1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anit [1.1K]
3 years ago
15

E is the midpoint of DF⎯⎯⎯⎯⎯, DE=6x+1 and EF=7x−4. Find DE, EF, and DF

Mathematics
1 answer:
grandymaker [24]3 years ago
8 0

DE is 31 units, EF is 31 units and DF is 62 units

Step-by-step explanation:

A mid-point of a line segment

  • Divides it into two congruent parts
  • The length of each part is half the length of the line segment

∵ E is the mid-point of segment DF

- That means E divides DF into two parts DE and EF and the

   lengths of them are equal

∴ DE ≅ EF

∵ DE = 6x + 1

∵ EF = 7x - 4

- Equate them

∴ 6x + 1 = 7x - 4

- Add 4 to both sides

∴ 6x + 5 = 7x

- Subtract 6x from both sides

∴ 5 = x

Substitute the value of x in DE and EF to find their length

∵ DE = 6(5) + 1

∵ DE = 30 + 1

∴ DE = 31 units

∵ EF = 7(5) - 4

∴ EF = 35 - 4

∴ EF = 31 units

∵ DF = DE + EF

∴ DF = 31 + 31

∴ DF = 62 units

DE is 31 units, EF is 31 units and DF is 62 units

Learn more:

You can learn more about the mid-point in brainly.com/question/10480770

#LearnwithBrainly

You might be interested in
Simplify the sum: (5u^3+7u^2+7)+(7u^3-6u+5)
viktelen [127]
I hope you understand it

5 0
4 years ago
Three-fourths a number (b) divided by 5
Greeley [361]
3/28 because you need yo multiple
7 0
3 years ago
Read 2 more answers
One bread recipe calls for 2 1/3 cup of flour another bread recipe called for to 1/2 cup of flour Tim hair 5 cups of flour if he
yan [13]

Answer:

As per the statement:

One bread recipe calls for 2 1/3 cup of flour another bread recipe called for to 1/2 cup of flour .

First we calculate how much flour the two recipes combine call for, by adding the amount of flour needed for both the recipes:

⇒2\frac{1}{3}+\frac{1}{2}

⇒\frac{7}{3}+\frac{1}{2} = \frac{14+3}{6} = \frac{17}{6}

Tim would use \frac{17}{6} cup of flour for two recipe.

We have to find how much flour will he have left over.

Tim has 5 cup of flour.

Subtract 17/6 from 5

5-\frac{17}{6} = \frac{30-17}{6} = \frac{13}{6}= 2\frac{1}{2}

Therefore, Tim would have 2\frac{1}{2} left over.

7 0
4 years ago
Refer to the Teaching Psychology (May 1998) study of how external clues influence performance. Two different forms of a midterm
kozerog [31]

Answer:

P(X

P(Y

So for this case we have a higher probability for the red exam so we can conclude that the student is more likely to score below 20% on the difficult questions in the red one.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the scores for the blue exam, and for this case we know the distribution for X is given by:

X \sim N(53,15)  

Where \mu=53 and \sigma=15

We are interested in the probability that P(X<20%)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

And if we replace we got:

P(X

Let Y the random variable that represent the scores for the red exam, and for this case we know the distribution for X is given by:

Y \sim N(39,12)  

Where \mu=39 and \sigma=12

We are interested in the probability that P(Y<20%)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{y-\mu}{\sigma}

And if we replace we got:

P(Y

So for this case we have a higher probability for the red exam so we can conclude that the student is more likely to score below 20% on the difficult questions in the red one.

7 0
3 years ago
Use the intercept method to graph the equation y=-3
Strike441 [17]
What if I write the equation like this:
y = zero x - 3.
Now you know that the slope of the line is zero and its y-intercept is -3.
That's a horizontal line that crosses the y-axis at -3. And just like the equation says, the value of 'y' doesn't depend on 'x'. It's -3 everywhere.
6 0
3 years ago
Other questions:
  • 35 divided by 0.7 help me
    10·2 answers
  • Vivian is going to do some yard work, but she needs to leave her house at 1:00 to go to a football game. She is going to mow the
    8·2 answers
  • Bill has a set of 6 black cards and a set of 6 red cards. Each card has a number from 1 through 6, such that each of the numbers
    11·1 answer
  • How many solutions are there to the system of equations?
    6·2 answers
  • Arianna and Blair are working on a problem together: Solve x/3 + 8 = -2. Blair thinks the first step is to multiply by 3. Ariann
    13·2 answers
  • If -(x - 1) = 5, find the value of -4x. Show your work.<br> PLEASEEEE !!!
    14·1 answer
  • an examination ,60% of the candidates failed the number of candidates who passed was 500 .find the number that failed​
    5·1 answer
  • What is the value of the interior angle
    7·1 answer
  • How long of a ladder is needed to reach a window sill 50 feet above the ground if the ladder rests against the building making a
    8·1 answer
  • What is the difference?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!