Determine whether the equation below has one solution, no solution, or infinitely many solutions: 3x − 15 = 3(x − 6)

Answer:

The correct option is (b).

Step-by-step explanation:

Given that,

The length of the string = 39 m

The kite is level with the top of a building that is 24 meters high.

We need to find the angle of elevation of the kite.

A right-angled triangle will form such that its hypotenuse is 39 m and height is 24 m. Using trigonometry to solve this.

[tex]\sin\theta=\dfrac{P}{H}\\\\\sin\theta=\dfrac{24}{39}\\\\\theta=\sin^{-1}\left(0.61538\right)\\\\\theta=37.98^{\circ}[/tex]

So, the angle of elevation of the kite is 37.97°. The correct option is (b).

Answer:

t = (t₁ · vr)/ (vj - vr) = 45 seconds

Step-by-step explanation:

Given:

Initial time from Ricardo  t₁ = 15 seconds, Ricardo's velocity (speed) vr = 3 ft/s,

John's velocity (speed) vj = 4 ft/s

Requested time when John catch Ricardo t = ?

During 15 seconds, Ricardo moved away

S = vr · t₁ = 3 ft/s · 15 s = 45 feet.

From that moment, the same time runs for both of them

Ricardo's path is S₁ = vr · t  and John's path is S₂ = vj · t

S + S₁ = S₂ =>  S = S₂ - S₁  => 45 = vj · t - vr · t  

When we draw t we get:

t ( vj - vr) = 45   t = 45 / (vj - vr) = 45 / (4 - 3) = 45 / 1 = 45 seconds

t = 45 seconds

S₁ = vr · t = 3 · 45 = 135 ft

S₂ = vj · t = 4 · 45 = 180 ft

Answer:

option B

Step-by-step explanation:

The figure is combination of parallelogram and semi- circle. So,

area = area of parallelogram + area of semi-circle

[tex]Area \ of \ parallelogram = base \times height = 7 \times 6 = 42 cm^2\\\\Area \ of \ semi-circle = \frac{1}{2} \pi r^2 = \frac{1}{2} \times 3.14 \times 3.5^2 = 19.2cm^2\\\\Therefore \ Area = 42 + 19.23 = 61.2cm^2[/tex]

Answer:

C

Step-by-step explanation:

Trust me bro.

Answer:

-12 w^3

Step-by-step explanation:

-9w^3  - 3 w^3

Factor out the common term

w^3( -9-3)

w^3 (-12)

Answer:

Value of F(x) when x = -5 is 20

Step-by-step explanation:

Given equation;

f(x) = x² + 2x + 5

f(x) = f(-5)

Find:

Value of F(x) when x = -5

Computation:

Given function;

f(x) = x² + 2x + 5

By putting value of x in given function

f(-5) = (-5)² + 2(-5) + 5

f(-5) = (-5 x -5) + 2(-5) + 5

f(-5) = (25) - 10 + 5

f(-5) = (25) - 5

f(-5) = 20

Value of F(x) when x = -5 is 20

Answer: I think the answer would be 10

Step-by-step explanation:

5/8 * 16/1 = 80/8 = 10

She needs 10 sub sandwiches if there are 16 students and Mrs Bryant wants to give them 5/8 of a large sub sandwiches

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

Total number of students = 16

Each student receive = 5/8 of a large sub sandwich

Total sandwich receive = 16(5/8) = 10

Thus, she needs 10 sub sandwiches if there are 16 students and Mrs Bryant wants to give them 5/8 of a large sub sandwiches

Learn more about the fraction here:

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Answer:

SAS

Step-by-step explanation:

One of the postulates is called SAS and it states that if two triangles have 2 sides with the same length and the angles between the two sides are the same then the two triangles are congruent. This is exactly what we see on the diagram shown in the question, therefore the correct postulate is SAS

Answer:

13 cm

Step-by-step explanation:

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

Answer:

10 units

Step-by-step explanation:

point A has the coordinate (1,6) and point B has the coordinates (1,2), so the difference in the y values will give height of the triangle which is 6-2 = 4

similarly the point B has the coordinates (1,2) and point C has the coordinates (6,2). Calculate the difference in x values which is 6-1 = 5 which is the base of the triangle

now use the area of a triangle formula which is 1/2 * b * h

= 1/2 * 5 * 4

= 1/2 * 20

= 10

Answer:

Se debe fabricar y vender 553 escritorios para lograr una utilidad de S/ 25000.

Step-by-step explanation:

La utilidad por cada escritorio se obtiene al sustraer los costes fijos y variables del precio, es decir:

[tex]u = S/ \,125 -S/\,4,75 - S/\,75[/tex]

[tex]u = S/\,45.25[/tex]

El número de escritorios a vender para obtener [tex]S/\,25000[/tex] se calcula mediante la siguiente regla de tres simple:

[tex]x = \frac{S/\,25000}{S/\,45,25} \times 1\,esc[/tex]

[tex]x = 552.486[/tex]

Puesto que la cantidad a vender es una variable entera, se debe redondear al entero más cercano. En consecuencia, se debe fabricar y vender 553 escritorios para lograr una utilidad de S/ 25000.

By looking at the table, you can see that we have an x

that is paired with two different y's so this does not fit the

definition of a function which states that each x must

be paired with exactly one y.

