Answer:
150 miles
Step-by-step explanation:
If they drove the same speed throughout the trip, we can find the speed from
d= rt
Solving for r
d/t =r
300 miles/ 6 hours = r
50 miles per hour = rate ( or speed)
On the last day, the drove 3 hours.
d =rt
d = 50 miles per hour * 3 hours
d = 150 miles
Which question shows the quadratic fomula used correctly to solve 7x^2=9+x for x
Answer:
x = [tex]\frac{-b\pm\sqrt{b^{2}-4ac} }{2a}[/tex]
Step-by-step explanation:
We have
7x²=9+x
Subtracting x from both sides, we get
7x²-x=9+x-x
Cancelling out +x and -x from the right side, we get
7x²-x=9
Subtracting 9 from both sides, we get
7x²-x-9=9-9
Cancelling out 9 and -9 from the right side, we have
7x²-x-9 = 0
The above equation is in the form ax²+bx+c=0 where upon comparing we get a= 7 , b = -1 and c= -9
We can solve for x using the below quadratic formula:-
x = [tex]\frac{-b\pm\sqrt{b^{2}-4ac} }{2a}[/tex]
Upon solving we'll get two values for x, one positive an the other negative.
State whether each question below represents a proportional relationship. How can you tell?
a. y= x+ 2.3
b. y=6\13x
c. 7-y=2x
Among the given equations, only 'y = 6/13x' shows a proportional relationship because the ratio between x and y remains constant. The other two equations-'y = x + 2.3' and '7 - y = 2x' are not showing proportional relationships because the ratio between the variables doesn't remain constant.
Explanation:A proportional relationship is one where the ratio between two variables remains constant. This relationship can be represented by the equation y = kx, where k is the constant of proportionality.
a) The equation y = x + 2.3 is not a proportional relationship because it involves an added constant. If x is zero, y is not zero, thus it's not proportional.
b) The equation y = 6/13x is a proportional relationship, because there is a direct proportion between x and y. If x is multiplied by a certain factor, y will be multiplied by the same factor, thus maintaining the ratio.
c) The equation 7 - y = 2x rearranges to y = 7 - 2x, which is not a proportional relationship. Again, if x is zero, y is not zero, thus it's not proportional.
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A construction worker has a rope that is 6 m long. She needs to cut it into pieces that are each 3/7 m long. How many such pieces can she cut without having any rope leftover?
Answer:
14 pieces
Step-by-step explanation:
We will divide 6 m into 3/7 m pieces
6 ÷ 3/7
Use copy dot flip
6 * 7/3 =
42/3
14
She will have 14 pieces
The sum of the speeds of two trains is 718.7 miles per hour. If the speed of the first train is 3.3 mph faster than that of the second train, find the speeds of each.
Answer:
2x + 3.3 = 718.7 mph
Step-by-step explanation:
Charlene sold 15 magazines subscriptions for the fundraiser. Mark sold 17 subscriptions and Paul sold 12. How many magazine subscriptions did they sell in all?
Let s represent subscriptions
Equation:______
They sold_____ subscriptions in all.
Charlene, Mark, and Paul sold a combined total of 44 magazine subscriptions for their fundraiser.
Explanation:In this problem, Charlene, Mark, and Paul collectively sold magazine subscriptions. We need to find the total number of subscriptions sold. We can do this using simple addition: Charlene sold 15 subscriptions, Mark sold 17 subscriptions, and Paul sold 12 subscriptions. Therefore, using s to represent total subscriptions, our equation would be: s = 15 (Charlene's sales) + 17 (Mark's sales) + 12 (Paul's sales). Summing the numbers, s = 44. Hence, they sold 44 subscriptions in total.
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Making sure I’m doing this write... please give a walkthrough explanation! :)
144= -12(x+5)
(I’m solving for x)
Start by distributing:
-12(x+5) = (-12 * x) + (-12 * 5) = -12x - 60
144 = -12x - 60
Add 60 to both sides to start isolating your variable:
204 = -12x
Solve for x by dividing both sides by -12:
x = -17
Step-by-step explanation:
multiply -12 with x and 5, after you get the answer. subtract 60 on the left and right, after getting 84 divide it by -12 and the final answer will be -7
Type the correct answer in each box. Spell all words correctly.
