Which two points on the number line represent numbers that can be combined to make zero?

B and D
A and B
C and D
A and C

Step-by-step explanation:

[tex] {x}^{2} - 14x - 25 {y}^{2} + 100y = 76[/tex]

Factor by grouping,

[tex]( {x}^{2} - 14x) - (25 {y}^{2} - 100y) = 76[/tex]

Complete the square, with the x variables,

[tex]( {x}^{2} - 14x + 49) - (25 {y}^{2} - 100y) = 125[/tex]

Factor out 25 for the y variables

[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y) = 125[/tex]

Complete the square

[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y + 4) = 25[/tex]

Simplify the perfect square trinomial

[tex](x - 7) {}^{2} - 25(y - 2) {}^{2} = 25[/tex]

Make the right side be 1 so divide everything by 25.

[tex] \frac{(x - 7) {}^{2} }{25} - (y - 2) {}^{2} = 1[/tex]

Here our center is (7,2).

If 24 marbles have a mass of 60 g, then each marble has a mass of [tex]60/24=2.5 \text{ g}[/tex].

So, 60 marbles have a mass of 60(2.5)=150 g

Answer:

150 g

Step-by-step explanation:

24 marbles = 60 g

1 marble = 60÷24 = 2.5 g

60 marbles = 2.5 × 60 = 150 g

Hope this helped and have a good day  

Step-by-step explanation:

We will need to use logs here...

First divide each side by 3

[tex]3(10)^x=30000[/tex]

[tex]10^x=10000[/tex]

Then take the log of each side

Keep in mind that [tex]log_{10} (10)[/tex] gets canceled out to leave x

[tex]log_{10} (10^x)=log(10000)[/tex]

Finally, log(10000) = 4 because [tex]10^4=10000[/tex]

[tex]x = 4[/tex]

The maximum number of visits you can make with each membership is 104.

Gym membership refers to the cost to register, attend, and use a gym as a member for an agreed period.

Some gym memberships require one-time payments made monthly or annually.

Assume that the annual gym fee is $200 for Saturdays and Sundays only.

Thus, in this scenario, the maximum number of visits you can make with each membership is 104.

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1). Option C

2). Option A

Polygon is given as a closed two-dimensional figure with three or more straight lines.

The given vertices of polygon ABCDE are A(2, 8), B(4, 12), C(10, 12), D(8, 8) and E(6, 6)

After reflection new polygon formed MNOPQ has the vertices M(-2, 8), N(-4, 12), O(-10, 12), P(-8, 8) and Q(-6, 6).

By comparing the vertices we find the x-coordinates of polygon ABCDE have been changed to MNOPQ by negative notation only. Y- coordinates are same.

Therefore, polygon ABCDE has been reflected across the y-axis.

Option C. is the answer.

If polygon MNOPQ is translated 3 units right and 5 units down then the new vertices of congruent polygon VWXYZ will be

M(-2, 8) = [(-2 - 3), (8 + 5)] = (-5, 13)

N(-4, 12) = [(-4 - 3), (12 + 5)] = (-7, 17)

O(-10, 12) = [(-10 - 3),(12 + 5)] = (-13, 17)

P(-8, 8) = [(-8 - 3), (8 + 5)] = (-11, 13)

Q(-6, 6) = [(-6 -3),(6 + 5)] = (-9, 11)

Thus, Option A. is the correct option.

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Answer:

Step-by-step explanation:

the

Answer:

Step-by-step explanation:

how many triangles are in a 18 sided polygon

An 18 sided polygon, sometimes also called an octakaidecagon, it has 18 sides and therefore is made up of 18 triangles and has 18 vertices.

(look at the picture)

By functional analysis we have the following conclusion about the function given: The domain for f(x) is all real numbers greater than or equal to 2.

Domain is the set of x-values such that the value of the function exists. By algebra we know that the domain of polynomials is the set of all real numbers, whereas the domain of radical functions is the set of x-values such that y ≥ 0. If we know that f(x) = 2 · x² + 5 · √(x - 2), then the domain is restricted by the radical component and defined by x ≥ 2.

By functional analysis we have the following conclusion about the function given: The domain for f(x) is all real numbers greater than or equal to 2.

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Answer:

B

Step-by-step explanation:

five times x cubed plus/and two times x squared minus nine.

According to the given values, the numbers from least to greatest is ∛64, 4.222.. √19

Ordering a sequence of number from least to greatest is known as the ascending order of magnitude

Given the following parameters

∛64, √19 and 4.222...

The cube root of 64 is 4

The square root of 19 is 4.36

While the repeating decimal 4.2. can be 4.2222...

Ordering from least to greatest is 4, 4.2222, 4.36

According to the given values, the numbers from least to greatest is ∛64, 4.222.. √19

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Based on the given options, the inequality for the acceptable weights of the suitcase is 32.5 ≤ x ≤ 47.5.

You didn't include the full question but this question can be answered based on the given options.

When inequalities are written, there is no inclusion of "or" which eliminates options A and C.

It is illogical to have an inequality as 32.5 ≥ x ≥ 47.5. This is because if 32.5 is larger or equal to x, then x cannot be larger than 47.5. This is mathematically impossible.

This leaves the likely answer as 32.5 ≤ x ≤ 47.5 which means that the weight of the suitcase has to be larger than or equal to 32.5 but less than or equal to 47.5.

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Answer:

32.5 ≤ x ≤ 47.5

Step-by-step explanation:

Part (i)

1) AB is perpendicular to BC, ED is perpendicular to CD, BC = CD (given)

2) Angles ABC and CDE are right angles (perpendicular lines form right angles)

3) Angles ABC and CDE are equal (all right angles are equal)

4) Angles ACB and DCE are equal (vertical angles are equal)

5) Triangles ABC and EDC are congruent (ASA)

Part (ii)

6) AB = DE (corresponding parts of congruent triangles are equal)

Compare the quantity in Column A with the quantity in Column B.

Column A Column B, The two quantities are equal.

Generally, the surface that has one end or side that is higher than the other (or vice versa); is a surface that slopes up or down.

In conclusion, Compare the number in Column A with the number in Column B.

The two amounts are identical in Columns A and B.

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Answer:

? i need help

Step-by-step explanation:

Answer:

[tex]n {}^{2} + 3[/tex]

Answer:

4 is my answer:))))) maybe this will help

Answer:

1

Step-by-step explanation:

it depends on how many choices there are

If there is 1 choice for an appetizer, 1 choice for an entrée, and 1 choice for a dessert

(1 * 1 * 1 = 1)

then there is 1 meal choice

If there are 7 choices of appetizers, 12 choices of entrée, and 6 choices of dessert.

(7 * 12 * 6 = 504)

then there are 504 different options

If there are 5 choices for an appetizer, 12 choices for an entrée, and 3 choices for a dessert

(5 * 12 * 3 = 180)

then there are 180 options

12 choices for entrées, 10 choices for side dishes, and 6 choices for dessert

(12 * 10 * 6 = 3240)

then there are 3240 meal options

you have to multiply the number of entrées (e), meals (m), and desserts (d)

e * m * d = x

you are solving for x, which is the different meals available aka your answer.

so plug in the numbers and that should give you the answer!

hope this helps:)

The vertices of the image of dilation are (4, 2), (-1, 2) and (3, 4)

The given parameters are:

Center, (a, b) = (-3, 0)

Scale factor, k = 1/2

The vertices of the figure are

(5,4), (-5, 4) and (3,8)

The rule of dilation is represented as:

(x, y) ⇒ (k(x -a), k(y -b))

So, we have:

Point (5,4)

(x, y) ⇒ (1/2(5 + 3), 1/2(4 -0))

(x, y) ⇒ (4, 2)

Point (-5,4)

(x, y) ⇒ (1/2(-5 + 3), 1/2(4 -0))

(x, y) ⇒ (-1, 2)

Point (3,8)

(x, y) ⇒ (1/2(3 + 3), 1/2(8 -0))

(x, y) ⇒ (3, 4)

So, the vertices of the image of dilation are (4, 2), (-1, 2) and (3, 4)

See attachment for the image

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Yes, the triangles are congruent if AB ≅ DE.

Criteria for the Congruency of two Triangles

If two triangles share the same sides and angles, they are said to be congruent triangles.

Triangles are tested for congruence using the following 4 criteria:

1) Angle-side-angle(ASA): Two angles and a side of a triangle are congruent if they are equal to two angles and the corresponding side of another triangle.

2) Side-side-side(SSS): Two triangles make congruent triangles if all three sides of one triangle are equal to three sides of another.

3) Side angle side(SAS): A triangle is congruent if its two sides and any included angles are equivalent to those of another triangle's two sides and corresponding angle.

4) Hypotenuse - leg(HL): If a triangle's hypotenuse and one of its legs are equal, then the triangle's hypotenuse and leg are also equal.

Checking for Congruency in the Given Triangles

ΔDEF and ABC have a equal angles, ∠F=∠B, as well as a pair of equal sides,  DF = AC.

Thus, in order to satisfy the SAS criterion of congruent triangles, AB = DE

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Answer:

(D) no, because the hypotenuses must have different lengths

Step-by-step explanation:

Answer:I think observational

Step-by-step explanation:They want to study it so they trying it on people who are willing so they are looking closely to what happens.

Answer

100 multiples of 5 greater than 100 are:

Step-by-step explanation:

105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275, 280, 285, 290, 295, 300, 305, 310, 315, 320, 325, 330, 335, 340, 345, 350, 355, 360, 365, 370, 375, 380, 385, 390, 395, 400, 405, 410, 415, 420, 425, 430, 435, 440, 445, 450, 455, 460, 465, 470, 475, 480, 485, 490, 495, 500, 505, 510, 515, 520, 525, 530, 535, 540, 545, 550, 555, 560, 565, 570, 575, 580,

Answer:

Step-by-step explanation:

If is -(-13/12) then A. -13/-12

If is -13/12 then B. 13/-12

[tex]-\dfrac{-13}{12}=\dfrac{-13}{-12}=\dfrac{13}{12}\\\\\dfrac{-13}{12}=-\dfrac{13}{12}=\dfrac{13}{-12}[/tex]

Answer:

x = 120

y = 21

Step-by-step explanation:

Since j and k are parallel, the sum of x and 60 would be 180 because they are supplementary:

x + 60 = 180 subtract 60 from both sides

x = 120

The measure of x and (4y+36) is equal because they are alternate angles since the horizontal lines are also stated as parallel:

we know x = 120 so

120 = 4y + 36 subtract 36 from both sides

84 = 4y divide both sides by 4

21 = y

Using the slope concept, it is found that the change of elevation for a car at the end of the 5 mile drive is of 0.3672 miles.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, we have that:

Hence:

tan(4.2º) = h/5

h = 5 x tan(4.2º)

h = 0.3672.

The change of elevation for a car at the end of the 5 mile drive is of 0.3672 miles.

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Answer:

ab(7a+b-2)

Step-by-step explanation:

see the common and take out the common parr

Answer:

its all about the formula =

(a+b)2 =a2 +2ab=b2

Step-by-step explanation:

[tex]\log_3|5-2x| > 4\\\log_3|5-2x| > \log_33^4\\|5-2x| > 3^4\\|5-2x| > 81\\5-2x > 81 \vee 5-2x < -81\\2x < -76 \vee 2x > 86\\x < -38 \vee x > 43\\x\in(-\infty,-38)\cup(43,\infty)[/tex]

The equation of the appropriate line of best fit is y = 1.25x + 2

Start by drawing a line through the points (see attachment)

From the attached graph, we have:

(x, y) = (0,2) and (4,6.5)

Calculate the slope (m) using:

m = (y2 - y1)/(x2 - x1)

This gives

m = (6.5 - 4)/(2 - 0)

Evaluate

m = 1.25

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 1.25(x - 0) + 2

Expand

y = 1.25x + 2

Hence, the equation of the appropriate line of best fit is y = 1.25x + 2

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Answer:

[tex]\sf \dfrac{11}{20} \quad or \quad 0.55[/tex]

Explanation:

[tex]\rightarrow \sf \dfrac{3}{4} - \dfrac{1}{5}[/tex]

make the denominators same by lcm

[tex]\rightarrow \sf \dfrac{5(3)}{20} - \dfrac{4(1)}{20}[/tex]

expand the following

[tex]\rightarrow \sf \dfrac{15}{20} - \dfrac{4}{20}[/tex]

Join the fractions together

[tex]\rightarrow \sf \dfrac{15-4}{20}[/tex]

Subtract the integers

[tex]\rightarrow \sf \dfrac{11}{20} \quad or \quad 0.55[/tex]

Answer:

11/20 or 0 whole 11/20 or 0.55

Step-by-step explanation:

Find the least common multiple (LCM) of 4 and 5 at first:

We can't do the LCM of 5 and 4,so just multiply them, 5*4 = 20

Now,

For 3/4 : divide 20 by 4,then multiply the result by 3.For 1/5 : divide 20 by 4, then multiply the result by 1. Simple!

Subtracting the numerators,

As a whole number:

As a decimal:

Answer:

$206

Step-by-step explanation:

Lyanna will earn 3% on her capital within 1 year.
In total, she will have 103%.
$200 x 103% = $206