Question 12
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1
The tank for a car holds 17 gallons. The gasoline gauge shows the tank is full. How much gas is still in
4
the tank? Give your answer as a whole number or as a mixed fraction reduced to lowest terms.
​

Answer:

Step-by-step explanation:

Applying the formula for the car deprecation we have

[tex]f(t)=P(1-\frac{r}{100} )^n[/tex]

Where,

A is the value of the car after n years,

P is the purchase amount,

R is the percentage rate of depreciation per annum,

n is the number of years after the purchase.

1. The depreciated value of the car after 1 yr is ​

n=1

[tex]f(t)= 15000(1-\frac{12}{100} )^1\\\f(t)= 15000(1-0.12 )\\\f(t)= 15000(0.88)[/tex]

Answer:

2√137

Step-by-step explanation:

To find AB, we can use the Pythagorean Theorem (a² + b² = c²). In this case, a = 22, b = 8 and we're solving for c, therefore:

22² + 8² = c²

484 + 64 = c²

548 = c²

c = ± √548 = ± 2√137

c = -2√137 is an extraneous solution because the length of a side of a triangle cannot be negative, therefore, the answer is 2√137.

Answer:

Step-by-step explanation:

Given,

Hypotenuse ( h ) = 158 cm

Perpendicular ( p ) = 83

Base ( b ) = ?

Now, Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {b}^{2} = {h}^{2} - {p}^{2} [/tex]

Plug the values

[tex] {b}^{2} = {158}^{2} - {83}^{2} [/tex]

Evaluate the power

[tex] {b}^{2} = 24964 - 6889[/tex]

Calculate the difference

[tex] {b}^{2} = 18075[/tex]

[tex]b = \sqrt{18075} [/tex]

Calculate

[tex]b = 134.4 \: cm[/tex]

Hope this helps..

Best regards!!

Answer: the slope is 1.5 and the y-intercept is -2.

Step-by-step explanation:

Assuming you meant 1.5x-2 and accidentally pressed shift to turn - into _.

This equation is in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

Thus, the slope is 1.5 and the y-intercept is -2.

Hope it helps <3

━━━━━━━☆☆━━━━━━━

▹ Answer

[tex]Slope = 1.5\\\\Y-intercept = -2[/tex]

▹ Step-by-Step Explanation

(I'm assuming the underscore was meant as a minus sign)

[tex]Slope \\equation \\\\ y = mx + b\\\\[/tex]

mx represents the slope and b represents the y-intercept.

Therefore:

1.5 is the slope, and -2 is the y-intercept.

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

No.

Step-by-step explanation:

Substitute 4 (as x) and 2 (as y) into the 2 equations to see if they fit.

y = x - 2

2 = 4 - 2

2 = 2

The first equation is true for (4,2).

Now try the 2nd one.

y = 3x + 4

2 = 3(4) + 4

2 ≠ 16

So the 2nd equation is not true for (4,2).

Either one not true makes the solution incorrect.

No, (4, 2) is not the solution for system of Equation.

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution.

To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

Equations:

y= x-2 ............(1)

y= 3x+ 4.................(2)

Put the value of y from equation 1 to equation (2), we get

x- 2 = 3x+ 4

x- 3x = 4+ 2

-2x = 6

x= -3

and, y= -3 -2 = -5

So, the solution to the system is (-3, -5)

and, (4, 2) can only satisfy the Equation y= x-2 but does not satisfy y= 3x+ 4.

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Here is the step by step answer. hope it helps!

The solution to the quadratic equation x² - 3x + 8 = 0 is given by

x = ( 3/2 ) ± i ( √23/2 )

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² - 3x = -8  

Adding 8 on both sides of the equation , we get

x² - 3x + 8 = 0   be equation (1)

Now , on simplifying the equation , we get

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

Substituting the values in the equation , we get

x = [ - ( -3 ) ± √ ( -3 )² - ( 4 ) ( 1 ) ( 8 ) ] / 2

On simplifying the equation , we get

x = [ 3 ± √ ( 9 - 32 ) ] / 2

x = ( 3/2 ) ± √ ( -23 ) / 2

x = ( 3/2 ) ± i ( √23/2 )

where i² = -1

Therefore , the value of x is  x = ( 3/2 ) + i ( √23/2 ) , x = ( 3/2 ) - i ( √23/2 )

Hence , the solution to the equation is x = ( 3/2 ) ± i ( √23/2 )

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so amnt of money is x

x - 5 is Mark's remaining amnt

x - 20 is Susan's remaining amount

x - 5 = 2( x - 20) as he has twice the amnt of Susan

x - 5 = 2x - 40

40 - 5 = 2x - x

35 = x

the original amnt is $35

Answer:

2 and angle that is left of 5

Step-by-step explanation:

Angle 2 is vertical from 110, and vertical angles are congruent. From this, we can figure out that 2 and 3 (they're supplementary) are 70. Angles 5 and 3 are Alternate Interior Angles, and therefore must be congruent. The one to the left of 5 is supplementary to it, and therefore must be 110. Your answers are angle 2 and the angle that is left of 5.

