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3 years ago

Need Help ASAP! Provide the missing statements and reasons for the following proof. Please provide proof.

Mathematics

1 answer:

Dafna11 [192]3 years ago

8 0

Answer/Step-by-step explanation:

The following shows the reasons for each step taken in proving that $x = \frac{61}{9}$ :

Step 1:

$9(x - 2) + 32 = 75$ => R1: Given

Step 2: apply the subtraction property of equality by subtracting 32 from each side of the equation.

$9(x - 2) + 32 - 32 = 75 -32$

$9(x - 2) = 43$ => R2: Subtraction property of equality

Step 3: Eliminate the parentheses by applying the distributive property of multiplication

$9x - 18 = 43$ => R3: distributive property of multiplication

Step 4: Apply the addition property of equality by adding 18 to each side.

$9x - 18 + 18 = 43 + 18$

$9x = 61$ => R4: Addition property of equality

Step 5: Apply the division property if equality by dividing both sides by 9.

$\frac{9x}{9} = \frac{61}{9}$

$x = \frac{61}{9}$ => R5: Division property of equality

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Precalculus question. Please help me and thank you .

VLD [36.1K]

We know,

sin(x) and cos(x) have minimum value equal to -1 and maximum value is 1.

Maximum value of sin(x) is 1

So we replace sin by 1 in our given equation

$y=-2+5sin(\frac{\pi }{12}(x-2))$

When we replace sin by 1 we will get

$y=-2+5(1))$

y= -2+5 = 3

So maximum value is 3

4 0

4 years ago

The triangles are similar. What is the value of x? Enter your answer in the box. x = two right triangles. the larger triangle ha

grandymaker [24]

<h2>Answers:</h2>

These problems can be solved by the Thales’s Theorem, which states:

Two triangles are similar when they have equal angles and proportional sides

In addition, if two triangles are similar, their angles are similar as well. This means that the relation between two sides of the big triangle is equal to the relation between two sides of the small triangle, as follows:

$\frac{B}{A}=\frac{b}{a}$

Knowing this, lets’s begin with the answers:

1. For this first problem, see the first figure attached. There are shown the two triangles, and we are told both are similar, this means (according the prior explanation above) that we can use the Thale’s Theorem to find $x$ .

Therefore, we can establish a relation between two sides of the big triangle which is equal to the relation between two sides of the small triangle; in this case let’s use $B$ and $C$ for the first triangle and $b$ and $c$ for the second:

$\frac{C}{B}=\frac{c}{b}$

$\frac{6x+28}{96}=\frac{25}{24}$

Now we find $x$ :

$6x+28=\frac{(25)(96)}{24}$

$6x+28=100$

$6x=100-28$

$x=\frac{72}{6}$

$x=12$

Finally, the value of $x$ is 12 units.

2. For this problem, see the second figure attached. In order to find the values of the segments BE and EC, we will use two sides of each triangle (ABE and DCE) according to the Thale’s Theorem:

For the segment BE:

$\frac{BE}{10}=\frac{x+3}{4}$

$BE=\frac{(x+3)(10)}{4}$

Simplifying:

$BE=\frac{5}{2}(x+3)$ >>>>>This is the length of the segment BE

For the segment EC:

$\frac{EC}{4}=\frac{2x+10}{10}$

$EC=\frac{(2x+10)(4)}{10}$

Simplifying:

$EC=\frac{4}{5}(x+5)$ >>>>>This is the length of the segment EC

3. For this problem, see the third figure attached:

$\frac{12 inches}{8 inches}=\frac{x}{7 inches}$

Solving for $x$ :

$x=\frac{(12 inches)(7 inches)}{8 inches}$

Finally:

$x=10.5 inches$ >>>>>This is the height of the smaller sail

4. For this problem, see the fourth figure attached.

$\frac{80 inches}{45 inches}=\frac{x}{40 inches}$

Solving for $x$ :

$x=\frac{(80 inches)(40 inches)}{45 inches}$

$x=71.11 inches$ >>>>>This is the height from the floor to the son's hand

6 0

3 years ago

Which statement MUST be true?

romanna [79]

The answer is C

The reason being these two sets of angles are opposite angles (also known as vertical angles) and opposite angles are always congruent.

7 0

4 years ago

A total of 476 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student t

stiks02 [169]

Answer:

357

Step-by-step explanation:

476÷4=119

119×3=357

5 0

4 years ago

David bought 3.5 pounds of apples that sell for $1.28 per pound and 2.4 pounds of bananas that sell for $0.55 per pound. How muc

Allushta [10]

3.5*1.28=4.48
2.4*0.55=1.32
4.48+1.32=5.8
5.8/5.9=0.98
the answer is C

7 0

3 years ago