Suppose a triangle has two sides of length 2 and 3 and that the angle
between these two sides is 60°. What is the length of the third side of the
triangle?
ОА. 7
В. 2
ооо
SUBMIT

Answer:

Let's write this out in an equation.

y = 4 + 7x

The mathematical equation 'Y is 4 more than the product of 7 and x' can be written as 'Y = 7x + 4' where Y is the dependent variable and x is the independent variable. This is a standard form linear equation.

The subject of this question is Mathematics, and it appears to be targeted at a Middle School level. The statement 'Y is 4 more than the product of 7 and x' is a mathematical equation that can be written as Y = 7x + 4. Here, '7x' refers to the product of 7 and x, and the '+ 4' indicates that Y is 4 more than this product. It is a linear equation in variable x.

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Answer:

slope = - 1

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 4, 7) and (x₂, y₂ ) = (0, 3) ← 2 ordered pairs from the table

m = [tex]\frac{3-7}{0+4}[/tex] = [tex]\frac{-4}{4}[/tex] = - 1

Answer:

Function 1.

Step-by-step explanation:

The rate of change of Function 2 = (18.75 - 14.25)/ (5 - (-1))

=  4.5 / 6

= 3/4 or 0.75.

For Function 1 it is  5/6 or 0.83

So Function 1 has greatest rate of change.

Answer:

The length of the intercepted arc for circle S is  (1/2)π ft

Answer:

product

Step-by-step explanation:

Answer:

The Correct Answer is product of powers

Step-by-step explanation:

Answer:

5+4w=7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sin x = opp/hyp

Sin x = 4/7

Sin x = 0.5714

X =sin-¹(0.5714)

X = 34.8

X = 35°

The required measure of angle x in the triangle is 35°.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

From triangle,

Sin x = perpendicular/hypotenuse

Sin x = 4/7

Sin x = 0.57

X =sin⁻¹(0.57)

X = 34.9
x = 35°

Thus, the required measure of angle x in the triangle is 35°.

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Answer:

Look at the picture.

x < 0 and y < 0

Answer:

2. The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r + t = 20 and 5 r + 5 t = 150.

Step-by-step explanation:

The total lunch budget of the company  =  $150

Total number of employees  = 20

The cost of 1 roast beef sandwich = $5

The cost of 1 tuna sandwich = $5

r represents the number of roast beef sandwiches provided.

t represents the number of tuna sandwiches provided.

Now, consider the given statements:

Here, total number of sandwiches purchased  = Total number of employees

⇒ r +  t = 20   .... (1)

Also, as each type of sandwich costs $5.

So, the cost of r roast beef sandwiches = r x ( Cost of  1  beef sandwich)

= r x ( $5) = 5 r

And, the cost of t tuna sandwiches = t x ( Cost of  1  tuna sandwich)

= t x ( $5) = 5 t

Total cost of (r +t) sandwiches = Total Lunch Budget

⇒ 5 r +  5 t = 150   .... (2)

Hence, from (1) and (2) the above situation can be represented as:

r +  t = 20  

5 r +  5 t = 150

Hence, the company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r + t = 20 and 5 r + 5 t = 150.

Answer:

[tex]10\frac{1}{2}\ \frac{acres}{hour}[/tex]

Step-by-step explanation:

The correct question is:

Darcy harvests 8 3/4 ​ acres of corn every 5/6​  of an hour. Darcy harvests corn at a constant rate. How many acres does she harvest per hour?

we know that

To find out the corn rate harvested per hour or the unit rate, divide the number of acres of corn harvested by the total time it takes

so

[tex]8\frac{3}{4} :\frac{5}{6}[/tex]

Convert mixed number to an improper fraction

[tex]8\frac{3}{4}=8+\frac{3}{4}=\frac{8*4+3}{4}=\frac{35}{4}[/tex]

substitute

[tex]\frac{35}{4} :\frac{5}{6}=\frac{210}{20}=\frac{21}{2}\ \frac{acres}{hour}[/tex]

Convert to mixed number

[tex]\frac{21}{2}\ \frac{acres}{hour}=\frac{20}{2}+\frac{1}{2}=10\frac{1}{2}\ \frac{acres}{hour}[/tex]

Answer:

[tex]10\frac{1}{2}[/tex] or [tex]\frac{21}{2}[/tex]

Answer:

y=0

Step-by-step explanation:

Parallel lines never intersect therefore you need to find what y=-5 would look like on a graph (look at the image for reference, it is the blue line). Because it is a straight line then you just need to find what would make a straight line across the origin, therefore you would have to do y=0 (the red line on the image.)

The reason for putting y=0 or y=-5 is because the y value will ALWAYS stay the same and the x value will continue going on and on, without intersecting.

We can ise Pythagorean triplet which is ( 12 , 16 , 20 )

Therefore the answer is 16.

Step-by-step explanation:

Or we can use Pythagoras theorem , stated as ;

( hyp )^2 = ( adj )^2 + ( opp )^2

hyp ( hypotenuse ) = 20

We can assume the adj ( adjacent ) = 12

By substituting the values ,

20^2 = 12^2 + ( adj )^2

400 = 144 + ( adj )^2

400 - 144 = ( adj )^2

256 = ( adj )^2

Take the square root of both sides

✓256 = adj

16 = adj

Therefore the length of the other leg which is the adjacent( adj ) side is 16.

The length of the other leg is 16

To find the length of the other leg of a right triangle, given one leg is 12 and the hypotenuse is 20, we use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the legs (a and b) is equal to the square of the length of the hypotenuse (c).

This relationship is given by:

a² + b² = c²

1.  Here, one leg (a) is 12 and the hypotenuse (c) is 20. So we can write:

12² + b² = 20²

2.  Calculating the squares gives:

144 + b² = 400

3. Subtract 144 from both sides to find b²:

b² = 256

4. Finally, take the square root of both sides to find b:

b = √256 = 16

Thus, the length of the other leg is 16.

Answer:

B: 3.844x10^5

E: 3.844x10^6

Step-by-step explanation:

Answer:

(y + 2)(y + 3)

Step-by-step explanation:

Hey!

~Set up the equation: -5(x-1)=40

~ Divide 5 on both sides: 40/-5

~ Simplify: x-1=-8

~ We want to get x by itself, so subtract +1 to both sides.

~ Simplify: x = -7

~ Therefore, x = -7.

Answer:

x = - 7

Step-by-step explanation:

-5(x - 1) = 40

-5x + 5 = 40

- 5x = 40 - 5

- 5x = 35  | x(-)

5x = - 35

x = - 35 : 5

x = - 7

Final answer:

The total length of a race course would be the perimeter if it's a closed loop. Without specific details of the race course, the exact measurement cannot be provided, but several examples hint at how the length can be determined if more information is available.

Explanation:

The student's question pertains to the total length of a race course. To ascertain the total length, one would typically consider the perimeter of the race track if the course returns to the start line or the straight distance from start to finish if not returning. This question does not provide specific details about the dimensions or shape of the race course, which are necessary to give an exact measurement. However, if we refer to the provided information, option (a) says that the perimeter is the distance, and the shortest distance between the start and finish line is the magnitude of displacement. This suggests that the total length could be measured by the perimeter if it's a closed loop.

Some examples include a marathon which has a set length of 42.188 km, or a soccer field where the perimeter would be the sum of all sides, assuming the field was used for a running event. For an actual racecourse, you would need to know the specific dimensions or shape to calculate the total length.

Answer:

[tex]k=-5[/tex]

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]6x^{2} +7x+k=0[/tex] 

so

[tex]a=6\\b=7\\c=k[/tex]

substitute in the formula

[tex]x=\frac{-7\pm\sqrt{7^{2}-4(6)(k)}} {2(6)}\\\\x=\frac{-7\pm\sqrt{49-24k}} {12}[/tex]

so

[tex]x_1=\frac{-7+\sqrt{49-24k}} {12}\\\\x_2=\frac{-7-\sqrt{49-24k}} {12}[/tex]

Remember that

[tex]2x_1+3x_2=-4[/tex]

substitute

[tex]2(\frac{-7+\sqrt{49-24k}} {12})+3(\frac{-7-\sqrt{49-24k}} {12})=-4\\\\(\frac{-14+2\sqrt{49-24k}} {12})+(\frac{-21-3\sqrt{49-24k}} {12})=-4[/tex]

Multiply by 12 both sides

[tex](-14+2\sqrt{49-24k})+(-21-3\sqrt{49-24k})=-48\\\\-35-\sqrt{49-24k}=-48\\\\\sqrt{49-24k}=48-35\\\\\sqrt{49-24k}=13[/tex]

squared both sides

[tex]49-24k=169\\24k=49-169\\24k=-120\\k=-5[/tex]

therefore

The equation is

[tex]6x^{2} +7x-5=0[/tex]

The roots are

[tex]x=\frac{-7\pm\sqrt{49-24(-5)}} {12}\\\\x=\frac{-7\pm\sqrt{169}} {12}\\\\x=\frac{-7\pm13} {12}\\\\x_1=\frac{-7+13} {12}=\frac{1} {2}\\\\x_2=\frac{-7-13} {12}=-\frac{5} {3}[/tex]

Answer:

Eric earned last month US$ 9,786.25

Step-by-step explanation:

Commission of Eric on each house sold = 5% = 0.05

House 1 $55,000

55,000 * 0.05 = $ 2,750

House 2 $105,525

105,525 * 0.05 =  $ 5,276.25

House 3 $35,200

35,200 * 0.05 = $ 1,760

Eric earned last month =  $ 2,750 +  $ 5,276.25 + $ 1,760

Eric earned last month US$ 9,786.25

Answer:

Step-by-step explanation:

Let, it will take x years to be of same height for these trees.

We know that 1 ft = 12 inches.

8 ft = [tex]12\times8 = 96 inch[/tex]. 2 ft = 24 inch.

After x years, the height of type A will be (96 + 6x) inch and the height of type B will be (24 + 15x) inch.

We need find the value of x, for which 96 + 6x = 24 + 15x or, 9x = 72 or, x = 8.

Answer:

more than 16 squares

Answer:

a

Step-by-step explanation:

The diagonal of square is 9.90 units long.

Step-by-step explanation:

Given,

Length of each side of square= s = 7 units

Diagonal of square = s√2

Putting s = 7

Diagonal of square = [tex]7*\sqrt{2}[/tex]

Diagonal of square = 7 * 1.414

Diagonal of square = 9.898

Rounding off to nearest hundredth

Diagonal of square = 9.90 units

The diagonal of square is 9.90 units long.

Keywords: square, diagonal

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Answer:

d = 9.9 units

Step-by-step explanation:

The step by step explanation is in the picture below

The value of the square root of negative 49 will be ± 7i.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ √(-49)

We know that √-1 = i, then we have

⇒ √(-1 x 49)

⇒ ± 7i

The value of the expression √(-49) will be ± 7i.

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Final answer:

The square root of negative 49 simplifies to 7i, where i is the imaginary unit.

Explanation:

The simplify question involves finding the square root of negative 49, which is a mathematical operation dealing with complex numbers. To simplify the square root of a negative number, we use the imaginary unit i, where i is defined as the square root of negative one. Therefore, to simplify √-49, we break it down into the product of √-1 and √49. Since √-1 equals i, and √49 equals 7, the simplification results in 7i.

Answer:

E

Step-by-step explanation:

7+8+4=19

4/6 + 3/6 + 1/6 = 1 2/6

19 + 1 1/3

20 1/3

Volume is length x width x height.

A cube has the same length, width and height.

The volume of the cube is 2 x 2 x 2 = 8cm

Answer: 8 cm

Happy to help!

Answer: the answer is 8

Step-by-step explanation: The answer is 8 because the equation LxHxW and since It is a cube it is 2x2x2

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]x+2y > 4[/tex]

Isolate the variable y

subtract x both sides

[tex]2y > -x+4[/tex]

Divide by 2 both sides

[tex]y > -\frac{1}{2}x+2[/tex]

The solution of the inequality is the shaded area above the dashed line

[tex]y=-\frac{1}{2}x+2[/tex]

The slope of the dashed line is negative

The y-intercept of the dashed line is (0,2)

The x-intercept of the dashed line is (4,0)

therefore

The graph in the attached figure

Answer:

-95/36

Step-by-step explanation: I think that's right.

Answer:

w = I /2 - 4

Step-by-step explanation:

half the length : I /2

4 less than half the length : I /2 - 4

To match the requirements : w= I /2 - 4