Given: g(x) = 2x2 + 3x + 10
k(x) = 2x+16
Solve the equation g(x) = 2x(x) algebraically for x, to the nearest tenth. Explain why you
shose the method you used to solve this quadratic equation.​

Answer:

2 roots, 1 root, or no roots

Step-by-step explanation:

There is a maximum of two roots

If the maximum or minimum is on the x-axis there is 1 repeated root

The roots are imaginary if it does not touch the x-axis

Step-by-step explanation:

It all depends on the discriminants sign.

The quadratic equation:

[tex]ax^2+bx+c=0[/tex]

The discriminant:

[tex]\Delta=b^2-4ac[/tex]

If Δ < 0, then the equation has no real solution

If Δ = 0, then the equation has one solution [tex]x=\dfrac{-b}{2a}[/tex]

If Δ > 0, then the equation has two different solution

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Answer:

m∠CGF=25°

Step-by-step explanation:

we know that

In a circle, a radius that bisects a chord is perpendicular to the chord

so

CS is perpendicular to AC

The triangle GFC is a right triangle

Remember that the sum of the measures of the interior angles in a triangle must be equal to 180 degrees

m∠CGF+m∠GFC+m∠GCF=180°

we have

m∠GFC=90°

m∠GCF=65°

substitute

m∠CGF+90°+65°=180°

m∠CGF+155°=180°

m∠CGF=180°-155°

m∠CGF=25°

Answer:

Printer: $257, Computer: $771

Step-by-step explanation:

First you want to make a part to part diagram. It sounds stupid at first but trust me it works, We assume the both have the same amount. Now we draw 3 boxes for printer because it is 3 times as much. Now we have 4 boxes. divide 1028 by 4 and get 257. That is the amount for each box. You now know the printer is 257 dollars. Now multiply that by 3 to find cost of printer. 257x3=771.

Now you know the computer cost 771 dollars. You can check your work by adding them up. Hope this helped!!!!

Printer | []

Computer| [] [] []

The expression 56x+40y−48z can be rewritten as a product of the greatest common factor and one other factor, which is 8(7x+5y−6z). Therefore, the correct answer is A.

The expression 56x+40y−48z can be factored by identifying the greatest common factor (GCF). In this case, the GCF of 56, 40, and 48 is 8. Therefore, you divide each term in the expression by the GCF which will give you 7x+5y-6z. Hence, the expression can be rewritten as a product of the GCF and one other factor, which is 8(7x+5y−6z). So, the correct answer is A - 8(7x+5y−6z).

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Answer:

20 points

Step-by-step explanation:

key words: difference

Take the amount of points she has and subtract what she has

25-5

Answer:

From given option ,  the equation of parabola is                                            y = negative x² divided by 12

Step-by-step explanation:

Given as for parabola :

The focus is at (0 , - 3)

The directrix equation is y = 3

Now, equation of parabola parallel to y-axis is

( x - h )² = 4 p ( y - k )

where focus is ( h , k+p )   and  directrix equation is y = k - p

So, from equation

h  = 0     and   k + p = - 3

And y = k - p   i.e k - p = 3

Now solving  ( k + p ) + (  k - p ) = - 3 + 3

or, 2 k = 0  ∴ k = 0

Put the value of k , k + p = - 3

So, 0 + p = - 3    ∴ p = - 3

Now equation of parabola with h = 0  , k = 0  , p = - 3

( x - h )² = 4 p ( y - k )

I.e ( x - 0 )² = 4 × ( - 3 ) ( y - 0 )

Or, x² = - 12 y   is the equation of parabola

Hence  From given option ,  the equation of parabola is                                y = negative x² divided by 12       Answer

The first five terms of the sequence are:

6 , 8 , [tex]\frac{32}{3}[/tex] , [tex]\frac{128}{9}[/tex] , [tex]\frac{512}{27}[/tex]

Step-by-step explanation:

The recursive formula of the sequence is

[tex]a_{1}=6[/tex] and [tex]a_{n}=\frac{4}{3}*a_{n-1}[/tex]

To find the first five terms do that:

∵ [tex]a_{1}=6[/tex]

∴ [tex]a_{2}=\frac{4}{3}*6[/tex]

