Find the measure. (Lesson 5-1)
TQ

150 is   the cost of renting a car from YourPal.

What is surface area of cuboid ?

Proxy car equation: y = 0.32x + 18

YourPal equation: y = 0.36x + 12

Set equations right sides equal to each other... meaning their cost, y, are equal

0.32x + 18 = 0.36x + 12

18 = 0.04x + 12  (subtract 0.32x from both sides of the equation)

6 = 0.04x            (subtract 12 from both sides of the equation)

150 = x               (divide both sides of the equation by 0.04)

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Answer:

Frictional force (F(frict)) = 17.1 N

Normal force (F(norm)) = 78.0 N

Gravitational force (F(grav)) = 63.7 N

Acceleration (a) = 1.2 ms⁻²

Step-by-step explanation:

Newton's second law:

[tex]\boxed{F_{net}=ma}[/tex]

where:

Use trigonometry to resolve the 28.5 N force into its horizontal and vertical components since it is acting on the particle at 30°:

[tex]\implies F_x=28.5 \cos 30^{\circ}[/tex]

[tex]\implies F_y=28.5 \sin 30^{\circ}[/tex]

Due to the particle's mass, m, and the acceleration due to gravity, g:

[tex]\boxed{W=mg}[/tex]

Given:

[tex]\begin{aligned}W & = mg\\\implies W & = 6.5 \times 9.8\\W & = 63.7\;\sf N\end{aligned}[/tex]

The particle is moving parallel to the plane (the horizontal), so acceleration perpendicular to the plane is zero.

Resolving forces vertically (taking ↑ as positive):

[tex]\begin{aligned}F & = ma\\\implies R-W-28.5 \sin 30^{\circ}&=6.5 \times 0\\R-W-28.5 \sin 30^{\circ}&=0\\R & = W+28.5 \sin 30^{\circ}\\R & = 6.5(9.8)+28.5(0.5)\\R & = 63.7+14.25\\R & = 77.95\\R & = 78.0 \;\; \sf N\; (1\:d.p.)\end{aligned}[/tex]

When a moving object is acted on by a frictional force, fiction is limiting, and the frictional force F is at its maximum value:

[tex]\boxed{F = \mu R}[/tex]

(Where μ is the coefficient of friction and R is the normal reaction).

[tex]\begin{aligned}F & = \mu R\\\implies F & = 0.22 \times 77.95\\F & = 17.149\\F & = 17.1 \;\; \sf N\;(2\:d.p.)\end{aligned}[/tex]

Friction always acts in the opposite direction to motion (or potential motion).

Resolving forces horizontally (taking → as positive):

[tex]\begin{aligned}F & = ma\\\implies 28.5 \cos 30^{\circ}-F & = 6.5a\\28.5 \left(\dfrac{\sqrt{3}}{2}\right)-17.149 & = 6.5a\\\dfrac{57\sqrt{3}}{4}-17.149 & = 6.5a\\7.532724008 & = 6.5a\\a & = 1.158880617\\a & = 1.2\; \sf ms^{-2}\;\;(1\:d.p.)\end{aligned}[/tex]

The product in scientific notation of (4.12 × 10^−9)(8.3 × 10^15) is  3.4196 * 10^7

The product expression is given as

(4.12 × 10^−9)(8.3 × 10^15)

Rewrite properly as

(4.12 × 10^−9)(8.3 × 10^15) =  (4.12 × 10^−9) * (8.3 × 10^15)

Evaluate the product of 4.12 and 8.3 in the above expression

So, we have

(4.12 × 10^−9)(8.3 × 10^15) =  34.196 * 10^−9 × 10^15

Evaluate the product of 10^−9 and 10^15 in the above expression

So, we have

(4.12 × 10^−9)(8.3 × 10^15) =  34.196 * 10^6

Rewrite the expression as

(4.12 × 10^−9)(8.3 × 10^15) =  3.4196 * 10^7

Hence, the product in scientific notation of (4.12 × 10^−9)(8.3 × 10^15) is  3.4196 * 10^7

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Answer:

Its B. 3.4196 x 10^7

Step-by-step explanation:

This is correct answer :))

Answer:

Step-by-step explanation:

The length and the width of the rectangle basee on the perimeter will be 2 and 4cm.

How to calculate the value?

