Time taken to cover path around the park if he runs at speed 5miles/hour is 15.96min
What is Speed ?
Speed indicates how quickly something or someone is moving. If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance x time.
Given that,
Time taken when Bob runs 4miles/hour = 20min
Time taken when Bob runs 5miles/hour = ?
First we have to find the distance of the path around the circle
Distance = speed x time
= 4 x 20/60
= 4/3 miles
= 1.33 miles
Now to calculate the time when he ran 5 miles/hours:
Time = distance / speed
= 1.33 / 5
= 0.266hours
0r
= 0.266 x 60 min
= 15.96 min
Hence, its will take 15.96min to cover the path around the park
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thank u plssssssss do it
Answer:
63
Step-by-step explanation:
23 + 94 = 117
180 degrees ( sum of all angles in a triangle)
180 - 117 = 63
Divide: (u² - 3u - 5) ÷ (u+3).
Answer:
u - 6 + 13/u+3
Step-by-step explanation:
Have a good day :)
if f(x)=-5, what is x?
Answer:
x is any real number from -infinity to infinity.
Donna bought a desk on sale for $343. This price was 35% of the original price.
The original price for the desk is $980.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.
Given:
Sale price = 343
price was 35% of the original price.
let the original price be x
35% of x = 343
35 / 100 * x = 343
x= 343 * 100/ 35
x=980
Hence, the original price of the desk was $980.
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please help me out i’ll give you brainlist !
Answer:
In order, the answers are d, b, c, a
Step-by-step explanation:
[tex] \frac{ {x}^{7} }{ {x}^{4} } = {x}^{3} [/tex]
[tex] {x}^{ - 3} = \frac{1}{ {x}^{3} } [/tex]
[tex] {x}^{0} = 1[/tex]
[tex] \frac{ {x}^{4} }{ {x}^{3} } = x[/tex]
i need help with question 17
Answer:
[tex]42[/tex]Step-by-step explanation:
To find the median of a stem and leaf plot, use the equation:
[tex]\begin{gathered} median=\frac{n+1}{2} \\ where, \\ n=\text{ number of data} \end{gathered}[/tex]Therefore, for the given plot, there are 16 elements.
[tex]\begin{gathered} \text{ median=}\frac{16+1}{2} \\ \text{ median=8.5} \end{gathered}[/tex]When there are two middle values, the median is the mean of these two values:
[tex]\begin{gathered} \frac{3+1}{2}=2 \\ \text{ Hence, the median is 42.} \end{gathered}[/tex]The ages of the signers of the Declaration of Independence are shown. (Age is approximate since only the birth year appeared in the source, and one has been omitted since his birth year is unknown.) Construct a grouped frequency distribution and a cumulative frequency distribution for the data, using 7 classes.
Answer:
Step-by-step explanation:
The ages of the signers of the Declaration of Independence are shown. (Age is approximate since only the birth year appeared in the source, and one has been omitted since his birth year is unknown.) Construct a grouped frequency distribution and a cumulative frequency distribution for the data using 7 classes. Limits Boundaries 27-33 26.5-33.5 7 41 54 47 40 39 35 50 37 49 42 70 32 44 52 39 50 40 30 34 69 39 45 33 42 44 63 60 27 42 34 50 42 52 38 36 45 35 43 48 46 31 27 55 63 46 33 60 62 35 46 45 34 53 50 50 34-40 33.5-40.5 14 41-47 40.5-47.5 15 48-54 11 47.5-54.5 54.5-61.5 55-61 3 62-68 61.5-68.5 3 69-75 68.5-75.5 55
Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function.
By graphing both equations and finding where the graphs intercept, we can see that the solution for the system is x = 3.
For which value of x both functions give the same output?Here we have the functions:
f(x) = -2x +4
g(x) = 2x - 8
We want to find the value of x such that:
f(x) = g(x).
If we graph the two functions, we just need to identify the x-value of the point where the functions intercept.
The graph can be seen in the image below.
There we can see that the graphs intercept at (3, -2), meaning that the solution of:
f(x) = g(x) is x = 3.
Which is the same thing that if we write:
f(x) = g(x)
-2x + 4 = 2x - 8
4x = 12
x = 12/4 = 3
x = 3
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4) A done relevant a bomb witha velocity of 20m/s horizotally from a hieght of 50m the ground clculate time
The time taken for the bomb to fall to the ground is 2.5 sec.
What is a projectile motion?In this case, the bomb is moving like a projectile and has projectile motion.A body can only move in a projectile motion when it is affected by gravity. A body moving as a projectile is a projectile motion.We model a particle as having zero acceleration (and thus constant velocity) when it is projected horizontally.The particle in this instance has a zero initial velocity and a constant downward vertical acceleration of g.Given:
Height (h) = 50 m
Horizontal velocity(u) = 20 m/s
Time (t) =?