A sequence of transformations maps ∆ABC onto ∆A″B″C″. The type of transformation that maps ∆ABC onto ∆A′B′C′ is a
.
When ∆A′B′C′ is reflected across the line x = -2 to form ∆A″B″C″, vertex
of ∆A″B″C″ will have the same coordinates as B′.
Answer:
Reflection
Step-by-step explanation:
When we reflect a point on the x axis, the y coordinate changes its sign.
For example if a Point P has coordinates (x,y), it will be (x, -y) after reflection on the x axis.
A (-6,2) reflected on the x axis becomes A' (-6, -2)
B (-2,6) reflected on the x axis becomes B' (-2, -6)
C (-4,2) reflected on the x axis becomes C' (-4, -2)
So, the type of transformation that maps ∆ABC onto ∆A′B′C′ is a reflection on the x axis.
Answer:
Reflection
Step-by-step explanation:
When we reflect a point on the x axis, the y coordinate changes its sign.
For example if a Point P has coordinates (x,y), it will be (x, -y) after reflection on the x axis.
A (-6,2) reflected on the x axis becomes A' (-6, -2)
B (-2,6) reflected on the x axis becomes B' (-2, -6)
C (-4,2) reflected on the x axis becomes C' (-4, -2)
So, the type of transformation that maps ∆ABC onto ∆A′B′C′ is a reflection on the x axis.
Step-by-step explanation:
There are 96 coins in a bottle. 1\2 of the coins are £1 coins. The rest of the coins are 50p coins. work out the total value of the 96 coins I need help with this
Answer:
£72
Step-by-step explanation:
Firstly, if half of 96 coins are £1 coins then:
96/2 * 1 = value of half the coins = £48
Now, we simply need to multiply 96/2 by 0.5 to find the value of these coins:
48 * 0.5 = 24
Now we can add the two:
48 + 24 = 72
So the value of the 96 coins are £72.
How many solutions are there to the equation below? 4(x-5)=3x+7
A. 1
B. 0
C. Infinitely Many
Answer:
A. 1
Step-by-step explanation:
4(x - 5) = 3x + 7
4x - 20 = 3x + 7
+ 20 = + 20
4x = 3x + 27
-3x -3x
1x = 27
x = 27
The answer is A.1
An equation is formed of two equal expressions. There exists only one solution to the problem which is equal to 27. Thus, the correct option is A.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the equation can be found as shown below,
4(x-5)=3x+7
4x - 20 = 3x + 7
4x - 3x = 20 + 7
x = 27
Hence, there exists only one solution to the problem which is equal to 27. Thus, the correct option is A.
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the school fit 72 students onto 3 buses. find the unit rate for number of students per bus.
ll the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. a How many hours would this job take if the number of workers decreased by factor of 2?
Answer:
44 hours
Step-by-step explanation:
Decreasing the people by a factor of 2 means we have 3 people
The job takes 6* 22 = 132 people hours
When we decrease the people, it will take more hours
132 people hours = 3 people * t hours
Divide each side by 3
132/3 = 3t/3
44 = t
It will take 44 hours
y = 15x
y = 25 + 12.5x
Substitute y = 15x to the equation y = 25 + 12.5x:
15x = 25 + 12.5x subtract 12.5x from both sides
2.5x = 25 divide both sides by 2.5
x = 10
Substitute the value of x to the equation y = 15x:
y = (15)(10)
y = 150
Answer: x = 10 and y = 150Which equations contain the point (0.5, –6.75). Check all that apply.
2x + 4y = –26
y = x – 7.5
2y = x + 13
y = 0.5x – 7
Answer:
(A) 2x + 4y = –26
(D) y = 0.5x – 7
The equations satisfying the points (0.5, –6.75) will be 2x + 4y = –26 and y = 0.5x – 7. The correct options are A and D.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The given point is (0.5, –6.75). Check whether all the equations satisfy the point or not.
A) 2x + 4y = –26
2 x 0.5 + 4 x -6.75 = -26
1 - 27 = -26
-26 = -26
Satisfying
B) y = x – 7.5
-6.75 = 0.5 - 7.5
-6.75 ≠ -7
C) 2y = x + 13
2 x -6.75 = 0.5 + 13
-13.5 ≠ 13.5
y = 0.5x – 7
-6.75 = 0.5 x 0.5 -7
-6.75 = -6.
Satisfying.
Therefore, the equations satisfying the points (0.5, –6.75) will be 2x + 4y = –26 and y = 0.5x – 7. The correct options are A and D.
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Yesterday, Julie’s bank account balance was $39.99. Today, she made a withdrawal from her account. The current balance is –$10.28.
How much did she withdraw from her account?
A). $50.27
B). $29.71
C). $0.00
D). $19.61
Answer:
A). $50.27
Step-by-step explanation:
Add $39.99 and -$10.28 to get $50.27
Final answer:
Julie withdrew $50.27 from her account, which can be calculated by adding her previous balance of $39.99 to the absolute value of her negative current balance, $10.28.
Explanation:
The question asks to determine how much was withdrawn from Julie's bank account, given that her balance went from $39.99 to -$10.28. To do this, we subtract the current balance from the previous balance. So the calculation is $39.99 - (-$10.28).
First, subtracting a negative is the same as adding its absolute value, so the equation can be rewritten as $39.99 + $10.28.
When these two values are added together, we get a total of $50.27. This means that Julie withdrew $50.27 from her account.
Therefore, the correct answer is A). $50.27.
Find dy, dx if f(x) = (x + 8)3x. 3xln(x + 8) the product of the quantity 3 times the natural log of the quantity x plus 8 plus 3 times x divided by the quantity x plus 8, and the quantity x plus 8 raised to the 3x power 3 times the natural log of the quantity x plus 8 plus 3 times x divided by the quantity x plus 8 3x(x + 8)(3x − 1)
Answer:
[tex]\displaystyle \frac{dy}{dx} = 3(x + 8)^{3x} \bigg[ \ln (x+ 8) + \frac{x}{x + 8} \bigg][/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]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle f(x) = (x + 8)^{3x}[/tex]
Step 2: Differentiate
Exponential Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \frac{d}{dx} \bigg[ 3x \ln (x + 8) \bigg][/tex]Derivative Rule [Product Rule]: [tex]\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ \frac{d}{dx}(3x) \ln (x + 8) + 3x \frac{d}{dx}[ \ln (x + 8)] \bigg][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \frac{d}{dx}(x) \ln (x + 8) + 3x \frac{d}{dx}[ \ln (x + 8)] \bigg][/tex]Derivative Rule [Basic Power Rule]: [tex]\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \ln (x + 8) + 3x \frac{d}{dx}[ \ln (x + 8)] \bigg][/tex]Logarithmic Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \ln (x + 8) + \frac{3x}{x + 8} \frac{d}{dx} (x + 8) \bigg][/tex]Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \ln (x + 8) + \frac{3x}{x + 8} \Big[ \frac{d}{dx}(x) + \frac{d}{dx}(8) \Big] \bigg][/tex]Derivative Rule [Basic Power Rule]: [tex]\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \ln (x + 8) + \frac{3x}{x + 8} \bigg][/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = 3(x + 8)^{3x} \bigg[ \ln (x+ 8) + \frac{x}{x + 8} \bigg][/tex]∴ we have found the derivative of the given function.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Given the sequence -1,3,7,11 find a25
It'a an arithmetic sequence.
[tex]a_1=-1\\a_2=-1+4=3\\a_3=3+4=7\\a_4=7+4=11\\\vdots\\\\\text{The general formula of nth term of an arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\\text{We have:}\\\\a_1=-1,\ d=4\\\\\text{Substitute:}\\\\a_n=-1+(n-1)(4)=-1+4n-4=4n-5\\\\\text{We want }\ a_{25}.\ \text{Substitute n = 25 to the formula:}\\\\a_{25}=4(25)-5=100-5=95\\\\Answer:\ \boxed{a_{25}=95}[/tex]
what type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue a.find a mixture that will make the same shade of green but a smaller amount
Answer:
Step-by-step explanation:
We are given that a shade of green is prepared using 2 cups of yellow and 3.5 cups of blue.
