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3 years ago

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Joel walked 2/5 of a mile to the store, 3/10 of a mile to the library, and 1/20 of a mile to the post office. Let x = the total

distance Joel walked. Hw far did he walk? Draw a picture.

1 answer:

nadezda [96]3 years ago

4 0

3/4 a mile is the answer

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Tell whether the graph of the equation is a horizontal or a vertical line. Explain your choice.

Orlov [11]

Answer:

horizontal line

Step-by-step explanation:

The equation of a horizontal line parallel to the x- axis is

y = c

where c is the value of the y- coordinates the line passes through.

The equation of a vertical line parallel to the y- axis is

x = c

where c is the value of the x- coordinates the line passes through.

Hence

y = - 1 is a horizontal line passing through all points with a y- coordinate - 1

4 0

3 years ago

The angle between a diagonal and the longer base of the isosceles trapezoid MNFD is 45°. NK is an altitude to the longer base. I

Elanso [62]

Answer:

$NK \approx 7.001$ , $MK = 2$ , $MF \approx 7.001$ , $A_{AMNFD} = 49.007$

Step-by-step explanation:

According to the statement, we find the following inputs:

$\angle MDK = \angle DMF = 45^{\circ}$ (Due to the condition of isosceles trapezoid)

$MD = 9$

$NF = 5$

Given than longer base and shorter base are parallel to each other, we conclude that:

$\angle KND = 180^{\circ} -\angle NKD - \angle KDN$

$\angle KND = 180^{\circ}-90^{\circ}-45^{\circ}$

$\angle KND = 45^{\circ}$

$\angle FND = 90^{\circ}-\angle KND$

$\angle FND = 45^{\circ}$ (By definition of complementary angles)

$\angle FND = \angle NFM = 45^{\circ}$ (Due to the condition of isosceles trapezoid)

$\angle MDK = \angle DMF = \angle FND = \angle NFM = 45^{\circ}$

$\angle NOF = \angle MOD = \angle MOF = \angle FOD = 90^{\circ}$ (By definitions of complementary and vertical angles and the theorem that states that sum of internal angles within a triangle equals 180º)

$MO = DO = \frac{\sqrt{2}}{2}\cdot MD$ (By theorem for 45-45-90 Right Triangle)

$NO = OF = \frac{\sqrt{2}}{2}\cdot NF$ (By theorem for 45-45-90 Right Triangle)

If we know that $MD = 9$ and $NF = 5$ , then we find that:

$DO = MO \approx 6.364$

$NO = OF \approx 3.536$

The value of MK is obtained from the following relationship:

$MK = \frac{MD-NF}{2}$

$MK = \frac{9-5}{2}$

$MK = 2$

And the value of KD is calculated from this expression:

$KD = MD-MK$

$KD = 9-2$

$KD = 7$

Now by the Pythagorean Theorem we find that:

$NK = \sqrt{(NO+DO)^{2}-KD^{2}}$

$NK = \sqrt{9.9^{2}-7^{2}}$

$NK \approx 7.001$

And considering the symmetry characteristics of an isosceles trapezoid, we determine MF:

$MF = NO + DO \approx 7.001$

Lastly, the area of the isosceles trapezoid is determined by the following formula:

$A_{AMNFD} = NF\cdot NK + MK\cdot NK$

$A_{AMNFD} = NK\cdot (NF+MK)$

If we know that $NK \approx 7.001$ , $NF = 5$ and $MK = 2$ , then the area of the figure is:

$A_{AMNFD} = (7.001)\cdot (5+2)$

$A_{AMNFD} = 49.007$

8 0

2 years ago

What is the slope of the line passing through the points (−1, 7) and (4, −1)?

Damm [24]

Hey!

------------------------------------------------

Formula: $m = \frac{y2 - y1}{x2 - x1}$

------------------------------------------------

Steps To Solve:

~Substitute

$m = \frac{-1 - 7}{4 - (-1)}$

~Simplify

$m = \frac{-8}{5}$

------------------------------------------------

Answer:

$\large\boxed{C)~\frac{-8}{5} }$

------------------------------------------------

Hope This Helped! Good Luck!

3 0

3 years ago

Read 2 more answers

The height, in feet, of a t-shirt launched from a t-shirt cannon high in the stands at a football stadium is given by h(x)=-16x^

Vilka [71]

max height is 144

take 3 seconds

5 0

3 years ago

Write the equation that represents each table of values

rewona [7]

9514 1404 393

Answer:

3. y = 3·4^x

4. y = 24·0.5^x

5. y = 45·0.9^x

Step-by-step explanation:

Each table appears to represent an exponential function. Such a function can be written in the form ...

y = a·b^x

where 'a' is the value of y when x=0, and 'b' is the ratio of the values of y when x=1 and x=0.

__

3. a = 3. b = 12/3 = 4

y = 3·4^x

__

4. a = 24. b = 12/24 = 0.5

y = 24·0.5^x

__

5. a = 45. b = 40.5/45 = 0.9

y = 45·0.9^x

4 0

2 years ago