GRAPH NUMBERS ON A NUMBER LINE
Identify the point on the number line that matches each number.
30. - 0.5
31.2.5
32.-3
A.
B с D
+
-3 -2 -1
А
0
E
1 2 3

Deductive Reasoning.

What's the difference between inductive and deductive reasoning?

Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down. Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.

Examples-

Inductive Reasoning: The first lipstick I pulled from my bag is red. The second lipstick I pulled from my bag is red. Therefore, all the lipsticks in my bag are red.

Deductive Reasoning: The first lipstick I pulled from my bag is red.

A deductive approach involves the learners being given a general rule, which is then applied to specific language examples and honed through practice exercises. An inductive approach involves the learners detecting, or noticing, patterns and working out a 'rule' for themselves before they practise the language.

A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.

Thus ,I know I'll have to work a double shift today because I have a migraine and every time I have a migraine I get stuck pulling a double is and example of Deductive reasoning . Because a  deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.

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Answer:

( x + y + z )( x^2 + y^2 + z^2 - xy - yz - zx )

Step-by-step explanation:

Use Identity to factor this long expression.

Hope this helps.

Answer:

s

sStep-by-step explanation:

The height of each story is 20 feet.

The value of x is 3 feet.

The score on the third quiz is 10

The number of action figures that would be produced on Friday is 182.

The equation that can be used to determine the height of each story is:

46 = x + x + 6

46 = 2x + 6

46 - 6 = 2x

40 = 2x

x = 40 / 2

x = 20 feet

The equation that can be used to solve for x is:

35 = 5x + 5x + 5

35 - 5 = 5x + 5x

30 = 10x

x = 30 / 10

x = 3 feet

Total quiz score = score on first quiz + score on second quiz + score on third quiz

(15 x 3) = 24 + 11 + score on third quiz

45 = 35 + score on third quiz

score on third quiz = 45 - 35

score on third quiz = 10

x = total amount of figures produced in a week - sum of figures produced from Monday to Thursday

(50 x 5) - (12 + 12 + 16 + 28)

250 - 68

X = 182

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Answer:

f(x) = 4x³ - 7x + 5

f(x) = 4x³ - 7x + 5(a). f(0) = 5

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Check

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula above

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) =

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above,

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5 = 4(343) - 49 + 5

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5 = 4(343) - 49 + 5 =1372 - 54

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5 = 4(343) - 49 + 5 =1372 - 54 = 1318

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5 = 4(343) - 49 + 5 =1372 - 54 = 1318

(c). f(-5) =

Using the formula above

f(-5) = 4(-5)³ - 7(-5) + 5

= 4(-125) + 35 + 5

= -500 + 40

= -460

*remember to use a calculator to check the answers

Hope this helps xoxo....

Answer: 1328

Step-by-step explanation:

4*7^3 - 7*7 + 5 = 1328

Answer:

4 lemons per pitcher basically by looking at the graph you can determine each pitcher increased by a steady pattern of 4 lemons per pitcher.

Example: 2x=8, x=4, 2(4)=8, 8=8 true, the x and y value is cannot be 0 for this equation since no workers means no lemons. If I subtract back by -4 the graph would look like: 1 4, 0 0. Proving this. Also another example I can do is 3x=12, divide 3 by both side x=4, plug them in, 12=12 which is true. Keep in mind X means Pitcher so 4 is correct.

Oh yea less compilcated way is to just look a graph I did all those step to prove to you. Good luck!

Step-by-step explanation:

Answer:

324309

 doctors were registered that year.

Step-by-step explanation:

The questions says, "18.1% of all registered doctors are females"

(Consider, total number of registered doctors as [tex]x[/tex])

that's, 18.1 % of [tex]x[/tex] are female.

and 18.1% of [tex]x[/tex] is 58,700

.

Answer:

Divide one number by the other, your quotient is the answer.

Question 1

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]-16x+10x+86=180 \\ \\ 10x+70=180 \\ \\ 10x=110 \\ \\ x=11[/tex]

Question 2

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]9x+30+7x-10=180 \\ \\ 16x+20=180 \\ \\ 16x=160 \\ \\ x=10[/tex]

Answer:

Step-by-step explanation:

Let the perimeter of the square with length of n be Pₙ.

According to given table we have:

We can put this as a sequence:

Common difference is:

The recursive formula for this sequence is:

The complementary angles are: 66.7° and 23.3°.

Two angles are said to be complementary if they both have a sum of 90 degrees when added.

Thus, we have the following:

One of the angles is represented as x.

Second angle = x - 43.4

Therefore:

x + x - 43.4 = 90

2x - 43.4 = 90

2x = 90 + 43.4

2x = 133.4

2x/2 = 133.4/2

x = 66.7°

First angle = x = 66.7°

Second angle = 66.7 - 43.4 = 23.3°

Therefore, the complementary angles are: 66.7° and 23.3°.

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Answer:

F=10, S=26

Step-by-step explanation:

We know that the base is 24. Using that information, 10^2+24^2=26^2 which is a pythagorean triple

The height of the tree in the mural should be 22.5 feet.To determine the height of the tree in the mural, we can set up a proportion using the given information:

Devon's height in the mural: 4.5 feet

Devon's actual height: 6 feet

Tree's height in the mural: Unknown (let's denote it as x)

Tree's actual height: 30 feet

The proportion can be set up as follows:

(Devon's height in the mural) / (Devon's actual height) = (Tree's height in the mural) / (Tree's actual height)

(4.5 feet) / (6 feet) = x / (30 feet)

Now, let's solve for x by cross-multiplying:

4.5 feet * 30 feet = 6 feet * x

135 feet = 6x

Now, divide both sides of the equation by 6 to find x:

x = 135 feet / 6

x = 22.5 feet

So, the height of the tree in the mural should be 22.5 feet.

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If the two angles are supplementary then the value of x is 33°.

Two angles that sum to a straight angle or 180° are called supplementary angles.

If the two given angles are supplementary then we can create a linear equation in x of the form:

m∠1+m∠2=180°

Substituting the values we get:

3x°+(x+48)°=180°

or, 4x°+48°=180°

or, 4x°=180°-48°

or,4x°=132°

or, x°=33°

Hence the value of x is 33°.

Disclaimer: The complete question should be: if m< 1=3x° and m2 = (x+48)° are supplementary find the value of x.

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The function (r •q)(-3) =(q •r)(-3)  and they are equal to -40

What are algebraic functions with example?

Given the following functions

q(x) = 2x+2

r(x) = x² +1

Taking the product

q(x)*r(x) = (2x+2)(x² +1)

Note that according to the communatative law, (r •q)(x) = (q •r)(x)

(r •q)(-3) =(q •r)(-3) = (2(-3)+2)((-3)² +1)

(r •q)(-3) =(q •r)(-3) = (-4)(9+1)

(r •q)(-3) =(q •r)(-3) = -4(10)

(r •q)(-3) =(q •r)(-3) =-40

Hence the function (r •q)(-3) =(q •r)(-3)  and they are equal to -40.

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If 2 and 6 were both negative, their combined value would be -2 + (-6) = -8. The arithmetic outcome of adding the magnitudes of the numbers, but with the opposite sign, yields the sum of negative integers. In this instance, the product of -2 and -6 is -8, which symbolises the joining of two negative values that produces a negative outcome.

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The value of x is for the given equation is 7/2.

An algebraic expression (or variable expression) is a term that has been combined with addition, subtraction, multiplication, and division operations.

To simplify an algebraic expression, we simply combine similar terms. As a result, variables with similar characteristics will be combined. The same abilities will now be created by combining similar variables.

The given equation is 4x-(10-x) =15/2.

4x - 10 + x + 15/2

5x - 10 = 15/2

Dividing both sides by 5 to obtain:

x - 2 = 3/2

Multiply both sides by 2 to get:

2x - 4 = 3

2x = 3 + 4
x = 7/2

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Answer: I think this is a trick question because they are always either greater or less than each other

Step-by-step explanation:

The probability that she selects all 4 blue disks is 0.0317.

The probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Now, according to the question;

There is a total of 2 green disks.

There is a total of 4 blue disks.

There is a total of 3 yellow disks.

The formula for selecting the combination of 4 blue disks are

Probability = (combination for 4 blue)/ Total combination for 9.

The combination is given by the relation;

ⁿCₓ = n!/{x!(n-x)!}

The combination for getting 4 blues is-

n is the total blue disks = 9

x is the selected blue disks = 4

⁹C₄ = 9!/{4!(9-4)!} = 126

The required probability = 4/126

The required probability = 0.0317

Thus, the probability that she selects all 4 blue disks is 0.0317.

