In order to answer the question correctly, please use the following image below:

Find the value of x.

X=(Blank)

Please show all the work on how you got your answer.

Answer: Angles who share the same initial side and terminal sides.

Answer:

El primer paso será darle un nombre a nuestras variables:

x= Numero de libros comprados inicialmente

y=Precio inicial de los libros

Ahora analizamos el enunciado,

Lorena ha comprado libros todos del mismo precio por valor de 120 €

x*y=120 € (1)

El librero le regala 3 libros por lo que en realidad cada libro que cuesta 2 € menos

(x+3)(y-2)=120€ (2)

Tenemos entonces dos ecuaciones con dos incógnitas, así que podemos resolver,

Despejamos en (1)

x=120/y

Sustituimos en (2)

(120/y +3)(y-2)=120

120 - 240/y + 3y -6 =120

3y-240/y =120-120+6

3y -240/y =6

y- 80/y=6

y²-80=6y

y²-6y-80=0

Resolvemos la ecuación de segundo grado

a=1

b=-6

c=-80

Aplicando la resolvente,

(6+- √36+320)/2

6+-√356/2

(6+-18,86)/2

Como el valor de y no puede ser negativo la unica respuesta válida será:

y=12,43

Cada libro le costo 12,43€

Sustituyendo en (1)

x=120/12,43

x=9,65 como no puede ser un número racional

x=9

Lorena ha comprado 9 libros

Ana originally bought 12 books.

Let's say Ana originally bought x books, each costing p euros.

The total cost of all the books is 120 euros, so we can write the equation:

x * p = 120

After the bookseller gives Ana 3 free books, the new total number of books she has is x + 3 and each book costs p - 2 euros.

The new total cost of all the books is still 120 euros, so we can write the equation:

(x + 3) * (p - 2) = 120

Simplifying this equation, we get:

px + 3p - 2x - 6 = 120

Combining like terms:

px - 2x + 3p - 6 = 120

Substituting the equation px = 120, we get:

120 - 2x + 3p - 6 = 120

Simplifying further:

3p - 2x - 6 = 0

Let's rewrite this equation:

3p - 2x = 6

When we substitute the equation px = 120 into this equation:

3p - 2(120/p) = 6

Simplifying:

3p - 240/p = 6

Multiplying through by p:

3p^2 - 240 = 6p

Rearranging:

3p^2 - 6p - 240 = 0

Using the quadratic formula to solve for p:

p = (-(-6) ± sqrt((-6)^2 - 4*3*(-240)))/2*3

p = (6 ± sqrt(36 + 2880))/6

p = (6 ± sqrt(2916))/6

p = (6 ± 54)/6

For the positive value of p:

p = (6 + 54)/6 = 60/6 = 10

Now, substituting p = 10 back into the equation px = 120:

10x = 120

x = 120/10 = 12

So, Ana originally bought 12 books.

Answer:

2/3

Step-by-step explanation:

Answer:

Part 1: 8 km per liter

Part 2: 0.125 liters per km

Step-by-step explanation:

Part 1:

6x=48

x=48/6

x=8

Part 2:

8km per liter

?liters per km

1/8 = 0.125

0.125 liters per kilometer

Final answer:

To find the probability of getting at least 2 heads in three coin tosses, count the favorable outcomes (HHH, HHT, HTH, THH) and divide by the total outcomes. The probability is 4/8 or 1/2, which is 50%.

Explanation:

The question asks to calculate the probability of getting at least 2 heads when flipping a coin three times. The sample space for three coin tosses consists of 8 possible outcomes: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. To find the probability of getting at least 2 heads, we need to count the favorable outcomes which are: {HHH, HHT, HTH, THH}, and then divide this number by the total number of possible outcomes.

There are 4 favorable outcomes out of 8 possible, so the probability is 4/8 or 1/2. Therefore, the probability of obtaining at least 2 heads in three coin tosses is 0.5 or 50%.

Answer:

280 miles of actual

Step-by-step explanation:

Given that:

<=> 1 inch on the map represents : 200/5 = 40 miles of actual

So the actual distance between the 2 cities is:

7*40 miles of actual

= 280 miles of actual

Hope it will find you well.

Answer:

Step-by-step explanation:

we know that the formula for the volume of cylinder is

=[tex]\pi r^{2} h[/tex]

Given

radius(r) = 4

height(h) = 10

NOW

Volume =  [tex]\pi r^{2} h[/tex]

             = [tex]\pi *4^{2} *10[/tex]

             =[tex]160\pi units^{3}[/tex]

or

if we use the value of pie then its answer is

= 160 * 3.14

= 502.4[tex]units^{3}[/tex]

Hope it was helpful:)

Final answer:

The best estimate for (6.3 x 10⁻²) (9.9 x 10⁻³) in scientific notation is approximately 6.237 x 10⁻⁵.

Explanation:

To find the best estimate for (6.3 x 10⁻²) (9.9 x 10⁻³) written in scientific notation, you need to multiply the coefficients and add the exponents.

The product of 6.3x 10⁻² and 9.9 x 10⁻³ can be calculated as (6.3 x 9.9) x (10⁻² x 10⁻³). The coefficients multiply to give 62.37 (approximately), and the exponents add to give -5.

Therefore, the best estimate for (6.3 x 10⁻²) (9.9 x 10⁻³) in scientific notation is approximately 6.237 x 10⁻⁵.

Answer:

The slope is -2

Step-by-step explanation:

-6-2/4-0=-8/4=-2

Answer:

The slope is -2

Step-by-step explanation:

We can find the slope of a line given two points using

m = (y2-y1)/(x2-x1)

    = (2 - -6)/(0 -4)

    = (2+6)/(0-4)

     = 8/-4

      = -2

Answer:

Vertex of parabola

Step-by-step explanation:

The red dot shows the extreme of parabola that is known as vertex.

The answer is C

Because the sum of the angles are not up to 180

which makes way for other angles.

Option B, three side lengths measuring 7m, 10m, and 12m can create more than one triangle because there are multiple ways the sides can be oriented to create different internal angles, therefore creating multiple triangles.

The question is about constructing triangles from given dimensions and determining which sets of dimensions can create more than one triangle. In geometry, for a set of dimensions to produce more than one unique triangle, it must not fully determine the shape of the triangle. The axiom that the sum of the angles in a triangle is exactly 180 degrees is key to answering part of this question. Here are the evaluations based on the given options:

Upon evaluating the provided dimensions:

Therefore, the correct answer is B: Three sides measuring 7m, 10m, 12m can create more than one triangle.

Answer:

There are 2 cups in a pint is correct

The correct measurement statement is that there are 4 pints in a quart. This conclusion is derived from understanding the relationship between cups, pints, and quarts in the customary system of measurement.

The correct measurement statement among the options provided is that there are 4 pints in a quart. This is because, in the customary system of measurement, one quart (qt) is equivalent to two pints (pt), and a pint is equivalent to two cups (c). Therefore, the relationship among these units of measure can be summarized as follows:

Thus, when we compare cups, pints, and quarts, we establish that the conversion factors are essential for accurate measurement in different scenarios, whether it be for cooking or scientific measurements.

Answer:

Kevin is 7

Step-by-step explanation:

In 56 years if Kevin is 7 now he will be 63 and 7X9 = 63

Answer:

The correct answer is 6 hours.

Step-by-step explanation:

Let Mrs. Long rent the bounce house for x hours.

Fixed price to be charged is 145.

Per hour price of the bounce house is 35. Total price of x hours is 35x.

Thus total amount charged by the rentals is 145 + 35x.

Mrs. Long paid 355 in total.

∴ 145 + 35x = 355

⇒ 35x = 210

⇒ x = 6.

Thus Mrs. Long rented the bounce house for 6 hours.

Answer:

  c.  2; no

Step-by-step explanation:

The inner product is the sum of the products of corresponding vector components. It is a scalar value, not a vector value.

  (3, 5)·(4, -2) = (3)(4) +(5)(-2) = 12 -10 = 2

When the inner product is non-zero, the vectors are not perpendicular. (The yes answers with a non-zero value can be rejected out of hand.)

