What is the first step to solve a system with substitution?

The time it would take the rocket to hit the ground upon launch is; 3 seconds.

It follows from the task content that the time taken for the rocket in discuss to hit the ground upon launch is to be determined.

Since the given formula for the height in terms of time, t is;

h = - 3t² + 3t + 18

It follows that ; when the rocket hits the ground; the height; h = 0.

Therefore;

0 = - 3t² + 3t + 18

0 = -3t² + 9t - 6t + 18

0 = -3t ( t - 3 ) - 6 ( t - 3)

-3t - 6 = 0 OR. t - 3 = 0.

t = -2. OR. t = 3.

Therefore, since the time after launch can only be positive; the time taken for the rocket to hit the ground is; 3 seconds.

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The responses for the confidence intervals of the 45 lbs weight and the set of data are;

3. D. (45.0472, 45.0928); The exercise equipment company can be 95% confident the population mean of their 45 lb weights lies between 45.0472 and 45.0928

4. C. The size of the confidence interval would increase because Raul would be multiplying by a larger z-score and dividing by a smaller sample size.

The confidence interval is the likelihood of a parameter of a population can be found within a range of values during a specified percentage or proportion of the time.

3. The confidence interval can be found using the formula;

[tex]CI = \overline x \pm z\cdot \dfrac{s}{\sqrt{n} }[/tex]

Where;

[tex]\overline x[/tex] = The mean of the sample = 45.07 lbs

s = The standard deviation of the sample = 0.09 lbs

n = The sample size

z = The confidence level = 1.96 at 95% confidence level

Therefore;

[tex]CI = 45.07 \pm 1.96\times \dfrac{0.09}{\sqrt{60} }[/tex]

45.0472 < μ < 45.0928

The correct option is therefore, option D

Therefore;

4. Decreasing the sample size, n, will decrease the value by which the term on the right of the ± is being divided, increasing the confidence interval.

Increasing the level of confidence will increase z, thereby also increasing the confidence interval.

The correct option is therefore, option C.

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The area of walk is 504 square feet

The area of rectangle is define as a  product of length L and width w

calculate the area of rectangle yard

Area = L x W,  

where A equal the Area, L equals the length and W equal width.

A = 35 x 55

A= 1925 square feet

Area of the rectangular yard is 1925 square feet

From the question, we have 3ft wide goes all the way along the fence inside.

Therefore, we subtract six feet from each of the value of length ( 35) and width (55) because each side has 3feet .

Area = L x W

A = 29 x 49

A = 1421 square feet

Area of new rectangle formed by allowing for three foot walk is 1421 square feet

Area of Walk

To get the area walk;  we subtract area of new rectangular formed from area of rectangular yard

Area of Walk = Area of Rectangular yard - Area of new rectangle

Area of Walk = 1925 - 1421

Area of Walk = 504 square feet.

Therefore, the area of walk is 504 square feet.

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Answer:

x = 0 , y = 0 , z = -3

Step-by-step explanation:

Solve the following system:

{x - 6 y + 4 z = -12 | (equation 1)

x + y - 4 z = 12 | (equation 2)

2 x + 2 y + 5 z = -15 | (equation 3)

Swap equation 1 with equation 3:

{2 x + 2 y + 5 z = -15 | (equation 1)

x + y - 4 z = 12 | (equation 2)

x - 6 y + 4 z = -12 | (equation 3)

Subtract 1/2 × (equation 1) from equation 2:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+0 y - (13 z)/2 = 39/2 | (equation 2)

x - 6 y + 4 z = -12 | (equation 3)

Multiply equation 2 by 2/13:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+0 y - z = 3 | (equation 2)

x - 6 y + 4 z = -12 | (equation 3)

Subtract 1/2 × (equation 1) from equation 3:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+0 y - z = 3 | (equation 2)

0 x - 7 y + (3 z)/2 = -9/2 | (equation 3)

Multiply equation 3 by 2:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+0 y - z = 3 | (equation 2)

0 x - 14 y + 3 z = -9 | (equation 3)

Swap equation 2 with equation 3:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x - 14 y + 3 z = -9 | (equation 2)

0 x+0 y - z = 3 | (equation 3)

Multiply equation 3 by -1:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x - 14 y + 3 z = -9 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Subtract 3 × (equation 3) from equation 2:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x - 14 y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Divide equation 2 by -14:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Subtract 2 × (equation 2) from equation 1:

