what are the two values of x that are roots of this equation x^2+3x-6=0​

Which point is an x-intercept of the quadratic function

f(x) = (x + 6)(x - 3)? THE ANSWER IS D.

Answer:

    [tex]c(x)=150+16.52x[/tex]

Explanation:

The total cost is comprised of three costs, namely the flat fee for the room rental ($150), the charge person for the Italian buffet ($14 per person), and the tip (18% added to the cost of the food). With this you can build your equation:

[tex]Total\text{ }cost=$150+$14x+18\%\times (14x)[/tex]

Where x respresents the number of people attending the party.

Convert 18% to its decimal form, which is 0.18 and simplify the equation:

      [tex]Total\text{ }cost=$150+$14x+0.18\times (14x)=150+14x+2.52x\\ \\ Total\text{ }cost=150+16.52x[/tex]

Hence, calling the function c(x), it is:

           [tex]c(x)=150+16.52x[/tex], with x being the number of people attending the party, and c(x) the cost in dollars.

The function which representing the total cost of party is [tex]150+16.52x[/tex]

Let us consider that number of people who attending part be x.

The room rental amount is $150.

The charge of the Italian buffet for per person = $14

For x number of people [tex]=14x[/tex]

Since, 18% tip  added to the cost of the food.

  Tip cost [tex]=14x*\frac{18}{100} =2.52x[/tex]

Total cost of the party [tex]=150+14x+2.52x=150+16.52x[/tex]

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Area of the heart is 178.5 cm² and Perimeter is 51.4 cm

Step-by-step explanation:

Total area of heart = Area of the square + 2 × area of the semi circle

Calculate the area of the square where side = 10 cm

⇒ Area of the square = side² = 10² = 100 cm²

Calculate the area of the 2 semicircles where radius = 10/2 = 5 cm

⇒ Area of the semicircle = 1/2 × π × r²

⇒ Area of the 2 semicircles = 2 × 1/2 × π × r² = 3.14 × 5² = 78.5 cm²

⇒ Total area of the heart = 100 + 78.5 = 178.5 cm²

Calculate the perimeter of the heart = length of 2 sides of the square + 2 × perimeter of the semicircle (since there are 2 semicircles)

⇒ Perimeter = 10 + 10 + 2 × π × r (since perimeter of semicircle = πr)

⇒ Perimeter = 20 + 2 × 3.14 × 5 = 20 + 31.4 = 51.4 cm

The area and Perimeter values of the figure are 178.5 cm² and 51.4 cm

The area of the square portion

We have;

Area of the Semicircle:

Area of Semicircle = 0.5×πr²

Area of Semicircle = 39.25

Since, we have 2 similar Semicircles :

Total Area = 100 + 78.5 = 178.5 cm²

2.)

The Perimeter of the figure ;

For the 2 Semicircles ;

Perimeter = 31.4 cm

Perimeter of the square ;

Total Perimeter = 20 + 31.4 = 51.4 cm

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Answer:7

Step-by-step explanation:

Gotta get rid of the shirts so 24x3 shirts is 72 and 79-72=7 which is the socks price

Answer:$7

Step-by-step explanation:3 Shirts at $24 each 24×3=$72 then subtract $72- from total cost for shirts and socks $72-$79=$7✔

Answer:

Step-by-step explanation:

T think its the 3rd option down

Answer:

b

Step-by-step explanation:

Answer:

length = 12

width = 4

Step-by-step explanation:

Width = w

Length = l

w = l-8

l-8 + l-8 + l + l = 32

4l - 16 = 32

4l = 48

length = 12

width = 4

Answer:

2/3

Step-by-step explanation:

photomath bud

i believe the answer is 2/3

There are only a handful of perfect squares in the given range: 16, 25, 36, and 49

The sum of their digits wil be odd if one digit is odd and the other is even, which is the case for 16, 25, and 49. So the answer is A.

Caedin runs fastest (he has the highest speed)

Step-by-step explanation:

The question in this problem is "who runs fastest": this means that the problem is asking us "which runner has the greatest speed?"

The speed of a body is a scalar quantity defined as

[tex]v=\frac{d}{t}[/tex]

where

d is the distance covered by the body

t is the time elapsed

In order to calculate the distance covered by each runner, we have to sum the length of all the pieces of motion, regardless of their direction.

From the graph, we observe that:

- Andy moves from x = 0 to x = 1.25 miles, so the distance covered is d = 1.25 miles. Since the time taken is 10 minutes, his speed is

[tex]v=\frac{1.25}{10}=0.125 mi/min[/tex]

- Berta moves from x = 0.5 miles to x = 1.15 miles, so the distance covered is

d = 1.15 - 0.5 = 0.65 miles

The time taken is 10 minutes, so her speed is

[tex]v=\frac{0.65}{10}=0.065 mi/min[/tex]

- Finally, Caeding moves first from x = 1.5 miles to x = 0, so he covers a distance of

[tex]d_1 = 1.5 mi[/tex]

Then he also moves from x = 0 to x = 1.0 miles, so he covers an additional distance of

[tex]d_2=1.0 mi[/tex]

So the total distance is

[tex]d=d_1+d_2=1.5+1.0=2.5 mi[/tex]

And since the time taken is 10 minutes, the speed is

[tex]v=\frac{2.5}{10}=0.25 mi/min[/tex]

Therefore, Caedin has the highest speed.

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Answer:

Scientific Notation:

4.2 × 10^-3

E-Notation:

4.2e-3

Engineering Notation:

4.2 × 10^-3

Real Number:

0.0042

Step-by-step explanation:

Answer:

x is either 2 or 3

Step-by-step explanation:

[tex] {x}^{2} - 5x + 6 = 0 [/tex]

(x-3)×(x-2) = 0

x- 3 = 0 ➡x = 3

x -2 = 0➡ x = 2

slope intercept form: y=mx+b

y=3x+6

y=3(2)+6

y=6+6

y=12

Final answer:

The two lines have different slopes, with the first line having a slope of -2 and the second line having a slope of 2. Since the slopes are different, the two lines intersect at exactly one point, indicating that there is one solution.

Explanation:

To determine if two lines have no solution, one solution, or an infinite number of solutions, we need to find the slopes of each line. If the slopes are different, the lines intersect at one point, indicating one solution. If the slopes are the same, but they have different y-intercepts, the lines are parallel and there is no solution. If the slopes and y-intercepts are the same, the lines coincide and there are an infinite number of solutions.

For the first line through (-1,3) and (0,1), the slope can be calculated using the formula slope (m) = (y2 - y1) / (x2 - x1). Plugging in the values, we get:

m = (1 - 3) / (0 + 1) = -2

The second line passes through (1,4) and (0,2). Using the same formula:

m = (2 - 4) / (0 - 1) = 2

Since the slopes of the two lines are different, they will intersect at exactly one point, indicating one solution.

The system of equations has one solution since the lines intersect at a single point, confirming a unique solution.

To determine if the system of equations has no solution, one solution, or an infinite number of solutions, we need to analyze the slopes and y-intercepts of the two lines.

Step 1:

Calculate the slope of each line using the formula [tex]\(m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\).[/tex]

For the first line passing through (-1,3) and (0,1):

[tex]\[ m_1 = \frac{{1 - 3}}{{0 - (-1)}} = \frac{{-2}}{{1}} = -2 \][/tex]

For the second line passing through (1,4) and (0,2):

[tex]\[ m_2 = \frac{{2 - 4}}{{0 - 1}} = \frac{{-2}}{{-1}} = 2 \][/tex]

Step 2:

Calculate the y-intercept for each line using the slope-intercept form [tex]\(y = mx + b\)[/tex], where (b) is the y-intercept.

For the first line:

[tex]\[ 1 = -2 \cdot 0 + b_1 \][/tex]

[tex]\[ b_1 = 1 \][/tex]

For the second line:

[tex]\[ 2 = 2 \cdot 0 + b_2 \][/tex]

[tex]\[ b_2 = 2 \][/tex]

Step 3: Compare the slopes and y-intercepts.

Since the slopes are different (-2 for the first line and 2 for the second line), the lines are not parallel. Therefore, they will intersect at exactly one point, resulting in one solution for the system of equations.

Conclusion:

The system of equations has one solution.

500 : 1 expresses the ratio of sheets of paper to reams in simplest form ⇒ D

Step-by-step explanation:

The given is:

We need to find the ratio between the sheets of paper to the reams in simplest form

∵ The number of the sheets is 4000

∵ The number of the reams is 8

→ sheet  :  ream

→ 4000  :  8

to simplify the ratio divide the two terms by the same number

∵ 4000 ÷ 2 = 2000 and 8 ÷ 2 = 4

∵ 2000 ÷ 2 = 1000 and 4 ÷ 2 = 2

∵ 1000 ÷ 2 = 500 and 2 ÷ 2 = 1

∴ 4000 and 8 can be divided by 8 to get the simplest form

   of the ratio

→ sheet        :  ream

→ 4000 ÷ 8  :  8 ÷ 8

→ 500           :  1

∴ The ratio of sheets to reams is 500 : 1

500 : 1 expresses the ratio of sheets of paper to reams in simplest form

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Ahmed cannot have total of 30 coins in his pocket

Solution:

Given that,

There are 5 pennies for every 6 quarters in Ahmed's pocket

We are asked if Ahmed can have a total of 30 coins in his pocket

From given,

5 pennies for every 6 quarters

Therefore, ratio is:

penny : quarter = 5 : 6

Total = 5 + 6 = 11

Then the total number of coins must be multiple of 11

But 30 is not a multiple of 11

Therefore, Ahmed cannot have total of 30 coins in his pocket

No, Ahmed cannot have a total of 30 coins in his pocket.

Yes, Ahmed could have a total of 30 coins in his pocket.

To determine how many quarters and pennies Ahmed could have, we can set up a ratio.

The ratio of pennies to quarters is 5:6.

Let the number of quarters be represented by 6x, where x is a positive integer. Then, the number of pennies would be 5x.

To find out if Ahmed could have a total of 30 coins, we need to solve the equation 6x + 5x = 30.

Combining like terms, we obtain 11x = 30. By dividing both sides of the equation by 11, we find that x = 2.7272 (repeating).

Since x must be a positive integer, we can conclude that Ahmed cannot have a total of 30 coins in his pocket.

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Answer:

  rhombus

Step-by-step explanation:

A quadrilateral with equal-length sides is a rhombus.

_____

A square is a special case of a rhombus.

Answer:

1 and 4.

Step-by-step explanation:

i just did it

Answer:

a) Length = (20 - 2x) inches

Width = (15 - 2x) inches

b) Volume = (20 - 2x)(15 - 2x)x cubic inches.

Step-by-step explanation:

A metalworker makes a box from 15 inches by 20 inches piece of tin by cutting a square with a side length x out of each corner and folding up the sides.

a) So, the length of the box will become (20 - 2x) inches.

And, the width of the box will become (15 - 2x) inches.

b) The volume of the box will be = (Length × Width × Height)

= (20 - 2x)(15 - 2x)x cubic inches. (Answer)

Answer:$3900

Step-by-step explanation:

Answer:

f(x)=-7x is the only one linear

Step-by-step explanation:

I'm wondering if this is mistake or not with your question, but if you graph each function, all but one graph is linear.

To find the height of a new right triangle similar to the original with a base of 26 yards, use the ratio of sides from the original triangle (7/12) to set a proportion. Solve the proportion to get the new height as 15.2 yards (or 45.5 feet).

Since the triangles are similar, the ratio of their corresponding sides must be the same. To find the height of the new triangle with a base of 26 yards, we set up a proportion using the corresponding sides of the original triangle:
7 yards / 12 yards = height / 26 yards

By cross-multiplying and solving for the unknown height, we get:

7 yards * 26 yards = height * 12 yards

182 y = height * 12 yards

height = 182  / 12 yards

height = 15.1666667 yards

Since 1 yard = 3 feet, we convert the height to feet:

15.1666667 yards * 3 feet/yard = 45.5 feet

Therefore, the height of the new right triangle is approximately 15.2 yards or 45.5 feet when rounded to the nearest tenth of a foot.

Answer:

0.2% of 50  = [tex]0.1[/tex]

Step-by-step explanation:

0.2% of 50

We have to find 0.2% of 50

     [tex]50*0.2*\frac{1}{100}[/tex]

       [tex]50*\frac{2}{10}* \frac{1}{100}[/tex]

          =[tex]\frac{5*2}{100}[/tex]

           =[tex]\frac{10}{100}\\\\ \frac{1}{10}\\\\0.1[/tex]

The 0.2% of 50 is 0.1

Answer:

0.1

Step-by-step explanation:

The values are [tex]m\angle \mathrm{ABC}=62^{\circ}[/tex], [tex]m\angle \mathrm{DBE}=62^{\circ}[/tex], [tex]m\angle \mathrm{CBE}=118^{\circ}[/tex] and [tex]m\angle \mathrm{ABD}=118^{\circ}[/tex]

Explanation:

It is given that [tex]\angle \mathrm{ABC}=4x+2[/tex] and [tex]\angle \mathrm{DBE}=5x-13[/tex]

The image having these measurements is attached below:

The angles ABC and DBE are vertically opposite.

Since, vertically opposite angles are equal, [tex]\angle \mathrm{ABC}=\angle \mathrm{DBE}[/tex]

Equating the values, we have,

[tex]\begin{aligned}4 x+2 &=5 x-13 \\2+13 &=5 x-4 x \\15 &=x\end{aligned}[/tex]

Thus, the value of x is 15. Let us substitute x in the equation to find [tex]\angle \mathrm{ABC}[/tex] and [tex]\angle \mathrm{DBE}[/tex]

Thus,

[tex]\begin{aligned}\angle A B C &=4(15)+2 \\&=60+2 \\&=62\end{aligned}[/tex]

Thus, [tex]m\angle \mathrm{ABC}=62^{\circ}[/tex]

Also, substituting x = 15 in [tex]\angle \mathrm{DBE}[/tex]

We have,

[tex]\begin{aligned}\angle DBE &=5(15)-13 \\&=75-13 \\&=62\end{aligned}[/tex]

Thus, [tex]m\angle \mathrm{DBE}=62^{\circ}[/tex]

Hence, the measure of [tex]\angle \mathrm{ABC}=62^{\circ}[/tex] and [tex]\angle \mathrm{DBE}=62^{\circ}[/tex]

To find the measure of [tex]\angle \mathrm{CBE}[/tex] and [tex]\angle \mathrm{ABD}[/tex]:

Since, the angles in a straight line add up to 180°

To find [tex]\angle \mathrm{CBE}[/tex], let us add the angles and equals to 180°

[tex]\angle \mathrm{CBE}+\angle \mathrm{DBE}=180[/tex]

Substituting the value of DBE, we have,

[tex]\angle \mathrm{CBE}+62=180[/tex]

Subtracting both sides by 62,

[tex]\angle \mathrm{CBE}=118[/tex]

Thus, the measure of [tex]\angle \mathrm{CBE}[/tex] is 118°

Since,  [tex]\angle \mathrm{CBE}[/tex] and [tex]\angle \mathrm{ABD}[/tex] are vertically opposite, they are equal.

Thus, [tex]\angle \mathrm{ABD}=118[/tex]

Thus, the measure of [tex]\angle \mathrm{ABD}[/tex] is 118°

Hence, the values of the angles are  [tex]m\angle \mathrm{ABC}=62^{\circ}[/tex], [tex]m\angle \mathrm{DBE}=62^{\circ}[/tex], [tex]m\angle \mathrm{CBE}=118^{\circ}[/tex] and [tex]m\angle \mathrm{ABD}=118^{\circ}[/tex]

Yo sup??

a:b=5:3

a/b=5/3

a=5x

b=3x

3a+4b:5a+2b

=15x+12x:25x+6x

=27x:31x

=27:31

Hope this helps.

Answer:

Step-by-step explanation:

a:b=5:3 the value of 3a+4b:5a+2b

(3*5)+(4*3):(5*5)+(2*3)

15+12:25+6

=27:31

Answer:

Amy has 310 small marbles, 62 medium marbles and 188 large marbles.

Step-by-step explanation:

i) Let the number of small marbles be x

ii) let the number of medium marbles be y

iii) let the number of large marbles be z

iv) Amy has 5 times as many small marbles as medium marbles therefore we can write  5y = x

v) the number of large marbles is two more than than three times the number of medium marbles therefore we can write

   z = 3y + 2

vi) Amy has a total of 560 marbles therefore we can write x + y + z = 560

vii) Therefore from i) we can write x  = 5y

viii) using vii) and v) in vi) we can write

    x + y + z  = 5y + y + 3y + 2 = 560

ix) Therefore 9y = 558   .... therefore y = [tex]\frac{558}{9}[/tex] = 62

x) Therefore from i) we get x  = y [tex]\times[/tex] 5 = 62 [tex]\times[/tex] 5 = 310

xi) Therefore z  = (3 [tex]\times[/tex] 62) + 2 =  188

Amy has 310 small marbles, 62 medium marbles and 188 large marbles.

Answer:

-7

Step-by-step explanation

The explicit rule for the number of marbles in 10th row is An= 12+ n-1.

Step-by-step explanation:

Therefore, for the remaining 9 rows out 10 rows ⇒ 9 marbles are added.

For n= 10, then

⇒ A10 = 12 + (10-1)

⇒ A10 =12+9 = 21

Answer:

A(n)=11+n

Step-by-step explanation: took test

Answer:47

Step-by-step explanation:

Answer:

47 feet

Step-by-step explanation:

92 feet-45 feet= 47 feet

Answer is 47 feet