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4 years ago

7

Mercury orbits the sun 87 24/25 earth days Venus orbits the sun in224 7/10 earth days and mars orbits the sun 686 49/50 earth da

ys express each mixed number as a decimal

1 answer:

Verizon [17]4 years ago

4 0

Oooh I miss these. Haven't done them since kindergarten! 24/25 would equal 0.96. 87+0.96 would get 87.96. 7/10 is 0.7 so 224+0.7=224.7. 49/50 is 0.98, so 0.98+686 is 686.98.

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What are the factors of 90?

Elina [12.6K]

1,2,3,6,9,10,15,30,45,90

8 0

3 years ago

Read 2 more answers

The parallelogram ABCD below, line AC is a diagonal, the measure of angle ABC is 40, and the measure of angle ACD is 57. What is

Strike441 [17]

Answer:

Using properties of parallelogram and angle sum property of a triangle in the figure as shown below in the attachment

In parallelogram ABCD, AC is a diagonal.

Given: $\angle ABC = 40^{\circ}$ and $\angle ACD= 57^{\circ}$

As, we know that opposite angles in parallelogram are equal.

therefore,

$\angle ABC =\angle ADC= 40^{\circ}$

Now, in ΔADC

Sum of the measures of angles in a triangle is 180 degree.

$\angle ACD+ \angle ADC+\angle DAC =180^{\circ}$

Substituting the values of $\angle ADC= 40^{\circ}$ and $\angle ACD= 57^{\circ}$ we have;

$57^{\circ}+40^{\circ}+\angle DAC =180^{\circ}$

or

$97^{\circ}+\angle DAC =180^{\circ}$

Subtract $97^{\circ}$ from both sides we get

$\angle DAC =180 -97 =83^{\circ}$

Therefore, the measure of angle CAD is $83^{\circ}$ .

3 0

3 years ago

If a weight hanging on a string of length 5 feet swings through 6° on either side of the vertical, how long is the arc through w

garik1379 [7]

Answer:

1.047 ft

Step-by-step explanation:

The length of an arc is given by ...

s = rθ

where s is the arc length, r is the radius, and θ is the central angle in radians. Your arc subtends an angle of 12° = (12·π/180) = π/15 radians. The length of the arc is then ...

s = (5 ft)(π/15) = π/3 ft ≈ 1.047 ft

6 0

4 years ago

(05.05)Polygon ABCD has the following vertices: A(−5, 4), B(1, 4), C(6, −4), and D(−5, −4) Calculate the area of the polygon.

ella [17]

The first thing you should do is draw the points in the Cartesian plane and then join them to find the polygon.
The searched polygon can be seen in the attached image.
The area of the polygon will be the area of the square plus the area of the triangle.
At = (6) * (8) + (1/2) * (5) * (8) = 68
At = 68
answer
the area of the polygon is 68units ^ 2

5 0

4 years ago

Use the equation below to answer the question.

JulijaS [17]

Answer:

The signa notation to represent the first five ten f(x) is given by $f(x)=\sum\limits^{5}_{n=1}a_n$

Step-by-step explanation:

Given sequence is -5, -9, 13...

Let f(x) be the given sequence and is denoted by

$f(x)=\{-5,-9,-13,...\}$

Let the first term be $a_1, 2^{\textrm{nd}}$ term be $a_3,...$

ie, $a_1=-5,a_2=-9, a_3=-13,...$

To find the common difference d:

$d=a_2-a_1$

$=-9-(-5)$

$=-9-(+5)$

$d=-4$

$d=a_3-a_2$

$=-13-(-9)$

$=-13+9$

$d=-4$

Therefore the common difference d is -4 for given sequence f(x) with $a_1=-5$ and d=-4, the seqence f(x) is an arithmetic sequence

By defintion of arithmetic sequence

$a_n=a+(n-1)d\hfill(1)$

Now to find $a_4, a_5$ :

put n=4 in equation (1)

$a_4=a+(4-1)d$

$a_4=-5+(3)(-4)$ [since a=-5, d=-4]

$=-5-12$

$a_4=-17$

in equation (1)

$a_5=a+(5-1)d$

$a_5=-5+(4)(-4)$ [since a=-5, d=-4]

$=-5-16$

$a_5=-21$

Therefore $a_4=-17$ and $a_5=-21$

Therefore $f(x)=\{-5,-9,-13,-17,-21,...\}$

Now to represent the sum of the first five terms of f(x) using sigma notation as below

$f(x)=\sum_{n=1}^5 a_n$

where $\sum_{n=1}^5 a_n=a_1+a_2+a_3+a_4+a_5$

$-5-9-13-17-21$

$\sum_{n=1}^5 a_n=-65$

4 0

4 years ago