Point A is located at (1, 10) and point B is located at (20, 18).

What point partitions the directed line segment ​ AB⎯⎯⎯⎯⎯ ​ into a 2:5 ratio?



(1025, 22)

(737, 1557)

​(637, 1227)​

​(5, 1715)​

Since all triangles in these questions are similar, we use that the ratios of corresponding sides are equal

(1)

[tex]\frac{y}{6}[/tex] = [tex]\frac{9}{x}[/tex] = [tex]\frac{5}{4}[/tex]

solving [tex]\frac{9}{x}[/tex] = [tex]\frac{5}{4}[/tex] ( cross-multiply )

5x = 36 ( divide both sides by 5 )

x = [tex]\frac{36}{5}[/tex]

solving [tex]\frac{y}{6}[/tex] = [tex]\frac{5}{4}[/tex]

4y = 30 ⇒ y = [tex]\frac{15}{2}[/tex]

(2)

let h be the height of the flagpole, then

[tex]\frac{h}{5.5}[/tex] = [tex]\frac{50}{4}[/tex]

4h = 275 ⇒ h = 68.75 feet

(3)

[tex]\frac{x}{6}[/tex] = [tex]\frac{93.5}{12.75}[/tex]

12.75x = 561 ⇒ x = 44 feet

Answer:

Copy the second line segment with one endpoint at the same endpoint of the first line segment.

c is correct a is wrong

Answer:

Option A : copy the angle

Step-by-step explanation:

We can see that to make congruent triangles he first copied the segments

He copied the segment and drew segment FG

Then he copied the length of BH  and then keeping compass on point F cut the line segment FG at I

Then he measured the angle ABC and then intersect the previous arc at J

So, we can see that he just copied the angle

So, his recent completed step was copy the angle .

So, Option A is correct

Hence Option A copy the angle is true .

Assuming that you meant "11 plus 1/6" written as the equivalent decimal expression, then it'd be 11.16666....     Here the 6 repeats indefinitely.

C'(2, 3 )

under a counterclockwise rotation about the origin

a point (x, y ) → (- y, x ) hence

C(3, - 2 ) → C'(2, 3 )

Answer:

C' (2, 3)

Step-by-step explanation:

Remember that when you are rotating something 90 degrees and counter clockwise you just need to interchange the X and Y values, and change the value of the new X to a negative position because it woul be located in the second quarter:

(x,y) rotated 90º counter clockwise= (-y,x)

(3,-2)=(-(y),x)=(-(-2),(3)=(2,3)

So the answer would be C' (2, 3)

The numbers are a bit ugly, but the equation can be solved as is.

... 1.2x/3.6 + (0.2/3.6) = 0.5x/9 . . . . use the distributive property on the left

... x(1/3 -1/18) + 1/18 = 0 . . . . . subtract the right side, simplify fractions

... x(6/18 -1/18) = -1/18 . . . . . . . use 18 for common denominator

... 5x = -1 . . . . . . . . . . . . . . . . . multiply by 18

... x = -1/5 . . . . . . . . . . . . . . . . divide by 5

_____

You can eliminate decimals and fractions by multiplying the given equation by 18.

... 6x +1 = x

... 5x +1 = 0

... 5x = -1

... x = -1/5

_____

The fraction simplification can work like this:

... 0.2/3.6 = 2/36 = 1/18

... 0.5/9 = (1/2)/9 = 1/(2·9) = 1/18 . . . . or . . . . (0.5)/9 × (2/2) = (0.5·2)/(9·2) = 1/18

Answer:

x=-0.2

Step-by-step explanation:

The given equation is

[tex]\frac{0.2(6x+1)}{3.6}=\frac{0.5x}{9}[/tex]

We need to solve the given equation for x.

On cross multiplication we get

[tex]9[0.2(6x+1)]=3.6(0.5x)[/tex]

[tex]1.8(6x+1)=1.8x[/tex]

Using distribution property, we get

[tex]1.8(6x)+1.8(1)=1.8x[/tex]

[tex]10.8x+1.8=1.8x[/tex]

Subtract 1.8x and 1.8 from both sides.

[tex]10.8x+1.8-1.8x-1.8=1.8x-1.8x-1.8[/tex]

[tex]10.8x-1.8x=-1.8[/tex]

[tex]9x=-1.8[/tex]

Divide both sides by 9.

[tex]x=-\frac{1.8}{9}[/tex]

[tex]x=-0.2[/tex]

Therefore, the value of x is -0.2.

since both points have a y- coordinate of zero, this is a horizontal line parallel to the x- axis

hence slope = 0

We want to find the slope of a line given that we know two points on the line.