Answer:

vertex(-2,4)

Step-by-step explanation:

f(x)=-3(x+2)^2+4

f(x)=-3(x²+4x+4)+4

f(x)=-3x²-12x-12+4

    = -3x²-12x-8

v(h,k)

h=-b/2a=-(12/-6)==2

substitute for x=-2

k=-3(2)²-12(-2)-8=-12+24-8=4

Answer:

critical point of the given function f(x,y) = x²+y²+2xy is from line y = -x is the critical point of the function f(x0,y0) = 0

and it local minimum.

Step-by-step explanation:

Let the given function be;

f(x,y) = x²+y²+2xy

From above function, we can locate relative minima, maxima and the saddle point

f(x,y) = x²+y²+2xy = (x+y)²

df/dx = 2x+2y = 0 ---- (1)

df/dy =2y+2x = 0 ---- (2)

From eqn 1 and 2 above,

The arbitrary point (x0,y0) from line y = -x is the critical point of the function f(x0,y0) = 0

Then, from f(x,y) >= 0 for arbitrary (x,y) € R^n, the arbitrary point from the line x = -y is local minima of the function f.

Answer: 9.0876544e+58

Step-by-step explanation:

Answer:

90876543579645968765443223456789009876543212345678909876544

Step-by-step explanation:

90876543579645968765443223456789009876543212345678909876543

+

1

=

90876543579645968765443223456789009876543212345678909876544

Answer:

The number of car they did quick wash is 75 and the number of car they did premium washes is 50 .

Step-by-step explanation:

The number of cars they washed is equals to 125 cars. They made a total of $775 from the wash. The wash is in two category the quick washes which is $5 and the premium washes which is $8.

Let

number of car for quick washes = x

number of car for premium washes = y

Base on the equation given below

x + y =125 .........(i)

5x + 8y = 775 .......(ii)

Let us find x and y

from equation (i)

y = 125 - x

inserting the value of y in equation (ii)

5x + 8(125 - x) = 775

5x + 1000  - 8x = 775

-3x = -225

divide both sides by -3

x = -225/-3

x = 75

insert the value of x in equation (i)

75 + y =125

y = 125 -75

y = 50

The number of car they did quick wash is 75 and the number of car they did premium washes is 50 .

Answer:

The Answer is A

Please leave an Exellent rating and press THANKS!

Answer:

see details below

Step-by-step explanation:

The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.

a. Determine the amount to be financed.​​​​​​​15a. ___$23450____________

29450 - 6000 = 23450

b. Determine the installment price.​​​​​​​​b. ___$792,22______________

"monthly payment of $792.22"

c. Determine the finance charge.​​​​​​​​c. __$5069.92_______________

A = 792.22

n = 36

finance charge = total paid - amount to be financed

= 36*792.22 - 23450

= 5069.92

Answer:

Remaining amount of the element = 31.5 mg

Step-by-step explanation:

Half life of radioactive Iodine is [tex](T_{\frac{1}{2}})[/tex] = 60 days

Formula to get the remaining element after t days is,

[tex]N=N_0(e)^{\lambda.t}[/tex]

Where [tex]\lambda[/tex] = decay constant of the radioactive element

t = duration of the decay (in days)

[tex]N_0[/tex] = Initial amount of the element

N = final amount after decay

For half life period 't' = 60 days

[tex]\frac{N_0}{2}=N_0(e)^{\lambda\times 60}[/tex]

[tex]e^{60\lambda}=0.5[/tex]

[tex]ln(e^{60\lambda})=ln(0.5)[/tex]

[tex]60\lambda =-0.069315[/tex]

[tex]\lambda=-0.0115524[/tex]

Remaining amount of the element after 40 hours,

N = [tex]50(e^{40\lambda} )[/tex]

   = [tex]50(e)^{-(0.0115524)\times 40}[/tex]

   = 50(0.62996)

   = 31.49

   ≈ 31.5 mg

Therefore, remaining amount of the element after 40 days is 31.5 mg.

Answer:

In 40 days, there would be approximately 31.5 mg remaining.

Step-by-step explanation:

Answer:

$960

Step-by-step explanation:

A shortcut method.

If you get a discount of 1/5, then that means you would end up paying 4/5 of the whole cost. That means all you have to do then is plug in what it costs, which in this case is 1200, and then multiply it by 4/5, so you end up with $960.

