The total number of miles for the four trips is 25 miles.
Given that;
Linda traveled for one hour each day for four days at a speed that made her cover one mile in an even number of minutes. After the first day, she started to lose speed, and it took her 5 minutes longer to complete a mile than the day before. Her journey distance was also an integer amount of miles throughout the four days.
We know that,
Distance is a product of speed and time. We need to find the distance here with the use of the given conditions, time is 1 hour.
Speed = Distance / Time
Hence, speed is 1 mile per x minutes because we want to distance by multiplying the time and speed together yielding 60 min * 1 mile / x mins.
Minutes cancel out, so now we have 60/x as our distance for the first day.
The distance for the given case;
⇒ [tex]\frac{60}{x},\frac{60}{x+5},\frac{60}{x+10},\frac{60}{x+15}[/tex]
It is given that x = 5;
⇒ [tex]\frac{60}{5},\frac{60}{10},\frac{60}{15},\frac{60}{20}[/tex]
= 12 + 6 + 4 + 3
= 25
The total number of miles for the four trips is 25 miles.
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lmn is straight line coordinates of L (-3,1) coordinates of M (4,9) LM:MN is 2:3 find coordinates of N
The coordinates of point N are (8.66, 21)
What is the general equation of a Straight line? What is Section Formula in 2 - D geometry?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The coordinates of a point dividing a straight line joining two coordinates in the ratio m : n is given by -
x = [tex]$\frac{mx_2+nx_1}{m+n}[/tex]
y = [tex]$\frac{my_2+ny_1}{m+n}[/tex]
We have LMN as a straight line such that the coordinates of L are (-3,1) , coordinates of M are (4,9) and LM : MN is 2 : 3.
Assume the coordinates of point N are (a, b).
We can write -
9 = (2b + 3)/5
4 = (-6 + 3a)/5
2b + 3 = 45
b = 21
3a - 6 = 20
3a = 26
a = 8.66
Therefore, the coordinates of point N are (8.66, 21)
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determine whether the lines are parallel, intersect, coincide y = x-7, y = -x + 3
The given two equations are Perpendicular to each other .
What is intersection of lines ?
It is known as an intersection of lines when two lines have exactly one point in common. A point is shared by the connecting lines. The point of intersection is the same place that may be found at the intersection of all intersecting lines. When two or more straight lines cross each other in a plane, they are said to be intersecting lines. An intersection point will be present for the two non-parallel straight lines that are coplanar. The point of intersection, which can be found on all intersecting lines, is where the intersecting lines share a common point.
Here the equation of line is y=mx+b .
Where m = slope . then,
=> y = x-7 where here slope m1= 1 and
=> y = -x+3 where here slope m2 = -1 .
Here the m1= -m2
Hence the given two equations are Perpendicular to each other .
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Which ordered pairs is a solution to 5x+3y>12 Question 2 options: (3, 9) (-5, 5) (3, -6) (-2, -5) (2, 8) (-6, 0)
The solution to the expression given as 5x + 3y > 12 has the ordered pair of (3, 0)
How to determine the ordered pair of the solution?From the question, we have the following inequality that can be used in our computation:
5x + 3y > 12
Solving further, we need to collect the like terms
So, the expression becomes
3y > 12 - 5x
Next, we divide through the inequality by 3
So, we have the following representation
y > 12/3 - 5/3x
Evaluate
The equation becomes
y > 4 - 5/3x
At this point, we assume any value for x and then solve for y
Assume that the value of x is 3
So, we have the following representation
y > 4 - 5/3 * 3
Evaluate the products
y > -1
A value greater than -1 is 0
So, we have
x = 3 and y = 0
Express as ordered pairs
(x, y) = (3, 0)
Hence, the ordered pair of the solution is (3, 0)
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Finding a Missing Endpoint
The new x-coordinate must be 2-2 = 0.
What are endpoints?Many objects in geometry such as line segments, angles, polygons, etc., can be named using endpoints:Points A and B are endpoints for the line segment below. The line segment is named by its endpoints, AB or BA.A ray on the other hand, has only one endpoint as shown below. The ray is named using its endpoint as the first letter, AB.An angle can be named using the common endpoint of the two rays, as shown below. Rays AB and BC share endpoint B and form an angle. This angle can be named as ∠ABC or, using just its endpoint, as ∠B.acc to our question-
Finding the distance between the known endpoint and the midpoint, then applying the same transformation to the midpoint, is the quickest technique to locate the missing endpoint. The x-coordinate changes in this situation from 4 to 2, or down by 2, hence the new x-coordinate is 2-2 = 0.
Hence,The new x-coordinate must be = 0.
