The proportional relationship between x and y is;
x 7 14 28 35
y 1 2 4 5
The correct option is D.
Proportional relationships;Proportional relationships between x and y satisfy the following equation;
[tex]\rm y=kx[/tex]
Where k is some constant.
Rearranging the equation;
[tex]\rm y=kx\\\\k=\dfrac{y}{x}[/tex]
Then,
The proportional relationship between x and y is;
[tex]\rm k = \dfrac{y}{x}\\\\\rm When \ x= 7 \ and \ y= 1\\\\K=\dfrac{1}{7}\\\\\rm When \ x= 14 \ and \ y= 2\\\\K=\dfrac{2}{14}=\dfrac{1}{7}\\\\\rm When \ x= 28 \ and \ y= 4\\\\K=\dfrac{4}{28}=\dfrac{1}{7}\\\\\rm When \ x= 35 \ and \ y= 5\\\\K=\dfrac{5}{35}=\dfrac{1}{7}[/tex]
Hence, the proportional relationship between x and y is the correct option is D.
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PLEASE HELP ME!
-----------------------------------
For the 1st question, the answer is A) Distributive Property:
The reason why Step 1 is A) Distributive Property is because you're distributing 2 to the #'s that are in the parenthesis().
For the 2nd question, it's either A) Reflexive Property or C) Symmetric Property...
the soccer team voted on what they wanted to eat. There are 20 members on the team. Six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs.
Answer:
4 people voted for hot dogs
Step-by-step explanation:
20-6-10=4
Answer:
Not sure what your exact question is, but I'll make an assumption that you are asking for the percentages of each statistic. It's going to be:
30% pizza
50% chicken
20% hot dogs
Step-by-step explanation:
Because you have 20 members, to get a total percentage, I divided by 2 to get to 10, which is going to make it easier to determine the percentages.
Next, because you divided the total players by 2, you have to do the same for each of the votes as well. Six becomes three, 10 becomes 5, and the rest (which is four) becomes two.
Now, you need to multiply by 10 to get the exact percentage. 10 becomes 100%, and the same for all the other numbers.
Hope this helps!
If x = 1 is a zero of the polynomial x3 – 7x + 6, find the other two zeroes.
Answer:
x = - 3, x = 2
Step-by-step explanation:
Since x = 1 is a zero then (x - 1) is a factor of the polynomial
dividing x³ - 7x + 6 ÷ (x - 1)
= (x - 1)(x² + x - 6)
= (x - 1)(x + 3)(x - 2)
equating (x + 3)(x - 2) = 0 gives the other zeros
equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 2 = 0 ⇒ x = 2
Which of the following could be the equation of the function below?
Answer:
[tex]y=-2cos (2(x+\pi ))-1[/tex]
Step-by-step explanation:
From the graph, we can see that y = -3 when x = 0.
So to check whether which of the given options is the equation of the given graph, we will set our calculator to the radian mode and then plug the value of x as 0.
1. y = -2 cos (4(x + pi)) - 1 = -2 cos (4(0 + pi)) - 1 = 3
2. y = 2 cos(x + pi) = 2 cos(0 + pi) = -1
3. y = -2 cos (2(x + pi)) - 1 = -2 cos (2(x + pi)) - 1 = -3
Therefore, the equation of this graph is y = -2 cos (2(x + pi)) - 1.
-10-|1+4b|=-19
Y = 0
Answer:
b=2 or b=-2.5
Step-by-step explanation:
We solve absolute value equations the same as any other equation using inverse operations. However, the inverse operation for absolute value requires one special condition. Since absolute values change a number to a positive regardless if it has a negative sign, we have two possible answers. When we have the absolute value operation isolated, we will set it equal to both the negative and positive option.
[tex]-10-|1+4b|=-19\\-10+10-|1+4b|=-19+10\\-|1+4b|=-9\\\frac{-|1+4b|}{-1} =\frac{-9}{-1} \\|1+4b|=9[/tex]
We now have the absolute value isolated. We will set it equal to both 9 and -9.
[tex]1+4b=9\\1-1+4b=9-1\\4b=8\\b=2[/tex]
and
[tex]1+4b=-9\\1-1+4b=-9-1\\4b=-10\\b=\frac{-10}{4}=\frac{-5}{2}= -2.5[/tex]
The company also discovered that it costs $25 to produce 2 camera cases, $59 to produce 4 camera cases and $305 to produce 10 camera cases . Find the total cost of producing 5 camera cases
Please help!!!
Answer:
Cost of 5 camera cases is $85.
Step-by-step explanation:
First we need to determine what type of function we're dealing with, is it linear, quadratic or exponential? We can determine this by calculating the first difference.
We can translate the number of cameras to correspond to the x axis and cost to the y axis. By doing this we can come up with the ordered pairs of (2,25), (4,59),(10,305). Let's get the first two ordered pairs and calculate the first difference:
[tex]\frac{59-25}{4-2}=17[/tex]
And now the second and third value:
[tex]\frac{305-59}{10-4}=41[/tex]
Notice how these values do not match, this means that this function is not increasing at a constant rate meaning that this function is not linear. Now let's calculate the second difference:
[tex]\frac{41-17}{10-2}=3[/tex]
This means our function is quadratic with a=3. Remember that generally speaking a quadratic function is such that:
[tex]y=ax^2+bx+c[/tex]
Where a,b,c are coefficients and in this case a=3. Now, let's solve for b and c values by using the coordinates given. Let's use the coordinates (2,25) where x=2 and y=25 and so:
[tex]f(x)=ax^2+bx+c\\\\25=3(2)^2+b(2)+c\\25=3(4)+2b+c\\25=12+2b+c\\13=2b+c\\\\b=\frac{13-c}{2}[/tex]
Now let's solve for "c" by using different coordinates (4,59) where x=4 and y=59 and also use the "b" value that we calculated above and so:
[tex]f(x)=ax^2+bx+c\\\\59=3(4)^2+(\frac{13-c}{2})(4)+c\\59=48+\frac{52-4c}{2}+c\\11=\frac{52-4c+2c}{2}\\11=26-2c+c\\-15=-c\\\\c=15[/tex]
Now that we know the value of "c" we can use the equation for b to solve for b and so:
[tex]b=\frac{13-c}{2}=\frac{13-15}{2}\\\\b=-1[/tex]
So this means in the quadratic equation a=3, b=-1 and c=15 therefore by using the general equation of a quadratic function we obtain or final equation:
[tex]f(x)=ax^2+bx+c\\\\f(x)=3x^2-x+15[/tex]
Since we want to find the total cost of producing 5 camera cases x=5 and so:
[tex]f(x)=3x^2-x+15\\\\f(5)=3(5)^2-(5)+15\\f(5)=75-5+15\\\\f(5)=85[/tex]
And so the cost of 5 camera cases is $85.
Simplify the expression. 3x2 + x − x2 − 2x
A. 2x
B. 2x2 − x
C. 3x2 − 2x
D. 4x2 − 3x
Answer:
B. 2x^2 − x
Step-by-step explanation:
3x^2 + x − x^2 − 2x
We need to combine like terms
3x^2 -x^2+ x − 2x
2x^2 -x
The expression 3x² + x - x² - 2x simplifies to 2x² - x, which is Choice B.
To simplify the expression 3x² + x - x² - 2x, you can combine like terms. The equation has two terms involving x squared (x²) and two terms involving x to the first power.
Combine the x² terms: 3x² - x² = 2x².
Next, combine the x terms: x - 2x = -x.
Putting them together, the simplified expression is 2x² - x.
Therefore, the answer is Choice B: 2x² - x. This step-by-step process demonstrates the importance of combining like terms and simplifying expressions to arrive at the correct solution.
which is the product of 4x^5-6x^4+4x^3-6x^2
Answer:
2 x^2 (2 x - 3) (x^2 + 1)
Step-by-step explanation:
Factor the following:
4 x^5 - 6 x^4 + 4 x^3 - 6 x^2
Factor 2 x^2 out of 4 x^5 - 6 x^4 + 4 x^3 - 6 x^2:
2 x^2 (2 x^3 - 3 x^2 + 2 x - 3)
Factor terms by grouping. 2 x^3 - 3 x^2 + 2 x - 3 = (2 x^3 - 3 x^2) + (2 x - 3) = x^2 (2 x - 3) + (2 x - 3):
2 x^2 x^2 (2 x - 3) + (2 x - 3)
Factor 2 x - 3 from x^2 (2 x - 3) + (2 x - 3):
Answer: 2 x^2 (2 x - 3) (x^2 + 1)
Answer:
[tex]2x^{2} (2x-3)(x^{2} +1)[/tex]
Step-by-step explanation:
what is 3/8+2/5 equal if someone answers can you guys please explain it to me please
Answer:
31/40
Step-by-step explanation:
LCD = 40
Multiplying numerators and denominators to get the LCD in all fraction denominators
Then rewriting the equation with the equivalent fractions
With like denominators we can operate on just the numerators
Answer:
31/40
Step-by-step explanation:
3/8+2/5
First make them both have same denominator:
3/8 8 x 5= 40 3 x 5=15/40
2/5 5 x 8=40 2x8=16 16/40
15/40+16/40=31/40
IN THE MIDDLE OF THE TEST PLEASE!!
