Which of the following represents the series in summation notation?
−2 + 4 − 8 + 16 − 32 + 64 − 128.

Answer:

○ [tex]x = -7[/tex]

Step-by-step explanation:

Given the equation:

[tex]10(x + 10) - 4 = 11 - 5(2x + 11)[/tex],

to solve for [tex]x[/tex], we have to rearrange the equation to make [tex]x[/tex] its subject.

[tex]10(x + 10) - 4 = 11 - 5(2x + 11)[/tex]

⇒ [tex]10x + 100 - 4 = 11 - 10x -55[/tex]      [expand brackets]

⇒ [tex]10x + 96 = -44 - 10x[/tex]

⇒ [tex]10x + 10x + 96 = -44[/tex]                   [add [tex]10x[/tex] to both sides]

⇒ [tex]20x + 96 = -44[/tex]

⇒ [tex]20x = -44 - 96[/tex]                             [subtract 96 from both sides]

⇒ [tex]20x = -140[/tex]

⇒ [tex]x = \frac{-140}{20}[/tex]                                        [divide both sides by 20]

⇒ [tex]x = \bf-7[/tex]

Answer:

B) x = -7

Step-by-step explanation:

Given equation: [tex]10(x+10)-4=11-5(2x+11)[/tex]

Step 1: Distribute [tex]10[/tex] and [tex]-5[/tex] through the parentheses.

[tex]\implies 10(x)+10(10)-4=11-5(2x)-5(11)[/tex]

[tex]\implies 10x+100-4=11-10x-55[/tex]

Step 2: Simplify (combine like terms).

[tex]\implies 10x+100-4=11-10x-55[/tex]

[tex]\implies 10x+96=-44-10x[/tex]

Step 3: Add [tex]10x[/tex] to both sides.

[tex]\implies 10x+10x+96=-44-10x+10x[/tex]

[tex]\implies 20x+96=-44[/tex]

Step 4: Subtract [tex]96[/tex] from both sides.

[tex]\implies 20x+96-96=-44-96[/tex]

[tex]\implies 20x=-140[/tex]

Step 5: Divide both sides by [tex]20[/tex] to isolate [tex]x[/tex].

[tex]\implies \dfrac{20x}{20}=\dfrac{-140}{20}[/tex]

[tex]\implies \boxed{x=-7}[/tex]

Answer:

A dealer bought digital watches at Rs 5500  per piece and fixed the price of each watch to make 20  profit. How much should a customer pay for it with 13  VAT? A trader purchased a laptop for Rs 45000   and marked its price to make 24  profit.

Step-by-step explanation:

Using the Fundamental Counting Theorem, it is found that the customer can put together 288 different outfits.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Bryan sells 3 types of shirts, 6 types of skirts, 8 types of bracelets and 2 types of hats, hence the parameters are given as follows:

[tex]n_1 = 3, n_2 = 6, n_3 = 8, n_4 = 2[/tex]

Hence the number of different outfits is given as follows:

N = 3 x 6 x 8 x 2 = 288

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The correct option is option (d) 8 hours.

Amelia need to work for 8 hours to buy new sweater $40.

When two expressions are connected with the equals sign (=) in a math equation, it expresses the equality of the two expressions. A number that may be entered for the variable to produce a true number statement is the solution to an equation.

Let the hours Amelia need to work=h

Amalia paid=$20

Payment of each hour=$2.50

So, we can make an equation with given problem

40=20+2.50h

40-20=2.5h

20=2.5h

[tex]h=\frac{20}{2.5}[/tex]

h= 8

So, Amelia need to work for 8 hours to get $40.

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Answer:

c=3.

Step-by-step explanation:

∵2*2*2=8,

∴2^3=8.

∵2^c=8,

∴c=3.

Answer:

[tex]y = - \frac{1}{4} x - 10[/tex]

Step-by-step explanation:

The negative reciprocal of 4 is -1/4.

Let's substitute in our values, to find the y-intercept:

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

[tex] - 11 = - 1 + c[/tex]

[tex]c = - 10[/tex]

Finally, our full equation is:

[tex]y = - \frac{1}{4} x - 10[/tex]

Answer: -2, -4, -1

Step-by-step explanation:

[tex]17-7x > 3(10x-4)+61\\\\17-7x > 30x-12+61\\\\17-7x > 30x+49\\\\-32 > 37x\\\\x < -\frac{32}{37}[/tex]

So, the values of x are -2, -4, -1.

Answer:

True

Step-by-step explanation:

All faces of a cube are the same.

The two ratios in the tables shown which have a common denominator you could use to compare is; 3/12 and 4/12

Machael's ratio:

lemons to water = 1:4

Equivalent ratio

= 3 : 12

= 4 : 16

Sondra's ratio:

lemons to water = 2 : 6

Equivalent ratio

= 4 : 12

= 6 : 18

Therefore, the two ratios in the tables shown which have a common denominator you could use to compare is; StartFraction 3 Over 12 EndFraction and StartFraction 4 Over 12 EndFraction

Complete question

Michael and Sondra are mixing lemonade. In Michael’s lemonade, the ratio of lemons to water is 1:4. In Sondra’s lemonade, the ratio of lemons to water is 2:6. Several equivalent ratios for each mixture are shown in the ratio tables. Imagine that you want to compare Michael’s ratio to Sondra’s ratio. Which two ratios in the tables shown have a common denominator you could use to compare?

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The probability that the first interview occurs on the fifth resume that you sent is 0.2592.

According to the given question.

The probability of being called for an interview, p = 0.40.

So, the probability of not being called for an interview, q = 1 - 0.40 = 0.60

As we know that binomial distribution summarizes the number of trials, or observations when each trial has the same probability of attaining one particular value. The binomial distribution determines the probability of observing a specified number of successful outcomes in a specified number of trials.

Therefore, the probability that the first interview occurs on the fifth resume that you send out

= [tex]^{5} C_{1} (0.40)^{1} (0.60)^{4}[/tex]

= 5(0.40)(0.1296)

= 0.2592

Hence, the probability that the first interview occurs on the fifth resume that you sent is 0.2592.

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Answer: [tex]\large\boxed{29}[/tex]

Step-by-step explanation:

The sum of 10 consecutive integersstarting with 11

= 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 155

Lets try 29:

29 + 30 + 31 + 32 + 33 = 155

Therefore our answer is:

[tex]\large\boxed{29}[/tex]

The intersection of the sets has the following properties: Commutative law – A ∩ B = B∩ A. Associative law – (A ∩ B)∩ C = A ∩ (B∩ C) φ ∩ A = φ

do mark brainliest

Answer:

Step-by-step explanation:

PS and QW intersect at U. PST = 136° and Q₁ =100°

tried my best to show the steps!! all i did was isolate to find the missing widths attached to the respective lengths (divided surface area by width) and then multiply both sides by two and add them together to find the perimeter.

The dimensions of the garden that would require the least amount of fencing are 6 ft in length and 6 ft in width.

The dimensions are the sides of a geometric shape.

The lengths of the three gardens are given as 6 ft, 9 ft, and 12 ft respectively.

If the area of the garden is 36 feet squared, then the widths for the three lengths will be as follows:

The width of the garden with a length of 6 ft [tex]= \dfrac{36}{6} = 6\ ft[/tex]

The width of the garden with a length of 9 ft [tex]= \dfrac{36}{9} = 4\ ft[/tex]

The width of the garden with a length of 6 ft [tex]= \dfrac{36}{12} = 3\ ft[/tex]

The parameters are calculated as:

The parameter of the garden with dimensions (6 ft, 6 ft) = 2(6 + 6) = 24 ft

The parameter of the garden with dimensions (9 ft, 4 ft) = 2(9 + 4) = 26 ft

The parameter of the garden with dimensions (12 ft, 3 ft) = 2(12 + 3) = 30 ft

The least of the parameter is of the garden with dimensions (6 ft, 6 ft).

Thus, the garden with dimensions (6 ft, 6 ft) would require the least amount of fencing.

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Answer:

91.5[tex]cm^{2}[/tex]

Step-by-step explanation:

The area of the rectangle:

a = lw

a =(21)(3) = 63

The area of the square:

a = lw

a = (5)(5) = 25

The area of a half circle:

a=[tex]\frac{\pi r^{2} }{2}[/tex]

a= [tex]\frac{3.14(1.5^{2}) }{2}[/tex]

a = [tex]\frac{3.14(2.25)}{2}[/tex]

a = [tex]\frac{7.065}{2}[/tex]

a = 3.5 rounded to the nearest tenth

63 + 25 + 3.5 =91.5

Answer:

m<C = 12.0 °

Step-by-step explanation:

Since we know that this is a non-right triangle, we must use either the law of sines or law of cosines to find m<C.  

The information we now have only allows us to use the law of sines, which focuses on proportions:

[tex]\frac{SinA}{a}=\frac{SinB}{b}=\frac{SinC}{c}[/tex]

Thus, we can use:

[tex]\frac{sin(98)}{19}=\frac{sinC}{4}\\ 4*sin(98)=19*sinC\\ \frac{4*sin(98)}{19}=sinC\\ sin^-1\frac{4*sin98}{19}=12.033=12.0[/tex]

The sin^-1 represents the sin inverse, which you must use to find angle measures.

A logarithmic equation exists as an equation that uses the logarithm of an expression containing a variable. The value of the logarithmic equation x = log 2.97/log 1.13.

A logarithmic equation exists as an equation that applies the logarithm of an expression having a variable. To estimate exponential equations, first, see whether you can note both sides of the equation as powers of the same number.

Given: [tex]$1.13^x = 2.97[/tex]

Taking log on both sides, we get

log [tex]$1.13^x[/tex] = log 2.97

x log 1.13 = log 2.97

x = log 2.97/log 1.13

Therefore, the value of logarithmic equation x = log 2.97/log 1.13.

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Answer:

p(t) = 2950^3t

Step-by-step explanation:

I’m not sure if this is exactly what you wanted or not. Please let me know more info and I’ll write any more answers for this question in the comments. Have a great day!!

The equation that represents the function g(x) is g(x) = log₅(x - 3)

The equation of the function f(x) is given as:

f(x) = log₅(x)

From the graph, we can see that the function g(x) is 3 units to the right of the function f(x)

This means that

g(x) = f(x - 3)

The function f(x - 3) is calculated as follows

f(x - 3) = log₅(x - 3)

Substitute f(x - 3) = log₅(x - 3) in g(x) = f(x - 3)

g(x) = log₅(x - 3)

Hence, the equation that represents the function g(x) is g(x) = log₅(x - 3)

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Answer:

[tex]y=-\frac{1}{3}x+7[/tex]

Step-by-step explanation:

Parallel lines have the same slope, so the slope of the line we need to find is -1/3.

Substituting into point-slope form and converting to slope-intercept form,

[tex]y-5=-\frac{1}{3}(x-6) \\ \\ y-5=-\frac{1}{3}x+2 \\ \\ y=-\frac{1}{3}x+7[/tex]

The theorems or postulates for the given pair of angles are as follows:

2. ∠2 ≅ ∠8 → Alternate exterior angles are congruent;

3. ∠2 ≅ ∠4 → Vertically opposite angles are congruent;

4. ∠3 ≅ ∠5 → Alternate interior angles are congruent;

5. ∠3 is supplementary to ∠6 → Consecutive interior angles are supplementary;

6. ∠4 ≅ ∠8 → Corresponding angles are congruent;

Consider two lines m and n are parallel. A transversal t is intersecting the lines m and n.

So, it forms 8 angles with the lines m and n. They are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8.

Based on their position, they are paired into different categories. Such as:

Interior angles: ∠3, ∠4, ∠5, ∠6

Exterior angles: ∠1, ∠2, ∠7, ∠8

Classifying the given pair of angles and their corresponding theorems:

2. ∠2 ≅ ∠8 → These angles belong to pair of Alternate exterior angles.

Theorem - "The alternate exterior angles are congruent"

3. ∠2 ≅ ∠4 → These belong to pair of vertically opposite angles.

Theorem - "The verticle angles are congruent"

4. ∠3 ≅ ∠5 → These belong to pair of alternate interior angles.

Theorem - "The alternate interior angles are congruent"

5. ∠3 is supplementary to ∠6 → These angles belong to pair of consecutive interior angles. Thus, they are supplementary.

Theorem - " The supplementary angles add up to 180°"

6. ∠4 ≅ ∠8 → These angles belong to pair of corresponding angles.

Theorem - " The corresponding angles are congruent".

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The distance from Humood's house to the school is 500m

The given parameters are:

Humood's house is (-5,7)

The school is (3,1)

The distance between both points is calculated using

[tex]d = \sqrt{(x_2- x_1)^2 + (y_2 - y_1)^2[/tex]

Substitute the known values in the above equation

[tex]d = \sqrt{(-5 - 3)^2 + (7 - 1)^2[/tex]

Evaluate

d = 10

Each unit in the graph is 50m.

So, we have

Distance =10 * 50m

Evaluate the product

Distance = 500m

Hence, the distance from Humood's house to the school is 500m

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[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

Given ,

[tex]2x = 100[/tex]

To find ,

value of x

Now ,

[tex]\longrightarrow{2x = 20}[/tex]

Dividing both sides by 2 , we get

[tex] \frac{2x}{2} = \frac{100}{2} \\ \\ \longrightarrow\boxed{ \: x = 50} [/tex]

nikal -,- xD

Answer:

Step-by-step explanation:

[tex]\bf 2x=100[/tex]

Divide both sides by 2:-

[tex]\bf \cfrac{2x}{2}=\cfrac{100}{2}[/tex]

Simplify:-

[tex]\bf x=50[/tex]

___________________

There is a maximum value of 7/6 located at (x, y) = (5/6, 7).

The function given to us is f(x, y) = xy.

The constraint given to us is 6x + y = 10.

Rearranging the constraint, we get:

6x + y = 10,

or, y = 10 - 6x.

Substituting this in the function, we get:

f(x, y) = xy,

or, f(x) = x(10 - 6x) = 10x - 6x².

To find the extremum, we differentiate this, with respect to x, and equate that to 0.

f'(x) = 10 - 12x ... (i)

Equating to 0, we get:

10 - 12x = 0,

or, 12x = 10,

or, x = 5/6.

Differentiating (i), with respect to x again, we get:

f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 5/6.

The value of y, when x = 5/6 is,

y = 12 - 6x,

or, y = 12 - 6*(5/6) = 7.

The value of f(x, y) when (x, y) = (5/6, 7) is,

f(x, y) = xy,

or, f(x, y) = (5/6)*7 = 7/6.

Thus, there is a maximum value of 7/6 located at (x, y) = (5/6, 7).

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The local minimum on the interval [-3, 0] is -16, the local maximum on the interval [0, 3] is 4 and the local minimum on the interval [0, 3] is -3

In a function, a point located at the local minimum is a point that is at a lower coordinate compared to the other neighboring points

In a function, a point located at the local maximum is a point that is at a higher coordinate compared to the other neighboring points

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In the first interval, [-3, 0], the lowest point in the interval is located at (-16, -1.5)

This means that the local minimum on the interval [-3, 0] is -16

In the second interval, [0, 3], the highest maximum in the interval is located at (4, 1)

This means that the local maximum on the interval [0, 3] is 4

In the second interval, [0, 3], the lowest minimum in the interval is located at (0, -3)

This means that the local minimum on the interval [0, 3] is -3

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The possible base and height of a second triangle are:

To find the base and height of the triangle:

First, we must find the constant of variation (k).

The problem indicates that the base of each triangle varies inversely with the height.

So, this can be represented as below:

B = k/H

When we clear "k", we obtain:

Now, we have:

We can give any value to "H" and you will obtain the base of the second triangle.

If H = 12, then:

Therefore, the possible base and height of a second triangle are:

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