Alexandra purchases two doughnuts and three cookies at a doughnut shop and is charged $3.30. Brianna purchases five doughnuts and two cookies at the same shop for $4.95. All the doughnuts and cookies have the same price. Find the cost of one doughnut and the cost of one cookie.

Answer:

a (5,2)

Step-by-step explanation:

To get to the smiley face, we move 5 units in the x direction from the origin, then we move 2 units up in the y direction  (x,y)  so the point is at (5,

The center of the circle described by the equation x^2 + (y+4)^2 = 64 is at the point (0,-4), and the radius is 8.

In the context of a circle, the general equation form is (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is its radius. Looking at your given equation x^2 + (y+4)^2 = 64, it is in this general format.

Here, the value of a is 0 (as there is no number being subtracted from x) and b is -4 (the y coordinate has been shifted 4 units down). Therefore, the center of the circle is at point (0,-4).

For the radius, since r^2 = 64, the radius r will be the square root of 64 which is 8.

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Answer:

Angle ABC is 22 degrees

Angle BAC is 68 degrees

======================================

Work Shown:

Because there are just 3 points, we can refer to "angle BAC" as "angle A" and "angle ABC" as "angle B". Focus on the middle letter of each three-letter sequence.

The three angles A, B, C add up to 180 degrees. This is true for any triangle.

A+B+C = 180

(6x+8) + (2x+2) + 90 = 180 ... substitution

6x+8 + 2x+2 + 90 = 180

8x+100 = 180

8x+100-100 = 180-100 ... subtract 100 from both sides

8x = 80

8x/8 = 80/8 ... divide both sides by 8

x = 10

If x = 10, then angle BAC is

angle BAC = 6x+8

angle BAC = 6*10+8

angle BAC = 60+8

angle BAC = 68

Use x = 10 to find angle ABC as well

angle ABC = 2x+2

angle ABC = 2*10+2

angle ABC = 20+2

angle ABC = 22

The three angles of this triangle are A = 68, B = 22, C = 90

As a check, the three angles must add to 180

A+B+C = 180

68+22+90 = 180

180 = 180

Answers are confirmed

Another thing to notice is that A+B = 90 meaning that A and B are complementary angles. A+B = 68+22 = 90.

Option: D is the correct answer.

  D.    The slope of is 3, and passes through O.

It is given that:

AB is dilated by a scale factor of 3 to form AB .

Also, the line AB pass through the origin.

So, if AB pass through (0,0) and some point (x,y) then the slope of line AB is:

[tex]Slope=\dfrac{y-0}{x-0}\\\\i.e.\\\\Slope=\dfrac{y}{x}=3[/tex]

( Since, it is given the slope of AB is 3 )

Now , if AB is dilated to A'B' by a scale factor of 3 then

(0,0) → (0,0)

and

(x,y) → (3x,3y)

i.e. (0,0) and (3x,3y) will lie on A'B'.

Hence, the slope of line A'B' is given by:

[tex]Slope=\dfrac{3y-0}{3x-0}\\\\i.e.\\\\Slope=\dfrac{3y}{3x}\\\\i.e.\\\\Slope=\dfrac{y}{x}=3[/tex]

Hence, both have the same slope.

                The answer is :  Option: D

Answer:

Step-by-step explanation:

Answer:

The mystery number is -3

Step-by-step explanation:

five more then -8 times a number is 29.

-8n +5 = 29

Subtract 5 from both sides

-8n +5-5 = 29-5

-8n = 24

Divide by -8 on each side

-8n/-8 = 24/-8

n= -3

The mystery number is -3

The mystery number in the equation is -3, determined by solving the algebraic equation 5 + (-8 × n) = 29.

The equation given in the problem statement translates to the mathematical expression 5 + (-8 × n) = 29, where n is the mystery number. To find the value of n, we can perform the following steps:

Subtract 5 from both sides to get -8n = 24.

Divide both sides by -8 to isolate n, giving us n = 24 / -8.

Calculate the result to find that n = -3.

Therefore, the mystery number is -3.

Answer:

4:2 is the same as:

2:1

8:4

or anything that is proportional to 4:2

Step-by-step explanation:

A proportion is anything that corresponds in size or amount to something else.

Answer:

2:1

Step-by-step explanation:

just reduce the ratio b and divivd bith sides by 2

Answer:

144

Step-by-step explanation:

4 x 4 x 4 = 64

100/5 = 20

20 x 4= 80

80 + 64 =144

Answer:

100 /( 5 x 4 + 4³) = 1 4/21  

100 / 5 x 4 + 4³ = 144

Step-by-step explanation:

100 /( 5 x 4 + 4³)

PEMDAS tells us to do what is inside the parenthses

We will do the power in side the parentheses first  4^3 = 64

100 /( 5 x 4 + 64)

Now we will multiply

100/(20+64)

Now we add inside the parentheses

100/84

Divide the top and bottom by 4

25/21

Changing from an improper fraction to a mixed number

1 4/21

OR  

100 / 5 x 4 + 4³

If the quantity is not in parentheses

We will do the power  first  4^3 = 64

100 / 5 x 4 + 64

Then we do the multiplication and division from left to right

20 *4+64

80+64

144

Answer: 0.44444444444....

Step-by-step explanation: 4/9 is the same as 4 ÷ 9. 9 does not divide into 4, so we add a 0 and bring down a 0 to get 9 divided by 40. 9 can be multiplied by 4 to get 36, 40 - 36 = 4, bring down another 0, 9 can be multiplied by 4 to get 36, 40 - 36 = 4.... this is a never ending decimal.

Answer:

see explanation

Step-by-step explanation:

To find the x- intercepts set y = 0, that is

- 2x² - 9x + 5 = 0

To factorise the quadratic consider the factors of the product of the coefficient of the x² term and the constant term that sum to give the coefficient of the x- term.

product = - 2 × 5 = - 10 and sum = - 9

The factors are - 10 and + 1

Use these factors to split the middle term

- 2x² - 10x + x + 5 = 0 ( factor the first/second and third/fourth terms )

- 2x(x + 5) + 1(x + 5) ( factor out (x + 5) )

(x + 5)(- 2x + 1) = 0

equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

- 2x + 1 = 0 ⇒ x = [tex]\frac{1}{2}[/tex]

x-intercepts are x = - 5 and x = [tex]\frac{1}{2}[/tex]

Answer:

25

Step-by-step explanation:

Answer:

100% profit of 1500

Step-by-step explanation:

One the first calculator David earns 25% profit:

25% + 1500 = 1,875

He gets a 25% on the second calculator:

1500 - 25% = 1,125

In total he receives 1125 + 1875 = 3000

Therefore he has 100% profit

Answer:

1,12/ Not a solution

2,10/ solution

4,5/ solution

6,10/ not a solution

12,8/ not a solution

18,6/ not a solution

Step-by-step explanation:

all you have to do is put it into the equation.

for example:

1,12

1x1+12x3= $37

1x1+12x1.5= 19lbs

This is not a solution because he can carry it but doesn't have the money to buy it.

Answer:

(1,12)=no solution

(2,10)=Solution

(4,5)=Solution

(6,10)=no solution

(12,8)=no solution

(18,6)=no solution

Step-by-step explanation:

You have to add the money and pounds each together. For example, the equation you would set up would be, for money: 1(1)=1 and the jars 3(12)=36. Together, it equals 37, which would be over the total amount that Tyler may buy. If you do all of these to show your work, then the answers are the ones shown above.

Answer:

Option B is correct

For [tex]n\geq 1[/tex] , the function for the given sequence is defined as; [tex]f[n] = 4 +3n[/tex]

Step-by-step explanation:

An arithmetic sequence is a sequence in which the difference between each consecutive term is constant.

An explicit formula for this arithmetic sequence given by;

[tex]a_n = a+(n-1)d[/tex] where a represents first term

Since, the given sequences; 7 , 10 , 13 , 16 and 19

⇒ common difference(d) = 3 and a = 7

Since.

10 -7 = 3

13- 10 = 3  ....

The function which defined this sequence is;

[tex]f[n]=a_n = 7 +(n-1)(3)[/tex]

using distributive property:

[tex]f[n] = 7 + 3n -3[/tex]

[tex]f[n] = 4 +3n[/tex]

therefore, the function for the given sequence for all integers [tex]n\geq 1[/tex] is;  [tex]f[n] = 4 +3n[/tex]

The correct option is D) f(n) = 4 + 3n.

Step-by-step explanation:

Given :

Arithmetic Sequence -- 7,10,13,16,19

Solution :

The explicit formula of arithmetic sequence is given by,

[tex]T_n = a+(n-1)d[/tex] ------- (1)

where, common difference (d) = 10 - 7 = 3

first term (a) = 7

So from equation (1),

[tex]T_n = 7+(n-1)3 = 7+3n-3[/tex]

[tex]T_n = 4 + 3n[/tex]

Therefore, the correct option is D) f(n) = 4 + 3n.

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Answer:

25%  

Step-by-step explanation:

Change = Final - initial

% Change =(Final - Initial)/Initial × 100%

% Change = (50 - 40)/40 × 100%

% Change = 10/40 × 100%

% Change = 25%

Answer:

25%

Step-by-step explanation:

1) Find the difference of the two numbers, do (Largest Number)-(Smallest Number).

2) Use your difference as a fraction. Use the difference over the initial value.

3) Create a proportion

10/40 = x/100

4) Cross multiply, 10*100 = 200, 40*p = 40p

5) Simplify expression 1,000=40p

6) Solve, 1,000/40 = 25

7) Put it as a fraction, 25/100

8) Make it a percent 25%

The proportional relationship:

y = ax for a > 0.

Therefore your answer is:

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (3, 0) and (6, -3). Substitute:

[tex]m=\dfrac{-3-0}{6-3}=\dfrac{-3}{3}=-1[/tex]

The point-slope form:

[tex]y-(-3)=-1(x-6)\\\\\boxed{y+3=-(x-6)}[/tex]

or

[tex]y-0=-1(x-3)\\\\\boxed{y=-(x-3)}[/tex]

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

From the second point-slope form we have slope-intercept form:

[tex]y=-(x-3)\\\\y=-x-(-3)\\\\\boxed{y=-x+3}[/tex]

Answer: [tex]\bold{\pm \{1, 2, 3, 4, 6, 12, \dfrac{1}{2}, \dfrac{3}{2}\}}[/tex]

Step-by-step explanation:

        Q                       P

f(x) = 2x³ - bx² + cx + 12

Possible rational roots are all of the factors of P divided by all of the factors of Q, including both positive and negative signs.

[tex]\quad \pm \dfrac{\text{factors of P}}{\text{factors of Q}}\\\\=\pm \dfrac{\text{factors of 12}}{\text{factors of 2}}\\\\=\pm \dfrac{1,2,3,4,6,12}{1,2}\\\\=\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm \dfrac{1}{2}, \pm \dfrac{3}{2}\\[/tex]

Answer:4/52=1/13

Step-by-step explanation:

The deck has 52 cards and contains 4 aces. When you draw a card, the probability of drawing an ace is 4/52=1/13

Answer:

327 FOR A FACTTTTT

Step-by-step explanation:

Answer:

the answer would be 327

Step-by-step explanation:

hope this helps :)

Answer:

the area of this trapezoid= 81 square inches

Step-by-step explanation:

To find area of trapezoid , we use formula

[tex]Area = \frac{a+b}{2} * h[/tex]

Where a,b are the base of the trapezoid

h is the height of the trapezoid

Here a= 3 in

b = 15 in

h = 9 in

Plug in all the values in the formula

[tex]Area = \frac{a+b}{2} * h[/tex]

[tex]Area = \frac{3+15}{2} * 9[/tex]

[tex]Area = \frac{18}{2} * 9[/tex]

Area = 9 * 9 = 81

the area of this trapezoid= 81 square inches

If an image is being enlarged by 15% you would take the base number multiply it by the percent in decimal form and add the result to the base number.

4.25*0.15=0.6275

0.6375+4.25=4.8875

Answer: 4.8875

To find out the height of the photocopied drawing, we first calculate 15% of the original height (4.25 inches) and add this to the original height. The photocopied drawing is approximately 4.89 inches tall.

The student photocopied a drawing with the copier set to enlarge the image by 15%. If the original drawing is 4.25 inches tall, the enlarged photocopied drawing would be larger by 15% of 4.25 inches.

Firstly, to find 15% of 4.25 inches, you multiply 4.25 by 0.15 (the decimal equivalent of 15%), which equals 0.6375 inches.

Adding this to the original height of the drawing, we get 4.25 inches + 0.6375 inches = 4.8875 inches, which is approximately 4.89 inches when rounded to two decimal places.

So, the photocopied drawing is approximately 4.89 inches tall.

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Answer:

The equation of this line would be 4x + y = 13

Step-by-step explanation:

In order to find this equation we must first find the slope of the original line. To do this, we solve the original equation for y.

4x + y - 2 = 0

4x + y = 2

y = -4x + 2

The original slope (the coefficient of x) is -4, which means the new slope will also be -4 because parallel lines have the same slope. Now, we can use this slope along with the point in point-slope form to find the equation of the line. Just plug in the numbers and solve for the coefficient.

y - y1 = m(x - x1)

y + 3 = -4(x - 4)

y + 3 = -4x + 16

4x + y + 3 = 16

4x + y = 13

Answer: The new price is $3350.

Answer:

$3350; $30 150  

Step-by-step explanation:

Original price = $33 500

Discount = 33 500 × 10 %

Discount = 33 500 × 0.10

Discount = $3350

New price = Original price - Discount

New price = 33 500 - 3350

New price = $30 150

Answer:

60%

Step-by-step explanation:

Use the equation a=pw. A= Part   P= Percent. W= Whole

A= $56.49

P = x (unknown)

W= $ 89.99

Equation = 56.49=89.99x

You divide 89.99 on both sides to be equal and isolate the variable x. You would divide 56.49 by 89.99 and will get 0.627736415. You would round it to the nearest tenth , 0.6 so the percent is 60%

The percent off is 37.2263 % of the sale price.

Calculations :

                with the same whole number                     =   3350/8999

              numerator and the denominator                 =  0.372263 x  [tex]\frac{100}{100}[/tex]

               equal to 100 as a percent                             = 37.2263 %

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Answer:

The 8th term is 23

Step-by-step explanation:

If we are given the formula for the sequence

an=2n+7,

then to find the 8th term we substitute n=8 into the formula.

a8 = 2(8) +7

a8 = 16+7

a8 = 23

The 8th term is 23

Answer:

A

Step-by-step explanation:

given sin x ≈ 0.2588, then

x = [tex]sin^{-1}[/tex](0.2588) ≈ 15°

using the cofunction identity

cos x = sin(90 - x)

the complement of 15° is 90° - 15° = 75°, hence

cos 75° = sin(90 - 75)° = sin15° ≈ 0.2588

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have the line

[tex]y-3=-\dfrac{1}{5}(x+2)\to m=-\dfrac{1}{5}[/tex]

If m₁ and m₂ are the slopes of the perpendicular lines, then

[tex]m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]

Therefore the slope of ouer line is

[tex]m=-\dfrac{1}{-\frac{1}{5}}=5[/tex]

We have the point (-2, 7). Put the coordinates to the equation of a line in the point-slope form:

[tex]y-7=5(x-(-2))[/tex]

[tex]y-7=5(x+2)[/tex]      use the distributive property

[tex]y-7=(5)(x)+(5)(2)[/tex]

[tex]y-7=5x+10[/tex]       add 7 to both sides

[tex]\boxed{y=5x+17}[/tex]

y=8.5x

y= money earned

x= hours worked

The equation to find Dianna's money earned as a lifeguard is e = 8.50h.

To find Dianna's money earned, we can write an equation using the formula for calculating earnings:

Earnings=Hourly Rate × Number of Hours Worked

In this case, Dianna's hourly rate is $8.50, and let's denote the number of hours she worked as ℎ.

So, the equation to find Dianna's money earned

E=8.50×h

Where:

E represents the total earnings

8.50 represents Dianna's hourly rate

h represents the number of hours worked

This equation will give us the total amount of money Dianna earned based on the number of hours she worked.

Answer:

f(x) = 34 + 25w

Step-by-step explanation:

First, we need to find the amount he was paid over the 35 weeks:

909 - 34 = 875

35w = 875

w = 875 / 35 = 25

So every week he is paid $25

The function has to start with 34, as that is the amount already in there, and as w is multiplying by 25, this can be written as 25w

So put these two together:

f(x) = 34 + 25w

Answer:

A. y = -(-x) +7 = x + 7

D. y = 0.05x + 10