A pair of linear equations is shown:

y = −3x + 5
y = x + 2

Which of the following statements best explains the steps to solve the pair of equations graphically?

On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1.
On a graph, find the point of intersection of two lines; the first line has y-intercept = −3 and slope = 5, and the second line has y-intercept = 1 and slope = 2.
On a graph, find the point of intersection of two lines; the first line has y-intercept = −5 and slope = 3, and the second line has y-intercept = −2 and slope = −1.
On a graph, find the point of intersection of two lines; the first line has y-intercept = 3 and slope = −5, and the second line has y-intercept = −1 and slope = −2.

Answer: Balloon B

Step-by-step explanation:

The distance, in feet, is always four times the time, in seconds.

The speed of the cyclist in miles per hour is 7.5 miles per hour. The distance covered by the cyclist in 5 hours is 30 miles.

According to the question,

We have the following information:

A cyclist rides his bike at the speed of 11 ft per second.

Now, it is given that we have to use 1 mile = 5280 ft.

So, we have:

1 ft = 1/5280 miles

We know that there 3600 seconds in 1 hour.

1 seconds = 1/3600 hour

So, we  have the speed in miles per hour:

11*(1/5280)/(1/3600)

(11*3600)/5280

7.5 miles per hour

Time taken = 5 hours

Speed = 7.5 miles per hour

Distance = speed*time

Distance = 7.5*5

Distance = 30 miles

Hence, the speed of the cyclist in miles per hour is 7.5 miles per hour. The distance covered by the cyclist in 5 hours is 30 miles.

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ANSWER

The system has no solution

EXPLANATION

We want to find the solution to the system of equations given:

From the first equation, make x the subject of the formula:

Substitute that into the second equation and simplify:

As we can see, the two sides of the equality sign have two different values.

This implies that the system of equations has no solution.

A) Check the graph below, please. B) Horizontal translation to the left in 2 units. C) Vertical shift 4 units

1) Given that we have the function h(x) = |x+2| and g(x)= |x| + 4

A) Let's set a pair of tables, and pick 3 arbitrary values for x and then plug into each one

h(x) = |x+2|

x | y = |x+2|

-1 | 1 y =|-1 +2| = |1| = 1

0 | 2 y =|0+2| = |2| = 2

1 | 3 y =|1+2| = |1| = 1

g(x) =|x| + 4

x | y

-1 | 5

0 | 4

1 | 5

Let's plot those absolute value functions:

B) Considering the parent function f(x) =|x| we can notice that h(x) is a translation to the left, in two units. This we can see better this way:

Note that f(x) is in red, and h(x) in pink or light red.

C) Considering that f(x) = |x| we can see that g(x) = is a vertical shift 4 units up.

Answer:

1018.3

Step-by-step explanation:

The volume of a cylinder=πr2h

=22\7*6*6*9

=1018.3

therefore, the of the cylinder is 1018.3

Let's rewrite it the first one

When we apply, log on both sides. We have the logarithm of a power equal to its exponent that is why we have y on the left side.

Rewriting the second one:

Since the Natural Logarithm is log in the base "e" we can say that x is equal to e raised to 9

Step 1:

Write the given vectors

Step 2

Resultant vector = [ 10 + (-6) , 9 + (-2) ]

= ( 4 , 7 )

Resultant vector = 4i + 7j

Step 3

Step 4:

6 bracelets Eva can make with the yarn she has left with .

The equation is [tex]\frac{3n}{2}=9[/tex]

Algebra is a branch of mathematics that helps translate real-world situations or problems into mathematical truths. Mathematical operations like addition, subtraction, multiplication, and division are needed in addition to variables like x, y, and z to construct a meaningful mathematical expression. All branches of mathematics, such as calculus, trigonometry, and coordinate geometry, employ algebra. A fundamental algebraic expression is 2x + 4 = 8, which results from operations like addition, subtraction, multiplication, and division on variables and constants. Algebraic expressions are obtained as the mathematical statement.

Eva has 11 meters of yarn and she gives 2 meters of the yarn to her friend

Now she left with 11 -2 = 9

As Each bracelet uses [tex]\frac{3}{2}[/tex] meters of yarn

n braclet = [tex]\frac{3n}{2}[/tex]

9= [tex]\frac{3n}{2}[/tex]

n = [tex]\frac{18}{3}[/tex]

=6

6 bracelets Eva can make with the yarn she has left with .

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The heighth of the cylinder if the surface area is 942 square feet is 25 feet.

From the information given, the S = 2π(25) + 2π(5h). We are to find the heighth of the cylinder if the surface area is 942 square feet.

