**Answer:**

42 cm

**Step-by-step explanation:**

7+4+2+4+2+4+7+12

If log3 x + logx 3= 2.5 find the value of x

The** value **of x is -0.004624

[tex]log_{3} (x)+log_{x} (3)=2.5[/tex]

[tex]log_{3} (x)+\frac{log_{3} (3)}{log_{3} (x)} =2.5[/tex]

Let z= [tex]log_{3} (x)[/tex]

[tex]z+\frac{1}{z} = 2.5[/tex]

[tex]3z^{2} + z-2.5z=0[/tex]

z= -0.166

[tex]log_{3} (x)=-0.166[/tex]

x = -0.004624

What is a **log**?

The** logarithm** is exponentiation's opposite function in mathematics. This indicates that the exponent to which a set number, base b, must be increased in order to create a specific number x, is represented by the **logarithm** of that number. The **logarithm**, in its most basic form, counts the number of times the same factor appears when multiplied repeatedly; for instance, since 1000 = 10 x 10 x 10 = 103, its "logarithm base 10" is 3, or log10 (1000) = 3. When there is no possibility of a mistake or when the base is irrelevant, as, in big O notation, the logarithm of x to base b is written as** log**a (x),** log**b x, or even without the explicit base, **log** x.

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help on the ones you know

**Answer:**

**2. y = x + 13**

**Step-by-step explanation:**

Your points are: (-4, 9) and (2, 15)

To write an equation of a line from two ordered pairs, you first find the slope (m)

To find the slope, you do **y2 - y1 / x2 - x1**

(-4 is x1, 9 is y1) (2 is x2, 15 is y2)

Plug in the numbers:

15 - 9 **/** 2 - (-4) ----------------------> 6/6 ----------> 1, **m = 1**

The next equation we'll use is **y - y1 = m(x - x1)**

**and slope intercept form is y = mx + b**

Pick either ordered pair to plug in the coordinates, but this time I'll use

(2, 15) -----> **2 is x1, 15 is y1**

**y - 15 = m(x - 2)**

Since we already know the slope, **m**, we can simplify the equation.

y - 15 = 1(x - 2)

Distributive property

y - 15 = x - 2

Add 15 on both sides,

**y = x + 13**

1. y=(2/3)x-4

slope is rise/run. starting at (0,-4), i counted up 4 to the x-axis then over 6 to the point (6,0). this gives a slope of 4/6, which is then reduced to 2/3. our b in the y=mx+b is found by looking for where the line crosses the y-axis, which is at (0,-4). b is this y value. plugging everything in (m for slope, b for y-intercept) gives y=(2/3)x-4

2. the other commenter did a great job at explaining 2

3. the line with a slope of -3 is steeper

start this problem by solving for y in the equation given. -5x+2y=8 becomes 2y=5x+8, then y=(5/2)x+4. all we need from this is the slope 5/2 to compare to -3. a steeper slope is given by the larger absolute value. |5/2| is 5/2, and |-3| is 3. 5/2<3, so the line with the slope -3 is steeper.

4a. the lines are neither perpendicular or parallel.

the slopes are different, so they cannot be parallel. the slope of the first equation and second equation (-4 and 4) are not inverse reciprocals of each other, so they cannot be perpendicular.

4b. the lines are parallel.

to find the answer of this question, solve for y in the first equation. 5x+15y=-8 becomes 15y=-5x-8, then y=-(1/3)x-(8/15). the slopes of the lines are both -1/3 with different y-intercepts, so the lines are parallel.

