What is the maximum value of 4(x + 7)(2 - x), over all real numbers x?

Answer:

x + 2 = 0 and y - 3 = 0

Step-by-step explanation:

We have to find the solution of the system of equations  

6x + 2y = - 6 ........... (1)

⇒ 12x + 4y = - 12 .......... (2) and  

3x - 4y = - 18 ........... (3)

Now, solving equations (2) and (3) we get,

15x = - 30

⇒ x = - 2

Hence, from equation (1) we get, 2y = - 6 - 6x = - 6 - 6(- 2) = 6

⇒ y = 3

Therefore, the solution of the given system of equations is (-2,3).

Now, x + 2 = 0 and y - 3 = 0 are another system of equations that have the same solutions. (Answer)

Answer:

$20,001

Step-by-step explanation:

Let $x be the amount of dollars Lincoln needs to make in sales to earn more than $1500.

His boss pays him $500 for the week, plus a 5% commission on each vehicle he sells.

5% of $x is $0.05x, the Lincoln earns

[tex]\$(500+0.05x)[/tex] in total.

Hence,

[tex]500+0.05x>1,500[/tex]

Solve this inequality:

[tex]0.05x>1,500-500\\ \\0.05x>1,000\\ \\5x>100,000\\ \\x>20,000[/tex]

Lincoln needs to make in sales more than $20,000, so the minimum amount of dollars Lincoln needs to make in sales is $20,001

Answer:

2.25 miles of road they have to build this week

Step-by-step explanation:

Given:

Total distance of the road = 3 miles

Distance constructed on Tuesday = 1/4 mile of road.

To Find:

Miles of road still have to be built this week=?

Solution:

Let the Distance that have  to be built be X

Then,  

X= total distance of the Road – the distance built on Tuesday

X = 3  –  [tex]\frac{1}{4} \text{ of the 3}[/tex]

X = 3 - [tex]\frac{3}{4}[/tex]

X =[tex]\frac{12 -3}{4}[/tex]

X= [tex]\frac{ 9}{4}[/tex]

X= 2.25  miles

Answer:

(0,3) (3,0)

Step-by-step explanation:

if your asking for y=-x+3

or y=x+3 is (0,3) (0,-3

The situation that can be represented by the inequality x < 3 is that the backpack is heavier than 3 kg.

The situation that can be represented by the inequality x < 3 is: The backpack is heavier than 3 kg.

This means that if the weight of the backpack is represented by 'x', then 'x' is less than 3 kg.

For example, if the weight of the backpack is 2 kg, then 2 is less than 3, which satisfies the inequality x < 3.

The situation that can be represented by the inequality x<3 is "The ceiling is lower than 3 m." This inequality shows that the value of x is less than 3. In real-world terms, it could mean the height of a ceiling, length of an object, or the age of a child, among other things. However, in the given options, it corresponds to a ceiling's height being less than 3 meters.

Let's explore a couple of examples to understand inequalities better with metric measurements:

Answer:

Step-by-step explanation:

The domain on all x-squared parabolas is all real numbers.  

The range of an x-squared parabola is always found at the y coordinate of its vertex, and then is determined by whether it opens upwards or downwards. Our vertex has a y coordinate of -1 and opens downwards, so the range is all real numbers less than or equal to -1.

There are no x-intercepts (aka places on the graph that go through the x-axis), but the y-intercept is also the vertex, which is (0, -1).

Because this is an upside down parabola, it has a max point, again at the vertex.  It has no min point.

It increases from negative infinity to its max point and is notated as follows: (-∞, 0]

and decreases from its max point to negative infinity: [0, -∞)

Answer:

C

Step-by-step explanation:

They're solid lines and overlap at that point

To find kilometers per hour, we need to multiply 2 1/6 by 3, because it took Linley 1/3 hour to ride that far.

2 1/6 * 3 = 6 1/2

So, her average speed in kilometers per hour is 6 1/2 kph

Answer:

y=1/2x+5

Step-by-step explanation:

y=mx+b

The equation of the line that passes through the point (6,8) and has a slope of 1/2 will be y=1/2x+10.

A straight line is a combination of endless points joined on both sides of the point. A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

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

It is given that the equation of the line that passes through the point (6,8) and has a slope of 1/2,

The standard equation of the line passes through the points (x₁,y₁) having slope m is,

y-y₁=m(x-x₁)

Substitute the given value as

y-8=-1/2(x-6)

2(y-8)=-1(x-6)

2y-16=x-6

2y=x-6+16

2y=x+10

y=1/2x+10

Thus, the equation of the line that passes through the point (6,8) and has a slope of 1/2 will be y=1/2x+10.

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Answer:

35.2

Step-by-step explanation:

1/22=1.6/?

Cross multiply: 1.6*22=35.2

Final answer:

To find the total distance driven to and from work over 3 days, multiply the daily round-trip distance of 4310 miles by 3, resulting in 12,930 miles.

Explanation:

The question asks how many miles you would drive to and from work in 3 days if your round-trip to work is 4310 miles. To calculate this, you just need to multiply the daily round-trip distance by the number of days you travel. In this case, you travel to and from work for 3 days.

Determine the daily round-trip distance. (Already provided as 4310 miles)

Multiply the daily round-trip distance by the number of days traveled: 4310 miles × 3 days.

The calculation would be 4310 miles × 3 which equals 12,930 miles. This is the total distance driven to and from work over the 3 day period.

Answer:

7000

Step-by-step explanation:

nhi batunga

Answer:

Hittites, Aryans, Portuguese.

Step-by-step explanation:

I just know for a fact. These are the correct answers.

Answer:

The graph of y + 1 = −3/5 (x − 4) would be a straight line. The graph figure is attached below.

Step-by-step explanation:

As the linear equation y + 1 = −3/5 (x − 4) is given.

Since y-y₁ = m (x - x₁) is the Point-slope form is the general form y-y₁=m(x-x₁) for linear equations.

Hence, from the linear equation we can determine the slop which is m = -3/5

Also, when we put x = 0 in the linear equation, we determine the y-intercept as follows:

                            y + 1 = −3/5 (x − 4)

                            y + 1 = -3/5(-4)      ∵x = 0

                            y = 12/5 - 1

                            y = 7/5

y-intercept: 7/5

Hence,

Table for some points can be made for x and values as:

0           7/5

1            4/5

The graph of y + 1 = −3/5 (x − 4) would be a straight line. The graph figure is attached below.

Keywords: graph, straight line

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Answer:

x=9

Step-by-step explanation:

8(2x-6)=96

2x-6=96/8

2x-6=12

2x=12+6

2x=18

x=18/2

x=9

Hello, thanks for usin Brainly. :)

Let's solve by using distributive property.

8(2x-6)=96

16x-6=96

16x-48=96

     +48 +48

16x = 144

x = 9

First, what we did was do 8 x 2 & 6 x 8.

Then, we got 16x-6=96.

We want to get X by itself, therefore we need to get rid of -48, so we 48 to all of our terms.

Then our equation should look like 16x = 144.

Divide and get 9!

Therefore, x = 9.

Wait, how can we be sure?

Let's check our answer.

Let's allow our x value to be 9.

Now, our equation should look like:

8(2(9)-6=96

Follow the PEMDAS rule.

8(18-6)=96

8(12)=96

8 times 12 is 96.

96 = 96 Done!

Therefore, we know our answer is correct.

Options A, B, and D each have exactly one solution. Option C has no solution because it simplifies to a contradiction.

To determine which of the given equations have exactly one solution, we will analyze each equation to see if it can be simplified or rearranged to form an identity (true for all values of [tex]\( x \))[/tex] or a contradiction (false for all values of [tex]\( x \))[/tex], or if it remains a valid equation with a unique solution for [tex]\( x \).[/tex]

An equation has exactly one solution if it can be simplified to the form [tex]\( ax = b \)[/tex] where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants, and [tex]\( a \)[/tex] is not zero.

Let's analyze each option step by step:

Option A: [tex]\( -5x + 12 = -12x - 12 \)[/tex]

1. Add [tex]\( 12x \)[/tex] to both sides: [tex]\( -5x + 12x + 12 = -12 + 12x \).[/tex]

2. This simplifies to [tex]\( 7x + 12 = -12 \).[/tex]

3. Subtract [tex]\( 12 \)[/tex] from both sides: [tex]\( 7x = -24 \).[/tex]

4. Divide by

  This equation has exactly one solution, [tex]\( x = -\frac{24}{7} \).[/tex]

Option B: [tex]\( -5x + 12 = 5x + 12 \)[/tex]

1. Add [tex]\( 5x \)[/tex] to both sides: [tex]\( -5x + 5x + 12 = 5x + 5x + 12 \).[/tex]

2. This simplifies to [tex]\( 12 = 10x + 12 \).[/tex]

3. Subtract \( 12 \) from both sides: [tex]\( 0 = 10x \).[/tex]

4. Divide by [tex]\( 10 \)[/tex]: [tex]\( x = 0 \).[/tex]

  This equation has exactly one solution, [tex]\( x = 0 \).[/tex]

Option C: [tex]\( -5x + 12 = -5x - 12 \)[/tex]

1. Subtract \( -5x \) from both sides: [tex]\( 12 = -12 \).[/tex]

  This simplifies to a contradiction since [tex]\( 12 \)[/tex] does not equal [tex]\( -12 \).[/tex]

  Therefore, this equation has no solution.

Option D: [tex]\( -5x + 12 = 5x - 5 \)[/tex]

1. Add \( 5x \) to both sides: [tex]\( -5x + 5x + 12 = 5x + 5x - 5 \)[/tex].

2. This simplifies to [tex]\( 12 = 10x - 5 \)[/tex].

3. Add [tex]\( 5 \)[/tex] to both sides: [tex]\( 17 = 10x \).[/tex]

4. Divide by [tex]\( 10 \)[/tex]: [tex]\( x = \frac{17}{10} \)[/tex].

  This equation has exactly one solution, [tex]\( x = \frac{17}{10} \)[/tex].

Based on this analysis, Options A, B, and D each have exactly one solution. Option C has no solution because it simplifies to a contradiction.

Answer:

shape and size

Step-by-step explanation:

we know that

If two figures are similar, then its corresponding sides are proportional and its corresponding angles are congruent

Similar figures have the same shape but not necessarily the same size

The focus must be the point (0, 4), because it is equidistant from the vertex (0, 2) as the focus is from the directrix, y = 0, which indicates that the focus is twice the distance from the vertex to the directrix or (0, 4)

The evaluation that shows the reasons the focus must be the point (0, 4) are as follows;

The location of the vertex of the parabola at the point (0, 2), and the location of the directrix on the x-axis, we get;

The location of the focus is on the line passing through the vertex, which is the line x = 0

The definition of a parabola is the path of a point that moves such that the distance from the focus and the directrix are the same

The equation of the directrix is; y = 0

The shortest distance of the vertex from the directrix is 2 - 0 = 2 units

The distance from the focus to the vertex is therefore 2 units

Whereby the focus is 2 units above the x-axis, the focus, which is 2 units from the vertex on the remote side of the directrix is 2 + 2 = 4 units above the x-axis and the coordinates of the vertex must be (0, 4)

The definition of a parabola indicates that the location of the focus should be 2 units from the

The complete question found through search can be presented as follows;

A parabola is shown graphed on the grid below. Its directrix is the x-axis

(a) Explain why the focus must be the point (0, 4)

The coordinates of  the vertex of the parabola is (0, 2)

The coordinates of other points on the parabola are (-8, 8), (8, 8)

Answer:

10

Step-by-step explanation:

10^0=1

1*10=10

Answer:

-5a - 4 is the expression equivalent

Following are the calculation to the given expression:

Given:

[tex]\bold{7a-8-12a+4}[/tex]

To find:

solve the expression=?

Solution:

[tex]\to \bold{7a-8-12a+4}\\\\\to \bold{-5a-4}\\\\[/tex]

Therefore, the final answer is "[tex]\bold{-5a-4}[/tex]".

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Answer:

B) y=1/2x-3/2

Step-by-step explanation:

y=2x+3

x=2y+3

2y=x-3

y=1/2x-3/2

Answer:

B

Step-by-step explanation:

EDGE 2020

Answer:

Option C

10%

Step-by-step explanation:

Given information

Cost of investment=$20000

Selling price=$22000

Profit=Selling price-Cost of investment=22000-20000=2000

Return on investment=profit/cost of investment

[tex]RoI=\frac {2000\times 100}{20000}=10%[/tex]

The amount of money on a property or good sold is known as ROI. Pete’s return on investment is 10%

The amount of money on a property or good sold is known as ROI.

Given the following

Cost price = $20000

Selling price = $22000

ROI = SP-CP/CP * 100

%ROI = 2000/20000 * 100

%ROI = 1/10 * 100
%ROI = 10%

Hence Pete’s return on investment is 10%

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Answer

Step-by-step explanation:

From the attached diagram below,

< ADC + <D = 180° (sum of linear angle) ------------(1)

<B + <C + <D = 180° (sum of interior angle in a triangle)---------(2)

Since the two equations are equal to 180°, We equate the two equation

i.e

(1) = (2)

< ADC + <D = <B + <C + <D

<D from the left hand side will cancel <D on the right hand side

We are now left with

<ADC = <B + <C

The Exterior Angle Theorem is proven by using the Triangle Sum Theorem, the Linear Pair Postulate, and the Subtraction Property of Equality to show that the sum of the interior opposite angles of a triangle equals the exterior angle.

To complete the proof of the Exterior Angle Theorem using the fact that angle ACD is an exterior angle of triangle BCD and prove that angle B + angle C = angle ACD, follow the steps below:

Answer:

The value of [tex]a_{4}=15[/tex]

Step-by-step explanation:

Given that [tex]a_{1}=6[/tex] and [tex]a_{n}=a_{n-1}+3[/tex]

Given sequence is of the form arithmetic sequence

For arithmetic sequence the sequence is [tex]a_{1},a_{2},a_{3},...[/tex]

The nth term is of the form  [tex]a_{n}=a_{n-1}+d[/tex]

Here  [tex]a_{1}=6[/tex] and [tex]a_{n}=a_{n-1}+3[/tex]

from this the common differnce is 3.

Therefore d=3

To find  [tex]a_{2}[/tex], [tex]a_{3}[/tex] , [tex]a_{4}[/tex]

[tex]a_{n}=a_{n-1}+d[/tex]

put n=2 and d=3 we get

[tex]a_{2}=a_{2-1}+3[/tex]

[tex]a_{2}=a_{1}+3[/tex]

[tex]a_{2}=6+3[/tex]   (here  [tex]a_{1}=6[/tex] )

Therefore [tex]a_{2}=9[/tex]

[tex]a_{n}=a_{n-1}+d[/tex]

put n=3 and d=3 we get

[tex]a_{3}=a_{3-1}+3[/tex]

[tex]a_{3}=a_{2}+3[/tex]

[tex]a_{3}=9+3[/tex]   (here  [tex]a_{2}=9[/tex] )

Therefore [tex]a_{3}=12[/tex]

[tex]a_{n}=a_{n-1}+d[/tex]

put n=4 and d=3 we get

[tex]a_{4}=a_{4-1}+3[/tex]

[tex]a_{4}=a_{3}+3[/tex]

[tex]a_{4}=12+3[/tex]   (here  [tex]a_{3}=12[/tex] )

Therefore [tex]a_{4}=15[/tex]

Therefore the sequence is 6,9,12,15,...

Therefore the value of [tex]a_{4}=15[/tex]

Good evening ,

Answer:

(x - 6 + i)(x - 6 - i) = x² - 12x + 37

Step-by-step explanation:

(x - 6 + i)(x - 6 - i) = [(x - 6) + i]×[(x - 6) - i] = (x-6)² - i² = (x-6)² + 1 = x² - 12x + 37 .

:)

Answer:

∠A= 112.5°, ∠B=67.5°, ∠C is 67.5° and ∠D 112.5°.

Step-by-step explanation:

Consider the provided information.

The sum of all interior angle of a polygon is: [tex](n-2)180[/tex]

Substitute n = 8.

[tex](8-2)180=1080[/tex]

Thus, the measure of each angle is: [tex]\frac{1080}{8}=135[/tex]

∠B and ∠C are congruent and their sum is 135°

∠B+∠C=135°

∠B=67.5°

Hence, the m angle B and m angle C is 67.5°.

The sum of all angles of a quadrilateral is 360°.

∠A+∠D+∠B+∠C=360°

∠A+∠D=360°-135°

∠A+∠D=225°

∠A and ∠D are congruent and their sum is 225°

∠A+∠D=225°

∠A=∠D=112.5°

Hence, the m angle A and m angle D is 112.5°.

Answer:

BC ≈ 11.9 cm

Step-by-step explanation:

Using the sine ratio in the right triangle

sin58° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{14}[/tex]

Multiply both sides by 14

14 × sin58° = BC, thus

BC ≈ 11.9 cm ( to 1 dec. place )

To find the length of side BC in a triangle, you would typically use the Pythagorean theorem if given a right triangle. Additional information or a diagram is required for a precise answer. The theorem can be rearranged to solve for any side of the triangle.

Finding the length of side BC requires you to use the principles of geometry, specifically the Pythagorean theorem if this is a right triangle context. However, without a provided diagram or additional information, it's impossible to give a specific answer. The Pythagorean theorem states that in a right-angle triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as a^2 + b^2 = c^2, where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. You could rearrange this equation to solve for b if you knew the lengths of a and c.

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Answer:

y = -3x + 6

Step-by-step explanation:

Distribute -

y + 6 = -3x + 12

Subtract 6 from both sides, final answer

y = -3x + 6

Final answer:

The equation y + 6 = -3(x - 4) in slope-intercept form is y = -3x + 6, where the slope is -3 and the y-intercept is 6.

Explanation:

To write the equation y + 6 = -3(x - 4) in slope-intercept form, which is y = mx + b, we need to solve the equation for y. First, distribute the -3 to both terms within the parentheses: y + 6 = -3x + 12. Next, subtract 6 from both sides to isolate y: y = -3x + (12 - 6). Simplifying the equation, we get y = -3x + 6. Thus, the slope-intercept form of the equation is y = -3x + 6, where the slope (m) is -3 and the y-intercept (b) is 6.

Answer:

The interest charged for this month is $7.5

Step-by-step explanation:

Given:

Principal = $300

Interest = 30%

Time =  1 month

To Find:  

The interest charged for this month = ?

Solution:

we know that the  interest charged = [tex]principal \times \text {Interest rate} \times time[/tex]

1 month can also be written as [tex]\frac{1}{12}[/tex]

Substituting the values,

interest charged:

=> [tex] 300 \times 30%  \times \frac{1}{12}[/tex]

=> [tex] 300 \times \frac{30}{100} \times \frac{1}{12}[/tex]

=> [tex] 300 \times \frac{3}{120}[/tex]

=>[tex] \frac{900}{120}[/tex]

=>[tex] \frac{30}{4}[/tex]

=>[tex] \frac{15}{2}[/tex]

=> 7.5

Answer:

The larger angle is 52. 4

The smaller angle is 37. 6

Step-by-step explanation:

The equation is:

(x-14. 8)+x=90

x+x-14. 8=90

2x=90+14. 8

2x=104. 8

x=52. 4

The value for the larger angle is x

and x =52. 4

The value for the smaller angle is x-14. 8

and x-14. 8=52.4-14.8

=37.6

Verification

(x-14.8)+ x=90

(52.4-14.8)+52.4=90

37.6+52.4=90

90=90

The smaller angle measures 37.6° and its complementary angle measures 52.4°. These measures satisfy the condition that one angle is 14.8° less than the measure of its complementary angle, and both angles sum to 90°.

To determine the measure of each angle when one angle is 14.8° less than its complementary angle, we need to set up an equation.

Complementary angles add up to 90°.

Let's denote the smaller angle as x, so the complementary angle is x + 14.8°. The equation becomes:

x + (x + 14.8°) = 90°

Combining like terms, we have:

2x + 14.8° = 90°

Subtracting 14.8° from both sides:

2x = 90° - 14.8°

2x = 75.2°

Dividing both sides by 2 to solve for x:

x = 75.2° / 2

x = 37.6°

So the smaller angle measures 37.6° and the complementary angle measures x + 14.8° = 37.6° + 14.8° = 52.4°.