Solve the given system of equations.S =t =-6s+ 3t = - 45-s-5t= -2

Answer:

use the property’s of equality to solve

Step-by-step explanation:

Use the properties of equality to solve, is not a step when we are solving an equation using distributive property.

Distributive property:- In general,

      distribute means to divide something or give a share or part of something. According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

             ex:-   a(b+c)=ab+ac

                       a(b-c)=ab-ac  ,also valid true for division

                  (b+c)/a = b/a + c/a

Steps involved while solving equations

1. If you see parenthesis, with more than one term inside, then distribute first.

2. Rewrite your equations with like terms together. Take the sign in front of each term.

3. Combine like terms.

4. Continue solving to get the answer.

Thus, Use the properties of equality to solve, is not a step involved in solving equation using distributive property.

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The relationship between the shoe's altitude (in meters relative to the water's surface) and time (in seconds) has been plotted in the graph shown below.

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + c

Where:

Next, we would determine the initial altitude as follows:

y = mx + c

0  = (0.1 × 35)  + c

0 = 3.5 + c

c  = -3.5

Substituting the given points into the formula, we have;

y  = 0.1x - 3.5

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Complete Question:

Elon sat on the dock with his fishing rod, when suddenly he felt the rod being pulled down! He reeled in his catch, causing it to ascend at a constant rate of 0.1 meters per second. When it reached the water's surface after 35 seconds, Elon found it was only an old shoe...

Graph the relationship between the shoe's altitude (in meters relative to the water's surface) and time (in seconds).

Ezzzzzzzzzzzzzzzzzzzzzzzzzzz

Answer:

3 and 2

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original

shape on left

consider the length of the horizontal sides

P = 2 and Q = 6 , then

scale factor = [tex]\frac{6}{2}[/tex] = 3

shape on right

consider the length of the horizontal sides

R = 2 and T = 4 , then

scale factor = [tex]\frac{4}{2}[/tex] = 2

In order to determine how many packages of diapers you can buy, it is only necessary to divide the total money you have, between the price of each package.

You have:

available money = 40$

package cost = 8$

Then, you calculate the quotient between available money and package cost:

Hence, you can buy 5 packages of diapers with 40$

Answer:[tex]26cm^{2}[/tex]

Step-by-step explanation: To do this you have to dissect the shapes into singular shapes.

First, you do the parallelogram at the bottom. 4×2

Then the middle rectangle. 3×4

Then the triangle at the top. 4×3÷2

Area= [tex]26m^{2}[/tex]

The price of 1 yard of blue fabric and 1 yard of green fabric is obtained by solving the system of linear equations and it is $8

Let

x = price of blue fabric per yard

y = price of green fabric per yard

"The blue fabric costs $2 more per yard than the green fabric" means:

x = y + 2  (Equation 1)

" LaTanya buys 6 yards of blue fabric and 9 yards of green fabric and pays $57" means:

6x + 9y = 57  (Equation 2)

Substitute equation 1 into equation 2:

6x + 9y = 57

6 (y + 2) + 9y = 57

6y + 12 + 9y = 57

15 y = 45

y = 3

Substitute y = 3 into equation 1

x = 3 + 2 = 5

Hence, the price of blue fabric is $5 per yard while the green fabric is $3 per yard.

The price of 1 yard of blue fabric and 1 yard of green fabric = x + y = 3 + 5 = $8

Complete question:

LaTanya buys 6 yards of blue fabric and 9 yards of green fabric. The blue fabric costs $2 more per yard than the green fabric. She pays a total of $57. What would be the combined cost of 1 yard of blue fabric and 1 yard of green fabric?

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ANSWER

B) y = 1/2x - 6

EXPLANATION

We have that the line passes through (6 -3) and has a slope of 1/2.

To find the point-slope form of the equation, we have to use the formula:

where m = slope = 1/2

(x1, y1) = (6, -3)

So, we have:

y - (-3) = 1/2 (x - 6)

y + 3 = 1/2 x - (1/2 * 6)

y + 3 = 1/2 x - 3

=> y = 1/2x - 3 - 3

y = 1/2x - 6

The answer is Option B

After using the linear equation - The smaller number is 7, and the greater number will be 23.

what is the substitution method?

Mathematicians frequently use the substitution method to resolve an equation system. With this method, you solve the equation for the first variable first, and then plug the answer into the second equation.

what is a linear equation in two variables?

When an equation is written in the form axe + by + c=0 and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero and the greater of the two numbers is four times the smaller number minus 5, that equation is said to be linear in two variables.

Let's assume that "x" is the smaller number, making "4x-5" the greater number. The requirement that the difference between the two numbers be 16 is also included.

thus,

4x - 5 - x = 16
3x -5 = 16
3x = 16 +5
3x =21
x = 21/3
x = 7
for the second number
4x-5
=4(7)-5
=28-5
=23

hence the smaller number is 7, and the greater number will be 23.

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The representation of the radical expression; the cube root of five to the seventh power as an expression with a rational exponent is; five to the seven thirds power.

It follows from the task content that the radical expression given; ³√5⁷ is to be expressed as a rational exponent expression.

Recall that the converse of the rational exponent law of indices is such that; ³√x = (x)^⅓.

Hence, it follows that the expression given;

³√5⁷ = (5⁷)^⅓.

Also, it follows from the power of power law of indices that the expression above can be written as;

5^(7/3).

Ultimately, the equivalent rational exponent expression is; five to the seven thirds power; 5^(7/3).

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a. The rocket splashes down after 31.23 seconds.

b.  The rocket is 1374.7 meters above sea level.

NASA launches a rocket at t=0 seconds.

Its height, in meters above sea-level, as a function of time is given by

h(t)=-4.9t²+142t+346.

Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?

When splash down occurs, h(t) = 0, therefore

-4.9t²+142t+346 = 0

find t using the quadratic formula; a=4.9, b=142, c=346

t = -142 ± √(142)² - 4(-4.9)(346) / 2(-4.9)

t = -142 ± 164.15 / -9.8

t = -142+164.15/-9.8 , -142-164.15/-9.8

t = 22.15/-9.8 , -306.15/-9.8

t = -2.26 , 31.23

time cannot be negative so t = 31.23

The rocket splashes down after 35.8229 seconds.

The max occurs on the axis of symmetry, use x=-b/(2a) to find it

t = -142/2(-4.9)

t = 142/9.8

t = 14.48 sec

replace t with 17.2449 in the equation

h(t) = -4.9(14.48)² + 142(14.48) + 346

= 1374.7 m

The rocket peaks at 1374.7 meters above sea-level.

Hence we get the answers.

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Answer:

Touchdowns: 6

Field goals: 3

PATS: 5

Step-by-step explanation:

6*6 = 36

3*3 = 9

5*1 = 5

9+5+36 = 50 points

6+3+5 = 14 scored times

Answers:

6 touchdowns (TD)

3 field goals (FG)

5 points after touchdown (PAT)

===============================================

Explanation:

Acronyms used in football

Define the following variables

"They had 3 more touchdowns than field goals", so,

TD = FG + 3

x = y + 3

They scored 14 times which means we can say

x+y+z = 14

Let's look at the point breakdown per type of score

Then we can add up those expressions to get us to 6x+3y+1z = 50 points total. This is the same as saying 6x+3y+z = 50.

--------------------------

Here's our system of equations

x = y+3

x+y+z = 14

6x+3y+z = 50

Let's replace each x with y+3 in the second equation. Then solve for z.

x+y+z = 14

y+3+y+z = 14

2y+z = 14-3

2y+z = 11

z = 11-2y

Now replace every x with y+3 in the third original equation

6x+3y+z = 50

6(y+3)+3y+z = 50

6y+18+3y+z = 50

9y+z = 50-18

9y+z = 32

Then plug in z = 11-2y and solve for y

9y+z = 32

9y+11-2y = 32

7y+11 = 32

7y = 32-11

7y = 21

y = 21/7

y = 3 is the number of FGs scored

Use this to find z

z = 11-2y

z = 11-2(3)

z = 11-6

z = 5 is the number of PATs scored

Now let's find x

x = y+3

x = 3+3

x = 6 is the number of TDs scored

--------------------------

Checking the answers:

x+y+z = 6+3+5 = 9+5 = 14 times they scored

6x+3y+z = 6*6+3*3+5 = 36+9+5 = 50 points scored

There are 3 more TDs than FGs since x = y+3 leads to 6 = 3+3 which is a true statement.

All three original equations we set up for the system of equations are true. Therefore, the final answers are confirmed.

The benzene has a volume value of 149.99 mL

From the question, the given parameters are

Density of benzene = 0.8787 g/mL

Mass of benzene = 131.8 g

The volume of the benzene is then calculated using

Density = Mass/Volume

Make Volume the subject of the formula

So, we have

Volume = Mass/Density

Substitute the known values in the above equation

So, we have the following equation

Volume = 131.8/0.8787

Evaluate the quotients in the equation

Volume = 149.99

Hence, the volume of the benzene is 149.99 mL

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Step-by-step explanation:

the slope of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

a slope = 0 means that the y coordinate change is always 0, so y does not change anywhere on the line.

that makes y a constant c, and x can be any value completely independent of y.

the line is the summary of all points that have c as their y coordinate.

so, the general equation for such a line is simply

y = c

what is c ?

as we have one point on the line, remember the statement above : the line is the summary of all points that have c as their y coordinate.

that means (3, -4) must have the same y coordinate.

so, c = -4.

the equation of the line is therefore

y = -4

a. The expected value is 0.40

b. The standard error is 0.0024

Given that:

Sample size, n=100

Population proportion, p=0.40

a) The expected value of the sample proportion is defined as:

E(^p)=p

now,

E(^p)=0.40

b) The standard error of the sample proportion is defined as:

SE(^p) = √p(1-p)/n

SE(^p) = √0.40(1-0.40)/100

SE(^p) = 0.0024

c) The sampling distribution of the sample proportion is normally distributed with the expected value of the sample proportion of 0.40.

Therefore,

E(^p) = 0.40

d) The central limit theorem states that the sample statistic (sample proportion) tends to the population parameter (population proportion) as the sample size tends to infinity (OR n→∞).

^P~N(p, p(-p)/n) as n→∞

Hence we get the required answers.

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Answer:

$100.14

Step-by-step explanation:

convert to a number

A line that passes through point (3,-5) and is perpendicular to y = -x+5 has the equation y = x - 8.

A straight line has an equation of y=mx + c, where m is the gradient and c is the constant, also known as the y-intercept, at which the line crosses the y-axis.

In order to put the equation in y-intercept (y = mx + b) form and determine the equation of a graphed line, first determine the slope and y-intercept.

It is given that a line's equation passes through point (3,-5) and is perpendicular to y = -x+5.

Slope of given line = -1

Slope of line perpendicular to the given line = Negative of the reciprocal of the slope of a given line = 1

We have the slope and point (3,-5) of the required line. So, we can find the constant of this equation.

y = mx + c

-5 = 1(3) + c

c = -5 - 3

c = -8

Substituting c = -8 and m = 1 to get the equation of required line.

y = mx + c

y = x - 8

As a result, the equation of a line passing through point (3,-5) and perpendicular to y = -x+5 is y = x - 8.

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Answer:

[tex]\sf Area = 10\dfrac{7}{8} \yd^2[/tex]

Step-by-step explanation:

     Area = length *breadth

Convert the mixed fraction to improper fraction.

