Line segment IK includes Point J. The length of the segment IK=15 and IJ=13. The length of the segment JK is 2.
Given that,
Line segment IK includes Point J.
We have to determine the length of segment JK.
We have length of the segment IK=15 and IJ=13.
Two unique points on a line define the boundaries of a line segment. A line segment is also known as a part of a line that connects two locations. A line and a line segment vary in that a line has no ends and can continue indefinitely in any direction.
We can write as,
IK=IJ+JK
15=13+JK
JK=15-13
JK=2
Therefore, The length of the segment JK is 2.
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In 5 months, firefighters responded to 80wildfires. At this rate, how many wildhres will the frefighters respond to in 8 months?
Given that, in 5 months, firefighters responded to 80 wildfires:
• You can determine the rate of wildfires per month firefighters respond to by dividing 80 wildfires by 5 months:
[tex]\frac{80\text{ }wildfires}{5\text{ }months}=16\text{ }\frac{wildfires}{month}[/tex]You can determine that each rectangle of the diagram provided in the exercise represents the rate obtained above.
• Assuming that the rate is the same in 8 months, you can multiply the rate obtained before by 8 months, in order to determine the number of wildfires the firefighters will respond to in 8 months:
[tex](16\text{ }\frac{wildfires}{month})(8\text{ }months)=128\text{ }wildfires[/tex]Hence, the answer is:
Mike solved a system of equations and found that it had infinite solutions. Which could be the system of equations mike solved?
A system of equations has infinite solutions when both equations are equivalent.
To check if two equations are equivalent, write both of them in the same form. If the coefficients are proportional, including the constant terms, then they are equivalent.
Option 1
The first equation is written in general form. Isolate the constant term on the second equation to write it in general form:
[tex]\begin{gathered} y=-2x-1 \\ \Rightarrow2x+y=-1 \end{gathered}[/tex]Notice that if we multiply the second equation by 3 on both sides, we will get the same coefficients as in equation 1:
[tex]\begin{gathered} 3(2x+y)=3(-1) \\ \Rightarrow6x+3y=-3 \end{gathered}[/tex]Then, both equations are equivalent.
Therefore, this system has infinite solutions.
Option 2
Since there is no constant term in the secon
Angel, Brandon, and Carla work in the same office.
•Angels age is 4 years more than twice than Carla’s age
•Brandon is 5 years younger than Carla
If N represents Carla’s age, write and expression for Angels age and Brandon’s age. The sun of Angels,Brandon’s, and Carla’s age is 123
what is the answer to 8+2(6-3)÷6 in pemdas form
8 + 2(6 - 3) / 6
we will be using order of operation
pemdas
firstly we will solve the parentheses
= (6 - 3)
= 3
8 + 2(3) / 6
Secondly we will open the parentheses with 2
= 8 + 6/6
thirdly, we will do the division
= 6/6 = 1
Lastly, Addition
8 + 1
= 9
The answer is 9
A force of 250 newtons stretches a spring 30 centimeters . Please find how much work is done in stretching the spring from 20 centimeters to 50 centimeters.
How many bushels will there been in the figure hold? (1 cu ft≈ 1.24 bushels)
Answer:
151.93 bushels
Explanation:
First, let's find the volume of the truncated cone using the following equation
[tex]V=\frac{1}{3}\pi h(r^2+rR+R^2)[/tex]Where h is the height of the cone, r is the smallest radio and R is the largest radio. So, replacing h = 4 ft, r = 1.5 ft and R = 4.5 ft, we get:
[tex]\begin{gathered} V=\frac{1}{3}(3.14)(4)((1.5)^2+(1.5)(4.5)+(4.5)^2) \\ V=\frac{1}{3}(3.14)(4)(29.25) \\ V=122.52ft^3 \end{gathered}[/tex]Because the radius is half the diameter, so r = 3ft/2 = 1.5 ft and R = 9ft/2 = 4.5 ft.
Now, we know the volume in cubic feet. To find the volume in bushels, we will use the conversion factor 1 ft³ = 1.24 bushels.