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Answer:

7.5 acres per hour

Step-by-step explanation:

1) You know that in 1/3 of an hour John waters 2 1/2, or 2.5, acres of farmland.

2) To get 1 hour we would multiply what John waters in 1/3 of an hour by 3.

2.5acres * 3 = 7.5 acres per hour

3) We multiply by 3 because 1/3 of an hour * 3 = 1 hour

so: 2.5acres * 3 = 7.5 acres per hour

Answer: y= -2/3 x + 1/3

Step-by-step explanation:

The first thing you need to do is but it into standard y = mx + b form, where m is the slope of the line and b is the y-intercept. Using algebra, we can turn 3y + 2x = 1 into y = -2/3x + 1/3. the slope is -2/3 which means you start at the y-intercept (0,1/3) and go down 2 and to the right 3. Putting it on paper or in a graphing simulator will give you this line. The point on the y-axis is the y-intercept and the point on the x-axis is the x-intercept.

Answer:

make 3y subjet of the fomulae then subtract 2x then divide by 3 both sides then the ans will be y= -2x+1/3

Answer:

The width is 16 cm.

Step-by-step explanation:

[tex]l = 4w[/tex]

[tex]lw = 4 {w}^{2} = 1024[/tex]

[tex] {w}^{2} = 256[/tex]

[tex]w = 16[/tex]

First substitute [tex]x=\tan^{-1}(y)[/tex] to rewrite the integral as

[tex]\displaystyle \int_0^{\pi/4} \sqrt{\tan(x) - \tan^2(x)} \, dx = \int_0^1 \frac{\sqrt{y-y^2}}{1+y^2} \, dy[/tex]

Now use an Euler substitution, [tex]z=\frac{\sqrt{y-y^2}}y[/tex] to rewrite it again as

[tex]\displaystyle \int_0^{\pi/4} \sqrt{\tan(x) - \tan^2(x)} \, dx = 2 \int_0^\infty \frac{t^2}{(t^2+1)^2 + 1) (t^2 + 1)} \, dt[/tex]

where we take

[tex]\sqrt{y - y^2} = \sqrt{-y(y-1)} = yt \implies y = \dfrac1{1+t^2} \text{ and } dy = -\dfrac{2t}{(1+t^2)^2} \, dt[/tex]

Partial fractions:

[tex]\displaystyle \frac{t^2}{((t^2+1)^2+1) (t^2 + 1)} = \dfrac{t^2+2}{t^4+2t^2+2} - \dfrac1{t^2+1}[/tex]

so that

[tex]\displaystyle \int_0^{\pi/4} \sqrt{\tan(x) - \tan^2(x)} \, dx = 2 \left(\int_0^\infty \frac{t^2+2}{t^4+2t^2+2} \, dt - \int_0^\infty \frac{dt}{t^2+1}\right)[/tex]

The second integral is trivial,

[tex]\displaystyle \int_0^\infty \frac{dt}{t^2+1} = \lim_{t\to\infty}\tan^{-1}(t) - \tan^{-1}(0) = \frac\pi2[/tex]

For the other, I'm compelled to use the residue theorem, though real methods are doable too (e.g. trig substitution). Consider the contour integral

[tex]\displaystyle \int_\Gamma f(z) \, dz = \int_\Gamma \frac{z^2+2}{z^4+2z^2+2} \, dz[/tex]

where [tex]\Gamma[/tex] is a semicircle in the upper half of the complex plane, and its diameter lies on the real axis connecting [tex]-R[/tex] to [tex]R[/tex]. The value of this integral is 2πi times the sum of the residues in the upper half-plane. It's fairly straightforward to convince ourselves that the integral along the circular arc vanishes as [tex]R\to\infty[/tex], so the contour integral converges to the integral over the entire real line. Note that

[tex]\displaystyle 2 \int_0^\infty \frac{t^2+2}{t^4+2t^2+2} \, dt = \int_{-\infty}^\infty \frac{t^2+2}{t^4+2t^2+2} \, dt[/tex]

since the integrand is even.

Find the poles of [tex]f(z)[/tex].

[tex]z^4 + 2z^2 + 2 = 0 \\\\ ~~~~ \implies (z^2+1)^2 = -1 \\\\ ~~~~ \implies z^2 = -1 \pm i \\\\ ~~~~ \implies z = \pm \sqrt{-1 \pm i} = \sqrt[4]{2}\, e^{\pm i(3\pi/8 + \pi k)}[/tex]

where [tex]k\in\{0,1\}[/tex].

The two poles we care about are at [tex]z_1=\sqrt[4]{2}\,e^{i\,3\pi/8}[/tex] and [tex]z_2=\sqrt[4]{2}\,e^{-i\,11\pi/8}[/tex]. Compute the residues at each one.

[tex]\displaystyle \mathrm{Res}\left\{f(z),z=z_1\right\} = \lim_{z\to z_1} \frac{f(z)}{z-z_1} = -\frac1{2^{7/4}}\,ie^{-i\,\pi/8} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~= -\frac1{2^{7/4}} \left(\sin\left(\frac\pi8\right) + i \cos\left(\frac\pi8\right)\right)[/tex]

[tex]\displaystyle \mathrm{Res}\left\{f(z),z=z_2\right\} = \lim_{z\to z_2} \frac{f(z)}{z-z_2} = -\frac1{2^{7/4}}\,ie^{i\,\pi/8} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~= \frac1{2^{7/4}} \left(\sin\left(\frac\pi8\right) - i \cos\left(\frac\pi8\right)\right)[/tex]

By the residue theorem,

[tex]\displaystyle \int f(z) \, dz = 2\pi i \sum_{\rm poles} \mathrm{Res}\{f(z)\} = \frac{4\pi}{2^{7/4}} \cos\left(\frac\pi8\right)[/tex]

We also have

[tex]\displaystyle \cos^2\left(\dfrac\pi8\right) = \dfrac{1 + \cos\left(\frac\pi4\right)}2 = \dfrac{2 + \sqrt2}4 \implies \cos\left(\frac\pi8\right) = \dfrac{\sqrt{2+\sqrt2}}2[/tex]

Then the remaining integral is

[tex]\displaystyle \int_0^\infty \frac{t^2+2}{t^4+2t^2+2} \, dt = \frac{4\pi}{2^{7/4}} \cos\left(\frac\pi8\right) = \sqrt{\frac12 + \frac1{\sqrt2}} \, \pi[/tex]

It follows that

[tex]\displaystyle \int_0^{\pi/4} \sqrt{\tan(x) - \tan^2(x)} \, dx = \boxed{\left(\sqrt{\frac12 + \frac1{\sqrt2}} - 1\right) \pi}[/tex]

The conditions on m and b such that the linear function y = mx + b is its own inverse is 1 and 0 respectively.

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. It's look like the slope-intercept form of a line which is expressed as y = mx + b.

Or, it is a function that represents a straight line on the coordinate plane.

It is given that the linear is b,

y = mx + b

So, inverse of this function will be :

x = my + b

my = x - b

y = (1/m)x - b/m

Then, for both functions equal

m = 1/m and -b = b

So, m must be 1 and b must be 0.

Therefore, the value is of the m and b of the given equation y = mx + b is its own inverse will be 1 and 0 respectively.

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The correct option is; Associative Property of Addition.

For the given question;

The equation formed by the given statement is -

5 + [(-3x) + 4] = [5 + (-3x)] + 4

Observe the stated equation and comparing with the general equation;

The values are arranged in the form of associative addition.

Check the values;

LHS = 5 + [(-3x) + 4] ; simplifying,

5 -3x + 4 = 9 - 3x

RHS =  [5 + (-3x)] + 4 ; simplifying,

5 - 3x + 4 = 9 -3x

As, LHS = RHS and addition is being done.

Thus, the given equation shows the associative property of addition.

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The slope of the line parallel to the line  –x + 3y = 6 is a 1/3 option (A) 1/3 is correct.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that:

The equation of the line:

–x + 3y = 6

Write the equation in standard form:

y = x/3 + 6/3

y = x/3 + 2

m = 1/3

The slope of the line parallel to the line  –x + 3y = 6

M = 1/3

Thus, the slope of the line parallel to the line  –x + 3y = 6 is a 1/3 option (A) 1/3 is correct.

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Answer: Zero

Step-by-step explanation: The bars are meant trick you. git cuh

Answer:

0

Step-by-step explanation:

−3+3

=−3+3

=0

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