please help me

3. What do you call a mathematical statement in two variables that uses equal sign (=)?
A. mathematical expression
B. mathematical equation
C. LinearvEquation in two variables
D. Linear inequality in two variables

​

The value of x in the expression given is -7/6

(6x + 9)/2 =

First step is to cross multiply

6x + 9 = 2

Collect like terms

6x = 2 - 9

6x = -7

divide both sides by 6 to isolate x

x = -7/6

Therefore the value of x in the expression given is -7/6

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Answer:

this list

Step-by-step explanation:

1×12000=12000

2×6000=12000

3×4000=12000

4×3000=12000

5×2400=12000

6×2000=12000

8×1500=12000

10 ×1200=12000

12 ×1000=12000

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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Answer:

The first design does not specify the age and the number of the group not exercising.

Step-by-step explanation:

The second design will produce more trustworthy data because there are equal number of men above the age of 40 grouped into two categories those who exercise and those who do not exercise.

The first design does not produce such accurate results because the two sample sizes may be quite different and the second group may have candidates of any age other than 40.

The null hypothesis for this design will be u ≠ 40 against the alternate hypothesis that u= 40.

This will give a two tailed test.

All the result possibilities will be for  both men aged above 40 and below 40 excluding out only the 40 aged men.

In the second design the sample sizes are same and the both samples may have men aged older than 40

The null hypothesis for this design will be u => 40 (Mean is greater and equal to 40) against the claim u < 40 .

This will give a one tailed test.

So this design will give better results.

All the result possibilities will be for men aged above 40.

Answer:

Short leg = 24inches

Long leg = 32inches

Hypotenuse = 40inches

Step-by-step explanation:

Given:

Pythagorean Theorem:

a²+b²=c² → (x-8)²+ x² = (x+8)²

Solving for both sides:

x² - 16x+ 64 + x² = x²+ 16x + 64

More Painful Solving:

x² - 32x = 0

x(x-32) = 0

x=0 or 32

Can't use the 0 so we trash it!

x=32

add 8 to get the hypotenuse and subtract 8 to get the short leg

Answer:

\(y = \frac{2}{3} x + 2\)

Step-by-step explanation:

Start by finding the slope of the given line.

\(\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }\)

Slope of given line

\( = \frac{5 - ( - 1)}{ - 2 - 2} \)

\( = \frac{5 + 1}{ - 4} \)

\( = \frac{6}{ - 4} \)

\( = - \frac{3}{2} \)

A perpendicular bisector cuts through the line at its midpoint perpendicularly.

The product of the slopes of two perpendicular lines is -1.

Let the slope of the perpendicular bisector be m.

\( - \frac{3}{2} m = - 1\)

\(m = - 1 \div ( - \frac{3}{2} )\)

\(m = - 1 \times ( - \frac{2}{3} )\)

\(m = \frac{2}{3} \)

\(y = \frac{2}{3}x + c\), where c is the y-intercept.

To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.

\(\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}\)

Midpoint of given line

\( = ( \frac{ - 2+ 2}{2} , \frac{5 - 1}{2} )\)

\( =( \frac{0}{2} , \frac{4}{2} )\)

= (0, 2)

\(y = \frac{2}{3} x + c\)

When x= 0, y= 2,

2= ⅔(0) +c

2= 0 +c

c= 2

Thus, the equation of the perpendicular bisector is \(y = \frac{2}{3} x + 2\).

Answer:

It is a positive number.

Step-by-step explanation:

Numbers that are above 0 are considered positive and numbers below 0 are considered negative.

~Anna

System A

This system of equations is: consistent dependent.

This means the system has: infinitely many solutions.

System B

This system of equations is: inconsistent.

This means the system has: no solution.

System C

This system of equations is: consistent independent.

This means the system has: solution (3, 1).

In Mathematics and Geometry, a system of equations has infinitely many solutions (infinite number of solutions) when both equations produce the same line and as such, it is consistent dependent i.e System A.

In Mathematics and Geometry, a system of equations has no solution when both equations produce parallel lines with no common point and as such, it is inconsistent i.e System B.

In conclusion, a system of equations has one solution when both equations produce lines that intersect and have a common point and as such, it is consistent independent i.e System C.

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Answer:

The range is (D) or '12'

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Base of the Pennant = 330 pixels

Scale Factor =0.6

Step-by-step explanation:

The base measure of the pennant on screen is 550 pixels.

The height  is 275 pixels.

\(A$spect Ratio=\dfrac{Base}{Height}=\dfrac{550}{275} =2:1\)

If Charlotte resizes the pennant, keeping the aspect ratio  constant.

Height = 165 pixels

Therefore:

\(\dfrac{Base}{165}=\dfrac{2}{1} \\\\$Base= 2 *165 =330\)

Therefore, the scale factor of the dilation  \(=\dfrac{330}{550}= \dfrac{165}{275}=0.6\)

Base of the Pennant = 330 pixels

Scale Factor =0.6

Answer:

2.5

Step-by-step explanation:

the length has increased by 7.5/3 = 2.5.

so the scale factor is 2.5

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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A=prt

A=2000×7%×4

=560

The simplified Expression of 2.5 x 10² / 5 x \(10^{-5}\) is 5 x \(10^6\).