We use, h = ut to determine the time
50 = 20 × t
Divide both sides by 20,
t = 50 / 20
t = 5/2 s ≅ 2.5 sec
Thus, the bomb will take 2.5 sec to land on the ground.
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The complete question is: "A bomb is projected horizontally downward from a height of 50m with a velocity of 20m/s. Calculate the time taken for the bomb to fall to the ground."
Find a with the given information.
m=-6/7 (-10,0) and (a,-6)
Based on the slope formula for a line, the value of a is: a = -3.
How to Calculate the Slope of a Line?If two points on a line have the following coordinates, (x1, y1) and (x2, y2), to find the slope (m) of the line, the formula that is applied is given as:
Slope (m) = change in y /change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = rise/run.
The given line has the following:
(-10, 0) = (x1, y1)
(a, -6) = (x2, y2)
Slope (m) of the line = -6/7.
Plug in the values into the slope formula for a line:
(-6 - 0) / (a - (-10)) = -6/7
-6/(a + 10) = -6/7
Cross multiply and solve to find the value of a in the equation:
-6(a + 10) = -6(7)
Apply the distributive property
-6a - 60 = -42
Add 60 to both sides
-6a - 60 + 60 = -42 + 60 [addition property of equality]
-6a = 18
Divide both sides by -6
-6a/-6 = 18/-6 [division property of equality]
a = -3
Therefore, the value of a is -3.
The line that has a slope of -6/7 will have the following points, (-10, 0) and (-3, -6).
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For
f(x) = 3x and g(x) = x4 + 2, find the following.
(b)(g ∘ f)(x)
A retailer owes a wholesaler $300,000 due in 45 days. If the payment is 15 days late, there is a 1% penalty charge. Since the bill isn't due immediately, the retailer can invest the $300,000 in a certificate of deposit and make money on the interest. The retailer has two options: a 45-day certificate of deposit (CD) earning 6% per year simple interest or a 60-day certificate earning 7% per year simple interest.
A 45-day certificate of deposit (CD) earning 6% per year simple interest. Simple interest and precise simple interest are the two types of simple interest. $2250 is simple interest for the 6% interest.
What is simple interest ?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Simple Interest is the amount repaid for using borrowed funds over a predetermined amount of time.
Simple interest=p*n*r
=300000*6/100*45/365
=2250
Ordinary simple interest and precise simple interest are the two types of simple interest. In order to calculate interest, a year is divided into 360 days for ordinary simple interest and 365 days (or 366 days for leap years) for exact simple interest.
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Jackie deposited $500 in an account for 10 years at 6% interest.How much money did she earn?
After 10 years, the money dis she earn is $800 with the interest of 6%.
Interest:
Interest is the amount for a particular principal amount of money at some rate of interest.
Given,
Jackie deposited $500 in an account for 10 years at 6% interest.
Here we need to find the money did she earned.
We know that, the interest for the amount is 6%.
So, the amount after 10 years is,
=> 500 x (6/100) x 10
=> 30 x 10
=> 300
Therefore, the interest amount is 300.
So, the total amount she will receive after 10 years is,
=> 500 + 300
=> 800
Therefore, she will earn $800 after 10 years.
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the graph of g(x) = (x + 2)2 is a translation of the graph of f(x) ___ by ___ units
The provided translated function, f(x), shifts left by two units on the horizontal axis.
Describe translation.One type of transformation is translation. Both the scaling calculation and the compression calculation are performed using it. This approach wouldn't change the object's form or shape.
The given graph equation for the translation, as per the query, is g(x) = (x + 2)²
The translation of the given quadratic function is: y = g(x) = (x + 2)²
Consequently, the parent function is written as y = g(x) = x2.
Additionally, the vertex should be known when graphing the translated function:
a(x - h)2 + k = y = g(x);
where the parent function is (0, 0) and the vertex values are (h, k).
(h, k) = is the vertex for the function that is provided (-2, 0)
This information causes the translation function to move the graph two units to the left.
Horizontal translation is the name given to the translation.
As a result, the given function, f(x), shifts horizontally, or left, by 2 units.
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Check all the angles that are congruent to angle 5.
The angles congruent to ∠5 are as follows:
∠8∠1∠4∠9∠12How to find angles in parallel lines?According to the diagram, line l, m and n are parallel lines.
Therefore, when parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertical opposite angle etc.
Hence, the angles that are congruent to ∠5 can be solved as follows:
∠5 ≅ ∠8 (vertically opposite angles)
Vertically opposite angles are congruent.
∠5 ≅ ∠1 (corresponding angles)
Corresponding angles are congruent.
∠5 ≅ ∠4 (alternate angles)
Alternate angles are congruent.
∠5 ≅ ∠9 (corresponding angles)
∠5 ≅ ∠12 (alternate exterior angles)
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Determine the distance between A(-3, 4) and B(2, -4).
5 units
Explanation
Step 1
the distance between 2 points P1 and P2 is given by:
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1_{})^2+(y_2-y_1)^2} \\ \text{where} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}[/tex]Let
P1=A(-3,4)
P2=B(2,-4)
Step 2
put the values into the equation
[tex]\begin{gathered} \text{distance}=\sqrt[]{(-4-4)^2+(2-(-3))^2} \\ \text{distance}=\sqrt[]{(0)^2+(2+3)^2} \\ \text{distance}=\sqrt[]{(0)^2+(5)^2} \\ \text{distance}=\sqrt[]{(25} \\ \text{distance}=5 \end{gathered}[/tex]Write an equation for the quadratic graphed below:
x-intercepts: (-3,0) and (-1,0); y-intercept: (0,-2)
The equation for the quadratic graphed as x-intercepts: (-3,0) and (-1,0); y-intercept: (0,-2) can be written as y = -1/2 (x+3)(x+1)
Which of these equations is quadratic?An equation of the second degree, or one with at least one squared term, is a quadratic equation. The equation in standard form is written as ax2 + bx + c = 0, where a, b, and c are numerical coefficients that are constants, and x is an unknown variable.
The initial constant, “a,” cannot be 0, and this is an unbreakable rule.
How do you translate a graph into some equation?In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change.
Thereafter draw a sloping triangle connecting the two spots you find on the line.
If the x intercepts are -3 and -1, then the factored form is y = a(x + 3)(x + 1). In order to find "a", we plug in the data point (x, y) of (0, -2) so:
-2 = a(0+3)(0+1)
-2 = 4a
a = -1/2
So the equation can be written as y = -1/2 (x+3)(x+1)
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Can someone please help with this
Answer:
x = 8
y = 8
Step-by-step explanation:
The two equations are:
x + y = 16 (1)
x = y (2)
Since x = y substitute for y in terms of x in (1):
x + x = 16
2x = 16
2x/2 = 16/2
x = 8
y = 8
f(x) = x + 3g(x) = 2x2 - 4Find (f ·g)(x)
SOLUTION
f(x) = x + 3
[tex]undefined[/tex]pls help i dont get it
Answer:
Step-by-step explanation:
Answer: You can add 5. The question is asking you what can you do to make both sides equal 8. I am not a professional but I hope that helped.
Phillip added 15 pencils to his collection. He then gave 30 pencils to a friend. Write and evaluate an expression
Answer:
x + 15 - 30
x -15
Step-by-step explanation:
For the triangle shown, find the length AD. (Assume u = 17, v = 17, ∠x = 25°, and ∠y = 25°
Using the law of Sines, the length of side AD, |AD|, is 7.44
Calculating lengthFrom the question, we are to determine the length of side AD
From the given information, we have that
u = 17 and v = 17
Then,
ΔBCD is an isosceles triangle
∴ m ∠DBC = m ∠ BCD
m ∠DBC = x = 25°
∴ m ∠BCD = 25°
Also,
m ∠BCA = ∠y + m ∠BCD
m ∠BCA = 25° + 25°
m ∠BCA = 50°
Now, we will determine the measure of ∠CAD.
m ∠CAD + m ∠DBC + m ∠BCA = 180° (Sum of angles in a triangle)
m ∠CAD + 25° + 50° = 180°
m ∠CAD = 180° - 25° - 50°
m ∠CAD = 105°
Now,
From law of Sines, we can write that
|AD| / sin DCA = |DC| / sin CAD
|AD| / sin y = u / sin CAD
|AD| / sin 25° = 17 / sin 105°
|AD| = (17 × sin 25°) / sin 105°
|AD| = 7.43795
|AD| ≈ 7.44
Thus,
Length AD is 7.44
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Match the following.
Matching the given mathematical operation equations to the specified choices, gives;
A•B = B•A ; Commutative Property of Multiplication
A + B = B + A ; Commutative Property of Addition
(A•B)•C = A•(B•C); Associative Property of Multiplication
A•0 = 0; Multiplicative Property of 0
(A + B) + C = A + (B + C); Associative Property of Addition
A•1 = A; Multiplicative Identity
A + 0 = A; Additive Identity
What are the properties of mathematical operations?The properties of mathematical operations includes; inverse, associative, distributive, associative and commutative properties
Commutative propertyCommutative property in mathematics is one in which for a binary operation, the result of an operation remains unchanged when the order in which the operands appears in the expression is changed.
Therefore;
Commutative property of multiplication is therefore; A•B = B•A
Commutative property of addition is; A+B = B+A
Associative propertyAssociative property relates with operations that have results which remains the same when the parentheses in the expressions are rearranged.
