A company manufactures school desks. The table shows the number of units that the company sold each month over a nine-month period
beginning in January.
Month, x
Units, y
Which equation best models the situation?
1
800
2
500
3
400
4
300
5
200
6
300
7
450
8
600
9
800

According to the plot of [tex]f(x)[/tex], whose curve passes through the point (-5, -3), we have

[tex]f(-5) = -3 \implies f^{-1}(-3) = \boxed{-5}[/tex]

From the power rules, the matching of  each expression with its equivalent expression is:

[tex]5^{-3}=\frac{1}{125}[/tex]

[tex]-5^{-3}=-\frac{1}{125}[/tex]

[tex](-5^{-3})^{-1}=-125[/tex]

[tex](-5^{-3})^{0}=1[/tex]

There are different power rules, see some them:

1. Negative exponent. For this rule when you have a negative exponent, you need to invert the number, i.e, the power base is converted to the denominator. After that, you should solve the power with a positive exponent.  See the  examples:

[tex]4^{-3}=\frac{1}{4^3} =\frac{1}{64} \\ \\ {\frac{4}{6} }^{-2}=( {\frac{6}{4} })^{2}=\frac{36}{16}[/tex]

2. Power. For this rule, you should repeat the base and multiply the exponents. See the  example, [tex](2^{2})^3=2^6=64[/tex].

3. Zero Exponent. When you have an exponent equals to zero, the result must be 1.  See the  example, [tex]2^0=1[/tex].

From this for your question, you have:

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Answer:

1.5 is the number.

Explanation:

Let the number be 'n', this is 100% - original number.

When increased by 40%, 100% + 40% = 140%.

140% × n = 2.1

1.4n = 2.1

n = 2.1/1.4

n = 1.5

Hence, the original number is 1.5.

Answer:

x=20

Step-by-step explanation:

The angles are 'Co-interior Angles', they make a C shape and add up to 180 degrees

so 4x +5x =9x

9x=180

x=20

4x=80

5x=100

The score of Jane is 27 and the score of Claire is 18.

A linear equation is an equation where highest degree of variables is 1.

Let the score of Jane's mark is x

Given, that score Jane is 9 more than the score of Claire.

So, the score of Claire= x-9

Given, the score of Jane is 60% of the sum of their scores.

the sum of their scores is = x+x-9= 2x-9

from the above it is clear that

the linear equation will be

x=60%(2x-9)

⇒x=0.6(2x-9)

⇒x= 1.2x -5.4

⇒1.2x-x= 5.4

⇒0.2x= 5.4

⇒x= 5.4/0.2

⇒x= 27

So the score of Jane is 27.

As score Jane is 9 more than the score of Claire.

the score of Claire is = x-9= 27-9=18

Therefore the score of Jane is 27 and the score of Claire is 18.

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Answer:

f(2) = 2

Step-by-step explanation:

Given function:

f(x) = 5x - 12

To Find:

f(2)

Solution:

Well,it is absolutely clear from the problem,that x = 2.So just substitute 2 in x's place on the function,then simplify using PEMDAS.

[tex]f(x) = 5x - 12[/tex]

[tex]f(2) = 5(2)- 12[/tex]

[tex]f(2) = 10 - 12[/tex]

[tex]\boxed{f(2) = - 2}[/tex]

Hence,f(2) is equal to -2.

Answer:

maybe minus 12 there was no number of cows

Answer:

x - 12

Step-by-step explanation:

x represents the number of cows since we do not know the number

then "minus 12"

bada bing bada boom

The triangle is congruent by SSS congruency because the corresponding two sides of two triangles are of the same measurement Hence, Option D is correct.

If the corresponding two sides of two triangles are of the same measurement, then the considered pair of triangles are congruent.

We have given two triangles that are congruent to each other;

LMN is congruent to OPQ

Given;

LM = OP

MN = PQ

LN = OQ

Thus, the triangle is congruent by SSS congruency because the corresponding two sides of two triangles are of the same measurement

Hence, Option D is correct.

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Answer:

C

Step-by-step explanation:

The contrapositive is always logically equivalent to the original statement.

Answer:

C

Step-by-step explanation:

Answer: down below

Step-by-step explanation:

1. How many hay bales did the farmer sell?

To do that, you need to divide the weight of a hay bale by the total weight of the hay bales that the farmer sold.

That will be 24,300 / 75 = 324 bales

2. Divide the new number (26,700) by the same number 75.

26,700 / 75 = 356 hay bales

Subtract the bales from last year to the bales from this year:

356 bales - 324 bales = 32 bales

Answer:

k = 11, if I understand the question.

Step-by-step explanation:

Please rephrase the question if my interpretation is incorrect.  (BTW, isn't (k,9) a dog?)

======================

I'll assume that we want to find the value of k as given by the equation of a line that has a slope of (1/2).  

Let's determine if we can establish an equation with what we know:

1.  It goes through point (3,5), and

2.  It has a slope of (1/2)

We'll look for a line with the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).

From (2) we know y = (1/2)x + b.

We can find b by using the one known point that lies on the line (3,5).  Use y = (1/2)x + b, insert the point (3,5), and solve for b:

y = (1/2)x + b

5 = (1/2)(3) + b

5 = 1.5 + b

b = 3.5

The line is y = (1/2)x + 3.5.

Now use the point (k,9):

y = (1/2)x + 3.5

9 = (1/2)k + 3.5

(1/2)k = 5.5

k = 11

The point is (11,9) so k = 9

See the attached graph.

The geometric mean of 9 and 9/4 will be 9/2 or 4 1/2.

It should be noted that in order to find the geometric mean of the numbers given, give to find the square root and then multiply.

This will be:

= ✓9 × ✓9/4

= 3 × 3/2

= 9/2 = 4 1/2

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Let's take this problem step by step:

To find the ordered pair of the system:

⇒ must set both equations equal to each other

    ⇒ must solve for 'x'

Let's solve:

 [tex]x^2-2x+3=-2x+28\\x^2-2x+3+2x-28=0\\x^2-25=0\\(x-5)(x+5)=0[/tex]

Let's find the x-values:

 [tex](x-5)=0\\x=5\\\\(x+5)=0\\x=-5[/tex]

Let's find f(x)'s value for each of the 'x':

[tex]x=5\\f(5)=-2(5)+28=18\\\\x=-5\\f(-5)=-2(-5)+28=38[/tex]

Answer: (5, 18), (-5,38)

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The least number of consecutive positive integer that is required to make the sum of the reciprocals greater than three is 7.

An integer is simply a number that is not  a  fraction.

The first four consecutive positive integers are:

1, 2, 3 , 4.

Their reciprocals are:

1/1, 1/2, 1/3, 1/4; and

The sum of them are greater than 2; that is

1/1 + 1/2 + 1/3 + 1/4 = 2.08333333333 > 2

to make the expression >3

We would require the following integers

1/1 + 1/2 + 1/3 + 1/4+ (1/5) + (1/6) + (1/7) + (1/8)+ (1/9) + (1/10) + (1/11) = 3.01987734488

Thus, the additional consecutive reciprocal integers that is required to make the sum of the reciprocal of the fist four greater than 3 is 7.

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Answer:

D

Step-by-step explanation:

Answer:

between 3 and 4

Step-by-step explanation:

3 squared is 9 and 4 squared is 16 so something in between 3 and 4 can be squared to equal 10 (since a square root is the opposite of squaring)

Answer:

Answer:

(x - 9)(x^2 + 18x + 81).

Step-by-step explanation:

Use the difference of cubes factorization, which claims that a^3 - b^3 = (a - b)(a^2 + ab + b^2)

x^3 - 729 = (x - 9)(x^2 + 18x + 81)

Answer:[tex](x-9) (x^{2} +9x + 81)[/tex]

Step-by-step explanation:

Answer:

  ia) center: (0, 0), the origin

  ib) angle: 90°

  ic) direction: CCW

  ii) LM ≅ L'M', ∠L ≅ ∠L'

  iii) (2, 1)

Step-by-step explanation:

A rigid transformation preserves size and shape of a figure, so the image is congruent to the original. The rigid transformations are rotation, reflection, and translation. Each has characteristics that allow one to determine the nature of the transformation(s) involved.

__

angle and direction

One way to determine the angle and direction of rotation of a figure is to compare a horizontal segment on the original with the corresponding segment on the image. Here, a convenient segment is NM, which is horizontal and points to the right. Its angle relative to the direction of the +x axis is 0°.

The transformed segment N'M' points upward, at an angle relative to the +x axis of 90°. This tells you the figure was rotated 90° in the CCW direction. (This is fully equivalent to a rotation of 270° in the CW direction.)

center

Points in a rotated image always remain at the same distance from the center of rotation as the original points. In most cases, the center of rotation is the origin. We can check to see if that is the case by looking at the distances of a couple of points from the origin.

  N is at coordinates (1, 1), so is √(1² +1²) = √2 from the origin

  N' is at coordinates (-1, 1), so is √((-1)² +1²) = √2 from the origin

  L is at coordinates (1, 3), so is √(1² +3²) = √10 from the origin

  L' is at coordinates (-3, 1) so is √((-3)² +1²) = √10 from the origin

This confirms that the origin is the center of rotation.

__

Since each point and its image are on a circle centered at the center of rotation, the line between them is a chord of that circle. The perpendicular bisector of that chord goes through the center of rotation. Here, we observe that the perpendicular bisector of NN' is the y-axis. The perpendicular bisector of LL' is a line with slope -2 through (-1, 2). It will intersect the y-axis at the origin, confirming the origin as the center of rotation.

__

A rigid transformation preserves lengths and angles, so any length or angle on the rotated figure is congruent to the original:

 LM ≅ L'M', MN ≅ M'N', NL ≅ N'L'

  ∠L ≡ ∠L', ∠M ≡ ∠M', ∠N ≡ ∠N'

__

The components of a translation vector add to the corresponding coordinates of a point.

  L +v = L'

  (1, 3) +(1, -2) = (2, 1) . . . image of point L

Answer:

A. a = 2s - b -c

Step-by-step explanation:

Rearrange the equation in a way that you have only a on one side. When solving equations you can add, subtract, multiply or divide by the same number/variable/expression on the both sides.

[tex]s = \frac{a + b + c}{2}[/tex]

Multiply by 2 to get rid of the fraction.

[tex]s \cdot 2 = \frac{a + b + c}{2} \cdot 2[/tex]

On the right side the 2 cancels out:

[tex]s \cdot 2 = a + b + c[/tex]

On the right side next to a are still b and c. But we want a alone. Subtract b.

[tex]s \cdot 2 - b = a + b + c - b[/tex]

b - b on right side gives 0.

[tex]s \cdot 2 - b = a + c + 0[/tex]

The step above is usually skipped, because number + 0 = number.

[tex]s \cdot 2 - b = a + c[/tex]

Next to a there is still c. Subtract c.

[tex]s \cdot 2 - b - c = a + c - c[/tex]

c - c on the left is 0.

[tex]s \cdot 2 - b - c = a[/tex]

So our answer is:

[tex]s \cdot 2 - b - c = a[/tex]

It can be rewritten to (change sides):

[tex]a = s \cdot 2 - b - c[/tex]

And s · 2 can be rewritten to 2s:

[tex]a = 2s - b - c[/tex]

The proof is shown below

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Given:

∠CBA ≅ ∠FBA; ∠CAB ≅ ∠FAB

Now, ∠BCA is congruent to ∠BFA      [reflexive property of congruence]

Also, AB= AB  (common)

Thus, we can conclude that Δ BCA≅ Δ BFA  by ASA criteria.

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In the given equation, the value of x is approximately 75°

From the question, we are to determine the value of x

The given equation is

sin x ≈ 0.965926

If sin x ≈ 0.965926

Then,

x ≈ sin⁻¹(0.965926)

∴ x ≈ 75.0°

Hence, the value of x is approximately 75°

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Answer:

Step-by-step explanation:

When 2 lines are perpendicular, their slopes are negative reciprocals of one another.  Here, if the slope of A is -1/2, the slope of B is +2/1, or just 2.

(f- g)(x) = 2x²-3x -8 , Option B is the correct answer.

A function is a mathematical statement that derives relation between two variables.

Two functions are given in the question

f(x) = 2x² - 5

g(x) = 3x + 3

(f- g)(x) = ?

(f- g)(x) = (2x² - 5 - (3x + 3))

(f- g)(x) = 2x²-3x -8

Therefore Option B is the correct answer.

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The standard equation is:  y = (-2)x² + 8x + 5

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0, with a ≠ 0 .

We know,

y = ax² + bx + c

For (-1, -5)

-5 = a - b + c..................(1)

For (0, 5)

5 = c

For (1, 11)

11 = a + b + c.....................(2)

From (1) and (2), we get

a=-2

and b= 8

Hence, the standard equation is:

y = (-2)x² + 8x + 5

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Answer:

Vertex: (1, 5)

Focus: (0, 5)

Step-by-step explanation:

Given that the parabola's equation is y² - 10y + 4x + 21 = 0, solve for the vertex and the focus.

Vertex:

Step 1: Isolate x to the left side of the equation; we get x = - (y² / 4) + (5y / 2) - (21 / 4).

Step 2: Complete the square of the previous equation; here we get - (1 / 4) * (y - 5)² + 1. x is squal to this.

Step 3: Use the vertex form, x = a(y - k)² + 1. a is - 1 / 4, h is 1, and k is 5.

Step 4: Fill in (h, k). We get the answer (1, 5) as the vertex.

Focus:

Step 1: Find p, and distance from the vertex to the focus. We can find p by using 1 / (4a).

Step 2: Simplify. This gives us -1 as p.

Step 3: We plug in the values we just got earlier to get the vertex. The focus of a parabola can be found by using: (h + p, k).

Step 4: Substitude the values. We have (1 + -1, 5).

Step 5: Simplify. Therefore, the answer is (0, 5).

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