Answer:
A
Step-by-step explanation:
y=3/2x+5
2(y+3/2x)=5(2)
2y+3x=10
Only answer if you are 100% sure!
Answer:
$29.865
Step-by-step explanation:
Because 3.75/2 =1.875 so $1.875 plus $15 Plus the flat $12.99
Using a linear function, it is found that he spent $29.865 for the 4.5 hours he was on the river.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The intercept is the flat rate of $12.99.The slope is the cost per hour of $3.75.Hence the cost of x hours is given by:
C(x) = 12.99 + 3.75x.
For 4.5 hours, the cost is given as follows:
C(4.5) = 12.99 + 3.75(4.5) = $29.865.
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find a degree 3 polynomial having zeros, -6, 2, and 7 and the coefficient of x^3=1
The polynomial of degree 3 is given by x³-3x²-40x+84.
The degree of a polynomial is the highest degree of the variables present with non-zero coefficients.
For example the polynomial [tex]{\displaystyle 2x^{2}y^{3}+8x+10}[/tex] has three terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term.
A degree 3 polynomial having zeros α,β and γ and the coefficient of x³ equal a is
a(x-α)(x-β)(x-γ)
So the given zeroes of the polynomial are -6,8 and 7 and the coefficient of x³ is 1. So the desired polynomial is given by:
1(x+6)(x-2)(x-7)
=(x²-4x-12)(x-7)
=x³-3x²-40x+84
Hence the polynomial of degree 3 is given by x³-3x²-40x+84.
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Alex wants to make a cake and has 50 1/2 cups of sugar, he needs 1/4 of a cup to make 1 cake. How many cakes can he make?
Alex makes 202 cakes with 50 (1/2) cups of sugar.
Given,
Quantity of sugar Alex with him = 50 (1/2) cups
Quantity of sugar needed for making 1 cake = 1/4 cup
We have to find the number of cakes Alex can make with 50 (1/2) cups of sugar.
Number of cakes = Quantity of sugar Alex with him / Quantity of sugar needed for making 1 cake
Number of cakes = 50 (1/2) ÷ 1/4
Number of cakes = 50 ÷ 0.25 + 0.5 ÷ 0.25
Number of cakes = 200 + 2
Number of cakes = 202
That is, Alex can make 202 cakes with 50 (1/2) cups of sugar.
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Beinggreat78 is a goddess fr
Answer:
C.
Step-by-step explanation:
[tex]\frac{3}{5} = 3 \div 5 = 0.6[/tex]
Answer: A
Step-by-step explanation:
0.6 converted to a fraction is 1/6
-1/2n = -8 PLEASEEEEEEE
Answer:
Step-by-step explanation:
D.16
95 +94/2
= 94.5
A. Identify and explain the error in this scenario.
B. Correct the error.
Answer:
did not do order of operations and added first
94/2 remember order of operations
94/2 = 47
47+95 = 142
There you go :)
A company that manufactures bicycles has costs given by the equation below in which x is the number of bicycles manufactured and C is the cost to manufacture each bicycle. Complete parts a. through c.
a) cost C of manufacturing 1000 bicycle is $170
b) cost C of manufacturing 7000 bicycle is $110
c) As more bicycle is manufactured the cost of manufacturing decreases
What is an mathematical expression?
Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
given expression of cost of bicycle C in terms of number of number of bicycles x is :
C = (100x + 70,000)/ x
a) Now, to get the cost C of manufacturing 1000 bicycle substitute x as 1000 in above expression :
C = (100x + 70,000)/ x
C = 100 + (70,000/ x)
C = 100 + 70,000/1000
C = 100 + 70
C = 170 bicycle's
b) Now, to get the cost C for 7000 bicycle substitute x as 7000 in above expression :
C = (100x + 70,000)/ x
C = 100 + (70,000/ x)
C = 100 + 70,000/7000
C = 100 + 10
C = 110 bicycle's
c) As it is observed from the above analysis as more bicycle is manufactured the cost of manufacturing decreases.
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What of the following is not a vertical asymptote of the function
f(x)= tan(pi x/4) / x^2-8x+15?
2
3
4
5
6
Rewrite the function as
[tex]f(x) = \dfrac{\tan(\left(\frac{\pi x}4\right)}{x^2 - 8x + 15} = \dfrac{\sin\left(\frac{\pi x}4\right)}{\cos\left(\frac{\pi x}4\right) (x-3) (x-5)}[/tex]
Vertical asymptotes occur wherever the denominator is zero (but not necessarily when the numerator is also zero).
We have
[tex]\cos\left(\dfrac{\pi x}4\right) (x-3) (x-5) = 0[/tex]
[tex]\implies \cos\left(\dfrac{\pi x}4\right) = 0 \text{ or } x - 3 = 0 \text{ or } x - 5 = 0[/tex]
In the first case, we have
[tex]\cos\left(\dfrac{\pi x}4\right) = 0 \implies \dfrac{\pi x}4 = \pm\dfrac\pi2 + 2n\pi \implies x = \pm 2 + 8n[/tex]
where [tex]n[/tex] is an integer. That is, any of [tex]x\in\{\ldots,-10,-2,\boxed{6},14,\ldots\}[/tex] and [tex]x\in\{\ldots,-6,\boxed{2},10,18,\ldots\}[/tex] are asymptotes.
In the latter two cases, we get [tex]x=\boxed{3}[/tex] or [tex]x=\boxed{5}[/tex]. The numerator is finite at these values [tex]\left(\sin\left(\frac{3\pi}4\right)=\frac1{\sqrt2}\text{ and } \sin\left(\frac{5\pi}4\right)=-\frac1{\sqrt2}\right)[/tex].
This means [tex]x=4[/tex] is not an asymptote. (C)
Alexandra is ordering a taxi from an online taxi service. The taxi charges $2 just for
the pickup and then an additional $1.75 per mile driven. How much would a taxi ride
cost if Alexandra is riding for 9 miles? How much would a taxi ride cost that is m
miles long?
Answer:$17.75
Step-by-step explanation:
2+1.75m
2+1.75(9)
2+15.75
17.75
Answer this volume based Question. I will make you brainliest + 50 points
Answer:
1.3 m
Step-by-step explanation:
Given dimensions of rectangle ABCD:
width = xlength = (x + 4)[tex]\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\\\\implies \sf Area\:of\:ABCD& = x(x+4)\\& = x^2+4x \end{aligned}[/tex]
Given dimensions of isosceles triangle ADE:
Base = DE = xHeight = AD = x[tex]\begin{aligned}\textsf{Area of a triangle} & = \dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of $\triangle$ADE}& = \dfrac{1}{2} \cdot x \cdot x\\& = \dfrac{1}{2}x^2\end{aligned}[/tex]
As the area of the portion remaining when ADE is cut off from ABCE is 6 m²:
[tex]\begin{aligned}\sf ABCD-ADE & = 6\\\implies x^2+4x-\dfrac{1}{2}x^2 & = 6\\2x^2+8x-x^2 & = 12\\x^2+8x & = 12\\x^2+8x-12 & = 0\end{aligned}[/tex]
Solve the found quadratic equation by completing the square.
Move the constant to the right side of the equation:
[tex]\implies x^2+8x-12+12=0+12[/tex]
[tex]\implies x^2+8x=12[/tex]
Add the square of half the coefficient of x to both sides:
[tex]\implies x^2+8x+\left(\dfrac{8}{2}\right)^2=12+\left(\dfrac{8}{2}\right)^2[/tex]
Simplify:
[tex]\implies x^2+8x+4^2=12+4^2[/tex]
[tex]\implies x^2+8x+16=12+16[/tex]
[tex]\implies x^2+8x+16=28[/tex]
Factor the perfect square trinomial on the left side:
[tex]\implies (x+4)^2=28[/tex]
Square root both sides:
[tex]\implies \sqrt{(x+4)^2}=\sqrt{28}[/tex]
[tex]\implies x+4=\pm \sqrt{28}[/tex]
[tex]\implies x+4=\pm \sqrt{4 \cdot 7}[/tex]
[tex]\implies x+4=\pm \sqrt{4}\sqrt{7}[/tex]
[tex]\implies x+4=\pm 2\sqrt{7}[/tex]
Subtract 4 from both sides:
[tex]\implies x=-4\pm 2\sqrt{7}[/tex]
As length is positive:
[tex]\implies x=-4+ 2\sqrt{7}\:\:\sf only[/tex]
Taking the value of √7 = 2.65:
[tex]\implies x \approx -4+ 2(2.65)[/tex]
[tex]\implies x \approx -4+5.3[/tex]
[tex]\implies x \approx 1.3[/tex]
Therefore, the width of the sheet is 1.3 m.
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A store has clearance items that have been marked down by 25%. They are having a sale, advertising an additional 45% off clearance items. What percent of the original price do you end up paying?
we end up paying 41.25 % of the original price after the addition sale on the clearance.
Let the original price of the good be x
Now, there is a sale of 25 %.
So the price will become
Price = x - 25 % of x
Price = x - 25 / 100 x
Price = x - 0.25 x
Price = 0.75 x
Now, there is an addition 45 % sale on the price.
so the price become:
New price = P = 0.75 x - 45 % of 0.75 x
P = 0.75 x - 45 / 100 (0.75 x)
P = 0.75 x - 0.45( 0.75 x)
P = 0.75 x - 0.3375 x
P = 0.4125 x
percentage of original price is:
P = 41.25 % of x
Therefore, we get that, we end up paying 41.25 % of the original price after the addition sale on the clearance.
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In a conditional statement where do you find the conclusion
please im failing math and this is an extra credit problem.
Answer:
1:30 pm
Step-by-step explanation:
You want the time when Sahil catches up to Joaquin, who left at 8 am riding 50 mph when Sahil left at 8:30 am, riding at 55 mph.
Time, Speed, DistanceThe relation between time, speed, and distance is ...
distance = speed × time
time = distance / speed
Joaquin has a head start of 0.5 hours (30 minutes), during which time he traveled ...
head start distance = (50 mi/h) × (0.5 h) = 25 mi
Sahil is traveling 55 - 50 = 5 mph faster than Joaquin, so closes that gap at the rate of 5 mi/h. The time it takes to close the gap entirely is ...
time = distance / speed = 25 mi / (5 mi/h) = 5 h
So, 5 hours after Sahil starts at 8:30, the two riders will be at the same place.
Sahil catches Joaquin at 1:30 pm.
__
Additional comment
By the time the gap is closed at 1:30 pm, both riders will have traveled a distance of ...
distance = speed × time = 50 mi/h × 5.5 h = 55 mi/h × 5 h = 275 mi
In the attached graph, we have written equations for the total distance traveled by each motorcycle. The x-value used is the clock time on a 24-hour clock. That is, their meeting time of 13.5 hours corresponds to 13:30 hours or 1:30 p.m. on a 12-hour clock.
Grayson bought snacks for his teams practice. He bought a bag of popcorn for $3.50 and a five pack of juice bottles. The total cost before tax was $11.05. Right and solve an equation which can be used to determine J, how much each bottle of juice cost.
The each bottle of juice cost $ 7.55 before tax .
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Grayson bought bag of popcorn (P)= $3.50
Five pack of juice bottles.
The total cost before tax was $11.05.
According to given question we have
Let the cost of the juice bottles be x.
P+ x= $11.05.
$3.50+x=$11.05
x=$11.05-$3.50
x=$ 7.55
Therefore, the each bottle of juice cost $ 7.55 before tax .
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An aeroplane when flying at a height of 2000m from the ground passes vertically above a helicopter at an instant when their angles of elevation from the same point on the ground are 60⁰ and 30 respectively. Find the vertical distance of the helicopter from the ground.
The vertical distance of helicopter from the ground is equal to 2000 / 3 m.
Let the distance between the two planes A and B be x.
In △ ADC, we get that:
tan 60° = 2000 / y
√3 = 2000 / y ...(1)
Now, in △ BCD, we get that:
tan 30° = 2000 - x / y
1 / √3 = (2000 - x) / y ... (2)
Divide (1) from (2):
3 = 2000 / (2000 - x)
6000 - 3 x = 2000
3 x = 6000 - 2000
3 x = 4000
x = 4000 / 3
(2000 - x) = 2000 - 4000/3 = 2000 / 3
Therefore, the vertical distance of helicopter from the ground is equal to 2000 / 3 m.
