Solve 3x-y=7 and 3x+y=11 using substitution method

The solution of the expression is,

⇒ x = 2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ [tex]\frac{5^{6x + 5} }{125^{3x - 1} } = 5^{-5x + 2}[/tex]

Now, Solve the equation by rule of exponent as;

⇒ [tex]\frac{5^{6x + 5} }{5^{5 (3x - 1)} } = 5^{-5x + 2}[/tex]

⇒ [tex]\frac{5^{6x + 5} }{5^{15x - 5} } = 5^{-5x + 2}[/tex]

⇒ [tex]{5^{6x + 5} } * {5^{- (15x - 5)} } = 5^{-5x + 2}[/tex]

⇒ [tex]{5^{6x + 5} } * {5^{-15x + 5} } = 5^{-5x + 2}[/tex]

⇒ [tex]{5^{6x + 5- 15 x+ 5} }= 5^{-5x + 2}[/tex]

⇒ [tex]{5^{-9x + 10} } = 5^{-5x + 2}[/tex]

By comparing, we get;

⇒ - 9x + 10 = - 5x + 2

⇒ 10 - 2 = 9x - 5x

⇒ 8 = 4x

⇒ x = 8/4

⇒ x = 2

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The value of the $110 annuity given annual compounding is $9983.338.

The value of the annuity can be determining using this formula: amount deposited x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

n = number of years

r = interest rate

here, we have,

Periodic Deposit 110 at the end of every six months Rate Time 4.5 % compounded semiannually 25 years

now,

r=4.5%/2

 =0.0225

n= 25*2 = 50

using the formula, we get,

the value of the annuity =$9983.338

hence, The value of the $110 annuity given annual compounding is $9983.338.

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For the students collecting the data, it would be very difficult to select a random sample from this population.

The term Simple random sample, also known as an SRS, which is also a subset of people chosen at random from a larger group of people, all with the probability which is same. In this method samples are chosen at random. Each and every subset of k people in SRS has the equal opportunity of getting selected for the sample just like some other subset of k people.

An objective sampling strategy is a straightforward random sample. Simple random sampling is the most basic category of sampling that can be used in combination with other, more sophisticated sampling techniques.

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The linear equation that is represented in the table is:

y = 3*x + 2

A general linear equation can be written in the form:

y = m*x + b

Where m is the slope and b is the y-intercept.

First, notice that on the table we can see the point (0, 2), then the y-intercept of the linaer function is b = 2

Then we can write:

y = m*x + 2

Now we can use any other point on the table to find the value of the slope m.

Using the second point (1, 5),replacing the values we will get:

5 = m*1 + 2

Solving for m, we will get:

5 = m + 2

5 - 2 = m

3 = m

Then the linear equation is:

y = 3*x + 2

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The complete statement is ∠M = 40°

If the only difference between two triangles is their size (and perhaps the need to rotate or flip one), but not their shape, then they are similar.

In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "≅"

If ΔABC and ΔXYZ are similar triangles then

∠A = ∠X, ∠B = ∠Y, and ∠C = ∠Z  

Here we have

ΔXYZ and ΔLMN are similar triangles

=> ∠X = ∠L,  ∠Y = ∠M, and  ∠Z = ∠N    

From the given figure,

=> ∠X = ∠L = 25°

=> ∠Y = ∠N = 115°

=> ∠Z = ∠M    

From ΔLMN      

=> ∠L + ∠M + ∠N = 180°  

=> 25° + ∠M +115° = 180°    

=> ∠M = 180°- 115° - 25°  

=> ∠M = 40°    

Therefore,

The complete statement is ∠M = 40°

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Point A has coordinates (x1, y1). The x-coordinate, x1, is the horizontal distance from the origin, while the y-coordinate, y1, is the vertical distance from the origin.

Coordinates in math refer to a pair of numbers that indicate the position of a point on a two-dimensional graph or in a three-dimensional space. The two numbers are usually referred to as the x-coordinate (or abscissa) and the y-coordinate (or ordinate). In three-dimensional space, the third number is referred to as the z-coordinate (or applicate). A point located at (3, 4) on a two-dimensional graph would be located 3 units along the x-axis and 4 units along the y-axis. Similarly, a point located at (3, 4, 5) in three-dimensional space would be located 3 units along the x-axis, 4 units along the y-axis, and 5 units along the z-axis.

Both coordinates indicate the exact location of Point A in a coordinate system. For example, if Point A is located at (2, 4), it means that the x-coordinate of Point A is 2, which is 2 units away from the origin in a horizontal direction, and the y-coordinate of Point A is 4, which is 4 units away from the origin in a vertical direction. The origin is usually located at (0, 0) in a coordinate system.

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1000

Step-by-step explanation:

5000

The evaluation of the equation in the question for the number of solutions is as follows;

2) The values of S and T for which the equation Sx + 81 = -24x + T have infinitely many solutions is S = 24 and T = -81

c. S = 24 and T = -81

An equation is a statement of equivalence of two expressions.

