Given: KLMN is a trapezoid, m∠N=m∠KML, FD=8, LM KN = 3 5 F∈ KL , D∈ MN , ME ⊥ KN KF=FL, MD=DN, ME=3 5 Find: KM

D) The function g(x) has a larger slope

The change between any two y-coordinates in g(x) is greater than any change in the y-coordinates in f(x)

Answer:

The area of △MNP is one fourth of the area of △ABC.

Step-by-step explanation:

It is given that the points M, N, and P are the midpoints of sides AC, BC and AB respectively. It means AC, BC and AB are median of the triangle ABC.

Median divides the area of a triangle in two equal parts.

Since the points M, N, and P are the midpoints of sides AC, BC and AB respectively, therefore MN, NP and MP are midsegments of the triangle.

Midsegments are the line segment which are connecting the midpoints of tro sides and parallel to third side. According to midpoint theorem the length of midsegment is half of length of third side.

Since MN, NP and MP are midsegments of the triangle, therefore the length of these sides are half of AB, AC and BC respectively. In triangle ABC and MNP corresponding side are proportional.

[tex]\triangle ABC \sim \triangle NMP[/tex]

[tex]MP\parallel BC[/tex]

[tex]MP=\frac{BC}{2}[/tex]

By the property of similar triangles,

[tex]\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{PM^2}{BC^2}[/tex]

[tex]\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{(\frac{BC}{2})^2}{BC^2}[/tex]

[tex]\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{1}{4}[/tex]

Hence proved.

The area of triangle MNP is one-fourth that of triangle ABC, because M, N, and P are midpoints leading to the smaller triangle being similar to the larger, and thus their area ratio due to the proportional side lengths is 1:4.

In Mathematics, proving that the area of △MNP is a fourth of that of △ABC involves the concept of similar triangles and their properties. We know that M, N, and P are the midpoints of BC, AC, and AB. Due to this, triangle MNP is similar to triangle ABC as per the Midpoint theorem. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. In this case, the ratio of the sides would be 1:2 (since M, N, P are midpoints).

Therefore, the ratio of their areas (△MNP:△ABC) would be (1⁄2)², which is 1/4. Hence, the area of △MNP is one-fourth of the area of △ABC.

This clearly demonstrates that the area of the smaller triangle formed by the midpoints of a larger triangle equates to a fourth of the total area of the initial triangle.

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Answer:

P(A ∩ B) = 0.75 (option d)

Step-by-step explanation:

P(A)=0.50

P(B)=0.40

P(A U B)=0.15

P(A ∩ B)=?

P(A U B)=P(A)+P(B)-P(A ∩ B)

Replacing the given values:

0.15=0.50+0.40-P(A ∩ B)

Adding like terms:

0.15=0.90-P(A ∩ B)

Solving for P(A ∩ B):

Subtracting 0.90 both sides of the equation:

0.15-0.90=0.90-P(A ∩ B)-0.90

Subtracting:

-0.75 = -P(A ∩ B)

Multiplying both sides of the equation by -1:

(-1)(-0.75) = (-1) ( -P(A ∩ B) )

0.75 = P(A ∩ B)

P(A ∩ B) = 0.75

Answer:

d=0.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\int 3x(x^2+3)^4 \ dx[/tex].

It is apparently obvious we could expand the bracket and integrate term-by-term. This method would work but is very time consuming (and you could easily make a mistake) so we use a different method: integration by substitution.

Integration by substitution involves swapping the variable [tex]x[/tex] for another variable which depends on x: [tex]u(x)[/tex]. (We are going to choose [tex]u[/tex] for this question).

The very first step is to choose a suitable substitution. That is, an equation [tex]u=f(x)[/tex] which is going to make the integration easier. There is a trick for spotting this however: if an integral contains both a term and it's derivative then use the substitution [tex]u=\text{The Term}[/tex].

Your integral contains the term [tex]x^2 + 3[/tex]. The derivative is [tex]2x[/tex] and (ignoring the constants) we see [tex]x[/tex] is also in the integral and so the substitution [tex]u=x^2+3[/tex] will unravel this integral!

Step 2: We must now swap the variable of integration from x to u. That means interchanging all the x's in the integrand (the term being integrated) for u's and also swapping (dx" to "du").

[tex]u=x^2+3 \Rightarrow \frac{du}{dx}=2x \Rightarrow dx = \frac{1}{2x} du[/tex]

Then,

[tex]\int 3x(x^2+3)^4 \ dx = \int 3x \cdot u^4 \cdot \frac{1}{2x} du = \int \frac{3}{2}u^4\ du[/tex].

The substitution has made this integral is easy to solve!

[tex]\int \frac{3}{2}u^4\ du= \frac{3}{10}u^5 + C[/tex]

Finally we can substitute back to get the answer in terms of x:

[tex]\int 3x(x^2+3)^4 \ dx = \frac{3}{10}(x^2+3)^5+C[/tex]

[tex]|a|<b\iff a< b\ and\ a > -b\\\\|a|>b\iff a>b\ or\ a<-b[/tex]

[tex]-2|3-2r|<-34\qquad\text{change the signs}\\\\2|3-2r|>34\qquad\text{divide both sides by 2}\\\\|3-2r|>17\iff3-2r>17\ or\ 3-2r<-17\qquad\text{subtract 3 from both sides}\\\\-2r>14\ or\ -2r<-20\qquad\text{change the signs}\\\\2r<-14\ or\ 2r>20\qquad\text{divide both sides by 2}\\\\\boxeD{r<-7\ or\ r>10}[/tex]

Answer:

The correct answer on Odyssey is Ellipse

Step-by-step explanation:

I got it correct on Odyssey

Answer:

12/35

Step-by-step explanation:

"2fifth" = 2/5

"6seventh" = 6/7

"times" = *

Multiply across:

(2/5) * (6/7) = 12/35

12/35 is your answer

~

Answer:

12/35

Step-by-step explanation:

2/5 times 6/7

First multiply the numerators.

2 x 6 = 12

Then multiply the denominators.

5 x 7 = 35

Your answer is 12/35

balance = $360

2% of balance = 0.02*360 = 7.20

Since $10 is larger than $7.20, this means the min monthly payment is $10

Answer: 10

simplify to get 1/3 times 17/4 which simplifies to 17/12 or 1 and 5/12.

Answer:

17/12

Step-by-step explanation:

1/3 x 4 1/4 change to

1/3 x 17/4

multiply the top and then the bottom : 17/12

Answer:

It would be C

Answer:

$1.02

Step-by-step explanation:

9.25+4.35=13.60

13.60X0.075=1.02

Tax= 1.02

Answer:

$1.02

Step-by-step explanation:

$9.25+$4.35=$13.60

7.5----0.075

$13.60 times 0.075

$1.02

To add tax you take the decimal and move it to the left 2 times,

example: 6%---- .06

you then would multiply .06 by the price to get the price of the tax.

Answer:

49.5

Step-by-step explanation:

76-42+65 is 99, the you divide by 2, and that is 49.5

Answer:

I graphed it and u can find the two solutions :)

Step-by-step explanation:

Answer: the answer is C . 19.5 units - APEX :D

Answer:

Answer is 19.5 units

Step-by-step explanation:

Given that there is a trapezoid.

Its bases are 13 and 26 respectively.

Non parallel sides are congruent

To find the median that is the length of line connecting the midpoints of the non parallel sides

If we draw any one diagonal we see that median is the line connecting the mid point of two triangles with the parallel sides as bases

Hence length of median= 1/2 (base 1+base 2)

(By triangle mid point theorem)

= 1/2 (13+26)

=19.5 units

Answer:

The slope is -1/3

Step-by-step explanation:

We can find the slope of a line using the formula

m = (y2-y1)/(x2-x1)

  = (2-3)/(3-0)

  = (-1/3)

  =-1/3

Answer:

m= -1/3

Step-by-step explanation:

Slope is determined from the formula:

y2-y1/x2-x1

Input the corresponding numbers in the formula.

2-3/3-0

-1/3

m= -1/3

Answer:

A discrete graph

Step-by-step explanation:

It would make sense because you can track the distances on the coordinate plane

Answer:

The first graph or A.

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

The correct option is A. (F(x)=-x^{7}+4x^{3}-2x^{2}). This function matches all the key properties observed in the graph.

Sure, I've analyzed the image you sent and I can help you determine the correct option.

Based on the graph, we can see that it has the following properties:

It has three turning points, one minimum point and two maximum points.

The end behavior as x approaches positive or negative infinity is that the function increases without bound.

It intersects the x-axis three times.

Let's analyze the answer choices based on these observations:

This function has an odd leading term, which aligns with the increasing end behavior.

It has three factors, matching the number of x-intercepts.

By graphing this function, we can see that it matches the shape of the given graph with a minimum point followed by two maximum points.

This function has an even leading term, which does not align with the increasing end behavior.

Even though it has four factors, it intersects the x-axis only twice.

This function has an odd leading term, which aligns with the increasing end behavior.

However, it only has two factors, not matching the three x-intercepts of the graph.

This function has an even leading term, which does not align with the increasing end behavior.

It also only has two factors, not matching the three x-intercepts of the graph.

We have the supplementary angles.

The sum of the measures of the two Supplementary Angles is 180°.

Therefore we have the equation:

13x - 2 + 39 = 180

13x + 37 = 180     subtract 37 from both sides

13x = 143      divide both sides by 13

x = 11

Answer:

Where is the diagram

Step-by-step explanation:

Answer:

36 ft

Step-by-step explanation:

So the proportion of the big triangle is 48:4 or 12:1. So if the small triangle’s height is 3 feet, then 3*12 is 36 feet.

Answer: 36 ft

Step-by-step explanation:

Similar triangles means there is a constant proportion between the left legs, the base legs, and the hypotenuses.

[tex]\frac{LeftLeg(large)}{LeftLeg(small)}= \frac{BaseLeg(large)}{BaseLeg(small)}[/tex]

                  [tex]\frac{x}{3}= \frac{48}{4}[/tex]

Cross multiply: x(4) = 3(48)

solve for x:        ÷4     ÷4    

                          x    =  3(12)

                                =  36

The student that solved at a rate of 28 per minutes was Logan

Answer:

Logan

Answer:

Logan solved problems at a rate of 28 problems per minute.

Step-by-step explanation:

To find the number of problems per minute that a person solved, you will divide the number of problems that they solved by the number of minutes that they took.

Murray:

58 problems in 2 minutes,

58 / 2 = 29

He solved problems at a rate of 29 problems per minute.

Kris:

78 problems in 3 minutes,

78 / 3 = 26

He solved problems at a rate of 26 problems per minute.

Logan:

84 problems in 3 minutes,

84 / 3 = 28

He solved problems at a rate of 28 problems per minute.

Since you found that Logan solved problems at a rate of 28 problems per minute, Logan is the student that solved problems at a rate of 28 per minute.

The SSE for the data set is:  24

The data points are given by:

        (3,6),(6,2),(9,10)

The data points are as follows:

when x=3   y=6

when x=6   y=2

and when x=9   y=10

Also, the line of best fit is as follows:

[tex]y=\dfrac{2}{3}x+2[/tex]

The SSE( sum of square for error ) is calculated as follows:

when x=3

from the line of best fit we have: y=4

when x=6

then y=6

when x=9

then y=8

when x=3        6-4= -2

when x=6       2-6= -4

and when x=9      10-8=2

Hence, the square of these difference quantity is:

(-2)²=4

(-4)²=16

and (2)²=4

Hence, the sum of these square quantity is: 4+16+4=24

Hence, the SSE of data is:  24

Final answer:

An acrostic poem for the word 'percent' is crafted with each line pertaining to the process and concept of calculating percents, expressed as a part of 100, or ratios with a denominator of 100.

Explanation:

An acrostic poem for the word percent could be:

Perusing numbers, calculations at hand,

Every figure is neatly planned.

Ratios and fractions - they all fit,

Calculations to make you think a bit.

Each part of a hundred, clearly set,

Numerical values that we get,

Twenty, fifty, seventy-five, all to percent we convert and drive.

This acrostic poem takes the word percent and creates a line for each letter that relates to the concept of percentages, which are ratios with a denominator of 100. Calculating percents involves setting up equivalent fractions or converting to decimals and fractions for ease of use in various mathematical situations. An understanding of this concept is essential for mathematical proficiency.

Answer:

I.3 is the answer

Answer:

It would be 1.30

Step-by-step explanation: It would be 1.3 because to round up it has to be over 5 and to round down it has to be under 5. So in this case it is 28 and 8 is over 5, so you would round to the nearest tenth which would be 1.30.

10b+6=7b-6.

3b=-12

b=-4.

*Note that you can just divide by 12 on both sides to simplify the equation.

Answer: 20% off sale because Daisey will have to pay a total of 72

Step-by-step explanation:

Answer:

4 - x

Step-by-step explanation:

product means multiply

the product of 1 and x = 1 × x = x

This is then subtracted ( minus ) from 4 giving

4 - x ← expression representing the situation

Answer:

2*4-6

Step-by-step explanation:

Answer:

c ÷ 7 + 5 = 8

Step-by-step explanation:

The Translate the sentence into an equation is c/7 +5 =8.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

given variable is given as c therefore, the translation of the given equation  Five more than the quotient of a number and 7 is equal to 8 will be :

c/7 +5 =8

Therefore, the Translate the sentence into an equation is c/7 +5 =8.

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Answer:  Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.

Step-by-step explanation:

Given : ABCD is a parallelogram.

That is, AB ║ CD and AD ║BC

We have to prove that: AB≅CD and AD≅BC

Proof:

Construct diagonal AC in the parallelogram ABCD.

Since, AC ≅ AC ( reflexive)

∠ BAC ≅ ∠ DCA  ( By the alternative interior angle theorem)

∠ BCA ≅ ∠ DAC   ( By the alternative interior angle theorem)

⇒ Δ BCA ≅ Δ DAC ( By ASA congruence postulate )

⇒ AB≅CD as well as AD≅BC ( BY CPCTC )

Thus, the opposite side of the parallelogram are congruent.

Diagonal AC is congruent to itself by the Reflexive Property of Equality.