What is the solution to this system of equations? y=3xy=x+2
Y = 3x
Y = x+2
set the two y's equal to each other
3x=x+2
Isolate the x
2x=2
divide
ANSWER: x=1 y=3 or (1,3)
Answer:the anwser is (3,9)
Step-by-step explanation:I orgainly thought 1,3
Karonlina flips a coin 60 times. how many times would you expect it's to land heads up?
Answer:
30 times
Step-by-step explanation:
There's a 50% chance that they will get heads.
60 divided by 2 is 30
50% of 60 is 30
Answer:
We expect 30 heads.
Step-by-step explanation:
There are 2 sides to a coin, heads and tails. They are equally likely. So the probably of getting a heads is 1/2
If we want to know how many times we will get heads, we multiply the number of flips by the probability of getting heads.
number of heads = 60 * 1/2
= 30
Using the slope formula, find the slope of the line through the given points.
(-8, -5) and (9, -5)
Simplify
Answer:
0
Step-by-step explanation:
Slope = (y2-y1)/(x2-x1)
= (-5--5)/ (9--8)
= (-5+5)/(9+8)
= 0/17
=0
The slope it 0
This is a horizontal line because the y value doesn't change. If the y value doesn't change, the slope it zero.
2. Sally buys a hand bag. There was a discount of 30%. If Sally paid $20, what was the original price?
Answer:
the original price is $28.57
Step-by-step explanation:
If the discount is 30% then the amount paid is 70% of the original price. Sally paid $20, it is the discounted price, equivalent to 70%.
We need to divide $20 by 70% to get the original price or the 100%.
$20 / 70% = $28.57 original price.
Since the handbag was has discount of 30%, we multiply the original price with the 30% to get the discount value.
$28.57 * 30% = $8.57 discount
To check: deduct the discount from the original price to get the discounted price.
$28.57 - $8.57 = $20
Simplify
[tex]\frac{(3 + i)}{(5 + 2i)} [/tex]
Answer:
17-i
--------
29
Step-by-step explanation:
To simply fractions with complex numbers, we have to multiply by the complex conjugate of the denominator.
The denominator is 5+2i, so the complex conjuate is 5-2i
3+i 5-2i
------ * ---------------
5+2i 5-2i
Simplifying the numerator
(3+i) * (5-2i) = 3*5 + 5i -3*2i -2i^2 = 15 +5i -6i -2(-1) = 15-i+2 = 17-i
Simplifying the denominator
(5+2i) (5-2i) = 25 -10i + 10i -4i^2 = 25 -4(-1) = 29
17-i
--------
29
Answer:
- [tex]\frac{1}{29}[/tex] i + [tex]\frac{17}{29}[/tex]
Step-by-step explanation:
to simplify the fraction ewe require to rationalise the denominator.
This is done by multiplying the numerator/ denominator by the conjugate of the denominator.
the conjugate of 5 + 2i is 5 - 2i, hence
= [tex]\frac{(3+i)(5-2i)}{(5+2i)(5-2i)}[/tex]
= [tex]\frac{15-i-2i^2}{25-4i^2}[/tex]
[ i² = ([tex]\sqrt{-1}[/tex])² = - 1 ]
= [tex]\frac{-i+17}{29}[/tex] = - [tex]\frac{1}{29}[/tex] i + [tex]\frac{17}{29}[/tex]
2350 meters is how many kilometers
Answer:
Your answer would be 2.35. All you have to do id divided how many meters you have by 1000. Hope it Helped
Step-by-step explanation:
km=m times 1000
Rachel has 30 pounds of a mixture of candy that sells for $1.00/lb. If lollipops sell for $0.95/lb and caramel candies sell for $1.10/lb. How many pounds of lollipops are in the mixture?
