Two tankers contain 35 litres and 50 litres of petrol, the maximum capacity of a container which can measure the petrol of either tanker in exact number of times : *

Answer:

[tex]a^3 + 1 = 0[/tex]

Step-by-step explanation:

We start with the equation:

[tex]a + \frac{1}{a} = 1[/tex]

We want to find the value of:

[tex]a^3 + 1 =[/tex]

We can start with our previous equation and multiply both sides by a:

[tex](a + \frac{1}{a})*a = 1*a\\a^2 + 1 = a[/tex]

Now we can rewrite our initial expression as:

[tex]a = 1 - \frac{1}{a}[/tex]

Replacing that in the right side, we get:

[tex]a^2 + 1 = a = 1 - \frac{1}{a}[/tex]

Now again, let's multiply both sides by a

[tex]a*(a^2 + 1) = a*(1 - \frac{1}{a} )\\a^3 + a = a - a/a\\a^3 + a = a - 1\\a^3 = -1\\a^3 + 1 = 0[/tex]

So we can conclude that:

[tex]a^3 + 1 = 0[/tex]

Answer-

a. no

b. yes

c. no

Answer:

x = 16

Step-by-step explanation:

These are corresponding angles meaning they are equal to each other.

4x + 30 = 94

4x = 64

x = 16

the bottom one... i think

Answer:

∠ 1 = 53°, ∠ 2 = 37°

Step-by-step explanation:

let ∠ 2 be x then ∠ 1 = x + 16

Complementary angles sum to 90° , then

x + 16 + x = 90

2x + 16 = 90 ( subtract 16 from both sides )

2x = 74 ( divide both sides by 2 )

x = 37

Then

∠ 2 = 37° and ∠ 1 = 37 + 16 = 53°

Answer:

[tex]\displaystyle y=-\frac{1}{6}x-\frac{1}{2}[/tex]

Step-by-step explanation:

We want to write the equation of a line that passes through the point (3, -1) and is perpendicular to the line:

[tex]y=6x-4[/tex]

Remember that the slopes of perpendicular lines are negative reciprocals of each other.

The slope of the given equation is 6.

So, the slope of our perpendicular line is the negative reciprocal of 6, which is -1/6.

Next, we are given that it passes through the point (3, -1). Since we are given a point and know the slope, we can use the point-slope form. Point-slope form is given by:

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope and (x₁, y₁) is a point.

We will substitute -1/6 for m and (3, -1) for (x₁, y₁). Hence:

[tex]\displaystyle y-(-1)=-\frac{1}{6}(x-(3))[/tex]

Simplify:

[tex]\displaystyle y+1=-\frac{1}{6}(x-3)[/tex]

Our answer is valid as it as, but we can simplify this into slope-intercept form. Distribute:

[tex]\displaystyle y+1=-\frac{1}{6}x+\frac{1}{2}[/tex]

And subtract one from both sides. Therefore, our equation is:

[tex]\displaystyle y=-\frac{1}{6}x-\frac{1}{2}[/tex]

Answer:

gyufigaruofhasidjfdskcm

Step-by-step explanation:

Answer:

8x.

Step-by-step explanation:

coordinates: (3,10) (5,26)

use slope formula (y2 - y1/x2-x1)

26-10/5-3

16/2

= 8

Answer:

A   y ≥ (1/2)x + 5

Step-by-step explanation:

The shaded area is above the solid line

the correct symbol is ≥

Answer:

x = 2

Step-by-step explanation:

In a vertical line, all x-coordinates are the same.

x = 2

Answer:

x =2

Step-by-step explanation:

A vertical line means the x value remains constant

The x value is 2

x =2

Answer:

x=-20

Step-by-step explanation:

x=-10•2

• means multipled

Answer:

3,375mm^3

Step-by-step explanation:

To find the volume, you do the length times the width times the height. Since this is a cube, the length, width, and height are all 15 mm. Multiply 15 times 15 times 15 to get 3375. The answer is 3375 cubic inches or 3375mm^3

Answer:

x +(2x + 3) = 33

Step-by-step explanation:

two equations can be derived from the question

c = 3 + 2x equation 1

c + x = 33 equation 2

where :

c =  cappuccinos

x =  lattes

make c the subject of the formula in equation 2

c = 33 - x equation 3

equate 3 and 1

x +(2x + 3) = 33

Answer:

82

Step-by-step explanation:

82x.55=45.10

45.10+29.50=74.60

Answer:

2, 5, 6

Step-by-step explanation:

The volume of a rectangular prism is given by [tex]V=l\cdot w\cdot h[/tex], where all variables to the right are dimensions of the prism.

Therefore, we're looking for three numbers that multiply to be 60.

Since the question stipulates that no side length may be 10, we have:

[tex]2\cdot 5\cdot 6=60[/tex]

Answer:

[tex]81[/tex]

Step-by-step explanation:

The average of a set of [tex]n[/tex] values is equal to the sum of the values in that set divided by [tex]n[/tex].

Therefore, the average of your 5 scores is equal to [tex]\frac{73+86+91+88+67}{5}=\boxed{81}[/tex]. Since evidently your grade is represented by the average of all your scores, your new grade is 81.

Answer:

24

Step-by-step explanation:

15 - 3d

Let d = -3

15 - 3(-3)

Multiply

15 +9

Add

24

Answer:

24

Step-by-step explanation:

15 - 3d

* plug in -3 *

15 - 3(-3)

simplify -3(-3)

-3(-3) = + 9

add

15 + 9 = 24

Answer:

Step-by-step explanation:

comparing corresponding elements

x + y = 13

2x - y = 2

Now use substitution method.

x + y = 13

x = 13 - y                 equation(i)

substitute the value of x

2x - y = 2

2(13 - y) - y = 2

26 - 2y - y = 2

-3y = 2 - 26

y = -24/-3

y = 8

substitute the value of y in eqaution(i)

x = 13 - y

x = 13 - 8

x = 5

therefore , x = 5 and y = 8

To check :

x + y = 13

when we add x and y then must come 13

5 + 8 = 13

13 = 13

2x - y = 13

substitute the value of x and y . REsult must come 2

2*5 - 8 = 2

10 - 8 = 2

2 = 2

10 - 8 = 2

Answer:

x = 5, y = 8

Step-by-step explanation:

Another way to write  (x+y, 2x-y)= (13, 2) is

x + y = 13 -- (1)

2x - y = 2 -- (2)

using the elimilation method,

Rewriting (1), y = 13 - x --(1)'

Replacing (1)' into (2),

2x - ( 13 - x) = 2

2x - 13 + x = 2

3x = 15

x = 5 -- (3)

Replacing (3) into (1),

5 + y = 13

y = 8 -- (4)

Accorindg to (3) and (4),

x = 5, y = 8

If this helps you, please give brainliest!

Answer:

165 cm

Step-by-step explanation:

We solve using the rule

Shadow of ruler/Length of ruler = Shadow of the girl /Length of the girl

Shadow of ruler = 20cm

Length of ruler = 30cm

Shadow of the girl = 110cm

Length of the girl = x

Hence:

20/30 = 110/x

Cross Multiply

20x = 30 × 110

x = 30 × 110/20

x = 165 cm

Therefore, Sierra(the girl) is 165cm tall

Answer:

625 cubic feet

Step-by-step explanation:

Given data

Base area= 125 square feet

Height = 15feet

The expression for the volume of a pyramid is given as

V= a^2*h/3

but a^2= 125 square feet

V= 125*15/3

V= 1875/3

V=625 cubic feet

Answer:

120° = CAB

arc lenght = CÁB/ 360 × 2(pi)(4)

a/2pi(4) = CAB/360

8/3(pi)/2(pi)(4) × 360 = CÁB

120 = CAB

Answer:

120°

Step-by-step explanation:

that is the procedure above

Answer:

91.7%

hope I helped

Answer:

12.75

Step-by-step explanation:

c = π x d

40.035= 3.14 x d

40.035/3.14 = 12.75

⭐Answer:

✰According to angle property between tangent and secant✰

[tex](4x-8)=1/2(80)[/tex]

[tex]4x-8=40[/tex]

[tex]4x=40+8[/tex]

[tex]4x=48[/tex]

[tex]x=48/4[/tex]

[tex]x=12[/tex]

〖D) 12〗

☁☁☁☁☁☁☁

hope it helps...

The value of x is 12

Circle is the collection of all points in a plane at a constant distance from a fixed point. The fixed point is known as the centre, and the constant distance is the circle’s radius. A line that intersects a circle in two distinct points is called a secant to the circle.

A line meeting a circle only in one point is called a tangent to the circle at that point. In this article, we will talk about the relative position of the circle and a line in the same plane. We will also examine the existence of tangents to a circle and their properties.

Using angle property between tangent and secant

(4x - 8) = 1/2*80

4x- 8 = 40

4x= 48

x= 12

Learn more about tangent here:

https://brainly.com/question/19064965

#SPJ5

Answer:

49

Step-by-step explanation:

Answer:

[tex]\text{A. }\frac{5}{6}\pi x^2[/tex]

Step-by-step explanation:

The area of a sector with measure [tex]\theta[/tex] is equal to [tex]r^2\pi\cdot \frac{\theta}{360}[/tex]

Since there are 360 degrees in an angle, the measure of sector K must be 360-60=300 degrees.

What we know:

Thus, the area of the sector is [tex]x^2\pi\cdot \frac{300}{360}=\boxed{\text{A. }\frac{5}{6}\pi x^2}[/tex]

Answer:

(a+b)/2(a-b)

Step-by-step explanation:

Explained in the paper

Goodluck

Answer:

The equation would be (x – 3)^2 + (y – 4)^2 = √26^2 or 26.

Step-by-step explanation:

Firstly, we need to find the radius of the circle. In this case, through the Pythagorean theorem, we can find it to be √(9-4)^2 + (4-3)^2 = √25 + 1 = √26.

Therefore, the equation of the circle would be (x – h)^2+ (y – k)^2 = r^2, where h and k are the x and y-coordinates of the center of the circle respectively, and r is the radius. Hence, the equation of this circle would be (x – 3)^2 + (y – 4)^2 = √26^2 or 26.

Hope this helped!

Answer:

Step-by-step explanation:

Equation in standard form:

where (h, k) is the center and r- radius

On the graph we have (h, k) = (3, 4)

Find the r² using the distance formula:

The equation is:

Answer:

Answer is 3 because

Step-by-step explanation:

a=2

20*2= 40

40-1 = 39

b = 13

so 39/13 = 3