5. y=(1/3)x-(14/3)

use point-slope form and simplify. plugging into point slope gives us y+2=m(x-8). m is found by taking the inverse reciprocal of the equation given to us. the inverse reciprocal of -3 is 1/3, so m=1/3. the equation is y+2=(1/3)(x-8). distribute to get y+2=(1/3)x-(8/3). solve for y. y=(1/3)x-(8/3)-2. y=(1/3)x-(8/3)-(6/3). y=(1/3)x-(14/3)

slope is rise/run. starting at (0,-4), i counted up 4 to the x-axis then over 6 to the point (6,0). this gives a slope of 4/6, which is then reduced to 2/3. our b in the y=mx+b is found by looking for where the line crosses the y-axis, which is at (0,-4). b is this y value. plugging everything in (m for slope, b for y-intercept) gives y=(2/3)x-4

2. the other commenter did a great job at explaining 2

3. the line with a slope of -3 is steeper

start this problem by solving for y in the equation given. -5x+2y=8 becomes 2y=5x+8, then y=(5/2)x+4. all we need from this is the slope 5/2 to compare to -3. a steeper slope is given by the larger absolute value. |5/2| is 5/2, and |-3| is 3. 5/2<3, so the line with the slope -3 is steeper.

4a. the lines are neither perpendicular or parallel.

the slopes are different, so they cannot be parallel. the slope of the first equation and second equation (-4 and 4) are not inverse reciprocals of each other, so they cannot be perpendicular.

4b. the lines are parallel.

to find the answer of this question, solve for y in the first equation. 5x+15y=-8 becomes 15y=-5x-8, then y=-(1/3)x-(8/15). the slopes of the lines are both -1/3 with different y-intercepts, so the lines are parallel.

5. y=(1/3)x-(14/3)

use point-slope form and simplify. plugging into point slope gives us y+2=m(x-8). m is found by taking the inverse reciprocal of the equation given to us. the inverse reciprocal of -3 is 1/3, so m=1/3. the equation is y+2=(1/3)(x-8). distribute to get y+2=(1/3)x-(8/3). solve for y. y=(1/3)x-(8/3)-2. y=(1/3)x-(8/3)-(6/3). y=(1/3)x-(14/3)

What products are defined for these matrices?

Drag the operation to the boxes to correctly complete the table.

The **allocation **for product defined and **product **not defined are

PD(product defined)

PM, QP, LMPND

MLThis is further explained below.

What is an allocation for product defined?Generally, the rule for matrix multiplication

no. of columns for the first matrix should be equal to no. of rows in the second matrix" that is if

1st matrix has =m * n

2nd has =k *l

Therefore

m=l

L=2*2, M=4*2,

The **matrix **is defined as the row and the column tally

M=4*2 and L=2*2

The **matrix **is not defined as a row and the column do not tally

In conclusion, Q=2*1, and P=2*2 equal so the product is defined.

P=2 *2,M=4 *2, equal so **product **is defined.

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jane had overdrafted her bank account and had a balance of -$24.62. She picked up her paycheck from work and deposited $154.88. What is her new balance?

answer for 100 points

Your answer would be 179.5

Write each number as a power of 4

a) 1/4

b) 1/64

**Answer: I am going to assume that 1/4 is 1 over 4 ( a fraction ) and that it is the same for 1/64**

**A) 0.00390625**

**B) 0.015625^4 <------( Here is the equation. when i put it in a calculator it was too long. here is the answer that gave me: 5.96046448 e-8 )**

Please help!! I’ve been struggling

Explain how to solve this question by multiplying, dividing, adding, or subtracting both sides by 2

**Answer:**

x=16

**Step-by-step explanation:**

x/2 = 8

Multiply both sides by 2

x=16

:] Hope this helps

**the answer would be x=16**

**you would multiply both sides by 2 **

a certain area of the eastern united states is, on average, hit by 6 hurricanes a year. find the prob- ability that in a given year that area will be hit by (a) fewer than 4 hurricanes; (b) anywhere from 6 to 8 hurricanes.

By applying **probability** method in a **Poisson** distribution, we find out that the probability that in a given year that area will be hit by fewer than 4 hurricanes is 0.1512 and the probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes is 0.4015.

It is given that -

On an **average**, Eastern United States is hit by 6 hurricanes in a year.

We have to find out -

(a) Probability that in a given year that area will be hit by fewer than 4 hurricanes

(b) Probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes

This is a case of probability which relates to Poisson distribution that provides probability of any **random event** that occurs within a specific **time interval**.

Let us assume the **number** of hurricanes is represented by [tex]X[/tex]. The Poisson distribution can be represented as -

[tex]P(X) = \frac{(lambda)^{X}*e^{-lambda}}{X!}[/tex] -------(1)

Here, [tex]X\\[/tex] = 1,2,3,...

**lambda** = Average = 6 (in this question)

[tex]e[/tex] = 2.718

(a) Probability that in a given year that area will be hit by fewer than 4 hurricanes

[tex]P(X < 4) = P(X=0) +P(X=1)+P(X=2)+P(X=3)\\= \frac{6^{0}*e^{-6}}{0!}+\frac{6^{1}*e^{-6}}{1!}+\frac{6^{2}*e^{-6}}{2!}+\frac{6^{3}*e^{-6}}{3!}\\=0.0025+0.0149+0.0446+0.0892\\=0.1512[/tex]

Thus, the probability that in a given year that area will be hit by **fewer than 4 hurricanes** is 0.1512.

(b) Probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes

[tex]P(6\leq X\leq 8)=P(X=6)+P(X=7)+P(X=8)\\=\frac{6^{6}*e^{-6} }{6!}+\frac{6^{7}*e^{-6} }{7!}+\frac{6^{8}*e^{-6} }{8!}\\=0.1606+0.1376+0.1033\\=0.4015[/tex]

Thus, the probability that in a given year that area will be hit by anywhere from **6 to 8 hurricanes** is 0.4015.

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HELLLP khan academy !! due tonight

Equation of the line is **y = -(1/3)x+5**

The figure shows a **straight line** of which two points and thereby the **slope** can be found out.

Equation of a line is in the **slope-intercept** form is,

**y = mx +c,**

where m is the** slope** of the line and c is the **y-intercept** of the line.

From the figure, two points on the line are, (0,5) and (3,4).

Then **slope =** (4-5)/(3-0)

= -1/3

Now** y-intercept**, c is the y-co-ordinate when x = 0.

From the figure, when x = 0, y = 5

So** y-intercept,** c = 5.

Thus the **equation** of the line is, **y = -(1/3)x+5**

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!!20 Points!! Solve using augmented matrices.

x+y=1

3x-y=7

x=2

y=-1

You have to do subtitution

y=-1

You have to do subtitution

What will be the location of T′ in the image trapezoid S′T′U′V′? (10, −1) (10, 1) (13, 1) (13, −1)

By **translating** trapezoid S′T′U′V 7 using the same **translation** rule, the location of T′ in the image trapezoid S′T′U′V′ is: D. (13, -1)

Generally, there are four (4) main types of **transformation** and these include the following:

In Geometry, a **translation** can be defined as a type of **transformation** which moves every point of a geometric figure or object in the same direction, as well as for the same distance.

By critically observing the graph (see attachment), we can logically deduce that rectangle JKLM was **transformed** to rectangle J'K'L'M' by **translating** it 7 units to the right and 5 units up.

Next, we would apply the same **translation** rule to T' which is located at point (6, -6) as follows:

(x, y) → (x + 7, y + 5)

Point T (6, -6) → Point T' = (6 + 7, -6 + 5) = (13, -1)

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Complete Question:

Rectangle J'K'L'M' shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied on trapezoid STUV.

What will be the location of T′ in the image trapezoid S′T′U′V′? (10, −1) (10, 1) (13, 1) (13, −1)

standard to slope intercept form

**Answer: y = 1/6x + 1**

**Step-by-step explanation:**

12y - 2x= 12

+2x +2x

12y = 12 + 2x

DIVIDE BOTH SIDES BY 12

y = 1 + 1/6x

THEN PUT IN SLOPE INTERCEPT FORM

y = 1/6x + 1

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 12y - 2x = 12[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 12y = 2x + 12[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{2}{12} x + \frac{12}{12} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{1}{6} x + 1[/tex]

Slope = 1/6, y - intercept = 1

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Which of the following is equal to (2x/5 - 9) +9?

**Answer:**

**I don't see any answer options, and the equation doesn't look correct.**

**I'll assume the equation is meant to be:**

**Step-by-step explanation:**

(2x/5 - 9) = 9

2x/5 = 18

2x = 90

**x = 45**

**if the modified equation is correct.**

Write an explicit formula for an, the nth term of the sequence

6, -12, 24,....

**Answer:**

6,12,24,48,96

**Step-by-step explanation:**

Which postulate could we use to prove that the angles

The angle postulate that best defined angles CAB and CAD is; **Supplementary Angles**

We know that there are different **angle postulates** such as Corresponding angles, complementary angles, supplementary angles and others.

Now, in this case we want to find the angle theorem that best describes angles CAB and CAD. Now, from the given image, it is clear that both angles form a **straight line **and we know that the sum of angles on a straight line equals 180 degrees.

Since both angles sum up to 180 degrees and we know that these angles are defined as **supplementary angles** which are linear pairs.

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Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the force exerted on the object. If an object accelerates at a rate of 3 m/s2, it will exert a force of 15 N. How much force will the same object exert if it accelerates at a rate of 7 m/s2 ?

**Answer: 35N**

**Step-by-step explanation:**

**Cross multiply and divide to find the missing value**

**Answer: 35N :)))))))))))))))))))))))))))))**

98

7. A bag contains 100 marbles. Some are red and the rest are blue. If there are no

more than 12 times as many red marbles as blue marbles in the bag, at most how

re in the bag? At least, how many blue marbles are in the

many red marbles are

bag?

At least 84** blue marbles** and 7 **red marbles** are there in the bag.

Let the bag contain x red marbles therefore there are 12x blue marbles.

Therefore according to the question,

12x + x = 100

13x = 100

= 100/13

=7.69 approx

Which is not possible as the no,of marbles cannot be in decimals therefore there must be atleast 7 marbles of red colour and 84 blue marbles.

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Put the following equation of a line into slope-intercept form, simplifying all fractions. 6x-3y=15

**Answer: **y=2x-5

**Step-by-step explanation:**

6x-3y=15

6x-6x-3y=-6x+15

-3y=-6x+15

-(3y=6x-15)

3y=6x-15

3y/3=(6x-15)/3

y=6x/3-15/3

**y=2x-5**

use the properties of vector addition and scalar multiplication from the following theorem. properties of vector addition and scalar multiplication in rn let u, v, and w be vectors in rn, and let c and d be scalars.

The set R^2 with x ≤ 0 and y ≤ 0 is not a **vector **space.

The 10th axiom cv∈ V does not hold

Let u, v and w be vectors in the vector space V, and let c and d be **scalars**. A set S is defined as a **vector **space if it satisfies the following conditions:

1. u+ v ∈V

2. v + w = w + v

3. (u + v) + w = u + (v + w)

4. v + 0 = v = 0 + v

5. v + (−v) = 0

6. 1v = v

7. c(dv) = (cd)v

8. c(v + w) = cv + cw

9. (c + d)v = cv + dv

10. c v ∈V

Given the set of all vectors x, y in R^2 with x ≤ 0 and y ≤ 0

If the **scalar **c is such that c<0 then c v ∉R^2as cv>0

Therefore, the 10th axiom is not satisfied and thus the set R^2 with x ≤ 0 and y ≤ 0 is not a vector space.

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What is an equation of the line that passes through the point (2,-3) and is parallel to the line 2x+5y=10

The **equation of the line** that passes through the point (2,-3) and is parallel to the line 2x + 5y = 10** **is y = - 2 / 5 x - 11 / 5

The** equation of a line** can be represented in various form such as point slope form, slope intercept form and standard form.

Therefore, let's find the **equation of the line** that passes through the point (2, -3) and is parallel to the line 2x + 5y = 10.

Hence, parallel lines have the same slope.

5y = -2x + 10

y = - 2 / 5 x + 2

Therefore, the slope of the line is - 2 / 5.

Let's find the y-intercept using the slope intercept equation.

y = mx + b

where

m = slopeb = y-interceptHence, (2, -3)

-3 = - 2 / 5(2) + b

-3 = - 4 / 5 + b

b = - 3 + 4 /5

b = - 11 / 5

Therefore, the **equation of the line** is y = - 2 / 5 x - 11 / 5

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The required **equation **of the **line **y = - (2/5)x - 11/5 passes through the **point **(2,-3) and is **parallel **to the line 2x + 5y = 10.

We have to determine the **line **that passes through the **point **(2,-3) and is parallel to the line 2x+5y=10

**Parallel lines **are known to have the same **slope**.

Firstly, we have to find its slope by the given line

⇒ 5y = -2x + 10

⇒ y = - (2/5)x + 2

Thus, the **slope **of the **line **is - 2/5.

Let the required **equation **of the line is y - y₁ = m(x -x₁ )

Here x₁ = 3, y₁ = 1 and m = -2/5

y - 1 = (-2/5)(x - 3)

y - 1 = (-2/5)x + 3(-2/5)

y = - (2/5)x - 6/5 +1

y = - (2/5)x - 11/5

Therefore, the required **equation **of the **line **is y = - (2/5)x - 11/5.

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Can you please help me with this question I don’t understand it.From DA to the angle BAC

**INFORMATION:**

We have the next rhombus

And we must find the measure of

Knowing that DB = 10, BC = 13, and m∠WAD = 25°

**STEP BY STEP EXPLANATION:**

To find all measures, we need to use properties or the rhombus:

- DA: To find DA we need to know that all sides of the rhombus are equal. So, if BC measures 13, then DA measures 13 too.

- BW: To find BW we need to know that in a rhombus, diagonals bisect each other at right angles. That means, diagonals intersect in the middle. So, if DB = 10, then BW will be half of BD. BW = 10/2 = 5.

- WC: We can find it as one of the legs of the right triangle formed by BW, BC and WC. Where, BC is the hypotenuse.

[tex]\begin{gathered} 13^2=5^2+WC^2 \\ WC=\sqrt{13^2-5^2} \\ WC=12 \end{gathered}[/tex]So, WC = 12.

- Angle BAC: To find this angle, we need to use that the interior triangles formed in the interior of the rhombus are congruent. So, angle BAC is congruent with the angle DAC. Then, BAC = 25°.

**ANSWER:**

**DA = ****13**

**BW = ****5**

**WC = ****12**

**BAC = ****25**** degrees**

Can someone help me find the slope???

**Answer:**

The slope is -1/3.

**Step-by-step explanation:**

When you count the rise/run, which is how much it goes up/down and left/right, you get -4/12. Simplify -4/12 and you'll get -1/3.

22 Which inequality is equivalent to 7x - 2y > 8?

Fy> / x+8

8

5 y> - ²/x + ²

Hy< ²x -

3

4

417

<-²/x-4/

32

**Inequality** which is equivalent to 7x - 2y > 8 x>[tex]\frac{2y}{7}[/tex] + [tex]\frac{8}{7}[/tex] and y <[tex]\frac{7x}{2} -4[/tex]

**Equations** don't always need to have a "equal to" symbol on both sides to be balanced. Sometimes it can be about a "not equal to" relationship, meaning that something is superior to or inferior to another. In mathematics, an inequality is a relationship between two numbers or other **mathematical expressions** that results in an **unequal comparison**. **Inequalities** are the name given to certain** algebraic **mathematical expressions.

7x - 2y>8

-2y > 8 -7x

=y <[tex]\frac{7x}{2} -4[/tex]

or

7x >2y + 8

=x>[tex]\frac{2y}{7}[/tex] + [tex]\frac{8}{7}[/tex]

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please answer question 98 please!

thanks

Answer: 1.6 hours (when rounded to nearest tenth)

Steps: 3, 2, 2, 1, 1.5, 2. Add together; 9.5

divide; 9.5 / 6 = 1.583333

round up to nearest tenth; 1.6

Explanation: To calculate average (also called “mean”), you have to add all the numbers together, and divide that number by how many numbers there were. ex: 5, 2, 7, 4, 2. First you would add the numbers together: 20. There were 5 numbers I added together; 20 / 5 = 4. The average would be four.

Steps: 3, 2, 2, 1, 1.5, 2. Add together; 9.5

divide; 9.5 / 6 = 1.583333

round up to nearest tenth; 1.6

Explanation: To calculate average (also called “mean”), you have to add all the numbers together, and divide that number by how many numbers there were. ex: 5, 2, 7, 4, 2. First you would add the numbers together: 20. There were 5 numbers I added together; 20 / 5 = 4. The average would be four.

Evaluate. Write your answer as a whole number or as a simplified fraction.

Submit

**Answer:**

1 / 121

**Step-by-step explanation:**

4^0 / 11^2

= 1 / 11^2

= 1 / 121

PLEASE HELP ME! QUICK!

The **volume** of the given triangular prism to the **nearest tenth** is; 171.5 in³

What is the Volume of the triangular prism?

The volume of a triangular prism of the kind given to us is expressed as;

**Volume** of a triangular prism = area of base triangle × length of the prism

Now, the formula for **area** of base triangle is;

Area = 1/2 * base * height

From the question, we have;

**base** = 9.8 in

**height** = 14 in

Now, the **length** of **prism** is 2.5 inches. Thus;

Volume of prism = (1/2 * 9.8 * 14) * 2.5

**Volume** of prism = 171.5 in³

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Cathy has 48m of fencing to make a rectangular pen for her pets. What is the

maximum area?

The area of the square will be 100 square meters. Then the dimensions of the pen of the rectangle will be 10 by 10 which is a square.

**What is the area of the square?**

Let a be the side length of the square.

Then the area of the square will be

Area of the square = a² square units

Cathy has 40 meters of fencing to build a rectangular pen for her pets.

For the maximum area of the rectangle, the length and width should be congruent.

40 = 4a

a = 10

Then the area of the square will be

**A = 10²**

**A = 100 square meters**

The dimensions of the pen of the rectangle will be 10 by 10 which is a square.

a hypothesis test is conducted at the 0.05 level of significance to test whether or not the population correlation is zero. if the sample consists of 41 observations and the correlation coefficient is 0.60, what is the computed value of the test statistic? round to two decimal places.

The computed value of the test **statistic** is 4.65 or 4.7

Information given in the query:

significance level = 0.05

**Sample size** is 41 observations, and the **correlation** value is 0.60.

Now,

Using the formula, the test statistic to determine whether the population correlation is zero is provided.

:

t =[tex]r\sqrt{n-2} /\sqrt{1-r^{2} }[/tex]

on substituting the respective values, we get

test statics , t = 4.65

or

t=4.7

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13 people on a softball team show up for a game. how many ways are there to choose 10 players to take the field? (you must provide an answer before moving to the next part.)

858 **combinations** are there to choose 10 players to take the field.

Pick 10 people from 13,

[tex]C^{13} _{10}[/tex] = [tex](^{13} _{2} )[/tex]

Splitting the combination,

[tex]C^{13} _{10}[/tex] = (13 × 12 × 11) ÷ 2

[tex]C^{13} _{10}[/tex] = 1716 ÷ 2

[tex]C^{13} _{10}[/tex] = 858 ways to pick the 10 to play.

There are 858 different methods to select 10 players to take the pitch.

The **permutations** of a set are the vaguely defined community of its members in arrangement or linear order, or the permutation of its components if the set is already collected. The act or procedure of adjusting the linear ordering of a sorted set is often named "permutation".

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Susie started a rock collection. she started with 26 rocks. each month she adds 5 to the collection. which equation can be used to find y, the total number of rocks in susie's collection after x months?

Answer:

26 + 5x = y

Step-by-step explanation:

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EFG and GFH are a linear pair, m EFG = 4n+ 15, and mGFH = 2n + 39. What are mEFG and mGFH?

mEFG=

mGFH=

**Answer:**

Find value of n first to find out what the angle measures are.

Linear angles have a sum of 180°.

Angle EFG + Angle GFH = 180

4n + 15 + 2n + 39 = 180

6n + 54 = 180

6n = 126

n = 21

Substitute n into the angles.

Angle EFG = 4(21) + 15 = 99°

Angle GFH = 2(21) + 39 = 81°

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