{2 x + 0 y+5 z = -15 | (equation 1)

0 x+y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Subtract 5 × (equation 3) from equation 1:

{2 x+0 y+0 z = 0 | (equation 1)

0 x+y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Divide equation 1 by 2:

{x+0 y+0 z = 0 | (equation 1)

0 x+y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Collect results:

Answer: {x = 0 , y = 0 , z = -3

Step-by-step explanation:

The steps in solving two rational numbers is using the cross multiplication method and then do the arithmetic operation on the numerator

The rational expression is defined as the expression with both numerator and denominator has polynomials.

Consider two rational expressions

Add two expression using cross multiplication

a/b + c/d

Cross multiply the expression

a/b + c/d = (ad + cb) / bd

Subtract two expression using cross multiplication

a/b - c/d

Cross multiply the expression

a/b + c/d = (ad - cb) / bd

Therefore, the two rational expression can be solved by using the cross multiplication method and do the arithmetic operation

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The function‘s end behavior is falls to the left and rises to the right.

The given function is [tex]f(x)=-10+2x^5-9x^3[/tex].

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Use the degree and the leading coefficient to determine the behavior.

Falls to the left and rises to the right.

Find where the first derivative is equal to 0 to find the local maxima and minima.

x =−3√30/10 is a local maximum

x = 3√30/10 is a local minimum

Therefore, the function‘s end behavior is falls to the left and rises to the right.

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Initial liquid volume is x.

3/4 of the liquid was removed:

Then 1/2 quarts added, the expression including the addition is:

Simplify to get equivalent expression:

Tom's growth chart  is a continuous graph.

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Divide the numerator and denominator by the GCF to reduce a fraction. (This is also referred to as "writing a fraction in the simplest terms.") The common factors are sometimes shown to be "cancelled." It is worth noting that the result is an equivalent fraction in its simplest form.

To put it simply, we must divide the numerator (x) by the denominator (y) to simplify it. For example, after simplifying 3 6, represent it as a fraction and identify the numerator and denominator. 3 6 can be written as 3/6. Further simplification yields 1/2.

Let's pretend the fraction is a proper fraction. The denominator is the numerator. We want to reduce the fraction to its simplest form.

a) Use Numerator =Remainder* as the denominator.

Now Numerator >Remainder* b)Numerator Remainder*=Remainder** c) ••• (keep going until Remainder =0)

d) When the Remainder equals zero, the Divisor is the GCD (or GCF, as you say). GCF is a misnomer because it only deals with numbers. Only the term GCF applies to variables (with numerical values, as in algebraic expression).

Let us look at an example.

407/3367 is the fraction.

As evident, the numbers407 ,3367 does not appear to have share Divisors 2 or 3 or 5 or 7 or 11 from prima facie considerations. So we may take recourse of successive division method.

3367 ÷407 =Remainder 111 (quotient 8)

407 ÷ 111 =Remainder 74 (quotient 3)

111 ÷74=Remainder 37 (quotient 1)

74 ÷37 =Remainder 0 (ZERO )

Here 37 divides leaving Remainder zero. Therefore the GCD is 37

Fraction 407 /3367 =(407 ÷37)/(3367÷37)=11/91

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Answer please anyone help same doubht

Step-by-step explanation:

Answer:

Refer to the photos taken.

Step-by-step explanation:

Answer:

[tex]y^6[/tex]

Step-by-step explanation:

1) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].

[tex]y^{1+3+2[/tex]

2) Simplify 1 + 3 to 4.

[tex]y^{4+2}[/tex]

3) Simplify 4 + 2 to 6.

[tex]y^6[/tex]

Thank you,

Eddie

The solution is Option D.

The equation is w - 23 = 84

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of wolves on January 1 = w

Now , after 1 year

The number of wolves in the state is = 84

And , number of wolves in the state after 1 year = 23 less than previous year

So ,

84 = 23 less than w

84 = w - 23   be equation (1)

Adding 23 on both sides of the equation , we get

w = 107

Therefore , the value of w = 107

And the equation is w - 23 = 84

Hence , The equation is w - 23 = 84

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Answer: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Step-by-step explanation: Add 5 until you get to 50.

Answer:

26

Answer choice 1.

Step-by-step explanation:

6 1/2 ÷ 1/4 is our equation.

6 1/2 as an improper fraction is 13/2

Our new equation is 13/2÷1/4

flip the divisor into a reciprocal and multiply:

13/2×4/1

simplify:

13/1×2/1

26/1

=26

Answer: The answer is A or 26

Step-by-step explanation: I have my ways ;>

To find equivalent expression in math is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.

In mathematics, equivalent fractions are those with the same denominator and differing numerators.

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.

This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.

For instance, if we simplify 5/15, we get a fraction that is equal to 1/3, which is equal to 5/15.

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The length of t will be;

⇒ t = 294.30 inches.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In ΔSTU, s = 250 inches, ∠U=17° and ∠S=52°.

Now,

Since, In ΔSTU, s = 250 inches, ∠U=17° and ∠S=52°.

Hence, ∠ T = 180 - (17 + 52)

∠ T = 180 - 69

∠ T = 111°

Now, We use the sin rule as;

⇒ t / sint = s / sin s

⇒ t / sin 111° = 250 / sin 52

⇒ t = sin 111° × 250 / sin 52

⇒ t = 0.93 × 250 / 0.79

⇒ t = 294.30 inches.

Thus, The length of t will be;

⇒ t = 294.30 inches.

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Answer: 296.2

Step-by-step explanation:

t/sin111 = 250/sin52

t=250 sin111/52 = 296.1826 = 296.2

Triangle DEF is congruent to triangle GHI is correct.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. A triangle having vertices A, B, and C is known as triangle ABC. Any three points in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.

A triangle is a polygon with three edges and three vertices. A triangle's total number of angles equals 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

Equilateral, scalene, isosceles, and other triangles are used.

Given are three triangles ΔABC, ΔDEF, ΔIHG.

ΔDEF is congruent to ΔGHI as -

EF = IH (given)

∠E = ∠H (right angle)

FD = IG (given)

Using SAS congruent rule, ΔDEF ≅ ΔGHI

Therefore,  triangle DEF is congruent to triangle GHI is correct.

The complete question is : Which of the following statements are correct?

Select all that apply.

Triangle ABC is congruent to triangle DEF.

Triangle DEF is congruent to triangle GHI.

All three triangles are congruent.

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The motion of the dolphin, evaluated using the kinematic equations and Newton's second law of motion are;

Mathematically, Newton's second law of motion states that force is the product of mass and acceleration.

The mass of the dolphin = 230 kg

Height to which the dolphin leaps = 6.4 m

The distance the drag brings the dolphin to a stop = 6.4 meters

First part;

The time it takes the dolphin to stop can be found from the equation;

At the water surface;

m·g·h = 0.5·m·v² (conservation of energy)

g·h = 0.5·v²

v² = 2·g·h

Therefore;

v² = 2 × 9.81 × 6.4 = 125.568

In the water, the initial velocity is v, the velocity at 1.5 meters depth is u, we get;

u² = v² - 2·a·s

Therefore;

v² = 2·a·s

a = v²/(2·s)

a = 125.568/(2 × 1.5) = 41.856

a = 41.856 m/s²

v = u - a·t

t = (u - v)/a

Therefore;

t = (√(125.568))/41.856 ≈ 0.268

The time it takes the dolphin to stop is about 0.268 seconds

Second part

Newton's second law of motion states that force is directly proportional to the rate of change of momentum produced

Mathematically

Force = Mass × Acceleration

Force on the dolphin, F = 230 kg × 41.856 m/s²= 9626.88 N

The possible parts of the question, obtained from a similar question are;

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0.85 millimeter the nurse will administer

What is division ?

One of the four fundamental arithmetic operations, or the process by which two or more numbers are added together to create a new number, is division. Multiplication, addition, and subtraction round out the list of operations.

The act of dividing anything into equal parts is called a division. As an illustration, we could divide a group of 20 people into 4 groups of 5, 5 groups of 4, and so on.

1 ml contain 200 mg of hormone

    200 mg = 1 ml

     1 mg = 1 / 200 ml

1 mg contain 1/200 ml of hormone

170 mg = 1/200 * 170 ml

            = 170 / 200

170 mg = 0.85 ml

The nurse will administer 0.85 ml

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Cindy's monthly payment of $609.63 will cost her $29,262.24 in 4 years at a 4% APR.

The total cost that Cindy will spend on the car which costs $27,000 is computed by multiplying the monthly payment by 48 months (the payment period).

The monthly payment can be determined using an online finance calculator that compounds the interest rate monthly for four years.

Cost of car = $27,000

Annual Percentage Rate (APR) = 4%

Payment period = 4 years (monthly)

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $27,000

FV (Future Value) = $0

Results:

PMT = $609.63

Sum of all periodic payments = $29,262.24

Total Interest = $2,262.45

Thus, Cindy will spend $29,262.24 for a car that costs $27,000, if she repays monthly for 4 years.

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The value of x is 19 and the measure of angles in triangle ABC are 75°, 75° and 30° respectively.

triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

If ABC is a triangle, then it is denoted as ∆ABC, where A, B and C are the vertices of the triangle. A triangle is a two-dimensional shape, in Euclidean geometry, which is seen as three non-collinear points in a unique plane.

The sum of ∠A + ∠B + ∠C = 180°( sum of angles in a triangle )

3x + 18 + 7x - 58 + 2x - 8 = 180°

12x -48° = 180°

12x = 228

x = 228/12

x = 19

but ∠A = 3x + 18, but x = 19

∠A = 3(19) + 18 which is 75°

Also ∠B = 7x -58

∠B = 7(19) - 58 which is 75°

∠C = 2x -8

∠C = 2(19) - 8 which is 30°

In conclusion, the value of x = 19, ∠A = 75°, ∠B = 75° ∠C = 30°

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The total monthly charges for the mobile plan if the usage is 120 minutes is $480.

Given that,

A mobile plan's total monthly costs, $C, are made up of a fixed fee of $ 20 and a variable fee that is based on usage. The cost is $0.20 per minute used.

We have to calculate the total monthly charges for the mobile plan if the usage is 120 minutes.

We know that,

A mobile plan fee is $20

For 1 min $0.20 for mobile plan

For 120 minutes

=120×0.2

=24

=24×20

=480

Therefore, the total monthly charges for the mobile plan if the usage is 120 minutes is $480.

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Using half-life and disintegration constant, the sample that will remain 4 seconds 2.03g

This is the spontaneous decay of an active radioactive sample. The decay curve is exponential and it slope is constantly changing.

The half-life of this sample given can be used to find the disintegration constant of the sample.

The formula of half - life is given as

T₁/₂ = ln2 / λ

Substitute the values into the equation;

7.13 = 0.693 / λ

λ = 0.693 / 7.13

λ = 0.0972

The amount of sample left after 4 seconds will be

A = Ne⁻(λt)

A = 3e⁻(0.0972 * 4)

A = 2.03g

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Answer:

neither narrower or broader

Step-by-step explanation:

if you look at your problem it says identical so that means exactly the same so it would be the second choice neither narrower or broader

ASA stands for "Angle-Side-Angle." Triangles classified as ASAs have two known angles and a common side. The ASA triangle ABC, with provided angles B and C and their common side a between them, is depicted below.

What does a congruence mean in mathematics?

If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.

Describe ASA congruence through an example.

ASA (Angle-Side- Angle) 

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

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The number 5i located on the complex plane in I Quadrant.

What is Complex Plane?

The real axis and the imaginary axis are the graph's horizontal and vertical axes, which are orthogonal (or perpendicular). The labels Re and Im are typically present. The complex plane is the plane defined by these coordinates.

We are aware that in a two-dimensional plane, an ordered pair's x- and y-coordinates are treated as the real and imaginary parts of the complex number, respectively.

i.e., a+bi=(a,b) -- Quadrant I,

    -a+bi=(-a,b) -- Quadrant II,

     a-bi=(a,-b) -- Quadrant III

and

     -a-bi=(-a,-b) -- Quadrant IV

The complex number that is being presented is 5i, aland it is located in quadrant I.

As a result, the complex number in question belongs in Quadrant I.

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Step-by-step explanation:

Answer:

∠ R = 115°

Step-by-step explanation:

• each lower base angle is supplementary to the upper base angle on the same side, that is

∠ R + ∠ S = 180°

∠ R + 65° = 180° ( subtract 65° from both sides )

∠ R = 115°

You have to divide 27 by 100 and that gives you .27.

If you multiply until you reach 32.13 with different numbers you get 19. It is a 19% increase.