Bryan and Yuan started out at their houses and are biking towards each other. Bryan started
out first, and has already gone 5 miles. He bikes at a constant speed of 3 miles per hour.
Yuan just left, and rides at 4 miles per hour. When the boys meet halfway between their
houses, they will continue to the park together. How long will that take? How far will each
boy have ridden?

Answer:

1. UW // TX

2. VX // UY

3. UW ≅ TY ≅ YX

4. YW = [tex]\frac{1}{2}[/tex] TV

5. TX = 2 UW

6. ∠TXV ≅∠WUY

Step-by-step explanation:

The line segment joining the midpoint of two sides of a triangle is parallel to the third side and equal to half its length

In Δ XVT

∵ U is the midpoint of VT

∵ W is the midpoint of VX

∵ XT is the 3rd side of the triangle

→ By using the rule above

∴ UW // TX ⇒ (1)

∴ UW = [tex]\frac{1}{2}[/tex] TX

→ Multiply both sides by 2

∴ 2 UW = TX

∴ TX = 2 UW ⇒ (5)

∵ Y is the midpoint of TX

∴ TY = YX = [tex]\frac{1}{2}[/tex] TX

∵ UW = [tex]\frac{1}{2}[/tex] TX

∴ UW ≅ TY ≅ YX ⇒ (3)

∵ U is the midpoint of VT

∵ Y is the midpoint of XT

∵ VX is the 3rd side of the triangle

→ By using the rule above

∴ UY // VX

∴ VX // UY ⇒ (2)

∴ UY = [tex]\frac{1}{2}[/tex] VX

∵ W is the midpoint of VX

∵ Y is the midpoint of XT

∵ TV is the 3rd side of the triangle

→ By using the rule above

∴ YW // TV

∴ YW = [tex]\frac{1}{2}[/tex] TV ⇒ (4)

∵ 2 Δs UYW and XVT

∵ UY = [tex]\frac{1}{2}[/tex] XV

∵ YW = [tex]\frac{1}{2}[/tex] VT

∵ WU = [tex]\frac{1}{2}[/tex] TX

∴ [tex]\frac{UY}{XV}[/tex] = [tex]\frac{UW}{VT}[/tex] = [tex]\frac{WU}{TX}[/tex] = [tex]\frac{1}{2}[/tex]

→ By using the SSS postulate of similarity

∴ ∠TXV ≅∠WUY ⇒ (6)

9514 1404 393

Answer:

  3

Step-by-step explanation:

Vertical angles share a vertex point, and have opposite rays for sides. In short, they are across the point of intersection from each other. Vertical angles do not have a common side (they are not adjacent).

The first part of the problem is to identify angle NCA. That is shown in red in the attachment. The vertical angle is across the point of intersection. It is angle 3.

Given that,

∠C = (6x-21)° and ∠A = (4x+11)°

To find,

Choose the correct option.

Solution,

For a parallelogram, the opposite angles are equal. ATQ,

(6x-21)° = (4x+11)°

Taking like terms together,

6x-4x = 21 + 11

2x = 32

x = 16

∠C = (6x-21)° = 6(16) -21 = 75°

So, ∠A = 75°

So, ∠A = ∠C = 75°. Hence, the correct option is (B).

Answer:

10 persons

Step-by-step explanation:

Step one:

given data

We are told that they have a total of $275

also, they want to spend $5 on packing space

and a ticket cost $27 per person.

Step two:

let the number of persons be x

and let the total amount to be spent be y

hence the inequality is

y≤ 5+ 27x

now for y= $275, let us find x

Substitute into the inequality we have

275≤5+27x

275-5≤27x

270≤27x

Divide both sides by 27

x ≤ 270/27

x ≤ 10

Hence the number of persons should not be more than 10

Answer:

Inequality: 25x+10_<275

Answer: x_<10.6

Step-by-step explanation:

I have delta math also. This is the exact ANSWER! So i am too lazy to explain it but actually that is correct. I tried to put a screenshot in here but it wont let me for some reason? BUT THIS IS THE ANSWER!

Your welcome (○｀ 3′○)

Answer:

[tex] \frac{1}{6} t + \frac{5}{18} \\ (\frac{1}{6} \times \frac{1}{3} ) + \frac{5}{18} \\ \frac{1}{18} + \frac{5}{18} = \frac{(1 + 5)}{18} \\ \frac{6}{18} = \frac{1}{3} [/tex]

Answer:

perpendicular

Step-by-step explanation:

L1: find the slope

rise: 2 - (-5) = 7

run: -1 - (-3) = 2

m1 = 7/2

L2:

rise: 2 - 4 = -2

run: 7 - 0 = 7

m2 = -2/7

parallel means same slope m1 = m2

perpendicular means opposite reciprocal (flip and change signs)

7/2 flip and change signs = -2/7, yes thus it is perpendicular

Answer:

x^3 - 9[tex]x^{2}[/tex] + 27x - 27

Step-by-step explanation:

Answer:

How much is her raise?

Her raise is at 0.345$

Hourly pay after raise?

Her new pay rate is 11.845$/h

Step-by-step explanation:

New hourly pay:

[tex]11.50 \times 1.03 = 11.845[/tex]

Actual raise:

[tex]11.845 - 11.50 = 0.345[/tex]

Answer:

We conclude that

[tex]a\times \left(b-c\right)=\:a\times b-a\times c[/tex]

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

        L.H.S = R.H.S    

Step-by-step explanation:

Given the property expression

[tex]a\times \left(b-c\right)=\:a\times b-a\times c[/tex]

Given that:

Determining the LEFT-HAND SIDE

[tex]a\times \left(b-c\right)[/tex]

substituting a= -3/5, b= 5/9 and c= -10/3​

[tex]a\times \left(b-c\right)\:=\:\:-\frac{3}{5}\times \left(\frac{5}{9}-\left(-\frac{10}{3}\right)\right)\:\:\:\:\:\:\:\:\:\:\:\:[/tex]

                  [tex]=-\frac{3}{5}\times \:\left(\frac{5}{9}+\frac{10}{3}\right)\:\:\:[/tex]

                  [tex]=-\frac{3}{5}\times \frac{35}{9}[/tex]

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

Determining the RIGHT-HAND SIDE              

[tex]\:a\times \:b-a\times \:c[/tex]

substituting a= -3/5, b= 5/9 and c= -10/3​

[tex]\:a\times \:b-a\times \:c=ab-ac[/tex]

                      [tex]=-\frac{3}{5}\left(\frac{5}{9}\right)-\left(-\frac{3}{5}\right)\left(-\frac{10}{3}\right)[/tex]

                      [tex]=-\frac{3}{5}\cdot \frac{5}{9}-\frac{3}{5}\cdot \frac{10}{3}[/tex]

                      [tex]=-\frac{15}{45}-\frac{30}{15}[/tex]

                      [tex]=-\frac{1}{3}-2[/tex]

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

Apply the fraction rule:  [tex]\frac{-a}{b}=-\frac{a}{b}[/tex]

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

Therefore, we conclude that

[tex]a\times \left(b-c\right)=\:a\times b-a\times c[/tex]

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

        L.H.S = R.H.S                                          

Answer:

decreasing, linear

Step-by-step explanation:

you could find the first differences and then the secon ddifferences, but when it's allowed to use Desmos, why not, lol, so, looking at the 4 points plotted on Desmos, it is decreasing, and linear

Answer:

Decreasing; Linear

Step-by-step explanation:

This is a linear line for a fact.

And the line is decreasing. I used desmos to graph these points.

You can see for yourself, in the image I provided

Answer:

The answer is 40.

Step-by-step explanation:

I just got it correct.

Answer:

15 foot

Step-by-step explanation:

6 foot = 8 foot shadow

3 foot= 4 foot shadow

15 foot=20 foot shadow

please give me brainliest!!!

Answer:

C

Step-by-step explanation:

For A, only two sides are congruent, while the third is not

For B, You have two sides and an angle, which is SAS, not SSS

Answer:

Applying the quadratic formula.

Exact Form:

x=32,−92

Decimal Form:

x=1.5,−4.5

Mixed Number Form:

x=112,−412

Step-by-step explanation:

Solve the equation: x2 + 3x -27/4 = 0 With the coefficients: a = 1, b = 3, c = -6.75 a ≠ 0 With ∆ = 36> 0 => Equation has 2 distinct solutions

 x1 = 1.5, x2 = -4.5

Answer:

fraction- 1/4

Answer:

Approximately 50 square feet (50.24 to be exact)

Step-by-step explanation:

If you're using 3.14 for π, and the area of a circle is A=πr2,

(3.14)(4)^2 =?

(3.14)(16) = 50.24

Therefore the answer would be about 50 square feet.  

Answer:

25.12

Step-by-step explanation:

Answer:

2037.89

Step-by-step explanation:

The area of a circle is πr²

This means that the area of the pizza is π*17.5^2

This means that the area =962.11275016187

We then need to find the area of a rectangle which is shown throuhg lenght*width

50*60=3000

We then need to find out the area of the box excluding the pizza so we subtract the area of a pizza

so we have

3000-962.11275016187=2,037.88724983813

Round and get 2037.89

Answer:

c 3/4, 0.8, 94%

Step-by-step explanation:

I would convert all of these to decimals first so its not as confusing

a). 0.54, 0.70, 0.40 not in order

b). 0.67, 0.50, 0.80 not in order

c). 0.75, 0.80, 0.94 in order

d). 0.70, 0.54, 0.67 not in order

Answer:

17/5

Step-by-step explanation:

Multiply 3 with the denominator 5.

3 * 5 = 15

Then add the product to the numerator

15 + 2 = 17

Keep the 5 as the denominator.

So the final answer is 17/5

The mixed fraction [tex]3\frac{2}{5}[/tex] as improper fraction is 17/5.

To convert the mixed number [tex]3\frac{2}{5}[/tex] to an improper fraction, we need to combine the whole number part with the fractional part.

The whole number 3 can be written as a fraction with the same denominator as the fractional part (5):

3 = 3/1

Now, add the fractional part 2/5 to the whole number 3/1:

3 + 2/5

To add fractions, we need a common denominator.

In this case, the common denominator is 5.

Now, rewrite 3 as a fraction with the common denominator 5:

3 = (3 × 5)/5

= 15/5

Now, add the fractions together:

15/5 + 2/5 = 17/5

So, the mixed number [tex]3\frac{2}{5}[/tex] as an improper fraction is 17/5.

To learn more on Fractions click:

https://brainly.com/question/10354322

#SPJ6

Answer:

D.) 3x - 3

Step-by-step explanation:

X - 4 + 2x + 1

= X + 2x - 4 + 1

= 3x - 4 + 1

= 3x - 3

I hope this helps!

In a table of a proportional relationship, there is always some number that you can multiply by the number in the first column to get the number in the second column for any row. This number is called the constant of proportionality. In the fruit juice example, the constant of proportionality is 0.4.

Answer:

The probability of the frog landing on a complement of yellow lily is 0.57

Step-by-step explanation:

PLANTS Of the water lilies in the pond, 43% are yellow. The others are white.

The complement is  [tex]1-p[/tex].

It is given that 43% of plants are lilies it means the probability of a frog randomly jumps onto a lily is: [tex]p=0.43[/tex]

Now the complement is:

[tex]1-p=1-0.43[/tex]

[tex]1-p=0.57[/tex]

Hence, the probability of the frog landing on a complement of yellow lily is 0.57

Answer:

27 Centimeters

Step-by-step explanation:

Calculation for how many centimeters on the

treasure map is equivalent to 135 miles

Number of Centimeters to 135 miles=[135 miles/(15 miles÷3 centimetres)]

Number of Centimeters to 135 miles=135 miles/5

Number of Centimeters to 135 miles=27 Centimeters

Therefore the numbers of centimeters on the

treasure map that is equivalent to 135 miles is

27 Centimeters

Answer:

your awnser is 3 3/5

Step-by-step explanation:

all u do is 18 divided by 5 wich gives u 3 with a leftover of 3 so that gives u 3 3/5

Answer:

3 3/5

Step-by-step explanation:

You count by 5 until it wont fit in to 18 what you have left over ( 3 ) is your numerater. However many times 5 went into 18 Is your whole number.

Answer:

Angle 1 is 105 as Z rule

Angle 2 is 75 per the angles of the straight line

Angle 3 is 90, and in turn as angles around a point, so is 4

I may be wrong...angles arent my strength, but I think its pretty accurate

Step-by-step explanation:

Answer:

A 7-digit number is read as millions or ten-lakhs.

10 ones make a ten, 10 tens make a hundred, 10 hundreds make a thousand, 10 thousands make a ten-thousand, 10 ten-thousands make a hundred-thousand and 10 hundred-thousands make a million.

Step-by-step explanation:

please mark me as brainliest thank you

Answer:

The answer is 41.50 i just took it

Step-by-step explanation:

i just took it

Answer:

[tex]\sqrt{ 105}[/tex]

Step-by-step explanation:

→ Utilise Pythagoras theorem

[tex]\sqrt{11^{2} -4^{2} } =\sqrt{121-16} =\sqrt{105}[/tex]