The arm and blade of a windshield wiper have a total length of 30 inches. The blade is 24 inches long and the wiper sweeps out an angle of 125 degrees.

Answer:

f(x) = 4x² + 48x + 149

Step-by-step explanation:

Given

f(x) = 4(x + 6)² + 5 ← expand (x + 6)² using FOIL

     = 4(x² + 12x + 36) + 5 ← distribute parenthesis by 4

     = 4x² + 48x + 144 + 5 ← collect like terms

     = 4x² + 48x + 149 ← in standard form

Answer:

[tex]f(x)=4x^{2} +149[/tex]

Step-by-step explanation:

Start off by writing the equation out as it is given:

[tex]f(x)=4(x+6)^{2} +5[/tex]

Then, get handle to exponent and distribution of the 4 outside the parenthesis:

[tex]f(x)=4(x^{2} +36)+5\\f(x)=4x^{2} +144+5[/tex]

Finally, combine any like terms:

[tex]f(x)=4x^{2} +149[/tex]

Answer:

The number of pink roses bloomed are 4.    

Step-by-step explanation:

Answer:

[tex]\large \boxed{\sf \ \ \ 4 \ \ \ }[/tex]

Step-by-step explanation:

Hello, please find below my work.

[tex]x^2-4x-1=0 \ \ \text{add 1 to both parts of the equation}\\\\<=> x^2-4x-1+1=0+1=1\\\\<=> x^2-4x=1[/tex]

We know that for any a and x real numbers we can write

[tex](x-a)^2=x^2-2ax+a^2[/tex]

When we compare with the left part of the equation we can identify the term in x so that -4=-2a (multiply by -1) <=>4=2a (divide by 2) <=> a = 4/2 = 2

So we can write

[tex](x-2)^2=x^2-4x+2^2=x^2-4x+4[/tex]

So we have to add 4 to both sides of the equation to complete the square and it comes:

[tex]x^2-4x-1=0 \ \ \text{add 1 to both parts of the equation}\\\\<=> x^2-4x-1+1=0+1=1\\\\<=> x^2-4x=1 \ \boxed{\text{ add 4 to complete the square}} \\\\<=>x^2-4x\boxed{+4}=1+4=5\\\\<=>(x-2)^2=5 \ \text{ we take the root } \\ \\ <=>x-2=\pm \sqrt{5}\ \text{ we add 2 } \\ \\ <=> x = 2+\sqrt{5} \ \text{ or } \ x = 2-\sqrt{5}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

30°, 60° and 90°

Step-by-step explanation:

Given the expression Arccos (√3/2)=β, we can use the expression to calculate one of the acute angles in a right angled triangle.

Note that a right angled triangle is made up of two acute angles and a right angled (90°)

Let's get one of the acute angles first

If Arccos (√3/2)=β

β = cos^-1 √3/2

β = 30°

This shows that one of the acute angles is 30°

To get the third angle, we know that sum of angles in a triangle is 180° and since we already know two of the angles, i.e 90° and 30°, we can get the third angle.

90+30+x = 180

120+x = 180

x = 180-120

x = 60°

All the angle measurement for the right angled triangle are 30°, 60° and 90°

Answer:

a = 1, b = - 2

Step-by-step explanation:

The points that lie on the curve and straight line satisfy the corresponding equations.

Substitute the points into their corresponding equations, that is

(1, - 1 ) → - a = 1² + b = 1 + b ( multiply both sides by - 1 )

a = - 1 - b → (1)

(3, 3 ) → [tex]\frac{-3b}{2}[/tex] = [tex]\frac{3}{a}[/tex] ( cross- multiply )

- 3ab = 6 ( divide both sides by - 3 )

ab = - 2 → (2)

Substitute a = - 1 - b into (2)

(- 1 - b)b = - 2 , distribute left side

- b - b² = - 2 ( multiply through by - 1 )

b² + b = 2 ( subtract 2 from both sides )

b² + b - 2 = 0 ← in standard form

(b + 2)(b - 1) = 0 ← in factored form

Equate each factor to zero and solve for b

b + 2 = 0 ⇒ b = - 2

b - 1 = 0 ⇒ b = 1

Substitute these values into (1) for corresponding values of a

b = - 2 : a = - 1 - (- 2) = - 1 + 2 = 1

b = 1 : a = - 1 - 1 = - 2

Thus a = - 2, b = 1 or a = 1, b = - 2

Given that a > b then a = 1, b = - 2

Answer:

The average rate of change from x=-7 to x=-5 is -3

Step-by-step explanation:

In order to calculate average rate of change we would have to make the following calculation:

According to the given data we have the following:

x=-7 so, f(-7) is to be calculated in the graph y

x=-5 so, f(-5) is to be calculated in the graph y

Therefore, average rate of change=f(-5)-f(-7)/-5-(-7)

average rate of change=3-9/2

average rate of change=-6/2

average rate of change=-3

The average rate of change from x=-7 to x=-5 is -3

The average rate of change of a function is the unit change of the function.

The average rate of change from x = -7 to x = -5 is -3

The average rate of change is calculated as:

[tex]\mathbf{f'(x) = \frac{f(b) - f(a)}{b - a}}[/tex]

The interval is given as: x = -7 to x = -5.

This means that:

a = -5 and b = -7

So, we have:

[tex]\mathbf{f'(x) = \frac{f(-7) - f(-5)}{-7 - -5}}[/tex]

This gives

[tex]\mathbf{f'(x) = \frac{f(-7) - f(-5)}{-2}}[/tex]

From the graph

f(-7) = 9 and f(-5) = 3.

So, we have:

[tex]\mathbf{f'(x) = \frac{9 - 3}{-2}}[/tex]

Subtract

[tex]\mathbf{f'(x) = \frac{6}{-2}}[/tex]

Divide

[tex]\mathbf{f'(x) = -3}[/tex]

Hence, the average rate of change from x = -7 to x = -5 is -3

Read more about average rate of change at:

https://brainly.com/question/23715190

the answer is A,when X=0

Answer:

3/4

Step-by-step explanation:

We can use the slope of the line by using the slope formula

m = (y2-y1)/(x2-x1)

   = (7-1)/ ( 9-1)

    = 6/8

    = 3/4

Answer: 3/4

Step-by-step explanation: To find the slope of this line, I will be showing you the graphing method.

To find the slope of the line using the graphing method,

we first set up a coordinate system.

Next, we plot our two points, (1, 1), which we label point A, and (9, 7), which we label point B, and we graph our line, as shown below.

Now, remember that the slope, or m, is equal to

the rise over run from point A to point B.

To get from point A to point B, we rise

6 units and run 8 units to the left.

So our slope, or rise over run, is 6 over 8, which reduces to 3/4.

Answer:

28>x

Step-by-step explanation:

7>x/4

remove the denominator by multiplying both sides by 4

4×7>x/4×4

28>x

Answer:

                [tex]8\frac23\ cm^2[/tex]

Step-by-step explanation:

sector of the circle if the angle at the center is 150° means  [tex]\frac{150^o}{360^o}[/tex] of full circle of given radius

area of a circle of given radius R is:  πR²

so area of given sector:

[tex]A=\dfrac{150^o}{360^o}\cdot \pi\cdot8^2=\dfrac5{12}\cdot3.1\cdot64=82,(6)=8\frac23\ cm^2[/tex]

The area of a sector of the circle if the angle at the center is 150° is 82.67 square centimeter.

A circle is a locus of a point whose distance always remains constant from a given specific point. The general equation is -

x² + y² = r²      (for circle centered at origin)

Given is a circle has a radius of 8 cm.

The area of the sector subtending the angle 150° at center is -

A = (150/360) x 3.1 x 8 x 8

A = 82.67 square centimeter.

Therefore, the area of a sector of the circle if the angle at the center is 150° is 82.67 square centimeter.

To solve more questions on circles, visit the link below-

https://brainly.com/question/17006280

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Answer:

answer is 1 answer is 4-5 = 1 is 3-6 answer is only 3

Answer:

38

Step-by-step explanation:

f(-9) is the value of f(x) when x = -9. Therefore, f(-9) = 4 from the graph. Doing the same with g(6), we can see that g(6) = 6. Our expression becomes:

-1 * 4 + 7 * 6

= -4 + 42

= 38

Answer:

D

Step-by-step explanation:

Apply rule : [tex]-(-a)=+a[/tex]

Negative times negative is positive.

The expression turns into a sum of fractions.

Answer:

2

Step-by-step explanation:

substitute n=1 and n=3 in the given equation

1 st term is (1)^2-1-2 = 1 -1 -2 = -2

3rd term is (3)^2-3-2 = 9-3-2=4

sum of 1st and 3rd term is -2 + 4 = 2

Answer:

AAS

Step-by-step explanation:

As we can see, they tell us that both of the angles on the bottom are congruent. Since they share a side, that means that one side is congruent too. So it must be two angles and one side. It can't be ASA, because the congruent side is not in between the two congruent angles, so it must be AAS

Hey There!!

Your correct choice will be AAS Theorem.

Step-by-step explanation:

Because, two angles and any side of one triangle are congruent to two angles and any side of another triangle, then these triangles are congruent Thus, given a triangle ADB and CDB. ∠BAD = ∠BCD = 90°. (Angle), Then, BD = BD (The common side) As given AAS Theorem. Therefore, ∆ADB ≅ ∆CDB by the AAS theorem.

Hope This Explaining was not confusing . . .

By ☆Itsbrazts☆

Hey Mate !

Your Answer is given in the snip below !!

Please do mark me as brainliest !!!

(ANSWER=  (D)   [tex]\frac{1}{6}[/tex] )

Explanation

Answer:

You have a standard number cube.

