I'm not sure what the ratio would be as a fraction (maybe 2/3?), but I do know that the fraction for the number of raisins in the whole bag is 2/5 and the fraction for the number of M&Ms is 3/5.
Hope this helps!
(If the answer is even right, that is...)
65% of 40 is what number?
ahh this was supposed to be done yesterdayyy..
Answer:
65% of 40 is 26
26 is answer
Step-by-step explanation:
Percentage solution with steps:
Step 1: Our output value is 40.
Step 2: We represent the unknown value with $x$.
Step 3: From step 1 above,$40=100\%$.
Step 4: Similarly, $x=65\%$.
Step 5: This results in a pair of simple equations:
$40=100\%(1)$.
$x=65\%(2)$.
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
$\frac{40}{x}=\frac{100\%}{65\%}$
Step 7: Again, the reciprocal of both sides gives
$\frac{x}{40}=\frac{65}{100}$
$\Rightarrow x=26$
Therefore, $65\%$ of $40$ is $26$
jOE TRAVEL TO SCHOOL ON A BUS. ON ANY DAY THE PROBABILITY THAT HE MISSES THE BUS IS 1/3. WHAT IS THE PROBABILITY THAT HE WILL MISS THE BUS ON TWO CONSECUTIVE DAYS AND THE PROBABILITY THAT HE WILL MISS THE BUS ON ONE DAY OUT OF TWO CONSECUTIVE DAYS
Answer:
1/6 of 2 dayas an 1/3 on 1 day
Step-by-step explanation:
work out the coordinates of c
the answer
Answer:
y = 30- 2 = 28
28/4=7
So 7 per side of the square. x would then be 27-7-7= 13 counting from the top
y would be 2+7+7=16
(13,16)
A proportional relationship between the number of pounds of pickling cucumbers (x) and the price in dollars (y) can be graphed, and the ordered pair (6, 4) would be on the graphed line.
Part A: What is the price of 1 pound of pickling cucumbers? Show your work. (8 points)
Part B: What does the ordered pair (12, 8) on the graph represent? Explain in words. (2 points)
Part A: What is the price of 1 pound of pickling cucumbers?
Answer: after surveying the selection, we discovered that 1 pound is equal to 6 to 7 pickling cucumbers that are 3 to 4 inches in length. We decided to use 1 pound of pickling cucumbers for ours calculation sample.
Part B: What does the ordered pair (12, 8) on the graph represent?
Answer: number are plotted on graph quadrants in what are known as ordered pair. An ordered pair consists of two values, x and y. In an ordered pair, x is always the first value and y is always the second value.
Step-by-step explanation: I think this is what you want, hope this help
Find the answer (5x) + (4x) + (6y)
Answer:
9 x + 6 y
Step-by-step explanation:
Determine the value of y, if x is -2.
y = |x – 12|
Answer:
y=14
Step-by-step explanation:
Solve x2 - 13x + 30 = 0
Answer:
or, x2-(2-15)x +30= 0
or, x2-2x-15x + 30= 0
or,x(x-2)-15(x-2)=0
or, (x-2) (x-15)=0
either, or,
x-2=0 x-15=0
Answer:
x2-(10+3)x+30=0
x2-10x-3x+30=0
x(x-10)-3(x-10)=0
(x-10)(x-3)=0
either, or,
x-10=0 x-3=0
x=10 x=3
therefore,x=10,3
A 38-ounce bottle of juice drink contains 6 percent water. Than computed 6 percent of 38. His work is shown below.
6 percent of 38 0.6 times 38 = 22.8
Which statement explains Than’s error?
Than did not multiply 0.6 and 38 correctly.
Than did not use 0.06 for 6 percent.
Than did not move the decimal point three places to the left in the answer.
Than did not use 6 for 6 percent.
Answer: Than did not use 0.06 for 6 percent.
Step-by-step explanation:
From the question, we are informed that Than computed 6 percent of 38 as 6 percent of 38 = 0.6 times 38 = 22.8.
His above solution is wrong. We should note that:
6% × 38
= 6/100 × 38.
= 0.06 × 38
= 2.28
The mistake that he made was that Than did not use 0.06 for 6 percent.
Answer:
b
Step-by-step explanation:
edge
A fireplace burn 6 same-sized logs in 3 hours. How many logs does the fireplace burn in 9 hours?
Answer:
18 logs
Step-by-step explanation:
because 9 is three times 3, just multiply the 6 by three as well.
Is this a parallelogram if so by which theorem
Answer:
Egghead
Step-by-step explanation:
Write an equation for the nth term of the geometric sequence 2, 8, 32, 128, ...
Then find a6. Round to the nearest tenth if necessary.
Answer:
Equation: x(n)=2*4^(n-1)
a6=2048
Step-by-step explanation:
Take note that the common ratio is 4 because 2*4=8, 8*4=32, 32*4=128, and so on...
We will use the equation x(n) = ar^(n-1) where n represents the nth term, r stands for the common ratio, and "a" stands for the first term. We use (n-1) because ar^0 is for the 1st term
Given the first term is a=2, the common ratio is r=4, then we have the equation x(n)=2*4^(n-1)
So, 128*4=512 would be the 5th term, and the 6th term would be 512*4=2048
So a6=2048
We want to find an equation and the sixth term of the given geometric sequence.
