A 15-foot board rests against a wall. The angle that the board makes with the
ground is 60°. How far is the base of the board away from the wall?
Select the correct trig ratio and distance from wall.

Answer:   The perimeter of ΔYXZ6.4

Answer:6.4

Step-by-step explanation:

Answer:

1200 cm²

Step-by-step explanation:

width = x cm

length = 3x  cm

perimeter = 160 cm

2(x + 3x) = 160

4x = 160/2

4x = 80

x = 80/4

x = 20  cm  - width

length = 3x = 3 · 20 = 60 cm

Area = length · width = 60 · 20 = 1200 cm²

The rectangle's width is 20 cm and its length is 60 cm. Thus, the area of the rectangle is 1200 square centimeters.

We are given that the length of a rectangle is three times its width. Let's denote the width as 'w'. Consequently, the length would be '3w'.

The perimeter of a rectangle is given by the formula: 2*(length + width). Given that the perimeter is 160 cm, we can substitute our variables into the formula: 2*(w + 3w) = 160. This simplifies to 8w = 160. Therefore, the width (w) equals 20 cm, and the length is 60 cm (3w).

The area of a rectangle is calculated by multiplying its length and width. Hence, the area of our rectangle is: 60 cm * 20 cm = 1200 square centimeters.

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Answer:

Step-by-step explanation:

y-intercept: (0, y)

x-intercept: (x, 0)

Therefore the y-intercept is only (0, 1).

Answer:

see explanation

Step-by-step explanation:

The range is the set of y- values of the ordered pairs without repeats.

3

given

(4, 7), (4, - 3), (- 5, - 9)

Then the values of y are 7, - 3, - 9

hence range is { - 9, - 3, 7 }

For

(- 4, - 2), (2, 1), (4, 1)

Then the values of y are - 2, 1, 1

Hence range is { - 2, 1 }

Step-by-step explanation:

i think its 4.2m^2+1.5n

Answer:

4.2m^2+1.5n

Step-by-step explanation:

1.7m^2 + 6.5n - 4n + 2.5m^2 - n

First, rearrange the numbers so that they can be added or subtracted with their like terms.

It would look like this:

(1.7m^2 + 2.5m^2) + (6.5n - 4n - n)

All you have to do is solve from here

this would simplify into:

4.2m^2+1.5n

Hope this helped!

See the attached picture:

Answer:

rxch.ace_

Step-by-step explanation:

Final answer:

Bus 2 is scheduled to leave at 3:00 pm, but if it leaves 15 minutes early, it departs at 2:45 pm and arrives at the shops at 3:00 pm. If Bus 1 is 15 minutes late, it arrives at 2:45 pm, the same time Bus 2 leaves, preventing the transfer.

Explanation:

To solve the question regarding bus schedules and arrival times, let's break down each part of the problem step by step.

Part (a): Scheduled Departure Time of Bus 2

Bus 1 arrives at the first stop at 2:30 pm. There is a half-hour wait, so the earliest you can board Bus 2 is at 3:00 pm. Since Bus 2 arrives at the shops at 3:15 pm, and it leaves 15 minutes before its scheduled arrival time, Bus 2 is scheduled to leave at 3:00 pm.

Part (b): Bus 2 Leaves Early

Bus 2 is supposed to leave 15 minutes early. If its scheduled departure was 3:00 pm, it actually leaves at 2:45 pm. Since it leaves 15 minutes early and the travel time remains unchanged, Bus 2 would still arrive at 3:00 pm at the shops.

Part (c): Bus 1 is Late

Bus 1 is 15 minutes late. Instead of leaving at 2:00 pm, it leaves at 2:15 pm and arrives at the first stop at 2:45 pm. Since Bus 2 leaves at 2:45 pm, you would not be able to transfer from Bus 1 to Bus 2 since their arrival and departure times coincide.