Answer:

c

Step-by-step explanation:

Answer:

D. by multiplying 58 by 0.17

[tex]17\% \: of \: 58 \\ = \frac{17}{100} \times 58 \\ = \frac{986}{100} \\ = 9.86[/tex]

Answer:

08 units, 3 units, V73 units

Step-by-step explanation:

Pythagoras theorem can be used to determine which  sets of side lengths are for a right triangle

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

8² + 15² = √289

8² + 3² =  √73

16² + 30² =  √1156

only the second option is correct

Answer: 4/5

Step-by-step explanation:

Answer:

Consistent

Step-by-step explanation:

It was a solution.

Answer:

22 square units

Step-by-step explanation:

Area of a triangle formula:

A = 0.5bh

Given:

b = 11

h = 4

Work:

A = 0.5bh

A = 0.5(11)(4)

A = 5.5(4)

A = 22

an isotope is an atom with a different number of____neutrons____ ,than a normal atom

Answer:

I cant see the different side measurements

Answer:

√7 / 4

Step-by-step explanation:

Trigonometrical identity are used to show the relationship between the sides and angles of a right angled triangle. Some trigonometric identities are:

sinΘ = opposite / hypotenuse, cosΘ = adjacent / hypotenuse, tanΘ = opposite / adjacent.

Given that cosΘ = 3 / 4

Therefore, cosΘ = adjacent / hypotenuse = 3 / 4

adjacent = 3, hypotenuse = 4. Let x be the opposite side, to get the opposite side, we use Pythagoras theorem:

opposite² + adjacent² = hypotenuse²

x² + 3² = 4²

x² + 9 = 16

x² = 7

x = √7

sinΘ = opposite/hypotenuse = √7 / 4

Answer:

Solution given:

[tex]\frac{1}{5}(6+3+1)²[/tex]

[tex]\frac{1}{5}(10)²[/tex]

[tex]\frac{1}{5}100[/tex]

=20 is a required answer.

Answer:

11 hours

Step-by-step explanation:

Using an inequality, find how many additional hours must she work in order to reach this goal?

From the above question, the term at least means less than or equal to and it is represented by the inequality = ≤

Hence,

Let the number of additional hours = h

Last summer Myrtle, worked 45 hours and earned $443.70.

The amount she earned per hour = $443.70/45

= $9.86

Our inequality equation is written as;

She wanted to make at least $550 this summer.

$9.86 × h ≤ $550

= 9.86h ≤ 550

h = 550/9.86

h = 55.780933063 hours

Approximately the additional hours she has to work =

55.780933063 - 45 hours

= 10 .780933063 hours

Approximately = 11 hours

Answer:

-3 and -4

Step-by-step explanation:

x = 1st number

y = 2nd number

2x-4y=10

4x-4y=4

distribute first equation by -2 to eliminate x-values:

 -4x + 8y = -20

+ 4x - 4y = 4

4y = -16

y = -4

solve for 'x':

2x - 4(-4) = 10

2x + 16 = 10

2x = -6

x = -3

The solution for the given system of equations is x = -3 and y = -4.

A linear equation is defined as an equation in which the highest power of the variable is always one.

This is a system of linear equations in two variables, x and y.

The first equation is:

2x - 4y = 10

The second equation is:

4x - 4y = 4

You can solve one of the equations for one of the variables, and then substitute that expression into the other equation.

From the first equation:

2x - 4y = 10

2x = 4y + 10

x = 2y + 5

Substitute this expression of x in the second equation,

4(2y+5) - 4y = 4

8y + 20 - 4y = 4

4y = -16

y = - 4

Now, substitute this value of y in x = 2y + 5

x = 2 × -4 + 5

x = - 3

Hence, the solution for the system of equations is x = -3 and y = -4.

Learn more about the Linear equations here:

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Answer:

Let's walk through the steps together!

Step-by-step explanation:

1

a) we know that the Pythagorean theorem is a^2+b^2=c^2

a^2+b^2=c^2 means that if we add the squared values for each of the two sides of the triangle (these sides need to have an angle of 90 degrees together. Basically they are the ones that aren't the hypotenuse) we get the value of the hypotenuse (the longest side that doesn't help to make the right angle).

We see that we have the values of a and b in this formula (these sides need to have an angle of 90 degrees together.) Plugging the values in problem 1a into this formula, we see that 16^2+12^2=x^2 (x is the value we need to find)

16^2=236

12^2=144

so the formula now says that 236+144=x^2

236+144=400, so x= [tex]\sqrt{400}[/tex] , which is 20.

so x=20

b) we can use the same knowledge we used in the first problem in this problem as well. In this problem, we are given the values of c (the hypotenuse) and one of the sides (which for our purposes can be a).

a^2+b^2=c^2     ->      100+b^2=289

This means that b=[tex]\sqrt{289-100}[/tex]

so b=[tex]\sqrt{189}[/tex]

so b=[tex]3\sqrt{21}[/tex]

2

These ones are pretty basic, having any common knowledge of ratios should lead you right to the answer. I will help you with a and d

a) we are given the values 6 and 9 as a ratio, which is the same as a 2:3 ratio. 12 corresponds to 6, so 12 would be the 2 in 2:3, meaning the answer (for the value of x) is 18

d) we are given the values 6 and 8, and the corresponding value to 8 is 12. 6 and 8 make a ratio of 3:4, and if we plug 12 in as the 3, the 4->4*4=16

3

I can't see the full problem so unfortunately, I cannot help you

I hope this helped in your understanding!

-Suvi