What is the sum of 6/7 and 1/2?

Answer:

all real numbers greater than or equal to 175

Step-by-step explanation:

The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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Answer: 4 1/2

Step-by-step explanation:

Answer:

9/64

Step-by-step explanation:

\(=0.75\times \frac{\left(3.75+-3.5\right)}{1.3}\\0.75\times \frac{\left(3.75+-3.5\right)}{1.3}\\=0.75\times \frac{0.25}{1.3}\\=0.75\times 0.1875(\left a.k.a\:\frac{3}{16}\right)\\\frac{\left(3\times 0.1875\right)}{4}\\\mathrm{\left(Clarification:\:The\:\:math\:\:above\:\:is\:\:a\:\:broken\:\:down\:version\:of\:the\:original\:problem.\right)}\\=\frac{0.5625\left(\frac{9}{16}\right) }{4}\\=0.1406\left(\frac{9}{64}\right)\)

Hope this helps!

Yes, the proof of congruence of two triangles ∆ABC ≅ ∆GHF is possible.

The convergence method which proves this congruence is SSS(side-side-side) congruence.

We have given the sketch of two triangles as seen above. We have to prove ∆ABC ≅ ∆GHF

Now , AB = √(-7+7)² + 5² = 5 in triangle ABC and FG = 5 in triangle FGH,

so, AB ≅ FG

Because AC = 3 in triangle ABC and FH = 3 in triangle FGH,

so, AC ≅ FH

To find the lengths of BC and GH , we can use distance formula.

Length of BC :

BC = √[(x₂ - x₁)² + (y₂ - y₁)²]

(x₁, y₁) = B(-7, 0) and (x₂, y₂) = C(-4, 5).

BC = √[(-4 + 7)² + (5 - 0)²]

= √[32 + 52]

= √[9 + 25]

= √34

Length of GH :

GH = √[(x₂ - x₁)² + (y₂ - y₁)²]

(x₁, y₁) = G(1, 2) and (x₂, y₂) = H(6, 5).

GH = √[(6 - 1)² + (5 - 2)²]

= √[52 + 32]

= √[25 + 9]

= √34

Conclusion :because BC = √34 and GH = √34,

=>BC ≅ GH

All the three sides of one triangle is congruent to the corresponding sides of other triangle.

By SSS congruence postulate,

ΔABC ≅ ΔFGH

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Answer:

45000

Step-by-step explanation:

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Answer:

4500

Step-by-step explanation:

The angle m∠J  in the right angle triangle is 58.1 degrees.

One of the angle of a right tangle triangle is 90 degrees. The sum of

angles in a triangle is 180 degrees.

Therefore, the side length LK can be found using Pythagoras's theorem and the angle can be found using trigonometric ratios.

Hence,

tan ∠J = opposite / adjacent

tan ∠J = 15.1 / 9.4

∠J = tan⁻¹ 1.60638297872

∠J = 58.0909229196

Therefore,

m∠J = 58.1 degrees

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Answer:

1. $6.00 to 95 cents  = 6.32

2. 3 hours to 35 minutes  = 5.14

3. 42 inches to 2 feet = 1.75

Step-by-step explanation:

Given

$6.00 to 95 cents

3 hours to 35 minutes

42 inches to 2 feet

Required

Express in 2 decimal places

1. $6.00 to 95 cents

Express as ratio

\(\$6.00 : 95\ cents\)

Convert dollars to cents

\(6.00 * 100\ cents: 95\ cents\)

\(600\ cents: 95\ cents\)

Convert ratio to division

\(\frac{600\ cents}{95\ cents}\)

\(6.31578947368\)

Approximate

\(6.32\)

2. 3 hours to 35 minutes

Express as ratio

\(3\ hours : 35\ minutes\)

Convert hours to minutes

\(3 * 60\ minutes: 35\ minutes\)

\(180\ minutes: 35\ minutes\)

Convert ratio to division

\(\frac{180\ minutes}{35\ minutes}\)

\(5.14285714286\)

Approximate

\(5.14\)

3. 42 inches to 2 feet

Express as ratio

\(42\ inches: 2\ feet\)

Convert feet to inches

\(42\ inches:2 * 12\ inches\)

\(42\ inches : 24\ inches\)

Convert ratio to division

\(\frac{42\ inches}{24\ inches}\)