Answer:

1/56 gallon

Step-by-step explanation:

The car wash has 1/7 gallons of soap and they can use 1/8th of it each day. So, you would set up [tex]\frac{1}{7}[/tex] x [tex]\frac{1}{8}[/tex] = [tex]\frac{1}{56}[/tex].

Answer: B) 15 + 5i

Step-by-step explanation:

(7 + 4i) + (8 + i)

Add like terms: (7 + 8) + (4i + i)

Simplify: 15 + 5i.

Answer:

20875

Step-by-step explanation:

Given:

y = 5500 ln (9t + 4

y is number of mowers sold

t is years after a particular model is introduced

f(t)= 9t+4

How many mowers will be sold 4.5 years after a model is introduced?

t=4.5

putting t=4.5 in given function we get,

y= 5500ln(9(4.5) +4)

       = 20875.19

20875 mowers will be sold 4.5 years after a model is introduced!

Intersecting chord rule:

DK x KB = AK x CK

12 x 4x+1 = 14 x 3+3x

Simplify:

48x +12 = 42x +42

Subtract 12 from each side:

48x = 42x + 30

Subtract 42x from each side:

6x = 30

Divide both sides by 6:

x = 5

Now find the length of KB: 4x +1 = 4(5) +1 = 20 +1 = 21

Now add KB and AK:

21 + 14 = 35

The answer is D. 35

The required length of KB(21) + AK(14) is 35. Option D is correct.

The figure is given,
where AK = 14. DK = 12, KB = 4x+1 and  KC =3+3x.
KB + AK to be determined.

The ratio can be defined as the relativeness of the fraction of one quantity towards others.

Here,
The ratio of AK: DK = KB:KC

[tex]14/12= 4x+1/3+3x\\14*(3+3x) = 12*(4x+1)\\2+42x = 48x+12\\42-12=48x-42x\\6x= 30\\x = 5[/tex]

Now,
= KA + KB
= 14 + 4x+1
= 14+ 4(5)+1
= 35

Thus, the required length of KB + AK is 35.

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Answer: A. yes, by SSS Similarity Theorem

Step-by-step explanation:

From the given picture, it can be seen that we have all the sides of bothe the triangles.

SSS Similarity Theorem says that if the ratio of lengths of the corresponding sides of two triangles are then the triangles must be similar.

From the given picture , the ratio of the sides is given by :-

[tex]\dfrac{10}{35}=\dfrac{2}{7}\\\\\dfrac{12}{42}=\dfrac{2}{7}\\\\\dfrac{11}{36.5}=\dfrac{2}{7}[/tex]

Thus, the ratio of lengths of the corresponding sides of two triangles are equal.

Hence, the triangles must be similar by SSS similarity theorem.

Answer:

The answer is (5*2x) - (5*3)

Step-by-step explanation:

You just have to multiply the coefficient by the individual numbers and variables inside the parentheses. :)

Answer:

Step-by-step explanation:

[tex](a+b)^2=a^2+2ab+b^2\qquad(8)\\\\x^2+2x=17\\\\x^2+(2)(x)(1)=17\qquad\text{add}\ 1^2\ \text{to both sides}\\\\\underbrace{x^2+(2)(x)(1)+1^2}_{(*)}=17+1^2\\\\(x+1)^2=18\iff x+1=\pm\sqrt{18}\qquad\text{subtract 1 from both sides}\\\\x=-1\pm\sqrt{18}\\\\x\approx-1-4.24=-5.24\ \vee\ x\approx-1+4.24=3.24[/tex]

Answer:

25 degrees.

Step-by-step explanation:

The 3 angles in a triangle  add up to 180 degrees therefore:

m < C = 180 - 72 - 83

=  180 - 155

= 25 degrees.

Answer:

25

Step-by-step explanation:

Theorem:

The sum of the measures of the interior angles of a triangle is 180 degrees.

The theorem is can be written as the equation below.

m<A + m<B + m<C = 180

We know the measures of angles A and B, so we substitute the values for those measures, and we solve for the measure of angle C.

