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3 years ago

Which expressions equal 9 when x=4 and y=1/3

Mathematics

2 answers:

Maslowich3 years ago

6 0

B.
$4 \times 2 = 8$
$3 \times \frac{1}{3} = 1$
$8 + 1 = 9$

babymother [125]3 years ago

6 0

I think there are 3 answers, B, D, and E.

For B: 2(4)+3(1/3)=8+1=9
For D: 5(4/2)-3(1/3)=5(2)-1=10-1=9
For E: 3(4)-9(1/3)=12-3=9

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Hello! Please help thanks

kogti [31]

Answer:

A. $\frac{5}{13}$

Step-by-step explanation:

Hi there!

We are given right triangle PQR, with PR=5, RQ=12, and PQ=13

We want to find the value of sin(Q)

Let's first recall that sine is $\frac{opposite}{hypotenuse}$

In reference to angle Q, PR is the opposite side, RQ is the adjacent side, and PQ is the hypotenuse

So that means that sin(Q) would be $\frac{PR}{PQ}$

Substituting the values of PR and PQ gives sin(Q) as $\frac{5}{13}$ , which is A

Hope this helps!

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3 years ago

How many feet tall is the taller tree?

Temka [501]

Answer:

16.33 feet

Step-by-step explanation:

17.5 / 11.25 = x / 10.5

x = 17.5 * 10.5 / 11.25 = 16.33

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3 years ago

Bowie used 1/6 cup of rasperries and 1/5 cup of blueberries to make a berry smoothie. How much fruit did he use in total?

guapka [62]

Answer: 11/30

Step-by-step explanation:

5 0

3 years ago

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What is the answer to 2(17+3)=?

Effectus [21]

The answer is 40 easy

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3 years ago

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Tomika heard that the diagonals of a rhombus are perpendicular to each other. Help her test her conjecture. Graph quadrilateral

Stella [2.4K]

Answer:

a. The four sides of the quadrilateral ABCD are equal, therefore, ABCD is a rhombus

b. The equation of the diagonal line AC is y = 5 - x

The equation of the diagonal line BD is y = 5 - x

c. The diagonal lines AC and BD of the quadrilateral ABCD are perpendicular to each other

Step-by-step explanation:

The vertices of the given quadrilateral are;

A(1, 4), B(6, 6), C(4, 1) and D(-1, -1)

a. The length, l, of the sides of the given quadrilateral are given as follows;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

The length of side AB, with A = (1, 4) and B = (6, 6) gives;

$l_{AB} = \sqrt{\left (6-4 \right )^{2}+\left (6-1 \right )^{2}} = \sqrt{29}$

The length of side BC, with B = (6, 6) and C = (4, 1) gives;

$l_{BC} = \sqrt{\left (1-6 \right )^{2}+\left (4-6 \right )^{2}} = \sqrt{29}$

The length of side CD, with C = (4, 1) and D = (-1, -1) gives;

$l_{CD} = \sqrt{\left (-1-1 \right )^{2}+\left (-1-4 \right )^{2}} = \sqrt{29}$

The length of side DA, with D = (-1, -1) and A = (1,4) gives;

$l_{DA} = \sqrt{\left (4-(-1) \right )^{2}+\left (1-(-1) \right )^{2}} = \sqrt{29}$

Therefore, each of the lengths of the sides of the quadrilateral ABCD are equal to √(29), and the quadrilateral ABCD is a rhombus

b. The diagonals are AC and BD

The slope, m, of AC is given by the formula for the slope of a straight line as follows;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Therefore;

$Slope, \, m_{AC} =\dfrac{1-4}{4-1} = -1$

The equation of the diagonal AC in point and slope form is given as follows;

y - 4 = -1×(x - 1)

y = -x + 1 + 4

The equation of the diagonal AC is y = 5 - x

$Slope, \, m_{BD} =\dfrac{-1-6}{-1-6} = 1$

The equation of the diagonal BD in point and slope form is given as follows;

y - 6 = 1×(x - 6)

y = x - 6 + 6 = x

The equation of the diagonal BD is y = x

c. Comparing the lines AC and BD with equations, y = 5 - x and y = x, which are straight line equations of the form y = m·x + c, where m = the slope and c = the x intercept, we have;

The slope m for the diagonal AC = -1 and the slope m for the diagonal BD = 1, therefore, the slopes are opposite signs

The point of intersection of the two diagonals is given as follows;

5 - x = x

∴ x = 5/2 = 2.5

y = x = 2.5

The lines intersect at (2.5, 2.5), given that the slopes, m₁ = -1 and m₂ = 1 of the diagonals lines satisfy the condition for perpendicular lines m₁ = -1/m₂, therefore, the diagonals are perpendicular.

5 0

3 years ago