A particle is moving on the x-axis. Its position is given by x = 2t^2 - 12t + 4 for times t ≥ 0

Answer: There is no x-intercept for this quadratic equation.

Step-by-step explanation:

An x-intercept is when the y-value of the point if equal to zero. There is no x-intercept for this quadratic equation. This can be supported by the fact that this equation cannot be factored.

Answer:

-1 and -8

Step-by-step explanation:

x^2+2*9/2*x+(9/2)^2-(9/2)^2+8=0

(x+9/2)^2+32/4-81/4=0

(x+9/2)^2-49/4=0

(x+9/2)^2=(7/2)^2

so

x+9/2=7/2

x=7/2-9/2

x=-2/2

x=-1

or

x+9/2=-7/2

x=-7/2-9/2=-16/2

x=-8

Answer:

n = 3

Step-by-step explanation:

Hello!

p = 2n - 3

the question asks for when p is equal to 3 so we put 3 in for p

3 = 2n - 3

Now we can solve this

3 = 2n - 3

Add 3 to both sides

6 = 2n

Divide both sides by 2

3 = n

The answer is n = 3

Hope this Helps!

Answer:

[tex]\displaystyle \int\limits^5_1 {(x^2 - x + 1)} \, dx = \frac{100}{3}[/tex]

General Formulas and Concepts:

Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^5_1 {(x^2 - x + 1)} \, dx[/tex]

Step 2: Integrate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer: 5\int_0^5 3^(3)\sqrt(x^(2)) dx

Step-by-step explanation:

Answer:

see below (I hope this helps!)

Step-by-step explanation:

When n < 1, Declan's statement is incorrect because 4 * 0 = 0 which is not greater than 4 and this continues for all n values that are less than 1.

Answer:

1/273

Step-by-step explanation:

5/15 * 4/14 * 3/13 * 2/12

= 1/3 * 2/7 * 3/13 * 1/6

= 1/273

Answer:

ŷ = 6.69X - 706.18 ; ŷ = 270.56 ; B. The predicted value is not close to the actual diastolic reading.

Step-by-step explanation:

Systolic reading(x) :

117

134

150

113

138

113

144

145

Diastolic (y) :

85

74

86

55

75

80

106

841

Using the online regression calculator, the regression equation obtained using the data values provided above is:

ŷ = 6.69X - 706.18

Comparing with the regression equation formula: ŷ = mX + c

Where :

ŷ = predicted variable (Diastolic)

m = 6.69 = gradient or slope of the regression line

c = - 706.18 = intercept ( where the regression line intersects the y-axis).

2.) What is the best predicted diastolic pressure for a person with a systolic reading of 146

X = 146

ŷ = 6.69(146) - 706.18

ŷ = 976.74 - 706.18

ŷ = 270.56

The predicted value, 270.56 is not close to the actual Diastolic reading of 91.0

Answer:

(B) [tex]b + 2b - 83 = 259[/tex]

Step-by-step explanation:

We can first create the equation [tex]b + g = 259[/tex], since we know that there are a total of 259 students in this freshman class.

Now, the amount of girls is 83 less than twice the number of boys, so that is [tex]2b - 83[/tex].

Now, we can substitute this in the previous equation as g.

[tex]b + 2b - 83 = 259[/tex]

Hope this helped!

Answer:

b

Step-by-step explanation:

Step-by-step explanation:

Hey, there!!

I hope you mean to subtract (-137) +(-43) from sum of -103 and 27.

First, add -103 + 27

[tex] = - 103 + 27[/tex]

[tex] = - 76[/tex]

{As ( minus + plus )= subtracts with sign which has greator value. }

now,

[tex]( - 137) + ( - 43) = - 180[/tex]

{ minus + minus = add with minus sign}.

Now, subtracting -180 from -76.

=(-76) - (-180 )

Now, multiply the sign (- × -)= +

so, -180 becomes +180

= -76+180

= 104..... is answer.

Hope it helps...