What is the probability of rolling a number less than 3, and then rolling a prime number?

D. 1/6

Answer:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Answer:

Two remote interior angles.

Answer:

A=3244.8 dollars

Step-by-step explanation:

A=p(1+r)^t

A=3000(1+0.04)^2

A=3244.8 dollars

Answer:

subtract 3, because that'll allow the variables to be on one side and the constants on the other

Step-by-step explanation:

Answer: is your  first option

Step-by-step explanation:

after going over all the available equations, your first option is the only one that had results that were much more reasonable than the others. hope it helps.

Answer:

  £531.52

Step-by-step explanation:

We are given the profit in week 1 and information about week 2. We are asked for the difference between week 2 profit and week 1 profit.

__

In week 2, pizza is sold 4 ways. The diagram shows the numbers of pizzas sold each way. The table shows the profit made for each way the pizza was sold. We need to add up the profits from each of the sales to find the profit for week 2.

Then the total profit in week 2 is ...

  £1514.04 -175.42 +888.94 -5.68 = £2221.88

So, profit in week 2 exceeds profit in week 1 by ...

  £2221.88 -1690.36 = £531.52 . . . more profit in week 2

Answer:

2 by 3

Step-by-step explanation:

please mark brainliest if it helped

Answer:

2/6 < 4/6 < 5/6

Step-by-step explanation:

2 < 4 => 2/6 < 4/6

4 < 5 => 4/6 < 5/6

=> 2/6 < 4/6 < 5/6

Answer:

2/6, 4/6 5/6

Step-by-step explanation:

Answer:

12.8

Step-by-step explanation:

you have to use the law of sines to calculate it. the measure of angle c is 110 and you have to do

Sin(110)x=17sin(45)

and then it turns into 17sin(45)/sin(110)

then put it into desmos with it being in degrees mode

Answer:

Step-by-step explanation:

From the expression xy = 4, y = 4/x

Substituting y = 4/x into the expression  y(x-4)(x+2) and expanding;

=  y(x-4)(x+2)

= 4/x(x-4)(x+2)

On expansion;

= (4-16/x)(x+2)

= 4x+4(2)-(16/x)x-(16/x)2

= 4x+8-16-32/x

= 4x-8-32/x

The equivalent expression is 4x - 8 - 32/x

Answer:

The greatest possible time taken by Maria is 97.4 seconds.

Step-by-step explanation:

The greatest possible time taken by Maria occurs when she moves at constant rate and is equal to the length of the road divided by the length of the road. That is to say:

[tex]t = \frac{\Delta s}{v}[/tex]

Where:

[tex]\Delta s[/tex] - Length of the road, measured in meters.

[tex]v[/tex] - Average speed, measured in meters per second.

Given that [tex]\Delta s = 380\,m[/tex] and [tex]v = 3.9\,\frac{m}{s}[/tex], the greatest possible time is:

[tex]t = \frac{380\,m}{3.9\,\frac{m}{s} }[/tex]

[tex]t = 97.4\,s[/tex]

The greatest possible time taken by Maria is 97.4 seconds.

Answer:

tan (40°) = [tex]\frac{x}{100}[/tex]

Step-by-step explanation:

tan [tex]\theta[/tex] = [tex]\frac{opposite}{adjacent}[/tex]

The opposite side to angle B is x. The adjacent side to angle B is 100 ft.

tan (40°) = [tex]\frac{x}{100}[/tex]

Answer:

tan 40° = x/100

Step-by-step explanation:

As, AC is perpendicular and BC is the with respect to angle ABC. So, tan 40° will be use to determine the distance in feet from point C to point A.

tan ABC = perpendicular/base

tan 40° = AC/BC

tan 40° = x/100 feet

Answer:

17.32m ; 110°

Step-by-step explanation:

Distance between X and Z

To calculate the distance between X and Z

y^2 = x^2 + z^2 - (2xz)*cosY

x = 20, Z = 10

y^2 = 20^2 + 10^2 - (2*20*10)* cos60°

y^2 = 400 + 100 - (400)* 0.5

y^2 = 500 - 200

y^2 = 300

y = sqrt(300)

y = 17.32m

Bearing of Z from X:

Using cosine rule :

Cos X = (y^2 + z^2 - x^2) / 2yz

Cos X = (300 + 100 - 400) / (2 * 20 '*10)

Cos X = 0 / 400

Cos X = 0

X = cos^-1 (0)

X = 90°

Bearing of Z from X

= 20° + X

= 20° + 90°

= 110°

Answer:

[tex]\boxed{-10000}[/tex]

Step-by-step explanation:

[tex]F(x)=\frac{1}{x}[/tex]

Let x = -10000

[tex]F(-10000)=\frac{1}{-10000}[/tex]

[tex]F(-10000)= -0.0001[/tex]

-0.0001 is closest to 0 when x value is -10000.

No other value can work from the other options, options B and C increase the value from 0. Option D would make the function undefined.