We want to make the same shade of green, but lesser quantity. We can assume a smaller value for either of the yellow or the blue colors, and find the corresponding value of the other to figure out the answer.
Let us assume that 1 cup of yellow is mixed with x cups of blue to prepare the same shade of the green. Now we can set up the ratios as shown below:
[tex]\frac{1}{x}=\frac{2}{3.5}\\2x=3.5\\x=1.75[/tex]
Therefore, 1 cup of yellow and 1.75 cups of blue color will also make the same shade of green
x square plus 3x minus 18 equal 0 by using quadratic formula
Answer:
Step-by-step explanation:
x^2 + 3x - 18 = 0
(x+6)(x-3)=0
x=-6 x=3
i had this on my book so i just wanted to help.
Final answer:
The quadratic equation x^2 + 3x - 18 = 0 can be solved using the quadratic formula, resulting in two solutions, x = 3 and x = -6.
Explanation:
To solve the quadratic equation x^2 + 3x - 18 = 0 using the quadratic formula, we must first identify the coefficients a, b, and c in the standard form ax2 + bx + c = 0. In our equation, a = 1, b = 3, and c = -18. Substituting these values into the quadratic formula gives us:
x = [-b ± √(b^2 - 4ac)] / (2a)
By substituting the values we have:
x = [-(3) ± √((3)^2 - 4(1)(-18))] / (2(1))
Which simplifies to:
x = [-3 ± √(9 + 72)] / 2
x = [-3 ± √(81)] / 2
x = [-3 ± 9] / 2
Therefore, we have two possible solutions for x:
x = (-3 + 9) / 2 = 3
x = (-3 - 9) / 2 = -6
So, the solutions to the equation x2 + 3x - 18 = 0 are x = 3 and x = -6.
50 POINTS PLEASE HELP FAST DUE TODAY: Explain why any of the four operations (+ - × ÷) placed between the two terms 5 and -3√8 will result in an irrational number.
Answer:
Because -3-/8 itself is an irrational number. No matter the operation it wil always be irrational
Step-by-step explanation:
PLZ HELP URGENT 30 POINTS!!!!!
Which of the following
functions maps 3 to -5
F(x)=4-x^2
F(x)=x-5
F(x)=-x+2
F(x)=x+8
Answer:
F(x)=4-x^2
Step-by-step explanation:
I am assuming that x=3 and y=-5
Put in x =3
F(3)=4-3^2 = 4-9 =-5 Yes
F(3)=3-5 = -2 No
F(3)=-3+2 = -1 No
F(3)=3+8=11 No
A small airplane takes off from point A and continues to climb upward in a straight line, as shown in the diagram. What is the plane’s distance from point A when it reaches point C?
A. 6,900 feet
B. 7,000 feet
C. 11,636 feet
D. 12,600 feet
E. 13,400 feet
Answer:
The distance from A to C is 12600 ft
Step-by-step explanation:
We can use similar triangles to help us solve the problem.
5600 ft AC
------------- = --------------
5200 ft 5200 + 6500
5600 ft AC
------------- = --------------
5200 ft 11700
We can solve using cross products
11700* 5600 = AC *5200
65520000=5200 AC
Divide each side 5200
65520000/5200 = AC
12600 =AC
Answer:
12600
Step-by-step explanation:
Which data set matches the box and whisker plot? A. 12.5, 15, 17, 23, 23, 24, 26, 29, 31, 32, 33 B. 11, 13, 16, 19, 23, 23, 24, 29, 31, 33, 34 C. 11, 12, 15, 18, 24, 24, 25, 27, 30, 32, 34 D. 10.5, 12, 15, 17, 23, 23, 24, 26, 29, 34
Answer:
c
Step-by-step explanation:
What does pathagery and theorem solve for? Please help!!!
Answer:
The Pythagorean theorem shows that one leg squared plus the other leg squared is equal to the hypotenuse squared
Step-by-step explanation:
According to the manufacturer, about 26% of sour candy in a package of Sandy's Sours are grape. What is the probability that the first grape candy chosen from the bag will be, at LEAST, the third candy chosen overall?
To find the probability that the first grape candy chosen from the bag will be, at least, the third candy chosen overall, you multiply the probability that a candy is not grape (0.74) by itself (since we're considering two independent events, both candies not being grape). The answer is 0.5476.
Explanation:The subject of this question is probability which is a branch of mathematics. You're looking to find the probability that the first grape candy drawn from a bag of Sandy's Sours will be, at least, the third candy chosen overall.
Given that 26% of the candies are grape, the probability that the first candy drawn is not grape is 1 - 0.26 = 0.74 (or 74%). Since we're looking for the first grape candy to be the third candy drawn or later, we need the first two candies to be not grape.
The probability that the first candy drawn is not grape is 0.74. Because each candy draw is an independent event (the result of one draw does not affect the results of any other draws), the probability that neither the first nor the second candy drawn is grape is 0.74 * 0.74 = 0.5476 (or 54.76%).
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Determine ‘a’ and ‘d’ for t7= 3 + 5x and t11= 3 + 23x (formula is tn= a + (n-1) x d)
(25 POINTS!!)
Final answer:
To determine 'a' and 'd' for tn = a + (n-1)x, substitute the values of 'n' and 't' into the equations and solve the system of equations.
Explanation:
To determine 'a' and 'd' for tn = a + (n-1)x, we need to find the values of 'a' and 'd' that satisfy both t7 = 3 + 5x and t11 = 3 + 23x.
Step 1: Set up two equations
t7 = 3 + 5x
t11 = 3 + 23x
Step 2: Use the formula tn = a + (n-1)x to substitute the values of 'n' and 't' in the equations.
a + 6d = 3 + 5x (equation 1)
a + 10d = 3 + 23x (equation 2)
Step 3: Solve the system of equations.
Subtract equation 1 from equation 2: (a + 10d) - (a + 6d) = (3 + 23x) - (3 + 5x)
Cancel out the 'a' terms and simplify the 'd' and 'x' terms: 4d = 18x
Divide both sides by 18: d = 4.5x
Substitute the value of 'd' in equation 1 to solve for 'a': a + 6(4.5x) = 3 + 5x
Expand and simplify the equation: a + 27x = 3 + 5x
Subtract 5x from both sides: a + 22x = 3
Subtract 22x from both sides: a = 3 - 22x
So, the values of 'a' and 'd' are a = 3 - 22x and d = 4.5x.
Here is the new question, plz solve this one for me
Answer:
1805.4
Step-by-step explanation:
Answer:
the answer is 1,710 it is adding 30 each time
Step-by-step explanation:
1 month=1,500
2 months=1,530
3 months=1,560
4 months=1,590
5 months=1,620
6 months=1,650
7 months=1,680
8 months=1,710
A developer has 7 1/2 acres of land to build houses on. If each house is to be built on 1/4 acre plot, how many houses can he build?
Answer:
He could build 30 houses.
Step-by-step explanation:
7 1/2 divided by 1/2 equals 30!
Answer: 30 houses can be built
Step-by-step explanation:
to make 5 dinner rolls 1/3. How much flour is need to make 1 diner roll
Find the circumference of each circle. Use 3.14 for the value of π . Round answer to the nearest tenth.
Answer:
[tex]C=9.4\pi[/tex] meters
Step-by-step explanation:
Recall to find the circumference of a circle the formula is [tex]C=\pi d[/tex] or [tex]C=2\pi r[/tex].
We start by substituting 4.7m for r in the second circumference formula.
[tex]C=2\pi r\\C=2\pi (4.7)\\C=9.4\pi [/tex]. We input this value of r into the area formula.
Answer:
its C.
Step-by-step explanation:
Y=-4x y=x^2-12 solve the system of equations
Answer:
(-6, 24) and (2, -8)
(-6, 24) and (2, -8) is the answer.
What's the easiest way to remedy a system of equations?
There are three strategies used to resolve structures of equations: graphing, substitution, and elimination. To solve a gadget via graphing, you honestly graph the given equations and locate the factor(s) in which they all intersect. The coordinate of this point will provide you with the values of the variables that you are fixing.
How do you remedy a gadget of equations without graphing?To remedy a machine of linear equations without graphing, you may use the substitution technique. This method works by way of solving one of the linear equations for one of the variables, then substituting this price for the same variable in the different linear equation and solving for the other variable.
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