The appropriate choice is ...

  2; no

Final answer:

The inner product of the vectors (3,5) and (4,-2) is 2. As the dot product is not zero, the vectors are not perpendicular. Therefore, the correct answer is c.2; no.

Explanation:

To find the inner product of two vectors, we use the dot product formula. The dot product of two vectors u = (a1, b1) and v = (a2, b2) is calculated as u · v = a1 × a2 + b1 × b2. For the vectors (3,5) and (4,-2), we calculate as follows:

Inner product = 3 × 4 + 5 × (-2) = 12 - 10 = 2.

Two vectors are perpendicular if their dot product is zero. Since the dot product here is 2, not zero, the given vectors are not perpendicular.

Therefore, the correct answer is: c.2; no.

Answer:

The x intercept is (7/5,0)

Step-by-step explanation:

y=−5x+7

To find the x intercept, set y=0 and solve for x

0 = -5x+7

Subtract 7 from each side

0-7 = -5x+7-7

-7 = -5x

divide each side by -5

-7/-5 = -5x/-5

7/5 =x

The x intercept is (7/5,0)

Answer:

y = (3x² + x - 2)/(x² - 1)

Step-by-step explanation:

(x - 1)(x + 1) = x² - 1

In the denominator

f(x)/(x² - 1)

f(x) has a factor (x + 1)

3 + (x + 1)/(x² - 1)

(3x² - 3 + x + 1)/(x² - 1)

y = (3x² + x - 2)/(x² - 1)

Answer:

a) 32, 52

b) 18n

Step-by-step explanation:

a)

12+20=32

20+32=52

b)

4th element = 3n+4n=7n

5th element = 4n+7n=11n

6th element = 7n+11n=18n

Answer:

a) 32, 52  

b) 18n

Step-by-step explanation:

because 7n+n

3n+7

4

Answer:

the answer is C. (1/7)

Step-by-step explanation:

I did it on edge

THE ANSWER WOULD BE 40 × d

or 40d

Answer:

3 feet

Step-by-step explanation:

GIVEN: A filing cabinet has a height of [tex]6\text{ feet}[/tex] and a length of [tex]2\text{ feet}[/tex]. The volume of the filing cabinet is [tex]36\text{ feet}^3[/tex].

TO FIND: What is the width of the filing cabinet.

SOLUTION:

Let the width of filing cabinet be [tex]x\text{ feet}[/tex]

length of filing cabinet  [tex]=6\text{ feet}[/tex]

height of filing cabinet  [tex]=2\text{ feet}[/tex]

Volume of filing cabinet [tex]=\text{length}\times\text{height}\times\text{width}=36\text{ feet}^3[/tex]

putting values,

[tex]6\times2\times x=36[/tex]

[tex]12\times x=36[/tex]

[tex]x=3[/tex]

Hence the width of filing cabinet is 3 feet.

Answer:

A) 0.685

Step-by-step explanation:

P(no snow) = 1 - P(snow)

1 - 0.315

0.685

Answer:

Between 36 and 38

Answer:

girl, is that USA Test Prep???

im doing that also!!

i think its between 36 and 38 basically.

Step-by-step explanation:

hope it helps i guess!! <33

Answer:

20 meters

Step-by-step explanation:

Seeing the image attached, we can observe that there is a triangle formed by half of the chord of the arc, the radius (hypotenusa) and part of the radius (r-4). Using pythagoras theorem in this triangle, we have:

(r-4)^2 + 12^2 = r^2

r^2 - 8r + 16 + 144 = r^2

8r = 160

r = 20

So the radius of the circle that contains this arc is 20 meters.

Answer:

20 m

Step-by-step explanation:

radius 'r', half the chord, and dist from center to the chord  has formed a right angle triangle

where,

r  is hypotenuse

(r-4) = one side i.e dist from center to chord)

12 = other side i.e half the length of the chord)

By applying Pythagoras theorem, we will have

r² = 12² + (r-4)²

 r²= 144 + r² - 8r + 16  --->(cancel out r²)

0 = -8r + 160

8r = 160

r = 160/8

r = 20 m

Thus, the radius of the circle containing this arc  is 20m

You can also verify this :

distance from center to chord: 20 - 4 = 16

r = [tex]\sqrt{16^{2}+12^{2} }[/tex]

r = 20

Answer:

H₀: p=0.76

Ha :p < 0.76

Step-by-step explanation:

A null hypothesis is the common accepted fact that the researcher works to prove it wrong. In this case, the survey revealed that 76% of US adults admit they lie to their doctor about how often they exercise. This forms the null hypothesis.

The alternative hypothesis suggest that a new theory is happening unlike the original one.In this case,  Dr. Moffett believes the percentage seems high, so the alternative hypothesis is that the percentage is lower than 76%

Answer:

H0: p = 0.76; Ha: p < 0.76

Step-by-step explanation:

I took the quiz and got it right

Answer:

610 and 970

Step-by-step explanation:

Answer:

610 and 970

Step-by-step explanation:

The population of Leavetown after 100 years would be 111,17.5681.

Step-by-step explanation:

Given that,

Initial Population = I = 123,000

Decreasing Rate = r = 2.375 = 0.02375

We have to find the population after 100 years. So,

n = 100

The formula to calculate the population (P) after n years with a decreasing rate r is:

[tex]P = I (1-r)^{n}[/tex]

Now, put the values in this formula.

[tex]P = 123,000 (1-0.02375)^{100}[/tex]

[tex]P = 123,000 (0.97625)^{100}[/tex]

[tex]P = 11117.5681[/tex]

Hence, the population of Leavetown after 100 years would be 111,17.5681.

Answer:

0.42074

Step-by-step explanation:

In this question, we are asked to calculate the probability that a car will get less than 21 miles per gallon.

This is P(x < 21)

z = 21-22/5 = -1/5 = -0.2

Therefore the probability of getting less than 21 miles per gallon will be;

P(x<21) = P (z < -0.2)

= 0.42074

Answer:

8 cup of blue

12 cup of red

Step-by-step explanation:

The first thing is to calculate how much black paint is produced, assuming that the volumes add up, we have to:

1/2 + 1/3 = 5/6

5/6 cup of paint is produced, I want to know how much I need to produce 20 cups, I divide the value I want by the ideal value, that is, 5/6 and thus I obtain the factor that I require:

20 / (5/6) = 24

Now I multiply by 24 each quantity of blue and red paint

1/2 * 24 = 12

1/3 * 24 = 8

Which means you need 12 cups of red paint and 8 cups of blue paint

Answer:

Monthly deposit, P = $776.41

Step-by-step explanation:

Interest rate per annum = 5.5%

number of years = 25

Since she pays monthly, number of payments per annum = 12

Interest rate per period, r = (Interest rate per annum)/(number of payments per annum)

r = 5.5%/12 = 0.46%

Number of periods, n = number of years * number of payments per annum

n = 25 * 12 = 300

Future value of annuity, FVA = $500,000

Monthly deposit will be:

[tex]P = \frac{(FVA) * r}{(1+r)^{n} -1} \\P = \frac{(500000) * 0.46/100}{(1+0.46/100)^{300}-1 }[/tex]

P = $776.41

Answer:

MP = $778.77

she should put $778.77 into the account each month

Step-by-step explanation:

This problem can be solved using the compound interest formula;

FV = MP{[(1+r/n)^(nt) - 1]/(r/n)} .......1

Where;

FV = Future value

MP = monthly contribution

r = yearly rate

n = number of times interest is compounded per year.

t = number of years

Given

FV = $500,000

t = 25 years

r = 5.5% = 0.055

n = 12 months/year

From equation 1, making MP the subject of formula;

MP = FV/{[(1+r/n)^(nt) - 1]/(r/n)}

Substituting the given values we have;

MP = 500,000/(((1+0.055/12)^(12×25) -1)/(0.055/12))

MP = $778.77

she should put $778.77 into the account each month