Which best describes the relationship between the successive terms in the sequence shown?

9, –1, –11, –21, …

The common difference is –10. 

The common difference is 10. 

The common ratio is –9.

The common ratio is 9.

the answer is 0.5531 (✿◠‿◠)

To find the probability that the car will travel a maximum distance between 125 and 135 miles, we need to calculate the z-scores for these distances and find the corresponding probabilities using a standard normal distribution table or calculator.

To find the probability that the car will travel a maximum distance between 125 and 135 miles, we need to calculate the z-scores for these distances using the formula: z = (x - mean) / standard deviation.

For 125 miles: z = (125 - 134) / 4.8 = -1.875.

For 135 miles: z = (135 - 134) / 4.8 = 0.208.

Next, we need to find the corresponding probabilities for these z-scores using a standard normal distribution table or calculator. The probability of a z-score less than -1.875 is approximately 0.0301, and the probability of a z-score less than 0.208 is approximately 0.5829.

To find the probability between 125 and 135 miles, we subtract the probability of a z-score less than 125 from the probability of a z-score less than 135: 0.5829 - 0.0301 = 0.5528.

Therefore, the probability that the car will travel a maximum distance between 125 and 135 miles is approximately 0.5528 or 55.28%.

Answer:

4.4

Step-by-step explanation:

The answer is 4.4 because if you know that 5*4 equal 20 so 4 can go each of the 5 groups so 24-20 leaves you with 4 so your answer is 4 remainder 4

Answer: x = 7.2

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

Explanation:

As shown in the diagram (see attached image below), the red interior angles are

180-10x

180-15x

180-20x

180-5x

Each of those expressions is in the form 180-E, with E as the exterior angle. Add up the interior angles. Set the sum equal to 360 and solve for x. For any quadrilateral, the four interior angles always add to 360.

(angle1)+(angle2)+(angle3)+(angle4) = 360

(180-10x) + (180-15x) + (180-20x) + (180-5x) = 360

(180+180+180+180)+(-10x-15x-20x-5x) = 360

720-50x = 360

-50x = 360-720

-50x = -360

x = -360/(-50)

x = 36/5

x = 7.2

Answer: D

Step-by-step explanation:

A. False

f(x): x → -∞, y → -∞

g(x): x → -∞, y → 1  

B. False

at x = -1, f(x) = -7

at x = -1, g(x) = 1.5

C. False

refer to A

g(x) → 1 and f(x) → -∞   so g(x) > f(x)

D. TRUE

It is hard to tell from the graph so plug in a value to check.

f(10) = 5(10) - 2

       = 50 - 2

       = 48

g(10) = 2¹⁰ + 1

        = 1024 + 1

        = 1025

g(10) > f(10)

Answer:

x=9, y=-4

C (9,-4)

Step-by-step explanation:

−4y − 3x = −11

x − 2y = 17

WE are using substitution, so solve the second equation for x

Add 2y to each side

x -2y+2y = 17+2y

x = 17+2y

Substitute this into the first equation

-4y -3x = -11

-4y -3(17+2y) = -11

Distribute the 3

-4y -3*17 -3*2y = -11

-4y -51 -6y = -11

Combine like terms

-10y-51=-11

Add 51 to each side

-10y-51+51=-11+51

-10y = 40

Divide by -10

-10y/-10 = 40/-10

y = -4

Now we need to find x

x= 17+2y

x = 17+ 2(-4)

x =17-8

x=9

By solving the second equation for x, substituting into the first equation, and simplifying, we find the solution to the system is (9, -4), which corresponds to Option C.

In order to find the solution of the system using substitution, we first solve one of the equations for x or y. Looking at the second equation x - 2y = 17, we can solve for x to get x = 2y + 17. Now we substitute this expression for x into the first equation - 4y - 3x = - 11, which gives us:

- 4y - 3(2y + 17) = - 11

Simplifying this equation, we obtain:

- 4y - 6y - 51 = - 11

Combine like terms:

- 10y - 51 = - 11

Add 51 to both sides:

- 10y = 40

Now, divide both sides by - 10 to find y:

y = - 4

After obtaining the value for y, we substitute it back into the equation we derived for x (x = 2y + 17):

x = 2( - 4) + 17

Which simplifies to:

x = - 8 + 17

Finally, we get x = 9.

The solution for the system is therefore (9, - 4), which corresponds to Option C.

Answer:

The store has 100 cans of soup

Step-by-step explanation:

20x5=100

Answer: 100 cans

Step-by-step explanation:

20 times 5 = 100

Answer:

p = 12+5n

Step-by-step explanation:

For every added triangle, the perimeter only increases by 5.

For n=1, the perimeter is 6+6+5 = 17

For n=2, the perimeter is 6+6+5+5 = 22

So in general, the perimeter is 12 + 5n

Answer:

Q12. p = 5n + 12

Q13. See below.

Q14. y-intercept = (0, -3); x-intercept = (-3/2, 0).

Step-by-step explanations:

Question 12. Perimeter

      One triangle: p₁ = 2×6 + 1×5

    Two triangles: p₂ = 2×6 + 2×5

Three triangles : p₃ = 2×6 + 3×5

         n triangles: pₙ = 2×6 + n×5

General formula: p = 5n + 12

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

Question 13. Modelling a function

Here's one possible table of values.

x   y

-3    3

-2    1

-1   -1

0  -3

1   -5

You can see the graph of the function in Fig. 1 below.

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

Question 14. x- and y-intercepts

y- intercept

y = -2x – 3     Set x = 0

y = -2×0 – 3

y = 0 – 3

y = -3

The y-intercept is at (0, -3).

=====

x-intercept

y = -2x – 3      Set y = 0

0 = -2x – 3     Add 3 to each side

3 = -2x            Divide each side by -2

x = -3/2

The x-intercept is at (-3/2, 0).

Answer:

two real different roots

Step-by-step explanation:

Consider polynomial function

[tex]M(x)=-4x^2+x+1.[/tex]

The discriminant is

[tex]D=b^2-4ac=1^2-4\cdot (-4)\cdot 1=1+16=17.[/tex]

Since [tex]D>0,[/tex] the polynomial function [tex]M(x)[/tex] has two real different roots.

Answer:

±sqrt(7) = r

Step-by-step explanation:

21 = 3r^2

Divide each side by 3

21/3 = 3r^2/3

7 = r^2

Take the square root of each side

±sqrt(7) = sqrt(r^2)

±sqrt(7) = r

Answer:

see explanation

Step-by-step explanation:

Check the value of the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 then roots are real

• If b² - 4ac = 0 roots are real and equal

• If b² - 4ac < 0 then roots are not real

given (x - a)(x - b) = k² ( expand factors )

x² - bx - ax - k² = 0 ( in standard form )

x² + x(- a - b) - k² = 0

with a = 1, b = (- a - b), c = -k²

b² - 4ac = (- a - b)² + 4k²

For a, b, k ∈ R then (- a - b)² ≥ 0 and 4k² ≥ 0

Hence roots of the equation are always real for a, b, k ∈ R

Jay has run two-thirds of 6 miles, that is, 4 miles. When converted to yards, it is approximately 7040 yards.

To find out how far Jay has run to the nearest yard, we first need to find out 2/3 of 6 miles since Jay has run this fraction of the distance. You can calculate two-thirds of a total by multiplying the total by 2/3. So, Jay has run 2/3 * 6 miles, which equals 4 miles.

Since we want to find out how far he has run in yards, we need to convert these miles to yards. We know that 1 mile is approximately 1760 yards. Hence, Jay has run approximately 4 * 1760 = 7040 yards.

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To find the real solutions of the equation x^3-8x^2+17x-10=0 using the x-intercept method, factor the equation and set each factor equal to zero. The real solutions are x=2, x=1, and x=5.

To find the real solutions of the equation x^3-8x^2+17x-10=0 using the x-intercept method, we need to find the x-values where the graph of the equation intersects the x-axis. This is done by factoring the equation and setting each factor equal to zero.

Step 1: Factor the equation: (x-2)(x-1)(x-5)=0

Step 2: Set each factor equal to zero and solve for x:

Therefore, the x-intercepts or real solutions of the equation are x=2, x=1, and x=5.

Answer:

The above result is proved with the help of Pythagoras theorem and explained below.

Step-by-step explanation:

Given figure ABCD in which AD=BC and all angles intersect at right angle. Hence, the triangle formed inside ADC and ABC are right angled triangle.

In triangle ADC,

By applying Pythagoras theorem, we get

[tex]AC^{2}=AD^{2}+DC^{2}[/tex]    →  (1)

In triangle ABC,

[tex]AC^{2}=AB^{2}+BC^{2}[/tex]    →  (2)

Now, from eq (1) and (2)

Peach Tree Dr. is the same distance as Sycamore Ln.

[tex]AD^{2}+DC^{2} = AB^{2}+BC^{2}[/tex]

⇒ [tex]DC^{2} = AB^{2}[/tex]              (∵ AD=BC)

⇒ DC=AB                    (∵Distance can never negative)

Therefore, Peach Tree Dr. is the same distance as Sycamore Ln.

Answer: y = 0.4

Step-by-step explanation: Using the distributive property, first by distributing the numbers outside the bracket to the ones inside.

( - 3 * 2 ) (- 3 *-0.4y) +5.6 = (0.4*3y) (0.4*1)

   - 6     +       1.2y  +   5.6  =  1.2y  +   0.4

Next step is to collect like terms :

(- 6 + 5.6) +1.2y  =  1.2y +0.4

- 0.4 +1.2y =1.2y +0.4

Next step is to get rid of of the 0.4 :

- 0.4 +1.2y =1.2y +0.4

+0.4                     +0.4

= 1.2y=1.2y+0.4

=1.2y-1.2y=0.4

y=0.4.

About 16/25 fraction of the animal shelter are dogs.

Hope helps!-Aparri

Answer:

[tex]\frac{16}{25}[/tex]

Step-by-step explanation:

64% of the animals at an animal shelter are dogs.

This can also be expressed as: [tex]\frac{64}{100}[/tex] of the animals are dogs

Simplifying gives a fraction: [tex]\frac{16}{25}[/tex] of the animals are dogs.

Answer:

The value of y is 6.

Step-by-step explanation:

To find the value of y, start by using the known information we have in the equation for slope. The equation is below.

m(slope) = (y2 - y1)/(x2 - x1)

In this equation, the first ordered pair would be (x1, y1) and the second would be (x2 , y2). So we put the values in for these variables and we get.

1/2 = (7 - y)/(2 - 0)

1/2 = (7 - y)/2

Now we can use cross multiplication to solve for y.

1/2 = (7 - y)/2

1*2 = 2(7 - y)

2 = 14 - 2y

-12 = -2y

6 = y

Answer:  The volume of the cuboid  is:  " 11 ,200 cm³ " .

_________________________________________________

Step-by-step explanation:

____________________________________________________

The formula for the volume of a "cuboid" ;

      which is given in:  "cubic units" ;  or,  "units³ " ;  is:

____________________________________________________

        →    Volume, "V" = length (L)  * width (w) * (height)  ;

____________________________________________________

 →  The 3 (three given values are "4m" , "4 cm" and "7cm" .

We need the units of measurement to be equal;  so we need to convert the " 4m " to "cm" :

 Note that:  " 1 m = 100 cm " ; {exact conversion} ;

 So:   4m ( 100 cm / 1 m) = (4 * 100) cm = 400 cm.

_____________________________________________________

Now, we can plug these values and solve for the volume; in units of "cm³ " ;

_____________________________________________________

 V = 400 cm * 4 cm * 7 cm ;

    =  400 * 4 * 7 * cm * cm * cm ;

    =  400 * 4 * 7 cm³ ;

    =  1600 * 7 cm³ ;

     =  11, 200 cm³

_____________________________________________________

The answer is:  " 11 ,200 cm³ " .

_____________________________________________________

Answer:

put the sum on 0, put 1.4 4 spaces away from the positive 1 and put k four spaces away from the negative 1

Step-by-step explanation:

The  number sentence that  is not true is |-20| < 20 , option A

Let us consider each of the options;

Option A;

|-20| < 20

20<20

This statement is wrong because 20 is not less than 20

Option B

|9|=9

9=9

This statement is correct mathematically, hence the correct statement

Option C

|-20|>|9|

20>9

This statement is correct mathematically, hence the correct statement

Option D

|9|<|20|

9<20

This statement is correct mathematically, hence the correct statement

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8 am to 10:30 am is 2.50 hours.

Old Steamy is going 6.14 mph for 2.5 hours so travels : 6.14 * 2.5 = 15.35 miles.

This means Chug a lug has to travel 290 - 15.35 = 274.65 miles in 2.5 hours.

The speed would be 274.65 / 2.5 = 109.86 miles per hour.

Answer:

The speed of Old Steamy train = 6.14 mph

Train started at 8 a.m. and arrived at 10.30 a.m, this becomes 2.5 hours.

So, distance traveled by Old Steamy train = [tex]Speed\times time[/tex]

=> [tex]6.14\times2.5=15.35[/tex] miles

Now we get that Chug-a-Lug was 290 miles behind the Old steamy.

To know the distance traveled by Chug-a-Lug, we will add distance traveled by Old Steamy to the station plus the distance between the trains.

So, distance traveled by Chug-a-Lug = [tex]15.35+290=305.35[/tex] miles

The speed of Chug-a-Lug =[tex]\frac{Distance}{Time}[/tex]

= [tex]\frac{305.35}{2.5}=122.14[/tex] mph

Answer:

The y intercept is -2

Step-by-step explanation:

To find the y intercept, set x = 0 and solve for y

2x-5y=10

0  -5y = 10

Divide each side by -5

-5y/-5 = 10/-5

y = -2

Answer:

1. (h + p)(x) = 2x^2 - 11x + 16

2. It is the same problem as #1.

3. (k - f)(x) = 5x^3 + x^2 - 17x + 2

4. (q - g)(x) = 4x^2 + 7x - 14

Step-by-step explanation:

We are given that the values of h(x) = 2x^2 - 5x + 15 and p(x) = -6x + 1. Using these values you can substitute them into (h + p)(x).

(2x^2 - 5x + 15) + (-6x + 1)

Start by combining like terms. -5x and -6x will combine; 15 and 1 will also combine. 2x^2 will stay the same since there is no other term for it to combine with.

2x^2 - 11x + 16

Combine like terms. We will be adding since h(x) and p(x) are being added together.

We are given that k(x) = 8x^3 - 12x + 2 and f(x) = 3x^3 - x^2 + 5x. Knowing these values we can substitute k(x) and f(x) into (k - f)(x). This will look like:

(8x^3 - 12x + 2) - (3x^3 - x^2 + 5x)

Start by combining like terms. The terms to the same power can be combined (keep in mind we are finding the difference, in other words: subtracting). The terms with "x" can be combined as well. After doing so, your evaluated expression will look like:

5x^3 + x^2 - 17x + 2

q(x) = 4x^2 + 9x - 10 and g(x) = 2x + 4. Substitute q(x) and g(x) into (q - g)(x).

(4x^2 + 9x - 10) - (2x + 4)

Use the same rules I said above. The simplified expression will look like:

4x^2 + 7x - 14

Answer:

x = 12        and    x = -4

Step-by-step explanation:

abs (x-4) = 8

When we have absolute value equations, we get two solutions, one positive and one negative

x-4 = 8        and   x-4 = -8

Add 4 to both sides

x-4+4 = 8+4       x-4+4=-8+4

x = 12        and    x = -4

[tex]|x-4|=8\iff x-4=8\ \vee\ x-4=-8\qquad\text{add 4 to both sides}\\\\\boxed{x=12\ \vee\ x=-4}[/tex]

It is closer to 1/4.

Hope this helps.

-TheOneandOnly003

Answer:

[tex]A(x)=5\cdot 2^x[/tex]

Step-by-step explanation:

The given scenario can be represented by an exponential growth function. The general form if the exponential growth function is,

[tex]y=a(1+r)^x[/tex]

where,

y = the future amount after time x,

a = initial amount,

r = rate of growth.

As here A(x) represents the amount of money after x years with initial deposit of  $5 and in each year the amount doubles or duplicates itself i.e r=100% = 1, so the function would be,

[tex]A(x)=5(1+1)^x=5\cdot 2^x[/tex]

At the beginning the amount was $5, so the y intercept of the graph will be at 5.

Answer:

It’s Z Bc that’s the only one that starts at 5 and then doubles each year

If we start from the origin, then the vector would be v = (52, 12) as given. But suppose we shift its initial point. Doing so would preserve its direction. For example, if we move its initial point to (1, 1), we'd have to shift its terminus by the same amount (1 unit to the right, 1 unit up) so that its terminal point would be (52 + 1, 12 + 1) = (53, 13).

Option A is not correct. If we want the vector to start at (52, 12), we have to adjust the terminus by the same distance by adding (52, 12) to the terminus. This means the resulting vector would start at (52, 12) and end at (52 + 52, 12 + 12) = (104, 24).

One important thing to observe here is that the difference between the terminal and initial points always returns v. In the first example: (53, 13) - (1, 1) = (52, 12). In checking option A: (104, 24) - (52, 12) = (52, 12). So to eliminate any other answer choices, all you need to do is subtract.

Option B is correct by this "rule". (66, 7) - (14, -5) = (52, 12).

Options C and D are not. (0, 12) - (52, 0) = (-52, 12), and (64, -4) - (-12, 16) = (76, -20).

Final answer:

The initial and terminal points that correctly represent the vector v = (52, 12) in component form are option B: initial (14, -5); terminal (66, 7), as these points give the same components when subtracted (terminal - initial).

Explanation:

The student is asking about the initial and terminal points for a vector given in component form. The vector v is (52, 12), which means it has an x-component of 52 and a y-component of 12. This can be visually represented as a directed line segment with an initial point and a terminal point. The correct initial and terminal points for vector v would result in the same component form when subtracting the coordinates of the initial point from the coordinates of the terminal point (terminal - initial).

Option B has the initial point (14, -5) and terminal point (66, 7). By calculating the difference between the terminal and initial points: (66 - 14, 7 - (-5)) = (52, 12), we can see that these points correctly represent the vector v in component form. Therefore, the answer is B.

Answer:

(3 1/2, 7 1/4)

Step-by-step explanation:

A 1:3 ratio means we want 4 equal parts  (1+3 = 4)

Find the distance of the segment and divide by 4

(x2+x1)/4,  (y2+y1)/4

(8-2)/4 , (5-8)/4

6/4, -3/4

Since the first part is of ratio 1, we multiply by 1

Now add this to the starting point

(2 + 6/4, 8+ -3/4)

Getting a common denominator of 4

2*4/4 = 8/4

8 *4/4 = -3/4

(8/4 + 6/4, 32/4 -3/4)

(14/4, 29/4)

Now change back to a mixed number

(3 2/4 , 7 1/4)

(3 1/2, 7 1/4)

Answer:

x=2 ,y=-6

B (2,-6)

Step-by-step explanation:

y = -3x

x+y = -4

Substitute -3x for y in the second equation

x+y = -4

x+ (-3x) = -4

Combine like terms

-2x = -4

Divide by -2 on each side

-2x/-2 = -4/-2

x = 2

Now we still need to find y

y = -3x

Substitute x=2

y = -3(2)

y = -6

Answer:

y=-0.75x+16

Step-by-step explanation:

Answer:

y=-0.75x+16

Step-by-step explanation:

Answer:

16 2/3 %

Step-by-step explanation:

To put this in a percentage, they need to have the same units.

Let convert days to hours

1 day = 24 hours

Multiply by 3

3 days = 72 hours

The percentage is part over whole

12 hours / 72 hours

We can simplify by dividing top and bottom by 12

1/6

This is a fraction, change this to a decimal

.166666666

Now multiply by 100

16.666666 %

16 2/3 %