1
Which is the equation of a line that has a slope 1/2 and passes through point (2, -3)?
Oy-x-4
0y=x-2
Oy-x+2
Oy=x+3

Using proportions, the scenario modeled by the equation 0.6x = 86.46 is:

D. A picnic table is on sale for 40 percent off. The original price of the picnic table is x, $144.10.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

When a product is 40% off, 100 - 40 = 60% of the original price x is paid, hence the expression for the price is:

0.6x.

In this problem, the expression is:

0.6x = 86.46

x = 86.46/0.6

x = 144.1.

Hence option D is correct.

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Recall the Pythagorean identity,

[tex]\sin^2(x) + \cos^2(x) = 1[/tex]

Then we can rewrite the equation as

[tex]\sin(3x) + 2 \cos^2(3x) = 1[/tex]

[tex]\sin(3x) + 2 (1 - \sin^2(3x)) = 1[/tex]

[tex]1 + \sin(3x) - 2 \sin^2(3x) = 0[/tex]

Factorize the left side.

[tex](1 + 2 \sin(3x)) (1 - \sin(3x)) = 0[/tex]

Then we have

[tex]1 + 2\sin(3x) = 0 \text{ or } 1 - \sin(3x) = 0[/tex]

[tex]\sin(3x) = -\dfrac12 \text{ or } \sin(3x) = 1[/tex]

Solve for [tex]x[/tex]. We get two families of solutions:

[tex]3x = \sin^{-1}\left(-\dfrac12\right) + 2n\pi \text{ or } 3x = \pi - \sin^{-1}\left(-\dfrac12\right) + 2n\pi[/tex]

[tex]\implies 3x = -\dfrac\pi6 + 2n\pi \text{ or } 3x = \dfrac{7\pi}6 + 2n\pi[/tex]

[tex]\implies \boxed{x = -\dfrac\pi{18} + \dfrac{2n\pi}3} \text{ or } \boxed{x = \dfrac{7\pi}{18} + \dfrac{2n\pi}3}[/tex]

and

[tex]3x = \sin^{-1}(1) + 2n\pi[/tex]

[tex]\implies 3x = \dfrac\pi2 + 2n\pi[/tex]

[tex]\implies \boxed{x = \dfrac\pi6 + \dfrac{2n\pi}3}[/tex]

(where [tex]n[/tex] is any integer)

Cubing of integers from 1 to 5 will have their cubes in the interval 1 to 200. There are such 5 positive numbers (1,2,3,4,5).

To calculate the variety of integers, locate and subtract the integers of the hobby after which subtract 1. As evidence of the concept, calculate the wide variety of integers that fall between five and 10 on more than a few lines. We realize there are four (6, 7, 8, 9).

All entire numbers are integers (and all herbal numbers are integers), however now not all integers are whole numbers or natural numbers. as an example, -five is an integer but not an entire variety or a natural quantity. An integer is an entire variety (not a fractional number) that can be fine, bad, or 0. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.forty three, 1 3/four, three.14, . 09, and five,643.1.

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The equivalent expressions for the costs are 8 * (14 + c) and 112 + 8c

The given parameters are:

Number of uniform = 8

Cost of each = $14

The cost of the uniforms and the shorts is then calculated as:

Cost = Number of uniforms * (Cost of uniform + Cost of short)

This gives

Cost= 8 * (14 + c)

Expand

Cost = 112 + 8c

Hence, the equivalent expressions for the costs are 8 * (14 + c) and 112 + 8c

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Hello !

[tex]a_{n} = a_{1} + (n - 1) \times d[/tex]

[tex]a_{39} = - 28 + (39 - 1) \times ( - 4) = - 28 + 38 \times ( - 4) = - 180[/tex]

The required a39 of the arithmetic sequence is -180.

Given that,
To find a39 of the arithmetic sequence given a1 = -28 and d = - 4.

Arithmetic progression is the series of numbers that have common differences between adjacent values.

