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2 years ago

Can someone please do these for me?

Mathematics

1 answer:

Gennadij [26K]2 years ago

3 0

$\rm \: y = 100 + 65x \\ \rm y = 40 + 80x$

$\rm 100 + 65x = 40 + 80x$

$\rm \: - 65x + y = 100 \\ \rm \: - 80x - y = - 40$

$\rm \: x = 4$

Now, Substitute the given value of x into the second equation

$\rm y = 40 + 80 \times 4$

$\rm \: y = 360$

The possible solution of the system is the ordered pair (x,y)

$\rm(x,y) = ( 4 , 360 )$

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<h3>Part 2 is attached!!</h3>

$\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}$

To solve this we will need to put the value of x as 3 in both equations and solve for y

$\rm \: y = 100 + 65 \times 3 \\ \rm \: y = 40 + 80 \times 3$

$\rm \: y = 100 + 195 \\ \rm \: y = 295$

$\rm \: y = 40 + 240 \\ \rm \: y= 280$

Therefore, Amy's auto repair shop is cheapest...~

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3 years ago

Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let t

katrin2010 [14]

Answer:

$\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24$

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of $\triangle ACD$ and the hypotenuse of $\triangle ADB$ .

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

$\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}$

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is $\angle CAD$ . The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

$\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}$

Now use this value in the Law of Sines to find AD:

$\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}$

Recall that $\sin 45^{\circ}=\frac{\sqrt{2}}{2}$ and $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ :

$AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}$

Now that we have the length of AD, we can find the length of AB. The right triangle $\triangle ADB$ is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio $x:x\sqrt{3}:2x$ , where $x$ is the side opposite to the 30 degree angle and $2x$ is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent $2x$ in this ratio and since AB is the side opposite to the 30 degree angle, it must represent $x$ in this ratio (Derive from basic trig for a right triangle and $\sin 30^{\circ}=\frac{1}{2}$ ).

Therefore, AB must be exactly half of AD:

$AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24$

3 0

3 years ago

Read 2 more answers

Read paragraphs 4-5 from the passage.

rodikova [14]

Answer: C

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I recognize this as coming from an old 1912 novel published as "A Princess of Mars", by Edgar Rice Burroughs. I read the book as a teenage boy. A 2012 movie, called "John Carter", was based on this same book.

Answer A - No, because the character (Carter) says, "My muscles, perfectly attuned and accustomed to the force of gravity on Earth". Perfectly attuned is an athlete, not a clumsy person.

Answer B - No, because the character just doesn't sound all that frustrated. The experience is strange and inconvenient, yet he is handling his emotions pretty well for how weird it must be. It is more like he is writing about an amazing experience, not just complaining.

Answer D - No, because he never says that the experience was making him happy. He does not say that he was laughing or smiling or that it reminded him of some pleasant time he had as a boy.

Answer C - Yes. - Creation of vivid imagery. In a novel, the author must paint pictures with their words. Part of how the author does this is by giving you the picture of a man who feels very comfortable with his coordination on Earth, but keeps winding up about 9 feet off the ground without trying. He doesn't just "I kept falling". He tells you in vivid detail - "... landed me sprawling on my face or back ..."

Hope this helps!

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1 year ago

The perimeter of a rectangular painting is 310 centimeters. If the width of the painting is 56 centim

gtnhenbr [62]

Answer:

The length is 99 cm

Step-by-step explanation:

The perimeter of a rectangle is

P = 2 (l+w)

310 = 2( l+56)

Divide each side by 2

310/2 = 2/2( l+56)

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155-56 = l+56-56

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3 years ago

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