Answer:
x = 12 and x = -4
Step-by-step explanation:
abs (x-4) = 8
When we have absolute value equations, we get two solutions, one positive and one negative
x-4 = 8 and x-4 = -8
Add 4 to both sides
x-4+4 = 8+4 x-4+4=-8+4
x = 12 and x = -4
[tex]|x-4|=8\iff x-4=8\ \vee\ x-4=-8\qquad\text{add 4 to both sides}\\\\\boxed{x=12\ \vee\ x=-4}[/tex]
A restaurant cook earns $8 per hour for the first 40 hours worked and $12 per hour for over time (hours worked in addition to the 40 hours a week). Last week the cook worked 60 hours. Calculate the cooks total pay for that week.
Answer:the answer is 560
Step-by-step explanation:
The reason is because you multiply to get 8 and 40 to get the amount for regular time which is 320.Then you subtract 60 from 40 which is 20.You multiply that amounnt by 12 because that is the overtime which will equal 240.Add them together and you get 560. ☺
if two lines are the same slope and diffrent y-intercepts then the lines are
Answer:
The lines would be parallel
Step-by-step explanation:
They have the same slope, but they sit on different y values. Therefore, they are parallel.
A pet store has two gray rabbit 1/8 of the rabbits at the pet store are gray how many rabbits does the pet store have
Given that two rabbits are gray and they represent 1/8 of all rabbits at a pet store, calculated using ratios, it can be inferred that the total number of rabbits is 16.
Explanation:The question is asking about the total number of rabbits in a pet store given that 1/8 of the total rabbits are gray and there are two gray rabbits. We can use this information to set up a ratio to calculate this.
To find out the total number of rabbits, we can set up a proportion where 2/total rabbits = 1/8. By cross multiplying, we find that 2 * 8 = total rabbits. Therefore, the pet store has 16 rabbits.
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Remy drinks 214 cups of water every 145 hours.
How many cups of water does he drink in 1 hour?
Answer:
Approximately 1.5 cups/hour
Step-by-step explanation:
Divide 214 cups by 145 hours.
(214 cups)/(145 hours) = 1.47586... cups/hour
Remy drinks around 1.47 cups of water in an hour. This was calculated by dividing the total cups (214) by total hours (145).
Explanation:To solve this question, we need to calculate the rate at which Remy drinks 214 cups of water every 145 hours. This can be done by dividing the total number of cups by the total number of hours.
So, the formula we have is:Cups per hour = Total Cups / Total hours
This gives us:Cups per hour = 214 / 145
After calculating this, you will find that Remy drinks approximately 1.47 cups of water in 1 hour.
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a−2>4. What is a's solution?
From net earnings of 740 per month Lisa Jones must spend 200 for her portion of the rent on an apartment she shares with two friends what percent of her net income is her rent payment
Answer:
27% of her net income is her rent payment
Step-by-step explanation:
Net earnings = $740
Lisa spend $200 for rent payment
We need to find out what percent of net earning is her rent payment
Let x be the percentage
x% of net income = rent
x% * 740 = 200
[tex]\frac{x}{100} * 740 = 200[/tex]
Multiply both sides by 1004
740x = 20000
divide both sides by 740
x=27.02702703
So its approximately 27%
Shana, who lives in Canada, and Pearl, who lives in Pennsylvania, were discussing the weather. Shana complained about the cold temperature of -20 C. Pearl, who lives in Pennsylvania, mentioned that her temperature was the opposite of Shana’s. Which is the correct way to represent “the opposite of Shana’s temperature is equal to Pearl’s”?
- -20 = 20
- (-20) = -20
- (20) = - 20
- -(20) = 20
Answer:
- -20 = 20
Step-by-step explanation:
The "opposite" here means we take the negative of -20 C.
So we can write - -20 which is equal to 20.
So the first option is correct, - -20 = 20.
Answer:
d
Step-by-step explanation:
Hello, I have a question about quadratic equations. I don’t know how to slove these:
1. (x-6)(2x-6)=20
2. (x+3) ² = 8x+12
3. (3x-1)(x+5)=3x ²
can somebody help me?
Answer:
Step-by-step explanation:
Answer:
1.X= 8 or 1
2.X= 3 or -1
3. X = 5/14
Step-by-step explanation:
1. Expanding your original equation (x-6)(2x-6)=20) , you get 2x^2-18x+36=20. Then, subtract 20 from both sides. You get 2x^2-18x+16=0. Now this is a standard Quadratic equation. Use the quadratic Formula to solve this, you get X= 8 or 1.