This will be:

S = 2π(25) + 2π(5h).

2π(25) + 2π(5h) = 942

50π + 10πh = 942

(50 × 3.14) + (10 × 3.14 × h) = 942

157 + 31.4h = 942

Collect like terms

31.4h = 942 - 157

31.4h = 785

h = 785/31.4

h = 25

The height of the cylinder is 25 feet

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We have the next information

Let X be the number of customer purchased coffee

Let Y be the number of customer pwho urchased donuts

X∩Y Then is the number of customers who purchased both coffee and donuts

X∪Y is the number of customers who purchased both coffee or donuts

The number of customers who purchase only coffee is

48 customers purchased only coffee

The number of customers who purchase only donuts is

22 customers purchased only donuts

In order to know how many customers did not purchase either of these items

First we will calculate the customers that purchase something

then we know that the total number of customers is 110

21 customers did not purchase either of these items

Given:

Commutative law of addition.

2 only is the correct answer.

When pH is 2, the hydrogen ion concentration in [tex]litre^{-1}[/tex] is [tex]10^{-2}[/tex]

The pH value of water indicates how acidic or basic it is. The negative log of the hydrogen ion concentration is defined as pH. The pH scale starts from 0 and ends at 14. A pH of 7 is considered neutral because pure water has a pH of exactly 7. Acidic values are less than 7; basic or alkaline values are greater than 7.

Given that,

pH = 2 for HCl acid

We know that,

The relation between concentration of acid and pH is,

pH = -log[[tex]H^{+}[/tex]]

2 = -log[[tex]H^{+}[/tex]]

[tex][H^{+} ][/tex]  = [tex]10^{-2}[/tex]

Hence, the hydrogen ion concentration in a solution with a pH of 2 is [tex]10^{-2}[/tex].

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Given:

Given the diagram

Required: The measure of angles 1, 2 and 3.

Explanation:

The sum of interior angles of a triangle is 180 degrees. So,

The angles x and 1 are supplementary angles, that is, the sum of angles 1 and x gives 180 degrees.

The angle 2 is the opposite angle of 55 degrees. Hence angle 2 equals 55 degrees, that is,

Angle y and 150 degrees are supplementary angles. So,

The sum of the interior angles of a triangle equals 180 degrees.

Final Answer:

Answer:

The right option is 1) 27

Explanation:

According to the given data we have the following:

K is the midpoint of JL.

JK = 6x + 9

KL = 5x + 12

K is the midpoint of JL, hence, JL=JK+KL

So, to find JK we would equal JK with KL

So, 6x + 9=5x + 12

6x-5x=12-9

x=3

Therefore, JK=6(3)+9

JK=18+9

JK=27

Therefore, the right option is 1) 27

Given

height of cone = 4cm

Base radius of cone = 3cm

Find

TSA of cone

Explanation

We know that TSA of cone is

Final Answer

Part a

Remember that the ordinate is the y-coordinate and the abscisa is the x-coordinate

so

(x, 2x+1)

y=2x+1

Part b

x=(1/2)y^2

Part c

x^2+y^2=25

Part e

y=2

Part f

x=7

Part g

x=y

Part h

Part i

In order to solve the expression:

We operate inn such a manner that x is left alone, that is:

We have our expression 9 - 2x = 35.

In order to solve for x, we try and leave x alone, that is, we sustract 9 from both sides of the operation:

9 - 9 - 2x = 35 -9 => -2x =26

Now that we have this, we proceed to eliminate -2 from the side of x, for that we divide both sides by -2, that is:

(-2/-2)x=(26/-2) => x = -13

Input data

Graph

Procedure

y-intercept

Y-Intercept of a Straight Line. Where a line crosses the y-axis of a graph.

(0, -6)

x-intercept

The x-intercept is the point where a line crosses the x-axis

(-8,0)

X₁: science GPA for those who left their profession after graduation

X₂ science GPA for those who remained in their profession after graduation.

The working hypothesis is that the GPA of those who stayed is higher than those who left.

Which is the same as saying that the GPa of those who left is less than those who stayed.

μ₁ represents the population mean of the science GPA of those who left.

μ₂ represents the population mean of the science GPA of those who remained.

Part one

You can express the working hypothesis as follows:

The hypothesis does not include the equal sign, so this hypothesis can be considered as the alternative hypothesis.

The null hypothesis of this test will be the complement of the alternative hypothesis, and always carries the equal sign within. So if the alternative hypothesis states that "the mean of the leavers is less than the mean of the stayers", then the null hypothesis will be that "the mean of the leavers is greater than or equal to the mean of the stayers" you can symbolize this as:

Since the null hypothesis carries the equal sign you can also write it as:

Both options are equally valid.