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as \(3^4\), where 4 is the exponent and 3 is the base.

Given:

2.5 x 10² / 5 x \(10^{-5}\)

Now, using Exponents and powers

\(a^{-m}\) = 1/ \(a^m\)

So, 2.5 x 10² / 5 x \(10^{-5}\)

= 2.5 /5 x \(10^{2-(-5)}\)

= 25/50 x \(10^{2+5]\)

= 1/2 x \(10^7\)

= 0.5 x \(10^7\)

= 5 x \(10^6\)

Hence, the simplified Expression is 5 x \(10^6\).

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Answer:

d² - 24d + c = (d - 12)² - 144 + c

Answer:

2

Step-by-step explanation:

The constant of proportionality k is given by k=y/x

y=2, x=1,

k=2

Answer:

a.)

Open statement : P(X,Y) = The square of X is larger than the cube of Y.

b.)

Open Statement : P(X,Y,Z) = X.Y + 8 = Z.

c.)

Open Statement : P(X,Y) = The population of X is larger than the population of Y.

Answer:

Step-by-step explanation:

Answer:

B) I, II, III, and IV

Step-by-step explanation:

Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.

In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;

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Complete Question:

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS

We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.

NS and NS

NS and RS

MS and RS

MS and QS

When a man selects 3 items, the probability that they're all defective will be 1/64.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

From the information, bag contains 8items of which two are deffective. The probability of a defective item is:

= 2/8

= 1/4

When a man selects 3 items, the probability that they're all defective will be:

= (1/4)³

= 1 / 64

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Complete question

A bag contains 8items of which two are deffective. A man selects 3 items, what is the probability that they're all defective?

Answer:

Step-by-step explanation:

27/54   = .54

4/5 = .80

.45 = 9/20

38% = 19/50

17/25 = 0.68

On solving the provided question we can say that The following is the data table of the function.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

the provided functions that can be formed are

           x            -infinity < x < -10

f(x) =    2x + 10          -10 < x < 10

           4X - 10       10 < x < infinty

The following is the data table of the function.

x              y

-20          -20

-15          -15

-10          -10

-5             0

0              10

5               20

10              30

15              50

20              70

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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.

A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.

Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

The following is the data table of the function.

x               y

-20          -20

-15           -15

-10           -10

-5              0

0              10

5              20

10              30

15              50

20             70

The provided functions that can be formed are

\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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To calculate the circumference of a circle, you can use the formula:

\(\displaystyle C=2\pi r\)

Where \(\displaystyle C\) represents the circumference and \(\displaystyle r\) represents the radius of the circle.

Given that the radius \(\displaystyle r\) is 8 inches, we can substitute this value into the formula:

\(\displaystyle C=2\pi (8)\)

Simplifying the expression:

\(\displaystyle C=16\pi \)

Thus, the circumference of a circle with a radius of 8 inches is \(\displaystyle 16\pi \) inches.

Note: \(\displaystyle \pi \) represents the mathematical constant pi, which is approximately equal to 3.14159.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Measurement of weight 6 is in ounces and the measurement of weight 170 is in grams.

What is measurement?

An object or event's attributes are quantified through measurement so that they can be compared to those of other things or events. Measurement, then, is the process of establishing how big or small a physical quantity is in relation to a fundamental reference quantity of the same kind.

Given:

Elena has a pet parakeet that weighs 6 when measured in one unit and

170 when measured in a different unit.

We have to find the correct units from grams and ounces for these.

We know that, 1 ounce is greater than 1 gram.

1 ounce = 28.3495 grams

Multiply both sides by 6.

6 ounces = 170.097 grams

Approximate the values to the nearest whole number.

6 ounces = 170 grams

Therefore, 6 ounces = 170 grams.

Hence, measurement of weight 6 is in ounces and the measurement of weight 170 is in grams.

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Answer: On Tuesday and Thursday

Step-by-step explanation:

On Tuesday, Mrs. Smith rode her favorite horse for 1 9/15 miles. Taking it to its simplest form by dividing it by 3 would yield a mixed fraction of 1 3/5 which is the same as the distance that the horse was ridden on Thursday.

Another method is to convert them back into their original improper fractions.

Tuesday;                                                              Thursday

= 1 9/15                                                                 = 1 3/5

= (15 * 1 + 9) / 15                                                   = (5 * 1 + 3)/5

= 24/15                                                                 = 8/5

= 8/5

Notice how again they are the same at their simplest forms.

Answer: The percentage change is 56.67%.

Step-by-step explanation:

From 120 meals to 52 meals, change in meals = ( 120- 52) meals

= 68 meals

The percentage change = \(\dfrac{\text{change in meals}}{\text{Original quantity of meals}}\times100\)

\(=\dfrac{68}{120}\times100\\\\=56.67\%\)

Hence, the percentage change is 56.67%.