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2 years ago

If PR = 4x – 2 and RS = 3x – 5, which expression represents PS?

Mathematics

1 answer:

klasskru [66]2 years ago

8 0

Answer:

$PS = 7x- 7$

Step-by-step explanation:

Given

Straight Line, PS

Such that

$PR = 4x -2$

$RS = 3x - 5$

Required

Find PS

From the attachment above, it can be seen that RS is a continuation of PS;

This implies that

$PS = PR + RS$

Substitute $PR = 4x -2$ and $RS = 3x - 5$

$PS = 4x - 2 + 3x - 5$

Collect like terms

$PS = 4x + 3x- 2 - 5$

$PS = 7x- 7$

Hence, the length of PS is $PS = 7x- 7$

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2 years ago

Read 2 more answers

You have a budget of $48. You want to buy fruit and granola bars. Fruit costs $4 per pound, and the granola bars are $1 each. Yo

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1)Define the variables you will use in your model.

Let

x------->total pounds of the fruit

y-------> the total number of granola bars

TC----> total cost

Tf------> total cost of the fruit

Tg----> total cost of the granola bars

2) Write an inequality representing the total cost of your purchase. (3 points)

a. Each pound of fruit costs $4. Write an expression that shows the total cost of the fruit. Use the variable you identified in question 1

Tf=4*x

b. Each granola bar costs $1. Write an expression that shows the total cost of the granola bars. Use the variable you identified in question 1.

Tg=1*y--------> Tg=y

c. Combine the expressions from parts a and b to write an expression for the total cost. Then use this expression to write an inequality that compares the total cost with the amount you have to spend.

TC=Tf+Tg

TC=4*x+y

inequality-------> $4x+y \leq 48$

3. Write the inequality that models the number of granola bars you need to buy.

You need at least 10 granola bars

$y\geq 10$

4. Describe in words what each of your inequalities means

inequality 1

$4x+y \leq 48$

the total cost of fruits plus the total cost of granola bars must be less than or equal to 48 dollars

inequality 2

$y\geq 10$

5. Graph your system of inequalities.

using a graph tool

see the attached figure

6. Identify one point on the graph that represents a viable solution to the problem, and then identify one point that does not represent a viable solution.

Let

A-------> one point on the graph that represents a viable solution

B-------> one point on the graph that does not represent a viable solution

A(4,20)

x=4-------> total pounds of the fruit

y=20------> the total number of granola bars

check point A

substitute the values of x and y in the inequality 1

$4x+y \leq 48$

$4*4+20\leq 48\\ 36\leq 48$ -------> is ok

substitute the values of x and y in the inequality 2

$y\geq 10$

$20\geq 10$ --------> is ok

the point A represents a viable solution, because satisfies both inequalities

B(10,30)

x=10-------> total pounds of the fruit

y=30------> the total number of granola bars

check point B

substitute the values of x and y in the inequality 1

$4x+y \leq 48$

$4*10+30\leq 48\\ 70\leq 48$ -------> is not a viable solution

substitute the values of x and y in the inequality 2

$y\geq 10$

$30\geq 10$ --------> is ok

the point B is not a viable solution because does not satisfy the inequality 1

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1 year ago

Identify the triangle that contains an acute angle for which the sine and cosine ratios are equal. 1. Triangle A B C has angle m

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Answer:

The correct option: (2) Triangle ABC that has angle measures 45°, 45° and 90°.

Step-by-step explanation:

It is provided that a triangle ABC has an acute angle for which the sine and cosine ratios are equal to 1.

Let the acute angle be m∠A.

For the sine and cosine ratio of m∠A to be equal to 1, the value of Sine of m∠A should be same as value of Cosine of m∠A.

The above predicament is possible for only one acute angle, i.e. 45°, since the value of Sin 45° and Cos 45° is,

$Sin\ 45^{o} =Cos\ 45^{o} = \frac{1}{\sqrt{2} }$

So for acute angle 45° the ratio of Sin 45° and Cos 45° is:

$\frac{Sin\ 45^{o}}{Cos\ 45^{o}} = \frac{\frac{1}{\sqrt{2} } }{\frac{1}{\sqrt{2} } } = 1$

Hence one of the angles of a triangle is, m∠A = 45°.

Comparing with the options provided the triangle is,

Triangle ABC that has angle measures 45°, 45° and 90°.

Thus, the provided triangle is a right angled isosceles triangle, since it has two similar angles.

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2 years ago

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x < 3/4 is your answer.

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2 years ago

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tia_tia [17]

Answer:

<h3>The missing value in the solution to the equation is 6.</h3><h3>So, the complete solution is (6, -4).</h3>

Step-by-step explanation:

Given:

6x+7y=4x+4y.

( ,-4)

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As, the equation is: