Following a severe snowstorm, Ken and Bettina Reeves must clear their driveway and sidewalk.Ken can clear the snow by himself in 3 hours, and Bettina can clear the snow by herself in 4 hours. After Bettina has been working for 1 hour, Kane is able to join her. How much longer will it take them working together to remove the rest of the snow?

Answer:

opposite side = 8.27cm

adjacent = 12.5cm

Step-by-step explanation:

to work out the other side of the triangle

give the angle = 32

using SOH CAH TOA

sineФ = opposite/ hypoteneus

sin32° = opposite/ 15cm

using cross multiplication

opposite side = sine32 x 15cm

opposite side = 0.551 x 15cm

opposite side = 8.27cm

to find the other side of the triangle using pythagoras theorem

hypotheneus ² = opposite² + adjacent²

15² = 8.27² + adjacent ²

collect the like terms

15² - 8.27² = adjacent ²

225  - 68.42 = adjacent²

156.58 = adjacent²

squaring both sides

adjacent = √ 156.58

adjacent = 12.5cm

Answer:

2/3

Step-by-step explanation:

Calculators help :)

To divide 2 1/2 by 3 3/4, convert the mixed numbers to improper fractions, change division to multiplication of the inverse, multiply, and simplify the result to 2/3.

To divide and simplify the expression 2 1/2 divided by 3 3/4, we begin by converting the mixed numbers into improper fractions. The mixed number 2 1/2 becomes 5/2 (2 times 2 + 1), and 3 3/4 becomes 15/4 (3 times 4 + 3).

Next, we use the rule for dividing fractions: invert the second fraction and change the division to multiplication. Therefore, the division becomes 5/2 times 4/15. We can now multiply the numerators together and the denominators together, resulting in 20/30.

To simplify, we can reduce the fraction by dividing both the numerator and the denominator by the greatest common factor, which is 10. Simplifying gives us 2/3, the final answer.

If discriminate is less than zero, the quadratic will have no real solution.

Answer: B

Answer:

the outlier is 20 and 24

Step-by-step explanation: An outlier, in mathematics, statistics and information technology, is a specific data point that falls outside the range of probability for a data set. In this Case 20 and 24 are outliers because they are not in the range of 58, 59, 63, 63, 65, 66. :) your welcome.

Let's make a table of differences

0 3 8 15 24

3  5 7  9

 2  2  2

Constant second difference means a quadratic polynomial,

f(n)=an² + bn +c

f(1)=0, f(2)=3, f(3)=8

0 = a+b+c

3 = 4a + 2b + c

8 = 9a + 3b + c

Subtracting pairs

3 = 3a+b

5 = 5a + b

Subtracting,

2 = 2a

a = 1

b = 5 - 5a = 0

c = -a-b = -1

f(n)=n² -1

Duh, shoulda noticed that at the beginning.

f(17)=17²-1 = 288

a₁ =5

aₙ = aₙ₋₁ - 7

aₙ = a₁ + d(n-1)

aₙ = 5 - 7(n-1)

a₇ = 5 - 7(6) = -37

Answer: -37

Answer:

B.

Step-by-step explanation:

Sorry I am late. Here's the answer for everybody else. :)

To convert 2 and 5/6 to a percent, convert the fraction to a decimal and add it to the whole number. Then multiply by 100 to find the percentage (approximately 283.3%).

In mathematics, to convert a mixed number like 25/6 to a percentage, you can first convert it to a decimal and then multiply by 100. The fraction can be converted into decimal by dividing the numerator by the denominator. In this case, 5 divided by 6 is approximately 0.8333. Since we have 2 whole and 0.8333, we can add them to get approximately 2.8333. By multiplying this by 100, we get 283.33% which we can take as an approximate value of 283.3% because it's the closest listed option in the question.

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Answer:

Step-by-step explanation:

3ft x 5 ft x 6 ft

15 x 6 = 90 cubic feet

Step-by-step explanation:

To get the volume, you have to do LxWxH so its 3x5x6=90

so its 90 cubic feet.

Answer:

C. 2(2x + 3)(2x - 3)

Step-by-step explanation:

[tex]8 {x}^{2} - 18 \\ = 2 \times 4 {x}^{2} - 2 \times 9 \\ = 2(4 {x}^{2} - 9) \\ = 2 \{( {2x})^{2} - ( {3)}^{2} \} \\ = 2(2x + 3)(2x - 3) \\ [/tex]

Final answer:

The expression 8x² - 18 is factored by first taking out the common factor of 2, and then applying the difference of squares formula to get the fully factored form, 2(2x + 3)(2x - 3). Option C is accurate.

Explanation:

To factor the expression 8x² - 18, we need to first take out the common factor. Here, we can see that both terms are multiples of 2. Thus, we can factor out a 2, which gives us:

2(4x² - 9)

Now, we recognize that the expression inside the parentheses is a difference of squares because 4x² is (2x)² and 9 is 32. A difference of squares can be factored into:

(a² - b²) = (a + b)(a - b)

Applying this to our expression, we get:

2((2x) + 3)((2x) - 3)

Hence, the fully factored form of the expression 8x² - 18 is:

2(2x + 3)(2x - 3) (Option C)

Answer:

6

Step-by-step explanation:

IQR is the distance between the ends of the box. The ends of the box are 15 and 21, so the IQR is 21-15, which is 6.

Answer: m = 7 and b = 0

Step-by-step explanation:

y = mx + b is slope-intercept form

m = slope

b = y-intercept

You would put +0 on the end of the equation because it doesn't change anything

Answer:

a parabola is a curve often resembling a U and follows a mathematical equation

Step-by-step explanation:

for example:

Answer:

In mathematics, a parabola is a plane curve

Step-by-step explanation:

Step-by-step explanation:

Use Desmos

Answer:

The recipe makes 1/2 cup of salad dressing assuming that the salt and herbs do not make a difference.  Each serving has 1/12 of a cup.  I am not gifted in the number sentence and equation department

Step-by-step explanation:

1/3=2/6

         +

1/6=1/6

--------------

3/6=1/2

The recipe will make 1/2 cup of salad dressing. Each serving would have 1/12 cup of dressing.

To find out how many cups of salad dressing the recipe will make, we can add the quantities of olive oil and balsamic vinegar. We have 1/3 cup of olive oil and 1/6 cup of balsamic vinegar, so the total is 1/3 + 1/6 = 1/2 cup. Therefore, the recipe will make 1/2 cup of salad dressing.

To determine how much dressing there would be in one serving, we divide the total quantity of dressing (1/2 cup) by the number of servings (6). This can be represented as the number sentence: 1/2 ÷ 6 = 1/12 cup per serving.

Answer:

2.95 is bigger

Step-by-step explanation:

Always remember that each place after the integer in a decimal spot ends are all 0's.

This helps when we are comparing decimals.

In that case we really have:

2.9500 and 2.9490

Since 9500 is bigger than 9490, we can see that the one's digits are the same.

Since they are, 2.95 is the bigger number.

Answer:

36250

1450/ 1/25= 36250

72500

1450/ 1/50

Answer:

Drink=5.75

Popcorn=1.83

Percentage for drink=75.9%

Step-by-step explanation

Let the popcorn be p

the drinks be d

6p+4d=34....(1)

12p+7d=66.25...(2)

Multiply (1) by 2

12p+8d=72....(3)

Substrate (2) from (3)

d=5.75

Substitute the value for d into (1)

6p+4(5.75)=34

6p+23=34

Substrate 23 from both sides

6p=11

Divide both sides by 6

p=1.83

So for one drink=$5.75

For one popcorn=$1.83

To determine the% for drink

5.75+1.83=7.58

5.75/7.58 ×100

575/7.58

75.858~75.9%

The percentage for drink is 75.9%

Answer:

the answer is -1/3

Step-by-step explanation:

here is your step by step solution

Answer:

[tex]- \frac{1}{3} [/tex]

Step-by-step explanation:

The product of the gradients of perpendicular lines is -1.

Let the slope of the line perpendicular to line C be x.

(slope of Line C)(x)= -1

x= -1 ÷ (slope of Line C)

Let's find the slope of line C using the gradient formula.

[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]

Gradient of Line C

[tex] = \frac{ - 6 - ( - 12)}{ - 3 - ( - 1)} \\ = \frac{ - 6 + 12}{ - 3 + 1} \\ = \frac{-6}{ - 2} \\ = 3[/tex]

Thus substituting gradient of Line C= 3,

x= -1÷ (3)

x= [tex]- \frac{1}{3} [/tex]

Answer:

1077

Step-by-step explanation:

A term in a math expression is single number or variable and are separated by a + or - or × or ÷

This expression has 4 terms

2r

1c

.5d

and 8

This expression has 4 terms 2r, 1c, 0.5d, and 8.

One mathematical expression makes up a term. It could be a single variable (a letter), a single number (positive or negative), or the number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given an expression 2r+c+0.5d+8 to find the term of the given expression

A term in a math expression is a single number or variable and is separated by a + or - or × or ÷

thus this equation has four terms

that is:

2r

1c

0.5d

and 8

therefore, Given expression 2r+c+0.5d+8 has 4 terms 2r, 1c, 0.5d, and 8.

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The radius of the oblique cone is; B: 3 units

Formula for the volume of an oblique cone is;

V = ¹/₃πr²h

where;

V is volume

r is radius

h is height

We are told that diameter is equal to the height. Thus;

diameter = 2r = h

Thus;

V = ¹/₃πr²(2r)

18π = ¹/₃πr²(2r)

r = ∛(18π * 3/2π)

r = 3 units

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The radius of the cone is approximately 3 units.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is 1/3πr²h.

We have,

We know that the height of the cone is equal to the diameter of the base, which means h = 2r.

Substituting this into the formula for the volume, we get:

V = (1/3) x π x r² x (2r) = (2/3) x π x r³

We are given that the volume of the cone is 187 cubic units, so we can set up an equation:

(2/3) x π x r³  = 187

Multiplying both sides by 3/2π, we get:

r³ = (187 x 3)/(2π)

Taking the cube root of both sides, we get:

r = (187 x 3/(2π))^(1/3) ≈ 3.00

Therefore,

The radius of the cone is approximately 3 units.

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Answer:

A) resturant is at (-4,5)

A)the equation is: [tex](x-0)^2+(y-0)^2=6^2[/tex]

B) Consuela can get free delivery

Step-by-step explanation:

see picture

Answer:

80°

Step-by-step explanation:

Just multiply 40° by 2 to get the arc

Answer:

80

Step-by-step explanation:

An arc's measurement is always twice the amount of its angle.

40 x 2 = 80

Answer:

7root2/2

Step-by-step explanation:

You can solve this by multiplying by a version of 1 which will simplify but not change the expression. If you multiply this by root2/root2, you will have 7root2 in the numerator and 2 in the denominator, which is simplified. Hope this helps!

Answer:

b. $9000

Step-by-step explanation:

Quick way of doing this:

10% is one-tenth. 10% of $180,000 is $18,000.

5% is half of 10%, so it's half of $18,000.

Answer: b. $9000

Conventional way of doing this:

To find a percent of a number, multiply the percent by the number. To change the percent to a decimal, move the decimal point of the percent two places left.

5% of $180,000 = 5% * $180,000 = 0.05 * $180,000 = $9,000

Answer: c. $9000

Mrs. Henderson's commission for selling a house worth $180,000 is $9000.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Mrs. Henderson sells houses. She gets a 5% commission on all sales.

∴ His commission for selling a house worth $180,000 is 5% of  $180,000 which is,

=(5/100)×180000.

= $9000.

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Answer:

both are one

Answer:

det = 1 and det = 1

Step-by-step explanation:

just took the lesson on ed-genuity, these are both right :)

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be perpendicular, their slopes have to be the negative reciprocal of each other. (Basically flip the sign +/- and the fraction(switch the numerator and the denominator))

For example:

Slope = 2 or [tex]\frac{2}{1}[/tex]

Perpendicular line's slope = [tex]-\frac{1}{2}[/tex]   (flip the sign from + to -, and flip the fraction)

Slope = [tex]-\frac{3}{4}[/tex]

Perpendicular line's slope = [tex]\frac{4}{3}[/tex]  (flip the sign from - to +, and flip the fraction)

y = 1/3x + 4        The slope is 1/3, so the perpendicular line's slope is [tex]-\frac{3}{1}[/tex] or -3.

Now that you know the slope, substitute/plug it into the equation:

y = mx + b

y = -3x + b       To find b, plug in the point (1, 2) into the equation, then isolate/get the variable "b" by itself

2= -3(1) + b     Add 3 on both sides to get "b" by itself

2 + 3 = -3 + 3 + b

5 = b

y = -3x + 5

The equation of the line that passes through (1,2) and is perpendicular to the line (y = 1/3x + 4) is (y = -3x + 5) and this can be determined by using the given data.

Given :

The line that passes through (1,2) and is perpendicular to the line (y = 1/3x + 4).

The following steps can be used in order to determine the equation of the line:

Step 1 - When two lines are perpendicular to each other then their slopes are:

mm' = 1

where m and m' are the slopes of the lines.

Step 2 - So, the slope of the line which is perpendicular to the line (y = 1/3x + 4) is:

[tex]\rm \dfrac{1}{3}\times m' = -1[/tex]

m' = -3

Step 3 - Now, the equation of a line that passes through the point (1,2) and has a slope -3 is:

[tex]\rm (y -2) = -3(x-1)[/tex]

Step 4 - Simplify the above equation.

y = -3x + 5

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Answer:

14

Step-by-step explanation:

You fins the measure of angle C, and get 180-(118+22) = 40 degrees

You use law of sines, and get:

24/(sin40) = AC/(sin22)

Multiply both sides by sin(22)

24sin(22)/sin(40)=AC

Plug into a calculator, and get: 13.9868256738, which rounds to 14

Answer:

See explanation

Step-by-step explanation:

You question is missing some necessary information.

However these are the mappings for the following transformation.

Rotate 180° counterclockwise about the origin. The mapping is

[tex](x,y)\to(-x,-y)[/tex]

Reflect across the line y=x.

The mapping is

[tex](x,y)\to(y,x)[/tex]

Reflect across the line y=-x

The mapping is:

[tex](x,y)\to(-y,-x)[/tex]

Rotate 270° counterclockwise about the origin. The mapping is

[tex](x,y)\to(-y,x)[/tex]

Hope this is helpful.

Please try post complete questions to get the exact answer you are looking for .

Answer:

reflect across the line y = –x (C)

Step-by-step explanation:

If you multiply the point 1,4 by the matrix you get -4, -1

it cant be 180 since that would make it -1,-4 not -4,-1.

y=x would mean its positive making it 4,1

y=-x would mean atleast -x is present and if you use other values it swaps x and y

270 would be x,-y