The sum of the measures of the angles in △ABC is 180°. The sum of the measures of angle B and angle C is twice the measure of angle A. The measure of angle B is 32° less than the measure of angle C.

By finding the positive root of the quadratic equation, we conclude that the rock will hit the ground 7 seconds after it is thrown.

We know that a rock is thrown from a cliff whose height is 224 ft. And the equation that models the height of the rock as is the quadratic equation:

h(t) = -16t² + 80t + 224

The rock will reach the ground when its height is equal to zero, so what we need to find is the positive root of the quadratic equation, so what we need to solve is:

-16t² + 80t + 224 = 0

Solving it we get:

t = (-80 ± √(80² - 4*(-16)*224)/(2*-16)

t = (-80 ± 144)/(-32)

The positive solution is:

t = (-80 - 144)/(-32) = 7

This means that the rock will hit the ground 7 seconds after it is thrown.

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Answer:

dbc

Step-by-step explanation:

thats the only one that is obtuse

Answer:

473085 is the answer

Step-by-step explanation:

Hope it helps you

Wayne bought 72 ounces of blueberries.

A fraction is a non-integer that is made up of a numerator that is divided by a line from the denominator. An example of a fraction is 1/2. 1 is the numerator and 2 is the denominator.

The first step is to determine the total fraction of blueberries that was used.

[tex]\frac{3}{8} + \frac{1}{6} + \frac{5}{12}[/tex]

[tex]\frac{27 + 12 + 30}{72}[/tex] =  [tex]\frac{69}{72}[/tex]

Ounces of blueberries he bought = (ounces used ÷  fraction of blueberries used)

69 ÷  [tex]\frac{69}{72}[/tex]

69 x 72/69 = 72 ounces

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Answer:

10.63

Step-by-step explanation:

If Mohammad leaves home walks 5 blocks to the library and he then walks 2 blocks toward home to meet up with his friend and then together, he and his friend walk to the library together, then Mohammad walked for 9 blocks.

To calculate how far Mohammad walked we use addition.

Total blocks Mohammad walked = blocks to the library + blocks towards home to meet up with friend + blocks back to the library together

blocks to the library = 5

blocks towards the home to meet up with friend = 2

blocks back to the library together = 2 (As he walked 2 blocks towards home from the library, he will walk the same number of blocks again to reach the library)

Therefore,

total blocks Mohammad walked = 5 + 2 + 2

total blocks Mohammad walked = 9

Hence, the number of blocks Mohammad walked for is calculated to be 9.

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[tex]4x-2=-12\\\\4x=-10\\\\\frac{4x}{4} =\frac{-10}{4} \\\\x=\boxed{-\frac{5}{2} }[/tex]

to get the equation of any straight line, we simply need two points off of it, let's use the points from the table in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 3 }\implies -1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-1}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-x+2\implies {\LARGE \begin{array}{llll} y=-x+6 \end{array}}[/tex]

Answers:

14 rides: 52

and

r rides: 3r + 10

Step-by-step explanation:

3(14) + 10

52

probability that a randomly chosen colony diameter is greater than or equal to 10 =P(10<X<12)+P(12<X<14)

=0.14+0.02 = 0.16

Probability is basically how likely something is to happen. Whenever we're uncertain around the outcome of an occasion, ready to talk approximately the probabilities of certain outcomes—how likely they are. The analysis of occasions administered by probability is called statistics.

Probability may be a measure of the probability of an event to occur. Numerous events cannot be predicted with add up to certainty. Able to predict as it were the chance of an occasion to happen i.e. how likely they are to happen, using it.

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Answer:

Yes OFC

Step-by-step explanation:

As you can see at the 12-second mark the graph shows 1466 wave length for air so the density of the mass will be subtracted from the height

An angle is a figure formed by two rays with a common initial point called a of the angle.

What does a math angle mean?

What is type of angle ?

What is acute angle?

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Answer:

I agree thanks for the points

Step-by-step explanation:

Answer:

Rita: r - 5= 2c, or r - 5= 2(36), or r - 5 = 72

Cora: (r - 5)/2 = 36

Step-by-step explanation:

The coordinate of another point will be (a/2,y) where y can be any value.

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.

An isosceles triangle is a triangle whose two sides are equal.

Let's say AB = AC

So,

Distance associate to AB = Distance associate to AC

(x- 0)² + (y - 0)² = (x - a)² + (y - 0)²

x² + y² = (x - a)² + y²

x = a/2

So the coordinate of the third vertex is (a/2,y)

Hence "The coordinate of another point will be (a/2,y) where y can be any value".

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Answer:

its option C: x = 3

Step-by-step explanation:

The distance between the cars, x = 3 miles

The equation representing two cars traveling in opposite directions is given by, 8x-12 = 4x,

where 'x' is the distance (in miles) between the cars.

We need to find 'x'.

The equation given is a linear equation in x. So we will solve for 'x'.

8x-12 = 4x

⇒ 8x-4x = 12

⇒ 4x = 12

⇒ x = 12/4

⇒ x = 3

So the distance between the cars = 3 miles

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The ratio of the volumes of the Spaceship Earth to a golf ball = 1926949795 : 1

We need to find the volumes of the Spaceship Earth and a golf ball.

Spaceship Earth

Radius, R = 165/2 ft = 82.5 ft

Volume of the Spaceship Earth = [tex]\frac{4\pi R^3}{3}[/tex] = (4 x 3.14 x 561515.625)/3

                                                    = 2350878.75 cubic ft.

A golf ball

Radius = 1.5/2 inches = 0.75 inches

1 ft = 12 inches

So 0.75 inches = 0.75/12 = 0.0625 ft.

So radius, r = 0.0625 ft

Volume of a golf ball =  [tex]\frac{4\pi r^3}{3}[/tex] = (4 x 3.14 x [tex]0.0625^3[/tex])/3

                                   = 0.00122 cubic ft.

Ratio of the volumes of Spaceship Earth to a golf ball

                    = 2350878.75:0.00122

                    = 1926949795 : 1

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Answer:

z = 9

Step-by-step explanation:

Divide both sides by 3 to get z by itself

So we are provided with the equation,

x2 + 10x + 40 = 5

To simplify it, we will first reorder the terms,

40 + 10x + x2 = 5

Now we will solve the equation to find the value of the unknown variable that we declared here as x.

40 + 10x + x2 = 5

Solving for variable 'x.'

40 + -5 + 10x + x2 = 5 + -5

We will combine similar terms; the variables and the constants.

40 + -5 = 35

35 + 10x + x2 = 5 + -5

Combine the like terms again:

5 + -5 = 0

35 + 10x + x2 = 0

Adding -35 on both sides

35 + 10x + -35 + x2 = 0 + -35

35 + -35 + 10x + x2 = 0 + -35

35 + -35 = 0

0 + 10x + x2 = 0 + -35

10x + x2 = 0 + -35

0 + -35 = -35

10x + x2 = -35

The x term is 10x.

Take half its coefficient (5) to make it a perfect square.

Square it (25) and add it to both sides.

10x + 25 + x2 = -35 + 25

25 + 10x + x2 = -35 + 25

-35 + 25 = -10

25 + 10x + x2 = -10

Perfect square on the left side:

(x + 5) (x + 5) = -10

We can see that the Square root of the right side can’t be calculated.

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In rational functions, the discontinuities are caused by the denominator terms. Since the denominator of a fraction is non-zero, any term multiplied by the denominator is also non-zero.

To find the discontinuities, we need to factor the polynomial below. Once we have the two binomials, we set each to 0. This way, you can find the value that produces 0 in the denominator.

If x = -2 then (x^2) + 4 is 0.

So, the discontinuities are shown as x = -2

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The summation notion of given series is ∑10-3n , here n starts from 0 and the sum of given arithmetic series is 20.

The given arithmetic series is 10+7+4+ . . .

The summation notion of given series is ∑10-3n , here n starts from 0.

The sum of arithmetic series can be written as,

[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]

n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.

We have, n=5, [tex]a_{1}[/tex] = 10

To calculate sum of arithmetic series, we need to find [tex]a_{5}[/tex] .

[tex]a_{5} = a_{1} + (n-1)d[/tex]

d = -3 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get

[tex]a_{5}[/tex] = 10 + (5-1)(-3)

[tex]a_{5}[/tex] = 10-12 =-2

On substituting values in sum of arithmetic series formula, we get

[tex]S_{5}[/tex] = (5(10 + (-2)))/2 = 20

The summation notion of given series is ∑10-3n , here n starts from 0 and the sum of given arithmetic series is 20.

