Alan bought 3 pencils and a notebook. The notebook cost $6, and he spent a total of $12. How much did each pencil cost? Use p to represent how much each pencil costs.

Answer:

70

Step-by-step explanation:

The solution to the system of equations is the point of intersection of the two lines which is at; (0.88, 0.65)

The two simultaneous equations of the line are given as:

y = -²/₅x + 1 -----(1)

y = 3x – 2   -----(2)

Subtracting equation 1 from equation 2 gives;

3.4x - 3 = 0

3.4x = 3

3.4x/3.4 = 3/3.4

x = 0.88

Substitute x = 0.88 in equation 2 to get;

y = 3(0.88) - 2

y = 2.65 - 2

y = 0.65

Thus, the solution to the system of equations is the point of intersection of the two lines which is at (0.88, 0.65).

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If Edward rewrote the product of [tex](5y/9)(x//3)(5y)(x^{3}/9)(4x)[/tex] is [tex](100x^{5}y^{2} )/243[/tex].

Given Expressions [tex](5y/9)(x/3)(5y)(x^{3}/9)(4x)[/tex].

We have to solve this expression by finding product and product is the result of multiplication of two numbers.

Expression is a combination of numbers, symbols, variables, coefficients, fraction of numbers. It is not expressed in equal to form. It is generally evaluated to form full expression not to find the value of variables. Numerator is the number above division sign and number below the division sign is known as denominator.

(5y/9)(x/3)(5y)(x^{3}/9)(4x)=

We have to first add powers of same variables. and multiply the coefficients of all the variables whether they are in numerator and denominators.

=[tex](4x^{5} *25y^{2}) /27*9[/tex]

=[tex](100x^{5} y^{2} )/243[/tex]

Hence the product of expressions (5y/9)(x/3)(5y)(x^{3}/9)(4x) is

(100x^{5} y^{2} )/243.

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Answer:

5xy + 15y / 36x

Step-by-step explanation:

B.

The ratio of the combined volume of these pyramids to the volume of the prism as a fraction is equal to 1/3.

Mathematically, the volume of a pyramid can be calculated by using this formula:

Volume = 1/3 × b × h

Where:

Since both pyramids have the same base area as the prism, their combined volume is given by:

Combined volume = (1/3 × b × h) + (1/3 × b × h)

Combined volume = 2/3 × b × h

Also, the volume of this prism = 1/2 × b × h

Thus, the ratio is given by:

Ratio = (2/3 × b × h)/(1/2 × b × h)

Ratio = 2/3 × 1/2

Ratio = 1/3.

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It has the same slope and the same y-intercept, that is, option a is the right choice.

A linear function in the slope-intercept is written as y = mx + b, where m represents the slope of the line and b represents the y-intercept.

We are given two linear functions and are asked to compare them.

First linear function:

Slope (m) = -7/9.

y-intercept (b) = 3.

Therefore, the linear function is: y = (-7/9)x + 3.

Second linear function:

Function given: y + 11 = (-7/9)(x - 18)

or, y + 11 = (-7/9)x + (-7/9)(-18)

or, y = (-7/9)x + 14 - 11 = (-7/9)x + 3.

Therefore, slope (m) = (-7/9)

y-intercept (b) = 3.

Therefore, we can say that it has the same slope and the same y-intercept, that is, option a is the right choice.

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60+90+ angle U = 180 {sum of angle of triangle}

or, 150+ U= 180

or, angle U = 30°

From here we got that ,

angle U is smallest.

We know that, side opposite to the shortest angle is shortest side. So , short leg is side PM

In right angled triangle PMU,

hypotenuse(h) = 10

angle theta = 60°

perpendicular (PM)= ?

NOW,

sin theta = Perpendicular/ hypotenuse

or, sin 60° = P/10

[tex] \\or \frac{ \sqrt{3} }{2} = p \div 10[/tex]

[tex] or\frac{10 \sqrt{3} }{2} = p[/tex]

[tex]or \: 5 \sqrt{3 } = p[/tex]

Therefore,

[tex]short \: leg = 5 \sqrt{3} [/tex]

The expression 21x⁴ + 56x³ + 49x² represents the area of the entire rectangle.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

The area of the rectangle = length x width

= (3x² + 8x + 7)(7x²)

[tex]\rm =7x^2\cdot \:3x^2+7x^2\cdot \:8x+7x^2\cdot \:7[/tex]

= 21x⁴ + 56x³ + 49x²

Thus, the expression 21x⁴ + 56x³ + 49x² represents the area of the entire rectangle.

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Answer:

one possible solution is 5/6

Step-by-step explanation:

Solving for x

0 < 3x - 2 < 1

Add 2 to each side

0+2 < 3x - 2+2 < 1+2

2 < 3x<3

Divide each side by 3

2/3 < 3x/3 < 3/3

2/3 < x < 1

X must be between 2/3 and 1

Getting a common denominator

4/6 < x < 6/6

So x can be 5/6

Answer:

Triangles a, b, and d

Step-by-step explanation:

The three triangles have a side length measurement, an angle measure, then another side length measurement

in that order (the order matters)

Triangle a,b and d are the answers.

"SAS" is when you know the two sides and the angle between them. Use the cosine theorem to calculate the unknown edge, then use the sine and cosine theorem to find the smaller of the other two angles, and then use the three angles that are 180 ° to find the last angle. .. The side of the

angle refers to the two rays or line segments that form the angle. In the figure below, the rays BA and BC are the sides of the angle ABC. An angle is formed by rotating a ray around its endpoint.

Edge-side assumptions-> If the two sides and edges of a triangle are congruent with the two sides and the edges of another triangle, the two triangles are congruent by the side-angle assumptions.

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By applying operations for complex numbers, we have these:

Herein we must apply the operations of summing two complex numbers, multiplying two complex numbers and multiplying a complex number by a real number, which are defined below:

Addition between two complex numbers

(a + i b) + (c + i d) = (a + c) + i (b + d)     (1)

Multiplication between two complex numbers

(a + i · b) · (c + i d) = (a · c - b · d) + i (b · c + a · d)

Multiplication of a complex number by a real number

k · (a + i b) = k · a + i k · b      (2)

Now we proceed to find the equivalent expressions:

- 5 · x + y = - 5 · (3 + i 8) + (7 - i) = (- 15 - i 40) + (7 - i) = - 8 - i 41

- x · y = - (3 + i 8) · (7 - i) = (- 3 - i 8) · (7 - i) = (- 21 - 8) + i (- 56 + 3) = - 29 - i 53

x · 2 · y = (3 + i 8) · 2 · (7 - i) = (3 + i 8) · (14 - i 2) = (42 + 16) + i (112 - 6) = 58 + i 106

2 · x - 3 · y = 2 · (3 + i 8) - 3 · (7 - i) = (6 + i 16) + (- 21 + i 3) = - 15 + i 19

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Using a decaying exponential function, it is found that the maximum height reached after the 10th bounce is of 20.62 cm.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, the parameters are:

A(0) = 192, r = 0.2.

Hence the maximum height after the nth bounce is:

[tex]A[n] = 192(0.8)^n[/tex]

After the 10th bounce, the maximum height in cm is of:

[tex]A[10] = 192(0.8)^10 = 20.62[/tex]

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Answer:

I don't know

Step-by-step explanation:

980-788711758c75ds47c75c70rz76vyif7cuc8f58x85c7f85f8c

The total amount of money I have paid from May 2014 to July 2022 is $75,319.86.

The first step is to determine the total number of months from  May 2014 to July 2022.

12 months = 1 year

May 2022 - May 2014 = 8 years x 12 = 96 months

Number of months from may 2022 to july 2022 = 2 months

Total number of months = 96 + 2 = 98 months

Total amount paid = 98 x 768.57 = $75,319.86

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Answer:

The number that could not be a value of y if y = 4x² - 6 is -12.

Step-by-step explanation:

The value of y for which a function f(x) = y = 4x² - 6 can be determined by knowing the smallest value of y for which x is equal to zero.

So, from the equation y = 4x² - 6, we will replace the value of x with zero to determine the smallest value of y.

y = 4(0) - 6

y = 0 - 6

y = -6

Thus, any number smaller than -6 could not be a value of y for the equation y = 4x² - 6.

Therefore, we can conclude that the number that could not be a value of y if y = 4x² - 6 is -12.

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

If x=-5, what is y is y=4-x²?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Put in the value of x.

[tex]\bf{y=4-(-5)^2}[/tex] | evaluate using Bodmas

[tex]\bf{y=4-25}[/tex] | subtract

[tex]\bf{y=-21}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

             [tex]\bf{=y=-21}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]

The true statement is (b) It is a reduction because 0 < n < 1.

The scale factor of dilation is given as:

n = 1/3

When the scale factor (n) is between 0 and 1, then the dilation is considered reduction or compression;

Otherwise, the dilation is considered enlargement or stretch

Because n is between 0 and 1, then the dilation is a reduction

Hence, the true statement is (b) It is a reduction because 0 < n < 1.

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Answer:

b

Step-by-step explanation:

The common difference for the arithmetic sequence in the task content is; -5.

The common difference of the sequence which is arithmetic can be evaluated as the difference between each successive term.

Hence, it follows that the common difference is;

-1-(-6) = 4-(-1) = 9-4 = 5.

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3²×5, 2⁴×5, 2²×3×5×7, 5⁴ and 3⁴ are the index notations of the numbers 45, 80, 420, 625 and 81 respectively. This can be obtained by taking the factors of these numbers and wring as the powers as shown below.

It is a method of representing numbers and variables that are multiplied by themselves a number of times.

For example, 7³, a²

The given numbers can be represented as the following:

(1) 45 =3×3×5 = 3²×5

(2) 80 =2×2×2×2×5 = 2⁴×5

(3) 420 =2×2×3×5×7 = 2²×3×5×7

(4) 625 =5×5×5×5 = 5⁴

(5) 81 =3×3×3×3 = 3⁴

Hence 3²×5, 2⁴×5, 2²×3×5×7, 5⁴ and 3⁴ are the index notations of the numbers 45, 80, 420, 625 and 81 respectively.

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The height of the smaller building is 94.63 feet, computed using the trigonometric ratios.

In the question, we take AB to be the taller building, where A is its top and B is its base, CD to be the shorter building, where C is its top and D is its base, and CE to be the perpendicular from C to AB.

Given that the horizontal distance between the two buildings is 260 feet, we can say that BC = CE = 260 feet.

The angle of elevation from the top of the shorter building to the top of the taller building is 30°, that is, ∠ECA = 30°.

The angle of depression from the top of the shorter building to the base of the taller building is 20°, that is, ∠ECB = 20°.

When ∠ECB = 20°, then ∠CBD = 20°, as they are alternate angles.

We are asked to find the height of the shorter building, that is, we are asked to find CD.

In ΔCBD,

tan ∠CBD = CD/BD {perpendicular/base},

or, tan 20° = CD/260,

or, CD = 260*tan 20° = 260*0.36397023426 {∵ tan 20° = 0.36397023426},

or, CD = 94.6322609092.

Therefore, the height of the smaller building is 94.63 feet, computed using the trigonometric ratios.

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An equation is formed of two equal expressions. The length of the sides QT and SV are 21 units and 41 units respectively.

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

Given the length of TR is 17 and it is equal to side VR, therefore,

VR = VT

3x + 2 = 17

x = 5

Since the given figure is a kite, therefore,

QT= QV = 4x + 1

QT = 4(5) + 1

QT = 21 units

Similarly, the sides SV will be equal to ST,

SV =ST = 9x - 4

SV = 9(5) - 4

SV = 41 units

Hence, the length of the sides QT and SV is 21 units and 41 units respectively.

The complete question is:

The length of TR is 17 units. What are the lengths of SV and QT?

SV=___ units

QT=___ units

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Answer:

[tex] {x}^{4} - {y}^{2} [/tex]

Step-by-step explanation:

This is a difference of squares, so its the square of the first term minus the square of the second term.

Answer:

Step-by-step explanation:

Discussion

First draw FH

<FOH and <FGH share the end points of the chord FH

<FOH is a central angle.

<FGH touches the circumference of the circle in the on the same side of the point of angle <FOH is closest to

Therefore <FGH  is 1/2 <FOH. That is always true of central angles and the smaller angle touching the circumference that <FOH points to

Conclusion

<FGH = 1/2 < FOH

58 = 1/2 <FOH

Therefore <FOH = 2 * 58 = 116

y = < FOH

Answer

y = 116

Answer: [tex]\frac{1}{3}[/tex] or about 33%

Step-by-step explanation:

       We will divide the wanted outcomes by the possible outcomes.        

[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{Number of numbers greater than 4}}{\text{number of numbers 1 through 6}} =\frac{2}{6}=\frac{1}{3}\;\; \text{or about 33\%}[/tex]

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Answer: 1/3

Step-by-step explanation:

There are only 2 numbers greater than 4. 5 and 6.

2/6= 1/3 chance

Answer:

6/17

Step-by-step explanation:

Robyn paid $45,

Rachel paid $65

Rocky paid $60.

Total amount paid = $45 + $65 + $60 = $170

Fraction paid by Rocky will be:

= 60/170

= 6/17

The length of DC based on the information given about the triangle is 19.37.

Based on the given information, it should be noted that:

AB² = AD² + BD²

25² = AD² + 5²

625 = AD² + 25

AD² = 625 - 25

AD² = 600

AD = √600

AD = 24.5

DC² = AD² + - AB² (Pythagoras theorem)

DC² = 24.5² + 15²

DC² = 375.25

DC = 19.37

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Hello !

We solve this system:

[tex]\begin{cases} 2y + 2 &=3y - 9 \: \: \: \: (1)\\ 3x + 6 &=y + 4 \end{cases}[/tex]

[tex](1) : 2y + 2 = 3y - 9 \\ - y + 2 = - 9 \\ - y = - 11\\ y = 11[/tex]

We replace y by 11 in the second equation:

[tex]3x + 6 = 11 + 4 \\ 3x + 6 = 15 \\ 3x = 9 \\ x = \frac{9}{3} = 3[/tex]

_____________

[tex]x = 3[/tex]

[tex]y = 11[/tex]

Have a nice day ;)

Answer:

x = 3

y = 11

Step-by-step explanation:

Since DRWH is a parallelogram

Then ,the opposite sides are congruent

Then , DR = HW and DH = RW

………………………………………………

DR = HW

⇔ 2y + 2 = 3y - 9

⇔ 9 + 2 = 3y - 2y

⇔ 11 = y

⇔ y = 11

DH = RW

⇔ 3x + 6 = y + 4

⇔ 3x + 6 = 11 + 4

⇔ 3x + 6 = 15

⇔ 3x = 15 - 6

⇔ 3x = 9

⇔ x = 9/3

⇔ x = 3

Answer: See attached.

Step-by-step explanation:

   For [a], we graph the parent function (y = x²), but shift it downwards 2 units.

   For [b], we graph the parent function (y = x²), but shift it downwards 6 units, shift it to the right 2 units, and apply a compress factor of 3.