Latoya drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 6 hours. When Latoya drove home, there was no traffic and the trip only took 4 hours. If her average rate was 22 miles per hour faster on the trip home, how far away does Latoya live from the mountains

Answer:

Step-by-step explanation:

( x² + 3 ) ( x³ - x² + 4 )

Multiply the second parentheses by each term from the first parentheses

x² ( x³ - x² + 4 ) + 3 ( x³ - x² + 4 )

Distribute x through the parentheses

x⁵ - x⁴ + 4x² + 3 ( x³ - x² + 4 )

Distribute 3 through the parentheses

x⁵ - x⁴ + 4x² + 3x³ - 3x² + 12

Collect like terms

x⁵ - x⁴ + x² + 3x³ + 12

Use the commutative property to reorder the terms

x⁵ - x⁴ + 3x³ + x² + 12

Hope this helps..

Best regards!!

Answer:

x^5-x^4+3x^3+x^2+12

Step-by-step explanation:

Mulitply each term:

x^5-x^4+4x^2+3x^3-3x^2+12

Now simplify.

x^5-x^4+3x^3+x^2+12

I hope this helps....

Please mark me brainliest!!

Let d equal the final amount it depreciates.

Let m equal the number of months.

Since d is the final amount, we put this at the very end of the equation.

Since it depreciates $25 every month, this number is going to be subtracted from the total price of the tablet ($650).

The final equation comes out too: d = 650 - 25m

Best of Luck!

Answer:

Hamish's earning = $20

Harry's earning = $26

Step-by-step explanation:

Given the following :

Let Harry's earning per hour = x

Let Hamish earning per hour = y

Harry earns a dollar more than more than 5/4 the amount hamish earns per hour;

Therefore,

x = 5/4y + 1

x - 5/4y = 1 - - - - (1)

the amount Harry earns per hour is $2 less than 7/5 the amount Hamish earns per hour

x = 7/5y - 2 - - - - (2)

Substituting (2) into (1)

7/5y - 2 - 5/4y = 1

7/5y - 5/4y = 1 + 2

7/5y - 5/4y = 3

Taking the L. C. M

(28y - 25y) / 20 = 3

28y - 25y = 60

3y = 60

y = 20

Substitute y = 20 into (1)

x - 5/4(20) = 1

x - 100/4 = 1

x - 25 = 1

x = 1 + 25

x = 26

y = Hamish's earning = $20

x = Harry's earning = $26

Answer:

Hey there!

Angles in a quadrilateral add to 360 degrees, so we have 56+78+90+x=360

Solving, we see that the missing angle, x, is 136 degrees.

Hope this helps :)

Answer:

Hey.... Ans is 154°

The mate who ans before me HAVE TO FIND x TOO

Step-by-step explanation:

For example take a quadrilateral ABCD (refer to the pic)

Then solution is...

In quadrilateral ABCD

            Sum of all sides of a quadrilateral= 360°

           =angle A + angle B+ angle C+ angle D=

Given,

          Angle A= 56° + angle B=78° + angle C=90° + angle D=x

        =56° + 78° + 90° + x.            (add all the numbers)

         x+226=360°                           (56+78+90=226)

         x=360° - 226°

         x=154°

Therefore the largest angle = x = 154°

Hope it helped u!!

The correct answer is C) The initial population at the time of the estimation

Explanation:

A mathematical function represents the relationship between two variables by showing how one increases or decreases as the other changes. In the case presented, the variables are the time in years represented by x and the population represented by f (x). In this context, the value 160.000 in column f(x) represents the population on the year 0, this means the current population or initial population when the function or estimation is created. On the other hand, other values represent the population in the future, for example, the value 173189 represents the population in 4 years.

Answer:

yes the 3ed answer in correct on ENG 2022

Answer:

1. Cash flow statements; the investing section

Step-by-step explanation:

The cash flow statements is a useful document that shows where the company receives funds and uses it. Thus, it shows both incoming and outgoing cash flow.

The investment section of the cash flow statement is where all the amount of cash paid for acquisitions of property and equipment is imputed. Usually the transactions are written as capital expenditure.

Answer:   y ≤ x² + 8x + 7  

Step-by-step explanation:

x ≤ -7     --> x + 7 ≤ 0

x ≥ -1      --> x + 1 ≥ 0

        y = (x + 7)(x + 1)

        y = x² + 8x + 7

        The quadratic is positive so it is U-shaped

        x ≤ -7    and    x ≥ -1    

       means the outside of the U-shaped parabola is shaded

        so we need to use the ≤ symbol

Note: if the inequality symbols were reversed, the shading would be inside the U-shaped parabola so we would use the ≥ symbol.

Answer:

Shape - Cube

Area= 864

Step-by-step explanation:

The shape folds to become a cube and all the edges are the same size.

Area of a cube is Length * Width * Height = Area

12*12*12= 864

Answer:

Shape - Cube

Area= 864

Step-by-step explanation:

The shape folds to become a cube and all the edges are the same size.

Area of a cube is Length * Width * Height = Area

12*12*12= 864

Answer: A) 2.95 units

Step-by-step explanation:

The diameter of a circle is twice the radius.  Thus, simply do 5.9/2 to get that the radius is 2.95 units long.

Hope it helps <3

Answer:

your answer would be A-2.95

5.9/2=2.95

Step-by-step explanation:

Answer: -1

Step-by-step explanation:

[tex]5t-3=3t-5[/tex]

Add 3 to both sides.

[tex]5t=3t-2[/tex]

Subtract 3t from both sides.

[tex]2t=-2[/tex]

[tex]t=-1[/tex]

Hope this helps!

Answer: t=-1

Step-by-step explanation:

1) add 3 to both sides

2) subtract 3t from both sides

3) Divide both sides by 2

Answer:

Slope = -6/7

Step-by-step explanation:

You need to use the formula m = y2 - y1 ÷ x2 - x1

The formula means: slope = the y coordinate of point 2 subtract the y coordinate of point 1, divided by the x coordinate of point 2 subtract the x coordinate of point 1

So,

m = 2 - 5 ÷ 3/2 - (-2)

m = -3 ÷ 7/2

m = -6/7

Hope this helps :)

Answer:

x = 1

Step-by-step explanation:

Using the rules of logarithms

log [tex]x^{n}[/tex] ⇔ n log x

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

3[tex]log_{2}[/tex] (2x) = 3

[tex]log_{2}[/tex] (2x)³ = 3

(2x)³ = 2³

8x³ = 8 ( divide both sides by 8 )

x³ = 1 ( take the cube root of both sides )

x = 1

Answer:

x=1 is the correct answer

Step-by-step explanation:

got it right on edge!!!!

Answer:

3, 8, 12, 12, 14, 20, 21, 23, 26, 34

stem         leaf

0               3     8

1                 2     2       4               (you have 12,12,14)

2                0      1       3        6    ( numbers 20,21,23,26)

3                 4                               ( number 34)

Answer:

10x1.4^6

Step-by-step explanation:

Answer:

The common difference = 2.

Step-by-step explanation:

An AP can be written as  a1,  a1 + d,  a1 + 2d,  a1 + 3d,  a1 + 4d,  a1 + 5d, a1 + 6d , a1 + 7d.    

 where a1 = first term and d is the common difference.

Here first term = a1 = 8

3rd term = a1 + 2d = 8 + 2d

5th term = a1 + 4d = 8 + 4d

8th term = 8 + 7d

First 3 terms of a GP are  a , ar and ar^2

So from the given information:

a = 8 + 2d

ar = 8 + 4d

ar^2= 8 + 7d

Dividing the second equation by the first  we have

r = (8 + 4d)/(8 + 2d)

Dividing the third by the second:

r = (8 + 7d) / (8 + 4d)

Therefore, eliminating r we have:

(8 + 4d)/(8 + 2d)  =   (8 + 7d)/(8 + 4d)

(8 + 4d)^2 = (8 + 2d)(8 + 7d)

64 + 64d + 16d^2 =  64 + 72d^ + 14d^2

2d^2 - 8d  = 0

2d(d^2 - 4) = 0

2d = 0 or d^2 = 4, so

d =  0, 2.

The common difference can't be zero so it must be 2.

Answer:

The Answer Is C The fist poster is the proper representation, because find the areas compare the paintings to the first poster it is 360 to 3240 which shows the poster is 9x bigger but compared to the second one it is out of proportion for the painting and first poster

Answer: 16 units

Step-by-step explanation:

Given that in triangle ABC, m∠C=90,

it means m∠A +∠B= m∠BAC + m∠ABC = 90

m∠ABC = 90 - m∠BAC

Also given that;m∠BAC = 2m∠ABC

So,

m∠BAC = 2(90 - m∠BAC) = 180 - 2m∠BAC

m∠BAC +2m∠BAC = 180

3m∠BAC = 180

m∠BAC=180/3 = 60

m∠ABC = 60/3 = 30

thus,ΔBAC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:BC=1:√3, AC=BC/√3BC=24, So,

AC=24/√3=8√3AL bisects angle A =>m∠LAC=30

ΔALC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:AL=√3:2AL=2AC/√3=2x8√3/√3=16

Answer:

Option A is the correct option.

Step-by-step explanation:

Let the points be A and B

A ( 2 , 2 ) ------> ( x1 , y1 )

B ( 3 , 5 ) -------> ( x2 , y2)

Now, let's find the mid-point :

Midpoint = [tex] (\frac{x1 + x2}{2} \:, \frac{y1 + y2}{2} )[/tex]

plug the values

[tex] = ( \frac{2 + 3}{2} \: , \frac{2 + 5}{2} )[/tex]

Calculate the sum

[tex] = \: ( \frac{5}{2} \:, \frac{7}{2} )[/tex]

Hope this helps..

Best regards!!

Answer:

74°

Step-by-step explanation:

A rhombus is a quadrilateral that has its opposite sides to be parallel to be each other. This means that the two interior opposite angles are equal to each other. Since the sum of the angles of a quadrilateral is 360°.

According to the triangle, since one of the acute angle is 32°, then the acute angle opposite to this angle will also be 32°.

The remaining angle of the rhombus will be calculated as thus;

= 360° - (32°+32°)

= 360° - 64°

= 296°

This means the other two opposite angles will have a sum total of 296°. Individual obtuse angle will be 296°/2 i.e 148°

This means that each obtuse angles of the rhombus will be 148°.

To get the unknown angle m°, we can see that the diagonal cuts the two obtuse angles equally, hence one of the obtuse angles will also be divided equally to get the unknown angle m°.

m° = 148°/2

m° = 74°

Hence the angle measure if m(1) is 74°

Answer: w=5

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

The midsegment ( median is equal to half the sum of the parallel bases, that is

[tex]\frac{AB+CD}{2}[/tex] = EF, substitute values

[tex]\frac{4x-10+3x+8}{2}[/tex] = 13 ( multiply both sides by 2

7x - 2 = 26 ( add 2 to both sides )

7x = 28 ( divide both sides by 7 )

x = 4

Answer:

i) Estimate the value of the population proportion = 0.8

ii) 95% confidence interval for the population proportion

(0.7214 , 0.8784)

iii)    Lower bound = 0.7214

     upper bound = 0.8784

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 100

Given data  he surveys 100 customers and finds that 80 paid at the pump

sample proportion

                     [tex]p = \frac{x}{n} = \frac{80}{100} = 0.8[/tex]

Step(ii):-

95% confidence interval for the population proportion is determined by

[tex](p^{-} - Z_{\alpha } \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{\alpha } \sqrt{\frac{p(1-p)}{n} })[/tex]

Level of significance  

∝ =0.05

Z₀.₀₅ = 1.96

[tex](0.8 - 1.96 \sqrt{\frac{0.8 X 0.2)}{100} } , 0.8 + 1.96 \sqrt{\frac{0.8 X 0.2}{100} })[/tex]

On calculation , we get

(0.8 - 0.0784 , 0.8 + 0.0784)

(0.7214 , 0.8784)

Conclusion:-

95% confidence interval for the population proportion

(0.7214 , 0.8784)

Hey there! I'm happy to help!

There are 31 days in March, so there are 11 days left in March. We add this to the 20 days in April, giving us 31 total days this interest is compounded.

We could calculate the amount compounded each day for 31 total days, but that would take a long time. Instead, there is a formula we can use to calculate compound interest instead.

[tex]Total= P(1+i)^n\\\\P=Principal Amount\\i=interest rate\\\\n=number of times compounded[/tex]

So, let's plug in those numbers! Remember to convert the percent to a decimal so it works in the equation!

[tex]Total=1000(1+0.055)^3^1\\Total=1000(5.258068609)\\Total=5258.068609[/tex]

Now, we subtract the initial amount just to see how much interest was earned.

5258.068609-1000=4258.07 (rounded to nearest cent).

Therefore, the money will have earned $4,258.07 by April 20.

Have a wonderful day!

Answer:

Distance between balloon and a is = 383.67 m

Step-by-step explanation:

The given situation can be represented as the given diagram as attached in the answer area.

cd = 384 m

cb = 200 m

[tex]\angle adb = 33^\circ[/tex]

To find:

Distance between balloon and a i.e. side ad = ?

Solution:

First of all, let us consider the right angled [tex]\triangle bcd[/tex].

We know the trigonometric identity that:

[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]

[tex]tan\angle cbd =\dfrac{cd}{cb}\\\Rightarrowtan\angle cbd =\dfrac{384}{200}\\\Rightarrowtan\angle cbd =1.92\\\Rightarrow \angle cbd = tan^{-1}(1.92) = 62.49^\circ[/tex]

Now, using the external angle property for the external [tex]\angle cbd[/tex] for the [tex]\triangle abd[/tex]:

(External angle is equal to the sum of two opposite angles of the triangle.)

[tex]\angle cbd = \angle adb+\angle a[/tex]

[tex]\Rightarow \angle a =62.49-33 =29.49^\circ[/tex]

Now, let us consider the right angled [tex]\triangle acd[/tex].

We have the value of [tex]\angle a[/tex] and perpendicular dc.

We have to find the hypotenuse ad.

Let us use the sine identity:

[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin\angle a =\dfrac{cd}{ad}\\\Rightarrow sin(29.49^\circ) =\dfrac{384}{ad}\\\Rightarrow ad = \dfrac{384}{0.49}\\\Rightarrow \bold{ad = 783.67\ m}[/tex]

So, the answer is:

Distance between balloon and [tex]\bold{a}[/tex] is = 383.67 m

Answer:

Step-by-step explanation:

Given the surdic expression [tex]\frac{2}{3\sqrt{5} + 2\sqrt{11}}\\[/tex], to rationalize the expression, we will have to multiply the numerator and denominator of the expression by the conjugate of the denominator as shown;

[tex]= \frac{2}{3\sqrt{5} + 2\sqrt{11}} * \frac{3\sqrt{5} - 2\sqrt{11}}{3\sqrt{5} - 2\sqrt{11}}\\\\= \frac{2(3\sqrt{5} - 2\sqrt{11})}{(3\sqrt{5} + 2\sqrt{11})(3\sqrt{5} - 2\sqrt{11})}\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{9\sqrt{25}+6\sqrt{55}- 6\sqrt{55}-4\sqrt{121} } \\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{9(5)-4(11) }\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{45-44 }\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{1}[/tex]

Comparing the result [tex]\frac{6\sqrt{5} - 4\sqrt{11} }{1}[/tex] with the expression [tex]\frac{A\sqrt{B} + C\sqrt{D}}{E}[/tex], it can be seen that A = 6, B = 5, C = -4, D = 11 and E = 1

A+B+C+D+E = 6+5+(-4)+11+1

A+B+C+D+E = 11-4+12

A+B+C+D+E = 19

Hence the value of A+B+C+D+E is 19

Answer:

x=-2 and y=-1

Step-by-step explanation:

If x = -2 then:

y = -(-2)-3

y = 2-3

so y = -1

I hope this helps! And plz mark me brainliest!!!

Answer:

(-2,-1)

Step-by-step explanation:

Well if x is -2 we can plug it in to find y,

y = -(-2) - 3

y = 2 - 3

y = -1

(-2, -1)

Thus,

the solution is (-2,-1)

Hope this helps :)

Answer:

x=3

Step-by-step explanation:

-2x-3=-9

Add 3 to each side

-2x-3+3=-9+3

-2x = -6

Divide by -2

-2x/-2 = -6/-2

x = 3

Answer:

x =3

Step-by-step explanation:

[tex]-2x-3=-9. \\ - 2x = - 9 + 3 \\ - 2x - 6 \\ \frac{ - 2x}{ - 2} = \frac{ - 6}{ - 2} [/tex]

[tex]x = 3[/tex]

Answer:

120

Step-by-step explanation:

12 x 6 = 72

8x(12/2)=48

72+48 =120

Answer:

16 and 40

Step-by-step explanation:

Hello,

We need to find the factors of 80

1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.

Which can be 2, 2, 2, 2, and 5 (these numbers would go into all the factor completely without any reminder.)

This leaves us with two numbers 2 and 5

If the highest common factor (H.C.F) of both numbers is 8

And the lowest common multiple (L.C.M) = 80

Multiply the numbers by the highest common factor (H.C.F)

2 × 8 = 16

5 × 8 = 40

The numbers are 16 and 40

Answer:

1. a=9     2. f=1    3. b=6

Step-by-step explanation:

1.) 4a-1=3a+8

subtract 3a from both sides

a-1+8

add 1 to both sides

a=9

2.) 1+f+3+f=f+5

combine like terms that are on the same side

2f+4=f+5

subtract f from both sides

f+4=5

subtract 4 from both sides

f=1

3.) construct a equation

b+5=11

subtract 5 from both sides

b=6