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Reil [10]
3 years ago
11

Date:

Mathematics
1 answer:
icang [17]3 years ago
7 0

Answer:

1. D. n + 4 = 30

2. A. 5h \ge 15

3. D. p + 5 \le 40

Step-by-step explanation:

1. Initial number of students = n

Number of new students that joined the class = 4

New total number of students after 4 students joined the class (n + 4) = 30

The equation that can be used to find the number of students in the class before new students joined, n, is represented by the equation below:

n + 4 = 30

2. The goal of Lucy is to walk at least 15 miles. This means, she must walk a distance that is equal to 15 or greater than 15 (goal: ≥ 15).

Rate of walking = 5 miles per hour

Number of hours = h

To determine how many she would walk in order to attain her goal, the inequality below represents the situation:

5h \ge 15

3. Mr Sanchez has $40 as the maximum he can spend. This means the total of all his spending must be equal to or less than $40 (total spending: ≤ 40).

Cost of ticket to the museum = $5

Cost of spending on other things at the museum = p dollars

Total spending = p + 5

Since total spending limit is $40, the following inequality can be used to determine the possible values for p:

p + 5 \le 40

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Find b and then solve the equation:(b−5)x2−(b−2)x+b=0, if one of its roots is0.5
grigory [225]

Answer:

b = ⅓

x = ½, -1/7

Step-by-step explanation:

(b−5)x² − (b−2)x + b = 0

(b - 5)(0.5)² - (b - 2)(0.5) + b = 0

0.25b - 1.25 - 0.5b + 1 + b = 0

0.75b = 0.25

b = ⅓

(⅓−5)x² − (⅓−2)x + ⅓ = 0

(-14/3)x² + (5/3)x + 1/3 = 0

14x² - 5x - 1 = 0

14x² - 7x + 2x - 1 = 0

7x(2x - 1) + (2x - 1) = 0

(7x + 1)(2x - 1) = 0

x = 0.5, -1/7

4 0
4 years ago
Read 2 more answers
-6x-3y=-30<br> -9x-y=-24<br> Solve by elimination
german

Answer:

x=2. y=6

Step-by-step explanation:

Step (1)

-6x-3y=-30

-3(-9x-y=-24)

Step (2)

-6x-3y=-30

27x+3y=72

Step (3)

-6x+27x=21x

-30+72=42

Step (4)

21x=42

divide 21 on each side

x=2

Plug x in one of the two equations

to get the y

-6(2)-3y=-30

-12-3y=-30

+12. +12

-3y=-18

divide negative 3

y=6

8 0
3 years ago
In order to evaluate 7 sec(θ) dθ, multiply the integrand by sec(θ) + tan(θ) sec(θ) + tan(θ) . 7 sec(θ) dθ = 7 sec(θ) sec(θ) + ta
Maurinko [17]

Answer:

\int {7 \sec(\theta) } \, d\theta = 7\ln(\sec(\theta) + \tan(\theta)) + c

Step-by-step explanation:

The question is not properly formatted. However, the integral of \int {7 \sec(\theta) } \, d\theta is as follows:

<h3></h3>

\int {7 \sec(\theta) } \, d\theta

Remove constant 7 out of the integrand

\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) } \, d\theta

Multiply by 1

\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) * 1} \, d\theta

Express 1 as: \frac{\sec(\theta) + \tan(\theta) }{\sec(\theta) + \tan(\theta)}

\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) * \frac{\sec(\theta) + \tan(\theta) }{\sec(\theta) + \tan(\theta)}} \, d\theta

Expand

\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{\sec^2(\theta) + \sec(\theta)\tan(\theta) }{\sec(\theta) + \tan(\theta)}} \, d\theta

Let

u = \sec(\theta) + \tan(\theta)

Differentiate

\frac{du}{d\theta} = \sec(\theta)\tan(\theta) + sec^2(\theta)

Make d\theta the subject

d\theta = \frac{du}{\sec(\theta)\tan(\theta) + sec^2(\theta)}

So, we have:

\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{\sec^2(\theta) + \sec(\theta)\tan(\theta) }{u}} \,* \frac{du}{\sec(\theta)\tan(\theta) + sec^2(\theta)}

Cancel out \sec(\theta)\tan(\theta) + sec^2(\theta)

\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{1}{u}} \,du}}

Integrate

\int {7 \sec(\theta) } \, d\theta = 7\ln(u) + c

Recall that: u = \sec(\theta) + \tan(\theta)

\int {7 \sec(\theta) } \, d\theta = 7\ln(\sec(\theta) + \tan(\theta)) + c

8 0
3 years ago
Factor the expression. 16j2 + 24j + 9
ohaa [14]
A² + 2ab + b² = (a+b)²<span>
</span><span>
So we get 
</span><span>16j</span>² + 24j + 9 = (4j+3)²
5 0
4 years ago
Read 2 more answers
Please I have a 8th grade math question
Soloha48 [4]
<h3>Answer:  2</h3>

==========================================================

Explanation:

x = number of years

y = height in feet

The equation for the first tree is

y = x+3

The slope is 1 to represent a rate of 1 ft per year of growth. The y intercept of 3 is the starting height. Refer to y = mx+b form.

For the second tree, the equation is:

y = 0.5x+4

This time we have a slope of 0.5 and a y intercept of 4.

Apply substitution to solve for x

y = x+3

0.5x+4 = x+3

0.5x-x = 3-4

-0.5x = -1

x = -1/(-0.5)

x = 2

The trees will be the same height in <u>  2  </u> years.

What will that height be? Plug x = 2 into either equation to find y. We should get the same y value.

y = x+3

y = 2+3

y = 5

Or we could say

y = 0.5x+4

y = 0.5*2+4

y = 1+4

y = 5

We've shown that both equations lead to y = 5 when x = 2. This means that at the 2 year mark, both trees are 5 feet tall. This helps confirm we have the correct x value.

8 0
2 years ago
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