Find the least number which must be subtracted from each of the following numbers
so as to get a perfect square. Also find the square root of the perfect square so
obtained.
1989

Answer:

4

Step-by-step explanation:

3a, 2b, (1)c, and 100 are all their own terms. None of them having the same variable making them each their own. (including whole numbers without a variable, the absence of a variable still means its a term)

Using the inverse of the function from the table, the value of f⁻¹(4) is 107/3

The inverse of a function is a new function that "undoes" the original function. It reverses the mapping of inputs and outputs, allowing you to find the original input value when you know the output value.

In this problem, we have to use the table to find the original function which is f(x) and use it to find the inverse of the function;

Taking two points from the table;

m = y₂ - y₁ / x₂ - x₁

m = 0 - (-3) / -9 - (-11)

m = 3 / 20

Using the slope and one point on the table;

y = mx + x

-3 = 3/20(-11) + c

-3 = -1.65 + c

c = -3 + 1.65

c = -1.35

Putting the slope and y - intercept together;

y = 3/20x - 1.35

y = 3/20x - 27/20

f(x) = 3/20x - 27/20

Taking the inverse of the function;

f⁻¹(x) = (20x + 27)/3

To find the value of f⁻¹(4), we just need to substituting the value of x in the function;

f⁻¹(4) = (20(4) + 27)/3

f⁻¹(4) = 107/3

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Answer:

Some of the 50 students should have been assigned to a control group that used the in-person course

Step-by-step explanation:

Some of the 50 students should have been assigned to a control group that used the in-person course is the concerns makes their conclusion inappropriate.

A learning program that is done in a virtual setting and is organized in accordance with a syllabus is known as an online course. Online courses can be informal and focused on learning a specific skill, or formal and leading to a certification or degree.

Because you may arrange the learning materials so that students can deepen their understanding of a particular subject, online courses are the modernized form of traditional courses. The main component of it is a curriculum, or study plan, broken down into modules.

Hence, Some of the 50 students should have been assigned to a control group.

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In the event that cells B1, C1, and D1 were highlighted and then used to fill E1, F1, and G1, the values we would see are A. Seat1Row2, Seat2Row2, Seat3Row2.

When using a spreadsheet, you can autofill succeeding cells if you highlight the preceding ones and then drag the cursor.

If Seat1Row1, Seat2Row1, and Seat3Row1 are in the cells B1, C1, and D1, then the spreadsheet would take note of the "1s" at the end of the values.

When it is then used to autofill the next cells, it would make this a 2 such that we see Seat1Row2, Seat2Row2, Seat3Row2.

If cells H1, I1, and J1 are filled, we would then see Seat1Row3, Seat2Row3, Seat3Row3.

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Answer: 60 miles

Step-by-step explanation:

1 in. times 3 = 3 in

20 mi times 3 = 60 mi.

Answer:

5b* because we have no idea what it could stand for

Answer:

5b

Step-by-step explanation:

However many b's there are that's your number so in this case its 5 and then you just add be to it so 5b

Answer:

Step-by-step explanation:

Answer:13

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Ok, so I see that the x-intercept is (4,0), while the y-intercept is(-3,0)

Slope is rise/run

Between these two points, the line rose 3 and horizontally went 4 units to the right. Therefore, the slope is 3/4.

Feel free to tell me if I did anything wrong! :)

Also, if you're still confused, I could explain it another way.

Answer:

  34 hours or more

Step-by-step explanation:

If h is the number of hours Jack works, then his earnings will total 15h. He wants that to be at least 500. The appropriate inequality is ...

  15h ≥ 500

  h ≥ 33 1/3 . . . . . divide by 15

Jack needs to work 34 hours or more to earn at least $500.

The domain of the function above is [-2, 3].

The range of the function above is [-2.5, 2].

The intervals over which the function is increasing is [-2, 1.5] U [-2.5, 2].

The intervals over which the function is decreasing is [1.5, -2.5].

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of this rational expression (function)   shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = [-2, 3] or -2 ≤ x ≤ 3.

Range = [-2.5, 2] or -2.5 ≤ y ≤ 2.

Additionally, the intervals over which the function is increases over the interval [-2, 1.5] and [-2.5, 2], while it decreases over the interval [1.5, -2.5].

In conclusion, the given function is not constant over any interval.

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Answer:

b

Step-by-step explanation:

mark brainliest pls....

The length of the rectangle is 19.25 cm when it is 2 more than three times the width of 5.75 cm.

A perimeter is a closed path that encompasses, surrounds, or outlines a two-dimensional shape or length in one dimension. A circle's or an ellipse's circumference is its perimeter. There are several applications for calculating the perimeter. The length of fence required to encircle a yard or garden is known as the calculated perimeter.  

The perimeter (circumference) of a wheel/circle describes how far it can roll in one revolution.  Similarly, the amount of string wound around a spool is proportional to the perimeter of the spool; if the length of the string were exact, it would equal the perimeter.

Given that,

Perimeter = 2(l + b) = 50cm

And also given that,

l = 2 + 3b

Substituting the value of l in perimeter we get

2((2 + 3b) + b) = 50cm

2(2 + 4b) = 50cm

4 + 8b) = 50cm

8b = 50 - 4

b = 46/8

b = 5.75

Substituting the value of b in l, we get

l = 2 + 3(5.75)

l = 19.25

Therefore, the length of the rectangle is 19.25 cm when it is 2 more than three times the width of 5.75 cm.

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The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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The value of measure of x in the triangle is,

⇒ x = 4√3 units

We have to given that,

A triangle is shown in image.

Now, WE can formulate by trigonometry formula we get;

⇒ tan 30° = Opposite / Base

⇒ tan 30° = 4 / x

⇒ 1/√3 = 4/x

⇒ x = 4√3 units

Thus, The value of measure of x in the triangle is,

⇒ x = 4√3 units

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Answer:

0.339

Step-by-step explanation:

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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Answer:

b. 4.9 × 1011

Step-by-step explanation:

Using scientific notation is similar to expressing in standard form. Given that (7 × 105)2

We open the parenthesis. This may first be expressed as

7² × 10⁽⁵⁾²

Then expand,

= 49 × 10¹⁰

To put in scientific notation, 49 = 4.9 × 10

Hence the expression becomes

= 4.9 × 10 × 10¹⁰

Using the laws of indices

= 4.9 ×  10¹¹ in scientific notation

Answer:

4.9 × 1011

Step-by-step explanation:

I did it in grandpoint

Answer:16x16

Step-by-step explanation:

Using the combination formula, it is found that there is a \(\frac{1}{78}\) probability that the first winner randomly selects the card for the pizza topped with banana peppers and Kalamata olives.

The order in which the toppings are chosen is not important, hence the combination formula is used to solve this question.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

Researching the problem on the internet, it is found that 2 toppings will be chosen from a set of 13, hence:

\(C_{13,2} = \frac{13!}{2!11!} = 78\)

The pizza topped with banana peppers and Kalamata olives is one outcome, hence:

p = 1/78.

There is a \(\frac{1}{78}\) probability that the first winner randomly selects the card for the pizza topped with banana peppers and Kalamata olives.

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Two bikers meet at a park at A

The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°

Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles.

By following of the above statement the triangle is formed shown in  the image attached below.

Thus, without using cosine formula, by drawing the triangle according to
the statement. At point A both the bikers were meet

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Answer:

The answer is number 2

With the application angular momentum algebra Jy is Hermitian, Jy has imaginary matrix elements is proved.

What is Matrix?

a matrix is a collection of numbers that have been put in rows and columns to make a rectangular array. The entries of the matrix are the numbers, which are referred to as its elements. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics.

Solution:

Recall the angular momentum algebra:

[Jx, Jy] = ihJz, [Jy, Jz] = ihJx, [Jz, Jx] = ihJy

Given a basis | ii, the matrix representations for the Jx is [Jx]ij ≡ hi | Jx | ji, and likewise for

Jy and Jz. Thus, since Jx and Jz have real matrix elements, we find:

hi | Jx | ji = hj | Jx | ii, hi | Jz | ji = hj | Jz | ii

where we use the Hermiticty of Jx and Jz. Taking the matrix elements of the third commutator

given above, we find:

hi | [Jx, Jz] | ji = −i~ hi | Jy | ji

where

hi | [Jx, Jz] | ji = Summation k(hi | Jx | ki hk | Jz | ji − hi | Jz | ki hk | Jx | ji)

                      = − hj | [Jx, Jz] | ii

       hi | Jy | ji = − hj | Jy | ii

Therefore, Jy is Hermitian, Jy has imaginary matrix elements.]

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Given equations are,

4x - y = -2 ------(1)

x - 3y = 5 ------(2)

There are two variables in the equations 'x' and 'y'.

Coefficients of these variables in equation (1),

Coefficient of x = 4

Coefficient of y = -3

Similarly, constant terms of equations (1) and (2) are -2 and 5 respectively.

Matrix to solve these equations will be,

\(\begin{bmatrix}4 &-1 \\ 1 & -3\end{bmatrix}\begin{bmatrix}x\\y \end{bmatrix}=\begin{bmatrix}-2\\ 5\end{bmatrix}\)

Therefore, Option (A) will be the correct option.

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Answer:0.25

Step-by-step explanation:

Answer:

i = 77.5°

k = 77.5°

j = 102.5°

h = 155°

Step-by-step explanation:

Since we have an isosceles triangle, we know that ∠i and ∠k are equal. So,

180 - 25 = 2x

155 = 2x

x = 77.5

So m∠i = m∠k = 77.5°

To find m∠j, we use Supplementary Angles:

180 - 77.5 = 102.5°

To find m∠h, we also use Supplementary Angles:

180 - 25 = 155°

When the domain is substituted, the Range of the function will be

7 ≤ y < ∞

The range of a function is the the spread of minimum value of the function to maximum value. We can find the range by substituting different domains into the function.

Given a function  f(x) = |x| + 7

This |x| show that it is a modulus. That is, the domain will always be positive numerals.

The minimum domain = 0, so the minimum f(x) = 0 + 7 = 7

The maximum domain = ∞, so the maximum f(x) = ∞ + 7 = ∞

y = f(x)

Therefore, the range of of the function f(x) = |x| + 7 will be 7 ≤ y < ∞

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Answer:

Step-by-step explanation:

The volume is found by multiplying all the sides of the rectangular shape.

Thus the volume = 6 * 8 * 10 = 480 cubic feet

Hope that helps!

Answer:

480 cubic feet

Step-by-step explanation:

The volume of any prism is Bh, where B = AREA of the base and h = height of prism.

We're given:

Now, we solve the volume.

Therefore, the answer is 480 cubic feet.

Answer:

A. 1 milliliter

Step-by-step explanation:

1000 milliliters = 1 liter

0.001 liters = 1 milliliter

The angles <1, <2, and <3 will not add up to 180 degrees. The angles <1 and <2 are alternate interior angles, and the angles <2 and <3 are also alternate interior angles, AB is parallel to CD.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is always equal to 180 degrees. This means that if you measure the angles inside any triangle and add them up, the result will always be 180 degrees. This property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene.

To understand this property, consider a triangle ABC with interior angles angle A, angle B, and angle C. If we draw a line segment from vertex A to a point D on side BC such that it is parallel to the side AB, then we can see that angle A and angle C are alternate interior angles of the parallel lines AB and CD. Similarly, angle B and angle C are alternate interior angles of the parallel lines BC and AD.

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