Hazel runs for 3/4 hour and stretches For 1/5 hour. Complete the expression to model the time hazel exercises. Write equivalent fractions using the least common denominator. +

Please respond quickly will give brainliest ‼️‼️

Answer:

Option B

Step-by-step explanation:

We have to solve this system of equations by using the Substitution method so here goes,

\(Equation\ 1\\\\\y=x^2+5x+3\\\\Equation\ 2\\\\\ y=\sqrt{2x+5}\\\)

We insert equation 2 in equation 1 since both equations are equal to y so we equate both of them,

\(\sqrt{2x+5}=x^2+5x+3\\Square\ both\ sides\\\\\2x+5=(x^2+5x+3)^2 \\\)

To square the right hand side suppose

\(a=x^2+5x\\b=3\\(a+b)^2=a^2+2ab+b^2\\(x^2+5x)^2+2(x^2+5x)(3)+(3)^2\\\\((x^2)^2+2(x^2)(5x)+(5x)^2)+6(x^2+5x)+9\\x^4+10x^3+25x^2+6x^2+30x+9\\x^4+10x^3+31x^2+30x+9\\\)

Now,

\(2x+5=x^4+10x^3+31x^2+30x+9\\x^4+10x^3+31x^2+30x-2x+9-5=0\\x^4+10x^3+31x^2+28x+4=0\\\)

Apply Newton-Raphson method to quickly determine the approximate solution of the polynomial we get the values of x to be,

x ≈ -0.175 and x ≈ -1.22

now insert these values into equation 1 or 2 to get the values of y

we use the first value ,

\(y=x^2+5x+3\\y=(-0.175)^2+5(-0.175)+3\\y=2.155\\\)

now for the second value of x,

\(y=x^2+5x+3\\y=(-1.22)^2+5(-1.22)+3\\y=-1.612\)

now since the second set of values are not in the options we ignore the second set of values which are ( -1.22 , -1.612)

we use the first set of values which are (-0.175 , 2.155) which rounded off lead to (-0.2 , 2.1), so Option B is your answer

I also attached a graphical representation so you can verify the answer yourself , The approximate solution of this system of equation is the point of intersection between both the graphs which is marked on the image.

The justification for each step in the flowchart proof is given as:

A. given

B. definition of congruent

C. definition of bisect

A segment that divides an angle into two equal halves is known as an angle bisector.

In the image attached below, we want to prove that BC is an angle bisector of angle ABD.

The following justofy each step in the flowchart proof:

m∠ABC ≅ ∠CBD (given)

m∠ABC ≅ ∠CBD (definition of congruent)

BC bisects ABD (definition of bisect)

Learn more about angle bisector on:

https://brainly.com/question/24677341

#SPJ5

Answer:

Step-by-step explanation:

Answer:

brainliest please i work really hard for this

Step-by-step explanation:

Hit Water:

He hits the water when his height, h(t), is 0 meters above water.

0 =  

This is no factorable so we use the quadratic formula.

(-b±√(b²-4ac))/2a

(-10±√(10²-4*-5*3))/2*-5

(-10±√(100+60))/-10

(-10±√160)/-10

(-10±√16*10)/-10

(-10±4√10)/-10

(-10±4√10)/-10         Seperate to two equations

(-10+ 4√10)/-10                          and                (-10- 4√10)/-10

(-10+12.65)/-10                                                 (-10-12.65)/-10  

-.265 Not Solution                                          2.265 Seconds

Becasue there is no negative time

The diver hits the water at 2.265 seconds

For when he is at the same height as the spring board, we need to find the height of the spring board, and we do that by substituting 0 for t because we need the height 0 seconds after he jumps.

h(0) = -5*0^2 +10*0 +3

h(0) = 3   The height of the spring board is 3 so we need to know when he is at 3 meters again.

3= -5t^2 + 10t + 3       Subtract 3 from both sides

0= -5t^2 +10t

0= -5(t^2-2t)       Factor out -5 and divide both sides by -5

0= t^2-2t    

0= t(t-2)      Factor out t.

Solve.

t= 0               t-2=0

                    t= 2

He will be at the same height as the spring board at t= 2 seconds

Answer:

The area of the new rectangle is 9 times larger than the original rectangle

Step-by-step explanation:

For example if the length of a rectangle was 7 and the width was 6, to find area we multiply them. So 7×6=42

If we triple the length and width, we get 21×18=378.

378÷42=9.

This means the new rectangle's area is 9 times larger than that of the original.

Answer:

13%

Step-by-step explanation:

21-18.27=2.73

2.73/21= 0.13

0.13 x 100=13%

Answer:

x = 28 degrees. 180 degrees in a triangle, 180-85-67=28

Answer:

28 degrees

Step-by-step explanation:

The interior angles of a triangle add up to 180 degrees.

The three angles given are: x, 85, and 67.

Therefore, these three angles must add to 180.

x+85+67=180

Combine like terms on the left. Add 85 and 67.

x+ (85+67)=180

x+152=180

We want to find x. We need to get x by itself. 152 is being added to x. The inverse of addition is subtraction. Subtract 152 from both sides.

x+152-152=180-152

x=180-152

x=28

x is 28 degrees.

Answer:

5 out of 6, or 83%

Step-by-step explanation:

There are 6 sides and since it will not land on 3.  It will be \(\frac{5}{6}\) which equals 83%

The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

To know more about ratio visit:

https://brainly.com/question/13419413

#SPJ11

The average score of all students, calculated by taking a weighted average based on the number of students in each group, is 38. The overall performance is slightly below the group averages.

The average score of students in the first, second, and third groups are 39, 32, and 43, respectively. There are 24 students in the first group, 26 students in the second group, and 27 students in the third group.

To find the average score of all students, we need to take a weighted average of the scores in each group, with the number of students in each group as the weights.

Here's how to do it: First, we calculate the total number of students:24 + 26 + 27 = 77. Then, we calculate the total score across all students: 39*24 + 32*26 + 43*27 = 936 + 832 + 1161 = 2929

Finally, we divide the total score by the total number of students to get the average score:2929/77 = 38. The average score of all students is 38.

This means that the overall performance of all the students is slightly below the average of the scores in each group.

For more questions on average score

https://brainly.com/question/13832161

#SPJ8

Answer:

18 liquid quarts ≈ 17 litres

Answer:

18 us liquid quart =17.034 liters

Step-by-step explanation:

1) 1 us liquid quart = 0.946 liter

2) Multiply 0.946 *18 = 17.034

The cost of the calculator before the total is $24.95

From the question, we have the following parameters that can be used in our computation:

Total cost = $28.19

Tax = 13%

Using the above as a guide, we have the following:

Total cost = Initial cost * (1 + Tax)

substitute the known values in the above equation, so, we have the following representation

Initial cost  * (1 + 13%) = 28.19

So, we have

Initial cost   = 28.19/(1.13)

Evaluate

Initial cost = 24.95

Hence, the cost of the calculator before the total is $24.95

Read more about percentage at

brainly.com/question/843074

#SPJ1

Answer:

-4

Beni beyinsiz yap lütfen

Step-by-step explanation:

D Quadrilaterals ABCD and A'B'C'D' have the same orientation and are congruent.

What is an Quadrilaterals ?

To determine the answer, we can check whether the sides and angles of ABCD and A'B'C'D' are proportional to each other. If they are, then the quadrilaterals are similar, and if they are also congruent, then they have the same orientation.