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Answer:

40 psi

Step-by-step explanation:

We can see that the relationship is linear with pressure increasing by 5 psi for every extra 15 feet depth

The data is given from depth of 40 feet

At 40 feet, pressure = 10 psi  

At 55 feet, pressure = 15 psi

At 70 feet pressure = 20 psi

We have to use 40 as the base depth since there are no measurements less than that value. So relative depth is d - 40 and since for every 15', there is an increase of 5psi, the relative increase in pressure  per 15' is [tex]= \dfrac{d-40}{15}\cdot 5[/tex]

But the base pressure is 10psi not 0 so we have to add 10 to this equation to get the absolute psi

So the equation that connects depth (d) and pressure (p) is:

[tex]p = \dfrac{d - 40}{15}\cdot 5 + 10\\\\\textrm{At 130' depth},\\p = \dfrac{130-40}{15}\cdot 5 + 10\\= \dfrac{90}{15}\cdot 5 + 10\\\\= 30 + 10 = 40 psi\\[/tex]

If we plot these values, we can see they fit a straight line with slope = 1/3 and y-intercept = -10/3

Hope that helps

Using substitution method, the solution of the given system of equations is (-3,0)

A system of equation can be solved using:

The given system of equations:

4y - 6 = 2x   ............   (1)

y - 3x = 9  .............. (2)

We need to find the solution using substitution method.

In equation (2), add 3x to both sides:

y - 3x + 3x = 9 + 3x

y =  9 + 3x   ........ (3)

Substitute y =  9 + 3x into equation (1):

4y - 6 = 2x

4.(9 + 3x) - 6 = 2x

36 + 12x - 6 = 2x

12x - 2x = 6 - 36

10x = -30

   x = -3

Substitute back x = -3 into equation (3)

y =  9 + 3x

  = 9 + 3.(-3)

  = 9 + (-9) = 0

Hence, the solution is (-3, 0)

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If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped, then the distance the object falls during 10 seconds is 1600 foot

Given,

The algebraic expression of the distance in feet that an object falls = [tex]16t^{2}[/tex]

Where t is the time in seconds

Here,

time t = 10 seconds

Substitute the value in the expression

[tex]16t^{2}=16(10)^{2}[/tex]

=1600 foot

Hence, If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped, then the distance the object falls during 10 seconds is 1600 foot

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Hello and Good Morning Afternoon:

Let's take this problem step-by-step:

   [tex](5x + 9) + (8x-30)=180\\\\\text{Take out the parentheses as they are unnecessary to solve this problem}\\5x + 9+8x-30=180\\\\\text{Combine like terms like variables to variables and constants to constants}\\5x + 8x + 9-30 = 180\\13x - 21=180\\13x = 201\\x = 15.46 \text{ or }\dfrac{201}{13}[/tex]

Answer: 15.46 or 201/13

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Just like polynomials and other expressions, you can perform basic arithmetic operations on rational expressions: addition, subtraction, multiplication, and division. A rational expression is a fraction whose numerator and the denominator is a polynomial. If f is a logical expression, then we can write f in the form of p/q, where p and q are polynomials.

Solution:

To find the restriction on a variable in the denominator, we Set the denominator equal to zero. Then we solve for X

So,

X+1 = 0

X = -1

X-4 = 0

X = 4

When we put the X= -1 or X= 4, we get 0 in the denominator, so these are restrictions variables

= (x2+4x+3)/(x2-3x-4)

= (x+1) (x+3)/(x+1) (x-4)

Now cancel the common factor (x+1)

= x+3x-4

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Answer:

The answer is A because both equations are true

[tex] a) \: {x}^{3} - 2 = {1}^{3} - 2 \\ = 1 - 2 \\ = - 1 \\ \\ b) \: {x}^{2} + 4 = {1}^{2} + 4 \\ = 1 + 4 \\ = 5 \\ \\ [/tex]

The simplified form of the given expression 3[2(x - 3) + 2] + 5(x - 3)  is 12x - 63.

According to the given question.

We have an expression 3[2(x - 3) + 2] + 5(x - 3).

To simplify the above expression we will use the distributive law and add and subtract the like terms.

Therefore,

3[2(x - 3) + 2] + 5(x - 3)        

= 3[2x - 6 + 5x - 15]      (distributive rule)

= 3[7x - 21]             (adding the like terms)

= 21x - 63

Therefore, the simplified form of the given expression 3[2(x - 3) + 2] + 5(x - 3)  is 12x - 63.

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