2. 1. Expand : x²+6x+9-8x-12=0 2. Simplify : x^2-2x-3=0 3. Solve as a quadratic equation : x= 3 or -1.
3. Same thing as the first one!
Hope I helped! <3
It says to find the value of x.
Answer:
x = 23
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
the third angle forms a straight angle with 100°, hence
third angle in triangle = 180° - 100° = 80°
Summing the 3 angles gives
2x + 3 + 80 + 51 = 180
2x + 134 = 180 ( subtract 134 from both sides )
2x = 46 ( divide both sides by 2 )
x = 23
How do I even do this?
Answer:
[tex]y\leq -x-5[/tex]
Step-by-step explanation:
First you find the equation of the line. Start by finding the slope of the line, using the two points given: (-5,0), (0,-5).
[tex]\frac{0--5}{-5-0} = \frac{5}{-5} = -1[/tex]
The y intercept is -5.
Your equation is then y = -1x-5.
To find which inequality to use, plug in a point within your region and see if the statement is true. I would choose (-3,-3)
-3 __ -1(-3)-5
-3 __ -2 you would fill this in with a <, so that is what goes in your equation. since the line is solid and not dotted, you include the underline in the sign.
point a has the coordinates(2,5) point B has the coordinates (6,17) how long is segment ab in simplified radical form
Answer:
[tex]4\sqrt{10}[/tex]
Step-by-step explanation:
We have been given that point A has the coordinates(2,5) point B has the coordinates (6,17).
To find the length of segment AB we will use distance formula.
[tex]\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Upon substituting coordinates of point A and point B in distance formula we will get,
[tex]\text{Distance between point A and point B}=\sqrt{(6-2)^2+(17-5)^2}[/tex]
[tex]\text{Distance between point A and point B}=\sqrt{(4)^2+(12)^2}[/tex]
[tex]\text{Distance between point A and point B}=\sqrt{16+144}[/tex]
[tex]\text{Distance between point A and point B}=\sqrt{160}[/tex]
[tex]\text{Distance between point A and point B}=4\sqrt{10}[/tex]
Therefore, the length of segment AB is [tex]4\sqrt{10}[/tex].
If,
a + b = 8,
ab + c + d = 23,
ac + bd = 28, and
cd = 12,
find the values of a, b, c, and d.
Answer: There are four possible solutions
a = 3, b = 5, c = 6, d = 2a = 4, b = 4, c = 3, d = 4a = 4, b = 4, c = 4, d = 3a = 5, b = 3, c = 2, d = 6Step-by-step explanation:
I was unable to manipulate this system to develop solvable equations, so I made a table consisting of 7 rows with the following 5 columns:
a (values of 1 thru 7)b (values of 7 thru 1)a·b (multiplying column 1 by column 2)c + d (subtracting column 3 from 23)cd=12 (two addends from column 4 that create a product of 12)Table 1
[tex]\begin{array}{c|c|c|c|c}{a&b&ab&c+d&cd\\1&7&7&16&\text{null}\\2&6&12&11&\text{null}\\3&5&15&8&2,6\\4&4&16&7&3,4\\5&3&15&8&6,2\\6&2&12&11&\text{null}\\7&1&7&16&\text{null}\\\end{array}[/tex]
I used the valid solutions (rows 3 thru 5) to determine which combinations satisfied ab + cd = 28.
Table 2
[tex]\begin{array}{c|c|c|c|c}a&b&c&d&ab+cd\\3&5&2&6&6+11=17\\3&5&6&2&18+10=28^*\\4&4&3&4&12+16=28^*\\4&4&4&3&16+12=28^*\\5&3&2&6&10+18=28^*\\5&3&6&2&30+6=36\\\end{array}[/tex]
* represent the valid solutions
Which equations are equivalent to Y=2/3X-4 when written in slope-intercept form? Check all that apply. A =3X-2Y=4. B=2X-3Y=12. C-4(2X-3Y)=-4(12). D=2(X+6)=3Y. E=2X-3Y=4
Answer:
B 2X-3Y=12
C -4(2X-3Y)=-4(12)
Step-by-step explanation:
y = 2/3 x -4
multiply by 3
3y = 2x -12 factor out a 2 3y = 2(x-6)
subtract 2x from each side
-2x+3y = -12
multiply by -1
2x-3y = 12
multiply by -4
-4(2x-3y) = -4(12)
The slope-intercept form: y = mx + b.
The standard form: Ax + By = C.
