Paisley took a taxi from her house to the airport. The taxi company charged a pick-up fee of $1.70 plus $1.75 per mile. The total fare was $17.45, not including the tip. Which equation or tape diagram could be used to represent the context if a represents the number of miles in the taxi ride?​

By substitution, the solution of the system of equations, x - 2y + z = -4, -4x + y -2z = 1 and 2x + 2y - z = 10, is (x , y , z) = (2 , 1 , -4).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given three equations in x, y, and z,

x - 2y + z = -4     (equation 1)

-4x + y -2z = 1     (equation 2)

2x + 2y - z = 10     (equation 3)

Using the equation 1, find the value of one variable, lets say x, in terms of the other variables.

x - 2y + z = -4     (equation 1)

x = 2y - z - 4     (equation 4)

Substitute the equation 4 to equation 2 and 3 and find the value of another variable, lets say y, in terms of the other variable.

-4x + y -2z = 1     (equation 2)

-4(2y - z - 4) + y -2z = 1

-8y + 4z + 16 + y -2z = 1

-8y + y = 2z - 4z + 1 - 16

-7y = -2z - 15

y = -(2z + 15)/-7

y = (2z + 15)/7     (equation 5)

2x + 2y - z = 10     (equation 3)

2(2y - z - 4) + 2y - z = 10

4y - 2z - 8 + 2y - z = 10

4y + 2y = 2z + z + 10 + 8

6y = 3z + 18

y = (1/2)z + 3     (equation 6)

Substitute the value of y from equation 5 to equation 6 and solve for z.

y = (1/2)z + 3     (equation 6)

(2z + 15)/7 = (1/2)z + 3

2z + 15 = 7[(1/2)z + 3]

2z + 15 = (7/2)z + 21

2z - (7/2)z = 21 - 15

(-3/2)z = 6

z = -4

Substitute the value of z in either equation 5 or 6.

y = (1/2)z + 3     (equation 6)

y = (1/2)(-4) + 3

y = -2 + 3

y = 1

Finally, substitute the value of y and z to equation 4 and solve for x.

x = 2y - z - 4     (equation 4)

x = 2(1) - (-4) - 4

x = 2 + 4 -4

x = 2

Hence, the solution of the given system of equations is (x , y , z) = (2 , 1 , -4).

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answer

3 Laps

Step-by-step explanation:

The triangles are congruent by SSS.

What exactly do you mean by congruent?

Given:

First Label the Diagram:

AB ≅ CD

AD ≅ BC

To Prove:

Δ ABC ≅ Δ CDA

Proof:

In  Δ ABC and Δ CDA

AB ≅ CD     ....……….{Given}

BC ≅ DA     …………..{Given}

AC ≅ AC     ……….{Reflexive Property}

Δ ABC ≅ Δ CDA  ….{ By Side-Side-Side test}

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By elimination, the system of equations, 4x - 6y = -26 and -2x + 3y = 13, has infinite solutions.

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

First, simplify the first equation by dividing it by -2.

4x - 6y = -26 ⇒ -2x + 3y = 13     (equation 1)

-2x + 3y = 13     (equation 2)

Since the simplified equation of the first equation is the same as the second equation, then the two lines are exactly the same or overlapping.

Hence, the system of equations has infinite solutions.

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The numeric values for the functions are given as follows:

To find the numeric value of a function, we replace each instance of the variable by the desired value.

For the first problem, we have that:

For the second problem, we have that:

For the third problem, we have that:

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What error did your classmate make? This series is divergent so does not have a sum.

How is the divergence of the series proved?

Given:

[tex]a(\text{ the first term })=1\\\\r(\text{ the common difference })=1.1[/tex]

Since, [tex]\vert r \vert > 1[/tex] the infinite series diverges.

What is an infinite geometric series?

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Answer:

The sun of 10 is 2 times much 4.

Answer:

x=3

Step-by-step explanation:

➡️ Let x be the number;

4(x+2)=20

x+2=5

x=3

The number is 3.

Answer:

Step-by-step explanation:

the answer is -26 but it is not in the choices

-32+(-4+7)*(2)=

-32+3*2=

-32+6=

-26

Answer:

So C

Step-by-step explanation:

Average = all values added up/ how many numbers there are

(400.5+560.35+628.29)/3=Average

Average = 529.71

The value of b (real number) can be anything greater than zero so we cannot be determined with the given information so option (C) will be correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

Given the absolute equation,

|x| = b for b >0

b is a set of all positive real numbers and we know that real number goes 0 to infinite means,

b could be 1,2,3... anything.

It means the corresponding solution will also be 1,2,3... anything.

Therefore we cannot determine the solution.

Hence "We cannot predict the number of solutions of the given mode function  |x| = b, such that b>0 without more information".

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Answer: It is irrelevant if multiplying or dividing decimal numbers. For addition and subtraction it is not sufficient: you need to line up the decimal points as well as the digits according to their place values. If you intend to simply align the decimal points then you may as well not bother.

Step-by-step explanation:

Applying the triangle sum theorem, the measures of the angles in △CBD are: m∠CDB = 90°; m∠BCD = 65°; m∠CBD = 25°

In △CAD, they are: m∠A = 65°; m∠ADC = 90°; m∠ACD = 25°

All interior angles of a triangle have a total sum of 180 degrees when added together, according to the triangle sum theorem.

Given:

Measure of angle C = 90 degrees

In △CAD, we have the following angle measures:

m∠A = 65° (given)

m∠ADC = 90° [right angle]

m∠ACD = 180 - 90 - 65 [triangle sum theorem]

m∠ACD = 25°

In △CBD, we have the following angle measures:

m∠CDB = 90° [right angle]

m∠BCD = 90 - m<ACD [complementary angle]

m∠BCD = 90 - 25

m∠BCD = 65°

m∠CBD = 180 - m∠BCD - m∠CDB [triangle sum theorem]

m∠CBD = 180 - 65 - 90

m∠CBD = 25°

In summary, applying the triangle sum theorem, the measures of the angles in △CBD are: m∠CDB = 90°; m∠BCD = 65°; m∠CBD = 25°

In △CAD, they are: m∠A = 65°; m∠ADC = 90°; m∠ACD = 25°

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Answer:

1 dollar and 6 cents

Step-by-step explanation:

Answer:

The point of intersection is the number of gigabytes and the total cost when the two plans cost the same.

Step-by-step explanation:

Company A doesn't charge a fee "per gigabyte", there's just a flat fee and it is $100. Company B only charges a flat fee of $20, BUT there IS a "per gigabyte" charge. These two plans actually cost exactly the same when the customer uses 16 gigabytes.

The ratio of the surface area of the large sphere to the surface area of the small sphere of radius 20π meters and 6π meters, respectively, is B. 100/9.

Surface area refers to the total area covering the outside of a three dimensional shape. The surface area of a sphere is given by the formula:

A = 4πr^2

Solving for the surface area of each sphere:
1. larger sphere, r = 20π meters

A = 4πr^2

A = 4π(20π meters)^2

A = 4π(400π^2 square meters)

A = 1600π^3 square meters

2. smaller sphere, r = 6π meters

A = 4πr^2

A = 4π(6π meters)^2

A = 4π(36π^2 square meters)

A = 144π^3 square meters

Getting the ratio of the surface area of the large sphere to the surface area of the small sphere:

1600π^3 square meters / 144π^3 square meters = 100/9

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Using the Fundamental Counting Theorem, it is found that the website would have 30,891,577,600 passwords.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, the first six spaces of the password are letters, and each can assume 26 values, hence the parameters are:

[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = 26[/tex]

The last two spaces are composed by digits, and each can assume 10 values, hence the parameters are:

[tex]n_7 = n_8 = 10[/tex]

Hence the number of possible passwords is given by:

N = 26^6 x 10² = 30,891,577,600.

The website would have 30,891,577,600 passwords.

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Answer:

42 feet

Step-by-step explanation:

1 1/2 * 28 = 42

We can conclude that ΔMSP ≅ ΔRQP under SAS conditions.

So,

Given: MS ≅ RQ, MS || RQ

To Prove: ΔMSP ≅ ΔRQP

ΔMSP ≅ ΔRQP is proved.

Therefore, ΔMSP ≅ ΔRQP under SAS condition.

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Answer: -41.5

Hope that helped.

Answer:

24 pots 2 plates

Step-by-step explanation:

Answer:

24 pots and 2 plates

Step-by-step explanation:

Answer:

x= 42°

Step-by-step explanation:

The missing angle can be found by using the property '∠ sum of Δ'. The sum of the interior angles in a triangle is 180°.

The square symbol in the triangle represents a right angle, i.e. 90°.

Form an equation:

x +90° +48°= 180° (∠ sum of Δ)

x +138°= 180°

x= 42°

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The value of x will be 1099.8 when rounded it to the nearest decimals.

㏑(x-4)=7

Taking the exponential (e) both side, we get

[tex]e^{ln(x-4)} = e^{7}[/tex]

since 'e' and 'ln' cancels each other,

therefore

[tex]x-4 = e^{7}[/tex]

[tex]x = e^{7} + 4[/tex]                                                                                                  ..eq 1

Exponential 'e' is the Euler's number, which is a constant having the value of around 2.718281828459045235360.

so putting the value of 'e' in eq 1

[tex]x = (2.718)^{7} + 4[/tex]

x = 1095.838 + 4

x = 1099.838

therefore when ㏑(x-4)=7 is solved the value of x will be 1099.8.

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According to the arithmetic progression, explicit formula for this sequence can.be depicted by:

aⁿ =  a + ( n -1 ) d.

This sequence is in arithmetic progression, and an explicit formula for this sequence is

aⁿ =  a + ( n -1 ) d

where n is the number of terms,  d = the difference between two-term, and a is the first term of this sequence.

For example, We have to determine the 8th term of this sequence, so n = 8, and the difference between two correspondent numbers, ( 7 - 4 = 3 )

a⁸ = 1 + ( 8 - 1 ) 3 = 1 + 21 = 22.

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The number of students that did major in the north is 300 and the number of student that do major in the south is 700.

At the north campus of a performing arts school, 30% of the students are music majors.

At the south campus, 80% of the students are music majors.

let

x = number of student at the north campus before the merger

Therefore,

1000 - x = number of students at the south campus before the merger

Hence, the equation for the music majors in the merger is as follows:

0.3x + 0.8(1000 - x) = 0.65(1000)

0.3x + 800 - 0.8x = 650

-0.5x = 650 - 800

-0.5x = -150

divide both sides by -0.5

x = -150 / -0.5

x = 300

Therefore, the number of students that did major in the north is 300 and the number of student that do major in the south is 700.

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Answer:

[tex]x = -1, -3[/tex]

To solve by factoring, we will split up the equation using our factoring rules.

In this particular instance, we will factor out common variables.

We need to ensure that we get two numbers that add to equal 4 and two numbers that multiply to equal 3.

[tex]x^2 + 4x + 3 = 0[/tex]

[tex](x+3)(x+1)=0[/tex]

Set each factor equal to zero and solve.

Root 1

[tex]x+3=0[/tex]

[tex]x=-3[/tex]

Root 2

[tex]x+1=0[/tex]

[tex]x=-1[/tex]

The final answer is [tex]\boxed{x = -1, -3}[/tex].

As requested in the question, we must now check with the quadratic formula.

To solve this quadratic equation, we will utilize the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The parent formula for a quadratic equation is [tex]ax^2+bx+c=0[/tex].

We will define our variables:

Now, we will plug these into the equation and solve the equation.

[tex]\displaystyle x=\frac{-4\pm\sqrt{4^2-4(1)(3)}}{2(1)}[/tex]

[tex]\displaystyle x=\frac{-4\pm\sqrt{16-12}}{2}[/tex]

[tex]\displaystyle x=\frac{-4\pm\sqrt{4}}{2}[/tex]

[tex]\displaystyle x=\frac{-4\pm2}{2}[/tex]

Root 1

[tex]\displaystyle x=\frac{-4+2}{2}[/tex]

[tex]\displaystyle x=\frac{-2}{2}[/tex]

[tex]\boxed{x=-1}[/tex]

Root 2

[tex]\displaystyle x=\frac{-4-2}{2}[/tex]

[tex]\displaystyle x=\frac{-6}{2}[/tex]

[tex]\boxed{x=-3}[/tex]

The final answer is [tex]\boxed{x = -1, -3}[/tex].

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Given the equation, we can start by rewriting:

x^2 + 4x + 3 = 0

Now, let’s write in factored form:

(x + 1) (x + 3) = 0

since x is the only variable and there are 2 numbers, we can make 2 equations:

x + 1 = 0

x + 3 = 0

This forms:

(X + 1) (x + 3) = 0

Now, we can solve:

? + 1 = 0

? + 3 = 0

-1 + 1 = 0 and -3 + 3 = 0

x = -1 AND -3

The equation of the circle with radius 4.5 and center at (2 , 3) is (x - 2)^2 + (y - 3)^2 = 20.25.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (2 , 3)

r = 4.5

(x - 2)^2 + (y - 3)^2 = 4.5^2

(x - 2)^2 + (y - 3)^2 = 20.25

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