∴ [tex]a_{2}=8[/tex]

∵ [tex]a_{2}=8[/tex]

∴ [tex]a_{3}=\frac{4}{3}*8[/tex]

∴ [tex]a_{3}=\frac{32}{3}[/tex]

∵ [tex]a_{3}=\frac{32}{3}[/tex]

∴ [tex]a_{4}=\frac{4}{3}*\frac{32}{3}[/tex]

∴ [tex]a_{4}=\frac{128}{9}[/tex]

∵ [tex]a_{4}=\frac{128}{9}[/tex]

∴ [tex]a_{5}=\frac{4}{3}*\frac{128}{9}[/tex]

∴ [tex]a_{5}=\frac{512}{27}[/tex]

The first five terms of the sequence are:

6 , 8 , [tex]\frac{32}{3}[/tex] , [tex]\frac{128}{9}[/tex] , [tex]\frac{512}{27}[/tex]

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Answer:

The range of a set of data is the difference between the highest and lowest values in the set

Step-by-step explanation:

Answer:

point blank range is the range at which you don’t need to aim high or low to hit your aiming point. Maximum Point Blank Range (MPBR) is simply the farthest end of that distance.

Step-by-step explanation:

Answer:

14b - 10ab + 34a²b - 64a²b²

Step-by-step explanation:

We have to simplify the expression

2ab + 3b + 7b + 3a × 3a × b + 4b - 8ab × 8ab + 5a × 5a × b - 12ab

= 2ab + 3b + 7b + 9a²b + 4b - 64a²b² + 25a²b - 12ab

{Since (3a × 3a × b) = 9a²b, (8ab × 8ab) = 64a²b² and (5a × 5a × b) = 25a²b}

= 2ab + 10b + 9a²b + 4b - 64a²b² + 25a²b - 12ab  

= 14b - 10ab + 34a²b - 64a²b² (Answer)

Answer:

x=-1 and x=-2

Step-by-step explanation:

Given

[tex]f(x)=\dfrac{1}{(x+1)(x+2)}[/tex]

This function is undefined when the denominator becomes 0. Find values of x for which the denominator is 0:

[tex](x+1)(x+2)=0\\ \\x+1=0\ \text{or}\ x+2=0\\ \\x=-1\ \text{or}\ x=-2[/tex]

Thus, the lines with equations [tex]x=-1[/tex] and [tex]x=-2[/tex] represent vertical asymptotes (see attached graph)

Answer: -1 and -2

Step-by-step explanation:

Answer:

The segment area [tex]= 113.09\ unit^2[/tex]

Step-by-step explanation:

Area of the segment = [tex]\frac{(\theta)}{360} \times \pi r^2[/tex],where [tex]\theta[/tex] is the angle.

We can also say that [tex]90\ degrees[/tex] is covered with one segment and we have total [tex]4[/tex] segments (quadrants),so area of the circle divided by [tex]4[/tex] will give us the segement area of the arc.

So area [tex]\frac{\pi r^2 }{4} =\frac{\pi(12)^2}{4} = 113.09\ units^2[/tex]

So the area of the segment [tex]= 113.09 \ units^2[/tex]

Answer:

y = -2

Step-by-step explanation:

to do this, you have to plug in -8 for x

7(-8) - 2y = -52

-56 - 2y = -52

+56          +56

-2y = 4

/-2     /-2

y = -2

Answer:

1. The required slope m, for the context is[tex]m = \frac{-25}{3}[/tex]

2. The y-intercept in the context is [tex]P_{2}(d) = y = 100[/tex]

3. The x-intercept of the linear model is [tex]d = x = 12[/tex]

Step-by-step explanation:

Given:

[tex]P_{2}(d) = \frac{-25}{3}\times d + 100[/tex]

Where,

[tex]P_{2}[/tex] is the number of phones.

d is the number of days he has worked that week.

This is a linear model type equation.

Can be represented in the slope intercept form  which is equal to

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

Where,

m = Slope of the line.

c = y-intercept.

