A garment shop announces a flat 50% discount on every purchase of items for their customers. Draw that graph for the relation between the market price and the discount.
Hence find (1) the marked price when a customer gets a discount of Rs3250(from graph)
(2)the discount when the market price is rs2500

So, Sarah receives $9 as her allowance every week.

Sarah wants to deposit her allowance for 16 weeks straight, so she will have a total of $355 in her account.

We know that she had $211 initially in her account and after 16 weeks, she will have $355.

So the amount she will have to deposit every week as her allowance is:

$355 - $211 = $144

We can divide the total amount of allowance by the number of weeks to find out how much she receives per week:

$144 / 16 = $9

Therefore, Sarah receives $9 as her allowance every week.

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In case of parallel lines, the of the lines are always equal.

And the product of slopes of perpendicular lines is -1.

We know that the parallel lines are the lines in a plane that are always the same distance apart.

Also, the parallel lines never intersect.

The slopes of parallel lines are always equal.

The y-intercept of parallel lines is different.

Whereas, the perpendicular lines are the lines that intersect at a right angle (90 degrees angle).

The product of slopes of perpendicular lines is -1.

All perpendicular lines are always intersecting lines, but all intersecting lines need not be  perpendicular.

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Answer:

2y-7=5

Step-by-step explanation:

since the number represents y

the product of 2 and a number would be 2y

then since it says seven less than that you subtract 7 from 2y

this gives you 2y-7

finally, it says its equal to 5

so then all you have to put is 2y-7=5 as your answer since it only asks you to make the equation based off the sentence, not solve it.

The Booster Club sold 45 tickets to the adults and 110 tickets to the students.

In the given question, the Booster Club selling tickets wants to keep track of how many adult and student tickets they sold.

At a recent cross country meet, spectators had to pay to get in.

It cost $7 for adults and $3 for students.

However, they did know they sold 155 total tickets and made $645.

Let total x tickets sold to adults.

Let total y tickets sold to students.

They sold total 155 tickets. So the required equation is:

x + y = 155...(1)

The cost of one adult ticket is $7. So the cost of x tickets are 7x.

The cost of one student ticket is $3. So the cost of y tickets are 3y.

They earned total $645. So the required equation is:

7x + 3y = 645...(2)

Now solving the both equation using the elimination method

Multiply the equation 1 by 3 and then subtract by equation 2, we get

7x + 3y - (3x + 3y) = 645 - 465

After solving, we get

4x = 180

Divide by 4 on both side, we get

x = 45

Now putting the value of x in equation 1, we get

45 + y = 155

Subtract 45 on both side, we get

y = 110

Hence, the Booster Club sold 45 tickets to the adults and 110 tickets to the students.

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Answer:

=4r⁷

Step-by-step explanation:

(2r⁹) (8r⁴)

=_____

4r⁶

16r¹³

=______

4r⁶

=16r¹³ ÷ 4r⁶

=4r⁷.

Answer: 4r⁷

Step-by-step explanation: (2r⁹) (8r⁴) = _____ 4r⁶ 16r¹³ = ______ 4r⁶ 16r¹³ ÷ 4r⁶ 4r⁷

When triangle KLM is dilated with a scale factor of 0.75  the image K'L'M' will have sides reduced by the factor 0.75

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor.

The scale factor determines magnification or shrinking as follow

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

Hence for the triangle KLM, with a scale factor of 0.75, the sides will shrink by 0.75 = 3/4

Resulting to a smaller image K'L'M'

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Using BODMAS, the answer of the given question is  13232 / 15.

The brackets must be solved first, then powers or roots (i.e. of), Division, Multiplication, Addition, and finally Subtraction, according to BODMAS rule. Any expression can only be solved correctly if the BODMAS rule or the PEDMAS rule are applied.

The other operations must be solved in the same order. Brackets (B) are followed by the order of powers or roots, which is then followed by multiplication, addition, subtraction, and finally division.

