Sophie and Marcos are each saving for new bicycles. So far, Sophie has $7 saved and can earn $4 per hour walking dogs. Marcos has $3 saved and can earn $6 per hour at his family's plant nursery. After how many hours of work will Sophie and Marcos have saved the same amount? What will that amount be? Use the system of equations below to complete the graph.

Answer:

Hi mate!

[tex] \bf \sqrt{ \frac{1 + \sin( \theta)}{1 - \sin( \theta)} } = \sec( \theta) - \tan( \theta) [/tex]

Step-by-step explanation:

By taking LHS,

[tex] \maltese \: \: \large \bf \sqrt{ \frac{1 + \sin( \theta)}{1 - \sin( \theta)} } [/tex]

[tex] : \longrightarrow \bf \sqrt{ \frac{1 + \sin( \theta)}{1 - \sin( \theta)} \times \frac{1 + \sin( \theta)}{1 + \sin( \theta)} } \\ \\ : \longrightarrow \frac{ {( \sqrt{1 + \sin\theta }) }^{2} }{( \sqrt{1 - \sin( \theta)})(\sqrt{1 + \sin( \theta)}) } \\ \\ : \longrightarrow \frac{ {( \sqrt{1 + \sin\theta }) }^{2} }{ \sqrt{ {1}^{2} - { \sin}^{2} \theta } } \: \\ \\ : \longrightarrow \: \frac{1 + \sin \theta}{ \cos \theta } \\ \\ \longrightarrow \: \frac{1}{ \cos \theta } + \frac{ \sin \theta}{ \cos \theta} [/tex]

[tex] \: \: \: \: \: \bigg\lgroup \because \: \frac{1}{ \cos \theta }\: = \sec \theta \: \\ \: \: \: \: \: \: \: \: \: \: \: \frac{ \sin \theta}{ \cos \theta} = \tan \theta \bigg \rgroup[/tex]

[tex] \implies \boxed{\pink{ \sec \theta + \tan \theta }}[/tex]

Now taking RHS

[tex] \sf \sec \theta + \tan \theta [/tex]

[tex]\implies \: \: \frac{1}{ \cos \theta } + \frac{ \sin \theta}{ \cos \theta} \\ \\ \implies \frac{1 + \sin \theta }{ \cos \theta } [/tex]

Hence, proved

Answer:

[tex]\large{\pink{\underline\textsf{To Prove :-}}}[/tex]

[tex] \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } = \sec \theta + \tan \theta[/tex]

[tex] \huge{\orange{\underline{\textsf{Solution :-}}}}[/tex]

[tex] \sf \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } [/tex]

[tex] \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } \times \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } \\ \sqrt{ \frac{ {(1 + \sin \theta) }^{2} }{(1 + \sin \theta)(1 - \sin \theta) } } \\ \sqrt{ \frac{ {(1 + \sin \theta) }^{2} }{1 - { { \sin}^{2} \theta } } }[/tex]

[tex] \sqrt{ \frac{( {1 + \sin \theta })^{2} }{ { \cos}^{2} \theta} } \\ \frac{1 + \sin \theta }{ \cos \theta } \\ \frac{1}{ \cos \theta} + \frac{ \sin \theta }{ \cos \theta } [/tex]

[tex]\sf{\red { \sec \theta + \tan \theta}}[/tex]

[tex] \sf \huge \purple {HENCE \: \: PROVED! }[/tex]

Answer:

A

Step-by-step explanation:

because it A because I can done that fast

Answer:

15.5 is the median.

The mean of the data is 22

Step-by-step explanation:

First, the median of a data set is found by sorting the numbers in order, from least to greatest. Then you count inwards one at a time on both sides until you reach a center number.

4 , 12, 15, 16, 40, 45

     12, 15, 16, 40

          15, 16

               15.5

This means, 15.5 is the median

Next, to find the mean, you add up all the numbers and divide it by however many numbers there are. In this case there are 6 numbers, so we divide the total by 6.

40 + 4 + 12 + 15 + 45 + 16 = 132

132 / 6 = 22

The mean of the data is 22

Answer:

Mean: 22

Median: 15.5

Step-by-step explanation:

hope this helps :)

Answer:

The answer is exactly -2,299. But since this is a mental math question it's okay if it's not the exact answer. The answer would be "A"

Answer:

k=10

Step-by-step explanation:

The reason is that we should solve the following equation:

4k+5 + 6k+10 + (180-115) = 180

by doing some basic algebra we get:

10k = 100

thus: k=10

The equation it has solutions of –5 and 7  is x^2-2x-37=0

We have equation

solutions of equation are –5 and 7.

We have to find complete the equation.

We have given that solutions of the equation are -5, 7.

The standard form of a quadratic equation.

[tex](x -\alpha) (x- \beta)[/tex]

Where we have

[tex]p = -(\alpha+\beta) and q = (\alpha\times \beta)[/tex]

So, roots are

[tex]( x- (-5)) (x-7)[/tex]

[tex]p = -( -5+7)[/tex] , [tex]q =(-5)(7).[/tex]

[tex]p = -2 and q = -35.[/tex]

On substituting p and q in equation

[tex]x^2+(-2)x-37=0[/tex]

[tex]x^2-2x-37=0[/tex]

Therefore,x^2-2x-37=0  is the equation of solution -5,7.

To learn more about the quadratic factor visit:

https://brainly.com/question/472337

Answer:

-2, -35

Step-by-step explanation:

Answer: 14.3178210633

Step-by-step explanation: d=√((x_2-x_1)²+(y_2-y_1)²)

Answer:

9

Step-by-step explanation:

4+4=8, 26-8=18, 18 / 2 = 9, and this is 100% right becuase I got it right on Khan Academy

Answer:x^2-9y^2

Step-by-step explanation:

x timesx +x(-3y)+3yx+3y(-3y)

Then simplify

X^2-9y^2

Answer:

The sum of all the sides to this quadrilateral will equal a total of 20 inches, so you set up the equation:

2 + 2x + 7 + x + 2 = 20

Solve for x by combining like terms;

(2 + 7 + 2) + (2x + x) = 20

Which simplifies to;

11 + 3x = 20

Get rid of constants;

-11          -11

3x = 9

Isolate x by getting rid of it's coefficient;

/3  /3

x = 3

Now, to find the length of PQ, we plug in the value of x(3) into the equation that contains the line PQ.

x + 2

3 + 2

= 5 inches.

Now, to find the length of RS, we plug in the value of x(3) into the equation that contains the line RS.

2x

2(3)

= 6 inches.

To maintain the ratio, the amount of salt required when 1 cup of brown sugar is used is 1.5teaspoon

Fractions are written as a ratio of two integers.

From the gven question, we are told that a recipe requires 3/4 cups of brown sugar and 1 1/8 teaspoons of salt, this can be expressed as:

3/4 cups = 1 1/8 teaspoons

To maintain the ratio, the amount of salt that is required when 1 cup of brown sugar is used is given as:

amount of salt required = (1 1/8)/3/4

amount of salt required =9/8 * 4/3
amount of salt required = 3/2
amount of salt required = 1 1/2 teaspoon

Hence to maintain the ratio, the amount of salt required when 1 cup of brown sugar is used is 1.5teaspoon

Learn more on ratio and proportion here: https://brainly.com/question/2914376

Answer:

The axis of symmetry of the graph of the parabola is -2

Step-by-step explanation:

Since the sharks depth in meters is relative to sea level over time in minutes we need to model this as x= 7-2x so 2 times 3 is 6 7-6=1

1 plus 1 equals 2

Answer:

C

Step-by-step explanation:

Step 1

Step 2

Answer:

............

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

[tex]1.40(8000) = 11200[/tex]

[tex].15(11200 - 8000) = .15(3200) = 480[/tex]

Step-by-step explanation:

Set the parameters,

Let the width be 'X' inhes

Therefore,

Length = "5X" inches

According to the given condition,

Perimeter = sum of the sides = 2(l+b) = 40 inches,

Equation = 2(5X+X) = 40

2(6X) = 40

12X= 40

X= 3.33

Therefore,

Width = X = 3.33 inches

An equation is formed of two equal expressions. The equation that has solutions of m=–5 and m=9 is (m+5)(m-9)=0.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

As it is given that the solution of m is -5 and 9. Therefore, the equation which will represent the solution of m as -5 and 9 is

(m+5)(m-9)=0

Hence, the equation that has solutions of m=–5 and m=9 is (m+5)(m-9)=0.

Learn more about Equation:

https://brainly.com/question/2263981

Answer:

Answer to question 1 is 18

Answer to question 2 is 4/5

Step-by-step explanation:

Question one simply asks how much one controller is

Being that both controllers = 36$

And to find one controller price you would just divide the price by the number of units

36/2= 18

The second question asks how much pizza would be more .6, 4/5 or .8, or .75

Since .8 has the most value or in this case pizza 4/5ths is the answer

The area of the composite figure if ab ≅ bc ≅ cd ≅ da ≅ dn is (2π + 40) mm².

The area of a semicircle is the space contained by the circle. The area is the number of square units enclosed by the sides of the shape.

The area of the composite figure if ab ≅ bc ≅ cd ≅ da ≅ dn is given by adding an  area of MKCD , area of ABCD, area of a semi-circle with AB as diameter.

Area of the composite figure = area of MKCD + area of ABCD + area of a semi-circle with AB as diameter.

The area of the composite figure is;

Area A = (DC + MK)/2 × DN + AB² + (1/2)×π×2²

Area A = (4 + 8)/2 × 4 + 4² + (1/2)×π×4

Area A = 24 + 16 + 2π = (2π + 40) mm²

Hence, the area of the composite figure if ab ≅ bc ≅ cd ≅ da ≅ dn is (2π + 40) mm².

To know more about the area of the semicircle click the link given below.

https://brainly.com/question/17098710

Answer:

please see photo above for details

3a. Area  = 2 (5×7 + 5×3 + 7×3)

3b. Area = 2 (6×6 + 6×5 + 6×5)

3c. Area = 2 (6.5×10 + 6.5×3 + 3×10)

4a. Area = 2(1/2 × 4 × 6) + 2(7×5) + 7×6

4b. Area = 2(1/2 × 6 × 6) + 2(10×8.5) + 10×6

4c. Area = 2(1/2 × 10.2 × 3.6) + 15×8.3 + 15×4.5 + 10.2×15

Using proportions, it is found that the speed of the sports car is of 85 miles per hour.

A proportion is a fraction of a total amount.

The cars are moving in the same direction, hence their relative speed is the difference of them.

The sports car is 0.5 miles faster over one minute, hence over one hour the difference is:

60 x 0.5 = 30 miles per hour.

Considering that the utility vehicle has a speed of 55 mph, the speed of the sports car is given by:

55 + 30 = 85 miles per hour.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

True, because if price changes, dod oes average of money. So if you get 5 bucks per 10 scarfs, you'll get 5.50$ for 11 scarfs

Step-by-step explanation:

Lets just say she gets half of what the actual cost is. In total.

Answer:

This is true

Step-by-step explanation:

Answer:

244 miles (nearest whole number)

Step-by-step explanation:

We can model this as a geometric series.

General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]

(where a is the first term and r is the common difference)

Given information:

Therefore:

Sum of the first n terms of a geometric series:

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

Therefore, sum of the first 19 terms:

[tex]\implies S_{19}=\dfrac{8(1-1.05^{19})}{1-1.05}[/tex]

[tex]\implies S_{19}=244.3120313...[/tex]

So Levi ran a total of 244 miles (to the nearest whole number)

Answer:

Graph= (-1,-8)

y= -8

x=-1

Step-by-step explanation:

Answer:

[tex]\red{ \bold{m \angle \: 1 = 54 \degree}} \\\: \purple{ \bold{m \angle \: 2 = 54 \degree}} [/tex]

Step-by-step explanation:

[tex](a) \: \: \: \\ r || s \: \: \: (given) \\ \implies \: m \angle \: 1 = m \: \angle \: 2 \\ (corresponding \: \angle s) \\ \implies \: (63 - x) \degree = (72 - 2x) \degree \\ \implies \: 63 - x = 72 - 2x \\ \implies \: 2x - x = 72 - 63 \\ \implies \: \huge \orange{ x = 9} \\ \\ (b) \\ m \angle \: 1 = (63 - x) \degree \\ \implies \: m \angle \: 1 = (63 - 9) \degree \\ \implies \: \red{ \bold{m \angle \: 1 = 54 \degree}} \\ \implies \: \purple{ \bold{m \angle \: 2 = 54 \degree}} \\ ( \because \: m \angle \: 1 = m \: \angle \: 2)[/tex]

Step-by-step explanation:

take the rectangle as whole with dimensions 16*8

area = 128 in^2

area of rectangle of dimensions 10*2 =20

required area = 108 in^2

The correct statements about the two-way frequency table are:

Option A, Option C, and Option E.

In Mathematics and statistics, A two-way frequency table is a tabular method for displaying relative data for two categories of variables. (See the attached).

The question (attached) shows that:

Learn more about a two-way frequency table at:

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Answer:

The answer is a,c, e

Step-by-step explanation:

Answer:

Step-by-step explanation:

x1= -3

y1= -4

m=5

y-y1=m(x-x1)

y-(-4)=5(x-(-3))

y+4=5(x+3)

y+4=5x+15

y=5x+15-4

y=5x+11