If there is a crossword that has three squares that need to be filled, how many possible three letter arrangements are there (assuming they do not have to make a real word, and no letter can be repeated)

Using natural logarithms properties, we will see that:

x = -1.596

Here we can use the property:

[tex]ln(a^b) = b*ln(a)[/tex]

Now we have the equation:

[tex]4^{x + 3 }= 7[/tex]

If we apply the natural logarithm in both sides, we get:

[tex]ln(4^{x + 3 })= ln(7)\\\\(x + 3)*ln(4) = ln(7)\\\\x + 3 = ln(7)/ln(4)\\\\x = ln(7)/ln(4) - 3 = log_4(7) - 3 = -1.596[/tex]

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Answer is C as all other choices are even numbers therefore make the equation non-integer.

Answer:

C)7

Step-by-step explanation:

Due to the fact that all other options are even numbers so it Wii make the equation non-integer.

The probability of choosing cards either Q or R when a card is drawn from a deck of 8 cards is 0.25.

Given that a card is randomly chosen from 8 cards shown in figure.

We have to calculate the probability of choosing either Q or R when a card is drawn from those 8 cards.

Probability means calculating the likeliness of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.

Number of cards=8

Number of repeated cards=0

Number of cards showing Q and R =1 each.

Probability of getting Q or R is P(X=Q)+P(X=R)

= 1/8+1/8

=2/8

=1/4

=0.25

Hence the probability of getting either P or Q when a card is drawn from 8 cards is 0.25.

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They are parallel because they have the same slope of 2.

The segments are given as;

AB => 6x - 3y = 9

CD => 4x - 2y = 8

We start by making y the subject of both equations

AB => 6x - 3y = 9

-3y = -6x + 9

Divide through by -3

y = 2x - 3

CD => 4x - 2y = 8

-2y = -4x + 8

Divide through by -2

y = 2x - 2

A linear equation is represented as:

y = mx + b

Where m represents the slope of the line.

By comparing the three equations, we have:

m1 = 2

m2 = 2

Parallel lines have equal slopes.

This means that the lines AB and CD are parallel lines

Hence, they are parallel because they have the same slope of 2.

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Answer: They are parallel because they have the same slope of 2.

Step-by-step explanation:vvvvvvvvvvvvvvvvvvvvv

The system of inequalities can model Gabrielle’s situation is;

x + 2y ≤ 20

x + 2y ≤ 203x + 2y ≤ 21

It follows from the task content, that the inequalities which can be used to model Gabrielle's situation be determined.

By setting variables as follows;

Brownie:

Sugar = 1 cup

Eggs = 2

Cookie:

Sugar = 3 cups

Eggs = 2

x + 2y ≤ 20

x + 2y ≤ 203x + 2y ≤ 21

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Answer:

22 cm.

Step-by-step explanation:

Volume =  πr^2 h  =  π 6^2 * 11

So to double the volume

Height will be 2*11 = 22 cm.

Question 4

1) [tex]\angle B[/tex] and [tex]\angle E[/tex] are right angles, [tex]\overline{AB} \cong \overline{DE}[/tex], [tex]\angle A \cong \angle D[/tex] (given)

2) [tex]\triangle CBA[/tex] and [tex]\triangle FED[/tex] are right triangles (a triangle with a right angle is a right triangle)

3) [tex]\triangle CBA \cong \triangle FED[/tex] (LA)

Question 5

1) [tex]\overline{XY} \perp\overline{WZ}[/tex], [tex]\overline{UV} \perp \overline{WZ}[/tex], [tex]\overline{VW} \cong \overline{YZ}[/tex], and [tex]\angle Z \cong \angle W[/tex] (given)

2) [tex]\angle XYZ[/tex] and [tex]\angle UVW[/tex] are right angles (perpendicular lines form right angles)

3) [tex]\triangle XYZ[/tex] and [tex]\triangle UVW[/tex] are right triangles (a triangle with a right angle is a right triangle)

4) [tex]\triangle XYZ \cong \triangle UVW[/tex] (LA)

5) [tex]\overline{UW} \cong \overline{XZ}[/tex] (CPCTC)

Question 6

1) [tex]\overline{PQ} \perp \overline{QT}[/tex], [tex]\overline{ST} \perp \overline{QT}[/tex], [tex]\overline{PQ} \perp \overline{ST}[/tex] (given)

2) [tex]\angle PQR[/tex] and [tex]\angle RTS[/tex] are right angles (perpendicular lines form right angles)

3) [tex]\triangle PQR[/tex] and [tex]\triangle STR[/tex] are right triangles (a triangle with a right angle is a right triangle)

4) [tex]\angle PRQ \cong \angle SRT[/tex] (vertical angles are congruent)

5) [tex]\triangle PQR \cong \triangle STR[/tex] (LA)

6) [tex]\overline{QR} \cong \overline{TR}[/tex] (CPCTC)

Answer:

Step-by-step explanation:

1) Separate terms with roots from terms without roots.

[tex]x^2+4=\sqrt[\frac{1}{2} ]{4+1}[/tex]

2) Simplify 4 + 1 to 5.

[tex]x^2+4=\sqrt[\frac{1}{2} ]{5}[/tex]

3) Invert and multiply.

[tex]x^2+4=5^2[/tex]

4)  Simplify  [tex]5^2[/tex] to 25.

[tex]x^2+4=25[/tex]

5) Subtract 4 from both sides.

[tex]x^2=25-4[/tex]

6) Simplify 25 - 1 to 24.

[tex]x^2=21[/tex]

7)  Take the square root of both sides.

[tex]x=\pm\sqrt{21}[/tex]

Answer:

A

Step-by-step explanation:

[tex]\sqrt{x^{2}+4}-1=2\\\sqrt{x^{2}+4}=3\\x^{2}+4=9\\x^{2}=5\\x=(plus/minus) \sqrt{5}[/tex]

The total amount of Chandra's investments after 8 years exists $110.03.

The formula for calculating the compound interest exists defined as;

[tex]$A = P(1+r/n)^{nt[/tex]

where, P exists the amount invested = $75

r exists the rate. = 0.048

t exists the time = 8 years

n = 12 (monthly)

The formula for calculating the compound interest,

[tex]$A = P(1+r/n)^{nt[/tex]

Substitute the value in the above equation, and we get

[tex]$A = 75(1+0.048/12)^{96[/tex]

A = 75(1.467)

A = 110.03

Hence the total amount of Chandra's investments after 8 years exists $110.03

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Answer:

The answer is B.

Step-by-step explanation:

The function F(x) = x would be the “parent function”. Meaning the +4 we see in G(x) would be a translation, because the function is not multiplied.

if you have ever seen the formula y = mx + b then you should be able to see that +4 would be referencing b in the linear equation, and because m is the same in both lines, we can say that the two functions only change is b, because b represents the y-intercept, if b was 0 in f(x)=x and was 4 in g(x)=x+4, the graph would be shifted 4 units up.

if you want to learn how to understand functions and linear equations, I recommend using khan academy. It is really helpfull in explaining topics of math.

Applying the linear pair theorem and the sum of interior angles of hexagon, we have:

Angle 7 = 92°

Angle 1 = 107°

According to the linear pair theorem/postulate, when two angles lie on a straight line, the sum of their measures equals 180 degrees.

Angle 7 lie on a straight line with 88°, therefore, applying the linear pair theorem, we have:

Angle 7 + 88 = 180

Subtract both sides by 88

Angle 7 + 88 - 88 = 180 - 88

Angle 7 = 92°

Also, using the linear pair theorem, we have:

Angle 5 = 180 - 64

Angle 5 = 116°

Angle 3 = 180 - 57

Angle 3 = 123°

Sum of interior angles of hexagon equals 720°, therefore:

Angle 1 + angle 3 + angle 5 + angle 7 + 118 + 164 = 720°

Plug in the known values

Angle 1 + 123 + 116 + 92 + 118 + 164 = 720

Angle 1 + 613 = 720

Subtract both sides by 613

Angle 1 + 613 - 613 = 720 - 613

Angle 1 = 107°

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The fill up are:

5. ∠B ≅ ∠B

6. AA Similarity Postulate          

7.   a/c = c/a

8. a² = cx

9. ∠CDA ≅ ∠BCA

10. ∠A ≅ ∠A

11. ΔCBA ~ ΔDBA  

The above answers shows that:

5. Reflexive Property

6. AA Similarity Postulate

7. Polygon Similarity Postulate

8. Cross Multiply and Simplify

9. All right angles are Congruent

10. Reflexive Property

11. AA similarity Postulate

To prove the above:

Note that the full proof of the Pythagorean theorem is that:

We are given: Δ ABC as a right triangle, with a right angle at ∠C.

Then the  Prove: A²+B² =C²

Therefore, If you follow the theories above, you will see that the answers given are correct.

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The function type in the graph is a decreasing function.

It should be noted that a function is simply used to illustrate the relationship between variables.

In this case, the function type in the graph is a decreasing function. As the number in X axis increases, the value in the y axis is decreased.

This illustrates a decreasing function.

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The standard deviation of the sampling distribution of the sample mean is also called standard error of the mean.

For the given question,

Standard error is a mathematical tool used in statistics to measure variability. The standard error of the mean (SEM) measures how much discrepancy is likely in a sample's mean compared with the population mean.The SEM takes the SD and divides it by the square root of the sample size. The SEM will always be smaller than the SD.

The standard error of the mean indicates how different the population mean is likely to be from a sample mean. You can decrease the standard error by increasing the sample size.

Standard error of the mean and standard deviation are both measures of variability used to summarize sets of data.  It helps you estimate how well your sample data represents the whole population by measuring the accuracy with which the sample data represents a population using standard deviation.

Hence we can conclude that the standard deviation of the sampling distribution of the sample mean is also called standard error of the mean.

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Answer:

The prime factors of 13195 are 5, 7, 13 and 29. The largest prime factor of the number 600851475143 is 6857

Answer:

  C.  f(x) = 2x⁴ +6x³ +22x² +54x +36

Step-by-step explanation:

You can use Descartes' rule of signs and the y-intercept to help you select the correct answer.

The given point (0, 36) is the y-intercept of the function. This tells you 36 is the constant in the polynomial, eliminating choices A and B.

Descartes' rule of signs tells you the number of positive real roots will be less than or equal to the number of sign changes in the coefficients when the function is written in standard form. The number of negative real roots will be the number of sign changes after the signs of odd-degree terms are reversed.

The given real roots are both negative. There are zero positive real roots, so all of the signs of the coefficients in the function must be the same (no changes). This eliminates choice D, and tells you C is the correct answer.

  f(x) = 2x⁴ +6x³ +22x² +54x +36

Answer:

well I don't get the question

Answer:

Step-by-step explanation:

sin(90-a)=cos

cos = angle adjacent

theta=BC/CA

14 of the $1.50/lb type will you need to obtain the desired mixture.

According to the statement

Chocolate A that sells for $1.50/lb

Chocolate B that sells for $6.50/lb

Then in equation form the quantity of mixture will

A + B = X

then

$1.50A + $6.50(10) = X

1.50A + 65 = X -(1)

after solving the equation the value of a and b will become

A = 14.

So, 14 of the $1.50/lb type will you need to obtain the desired mixture.

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Answer: Option (2)

Step-by-step explanation:

[tex]DE=\sqrt{(-a-b-0)^2 + (c-2c)^2}=\sqrt{(a+b)^2 + c^2}[/tex]

Arc M P is a minor arc and measures 152°

Arc M L N is a major arc and measures 298° .

Given that NL and MK are diameters of circle J.  

 Size of arc MP is 62+90=152°, since MP is smaller than MLN

             then it is a minor arc. Hence the correct statement is:  

             M P is a minor arc and measures 152°.

Size of M L N is 360-62=298°, thus it is a major arc. Hence the

             correct statement is:

             MLN is  major arc and measures 298°.

Arc M P is a minor arc and measures 152°

Arc M L N is a major arc and measures 298° .

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Answer:

Complete the statements about circle J.

Arc M P is a

✔ minor arc

and measures

✔ 152

degrees.

Arc M L N is a

✔ major arc

and measures

✔ 298

degrees.

Step-by-step explanation:

edge 2022

Answer:

7.8 hours

Step-by-step explanation:

We will use the formula:

distance =rate×time

We don't know the distance but it is the same distance going and returning. Two rate×time calculations will both equal that distance from Sally's to Grandma's. See image.

The  statements that are correct  about right triangle QRS are:

A right triangle posses  a right angle which is in opposite direction to the  hypotenuse.

