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Keith_Richards [23]
2 years ago
8

5. State the missing reasons in this proof.

Mathematics
1 answer:
hammer [34]2 years ago
3 0

Answer:

a.) Vertical Angles

b.) Given (Parallel)

c.) Substitution

Step-by-step explanation:

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Claire traveled 701 miles. She drove 80 miles every day. On the last day of her trip she only drove 61 miles. Write and solve an
mina [271]

Answer:

Claire traveled for 9 days.

Step-by-step explanation:

Given:

Total Distance traveled = 701 miles

Distance traveled each day = 80 miles

Distance traveled on last day = 61 miles

We need to find the number of days Claire traveled.

Solution:

Let the number of days Claire traveled be denoted by 'd'.

Now we can say that;

Total Distance traveled is equal to sum of Distance traveled each day multiplied by number of days and Distance traveled on last day.

framing in equation form we get;

80d+61=701

Now Subtracting both side by 61 using Subtraction Property of Equality we get;

80d+61-61=701-61\\\\80d = 640

Now Dividing both side by 80 we get;

\frac{80d}{80}=\frac{640}{80}\\\\d=8

Hence Claire traveled 80 miles in 8 days and 61 miles on last day making of total <u>9 days</u> of travel.

7 0
3 years ago
Can somebody help me with this question. Thank you!
Alex_Xolod [135]

Answer:

where is question ???

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
F−1(−2) = <br><br> f(−4) = <br><br> f(f−1(−2)) =
Sauron [17]

need more information

7 0
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
What are the correct answers?
Delvig [45]
1. y= -x - 15
2. y= -4x + 1/2
3. y= 2x + 1
4. y= 2/3x + 3
5. y= -1/2x - 4
6. y= -3x + 13

Glad I could help
8 0
3 years ago
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