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

The nth term of an arithmetic sequence is given as
an = a1 + (n - 1) * d
for term n = 39
a39 = -28 + (39 - 1) * -8
a39 = -28 - 152
a39 = - 180

Thus, the required a39 of the arithmetic sequence is -180.

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Using the bisection concept, it is found that the measure of angle PQR is of 130º.

A bisection divides an angle into two equal angles. In this problem, the angles are given as follows:

Hence the value of x is given as follows:

3x + 5 = 2x + 25

x = 20º.

Hence the measure of angle PQR is given as follows:

m<PQR = 3x + 5 + 2x + 25 = 5x + 30 = 5 x 20º + 30º = 130º.

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The required equation is g+300-900-900=1300.

The value of g is 2800 pounds.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Initially, there is a mound of g pounds of gravel, then 300 pounds are added, and then two orders of 900 pounds are sold. At the end of the day, the mound has 1,300 pounds of gravel.

The equation for the given information is formed as follows:

g+300-900-900=1300

Solve the equation to find the value of g,

g+300-1800=1300

g-1500=1300

g=1300+1500

g=2800

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Answer:

Volume = 64

Step-by-step explanation:

To find the volume of the cube use the formula.

Formula: l×b×h

l=length

b=base

h=height

Use the information given to solve using the formula.

4×4×4=64

The volume of this cube is 64.

Hope this helps!

If not, I am sorry.

Answer:

8x^2

Explanation:

First, do prime factorization of each of the coefficients:

32   ⇒   2^5

24   ⇒   2^3, 3

The greatest common factor (GCF) of the coefficients is 2^3 = 8.

Next, find the GCF of the variables:

x^2

x^2, y

The GCF of the variables is x^2.

Finally, multiply the GCF of the coefficients by the GCF of the variables to get:

8x^2

Answer: 4x^2

Step-by-step explanation: I took the test and got this answer right

Answer:

False, False, True

Step-by-step explanation:

Matrix addition or subtraction can only be performed on two matrices if they are the same dimensions.  The number of rows for both must match, and the number of columns for both must match.  If either is different, they cannot be combined with addition or subtraction.

So, the first two questions are false because the first number from each pair doesn't match (and neither does the second number from each pair, but we just need one mismatch for it to fail).

The last question is true because both of the first numbers are a 3, and both of the second numbers are a 4.

The given relation is function, because the curve of y = p(x) has its exist for every x in its domain(-6, 3) and the range of the function is lies between (-1, 9).

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent while Y is dependent variable.

As Clearly the shows in the graph the structure is decreasing, increasing and then decreasing. And implies, curve is continuous in its limits and for every x (-6,3) there is exist in range of y(-1, 9).

Thus, The given relation is function, and domain is (-6, 3) and the range of the function is lies between (-1, 9).

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First of all, a pair of angles that are complementary means that they add up to 90 degrees. In this case, angle b + 63 degree = 90 degree (because they are complementary), which mean angle b = 90 - 63 = 27 degree.

Answer: 27°

Step-by-step explanation:

Hello.

Complementary angles add up to 90°

Therefore,

63° + ? = 90°

Now we can subtract!

90° - 63° = 27°

Hope this helps and have a nice day :)

Answer:

C. 2y²

Step-by-step explanation:

[tex] \sf{( {3}^{0}y) {}^{2} \times 2(xy {)}^{0} = }[/tex]

[tex]\sf{ = (\red{1} \times y)^{2} \times (2 \times \red{1}) }[/tex]

[tex]\sf{ = (y)^{2} \times 2 }[/tex]

[tex]\sf{ =2 {y}^{2} }[/tex]

Answer:

[tex]\textsf{C.} \quad 2y^2[/tex]

Step-by-step explanation:

Given:

[tex](3^0y)^2 \times 2(xy)^0[/tex]

[tex]\textsf{Apply exponent rule} \quad a=a^1:[/tex]