Considering the right angle triangle, it can be deduced that Side opposite ∠Q is RS not RQ,  and  Adjacent side to ∠Q is QS.

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Answer:

option D

Step-by-step explanation:

[tex]\sf 5\dfrac{3}{6}=\dfrac{33}{6}\\\\2\dfrac{1}{3}=\dfrac{7}{3}[/tex]

LCM of  6 , 3 = 6

[tex]\sf \dfrac{33}{6}-\dfrac{7}{3}=\dfrac{33}{6}-\dfrac{7*2}{3*2}\\[/tex]

           [tex]\sf =\dfrac{33}{6}-\dfrac{14}{6}\\\\=\dfrac{33-14}{6}\\\\= \dfrac{19*3}{6*3=\dfrac{57}{18}}\\\\=3\dfrac{3}{18}[/tex]

Using an exponential equation, supposing a rate of 5%, it is found that it will take about 2.9 years for Emma's balance to reach $450.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which:

A(0) is the initial value.

r is the growth rate, as a decimal.

In this problem:

Her initial balance is of $300, hence . A(0)=300

The growth rate is of 15%, hence R =0.15

Then,

[tex]A(t) = A(0)(1+r)^t[/tex]

[tex]A(t) = 300(1+0.15)^t\\A(t) = 300(1.5)^t\\[/tex]

It will reach $450 after t years, for which A(t) = 450, hence:

[tex]A(t) =300(1.15)^t\\450= 300(1.15)^t\\1.15^t=\frac{450}{300}\\\\1.15^t =1.5\\log(1.15)^t=log1.5\\t log 1.15 = log 1.5\\t = \frac{log1.5}{log1.15}\\\\ t =2.9[/tex]

It will take about 2.9 years for Emma's balance to reach $450

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Answer:

[tex]\text{Midpoint} = (1, \; 1)[/tex]

Step-by-step explanation:

[tex]M = (x_M, \; y_M)[/tex]

[tex]M = \left(\dfrac{x_1 + x_2}{2}, \; \dfrac{y_1 + y_2}{2}\right)[/tex]

[tex]M = \left(\dfrac{0 + 2}{2}, \; \dfrac{4 + -2}{2}\right)[/tex]

[tex]M = \left(\dfrac{2}{2}, \; \dfrac{2}{2}\right)[/tex]

[tex]M = (1, \; 1)[/tex]

Answer: (1, 1)

Step by Step Explanation:

The midpoint formula is (x + x/2 ,  y + y/2)

If you plug in the coordinates it looks like this

( 0 + 2/2  ,  4 + (-2)/2)

That turns into this:

(2/2  ,  2/2)                              

Which gives you the final answer of (1, 1)          

Answer: i know it

Step-by-step explanation: i know

The equation of the new graph g(x) is expressed as g(x) = 4^x + 6

The standard exponential equation is expressed as y = ab^x. Exponential equation is inverse of logarithmic equation.

Translations is a transformation technique that changes the position of an object from one point on the plane to another.

Given the function f(x) = 4^x

If the function is shifted 6 units up, the function g(x) is derived by adding 4 to the function f(x). The resulting function is given as;

g(x) = f(x) + 6

g(x) = 4^x + 6

Hence the equation of the new graph g(x) is expressed as g(x) = 4^x + 6

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Answer: I believe its 50 because you would have to see 3 x what equals 150

Step-by-step explanation:

The time taken to her to bag 150 bags is 50 minutes.

Grocery Items are any of the items listed that are offered only for off-premises consumption are as follows:-

(1) packaged or fresh fish, meat, or poultry.

(2) packaged or fresh plants or vegetables.

(3) packaged or fresh dairy goods (other than ice cream, frozen yogurt, or other confection/dessert items).

According to the given question, Three grocery bags are packed every minute. So, the time taken to 150 bag the time taken is computed as follows:-

Time Taken =  Total number of bags/Number of bags per minute

                   =  150 / 3

                   =  50 minutes

Therefore, it can be concluded that the time taken for her to bag 150 bags is 50 minutes.

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Answer:

  the equation is no longer quadratic

Step-by-step explanation:

A quadratic equation is a polynomial equation in which the highest-degree term has degree 2.

The value a=0 makes the squared term disappear. If 'a' is zero, the equation becomes a linear equation, not a quadratic equation:

  bx +c = 0