Could I have an equation for the problem.
Thank you so Much!
Answer:
Twenty Pounds
Step-by-step explanation:
Equation #1:
30lbs x Mix Price = (Lollipop Lbs x 0.95) + (Caramel Lbs X 1.10)
Equation #2:
Lollipops Lbs + Caramel Lbs = 30 Lbs
Rearrange expressions to solve for different variables
EQ1: Caramel Lbs = (30 - .95 Lollipop Lbs)/ 1.10 NOTE: (mix price = 1.00)
EQ2: Lollipop Lbs = 30 - Caramel Lbs
Substitute formula 1 into formula 2
Lollipop Lbs = 30 - [(30 - .95 Lollipop Lbs)/1.10]
Distribute divisor
Lollipop Lbs = 30 - 27.2727 + .8636 Lollipop Lbs
Collect terms
Lollipop Lbs = 2.7273 + .8636 Lollipop Lbs
Remove .8336 Lollipops from both sides of the equation
.1364 Lollipop Lbs = 2.7273
Divide both sides by .1364 (Answer is 19.9949 which rounds to 20)
Lollipop Lbs = 20
PROOF:
30 = (20 x 0.95) + (10 x 1.10)
30 = 19 + 11
30 = 30 TRUE!
To determine the number of pounds of lollipops in the mixture, we can set up an equation with the total weight of the mixture and the weight of the lollipops. Solving the equation, we find that there are 15 pounds of lollipops in the mixture.
Explanation:
To solve this problem, we can set up an equation using the given information.
Let x represent the number of pounds of lollipops in the mixture.
Since Rachel has a total of 30 pounds of the mixture, we can write the equation: x + (30 - x) = 30
Simplifying the equation, we have: 2x = 30
Dividing both sides by 2, we find that x = 15.
Therefore, there are 15 pounds of lollipops in the mixture.
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20 Points!! Plzz Help!!! Will give brainliest!!! Hurry Plzz Need Help ASAP!!!
If l || m, m<7 = 2x and m<2 = x, then what is the measure of angle 2?
A. 30°
B. 60°
C. 90°
D. 120°
Answer:
60
Step-by-step explanation:
anwser: B.
see explanation
A 3-ounce package of pistachios cost $5.99 what is the unit rate???!
Answer: 1.996666666666667
Step-by-step explanation:
3ounces divided by 5.99
Answer:If you round 5.99 it would be 6.00 and then dived 3 and 6.00 its going to be 1.5 because you have to split it up
Step-by-step explanation:
Express as a fraction or a mixed number.
0.15%
Answer:
15/100
Step-by-step explanation:
If the the number as a decimal is in the hundredths place you put the number over 100
Math help quickkk! How many cupcakes can the baker decorate per minute
Answer:
It would be 1 and 2/5 or 1.4 per minute.
Step-by-step explanation:
Need help with 21-22, 27-34 plz
5/6 + (-1/2)value of sum
Answer:
it's 1/3
Step-by-step explanation:
5/6+(-1/2)
5/6-1/2
LCM= 6
(5-3)/6
2/6
1/3
the sum of 9 and twice a number use the variable n to represent the unknown number
Answer:
9 + 2n =
Step-by-step explanation:
9 + 2n =
Answer:
It would be 9+2n.
Step-by-step explanation:
Sinve you have not given us an equation, twice a number can also be reresented as 2n. Since 9 is the constant, you can say 9+2n.
When you own a pet, there are one-time costs, such as a leash, and continuing costs, such as food. Suppose the one-time costs for owning a small dog are $180, and the continuing costs are $400 per year Which function models the average annual cost of owning a small dog for x years?
Answer:
Average cost per year = 400 + 180/x
Step-by-step explanation:
Using the formula y=mx+b
We know that b is the y intercept or initial value. That would be the start up costs
m is the slope on costs each time x increases, that would be 400 per year
Costs = 400x + 180
To find the average cost per year, we need to divide by x
Average cost per year = (400x + 180)/x
= 400 + 180/x
Answer:
answer to this question is f(x) = (180 + 400x)/x
Multiply: (3x + 7)(5x2 − 3x + 6)
Answer:
15x^3+26x^2-3x+42
Step-by-step explanation:
The multiplication is 15x³ +26x² - 3x + 42.
What is multiplication?Multiplication is the process of adding a number up to a given number.
The multiplication (3x + 7)(5x²-3x+6) is as shown:
(3x + 7)(5x²-3x+6)
= 15x³ - 9x² + 18x +35x²- 21x +42
= 15x³ +26x² - 3x + 42
Hence, the multiplication is 15x³ +26x² - 3x + 42.
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A computer is normally $550 but is discounted to $385 which precent of the original price does mark pay
Answer:
70%
Step-by-step explanation:
We assume, that the number 550 is 100% - because it's the output value of the task.
We assume, that x is the value we are looking for.
If 100% equals 550, so we can write it down as 100%=550.
We know, that x% equals 385 of the output value, so we can write it down as x%=385.
Now we have two simple equations:
1) 100%=550
2) x%=385
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=550/385
Now we just have to solve the simple equation, and we will get the solution we are looking for.
Solution for 385 is what percent of 550
100%/x%=550/385
(100/x)*x=(550/385)*x - we multiply both sides of the equation by x
100=1.4285714285714*x - we divide both sides of the equation by (1.4285714285714) to get x
100/1.4285714285714=x
70=x
x=70
An investor invested a total of $3 comma 500 in two mutual funds. One fund earned a 4% profit while the other earned a 2% profit. If the investor's total profit was $110, how much was invested in each mutual fund
Answer:
$2000 invested in first fund
$1500 invested in second fund
Step-by-step explanation:
An investor invested a total of $3,500 in two mutual funds.
Let x be the amount invested in first fund
first fund earned a 4% profit (4%= 0.04)
So interest is 0.04x for first fund
Let x be the amount invested in first fund
first fund earned a 4% profit (4%= 0.04)
So interest is 0.04x for first fund
Let y be the amount invested in second fund
second fund earned a =2% profit (2%= 0.02)
So interest is 0.02y for second fund
An investor invested a total of $3,500 in two mutual funds.
So x+y = 3500----> equation 1
y= 3500-x
the investor's total profit was $110
0.04x + 0.02y = 110----> equation 2
Plug in 3500 -x for y
0.04x + 0.02(3500-x) = 110
0.04x + 70 - 0.02x = 110
0.02x + 70 = 110
Subtract 70 onboth sides
0.02x = 40
Divide both sides by 0.02
x= 2000
y= 3500-x
so y= 3500 - 2000 = 1500
$2000 invested in first fund
$1500 invested in second fund
x-y<3
Do I need to flip the sign?
the price of family dinner was $48.00 . A sales tax of 5% to the final bill. The family left a $10.08 tip. If the family included the sales tax when calculating the tip, what percent tip did the family leave?
Answer:
20% tip
Step-by-step explanation:
Dinner: $48.00
Tax: 0.05($48.00) = $2.40
Total (final) bill before tip: $50.40
Tip: $10.08
Percentage tip was then $10.08 (100%) / $50.40 = 20%
The family left a 20% tip.
James has a model helicopter. The model is 8 inches long and 7 inches wide. The actual helicopter is 56 inches long. What is the helicopters actual width, if we assume the models proportions are accurate?
A: 40 inches
B: 49 inches
C: 56 inches
D: 60 inches
Answer:
49 inches
Step-by-step explanation:
Write and solve an equation of ratios, as follows:
7 inches x
-------------- = -----------------
8 inches 56 inches
Then (8 ")x = (7 ")(56 "), and
x = 392/8 inches = 49 inches.
The actual width of the helicopter is 49 inches.
The actual width is found to be 49 inches, which corresponds to answer choice B.
The question is asking us to determine the actual width of a helicopter given its scale model dimensions and the actual length. To solve the problem, we use the concept of ratios or proportions. The scale model is 8 inches long and 7 inches wide, and the actual helicopter is 56 inches long.
We set up a proportion to find the actual width:
Model length : Actual length = Model width : Actual width8 inches : 56 inches = 7 inches : x inchesTo solve for x, we cross multiply:
8 * x = 56 * 7
x = (56 * 7) / 8
x = 392 / 8
x = 49 inches
Therefore, the correct answer is B: 49 inches, which is the actual width of the real helicopter.