The length of DP is:
DP=14 units
Step-by-step explanation:It is given that:
Point P is the midpoint of DE.
DP =3x + 2 and DE = 10x - 12.
We know that a midpoint divides the given line segment into two equal parts (i.e. it bisects a line segment)
Hence, we have:
DP+PE=DE
Also, DP=PE
This means that:
2DP=DE
2(3x+2)=10x-12
2×(3x)+2×2=10x-12
6x+4=10x-12
10x-6x=4+12
4x=16
x=16/4
x=4
Hence,
DP=3x+2=3×4+2
i.e.
DP=14
If 15.9 out of every 100 pregnant women in Georgia deliver their babies by C-section, how many pregnant women out of 25,250 would be expected to deliver by C-section?
I really don't understand this absolute value. please help
James thinks they could have paddled down the river in 5 days. If they had pushed their limits. How many miles per day would they have had to paddle to finish the trip in 5 days.
Change the order and the grouping of the addends so that you can use mental math to find the sum. Then find the sum. 43+39+43+11=
Final answer:
By applying the commutative property of addition and rearranging the numbers for easier mental calculation, the sum of 43 + 39 + 43 + 11 can be found to be 136.
Explanation:
The question asks to change the order and the grouping of the addends for easier mental calculation, and then to find the sum of 43 + 39 + 43 + 11. By understanding the commutative property of addition, which states that numbers can be added in any order without changing the sum, we can rearrange these numbers for easier addition.
To use mental math effectively, grouping numbers that make round numbers or those that are easier to add can simplify the process. Here, we can group 43 and 43, which are identical, and 39 and 11, which sum up to a round number.
Therefore, by rearranging:
43 + 43 = 86
39 + 11 = 50
Adding these sums together:
86 + 50 = 136
By changing the order and grouping of the addends, we find that the sum is 136.
1. Is it possible for a composite number to have more than one prime factorization? Is it possible for a number to have no prime factors? Why?
2.Give and example of how prime factorization could be used in the real world
in which square is 25% not shaded
-4+6(-4x+3) combining like terms & distributive property
The table shows the earnings and the number of hours worked if three employees . Complete the table by finding the missing values . Which employee earned the least per hour ? EXPLAIN.
of the 150 people surveyed seven out of 10 said they owned at least one pet how many of the people surveyed owned pets
how is 2.25 written as a fraction
What is the answer to -1 = 5+x divided by 6
A water cooler fills 150 glasses in 30 minutes. How many glasses of water can the cooler fill per minute?
Avery and her friends attend a museum. It costs $5 to enter the main exhibit hall, with an added charge of $3 to view each special exhibit. Avery writes an equation that models the total price of visiting the museum as a function of the number of special exhibits they view. What is the slope and y-intercept of Avery’s model?
Hence, slope = 3 and, y-intercept = 5.
What is function?
Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
Here, given that,
Avery and her friends attend a museum. It costs $5 to enter the main exhibit hall, with an added charge of $3 to view each special exhibit.
Avery writes an equation that models the total price of visiting the museum as a function of the number of special exhibits they view.
Now, let the function be,
f(x)= 3x+5 = the total price of visiting the museum
[where, x= special exhibit & 5=the main exhibit hall]
Let, y = f(x)
So, w get, y=3x+5
Hence, slope = 3
and, y-intercept = 5.
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Which is the best estimate for the sum of 31,096 and
58,721?
The teacher separated her class of twenty-eight student into two group. one group has 4 more than twice as many students as the other group. how many students are in each group?
Find the value of y if B is between A and C, AB is 2y, BC is 6y, and AC is 48.
a) 6
b) 4
c) 24
d) 8
The value of y is 6 and this can be determined by using the arithmetic operations and the given data.
Given :
B is between A and CAB is 2y, BC is 6yAC is 48The following steps can be used in order to determine the value of y:
Step 1 - The arithmetic operations can be used in order to determine the value of y.
Step 2 - According to the given data, B is between A and C.
Step 3 - The mathematical expression of the above expression is:
AC = BC + AB
Step 4 - Now, substitute the value of the known terms in the above expression.
48 = 6y + 2y
Step 5 - Simplify the above expression.
48 = 8y
y = 6
Therefore, the correct option is a).
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ax-x=c
solve the equation for x
X to 2nd power equals 9/256
4,444,444 the digit in the hundreds thousands place is 10 times the value of the digit in the ten thousands place?
(3 – 6y2)(y2 + 2) what is this
What is 40/3 simplified
Study the number 31,342. How many times less is the three in the hundreds place as compared to the three in the 10,000 place?
An airplane can travel at a speed of 550 mph. Write and solve an equation to find the time it will take to fly from London to Montreal, a distance of approximately 3300 miles
The time it will take for an airplane to fly from London to Montreal at a speed of 550 mph covering a distance of 3300 miles is approximately 6 hours.
Explanation:To find the time it will take for an airplane to fly from London to Montreal, we can use the equation for speed, which is:
Speed = Distance \u00f7 Time
Knowing that the plane can travel at a speed of 550 mph and the distance from London to Montreal is 3300 miles, we can rearrange the equation to solve for time:
Time = Distance \u00f7 Speed
Time = 3300 miles \u00f7 550 mph
After calculating, we find that:
Time = 6 hours
Therefore, it will take the airplane approximately 6 hours to fly from London to Montreal at a constant speed of 550 mph, ignoring any other factors such as wind or air traffic delays.
To find the time it will take, we can use the formula Time = Distance/Speed. In this case, it will take approximately 6 hours to fly from London to Montreal.
Explanation:To find the time it will take to fly from London to Montreal, we can use the formula Time = Distance/Speed. In this case, the distance is approximately 3300 miles and the speed is 550 mph.
Plugging in the values into the formula, we get Time = 3300 miles / 550 mph = 6 hours. So, it will take approximately 6 hours to fly from London to Montreal.
Therefore, the time it will take to fly from London to Montreal is 6 hours.
<ABD has a measure of 36 degrees. a)find the compliment of the angle b)find the supplement of that angle
A crane cable can support a maximum load of 17,000 kg. If a bucket has a mass of 4,000 kg and gravel has a mass of 1,500 kg for every cubic meter, how many cubic meters of gravel (g) can be safely lifted by the crane? Enter any fractions as reduced improper fractions.
if you forget to bring the book back to the library, you will pay a fine. is this a negation, conjunction, disjuntion, conditional or biconditional?
The sentence is a conditional statement where the payment of a fine depends on forgetting to return the book. Hence the correct option is Option 4 , conditional
The sentence 'if you forget to bring the book back to the library, you will pay a fine' is a conditional statement. In logic and English grammar, a conditional statement is one where the outcome (the consequent) depends on a certain condition (the antecedent). Here, the antecedent is 'if you forget to bring the book back to the library', and the consequent is 'you will pay a fine'. The structure of this sentence follows the 'if (condition), then (result)' pattern typical of standard conditionals.
For example:
If it rains, the picnic will be canceled.If you study hard, you will pass the exam.In both examples and the original sentence, the outcome is contingent on the condition being met, which is the hallmark of a conditional statement.
Please help me with my math homework! 20 points!
A culture of 1.08×10^15 bacteria is in petri dish A. A culture of 2.7×10^11 bacteria is in petri dish B.
How many times greater is the number of bacteria in petri dish A than petri dish B?
Enter your answer, in standard notation, in the box.
To find the number of times the bacteria in petri dish A than petri dish B, let us divide.
So, number of times = [tex]\frac{Number of times bacteria in petri dish A}{Number of times bacteria in petri dish B}[/tex]
[tex]= \frac{1.08(10^{15} )}{2.7(10^{11} )}[/tex]
= 0.4 × [tex]10^{4}[/tex]
= 4000
Hence, the number of bacteria in petri dish A is 4000 times the number of bacteria in petri dish B.
How many shapes are in the world
Quinn runs 3 miles 3 times every week. How many miles does Quinn run in 6 weeks
What is the value of the expression 3^−4 ?
The required simplified value for the expression [tex]3^{-4}[/tex] is 1 / 81.
Given that,
To determine the simplified value of the expression [tex]3^{-4}[/tex] .
The process in mathematics to operate and interpret the function or expression to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
[tex]3^{-4} = 1/3^4[/tex]
3 * 3 * 3 * 3 = 9 * 9 = 81
[tex]3^{-4} = 1 / 81[/tex]
Thus the required simplified value for the expression [tex]3^{-4}[/tex] is 1 / 81.
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