THINKING
4. Given is the Linear and Quadratic System g(x) = 3x2 + 8x + k and f(x) = 2x – 1.
Determine k such that g(x) = 3x2 + 8x + k intersects f(x) = 2x – 1 at one point.

Answer:

The answer is 3.5

Step-by-step explanation:

Answer:

45 square units

Step-by-step explanation:

In the above question, we are given the following values

The ratio of the lengths of the corresponding sides of two regular octagons is 8 to 3.

This means the length of the larger octagon = 8

The length of the smaller octagon = 3

Using scale factor denoted as k and because we are dealing with area of the octagon

k = 3²/8²

The area of the larger octagon is 320 ft².

The area of the smaller octagon s represented as y and is calculated as

k = y/Area of larger octagon

3²/8² = y/320

Cross multiply

8² × y = 3² × 320

y = 3² × 320/8²

y = 45 square units

Area of smaller octagon = 45 square units.

Answer:

B

Step-by-step explanation:

Interior angles of a triangle = 180°

3x°+3x+10°+4x-30°=180°

10x°-20°=180°

10x°=180°+20°

10x°= 200°

10x°/10=200°/10

x°=20°

Hence, the angle is [tex]x=20[/tex] degree.

What is the angle?

An angle can be defined as the figure formed by two rays meeting at a common end point.

Here given that,

As we know that the sum of interior angles of a triangle is [tex]180[/tex] degree.

[tex]3x+3x+10+4x-30=180\\\\10x-20=180\\\\10x=180+20\\\\10x= 200\\\\\frac{10x}{10}=\frac{200}{10}\\\\x=20[/tex]

Hence, the angle is [tex]x=20[/tex] degree.

To know more about the angle

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Answer:

L'(-7, -7), M'(-9, 9), and N'(5, 5)

Step-by-step explanation:

Assuming you mean 90° counterclockwise, you would use the formula: A(x,y) becomes A'(-y,x)

so L'(-7, -7), M'(-9, 9), and N'(5, 5)

The question was incomplete. Please check below the full content.

Which of the following represents a rotation of ΔLMN. which has vertices L (-7,7), M (9,9), and N(5, -5) about the origin by 90°?            

a) L(-7, -7) M(-9. -9) N(5, 5)

b) L(-7. -7) M(-9. 9) N(5, 5)

c) L(-7, -7) M(-9, 9) N(5, -5)

d) L (7, -7) M(9, 9) N(-5, 5)      

The rotation of the vertices L (-7,7), M (9,9), and N(5, -5) are

L'(-7,-7), M'(-9,9) and N'(5,-5) respectively.

Rotation of a point :

Let the rotations of L, M, and N are L', M', and N' respectively.

Hence  L'(-7,-7), M'(-9,9), and N'(5,-5) are the rotation of vertices

 L, M, and N of ΔLMN about the origin by 90°.

To know more about the rotation of a point:

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Answer:

Step-by-step explanation:

We khow that ABCD is a parallelogram so its area is the product of the base (DC) and the the height

ADE is a triangle . Its area is the product of the height and the base(DE) over 2

So the triangle and the parallelogram have the same area

Answer:

5 1/2 MILES

Step-by-step explanation:

$5.00-$.80=$4.20

4.20/.20=21/4= 5 1/4+1/4= 5 2/4 OR 5 1/2 MILES

Hope this help!

Answer:b because if there is 4 more sheep than cows just subtract 4 and you get the number of cows

Step-by-step explanation:

Answer:  the answer that I got was 24

Step-by-step explanation:

I hope it’s right and it helps!

Answer:

[tex]24[/tex]

Step-by-step explanation:

[tex](-1)\times (-(-2)) \times (-(-(-3))) \times (-(-(-(-4)))[/tex]

Negative times negative is positive.

Negative times negative times negative is negative.

Negative times negative times negative times negative is positive.

[tex](-1)\times (+2) \times (-3) \times (+4)[/tex]

Multiply.

[tex]-1 \times 2 \times -3 \times 4[/tex]

[tex]= 24[/tex]

Answer:

shown above

move active check

Answer:

Option D

Step-by-step explanation:

A. [tex]\sqrt{15}[/tex] = 3.87298

B. 11/25 = 0.44

C. 3/20 = 1.25

D. 2/6 = 0.333........

So, D had a repeating decimal form because it repeats the number 3.

Answer:

Step-by-step explanation:

D:  2/6.  Note that 2/6 = 1/3 = 0.3333333....  (repeating decimal form)

Answer:171.5

Step-by-step explanation:

7=✓3.5*x

49=3.5 x

x=48/3.5

x=48*35/10=24*35/5=24*7=168

AW=168

LW=3.5+168=171.5

Answer:

y = -2x + 8

Step-by-step explanation:

The slope is given, and if we plug in 2 and 3 for y and x respectively, we can solve to get b=8. When graphed, it looks like the picture below.

Answer:

1

Step-by-step explanation:

The n th term of cube numbers is calculated as

[tex]a_{n}[/tex] = n³

To find the first term let n = 1, that is

a₁ = 1³ = 1

Answer:

1.

Step-by-step explanation:

1 is the first term in the square numbers, as it is in the sequence of cube numbers.

1^3 = 1 * 1 * 1 = 1.

Hope this helps!

Answer:

(6,0)

Step-by-step explanation:

A zero of an equation is the x-intercept of the graph, meaning whenever the graph hits the x-axis. You can see that (2,0) and (6,0) are the x-intercepts, as I can see from the picture of the graph. There are other ways to solve this as well, but there is no need since the graph is provided. I hope this helps you!! Have a great rest of your day.

Answer:

150 paperclips

Step-by-step explanation:

set up the equation as a fraction equaling a fraction i.e. volume 16/ 50 paperclips = volume 48/ x paperclips

cross multiply so you get 16x = 2400

solve for x by dividing 2400 by 16

you should get x = 150

Answer: y≤ [tex]\frac{7}{3}x+2[/tex]

Step-by-step explanation:

Since we are given the equation, all we have to do is to fix the inequality. We have four options: <, >, ≤, and ≥. The line in the graph is a solid line. This means the line reaches and is equal to the points on the line. We can automatically eliminate ≤ and ≥. Now, we know the answer is ≤. The shading shows that the answer is less than 7/3x+2. In other words, y≤ [tex]\frac{7}{3} x+2[/tex].

Answer: 1/250

Step-by-step explanation:

Given the recurring decimal : 0.004

Firstly:

Let x = 0.004 - - - (1)

Due to the number of decimals places and value of x;

We multiply (1) by 1000 to obtain an integer

Multiply (1) by 1000

1000x = 4 - - - (2)

From (2) we can solve for x and leave our answer as a fraction.

Divide (2) by 1000 to obtain the value of x

1000x / 1000 = 4 / 1000

x = 1 / 250

Recall x = 0.004

Therefore, x = 0.004 = 1/250

B) 3/2

The radius of a circle is half its diameter.

Thus, the radius of the orange circle is 6, and the blue circle is 4

Thus the ratio is 4/6, which can be simplified to 3/2

Hope it helps <3 (Also, just answered this question for someone else!!)

Answer:

B. 3/2

Step-by-step explanation:

EDG

Answer:

15 cm

Step-by-step explanation:

Circumference of circle= 2πr, where r us the radius of the circle.

Given that the circumference of circle is 60πcm,

60π= 2πr

Divide by 2 on both sides,

15π= πr

Divide by π on both sides,

15= r

Thus, radius of circle= 15cm.

