The number of hours Nick took to reach the shopping mall in terms of r is ; 3.14 hours.
What is rate?Rate is a measure of a quantity using another quantity as the basis.
Analysis:
speed travelling on foot = r
distance travelled on foot = 5 miles
time taken = 5/r
speed travelling on bicycle 80 percent faster than on foot is 1.8r
distance travelled on bicycle = 8 miles
time taken = 8/1.8r = 40/9r
total time taken to get to the mall = 5/r + 40/9r = 85/9r
speed while walking = 3 miles per hour = r
time taken = 85/9 x 3 = 3.14 hours
In conclusion, number of hours Nick took to reach the shopping mall in terms of r is 85/9r is 3.14 hours.
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Answer:
3 hours 9 minutes
he triangle on the grid will be translated two units down. On a coordinate plane, triangle A B C has points (2, 1), (0, negative 1), (2, negative 1). Which shows the triangle when it is translated two units down? On a coordinate plane, triangle A prime B prime C prime has points (0, negative 1), (0, negative 3), (2, negative 3). On a coordinate plane, triangle A prime B prime C prime has points (0, 1), (negative 2, negative 1), (0, negative 1). On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 3). On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 1).
If these coordinates are translated two units down, we will subtract 2 units from the y axis to have A(2, -1), B(0, -3) and C(2, -3)
Translation of coordinate pointTranslation is a transformation technique of changing the position of an object on the xy-plane.
Given the following coordinate of a triangle expressed as:
A(2, 1)
B(0, -1)
C(2, -1)
If these coordinates are translated two units down, we will subtract 2 units from the y axis to have:
A(2, -1)
B(0, -3)
C(2, -3)
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Find the probability that a randomly
selected point within the circle falls
in the red shaded area.
r = 4 cm
[?]%
Round to the nearest tenth of a percent.
Enter
Answer:
[tex]31.8\%[/tex]
Step-by-step explanation:
The area of the circle is [tex]A=\pi r^2=\pi(4)^2=16\pi[/tex]
The area of the triangle is [tex]A=\frac{bh}{2}=\frac{8*4}{2}=\frac{32}{2}=16[/tex]
Hence, the probability of a randomly selected point within the circle falls in the red shaded area is [tex]\frac{16}{16\pi}=\frac{1}{\pi}\approx0.318\approx31.8\%[/tex]
Two trains, Train A and Train B, weigh a total of 526 tons. Train A is heavier than Train B. The difference of their weights is 466 tons. What is the weight of each train?
Answer:
Train A = 466
Train B = 60
Step-by-step explanation:
Last month David and Mary saved some money in a ratio of 3:5. This month they saved an additional $154 together, and David now has three times as much money as he had last month and Mary has two times as much as she had last month. How much money did they save last month?
Answer:
David: $42Mary: $70Step-by-step explanation:
The two relations can be translated to a system of linear equations in two variables. These can be solved in any of the usual ways.
__
setupLet d and m represent the amounts David and Mary saved last month, respectively.
The first relation tells us
d/m = 3/5 ⇒ 5d = 3m ⇒ 5d -3m = 0
The second relation tells us that adding 3 times what David had last month to 2 times what Mary had last month will give a total that is 154 greater than the sum of their funds last month.
d +m + 154 = 3d +2m ⇒ 2d +m = 154
__
solutionWe can add 3 times the second equation to the first to eliminate m.
(5d -3m) +3(2d +m) = (0) +3(154)
11d = 462 . . . . . . . . simplify
d = 42 . . . . . . . . . divide by 11
Using the second equation, we can find Mary's savings:
m = 154 -2d
m = 154 -2(420 = 70
David saved $42 last month; Mary saved $70.
What is the domain of the piecewise function?
A. x<0, x>4
B. -∞ 4
C. all real numbers
Answer:
C. All real numbers
Given a polynomial function f(x) = –x2 + 2x + 1 and an exponential function g(x) = 2x, what key features do f(x) and g(x) have in common?
A.)Both f(x) and g(x) decrease over the interval of [1 , ∞).
B.) Both f(x) and g(x) have the same range of (–∞, 2).
C.) Both f(x) and g(x) have the same x-intercept of (–1, 0).
D.)Both f(x) and g(x) have the same y-intercept of (0, 1).
The only key feature that these functions have in common is that they have the same y-intercept. So the correct option is D.
What do these functions have in common?
Here we have the functions:
[tex]f(x) = -x^2 + 2x + 1\\\\g(x) = 2^x[/tex]
f(x) is quadratic, and g(x) is exponential.
Notice that the exponential function has a positive base, so it is increasing. For the quadratic equation we can see a negative leading coefficient, so it opens downwards. So first and second options are false.
Also, g(x) never intersects the x-axis, so third option is false.
Finally, the y-intercepts of the given functions are:
[tex]f(0) = -0^2 + 2*0 + 1 = 1\\\\g(0) = 2^0 = 1[/tex]
So the y-intercepts are equal, meaning that the correct option is D.
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Answer:
Both f(x) and g(x) have the same y-intercept of (0, 1).
Step-by-step explanation:
I got it right on the test.
What is the volume of the rectangular prism?
A prism has a length of 8 inches, width of 2 inches, and height of 12 and one-half inches.
16 in.3
22 and one-half in.3
200 in.3
212 and one-half in.3
Volume is a three-dimensional scalar quantity. The volume of the rectangular prism is 200 in³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the rectangular prism of the length of 8 inches, the width of 2 inches, and the height of 12 1/2 inches can be written as,
The volume of the rectangular prism = 8in × 2in × 12.5in
= 200 in³
Hence, The volume of the rectangular prism is 200 in³.
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You have a glass paperweight that is shaped like a cone. The diameter of the paperweight is 7 centimeters. The slant height is 4 centimeters. Find the surface area of the cone. Use 3.14 to approximate pi.
Step-by-step explanation:
please mark me as brainlest
A bag contained $24.20 worth of coins. There were 20-cent and 50-cent coins only. The number of 20-cent coins was 5 fewer than the number of 50-cent coins. How many coins were there in the bag
Answer:
Their will be 2 coins in allThere were 67 coins in the bag, 36 of which were 50-cent coins and 31 of which were 20-cent coins.
Let x be the number of 50-cent coins in the bag,
And y be the number of 20-cent coins.
From the problem,
we know that y = x - 5,
Since there were 5 fewer 20-cent coins than 50-cent coins.
We can also set up an equation for the total value of the coins in the bag,
⇒ 0.5x + 0.2y = 24.20
Now we can substitute y = x - 5 into the equation,
⇒ 0.5x + 0.2(x - 5) = 24.20
Simplifying, we get,
⇒ 0.7x - 1 = 24.20
⇒ 0.7x = 25.20
⇒ x = 36
So there were 36 50-cent coins in the bag.
Using y = x - 5,
We can find that there were 31 20-cent coins.
Therefore, there were a total of 67 coins in the bag (36 + 31 = 67).
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How to find x=?
How to solve step by step
Answer:
230 degrees
Step-by-step explanation:
draw a horizontal line from x and use congruent rule to have a full 360 degree circle. You can now subtract 60 and 70 from 360 degrees leaving you with 230 degrees as x
Paul and Krystal spent 1 1/2 hours at the pool
Answer:
Paul and Krystal spent 13 hours at the pool
Step-by-step explanation:
I Thank
State your conclusion in the form of a theorem, and then prove the theorem using a two-column proof. When you write the proof, refer to the diagram you created in part A. It will be helpful to use point labels to state what is given and what you have to prove and to use those labels throughout the proof.
As part of the proof, you’ll have to construct a line segment connecting the top intersection point on one of the transversals with the lowest intersection point of the other transversal, thus forming two triangles. Take a screenshot of the construction, save it, and insert the image in the space below before you begin your written proof.
The midpoint theorem simply states that the line segment that joins the two sides of the triangle is parallel to the third side.
How to illustrate the theorem?Your information is incomplete. Therefore, an overview of the theorem will be given. It should be noted that the midpoint theorem states that the line drawn through the mid point of one side of the triangle is parallel to another side.
To find the midpoint, one can measure the distance between the two end points and divide the results by 2.
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40 POINTS!!
Which statement matches the vector operation shown on the coordinate grid?
The statement that matches the vector operation shown on the coordinate grid is v + w = u.
How to add two vectors graphically?In order to add two vectors a and b graphically by using the tail and tip method, we must draw the tail of b at the tip of vector a.
Then we must draw a line that goes from the tail of vector a to the tip of vector b.
This line represents the sum of a + b.
In the given problem, we notice that the tail of the vector w is on the tip of the vector v.
The line that joins the tail of vector v with the tip of vector w is vector u.
Therefore we can say that v + w = u
The statement that matches the vector operation shown on the coordinate grid is v + w = u.
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the zeros of the function f(x) = x² + 5x - 6 are show your work
Answer:
x = - 6 , x = 1
Step-by-step explanation:
to find the zeros let f(x) = 0 , that is
x² + 5x - 6 = 0
consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term ( + 5)
the factors are + 6 and - 1 , since
6 × - 1 = - 6 and 6 - 1 = + 5 , then
(x + 6)(x - 1) = 0 ← in factored form
equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
x - 1 = 0 ⇒ x = 1
which choices are in the solution set of the equation below check all that apply 4x=30
The choice in the solution set of the equation 4x = 30 is x = 7.5
How to determine the solution set?The equation is given as:
4x = 30
Divide both sides of the equation by 4
4x/4 = 30/4
Evaluate the quotients
x = 7.5
Hence, the choice in the solution set of the equation 4x = 30 is x = 7.5
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Without calculating the cubes find 1 cube+2cube+2(4) cube+(-5)cube+(-6)cube .
Can you help me please!!
The ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.
What is parallelogram?In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
We have ABCD is a parallelogram.
BE is perpendicular to FC
FA is perpendicular to FC
As we know in the parallelogram ABCD:
AB ≅ DC
AD ≅ CB
As the DC is extended to F
So, AB ≅ FE
And BE is perpendicular to FC
FA is perpendicular to FC (given)
∴ FA ≅ BE
∴ ABEF is a parallelogram.
Thus, the ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.
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Tera buys 10 pencils for $1.99.
About how much $ does each pencil
cost?
Answer:
19 cents or 0.199
Step-by-step explanation:
Hope it helped!
Answer:
19 cents
Step-by-step explanation:
divide total cost by amount of items
Krista got paid $43.75 for working 3.5 hours. How much did she earn per hour?
Answer:
12.5
Step-by-step explanation:
divide 43.75 by 3.5 to get your answer
Calculate the area of the alarm clock.
Given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².
What is the area of the alarm clock?Note that: Area of a circle is expressed as;
A = πr²
Where r is radius and π is constant pi ( π = 3.14 )
Given that;
Diameter d = 70cm Radius r = d/2 = 70cm/2 = 35cmArea = ?A = πr²
A = 3.14 × ( 35cm )²
A = 3.14 × 1225cm²
A = 3846.5cm²
Therefore, given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².
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PLEASE HELP ME I WILL GIVE BRAINLYEST
Answer:
your answer will be 85 1/3ins
Step-by-step explanation:
16x 5 1/3 = 85.3333333333
then I took the 85 and the 1/3
and just put em together
At 3:40 P.M, the hour hand and the minute hand of a clock form an angle of:
Answer:
130 degrees
Step-by-step explanation:
3:40, it has traveled 6 * 40 = 240 degrees which is 110 degrees from vertical The difference is 240 - 110 = 130 degrees, which is the final answer.
Hope This Helped
n⃗ =〈−2,−1〉 and D=[−4 4 2 3].
What is D⋅n⃗ ?
Enter your answer as a vector by filling in the boxes.
The dot product of the two matrices D and n is determine as (4, - 7).
Dot product of the vector
The dot product of the two matrices is calculated as follows;
n = (-2, -1), and D = [-4 2]
[4 3]
D.n = (-2, -1). [-4 2] = (-2 x -4) + (-1 x 4) = 4
[4 3] = (-2 x 2) + (-1 x 3) = -7
D.n = (4, - 7)
Thus, the dot product of the two matrices D and n is determine as (4, - 7).