We have:
[tex]y=\dfrac{2}{3}x-4[/tex] multiply both sides by 3
[tex]3y=2x-12[/tex] subtract 2x from both sides
[tex]-2x+3y=-12[/tex] change the signs
[tex]2x-3y=12\to\boxed{B.}[/tex] multiply both sides by (-4)
[tex]-4(2x-3y)=-4(12)\to\boxed{C.}[/tex]
Answer: B and C.A. 3x - 2y = 4 - NOT
D. 2(x + 6) = 3y → 2x + 12 = 3y → 2x - 3y = -12 - NOT
E. 2x - 3y = 4 - NOT
Charlotte is running at a rate of 9\,\dfrac{\text{km}}{\text{h}}9
h
km
.
What is Charlotte's speed in \dfrac{\text{m}}{\text{s}}
s
m
?
Step-by-step explanation:
Given speed of Charlotte in kilometer per hour = 9 km/h
We need to find the Charlotte's speed in meter per second.
We know 1 kilometer = 1000 meter
And 1 hour = 3600 seconds.
Plugging those values of km and hour in given speed in km/h, we get
[tex]9\ \frac{km}{h} = 9\times \ \frac{1000m}{3600 seconds}[/tex]
[tex]=\frac{10m}{4s}= 2.5\ m/s[/tex].
Therefore,
Charlotte's speed in meter/second is 2.5m/s.Answer:
Speed of Charlotte in a Unit which includes Km and hour [tex]=9 \frac{\text{Km}}{\text{hour}}[/tex]
1 Km=1000 meter
1 hour=60 minutes=3600 seconds
Speed of Charlotte in a Unit which includes meter and second is
[tex]=\frac{9 \times 1000}{3600}\frac{\text{meter}}{\text{seconds}}\\\\=\frac{90}{36}\frac{\text{meter}}{\text{seconds}}\\\\=\frac{5}{2}\frac{\text{meter}}{\text{seconds}}[/tex]
Why were measurements originally started?
Answer:
Measurements were needed for multiple things, such as agriculture, construction, and trade. Also, many areas developed their own systems for measuring objects making it difficult as people from different places had different results. Eventually, the same system was adopted by the majority of people.
Step-by-step explanation:
Brandon buys a radio for $46.49 in a state where the sales tax is 7%.
I couldb't understand you're question but here are possible answers and explanations
What is the total price: $49.74
$46.49 • 0.07 = 3.25
46.49 + 3.25 = 49.74
What was the sales tax amount: 3.25
$46.49 • 0.07 = 3.25
Hope this helps.
the length of a rectangle is 4 times its width. write an expression for the area of the rectangle.
Please help me with these two problems. It's fine if you only do one though. All help is welcomed. THANK YOU!!!
Answer:
a) x=38
b) x=19
Step-by-step explanation:
a) The interior angles at L and M can be found by subtracting 134 and 84 from 180 respectively:
∠L = 180 - 134 = 46
∠M = 180 - 84 = 96
The angles of a triangle sum up to 180, so x + 46 + 96 = 180.
From this you find that x = 180 - 46 - 96 = 38
b) Because YZ and XW are parallel, ∠Y=∠W = 2x
The sum of the angles in the triangle must be 180, so
3x-5 + 90 + 2x = 180
Which simplifies to
5x +85 = 180
5x = 95
x = 19
Answer:
a) x = 38°; b) x = 19°
Step-by-step explanation:
a)
∠OLM = 180 - 134 = 46° Supplementary angles
∠OML =180 - 84 = 96° Supplementary angles
x + 46 + 96 = 180 Interior angles of triangle
x + 142 = 180
x = 38°
===============
b)
∠XWY + 3x - 5 + 90 = 180 Interior angles of triangle
∠XWY + 3x + 85 = 180
(1) ∠XWY + 3x = 95
∠XWY = 2x
(2) ∠XWY - 2x = 0 Alternate interior angles
5x = 95 [2 subtracted from (1)]
x = 19°
the sum of two numbers that differ by 3 is x, what is the value of the greater of the two numbers?
Answer:
Step-by-step explanation:
You really don't have enough information to solve this with one answer. You want a value for y and there is no what to limit it to just 1 set of values. For example if x = 23 then
x = y + y - 3
x = 2y - 3
23 = 2y - 3 Add three to both sides
23+3 = 2y Combine
26 = 2y Divide by 2
26/2 = 2y/2 Do the division
13 = y
The smaller number is 13 - 3 = 10
Their sum is 13 + 10=23 But that answer is not unique.
====================
Suppose x = 13
13 = 2y - 3 Add 3
13 + 3 = 2y
16 = 2y
y =8
The larger number = 8
The smaller number = 5
=======================
The best I can do is give you the equation which is
x = 2y - 3
The ratio of the measures of the three angles to a triangle is 2:9:4. Find the measures of the angles.
