Solve for f. –9 + 2f >

Click or touch the graph to plot the points.

lina2011 [118]

Answer:

the answer is C

Step-by-step explanation:

the y intercept is on the right, so (x, y)

and the third option has (4,8) so 8 is on the y

4 0

4 years ago

Sally used 5 gallons of ginger ale, 1 gallon of orange juice, and 2 gallons of pineapple juice, to make a punch for her family h

ikadub [295]

The answer is 32 quarts

7 0

3 years ago

Arithmetic of Functions problem Open ended

VladimirAG [237]

Answer: (gºh)(25)=2

Step-by-step explanation:

1. This exercise is about Composition of functions, then you have:

2. Then, you have that

(gºh)(25) $=g(h(x))=\sqrt{x}-3$

3. Now, you must substitute 25 into the function, as you can see below:

(gºh)(25) $=\sqrt{25}-3$

4. Simplify the fucntion.

5. Therfore, you obtain:

(gºh)(25) $=5-3=2$

3 0

3 years ago

Read 2 more answers

(Recall, to solve |u| = c, one must solve u = c and u = −c.) Solve: |3x-1| +2=8

11Alexandr11 [23.1K]

Answer:

The answer is 5/3, 1 2/3, and 1.67

Step-by-step explanation:

The answer to this problem is simple as everything between the two lines will come out to be a positive. So the equation will end up coming out to be 3x+1+2=8.

Now we add the 1 and 2....

3x+3=8

To make this problems simple we can subtract the 3 from the left side and do the same on the right side making the equation say...

3x=5

Now we can make it easier to solve but it will not be a whole number. We now divide 3 from the left and right side leaving us with....

x = 5/3

So this answer could be 5/3 , 1 2/3, and 1.67

4 0

1 year ago

The figure below shows two triangles EFG and KLM.

grandymaker [24]

A right triangle is a triangle that has a right angle of 90 degrees. In this exercise, we have two of this type of triangles. To solve this problem, we will apply some properties of triangles, so:

1. Which step can be used to prove that triangle EFG is also a right triangle?

To prove this, we need to use Pythagorean Theorem. So, for triangle EGF, if the formula:

$c^{2}=a^{2}+b^{2}$

is true, then EFG is also a right triangle. The steps are:

Square a

Square b

Square c

If the sum of the square of a and the sum of the square of b equals the square of c, then this is a right triangle.

2. Prove that the sum of a and c is greater than b.

We need to prove that:

$a+c>b$

From trigonometry, we know that:

$a=c \times sin(\theta) \\ \\ b=c \times cos(\theta) \\ \\ where \ \theta=\angle EFG \\ \\$

By substituting these values in the previous inequality:

$c \times sin(\theta)+c>c \times cos(\theta) \\ \\ Since \ c>0 \\ \\ sin(\theta)+1>cos(\theta) \\ \\ 1>cos(\theta)-sin(\theta)$

Since $\theta$ is an angle greater than 0 and less than 90 degrees, $cos(\theta) \ and \ sin(\theta)$ are numbers between 0 (greater than) and 1. Therefore, this inequality is always true. So, the statement has been proved.

3. Prove that the sum of a and b is greater than c.

We need to prove that:

$a+b>c$

Applying the same reasoning as in 2:

$c \times sin(\theta)+c \times cos(\theta)>c \\ \\ Since \ c>0 \\ \\ sin(\theta)+cos(\theta)>1$

This inequality is always true. So, the statement has been proved.

4. Prove that triangles are congruent by SSS property and hence angle EGF is equal to angle KML.

SSS means that we know the three sides of the triangle and want to find the missing angles. For ΔEGF, we know the three sides, and for KML, since this is a right triangle KL = c, therefore the corresponding sides of these two triangles are equal. Accordingly, these two triangles are congruent by SSS and angle EGF is equal to angle KML.

5. Prove that the ratio of EF and KL is greater than 1 and hence the triangles are similar by AA postulate.

The ratio of EF and KL is:

$\frac{EF}{KL}$

The statement is true if and only if EF > KL. Then, according to AA postulate, two triangles are similar if they have two corresponding angles congruent. So:

EGF is congruent to KML and equals 90 degrees
GEF is congruent to MKL
EFG is conguent to KLM

Accordingly, the triangles are similar.

3 0

4 years ago

Read 2 more answers

Solve for f. –9 + 2f > – 3