Select all the expressions that cannot be factored using intergal coefficients and intergal constants
A. X^2 + 5x + 3
B. 25 - 20x + 4x^2
C. -2x^2 + 7x - 3
D. 2x^2 - 5x + 4

[tex] \sf \: {x}^{2} - 5x - 24 \\ \sf \: {x}^{2} + 3x - 8x - 24 \\ \sf \: x \times (x + 3) - 8(x + 3) \\ \sf \: (x - 8) \times (x + 3)[/tex]

➪Therefore the factors are: (x-8) & (x+3)

[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]

[tex] \tt \: {13x}^{2} - 52 \\ \tt13( {x}^{2} - 4) \\ \tt13(x - 2) \times (x + 2)[/tex]

➪ Therefore the factors are: 13(x-2) & (x+2)

[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]

Substitute the values into 3x-9y=14

[tex] \bf 3( - 6) - 9(3) = c[/tex]

[tex] \bf \: - 3 \times 6 - 9 \times 3 = c[/tex]

[tex] \bf \: 3( - 6 - 9) = c[/tex]

[tex] \bf \: 3( - 15) = c[/tex]

[tex] \bf \: - 45 = c[/tex]

[tex] \boxed{ \bf \: c = - 45}[/tex]

➪ So, the equation parallel to 3x-9y=14 is: 3x-9y=-45

[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]

[tex] \rm \: (5x + 4)(3x - 7) = 0[/tex]

[tex] \rm \: 5x + 4 = 0 \\ \rm \: 3x - 7 = 0[/tex]

[tex] \rm \: 5x = - 4 \\ \rm 3x = 7[/tex]

[tex] \rm \: x_{1} = - \frac{4}{5} , x_{2} = \frac{7}{3} [/tex]

➪ The values of x1 and x2 are: -4/5 & 7/3

Answer:

Layers of rock

Fossils

Step-by-step explanation:

Layers of rock and fossils are types of information the scientists use to determine the approximate age of the earth.

Fossils found in rocks and the layering in rock formations play a vital role for the scientists to determine the approximate age of the earth.

The required measure of angle ∠NQS = 30°.

Given that,
The measure of ∠QBS is 78°. What is m∠NQS is to be determined?

The angle can be defined as the one line inclined over another line.

In mathematics, it deals with numbers of operations according to the statements.

Here,
∠NQS + ∠BQN = ∠BQS
∠NQS + 48 = 78
∠NQS = 78 - 48
∠NQS = 30

Thus, the required a measure of angle ∠NQS = 30°.

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Answer:

The ball will land inside the goal.

Step-by-step explanation:

Given : The flight of the ball is modeled by a parabola.

To find : Will the soccer ball land in the goal?

Solution :

Let the equation of the parabola be,

[tex]y=a(x-h)^2+k[/tex]

Where, (h,k) are the vertex of the parabola,

According to question,

A soccer player who is 27 feet from a goal.

Let A be the point where player stand i.e, (27,0)

The height of the goal is 8 feet.

Let B be the point of height of goal i.e, (0,8)

The ball reached a maximum height of 10 feet when it was 15 feet from the soccer player.

The distance from goal to the distance 15 feet away from the player is

27-15=12 feet

Let C be the point with maximum height i.e, (12,10)

C is the vertex of the parabola and A is the point on the parabola.

Then, The equation of parabola is

[tex]y=a(x-12)^2+10[/tex]

Point A satisfy the equation,

[tex]0=a(27-12)^2+10[/tex]

[tex]0=a(15)^2+10[/tex]

[tex]a=-\frac{10}{225}[/tex]

Substitute back in equation,

[tex]y=-\frac{10}{225}(x-12)^2+10[/tex]

Now, we find the y-intercept of the equation i.e, x=0,

[tex]y=-\frac{10}{225}(0-12)^2+10[/tex]

[tex]y=-\frac{10}{225}(144)+10[/tex]

[tex]y=3.6[/tex]

If the y-intercept is greater than 8 then the ball will land outside the goal.

If the y-intercept is less than 8 then the ball will land inside the goal.

As 3.6<8

Therefore, The ball will land inside the goal.

Refer the attached figure below.

Final answer:

The soccer ball will not land in the goal due to its maximum height being above the height of the goal.

Explanation:

To determine if the soccer ball will land in the goal, we need to analyze its flight path. From the given information, we know that the ball reached a maximum height of 10 feet when it was 15 feet from the soccer player. This indicates that the ball's flight path is modeled by a downward-opening parabola.

Since the soccer player is 27 feet from the goal, we can consider the ball's horizontal distance from the player to the goal as the x-coordinate, and its height above the ground as the y-coordinate.

Based on the given information, the soccer ball will not land in the goal. The ball's maximum height is 10 feet, but the goal has a height of 8 feet. This means that at any point along its flight path, the ball's height will be above the height of the goal.

The real numbers between 1 and 4, inclusive, are all the numbers that lie on the interval [1, 4]. In interval notation, this can be represented as [1, 4].

In set-builder notation, the set of real numbers between 1 and 4, inclusive, can be written as:

{x | 1 ≤ x ≤ 4}

This set includes all real numbers greater than or equal to 1 and less than or equal to 4. It includes the numbers 1 and 4 as well. Some examples of numbers in this set are 1, 2, 3, 4, 1.5, 2.718 (approximation of Euler's number), etc.

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Answer:

D. [tex]\angle AOB[/tex]

Step-by-step explanation:

Since we know that complementary angles add up-to 90 degrees.

We can see from our given diagram that angle EOA and angle EOC is a linear pair of angles. The measure of angle EOA is 90 degrees, so EOC will be 90 degrees as well (Linear pair of angles must add up to 180 degrees).

We can also see that [tex]\angle EOC=\angle EOD+\angle COD[/tex].

Upon substituting value of angle EOC we will get,

[tex]90^o=\angle EOD+\angle COD[/tex]

We can see from our given diagram that angle COD and angle AOB are vertical angles.

[tex]\angle COD=\angle AOB[/tex]

Since vertical angles are equal, so by substitution property of equality we will get,

[tex]90^o=\angle EOD+\angle AOB[/tex]

Therefore, [tex]\angle AOB[/tex] is complementary to  [tex]\angle EOD[/tex] and option D is the correct choice.

Answer:

Distribute 2 inside the parenthesis

Step-by-step explanation:

Julie started solving the equation

3x=4+2(3−x)

To simplify any expression we use order of opeation PEMDAS

Always start simplifying the parenthesis

To remove parenthesis we apply distributive property

Distribute 2 inside th4e parenthesis

3x=4+2(3−x)

3x=4+6-2x

So next step is distributing 2 inside the parenthesis

3x=4+6-2x

there are 4 eggs total 3 plain and 1 gold

so you have a 1/4 probability of picking the gold egg

"Cary is 8 years older than Dan. In 5 years the sum of their ages wil equal 96. Find both their ages now. Solve using equations." 

x = Dan's age now
x + 8 = Cary's age now {Cary is 8 yrs older than Dan} 

x + 5 = Dan's age in 5 years
x + 13 = Cary's age in 5 years 

x + 5 + x + 13 = 96 {in five years the sum of their ages will be 96}
2x + 18 = 96 {combined like terms}
2x = 78 {subtracted 18 from both sides}
x = 39 {divided both sides by 39}
x + 8 = 47 {substituted 39, in for x, into x + 8} 

Dan is 39 years old
Cary is 47 years old

Final answer:

To find the constant of proportionality k when y varies directly as x^2, given that x=2 and y=8, set up the equation y = k × x^2 and solve for k, resulting in k = 2.

Explanation:

If y varies directly as x2, it means that y is equal to k times x2, where k is the constant of proportionality. To find k when x is 2 and y is 8, we set up the following equation based on the definition of direct variation:

y = k × x^2

Substitute the given values into the equation:

8 = k × (2^2)

Solve for k:

8 = k × 4

k = 8 / 4

k = 2

Thus, the constant of proportionality, k, is equal to 2 when x is 2 and y is 8.

Final answer:

The two solutions of the quadratic equation 2x squared + 1 = 5x are j = 1 and k = 1/2. The value of (j-1)(1-k) with these solutions is 0.

Explanation:

To solve the equation 2x squared + 1 = 5x, we first bring all terms to one side to get a quadratic equation:

2x2 - 5x + 1 = 0
Using the quadratic formula, x = [-b ± √(b2 - 4ac)]/(2a), where a = 2, b = -5, and c = 1, we find that the two solutions (j and k) of the equation are j = 1 and k = 1/2.

The value of (j-1)(1-k) with these values is:
(j - 1)(1 - k) = (1 - 1)(1 - 1/2) = (0)(1/2) = 0
Therefore, the value of (j-1)(1-k) is 0.

ivied 11 1/4 by 3/4

 11 1/4 = 45/4

45/4 / 3/4 =

45/4 *4/3 = 180/12 = 15

 there are 15 servings

Answer:

there are 11 servings in all

let x = angle

x = 1/2(90-x)

2x = 90-x

3x=90

x = 90/3 = 30

x = 30 degrees

To avoid getting a flat tire, one should maintain correct tire pressure, avoid sharp objects on the road, inspect the tires frequently, and consider using tire liners or puncture-resistant tires.

To avoid getting a flat tire on a bicycle, regular maintenance is important. This includes checking the tire pressure routinely, which should be ideally conducted every few weeks. Correct tire pressure prevents the tires from getting punctured easily. It's also essential to avoid sharp objects on the road, as these can cause punctures. Regularly inspecting the tires for small cuts and objects stuck into them can also help prevent a flat tire. Lastly, using tire liners or puncture-resistant tires can further protect your tires from getting flat.

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x + y ≥ 20 ( total number of shirts at least 20)

15x + 10y ≤ 250 ( total amount spent no more than $250)

These are the answers.

3. x + y ≥ 20 

5. 15x + 10y ≤ 250 

Hope this helps and have a wonderful day!

Final answer:

The base of the triangle is 8 inches, one side is 12 inches (base + 4), and the other side is 14 inches (base + 6). Hence, the side lengths of the triangle are 8 inches, 12 inches, and 14 inches, with a total perimeter of 34 inches.

Explanation:

The question describes a triangle with sides of varying lengths relative to what is defined as the base of the triangle. To find the length of each side, we'll use algebra and the fact that the perimeter of the triangle is given as 34 inches.

Let's denote the base as b. According to the problem, one side is 4 inches longer than the base, which would be b + 4 inches. The third side is 6 inches longer than the base, which would be b + 6 inches. The perimeter of a triangle is the sum of all its sides, so we have:

b + (b + 4) + (b + 6) = 34

Combining like terms, we get:

3b + 10 = 34

Subtracting 10 from both sides gives us:

3b = 24

Dividing by 3 gives us the length of the base:

b = 8 inches

Now, we can find the lengths of the other two sides:

b + 4 inches is 12 inches and b + 6 inches is 14 inches.

So, the lengths of the sides of the triangle are 8 inches, 12 inches, and 14 inches.

Answer:

Daily Payment = 5h+8

Step-by-step explanation:

Here we are given that in seven days the amount Harriet earned is given as

35h+56

It is also given that the amount earned each day is same.

We have to determine the amount earned each day. Total number of days is 7 . Hence in order to find the daily earning we divide the total earning by 7

Daily earning =

[tex]E=\frac{35h+56}{7}\\E=\frac{7(5h+8)}{7}\\E=5h+8[/tex]

Hence answer is 5h+8