72 + 83 + m<C = 180

Add like terms on the left side.

155 + m<C = 180

Subtract 155 from both sides.

m<C = 25

Answer: m<C = 25

Answer:

x=-5

Step-by-step explanation:

Vertical lines have the same x value all the time.  They are of the form x=

Since it passes through the point (-5,-2) the x value must be -5

x=-5

Answer:

the answer will be verticle angles

Step-by-step explanation:

∠4 and ∠5 form vertical angles.

When two lines intersect each other, then non-adjacent opposite angles are called vertical angles.

Vertical angles are always equal in measurement.

If line AB and CD intersect each other at point O, ∠AOC and ∠BOD are vertical angles, similarly, ∠AOD and ∠BOC are also vertical angles.

Here lines 1 and 2 intersect each other.

So ∠4 and ∠5 are formed which are non-adjacent and opposite also.

Therefore ∠4 and ∠5 form vertical angles.

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Answer:

-3,0

Step-by-step explanation:

this is the answer hope u like it

Answer:

2x-3

Step-by-step explanation:

4(x - 3) - 2x + 9

Distribute the 4

4x -12 -2x+9

Combine like terms

4x-2x  -12+9

2x -3

Answer:

987.

Step-by-step explanation:

The terms in a Fibonacci series are obtained form the sum of the previous 2 terms. So the next number F(16) = 377 + 610 = 987.

APEX ANSWER: 987

Step-by-step explanation:

377 + 610 = 987

Answer:

{-3,0,4,11}

Step-by-step explanation:

{(-3,6),(0,2),(4,7),(11,15)}

The domain is the input values, or x coordinates

{-3,0,4,11}

Answer:

Option B 6 30 am

Step-by-step explanation:

step 1

Sum all the times

(45+5+10+30+15)=115 minutes

Convert minutes to hours

we know that

60 minutes = 1 hour

so

115 minutes=60+55= 1 hour 55 minutes

Subtract 1 hour 55 minutes from 8 25 am

(8 25 am)-(1 hour 55 minutes)=(8 25 am-1 hour)-(55 minutes)

=7 25 am-55 minutes

=7 25 am-(25+30) minutes

=(725 am-25 minutes)-(30 minutes)

7 00 am-30 minutes

=6 30 am

no your wrong its 85.2

Answer:

-7

Step-by-step explanation:

Mischa's equation is   -x² + 4x - 7 = 0

The standard form is ax² + bx + c = 0

c is the constant term in the quadratic equation.

If we compare terms, we find that c = -7.

[tex](6x^2+5)-(4x-3)=6x^2+5-4x+3=6x^2-4x+8[/tex]

ANSWER B

I took the test and that was the correct answer

Answer:

The interval of the decreasing function is (-∞ , -1) ⇒ g(x)

The interval of the decreasing function is (-∞ , 0) ⇒ f(x)

Step-by-step explanation:

* Lets explain how to solve it

- Decreasing function means a function with a graph that moves

 downward as it is followed from left to right.

- For example, any line with a negative slope is decreasing function

- Lets look to the attached graph to understand the meaning of the

 decreasing function

∵ f(x) = IxI ⇒ green graph

∵ g(x) = Ix + 1I - 7 ⇒ purple graph

- From the graph f(x) translated 1 unit to the left and 7 units down to

 form g(x)

- The domains of f(x) and g(x) are all real numbers {x : x ∈ R}

- The range of f(x) is {y : y ≥ 0}

- The range of g(x) is {y : y ≥ -7}

# For f(x)

- The slope of the green line from (-∞ , 0) is negative

- The slope of the green line from (0 , ∞) is positive

# For g(x)

- The slope of the purple line from (-∞ , -1) is negative

- The slope of the purple line from (-1 , ∞) is positive

∵ The line with negative slope represent decreasing function

∴ The interval of the decreasing function is (-∞ , -1) ⇒ g(x)

∴ The interval of the decreasing function is (-∞ , 0) ⇒ f(x)

The function g(x) = |x+11|-7 is a transformed absolute value function, which is decreasing on the interval (-infinity, -11) due to the horizontal shift to the left by 11 units.

The question is asking about the transformation of the absolute function f(x) = |x| into a new function g(x). The function provided, g(x) = |x+11|-7, is a transformed version of f(x) where the graph has been shifted horizontally and vertically. To determine on which interval g(x) is decreasing, we need to consider the properties of the absolute value function and its transformations.

The graph of the standard absolute value function, f(x) = |x|, is shaped like a 'V', increasing for x > 0 and decreasing for x < 0. When we introduce a horizontal shift to the function (such as adding 11 to x), this shifts the vertex of the 'V' horizontally. For g(x), the graph is shifted to the left by 11 units due to the '+11' inside the absolute value. Therefore, the function will be decreasing on the interval (-infinity, -11) since the function will decrease to the left of the vertex (which is now located at x = -11). The vertical shift (subtracting 7) simply moves the graph down but does not affect the intervals of increasing or decreasing behavior.

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b)

If m > 0, then the function is increased

If m < 0, then the function is decreased

We have

[tex]m=\dfrac{2}{3}>0[/tex] - the function is increased

[tex]b=-4[/tex] - the y-intercept is -4 → (0, -4)

Therefore the line passes through III, IV and I quadrant.

========================================

<, ≤ - shaded region below the line

>, ≥ - shaded region above the line

========================================

We have [tex]y\leq\dfrac{2}{3}x-4[/tex] → ≤ - shaded region below the line.

Therefore the inequal the inequality exist in I, III and IV quadrant.

Look at the picture.

The inequality exists in quadrants A.I, III, and IV.

The answer is option A

            slope(m)=tan∅=y axis/x axis.

If m > 0, then the function is increased

If m < 0, then the function is decreased

=function is increased

=y-intercept is -4 = (0, -4)

    Therefor the line passes through III, IV and I quadrant.

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Answer:

[tex]h(x)=\frac{1}{4}x[/tex].

Step-by-step explanation:

The inverse is basically you just swapping x and y.  People want to solve it for y to make it a function of x.

[tex]y=4x[/tex]

Swap x and y:

[tex]x=4y[/tex]

Now solve for y by dividing y on both sides:

[tex]\frac{x}{4}=y[/tex]

[tex]\frac{1}{4}x=y[/tex]

[tex]y=\frac{1}{4}x[/tex].

Answer:

f(-3) = 12

Step-by-step explanation:

-3 < 2; 9 + 3 = 12 [(-3)² - -3 (double negative)]; DO NOT change -3 to 3.

I hope this helps, and as always, I am joyous to assist anyone at any time.

Answer:

She made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also results in incorrect cosecant, secant, and tangent functions.

Step-by-step explanation:

Francesca made her first error in step 3 because her sine, cosine, and tangent trigonometric ratio values are incorrect.

The correct steps to use in this regards are as follows;

Step 1;

A unit circle is shown. A ray intersects point (-2, -10) in quadrant 3. θ is the angle formed by the ray and the x-axis in quadrant 1.

Step 2;

r = √[(-2)² + (-10)²] = √104 = 2√26

Step 3;

cos θ = -2/(2√26) = -1/√26 = -(√26)/26

sin θ = -10/(2√26) =-5/√26 = -5(√26)/26

tan θ = -10/-2 = 5

sec θ = 1/sin θ = 1/-(√26)/26 = -26/√26

cosec θ = 1/cos θ = 1/-5(√26)/26 = -(√26)/5

cot θ = 1/tan θ = 1/5

Thus, Francesca made her first error in step 3 because the correct sine, cosine, and tangent ratios above differ from hers which was incorrect which lead to incorrect values of cosecant, secant, and tangent functions.

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