From the given rectangle,

Length of the rectangle = 5 cm

Width of the rectangle = 10 cm

Ratio of length : width = 1 : 2

Perimeter of the rectangle = 2(l + b)= 150 cm

l + b = 75 -----(1)

Since, l : b = 1 : 2

b = 2l ------(2)

From equations (1) and (2)

l + 2l = 75

3l = 75

l = 75/3

l = 25 m

Width 'b' = 2(25) = 50 m

Now we have to draw a rectangle with a scale = 25 : 2

Therefore, the scale factor =

l = 2 cm

Similarly,

w = 4 cm

Now we can draw a rectangle with length = 2 cm and width = 4 cm.

Answer:

Perimeter = 2(Length + Width)     | Formula for perimeter

102 = 2(3m + m)                             | Plug in value of length and width

102 = 2(4m)                                    | Combine like terms

102 = 8m                                        | Distribute 2

8m = 102                                        | Flip LHS and RHS

m = 12.75m                                    | Divide by 8 on both sides

Answer m = 12.75 ft

The number of packs of hot dogs bought is 2 packs

The number of packs of hamburgers bought is 4 packs

Let x represent the number of hot dogs bought and y represent the number of hamburgers bought

x + y= 6.........equation 1

2.65x + 6.29y= 30.46.........equation 2

From equation 1

x + y= 6

x= 6 - y

Substitute 6 - y for x in equation 2

2.65(6-y) + 6.29y = 30.46

15.9 - 2.65y  + 6.29y = 30.46

3.64y = 30.46 - 15.9

3.64y= 14.56

y= 14.56/3.64

y= 4

Substitute 4 for y in equation 1

x + y= 6

x + 4= 6

x= 6 - 4

x= 2

Hence 2 packs of hot dogs and 4 packs of hamburgers were bought

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The equation of the line y = -3x + 17 would have a graph that is shown in the diagram attached below.

Given that the line y = -3x + b goes through the point B(5, 2), it means that the slope (m) of the line would be -3, while the line would intercept the y-axis at b.

To find the value of b, substitute (x, y) = (5, 2) into y = -3x + b:

2 = -3(5) + b

2 = -15 + b

2 + 15 = b

17 = b

b = 17

Thus, the equation of the line y = -3x + 17 would have a graph that is shown in the diagram attached below.

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If m FH = (31x + 3°), m GH = (33x + 3°) and m ∠FHG = (28x − 3°) then the measure of ∠FGH is 48°.

Given: m FH = (31x + 3°), m GH = (33x + 3°) and m ∠FHG = (28x − 3°)

Based on the above information, we get

m FG = 2(m ∠FHG) = 2(28x - 3)°= (56x - 6)°

The arcs in the circle add up to 360 degrees, then

m FG + m FH + m GH = 360°

120x = 360°

x = 3

Substitute the value of x in  m ∠FHG in we get

28(3) - 3 = 81°

The measure can be found using the triangle sum theorem (all angles in a triangle must add up to 180°).

Firstly, it is known that ∠GFH would be an inscribed angle if the chord from F to G is drawn, and the arc GH would be twice its measure.

m GH = 33(3) + 3 = 102°

Half of that would be m ∠GFH = 51°

According to the triangle sum theorem all angles of the triangle must add up to 180°:

Therefore, m ∠GFH+ m ∠FGH +m ∠FHG= 180°

m ∠FGH = 48°

Therefore, the measure of ∠FGH is 48°.

The complete question is:

Given: circle k(O), m FH = (31x + 3°) m GH = (33x + 3°)

m ∠FHG = (28x − 3°) Find: m ∠FGH

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Functions can be reflected on the x-axis, the y-axis, or both axes. For example, function reflection y= f(x) can be written as y= -f(x) or y= f(-x) even y= -f(-x). There are four types of function or graph transformations: reflection, rotation, translation, and dilation. In mathematics, especially geometry, mirror or mirroring means flipping, so basically, the mirroring of a function is the mirror image of a given function or graph. Hence the reflection function is commonly known as the reflection function.

The reflection of the given function should be similar in size and shape to the original function.

f(x)=x+1; x-axis

(consult the pictures attached)

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Conversion a mixed number 9 7/

8

to a improper fraction: 9 7/8 = 9 7/

8

= 9 · 8 + 7/

8

= 72 + 7/

8

= 79/

8

To find a new numerator:

a) Multiply the whole number 9 by the denominator 8. Whole number 9 equally 9 * 8/

8

= 72/

8

b) Add the answer from previous step 72 to the numerator 7. New numerator is 72 + 7 = 79

c) Write a previous answer (new numerator 79) over the denominator 8.

Nine and seven eighths is seventy-nine eighths

Conversion a mixed number 2 3/

8

to a improper fraction: 2 3/8 = 2 3/

8

= 2 · 8 + 3/

8

= 16 + 3/

8

= 19/

8

To find a new numerator:

a) Multiply the whole number 2 by the denominator 8. Whole number 2 equally 2 * 8/

8

= 16/

8

b) Add the answer from previous step 16 to the numerator 3. New numerator is 16 + 3 = 19

c) Write a previous answer (new numerator 19) over the denominator 8.

Two and three eighths is nineteen eighths

Subtract: 79/

8

- 19/

8

= 79 - 19/

8

= 60/

8

= 4 · 15/

4 · 2

= 15/

2

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 8 = 64. In the following intermediate step, cancel by a common factor of 4 gives 15/

2

.

In other words - seventy-nine eighths minus nineteen eighths is fifteen halfs.

Conversion a mixed number 24 4/

5

to a improper fraction: 24 4/5 = 24 4/

5

= 24 · 5 + 4/

5

= 120 + 4/

5

= 124/

5

To find a new numerator:

a) Multiply the whole number 24 by the denominator 5. Whole number 24 equally 24 * 5/

5

= 120/

5

b) Add the answer from previous step 120 to the numerator 4. New numerator is 120 + 4 = 124

c) Write a previous answer (new numerator 124) over the denominator 5.

Twenty-four and four fifths is one hundred twenty-four fifths

Conversion a mixed number 6 3/

5

to a improper fraction: 6 3/5 = 6 3/

5

= 6 · 5 + 3/

5

= 30 + 3/

5

= 33/

5

To find a new numerator:

a) Multiply the whole number 6 by the denominator 5. Whole number 6 equally 6 * 5/

5

= 30/

5

b) Add the answer from previous step 30 to the numerator 3. New numerator is 30 + 3 = 33

c) Write a previous answer (new numerator 33) over the denominator 5.

Six and three fifths is thirty-three fifths

Subtract: 124/

5

- 33/

5

= 124 - 33/

5

= 91/

5

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Answer:

B

Step-by-step explanation:

-20+-32.5= -52.5

-52.5+ 40= -12.5

For 2 hours the cost will be same.

Firstly forming the equation as per the given information in question. Let us assume the number of hours to be t.

Cost on choosing first campus -

Cost = 25 × t

Cost on choosing second campus -

Cost = 10 + 20 × t

Now, equating both the equations to find the required time..

25t = 10 + 20t

Shifting 20t to Left Hand Side of the equation

25t - 20t = 10

Performing subtraction to find the value of t

5t = 10

Shifting 5 to Right Hand Side of the equation at denominator

t = 10÷5

Performing division to find the value of t

t = 2

Therefore, the number of hours for which the costs are the same is 2.

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Answer:

Yes.

Step-by-step explanation:

Is it possible to find the area of a parallelogram by just multiplying the lengths of two adjacent sides?

It is to find the area of a parallelogram by just multiplying the lengths of two adjacent sides. Let us now find a relation, if any, between the areas of two parallelograms on the same base and between the same parallels.

Answer:

6

Step-by-step explanation:

Let the amount of cars washed be x

120-12

---------- = x

18

108/18 =x

x=6

The value of the polynomial at the point [tex]x=a[/tex], just replace [tex]x[/tex] with [tex]a[/tex] in the polynomial equation.

Verify the following equation:

[tex]=4x^{2} -7x+5[/tex]

The given solution:

[tex]x=-3[/tex]

[tex]4x^{2} -7x+5[/tex]

Find the equation:

[tex]4x^{2} -7x+5[/tex]

[tex]4(-3x)^{2} -7(-3)+5[/tex]

[tex]=4(9)+21+5[/tex]

[tex]=36+26[/tex]

[tex]=62[/tex]

Therefore,The option E [tex]62[/tex] is the correct answer

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Answer:

The segment bisector of RS is KM and RS Lenght is 34CM

Step-by-step explanation:

17+17=34

The largest integer of the three even consecutive integers is 24

We have been given that there are 3 even consecutive integers.

Let the first integer be = x

Let the second integer be = (x+2)

Let the third integer be = (x+4)

According to the question, the equation according to the condition given will be

x + 3(x+2) = 38 + 2(x+4)

Solving the equation, the value of x will be

x + 3x + 6 = 38 + 2x + 8

4x + 6 = 46 + 2x

2x = 40

x =20

Hence, the integers are

            first term = x =20

            Second term = x+2 = 20+2 = 22

           Third term = x+4 = 20+4 = 24

Thus the largest integers is 24

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The numbers in order from the least to the greatest is  5, -45/7, -2.2, 13/7, 2.5, √9, 3.5.

When ordering a number from the least to the greatest, the negative number is smaller than the positive numbers. The farther a negative number is from 0 on the number line, the smaller the number is. The farther a positive number i from 0 on the number line, the larger the number is.

To order a number from least to greatest, convert al the numbers to decimals. A decimal is a number that is made up of integers and non-integers. The integers are separated from the non integers by a decimal point.

√9 = 3

-30/6 = - 5

13 / 7 = 1.857

- 4 5/9 = -4.56

The numbers ordered from least to greatest is:- 5, -45/7, -2.2, 13/7, 2.5, √9, 3.5

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Answer:

x+3=3+x

x+3=x+3

Step-by-step explanation:

Answer:

Step-by-step explanation:

10)99

16)a)4/13

b)8/13

c) 7/13

Using translation concepts, the equation for the translated graph is given by:

g(x) = |x + 2| + 1.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis, or rotations of a degree measure around the origin.

From the graph, we have that the parent function was:

Hence, considering the parent function f(x) = |x|, the equation for the translated graph is given by:

g(x) = |x + 2| + 1.

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   The function g(x) is a quadratic function:

 Functions are algebraic expressions that have at least two variables, in order to make their visual representation through a graph and evaluate their behavior.

 This problem deals with linear or quadratic functions, and these differ in the degree of the exponent of the variable:

  1 : linear

  2 : quadratic

  The function:

g(x) = -2x² - 3(x- 2).

g(x) = -2x² - 3x + 6 , we have a quadratic function.

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The order from least to greatest is negative 7.7 repeating, negative seven and one sixth,  forty-four sixths and square root of 60

To determine the order from least to greatest is to arrange the values in an ascending order.

Given the values as;

This is expressed as;

√60 = 7. 75

-7. 7

44/ 6 = 7. 33

-7 1/6 = -43/ 6 = -7. 17

The order from least to greatest is -7. 7, -7. 17 , 7. 33 and 7. 75

Thus, the order from least to greatest is negative 7.7 repeating, negative seven and one sixth,  forty-four sixths and square root of 60

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Both Fahrenheit and Celsius scales will have the same reading at temperature -40⁰.

The equation to convert temperature reading from Celsius to Fahrenheit degree is:

     F = (9/5) C + 32

Where:

F = Fahrenheit reading

C = Celsius reading

The equation tells us that the ratio of increment in Fahrenheit to Celsius scale is 9 : 5, and there is an offset 32 degree in Fahrenheit scale.

Suppose a specific temperature has the same number reading on both scales, then:

F = C

Substitute this into the equation:

F = (9/5) C + 32

C = (9/5) C + 32

C - (9/5) C = 32

-4/5 C = 32

C = 32 . (-5/4) = -40

Hence, both Fahrenheit and Celsius scales have the same reading at temperature -40⁰.

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The answer type is interval and the interval is (-∞,5).

The value of x is the domain for which the function is defined. Function in this case can use value from (-∞,5).

Graphs can be used to specify the domain and set of functions. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The range is the collection of potential output values, as displayed on the y-axis. Remember that the domain and range of the graph may be larger than the values seen if the graph extends beyond the area that is visible.

Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

Hence, The type of answer is interval and the values of interval is (-∞,5).

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The required no . is 1 / q where q > 2 and q is natural no .

For instance , let's take 1 / 2 ,

1 / 2 is one possible solution to this .

1 / 2 is not irrational .

Opposite of 1 / 2 is 2 which is a natural no .

Clearly , 1 / 2 is not a whole no .

Even it is greater than - 13 .

All the conditions are satisfied , hence 1 / 2 is one possible solution to this problem .

All the nos . of the form 1 / q where q > 2 and q is natural no . will satisfy the conditions of the question .  

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The ratio of quarts of punch to cans of frozen orange is 3/2 with maintaining the ratio to make 4 quarts of a punch we need 2 2/3 cans of frozen orange.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Given that,

2 cans of frozen oranges are used to make 3 quarts of punch.

So,

quarts of punch/cans of frozen oranges = 3/2

Now with the same ratio if we use 4 quarts of punch

Then,

3/2 = 4/ cans of frozen orange

Cans of frozen orange = 4(2/3)

⇒ 8/3 = 2 2/3.

Hence " To make 4 quarts of a punch we need 2 2/3 cans of frozen orange".

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