[tex]122.52ft^3\times\frac{1.24\text{ bushels}}{1ft^3}=151.93\text{ bushels}[/tex]Therefore, the answer is 151.93 bushels
Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form
The ratio of a 30-60-90 triangle is the following:
This means that the side that is opposite to the 60 degrees angle is "a" times the square root of 3, where "a" is the side adjacent to the 60 degrees angle. Therefore, applying this to the given triangle we get:
[tex]m=n\sqrt[]{3}[/tex]Also, the hypotenuse is "2a", therefore, we have:
[tex]84=2(n)[/tex]From there we can solve for "n" by dividing both sides by 2:
[tex]n=\frac{84}{2}=42[/tex]Now we can use this value to determine the value of "m":
[tex]m=42\sqrt[]{3}[/tex]how to find the area of a circle
Area of a circe = Pi x radius^2
To find a weekly average temperature, you add up all of the temperatures
and then divide by the number of days. Using the table of temperatures
below from Anchorage, Alaska, determine the average temperature for the
week given.
MONDAY
-31.4
TUESDAY
-35.2
WEDNESDAY
-33.8
THURSDAY
-34.9
FRIDAY
-32.7
The most appropriate choice for average will be given by-
Weekly average temperature of Anchorage = -33.6
What is average?
In a data set, there are many numbers. There has to be a number which will represent all the numbers in a data set. That representative is called average.
Average is calculated by dividing the sum of all observations by the number of observation.
Temperature on monday at Anchorage = -31.4
Temperature on monday at Anchorage = -35.2
Temperature on monday at Anchorage = -33.8
Temperature on monday at Anchorage = -34.9
Temperature on monday at Anchorage = -32.7
Weekly average temperature =
[tex]\frac{(-31.4) + (-35.2) + (-33.8) + (-34.9) + (-32.7)}{5}\\\\-\frac{168}{5}\\\\-33.6[/tex]
Weekly average temperature of Anchorage = -33.6
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Tiana said that her cable bill of $25 is less than $3 more than 5 times what Lottie pays for cable. Write an inequality that shows Tiana's comparison.
If c is the bill that Lottie pays for cable, the given situation can be represented by the following inequality:
25 < 3 + 5c
in the previous inequality, you have that 25 is less (<) than 3 more (3 + ) than 5 times (5x) what Lottie pays for cable.
The previous inequality can be also written as follow:
3 + 5c > 25
identify the place occupied by the digit 9. 1,664,963
Let us define place value
Place value is the value of each digit in a number. For example, the 5 in 350 represents 5 tens, or 50; however, the 5 in 5,006 represents 5 thousands, or 5,000. It is important that we understand that whilst a digit can be the same, its value depends on where it is in the number.
Given the number 1,664,963, the place values of each of the numbers are
1= 1 Million
the first 6 from the left= 6 hundred thousands
the second 6 from the left = 6 ten thousands
4= 4 thousands
9= 9 hundreds
the last 6 from the left = 6 tens, and
3= 3 units
Hence, the place occupied by 9 in the number 1,666,963 is 9 hundreds
593 divided 60 with remainder
Identify the arc length of BD in terms of pi and rounded to the nearest hundredth.
The radius of the circle, r = 8 in
m
That is the angle, θ = 92°
The length of arc BD is given by the formula:
[tex]\begin{gathered} \text{Arc BD = }\frac{\theta}{360}\times2\pi r \\ \text{Arc BD = }\frac{92}{360}\times2(8)\pi \\ \text{Arc BD = }4.09\pi\text{ in} \end{gathered}[/tex]If π = 3.142
Arc BD = 4.09 (3.142)
Arc BD = 12.85 in
The data set shown below represents the time in minutes spent using a computer at Kinko's copy center by 25 people on a randomly selected day construct a stem and leaf plot for the data and analyze the results 16, 25, 18, 39, 25, 17, 29, 14, 37 22, 18, 12, 23, 32, 35, 24, 26 20, 19, 25, 26, 38, 38, 33, 29
areTo produce a stem and leaf plot, we should follow these steps:
Step 1- Rearrange the numbers in ascending or descending order: This will make the plotting of the stem and leaf plot a lot easier.
Step 2- Next, we select the stems from each number in the data. the stem is the first digit in the number in consideration. For example, the stem of 16 is 1 because it is the first digit. We do this selection of stems for all the numbers in the dataset.
Step 3- Next, we select the leaves. The leaves are the digits that come after the stem in a number. For example, in the number 16, while 1 is the stem, 6 is the leaf of the number.
Step 4- We arrange the stems and leaves in a table and this represents the stem and leaf plot.
With this information, we can proceed to solve the question
Solution
Step 1:
Rearranging the numbers, we have:
12, 14, 16, 17, 18, 18, 19, 20, 22, 23, 24, 25, 25, 25, 26, 26, 29, 29, 32, 33, 35, 37, 38, 38, 39
Step 2:
The stems of this data are just the first digit of each number.
12, 14, 16, 17, 18, 18, 19 all have a stem of 1
20, 22, 23, 24, 25, 25, 25, 26, 26, 29, 29 all have a stem of 2
32, 33, 35, 37, 38, 38, 39 all have a stem of 3.
Thus, the stems of this data are: 1, 2, and 3.
Step 3:
The leaves of the data are the second digits of the numbers. Thus, we have that
The leaves of these numbers 12, 14, 16, 17, 18, 18, 19 are: 2, 4, 6, 7, 8, 8, 9.
The leaves of these numbers 20, 22, 23, 24, 25, 25, 25, 26, 26, 29, 29 are: 0, 2, 3, 4, 5, 5, 6, 6, 9, 9
The leaves of these numbers 32, 33, 35, 37, 38, 38, 39 are: 2, 3, 5, 7, 8, 8, 9.
Step 4:
Thus, we can proceed to generate the leaf plot as follows:
Sam weighed and measured an infant at the clinic today The baby weighed 8.5 kg and was 60.5 cm long The baby's mather wanted the baby's weight in pounds and length in inches . Use the lowing conversion factors 22 1in = 2.54 cm Round your answers to the nearest tenths place .
We know that
• The baby weighed 8.5 kg and was 60.5 cm long.
We have to transform 8.5 kg into pounds. We know that 1 kg is equivalent to 2.2 pounds. So, we just have to multiply.
[tex]8.5\operatorname{kg}\cdot\frac{2.2lb}{1\operatorname{kg}}=18.7lb[/tex]Therefore, the baby weighed 18.7 pounds.Then, we transform 60.5 cm into inches. We know that 1 inch is equivalent to 2.54 cm. So,
[tex]60.5\operatorname{cm}\cdot\frac{1in}{2.54\operatorname{cm}}=23.82in[/tex]Therefore, the baby was 23.82 inches long.A RICH DONOR GIVES A HOSPITAL $500000ONE YEAR FROM TODAY.
Answer:
what do you need to be helped with please
If x and y are in direct proportion and y is 2 when x is 4, what is y when x is 12.
If x and y are in direct proportion and y is 2 when x is 4 and y is 6 when x is 12.
By definition of proportionality,
If y is directly proportional to x,
y α x
i,e y = k(x)
K is the constant of proportionality
when x = 4, y =2
2 = k(4) --> k = 1/2
Now y = k.x
y = 1/2 (12)
y = 6
What is the Constant of Proportionality?
The proportional constant is a ratio that connects two given values in a so-called proportional relationship. Other names for the constant of proportionality are constant ratio, constant rate, unit rate, constant of variation, or even rate of change.
To find the constant of proportionality, first identify the variables x and y. To find out the relationship between weight and number of sticks, x is the weight and y is the number of butter sticks. Use the equation k = y÷ x to find the constant of proportionality.
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Use each of the numbers from 1 to 9 exactly once to create three mixed numbers with the greatest possible product. Then use each of the numbers exactly once to create three mixed numbers with the least possible product. Find each product. Explain your reasoning. The fraction portion of each mixed number should be proper.
Answer:
here
Step-by-step explanation:
hitler demanded to be appointed as chancellor. German President Paul von Hindenburg initially resisted this demand. However, he gave in and appointed Hitler as Chancellor of Germany on January 30, 1933. Hindenburg appointed Hitler to this position as the result of a political deal.
Use the Pythagorean theorem to determine the unknown length of the right triangle Determine the length of side c in each of the triangles that followers Do not include any units in your answer
Recall the Pythagorean Theorem:
For a right triangle with legs of lengths A and B and hypotenuse C, the following relation is satisfied:
[tex]A^2+B^2=C^2[/tex]If two variables are known (it could be the hypotenuse and one leg, or both legs), then the third can be calculated. If the hypotenuse is not known, it can be calculated as:
[tex]C=\sqrt[]{A^2+B^2}[/tex]If one of the legs is not known, then we can substract the other length squared, and then take the square root:
[tex]\begin{gathered} A^2=C^2-B^2 \\ \Rightarrow A=\sqrt[]{C^2-B^2} \end{gathered}[/tex]For problems involving the Pythagorean Theorem, use these equations by replacing the corresponding numerical values of A, B or C. Remember that C does not always stand for the hypotenuse, it always depend on the diagram. For example, if the legs of the right triangle were labelled as X and Y, and the hypotenuse was A, then:
[tex]X^2+Y^2=A^2[/tex]Be careful with that.
A sign above a basket of DVD reads "3 for $17." Kellen decides to buy 6 DVDs and use a coupon for 25% off. If sales tax is 6%, what will he pay in total?
The pay in total will be:
since 3 cost $17then 6 will cost 2(17)=$34
then we apply the coupon for 25% off, obtainning 34-0.25(34)=$25.5
now we add the taxes, 25.5+0.06(25.5)=$27.03
Then the final price will be 27.03 dollarsWhich of the following phrases translates to m - 7?
A. the difference between seven and a number
B. a number subtracted from seven
C. seven minus a number
D. a number decreased by seven
m is an unknown number that is being decreased by 7.
OPTION A IS WRONG BECAUSE MATHEMATICALLY IT IS WRITTEN AS
[tex]7 - m[/tex]
B IS WRONG BECAUSE IT MEANS
[tex]7 - m[/tex]
C IS WRONG BECAUSE IT MEANS
[tex]7 - m[/tex]
BUT D IS THE ANSWER BECAUSE IT MEANS
[tex]m - 7[/tex]
SINCE m IS TREATED AS AN UNKNOWN NUMBER.
GOODLUCK!!!!
Write an equation of variation to represent the situation and solve for the indicated information A bottle of 150 vitamins costs $5.25. If the cost varies directly with the number ofvitamins in the bottle, what should a bottle with 250 vitamins cost?Wei received $55.35 in interest on the $1230 in her credit union account. If the interestvaries directly with the amount deposited, how much would Wei receive for the sameamount of time if she had $2000 in the account?
A bottle of 150 vitamins costs $5.25.
The cost varies directly with the number of vitamins in the bottle.
What should a bottle with 250 vitamins cost?
Let C denotes cost and V denotes the number of vitamins.
The direct variation equation is
[tex]C=kV[/tex]Let us first find the value of k (constant of proportionality)
[tex]k=\frac{C}{V}=\frac{5.25}{150}=0.035[/tex]Now the cost of 250 vitamins may be found as
[tex]\begin{gathered} C=kV \\ C=0.035\times250 \\ C=\$8.75 \end{gathered}[/tex]Therefore, the cost of 250 vitamins is $8.75.
more help need 50 points
Answer:
9p-25
Step-by-step explanation:
always do parentheses first
-5(-10p + 8p -5)-p
multiply negative with negative gives positive
-5(-2p-5)-p
variable always has a 1 in front
10p-1p-25
9p-25
Evaluate.
(15+12)2+310⋅5
Enter your answer as a mixed number in simplest form.
Answer:
337.5
Step-by-step explanation:
first you solve what is in the bracket and add the 2 to give you 27 then add the 310.5
hello I'm a 7th grader can you please help me with my math summer package and explain it in a way that a 7th grader can understand it.....I need help with number 1 ...
Suppose that both Brian and Kristen pay $18.42 in order to diminish their checkbook balance. Then, after the payment, their current balances would be
[tex]\begin{gathered} Brian:-23.45+18.42=-5.03 \\ Kristen:18.42-18.42=0 \end{gathered}[/tex]Therefore, after paying the same amount ($18.42), Kristen's debt has reduced to zero while Brian still owes $5.03.
Thus, Brian owes more money than Kristen.In the diagram, AC = 12 V3. Find BC and AB. Write your answers in simplest form.B60930O BC = 72. AB = 36O BC = 36. AB = 72O BC = 24, AB = 12O BC = 12. AB = 24
constructing the triangle
From the figure,
We will be applying trig. ratios
[tex]\text{SOH CAH TOA}[/tex]Finding BC with respect to angle 30
[tex]\begin{gathered} \text{Tan 30 = }\frac{opp}{adj} \\ \text{Tan 30 = }\frac{BC}{12\sqrt[]{3}} \\ \text{cross multiply} \\ BC\text{ = Tan 30 }\times12\sqrt[]{3} \\ BC\text{ = }\frac{\sqrt[]{3}}{3}\text{ }\times\text{ 12}\sqrt[]{3} \\ BC\text{ = }\sqrt[]{3\text{ }}\text{ }\times\text{ 4}\sqrt[]{3} \\ BC\text{ = 4 }\times3 \\ BC\text{ = 12} \end{gathered}[/tex]Finding AB with respect to angle 30
[tex]\begin{gathered} \cos \text{ 30 = }\frac{adj}{hyp} \\ \cos \text{ 30 = }\frac{12\sqrt[]{3}}{AB} \\ \text{cross multiply} \\ \cos \text{ 30 }\times\text{ AB = 12}\sqrt[]{3} \\ \text{divide both sides by cos30} \\ AB\text{ = }\frac{12\sqrt[]{3}}{\cos \text{ 30}} \\ AB\text{ = }\frac{12\sqrt[]{3}}{\frac{\sqrt[]{3}}{2}} \\ AB\text{ = 12}\sqrt[]{3}\text{ }\times\text{ }\frac{2}{\sqrt[]{3}} \\ AB\text{ = 12 }\times2 \\ AB\text{ = 24} \end{gathered}[/tex]Therefore,
BC = 12 and AB = 24
write a complete sentence that makes a relative comparison of the density of castle in the two countries
Before we write the sentence comparing the densities, let's first calculate them. The density is given by the ratio between the amount of cattle and the area of the country.
The ratio for United States is:
[tex]\frac{75.9}{3.797}=19.9894653674\ldots\approx19.989[/tex]The density of cattle for United States is 19.989 cattle/square mile.
Doing the same calculation for the other country:
[tex]\frac{41.1}{1.013}=40.5725567621\ldots\approx40.573[/tex]The density of cattle for Republica is 40.573 cattle/square mile.
To do a relative comparison, we can do it by finding the ratio between those densities.
[tex]\frac{19.989}{40.573}=0.49266753752[/tex]A sentence that makes a relative comparison would be:
The density of cattle in United States is less than the density of cattle in Republica, representing only 49.27% of the density of cattle in Republica.
Find the I- and y-intercepts of the following equation: 2x + 3y = -24 Choose one · 1 point Oy, intercept: (0,8) intercept: (12,0) Oy- intercept: 0,-8) I - intercept: (-6,0) Oy- intercept : (0,8) I - intercept: (-12,0) Oy- intercept : (0,8) intercept: (-6,0)
The x-intercept and y-intercept are (-12,0) and (0,-8) for the equations is 2x+3y=-24.
Given that,
The equation of 2x+3y=-24
We must determine the equation's x-intercept and y-intercept.
In the cartesian coordinate system, the horizontal X-axis and the vertical 'Y-axis' are two perpendicular axes that make up the coordinate plane. The line's intercepts—where it crosses the two axes are referred to as.
We have to find x-intercept.
To find x-intercept take the y value as zero.
2x+3y=-24
2x+3(0)=-24
2x=-24
x=-24/2
x=-12
Now, To find y-intercept take x value as zero.
2x+3y=-24
2(0)+3y=-24
3y=-24
y=-24/3
y=-8
Therefore, The x-intercept and y-intercept are (-12,0) and (0,-8) for the equations is 2x+3y=-24.
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a survey about favorite sports. suppose 200 people were surved. how many more people favor soccer than swimming. 40% soccer 10% swimming 20%tennis 30%basketball
People surveyed P = 200
Then
40% soccer= 200x40/100= 80
10% swimming= 200x10/100= 20
20% tennis= 200x 20/100= 40
30% basketball= 200x 30/100= 60
))How many favor soccer than swimming?
= 80 - 20= 60
Then answer is 60 people
3. David’s watch broke. He decides to get it fixed instead of replacing it. Since David is a loyal customer, he received a coupon in the mail for a discount. The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair. Explain what each part of the expression represents in the context of the problem.
Please show work :)
What each part of the expression represents in the context of the problem include the following:
r represents the original cost of the repair.0.07r represents the tax.(r – 20) represents the discount.What is an algebraic expression?An algebraic expression is a mathematical equation that can be used for showing the relationship which exist between two or more variables, numerical quantities, as well as in conjunction with different mathematical operations.
What is a coefficient?In Mathematics, a coefficient simply refers to a constant numerical value (number or numeral) that written before the variable in any algebraic expression.
Given the following algebraic expression:
0.07r + (r – 20)
In the context of fixing David’s broken watch, the variable r represents the original cost of the repair while 0.07r most likely represents the amount of money charged as tax. Lastly the expression (r – 20) represents the discount on fixing David’s broken watch.
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