Let's first check if the sides are proportional. We can calculate the lengths of the sides of ABCD and A'B'C'D' using the distance formula:

AB = √[(3+3)² + (-3-(-3))²] = 6√(2)

BC = √[(6-(-3))² + (0-3)²] = 3√(10)

CD = √[(0-6)² + (-3-0)²] = 3√(10)

DA = √[(-6-0)²+ (-3-(-3))²] = 6

A'B' = √[(1+2)² + (1+1)²] = √(10)

B'C' = √[(2-(-1))² + (0-1)²] = 3

C'D' = √[(0-2)² + (-1-0)²] = √(5)

D'A' = √[(-2-0)² + (-1-(-1))²] = 2

Now let's check if the corresponding angles are congruent. We can calculate the angles using the dot product formula:

cos(AB, A'B') = [(3+3)(-1-2) + (-3-(-3))(1+1)] / (6√(2)√(10)) = -1/3

cos(BC, B'C') = [(6-(-3))(2-(-1)) + (0-3)(0-1)] / (3√(10)3) = 1

cos(CD, C'D') = [(0-6)(0-2) + (-3-0)(-1-0)] / (3√(10)√(5)) = 1/3

cos(DA, D'A') = [(-6-0)(-2-0) + (-3-(-3))(-1-(-1))] / (6√(2)2) = 1

Since the sides are proportional and the corresponding angles are congruent, we can conclude that quadrilaterals ABCD and A'B'C'D' are similar. Furthermore, since they have the same orientation (i.e., they can be mapped onto each other by a rotation and/or reflection), they are also congruent. Therefore, the correct statement is:

D Quadrilaterals ABCD and A'B'C'D' have the same orientation and are congruent.

To know more about quadrilaterals, visit:

https://brainly.com/question/29934440

#SPJ1

Answer:

x = 7

Step-by-step explanation:

3x - 9 = 12

3x = 12 + 9

3x = 21

x = 21 ÷ 3

x = 7

Aldolases and ketolases are enzymes involved in the aldol and ketol reactions, respectively, in organic chemistry. These reactions are important in various biochemical pathways, including carbohydrate metabolism and the synthesis of complex organic molecules.

Aldolases are enzymes that catalyze the aldol reaction, which involves the formation of a carbon-carbon bond between an aldehyde or ketone and a carbonyl compound. This reaction typically results in the formation of a β-hydroxy aldehyde or β-hydroxy ketone.

Example of Aldolase: Fuctose-1,6-bisphosphate aldolase (aldolase A)

Fructose-1,6-bisphosphate aldolase is an enzyme that plays a crucial role in glycolysis, the metabolic pathway that breaks down glucose to produce energy. It catalyzes the cleavage of fructose-1,6-bisphosphate into two three-carbon molecules, glyceraldehyde-3-phosphate, and dihydroxyacetone phosphate.

Ketolases are enzymes that catalyze the ketol reaction, which involves the rearrangement of a ketone into an aldose (an aldehyde with a hydroxyl group on the terminal carbon). This reaction can lead to the formation of complex sugars and other organic molecules.

Example of Ketolase: Transketolase

Transketolase is an enzyme involved in the pentose phosphate pathway, a metabolic pathway that generates pentose sugars and reducing equivalents (NADPH) from glucose. Transketolase catalyzes the transfer of a two-carbon fragment, such as a ketose, to an aldose, resulting in the formation of two different aldose sugars.

In summary, aldolases catalyze the formation of carbon-carbon bonds in the aldol reaction, while ketolases catalyze the rearrangement of ketones into aldoses in the ketol reaction. These enzymes play essential roles in various metabolic pathways and are involved in the synthesis and degradation of complex organic molecules in living organisms.

To know more about metabolism:

https://brainly.com/question/19664757

#SPJ4

In this refinery-type problem, we are given the equation: 10x1 + 5x2 + 5x3 = 300 and 5x1 + 10x2 + 8x3 = 300

The goal is to find the values of x1, x2, and x3 that satisfy both equations simultaneously.

The given refinery-type problem consists of two equations that need to be solved simultaneously to find the values of x1, x2, and x3. To solve this problem, we can use a method called simultaneous equation solving. However, since the problem does not specify a method, I will  provide the steps to set up the equations for further solving.

The steps are explained as follows to find the values of x1, x2, and x3:
1. Choose one of the equations and solve it for one variable in terms of the other variables. Let's choose the first equation and solve it for x1:
  10x1 = 300 - 5x2 - 5x3
  Divide both sides by 10:
  x1 = (300 - 5x2 - 5x3)/10
2. Substitute the expression for x1 obtained in step 1 into the second equation:
  5((300 - 5x2 - 5x3)/10) + 10x2 + 8x3 = 300
3. Simplify the equation obtained in step 2:
  (1500 - 25x2 - 25x3 + 20x2 + 16x3)/10 = 300
  Combine like terms:
  (1500 - 5x2 - 9x3)/10 = 300
4. Multiply both sides of the equation by 10 to eliminate the fraction:
  1500 - 5x2 - 9x3 = 3000
5. Rearrange the equation to isolate the variables:
  -5x2 - 9x3 = 3000 - 1500
  -5x2 - 9x3 = 1500
Now we have a system of two equations with two variables:
x1 = (300 - 5x2 - 5x3)/10
-5x2 - 9x3 = 1500
To find the values of x2 and x3, we can use various methods such as substitution or elimination.
In summary, the given refinery-type problem consists of two equations that need to be solved simultaneously to find the values of x1, x2, and x3. The steps provided above outline how to set up the equations and begin the solving process. Further solving would require using a specific method to find the values of x2 and x3.

Learn more about simultaneous equation solving here:

https://brainly.com/question/148035

#SPJ11

Answer:

x=3

Step-by-step explanation:

6 times 3 equals 18. 18+2 equals 20. So X=3

Answer:

\( \sf \: x = 3\)

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 2 + 6x = 20

Then the value of x will be,

→ 2 + 6x = 20

→ 6x = 20 - 2

→ 6x = 18

→ x = 18 ÷ 6

→ [ x = 3 ]

Hence, the value of x is 3.

Yes, because theory provides the foundation and framework for conducting research and analyzing data in a meaningful and systematic manner.

By giving them a conceptual framework for their research, theory aids in the formulation of research questions. It aids in defining the scope and goals of the research investigation, producing hypotheses, and identifying knowledge gaps.

The conceptual foundations for research and statistics are provided by theory. It directs the creation of research questions, the development of hypotheses, the design of the study, the analysis of the data, and the interpretation of results. Research becomes more methodical, rigorous, and relevant when theory is incorporated, which advances knowledge and our understanding of complicated processes.

Learn more about statistics:https://brainly.com/question/32201536

#SPJ4

Answer:

29

Step-by-step explanation:

Given

- 5x + 4 ← substitute x = - 5 into the expression

= - 5(- 5) + 4 = 25 + 4 = 29

The square number from that list is the one at option B:

9*10⁴

A square number is any number that can be written as the square of an integer.

Here we have some numbers written in scientific notation, so, these numbers will be a perfect square if and only if the first factor is square, and the exponent on the 10 is even.

The only option that meets the two conditions is B, which we can write as:

9*10⁴ = (3*10²)²

That is a square number.

Learn more about square numbers:

https://brainly.com/question/21694652

#SPJ1

Answer:

3/100  

Step-by-step explanation:

:)

Answer: 300 centimeters

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

1.5*10 =15

Answer:

15.

Step-by-step explanation:

1.5 x 10 is expanded notation, so you just solve it (by multiplying) to convert it into standard notation.

Answer:

$42

Step-by-step explanation:

Substitute:

Y = 6x

F = 7

So, Y = 6 * 7 = 42

Answer: 42

Step-by-step explanation:

The surface area of the rectangular pyramid is approximately 567.9 in².

What is rectangular pyramid?

A rectangular pyramid is a type of pyramid that has a rectangular base and four triangular faces that meet at a common vertex. The rectangular base of a rectangular pyramid can be any rectangle, meaning that the length and width can be different. The four triangular faces of a rectangular pyramid are congruent, which means they are the same size and shape. The height of the rectangular pyramid is the distance between the vertex and the center of the base. The surface area of a rectangular pyramid can be calculated by finding the area of each face and adding them together.

To find the surface area of the rectangular pyramid, we need to find the area of each face and add them together.

First, let's find the area of the rectangular base:

Area of base = length x width = 13 in x 17 in = 221 in²

Next, let's find the area of the larger triangular faces:

Area of each larger triangular face = (1/2) x base x height = (1/2) x 17 in x 11 in = 93.5 in²

Total area of both larger triangular faces = 2 x 93.5 in² = 187 in²

Finally, let's find the area of the smaller triangular face:

Area of smaller triangular face = (1/2) x base x height = (1/2) x 13 in x 12.3 in = 79.95 in²

Now, we can find the total surface area of the rectangular pyramid by adding the areas of all the faces:

Total surface area = area of base + area of both larger triangular faces + area of smaller triangular face

Total surface area = 221 in² + 187 in² + 79.95 in²

Total surface area = 488.95 in²

Therefore, the surface area of the rectangular pyramid is approximately 567.9 in².

To know more about rectangular pyramid visit:

https://brainly.com/question/27270944

#SPJ1

The coordinates in rectangular form are listed below:

(r, θ) = (9, π / 6): (x, y) = (7.79, 4.5)

(r, θ) = (3, 3π / 4): (x, y) = (- 2.12, 2.12)

(r, θ) = (0, π / 4): (x, y) = (0, 0)

(r, θ) = (10, - π / 2): (x, y) = (0, - 10)

In this question we must convert four coordinates in polar form into rectangular form, this conversion is defined by following expression:

(r, θ) → (x, y), where:

x = r · cos θ, y = r · sin θ

Where:

Now we proceed to find the rectangular coordinates for each case:

(r, θ) = (9, π / 6)

(x, y) = (9 · cos (π / 6), 9 · sin (π / 6))

(x, y) = (7.79, 4.5)

(r, θ) = (3, 3π / 4)

(x, y) = (3 · cos (3π / 4), 3 · sin (3π / 4))

(x, y) = (- 2.12, 2.12)

(r, θ) = (0, π / 4)

(x, y) = (0 · cos (π / 4), 0 · sin (π / 4))

(x, y) = (0, 0)

(r, θ) = (10, - π / 2)

(x, y) = (10 · cos (- π / 2), 10 · sin (- π / 2))

(x, y) = (0, - 10)

To learn more on rectangular coordinates: https://brainly.com/question/31904915

#SPJ1

Therefore, the equation of the plane through the point (1, -3, -2) and perpendicular to the line of intersection of the two planes x - 2y + z = -3 and 3x - 2y + z = 1 is -2x - 2y - 5z - 14 = 0.

To find the equation of the plane, we'll first determine the direction vector of the line of intersection between the two planes. The direction vector can be found by taking the cross product of the normal vectors of the two planes.

The normal vector of the first plane, x - 2y + z = -3, is <1, -2, 1>.

The normal vector of the second plane, 3x - 2y + z = 1, is <3, -2, 1>.

Taking the cross product of these two vectors, we get:

<1, -2, 1> x <3, -2, 1> = <(-2)(1) - (1)(-2), (1)(1) - (3)(1), (1)(-2) - (1)(3)> = <-2, -2, -5>

So, the direction vector of the line of intersection is <-2, -2, -5>.

Since the plane we are looking for is perpendicular to this line, the normal vector of the plane will be parallel to the direction vector. We can take the direction vector as the normal vector of the plane.

Now, let's find the equation of the plane through the point (1, -3, -2) using the normal vector < -2, -2, -5>.

The equation of the plane is given by:

A(x - x1) + B(y - y1) + C(z - z1) = 0,

where (x1, y1, z1) is the point on the plane and A, B, and C are the components of the normal vector.

Substituting the values, we have:

-2(x - 1) - 2(y + 3) - 5(z + 2) = 0,

Expanding and simplifying, we get:

-2x + 2 - 2y - 6 - 5z - 10 = 0,

Simplifying further, we have:

-2x - 2y - 5z - 14 = 0.

To learn more about  perpendicular

https://brainly.com/question/1202004

#SPJ11

Answer:

(-6,8)

Step-by-step explanation: