Which equation can be used to solve the problem below?

If four times a number is increased by 15, the result is three less than six times the number. Find the number.

Question 7 options:

4 (x + 15) = 6x -3


4x + 15 = 6(x-3)


4x + 15 = 6x -3


4x + 15 = 3-6x

Answer: [tex]x=18[/tex] ; [tex]y=6\sqrt{3}[/tex]

Step-by-step explanation:

You can write two expressions that are in terms of 'x' and 'y'. This is a right triangle, so Pythagorean's theorem can be used. We can also use the angle to find the sine of 30 degrees.

Pythagorean's Theorem:

The values 'a' and 'b' are the two shorter sides of the triangle, while the value 'c' is the longest side of the triangle; the hypotenuse.

[tex]a^2+b^2=c^2[/tex]

[tex]x^2+y^2=(12\sqrt{3} )^2[/tex]

[tex]x^2+y^2=12^2*\sqrt{3} ^2=432[/tex]

Sine of the Angle:

Sine is defined to be the opposite side divided by the hypotenuse. Let's take the sine of 30 degrees:

[tex]sin(\alpha )=opposite/hypotenuse[/tex]

[tex]sin(30)=y/12\sqrt{3}[/tex]

[tex]\frac{1}{2} =y/12\sqrt{3}[/tex]

[tex]y=6\sqrt{3}[/tex]

Plug this value of 'y' into the first expression derived from Pythagorean's theorem:

[tex]x^2+y^2=432[/tex]

[tex]x^2+(6\sqrt{3} )^2=432[/tex]

[tex]x^2+108=432[/tex]

[tex]x^2=432-108=324[/tex]

[tex]x=\sqrt{324}[/tex]

[tex]x=18[/tex]

Use this value of 'x' to solve for 'y' in the expression from Pythagorean's theorem:

[tex](\sqrt{324})^2+y^2=432[/tex]

[tex]324+y^2=432[/tex]

[tex]y^2=432-324=108[/tex]

[tex]y=\sqrt{108}[/tex]

[tex]y=\sqrt{36*3}[/tex]

[tex]y=6\sqrt{3}[/tex]

Answer:

Answer Linked below

Step-by-step explanation:

Pattern A = 1, 4, 7, 10, 13

Pattern B = 1, 5, 9, 13, 17

Each term is increases at a faster rate in pattern B; the difference between terms increases by one per step. In pattern A, 1 jumps to 4, while in pattern B, 1 jumps to 5. There is a difference of one. But when in pattern A, 4 jumps to 7, in pattern B, 5 jumps to 9. The is a difference of two between these two terms even though they are on the same "jump." This difference increases by one per "jump." (Jump is not the official word for this but I'm assuming this isn't a sequence problem.)

Answer:

Letter A is 100 degrees.

Letter B is 80 degrees.

Step-by-step explanation:

50+60= 110

180-110= 80 <- the leftover degrees for the triangle

a line is 180 degrees, so 100 degrees is left over for letter A.

Answer:

[tex]56[/tex]

Step-by-step explanation:

[tex]10 \times 5 + 6[/tex]

[tex]50 + 6 = 56[/tex]

Step-by-step explanation:

Pythagoras's rule:  [tex]a^2 + b^2 = c^2[/tex]  becomes  [tex]x^2 + 10^2 = y^2[/tex]

If we say b = 10: [tex]b = 10 = \sqrt{c^2 - a^2} = \sqrt{y^2 - x^2}[/tex]

You only need to look at the left triangle

Which of the options follows Pythagoras's rule?

Let's try the options until we get the right one (in no particular order)

If we try: 3) x = 4 y = [tex]29\sqrt{2}[/tex]...

[tex]\sqrt{(29\sqrt{2})^2 - 4^4} = 7\sqrt{34} \neq 10[/tex]

If we try: 4) x = 16 y = 116...

[tex]\sqrt{116^2 - 16^2} = 20\sqrt{3} \neq 10[/tex]

If we try: 2) x = 16 y = 29...

[tex]\sqrt{29^2 - 16^2} = 3\sqrt{65} \neq 10[/tex]

If we try: 1) x = 4 y = [tex]2\sqrt{29}[/tex]...

[tex]\sqrt{(2\sqrt{29})^2 - 4^2} = 10[/tex]

Answer:

C. (5,6)

Step-by-step explanation:

Hope this helps. please give brainliest

Answer:

3 1/5 meters

Step-by-step explanation:

1/4 in. on map ⇒ 1 meter in real life

⇒ 4/5 in. = 16/20 inches

⇒ 16/20 inches = 1/5 x 16 = 3 1/5 meters

Answer:

(x-8)(x-8) are the factors of the following biominals

Answer:

Step-by-step explanation:

Answer:

10.71

Step-by-step explanation:

You first convert 75.4 millimeters to centimeters, and you will get 7.54. Now you subtract 18.25 and 7.54 to get the answer 10.71

Answer:

y=-x2 - 8x – 18 is shown by graph D.

y=x2 - 4x + 7 is shown by graph A.

y=X+5 is shown by graph C.

y=-3x - 6 is shown by graph B.

Step-by-step explanation:

In y=-x2 - 8x – 18, the coefficient of x2 is less than 0.So the graph only has a maximum value.Thefore , the graph is point upward.

In y=x2 - 4x + 7, coefficient of x2 is greater than 0.

So the graph has a minimum point and is pointed downward.

for y =x + 5, the gradient is positive.so it is graph C.There is another way to find out too but this is quicker for now.

for y = -3x - 6, the gradient is negative ,-3.So it is the graph B.

Answer:

D A C B

Step-by-step explanation:

Answer:

there are three significant numbers

Answer:

three

Step-by-step explanation: 0.00509; the first three zeros are not significant since they come before a non-zero number, the final three digits are significant

By using what we know about intersecting lines, we will see that:

When two lines intersect, 4 angles are formed. There are two properties that these angles have.

a) We know that ∡5 = 47°

And 7 is not adjacent to 5, then 7 has the same measure:

∡7 = 47°

b) 6 and 5 are adjacent, then we must have that:

∡5 + ∡6 = 180°

47° + (2x - 5)° = 180°

That is the equation we need to solve to get the value of x.

c) To solve the linear equation we need to isolate x, let's do that:

47° + (2x - 5)° = 180°

(2x - 5)° = 180° - 47° = 133°

2x - 5 = 133

2x = 133 + 5 = 138

x = 138/2 = 69.

If you want to learn more about linear equations, you can read:

https://brainly.com/question/1884491

Answer:

a)  <5 and <7 have congruent angles. That means that both angles are equal, they have the same measure. This means that the measure of <7 is 47°.

<7 = 47°

b) 5 and 6 are adjacent, so this is the equation that we have to do to solve for the value of x.

<5 + <6 = 180°

47° + (2x - 5)° = 180°

c) To solve the linear equation we need to isolate x.

47° + (2x - 5)° = 180°

(2x - 5)° = 180° - 47° = 133°

2x - 5 = 133

2x = 133 + 5 = 138

x = 138/2 = 69

[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer}}[/tex]

Here we go ~

[tex]\qquad \tt \dashrightarrow \:16x - 4 = 0[/tex]

[tex]\qquad \tt \dashrightarrow \:16x - 4 + 4 = 0 + 4[/tex]

[tex]\qquad \tt \dashrightarrow \:16x = 4[/tex]

[tex]\qquad \tt \dashrightarrow \:x = 4 \div 16[/tex]

[tex]\qquad \tt \dashrightarrow \:x = \frac{1}{4} [/tex]

The Value of x is :-

16x - 4 = 0

16x = 4

x = 4/16

x = 1/4

Answer:

[tex]m = 3 m = - \frac{9}{4} [/tex]

Step-by-step explanation:

correct me if I'm wrong

Answer:D

Step-by-step explanation: Perimeter of field is 2(length +breadth)

=2(47+158)

=410 yards.

Convert to feet= 1230ft

1ft =$3.28

1230ft will be 1230×3.28

Ans $4034.4

[tex](110)_{2} = (1 \times 2^2 + 1 \times 2^1 + 0 \times 2^ 0)_{10}\\\\~~~~~~~~~~=(4+2+0)_{10}\\\\~~~~~~~~~~=(6)_{10}[/tex]

Answer:

C. 5,292[tex]\pi[/tex]ft²

Step-by-step explanation:

V=[tex]\pi r^2h[/tex]

V=[tex]\pi *14^2 *27[/tex]

[tex]14^2*27= 5,292[/tex]

Answer is C. 5,292[tex]\pi[/tex]ft²

Hope this helps! Have a good day! :)

Answer:

c

Step-by-step explanation:

hope this helps have a nice day:)

Answer:

x-4

Step-by-step explanation:

because a number could be x and all you have to do is subtract 4 from a number making it x-4

Answer:

4-x

Step-by-step explanation:

Because it says that x is subtracted from 4 which would make it understood that 4 is the first term and then x.

Let the tens digit of the number be x .

ones digit = ( 14 - x ) ( since the sum of the 2 digits is 14 )

Two - Digit number = 10 ( tens digit ) + ones digit

Required number ,

Reversed number ,

Given ,

Reversed number - Required number = 36

✯ 140 - 9x - ( 9x + 14 ) = 36

✯ 140 - 9x - 9x - 14 = 36

✯ 126 - 18x = 36

✯ 126 - 36 = 18x

✯ 18x = 90

✯ x = 5

♧ Thus , Required number is 10 × 5 + 9 = 59

Given -

i.e, if two numbers are x and y then, x + y = 14

i.e, if 10y + x then 10y + x = 10x + y + 36.

To find -

Concept -

If a, b and c are real number (and if a and b both are not equal to 0) then ax+by=c is called a linear equation in two variables (The two variables are x and y)

The numbers a and b are called the coefficient of the equation ax+by=c. The number r is called the constant of the equation ax+by = c

PS - first we will construct two linear equations and then we'll find the number.

Solution -

Let, x + y = 14

➜ y = 14 - x ----(i)

and we'll solve 10y + x = 10x + y + 36 further,

➜ 10y + x = 10x + y + 36

➜ 10y - y = 10x - x + 36

➜ 9y = 9x + 36

➜ 9x - 9y = -36

➜ 9(x - y) = -36

➜ x - y = -4 ----(ii)

Substituting the value of y (in equation (i)) in equation (ii),

➜ x - (14 - x) = -4

➜ x - 14 + x = -4

➜ 2x = -4 + 14

➜ 2x = 10

➜ x = 10/2

➜ x = 5

Now to find the value of y we will substitute the value of x in equation (i),

➜ y = 14 - 5

➜ y = 9

Therefore, the number is {10(5)+9,i.e,} 59.

1. The equation of the line of best fit is: y = -1.15x + 102.8

2. Using the equation of the line of best fit, the predicted cost is: $62.55

The equation of a line of best fit is represented by the equation, y = mx + b, where m is the slope and b is the initial value.

1. Using two points, (72, 20) and (20, 80):

Slope (m) = change in y / change in x = (80 - 20)/(20 - 72) = 60/-52

Slope (m) = -1.15.

Substitute m = -3 and (a, b) = (72, 20) into y - b = m(x - a)

y - 20 = -1.15(x - 72)

y - 20 = -1.15x + 82.8

y = -1.15x + 82.8 + 20

y = -1.15x + 102.8

The equation of the best line of fit is y = -1.15x + 102.8.

2. Monthly heating cost, y, for a month with an average temperature of 35°F (x) will be calculated by substituting x = 35 into y = -1.15x + 102.8.

y = -1.15(35) + 102.8

y = 62.55

The predicted monthly cost is $62.55.

Learn more about the line of best fit on:

https://brainly.com/question/17261411

Answer:

option I

Step-by-step explanation:

Option I 168 yd²

The surface area =168 yd²

I hope it helped you

Answer:

RANGE: y greater than or equal to -5 (b)

Graph the function

Attached

Then

We know

Vertex form of parabola

vertex:-

Range:-

Answer:

b = 9

Step-by-step explanation:

0.5 bh= 29.25

thus

(0.5)(b)(6.5)=29.25

thus

b= 58.5/6.5 = 9

Answer:

9?

Step-by-step explanation:

Answer:

7 songs costs $8.4

Step-by-step explanation:

6/5=  $1.2 for each song

1.2 times 7=  $8.4

7 songs costs $8.4

weekly raise= $145

let's assume the first paycheck as x.

she got a weekly raise of $145.

So, after concluding the first week she'll get $ (x+145).

likewise, after completing the second week she'll get $ (x + 145) + $ 145.

= $ (x + 145 + 145)

= $ (x + 290)

therefore, this is how her salary will get increased by $145 at the end of every week.

Answer:

25

Step-by-step explanation:

[tex]0.09a=75\\a=\frac{75}{0.09} \\0.03*a=0.03*\frac{75}{0.09} =25[/tex]

Answer:

The answer is A. Mean; because the data is skewed and there are outliers

Answer:

The answer is A