Solve the system of equations. 2x + 3y = 6 x + y = 4 (6, -2) (-2, 6) (-3, 4) (0, 2)

Answer:

Neither function A nor function B has an x-intercept.

Step-by-step explanation:

Function A has a y-intercept at (0, 5).

Function B is defined for negative numbers as well as positive numbers, but not for x=0.

These observations eliminate all answer choices but the first one.

The statement that best compares the two functions is; Neither function A nor function B has an x-intercept.

A y-intercept is the point where x = 0. Now, for function A we can see that when x = 0, y = 5. Thus, it has a y-intercept.

However, we are not given the point where y = 0 which is x-intercept. Thus, function A does not have an x-intercept.

Formula for Function B is y = 4/x.

This function does not have an x-intercept because at x = 0, the function is undefined.

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Answer:

-3

Step-by-step explanation:

In order to find the smallest zero, we will have to find out all the zeros of the function.

In case you are wondering what a zero is, it is the x-value or the domain intersections. The points where the parabola intersects the x-axis.

4x² - 8x - 60 = 0

Why zero?

We know that the parabola intersects the x-axis and when it does, the y-value is 0. h(x) is nothing but 'y'.

4(x²-2x-15) = 0 → I took the gcd as 4 and did it accordingly.

x² - 2x - 15 = 0 → Divide on both sides with 4

Now, what multiples to -15 but adds up to -2?

-5 and 3

x² + 3x - 5x - 15 → Grouping the terms

x ( x + 3 ) - 5 ( x + 3 ) → Taking the GCD in both groups

( x - 5 ) ( x + 3 ) = 0

x = 5 , -3

The smallest one out of these zeros is -3.

Hope it helps! :)

Answer:c

Step-by-step explanation:

Answer: D because they are all corresponding numbers.

Answer:

4.25

Step-by-step explanation:

To find the scale factor divide the image coordinates by the original coordinates, that is

scale factor = [tex]\frac{-12.75}{-3}[/tex] = [tex]\frac{29.75}{7}[/tex] = 4.25

The answer would be 4.25

At most means it can either equal 20 or be less than 20.

On a number line, there would be a closed circle on the number 20 and the area to the left of 20 would be shaded.

Number line graph with closed circle on 20 and shading to the left.

the expressions equivalent to [tex]\(k - \frac{k}{2}\)[/tex] are:

- Option C: [tex]\(\frac{1}{2}k\)[/tex]

- Option D: [tex]\(k + 2\)[/tex]

The correct option is (C) and (D).

the calculation step by step to find expressions equivalent to [tex]\(k - \frac{k}{2}\):[/tex]

1. Given Expression:

 [tex]\[ k - \frac{k}{2} \][/tex]

2. Step 1: Find a Common Denominator:

  To combine the fractions, we need a common denominator. The common denominator for \(2\) and \(1\) is \(2\). So, let's rewrite the expression:

[tex]\[ k - \frac{k}{2} = \frac{2k}{2} - \frac{k}{2} \][/tex]

3. Step 2: Subtract the Fractions:

  Subtract the numerators while keeping the common denominator:

[tex]\[ \frac{2k - k}{2} = \frac{k}{2} \][/tex]

4. Step 3: Simplify:

  Divide the numerator by (2):

[tex]\[ \frac{k}{2} = \frac{1}{2}k \][/tex]

Therefore, the expressions equivalent to [tex]\(k - \frac{k}{2}\)[/tex] are:

- Option C: [tex]\(\frac{1}{2}k\)[/tex]

- Option D: [tex]\(k + 2\)[/tex]

Answer:

-8/5

Step-by-step explanation:

The thing that makes lines different from other kinds of curves is their constant rate of change. We call this rate of change slope, and you usually see it represented with the letter m. We measure it as the rate our y-coordinate changes for some amount our x-coordinate changes.

We're given the two points (-1, 4), and (4, -4). From that first point to the second one, our x-coordinate increases by 5, while our y-coordinate decreases by 8, so our change in y is -8 for every 5 in the positive x direction, and we'd write our slope as

m = -8/5

Answer: $139.60  

Step-by-step explanation:

$40 for coming

$29.60 for parts

56 times 1.25 for labor  = 70

70 + 29.6 + 40  =  139.6

The total cost (c) of the repair is given by the sum of the costs for parts, labor, and the service call that is [tex]\$139.60[/tex]

First, we calculate the labor cost. The plumber charged $56 per hour and worked for 1 1/4 hours. To find the total labor cost, we multiply the hourly rate by the time worked:

Labor cost = [tex]hourly \ rate \times \ time \ worked[/tex]

Labor cost =[tex]\$56 \times 1 1/4 hours[/tex]

Labor cost =[tex]\$56 \times (1 + 1/4) hours[/tex]

Labor cost = [tex]\$56 \times (5/4) hours[/tex]

Labor cost = [tex]\$56 \times 1.25 hours[/tex]

Labor cost = $70

Next, we add the cost for parts and the service call to the labor cost to find the total cost:

Total cost (c) = cost for parts + labor cost + service call cost

Total cost (c) = $29.60 + $70 + $40

Total cost (c) = $139.60

Answer:

Option C is correct.

Step-by-step explanation:

Number of students of Deerlake middle school that voted = 442

Percentage of student that voted = 76%

Let x be the total number of student.

According to the Question,

[tex]\frac{76}{100}\times x=442[/tex]

[tex]x=442\times\frac{100}{76}[/tex]

[tex]x=582[/tex]

Therefore, Option C is correct.

Answer:

C = 7pi = 21.98 inches

Step-by-step explanation:

The circumference of a circle is given by

C = pi * d

 where d is the diameter

C = pi * 7

If we use 3.14 as an approximation for pi

C = 3.14 * 7

C =21.98 in

Answer:

14 and 18

Step-by-step explanation:

Small number : a

Larger number : a + 4

( a + 4 )^2 - a^2 = 128

a^2 + 8 a + 16    = 128

             8 a        = 128 - 16

                a         = 112 / 8

                a          = 14

And a + 4 = 18

Answer:

the diagonals intersect at right angle i.e. slope of AC = - 1/ slope of BD and

Midpoint of AC = Z₁ is equal to Mid point of BD = Z₂

so, the parallelogram is rhombus.

Step-by-step explanation:

A parallelogram is  a rhombus if diagonals intersect each other at right angle and the diagonals intersect at mid point.

We are given vertices:

A(-3,2)

B(-2,6)

C(2,7)

D(1,3)

The diagonals of the parallelogram will be:

AC and BD.

Slope of AC = y₂ - y₁ / x₂- x₁ where A = (-3,2)  and C = (2,7)

Putting values:

Slope of AC = 7-2/2-(-3) = 5/5  

Slope of AC = 1

Slope of BD = y₂ - y₁ / x₂- x₁ where B = (-2,6) and D = (1,3)

Putting values:

Slope of BD = 3-(6) / 1-(-2) = -3/3

Slope of BD = -1

AS, Slope of AC = - 1/ Slope of BD

So, the diagonals intersect and right angle.

Now finding the mid point Z₁ of AC and Z₂ of BD:

Midpoint of AC = Z₁ = A+C/2

Putting values:

=(-3,2) + (2,7) / 2

= (-1,9)/2

= (-1/2, 9/2)

Mid point of BD = Z₂ = B+D / 2

Putting values:

=(-2,6) + (1,3) / 2

= (-1,9)/2

= (-1/2, 9/2)

Midpoint of AC = Z₁ is equal to Mid point of BD = Z₂ i.e.

Z₁ = Z₂, the diagonals intersect at the same midpoint.

As,

the diagonals intersect at right angle i.e. slope of AC = - 1/ slope of BD and

Midpoint of AC = Z₁ is equal to Mid point of BD = Z₂

so, the parallelogram is rhombus.

Answer:

Step-by-step explanation:

B

Answer: Option A: A vertical line that the line of the graph aproaches but never intecepts it.

Step-by-step explanation:

An asymptote is a graph line that aproaches infinitely to something (in this case a vertical line), but it does not touch it (so never intercepts the graph).

This means that the graph aproaches but never intercepts the line, so the correct answer is A.

Answer:

Speed = Distance ÷ Time

time = distance ÷ speed

Step-by-step explanation:

248 ÷ 55 * 60 = 270.54 minutes

Answer:

The answer is G. (-2,3)

Step-by-step explanation:

The point where they meet is (-2,3), therefore that is the solution. Hope that helps! :)

Answer:20 students chose option 1

Step-by-step explanation:

20 students chose option 1

answer

Answer:

20

Step-by-step explanation:

In the sentence of = multiply. So you multiply 5/8 x 32

5/8 x 32/1  next you simply  

5/1 x 4/1   =20/1 = 20

Answer: 90[tex]\pi \\[/tex]

Step-by-step explanation:

Final answer:

The volume of a right circular cylinder with a radius of 3 inches and a height of 10 inches is calculated using the formula V = πr²h, which gives 282.74 cubic inches.

Explanation:

To calculate the volume of a right circular cylinder, you can use the formula V = πr²h, where 'V' is the volume, 'r' is the radius, and 'h' is the height of the cylinder. In this instance, the radius (r) is 3 inches, and the height (h) is 10 inches.

Using these values, you can plug them into the formula:

V = π × (3 in)² × 10 in

V = 3.14159 × 9 in² × 10 in

V = 3.14159 × 90 in³

V = 282.74 in³

Therefore, the volume of the cylinder is 282.74 cubic inches.

Answer:

Let's solve your equation step-by-step.

x2+4x+5=0

Step 1: Use quadratic formula with a=1, b=4, c=5.

x=

−b±√b2−4ac

2a

x=

−(4)±√(4)2−4(1)(5)

2(1)

x=

−4±√−4

2

Answer:

No real solutions.

Answer:

x=-2+-i

Step-by-step explanation:

Solve the equation for x by finding a, b, c of the quadratic then applying the quadratic formula.

Answer:

The length of the line segment is 13 units

Step-by-step explanation:

The line segment joining the two points is horizontal since the y co-ordinate is the same.

For a horizontal line, the length of the line segment is simply the difference between the x co-ordinate values.

In this case we have;

7 - (-6) = 7 + 6 = 13

Therefore, the length of the line segment is 13 units

Answer:

13 units

Step-by-step explanation:

We want to find the length  of the line segment with endpoints (-6,-8) and (7,-8).

Observe that, the y-coordinates are the same.

We can quickly use the absolute value method to find the required length.

According to this method the length of the line segment with endpoints (-6,-8) and (7,-8) is the absolute value of the difference between the x-values.

[tex]|7--6|=|7+6|=|13|=13[/tex]

The length of the line segment is 13 units.

Answer:

About 1,800 accidents

Step-by-step explanation:

Observing the attached figure

In 1965 ----> Approximately 260 accidents

In 1966 ----> Approximately 325 accidents

In 1967 ----> Approximately 300 accidents

In 1968 ----> Approximately 350 accidents

In 1969 ----> Approximately 360 accidents

In 1970 ----> Approximately 400 accidents

Total------> Approximately 1.920 accidents

Answer:

the desired equation is y = (-1/5)x - 5.

Step-by-step explanation:

Parallel lines have the same slope.  Here that slope is -1/5.

Let's use the slope-intercept form of the equation of a straight line:

y = mx + b

We know this new line passes through (-10, -3).  Substitute -3 for y in y = mx + b, as well as -10 for x and -1/5 for m:

-3 = (-1/5)(-10) + b and solve for b:

-3 = 2 + b.  Then b = -5, and the desired equation is y = (-1/5)x - 5.

Answer:

Obtuse triangle

Step-by-step explanation:

The longest side of the triangle is 26 in, so that will be the hypotenuse.

By an extension of the Pythagorean theorem:

Where a and b are the legs, and c is the hypotenuse.

Plug in: 3.5² + 25² ₙ 26²

Powers: 12.25 + 625 ₙ 676

Add: 637.25 < 676.

That means that this triangle is obtuse.

Answer:

Obtuse

Step-by-step explanation:

Using law of cosine, we can find the angle between the shorter sides:

c² = a² + b² − 2ab cos C

26² = 25² + 3.5² − 2(25)(3.5) cos C

cos C ≈ -0.221

C ≈ 102.8°

102.8° is greater than 90°, so the triangle is obtuse.

Answer:

together they can plant 175 seeds in 10 minutes

Answer with Step-by-step explanation:

Cara plants 5 seeds in 2 minutes.

⇒ Cara plants 5×5 seeds in 2×5 minutes

⇒ In 10 minutes Cara plant 25 seeds.

Wade plants 3 times as many seeds in half the time as Cara.

⇒ Wade plants 3×5 seeds in 2/2 minutes

i.e. Wade plants 15 seeds in 1 minute.

In 1×10 minutes Wade plants 15×10 seeds

i.e. In 10 minutes Wade plants 150 seeds.

150+25=175

Hence, they can together plant 175 seeds in 10 minutes.

Answer:

3 < x < 8

-2 < x < 4

12 < x ≤ 17

Step-by-step explanation:

x is less than 8 and greater than 3

i.e 3 < x < 8

x is less than 4 and greater than -2

i.e -2 < x < 4

x is greater than 12 and less than or equal to 17

i.e 12 < x ≤ 17

In order to answer this, you have to have the unit of measurement and an illustration.

I'm not sure if you meant to write 3x or [tex]x^{3}[/tex] instead of x3 but I will work out both versions just in case

In the equation 3x + 4 plug 6 in for x

3(6) + 4

Multiply 3 and 6 first

18 + 4

Add 18 and 4

22

OR

In the equation [tex]x^{3}[/tex] + 4 plug 6 in for x

[tex]6^{3}[/tex] + 4

Solve the exponent

(6*6*6) + 4

216 + 4

Add the numbers together

220

Hope this helped!

Answer:

220

Step-by-step explanation:

Im going to assume x3 equals x^3, so 6^3  is 216, add this to 4 and get 220

Answer:

Option C is correct.

Step-by-step explanation:

P(A or B) represents  that event A has occurred or event B has occurred or both events A and B are happening.

We are given P(A or B) = 0.60 or 0.60/100 = 60%

So, Option C The probability that a customer buys either a taco or a drink is 60% is correct.

Answer: Option C

Step-by-step explanation:

For two events A and B, P(A or B) represents the probability that event A occurs, or event B occurs.

In this case, event A represents a customer buys a taco and event B represents a customer buys a drink. We know that

[tex]P (A\ or\ B) = 0.60[/tex]

So this means that the probability that a customer buys either a taco or a drink is 60%

The answer is the option C

Answer:

[tex]\large\boxed{d=3\sqrt5}[/tex]

Step-by-step explanation:

[tex]\text{the formula of a distance between two points}\ A(x_1,\ y_1)\ \text{and}\ B(x_2,\ y_2):\\\\|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\=========================\\\\\text{We have}\ (4,\ 9)\ \text{and}\ (-2,\ 6).\ \text{Substitute:}\\\\d=\sqrt{(-2-4)^2+(6-9)^2}=\sqrt{(-6)^2+(-3)^2}=\sqrt{36+9}=\sqrt{45}\\\\\sqrt{45}=\sqrt{9\cdot5}=\sqrt9\cdot\sqrt5=3\sqrt5[/tex]

The distance between the points (4, 9) and (-2, 6) is approximately 6.71 units.

Identify the coordinates:

Let (x₁, y₁) = (4, 9) and (x₂, y₂) = (-2, 6).

Apply the distance formula:

The distance formula is given by:

d=√[tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]

Substitute the coordinates into the formula:

d= [tex]\sqrt{((-2)-4)^{2} +(6-9)^{2} }[/tex]²​

Simplify the terms inside the square root:

d=[tex]\sqrt{(-6)^{2} +(-3)^{2} }[/tex]

d=[tex]\sqrt{36+9}[/tex]

d=[tex]\sqrt{45}[/tex]

Simplifying further, we get:

d≈6.71

Answer:

[tex]\large\boxed{\text{Table 1:}\ y=4x+1}\\\boxed{\text{Table 2:}\ y=\dfrac{1}{2}x-1}[/tex]

Step-by-step explanation:

Tables show linear functions.

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

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

Table 1:

(0, 1) → b = 1, (1, 5)

[tex]m=\dfrac{5-1}{1-0}=\dfrac{4}{1}=4\\\\y=4x+1[/tex]

Table 2:

(4, 1), (6, 2)

[tex]m=\dfrac{2-1}{6-4}=\dfrac{1}{2}\\\\y=\dfrac{1}{2}x+b[/tex]

Put the coordinateso f the point (4, 1) to the equation of a line:

[tex]1=\dfrac{1}{2}(4)+b[/tex]

[tex]1=2+b[/tex]         subtract 2 from both sides

[tex]-1=b\to b=-1[/tex]

[tex]y=\dfrac{1}{2}x-1[/tex]

Answer:

[tex]\large\boxed{x\leq-27}[/tex]

Step-by-step explanation:

[tex]\dfrac{x}{-9}\geq3\qquad\text{change the signs}\\\\\dfrac{x}{9}\leq-3\qquad\text{multiply both sides by 9}\\\\9\!\!\!\!\diagup^1\cdot\dfrac{x}{9\!\!\!\!\diagup_1}\leq(-3)(9)\\\\x\leq-27[/tex]