Answer:
first angle is 24
second angle is 108
third angle is 48
all the three angles of the triangle add up to 180
(its a rule)
then 2+9+4=15
180÷15=12
12×2=24
12×9=108
12×4=48
Step-by-step explanation:
i got it right
What is the equation of this line?
a) y=2x−3
b) y=−12x−3
c) y=−2x−3
d) y=12x−3
Answer:
Not sure but i think its C. y=-2x-3
Answer:
y = 2x - 3
Step-by-step explanation:
15PTS!!
What is the best approximation of the solution to the system to the nearest integer values?
(−2, 6)
(7, −2)
(6, −2)
(−2, 7)
Answer:
(-2,6)
Step-by-step explanation:
The solution to a system of equations is where the two graphs intersection. By looking at the graph we can see that they cross at an x coordinate of approximately -2.4 and at a y coordinate of just above 6. We do not have to be too specific since we just have to be to the nearest integer.
(-2,6)
A model is created to show 5 thousands blocks, 4 hundreds blocks, and 9 ones blocks. How would this number be written in standard form?
Answer:
Five thousand- four hundred and nine.
Step-by-step explanation:
In what direction and by how many units is the graph of f(x) = −3 cos(2x − π) + 2 vertically and horizontally shifted
Answer:
Vertical shift is 2 units top and horizontal shift is [tex]\frac{\pi }{2}[/tex] units to the right
Step-by-step explanation:
Consider the function f(x) = a cos(bx + c) + d.
In this graph, the horizontal shift is -c/b and the vertical shift is d.
Let's compare our graph, f(x) = -3 cos(2x - π) + 2 with this graph.
Here, a = -3, b = 2, c = -π and d = 2.
So, vertical shift = d = 2 units top and
horizontal shift = [tex]-\frac{c}{b} =-\frac{-\pi }{2} =\frac{\pi}{2}[/tex] units to the right.
What is the 6th term in the arithmetic sequence defined by the explicit formula
an=8n-3?
Answer: The 6th term is 45
Step-by-step explanation:
for the 6th term you would substitute 6 for n
an = 8n - 3
an = 8 * 6 - 3
an = 48 - 3
an = 45
a deck 48 cards is divided equally among 6 colors if red is one of the colors in the deck what is the probability that the first card drawn will be red
Martin will earn $20 per hour at a new job. During training, he will earn $15 per hour. What percent of Martin's regular hourly rate will he earn during training?
Answer:the answer is 75%
Step-by-step explanation:
Martin will earn 75% of his regular hourly rate during his training period, which is calculated by dividing the training hourly rate ($15) by the regular hourly rate ($20) and multiplying by 100%.
Explanation:To determine what percent of Martin's regular hourly rate he will earn during training, we need to compare his training wage to his regular wage. Martin's regular hourly rate is $20 per hour, and during training, he earns $15 per hour.
The percentage can be calculated using the formula:
Percent Earned During Training = (Training Hourly Rate / Regular Hourly Rate) x 100%
Now, plug in Martin's earnings:
Percent Earned During Training = ($15 / $20) x 100%
Percent Earned During Training = 0.75 x 100%
Percent Earned During Training = 75%
Therefore, Martin will earn 75% of his regular hourly rate during his training period.
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cindy can bake 36 cupcakes in 1 hour. she needs a total of 144 cupcakes. she has already made 18 cupcakes. how many hours will it take cindy to bake the rest? write and solve the equation.
Answer:
The answer would be 4 more hours.
Step-by-step explanation:
Since she can make 36 cupcakes in 1 hour,
144 divided by 36 is 4, so it would take four more hours to make the rest.
Hope I helped! God bless you :-)
When Tom purchased a new motorcycle, he paid a 5% sales tax. The amount of sales tax he paid was $265. What was the total cost of the motorcycle including the sales tax? Enter your answer in the box. $
Answer:
$5565 PLEASE GIVE BRAINLIEST
Step-by-step explanation:
100% ÷ 5 = 20
265 x 20 = $5300
$5300 + $265 = $5565
TO CHECK YOUR ANSWER
5565 x .05 = 265 (amount of tax)
What ranges of scores have a frequency of 1
Answer:
20-30 & 40-50
Step-by-step explanation:
To find which range of scores have a frequency of 1, let's break it all down into separate ranges.
20-30: 1
30-40: 2
40-50: 1
50-60: 2
60-70: 6
70-80: 9
80-90: 13
90-100: 5
We can see in our different ranges that the range 20-30 and 40-50 have a frequency of 1.
How did we find this?
Analyze the chart and find which area shows the range, the bars are the frequencies of the different ranges.