[tex]\sf 1\dfrac{1}{2}=\dfrac{3}{2} \ yd[/tex]

[tex]\sf area = \dfrac{3}{2}*\dfrac{58}{8}\\\\[/tex]

      [tex]\sf = \dfrac{3*29}{8}\\\\=\dfrac{87}{8}\\\\= 10\dfrac{7}{8} \ yd^2[/tex]

Answer:

The vertical angles are

1 and 3

2 and 4

The linear equation which can be used to represents Curtis weekly salary is S = 8H + 0.02C

Weekly salary = Curtis wage per hour(Hours Worked) + Percentage commission(Commission earned on total sales)

S = 8(H) + 2%(C)

S = 8H + 0.02(C)

S = 8H + 0.02C

So therefore, Curtis linear equation for his weekly salary is S = 8H + 0.02C

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120 children and 120 adults were admitted to the amusement park if the admission fee collected was $1980.00

The number of children and adults that entered the park can be calculated using linear equations.

Considering x to be the number of adults and y to be the number of children;

As 240 people entered the park, therefore;

x + y = 240

As the fee for children is $3.50 and for adults is $13, therefore;

13x + 3.50y = 1980

Determining the value of y in the first equation;

x + y = 240

y = 240 - x

Putting this value of y in the second equation;

13x + 3.50y = 1980

13x + 3.50(240 - x) = 1980

13x + 840 - 3.50x = 1980

9.5x = 1980 - 840

9.5x = 1140

x = 1140 / 9.5

x = 120

To determine the value of y, we Substitute this value of x in the first equation;

y = 240 - x

y = 240 - 120

y = 120

Hence, 120 children and 120 adults entered the park if the admission fee for children was $3.50 and for adults was $13.00

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In order to find how many pounds are in each bag, we just need to divide the total amount of blueberries by the number of bags.

So we have:

So in each bag there are 1/16 pounds of blueberry.

Answer:-0.9.45

Step-by-step explanation:

-0945

Answer: -0.6i

Step-by-step explanation:

[tex]0.4i-i=\\\\i(0.4-1)=\\\\i(-0.6)=\\\\-0.6i[/tex]

The population for which 78% is a legitimate estimate of the percent of people that are 'very satisfied" with the yoga classes is C. anyone who has taken a yoga class at the gym in the past year but not before that.

An estimate is a rough calculation that may not be based on real figures or it may be based on rounded-off or appropriated facts and figures.

Estimates enable the decision-maker to make a quick guess or decision that cannot wait for all the facts to be collected.

Thus, the population of interest for the estimate includes members and non-members who have participated.

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Answer:

D

Step-by-step explanation:

By evaluating the equation in x = 2030, we can estimate the price to be $51.60.

We know that the equation:

y = 1.67*x - 3338.5

Models the relationship between the year, x, and the average ticket price of a Miami Marlins baseball ticket.

We know that this relationship works for the years 2006 to 2021, but can be used to estimate the price for years after and before that.

if we use x = 2030, we will get:

y = 1.67*2030 - 3338.5 = 51.6

This will be the price, in dollars, of a game in the year 2030.

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The equation of the line is y = -3x + 8.

The slope of a line, or angle between it and the horizontal, is stated numerically. The slope of a line, ray, or line segment in analytical geometry is the ratio of its vertical to horizontal distance between any two locations ("slope equals rise over run").

Given,

x1 = 1

y1 = 5

m = -3

From,

y-y1 = m(x-x1) (x-x1) (x-x1)

y - 5 = -3(x - 1) (x - 1) (x - 1)

y-5 = -3x + 3

y = -3x + 8

As a result, the equation for the line is y = -3x + 8.

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Answer:

Y=-3x+7

Step-by-step explanation:

it hit the y axis at 7

And it is going down by 3

For the given line, the graph is given below -

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

For the given line,

y = 1/4x + 2

the coordinates will be -

for x = 4, y = 3

(4,3)

for x = 8, y = 4

(8,4)

for x = 0, y = 2

(0,2)

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Answer:

y = x - 11

Step-by-step explanation: