Find two positive numbers whose difference is 3 and whose product is 1638.

Step-by-step explanation:

just insert a base of two at on both sides and solve.

The solution of the logarithmic equation ㏒ (x + 5) / ㏒ 2 = 4 will be 11.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The logarithmic equation is given below.

㏒₂(x + 5) = 4

Simplify the equation, then we have

㏒ (x + 5) / ㏒ 2 = 4

㏒ (x + 5) = 4 × ㏒ 2

㏒ (x + 5) = ㏒ 2⁴

Take antilog on both sides, then we have

(x + 5) = 2⁴

(x + 5) = 16

x = 11

The solution of the logarithmic equation ㏒ (x + 5) / ㏒ 2 = 4 will be 11.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

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Answer:

See Below.

Step-by-step explanation:

We can write a two-column proof.

Statements:                                                Reasons:

[tex]\displaystyle 1)\, \angle 4\cong \angle 2[/tex]                                                   Given

[tex]\displaystyle 2)\, \angle 3 \cong \angle 4[/tex]                                                   Vertical Angles are Congruent

[tex]\displaystyle 3) \, \angle 1 + \angle 2 = 180[/tex]                                          Linear Pair

[tex]\displaystyle 4)\, \angle 1 + \angle 4 = 180[/tex]                                          Substitution

[tex]\displaystyle 5) \, \angle 1 + \angle 3 = 180[/tex]                                          Substitution

[tex]\displaystyle 6) \, \text{$\angle 3$ and $\angle 1$ are supplementary}[/tex]                  Definition of Supplementary Angles

Answer:

19 trains

Step-by-step explanation:

Firstly, we need to calculate the difference in the number of hours

From the question, we have 7 am to 11 pm

7 am to 7 pm is 12 hours

7 pm to 11 pm is 4 hours

So total is 16 hours

16 hours to minutes is multiplied by 60 minutes

We have this as;

16 * 60 = 960 minutes

so to get the number of trains, we simply have to divide the number of minutes by 50

Mathematically, we have this as 960/50

= 19.2

Since we cannot have a fractional train stop, it means the number of trains that has stopped is 19

Step-by-step explanation:

The horizontal stretch or compression for a function f(x) is given by  g = f(bx) where b is a constant. If b> 0 then the graph of a function is compressed.

As it is given in the question that the function is transformed by a compression factor of 3.

Given function

The value of k will be 3 if the function is transformed by a compression factor of 3

Answer:

B

Step-by-step explanation:

When we reflect something across the y axis, the y axis stays the same but the x values change by a factor of -1.

B is the Answer

Answer:

c. switch the x-values and y-values in the table

Step-by-step explanation:

For any table or graph reflection over the line y=x

The rule is (x,y) ----> (y,x)

f(x) is reflected over the line y=x, so the coordinates of f(x) becomes

(-2,-31) becomes (-31,-2)

(-1,0) becomes (0,-1)

(1,2) becomes (2,1)

(2,33) becomes (33,2)

As per the rule, we switch the x-values and y-values in the table

For reflection over the line y=x , the coordinate becomes

(-31,-2)

(0,-1)

(2,1)

(33,2)

Answer:

"(5+x)/(6+2x) = 3/5" is the answer

Answer:

x = 4/3

Step-by-step explanation:

Answer:

x ≥ 3.5

y ≥ 2

2x + 1.5y ≤ 20

Step-by-step explanation:

Given :

Total Amount to spend ≤ $20

Let:

Amount of flour purchased = x

Amount of sugar purchased = y

Cost :

Flour = $2 per pound

Sugar = $1.5 per pound

Pounds of :

flour to be purchased ≥ 3.5

Sugar to be purchased ≥ 2

Hence, the system of inequalities :

x ≥ 3.5

y ≥ 2

Total Cost of x + total cost of y must be less than or equal to total amount

2x + 1.5y ≤ 20

Answer: x ≥ 3.5

y ≥ 2

2x + 1.5y ≤ 20

Step-by-step explanation: To write a system of inequalities, it is important to determine the restrictions. One restriction is that Sarah wants to buy at least 3.5 pounds of flour. "At least" means that 3.5 is the smallest amount she would buy and 3.5 can be included. This is expressed as x ≥ 3.5. She also wants at least 2 pounds of sugar, so similar to the flour, this can be written as y ≥ 2. Finally, the cost can be expressed as 2x + 1.5y. This is a restriction because Sarah can spend up to $20, so 2x + 1.5y is less than or equal to $20, or 2x + 1.5y ≤ 20.

