A line passes through the points ( – 4, – 2) and ( - 1, - 2). Determine the slope of the line.

Answer:

B. [tex] -3x [/tex]

Step-by-step explanation:

In algebra, a term could be a single negative or positive number (constant), a variable or a variable with a coefficient. It could also be 2 variables multiplied together.

The algebraic expression [tex] -3x - 7(x + 4) [/tex] , can be expanded and expressed as:

[tex] -3x - 7(x) -7(+4) [/tex]

[tex] -3x - 7x - 28 [/tex]

The three terms are: [tex]-3x, - 7x, -28[/tex]

Therefore, from the given answer choices, the term that is a term in the expression, [tex] -3x - 7(x + 4) [/tex] , is B. [tex] -3x [/tex]

Answer:

yyy = xxx + 151515

Step-by-step explanation:

Since you want to swim 151515 minutes longer one day at practice (note this time is actually 105 days), you simply need to swim the same amount of time as your friend, plus the extra time. Hence, your time will be equal to your friends time plus the extra time you plan to swim.

Answer:

(9, 3)  

Step-by-step explanation:

(1) 4(0.25x + 0.5 y) = 3.75 ⟶ x + 2y = 15

(2)                 4x - 8y = 12 ⟶ x  -  2y =   3

                                                   2x = 18

                                                      x = 9

                                              9 - 2y = 3

                                                  -2y = -6

                                                     y = 3

Answer:

  216

Step-by-step explanation:

  y = ±√36 = ±6

  y³ = (±6)³ = ±216

The largest of these values is 216, the greatest possible value of y.

Answer:

The graph of IxI is:

y = x for values of x ≥ 0

y = -x for values of x ≤ 0

Then you will see a "V", with the arms pointing up and the vertex in the point (0, 0)

(Something like in the image, but with the arms pointing upside instead of downside)

The actual graph is:

Answer:

  5

Step-by-step explanation:

The limit of f(x) at x=-1 is 5 when approached from the left or right. Since those limits are the same, the limit exists and is ...

  [tex]\boxed{\lim\limits_{x\to-1}f(x)=5}[/tex]

The question in part c is not clear, nevertheless, part a and part b would be solved.

Answer:

a. The first twelve terms are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

b. The first ten terms are:

1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.

Step-by-step explanation:

a. Given

an + 2 = an + an + 1

where a1 = 1 and a2 = 1.

a3 = a1 + a2

= 2

a4 = a2 + a3

= 3

a5 = a3 + a4

= 5

a6 = a5 + a4

= 8

a7 = a6 + a5

= 13

a8 = a7 + a6

= 21

a9 = a8 + a7

= 34

a10 = a9 + a8

= 55

a11 = a10 + a9

= 89

a12 = a11 + a10

= 144

The first twelve terms are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

(b)

Given

bn = an+1/an

b1 = a2/a1

= 1/1 = 1.000

b2 = a3/a2

= 2/1 = 1.000

b3 = a4/a3

= 3/2 = 1.500

b4 = a5/a4

= 5/3 = 1.667

b5 = a6/a5

= 8/5 = 1.600

b6 = a7/a6

= 13/8 = 1.625

b7 = a8/a7

= 21/13 = 1.615

b8 = a9/a8

= 34/21 = 1.619

b9 = a10/a9

= 55/34 = 1.618

b10 = a11/a10

= 89/55 = 1.618

The first ten terms are:

1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.

Answer:

Step-by-step explanation:

Let's create an equation:

[tex]5y = 135[/tex]

( Being vertically opposite angles)

Now, let's solve

Divide both sides of the equation by 5

[tex] \frac{5y}{5} = \frac{135}{5} [/tex]

Calculate

[tex] y = 27[/tex]

Hope this helps...

Best regards!!

Step-by-step explanation:

F (x)=x³-2x²+x+1,

Then F (-x)= - x³ - 2x² - x + 1

Tell me if I'm right.

Hope this helps.

Have a great day!

Answer:

The first step would be to look at the average for each brand.

The average can be calculated as:

A = (a1 + a2 + .... + an)/N

where a1 is the first lifetime, a2 is the second one, etc. And N is the total number of data points.

So, for Brand 1 we have:

A1 = (260 + 218 + 184 + 219)/4 = 220.25

Brand 2:

A2 = (181 + 240 + 162 + 218)/4 = 200.25

Brand 3:

A3 = (238 + 257 + 241 + 213)/4 = 237.25

So only from this, we can see that Brand 3 has the larger lifetime, then comes Brand 1 and last comes Brand 2.

Answer:

H₀ is accepted, we don´t have evidence to claim valves produces more than 4,1 pounds/square inch

Step-by-step explanation:

Normal Distribution

Population mean   μ₀  = 4.1

Population standard deviation  σ = 0,9

Sample size   n  = 260

Sample mean     μ  =  4,2

Level of significance 0,02       α = 0,02 form z-table we find z score

z(c) = 2,05  (critical value)

Test hypothesis      

Null hypothesis                       H₀            μ  =  μ₀

Alternative hypothesis           Hₐ            μ   >  μ₀

Is a one tail-test ( to the right. Values have a mean over the population mean)

z(s) = (  μ  -  μ₀ )/ σ /√n

z(s) =  4,2 - 4,1 / 0,9/√260

z(s) = 0,1 *16,1245 / 0,9

z(s) =  1,7916

To compare  z(s)   and z(c)

z(s) < z(c)

Then  z(s) is in the acceptance region, we accept H₀

Answer:

The plane is 388 miles far from the airport.

Step-by-step explanation:

We know that, the angle between southeast and south directions is [tex]135^\circ[/tex].

The plane travels as per the triangle as shown in the attached image.

A is the location of airport.

First it travels for 210 miles southeast from A to B and then 210 miles south from B to C.

[tex]\angle ABC = 135^\circ[/tex]

To find:

Side AC = ?

Solution:

As we can see, the [tex]\triangle ABC[/tex] is an isosceles triangle with sides AB = BC = 210 miles.

So, we can say that the angles opposite to the equal angles in a triangle are also equal. [tex]\angle A = \angle C[/tex]

And sum of all three angles of a triangle is equal to [tex]180^\circ[/tex].

[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow \angle A+135^\circ+\angle A = 180^\circ\\\Rightarrow \angle A = \dfrac{1}{2} \times 45^\circ\\\Rightarrow \angle A =22.5^\circ[/tex]

Now, we can use Sine Rule:

[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB}[/tex]

a, b are the sides opposite to the angles [tex]\angle A and \angle B[/tex] respectively.

[tex]\dfrac{210}{sin22.5^\circ} = \dfrac{b}{sin135^\circ}\\\Rightarrow \dfrac{210}{sin22.5^\circ} = \dfrac{b}{cos45^\circ}\\\Rightarrow b = 210\times \dfrac{1}{\sqrt2 \times 0.3826}\\\Rightarrow b = 210\times \dfrac{1}{0.54}\\\Rightarrow b \approx 388\ miles[/tex]

So, the answer is:

The plane is 388 miles far from the airport.

Answer:

80

Step-by-step explanation:

The quadrilateral is a kite.

The angle opposite to angle H is equal to angle H.

Angle F = 110 degrees

Angles in a quadrilateral add up to 360 degrees.

60 + 110 + 110 + G = 360

280 + G = 360

G = 360 - 280

G = 80

The measure of angle G is 80 degrees.

Answer: 80 degrees.

Step-by-step explanation:

In a kite, the angles formed by noncongruent sides are congruent.  Thus, <EFG is 110 degrees.  Then, because a kite is a quadrilateral, all of the angles in it add up to 360.  Thus, is <FGH = x, then 110+110+60+x=360.  Thus, x = 80.

Hope it helps <3

Answer:

-2 is a zero of the polynomial. 2 is not a zero of the polynomial.

Step-by-step explanation:

A value of x is a zero of a polynomial if when it is substituted for x in the polynomial, it makes the polynomial evaluate to zero.

The polynomial is x + 2

Let x = -2:

x + 2 = -2 + 2 = 0

-2 is a zero of the polynomial.

Let x = 2:

x + 2 = 2 + 2 = 4

2 is not a zero of the polynomial.

Answer:

Its B and D

Step-by-step explanation:

Because thats where the points intersects/meet.

Answer:

area = 1800 m²

Step-by-step explanation:

area of one triangle = 900 m²

if a parallelogram has the same height and base as the triangle, then that means the area or the two triangle and shaped as a parallelogram

is twice the area given.

area = 900 * 2

area = 1800 m²

Answer:

0.8 < x < 16.8

Step-by-step explanation:

8.0 + 8.8 = 16.8

The range of possible sizes for the side x are 0.8 < x < 16.8.

A triangle is a geometrical shape in two dimensional geometry which has three sides, three vertices and three angles.

The sum of all the three angles inside the triangle is supplementary.

This implies that if a, b and c are the three interior angles of a triangle, then, a + b + c = 180°.

If two sides of a triangle are given, then the third side of the triangle will always be in between the difference of the length of the other two sides and the sum of the length of the other two sides.

Here two lengths are given as 8.0 and 8.8.

Difference of the lengths = 8.8 - 8.0 = 0.8

Sum of the lengths = 8.8 + 8.0 = 16.8

So the x lies between 0.8 and 16.8.

Hence the range of the possible length of the given triangle is 0.8 < x < 16.8.

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Answer:

proved: see explanation below

Step-by-step explanation:

The parallelogram ABCD  has cordinates point A is (0,0) point B is (10,0) point C is (12,7) and point D is (3,7).

For the opposite sides of ABCD to be congruent, the slope of the opposite sides would be equal

If AB // CD, BC // AD, it’s a parallelogram.

If slope of AB = CD, BC = AD then it’s a parallelogram.

slope = Δy/Δx

slope AB = (0-0)/(10-0) = 0

slope BC =  (7-0)/(12-10) = 7/2

slope CD =  (7-7)/(12-3) = 0

slope DA =  (0-7)/(0-3) = 7/3

slope DA is supposed to be equal to slope BC

It means the coordinate of D is (2,7)

slope DA becomes=  (0-7)/(0-2) = 7/2

Therefore it would be proved that the opposite sides of ABCD are congruent as two pair of slopes are equal

Answer:

a =7.5

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+ b^2 = c^2  where a and b are the legs and c is the hypotenuse

a^2 + 10 ^2 = 12.5^2

a^2 + 100  =156.25

Subtract 100 from each side

a^2 = 56.25

Take the square root of each side

sqrt(a^2) = sqrt( 56.25)

a =7.5

Answer:

253°

Step-by-step explanation:

The central angle whose rays intercept a diameter of the circle has measure 180 deg.

m<AOD = 73 deg

m<DOB = 180 deg

m<ADB = m<AOD +m<DOB = 73 deg + 180 deg = 253 deg

The measure of an arc of a circle is equal to the measure of the central angle that subtends it.

m(arc)AOD = m<AOD = 253 deg

Answer: 253°

The solution is, the measure of Arc A D B is 253°.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

Here, we have,

given that AC and BD are diameters of circle O.

AC and BD intersect at point C the centre of the circle.

The central angle of a circle is the angle based at the circle's center. In other words, the vertex of the angle must be at the center of the circle. A central angle is formed by two radii that start at the center and intersect the circle itself.

The central angle whose rays intercept a diameter of the circle has measure 180 deg.

m<AOD = 73 deg

m<DOB = 180 deg

m<ADB = m<AOD +m<DOB = 73 deg + 180 deg = 253 deg

The measure of an arc of a circle is equal to the measure of the central angle that subtends it.

m(arc)AOD = m<AOD = 253 deg

Answer: the measure of Arc A D B is 253°.

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Answer:

No

Step-by-step explanation:

In exponential behavior each number increases by some some power in respect of previous number.

example

2,4,8,16

which is similar as 2 , 2^2,2^3,2^4

here it can be represented as y = 2^x

here we see that each number increases by power of 2, hence it shows exponential behavior.

____________________________________________

In the problem

(1,1), (2,2) ,(3,3), (4,4)

23 see that each number increases by one unit in respect of previous number

and also x is same as y

thus, it can be represented as

y = x which is linear behavior

hence , the given data set shows linear behavior rather than exponential behavior.

Step-by-step explanation:

Since you are given the values there is no need to try another method then replacing x by the values

㏑(2)= 0.69

㏑(1.35) = 0.3

so the right answer is D

Answer:

Possible solution 1: -4.5 and -8

Solution 2: 4 and 9.

Step-by-step explanation:

Let the two numbers be a and b.

One of them (let it be b) is 1 more than twice the other one. In other words,

b= 1+ 2a.

Their product is 36. Or:

a(b) = 36.

Substitute b:

a(1+2a) = 36

2a^2 + a = 36

2a^2 + a - 36 = 0

This is now a quadratic. We can factor to solve it. Find two numbers that equals 2(-36)=-72 and add to 1. We can use 9 and -8. Thus:

2a^2 - 8a + 9a - 36 = 0

2a(a - 4) +9(a-4) = (2a+9)(a-4) = 0

So, a = -9/2 = -4.5 or a = 4.

Thus, b can equal 1 + 2(-4.5) = -8 or 1 + 2(4) = 9

Answer:

the temperature reading that separates the bottom​ 4% from the others is -1.75°

Step-by-step explanation:

The summary of the given statistics data set are:

Mean [tex]\mu[/tex] : 0

Standard deviation [tex]\sigma[/tex] = 1

Probability of the thermometer readings = 4% = 0.04

The objective is to determine the temperature reading that separates the bottom​ 4% from the others

From the standard normal table,

Z score for the Probability P(Z < z) = 0.04

P(Z < -1.75) = 0.04

z = -1.75

Now, the z- score formula can be expressed as :

[tex]z = \dfrac{X-\mu}{\sigma}[/tex]

[tex]-1.75 = \dfrac{X-0}{1}[/tex]

-1.75 × 1 = X - 0

X = -1.75 × 1 - 0

X = -1.75

Therefore, the temperature reading that separates the bottom​ 4% from the others is -1.75°

Answer:

K = 40

Step-by-step explanation:

As they said that 28 is 12 less than K , it means that you've to add them to get the answer. So , 28 + 12 = 40 which is represented by the variable "K"

Hope it helps and pls mark as brainliest : )

Answer:

Step-by-step explanation:

28 is 12 less than k

Let's create an equation:

[tex]28 = k - 12[/tex]

Now, let's solve:

[tex]28 = k - 12[/tex]

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

[tex] - k = - 12 - 28[/tex]

Calculate the difference

[tex] - k = - 40[/tex]

Change the signs on both sides of the equation

[tex]k = 40[/tex]

Hope this helps...

Best regards!!

The expression that is equivalent to 6 cubed is: 6 times 6 times 6.

This is true since cubed indicates that the base number is multiplied by itself 3 times.

So, 6^3 equates to 6 x 6 x 6.

Answer:

The expression that is equivalent to 6 cubed is: 6 times 6 times 6.

This is true since cubed indicates that the base number is multiplied by itself 3 times.

So, 6^3 equates to 6 x 6 x 6.

Step-by-step explanation:

Answer:

Balance after one year will be $5830.

Answer:

a) percentage of the employees that will experience lost-time accidents in both years = 1.2%

b) percentage of the employees that will suffer at least one lost-time accident over the two-year period = 10.8%

Step-by-step explanation:

given

percentage of lost time accident last year

P(L) = 8% = 0.08 of the employees

percentage of lost time accident current year

P(C) = 4% = 0.04 of the employees

P(C/L) = 15% = 0.15

using the probability

P(L ∩ C) = P(C/L) × P(L)

= 0.08 × 0.15 = 0.012 = 1.2%

percentage of the employees will experience lost-time accidents in both years = 1.2%

b) Using the probability of the event

P(L ∪ C) = P(L) + P(C) - P(L ∩ C)

= 0.08 + 0.04 -0.012 = 0.108 = 10.8%

percentage of the employees will suffer at least one lost-time accident over the two-year period = 10.8%

Answer:

x = ln (5.2)

Step-by-step explanation:

e^x = 5.2

Take the natural log of each side

ln ( e^x) = ln( 5.2)

x = ln (5.2)

Answer:

x ≈ 1.91, if e refers to 2.718281828...

x = 5.2/e, if e is simply another variable

Step-by-step explanation:

We are given:

ex = 5.2

Now, if e is referring to the irrational value of e that is about 2.718281828..., then when we divide both sides by e to solve for x, we get:

ex = 5.2

x = 5.2 / 2.718281828... ≈ 1.91

However, if e is simply another varialbe, then we just have:

ex = 5.2

x = 5.2/e

~ an aesthetics lover

Answer:

50 meters

Step-by-step explanation:

The area of a circle is [tex]\pi r^2[/tex], so assuming that [tex]\pi[/tex] is 3.14, we can make the equation [tex]3.14 \cdot r^2[/tex].

Assuming the radius is r, which is 4, we can substitute the values into the equation.

[tex]3.14 \cdot 4^2\\3.14\cdot16\\50.24[/tex]

This question is asking for the area to the nearest square meter so rounding 50.24 to the nearest square meter results in 50.

Hope this helped!