\(1.75\)

The singer sold 512 music downloads.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

Let's use the following variables:

CD = the number of CD singles sold

DL = the number of music downloads sold

From the problem, we know the following:

CD + DL = total number of singles sold

CD = 456

The profit from selling CD singles is 35p = £0.35 per CD single

The profit from selling music downloads is 17p = £0.17 per music download

The total profit is £246.64

Using the information above, we can set up two equations based on the profits earned from selling CD singles and music downloads:

0.35 * CD = profit from CD sales

0.17 * DL = profit from download sales

And we know that the sum of these two profits equals the total profit:

0.35 * CD + 0.17 * DL = 246.64

Substituting CD = 456, we get:

0.35 * 456 + 0.17 * DL = 246.64

Simplifying this equation, we get:

159.6 + 0.17 * DL = 246.64

0.17 * DL = 87.04

DL = 512

Therefore, the singer sold 512 music downloads.

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Applying the slope-intercept form for perpendicular lines, we find out that no given pair of lines are perpendicular.

There are 4 different pairs of lines given to us.

We have to find out the pair of lines that are perpendicular to each other.

We know that the general equation of a line in slope-intercept form is represented as -

y = mx + c --- (1)

where

(x, y) = coordinates of the lines

m = slope of the line

c = y-intercept

It is also known to us that for two lines to be perpendicular the product of their slope must be equal to -1.

A. y = -8 and y = 2

Comparing these two lines to the general equation of a line in equation (1), we see that the slope of both these lines is equal to 0.

So, these two pair of lines are not perpendicular.

B. x = 4 and y = -1

Comparing these two lines to the general equation of a line in equation (1), we see that the slope of both these lines is equal to 0.

So, these two pair of lines are not perpendicular.

C. x - y = 7 and y = x + 3

Now, x - y = 7

=> -y = 7 - x

=> y = x - 7

Comparing this to the equation (1), we have slope of the line, m = 1.

Also, y = x + 3

Comparing this to the equation (1), we have slope of the line, m = 1.

We see that the product of the slope of these pair of lines is not equal to -1.

So, these two pair of lines are not perpendicular.

D. y = -4x + 1 and 8x + 2y = -10

Now, y = -4x +1

Comparing this to the equation (1), we have slope of the line, m = -4.

Also, 8x + 2y = -10

=> 2y = -8x - 10

=> y = -4x - 10

Comparing this to the equation (1), we have slope of the line, m = -4.

We see that the product of the slope of these pair of lines is not equal to -1.

So, these two pair of lines are not perpendicular.

Thus, according to the slope-intercept form for perpendicular lines, we find out that no given pair of lines are perpendicular.

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Answer:

6 days

Step-by-step explanation:

144/24(hours in a day)=6

Answer:

Step-by-step explanation:

6 Days are equal to 144 hours. Thus, option A is the answer.

We know that there are 24 hours in a day so,

when 144 hours are divided by 24 hours.

It will be 6 Days.

144/24 = 6

Therefore, 6 Days are the answer.

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Answer:

D

Step-by-step explanation:

integers are a whole number; a number that is not a fraction.

Answer:

  (b)  9.2 N

Step-by-step explanation:

The acceleration is the change in velocity divided by the change in time:

  a = (-4.4 m/s)/(0.072 s) = -61 1/9 m/s²

The force is given by ...

  F = ma = (0.150 kg)(-61 1/9 m/s²) = -9 1/6 N ≈ -9.2 N

The ground exerts a force of about 9.2 N upward on the egg.

There 211 number of coffee creamers left at the end of the week.

What is number ?

The arithmetic value of a number is one that is used to denote amount. As a result, a number is a mathematical concept used for counting, measuring, and labeling. As a result, mathematics is based on numbers.

An arithmetic value known as a number is used to represent a quantity and do calculations. Numbers are represented by written symbols, such as "3," which are referred to as numerals. A number system is a method of writing that uses logically ordered digits or symbols to represent numbers.

Numerology comes in a variety of forms. Organic Numbers entire numbers Integers Realistic Numbers Unreasonable Numbers True numbers complicated numbers Organic numbers numbers beginning with "1".

x will be equal to

x = 275 - 64

  = 211

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Answer:

Step-by-step explanation:

All you have to do is to be patient and then the moment will come and... POOF!

YoUr iN LOOOVeeeeE

I got you, buddy!

Let x be the length of the shortest side. Then, the length of the second side is 2x, and the length of the third side is x + y, where y is the additional length.

The perimeter of the triangle is the sum of the three sides, so we have:

x + 2x + (x + y) = 60

Simplifying this equation, we get:

4x + y = 60

We also know that the area of a triangle is given by:

A = (1/2)bh

where b is the length of the base, and h is the height. Since the base of the flower bed is the shortest side of length x, we can choose the height to be y. Therefore, we have:

A = (1/2)xy

Now we need to solve for x and y. We can use the equation for the perimeter to solve for y:

y = 60 - 4x

Substituting this into the equation for the area, we have:

A = (1/2)x(60 - 4x)

Simplifying and expanding, we get:

A = 30x - 2x^2

To maximize the area, we can take the derivative of A with respect to x and set it equal to 0:

dA/dx = 30 - 4x = 0

Solving for x, we get:

x = 7.5

Substituting this back into the equation for y, we get:

y = 60 - 4x = 45

Therefore, the dimensions of the flower bed are:

shortest side = x = 7.5 feet second side = 2x = 15 feet third side = x + y = 52.5 feet

Step-by-step explanation:

To find the total time required to produce each product, we can add up the machining, polishing, and assembling hours for each product. For example, for Product I, the total time required would be:

Total time for Product I = 3 hours + 1 hour + 2 hours = 6 hours

We can do this for each product to find the total time required for all four products:

Total time for Product I = 3 hours + 1 hour + 2 hours = 6 hours

Total time for Product II = 2 hours + 1 hour + 1 hour = 4 hours

Total time for Product III = 2 hours + 2 hours + 2 hours = 6 hours

Total time for Product IV = 4 hours + 3 hours + 1 hour = 8 hours

So, the total time required to produce all four products is 6 hours + 4 hours + 6 hours + 8 hours = 24 hours.

The total price of the vehicle would be $18,192.88.

The total deferred price of the car would be $11,191.60.

The length of the financing agreement is 68 months .

The total deferred price after the payments was $19,601.84.

The monthly payments would be $516.92.

Subtotal = Base price + Options + Destination charges

Subtotal = $14,500 + $982 + $592 = $16,074

Dealer preparation = 5% of subtotal

Dealer preparation = 0.05 x $16,074 = $803.70

Sales tax = 7% of subtotal

Sales tax = 0.07 x $16,074 = $1,125.18

Total price = Subtotal + Dealer preparation + Sales tax + Tag fee + Title fee

Total price = $16,074 + $803.70 + $1,125.18 + $145 + $45 = $18,192.88

Tax = 8% of selling price = 0.08 x $8,850 = $708

Tag fee = $130

Title fee = $35

Total amount financed = Amount financed + Tax + Tag fee + Title fee = $7,350 + $708 + $130 + $35 = $8,223

Annual interest rate = 9.5%

Number of years financed = 3

Total finance charges = $8,223 x 0.095 x 3 = $2,341.595

Total financed amount = $8,223 + $2,341.595 = $10,564.595

Monthly payments = Total financed amount / (Number of years financed x 12 months) = $10,564.595 / (3 x 12) = $293.4615

Total deferred price = Selling price + Total finance charges = $8,850 + $2,341.595 = $11,191.595

Total deferred price = $28,000

Down payment = $2,100

Total amount financed = Total deferred price - Down payment = $28,000 - $2,100 = $25,900

Monthly payments = $380

Number of months = Total amount financed / Monthly payments = $25,900 / $380 = 68.16

The financing agreement is approximately 68 months long.

Sticker price = $19,200

Discount = 6% of sticker price = 0.06 x $19,200 = $1,152

Selling price = Sticker price - Discount = $19,200 - $1,152 = $18,048

Sales tax = 8% of selling price = 0.08 x $18,048 = $1,443.84

Total price = Selling price + Sales tax + Tag fee + Title fee = $18,048 + $1,443.84 + $65 + $45 = $19,601.84

Using the formula for monthly payments on a loan:

P = (PV x r x (1 + r)^ n) / ((1 + r) ^ n - 1)

= ($26,515.80 x 0.005265 x (1 + 0.005265) ^ 60 ) / ((1 + 0.005265) ^ 60 - 1) = $516.92

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The value of side length x in diagram a) is 4.3mm and side length x in diagram b) is 309.7 m.

The figures in the image are right triangles.

A)

angle D = 17 degree

Adjacent to angle D = 14 mm

Opposite to angle D = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( 17 ) = x/14

x = tan( 17 ) × 14

x = 4.3mm

B)

angle Z = 82 degree

Adjacent to angle Z = 43.1 m

Hypotenuse = x

Using trigonometric ratio,

cosine = adjacent / hypotenuse

cos( 82 ) = 43.1 / x

x = 43.1 / cos( 82 )

x = 309.7 m

Therefore, the measure of x is 309.7 meters.

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Answer:

1. 1/6

2. 10/36

3. 1/12

Step-by-step explanation:

Answer:

What question do you need help with?

Step-by-step explanation:

Answer:

7x + 7y = 7(x+y)

Step-by-step explanation:

Factor out 7 from the expression.

The value of s for the given right angle triangle by Pythagoras' theorem will be 17.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

As per the given triangle, ABD is a right-angle triangle thus to Pythagora's theorem,

s² = 15² + 8²

s = 17

Hence "According to Pythagoras' Theorem, the value of s for the given right angle triangle is 17.".

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The time it will take for your account balance to reach $10,000 is given as follows:

t = 10.8 years.

The balance of an account after t years, using continuous compounding, is given as follows:

A(t) = A(0)e^(kt).

In which:

The parameters for this problem are given as follows:

A(0) = 6500, k = 0.04.

Hence the time needed for a balance of $10,000 is obtained as follows:

10000 = 6500e^(0.04t)

e^(0.04t) = 10000/6500

0.04t = ln(10000/6500) -> ln is the inverse operation of the exponential

t = ln(10000/6500)/0.04

t = 10.8 years.

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Answer:

lines which don't intersect at any point and having same distance between them at all points

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Complete question:

A police car is located 50 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. How fast is the red car actually traveling along the road.

Answer:

The red car is traveling along the road at 80.356 ft/s

Step-by-step explanation:

Given

Police car is 50 feet side off the road

Red car is 130 feet up the road

Distance between them is decreasing at the rate of 75 feet per sec

Let x be how far the police is off the road.

Let y be how far the red car is up the road.  

Let h be the distance between the police and the red car.

This forms a right triangle so we can use the Pythagorean theorem, to solve for h

h² = x² + y²

h² = 50² + 130²

h² = 19400

h = √19400

h = 139.284 ft

Again;

Let dx/dt be how fast the police is traveling toward the road.

Let dy/dt  be how fast the red car is traveling along the road.

Let dh/dt be how fast the distance between the police and the car is decreasing.

Recall that, h² = x² + y² (now differentiate with respect to time, t)

2h(dh/dt) = 2x(dx/dt) + 2y(dy/dt)

divide through by 2

h(dh/dt) = x(dx/dt) + y(dy/dt)

since the police car is not, dx/dt = 0

and dy/dt is the how fast is the red car actually traveling along the road

139.284(75) = 50(0) + 130(dy/dt)

10446.3 = 0 + 130(dy/dt)

dy/dt = 10446.3 / 130

dy/dt = 80.356 ft/s

Therefore, the red car is traveling along the road at 80.356 ft/s

Answer:

  (b)  -4.5

Step-by-step explanation:

Choosing the correct answer here is not the same as knowing what the correct value is.

You know that √30 < √100 = 10, so the sum must be negative. That is, 10 subtracted from a positive number less than 10 will give a negative result.

You know that 25 < 30 < 36, so √25 < √30 <√36. That is, √30 will be between 5 and 6. If we say √30 ≈ 5.5, then the sum is ...

  -10 +√30 ≈ -10 +5.5 = -4.5

__

Additional comment

Of course, a calculator can tell you the value to the desired precision.

Answer:

see below

Step-by-step explanation:

a) factors of 20 are, 1, 2, 4, 5, 10, 20

B) factors of 22 are, 1, 2, 11

C) factors of 26 are 1, 2, 3, 4, 6, 12,  13

D) factors of 65 are 1, 5, 13, 65

E) factos of 66 are 1, 2, 3, 11, 6, 22, 66

for all of these you stop dividing when there are no more numbers you can divide by that result in whole numbers.

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