Find the exact value of cos A in simplest radical form.

Answer:

Step-by-step explanation:

You cannot add these because they are not like. IF you have a value for x, then the expression could be evaluated at the x value, but you can't add them.

Answer:

The load weight is 2.29 N

Step-by-step explanation:

We note that  at equilibrium, the sum of the moment and the sum of forces about a point is zero, therefore, we have;

∑M =0

∑F = 0

The parameters given are;

The distance of the load from the hinge = 35 cm

The distance of the load from the spring balance = 15 cm

The applied force on the spring balance = 4 N↑

The direction of the applied force on the spring balance = Upwards

Let the weight of the load = W↓

The direction of the weight of the load = Downwards

We use downward negative and upward positive coefficients for the forces

We take moment about the hinge as follows;

Sum of moments equals zero gives;

4 × (35 - 15) - W × 35 = 0

∴ 4 × (35 - 15) = W × 35

4 × 20 = W × 35

W = 4 × 20/35 = 2.29 N

The weight of the load = 2.29 N.

Answer:

The load weight is 2.29 N

hope it helps

Answer:

The lines DE and BC have the same slope, therefore the two lines, DE and BC, are parallel

Step-by-step explanation:

To prove that DE is parallel to BC, we have;

The slope, m of the lines DE and BC are found from the following equation;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Where;

(x₁, y₁) and (x₂, y₂) = (b, c) and (a + b + c) for DE, we have;

[tex]Slope, \, m =\dfrac{c - c}{a + b-b} = 0[/tex]

Where we have (x₁, y₁) and (x₂, y₂) = (0, 0) and (2a, 0) for BC, we have;

[tex]Slope, \, m =\dfrac{0 - 0}{2a-0} = 0[/tex]

Therefore, because the lines DE and BC have the same slope, the two lines DE and BC are parallel.

Answer:

slope of DE = 0

slope Bc = 0

slopes are =

Step-by-step explanation:

Answer:

3.625 gpm

Step-by-step explanation:

Answer: Hi!

The solution to positive 6 and -6 is 0. A negative and a positive of the same absolute value cancel out.

Hope this helps!

Answer:

the answer is zero !

Step-by-step explanation:

when a negative and a positive of the same number  go against each other they cancel out

Answer:

3

Step-by-step explanation:

6(x+4)=42

x=3

check:

6*(3+4)=42

Step-by-step explanation:

100 - 25 = 75

75 + 90 = 165

= 165 strawberry .

Answer:

The correct option is;

c. Plot a point not on the original line segment

Step-by-step explanation:

The steps to copy a line segment are;

1) Plot a point that will be an endpoint of the new line segment

2) With the compass pin at the beginning of the original line segment, open the compass width to the end of the original line segment

3) With the adjusted compass width from the above step place the compass pin at the plotted point of the new line segment and draw an arc in the region the new line segment is to be located

4) Select a point on the arc where the other end of the new line will be

5) From the selected point from the above step, draw a line to the point plotted as the beginning of the new line segment

6) The length of the line drawn above is the same as the length of the original line segment.

Answer:

Hey there!

We have that 4/5, or 80% of the 60 students passed the exam.

Thus, we have:

0.8(60)=48

48 students passed the exam.

Let me know if this helps :)

Answer:

4. Meena- 3

Jerry- 6

5a. 5

5b. 6

Step-by-step explanation:

We can use the distance formula to solve all of these.

[tex]\sqrt{(x_{2} } -x_{1} )^2+(y_{2} -y_{1} )^2[/tex]

Plug the numbers in and make sure you understand how i got these answers :) Let me know if you see anything wrong about it, and i will try and fix it.

Answer:

Reflection.

Step-by-step explanation:

Reflection moves points across a specified line so that the line is the perpendicular bisector of each line segment connecting corresponding pre-image and image points.

On the other hand, "Translation" moves points the same distance along lines that are parallel to each other while "Rotation" moves points along concentric circles and through the same angle of rotation.

At an angle of 90°, a line of reflection intersects the line segments connecting corresponding points of the pre-image under a reflection.

Basically, a reflection allows us to flip an object or figure across a line, point or plane without any change in its shape or size.

Hence, to reflect an object or a figure such as a triangle simply means that its mirror image would be produced with respect to a line; this line is generally referred to as the line of reflection.

2^3 * 3^1

Go step by step. 24 = 2 x 12. 12 = 2 x 6. 6 = 2 x 3. We can't factor any more.

Therefore, we have 12 = 2 x 6, and since 6 = 2 x 3, we get 12 = 2 x 2 x 3.

Then 24 = 2 x 12, and 12 = 2 x 2 x 3, so 24 = 2 x 2 x 2 x 3.

There are 3 2's and 1 3's, so it's 2^3 * 3^1.

Hope that helped,

-sirswagger21

Answer:

24=2*12=2*6=2*3

Step-by-step explanation:

I could not draw the tree diagram

to do it you take a prime number it is divisible by and a composite number it is divisible by and you prime factorise the composite number and repeat until you get prime numbers

Answer:

5.25

Step-by-step explanation:

"The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average"

in that case

1.6, 3.2, 3.6, 4.6 , 4.7 , 5.2 , 5.3,  5.4 , 6.1 , 7.8 , 9.0 , 9.5 ,

1st  2nd 3rd 4th  5th    6th  7th .  8th . 9th  10th 11th 12th

as you can seem 5.2 and 5.3 are both in the middle. that means you take the average of those two numbers. so 5.25

Answer:

The median is 5.25

Step-by-step explanation:

Median is found in the middle of numbers.

First you arrange the number from descending to ascending order:

1.6, 3.2, 3.6, 4.6, 4.7, 5.2, 5.3, 5.4, 6.1, 7.8, 9.0, 9.5

There are 12 numbers.

Then find the number that is in the center. In this case, 5.2 and 5.3 are the numbers in the center. You add them together and divide them by 2:

5.2+5.3 = 10.5/2 = 5.25

The median is 5.25

Answer:

(4x + 5)²

4x² + 20x + 25

Step-by-step explanation:

Step 1: Factor 16x² + 40x + 25

(4x + __)(4x + __)

What multiplies to 25 and adds up to 40 with 4 multiplied as coefficient?

(4x + 5)(4x + 5) or (4x + 5)²

Step 2: Factor perfect square trinomial

36x² - 4x + 16 --> 4(9x² - x + 4) No

16x² - 8x + 36 --> 4(4x² - 2x + 9) No

25x² +9x + 4 --> 25x² + 9x + 4 No

4x² + 20x + 25 --> (2x + 5)(2x + 5) or (2x + 5)² Yes

Answer:

(4x + 5)(4x + 5).

4x^2 + 20x + 25.

Step-by-step explanation:

16x^2 + 40x + 25

= (4x + 5)(4x + 5)

= (4x + 5)^2.

36x^2 − 4x + 16: To be a perfect square trinomial, the factors would have to be (6x + 4) or (6x - 4). Since the value of b is only -4, this is NOT a perfect square trinomial.

16x^2 − 8x + 36: To be a perfect square, factors would have to be (4x + 6) or (4x - 6). Since the value of b is only -4, this is NOT a perfect square.

25x^2 + 9x + 4: To be a perfect square, factors have to be (5x + 2) or (5x - 2). Since b is positive, factors would be (5x + 2)(5x + 2) = 25x^2 + 20x + 4. 20x is not equal to 9x, so this is NOT a perfect square.

4x^2 + 20x + 25: Perfect square would have to have factors (2x + 5) or (2x - 5). b is positive, so factors are (2x + 5)(2x + 5) = 4x^2 + 10x + 10x + 25 = 4x^2 + 20x + 25. This IS a perfect square!

Hope this helps!

The angle is negative to indicate a clockwise rotation.

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

Explanation:

Z = -3 - 8i is in the form z = a+bi with a = -3 and b = -8

In the complex plane the point (a,b) represents the location of z = a+bi

Define three points with the locations

P = (a,b) = (-3,8)

Q = (0,0)

R = (10,0)

The angle PQR is the angle theta we're looking for. This is the angle formed between the positive x axis and the terminal point (a,b)

Use the arctan function to find theta

theta = arctan(b/a)

theta = arctan( (-8)/(-3) )

theta = 69.4439547804166

theta = 69.4 degrees approximately

Note how this theta value is in quadrant Q1, but (a,b) = (-3, -8) is in Q3

So we need to add 180 degrees to adjust this error.

69.4+180 = 249.4

and we're now in the proper quadrant. We would stop here if your teacher did not put the restriction that theta must be between -180 and 180.

However, this restriction is in place so we need to find the difference of 360 and 249.4 to get 360-249.4 = 110.6

-----------

The angle 249.4 degrees is coterminal to -110.6 degrees. They both point in the same direction.

angle 249.4 degrees is found by starting pointing directly east and rotating 249.4 degrees counterclockwise

angle -110.6 degrees is found by starting directly east and rotating 110.6 degrees clockwise.

Check out the diagram below. I used GeoGebra to make the diagram.

Answer:

-3.5 °F

Step-by-step explanation:

If the temperature change was the same each hour, we can find the change each hour by dividing -14 by 4.

-14/4= -3.5

= -3.5 °F

Answer:Answer:

[tex]\sum\left {{7} \atop {1}} \right -n(3+n)[/tex]

Step-by-step explanation:

Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;

The sum of an arithmetic series is expressed as [tex]S_n = \frac{n}{2}[2a+(n-1)d][/tex]

n is the number of terms

a is the first term of the sequence

d is the common difference

Given parameters

n = 7, a = -4 and d = -6-(-4) = -8-(-6) = -2

Required

Sum of the first seven terms of the sequence

[tex]S_7 = \frac{7}{2}[2(-4)+(7-1)(-2)]\\\\S_7 = \frac{7}{2}[-8+(6)(-2)]\\\\S_7 = \frac{7}{2}[-8-12]\\\\\\S_7 = \frac{7}{2} * -20\\\\S_7 = -70[/tex]

The sum of the nth term of the sequence will be;

[tex]S_n = \frac{n}{2}[2(-4)+(n-1)(-2)]\\\\S_n = \frac{n}{2}[-8+(-2n+2)]\\\\S_n = \frac{n}{2}[-6-2n]\\\\S_n = \frac{-6n}{2} - \frac{2n^2}{2}\\S_n = -3n-n^2\\\\S_n = -n(3+n)[/tex]

The sigma notation will be expressed as [tex]\sum\left {{7} \atop {1}} \right -n(3+n)[/tex]. The limit ranges from 1 to 7 since we are to  find  the sum of the first seven terms of the series.

Answer:

0.5+d=h

Step-by-step explanation:

If a plant is growing at a steady rate of 0.5 inches (h) in 1 day (d) then after one day your equation should look like: 0.5+1 which would give you the height of the plant in inches. If this is true, then you would keep the height per day the same (0.5) substitute the 1 for d (one day); then your equation would look like this: 0.5+d which would give you the height of the plant in inches (h).

0.5+d=h

The function that helps Yazmin to see how many days it takes is h = 1 + 0.5d.

Functions were originally the idealization of how a varying quantity depends on another quantity.

Now it is given that,

Height of sprout =  1 inch

Growth per day =  1/2 inch

Let h = height of the plant (inches), and let d = number of days (days)

∵ Growth per day =  1/2 inch

So, Growth of plant in d days = d * 1/2 = d/2 = 0.5d

Thus,  height of the plant, h = 1 + Growth of plant in d days

⇒ h = 1 + 0.5d

Thus, the function that helps Yazmin to see how many days it takes is h = 1 + 0.5d.

To learn more about the function :

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So our set of numbers is  5,8,b,9,4 . And we know the average is 7. So first, you have to add all the numbers in the set : 5+8+9+4 which gives you 26. We also know that to get the average of a set of numbers you have to add all the numbers and divide that sum by the how many numbers you have, in thsi case we have 5 numbers including b . So our equation now is : 26+b÷5=7. And if you plug in 9 for b you get 26+9÷5=7 and 26+9÷5  does equal 7 so therefore A is your answer

Answer:$60,000

Step-by-step explanation:

If he bought it for $50,000 and then spent $5,000 on repairs then he spent a total of $55,000. For a profit of $5,000 he would need to sell it for $60,000 Because

60,000 - 55,000 = 5,000

Step-by-step explanation:

[tex]c^{2} = {a}^{2} + { b}^{2} [/tex]

Pythagoras theorem

x²=12² + 5²

x²=144+25

x²=169

[tex]x = \sqrt{169} [/tex]

x=13

Answer:

x = 13

Step-by-step explanation:

Using the Pythagorean Theorem to find the missing hypotenuse side:

[tex]a^2+b^2=c^2[/tex]

12 and 5 are a and b. 'x' would be c.

[tex]12^2+5^2=c^2\\\\12^2=144\\5^2=25\\\\144+25=c^2\\\\169=c^2\\\\\sqrt{169}=\sqrt{c^2}\\\\\boxed{13=c}[/tex]

'x' should be equal to 13.

Answer:

Step-by-step explanation:

Given,

Principal ( P ) = N 250

Time ( T ) = 4 years

Amount ( A ) =N 330

Rate ( R ) = ?

First, finding the Interest :

According to definition of Amount ,

Amount = Principal + Interest

plug the values

⇒[tex] \sf{330 = 250 + I}[/tex]

Move i to left hand side and change it's sign

⇒[tex] \sf{ - I = 250 - 330}[/tex]

Calculate

⇒[tex] \sf{ - I = - 80}[/tex]

Change the signs of the both equation

⇒[tex] \sf{I = 80 }[/tex]

Interest = 80

Finding the rate :

Simple Interest = [tex] \sf{ \frac{PTR}{100} }[/tex]

plug the values

⇒[tex] \sf{80 = \frac{250 \times 4 \times R}{100} }[/tex]

Multiply the numbers

⇒[tex] \sf{80 = \: \frac{1000 \: R}{100} }[/tex]

Apply cross product property

⇒[tex] \sf{1000R = 100 \times 80}[/tex]

Multiply the numbers

⇒[tex] \sf{1000R = 8000}[/tex]

Divide both sides of the equation by 1000

⇒[tex] \sf{ \frac{1000R}{1000} = \frac{8000}{1000} }[/tex]

Calculate

⇒[tex] \sf{R = 8 \: \% \: }[/tex]

Thus, Rate = 8 %

-------------------------------------------------------------------------

Let's learn about Principal , Interest , Time , Rate and Amount :

Hope I helped!

Best regards!!

Answer:

D

Step-by-step explanation:

7 3 5 2

x     4 8

-----------

352,896

Hey There!!~

Because, First thing to do is mulpity 2 x 8 = 16 so, You bring the 6 and bring up the 1. Then, 5 x 8 = 40 + 1 = 41. So, we bring down the 1 and bring up the 4. Then, 3 x 8 = 24 + 4 = 28. Then, The same thing bring down the 8 and let the 2 stay up there. 7 x 8 = 56 + 2 = 58. So, Right now the answer is 58, 816. So, We just completed the first step, But we're are not done yet... 4 x 2 = 8. Then, 5 x 4 = 20. So, we bring down the 0 and bring up the 2. Then, 4 x 3 = 12 + 2 = 14. So, The 4 stay down and 1 goes up. Then, 7 x 4 = 28 + 1 = 29. So, we just completed the second step. The last step is to add 58, 816 + 29, 408 = 352, 896. Hope This helps!!

let the consecutive multiples be 7(n-1) , 7n and 7(n+1)

so 7(n-1)+7n+7(n+1)=777

or 3n=111,

n=37

252,259,266

[tex]7n+7n+7+7n+14=777\\21n=756\\n=36\\\\7n=252\\7n+7=259\\7n+14=266[/tex]

252,259,266

Answer:

x=3

Step-by-step explanation:

3x+6 =15

x=3

Answer:

3

Step-by-step explanation:

3x + 6 = 15

3x = 15 - 6 = 9

x = 9/3 = 3

Answer:

Step-by-step explanation:

convert mixed fraction into improper fraction

[tex]5\frac{3}{4}=\frac{23}{4}\\\\\\3\frac{7}{8}=\frac{31}{8}\\\\5\frac{3}{4}-[-3\frac{7}{8}]=\frac{23}{4}+\frac{31}{8}\\\\=\frac{23*2}{4*2}+\frac{31}{8}\\\\=\frac{46}{8}+\frac{31}{8}\\\\=\frac{46+31}{8}\\\\\\=\frac{77}{8}\\\\=9\frac{5}{8}[/tex]

Answer:

9 5/8.

Step-by-step explanation:

5 3/4 - (-3 7/8)

= 5 3/4 + 3 7/8

= 5 + 3 + 3/4 + 7/8

= 8 + 3/4 + 7/8    

The LCD of 4 and 8 is 8 so we get

8 + 6/8 + 7/8

= 8 + 13/8

= 8 + 1 5/8

= 9 5/8.

Answer:

Well, in the local reservoir we have an initial amount of water A.

And per hour, the amount of water in the reservoir decreases by 500 gals.

So after t hours, the amount of water in the reservoir is:

W = A - 500gal*t

This is a linear equation, so the model that fits best in the given situation is a linear model.

Where the only thing that you need to take in mind, is that the domain of this model is restricted:

This is because we can not have a negative amount of water in the reservoir, so the maximum value of t accepted is:

W = 0 = A - 500gal*t

t = A/500 hours

So the domain of this linear relation is:

t ∈ {0h, A/500 }

Answer: lin

Step-by-step explanation:

Answer:

list in the explanation

Step-by-step explanation:

BOOT x2

SKINNY x2

RELAXED x2

BOOT, SKINNY

BOOT, RELAXED

SKINNY, BOOT

SKINNY, RELAXED

RELAXED, BOOT

RELAXED, SKINNY

The solution set is given by Set A = { BB , SS , RR , BS , BR , SR } , where B , S and R are boot cut (B), skinny (S), and relaxed fit (R) respectively

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the set be represented as A

Now , the equation will be

Marcus is shopping for pants and the available pants are boot cut (B), skinny (S), and relaxed fit (R)

He wants to buy 2 pair of pants , and the possible ways of 2 pants are

Set A = { BB , SS , RR , BS , BR , SR }

So , the total number of elements in set A = 6 pairs

Therefore , the value of A is 6 pairs

Hence , the set A is { BB , SS , RR , BS , BR , SR }

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