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Wendy winholtz 8 year savings certificate pays an annual interest rate of 5.3% at the end of 5 years she cashed out the 6,000 CD and paid a penalty of 12 month simple interest. What penalty did she pay
Answer:
318
Step-by-step explanation:
The rate of 5.3% is an annual rate, and specifies the amount of interest earned in a 12-month period by the principal amount of the CD. The interest amount is found by multiplying the interest rate by the principal amount.
__
penaltyThe amount of the penalty is 5.3% of 6000:
0.053 × 6000 = 318
Wendy paid a penalty of 318 for her early withdrawal.
What is the volume of the solid
Answer:
A.264
Step-by-step explanation:
((Area Of triangle*height)=Volume
Area of triangle is the base of the triangle multiplied by height of triangle divided by 2
((8*6)/2)*11=264
What is the value of x? 2 3 6 7
Answer:
6
Step-by-step explanation:
Answer:
2 or A
Step-by-step explanation:
Correct on edge22
Beginning in the middle of summer, the average temperature for a certain year in Phoenix could approximately be modeled by the function f(x)=31cos(0.0055πx)+88, where x represents the number of days since the middle of the summer, and f(x) represents the average temperature in degrees Fahrenheit.
What was the lowest average temperature in Phoenix that year (approximately)?
A) 57∘F
B) 31∘F
C) 55∘F
D) 88∘F
By finding the minimum of the given function, we conclude that the lowest average temperature that year is 57°F.
What was the lowest average temperature in Phoenix that year?We know that the average temperature is given by the equation:
f(x)=31cos(0.0055πx)+88
And it is in Fahrenheit degrees.
To get the lowest average temperature, we just need to find the minimum of the above function.
Remember that the minimum of the cosine function is:
cos(x) = -1
Then the lowest value of the above function is:
f(x₀) = 31*(-1) + 88 = 57
From this, we conclude that the lowest average temperature that year is 57°F, so the correct option is A.
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the spec sheet for the actual 1968 corvette shows the front frame dimension to be 32.875 inches. what would this measurement be, in both fractional and decimal form, on the hot wheels 1:64 model? which form of the measurement would be easier to work with?
Answer:
0.513671875 = 263/512 inches
easier to use: depends on the measurement tool
Step-by-step explanation:
The model dimension is found by multiplying the actual dimension by the scale factor.
__
model dimensionmodel frame dimension = actual frame dimension × 1/64
= (32.875 inches)/64 = 0.513671875 inches
In fractional form, this is ...
(32 7/8) / 64 = (263/8) / 64 = 263/512 . . . inches
__
ease of useIt is unlikely that a casual hobbyist will have access to tools that measure with a resolution finer than 0.0001 inches. More common would be a measurement resolution of 0.001 inches. Using such tools, the rounded decimal value 0.5137 or 0.514 inches would be more useful than the fractional measurement.
It is possible that an optical measuring device could be available that would present its result as a fraction of an inch. If such a tool were used, the fractional measurement value would provide an appropriate point of comparison.
In short, the measurement easiest to work with depends on the tool being used to make the measurement.
Solve for x in the triangle. Round your answer to the nearest tenth.
X
9
64°
Answer:
x = 23.0
Step-by-step explanation:
To solve, you have to make the equation:
[tex]cos(64)=\frac{9}{x}[/tex]
Now multiply x to both sides:
[tex]cos(64)*x=9[/tex]
Next divide both sides by cos(64):
[tex]x=\frac{9}{cos(64)}[/tex]
x = 22.9675486404
Round to the tenth:
x = 23.0
Hope it helps and have a nice day!
x – y = 2 2x = 3y in elimination method
Answer:
x=6, y=4
Step-by-step explanation:
x - y = 2
2x = 3y => 2x - 3y = 0
x - y = 2 | ×(-2) => -2x + 2y = -4
2x - 3y = 0
-2x + 2y = -4
2x - 3y = 0
___________
0 - y = - 4 | ×(-1)
y = 4
Substitution in x - y = 2:
x - 4 = 2 | +4
x = 2+4 = 6