The equation is:
[tex]A_n = 4*A_{n-1}[/tex]
And the sixth term is equal to 512
Geometric sequences.In a geometric sequence, each term is a constant times the previous term, so the general relation is:
[tex]A_n = k*A_{n-1}[/tex]
Here we can use any pair of consecutive terms to find the value of the constant, for example, if we use the first two, we have:
8 = k*2
8/2 = 4 = k
Now we know the value of the constant, then the general formula is:
[tex]A_n = 4*A_{n-1}[/tex]
Now we can use this to get the sixth term:
[tex]A_6 = 4*A_5 = 4*128 = 512[/tex]
If you want to learn more about geometric sequences, you can read:
https://brainly.com/question/9300199
helppppo plss
zoom in on picture if u need but i need answer soon
Answer: third number line
Step-by-step explanation:
Find the derivative of a✓tan(5x-7)
Answer:
[tex]\displaystyle y' = \frac{5a \sec^2 (5x - 7)}{\sqrt{\tan (5x - 7)}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
*Note:
Treat a as an arbitrary constant.
Step 1: Define
Identify
[tex]\displaystyle y = a\sqrt{\tan (5x - 7)}[/tex]
Step 2: Differentiate
Derivative Property [Multiplied Constant]: [tex]\displaystyle y' = a\frac{d}{dx} \Big( \sqrt{\tan (5x - 7)} \Big)[/tex]Basic Power Rule [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = \frac{a}{\sqrt{\tan (5x - 7)}} \cdot \frac{d}{dx}[\tan (5x - 7)][/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = \frac{a \sec^2 (5x - 7)}{\sqrt{\tan (5x - 7)}} \cdot \frac{d}{dx}[5x - 7][/tex]Basic Power Rule [Derivative Properties]: [tex]\displaystyle y' = \frac{5a \sec^2 (5x - 7)}{\sqrt{\tan (5x - 7)}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Which graph represents the solution to the compound inequality?
-6<3x-12 s9
1 2
O
o3 6 9 12 15
O 30 369 12 15
Step-by-step explanation:
-6 < 3x - 12 <= 9
6 < 3x <= 21 (add 12)
2 < x <= 7 (divide by 3)
The graph that correct represents this solution set is the 2nd graph.
Which of the following lines is parallel to the line represented by 2y=4x+6?
y = -2x - 10
y = -3x + 10
y = 3x +10
y = 2x - 10
Pleaseeeee helppppp Asapppp!!!!!
What is the midline of this function ??
The midline is the line Y=0 .
(That's the x-axis.)
Put each line into slope-intercept form:
1. y=x + 3
2. 3x + 3y = -9
Can someone help me
Step-by-step explanation:
Slope-intercept form: y = mx + c
y = x + 3 is already in this form.
3x + 3y = -9,
3y = -3x - 9
y = -x - 3.
if a watch loses 30 seconds every 1 hour .if the watch was set right on sunday at 11:30pm what time did it show after 10hrs
Answer:
9:25
Step-by-step explanation:
Answer:
9:25 am
Step-by-step explanation:
losing 30 seconds every hour would be the same as losing one minute every 2 hours
since there are 5 2-hour intervals in 10 hours, the time if off by 5 minutes
instead of 9:30am it is 9:25 am
What is the distance between (–4, –10) and (–4, –4)?
Answer:
6 units
Step-by-step explanation:
(-4 , -10) ; (-4 , -4)
Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]= \sqrt{(-4-[-4])^{2}+(-4-[-10])^{2}}\\\\= \sqrt{(-4+4)^{2}+(-4+10)^{2}}\\\\=\sqrt{0+(6)^{2}}\\\\= \sqrt{36}\\\\= 6[/tex]
Answer:
6 units
Step-by-step explanation:
edge2021
If 12x - 3 = 17 + 7x, find the value of x.
Answer:
value of x is 4
Step-by-step explanation:
12x-3=17+7x
12x-7x=17+3
5x=20
x=4
Answer:
4
Step-by-step explanation:
Given that:
12x - 3 = 17 + 7x
Collect like terms
12x - 7x = 17 + 3
5x = 20
Divide both sides by 5
5x / 5 = 20 / 5
x = 4
Hence, x = 4
Which is a complete list of factors of each term in the expression 16 a + 18 a b?
16a: 1, 2, 4, 8, 16
18ab: 1, 2, 3, 6, 9, 18
16a: 1, 2, 4, 8, 16, a
18ab: 1, 2, 3, 6, 9, 18, b
16a: 2, 4, 8, a
18ab: 2, 3, 6, 9, a, b
16a: 1, 2, 4, 8, 16, a
18ab: 1, 2, 3, 6, 9, 18, a, b
Answer:
d
Step-by-step explanation:
Answer:
the answer is d.
Step-by-step explanation:
A tile backsplash is being installed. The installation fee is $150.00. The tile is priced at $2.75 per square foot, x. which equation best represents the total cost, y, of the backsplash?
Answer: y = 150 + 2.75x
Step-by-step explanation:
Since we are informed that the installation fee is $150.00 and that the tile is priced at $2.75 per square foot, x, the total cost, y, of the backsplash will be the addition of the fixed cost of $150.00 plus $2.75 multiplied by the number of square foot. This will be expressed as:
y = 150 + 2.75x
where,
x = number of square foot.