Answer:
The runners will be in a straight line after 1/2 seconds.
To solve this problem, we can set the y-coordinates of each runner equal to each other and solve for t. The y-coordinate represents the lane number, and if the lane numbers are equal, the runners are on a straight line.
Jon: y = 1
Laura: y = 2
Ellis: y = 4
Jon: 3t = 1
Laura: 4t = 2
Ellis: 6t = 4
Solving these equations simultaneously, we find that t = 1/2 seconds. This means that after 1/2 seconds, the runners will be in a straight line.
Consider the system of equations
5x+3y=30
−5x−2y=−25
Part A: Solve the system. Show your work.
Part B: Use the solution to your equation to find the value of x – y. Show your work.
x−y =
What is the perimeter of triangle mno
Answer:
[tex]\huge{\boxed{82.8\text{ units}}}[/tex]
Step-by-step explanation:
Because the triangles have all of the same angles, similarity can be proven via AAA.
Now that ΔJKL ~ ΔMNO, the sides must be proportional.
Because the sides are proportional, the following equation can be made:
[tex]\frac{24}{20}=\frac{x}{22}[/tex]
Via cross-multiplication, the equation simplifies to:
20x = 24 * 22
20x = 528
x = 26.4
Now, because perimeter is simple the sum of all sides, the perimeter of ΔMNO is simply 32.4 + 24 + 26.4, or 82.8.
Hope it helps :) and let me know if you want me to elaborate.
(25 points)
Which inequality is represented by this number line?
Answer:
C
Step-by-step explanation:
Pick point 7 and sub into the equations
eq 1 not equal to 10
eq 2 not equal to 12
eq 3 is equal to 15
eq 4 not equal to 18
Now sub in the value of -3 into equation 3 Yes equal to 15
so answer is eq 3
numbers greater than 7 and less than -3 are also true ....
Which function has the least slope?
OA.
B.
y =
x +15
y = x - 12
C. y = 5x + 23
D. y =
=
7x6
The perimeter of a rectangle i 104m the length i 7m more than twice the width. What are the dimenion of the rectangle
Size will be 37 L x 15 W.
What is perimeter?Perimeter is the distance around the edge of a shape. Discover how to calculate a shape's perimeter by adding its side lengths.
Finding the dimension is required, if the perimeter is 104 meters and the length is 7 meters longer than twice the breadth.
Let L be the length and W be the width
L = 7 + 2*W
P = 2(L + W) ; 104 = 2(7 + 2W + W) ; 104 = 2(7 + 3W) ;
104 = 14 + 6W
6*W = 90 ;
W = 15 L = 37
Hence the dimension is 37*15
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2. Multiply the polynomials (4a³-5a - 3) and (2a² - 7a+ 3). Simplify the answer. Show your work.
Can the answer be given by hand please
Answer:
Step-by-step explanation:
If f(x) = 2x² + 3x - 19, find f(-4)
Answer:
f(-4)=1
Step-by-step explanation:
f(x) = 2x² + 3x - 19
f(-4)=2(-4)² + 3(-4)-19
f(-4)=2(-16)+3(-4)-19
f(-4)=-32+3(-4)-19
f(-4)=32-12-19
f(-4)=20-19
f(-4)=1
Will mark as brainiest. Please help more points!
The total area of the two shaded faces of the cuboid below is = 112[tex]cm^{2}[/tex]
Since the two shaded faces of the cuboid shown are adjutant to each other and are of the same dimensions so according to the calculations -
Let us consider only one side of the shaded portion-
The length of the shaded part = 8cm
The width of the shaded portion = 7cm
So it appears that due to the uneven measure of length and breath this is a rectangle, so the area of a rectangle
= [ length (l) x width(w) ]
= 8cm x 7cm
= 56[tex]cm^{2}[/tex]
Since the question asks the total area of both sides so because both the shaded sides are equal then total area = 56 x 2 = 112 [tex]cm^{2}[/tex]
Therefore, the total area of the shaded faces of the cuboid = 112[tex]cm^{2}[/tex]
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fraction find the missing number 1/2 of 30= 1/4=
The missing number in the equation 1/2 of 30 = 1/4 is 60
How to determine the missing number?From the question, we have the following parameters that can be used in our computation:
1/2 of 30 = 1/4
This equation can be properly expressed as
1/2 of 30 = 1/4 of __
Represent the blank with a variable x
So, we have the following representation
1/2 of 30 = 1/4 of x
Express as products
1/2 * 30 = 1/4 * x
Multiply both sides by 4
This gives
x = 4 * 1/2 * 30
Evaluate
x = 60
Hence, the missing number is 60
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ABC has vertices at a(11,6), B(5,6), and (5,17).
The correct statements regarding the congruent triangles are given as follows:
Triangle ABC and triangle MNO are congruent by a sequence of rotations and translations.Triangle JKL and triangle ABC are congruent by a single rotation.What are congruent triangles?Congruent triangles are triangles in which the outer side lengths have the same measure.
Then the triangles ABC and triangle MNO are congruent by a sequence of rotations and translations, as both are right triangles.
Triangle JKL and triangle ABC are congruent by a single rotation, as the distances between the vertices of each triangle are equal.
Missing InformationThe problem is given by the image shown at the end of the answer.
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A rectangular fish tank has width w inches, length w + 8 inches, and height 18 - w inches. All dimensions are greater than 6 inches. The volume of the tank is 1440 cubic inches. Find the length, width, and height of the fish a. width: 12 in., length: 20 in., height: 6 in. b. width: 10 in., length: 18 in., height: 8 in. C width: 10 in., length: 8 in., height: 18 in. d. width: 12 in., length: 18 in., height: 8 in.
Answer:
To find the dimensions of the fish tank, we can set up the equation:
(width) * (length) * (height) = 1440 cubic inches
Substituting the given expressions for the dimensions of the tank, we get:
(w) * (w + 8) * (18 - w) = 1440
This is a quadratic equation in w, and we can solve it using the quadratic formula:
w = (-(w + 8) +/- sqrt((w + 8)^2 - 4*(18 - w)11440)) / (2*1)
This simplifies to:
w = (-(w + 8) +/- sqrt(w^2 + 16w + 64 - 72w + 5760)) / 2
= (-(w + 8) +/- sqrt(w^2 - 56w + 5760)) / 2
We can further simplify this equation by factoring:
w = (-(w + 8) +/- sqrt((w - 40)(w - 144))) / 2
We can then solve for w by setting each factor equal to zero:
w - 40 = 0 => w = 40
w - 144 = 0 => w = 144
Since the width of the fish tank must be greater than 6 inches, the only valid solution for w is 40 inches. Substituting this value back into the equation for the volume of the tank, we find that the length of the tank is 48 inches (w + 8 = 40 + 8 = 48) and the height of the tank is 12 inches (18 - w = 18 - 40 = 12).
Therefore, the dimensions of the fish tank are:
width: 40 inches
length: 48 inches
height: 12 inches
The correct answer is therefore (a) width: 12 in., length: 20 in., height: 6 in.
Step-by-step explanation:
How much compound interest will $50,000 have earned in 10 years at
6.4% annual interest compounded quarterly?
Answer:
Step-by-step explanation:
To find the compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly, we can use the formula:
compound interest = principal * (1 + rate/n)^(n*t) - principal
where "principal" is the initial amount of money, "rate" is the annual interest rate, "n" is the number of times the interest is compounded per year, and "t" is the number of years.
Plugging in the given values, we get:
compound interest = $50,000 * (1 + 0.064/4)^(4*10) - $50,000
= $50,000 * (1.016)^40 - $50,000
= $50,000 * 2.6335 - $50,000
= $78,167.50 - $50,000
= $28,167.50
Therefore, the compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly is $28,167.50.
a study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. it was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 2.75 days with an approximately normal distribution. (a) find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places.
Therefore, the probability that their hospital stay is from 5 to 6 days is 0.03310 .
What exactly is probability?Probability deals with calculating or making estimates of how probable or "possible" an event is to occur. To convey the probability of an event occurring, words like "certainly," "impossible," or "likely" might be employed. Probabilities are always represented in mathematics as fractional, decimals, or percentages, with values that range from 0 to 1.
Here,
Given:
Mean, μ =7.37 days
Standard Deviation, σ = 2.75 days
Given: hospital stays are distributed in a bell-shaped manner, which is a typical distribution.
Formula:
Z = [tex]\frac{x-u}{\alpha }[/tex]
a) P( 5 to 6 days are spent in the hospital.)
P(5≤x≤6)
=>P([tex]\frac{5-7.37}{2.75}[/tex] ≤x≤ [tex]\frac{6-7.37}{2.75}[/tex])
=>P(-0.861≤x≤-0.498)
=>P(Z≤-0.498) - P(Z<-0.861)
=>0.034 - 0.001 = 0.03310
=> P(5≤x≤6) =3.3%
Therefore the probability that their hospital stay is from 5 to 6 days is 3.3%.
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A small technology company started offering shares of stock to investors in 1987. At that time, the price of one share of stock was $0.39. Since then, the company has experienced rapid growth. Twenty-two years later, the price of a single share of stock has risen to over $110. One scatterplot shown summarizes the number of years since the initial stock offering in 1987 and the price of the stock, while the other compares years since 1987 to the log of stock price.
Based on these scatterplots, what type of model is most appropriate for summarizing the relationship between year and stock price?
A linear model is appropriate because the scatterplot of the transformed data is roughly linear.
An exponential model is appropriate because the scatterplot of time and log price is increasing.
An exponential model could be appropriate because the scatterplot of log height versus log weight is roughly linear. The next step is to look at the residual plot.
A power model is appropriate because the scatterplot of time and price shows a curved relationship.
PLS HURRY
These scatterplots show that model type A is best suited to summarize the relationship between year and stock price. The scatterplot of the processed data is nearly linear, so a linear model is suitable.
What is linear model ?These scatterplots show that model type A is best suited to summarize the relationship between year and stock price. The scatterplot of the processed data is nearly linear, so a linear model is suitable.
A linear model is applicable if we can create a linear equation based on the connection between the independent and dependent variables (because there is no constant rate of change).
Otherwise, we can simulate the relationship using an exponential model.
An exponential model is:When the rate of increase representing the relationship between the year and stock price is proportional or constant, we utilize the exponential model.
By determining whether the ratio of the dependent values is the same, one can choose to describe the connection as an exponential equation.
As a result, even though the time and price scatterplot is curved, a linear model is adequate.
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the number of cells in a specimen of bacteria doubles every hour. what type of function best represents the growth of the bacteria?
An example of an exponential function is the growth of bacteria. the growth of the bacteria is by exponential growth in the number of cells in a specimen of bacteria doubles every hour.
Some bacteria double her size every hour. Starting with 1 bacterium, every hour he doubles, after x hours he doubles as bacterium. This can be written as f(x) = 2x.
Bacteria replicate by binary fission, the process by which one bacterium divides into two. Bacteria therefore multiply in number by a geometric progression, doubling the population with each generation. The binary fission is the actual multiplication procedure of the cells division where cells grows fastly and further divided itself into other groups or colony.
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surveys, if not done correctly, can lead to seriously biased samples. which is not a bias due to the sampling plan?
Volunteer/voluntary response bias, also known as self-selection bias, occurs when research participants exert control over the decision to engage in the study.
What is Probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application.
Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
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Which expression is equivalent to x +11?
A. 11x
B. 11+x
C. 11-x
D. -x+11
Answer:
11x
Step-by-step explanation:
Which product is represented by the model?
A. 0.05×0.04=0.002
B. 5×0.4=2
C. 0.5×0.4=0.2
D. 0.5×0.04=0.02
The value of inserting area of an array is 0.02
What is meant by area ?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
The region that an object's shape defines as its area. The amount of space occupied by a figure or any other two-dimensional geometric shape in a plane is known as its area.
Given:
5 column (hundred grid) = 5/100 = 0.05
4 row (hundred grid) = 4/100 = 0.04
Find:
Area equation
Computation:
Area equation = 0.05 x 0.04
0.05 x 0.04 = 0.002
Therefore the value of inserting area of an array is 0.02
The complete question is : Which product is represented by the model? A hundred grid model shows 5 columns shaded and 4 rows shaded. The intersecting area is an array that is 5 by 4. A. 0 . 05 × 0 . 04 = 0 . 002 B. 5 × 0 . 4 = 2 C. 0 . 5 × 0 . 4 = 0 . 2 D. 0 . 5 × 0 . 04 = 0 . 02
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What will happen to the graph of the line y = -54x + 3 if you change -54 to 54?
Imagine Math
Ayuda, me gustaría su ayuda con mi tarea
Answer:
1.) x = 1, 2/3
2.) x = -3±[tex]\sqrt{6}[/tex]
3.) x = [tex]\frac{4+/-\sqrt{37} }{3}[/tex] or x = −3.36092084, 0.69425417
Step-by-step explanation:
These are quadratic equations so we use the quadratic formula method.
Use the quadratic formula by taking:
[tex]ax^{2}+bx^{2} +c=0[/tex]
1.) a = 3, b = -5, c = 2
2.) a = 1, b = 6, c = 3
3.) a = -3, b = -8, c = 7
Then, substitute into the quadratic formula:
(Check the picture provided for the quadratic formula)
Find the miing number
A number increaed by 25%. It i decreaed by __? But after decreaing it, it i the ame tarting number
When a number is first increased by 25% then if it is decreased by 25% , we will get the same starting number. hence the net increased or decreased value is zero.
What is net decrease?A decline in net income is a change from one period to the next in the amount of money you have after deducting your expenses from your revenues.
How do you calculate the net?There are two possible outcomes for net income. Your business has a positive net income when revenues exceed expenses. You have a negative net income, commonly referred to as a net loss, if all of your expenses exceed all of your revenues.
let the number is x
first it is increased by 25%
so,
x+(25/100)x=(125/100)x
now according to second condition,
we have to find a value by which it is decreased so we get the same number.
so, let that decreased value is y;
(125/100)x-y=x
-y=x-(125/100)x
-y=-(25/100)x
cancelation of sign;
y=25%
so this is our required value.
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What value of w makes the equation 3(−4w−5)=−7(5+w) true?
4 is the value of w which makes the equation true.
What is an equation?
There are many different ways to define an equation. A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.There are three main types of equations depending on the degree. More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.A quadratic equation must have at least one variable with an exponent of 2.A third-order equation is a cubic equation. Cubic equations need the exponentiation of at least one variable.It is given that,
3(−4w−5)=−7(5+w)
by solving the equation,
-12w-15=-35-7w
12w-7w=35-15
5w=20
w=20/5
∴w=4
Hence, 4 is the value of w which makes the equation true.
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Hello, can someone help me out with these two questions please!?!?!?
Answer: No solution
Step-by-step explanation:
3(2x + 3) - 3x = 9 + 3x
6x + 3 - 3x = 9 + 3x - 3x
6x + 3 - 6x = 9
3 = 9
No solution
What is an equation of the line that passes through the point (4,1) and is perpendicular to the line 2x-y=4
Answer: [tex]y-1=-\frac{1}{2}(x-4)[/tex]
Step-by-step explanation:
The equation of the given line can be rearranged as [tex]y=2x-4[/tex].
Perpendicular lines have slopes that are negative reciprocals, so the slope of the line we need to find is -1/2.
Using point-slope form, the equation is [tex]y-1=-\frac{1}{2}(x-4)[/tex].
Need help with this, Plot the points that represent the profit you can expect to earn each month, for each business, on a single xy-plane. You can create your plot by hand or you can use Desmos to help you. HINT: Use a different, single color for each business to help you keep track of your points
A value of lawn care is negetive because the profits are decreasing after month-3. So it is sloping downards. Had the profits been raising the a-value would have been positive.
Based on the plot the profits of each month can be found out using a qudratic function?
The lawn care business shows diminishing returns after month 3 . So it is not a viable business to conitnue for the long term. Based on the projections around month 8 profit becomes -$14.44. This is loss.
The other two businesses are profitable. The show upward growing trend as the months progress. Following table shows projected earnings for 1 year based on the equations showed in the graph.
3. A quadratic funtion can be used to represent the profits. The equation is given in the plots
4. A value of lawn care is negetive because the profits are decreasing after month-3. So it is sloping downards. Had the profits been raising the a-value would have been positive.
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A builder need 2,964 nail to finih a project. If the nail come in package of 52, how many package hould the builder purchae?
Number of nails to finish the project by buying are required = 2964 units
1 package of nails contains per unit = 52 units
To find the no. of packages we have to simply divide the total no. of nails required by the total of no. of nails of unit given in the one package of nails.
So,
Number of package required to the builder
= Total number of nails required to buy by the builder / no. of nails provided per package
=2964/52
=57 packages
Therefore, No. of packages required by the builder to buy to complete the project
=57 packages needed.
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Answer: 57
Step-by-step explanation:
Just plug it into a calculator.
2964/52 = 57
He needs to buy 57 packages
Calcula el número si 30 menos el triple del número es cuatro veces la diferencia del triple del número más 10
Answer:Calcula el número si 30 menos el triple del número es cuatro veces la diferencia del triple del número más 10
Step-by-step explanation:
4/5 divided by 1/3 equals?
Answer:
4/15
Step-by-step explanation:
reciprocal of 1/3 then cross multiply
If DG=FG=7, m∠DEG=u+21°, and m∠FEG=2u, what is the value of u?
The value of u is 21.
What is Congruence?Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
Given:
DG=FG=7, m ∠DEG=u+21°, and m ∠FEG=2u,
As, from the Diagram
DE = FE (Given)
DG= FG ( Given)
GE= GE (Common)
So, ΔDEG ≅ ΔFEG by SSS Rule.
<DEG = <FEG (CPCT)
u + 21 = 2u
2u - u= 21
u=21
Hence, the value of u is 21.
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Given the system below,
9x+3y=-18
y=x+7
What is the ordered pair for the intersection
)?
Answer:
(-3.25,3.75)
Step-by-step explanation:
Thuis can be answered with either of two approaches: Graphing and Matematical. We'll do both:
Graphing
Graph both equations. It is helpful to use a free online graphing utility: DESMOS.
The attached graph reveals the intersection of the lines at point (-3.25, 3.75).
Matematical
Solve the equations be using substitution. Rearrange either equation to isolate one of the two variables (x or y).
Lets use the second, since y is already isolated, making the task simple and fast. But the other equation could also be used, if desired.
y=x+7
Now use this expression of y in the other equation:
9x+3y=-18
9x+3(x+7)=-18
9x +3x +21 = -18
12x = -39
x = -(39/12)
x = -3 - (3/12)
x = -3.25
Now use x= -3.25 in either equation tand solve for y:
y=x+7
y=(-3.25)+7
y = 3.75
The solution to this series of equations is (-3.25,3.75)