Answer:

$960

Step-by-step explanation:

1200*1/5 = 240

1200 - 240 = $960

Would appreciate brainliest!! But it's ok if not

Answer:

1/4

Step-by-step explanation:

9 lbs

---------

36 lbs

We can write this because the units are the same

Divide the top and bottom by 9

9/9

----------

36 /9

1/4

Answer:

1/4

Step-by-step explanation:

9 pounds

36 pounds

Ratios are written as x:y, fractions are written as x/y.

9:36 as a fraction will be 9/36

Simplify the fraction.

1/4

Answer:

1) x=58, y=109

2) x=72, y=36

3) x=60, y=48

Step-by-step explanation:

1) 58 and x are so-called "F-angles" (a.k.a "corresponding angles), so x=58°

The angle on the other side of the 58 is 180-58 = 122 because they are supplementary. We need this one to calculate y.

The sum of angles in a quadrilateral is 360°, so 71 + 58 + 122 + y = 360, so y = 109

2) There are two isosceles triangles. Due to the symmetry, the bottom left angle is also 72, leaving 180-72-72 = 36 for y. The top triangle is the same triangle rotated, so x = 72.

3) Due to the parallel lines, the left angle of the top triangle is also 72, making the supplementary angle below it 180-72=108. The sum in the quadrilateral must be 360, so 72+108+2x+x=360, so 3x=180, x=60.

The sum in the outer triangle must be 180, so 72+y+x = 180, leaving y = 180-72-60 = 48

Answer:

[tex]\boxed{11m}[/tex]

Step-by-step explanation:

Method #1: 45-45-90 Triangle

You can use the rules for a 45-45-90 triangle. These are:

→ Each 45-45-90 triangle is a right triangle with two additional 45° angles.

→ The triangle will have 2 legs, x, and one hypotenuse, x√2.

Therefore, because the problem gives values for one leg and the hypotenuse, the value for the one leg is equal to the value for the unsolved leg.

Method #2: Pythagorean Theorem

You can use the Pythagorean Theorem to solve for a missing side in a triangle. Please note, however, that the Pythagorean Theorem only works on right triangles.

The Pythagorean Theorem is defined as [tex]a^{2} + b^{2} = c^{2},[/tex] where a and b are both legs of the triangle and c is the hypotenuse.

Therefore, substitute the known value for a, 11, and the known value for c, 11√2. Then, evaluate each value to its power (except for b - it is unsolved) and simplify the equation with basic algebraic methods. Once your equation is down to [tex]b^{2}= ?[/tex], you should take the square root of both sides of the equation to get the value for b.

[tex]11^{2} +b^{2} =(11\sqrt{2} )^{2}\\121 + b^{2} = 242\\b^{2}=121\\b=11[/tex]

Answer:

The map distance would be 2.8 cm

Step-by-step explanation:

Use the proportion given by the following relationship, where you use "x" as the unknown value in cm:

[tex]\frac{1\,\,cm}{5\,\,km} =\frac{x}{14\,\,km} \\\frac{1\,\,cm\.\,(14\,\,km)}{5\,\,km} =x\\x=2.8\,\,cm[/tex]

Answer:

x= -5, -1

Step-by-step explanation:

To find the zeroes of a function,

First expand the terms to get the form  [tex]ax^{2} + bx +c[/tex] where 'a, b, and c' are constants

     [tex]f(x)= (x+3)^{2} -4[/tex]

    [tex]f(x)= x^{2}+6x+9-4[/tex]

    [tex]f(x)= x^{2} +6x +5[/tex]

Now, factor the equation

This can be done using the quadratic formula or other methods

  One simple method is to find the two values that would get:

A good way to verify is to expand the terms and make sure the function looks the same

In this case, the equation can broken into

    f(x)= (x+1)*(x+5)

Now, look at each term individually and set each of them to equal 0

   x+1 =0

   x+5=0

Solve for x in each case

  x= -1

  x= -5

Now, ordering them from least to greatest would be: x= -5, -1

Answer:

Step-by-step explanation:

Given the values of the actual content of protein powder recorded as shown:

1530​, 1532​, 1495​, 1508​, 1528​, and 1511

a) We are to find the mean and median of the contents.

Mean is the average sum of the numbers. It is expressed mathematically as xbar = ΣXi/N

Xi are individual values

N is the total number of values present.

N = 6

xbar = (1,530​+1,532​+1,495​ +1,508​+1,528+1,511)/6

xbar = 9104/6

xbar = 1517.33

Median of the data is the value at the middle after rearrangement. On rearranging from lowest to highest:

1,495, 1508, 1511, 1528, 1530, 1532

The two values at the centre are 1511 and 1528.

Median = 1511+1528/2

Median = 1519.5

b) If the third value was incorrectly measured and is actually 1515, then our new data will become.

1530​, 1532​, 1515​, 1508​, 1528​, and 1511

xbar = (1,530​+1,532​+1,515​ +1,508​+1,528+1,511)/6

xbar = 9124/6

xbar = 1520.67

For median:

We arrange first

1508, 1511, 1515, 1528, 1530, 1532

The two values at the centre are 1515 and 1528.

Median = 1515+1528/2

Median = 1521.5

c) To know the measure of central tendency that was most affected, we will look at the difference in the values gotten for both mean and median.

∆Mean = 1520.67-1517.33

∆Mean = 3.34

∆Median = 1521.5 - 1519.5

∆Median = 2.0

It can be seen that the measure of central tendency with greater deviation is the mean. Therefore, the mean is more affected by the data entry error.

Answer:

Step-by-step explanation:

√7 /1 + 1/√2

= √7 + √2 / 2

Answer:

34.26 mm²

Step-by-step explanation:

To find the shaded region we must find the total area of the half-circle and then substract from it the area of the triangle

Let A be the area of the half circle

A = r²*π   where r is the radius

A = 4²π = 16π mm²

Let A' be the area of the triangle

A' = (b*h)/2   where b and h are respectively the base and the the height

A'= (8*4)/2 = 16

Let A" be the area of the shaded region

A" = A-A'

A" = 16π -16 = 34.26 mm²

Answer:

Below

Step-by-step explanation:

The initial length of the road was 56. 56 is the y-intercept assuming that the graph of this function is a line.

so the equation is:

y= mx+56

m is the slope of the function wich is by how much the function grows.

By analogy, m is the distance added to the road each day.

● y= 3x+56

X is the number of days.

■■■■■■■■■■■■■■■■■■■■■■■■■■

To find the length of the road after 33 days, replace x by 33.

y= 3*33+56 = 155

So after 33 days the road is 155 miles.

Answer:

The original number of men is 2

Step-by-step explanation:

Let the number of men be x

The amount each of the men will receive from the ten dinar since they all received equal amounts will be 10/x

Now, adding 6 more men, we have a total of x + 6 men now

Now we share 40 dinar amongst the x + 6 men and each will receive 10/x as received before

Mathematically;

40/x + 6 = 10/x

x(40) = 10(x + 6)

40x = 10x + 60

40x -10x = 60

30x = 60

x = 60/30

x = 2

There were originally 2 men

Hello!

Answer:

A) Yes.

B) No.

C) Yes.

D) Yes.

Step-by-step explanation:

To find the correct solutions to this question, we can go through each choice and check for their congruency:

A) Yes. ∠8 is congruent to ∠5 because ∠5 and ∠8 are vertical angles.

B) No. ∠5 is not congruent to ∠6 because ∠5 and ∠6 are supplementary to each other.

C) Yes. ∠5 is congruent to ∠1 because corresponding angles are congruent.

D) Yes. ∠5 is congruent to ∠4 because alternate exterior angles are congruent.

A) The angle 8 should be congruent so it should be Yes.

B) The angle 6 should be congruent so it should be No.

C) The angle 1 should be congruent so it should be Yes.

D) The angle 4 should be congruent so it should be Yes.

The congruent angles are those angles in which the corresponding sides and angles should be of equal measure.

A) Yes. ∠8 is congruent to ∠5 since ∠5 and ∠8 are vertical angles.

B) No. ∠5 is not congruent to ∠6 since ∠5 and ∠6 are supplementary to each other.

C) Yes. ∠5 is congruent to ∠1 since corresponding angles are congruent.

D) Yes. ∠5 is congruent to ∠4 since alternate exterior angles are congruent.

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Answer:

A. y ≤ 1/2x + 2

Step-by-step explanation:

Well look at the graph,

It is a solid line with it shaded down,

meaning it is y ≤,

So we can cross out B. and D.

So the y intercept is 2, we know this because the y intercept is the point on the line that touches the y axis.

now the slope can be found by seeing how far away each points are from each other,

Hence, the answer is A. y ≤ 1/2x + 2

Answer:

b

Step-by-step explanation:

A, b, c, and d are all points. the line segements are: ab, bc, cd, da, and ac

Answer:

12.5

Step-by-step explanation:

(7.5+2.5)x2.5/2

Answer:

12.5 units ^2

Step-by-step explanation:

This figure is a trapezoid

The area of a trapezoid is given by

A = 1/2 (b1+b2) *h

where b1 and b2 are the lengths of the bases and h is the height

A = 1/2 ( 2.5+ 7.5) *2.5

   = 1/2 ( 10) * 2.5

   =12.5 units ^2