Which graph represents the parametric equations x(t) = t – 4 and y(t) = t2 + 5 for –1 ≤ t ≤ 2?

Answer:

k = 0,  k = 4

Step-by-step explanation:

Given equation:

[tex]y=x^2+kx+3k+4x+4[/tex]

Rearrange into standard form [tex]ax^2+bx+c[/tex]:

[tex]\implies y=x^2+kx+4x+3k+4[/tex]

[tex]\implies y=x^2+(k+4)x+(3k+4)[/tex]

Therefore:

[tex]a=1, \quad b=(k+4), \quad c=(3k+4)[/tex]

If the vertex lies in the x-axis, then the quadratic has one (repeating) root at (x, 0).  Therefore, we can use the discriminant to find the values of k.

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]

Therefore, set the discriminant to zero and solve for k:

[tex]\implies (k+4)^2-4(1)(3k+4)=0[/tex]

[tex]\implies k^2+8k+16-12k-16=0[/tex]

[tex]\implies k^2-4k=0[/tex]

[tex]\implies k(k-4)=0[/tex]

[tex]\implies k=0, k=4[/tex]

So the vertex lies in the x-axis when k = 0 or k = 4

Answer:

D. but there should be an 8.33

Step-by-step explanation:

The answer should be 8.33 but in here it only says 7 which is the closest because the unit rate would be 8.33 miles an hour.

Answer: 5.13 square cm

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

So we have the set of numbers: 3,4,4,5,5,2,5,4,6,3,6,5,3.

Mode just means the most repeated number so let's sort them into groups.

(2) (3,3,3) (4,4,4) (5,5,5,5) (6,6).

the most repeated number is 5 which we see in the sequence about 4 times.

Answer:

9 5/6

Step-by-step explanation:

6 1/2 + 3 1/3

= (6 + 3) + (1/2 + 1/3)

= 9 + 1 * 3/ 2 * 3 + 1 * 2/ 3*2

= 9 + 3/6 + 2/6

= 9 + 3+2/6

= 9 + 5/6

= 9 5/6

Hey there!

6 1/12 + 3 1/3

= 73/12 + 10/3

= 73/12 + 40/12

= 73 + 40 / 12 + 0

= 113 / 12

= 9 5/12

Therefore, your answer is:

• 113/12

OR
• 9 5/12

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

3. First you should identify which line corresponds to which equation.

x + 2y = -8   ⇒   y = -x/2 - 4

is the line with slope -1/2 and intercept (0, -4), so the first inequality refers to the lower line in the graph.

For the inequality itself, the solution set that satisfies it is either the region above or below it. To decide which, pick any point in the plane and plug its coordinates into the inequality. The origin is a natural choice, since it's not on the line and working with 0s is easy.

In the first inequality, we have

x = 0 and y = 0   ⇒   0 + 2•0 = 0 < -8

which is not true. So (0, 0) is not in the solution set, and it stands to reason that any point in the same region will not be a solution. In other words, the region above the line x + 2y = -8 does not satisfy the inequality, while the one below it does.

In the second inequality,

x = 0 and y = 0   ⇒   2•0 + 0 = 0 ≥ -1

which is true. This means the region containing (0, 0) above the upper line solves the second inequality.

The solution to the system of inequalities is then the intersection of these two regions. (See attached; I've labeled the solution to the first inequality in blue, the solution to the second one in red, and the solution to both in green.)

All this work is kind of overkill for this particular question, though. All you really need to do is check if the given point satisfies the inequalities:

• (-5, 5) :

x = -5 and y = 5   ⇒   -5 + 2•5 = 5 < -8   ⇒   NO

• (2, -5) :

x = 2 and y = -5   ⇒   -2 + 2•5 = 8 < -8   ⇒   NO

• (-4, -6) :

x = -4 and y = -6   ⇒   -4 + 2•(-6) = -16 < -8   ⇒   MAYBE

x = -4 and y = -6   ⇒   2•(-4) + (-6) = -14 < -8   ⇒   YES

• (5, -7) :

x = 5 and y = -7   ⇒   5 + 2•(-7) = -9 < -8   ⇒   MAYBE

x = 5 and y = -7   ⇒   2•5 + (-7) = 3 < -8   ⇒   NO

4. x is the number of candy boxes with chocolates and y is the number of boxes without chocolates. Each of the x boxes cost $27.50, so if you have x boxes, their total cost is $27.5x. Each of the y boxes cost $25.00, so y boxes cost $25y. The sponsor doesn't want to order more than 100 boxes total, so

x + y < 100

but wants to raise at least $2000, so

27.5x + 25y ≤ 2000

Now do the same thing as before; plug in the listed x- and y-coordinates and pick the point that satisfies both inequalities. You will find that (50, 30) is the correct choice.

5. Consult the "overkill" part of problem 3. The line y = -3x + 6 has a negative slope, so it's the downward sloping one. Check if the origin satisfies the inequality:

x = 0 and y = 0   ⇒   0 ≤ -3•0 + 6   ⇒   0 ≤ 6   ⇒   YES

This means Regions II and III solve the first inequality.

Do the same with the other inequality:

x = 0 and y = 0   ⇒   0 ≥ 1/2•0 + 1   ⇒   0 ≥ 1   ⇒   NO

This tells us that Regions I and II solve the second inequality.

The intersection of these regions is of course Region II.

6. One of the plotted lines is apparently y = x + 4, which has a positive slope, so this must be the upper line. The shaded region below it corresponds to the solution of either y < x + 4 or y ≤ x + 4 and we eliminate B.

The other line has negative slope, which eliminates A and D since

3x - 4y = 20   ⇒   y = 3/4x - 5

has positive slope. This leaves D.

Answer:yes

Step-by-step explanation:

Answer:

5,000 is the correct answer

Answer:

the correct answer is D.

Step-by-step explanation:

d is the set of all rational numbers where (0 ≤ d ≤ depth of seafloor).

i just took the test on math nation and got it correct.

hope this helped! :)

Answer:

1/6

Step-by-step explanation:

6 = 6/1

Therefore, reciprocal= 1/6

Answer:

1/6

Step-by-step explanation:

Answer:

Last 3 digits 712 is divisible by 8 so 36712 is divisible by 8

Step-by-step explanation:

Step-by-step explanation:

there are 50 students and 5 prizes (1 + 1 + 3).

so, already in natural language we would say "there is 1 prize for every 10 students".

formally, remember the rule of probability : desired outcomes over total possible outcomes.

this is here

5/50 = 1/10 = 0.1

your can see it also this way :

if there was only 1 prize, each student would have a chance of 1/50 of winning.

now there are 5 prizes, which gives everybody 5 times the chance of winning. which is then 5×1/50 = 5/50 = 0.1

Answer:

x> 2

Step-by-step explanation:

Multiply by 6

2x6=12

5x+2>12

Move the 2 and make it subtraction

5x>12-2

Subtract 12-2=10

5x>10 divide by 5

X>2

Answer:

If ABC and XYZ are two similar triangles, then by the help of below-given formulas, we can find the relevant angles and side lengths. ∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z AB/XY = BC/YZ = AC/XZ

Answer:

-10

Step-by-step explanation:

Answer:

-10

Step-by-step explanation:

(3+(-7))+(-6)

=3-7+-6

=3-7-6=-10

Using the binomial distribution, it is found that there is a 0.011 = 1.1% probability that exactly one of their four children will have that trait.

For each children, there are only two possible outcomes, either they have the trait, or they do not. The probability of a children having the trait is independent of any other children, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X=x)=C_{n,x.}p^x.(1-p)^{n-x}[/tex]

[tex]C_{n,x}=\frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability is P(X = 1), hence:

[tex]P(X=x)=C_{n,x.}p^x.(1-p)^{n-x}[/tex]

[tex]P(X=1)=C_{4,1*}(0.85)^1.(0.15)^3=0.011[/tex]

0.011 = 1.1% probability that exactly one of their four children will have that trait.

A similar problem is given at https://brainly.com/question/24863377

Answer:

It's equal to itself. Here are the two ways to do this problem. ↓

Answer:

0.000299 in scientific notation

2.99 × 10-4

Step-by-step explanation:

To convert 0.000299 into scientific notation also known as standard form, follow these steps:

Move the decimal 4 times to right in the number so that the resulting number, m = 2.99, is greater than or equal to 1 but less than 10

Since we moved the decimal to the right the exponent n is negative

n = -4

Write in the scientific notation form, m × 10n

= 2.99 × 10-4

Answer:

0.000299

2.99 × 10^-4.

Step-by-step explanation:

Answer:

417.831823 [tex]in^{2}[/tex]

Step-by-step explanation:

surface area of cone ;

[tex]=\pi r^{2}+\pi rl\\ =\pi (7^{2}) +\pi (7)(12)=417.831823 in^{2}[/tex]

Answer:417.831823

Step-by-step explanation:

Answer:

[tex]y = \frac{x}{4} [/tex]

Step-by-step explanation:

we find the slope which also represented as m by the formula

[tex] m = \frac{(y2 - y1)}{(x2 - x1)} [/tex]

where from point (-4, -2) the x1 is -4 and the y1 is -2 and also from point (6, 3) the x2 is 6 and the y2 is 3.

so we substitute

[tex] \frac{(3 - ( - 2))}{(6 - ( - 4))} = \frac{(3 + 2)}{(6 + 4)} = \frac{5}{10} = \frac{1}{2} [/tex]

[tex]m = \frac{1}{2} [/tex]

after we have the slope, we calculate the equation of the line by using the formula

[tex](y - y1) = m(x - x1)[/tex]

but for now, we only have y1, m and x1 so can substitute

[tex](y - ( - 2)) = \frac{1}{2} (x - ( - 4))[/tex]

we have to get rid of the fraction 1/2 so we multiply it through by the denominator 2

[tex]2(y + 2) = 2 \times \frac{1}{2}(x + 4) [/tex]

we get

[tex]2(y + 2) = 1 \times (x + 4)[/tex]

so now we expand the brackets

[tex]2y + 4 = x + 4[/tex]

we make y stand alone by grouping liked terms.

[tex]2y = x + 4 - 4[/tex]

we get

[tex]y = \frac{x}{4} [/tex]

Answer:The probability that a couple will havenbaby boys in a row is given by the formula2Find the probability that a couple will have Sbaby boys in a row.

The probability that a couple will havenbaby boys in a row is given by the formula2Find the probability that a couple will have Sbaby boys in a row.

Step-by-step explanation:The probability that a couple will havenbaby boys in a row is given by the formula2Find the probability that a couple will have Sbaby boys in a row.

is your correct answer

Sawyer is 9 yrs old and his sister is 3 yrs old

hope it really helps...

Answer:

x^2 + x -20

Step-by-step explanation:

First, Multiply

(x)(x) + (x)(5) + (-4)(5) + (-4)(x)

Second, Add The Like Terms Together

X^2 + x + -20

Answer: Its  x^2 + 9x -20

Step-by-step explanation:

I did the test and got it wrong

4x + 8 > -x - 7

4x + x > - 7 - 8

5 x > - 15

x > -3

x > -3

4x + 8 > -x - 7

4x + x > -7 - 8

5x > -15

5x ÷ 5 > -15 ÷ 5

x > -3

☆...hope this helps...☆

Answer:

A) 29/8

Step-by-step explanation:

Identify the blocks. As you can see there are 5 x blocks on the left, and 9 -1 blocks on the left. On the right there are 3 -x blocks and 20 1 blocks. With this, form the equation.

5x - 9 = -3x + 20

Add 3x to both sides.

8x - 9 = 20

Add 9 to both sides.

8x = 29

Divide both sides by 28 to get:

x = 29/8.

Step-by-step explanation:

9.51 x 10^3    *    8.57 x 10^4    = ~~ 10000 * 90000 = 900, 000,000    est

Question was changed.....so answer was edited

Answer:

A=bxh

171 cm=18cmxh

h=171/18

= 9.5 cm

which is B no.