[tex](3^0y^1)^2 \times 2(x^1y^1)^0[/tex]

[tex]\textsf{Apply exponent rule} \quad(a^n)^c=a^{nc} \implies (a^nb^n)^c=a^{nc}b^{nc}:[/tex]

[tex]\implies 3^{(0 \times 2)}y^{(1 \times 2)} \times 2 \left(x^{(1 \times 0)}y^{(1 \times 0)} \right)[/tex]

[tex]\implies 3^0y^2 \times 2\left(x^0y^0\right)[/tex]

[tex]\textsf{Apply exponent rule} \quad a^0=1:[/tex]

[tex]\implies (1)y^2 \times 2\left(1 \times 1 \right)[/tex]

Simplify:

[tex]\implies (1)y^2 \times 2(1)[/tex]

[tex]\implies y^2 \times 2[/tex]

[tex]\implies 2y^2[/tex]

Formula:

[tex]\frac{1}{2}(Big Arc- Small Arc)[/tex]

[tex]\frac{1}{2} (118-26)[/tex]

[tex]\frac{1}{2}(92)\\[/tex]

=46

m∠DPR = 46°

I hope it helps! :)

Answer:

Yes, because they are congruent by AAS (angle angle side)

Step-by-step explanation:

One of the congruence theorem is AAS. If you follow the sides of the triangle, you will see that they are marked with an angle, another angle, and a side being congruent. I hope this helps!

Answer:

Step-by-step explanation:

33) [tex]AC=6[/tex] and [tex]BD=6[/tex], so [tex]AC/BD=1[/tex]

34) By the distance formula,

[tex]AE=\sqrt{(-2-4)^2 + (8-0)^2 }=10\\[/tex]

Also, EC = 8. So, [tex]AE/EC = 5/4[/tex].

35) [tex]\frac{8-0}{4-2}=4[/tex]

36) [tex]\frac{8-0}{4-8}=-2[/tex]

The expression 3⁴ × 3² when rewritten in the form 3ⁿ is;  (3²)³

We want to find the expression;

3⁴ × 3²

Now, according to law of exponents, we know that;

y² × y³ = y⁽² ⁺ ³⁾

Thus, applying that exponent form to our question gives us;

3⁴ × 3² = 3⁽⁴ ⁺ ²⁾ = 3⁶

Now, we want to find the answer in the form 3ⁿ. Thus;

3⁶ = (3²)³

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Answer: 3^6 on khan academy

Step-by-step explanation: add the exponents 4 and 2 and you get the exponent 6

The population of viruses in the dish A is 3,391 viruses.

Population density measures the amount of organisms in 1 square millimeters of a place (in this case the dish)

Population density = population / area

Population = population density x area

1.2 x 2826 = 3,391 viruses

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Answer:

y is the variable in that expression.

Answer:

Hence the expression [tex]$$(a+b)(2a+3b)=2a^2+5ab+3b^2$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{matrix}{} & {} & {} & {} & a & + & b \\ \times & {} & {} & {} & 2a & + & 3b \\ \end{matrix}$$[/tex]

___________________

[tex]$$\begin{matrix}{} & {} & {} & {} & 3ab & + & 3{{b}^2} \\ {} & {} & 2{{a}^2} & + & 2ab & {} & {} \\ \end{matrix}$$[/tex]

___________________

[tex]$$\begin{matrix}{} & {} & 2{{a}^2} & + & 5ab & + & 3{{b}^2} \\ \end{matrix}$$[/tex]

Based on the information provided and the requirements to organize the students, Jon most likely has 23 students.

In general, Jon will need a number that is not prime as this type of number will not allow him to complete all the grid.

20 = A rectangular grid of 5 x 4 seats can be arranged

21= A rectangular grid of 7 x 3 can be arranged

22 = A rectangular grid of 2 x 11 can be arranged

23 = It is impossible to organize 23 seats in a rectangular grid without gaps

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Jon has 23 students in his class.

Number of students = Least 20 and most 28

In this case, we are getting a 1 * x rectangle of desks, which is the only possible arrangement.

'x' is a prime number.

Since his classes can't have less than 20 and more than 28, it means we are  looking out for a prime number between 20 and 28.

Let's sort out a prime number between the numbers, 20 and 28

20: 1,2,4,5,10,20

21: 1,3,7,21

22: 1,2,11,22

23: 1,23

24: 1,2,3,4,6,8,12,24

25: 1,5,25

26: 1,2,13,26

27: 1,3,9,27

28: 1,2,4,7,14,28

From what we have, 23 is a prime number because it is only divisible by one and itself.

Therefore, Jon has 23 students in his class.

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Answer: m=-1.

Step-by-step explanation:

[tex]Q(x)=x^2+mx-12\ \ \ \ Q(-3)=0\ \ \ \ \ m=?\\Q(-3)=(-3)^2+m*(-3)-12=0\\9-3m-12=0\\-3m-3=0\\3m=-3\ |:3\\m=-1.[/tex]

Answer:

Step-by-step explanation:

Answer:

In slope-intercept form:

[tex]y = - \frac{1}{4} x - 5[/tex]

In standard form:

[tex]x + 4y = - 20[/tex]

Step-by-step explanation:

[tex] - 3 = - \frac{1}{4} ( - 8) + b[/tex]

[tex] - 3 = 2 + b[/tex]

[tex]b = - 5[/tex]

[tex]y = - \frac{1}{4} x - 5[/tex]

[tex] - 4y = x + 20[/tex]

[tex] - x - 4y = 20[/tex]

[tex]x + 4y = - 20[/tex]

Answer:

Step-by-step explanation:

1/2 pi is an angle ( in radians)

in degrees its 90 degrees.

cos 90 = 0.

The value of x is 103.

The value of x is 59.

The value of x is 134.

The value of x is 12

The value of x is 50

The value of x is 135

The sum of angles on a straight line add up to 180 degrees.

180 - 77 = 103

180 - 121 = 59

180 - 46 = 134

12 x + 36 = 180

12x = 180 - 36

12x = 144

x = 12

24 + 3x + 6 = 180

3x = 180 - 24 - 6

3x = 150

x - 50

[tex]\frac{x}{3}[/tex] + 99 + 36 = 180

[tex]\frac{x}{3}[/tex] = 180 - 36 - 99

[tex]\frac{x}{3}[/tex] = 45

x = 45 x 3

x = 135

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The points where both coordinates are integers lie within the intersection of these circles, including its boundary are 8 points.

To answer the question, we need to find the equation of the circles.

The equation of a circle with center (h, k) and radius r is

(x - h)² + (y - k)² = r²

Given that the first circle has

Its equation is

(x - 0)² + (y - 0)² = 5²

x² + y² = 25  (1)

Given that the second circle has

Its equation is

(x - 8)² + (y - 0)² = 5²

x² - 16x + 64 + y² = 25  (2)

To find the point of intersection of both circles, subtracting (1) from (2), we have

x² - 16x + 64 + y² = 25  (2)

-

x² + y² = 25  (1)

-16x + 64 = 0

-16x = -64

x = -64/-16

x = 4

Substituting x = 4 into (1), we have

x² + y² = 25

4² + y² = 25

16 + y² = 25

y² = 25 - 16

y² = 9

y = ±√9

y = ±3

So, the circles intersect at (4,-3) and (4, 3).

So, all the points that lie within their points of intersection where both coordinates are integers including their points of intersection are

So, there are 8 points.

So, all the points where both coordinates are integers lie within the intersection of these circles, including its boundary are 8 points.

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Step-by-step explanation:

the sum of all angles in a triangle is always 180°.

so,

180 = 60 + 45 + angle4 = 105 + angle4

75° = angle4

Step-by-step explanation:

ATTACHED IS THE SOLUTION!!