We will see that the slope of the line is 0.

Generally, if we know that a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we know that the line passes through (-4, 0) and (2, 0) then the slope will be:

[tex]a = \frac{0 - 0}{2 - (-4)} = 0[/tex]

The slope is equal to zero, meaning that this is a horizontal line (as you can see in the points, the y-component does not change).

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Filling in 16 for a, we have ...

... lower limit ≤ heart rate ≤ upper limit . . . . . . . this is the meaning of upper and lower limits

... 0.5×(220 -16) ≤ heart rate ≤ 0.9×(220 -16) . . . . . substitute given expressions

... 0.5×204 ≤ heart rate ≤ 0.9×204 . . . . . . . . . . . . . begin expression evaluation

... 102 ≤ heart rate ≤ 183.6

Answer:

204 students

just do 7140/35= 204

Step-by-step explanation:

Number of students who can get craft sticks are 204 .

To determine how many students can get craft sticks from the teacher, we need to divide the total number of craft sticks by the number of craft sticks each student needs.

Step-by-Step Solution

The total number of craft sticks is 7,140.

Each student needs 35 craft sticks.

To find out how many students can get the craft sticks, divide the total number of craft sticks by the number of craft sticks each student needs:

7,140 ÷ 35 = 204

Therefore, 204 students can get craft sticks from the teacher.

Estimation and Checking

To estimate the quotient, you can round the numbers to make the division easier. For example, round 7,140 to 7,000 and 35 to 30:

7,000 ÷ 30 ≈ 233.33

This estimation tells us that our division answer is reasonable, falling close to this rounded solution.

To check the division, multiply the quotient by the divisor and see if you get the original dividend:

204 × 35 = 7,140

Since the result matches the original number of craft sticks, the answer is verified as correct.

the correct answer is 63 because they are multiplying the length of each side by 7.

Answer: Option 'd' is correct.

Step-by-step explanation:

Since we have given two figures:

John's design is similar to Josh's project.

ML = 8 inches

CD = 56 inches

KL = 9 inches

We need to find value of 'BC'.

So, there ratio would be :

[tex]\dfrac{ML}{CD}=\dfrac{KL}{BC}\\\\\dfrac{8}{56}=\dfrac{9}{BC}\\\\\dfrac{1}{7}=\dfrac{9}{BC}\\\\BC=9\times 7\\\\BC=63\ inches[/tex]

Hence, Option 'd' is correct.

let a,b be the two numbers. we know that a2-b2=5 and a*b=6

using the formula we are given

[tex](a^2+b^2)^2 = 5^2 + 12^2 = 169[/tex] we get the solution [tex]\sqrt{169} = 13[/tex]

Answer:

13

Step-by-step explanation:

Let x and y are two numbers. The difference of the squares if the two numbers is 5 and the product of the numbers is 6 such that,

[tex](x^2-y^2)=5[/tex]......................(1)

[tex]xy=6[/tex]..........(2)

We need to find the sum of the squares of two numbers. By using following identities it can be calculated as :

[tex](x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2[/tex]

Using equation (1) and (2) in above equation, we get :

[tex](x^2+y^2)^2=5^2+(2\times 6)^2[/tex]

[tex]x^2+y^2=\sqrt{5^2+12^2}[/tex]

[tex]x^2+y^2=13[/tex]

So, the sum of squares of two numbers is 13. Hence, this is the required solution.

she needs to count how much 90% is so

85.00 times 90%

or 8500 times 0.9

Answer:

B) .95(53.75)

Step-by-step explanation:

5% is equal to 0.05. So the following expressions are equivalent.

5% × 53.75 = 0.05 × 53.75

To find the final price, she first takes the 5% and then subtracts the amount from 53.75. That is,

53.75 - 5% × 53.75 = 53.75 - 0.05 × 53.75

We can take out the common factor 53.75

53.75 . (1 - 0.05) = 53.75 . 0.95 = 0.95 . 53.75 = 0.95 (53.75)

The relationship between speed, distance, and time is easily remembered when you consider that speed is written in terms of units of distance per units of time. (miles per hour, or kilometers per hour, for example) Of course "per" means "divided by".

speed = distance/time

speed = (750 m)/(1/3 h) = 2250 m/h = 2.25 km/h

Logan's average speed is 2.25 kilometers per hour.

Answer:

i think is d

Step-by-step explanation:

Here we need to find the average rate of change of [tex]f(x)[/tex].

Now,

[tex]f(x)=-2x^2+4x+2[/tex]

Let us find out the value of [tex]f(x)[/tex] at the point [tex]x=1.2[/tex].

