11.) Mrs. Collins is buying supplies for her classroom. Pencils cost

labwork [276]

An algebraic expression is one that consists of both number(s) and an alphabet(s). The required answers are:

i. Distance from Chenoa's house to the coffee shop = 6.0 miles

ii. Distance from coffee shop to Chenoa's school = 1.5 miles

iii. Distance from Chenoa's house to her school = 7.5 miles

An algebraic expression is one that consists of both number(s) and an alphabet(s). The alphabet is referred to as the unknown whose value has to be determined.

In the given question, let the distance from the coffee shop to Chenoa's school be represented by y.

So that;

The distance from Chenoa's house to the coffee shop = (2y + 3) miles.

The total distance from Chenoa's house to her school = 5y.

This implies that:

(2y + 3) + y = 5y

3y + 3 = 5y

3 = 5y - 3y

2y = 3

y = $\frac{3}{2}$

= 1.5

The distance from the coffee shop to Chenoa's school is 1.5 miles.

Thus;

(2y + 3) = ( 2(1.5) + 3)

= 6

The distance from Chenoa's house to the coffee shop is 6 miles.

And,

5y = 5(1.5)

= 7.5

The total distance from Chenoa's house to her school is 7.5 miles.

For more clarifications on algebraic expressions, visit: brainly.com/question/12792264

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5 0

2 years ago

On the grid, draw the line with the equation x = -4

nexus9112 [7]

Answer:

Step-by-step explanation:

On a grid,

go to the middle, aka 0,0

move left 4 times, but stay on the same line. Then draw that line up and down on the -4 of x.

sorry if this isn't clear

6 0

3 years ago

Read 2 more answers

Evaluate the expression when b= 3 and c = -4 b - 4c

Sedaia [141]

Answer:

15.

c is a negative

3 - (-12)

15

5 0

3 years ago

Verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial

Mariulka [41]

Answer:

i) Since P(2), P(-1) and P(½) gives 0, then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

ii) - the sum of the zeros and the corresponding coefficients are the same

-the Sum of the products of roots where 2 are taken at the same time is same as the corresponding coefficient.

-the product of the zeros of the polynomial is same as the corresponding coefficient

Step-by-step explanation:

We are given the cubic polynomial;

p(x) = 2x³ - 3x² - 3x + 2

For us to verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial, we will plug them into the equation and they must give a value of zero.

Thus;

P(2) = 2(2)³ - 3(2)² - 3(2) + 2 = 16 - 12 - 6 + 2 = 0

P(-1) = 2(-1)³ - 3(-1)² - 3(-1) + 2 = -2 - 3 + 3 + 2 = 0

P(½) = 2(½)³ - 3(½)² - 3(½) + 2 = ¼ - ¾ - 3/2 + 2 = -½ + ½ = 0

Since, P(2), P(-1) and P(½) gives 0,then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

Now, let's verify the relationship between the zeros and the coefficients.

Let the zeros be as follows;

α = 2

β = -1

γ = ½

The coefficients are;

a = 2

b = -3

c = -3

d = 2

So, the relationships are;

α + β + γ = -b/a

αβ + βγ + γα = c/a

αβγ = -d/a

Thus,

First relationship α + β + γ = -b/a gives;

2 - 1 + ½ = -(-3/2)

1½ = 3/2

3/2 = 3/2

LHS = RHS; So, the sum of the zeros and the coefficients are the same

For the second relationship, αβ + βγ + γα = c/a it gives;

2(-1) + (-1)(½) + (½)(2) = -3/2

-2 - 1½ + 1 = -3/2

-1½ - 1½ = -3/2

-3/2 = - 3/2

LHS = RHS, so the Sum of the products of roots where 2 are taken at the same time is same as the coefficient

For the third relationship, αβγ = -d/a gives;

2 * -1 * ½ = -2/2

-1 = - 1

LHS = RHS, so the product of the zeros(roots) is same as the corresponding coefficient

7 0

3 years ago

I need some help with this, please explain well. It's Trigonometry with right triangles, please let me know if you need a better

andreyandreev [35.5K]

Answer:

x = 12

Step-by-step explanation:

First you figure out which function your going to use. I notice that from the angle we have 5 which is the opposite side and 23 which is the adjacent side. This means we have to use tangent.

Then set up your equation: tan(x)=5/23. This is because the opposite side is 5 and the adjacent is 23 and it must be set up in that order.

Next get x alone by making the equation: x=tan^-1(5/23).

Then put it into the calculator and round to get 12.

5 0

4 years ago