Therefore;
(A•B)•C = A•(B•C) represents the associative property of multiplication
The associative property of addition is represented by (A+B)+C = A+(B+C)
Multiplicative property of 0The multiplicative property of 0, which can be understood as the zero product property, states that the product of any number and 0 is 0
Therefore, the equation, A•0 = 0, represents the multiplicative property of 0
Multiplicative and additive identityThe multiplicative and additive identity states that an expression remains the same following the product of the expression with an identity element such as 1, or following the addition of the expression with an identity element such as 0
The multiplicative and additive identity are therefore represented by A•1 = A and A + 0 = A respectively
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please its due tomorrow
1 Answer:
Evaluate the following expression when q = 13.
q-10
2 Answer:
Evaluate the following expression when x = 4.2.
34.5x
3 Answer:
You deposit $70 in a savings account that pays an annual interest rate
of 3%. How much simple interest would you earn in 2.5 years?
1. The value of the expression when q = 13 in q - 10 is 3.
2. The value of the expression when x = 4.2.
34.5x is 144.9
3. The interest will be $5.25.
How to illustrate the information?It should be noted that an expression is simply used to show the relationship between the variables.
1. The expression when q = 13 in q - 10 will be:
= q - 10
= 13 - 10
= 3
2. The value in the expression when x = 4.2 will be:
= 34.5x
= 34.5 × 4.2
= 144.9
3. Principal = $70
Rate = 3%
Time = 2.5 years
Interest = PRT / 100
= (70 × 3 × 2.5) / 100
= $5.25
The simple interest would you earn in 2.5 years is $5.25.
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2(4x-3)-8-2x=4
someone please help me with this, fast
....................... .x=3
highest common factor of 106 and 104
The Greatest Common Factor (GCF) for 104 and 106, notation GCF(104,106), is 2.
Given that,
The numbers 106 and 104.
We have to find the greatest common factor of 106 and 104.
The greatest commo factor is nothing but the greatest common factor, which is the product of two or more numbers, is the largest number (GCF). By dividing them by the largest number, a natural number is produced (factor).There are a few factors that both share once all the number's factors have been identified. The common factor with the highest number among the others is said to be the greatest common factor. The GCF is often referred to as the highest common factor (HCF)
The factors of 104 are 1,2,4,8,13,26,52,104;
The factors of 106 are 1,2,53,106.
Therefore, as we can see, the Greatest Common Factor or Divisor is 2, because it is the greatest number that divides evenly into all of them.
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What is the equation of the following graph
Answer:
y = 1
The graph has no gradient and only intersects at the y-axis.
Please help I’ll mark you as brainliest if correct!
The value of a in the magic square is 25
The value of b in the magic square is 3
The value of c in the magic square is 14
The value of d in the magic square is 7
What are the missing values?The mathematical operations that would be used to determine the missing numbers are addition and subtraction. Addition is the process of determining the sum of two or more numbers. Subtraction is the process of determining the difference of two or more numbers.
According to the information provided in the question, all rows, diagonals and columns add to the same number. Thus, the first step is to determine the sum of all the squares.
The three squares of the diagonal from left to right has all the complete numbers.
Sum of the the squares = 5 + 16 + 27 = 48
a = 48 - 18 - 5 = 25
b = 48 - 18 - 27 = 3
c = 48 - 29 - 5 = 14
d = 48 - 27 - 14 = 7
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f(x) = c f(-x) = c
Does f(x) = f(-x)?
Does f(-x) = f(x)?
+c does not equal -c
The equation of the functions given as f(x) =f(-x) and f(-x) = f(x) are true
How to determine the true statements?The functions are given as
f(x) = c
Also, we have
f(-x) = c
In the above function definitions, we can see that
The functions f(x) and f(-x) have the same value
i.e. f(x) = f(-x) = c
This means that f(x) =f(-x)
By the symmetric property of an equation, the above can also be rewritten as
f(-x) = f(x)
Hence, the functions f(x) =f(-x) and f(-x) = f(x) are true
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Let f(x) = 5x²-2 and let g(x) = 3x + 1. Find (f + g)(2).
(f+g)(2)= (Simplify your answer.)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:(f+g)(x) = 5x² + 3x - 1 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: f(x) = 5 {x}^{2} - 2[/tex]
and
[tex]\qquad \tt \rightarrow \: g(x) = 3x + 1[/tex]
We need to find : (f + g) (x) = ?
[tex]\qquad \tt \rightarrow \: (f + g)(x) = f(x) + g(x)[/tex]
[tex]\qquad \tt \rightarrow \: (f + g)(x) = 5 {x}^{2} - 2 + 3x + 1[/tex]
[tex]\qquad \tt \rightarrow \: (f + g)(x) = 5 {x}^{2} + 3x - 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