Answer:

The correct option is;

C. 0.3337

Step-by-step explanation:

We note that for a binomial probability distribution, we have;

[tex]p(r\geq \gamma)=\sum_{\gamma = r}^{ n}\dbinom{n}{r}\cdot \left (p\right )^{\gamma }\cdot \left (1-p\right )^{n - \gamma}[/tex]

Which gives;

[tex]p(x \geq 90)=\sum_{r = 90}^{ 100}\dbinom{100}{90}\cdot \left (0.88\right )^{\gamma }\cdot \left (1-0.88\right )^{100 - \gamma}[/tex]

[tex]\dbinom{100}{90}\cdot \left (0.88\right )^{90 }\cdot \left (1-0.88\right )^{10} = 0.108033[/tex]

[tex]\dbinom{100}{91}\cdot \left (0.88\right )^{91 }\cdot \left (1-0.88\right )^{9} = 0.08706[/tex]

[tex]\dbinom{100}{92}\cdot \left (0.88\right )^{92 }\cdot \left (1-0.88\right )^{8} = 0.062456[/tex]

[tex]\dbinom{100}{93}\cdot \left (0.88\right )^{93 }\cdot \left (1-0.88\right )^{7} = 0.039399[/tex]

[tex]\dbinom{100}{94}\cdot \left (0.88\right )^{94 }\cdot \left (1-0.88\right )^{6} = 0.021516[/tex]

[tex]\dbinom{100}{95}\cdot \left (0.88\right )^{95 }\cdot \left (1-0.88\right )^{5} = 0.09965[/tex]

[tex]\dbinom{100}{96}\cdot \left (0.88\right )^{96 }\cdot \left (1-0.88\right )^{4} = 0.003806[/tex]

[tex]\dbinom{100}{97}\cdot \left (0.88\right )^{97 }\cdot \left (1-0.88\right )^{3} = 0.001151[/tex]

[tex]\dbinom{100}{98}\cdot \left (0.88\right )^{98 }\cdot \left (1-0.88\right )^{2} = 0.000258[/tex]

[tex]\dbinom{100}{99}\cdot \left (0.88\right )^{99 }\cdot \left (1-0.88\right ) = 0.0000383[/tex]

[tex]\dbinom{100}{100}\cdot \left (0.88\right )^{100 }\cdot \left (1-0.88\right )^{0} = 0.00000281[/tex]

P(r≥90)  is therefore 0.1083 + 0.08706 + 0.062456 + 0.039399 + 0.021516 +  0.09965 + 0.003806 + 0.001151 + 0.000258 + 0.0000383 + 0.00000281 = 0.333685 ≈ 0.3337.

Answer:

The area is 25 :)

Step-by-step explanation:

This Is An Obtuse scalene triangle.

Sides: a = 17.205   b = 13.454   c = 5

Area: T = 25

Perimeter: p = 35.658

Angle ∠ A = α = 131.987° = 131°59'14″ = 2.304 rad

Angle ∠ B = β = 35.538° = 35°32'16″ = 0.62 rad

Angle ∠ C = γ = 12.475° = 12°28'30″ = 0.218 rad

Height: ha = 2.906

Height: hb = 3.716

Height: hc = 10

Median: ma = 5.385

Median: mb = 10.735

Median: mc = 15.24

Inradius: r = 1.402

Circumradius: R = 11.573

Vertex coordinates: A[3; 4] B[8; 4] C[-6; -6]

Centroid: CG[1.667; 0.667]

Coordinates of the circumscribed circle: U[0; 0]

Coordinates of the inscribed circle: I[1.963; 1.402]

Exterior (or external, outer) angles of the triangle:

∠ A' = α' = 48.013° = 48°46″ = 2.304 rad

∠ B' = β' = 144.462° = 144°27'44″ = 0.62 rad

∠ C' = γ' = 167.525° = 167°31'30″ = 0.218 rad

Answer:

20.56 units.

Step-by-step explanation:

Perimeter of the shaded region is the sum of all straight sides and all 4 arcs.

Perimeter of 4 straight sides [tex]=4\times 2=8\text{ units}[/tex]

Perimeter of a arc [tex]=\dfrac{1}{4}\times 2\pi r[/tex]

Perimeter of 4 arcs [tex]=4\times \dfrac{1}{4}(2\pi r)=2\pi r[/tex]

Here, r is the radius. So,

[tex]r=\dfrac{6-2}{2}=\dfrac{4}{2}=2[/tex]

Perimeter of 4 arcs [tex]=2(3.14)(2)=12.56[/tex]

Perimeter of the shaded region = Perimeter of all straight sides + Perimeter of all 4 arcs

                             [tex]=8+12.56[/tex]

                             [tex]=20.56\text{ units}[/tex]

Therefore, the perimeter of the shaded region is 20.56 units.

Answer:

The number of people standing in the original line is 22 people

Step-by-step explanation:

The information given are;

The number of baguettes that was shared by the people on the line = 85

The number of baguettes each person received = 1 each

Therefore;

The number of people that were finally on the line = 85

Let the number of people in the original line = X

Then each space between two people in X was filled by 1 new person of the first set of people who joined the line

Therefore;

The number of the first set of people who joined the line = The number of spaces between two count of people in X

Which gives;

The number of people who joined the line = X - 1

The new total number of people on the line = X + X - 1 = 2·X - 1

As time passed, a second set of people joined the line such that each space between the people waiting was filled with a new person (from the second set) who joined the line

Therefore, the number of people in the second set = Number of people waiting - 1

Which gives;

The number of people in the second set = 2·X - 1 - 1 = 2·X - 2

The total number of people on the line becomes 2·X - 1 + 2·X - 2 = 4·X - 3

The 85 baguettes is then able to go round (each) among the total number of people on the line

Therefore;

The total number of people on the line = The number of baguettes sheared

4·X - 3 = 85

4·X = 85 + 3 = 88

X = 88/4 = 22

Therefore;

The number of people standing in the original line = 22.

Answer:

Equation of the line; y=x+3

Step-by-step explanation:

Graph the line that passes through the points (5,8) and (3,6) and determine the equation of the line.

Equation of a line: y=mx +b

Let's find the slope: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

8-6/ 5-3= 2/2 = 1

y=x+b

Substitute the points in.

y= 8

x = 5

8 = 5+b

b= 3

The y-intercept is 3.

y=x+3

Points on the line: (-2,1) (-1,2) (0,3) (1,4) (2,5)

Answer:

(f circle g) (x) = 3x^2 + 5

Step-by-step explanation:

To find (f circle g)(x), we substitute function g(x) for x in f(x) = 3x + 2:

(f circle g) (x) = 3(x^2 + 1) + 2, or

                         3x^2 + 3 + 2, or

(f circle g) (x) = 3x^2 + 5

Answer:

(f circle g) (x) = 3x^2 + 5

Step-by-step explanation:

Answer:

-2 2/5

Step-by-step explanation:

Barbara's method:

[tex]\frac{1}{2}*-4\frac{4}{5}=\frac{1}{2}*\frac{-24}{5}=\frac{-12}{5}=-2\frac{2}{5}\\[/tex]

Christopher's method:

[tex]\frac{1}{2}*-4\frac{4}{5}=\frac{1}{2}*(-4+\frac{-4}{5})=\frac{1}{2}*-4+\frac{1}{2}*\frac{-4}{5}=-2+\frac{-2}{5}=-2\frac{2}{5}\\[/tex]

Answer:

It will take 1 hour and 12 minutes for the two trains to be 192 miles apart

Step-by-step explanation:

The total distance between the two trains is the distance traveled by both trains. The distance traveled by the eastbound train is 85 mph * elapsed time and the distance traveled by the westbound train is 75 * elapsed time.

The combined formula is distance traveled = speed of first train * elapsed time + speed of second train * elapsed time.

Since the elapsed time is equal for both trains then the formula is modified as distance traveled = (speed of first train + speed of second train) * elapsed time.

Solving for the elapsed time

distance traveled = (speed of first train + speed of second train) * elapsed time

192 miles = (85mph + 75 mph) * elapsed time

192 miles = 160 mph * elapsed time

elapsed time = 192 miles / 160 mph

elapsed time = 1.2 hours

elapsed time = 1 hour and 12 minutes

It will take 1 hour and 12 minutes for the two trains to be 192 miles apart.

Answer:

need thiss

Step-by-step explanation:

Step-by-step explanation:

|-x|<1 --> -1<-x<1 --> -1<x<1

so the graph is the striped part