Answer:
B
Step-by-step explanation:
A cyclist travels north along a road at a constant speed of 18 miles per hour. At 1:00 P.M., a runner is 46 miles away, running south along the same road at a constant speed. They pass each other at 3:00 P.M.. What is the speed of the runner?
By forming and solving equations, we know that the speed of the runner is 4 miles per hour.
What are equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions. An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, we need to form an equation to get the speed of the runner:
2 × (18 + x) = 44'x' is the speed of the runner. Now, solve for x as follows:
2 × (18 + x) = 4418 + x = 44/218+x = 22x = 22 - 18x = 4 miles per bourTherefore, by forming and solving equations, we know that the speed of the runner is 4 miles per hour.
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I need helping answering 15. I need to create a table and graph the function.
ANSWER and EXPLANATION
We want to order the functions from widest to narrowest:
[tex]\begin{gathered} y=3x^2 \\ y=2x^2 \\ y=4x^2 \end{gathered}[/tex]To do this, we have to plot the graphs of the functions by using a table of values.
Let us find the values of the functions for values of x = -2, 0, 2
For the first function:
[tex]\begin{gathered} y=3x^2 \\ \Rightarrow x=-2: \\ y=3(-2)^2=3*4 \\ y=12 \\ \Rightarrow x=0: \\ y=3(0)^2=3*0 \\ y=0 \\ \Rightarrow x=2: \\ y=3(2)^2=3*4 \\ y=12 \end{gathered}[/tex]Hence, its table is:
For the second function:
[tex]\begin{gathered} y=2x^2 \\ \Rightarrow x=-2: \\ y=2(-2)^2=2*4 \\ y=8 \\ \Rightarrow x=0: \\ y=2(0)^2=2*0 \\ y=0 \\ \Rightarrow x=2: \\ y=2(2)^2=2*4 \\ y=8 \end{gathered}[/tex]Hence, its table is:
For the third function:
[tex]\begin{gathered} y=4x^2 \\ \Rightarrow x=-2: \\ y=4\left(-2\right)^2=4*4 \\ y=16 \\ \Rightarrow x=0: \\ y=4(0)^2=4*0 \\ y=0 \\ \Rightarrow x=2: \\ y=4(2)^2=4*4 \\ y=16 \end{gathered}[/tex]Hence, its table is:
Now, let us plot the graphs of the functions:
Therefore, from the graph, we see that the order of the functions from widest to narrowest is:
[tex]y=2x^2;y=3x^2;y=4x^2[/tex]PLEASE ANSWER QUICKLY I WILL GIVE BRAINLIEST!
Which of the following are measures of variation? Select two options.
median
standard deviation
mode
mean
range
Math stuff please help
How do I find the area of a trapezoid 6ft by 9ft
Given the following question:
Where the trapezoid is...
6ft by 9ft
Find the area:
[tex]A=(a+b)\times h\div2[/tex]Maggie and Amelia filled up 40 water balloons shaped like spheres. Each water balloon had a radius of 6.5 cm.
The total volume of the 40 sphere shaped water balloons is 46032.38 cubic cm.
Radius of 1 sphere = 6.5 cm
We know that the volume of the sphere is given by 4/3 π r³
We will take the radius as 6.5 cm and π as 22/7
Now we will find the volume : 4/3 ×22/7×6.5³ = 1150.81 cubic cm.
Volume of 40 such spheres = 40 × 1150.81 = 46032.38 cubic cm.
The radius of all the spheres are 46032.38 cubic cm.
A sphere is a geometrical entity with three dimensions that resembles a two-dimensional circle. A sphere is a group of points in three dimensions that are all situated at the same r-distance from one another.
The supplied point is the sphere's center, while the letter r stands for the sphere's radius which is half the diameter. The earliest known allusions to spheres are found in the works of two ancient Greek mathematicians.
Therefore total volume of the 40 sphere shaped water balloons is 46032.38 cubic cm .
Disclaimer: The complete question is : Maggie and Amelia filled up 40 water balloons shaped like spheres. Each water balloon had a radius of 6.5 cm.Find the total volume of water required.
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what is 178 x 82 ???????????????????????
Answer: It is 14,596.
If given f(x) = –4x – 2 and g(x) = 2x ^2 + 4x-5, what is (f · g)(x)?
The addition of the given two functions f(x) = –4x – 2 and g(x) = 2x ^2 + 4x-5 will be (f · g)(x) = 2x²-9
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
Given f(x)= -4x-2
g(x)=2x²+4x-5
For (f-g)(x) = -4x-2+2x²+4x-5
=2x²-9
(f-g)(x) = 2x²-9
Hence, The addition of the given two functions will be (f · g)(x) = 2x²-9
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PLEASE HELP IF YOURE GOOD AT GEOMETRY. TYSM. DUE TODAY
The image of the dilation is P'(-5, -5), Q'(0, -5), R'(10, 5) and S'(5, 5) and the graph is attached
How to graph the image of the rotation?The coordinates of the polygon are given as
P(-1, -1), Q(0, -1), R(2, 1) and S(1, 1)
The transformation is given as
A dilation with a scale factor of 5 about the origin
The dilation has the algebraic rule of
(x, y) ⇒ (5x, 5y)
So, we have
P'(-5, -5), Q'(0, -5), R'(10, 5) and S'(5, 5)
Hence, the coordinates of the image using the dilation rule is P'(-5, -5), Q'(0, -5), R'(10, 5) and S'(5, 5)
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Kim and steve went to dinner. kim has a coupon for a 25% discount of all meals not including tax and tip. if the original price of the meal was $75, how much money will they save?
The amount Kim and Steve will save is $18.75.
Define discountDiscount refers to a price decrease on items or services that merchants are willing to sell to customers at a marked-up price. Usually, this portion of the rebate is provided to boost sales or get rid of unsold inventory. The list price, also known as the marked price, is the cost of a product as stated by the manufacturer or the seller, and it does not include any discounts. After any reductions or discounts to the list price, the selling price is the actual price at which an item is sold. Discounts are frequently referred to as "off" or "reductions," among other names. It should be noted that the discounted price is always based on the marked price (also known as the list price or original price) of the product.
Given, the discount they have is of 25%.
Original price of the meal is $75.
Now find the discount on the original price.
Discount = Discount (%) * Original Price
= [tex]\frac{25}{100} *75[/tex]
= 0.25*75
= $18.75
Therefore, they saved an amount of $18.75.
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I have a i just need b and e
By using the formula of perimeter of square and triangle, the following results are obtained.
Length of the side of square = 9
length of the side of triangle = 12
Area of square = 81
What is perimeter of square and triangle?
Perimeter of square and triangle is the total space taken by the square and triangle.
If the side of the square is a, then perimeter of square is 4a
If the side of the equilateral triangle is a, then perimeter of square is 3a
Length of the side of square = 4x - 3
Length of the side of triangle = 5x - 3
Perimeter of square = 4(4x - 3) = 16x - 12
Perimeter of triangle = 3(5x - 3) = 15x - 9
By the problem,
[tex]16x - 12 = 15x - 9\\16x - 15x = 12 - 9\\x = 3[/tex]
Length of the side of square = [tex]4 \times 3 - 3 = 9[/tex]
Length of the side of triangle = [tex]5 \times 3 - 3=12[/tex]
Area of square = [tex]9 \times 9 = 81[/tex]
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The sketch below shows part of the graph of y = ab",
where a and b are constants.
YA
(0,8)
Work out the values of a, b and k.
(1.5, k)
(1, 18)
Answer:
y = 8*(9/4)^x
Point (1.5, 27)
Step-by-step explanation:
We can solve each unknown in separate steps. The first step is to take advantage of given point (0,8) to find the value of a. Since x is zero, b^x will just be 1, regardless of b. That makes it easy to solve for a, which is found to be 8.
Once a is known, we can use the next point (1,18) to solve for b. b is (9/4).
Once we have a and b, we have the full equation: y = 8*(9/4)^x
k is found by entering the x value and solving for y (which is k). k = 27
See attached worksheet
Identify the roots of:y = x² - 12x + 32
Okay, here we have this:
Considering the provided function, we are going to calculate the requested roots, so we obtain the following:
[tex]\begin{gathered} x^2-12x+32=0 \\ x_{1,2}=\frac{-(-12)\pm\sqrt{(-12^2)-4(1)(32)}}{2(1)} \\ x_{1,2}=\frac{12\pm\sqrt{144-128}}{2} \\ x_{1,2}=\frac{12\pm\sqrt{16}}{2} \\ x_{1,2}=\frac{12\pm4}{2} \\ x_{1,2}=6\pm2 \\ x_1=6+2,x_2=6-2 \\ x_1=8,x_2=4 \end{gathered}[/tex]Finally we obtain that the roots of the function are x=8 and x=4.
Question 2(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Approximate -16+√40 to the nearest tenth.
The value of an irrational number [tex]-16 + \sqrt{40}[/tex] Is approximate, the nearest tenth is -9.675.
What are irrational numbers?Irrational numbers include all real numbers that cannot be stated as the ratio of two integers, or p/q, where p and q are both integers.
Given expression:
[tex]-16 + \sqrt{40}[/tex]
Factorize the square part as
[tex]-16 + \sqrt{10\times2^2 }[/tex]
Simplify the above expression as
[tex]-16 + 2\times \sqrt{10}[/tex]
We know that [tex]\sqrt{10} = 3.132[/tex]
Hence, -16 + 2 × 3.132
= -9.675
Therefore, the value of an irrational number [tex]-16 + \sqrt{40}[/tex] is approximately the nearest tenth is -9.675.
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Given the linear function describe end behavior of the graph as x decreases. (Hint: manipulate the equation to either standard form or slope intercept form
For the negative slope equation y = -x as the value of x increases y decreases.
What is a slope?
Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
Given that the graph of a linear function has a negative slope. Suppose the equation with a negative slope is y = -x.
It would look like y = -m(x) + b.
As an illustration, m is 1 and b is 0. (You can try any random number; however, I looked for the most straightforward one so that we could easily observe it.) It will be written as y = -x. (You can also omit this and use random numbers)
If x = 3, y = -3 ; x = 5, y = -5 (x increases, y decreases)
If x = -1, y = 1 ; x = -5, y = 5 (x decreases, y increases)
Hence the answer is for the negative slope equation y = -x as the value of x increases y decreases.
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what is the point-slope form of an equation for the line that passes through (0, -5 )with a slope of 2 a.y=2x-5b. y+5=2xc.y-5=x-2d.y=2(x+5)
The point slope form is:
[tex]y-y_0=m(x-x_0)[/tex]where m is the slope and (x0,y0) is a point of the line.
In this case, we know the point (0,-5) and the slope is m=2.
Then, we can write the equation in slope point form as:
[tex]\begin{gathered} y-(-5)=2(x-0) \\ y+5=2x \end{gathered}[/tex]Answer: y+5=2x (option b)
I need help with my exam practice homework . Question 3 please
we have that
The double angles formula is equal to
[tex]\cos (2\theta)=\cos ^2(\theta)-\sin ^2(\theta)[/tex]and remember that
[tex]\begin{gathered} \sin ^2(\theta)+\cos ^2(\theta)=1 \\ \cos ^2(\theta)=1-\sin ^2(\theta) \end{gathered}[/tex]therefore
substitute in the original expression
[tex]\begin{gathered} \cos (2\theta)=1-\sin ^2(\theta)-\sin ^2(\theta) \\ \cos (2\theta)=1-2\sin ^2(\theta) \end{gathered}[/tex]therefore
The third option is incorrecthelp in mathematics pls i am troubled
Answer:
It's very blurry, try sending one section at a time.
Step-by-step explanation:
a) Complete the table of values for y = x² - 4x
-1 0
1 2
3
4 5
0
-3
X
y
5
b) Which of the three curves drawn
matches the graph of y = x² - 4x ?
A B YA C
-5-4-3-2
To complete the table of values for y = x² - 4x
The equivalent values to complete the table of values are 5, -1, -4 and 0
Given the function according to the table shown:
[tex]y = x^{2} -4x[/tex]
Now let us insert the values in the above given equation one by one
When we have x = -1
[tex]y = (-1)^{2} -4(-1)[/tex]
y = 1+4
y = 5
When we have x = 1
[tex]y = (1)^{2}-4(1)[/tex]
y = 1-4
y = -3
When we have x = 2
[tex]y = (2)^{2}-4(2)[/tex]
y = 4-8
y = -4
when we have x = 4
[tex]y = (4)^{2} -4(4)\\[/tex]
y = 16-16
y = 0
Hence the equivalent values to complete the table of values are 5, -1, -4 and 0
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Given the line below.
Graph image attached
a. Using variables, write out the formula for the point-slope form of the equation.
b. Determine the slope of the line.
c. Identify the point (-1,-2) as (x1, y1).
d. Write the equation of the line in point-slope form.
Show all work on how you found the slope or determined the slope from the graph. Use the box provided to submit all of your calculations and final answers. Simplify the answer as needed.
(a) A point-slope form of the line is y - y₁ = m(x - x₁)
(b) The slope of the line is 2.
(c) The point (x₁, y₁) = (-1, -2).
(d) The equation of a line in point-slope form is y + 2 = 2(x + 1).
What is point-slope form?The formula for a straight line: y - y₁ = m(x - x₁), where m is the slope of the line and (x₁, y₁) is the coordinates of a specific point on the line
(a) Let the two points are (x₁, y₁) and (x₂, y₂)
Then the slope of the lines is given as
m = (y₂ - y₁)/ (x₂ - x₁)
The point-slope form of the line is given as
(y - y₁) = [(y₂ - y₁)/ (x₂ - x₁)] (x-x₁)
y - y₁ = m(x - x₁)
(b) From the graph, (x₁, y₁) = (-1, -2) and (x₂, y₂) = (1, 2)
So, slope = (2 -(-2))/ (1-(-1))
= (2+2)/ (1+1)
= 4/2
= 2
c) (x₁, y₁) = (-1, -2)
d) The equation of a line in point-slope form is given as
y - (-2) = 2(x- (-1))
y + 2 = 2(x + 1)
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x/7=2
2x/3=8
7x-10=11
9x+2=20
pls give a step-by-step answer
ITS URGENT
Answer:
x=14
Step-by-step explanation:
x/7=2
7 x x/7 = 7x2
At work one day, Erica Franz received 11 packages. Speedy Delivery delivered four times as many as Ralph's Express, while Ralph's Express delivered one more than SendQuick Package Service. How many packages did each service deliver to Erica?
She received 1 package from SendQuick Package Service, 2 packages from Ralph's Express and 8 packages from Speedy Delivery
What is a word problem?A word problem is a mathematical exercise which is in the form of a hypothetical question that needs mathematical analysis and equations to be solved.
Let SQPS represent SendQuick Package Service
SD represent Speedy Delivery
RE represent Ralph's Express, then:
Let the number of packages from SQPS be x
The number of packages from RE will be x+1
The number of packages from SD will be 4(x+1)
Given that the total number of packages received is 11, then:
x + x+1 + 4(x+1) = 11
x + x+1 + 4x + 4 = 11
6x + 5 = 11
6x = 11-5
6x = 6
x = 1
x = 1 package from SQPS
x + 1 = 2 packages from RE
4(x+1) = 8 packages from SD
Therefore, Erica Franz received 1 package from SendQuick Package Service, 2 packages from Ralph's Express and 8 packages from Speedy Delivery
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is this relation a function? Justify your answer
Answer:A
Step-by-step explanation:
A city has 14,200 people. In a random sample
Answer:
43/80 * 14,200
Step-by-step explanation:
Since 80 random people were sampled its will become our denominator and out of 80 people there were 43 people and that 43 will become our numerator the next step is to mulitply 14,200 (im really bad at explaining stuff hope it helps!)
Answer:
43/80 * 14,200
Step-by-step explanation:
It was right when I answered it.
What is the solution to this equation?
−15(x+134)=−212
Responses
x=2114
x equals 21 and 1 over 4
x=1414
x equals 14 and 1 over 4
x=1034
x equals 10 and 3 over 4
x=334
Answer: 10 3\4
Step-by-step explanation:
I did the quiz
The library is installing new
Shelves. If the carpenter has
4/5 yard of wood to make
into 2 shelves of equal length,
how long will each shelf be?
Menth
The library is getting new shelves built. 40% will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.
Given that,
The library is getting new shelves built.
We have to find how long will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.
We know that,
We have to divide
4÷2÷5
2÷5
0.4
In percentage we write as 40%.
Therefore, The library is getting new shelves built. 40% will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.
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Ellen mix is 1/3 cup of orange juice with 5/6 cups of lemonade to make fruit punch. Then she adds 1 2/3 cups of soda. Use the properties of addition to find how many cups of fruit punch she makes show your work
ANSWER:
2 5/6 cups
STEP-BY-STEP EXPLANATION:
To find the total cups, we must add the number of cups in each case, like this:
[tex]\frac{1}{3}+\frac{5}{6}+1\frac{2}{3}[/tex]For ease, we'll convert each fraction so that they all have the same denominator:
[tex]\begin{gathered} \frac{1}{3}=\frac{2}{6} \\ \frac{5}{6} \\ 1\frac{2}{3}=\frac{5}{3}=\frac{10}{6} \\ \text{therefore:} \\ \frac{2}{6}+\frac{5}{6}+\frac{10}{6}=\frac{2+5+10}{6}=\frac{17}{6} \\ \frac{17}{6}=2\frac{5}{6} \end{gathered}[/tex]That is to say that in total there are 2 5/6 cups of fruit punch
Japanese adults eat about 79 pounds of fruit each year. How many years will it take for a Japanese adult to eat 1,100 pounds of fruit?
I need help on a problem
in this problem we have that
Triangle JTN is an isosceels triangle, because the triangle has two equal sides and two equal interior angles
segment TE is the altitude of triangle JTN, its a perpendicular bisector segment JN
that means
JE=NE
we have
JT=NT
mso
triangle TJE and triangle TNE are congruent by SAS
triangles TJE and trTNE are acute triangles
CAN SOMEONE PLS HELP W THE ANSWERS I DONT EVEN NEED A STEP BY STEP BUT PLS HELPPPP
The measure of each angle is A = 113°, B = 25° and C = 42°, the length is each side is a = 8 mm, b = 5 mm, c = 5.4 mm.
Triangles:
Triangles are geometric figures of three sides with three internal angles. We can apply different laws and rules to solve different types of triangles. For example, the law of cosines allows us to solve oblique triangles. We can find sides and angles by applying this law. We can use the law of cosines if we have the length of two sides of a triangle and the angle formed by them.
Given that
a = 8
b = 5
c = 42°
To solve the triangle, we are first going to make a diagram with the given information:
We start by applying the law of cosines to find the length of
[tex]c^{2} = a^{2}+ b^{2}-2abcosc[/tex]
Substituting a =8, b = 5 and c = 42°, we have
[tex]c^{2} = 8^{2}+5^{2} -2(8)(5)cos42^{0}[/tex]
[tex]c^{2} = 64+25 - 59.45[/tex]
[tex]\sqrt{c^2} =\sqrt{64-34.45}[/tex]
c = 5.435 = 5.4
Now, we apply the law of cosines to find the measure of angle B
[tex]b^2 = a^2+c^2-2accosB[/tex]
Substituting the lengths a = 8, b = 5, c = 5.4
[tex]5^2 = 8^2+5.4^2- 2(8)(5.4)cosB\\[/tex]
Note: we can substitute the lengths of the sides without the unit. Simplifying, we have:
25 = 64+29.16 - 86.4 cos B
25 = 96.16 - 86.4 cos B
cosB = 0.603
Now, we must apply inverse cosine on both sides of the equation:
[tex]cos^-1(cos B) = cos^-1(0.603)\\\\[/tex]
B = 25.256°
B = 25°
Lastly, we apply summation of internal angles of a triangle to find the angle A:
A + B + C = 180°
we need to isolate angle A:
A + 25°+ 42° = 180°
A + 67° = 180°
A = 113°
Hence the answer is, the measure of each angle is A = 113°, B = 25° and C = 42°, the length is each side is a = 8 mm, b = 5 mm, c = 5.4 mm.
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