The specified equation is presented as follows;

S·x + 81 = -24·x + T

The equation will have infinitely many solutions when both sides of the equation refer to the the sam line

The power of x on both sides of the equation is one, therefore, both expressions on the left and right side of the equation refer to linear relationships

The graph of two lines are the same if they have the same slope and the same y-intercept.

The slope of the expression on the left = S

The y-intercept of the expression on the left = 81

The slope of the expression on the right = -24

The y-intercept of the expression on the right = T

When both sides refer to the same line, we get;

S = -24, and T = 81

Therefore, both sides of the equation refers to the same line and therefore have infinitely many solutions when S = -24 and T = 81.

The correct option is option c

(c) S = -24 and T = 81

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The equation of the circle in the standard form is (x - 2)²+(y + 2)² = 34.

The fundamental form of an equation is the linear equation in standard form. Below is shown the standard form of a linear equation with two variables and more than two variables.

Here, a, b, (A)1, (A)2, (A)3,........ (A)n are referred to as the coefficients, and x, y, or (x)1, (x)2, (x)3,.... represent the variables. Constants are the numbers that appear after the equals to sign.

ax + by = c

A quadratic equation's standard form is a second-degree equation with a variable, coefficients, and constant term. X is a single variable of degree 2 in this situation. A quadratic equation has the following standard form.

ax² + bx + c = 0

We have given that:

[tex]$\left(x-x_0\right)^2+\left(y-y_0\right)^2=r^2$[/tex]

Lets solve

[tex]$P_0(2,-1)$[/tex]

[tex]$d^2=10^2+6^2$[/tex]

[tex]$r=\frac{d}{2}=5.831$[/tex]

[tex]$r^2=34$[/tex]

[tex]$(x-2)^2+(y+1)^2=34$[/tex]

Thus, the equation of the circle in the standard form is (x - 2)²+(y + 2)² = 34.

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Answer:

Step-by-step explanation: At the end of what? I need the rest of the question in order to help you.

The standard error of the estimate measures the vertical spread of the data points around the regression line.

The standard error of the estimate, a measurement of the average deviation of errors, is the difference between the y-values predicted by the multiple regression model and the y-values in the sample. This illustrates the precision of the regression model as well as the range of variation surrounding the estimated regression line.

The standard error of the estimate can be used to produce a confidence interval for the actual regression coefficient. The standard error is calculated by multiplying the standard deviation by the square root of the sample size. The standard deviation of the errors/residuals is the standard error of the estimate for the regression model.

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Based on the scatter plot shown, the correlation coefficient that best represents the scatter plot is r = 0.98.

Several dots are placed on a horizontal and vertical axis to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the degree of correlation, if any, between the values of observed quantities or occurrences called variables.

The scatter plot shown shows a highly positive correlation between the data. Hence, the value of the correlation coefficient is very nearly 1.

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The shape that results from a plane passing through a cone that is perpendicular to the base is option B: Circle.

When a plane passes through a cone perpendicular to the base, it intersects the cone at a circle. This is because the plane is cutting the cone at a 90-degree angle to the base, and so it is cutting through the circular cross-section of the cone.

Therefore, If the plane were to be tilted or angled, the shape of the intersection would be an ellipse, which is a flattened circle. This is because an ellipse is the shape that results when a plane intersects a cone at an angle that is not perpendicular to the base.

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Answer:

Alexander made $825 in commission last week. If he averaged the same amount each week, he would have made $42,900 in commission in 2011.

Step-by-step explanation:

$7,500 x 0.11 = $825 (Last Week's Commission)

$825 x 52 (weeks in a year) = $42,900 (2011 Commission)

Carly can walk 1 mile in 264 seconds.

Unit rate is the amount of one quantity for a unit amount of the other quantity.

In other words it compares 1 unit of some quantity with different amount of another quantity.

Unit rate of Carly is given.

Unit rate of an object in terms of distance covered and time taken is actually the speed of the object.

The formula for speed is,

Speed = Distance / Time

Speed = 20 feet per second

Distance = 1 mile = 5280 feet

Time taken be t.

20 = 5280 / t

t = 5280 / 20

t = 264 seconds

Hence it will take 264 seconds for Carly to walk a mile.

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Answer:

using the knowledge from the chapter similarity we can find how the two triangles are similar

Step-by-step explanation:

Triangle ABC and DEF

A B=DE

AC=DF

BC=EF

AB/DE=AC/DF=BC=EF

The final velocity of the car is given as follows:

25 m/s.

The velocity function is a linear function, modeled as follows:

v(t) = v(0) + at.

In which:

The parameter values for this problem are given as follows:

v(0) = 5, a = 2.

Hence the velocity function is given as follows:

v(t) = 5 + 2t.

At a time of 10 seconds, the velocity is given as follows:

v(10) = 5 + 2(10)

v(10) = 25 m/s.

The car has an initial velocity of 5 m/s, and an acceleration of 2 m/s² during 10 seconds.

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Answer:

Consolidation

Step-by-step explanation:

Maths is a great way to get a job and then you can give it a try for a few days and then again you can give it a try for a few days and then again you can give it a try for a few days

Answer:

30

Step-by-step explanation:

n^2-9n-6

(-3)^2-9(-3)-6

(-3)(-3)+27-6

9+27-6

36-6

30

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{n^2 - 9n - 6}[/tex]

[tex]\mathsf{= -3^2 - 9(-3) - 6}[/tex]

[tex]\mathsf{= -3(-3) - 9(-3) - 6}[/tex]

[tex]\mathsf{= -9 - (-27) - 6}[/tex]

[tex]\mathsf{= -9 + 27 - 6}[/tex]

[tex]\mathsf{= 18 - 6}[/tex]

[tex]\mathsf{= 12}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{12}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

35.26°

Step-by-step explanation:

You have to visualize this or draw a diagram

If a cube has side a, the face diagonal of the cube is √2a . The diagonal of the cube is √3a

One side of length a, another side of length √2a (face diagonal) and the third of √3a form a right triangle with the angle opposite √3a being the 90° angle

Therefore we can find the angle [tex]\theta[/tex]  which the cube diagonal makes with the face diagonal using the fact
[tex]\dfrac{a}{\sqrt{2}a} = \tan\theta[/tex]

[tex]\theta = tan^{-1}\left(\dfrac{1}{\sqrt{2}\right)} \\= 35.26^\circ[/tex]

The required, complete truth table has been shown, where (P→ Q) and (¬Q → ¬P) are logically equivalent.

A truth table is a table used in logic and mathematics to show the truth or falsehood of propositional statements or logical expressions. It lists all the possible combinations of the truth values of the variables in the expression and the resulting truth value of the entire expression for each combination.

Here,
Using the fact to construct a truth table,
For the implication P → Q only T → F = F or else T,
And ¬T = F, ¬F = T

The complete table has been shown in the image attached below,

In the table column for P → Q and (¬Q → ¬P) have the same truth values.

Thus, (P→ Q) and (¬Q → ¬P) are logically equivalent.

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Answer:

[tex]\textsf{1.\;\;Equation:\quad$A=720(1.048)^{t}$}[/tex]

    [tex]\textsf{Solution:\quad$\$1263.77$}[/tex]

[tex]\textsf{2.\;\;Equation:\quad$y=2^x$}[/tex]

    [tex]\textsf{Solution:\quad$8$}[/tex]

Step-by-step explanation:

Assuming the account earns annual compound interest.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ A=P\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

Substitute the given values or P and r into the annual compound interest formula to create an equation for the amount of money in the account after t years:

[tex]\implies A=720(1+0.048)^{t}[/tex]

[tex]\implies A=720(1.048)^{t}[/tex]

To find the amount of money in the account after 12 years, substitute t = 12 into the equation:

[tex]\implies A=720(1.75523549...)[/tex]

[tex]\implies A=1263.76955...[/tex]

[tex]\implies A=1263.77[/tex]

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

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given values:

Substitute the given values or a and b into the exponential function formula to create an equation for the number of bacteria after x days:

[tex]\implies y=1(2)^x[/tex]

[tex]\implies y=2^x[/tex]

To find the number of bacteria after 3 days, substitute x = 3 into the equation:

[tex]\implies y=2^3[/tex]

[tex]\implies y=8[/tex]

Answer:

21/8

Step-by-step explanation:

When you are dividing fractions, use Keep-Change-Flip. See image.

Keep-Change-Flip changes the problem to a multiplication.

To multiply fractions, multiply straight across:

top × top and bottom×bottom see image.

We get 21/8 is already in lowest terms.

Answer: After investing for 10 years at 8% interest

Step-by-step explanation: your $10,000 investment will have grown to $21,589 This calculator determines the future value of $10k invested for 10 years at a constant yield of 8.00% compounded annually

There were 10 hours of daylight on that particular day

Total number of hours in a day= 24

If the ratio of daylight to darkness is 5:7, the number of hours of daylight is 5x and that of darkness is 7x

Then, 5x + 7x= 24

=> 12x = 24

=> x= 2

Thus, 5x= 5×2= 10

Therefore, there were 10 hours of daylight on that particular day

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Answer:

Corp donates

Step-by-step explanation:

Consolidation is a great way to get a job and then she can u me a little more about it and let me know if

Answer:

A. The speed of the boat going against a current with a rate of x mph is (13 - x) mph.

B. The speed of the boat going with a current with a rate of x mph is (13 + x) mph.

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be triangle FUN and CAR is congruent thus it is proved that  m∠HAT = 50°

A triangle is a polygon since it has three parts and three vertices. It is a fundamental geometric figure. A triangle with the corners A, B, & C is referred to as triangle ABC. A single planar and triangle are found in geometric shapes when four elements are not collinear. Due of its three sides and top right corner, triangles are classified as polygons.

Here.

Triangle FUN is congruent with CAR , hence

then,

∠F equals ∠C

∠U is equivalent to ∠A.

∠N  equals ∠ R

and,

FN is equivalent to line CR

NU  is identical to line RA

UF  is equivalent to line AC

Cpct was used to resolve this.

congruent triangle's matching triangle segments

Therefore , the solution of the given problem of triangle comes out to be FUN is congruent with CAR .

For

m∠HAT = 50°

Thus triangle FUN and CAR is congruent thus it is proved that

m∠HAT = 50°

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