Find an expression which represents the sum of (9x+4y) and (-6x+4y) in simplest terms.

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.

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:

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)

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:

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:

The answer is 40.

Step-by-step explanation:

I just got it correct.

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

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:

75.5 % of all candidates passes

Step-by-step explanation:

36000 x .45 = 16200 x .7 = 11,340 girls passed

36000 x .55 = 19800 x .8 = 15,840 boys passed

total of boy and girls who passed = 27,180

27,180 out of 36,000 equals 75.5%

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).

Given: Points (-6, 2) and (3, -10).

To find: The y-coordinate of the midpoint of the line segment formed by the given points.

Answer:

Let's first find out the mid-point.

Formula to find the mid-point of a line segment:

[tex]\tt \bigg(\dfrac{x_1\ +\ x_2}{2}, \dfrac{y_1\+ \ y_2}{2}\bigg)[/tex]

From the given data, we have:

[tex]\tt x_1\ =\ -6\\\\x_2\ =\ 3\\\\y_1\ =\ 2\\\\y_2\ =\ -10[/tex]

Using these in the formula,

[tex]\tt Mid-point\ =\ \bigg(\dfrac{-6\ +\ 3}{2}, \dfrac{2\ +\ -10}{2}\bigg)\\\\\\Mid-point\ =\ \bigg(\dfrac{-3}{2}, \dfrac{-8}{2}\bigg)\\\\\\Mid-point\ =\ \bigg(\dfrac{-3}{2}, -4\bigg)[/tex]

The y-coordinate of the mid-point of the line segment formed by the points (-6, 2) and (3, -10) is -4.

Hope it helps. :)

Answer:

The answer is 41.50 i just took it

Step-by-step explanation:

i just took it

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:

12.8 and 20

Step-by-step explanation:

y=3.6x+2   [x=3 and x=5]

y=3.6(3)+2 = 10.8 + 2 = 12.8

y=3.6(5)+2 = 18 + 2 = 20

Answer:

4 T- shirts

Step-by-step explanation:

55- 14 = 41

41$ left and each T- shirt is 9$

count by 9s until you reach 41

9, 18, 27, 36 , 45

36 is the highest

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:

fraction- 1/4

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:

225

Step-by-step explanation:

X/500 = 45/100

100(x) = 45(500)

100x = 22500

X = 22500/100

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:

2 is true

Step-by-step explanation:

SInce the angles of a triangle add up to 180 c is equal to 50 because 100+30=130 and 180-130=50

By the Converse of the Base Angles Theorem or the Isosceles Triangle theorem if 2 angles of a triangle are congruent then the sides opposite are also congruent. By the definition of an isosceles triangle if a triangle has 2 equal sides it is isosceles.

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:

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:

Bear with me here

Step-by-step explanation:

I don't actually know how to solve this, I have geometry later this year. I just hope to be able to set it up for you.

Ok, so BE and CE are perpendicular. This means that they make a 90 degree angle. we can write in the boxes to signify if you want. We also know that the angles CDE and DCE have the same angle. I don't know how to put this is math terms, but that means that ADE and BCE have to be the same as well. If x(the angle of ADE and BCE)is the same, then CDA must be x + (mystery angle). if ADE and BCE are the same, and a triangle's angles add up to 180, then DAE and EBC must be the same as well. Not sure if this actually helps, I'm not able to give a straight answer but it's the best I can do with what I know.

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:

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:

It is the second one

Step-by-step explanation:

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: