If triangle ABC is similar WXY write a proportionality statement for the ratio of the sides of the triangle

Below is an image of what you have described. Since EF intersects GH perpendicularly - all resulting angles will be 90° by the definition of intersection of perpendicular lines.

This is to say that, Angle GDE, GDF, HDF, and HDE are all 90° angles.

Answer:

Where is the diagram

Step-by-step explanation:

Answer:

It is rational

Step-by-step explanation:

The pi terms cancel out when you divide. This is due to the rule x/x = 1 where x is any number you want except x cannot be zero. So replace x with pi and we have pi/pi = 1

Therefore,

(3pi)/(2pi) = (3/2)*(pi/pi)

(3pi)/(2pi) = (3/2)*1 .... use the rule mentioned above

(3pi)/(2pi) = 3/2

we get a fraction or a ratio of two whole numbers, so this proves that the given expression is rational.

Check out the attached image below. I've marked two red points on the line such that the points have whole number coordinates. This way I could compute the slope of this line to be -2/5

We move down 2 units (rise of -2) as shown by the blue arrows. Afterward, we move 5 units to the right as shown by the green arrows (which is the run). This gets us from the left red point to the right red point.

rise = -2, run = 5

slope = rise/run = -2/5

the original line shown has a slope of -2/5

----------------------------

Next we do two things to get the perpendicular slope.

Flip the fraction: -2/5 becomes -5/2

Flip the sign: -5/2 becomes +5/2 or simply 5/2

----------------------------

Final Answer: 5/2

Answer:

Step-by-step explanation:

You have to use Point Slope Form:

About Problem:

y - Y1 = m (x - X1)

y - -1 = -2/3 (x - -3)  ---- This is in Point Slope Form

If you want to solve it, & put it in Slope Intercept form, it would look like this:

y = mx + b

y = -2/3 - 2 --- This is in Slope intercept Form.... I might've solved it wrong... I'm not sure...

Really really sorry if I'm incorrect...

Answer:  The required equation of the line is [tex]2x+3y+9=0.[/tex]

Step-by-step explanation:  We are given to find the equation of a line that has a slope of [tex]-\dfrac{2}{3}[/tex] and passes through point (-3,-1).

SLOPE-INTERCEPT FORM :

The equation of a line having slope m and passing through the point (a, b) is given by

[tex]y-b=m(x-a).[/tex]

For the given line, we have

[tex]m=-\dfrac{2}{3},\\\\\\(a,b)=(-3,-1).[/tex]

Therefore, the equation of the line is given by

[tex]y-b=m(x-a)\\\\\Rightarrow y-(-1)=-\dfrac{2}{3}(x-(-3))\\\\\\\Rightarrow y+1=-\dfrac{2}{3}(x+3)\\\\\Rightarrow 3y+3=-2x-6\\\\\Rightarrow 2x+3y+9=0.[/tex]

Thus, the required equation of the line is [tex]2x+3y+9=0.[/tex]

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:

The temperature change per hour was -3 degrees per hour.

Step-by-step explanation:

We know that the temperature fell from [tex]0[/tex] degrees to [tex]-6\frac{3}{5}[/tex] degrees in a time period of [tex]2\frac{1}{5}[/tex] hours.

So to find the rate of change of the temperature, we will divide the change in temperature by the number of hours.

For that, we will change the mixed number into improper fractions and then solve:

[tex]-6\frac{3}{5}=-\frac{33}{5}degrees[/tex]

[tex]2\frac{1}{5}=\frac{11}{5} hours[/tex]

Temperature change per hour = [tex]\frac{-\frac{33}{5}}{\frac{11}{5}} = \frac{33}{5}*-\frac{5}{11}=-3[/tex]

Therefore, the temperature change per hour was -3 degrees per hour.

Answer:

Dan drove 23.7 miles each trip.

Step-by-step explanation:

If he drove a total of 71.10 miles in three trips and you are trying to find how many miles he drove each trip then you would divide the total miles by the number of trips. You would do, 71.10/3 which is equal to 23.7, which is your answer.

Hope this helps!

Answer:

132600

Step-by-step explanation:

I was always taught like this, and this should be the best estimate:

28 x 4417 --> 30 * 4420 --> 132600

Some other possible estimates with simpler values:

30 * 4400 --> 132000

30 * 4500 --> 135000

30 * 4000 --> 120000

Answer:

3/8

Step-by-step explanation:

there are 6 outcomes with two heads and two tails, and 16 total outcomes. 6/16=3/8

The probability of getting the same number of heads and tails is 3/8

The sample space (S) is given as:

S = {HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT}

The outcomes (E) that the number of heads and tail are the same is

E = {HHTT HTHT HTTH THHT THTH TTHH}

The probability of getting the same number of heads and tails is then calculated as:

[tex]Pr = \frac{n(E)}{n(S)}[/tex]

So, we have:

[tex]Pr = \frac{6}{16}\\[/tex]

Simplify

[tex]Pr = \frac{3}{8}[/tex]

Hence, the probability of getting the same number of heads and tails is 3/8

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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)

[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:

$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.

The solutions to the absolute value equation |y-9|=6 are y= 15 and y= 3. These values make the original equation true.

The mathematical question asked is: |y-9|=6. This represents an absolute value equation. In an absolute value equation, the quantity inside the absolute value brackets can either equal the positive or negative value on the other side of the equation. Therefore, you can create two separate equations out of this original equation: y-9 = 6 and y-9 = -6. Solving for y in these equations will give you the answers: y = 15 and y = 3.

So, the solutions to the absolute value equation are y = 15 and y = 3. These results mean that if y equals either 15 or 3, the original equation will hold true.

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The absolute value equation |y-9|=6 has two solutions: y= 15 and y= 3. The original equation is true with these values.

The |y-9|=6 is the mathematical question. This is an absolute value equation. The quantity inside the absolute value brackets in an absolute value equation can either equal the positive or negative value on the other side of the equation. As a result, you can deduce two independent equations from this original one: y-9 = 6 and y-9 = -6. Solving for y in these equations yields the following results: y = 15 and y = 3.

As a result, the absolute value equation answers are y = 15 and y = 3. These findings imply that the original equation will be true whether y equals either 15 or 3.

Answer:

The answer is y=1.4x

Step-by-step explanation:

You have to find the change of y over the change of x. So you have to find how much each value is changing by.

Y-side

5.6-2.8= 2.8

8.4-5.6=2.8

11.2-8.4=2.8

X-side

4-2=2

6-4=2

8-6=2

If you divide 2.8 by 2 you get 1.4

So the slope is 1.4

The idea is to pair up the terms, factor each sub-group, and then pull out the overall GCF to fully factor.

x^3+5x^2-6x-30

(x^3+5x^2)+(-6x-30)

x^2(x+5)+(-6x-30)

x^2(x+5)-6(x+5)

(x^2-6)(x+5)

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Answer: (x^2-6)(x+5)

Answer:

D) were laws passed by mainly Southern states to keep African Americans in a system of virtual slavery.

Step-by-step explanation:

The Black Codes were created by the Southern States and were extremely similar to slavery, in which the African Americans were not allowed many of their newly gotten rights, such as a right to education, voting, etc, and the African Americans had to endure a lot of codes that were created to make them feel inferior.

~

Answer:  D) were laws passed by mainly Southern states to keep African Americans in a system of virtual slavery.

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.

Point slope form?

Y- 10 = -6 ( X + 1 )

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:5

Step-by-step explanation:

Answer:

$ 5.25 per liter

Step-by-step explanation:

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:

[tex]d =30g[/tex]

Step-by-step explanation:

Sam drives his car at a constant speed. He travels a distance (d) of 15 miles with 1/2 of a gallon of gas (g)

Distance d= 15

Gallons of gas (g)= 1/2

Equation is d= rg

Now plug in the values

15 = r* 1/2

Now we divide by 1/2 on both sides

[tex]r=\frac{15}{\frac{1}{2}}=15 * \frac{2}{1}= 30[/tex]

r=30

Now we replace the value of 'r' in the equation d=rg

[tex]d = 30g[/tex]

Answer:

Step-by-step explanation:

i know it'

convert 2 1/4 into improper fraction or do it as same as it is

So, this is ratio and proportion. so, multiply 2 1/4 or 2.25 to 8 and divide it to 5. so, the answer is 3.6 or 3 3/5.

The simplification of the given expression is obtained as 1/216.

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

The given expression is 6⁻³.

It can be simplified as below,

Rewrite the given expression as,

6⁻³ = ((6)⁻¹)³

Now, (6)⁻¹ = 1/6

⇒ 6⁻³ = (1/6)³

⇒ 1/6 × 1/6 × 1/6 = 1/216

Hence, the given expression can be simplified as 1/216.

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Answer:

The equation of the line would be y = 3x - 8

Step-by-step explanation:

To find any equation when you have the slope and a point, start with point-slope form and then solve for y.

y - y1 = m(x - x1)

y - 1 = 3(x - 3)

y - 1 = 3x - 9

y = 3x - 8

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:

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.