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Which expression is equivalent to (5x^−5y^3)^
−2?
What is the probability of getting a 10 or a jack from a deck of pocker cards
Answer:
The probability of both outcomes is equal i.e. 50% or 1/2. So, the probability of an event is Favorable outcomes/Total number of outcomes. It is denoted with the parenthesis i.e. P(Event).
Answer: 8/52
Step-by-step explanation:
there are 4 jacks in a deck of 52 cards, and also 4 tens. The combined probability of picking a 10 or jack is 8 in 52, which is 15.38%.
The length of a rectangle is 5 times the width. If the perimeter of the rectangle is 108 feet, find the length
and the width.
Answers:
Length = 45 feet
Width = 9 feet
=========================================================
Work Shown:
x = width
5x = five times the width = length
P = perimeter of the rectangle
P = 2*(length + width)
P = 2*(5x+x)
P = 2*(6x)
P = 12x
Set this equal to the stated perimeter (108) and solve for x.
12x = 108
x = 108/12
x = 9 feet is the width
5x = 5*9 = 45 feet is the length
-------------
Check:
P = 2*(9+45) = 108
or you could add up the four sides like this
P = 9+45+9+45 = 108
Either way the answers are confirmed.
Solve for x
x + k
——- = r
m
So, we are to solve for x in:
[tex] \frac{x + k}{m} = r[/tex]
Cross multiply the above to solve for x
[tex]x + k = mr[/tex]
Now, collect like terms to find x
Therefore: [tex]x = mr - k[/tex]
A 55-inch is cut into two pieces. One piece is 4 times the length of the other. Find the length of the shorter piece.
The shorter section is x inches length, or 44.
What constitutes a length?
A line segment can be drawn on paper and has a set length. the measurement of the separation between the longest or longer side of an object's ends. 2: an exact distance The three miles of the road. 3: How much time something requires The movie lasts for two hours. 4: a lengthy fragment of something She purchased a length of pipe in
accordance with the instruction;
the shorter portion should be x.
It is 4x because the longer portion is 4 times as long as the other.
4x + x = 55
5x = 55
4x = 44
x = 11
The length of the shorter piece is x, which is 44
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a pebble dropped into a calm pond causing ripples in the form of concentric
Answer:
A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outer ripple is given by r ( t ) = 0.6 t r(t) = 0.6t r(t)=0.6t, where t is the time in seconds after the pebble strikes the water.
Step-by-step explanation:
Answer:
well dude it's because of the law of gravity
A car travels at an average speed of 52 miles per hour How many miles does it travel in 4 hours and 45 minutes
Answer: 247 miles.
Step-by-step explanation: First, we need to convert the 45 minutes into hours. we know that 1 hour = 60 minutes. Dividing any number of minutes by sixty gives us the number of hours along with the remaining minutes if there are any. so 45/60 simplifies to 3/4. Now for the miles, it's given that the speed is 52 mph. So we can put into the expression 52(4+3/4)= total miles. Once we distribute 52, we get 208 + 39, which equals to 247.
Answer:
247
Step-by-step explanation:
52÷60 mins x 45= 39 miles for 45 mins
45 mins + 4 x 52 =247
She begins at sea level, which is an elevation of o feet.
She travels down 27.2 feet.
She then ascends 2.1 feet.
Next, she descends a second time, 19.6 feet.
How many feet must she now rise to get back to sea level?
Answer:
She will need to rise 55.4 feet.
Step-by-step explanation:
-27.2 feet + 2.1 feet = -25.1
-25.1 + -19.6 = 44.6
100- 44.6 = 55.4 feet
please help it's matic
Answer:
6
Step-by-step explanation:
If there are 4 in each tank, that means there are 2 tanks. 4-2 = 2. 8-2 = 6.
Answer:
There 30 fish left at the store
Step-by-step explanation:
There are 8 tanks
If there are 4 fish in each tank, the total would be 32 fish. If Dalia buys 2 fish, you would do 32 - 2 = 30 fish.
Hope this helped!! ( >ᴗ<) xx
4. How many terms are there in the following sequence?
19, 21, 23, ..., 53
The answer is______ terms.
Please show work
Answer:
The answer is this sequence has 18 terms
Step-by-step explanation:
As you can see, the term-to-term rule of the sequence is +2
We can use that to calculate the amount of terms.
First, calculate the distance between the first and last terms
53 - 19 = 34
Then, use this and divide the term-to-term rule.
34/ 2 = 17
Remember to add 1 at the end :)
17 + 1 = 18
There are 18 terms in this sequence.
If you don't trust me, you can check it yourself :D
Find an equation of the line that satisfies the given conditions. Through (4, 9); parallel to the line passing through (5, 7) and (1, 3)
Answer:
y = 1x + 5
Step-by-step explanation:
First, lets calculate the equation of the line passing through (5, 7) and (1, 3) in slope-intercept form
The general equation of a line in slope-intercept form is
y = mx + b
where m = slope and b = y-intercept is rise over run =
[tex]m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}[/tex]
where (x₁, y₁) and (x₂, y₂) are any two points on the line
For the line passing through (5, 7) and (1, 3) , the slope
[tex]m = \dfrac{3 - 7}{1 - 5}[/tex]
[tex]m = \dfrac{-4}{-4}[/tex]
[tex]m = 1[/tex]
To compute the y-intercept, plug in any of the two points x and y values and solve for b
Take point 5, 7 ==> when x = 5, y must be 7
We get
7 = 1 x 5 + b
7 = 5 + b
2 = b (subtract 5 from both sides)
b = 2
So the equation of the line is
y = 1x + 2
A line parallel to another line will have the same slope and a different y-intercept
Therefore a parallel line will also have slope 1 and its equation will be of the form
y = 1x + b
To calculate this b, plug in the point (4, 9) into the equation and solve for b
9 = 1 x 4 + b
9 = 4 + b
b = 5
So the equation is
y = 1x + 5
Graph attached shows the real picture
24.56 divided by 1.2
Answer:20.4
Step-by-step explanation:
Change the divisor 1.2 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.
Find a. (f+g)(x) b. (f+g)(6).
f(x)=3x2−x−6, g(x)=x−4
We get that the value of (f + g)(x) is 3 x² - 2 x - 10 and (f + g)(6) is 86.
We are given the two functions:
f(x) = 3 x² - x - 6
g(x) = x - 4
We need to find:
(f + g)(x)
= f(x) +g(x)
= 3 x² - x - 6 + x - 4
= 3 x² - 2 x - 10
Now we have to find:
(f + g)(6).
Put x = 6, we get that:
= 3 (6)² - 2 (6) - 10
= 108 - 12 - 10
= 108 - 22
= 86
Therefore, we get that the value of (f + g)(x) is 3 x² - 2 x - 10 and (f + g)(6) is 86.
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at the valentines day dance the sponsors handed out candy kisses to each person entering the dance. one group received a total of 20 candy kisses as they entered. another group of dancers received a total of 52 candy kisses. each person received the same amount of candy. what was the greatest possible number of candy kisses each person could have received
the maximum number of candy kisses that each person could have received is 4.
What was the greatest possible number of candy kisses each person could have received?We know that each person receives the same number of candy.
Now, one group of K people receives 20 candy.Another group of N people receives 52 candy.Then the quotients between the number of candy and the number of people should give the same value:
20/K = 52/N
Let's find the common factors between 20 and 52, to do so, we need to rewrite the two numbers as a product of prime factors:
20 = 2*10 = 2*2*5
52 = 2*26 = 2*2*13
The greatest common factor between 20 and 52 is (2*2) = 4
Then, if each person receives 4 candy:
The group that receives 20 candy:
20/K = 4
20/4 = k = 5
That group has 5 people.
The group that receives 52 candy:
52/N = 4
52/4 = N = 13
This group has 13 people.
Then the maximum number of candy kisses that each person could have received is 4.
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The Jackman & Murohv partnership has the following balances on December 31, 2024:
H: (Click the icon to view the balances.)
Jackman and Murphy share profits 1:3, respectively. Jackman and Murphy decide to liquidate the partnership. Journalize the sale of the non-cash assets for $59,000, the payment of the liabilities.
and the payment to the partners. Assume Murphy contributes cash equal to the capital deficiencv. (Record debits first. then credits. Select the explanation on the last line of the journal entry table.)
Answer:
Step-by-step explanation: