what rational number lies in between -14/31 and -17/33? A. -989/3069 B. -123/276 C. -989/2046 D. -4/7

Answers

Answer 1

Answer: -14/31 and -17/33

-17/33 - (-14/31) = (-17/33*31/31) - (-14/31*33/33) = -527/1023 + 462/1023

= (-527+462)/1023 = -65/1023

-65/1023 ÷ 2 = -65/1023 * 1/2 = -65/2046

-17/33 - (-65/2046) = (-17/33*62/62) - (-65/2046) = -1054/2046 + 65/2046
= -989/2046 Choice C.

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1) Solve by using the perfect squares method. x2 + 8x + 16 = 0 2) Solve. x2 – 5x – 6 = 0

3) What value should be added to the expression to create a perfect square? x2 – 20x

4) Solve. x2 + 8x – 8 = 0

5) Solve: 2x2 + 12x = 0

6) Solve each problem by using the quadratic formula. Write solutions in simplest radical form. 2x2 – 2x – 1 = 0

7) Calculate the discriminant. x2 – x + 2 = 0

8) Calculate the discriminant and use it to determine how many real-number roots the equation has. 3x2 – 6x + 1 = 0

9) Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis. y = 2x2 + x – 3

10) Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis. y = x2 – 12x + 12

Answers

1)
$x^2+8x+16=0 \n(x+4)^2=0 \nx+4=0 \n\boxed{x=-4}$

2)
$x^2-5x-6=0 \nx^2-6x+x-6=0 \nx(x-6)+1(x-6)=0 \n(x+1)(x-6)=0 \nx+1=0 \ \lor \ x-6=0 \nx=-1 \ \lor \ x=6 \n\boxed{x=-1 \hbox{ or } x=6}$

3)
$\hbox{a perfect square:} \n (x-a)^2=x^2-2xa+a^2 \n \n 2xa=20x \n a=(20x)/(2x) \n a=10 \n \n a^2=10^2=100 \n \n \hbox{the expression:} \n x^2-20x+100 \n \n \boxed{\hbox{100 should be added to the expression}}$

4)
$x^2+8x-8=0 \n \na=1 \n b=8 \n c=-8 \n \Delta=b^2-4ac=8^2-4 * 1 * (-8)=64+32=96 \n√(\Delta)=√(96)=√(16 *6)=4√(6) \n \nx=(-b \pm √(\Delta))/(2a)=(-8 \pm 4√(6))/(2 * 1)=(2(-4 \pm 2√(6)))/(2)=-4 \pm 2√(6) \n\boxed{x=-4-2√(6) \hbox{ or } x=-4+2√(6)}$

5)
$2x^2+12x=0 \n2x(x+6)=0 \n2x=0 \ \lor \ x+6=0 \nx=0 \ \lor \ x=-6 \n\boxed{x=-6 \hbox{ or } x=0}$

6)
$2x^2-2x-1=0 \n \na=2 \n b=-2 \n c=-1 \n \Delta=b^2-4ac=(-2)^2-4 * 2 * (-1)=4+8=12 \n√(\Delta)=√(12)=√(4 * 3)=2√(3) \n \nx=(-b \pm √(\Delta))/(2a)=(-(-2) \pm 2√(3))/(2 * 2)=(2 \pm 2√(3))/(2 * 2)=(2(1 \pm √(3)))/(2 * 2)=(1 \pm √(3))/(2) \n\boxed{x=(1-√(3))/(2) \hbox{ or } x=(1+√(3))/(2)}$

7)
$x^2-x+2=0 \n \na=1 \n b=-1 \n c=2 \n\Delta=b^2-4ac=(-1)^2-4 * 1 * 2=1-8=-7 \n \n\boxed{\hbox{the discriminant } \Delta=-7}$

8)
$3x^2-6x+1=0 \n \na=3 \n b=-6 \n c=1 \n \Delta=b^2-4ac=(-6)^2-4 * 3 * 1=36-12=24 \n \n\boxed{\hbox{the discriminant } \Delta=24} \n \n\hbox{if } \Delta\ \textless \ 0 \hbox{ then there are no real roots} \n\hbox{if } \Delta=0 \hbox{ then there's one real root} \n\hbox{if } \Delta\ \textgreater \ 0 \hbox{ then there are two real roots} \n \n\Delta=24\ \textgreater \ 0 \n\boxed{\hbox{the equation has two real roots}}$

9)
$y=2x^2+x-3 \n \n a=2 \n b=1 \n c=-3 \n \Delta=b^2-4ac=1^2-4 * 2 * (-3)=1+24=25 \n \n \hbox{the function has two zeros} \n \boxed{\hbox{the parabola has 2 points in common with the x-axis}} \n \n a\ \textgreater \ 0 \hbox{ so the parabola ope} \hbox{ns upwards} \n \boxed{\hbox{the vertex lies below the x-axis}}$

10)
$y=x^2-12x+12 \n \na=1 \n b=-12 \n c=12 \n \Delta=b^2-4ac=(-12)^2-4 * 1 * 12=144-48=96 \n \n \hbox{the function has two zeros} \n \boxed{\hbox{the parabola has 2 points in common with the x-axis}} \n \n a\ \textgreater \ 0 \hbox{ so the parabola ope} \hbox{ns upwards} \n \boxed{\hbox{the vertex lies below the x-axis}}$

Find the indicated term of the given arithmetic sequence. a1 = 45, d = –6, n = 8a. 309
c. 3
b. –3
d. 87

Answers

an = a1+d*(n-1)
a8 = 45 - 6*(8-1) =3

The distance between Vancouver and Winnipeg is approximately 1850 km in a straight line. The distance on a map is 3.7 cm. Write a scale statement for the map. What scale factor was used to make the map.

Answers

3.7cm on the map represents 1850km in reality

3.7cm : 1850km

1cm : 1850/3.7 km

1cm : 500km

Scale statement for map is : 1cm : 500km.

That is 1cm on map represents 500km.

1cm : 500km. Recall 1km = 1000m = 100 000cm

1cm : 500* 100000cm

1cm : 50 000 000cm

1: 50 000 000.

Scale factor is 50 000 000.

Final answer:

The scale of the map is 1 cm : 500 km, meaning 1 cm on the map corresponds to an actual distance of 500 km on the ground. This is the scale factor used to create the map.

Explanation:

The scale of a map is a ratio that represents the relationship between the distance on the map and the actual distance on the ground. In this case, the actual distance between Vancouver and Winnipeg is 1850 km, while the distance on the map is 3.7 cm. Therefore, the scale of the map can be represented as 1 cm : 500 km (because 1850 km / 3.7 cm = approximately 500 km).

This means that 1 cm on the map represents an actual distance of 500 km on the ground, which is the scale factor used to create the map. Therefore, the scale statement for the map would be "1 cm on the map represents 500 km on the ground" or it can be written shorthand as 1:50,000,000 (considering 1 km = 1,000,000 cm).

Learn more about Map Scale here:

brainly.com/question/24486949

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Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete. What is the equation that can be used to find the value of y, the total time that Vlad spent on his homework, and what are the constraints on the values of x and y?y=2x+20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.
y=2x+20; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.
y=20x+2; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.
y=20x +2; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.

Answers

Answer:

The answer is A. y = 2x + 20; x is any integer greater than or equal to, 0 and y is any integer greater than or equal to 20

Step-by-step explanation:

Which ordered pairs make the equation true?4x – 3y = –10

Choose all answers that are correct.
(Points : 1)
(–4, –2)
(–1, 2)
(1, 4)
(3, –1)

Answers

$(-4,-2) \nx=-4 \n y=-2 \n \Downarrow \n4 * (-4)-3 * (-2) \stackrel{?}{=} -10 \n-16+6 \stackrel{?}{=} -10 \n-10 \stackrel{?}{=} -10 \n-10 = -10 \n \n(-1,2) \nx=-1 \n y=2 \n \Downarrow \n4 * (-1)- 3 * 2 \stackrel{?}{=}-10 \n-4-6 \stackrel{?}{=} -10 \n-10 \stackrel{?}{=} -10 \n-10 = -10 \n \n(1,4) \nx=1 \n y=4 \n \Downarrow \n4 * 1-3 * 4 \stackrel{?}{=} -10 \n4-12 \stackrel{?}{=} -10 \n-8 \stackrel{?}{=} -10 \n-8 \not= -10$

$(3,-1) \nx=3 \n y=-1 \n \Downarrow \n4 * 3- 3 * (-1) \stackrel{?}{=} -10 \n12+3 \stackrel{?}{=} -10 \n15 \stackrel{?}{=} -10 \n15 \not= -10$

The ordered pairs (-4,-2) and (-1,2) make the equation true.

(x,y)
1.
(-4,-2)
4*(-4)-3*(-2)= -10
-16+6= -10
- 10 = - 10

2. (-1,2)
4*(-1)-3*2= -10
-4-6= -10
-10 = -10

3. (1,4)
4*1-3*4= -10
8-12= -10
-4 ≠ -10

4. (3, -1)
4*3-3*(-1)= -10
12 + 3 = -10
15 ≠ -10

The correct answers:
(-4,-2) and (-1,2)

write an expression that shows how you can multiply 9*475 using expanded form and the distributive property

Answers

475 = 400 + 70 + 5

therefore

9 × 475 = 9 × (400 +70 + 5) = 9 × 400 + 9 × 70 + 9 × 5
=3600 + 630 + 45 = 4275

I think... It's better to use Distributive Property:
(a - b) × c = a × c - b × c

9 = 10 - 1

therefore:
(10 - 1) ×475 = 10 × 475 - 1 × 475 = 4750 - 475 = 4275

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