A bus traveled 40 miles during the second hour of a trip. This was 1/3 more than the distance traveled during the first hour. In the third hour the bus traveled a distance that was 1/4 more than in the second hour. What was the total distance that the bus traveled in 3 hours

[tex](-a+3)(a+4)=-a^2-a+12[/tex].

Hope this helps.

Answer:

-a²-a+12

Step-by-step explanation:

-a²+3a-4a+12

-a²-a+12

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex]

Required

Why is the function not continuous at x = 3

First substitute 3 for x at the denominator

[tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex]

Factorize the numerator and the denominator

[tex]f(x) = \frac{x^2 - 3x+2x -6}{x^2 - 3^2}[/tex]

[tex]f(x) = \frac{x(x - 3)+2(x -3)}{(x - 3)(x+3)}[/tex]

[tex]f(x) = \frac{(x+2)(x - 3)}{(x - 3)(x+3)}[/tex]

Divide the numerator and denominator by (x - 3)

[tex]f(x) = \frac{x+2}{x+3}[/tex]

Substitute 3 for x

[tex]f(3) = \frac{3+2}{3+3}[/tex]

[tex]f(3) = \frac{5}{6}[/tex]

Because [tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex] is defined when x = 3;

Then the function is continuous

Answer:

A: f is not defined at x = -3

Step-by-step explanation: EDGE 2020

Answer:

A square.

Step-by-step explanation:

Answer:

shape AREA= 35cm^2

Step-by-step explanation:

you should know that this shape is a combination of triangle and trapezoid. therefore you have to find the area of each shape and add them.

A=h/2(b1 + b2) for trapezoid

A=2/2((4+4)+4)

A=1*12

A=12cm^2

A=bh/2. for TRIANGLE

A=1/2((4+4)*5.75)

A=1/2(46)

A=23cm^2

shape AREA= triangle AREA + trapezoid AREA

shape AREA=12cm^2 + 23cm^2

shape AREA= 35cm^2

Answer:

[tex]\large \boxed{87.5 \, \%}[/tex]

Step-by-step explanation:

            Let x = the original number of books

Then 0.375x = the total number of biographies

 and 0.20  x = the original number of biographies

[tex]\text{Percent increase} = \dfrac{\text{ New number - Old number }}{\text{Old number }} \times 100\, \%\\\\= \dfrac{0.375x - 0.20x}{0.20x} \times 100\, \% = \dfrac{0.175x}{0.20x} \times 100\, \% = 0.875 \times 100\, \% = \mathbf{87.5 \, \%}\\\\\text{The number of biographies has increased by $\large \boxed{\mathbf{87.5 \, \%}}$}[/tex]

Answer:

a=-5

Step-by-step explanation:

When you do this every time the slope will go down 2 and over 1 which is rise over run or slope. You can see the y coordinates go down 4 points and every time is should go down 2 so you will know that it would have gone down 2 times so a+2 should equal -3 so if we subtract 2 from both sides we would get a=-5 and that is our answer.

Answer:

a = - 5

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to - 2

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

with (x₁, y₁ ) = (- 3, - 1) and (x₂, y₂ ) = (a, 3)

m = [tex]\frac{3+1}{a+3}[/tex] = [tex]\frac{4}{a+3}[/tex] = - 2 ( multiply both sides by a + 3 )

- 2(a + 3) = 4 ( divide both sides by - 2 )

a + 3 = - 2 ( subtract 3 from both sides )

a = - 5

Answer:

144 units²

Step-by-step explanation:

Surface area of a traingular prism is given as:

Area = 2(B.A) + P*L

Where,

B.A = base area of the triangular prism = ½*b*h

b = base of the triangular base = 4 units

h = height of the triangular base = 3 units

Base Area (B.A) = ½*4*3 = 2*3 = 6 units²

P = Perimeter of triangular face = sum of all sides the triangle = 3 + 4 + 5 = 12 units

L = length or height of prism = 11 units

Plug in all values into the formula for surface area of triangular prism = 2(B.A) + P*L

[tex] Area = 2(6) + 12*11 [/tex]

[tex] = 12 + 132 [/tex]

[tex] Surface Area = 144 [/tex]

Surface area of the triangular prism = 144 units²

Answer:

(A) No solution

(B) One solution

(C) One solution

(D) One solution

(E) No solution

Please tell me if this is incorrect. I hope this helps!

Answer:

  all real numbers

Step-by-step explanation:

There is nothing on the graph to indicate the function is undefined for any values of x. The domain is all real numbers.

Answer:

Domain is all real numbers.

Step-by-step explanation:

The domain of a quadratic function in standard form is always all real numbers, meaning you can substitute any real number for x.

Answer:

Andy's house to Billy's hometown 15 ways

Andy's house to Willie's hometown 2 ways.

Step-by-step explanation:

Andy's house to Billy's hometown there are 3 roads. There 5 road from billy's hometown to Willie's house . In total there will be 15 ways to travel which is calculated by 3 * 5. For traveling to Willie's hometown there will be two ways. There are two roads that are built to get to Willie's house.

Answer:

[tex]Domain: \{0,1,2,3,4,5,6\}[/tex]

Step-by-step explanation:

Given

[tex]m = 45 - 7.5b[/tex]

[tex]Values: \{0,1,2,3,4,5,6,7,8,9,10\}[/tex]

Required

Select all values that belongs to the domain of the given function

Analyzing the question;

The question says that the function, m represent the amount left after buying b number of books

This means that, after purchasing b books, I'm expected to have a certain m amount of dollars left with me;

This implies that the value of m can never be negative;

So, the domain of m are values of b such that [tex]m \geq 0[/tex]

When b = 0

[tex]m = 45 - 7.5(0)[/tex]

[tex]m = 45 - 0[/tex]

[tex]m = 45[/tex]

When b = 1

[tex]m = 45 - 7.5(1)[/tex]

[tex]m = 45 - 7.5[/tex]

[tex]m = 37.5[/tex]

When b = 2

[tex]m = 45 - 7.5(2)[/tex]

[tex]m = 45 - 15[/tex]

[tex]m = 30[/tex]

When b = 3

[tex]m = 45 - 7.5(3)[/tex]

[tex]m = 45 - 22.5[/tex]

[tex]m = 22.5[/tex]

When b = 4

[tex]m = 45 - 7.5(4)[/tex]

[tex]m = 45 - 30[/tex]

[tex]m = 15[/tex]

When b = 5

[tex]m = 45 - 7.5(5)[/tex]

[tex]m = 45 - 37.5[/tex]

[tex]m = 7.5[/tex]

When b = 6

[tex]m = 45 - 7.5(6)[/tex]

[tex]m = 45 - 45[/tex]

[tex]m = 0[/tex]

When b = 7

[tex]m = 45 - 7.5(7)[/tex]

[tex]m = 45 - 52.5[/tex]

[tex]m = -7.5[/tex]

There's no need to check for other values, as they will result in negative values of m;

Hence, the domain of m are:

[tex]Domain: \{0,1,2,3,4,5,6\}[/tex]

The values that are in the domain of the function are 7, 8, 9 and 10

Given the linear function  m=45−7.5b

where:

For th domain to exist, then;

45 - 7.5b< 0

7.5 b > 45

b > 45/7.5

b > 6

Hence the values that are in the domain of the function are 7, 8, 9 and 10

Learn more on domain here; https://brainly.com/question/10197594

Answer:

1and1/2yrs ago

Step-by-step explanation:

price dis year= 56545

reduction per year= 11309

...number of years ago = 73810-56545=17265

and is about 20% of annual deductions

so if 56545 +20% + 1/2 20% = 1nd1/2 yrs

Answer:

32 remainder 2

Step-by-step explanation:

To divide 162 by 5, we simply do the following:

5 goes into 16 => 3

Multiply 5 by 3 => 3 × 5 = 15

Subtract 15 from 16 => 16 – 15 = 1

Put the 1 before 2 => 12

5 goes into 12 => 2

Multiply 5 by 2 => 5 × 2 = 10

Subtract 10 from 12 => 12 – 10 => 2

In summary,

162 divided by 5 => 32 remainder 2

Please see attached photo for further details.

Answer:

A

Step-by-step explanation:

Here in this question, we want to select which of the options particularly represents what was given in the question.

Mathematically 10^4 means that we are raising 10 into a continued exponential raising up to 4 times.

So 10^4 is pronounced as the first option in the question.

10 raised to power 10 , raised to power 10 etc

Answer:

its harddd

Step-by-step explanation:

rightttttttt

Answer:

1) true

2) false

hope it worked

and pls mark me as BRAINLIEST

Answer:

First blank: Commutative

Second blank: Associative

Third blank: Same

Fourth blank and fifth blank: Rearranging them? (Not entirely sure)

Hope this helps :)

Answer:

A 95% confidence interval for the population average debt load of graduating students with a bachelor's degree is [$17,022.05, $20,577.94].

Step-by-step explanation:

We are given that a random sample of 28 students had an average debt load of $18,800. It is believed that the population standard deviation for student debt load is $4800. The α is set to 0.05.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample average debt load = $18,800

            [tex]\sigma[/tex] = population standard deviation = $4,800

            n = sample of students = 28

            [tex]\mu[/tex] = population average debt load

Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 5% level of

                                                      significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]

                        = [ [tex]\$18,800-1.96 \times {\frac{\$4,800}{\sqrt{28} } }[/tex] , [tex]\$18,800+1.96 \times {\frac{\$4,800}{\sqrt{28} } }[/tex] ]

                        = [$17,022.05, $20,577.94]

Therefore, a 95% confidence interval for the population average debt load of graduating students with a bachelor's degree is [$17,022.05, $20,577.94].

C. A line has one dimension, length.

E. A plane consists of an infinite set of lines.

Answer:

  -5x = 8

Step-by-step explanation:

The result is shown here. The y-terms cancel.

  [tex]\begin{array}{rccc}& -2x+7y &= &10 \\-&(\ \,3x+7y &= &2)\\\cline{1-4}&-5x+0y&=&8 \end{array}[/tex]

The simplified result is ...

  -5x = 8

Answer:

The result is that 5x = -8

Step-by-step explanation:

Here, we want to subtract 3x + 7y = 2 from -2x + 7y = 10

Mathematically that would be;

(-2x+7y)-(3x+7y) = 10-2

-2x + 7y -3x -7y = 8

-2x -3x + 0 = 8

-5x = 8 or 5x = -8

Answer:

4x^2 + 8x + 4

4(x^2 + 2x + 1) - remove GCF of 4

4(x + 1)(x + 1) - factor

4(x + 1)^2 - collect like terms

Step-by-step explanation:

Then also expand it out by distributing:

21x^3 + 35x²

Form 1:

21x^3 + 35x² - unfactored

Form 2:

7x²(3x + 5) - factored with GCF of 7x² brought to the front

Update:

You could also multiply two binomials and make a quadratic.

Example:

(7x + 2)(3x + 5)

7x(3x + 5) + 2(3x + 5)

= 21x² + 35x + 6x + 10

= 21x² + 41x + 10

The favorable polynomial with a GCF of 3x will be 21x² + 41x + 10.

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

The polynomial will be solved as below:-

21x³ + 35x²

Form 1:

21x³ + 35x² - unfactored

Form 2:

7x²(3x + 5) - factored with GCF of 7x² brought to the front

You could also multiply two binomials and make a quadratic.

E = (7x + 2)(3x + 5)

E = 7x(3x + 5) + 2(3x + 5)

E = 21x² + 35x + 6x + 10

E = 21x² + 41x + 10

To know more about polynomials follow

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Answer:

6 km

Step-by-step explanation:

Let us assume the following items

the Point at Train depot = T

The Point at Main gate =  M

The Point at Bird sanctuary =  B

The Point at Elephant house = E

The Point at manatee Springs =  S

As we can see that there are two triangles namely TMB and TSE.

Mentioned that

MTB = ∠STE

∠TMB = ∠TSE

∠TBM = ∠TES.

According to the Angle-angle-angle (AAA similarity)

So, the triangles TMB and TSE are the same.

[tex]\frac{TM}{TS} = \frac{TB}{TE} \\\\ \frac{TM}{4,200} = \frac{2,000}{3,500}[/tex]

So, the TM is 2400 yds

Now the Distance between Main gate M and manatee Spring S is

MS = MT + TS

= 2,400 + 4200

= 6600 yds

Now the MS is

= 6600 × 0.0009144 km

= 6.035 km

≅ 6 km

Answer:

1.1460277. Put in your decimal place given to you.

This is the percentage rate.

Step-by-step explanation:

f(x)=0=60100

55=120150

60100=a*b^0

120150/60100=60100/60100*b^5

b^5^(1/5)=5square root(120150/60100)=1.14860277

answer

-6r+-11=-37

-6r=-37+11

-6r=-48

r=8

Answer:

E: all real numbers

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

We can use the distance formula

d = sqrt (   ( y2-y1)^2 + ( x2-x1) ^2)

d = sqrt (   ( 4- -3)^2 + ( -4 -2) ^2)

   = sqrt (  ( 7^2  + ( -6)^2)

   = sqrt( 49+ 36)

   = sqrt(85)

      9.219544457

Rounding to the nearest whole number

 = 9

Answer:

x=-5

Step-by-step explanation:

The answer is x = -5. The explanation and answer is in the image below.

Answer:

Step-by-step explanation:

let the plane intersects the join of points in the ratio k:1

let (x,y,z) be the point of intersection.

[tex]x=\frac{3k+2}{k+1} \\y=\frac{5k+4}{k+1} \\z=\frac{-4k+16}{k+1} \\\because ~(x,y,z)~lies~on~the~plane.\\2(\frac{3k+2}{k+1} )-3(\frac{5k+4}{k+1} )+\frac{-4k+16}{k+1} +6=0\\multiply~by~k+1\\2(3k+2)-3(5k+4)+(-4k+16)+6(k+1)=0\\6k+4-15k-12-4k+16+6k+6=0\\-7k+14=0\\k=2\\x=\frac{3*2+2}{2+1} =\frac{8}{3} \\y=\frac{5*2+4}{2+1}= \frac{14}{3} \\z=\frac{-4*2+16}{2+1} =\frac{8}{3}[/tex]

point of intersection is (8/3,14/3,8/3)

and ratio of division is 2:1

Answer:

x = 60

Step-by-step explanation:

In a circle, the sum of the angles that meet at a point is 360 degrees. So now that we have the total, we can subtract all the given information in the picture. We have 84, 75, 68, and x + 73. Now let us set up and equation for this problem.

360 = 84 + 75 + 68 + x + 73

Now combine like terms.

360 = x + 300

Now subtract 300 on both sides.

x = 60

And this is the value of x.

Answer:

50 degrees

Step-by-step explanation:

84 + 75 + 68 = 227

227 - 360 = 133

133 - 73 = 50

The answer is 50 degrees.