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Using the slope concept, it is found that he stepped back 63.44 feet.

The slope is given by the vertical change divided by the horizontal change.

It's also the tangent of the angle of depression.

Initially, we have that:

Hence:

[tex]\tan{68^{\circ}} = \frac{85}{d}[/tex]

[tex]d = \frac{85}{\tan{68^{\circ}}}[/tex]

[tex]d = 34.34[/tex]

When he stepped back, the angle was of 41º, hence:

[tex]\tan{41^{\circ}} = \frac{85}{d}[/tex]

[tex]d = \frac{85}{\tan{41^{\circ}}}[/tex]

[tex]d = 97.78[/tex]

97.78 - 34.34 = 63.44.

Hence he stepped back 63.44 feet.

You can learn more about the slope concept at https://brainly.com/question/26291396

yea that is right, not sure why it says it's wrong, I'm sorry must be so frustrating

Answer: 6 and 84 degrees

Step-by-step explanation:

Let the measure of the angle = x.

Since complementary angles sum to 90 degrees,

x + (x+ 78) = 90

2x + 78 = 90

2x = 12

x = 6.

Therefore the angles are 6 and 84 degrees.

Answer: 4. 78,020,008 4. Seventy-eight million, twenty thousand, eight

5. 20,011,012 5. 20,000,000 + 11,000 + 12

6. 50,000 7. 900 8. 70,000,000 9. 30,000,000

Step-by-step explanation:

Answer: 1 is the only factor of 13

Step-by-step explanation:

Answer:

1 and 13

Step-by-step explanation:

becouse 13 is a prime number(wich means a number that can only be multiplied by 1 and itself) the ony factors are 1 and 13.

Answer:

24 is 3/4 of 32.

Step-by-step explanation:

if you understand:

24 divided by 3 (3 in 3/4) is 8.

8 x 3 = 24, so if we need to fill in the extra 1 in 3/4 (making it 4/4), we would need to add another 8. 24 + 8 = 32. (u can look up ' what is 3/4 of 32 too ')

Answer:

1 and 4

Step-by-step explanation:

Products of 4:  

Pairs of numbers that sum to 5:

Therefore, the two numbers that add up t o 5 and multiply to 4 are:  1 and 4

Answer: y = 5

You want to isolate the variable by dividing each side by factors that don't contain the variable. When doing this, we get that y = 5.

Step-by-step explanation:

Hope this helps =)

Answer: 5

Step-by-step explanation:

6y-(3y-6)=5y-4

6y-1(3y-6)=5y-4

6y-3y+6=5y-4

3y+6=5y-4

-3     -3

6=2y-4

+4     +4

10=2y

10/2=5

It appears the points are in the correct locations on the grid. Your graph is almost done. You need to draw a straight line through all of the points to finish off the graph of y = 1.49x

The origin represents the idea that 0 pounds of oranges cost $0

You have the correct unit rate. It indicates the oranges cost $1.49 per pound.

Answer:

10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

-1(2)(-5)

-1 (-10)=10

[RevyBreeze]

Answer:

the value is 52

Step-by-step explanation:

pls brain list me

Answer:

$16.10

Step-by-step explanation:

He spent $16.10 in total. Because 3.5 x 4.6 feet = 16.1

Answer:

$16.10

Step-by-step explanation:

3.50 x 4.6 = 14 + 2.10

the answer is m>1

I hope that helped!

Answer:

It's D. I did the test and got it right.

Answer:

1/5

Step-by-step explanation:

There is a total of 20 people. 4 out of 20 of them are left-handed. 4/20 simplified is 2/10. 2/10 simplified is 1/5.

Answer:

289 messages

equation: [tex]y=0.05x+45.5[/tex]

graph: attached below

Step-by-step explanation:

We can write this in slope-intercept form, or [tex]y=mx+b[/tex]. Since x is defined as the #of text messages, and 0.05 is the cost of a text message, 0.05 will be m. 45.5 is the base price, or the y-intercept, so it will be b.

Plugging in these numbers, we get [tex]y-0.05x+45.5[/tex]

now we make y = 60, since that is the total amount they have

[tex]60=0.05x+45.5\\14.5=0.05x\\x=290[/tex]

So, they can send 290 messages for 60, but they need the bill under 60, so 1 text message less will be 289, and that's enough.

Based on the SAS similarity theorem, both triangles are similar.

Similarity statement is: ΔSTV ~ ΔPQR by SAS Similarity Theorem.

Similar Polygons have different size but the same shape, and as such, the ratio of their corresponding side lengths are equal, while their corresponding angles are congruent.

Based on the SAS similarity theorem, two triangles are similar to each other if they have two pairs of corresponding sides that are proportional and an included pair of angles that are congruent.

In ΔSTV and ΔPQR:

m∠S ≅ m∠P = 86° (one pair of included congruent angles)

ST/PQ = SV/PR = 0.67 (proportional sides).

Therefore, based on the SAS similarity theorem, both triangles are similar.

Similarity statement is: ΔSTV ~ ΔPQR by SAS Similarity Theorem.

Learn more about similar polygons on:

https://brainly.com/question/2264759

Answer:

113.1

Step-by-step explanation:

Using the volume (for sphere) formula:

V = (4/3)*pi*(r^3)

You can plug in the radius (diameter/2, the diameter is 6m) to get a volume of 113.1.

Answer:

113.04m³

Step-by-step explanation:

[tex]Solution,\\\\Diameter(d)=6m\\\\Radius(r)=6m/2=3m\\\\Now,\\\\Volume=\frac{4}{3} \pi r^{3} \\\\Volume=\frac{4}{3} *3.14*(3m)^{3} \\\\Volume=113.04m^{3}[/tex]

Answer:The distribution of favorite color is the same for each eye-color group.

Step-by-step explanation: A EDGE22

Answer:

y = -2x - 3

Step-by-step explanation:

in the equation y = mx + b,

m = slope    b = y-intercept

The y-intercept is provided in the point, (0, -3), because that is where it crosses the y. You're y-intercept is -3

Now you need to find slope. You need to find the difference between these two points to find slope.

[tex]-2+0 = -2[/tex]

[tex]1-3=-2[/tex]

so your slope is going down by 2 and to the left by 2.

Hope this helps! Might be wrong. Try with another example and tell me if it works. <3

Answer: B

Step-by-step explanation:

m is the value of the slope between the two points on the graph

If the two coordinates is (x1,y1) and (x2,y2), the slope is (y1-y2) / (x1-x2)

So the slope for this question is (1-(-3)) / (-2-0) = -2 so the answer is B

The function value of (m × n)(7) is: C. 0.

To find the value of a function, plug in the given value of x and simplify.

Given:

m(x) = x - 7

n(x) = 1/x + 7

Find (m × n)(7)

(m × n)(7) = (x - 7)(1/x + 7)

Plug in x = 7

(m × n)(7) = (7 - 7)(1/7 + 7)

(m × n)(7) = (0)(1/7 + 7)

(m × n)(7) = 0

Therefore, the function value of (m × n)(7) is: C. 0.

Learn more about function value on:

https://brainly.com/question/2284360

Answer:

310

Step-by-step explanation:

1/10=0.1

3100 x 0.1=310

Answer:

x = 12, z = 109

Step-by-step explanation:

12x - 73 = 71

12x = 71 + 73 = 144

x = 144/12 = 12

z = 180 - 71 = 109

Step-by-step explanation:

Distribute the negative sign:

[tex]\frac{2}{7} x-3 -5/2-\frac{1}{5}y[/tex]

From the given, we can only find the difference with the integers.

Subtract the integers:

[tex]\frac{2}{7} x-\frac{1}{5}y-0.5[/tex]

Answer: 29/3 into a mixed fraction would be 9 2/3

I hope I helped you. Have a great day!

Step-by-step explanation:

Simplify:

29/3 = 9 2/3

Answer:

368 feet

Step-by-step explanation:

122 yards converted to feet is 366, and you have to add the 2 feet from before, which makes it 368 feet.

Answer:

A

Step-by-step explanation:

Answer:

4 girls to 7 students, and 3 boys to 7 students

(there are 7 students in total)