1.Construct a linear equation from the following statements.

(i) The quotient of three times a number and 5 is 9.
(ii) One-third a number added to 5 gives 25.

2. Solve the following equations.

15(x-1) – 3(x-2) + 7(x+3) = 0

3. What do you mean by SAS and RHS?

4. Find whether the pairs of triangles in each question below are congruent or not. If yes then state the criterion of congruence in each case.


P Q
_________
| |
3cm | | 3cm
|_________|
S R​

Answer:

the answer to your question is 3 and 34

Answer:

The HCF of [tex]a=2^1 \cdot 3^4 \cdot 5^1[/tex] and [tex]b = 2^3 \cdot 3^2 \cdot 5^2[/tex] is [tex]90[/tex].

Step-by-step explanation:

To calculate the HCF of two numbers given their prime factorization, we take the lowest exponent of every prime when comparing the two numbers.

So the HCF of [tex]a=2^1 \cdot 3^4 \cdot 5^1[/tex] and [tex]b = 2^3 \cdot 3^2 \cdot 5^2[/tex] is [tex]2^1 \cdot 3^2 \cdot 5^1 = 90[/tex].

Answer: there are 120 baloons in the bag

Step-by-step explanation:

10/ 600 = 4/x

10x = 1200

10/1200

x= 120

Answer:

Step-by-step explanation:

[tex]step - 1 : define[/tex]

[tex]2x - 9 = x + 5[/tex]

[tex]2x = x + 5+ 9[/tex]

[tex]2x = x + 14[/tex]

[tex]2x - x = 14[/tex]

[tex]x = 14[/tex]

KL=2x-9

=2.14-9

=28-9

=19

Answer:

The segment bisector of FG is HI because it splits it into two equal parts. Since point F to the bisector equals 33 and the bisector to point G is the same, that would also be 33. 33+33=66=FG

Step-by-step explanation:

The measurement of the line segment FG is 66 units.

We need to identify the segment bisector of FG and then find FG.

A segment bisector is a line, a ray, a line segment, or a point that cuts a line segment at the centre dividing the line into two equal parts. The word segment can also be referred to as line segment which means a segment is a part of the line that has fixed endpoints. The word bisect means cutting any object or line into two equal halves. Hence, a segment bisector is referred to as when two line segments bisect or cut each other at a point dividing the lines into equal halves.

From the given figure, HI is the bisector of the line segment FG.

Given that, 1/2 (FG)=33 units

⇒FG=66 units

Therefore, the measurement of the line segment FG is 66 units.

To learn more about the bisector of the line segment visit:

https://brainly.com/question/13792156.

#SPJ2

Answer:

x° = 145°

Step-by-step explanation:

x° + (2x - 255)° = 180°

3x = 180 + 255

3x = 435

x° = 145°

Answer:20

Step-by-step explanation:4:9

9x5=45

4x5=20

20:45

Answer:

it means positive 5. because negative + negative = positive or you can think like -1 times -5 which is 5.

Step-by-step explanation:

Answer:

Step-by-step874747634734634347

Answer:

I dont know

Step-by-step explanation:

sorrryy

Answer:

19

Step-by-step explanation:

Add 9 to 10

Given:

A directed line segment begins at F(-8, -2), ends at H(8, 6), and is divided in the ratio 8 to 2 by G.

To find:

The coordinates of point G.

Solution:

Section formula: If a point divide a line segment with end points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in m:n, then the coordinates of that point are

[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]

Point G divide the line segment FH in 8:2. Using section formula, we get

[tex]G=\left(\dfrac{8(8)+2(-8)}{8+2},\dfrac{8(6)+2(-2)}{8+2}\right)[/tex]

[tex]G=\left(\dfrac{64-16}{10},\dfrac{48-4}{10}\right)[/tex]

[tex]G=\left(\dfrac{48}{10},\dfrac{44}{10}\right)[/tex]

[tex]G=\left(4.8,4.4\right)[/tex]

Therefore, the coordinates of point G are (4.8, 4.4).

Answer:

Please check the explanation.

Step-by-step explanation:

Given

[tex]P(Z > 1.96)[/tex]

To determine

What probability expression is equivalent to [tex]P(Z > 1.96)[/tex].

Suppose Z is a standard normal variable.

Therefore,

P(Z > 1.96) = 1 - P(Z ≤ 1.96)

solving

                 = 1 - Ф(1.96)

                 [tex]= 1 - 0.9750[/tex]

                 [tex]= 0.0250[/tex]

Answer: x=12

Step-by-step explanation: 10(x−3)=90

(10)(x)+(10)(−3)=90 (Distribute)

10x+−30=90

10x−30=90

Step 2: Add 30 to both sides.

10x−30+30=90+30

10x=120

Step 3: Divide both sides by 10.

x=12

Answer:

wheres the end of the question

Step-by-step explanation:

Sam opens a savings account with $800. He saves $50 per month. Assume that he does not withdraw money or make any additional deposits.

Answer:

slope-intercept formula ----->  Y2-Y1/X2-X1

Step-by-step explanation:

X1= -5    X2= 1

Y1= -5     Y2= -3

-3+5/1+5=1/3

Answer:

The food will last for 10 days

Step-by-step explanation:

Proportions

The amount of food the farmer needs to feed his animals is proportional to the number of animals and to the number of days they are fed.

This can be written as:

Food=k*N*D

Where k is a constant, N is the number of animals and D is the number of days.

We know that the farmer has enough food to feed N=50 animals for D=15 days, thus:

Food=k*50*15=750k

If the same amount of food is used for 50+25=75 animals, then:

750k=k*75*D

Simplifying:

750=75*D

Dividing by 75:

D=10

The food will last for 10 days

Answer:

$27.5

Step-by-step explanation:

Let

x = pound over weight limit

Airline 1 = 20 + 10x

Airline 2 = 5 + 30x

Equate the fees

20 + 10x = 5 + 30x

20 - 5 = 30x - 10x

15 = 20x

x = 15/20

x = 0.75 pounds

How large was each airline's fee?

Airline 1 = 20 + 10x

= 20 + 10(0.75)

= 20 + 7.5

= $27.5

Airline 2 = 5 + 30x

= 5 + 30(0.75)

= 5 + 22.5

= $27.5

Answer:

Yoy add them to be 2n squared then divide by 2 on both sides then take the square root

Answer:180

Step-by-step explanation:

Answer:

15.59.

Step-by-step explanation:

The altitude of equilateral triangle bisects the base

So 1/2 base = 3.

Altitude of the triangle is found from Pythagoras theorem:

= sqrt(6^2 - 3^2)

= sqrt27

Area = 1/2 base * altitude

=  3 * sqrt27

= 15.59

Answer:

Step-by-step explanation:

3/4 + 3/4 + 3/4 + 3/4 + 3/4 + 3/4 = (6 x 3)/4 = 18/4 = 4 1/2

Answer:

80

Step-by-step explanation:

30 ÷ 6 = 5

16 × 5 = 80

I hope this helped!

Answer:

6 square units

Step-by-step explanation:

In oder to do this, you need graph paper to make it easier and then mark your graph paper with the quadrants.

I got 3 unites for the height and 4 units for the base

4 x 3 = 12 square units

however the formula for a triangle is Ab/2

so divide 12/2 = 6

So its 6 square units

Answer:

30

Step-by-step explanation:

- A number is divisible by 2 if its last digit is 2, 4, 6, 8 or 0

- A number is divisible by 3 if ist sum of digits is divisible by 3.

- A number is divisible by 5 if its last digit is a 5 or a 0.

_

The least 3 digit number divisible by 30 is 120 and the greatest is 990.

Answer: 30

Step-by-step explanation:

Divisible by 2,3 and 5 means divisible by 2*3*5=30

So we require to calculate number of multiples of 30 in the range 100 to 999.

The least 3 digit number divisible by 30 is 120 and greatest is 990.

This is an AP series with common difference 30.

First number is 120 and n'th number is 990.

We need to find n.

Using the AP series formula

120 + (n-1)*30= 990

or n= 30

There are 30 3-digit numbers divisible by 2,3 and 5.

Answer:

see attached

Step-by-step explanation:

pleass see attached