Solve. 3(x-2)+17=2(x+7)

Answer:

Profit % on skates = 8.7 %

Step-by-step explanation:

Step 1 : Find cost price of skates

Cost price of helmet = £45

Let cost price of skate be = x

Selling price = £224

Cost price = (x + 45)

Total profit % = 40%

\(Profit \% = \frac{Selling \ price - cost \ price }{Cost \ price} \times 100\)

\(\frac{40}{100} = \frac{224 - (x + 45)}{(x + 45)}\\\\40(x+ 45) = 100(224 - (x +45))\\\\40(x + 45) = 22400 - 100(x + 45)\\\\40(x +45) + 100(x+ 45) = 22400\\\\140(x + 25) = 22400\\\\x + 45 = \frac{22400}{140}\\\\x = 160 - 45 = \£ \ 115\)

Total cost price = 45 + 115 = £160

Step 2 : Selling price of Helmet

Cost price of Helmet = £45

Let selling price of helmet be = y

Profit % of helmet = 120 %

\(Profit \% = \frac{selling \ price - cost \ price}{cost \ price}\)

\(\frac{120}{100} = \frac{y -45}{45}\\\\\frac{120 \times 45}{100} = y -45\\\\54 = y - 45\\\\99 = y\)

Step 3 : Selling price of skates

Total selling = selling price of helmet + selling price of skates

224 = 99 + selling price of skates

224 - 99 = selling price of skates

125 = selling price of skates

Step 4 : Profit percentage on skates

Cost price of skate = £ 115

Selling price of skate = £ 125

\(Profit \% \ on \ skates = \frac{selling\ price- cost \ price }{cost \ price} \times 100\)

                           \(= \frac{125-115}{115} \times 100\\\\=\frac{10}{115} \times 100\\\\= 8.7 \%\)

Step-by-step explanation:

Use the first fundamental theorem of calculus.

∫₆¹⁰ f'(x) dx = f(10) − f(6) = 8 − 8 = 0

Answer:

x = 6

Step-by-step explanation:

First, we need to cross multiply on both sides, which gives us:

9 * (5x - 6) = 27 * (2 + x)

45x - 54 = 54 + 27x

Now, we want to isolate x on either side.

We can substract 54 from both sides:

(45x - 54 = 54 + 27x) - 54

45x - 108 = 27x

We then subtract 45 from both sides:

(45x - 108 = 27x) - 45

-108 = -18x

Finally, we divide both sides by -18:

(-108 = -18x) / -18

6 = x

y = 6x + 2 is the function which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

The linear function in the form y = mx + b represents the situation where y represents the cost of the babysitting job

x represents the number of hours, "m" represents the hourly rate, and "b" represents the additional fee (bus fare).

y = 3x + 2 represents an hourly rate of 3 and an additional fee of 2.

y = 3x + 1 represents an hourly rate of 3 and an additional fee of 1.

y = 6x + 2 represents an hourly rate of 6 and an additional fee of 2.

y = -6x + 2 represents a negative hourly rate of -6 and an additional fee of 2.

Hence, y = 6x + 2 is the which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

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Answer:

y=7 and x=52

Step-by-step explanation:

the first one

is to decide both side by 5

and the second one is too

subtract both sides with 24

If  a player hits a ball while a bird is flying across the field. The intersection points of the equations represent: C the time when the height of the ball and the bird are the same.

Intersection points  can be defined as the points in which two parallel lines meet each other.

Given data:

Height of the baseball over time = h = –16t² + 65t

Height of a bird over time = h = 8t + 20

Where:

t = time in seconds

h = height in feet

–16t² + 65t =  8t + 20

-16t² +57t -20 =0

So,

t = -57 ±√57² -4×(-16) × (-20) / 2× (-16)

t = -57±√3249  -1280/ -32

t = -57 ±√1969 /-32

t = -57 + 44.373 / -32

t =  -12.627 /-32

t =.395

And

t = -57 - 44.373 / -32

t =  -101.373 /-32

t =3.168

Based on the above of the height of both the baseball and the bird, the time when the height of the ball and the bird are the same  are the points were the two lines intersect.

Therefore the correct option is C.

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Answer:

(C) 1466

Step-by-step explanation:

The hour hand makes one revolution each 12 hours. So it makes 2 revolutions a day.

The minute hand makes one revolution each hour. So it makes 24 revoulutions a day.

The second hand makes one revolution each minute. So it makes 24*60 = 1440 revolutions a day.

In total:

2 + 24 + 1440 = 1466

The correct answer is C.

We learn from the query that Marcus will be preparing 10 vanilla sundaes.

An ice cream sundae is described as "A dessert of ice-cream topped or blended with squashed fruit, nuts, syrup, condensed milk, etc." in the Oxford English Dictionary. Simple explanation provided by Mark Dow's Famous Pizza manager: "As soon as we add a toppings, it's a sundae.

Total sundaes = 25

Mint sundaes = 1/5 x 25 = 5

Chocolate sundaes = 10

Total of mint and chocolate sundaes = 5 + 10 = 15

Vanilla sundaes = Total sundaes - Total of mint and chocolate sundaes

Vanilla sundaes = 25 - 15 = 10

Therefore, Marcus will be making 10 vanilla sundaes.

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ANSWER

B. 2.9 m

EXPLANATION

Let's draw the slide with the given information,

As we can see, the slide forms a right triangle with the ground. The length of the slide is the hypotenuse of the triangle and its height is the opposite leg to the given angle.

We have to use a trigonometric ratio to solve this problem and, with the given information, the one that best fits is the sine of the angle since it is the ratio between the opposite leg and the hypotenuse,

In this problem, the angle is 35°, the opposite leg is h and the hypotenuse is 5.1m,

Solving for h,

Hence, the height of the top of the slide is 2.9 m, rounded to the nearest tenth.

Answer: E, A

Step-by-step explanation:

Answer:

a-25

b-243

5^3 = 125/3 = 25

3^6 = 729/3 = 243

The answer to the equation is 63.275

First you must set up the equation.

\(\frac{2531}{40}\)

Then, divide the terms.

63.275

To calculate the circumference of a circle, you can use the formula:

\(\displaystyle C=2\pi r\)

Where \(\displaystyle C\) represents the circumference and \(\displaystyle r\) represents the radius of the circle.

Given that the radius \(\displaystyle r\) is 8 inches, we can substitute this value into the formula:

\(\displaystyle C=2\pi (8)\)

Simplifying the expression:

\(\displaystyle C=16\pi \)

Thus, the circumference of a circle with a radius of 8 inches is \(\displaystyle 16\pi \) inches.

Note: \(\displaystyle \pi \) represents the mathematical constant pi, which is approximately equal to 3.14159.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The required implicit solution to the initial-value problem would be  5x²- y² = 9.5 which is the equation of a hyperbola.

Hyperbola is defined as a conic section, a two-branched open curve, produced by the intersection of a circular cone.

(x-h)²/b² - (y-k)²/a² = 1

We have been given that 5x²- y² = c is a one-parameter family of solutions of the differential equation.

To determine an implicit solution to the initial-value problem ydy/dx = 5x

⇒ y dy/dx = 5x

⇒ y dy = 5x dx

⇒ y²/2 = 5x²/2 + c

If y(3) = −8 which is the means that when substitute x = 3 then y = -8

⇒ (-8)²/2 = 5(3)²/2 + c

⇒ 64/2 = 5(9)/2 + c

⇒ 32 = 22.5 + c

⇒ c = 9.5

Substitute the value of c in the given function 5x²- y² = c

⇒ 5x²- y² = 9.5 which is the equation of a hyperbola.

Therefore, the implicit solution to the initial-value problem would be  5x²- y² = 9.5.

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We can use the formula for the monthly payment of a loan to calculate the amount we need to pay each month:

M = (P * r * (1+r)^n) / ((1+r)^n - 1)

Where:

M = the monthly payment

P = the principal (the amount borrowed)

r = the monthly interest rate (which is the annual interest rate divided by 12)

n = the total number of months in the loan term (which is the number of years multiplied by 12)

Plugging in the given values, we get:

P = $3825

r = 15% / 12 = 0.0125

n = 4 years * 12 = 48 months

M = ($3825 * 0.0125 * (1+0.0125)^48) / ((1+0.0125)^48 - 1)

M ≈ $94.87

Therefore, the monthly payment will be approximately $94.87.

Answer:

cscθ = 5/4, secθ = 5/3

Step-by-step explanation:

First, let's view the drawing that I have attached, with the dot in the bottom left representing the origin. We know that cosecant and secant are the reciprocals of sin and cos respectively, and in order to find sin and cos, we must find the opposite, adjacent, and hypotenuse sides. The hypotenuse is opposite the right angle, equal to √(8²+6²) = 10

Next, we can find sin and cos of θ . sinθ = 8/10=4/5, making cscθ the reciprocal of 4/5, or 5/4

Similarly, cosθ = 6/10=3/5, and secθ = 5/3

Answer:

14.73.

Step-by-step explanation:

Answer:

See image below for answer:)

Step-by-step explanation:

Answer:

For every 1 cup of blue paint used, 1.5 cups of red paint are used.

Step-by-step explanation:

1. We know that constant of proportionality is 1.5 because when we divide the number of cups of red paint by the number of cups of blue paint, we get 1.5.

2. Since 1 cup of red paint is used every 1.5 cups of red paint, this is equivalent to the constant of proportionality.

Therefore, the answer is For every 1 cup of blue paint used, 1.5 cups of red paint are used.

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

\(y1 = 4 \\ x1 = 3\)

\(y - y1 = m(x - x1)\)

\(y - 4 = 0(x - 3)\)

\(y - 4 = 0\)

\(y = 4\)

The difference between the regression equation is Equation 2 is the estimated value of the model in equation 1, to be exact.

Regression analysis evaluates the association between the factors and variable and determines how changes in the independent variable impact the dependent variable. Equation Y is equal to aX plus b, where Y is the dependent variable, an is the slope of the regression equation, x is the independent factor, and b is a constant, is used to represent it.

Regression analysis is one of the most used statistical techniques for determining the relationships between a number of independent and dependent variables.

The two equations are:

y=b0+Bx .........(1)

y=b0+b1x............(2)

The parameter and estimate in the two equations are different.

Equation 1 contains the model that is presumptively present in the data collection. As a result, the parameters or actual values of the regression coefficient make up this model.

Now that these regression coefficients have been determined using the sample data, equation 2 is used to represent the result.

Equation 2 is the estimated value of the model in equation 1, to be exact.

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1) A(1,2),A'(-1,2) : a reflection across the y-axis

2) A(1,2), A'(-2,1): a rotation 270⁰ clockwise around the origin

3) A(1,2),  A'(-1,4):  a translation of 2 units left and 2 unit up

4) A(1,2),A'(-1,-2): a rotation 180⁰ around the origin

5) A(1,2),A'(-3,-7): a translation of 4 units left and 9 units down

What is the transformation of a point?

The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

The given point is A(1,2).

The rule of a rotation 180⁰ around the origin is (x,y)→(−x,−y).

Therefore, A(1,2)→A'(-1,-2).

A rule of translation of 2 units left and 2 unit up is (x,y)→(x-2,y+2)

Therefore, A(1,2)→A'(1-2,2+2) = A'(-1,4).

The rule of a reflection across the y-axis is (x,y)→(−x,y).

Therefore, A(1,2)→A'(-1,2)

A rule of translation of 4 units left and 9 units down is (x,y)→(x-4,y-9)

Therefore, A(1,2)→A'(1-4,2-9) = A'(-3,-7).

The rule of a rotation 270⁰ clockwise around the origin is (x,y)→(-y,x)

Therefore, A(1,2)→A'(-2,1)

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Answer:

Step-by-step explanation:

The equation that is equivalent to P = B + Brz is:

r = (P - B) / Bz

To see why, we can rearrange the original equation as follows:

P = B + Brz

P - B = Brz

(P - B) / Bz = r

Therefore, r = (P - B) / Bz is equivalent to P = B + Brz.

Now let's check the given options:

x = P/Br + 1/r

This equation is not equivalent to P = B + Brz.

r = (P - B) / Bz

This is the correct equation that is equivalent to P = B + Brz.

r = Bz / (P - B)

This equation is not equivalent to P = B + Brz.

B = P / (rz + 1)

This equation is not equivalent to P = B + Brz.

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Answer:

The answer is "0.869"

Step-by-step explanation:

Number of sample \((n) = 84\)

Number of correct response \((X) = 73\)

Calculating the Sample proportion:

Formula:

\(\text{Sample proportion}=\frac{\text{number of sample}}{\text{correct responses}}\)

                              \(=\frac{n}{X}\\\\= \frac{73}{84} \\\\=0.869\)

Answer:

$36

Step-by-step explanation:

The stock value of $40 increased by 20%.

Increased value

= 20% of $40

= (20/100) × $40

= $800/100

= $8

New stock value

= Initial value + increased value

= $40 + $8

= $48

Then, the value decreased by 25%.

Decreased value

= 25% of $48

= (25/100) × $48

= $1200/100

= $12

New stock value

= Initial value + decreased value

= $48 - $12

= $36

So, the resulting stock value is $36.

Answer:

The resulting value of the stock is $36.

Step-by-step explanation:

First, we need to find out what 20% of $40 is.

40 x 0.20 = 8

40 + 2 = $48

Therefore, the stock value, when increased, is $48.

Now, we need to see what 25% of $48 is.

48 x 0.25 = 12

48 - 12 = $36

Therefore, the resulting value of the stock is $36.

Answer:

x ≥ 1.5

Step-by-step explanation:

2x - 3 ≥ 0 ( add 3 to both sides )

2x ≥ 3 ( divide both sides by 2 )

x ≥ 1.5

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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