Answer:

104

Step-by-step explanation:

With what you provide, the expression would be:

[tex](-103+27)-(-137+-43)[/tex], which equals to:

[tex](-76)-(-180)= (-76)+(180)=104[/tex].      [negative minus a negative equals positive]

So, the answer would be 104.

Answer:

  1 foot

Step-by-step explanation:

Using the formula for the area of a triangle, fill in the given information and solve for the unknown.

  A = (1/2)bh

  0.75 = (1/2)b(1.5)

  b = 0.75/0.75 = 1 . . . . divide by the coefficient of b

The base is 1 foot.

Answer:

B-$100=$372

The is is the smartest way I could look at this

OR

$372 - $100= b

Hope this helps

MARNIE OUT!

Answer:

40

Step-by-step explanation:

First we need to subtract the 50 students enrolled in English class.

150 - 50 = 100

Next, let's add the mathematics students and the physics students.

80 + 60 = 140

Then we subtract the total amount of mathematics and physics students by the total number of students.

140 - 100 = 40

Therefore, there are 40 students who take both mathematics and physics.

Step-by-step explanation:

Hello!

For this you multiply the numbers that intersect at that box

Box A 2x and 4 intersect

2x * 4 = 8x

Box B 3 and 4 intersect

3 * 4 = 12

Box C 2x and x intersect

2x * x = [tex]2x^{2}[/tex]

Box D 3 and x intersect

3 * x = 3x

To solve this we put all these together

[tex]2x^{2} +3x+8x+12[/tex]

Combine like terms

[tex]2x^{2} +11x+12[/tex]

Hope this helps!

Answer:

(D) 2

Step-by-step explanation:

If two or more vectors are linearly dependent, then one of them can be expressed as a linear combination of the rest. In other words, vectors are dependent linearly on one another if the determinant of the matrix that they form is zero.

Given vectors:

i+j+2k

i+pj+5k

5i+3j+4k

Now, since they are linearly dependent, then the determinant of their matrix should be zero. i.e

Let their matrix be A and is given by;

A =   [tex]\left[\begin{array}{ccc}1&1&2\\1&p&5\\5&3&4\end{array}\right][/tex]

Where;

the first column holds the i components of the vectors

the second column holds the j components of the vectors and

the third column holds the k components of the vectors

=> |A| = det(A) = 0

 [tex]det(A) = det \left[\begin{array}{ccc}1&1&2\\1&p&5\\5&3&4\end{array}\right] = 0[/tex]

Now, let's calculate the determinant.

[tex]det \left[\begin{array}{ccc}1&1&2\\1&p&5\\5&3&4\end{array}\right] = 1(4p - 15) - 1(4 - 25) + 2(3 - 5p) = 0[/tex]

=> 4p -15 - 4 + 25 + 6 - 10p = 0

=> 4p - 10p + 12 = 0

=> 6p = 12

=> p = 2

Therefore, the value of p for which the vectors are linearly dependent is 2

Step-by-step explanation:

first you group like terms.

-3s-s+8+1-2

-4s+7

Answer:

-4s + 7

Step-by-step explanation:

We need to combine like terms. Like terms are terms whose variables (and exponents) are the same (note that they could be constants as well). Basically, they are "like" each other. In this case, the like terms are -3s and - s and also 1, 8, and -2. -3s - s = -4s and 1 + 8 - 2 = 7 so the answer is -4s + 7.

Answer:

Derek needs to add 3/4 cups of flour.

Step-by-step explanation:

If Derek has already used 1/4 cup of flour, he needs 3 more cups of flour to get to 1 full cup of flour.

Answer:

Step-by-step explanation:A batch of cookies requires 2 1/4 cup of flour and 1 egg. You have in your kitchen 8 cups of flour and a half dozen eggs. a) How many batches of cookies

Answer:

9.31

Step-by-step explanation:

Given the following :

- - - - - - - - - - df - - - - - SS - - - MS - - - F - - - signiF

Regression - 1 - 13555.42 - 13555.41 - 156.38 - 0

Residual - - 8.00 - 693.48 - - 86.68

Total - - - - 9.00 - 14248.90

What is the value of the standard error of estimate?

The standard error estimate :

Mean square error or Residual (MSE)

Standard Error (SE): √MSE

MSE = 86.68

Standard Error = √86.68

Standard error = 9.3102094

= 9.31

Answer:

y= -5/3x + 8

Step-by-step explanation:

parallel lines have the same slope

5x + 3y = 6

3y = -5x + 6

y = -5/3x + 2

the new line will have the slope (-5/3x)

y = (-5/3x) + b

plug in the (x, y) value to find b

-2 = -5/3(6) + b

-2 = -10 + b

b = 8

your equation is: y= -5/3x + 8

Answer:

|w - v| or |v - w|

Step-by-step explanation:

The answer is the absolute value of the difference of the two numbers written in either order.

|w - v| or |v - w|

Answer:

B |w-v|

Step-by-step explanation:

khan academy

Answer:

B

Step-by-step explanation:

So we have a 45-45-90 triangle.

This is a special right triangle. In a 45-45-90 triangle, the side lengths are x, and the hypotenuse will be x√2

Since the hypotenuse is 3, we can set it equal to x√2 to solve for x. Therefore:

[tex]x\sqrt2=3[/tex]

Divide both sides by √2:

[tex]x=\frac{3}{\sqrt2}[/tex]

Rationalize:

[tex]x=\frac{3\sqrt2}{2}[/tex]

Our answer is B.

Answer:

Step-by-step explanation:balls

Answer:

16Km due east of school P

Step-by-step explanation:

Given

A school P is 16km due west of a school Q

Thus, we can say that distance PQ = 16 km.

________________________________

now we have to find  the bearing of Q from P​

As distance is same

distance PQ = distance QP

Thus,

Distance will remain same of 16 km.

For direction,

If Q is west of P, then P will be east of Q[tex]P------------------>Q[/tex]

as shown in figure P is west of Q,

now from point P , Q is west P.

Thus,

Bearing of  School Q from P is 16Km due east of school P

Answer:

[tex]\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\[/tex]

Step-by-step explanation:

Given A = 5i + 11j – 2k and B = 4i + 7k​, the vector projection of B unto a is expressed as [tex]proj_ab = \dfrac{b.a}{||a||^2} * a[/tex]

b.a = (5i + 11j – 2k)*( 4i + 0j + 7k)

note that i.i = j.j = k.k  =1

b.a = 5(4)+11(0)-2(7)

b.a = 20-14

b.a = 6

||a|| = √5²+11²+(-2)²

||a|| = √25+121+4

||a|| = √130

square both sides

||a||² = (√130)

||a||²  = 130

[tex]proj_ab = \dfrac{6}{130} * (5i+11j-2k)\\\\proj_ab = \frac{30}{130} i+\frac{11}{130} j-\frac{12}{130} k\\\\proj_ab = \frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\\\[/tex]

Hence the projection of b unto a is expressed as [tex]\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\[/tex]

Answer:

3. C

Step-by-step explanation:

16 / 4 = 4 which is a counting number.

- 30 / 5 = -6 which is a integer.

-31/8 = -3.875 which is rational number

30/9 = 10/3 = 3.333333333.... which is an irrational number

So your answer is C

Answer:The answer is C

Step-by-step explanation:

I just had the question and i got it right :D

Answer:

The  probability is  [tex]P(14 < X < 20 ) = 0.5354[/tex]  

Step-by-step explanation:

From the question we are told that

   The  proportion that live with their parents is  [tex]\r p = 0.142[/tex]

   The  sample  size is n =  125

Given that there are two possible outcomes and that this outcomes are independent of each other then we can say the Recent census data follows a Binomial distribution

  i.e  

       [tex]X \ \~ \ B( \mu , \sigma )[/tex]

Now the mean is evaluated as

      [tex]\mu = n * \r p[/tex]

      [tex]\mu = 125 * 0.142[/tex]

      [tex]\mu = 17.75[/tex]

Generally the proportion that are not staying with parents is  

      [tex]\r q = 1 - \r p[/tex]

= >    [tex]\r q = 0.858[/tex]

The standard deviation is mathematically evaluated as

     [tex]\sigma = \sqrt{n * \r p * \r q }[/tex]

     [tex]\sigma = \sqrt{ 125 * 0.142 * 0.858 }[/tex]

    [tex]\sigma = 3.90[/tex]

Given the n is large  then we can use normal approximation to evaluate the probability as follows  

     [tex]P(14 < X < 20 ) = P( \frac{ 14 - 17.75}{3.90} <\frac{ X - \mu }{\sigma } < \frac{ 20 - 17.75}{3.90} )[/tex]

Now applying continuity correction

      [tex]P(14 < X < 20 ) = P( \frac{ 13.5 - 17.75}{3.90} < \frac{ X - \mu }{\sigma } < \frac{ 19.5 - 17.75}{3.90} )[/tex]

Generally  

    [tex]\frac{ X - \mu }{\sigma } = Z ( The \ standardized \ value \ of X )[/tex]

    [tex]P(14 < X < 20 ) = P( \frac{ 13.5 - 17.75}{3.90} < Z< \frac{ 19.5 - 17.75}{3.90} )[/tex]

     [tex]P(14 < X < 20 ) = P( -1.0897 < Z< 0.449 } )[/tex]

    [tex]P(14 < X < 20 ) = P( Z< 0.449 ) - P(Z < -1.0897)[/tex]

So  for the z -  table  

         [tex]P( Z< 0.449 ) = 0.67328[/tex]

         [tex]P(Z < -1.0897) = 0.13792[/tex]

 [tex]P(14 < X < 20 ) = 0.67328 - 0.13792[/tex]    

  [tex]P(14 < X < 20 ) = 0.5354[/tex]  

Hiroshi is correct; after you draw

the line from the first point to the other three, one of

the lines from the second point is already drawn.

Answer:

296.5 miles

Step-by-step explanation:

Round trip distance of City X to City Y is 647 miles.

Round trip includes to and fro.

i.e. City X to City Y and then City Y to City X back.

Let the distance between City X and City Y = D

Distance traveled in round trip between City X and City Y = D + D = 2D

Given than 2D = 647

OR

D = [tex]\frac{647}2[/tex] = 323.5 miles

Kindly refer to the attached diagram, for the location of City Z.

Distance between XY = Distance from X to Z + Distance from Z to Y.

Distance XY = XZ +ZY

323.5 = 27 +ZY

ZY =296.5 miles

Answer: B.) 1 and 111 only.

Step-by-step explanation:

75% = 75/100 = 0.75

0.75 falls into the category of rational numbers. Rational numbers comprises of numbers which can be expressed in the form a/b where a and b are integers and B is not 0. Here, both 75 and 100 are integers, thus 75% is a rational number.

Irrational numbers are the opposite of rational numbers thus, 75% is not irrational.

All rational numbers and irrational numbers are REAL numbers, hence, 75% is a real number.

Natural numbers are whole digits starting from 1 e.g ( 1, 2, 3,......). Hence 75% is not a natural number

Whole numbers are natural numbers including 0. (0, 1, 2,.....). Hence, 75% is not a whole number

Integer numbers are comprises of both positive and negative whole numbers. (..., - 1, - 2, 0, 1, 2,...). Hence, 75% is not an integer.

Answer:

8.25

Step-by-step explanation:

[tex]\frac{8r^2 - 14 r + 3}{r+5} = 4r -1[/tex]

[tex]8r^2 - 14r + 3= (4r -1)(r + 5)[/tex]

[tex]8r^2 - 14r + 3= 4 {r}^{2} + 19r - 5[/tex]

[tex]4 {r}^{2} - 33r + 8=0[/tex]

[tex]4 {r}^{2} - 32r - r + 8 = 0[/tex]

[tex]4r(r - 8) - 1(r - 8) = 0[/tex]

[tex](4r - 1)(r - 8)[/tex]

[tex]r = 8 \: or \: \frac{1}{4} [/tex]

Therefore the sum of all values of r

[tex]8 + \frac{1}{4} = 8 \frac{1}{4} [/tex]