100 Point! Need help please, thanks a lot!

How many solutions does the system of equations have?
2x = -10y + 6 and x + 5y = 3

How many solutions does the system of equations have?
y = 6x + 2 and 3y - 18x = 12


How many solutions does the system of equations have?
x - 3y = 15 and 3x - 9y = 45


How many solutions does the system of equations have?
y - 7x = -14 and 7y -49x = -2

Answer:

for the first one its the 3 answer

Step-by-step explanation:

i know because i had a similar quiz like yours and it was hard do i got a friend to help and i got 100% trust meeeeeeee

The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

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The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

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Answer:

-4 and 4

Step-by-step explanation:

Have a good day.

Answer:

answer is -4 and 4 ):(

Step-by-step explanation:

The given statement about inequality is true.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

The statement is true ''Pick a point on one side of the solid or dashed line and enter its coordinates into the original inequality to determine which side of a linear inequality to colour in for its graph. On that side of the plane, you should shade if the coordinates satisfy the inequality''.

The statement defines how to write an inequality the meaning of inequality is that one part of the inequality will be shaded by some colour indicating that the region is falling under the area of inequality.

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Answer:

Step-by-step explanation:

Hope this helps

The equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

We have to given that,

A number line is shown in image.

Since,

A number lines are the horizontal straight lines in which the integers are placed in equal intervals.

And, All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

Now, By given number line,

Point C is two point left from point 8.

Hence, The point C is denoted as,

⇒ C = 8.2

⇒ C = 82/10

⇒ C = 8 2/10

Therefore, the equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

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Answer:

C  DONT REPORT ME

Step-by-step explanation:

Applying the relevant tangents theorem, the answer to the circled questions are: 5. m(RU) = 190°;  7. m<T = 50°;   11. x = 9

5. Based on the secant-tangent theorem, we have:

m<S = 1/2(m(RU) - m(RT))

Given the following:

m<S = 45°

m(RT) = 100°

m(RU) = ?

Plug in the values:

45 = 1/2(m(RU) - 100)

90 = m(RU) - 100

90 + 100 = m(RU)

m(RU) = 190°

7. Using the same theorem, we have:

m<T = 1/2(160 - 60)

m<T = 50°

11. Based on the angle of tangents theorem, we have:

7x + 12 = 1/2((360 - 105) - 105)

2(7x + 12) = 150

14x + 24 = 150

14x = 150 - 24

14x = 126

x = 9

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The equation that represents the total number of black and white squares on the chess board is 8 * 2² = 32

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

The chess board

From the chess board, we have

Black squares = 32

White squares = 32

When factorized, we have

Black squares = 32 = 8 * 2²

White squared = 32 = 8 * 2²

Hence, the equation that represents the squares on the chess board is 8 * 2² = 32

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A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;

g(x) = kf(x)

g(x) = 1/2f(x)

\(g(x) = \frac{1}{2} e^x -4\)

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Answer:constant is 2/33

Step-by-step explanation:

1 min to fill 16.50 gallons

Time(t) varies directly as volume(v)

t α v

t =k x v Where k is constant

1=k x 16.50

k=1/16.50

k=2/33

Constant is 2/33

Answer:

\(\dfrac{5e^2}{2}\)

Step-by-step explanation:

Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.

Given function:

\(y=x^2\ln(2x)\)

Differentiate the given function using the product rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)

\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)

Input the values into the product rule to differentiate the function:

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)

To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:

\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)

Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:

\(\boxed{\dfrac{5e^2}{2}}\)

Answer:

D. X=-2

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

The question required attachment; however, follow the following steps to answer your question.

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Considering the horizontal plane of the gird.

Count the number of the squares in that plane;

This gives 4

Multiply 4 by length of each side of a square;

\(Perimeter = 8mm * 4\)

\(Perimeter = 32mm\)

The angle of the T in the ΔRST is 100° and the value of p is 11.

Define Triangle.

A triangle is a polygon that consists of three sides and three vertices. The fact that the interior angles of a triangle add up to 180 degrees is the most crucial aspect of triangles. This characteristic is known as the angle sum property of a triangle.

i.e., In a give ΔABC, ∠A + ∠B + ∠C = 180°.

Given:

∠R = 37°; ∠S = 43°; ∠T = 10p-10°

Let's take ∠T = x

In ΔRST,

∠R + ∠S + ∠T = 180°

37 + 43 + x =  180°

x = 180 - 80 ⇒ 100

∴ ∠T = 100°

To find the value of p,

 ∠T = 100

10p - 10 = 100

10p = 110 ⇒ 11

∴ p = 11

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Answer:

B

Step-by-step explanation:

a prime polynomial is one which does not factor into 2 binomials.

its only factors are 1 and itself

attempt to factorise the given polynomials

3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )

= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(3x² - 2) ← in factored form

--------------------------------------------------

3x³ - 2x² + 3x - 4 ( factor the first/second terms

= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored

thus this polynomial is prime

----------------------------------------------------

4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )

= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term

= (2x + 1)(2x² + 3) ← in factored form

-------------------------------------------------

4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )

= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(4x² - 3) ← in factored form

--------------------------------------------------

the only polynomial which does not factorise is

3x³ - 2x² + 3x - 4

Answer:

c. The period is 2π

Step-by-step explanation:

The period of a function is the smallest value of $p$ for which\( f(x+p) = f(x)\) for all x.

For the function f(x) = 2cos(x^2), we can see that f(x+2π) = f(x) for all x.

This is because the cosine function has a period of 2π. Therefore, the period of f(x) = 2cos(x^2) is \(\boxed{2\pi}\)

Answer:

x = 5

Step-by-step explanation:

Since Q is the midpoint of PR,

PQ = QR

=> 3x + 2 = 7x - 18

=> 3x - 7x = -18 - 2

=> -4x = -20

=> x = -20/-4

=> x = 5

Hope it helps :)

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Answer:

\(8.5x+4y=99.5,\ x+y=17\)

Step-by-step explanation:

\(\mathrm{System\ of\ equations:}\\8.5x+4y=99.5\\x+y=17\\\mathrm{where,}\ x\ \mathrm{is\ the\ number\ of\ popcorns\ and\ }y\mathrm{\is\ the\ number\ of\ candies}\)

"s" can be concluded from the premises

To use the rules of inference to show that "s" is a conclusion, we can use modus ponens,

This is a rule that allows us to infer a conclusion from a premise and its conditional statement.

Thus, "s" can be concluded from the premises "p → q", "q → r", "(q → r) → s", and "p".

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Answer:

2.72 inches

Step-by-step explanation:

1040/8.5=122.35

1 inch on the map = 122.35 miles actual distance

333/122.35=2.72

Answer:

THE ANSWER IS D

Step-by-step explanation:

D is correct. Subtract 3 from both sides, then divide by -2, and remember to reverse the inequality.

Answer:

24 ft

Step-by-step explanation:

Using the area formula

s = \(\sqrt{A}\)

when A = 36, then

s = \(\sqrt{36}\) = 6

perimeter of square = 4s = 4 × 6 = 24 ft

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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By creating a General Court made up of delegates from each town in the colony, this document reflects the principle of: D. republicanism.

Federalism simply refers to a form of government in which the federal government and other institutional bodies such as states, towns, smaller units, and provinces share power and authority.

Republicanism can be defined as a form of government that is centered around citizenship in a state and emphasizes their participation for the common good of a geographical area such as states, towns, and other smaller units in a colony.

This ultimately implies that, republicanism involves citizens selecting their representatives (delegates) from each town in a colony, especially through an electoral process such as in Article 8, Fundamental Orders of Connecticut.

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Answer:

republicanism

Step-by-step explanation:

Answer:

a) Then, t(s) is in the rejection region. We can not support that the mean annual premium in Pennsylvania is lower than the national mean annual premium

b) The point estimate of the difference is  59 $

Step-by-step explanation:

From sample we get:

sample size    n  =  25

annual mean   x  =  1440

standard deviation of the sample   s  =  150

mean for the mean annual premium    μ  = 1499

Hypothesis Test:

Null Hypothesis                      H₀           x  =   μ

Alternative Hypothesis          Hₐ           x  <   μ

Alternative Hypotesis indicates that the test is a one-tail test to the left

Let´s assume  confidence Interval 95 %    then  α  =  5 %   α = 0.05

As  n < 30 and we assume normality we will make a t-student test

degree of freedom    df  =  n  -  1    df  = 24

With df = 24  and  α = 0.05 and from t-student table we get t(c) =  - 1.711

To calculate t(s) we apply:

t(s)  =  (  x  -  μ ) / s/√n

t(s)  =  ( 1440  -  1499 ) * 5 / 150

t(s)  =  - 59/ 30

t(s)  =  - 1.96

Comparing t(s)  and t(c)  

|t(s)| > |t(c)|

Then, t(s) is in the rejection region. We can not support that the mean annual premium in Pennsylvania is lower than the national mean annual premium.

b) The point estimate for the difference is :   x  - μ  =  59 $

Answer:

C. (9, 26)

Step-by-step explanation:

By Substitution:

y = 2x + 8

y = 3x - 1

---------------------

2x + 8 = 3x - 1

-x + 8 = -1

-x = -9

x = 9

Now we can choose either of the two equations given to solve for y:

y = 2x + 8

y = 2(9) + 8

y = 18 + 8

y = 26

(9, 26)

By Elimination:

For this process, I am going to rewrite the equation in "x + y" for as it will make it easier to eliminate the variables

y = 2x + 8

2x - y = -8

y = 3x - 1

-3x + y = -1

-----------------

2x - y = -8

-3x + y = -1

-----------------

-x = -9

x = 9

2x - y = -8

2(9) - y = -8

18 - y = -8

-y = -26

y = 26

(9, 26)