Plugging [tex]x=1.2[/tex] in the equation we get:

[tex]f(1.2)=-2(1.2)^2+4(1.2)+2=-2\times 1.44+4.8+2=-2.88+4.8+2=3.92[/tex]

So,

[tex]f(1.2)=3.92[/tex]

Now calculating the value of [tex]f(x)[/tex] at [tex]x=3.8[/tex].

[tex]f(3.8)=-2(3.8)^2+4(3.8)+2=-2(14.44)+15.2+2=-28.88+15.2+2=-11.68[/tex]

So,

[tex]f(3.8)=-11.68[/tex]

Now that we have the values of the function at two distinct points, we can find the average by using the formula given below:

[tex]Avg= \frac{sum}{n}[/tex], where 'n' represents the number of values and that is two in our case and sum represents the sum of the values of the function.

Therefore,

[tex]Avg= \frac{3.92+(-11.68)}{2} =\frac{-7.76}{2} =-3.88[/tex]

So, the average rate of change of the function [tex]f(x)[/tex] from 1.2 to 3.8 is [tex]-3.88[/tex].

The law of cosines can be helpful here. The largest angle (C) will be opposite the longest side (c). That law tells us ...

... c² = a² + b² -2ab·cos(C)

Then

... cos(C) = (a² +b² -c²)/(2ab)

We don't actually need the angle. We only need to know the sign of the cosine.

... cos(C) = (7² +15² -17²)/(2·7·15) = -15/210 . . . . negative sign, so C > 90°

The sail has the shape of an obtuse triangle.

_____

A triangle solver app on your calculator, phone, tablet, or computer can give you the result easily.

The law of cosines can be helpful here. The largest angle (C) will be opposite the longest side (c). That law tells us ...

... c² = a² + b² -2ab·cos(C)

Then

... cos(C) = (a² +b² -c²)/(2ab)

We don't actually need the angle. We only need to know the sign of the cosine.

... cos(C) = (7² +15² -17²)/(2·7·15) = -15/210 . . . . negative sign, so C > 90°

The sail has the shape of an obtuse triangle.

_____

A triangle solver app on your calculator, phone, tablet, or computer can give you the result easily.

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In a previous question about this function, you determined that there were two (2) real zeros, near -1.4 and +3.4. (q: question/11280846)

Since this is a 4th degree polynomial, there are 4 zeros total, so two complex zeros.

_____

The factorization is

... f(x) = (x² -2x -5)(x² -x +1)

The latter factor has zeros at 0.5±i·0.5√3.

3/5 = blue shirts

5/8 of 3/5 = on sale blue shirts

1/3 of 5/8 of 3/5 = medium on sale blue shirts

‘Of’ can be replaced by multipication symbols.

1/3 • 5/8 • 3/5

1/3 • 3/5 = 3/15 (or 1/5)

3/15 • 3/5 = 9/75 (or 3/25)

9/75 of the shirts are medium, on sale, and blue. If you wanted to simplify this it would just be 3/25 of the shirts.

the answer is:

√100 = 0 + 10 i

hope this helps! :o)

Yes, the S. A. S. postulate is correct, because his proof stated two sides and the angle between those sides are congruent.

You're right. There is nothing in the text about a third side or a second angle, and doesn't say anything about the hypotenuse.

Remark

The line you want is parallel to y = - 2x + 3

That means it has the same slope as the given line.  The given line has a slope of  -2

y = -2x + b is what you have so far. Now you have to use the point to get b

y = - 100

x = - 100

Solve for b

-100 = -2(-100) + b

-100 = 200 + b       Notice the sign change. Two minus's make a plus. Subtract 200 from both sides.

- 100 - 200 = b

- 300 = b

Answer

y = - 2x - 100

The line with equation y = -2x + 3 has a slope of -2

The line parallel to line with equation y = -2x + 3 has a slope of -2

This is because parallel lines have the same slope

Taking a point (x,y) along the parallel line passing through (-100,-100)

Slope = change in y-axis divide by change in x-axis

-2 = (y - -100) ÷ (x - -100)

-2(x + 100)  = y + 100

y = -2x - 300

Answer:

The percent increase is [tex]13.33[/tex]%

Step-by-step explanation:

First we need to calculate the increase:

Increase in value = [tex]255-225[/tex]

                             =[tex]30[/tex]

Percent increase = [Increase in value / Initial value]*100

                             =[tex]\frac{30}{225} *100[/tex]

                             =[tex]13.33[/tex]%

Therefore,

the percent increase is [tex]13.33[/tex]%

First four is BBBC，The last one doesnt make sense to me，you probably didnt write it right

Answer:s

Step-by-step explanation:

Answer:

1/16 in

Step-by-step explanation:

The largest possible error in representing a number is half the unit of precision. Here, the error is said to be 1/32 in. That is half of 1/16 in. So, the unit of precision must be 1/16 in.