Now if we compare the given model by slope intercept formula we get

[tex]m = \frac{-25}{3}\\\\c = 100[/tex]

So ,the slope in the context of the problem is [tex]m = \frac{-25}{3}[/tex].

and the y intercept in the context of the problem [tex]P_{2}(d) = c = y = 100[/tex]

For finding x-intercept put y = 0

Here,[tex]P_{2}(d) = 0[/tex]

[tex]\therefore 0 = \frac{-25}{3}\times d + 100\\ \therefore \frac{25}{3}\times d = 100\\\therefore d=\frac{300}{25}\\\therefore d=12[/tex]

So, the x intercept of the linear model is [tex]d = x = 12[/tex]

Answer:Can You please like this I want to rank up

Step-by-step explanation:

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P.S. Please

One kilogram is made of 1000 grams. So, 1/2kg is made of 500 grams. If we add 250 grams, we have 750 grams, or 0.75kg.

To increase 1/2 kg by 250g, add the two values is 750g.

In mathematics, we often encounter situations where we need to perform operations with different units of measurement. In this case, you want to increase 1/2 kg by 250g. The first step is to convert both quantities to a common unit to facilitate the addition.

Step 1: Convert 1/2 kg to grams

We know that 1 kg is equal to 1000 grams (1 kg = 1000g). To find out how many grams are in 1/2 kg, we multiply 1/2 by 1000:

1/2 kg * 1000g/kg = 500g.

So, 1/2 kg is equivalent to 500g.

Step 2: Perform the addition

Now, we have both quantities in the same unit (grams). The addition becomes straightforward:

500g + 250g = 750g.

Thus, when you increase 1/2 kg by 250g, the result is 750 grams.

In summary, to add quantities with different units, it's crucial to convert them into the same unit before performing the operation. Here, we converted kilograms to grams and then added the values to get the final result of 750g.

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Answer:

c.)36

Step-by-step explanation:

Answer:

36 cm

Step-by-step explanation:

The area of a square is length times width. Since it is a square all sides are equal so you multiply 6×6.

Formula: A=s^2 or A=s×s

Answer: 42 pages

Step-by-step explanation: 6 pages x 7 days= 42 pages

Answer:

27/12

Step-by-step explanation:

6 3/4=27/4

(27/4)/3

(27/4)(1/3)=27/12

Answer:

Corn was planted in 24 sq.ft. of the vegetable garden.

Step-by-step explanation:

Length of garden = 9 ft

width of garden = 8 ft

Hence we will first find the total area of garden.

Total area of garden = length × width = [tex]8 \times 9 = 72ft^2[/tex]

He planted 1/2 of the garden with vegetables.

Hence.

Area of Vegetables garden = [tex]\frac{1}{2}\times \textrm{Total Area of Garden} = \frac{1}{2}\times 72 = 36ft^2[/tex]

He planted tomatoes in 1/3 of the vegetable garden and corn in the rest

Area in which tomatoes was planted = [tex]\frac{1}{3}\times \textrm{Area of Vegetables Garden} = \frac{1}{3}\times 36 = 12ft^2[/tex]

Hence Area in which corn were planted = Area of Vegetables garden - Area in which tomatoes was planted = [tex]36ft^2-12ft^2=24ft^2[/tex]

Hence Area of vegetable garden in which corn was planted is 24 sq.ft.

Answer:

Option 4 : 19

Step-by-step explanation:

For trapezoid ABCD : AB = 16 and CD = 28

E and F are midpoints of the legs

So, EF = (AB + CD)/2 = (16+28)/2 = 44/2 = 22

GH be the median of ABFE

So, GH = (AB + EF)/2 = (16+22)/2 = 38/2 = 19

Answer:

The answer would be 18/16 or 1 1/8.

Answer:

$697

Step-by-step explanation:

25% × 4 = 100%

174.25 × 4 = 697

Answer:

174.25

Step-by-step explanation:

174.25 × 4 = 697

697 × 0.25 = 174.25

Answer: 174.25

[tex]\bf 18-\sqrt{-25}\implies 18-\sqrt{-1\cdot 25}\implies 18-\sqrt{-1}\cdot \sqrt{25}\implies 18-5i[/tex]

Answer: 18-5i

Step-by-step explanation:

Answer:

Let x be the number

5 times a number:

5x

The quotient of the number and 2.

5x / 2

Final answer:

The 'quotient of 5 times a number and 2' can be expressed as '5x/2', where 'x' is the unknown number. Important mathematical concepts, such as order of operations, exponents, and percentages, influence how we calculate and understand such expressions.

Explanation:

The statement 'The quotient of 5 times a number and 2' represents a mathematical expression, where you are asked to first multiply a number by 5 and then divide that product by 2. To elucidate, let us assume the unknown number is represented by 'x'. So we multiply 5 by 'x' to get '5x', and then we divide that by 2 to get the final expression, which is '5x/2'. In this case, we are dealing with division, which is opposite to multiplication, and it's important to follow the correct order of operations when solving mathematical problems.

Answer:

12.  x = 50

13.  m∠M = 34°

Step-by-step explanation:

12.

Since the triangles are congruent, the sides' lengths are proportional. We can set up a ratio and solve for x.

Side JG corresponds to Side KM

Side HG corresponds to Side LM

Now, we can set up a ratio, cross multiply, and solve for x. Shown below:

[tex]\frac{35}{70}=\frac{25}{x}\\35x=70*25\\35x=1750\\x=\frac{1750}{35}\\x=50[/tex]

Thus, the value of x is 50

13.

The triangles are similar, so sides are proportional and angles are not related in the same way. Angles are same for both.

We want the value of Angle M, that angle corresponds to Angle G of the left triangle.

It is given that Angle G = 34, so Angle M would be the same degree measure as well.

Hence,

m∠M = 34°

Answer:

The absolute value of a number is its distance from zero on the number line. For example, -7 is 7 units away from zero, so its absolute value would be 7

|-4|=4

|1|=1

Step-by-step explanation:

the absolute value of - 4.5 = | - 4.5 | = + 4.5

the absolute value of 1 = | 1 | = + 1

To find out what percent of the distance Ava has walked so far, we can set up a proportion and solve for x. Ava has walked 60% of the distance to the train station.

To find out what percent of the distance Ava has walked so far, we can set up the following proportion:

15/25 = x/100

Where 15 is the distance Ava has walked, 25 is the total distance to the train station, x is the unknown percentage, and 100 represents 100%. To solve for x, we can cross multiply and divide:

15 * 100 = 25 * x

1500 = 25 * x

Dividing both sides by 25, we get:

x = 1500/25

x = 60

Therefore, Ava has walked 60% of the distance to the train station.

Final answer:

To find the percent of the distance Ava has walked so far to the train station, divide the distance she has walked by the total distance and multiply by 100. In this case, Ava has walked 15 blocks out of 25 blocks, so she has walked 60% of the distance.

Explanation:

To find the percent of the distance Ava has walked so far, you can divide the distance she has walked by the total distance to the train station and then multiply by 100.

In this case, Ava has walked 15 blocks out of 25 blocks to the train station. So, the percent of the distance she has walked so far can be calculated as:

Percentage = (15/25) * 100 = 60%

Answer:

66 pints of 70% pure fruit juice and 44 pints of 95% pure fruit juice must be used.

Step-by-step explanation:

Let

x ----> pints of pure fruit juice at 70%

y ----> pints of pure fruit juice at 95%

we know that

[tex]x+y=110[/tex] ----> [tex]x=110-y[/tex] ----> equation A

Remember that

[tex]70\%=70/100=0.70[/tex]

[tex]95\%=95/100=0.95[/tex]

[tex]80\%=80/100=0.80[/tex]

so

[tex]0.70x+0.95y=0.80(110)[/tex] ----> equation B

Solve the system by substitution

substitute equation A in equation B

[tex]0.70(110-y)+0.95y=0.80(110)[/tex]

solve for y

[tex]77-0.70y+0.95y=88[/tex]

[tex]0.25y=88-77[/tex]

[tex]0.25y=11[/tex]

[tex]y=44[/tex]

Find the value of x

[tex]x=110-y[/tex] ---> [tex]x=110-44=66[/tex]

therefore

66 pints of 70% pure fruit juice and 44 pints of 95% pure fruit juice must be used.

Answer:

30

Step-by-step explanation: