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2 years ago

10

Please help me with number ten and twelve

1 answer:

jasenka [17]2 years ago

5 0

Answer: $93,\ 34^{\circ}$

Step-by-step explanation:

Given

For figure (i) both triangles are congruent

$\therefore 8x-27=4x+33\\\Rightarrow 8x-4x=33+27\\\Rightarrow 4x=60\\\Rightarrow x=15$

$\Rightarrow PQ=8x-27\\\Rightarrow PQ=93$

For figure (ii)

Two triangles WXZ and WZY are congruent

$\therefore 9x-28=5x-8\\\Rightarrow 4x=20\\\Rightarrow x=5^{\circ}\\\Rightarrow \angle YWX=2(9x-28)\\\Rightarrow \angle YWX=2(17)\\\Rightarrow \angle YWX=34^{\circ}$

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A river is flowing at the rate of 2.4 miles an hour when a boy rows across it. If the boy rows at a still-water speed of 3.1 mil

Xelga [282]

Answer:

3.9 mi/h

Step-by-step explanation:

If the boy is rowing perpendicular to the current, the two vectors form a right triangle.

AB represents the downstream current, BC is the speed across the river, and AC is the ground speed of the boat

AC^2 = 2.4^2 + 3.1^2 =5.76 + 9.61 = 15.37

AC = sqrt(15.37) = 3.9 mi/h

The boat's speed over the ground is 3.9 mi/h.

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3 years ago

John's friend told him that he could earn $49 for handing out flyers at a local concert. John wants to calculate the hourly rate

gladu [14]

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3 years ago

Read 2 more answers

Find cot θ if csc θ = negative square root of thirty seven divided by six and tan θ > 0.

Ket [755]

You can use the trigonometric identity $1+\cot^2{x}=\csc^2{x}$ .

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\cot{\theta}=\frac{1}{6}$

The requirement that $\tan{\theta}\ \textgreater \ 0$ eliminates -1/6 from being another solution.

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3 years ago

What is the final price of a $30 item at 20% off and then %20 added?

stiv31 [10]

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3 years ago

-4x + 7 = 2y - 3<br> y-intercept:<br><br> x intercept:

pantera1 [17]

Answer:

x-intercept: $\bigg(\frac{5}{2}, \:0\bigg)$

y-intercept: $(0,\:5)$

Step-by-step explanation:

To find the x-intercept, substitute in $0$ for $y$ and solve for $x$ .

$-4x + 7 = 2y - 3$

$-4x+7=2\left(\bold{0}\right)-3$

Simplify 2(0): $-4x+7=2\cdot \:0-3$

Subtract 0 - 3 = -3: $-4x+7=-3$

Subtract 7 from both sides: $-4x+7-7=-3-7$

Simplify: $-4x=-10$

Divide both sides by -4 $\frac{-4x}{-4}=\frac{-10}{-4}$

$\bold{x=\frac{5}{2}}$

To find the y-intercept, substitute in $0$ for $x$ and solve for $y$ .

$-4x + 7 = 2y - 3$

$-4(\bold{0})+7=2y-3$

Switch sides: $y-3=-4\left(0\right)+7$

Simplify -4(0): $2y-3=-0+7$

Add 3 to both sides: $2y-3+3=7+3$

Simplify: $2y=10$

Divide both sides by 2: $\frac{2y}{2}=\frac{10}{2}$

$\bold{y=5}$

3 0

2 years ago