Answer:

15 per hour

Carl earns more

Step-by-step explanation:

Carl's earnings = earnings/no ofhours

We select any hour and corresponding earnings say 150 and 10

Earning per hour of Carl = 150/10 = 15 per hour.

b) Carl earns more as 15 >12 hourly rate of other person

c)

(A) For x representing the cost of one of Tanya's items, her total purchase cost 5x. The cost of one of Tony's items is then (x-1.75) and the total of Tony's purchase is 6(x-1.75). The problem statement tells us these are equal values. Your equation is ...

... 5x = 6(x -1.75)

(B) Subtract 5x, simplify and add the opposite of the constant.

... 5x -5x = 6x -6·1.75 -5x

... 0 = x -10.50

... 10.50 = x

(C) 5x = 5·10.50 = 52.50

... 6(x -1.75) = 6·8.75 = 52.50 . . . . . the two purchases are the same value

(D) The individual cost of Tanya's iterms was $10.50. The individual cost of Tony's items was $8.75.

When only angles are specified, the sides can be any length, so the triangle is not unique. In any event, the sum of angles must be 180°, so three angles measuring 50° cannot be closed to form a triangle.

Three sides measuring 4, 8, and 14 ft cannot be closed, either, as the long dimension exceeds the sum of the other two. The ends can't meet.

The appropriate choice is the 3rd one ...

... three sides measuring 5 in, 12 in, and 14 in.

Answer:

B three sides measuring 5 in, 12 in, and 14 in

Step-by-step explanation:

the three angles measuring 25, 65, and 90 is 180 and can make more triangle.

the three angles measuring 50, 50, and 50, doesn't even add up to 180 degrees.

the three sides measuring 4 ft, 8 ft, and 14 ft can make more triangles.

I got this right in my test and I got it right.I hope this helps you

Answer:

[tex]\frac{3}{7}[/tex]

Step-by-step explanation:

The number you thought of and original number = x

The number you thought of and added [tex]4\frac{5}{7}[/tex] and got the number equal to the original on times 12

[tex]x +4\frac{5}{7} = 12x[/tex]

Convert [tex]4\frac{5}{7}[/tex] to an improper fraction so it will be easier to work with.

[tex]x +\frac{33}{7} = 12x[/tex]

[tex]\frac{33}{7} = 12x - x[/tex]

[tex]\frac{33}{7} = 11x [/tex]

[tex]\frac{\frac{33}{7}}{11} = \frac{11x}{11} [/tex]

[tex]\frac{33}{7} * \frac{1}{11} = x [/tex]

[tex]\frac{3}{7} = x [/tex]

[tex]x = \frac{3}{7}[/tex]

The original number that the student thought of in the problem can be found by solving the algebraic equation x + 4 5/7 = 12x. After converting the mixed fraction to an improper fraction and simplifying, the original number is 33/77.

The original question is a kind of algebra problem. Let's denote the original number as x, according to the student's description, it follows this formula: x + 4 5/7 = 12x. To solve this equation, you need to collect terms involving x on one side. This gives you 11x = 4 5/7.

Next, convert 4 5/7 to an improper fraction. That gives you 33/7. So, your equation now is 11x = 33/7. Finally, solve for x by dividing both sides of the equation by 11, x = 33/77. This is your original number.

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Solve the given expression for the sum of the two numbers:

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

which you can rewrite as

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

Now, we are given the product of the numbers (i.e. xy) to be 10, the sum of the squares of the numbers (i.e. [tex] x^2+y^2 [/tex]) to be 29, and the sum of the cubes of the numbers (i.e. [tex] x^3+y^3 [/tex]) to be 133.

If we plug these values in the formula written above, we have

[tex] x+y = \dfrac{133}{29-10} = \dfrac{133}{19} = 7 [/tex]

The correct answers are;

A. [tex]3x^{2} =9[/tex]

C. [tex]4x^{2} =16[/tex]

E. [tex]13x^{2} =169[/tex]

F. [tex]25x^{2} =625[/tex]

Hope this helps!!!!

The numbers that are perfect squares include 9, 16, 169, and 625.

In conclusion, the numbers that are perfect squares include 9, 16, 169, and 625.

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