According to the question,

[tex]27 \frac{2}{3} \times 32 - \frac{2}{5} \div 64^{\frac{5}{6} }[/tex]

Using BODMAS,

⇒ 83/3 × 32 - [tex]\frac{2}{5}[/tex] ÷ [tex]64^{\frac{5}{6} }[/tex]

⇒ 83/3 × 32 - 2/5 ÷ [tex](2^{6})^{\frac{5}{6} }[/tex]

⇒ 83/3 × 32 - 2/5 ÷ 2⁵

⇒  83/3 × 32 - 2/5 × 1/2⁵

⇒  83/3 × 32 - 2⁴/5

⇒ 2656 / 3 - 2⁴/5

⇒ 2656 / 3 - 16/5

⇒ 13280 -  48 / 15

⇒ 13232 / 15

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Answer: x=3-4y

                 _____

                   5

Step-by-step explanation:

The inverse of a number is it's reciprocal. Consider a number y where y is not equal to zero. Then the inverse of y is the reciprocal of the y that is 1/y.

The inverse is a function or an operation which reverses the order of operation of another function or an operation”.

For example, Calculate the inverse of a number 5, 15, 35 and 46.

To find out the inverse of a number, we have to take the reciprocal of the given numbers.

So, the inverse of the number 5 will be 1/5.

The inverse of the number 15 will be 1/15.

The inverse of the number 35 will be 1/35.

The inverse of the number 46 will be 1/46.

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A system of linear equations can be classified into 3 different ways based on their nature of roots and their graphical representation.

Step 1: Examine the given graph.

Step 2: Determine if the lines cross exactly once, are exactly the same, or are parallel to each other.

Step 3: Classify the system of linear equations as consistent dependent, consistent independent, or inconsistent based on your findings in step 2.

A system of linear equations is consistent dependent if it has an infinite number of solutions i.e the graphs of the lines in the system are the same, it is consistent independent when it has exactly one solution i.e the graphs of the lines in the system cross exactly once and a system is inconsistent if it has no solutions i.e the graphs of the lines do not intersect and they are parallel.

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Place your protractor on a straight line to measure the acute angle. Line up the horizontal line on the baseline of your protractor, placing the centre of your protractor over the vertex. Examine where the diagonal line crosses the protractor to specify the number of degrees in the acute angle.

Measuring angles is a significant topic in geometry. An angle can be measured by operating a protractor, precisely. An angle is measured in degrees, hence it's called ‘degree measure’.

One complete revolution is equivalent to 360 degrees, hence it is divided into 360 parts. Each part of the one complete revolution is a degree. If we know how to measure angles, then it will be very easy to construct an angle using a protractor.

Any angle whether it is an obtuse, acute, right or reflex angle, can be calculated using a protractor. Although we are able to differentiate between acute, obtuse or reflex angles, based on the right angle.

If we have two acute angles to calculate, then we cannot calculate the greater angle among the two. Thus, we have to use a protractor to measure the angles accurately.

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Examining the right triangle figure attached the value of sin  A is

The trigonometry sin A is worked using the pneumonic SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

Information from the question, viewing from angle A

opposite = 20

adjacent = 15

hypotenuse = 25

The value of sin A is calculated using sin, SOH

et the angle be x

sin x = Opposite / hypotenuse

sin x = 20 / 25

sin x = 4 / 5

sin x is 4/5

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Answer: Common difference = -4, and 25th term = -56

Step-by-step explanation:

The common difference, d, is 20 - 16 or 16 - 12, which is -4.

Using the formula [tex]a_{n}=a_{1}+(n-1)d[/tex], [tex]a_{25}=20+(20-1)*-4[/tex]

= 20 + 19 * -4,

= 20 - 76

= -56

The number of times the length of the shorter piece is the longer piece is 5 and The total length could be 72 inches.

What is ratio ?

ratio can be defined as the given value divided by the total value.

Given ,

A ribbon is cut into two pieces. The length of the longer piece is 60 inches and the length of the shorter piece is 12 inches.

The number of times the length of the shorter piece is the longer piece is

let the number of times be x .

so,

x = 60/12

x = 5

The total length could be = 60+12 = 72

hence, The number of times the length of the shorter piece is the longer piece is 5 and The total length could be 72 inches.

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If x is the quantity of trick skis sold and y is the quantity of slalom skis sold, and x and y are both nonnegative numbers, then x 0 and y 0.

We can see from the first row of the table that 6x + 4Y 216 because 6x indicates the work hours required to make x number of trick skis and 4y is required to make y number of slalom skis. We get at 6X + 4Y 216 since the sum (6x+4y) cannot be greater than 216 hours.

Using a similar logic, the second row provides us with the following inequality:

X + Y ≤ 40

X 0 Y 0 6 X + 4 Y 216 X + Y 40

The points at the vertices are:

A = (0, 0)\sB = (0, 40)\sC = (12, 28)\sD = (33, 0) (33, 0)

By intersecting the border lines, one can locate each vertex point. For instance, the intersection of the boundary lines 6x+4y = 216 and x + y = 40 is point C.

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The definition of an equation is an algebraic expression that often connects unknown variables to known variables or constants.

A general rule is that the algebraic expression should take any of the following forms: addition, subtraction, multiplication, and division. Bring the variable to the left side and the other values to the right side in order to find the value of x. To determine the answer, simplify the values.

Equations are mathematical expressions that often connect unknown variables to known variables or constants. For instance, x + 2 = 15 and y2 = 4 are both equations. An equation's solution, also known as its root, is any value or group of values that may be used to transform the equation into a true statement.

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Answer:

45y2

Step-by-step explanation:

After 8years the investment will have worth 2800

Simple interest is the interest amount for a particular principal amount of money at some rate of interest. In contrast, compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

Simple interest is given as:

I = (P×R×T)/100

where P = principal

R = rate of the interest

T = time for the loan / savings

therefore I = 2000× 5× 8/100

I = 800

Therefore that amount realized after 8years

= 2000+800 = 2800

therefore the investment will worth 2800 after 8 years.

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Total Surface area of the inner cube = 6 * 2 = 12 m²

Take a vertical cross-section through the center of the arrangement as shown in the following figure —

The surface area of the outer cube is 24 m²

Therefore, each face of this cube equals  4 m²

=> Each edge of the larger cube is two meters

The inner sphere's diameter is 2 meters since it meets the surface of the outer cube.

Thus, the sphere's radius (Viz OR) is equal to 1 m.

Taking into account Right Triangle OQR, QR  = √ [ 1² + 1² ] = √2 m

=> The smaller cube's face area is equal to 2 m².

The inner cube's total surface area is equal to 6 * 2 = 12 m²

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The full question:

A sphere is inscribed in a cube that has a surface area of 24 m2. A second cube is then inscribed within the sphere. What is the surface area of the inner cube?

Answer: x = 32 & y = 51

Step-by-step explanation:

Since

ΔMNP ≅ ΔTUS

Therefore

NP ≅ US

2x - y = 13

y = 2x - 13 __eq_1

Since

ΔMNP ≅ ΔTUS

therefore

∠N ≅ ∠U

so, if we find ∠N we'll be able to find ∠U as well



since the sum of angles of a triangle is 180, therefore

∠N = 180 - (∠M + ∠P )

∠N = 180 - (142 + 24)

∠N = 14°

we know ∠N ≅ ∠U

therefore

14 = 2x - 50

2x = 64

x = 64÷2

x = 32 __eq_2

putting eq_2 in eq_1

y = 

2x - 13

y = 2 (32) - 13

y = 51 __eq_3

x = 32 & y = 51 ...Answer

hope that helps...

Answer:

a) 14/4 or 3.5

b.) 148/15 or 9.8667

Step-by-step explanation:

a) 5¾ - 2¼

=23/4 - 9/4

LCM = 4

=23/4 - 9/4

=23. - 9

4

=14/4 OR 3.5

b) 7⅔ + 2⅕

=23/3 + 11/5

LCM = 15

=23/3 + 11/5

115. + 33

15

=148/15 OR 9.8667

The derivative of e7 is 7e7. The derivative of e^x is e^x, so the derivative of e7 is e7 times the derivative of x, which is 1, so the derivative of e7 is 7e7

The derivative of e^x is e^x, so the derivative of e7 is e7 times the derivative of x, which is 1, so the derivative of e7 is 7e7

The derivative of a function is a measure of how the output of the function changes with respect to a change in the input. In this case, we are looking for the derivative of the function e^7. The derivative of e^x is e^x, so the derivative of e7 is e7 multiplied by the derivative of x, which is 1. Therefore, the derivative of e7 is 7e7. This means that for every one-unit increase in the input value, the output of the function is increased by 7e7. This is useful for understanding how the output of a function changes in relation to a change in the input value. Knowing the derivative of a function can help us to better understand its behavior and make predictions about its future values.

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Answer:

6x^2 - 5x - 4

Step-by-step explanation:

Here you go. A pic.

Answer:

8.3 miles

Step-by-step explanation:

1 2/3 times 5= 8.3. He rode 8.3 miles

Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value(s) for the variable are entered, two algebraic expressions that are equivalent will have the same value (s).

An algebraic expression is a mathematical expression made up of variables, coefficients, constants, and operations including addition, subtraction, multiplication, and division. In most cases, something is said to be equivalent if two of them are the same.

Similar to this, analogous expressions in mathematics are those that, despite their differences in appearance, have the same meaning.

The two expressions, however, produce the identical outcome when the values are inserted into them.

Example

If the provided expression has an equivalent, write it down: 3x+9

Solution:

expressed in this way: 3x+9

The analogous equation is equal to the expression when 3 is removed from it, which is = 3(x+3).

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The required equations are y = 3x + 2, y = 3x + 5 which have no solution.

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

For no solution of equation,

equation of line must be parallel and for parallel line, Slope should be same.

Or we can say There won't be a solution if (a1/a2) = (b1/b2) (c1/c2). An inconsistent pair of linear equations is the name given to this kind of equation.

y = 3x + 2

y = 3x + 5

Thus, required two equation are y = 3x + 2, y = 3x + 5 which have no solution.

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a. The null hypothesis (H0) is that the proportion of those who are adequately prepared financially for retirement is the same for people in the 66-69 age group who did not complete high school as it is for the population of the 66-69-year-old (71%).

The alternative hypothesis (Ha) is that the proportion of those who are adequately prepared financially for retirement is smaller for people in the 66-69 age group who did not complete high school than it is for the population of the 66-69-year-old.

b. To calculate the p-value for this hypothesis test, we can use a one-sample proportion test. The sample proportion (p-hat) is 165/300 = 0.55. Using a z-test, with a z-score of -2.35 and a standard deviation of 0.058, the p-value is 0.011.

c. At a significance level of 0.01, the p-value of 0.011 is less than the significance level, so we reject the null hypothesis. We can conclude that there is evidence that the proportion of those who are adequately prepared financially for retirement is smaller for people in the 66-69 age group who did not complete high school than it is for the population of the 66-69-year-old.

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There is no particular formula for substitution instead it is a method to solve the linear equations in two variables.

The substitution method is a simple method to solve a system of linear equations algebraically and find the solutions of the variables. As the name implies, it applies to finding the value of the x-variable in terms of the y-variable from the first equation and then substituting the value of the x-variable in the second equation.

In this method, we can find the value of the y-variable by solving the equation. And then, we can substitute the value of y in any of the given equations to find the value of x. 

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Answer:the frist one

Step-by-step explanation:

For each quadratic equation, the value of a, b and c are mentioned below. Also maximum or minimum points are mentioned here.

A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.

Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.

The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.

a. y = 3x²-3x + 5, comparing this with general quadratic equation ax² + bx + c and get a = 3 and b = -3 and c = 5

thus x = - (b/2a)

x = - (-3/6)

x = -1/2

as a > 0 thus the equation has the minimum value and that is:

y = 3(-1/2)² -3(-1/2) + 5

y = 3/4 + 3/2 + 5

y = 13/2

b. y = -2x² + x  comparing this with general quadratic equation ax² + bx + c and get a = -2 and b = 1 and c = 0

thus x = - (b/2a)

x = - (1/-4)

x = 1/4

as a < 0 thus the equation has the maximum value and that is:

y = -2(1/4)² + (1/2)

y = -1/8 + 1/2

y = 3/8

c. y = 1/2x² + 6 comparing this with general quadratic equation ax² + bx + c and get a = 1/2, b = 0 and c = 6

thus x = - (b/2a)

x = - (1/2×0)

x = 0

as a > 0 thus the equation has the minimum value and that is:

y = 1/2(0)² + 6

y = 6

d. y=-3x² + 1/2x - 2 comparing this with general quadratic equation ax² + bx + c and get a = -3, b = 1/2 and c = -2

thus x = - (b/2a)

x = - [(1/2)/-6]

x = 1/12

as a < 0 thus the equation has the maximum value and that is:

y=-3(1/12)² + 1/2 (1/12) - 2

y = - 1/48 + 1/24 - 2

y = -45/48

e. y=x²-2x+6 comparing this with general quadratic equation ax² + bx + c and get a = 1, b = -2 and c = 6

thus x = - (b/2a)

x = - (-2/2)

x = 1

as a > 0 thus the equation has the minimum value and that is:

y=(1)²-2(1)+6

y = 5

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