So, the second answer is null hypothesis.

Part two

Considering that we are studying the population means of two normal variables and that we know the population standard deviation for both populations, the test statistic to use is the standard normal for the difference of means which is defined as follows:

Subindex 1 indicates the values corresponding to the "leavers":

X₁bar= 3.16

n₁= 103

σ₁= 0.52 → σ₁²= 0.2704

Subindex 2 indicates the values corresponding to the "stayers":

X₂bar= 3.28

n₂= 225

σ₂= 0.46 → σ₂²= 0.2116

Under the null hypothesis both population means are equal, which means that their difference is equal to zero:

If μ₁ = μ₂, then μ₁ - μ₂ = 0

Replace all values on the formula to determine the Z-value under the null hypothesis, i.e. the test statistic:

To find the numerical value of the expression, we have to replace the variables for their given values. This way:

The numerical value of the expression is 85.

Answer:

4x_7+x=6 4x_x=7+6 3x=13 x=13÷3

The equation has no solution.

How to find the solution of the given equation?

-r + 23 = -7r +  3(2r + 8)

Applying distributive property A(B+C) = AB+AC

⇒  -r + 23 = -7r + 6r + 24

Combining like terms,

⇒  7r - 6r -r = 24 - 23

⇒  7r - 7 r = 1

⇒  0 = 1

L.H.S ≠ R.H.S

Since the two sides are unequal , there is no solution.

What is the distributive property ?

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The equation to describe the relationship between the height of the plant and the number of weeks is

y = x + 5

Given,

The height of the plant = x

The number of weeks = y

The height of plant at 6th week = 11 inches

The height of plant at 8th week = 13 inches

The height of plant at 10th week = 15 inches

We have to find the equation to describe the relationship between the height of the plant and the number of weeks.

Lets see,

x = 6 and y = 11, y – x = 11 – 6 = 5

x = 8 and y = 13, y – x = 13 – 8 = 5

x = 10 and y = 15, y – x = 15 – 10 = 5

That is,

y – x = 5.

y = x + 5

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The domain of a function is the set of x values the function uses as inputs; from a graph the domain is the x-values that the graph take on the x-axis; in this case, since we have an infinite amount of x-valeus the function uses we will write the domain as an interval. The domain is:

Similarly, the range is the set of values the function takes on the y-axis, from the graph we notice that the range is:

The value of given quadratic equation at -7 is 247.

What is quadratic equation?

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:

ax² + bx + c = 0

where x is the unknown variable and a, b and c are the constant terms.

given ,f(x) = [tex]4x^{2} -8x-5[/tex] to find f(-7)

f(-7)= 4(49)-8(-7)-5

=196+56-5

=247

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ANSWER

Atlanta is 20.62 miles away from the starting point

EXPLANATION

This is a diagram of this problem

We're looking for the hypotenuse of this right triangle. Using the Pythagorean theorem:

An equation is a collection of variables and constants. The value of p for the given equation p + 7 = −15 is p = -22 so option (A) is correct.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

The equation must be constrained with some constraints.

As per the given equation,

p + 7 = -15

Subtract both sides by 7

p + 7 - 7 = -15 - 7

p + 0 = -22

p = -22

Hence "An equation is a collection of variables and constants. The value of p for the given equation p + 7 = −15 is p = -22 so option (A) is correct".

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SOLUTIONS

The parallel line will be of form

the equation of the line that passes through the point (1/7,1) and is parallel to the line −4y−3x=−3

The equation of the line parallel to point(1/7 , 1)

1 .

Notice that 3/7 is close to 1/2 and 5/9 is also close to 1/2.

Therefore, an estimate for 3/7 + 5/9 is 1/2 + 1/2 = 1.

To estimate fractions using mental math, start by simplifying the fraction to the lowest possible denominator. Then, look at the fraction and round it to the nearest fraction that you feel comfortable working with which could be ¼, ⅓, ½, ¾, or even 1.

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The root mean square velocity of Neon, in m/s as required in the task content is; 18.45 m/s.

It follows from the task content that the root mean square velocity of Neon is to be determined.

Since the molar mass of Neon is; 20 while the gas constant, R = 8.314 and T = 273K.

It follows from the root mean square velocity formula that we have;

R.M.S = √(3RT/M)

R.M.S = √{(3×8.314×273)/20}

R.M.S = √340.46

R.M.S = 18.45 m/s.

Hence, the root mean square velocity of Neon, Ne under the given condition is; 18.45 m/s.

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