Please help with this lesson

Let [tex]y[/tex] be bags of chips and [tex]x[/tex] bottles of Gatorade.

The system of linear equations emerges.

[tex]3y+2x=7.35[/tex]

[tex]x=1.8[/tex]

Insert value of x from second equation into first to get rid of the system and get:

[tex]3y+2(1.8)=7.35[/tex]

Now solve for y.

[tex]y=\frac{7.35-2(1.8)}{3}=1.25[/tex].

A bag of chips costs $1.25.

Hope this helps.

The cost for 4 hours is 850, the cost for 7 hours is 1300 then the cost for 12 hours will be equal to 1906.8.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the data given in the question,

Cost for 4 hours = 850

4 × 212.5 = 850

Cost for 7 hours = 1300

7 × 185.7 = 1300

The rate at which it is increasing,

212.5 - 185.7 = 26.8

For 12 hours,

185.7 - 26.8 = 158.9

12 × 158.9 = 1906.8

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Answer:

The answer is "The total number of stamps is 35".

Step-by-step explanation:

There are many 35 stamps in total. The number of stamps during the first mixture is= 35  

Then let the other configurations be checked  

[tex]\to 20 + 15= 35 \\\to 22+13 = 35 \\\to 25 + 10 = 35 \\[/tex]

Therefore the correct answer is =35

The total number of stamps is 35. Therefore, the correct answer is option C.

From the given table,

Which ever the combination we choose, we get total number of stamps as 35.

Total cost of stamps in each case is

i) 18×0.45+17×0.65​

= $14.65

ii) 20×0.45+15×0.65​

= 9+9.75

= $18.75

iii) 22×0.45+13×0.65​

= 9.9+8.45

= $18.35

iv) 25×0.45+10×0.65​

= 11.25+6.5

= $17.75

Therefore, the correct answer is option C.

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Answer:

217.75

Step-by-step explanation:

Divide the distance traveled by the gallons used.  This will give you the distance that can be traveled using one gallon.

130/4 = 32.5

Now, multiply this value by 6.7 to find the distance that can be covered.

6.7 × 32.5 = 217.75

Answer:

[tex]\bold{x=\dfrac{-3\pm i\sqrt{7}}{2}}[/tex]

Step-by-step explanation:

Given quadratic equation is:

[tex]-x^2 - 3x = 4[/tex]

Rewriting the given equation:

[tex]-x^2 - 3x - 4 = 0[/tex]

OR

[tex]x^2 + 3x + 4=0[/tex]

Solution of a quadratic equation represented as [tex]ax^2+bx+c=0[/tex] is given as:

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Comparing the given equation with standard equation:

a = 1

b = 3

c = 4

So, the roots are:

[tex]x=\dfrac{-3\pm\sqrt{3^2-4\times 1 \times 4}}{2\times 1}\\\Rightarrow x=\dfrac{-3\pm\sqrt{9-16}}{2}\\\Rightarrow x=\dfrac{-3\pm\sqrt{-7}}{2}[/tex]

[tex]\sqrt{-7 }[/tex] can be written as [tex]7\sqrt{-1}[/tex]

and [tex]\sqrt{-1} = i[/tex]

So, [tex]\sqrt{-7} = i\sqrt7[/tex]

The numbers containing [tex]i[/tex] in them, are called as complex numbers.

Therefore, the roots of the equation can be written as:

[tex]\Rightarrow \bold{x=\dfrac{-3\pm i\sqrt{7}}{2}}[/tex]

Answer:

The correct option is;

720 unit²

Step-by-step explanation:

The given dimension of square pyramid is given as follows;

The length and width of the square prism = w = 12 units

The height of the square prism = x = 7 units

The base width of the pyramid = w = 12 units

The formula of the area of the square prism = 2 × w² + w × x × 4

∴ The area of the square prism = 2 × 12² + 12 × 7 × 4 = 624 unit²

The area of the square pyramid = w² + 1/2×4×w ×√((w/2)² + y²)

The area of the square pyramid = 12² + 1/2×4×12×√((12/2)² + 8²) = 12² +240 unit²

The formula for the surface area of the figure = The slant surface area of the square prism  + The area of the base of the square prism + The slant surface area of the square pyramid

The surface area of the figure = 12² + 12 × 7 × 4 + 1/2×4×12×√((12/2)² + 8²) = 720 unit²

The surface area of the figure = 720 unit².

Answer:

720 units2

Step-by-step explanation:

Hope this helps :)

Answer:

(4, -9)

Step-by-step explanation:

Find the distances between the x and y coordinates of point T and the midpoint:

2 - 0 = 2 (distance of x values)

-2 - 5 = -7 (distance of y values)

Add these two values to the coordinates of the midpoint:

2 + 2 = 4 (x value of point S)

-2 - 7 = -9 (y value of point S)

So, point S is at (4, -9)

Acceleration =‘change in speed / time:

Acceleration = (10-2)/4

Acceleration =8/4

Acceleration = 2 m/s^2

Answer:

The answer is A

Step-by-step explanation:

Answer:

Ratio = 5/12

Jack had = $972

Step-by-step explanation:

Given:

Since they spent same amount of money:

The ratio was 5/12

Sum of money:

As per ratio, x = 5/12y, substituting x in above equation:

Jack had $972

The graph is a representation of how the value of the variable y vary.

Given that y is equal to a constant, 8.4, the graph is an horizontal line.

Response:

The given equation is; -7 + 5·y = 35

The number of variables in the given equation is one (y), the

power of the variable is also one and the variable is y.

Therefore;

Solving the equation gives;

-7 + 5·y = 35

5·y = 35 + 7 = 42

[tex]y = \dfrac{42}{5} = \mathbf{8.4}[/tex]

The graph of the equation is the graph of the line, y = 8.4

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Answer:

C.) ΔXZY ≅ ΔLGM

Step-by-step explanation: I got it right on Edge

The correct congruency statement is: [tex]\triangle XZY \cong \triangle LGM[/tex]

From the graph, we have the following corresponding points

The above highlights mean that:

Triangle XZY corresponds to triangle LGM

Hence, the correct congruency statement is: [tex]\triangle XZY \cong \triangle LGM[/tex]

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Answer:

12

Step-by-step explanation:

Let x = number of 50.00 notes.

They are worth 50x

Then, 2x = number of 20.00 notes.

They are worth 2x * 20 = 40x

50x + 40x < 1100

90x < 1100

9x < 110

x < 12.2

Answer: 12

Check:

x = 12   (number of 50.00 notes)

2x = 24    (number of 20.00 notes)

12 * 50 + 24 * 20 = 1080

If she used one more 50.00 note, she'd go over 1,100, so 12 is correct.

Answer:

[tex]\Huge \boxed{\mathrm{B. \ 6}}[/tex]

Step-by-step explanation:

We can apply the Intersecting Secant-Tangent Theorem.

TV is the secant.

VW is the tangent.

VW² = VT × VU

(x+6)² = (5+x+4) × (x+4)

Combine the terms in bracket.

(x+6)² = (x+9)(x+4)

Expand brackets on both sides of the equation.

x²+12x+36=x²+13x+36

Subtract x² from both sides.

12x+36=13x+36

Subtract 12x from both sides.

36=x+36

Subtract 36 from both sides.

0=x

WV = x+6

x=0

WV = 0+6 = 6

The measure of the tangent WV is 6.

Answer:

l+3

Step-by-step explanation:

since Alma is 3 years older than Liz so then she would be l+3

Answer:

speed of Jim's train = 35 mi/h

speed of Sarah's train = 35 +20 mi/h = 55 mi/hour

Step-by-step explanation:

Let the speed of Jim's train be x mi/h

Given, Sarah and Jim leave a train station at the same time traveling 20mi/h faster that Jim’s train.

speed of Sarah's train = x + 20 mi/h

we know distance = speed * time

time = 3 hours

distance traveled by Sarah's train = 3*(x+20) = 3x+60 miles

distance traveled by Jim's train = 3*x =  3x miles

It is not given that if trains are moving in same or opposite direction.

__________________________________

if they are travelling in same direction

Then, then distance between them = total distance traveled by

faster train -  total distance traveled by

slower train = 3x +60 -3x = 60 miles

which is wrong as the two trains are 270 miles apart

hence, they are travelling in opposite direction

In this case

distance between them = total distance traveled by

faster train +  total distance traveled by

slower train = 3x +60 + 3x = 6x + 60 miles

given that the trains are 270 miles apart

6x + 60 miles = 270 miles

6x = 270 - 60 = 210

x = 210/6 = 35

Thus, speed of Jim's train = 35 mi/h

speed of Sarah's train = 35 +20 mi/h = 55 mi/hour

Answer:

C

Step-by-step explanation:

● 2.4 × 10^5

10^5 is 100000

● 2.4 × 100000

● 240 000

Answer:

C. 240,000

Step-by-step explanation:

This question is about using scientific notation.

In order to solve these types of questions, you move the decimal as many places as indicated by the Exponent ( which is given above the 10).

So in this example, we are given 2.4 x 10 ⁵. This means we would move the decimal 5 places. Since the exponent is positive, we will move the decimal to the right.

2 . 4         .

Which gives us option C. 240,000.

Answer:

The correct option is;

10.25 + (-3.5) = 6.75

Step-by-step explanation:

We note that when adding numbers the negative sign is equivalent to the minus sign which is a mathematical operator. Therefore, when we subtract one number from another, it is equivalent to adding the negative of the other number to the first number

The given expression is 10.25 - (3.5)

The result of the given expression is 10.25 - (3.5) = 6.5

Therefore, we have;

10.25 + (-3.5) = 6.75

Answer: B. The domain is {x|x<0 or x>0} and the range is {y|y>0}

Step-by-step explanation:

f(x)=x^-2

----------------------------

#1 Any negative (-) exponents means the answer will be 1/ the term

- for example, 3^-2=1/3^2=1/9

NOTE: NEGATIVE EXPONENTS DOES NOT MEAN IT IS A NEGATIVE NUMBER, IT IS STILL A POSITIVE NUMBER IF THE BASE IS POSITIVE.

-----------------------

The domain, which will be the value of x.

x can be any real number, except 0, because 0 can't go to negative exponents or else it will be undefined.

{x|x<0 or x>0}

-------------------------------------

The range, which will be the value of y.

Since the x value is being squared, it is always positive

{y|y>0}

Answer:

A. The first choice.

Step-by-step explanation:

[tex] f(x) = x^{-2} [/tex]

Let's rewrite the function in a more familiar way.

[tex] f(x) = \dfrac{1}{x^2} [/tex]

Domain:

We know that a denominator cannot equal zero, so we set the denominator equal to zero to find the values of x that must be excluded from the domain.

x^2 = 0

x = 0

The only value excluded from the domain is x = 0.

The domain is all reals except for zero.

Range:

Now that we know the domain is all real numbers except for 0, we look closely at the denominator.

What happens when you replace x with negative numbers? Since you are squaring x, all denominators will be positive. When you replace x with positive numbers, all denominators will also be positive. For values of x with a large absolute value, for example 1000, -1000, 1,000,000 or -1,000,000, as the absolute value of x increases, f(x) approaches zero. For values of x with a small absolute value, such as 0.0001, -0.0001, -0.00000001, or 0.00000001, as x approaches zero, f(x) approaches positive infinity.

The range is all positive real numbers.

Answer:

Domain: all real numbers except 0.

Range: all positive real numbers.

Answer:

14 square inches

Step-by-step explanation:

Since, three one inch cubes are stacked.

Therefore,

l = 1 in

w = 1 in

h = 3 in

Surface area of the composite figure

= 2(lw + wh + lh)

= 2( 1*1 + 1*3 + 1*3)

= 2 (1 + 3 + 3)

= 2 * 7

= 14 square inches

Answer:

money with Gopal rs. 60

money with laxmi Rs. 90

Total money with them = Rs. 150

Step-by-step explanation:

Let money with gopal be x

let money with laxmi be y

Given

Gopal gives Rs 10 from his money to Laxmi her money becomes double thanthat of the remaining money of Gopal

Money left with gopal after giving Rs 10 = x-10

money with Laxmi after getting rs 10 = y+10

according to given condition

money with laxmi = 2*money left with Gopal

y+10 = 2(x-10)

___________________________________________________

Laxmi gives Rs 10 to Gopal his moneyis still Rs 10 less than the remaining money of Laxmi.

Money left with Laxmi after giving Rs 10 = y-10

money with Gopal after getting rs 10 = x+10

according to given condition

money with laxmi -10 =money  with Gopal

y-10-10 =x+10

y-20 = x+10

=> y = x+10+20

y = x+30

substituting y = x+30 in    y+10 = 2(x-10)

x+30 +10 = 2(x-10)

x+40 = 2x-20

=>40+20 = 2x-x

=> x = 60

y = x+30 = 60+30 = 90

Thus,

money with Gopal rs. 60

money with laxmi Rs. 90

Total money with them = 60+90 = rs. 150

Answer:

first step to balance the equation is :

multiply AL by 2 to match the amount of aluminum on the other side

balanced equation : 4 Al +3O2 → 2 ALO3

Step-by-step explanation:

Al + O2 → Al2O3

first step to balance the equation is :

multiply AL by 2 to match the amount of aluminum on the other side

but then you have to deal with the amount of O from both sides, we need to find the least common multiple between 2 and 3 which is 6

the best thing to balance the equation is to multiply O2 by 3 and O3 by2, then deal with the amount of AL which is 4 on the other side. last step is to multiply AL by 4 to balance the equation.

Answer:

D. 63°

Step-by-step explanation:

a = 27°

b = 180° - (a + 27°)

b = 180° - (27° + 27°)

b = 180° - 54°

b = 126°

By inscribed angle theorem:

c = 1/2 b = 1/2 * 126°

c = 63°

The measure of angles a, b, and c in the given figure are 27°, 126°, and 63°, respectively.

An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.

In the triangle ORQ, the two sides of the triangle OR and OQ are the radius of the triangle, therefore, the length of the two sides will be.

Since the two sides of the triangle are equal, therefore, the triangle will be an isosceles triangle, with the angle opposite to the same length measuring the same. Therefore,

∠OQR = ∠ORQ

a = 27°

Now, in a triangle, the sum of the measure of all the angles is equal to 180°. Therefore, we can write,

∠OQR + ∠ORQ + ∠QOR = 180°

a + 27° + b = 180°

27° + 27° + b = 180°

b = 180° - 27° - 27°

b = 126°

Further, In a circle, the measure of the angle formed by the chord in the centre of the circle is twice the measure of the angle formed by the same chord on any point in the circle. Therefore,

∠QOR = 2∠QPR

b = 2 × ∠QPR

126° = 2 × ∠QPR

∠QPR = 126° / 2

∠QPR = 63°

Hence, the measure of angles a, b, and c in the triangle are 27°, 126°, and 63°, respectively.

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Answer:[tex]x^{2}[/tex]

Step-by-step explanation:

The highest degree is [tex]x^{2}[/tex]

quadratic equations are usually in this form: [tex]ax^{2}[/tex] +bx +c =0 (the signs may be positive or negative depending on the question given)

Answer:

Step-by-step explanation:

a. 2a(3+7a)

b.2x(x^3+x^4+x^9)

c.3z(z-5)

d i cant see

Answer:

1) 6a + 14a^2

2a(3+7a)

2) 2x^4 + 2x^5 + 2x^10

2x^4(1 + x + x^6)

3) 6z^2 - 15z

3z(2z - 5)

4) 42w^3 - 14w + 77w^2

42w^3 + 77 w^2 - 14 w

7w(6w^2 + 11w - 2)

Step-by-step explanation:

Answer:

  A, B, D, F

Step-by-step explanation:

The domain of a function is the range of its inverse.

The composition of a function and its inverse is an identity.

Answer:

3

Step-by-step explanation:

ok first multiply 6 and 4 it becomes 24 then we divide 24 with 8.

Answer:

12

Step-by-step explanation:

x + 1/4 x = 15

4/4 x + 1/4 x = 15

5/4 x = 15

x = 15 * 4/5

x = 12

Answer:

Its 12 trust me just did it

Step-by-step explanation:

Answer:

The second object (4000 grams) had more kinetic energy

Step-by-step explanation:

Use the equation KE = 0.5mv², where m is the mass and v is the velocity.

Find the kinetic energy of the first object:

KE = 0.5(2000)(2 m/s)²

KE = 4000 J

Find the kinetic energy of the second object:

KE = 0.5(4000)(3 m/s)²

KE = 18000 J

So, the second object (4000 grams) had more kinetic energy.

The second object of mass 4000 grams will have more kinetic energy than the first mass.

The energy that an object has as a result of motion is known as kinetic energy. It is described as the effort required to move a mass-determined body from rest to the indicated velocity.

Use the equation KE = 0.5mv², where m is the mass and v is the velocity.

The kinetic energy of the first object:

KE = 0.5(2000)(2 m/s)²

KE = 4000 J

The kinetic energy of the second object:

KE = 0.5(4000)(3 m/s)²

KE = 18000 J

Therefore, the second object (4000 grams) had more kinetic energy.

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Answer:

The simplified expression to represent the scenario is Y = 4·X - 0.48·X

Step-by-step explanation:

The given parameters are;

The number of tickets required = 4

The amount of discount offered = 12%

Let the selling price = X

Therefore the amount paid for each ticket = X - X×12 %

Which gives;

The amount paid for each ticket = X - X×0.12

The amount paid for the four tickets = 4 × (X - X×0.12) = 4·X - 4×0.12·X =  4·X - 0.48·X

Whereby the amount paid for the four tickets = Y, we have;

Y = 4·X - 0.48·X

Which gives, the simplified expression to represent the scenario as Y = 4·X - 0.48·X.