Answer:

39

Step-by-step explanation:

you just put it in a calculator

Answer:

The expression is not factorable with rational numbers.

2x^2+19x+12

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Sorry for the lat reply hopefully you still have that question ready. But basically in order for these equations to be considered inverses of one another it has to map its domain value and switch it to the range value and in this case it does not match the inverse when graphed.

Answer:

By similar triangles:    BE/20 = 18/25    BE 14.4

Also, (ED + 26) / 26 = 18/14.4

ED = 6.5   and AD = 32.5

Answer:

2 days

Step-by-step explanation:

Lets say that in one day, one cow eats 1 block of grass. So, six cows in three days would eat 18 blocks of grass in total. So 18 blocks of grass is how much we have. that means nine cows would eat that much in 2 days.

Answer:

2

Step-by-step explanation:

Given [tex]-6-2x[/tex] where [tex]x=-4[/tex], substitute [tex]x=-4[/tex] to find the value of the given equation.

Substituting [tex]x=-4[/tex]:

[tex]-6-2(-4)[/tex]

Multiply [tex]-2\cdot -4[/tex]:

[tex]-6+8[/tex]

Combine like terms:

[tex]-6+8=\boxed{2}[/tex]

Therefore, the value of [tex]-6-2x[/tex] when [tex]x=-4[/tex] is [tex]\boxed{2}[/tex].

In other words, choices B and C are the non-answers while everything else is an answer.

==============================================================

Explanation:

Let p represent the probability of an event. The value of p must be between 0 and 1, inclusive of both endpoints. Symbolically, we can write [tex]0 \le p \le 1[/tex]

In other words, p = 0 is the smallest it can get and p = 1 is the largest it can get, or it could be anything in between.

The probability p = 0 means that the event will never happen, or there's 0% of it happening. The probability p = 1 means there's 100% certainty the event will happen.

Something like p = 1.4 is not possible as this indicates it's over 100%. So that rules out choice B. Choice C is also ruled out because we can't have negative probabilities.

The table is not clear, so i have attached it.

Answer:

z statistic is -2.26

This is less than our alpha level,therefore we reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners between first generation and second generation Hispanic Americans

Step-by-step explanation:

From the attached table, we can see that;

first-generation hispanic americans; (N = 899 and percentage = 43%

second-generation hispanic americans; N = 351 and percentage = 50%

first-generation asian americans; (N = 2,684 and percentage = 58%

second-generation asian americans; N = 566 and percentage = 51%

Z-score formula in this case is;

z = (p1^ - p2^)/(√(p^(1 - p^)((1/n1) + (1/n2))

Where;

p^ = (p1 + p2)/(n1 + n2)

For, hispanic americans we have;

p1^ = 0.43 × 899 = 386.57

p2^ = 0.5 × 351 = 175.5

p^ = (386.57 + 175.5)/(899 + 351)

p^ = 0.45

Thus;

z = (0.43 - 0.5)/(√(0.45(1 - 0.45)((1/899) + (1/351))

z = -2.26

From z-distribution table, we have;

P-value = 0.01191

Since we have 2 samples, then probability = 2 × 0.01191 = 0.02382

This is less than our alpha level of 0.05,therefore we reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners between first generation and second generation Hispanic Americans.

Answer:

[tex]Weighted\ Average = 73[/tex]

Step-by-step explanation:

Given

[tex]Lab = 21\%[/tex]

[tex]Tests = 25\%[/tex]

[tex]Exam = 29\%[/tex]

[tex]Lab\ Score = 60[/tex]

[tex]First\ Test = 81[/tex]

[tex]Second\ Test = 69[/tex]

[tex]Exam = 79[/tex]

Required

The weighted average

To do this, we simply multiply each score by the corresponding worth.

i.e.

[tex]Weighted\ Average = Lab\ worth * Lab\ score + Tests\ worth * Tests\ score.....[/tex]

So, we have:

[tex]Weighted\ Average = 21\% * 60 + 25\% * 81 + 25\% * 69 + 29\% * 79[/tex]

Using a calculator, we have:

[tex]Weighted\ Average = 73.01[/tex]

[tex]Weighted\ Average = 73[/tex] --- approximated

Answer:

15.81 ft .

Step-by-step explanation:

This question is based on " Pythagoras Theorem " . If we imagine the given situation as a right angled triangle , then the base will be " 9ft " , and the perpendicular will be " 13 ft" . And the length of the ladder will be equal to hypontenuse of the triangle.

Using Pythagoras Theorem :-

[tex]\implies\rm h^2= p^2+b^2 \\\\\implies\rm h^2 = (9ft)^2+(13ft)^2 \\\\\implies\rm h^2 = 81 ft^2 + 169 ft^2 \\\\\implies\rm h^2 = 250ft^2 \\\\\implies \boxed{ \rm Ladder's \ Length = 15.81 \ ft }[/tex]

Hence the length of the ladder is 15.81 ft.

Answer:

[tex](x + y+ 1)^2[/tex]

Step-by-step explanation:

[tex]Using : (a + b)^2 = a^2 + 2ab + b^2\\\\(x+ y)^2 + 2(x +y) + 1 , \ where \ a = (x+y) , \ b = 1 \\\\= (x +y)^2 + ( 2 \times 1 \times (x+y)) + 1^2\\\\= (x +y+ 1)^2[/tex]

Step-by-step explanation:

Using:(a+b) ² =a²+2ab+b²

Hope it is helpful to you

Answer:

You MADE IT EASY

Step-by-step explanation:

[tex] {y - 5 \times 9}^{2} \: times \: sevem \\ n \: equals \sec(x + {}^{2} ) [/tex]

Answer:

​Robbin's grade point average must be at least 2.75 in order to be unconditionally accepted into the program. ​

Step-by-step explanation:

An unconditional acceptance into a graduate program at a university will be given to students whose GMAT score plus 100 times the undergraduate grade point average is at least 1075

Considering the GMAT score x, and the GPA y, this situation is modeled by the following inequality:

[tex]x + 100y \geq 1075[/tex]

Robbin's GMAT score was 800.

This means that [tex]x = 800[/tex], and thus:

[tex]x + 100y \geq 1075[/tex]

[tex]800 + 100y \geq 1075[/tex]

[tex]100y \geq 275[/tex]

What must her grade point average be in order to be unconditionally accepted into the​ program?

Solving the above inequality for y:

[tex]100y \geq 275[/tex]

[tex]y \geq \frac{275}{100}[/tex]

[tex]y \geq 2.75[/tex]

Thus:

​Robbin's grade point average must be at least 2.75 in order to be unconditionally accepted into the program. ​

Answer:

DGF = 106

Step-by-step explanation:

Bisects means to divide in half, with two equal parts

DGF = DGE + EGF

DGE = EGF

DGF = DGE + DGE

DGF = 53+53

DGF = 106

GE bisects ∠DGF, so it divides ∠DGF into 2 equal parts.

So, m∠EGF = m∠DGE

=> m∠EGF = 53°

m∠DGF = m∠EGF + m∠DGE

=> m∠DGF = 53° + 53°

=> m∠DGF = 106°

Answer:

80

Step-by-step explanation:

You mean the "interest on"

I=800×.1×1=80

Answer:

2

Step-by-step explanation:

Answer:

I think it would be 450 mm.

Answer:

5

Step-by-step explanation:

3-(-2) will become positive 5. so number line will go towards positive 5.

Answer:

-36m^3-21n^3+85mn^2+36m^2n

Step-by-step explanation:

That's what the calculator says:).

Answer:

2x - 1

Step-by-step explanation:

that is the procedure above