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The population of a pigeons in a city is 110 and is growing exponentially at 10% per
year. Write a function to represent the population of pigeons after t years, where the
quarterly rate of change can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the percentage
rate of change per quarter, to the nearest hundredth of a percent.
Answer:
The decemial is 7
Step-by-step explanation:
0.7. Because 04 plus 0.3 equal to 0.7
How many 8s in 72?
How many 800s in 72,000?
How many 5s in 450,000?
How many 3,000s in 270,000?
How many 90s in 63,000?
Find the inverse of A =
Answer:
(-4,-1) and (3,1), respectively.
Step-by-step explanation:
I am not quite sure if the question is necessarily asking for this, but the x and y values are switched to get the points of the inverse. (-1,-4) --> (-4,-1) and (1,3) --> (3,1). I hope that makes sense!
solve for x: 4x-3=2x+7
Answer:
x=5
Step-by-step explanation:
Follow the steps in the image.
-Hope this helped
How do I do this can someone help me plss
Answer:
I think is 50m.
Step-by-step explanation:
sophie's favorite number is a two-digit number. if she reverses the digits, the result is $45$ less than her favorite number. the sum of the digits in her favorite number is $11$. what is sophie's favorite number?
Sophie's favorite number is 83
We have that;
A two-digit number is Sophie's preferred number. Her favorite number is 45 less when the digits are in reverse. Her favorite number has digits that add out to 11 in total.
To get Sophie's favorite number, we need to assume the case as;
Let,
⇒10x + y = 10y + x + 45
x + y = 11
y = 11-x
⇒10x + 11 - x = 10(11 - x) + x + 45
10x + 11 - x = 110 - 10x + x + 45
9x + 11 = 155 - 9x
18x + 11 = 155
18x = 144
x = 8
Therefore, y = 11 - 8
y = 3
Sum = x + y = 8 + 3 = 11
Hence, the given condition is satisfied.
Sophie's favorite number is 83.
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"14 more than twice a number" translate expression
Answer: 14=2x
Step-by-step explanation:
the answer is 14=2x7=14
2. On which plane does the point (0,-1,5) lie? (1 point)
O the xy-plane
O the xz-plane
O the yz-plane
O the xyz-plane
( 0 , -1 , 5) point lies on xyz plane .
What is xyz plane ?The xy-plane is the plane that houses the x- and y-axes, while the yz-plane and the xz-plane house the y- and z-axes, respectively. Space is divided into eight sections known as octants by these three coordinate planes. The positive axes determine the first octant, which is in the front.
To be expressed, everything needs a perspective and a point of view. The three spatial dimensions are represented by the X, Y, and Z coordinates. These stand for length, width, and depth. We employ the same X, Y, and Z denotations when referring to machines, but we assign them different values or meanings. Even more intriguingly, there are no clear laws defining the meaning, which makes it difficult to converse on these levels.
Calculationthis given point lies on xyz plane bcz the point itself shows coordinates which is only possible in xyz plane .
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Jamal runs at a constant speed of 3.7 meters per second for
1/2
hour. Then he walks at a rate of 1.3 meters per seconds for 1/2 hour far did Jamal Uruk walk in 60 minutes
Answer:
9 km
Step-by-step explanation:
1/2 hr = 1800 seconds
3.7 m/s * 1800s + 1.3 m/s * 1800 s = 9000 m in 1 hr
( he walked AND ran this far)
Can write the equation of the graph?
The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (4,160) and (6,240) to find the number of soda bottles the machine can make each minute.
The number of soda bottles the machine can make each minute = 40
In this question, we have been given the graph shows the relationship between time and the number of soda bottles a machine can make.
Also, we have been given two points (4,160) and (6,240)
We need to find the number of soda bottles the machine can make each minute.
i.e., we need to find the slope of line passing through points (4,160) and (6,240)
Using the formula of slope,
m = (240 - 160) / (6 - 4)
m = 80/2
m = 40
Therefore, the number of soda bottles the machine can make each minute = 40
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please help what is the answer and how do you do it
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3 exponet 4 x (20.3 - 9) + 14.5
The solution to the expression is given as 3 exponent 4 x (20.3 - 9) + 14.5 is 929.8
How to determine solution to the expression?From the question, the expression is given as
3 exponent 4 x (20.3 - 9) + 14.5
When the expression is rewritten, we have the following representation
3⁴ x (20.3 - 9) + 14.5
Evaluate the exponent
So, we have
3⁴ x (20.3 - 9) + 14.5 = 81 x (20.3 - 9) + 14.5
Evaluate the expression in the bracket
3⁴ x (20.3 - 9) + 14.5 = 81 x 11.3 + 14.5
Solving further, we have
3⁴ x (20.3 - 9) + 14.5 = 915.3 + 14.5
Lastly, we have
3⁴ x (20.3 - 9) + 14.5 = 929.8
Hence, the solution is 929.8
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Divide [tex]4\frac{2}{15}[/tex] by 3.1.
[tex]\fbox{1.333333}[/tex]
[tex]4\frac{2}{15} \div3.1[/tex]
Simplify:
[tex]4\frac{2}{15} \div3.1[/tex]
[tex]=1.333333[/tex]
let's firstly convert the mixed fraction to improper fraction and the decimal one to a fraction.
[tex]\stackrel{mixed}{4\frac{2}{15}}\implies \cfrac{4\cdot 15+2}{15}\implies \stackrel{improper}{\cfrac{62}{15}}\hspace{10em} 3.\underline{1}\implies \cfrac{31}{1\underline{0}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{62}{15}\div \cfrac{31}{10}\implies \cfrac{62}{15}\cdot \cfrac{10}{31}\implies \cfrac{62}{31}\cdot \cfrac{10}{15}\implies \cfrac{2}{1}\cdot \cfrac{2}{3}\implies \cfrac{4}{3}\implies 1\frac{1}{3}[/tex]
Find the measurement of V.
Answer: 60 degrees
Step-by-step explanation: Because all sides are equilateral, and in an equilateral triangle all angles are 60 degrees, hope that helps.
Can somebody please explain what this question is asking, and how I solve it. I can not solve this, need help please.
Answer:
g(10)=-33, x=3
Step-by-step explanation:
g(x)=-4x+7. --------(1)
a) g(10)=?
since we know function x = -4x+7 to find function g(10) we will just place 10 whenever we see x
g(10)=-4(10)+7
g(10)=-40+7
g(10)= -33
b.)find x if g(x)=-5. ---------(ii)
g(x)=-4x+7. we will place (I) in (ii)
g(x)=-5
-4x+7=-5
-4x=-5-7
-4x=-12
cancel the minus(-) sign in both sides
4x=12
x=12/4
x=3
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find the volume, curved surface area and the total surface area of a cone having base radius 35 cm and height 12 cm.
The volume of the cone is 15393.80 cm³
The curved surface area of a cone is 4068.36 cm²
The total surface area of the cone is 7916.81 cm²
Given parameters;
The base radius( r ) of the cone is 35cm
The height( h ) of the cone is 12cm
Case (I): To find the volume of the cone;
The volume of the cone = [tex]\pi r^{2}\frac{h}{3}[/tex]
= π *(35)² * 12/3
= 15393.80 cm³
Case (II): To find the curved surface area of the cone;
The curved surface area of the cone = πrl
We know that;
Slant height l = [tex]\sqrt{(r^2 + h^2)}[/tex]
By substituting the values;
l = [tex]\sqrt{35^2 + 12^2}[/tex]
l = 37
We know that;
The curved surface area of a cone = πrl
= π * 35 *37
= 4068.36 cm²
Case (III): The total surface area of the cone;
The total surface area of the cone = πr(l + r)
= π * 35 * (37 + 35)
= 7916.81 cm²
Therefore,
The volume of the cone is 15393.80 cm³
The curved surface area of a cone is 4068.36 cm²
The total surface area of the cone is 7916.81 cm²
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Two cards are drawn without replacement from an ordinary deck. Find the probability that the second is not a red card, given that the first is not a red card.
What is the conditional probability?
Is it possible to apply the conditional probability in its alternative form, P(R2|R1) is n(R1⋂R2) divided n(R1) Given that the product rule hasn't yet been taught, we have advocated this approach.
What is the likelihood of receiving two red cards without being replaced?The probability of drawing a second red in the event that this red is not changed is 9/15,
hence the probability of A is 10/16 * 9/15, or 0.375.
The potential of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is determined by multiplying the likelihood of the earlier occurrence by the increased likelihood of the later, or conditional, event.Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.Is it possible to apply the conditional probability in its alternative form, P(R2|R1) is n(R1⋂R2) divided n(R1) Given that the product rule hasn't yet been taught, we have advocated this approach.To learn more about conditional probability refer to:
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Temperatures in °F can be converted in °C using the formula
5(F-32)
=
C=
Make F the subject of the formula.
aC + b
Give your answer in the form
C
Att
where a, b and c are all positive integers.
The given formula can be written as 5F = 9C + 160.
What is a Measurement unit?A measurement unit is a unit to measure certain quantities. To find the measurement of a new quantity knows units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.
Given that,
The conversion formula for °C into °F is 9C = 5(F - 32)
The given formula can be written in the form of cF = aC + b as,
9C = 5(F - 32)
⇒ 5F = 9C + 160
Hence, the given formula can be written by making F as the subject as 5F = 9C + 160.
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The temperature outside is 15°F. If the
temperature drops 20°, will the outside temperature be represented
by a positive or negative integer? Explain your reasoning.
simplify (55x + 46y) - (29x - 10y)
Answer:
26x-56y
Step-by-step explanation:
First you open the bracket and collect like terms
55x-29x-46y-10y
26x-56y
a 13 card hand is dealt from a well-shuffled standard 52-card deck. what is the probability that 2 red cards and 11 black cards are dealt?
The probability of an event is given by dividing the favorable outcomes by total number of outcomes. The sum of all the probabilities of events is always 1.
The probability that 2 red cards and 11 black cards are dealt is .
What is probability ?The probability of an event is given by dividing the favorable outcomes by total number of outcomes. The sum of all the probabilities of events is always 1. If for finding probability we have to select r out of n. Combination is used to select r items out of n, the formula is as follows,
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Finding the probability that 2 red cards and 11 black cards are dealt,
Number of favorable outcomes will be [tex]^{26}C_2\times^{26}C_{11}[/tex].
Total number of outcomes will be [tex]^{52}C_{13}[/tex]
Now, the probability will be,
[tex]P()=\frac{^{26}C_2\times^{26}C_{11}}{^{52}C_{13}} \\\\=\frac{325\times7726160}{635013559600} \\\\=0.00395[/tex]
Therefore, the probability that 2 red cards and 11 black cards are dealt is 0.00395.
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a solid box is 1515 cm by 1010 cm by 88 cm. a new solid is formed by removing a cube 33 cm on a side from each corner of this box. what percent of the original volume is removed?
9% of the volume of the original volume is removed.
Given that the dimensions of solid box is 15 cm by 10 cm by 8 cm.
So the volume of solid box = 15*10*8 cubic cm = 1200 cubic centimeter
The volume of the cube with side 3 cm = 3*3*3 = 27 cubic centimeter
For each corner one cube so the number of cube is 4
So total volume removed = 4*27 = 108 cubic centimeters
The percent of volume is removed = (108/1200)*100% = 9%
Hence the percentage of volume removed is 9%.
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Find x. Round your answer to the nearest tenth of a degree.
Answer:
~62.35°
Step-by-step explanation:
To find the degree of an angle from side lengths, use reverse trigonometric function.
arcsin, arccos, arctan / [tex]sin^-1, cos^-1, tan^-1[/tex]
Because we have adjacent and opposite, lets use arctan.
Set up the equation.
[tex]x = arctan\frac{21}{11}[/tex]
Use a calculator to solve.
A swimming pool is draining at a constant rate.
The table shows the proportional relationship between
the change in the water level and the number of hours
the pool has drained. Complete the table to show the change
in water level at 9 and 23 hours?
The level of water in the swimming pool after a specified duration of the water draining at a constant rate is found as follows;
10. a. The water level is changing (reducing) at a rate of 1.75 inches per hour.
b. After 9 hours, the change in the water ls 15.75 inches
c. The change in the water level after 23 hours is 40.25 inches
What is a constant rate?A constant rate is a rate that is fixed or steady and does not vary following a change of the other variables?
The table of values for the draining swimming pool obtained from a similar question on the internet is as follows;
Hours Draining [tex]{}[/tex] Change in Water Level (inches)
2 [tex]{}[/tex] -35
9 [tex]{}[/tex] ?
17 [tex]{}[/tex] -29.75
23 [tex]{}[/tex] ?
The relationship between the hours the swimming pool drains and the water level is a proportional relationship., such that the ratio of each coordinate pair in the table is a constant.
Let H represent the hours draining and let C represent the change in water level, we have;
C ∝ H
C = k·H
[tex]k = \dfrac{C}{H}[/tex]
Where;
k = The constant of proportionality, which is the rate at which the water level is changing per hour
a. The rate at which the water level changes per hour can be found from the first pair of points on the table as follows;
The first pair of points = (2, -3.5)
[tex]k = \dfrac{-3.5}{2} = -1.75[/tex]
The rate at which the water level is changing per hour is -1.75 inches per hour
The water level is decreasing at 1.75 inches per hour
b. The change in water level after 9 hours is found by using the formula;
C = k × H
Where, H = 9, we have;
Change in water level, C = -1.75 × 9 = -15.75
The change in water level after 9 hours is 15.75 inches
c. The change in water level after 23 hours is found by plugging in H = 23 as follows;
C = -1.75 × 23 = -40.25
The change in water level after 23 hours is -40.25 inches
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