10x² 18x -4
Factor number And find answer

The measure of angle that is an exterior angle to B is 95°.

The angle created by any extended side of a triangle and its neighboring side is referred to as the external angle of a triangle. A triangle has three external angles. It should be noticed that every outside angle and corresponding interior angle constitute a linear pair. We are aware that a triangle's internal angle is created when its sides come together at its apex.

Given that,

The measure of angle 4 is 120°, and the measure of angle 2 is 35°.

Triangle A B C. Angle A is 2, angle B is 1, and angle C is 3. The exterior angle to angle B is 5, and the exterior angle to angle C is 4.

The sum of an interior and exterior angle is 180°,

∠4 + ∠3 = ∠1 + ∠5 = ∠2 + ∠6 = 180°

and ∠2+ ∠1 +∠3 = 180°

Also, ∠3 = 180 - ∠4

∠3 = 180 - 120 = 60°

Substitute the values,

∠2+ ∠1 +∠3 = 180°

35 + ∠1 + 60 = 180

∠1 = 180 - 95

∠1  = 85°

Now, ∠1 + ∠5 = 180

∠5 = 180 - 85

∠5 = 95°

Hence, the measure of angle that is an exterior angle to B is 95°.

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The correct question is:

Answer: A) 95 Degrees

Step-by-step explanation:

There are 16% of the Green were Planes.

The percentage is defined as a ratio expressed as a fraction of 100.

Total number of green planes = 250

The total number of all planes = 1550

The percent of green planes = (number of green planes/number of total planes ) x 100

The percent of green planes = (250/1550) x 100

The percent of green planes = 0.1612 x 100

The percent of green planes = 16.129

Round to the nearest percent, and we get

The percent of green planes = 16%

Thus, 16% of the Green were Planes.

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Answer:

Step-by-step explanation:

Step 1: Understanding the Problem

The problem involves finding an equation to approximate the amount of fuel in Jon's semitruck after he drives x miles. Jon started with 240 gallons of fuel and his truck uses 0.15 gallons of fuel for each mile he drives.

Step 2: Writing the Equation

We know that the amount of fuel in Jon's tank decreases as he drives. So, we can write the equation as:

f(x) = 240 - 0.15x

This equation says that the amount of fuel in Jon's tank after he drives x miles is equal to 240 gallons (the amount of fuel he started with), minus 0.15 gallons for each mile he drives.

Step 3: Interpreting the Equation

The function f(x) = 240 - 0.15x is a linear equation, which means that it is a straight line on a graph. The value 240 is the y-intercept, which means that when x = 0, the y-value of the function is 240 (the amount of fuel in Jon's tank when he starts driving). The value -0.15 is the slope of the line, which tells us how much the y-value decreases for each unit increase in x (in this case, how much the fuel decreases for each mile Jon drives).

Step 4: Conclusion

So, the equation f(x) = 240 - 0.15x can be used to approximate the amount of fuel in Jon's semitruck after he drives x miles. The equation is linear and can be written in the form f(x) = mx + b, where m = -0.15 (the slope of the line) and b = 240 (the y-intercept).

The value of the variables in the parallelogram are such that:

This is a parallelogram which means that angles on the same line will add up to 180 degrees.

The value of x is therefore:

( x - 5 ) + ( 2x + 11 ) = 180

3x + 6 = 180

x = ( 180 - 6 ) / 3

x = 58

The value of y is:

2 y + ( 58 - 5 ) = 180

2 y = 180 - 53

y = 127 / 2

y = 63.5

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The probability that none of them will default 0.0066

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

(a) If 1,000 student loans are made, what is the probability of fewer than 50 defaults?

It's a binomial problem but the large n requires using a normal approximation.

mean = np = 1000*0.07 = 70

std = sqrt(npq) = sqrt(70*0.93) = 8.0685

z(50) = (50-70)/[8.0685] = -2.4788

P(# of defaults < 50) = P(z<-2.4788) = 0.0066

(b) More than 100?

z(100) = (100-70)/8.0685 = 3.7182

P(defaults > 100) = P(z>3.7182) = 0.00010035

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Correct question

The default rate on government-guaranteed student loans at a certaing public 4-year institution is 7% (a) If 1,000 student loans are made, what is the probability of fewer than 50 defaults? (b) More than 100? Show your work carefully.

Answer:

11/3

Step-by-step explanation:

-4(r-2/3)+4<-8

-4r+8/3+4<-8

8/3+4<-8+4r

8/3+4+8<4r

44/3<4r

44/12=r

11/3=r

Answer:

So the value of 5x-2w+t, with x=3, w=1/2, and t=8 is 22.

Step-by-step explanation:

Given,

The equation is  

5x-2w+t

and also given the

x=3

w=1/2

and t=8

Now ,

if we substitute the value of x,w and t,

We get,

5 × 3 - 2 × (1/2) + 8

= 15 - 1 + 8

= 22

So the value of 5x-2w+t, with x=3, w=1/2, and t=8 is 22.

Answer:

[tex]\sf \dfrac{p}{q}=\dfrac{\pm1}{\pm1},\dfrac{\pm1}{\pm3},\dfrac{\pm7}{\pm1},\dfrac{\pm7}{\pm3}=\pm 1, \dfrac{\pm1}{\pm3},\pm 7, \dfrac{\pm7}{\pm3}[/tex]

Step-by-step explanation:

Given polynomial:

[tex]f(x)=-3x^3-5x^2+x-7[/tex]

If P(x) is a polynomial with integer coefficients and if p/q is a root of P(x), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).

Possible p-values

Factors of the constant term:  ±1, ±7

Possible q-values

Factors of the leading coefficient:  ±1, ±3

Therefore, all the possible values of p/q:

[tex]\sf \dfrac{p}{q}=\dfrac{\pm1}{\pm1},\dfrac{\pm1}{\pm3},\dfrac{\pm7}{\pm1},\dfrac{\pm7}{\pm3}=\pm 1, \dfrac{\pm1}{\pm3},\pm 7, \dfrac{\pm7}{\pm3}[/tex]

Substitute each possible rational root into the function:

[tex]x=-1 \implies f(-1)=-3(-1)^3-5(-1)^2+(-1)-7=-10[/tex]

[tex]x=1 \implies f(1)=-3(1)^3-5(1)^2+(1)-7=-14[/tex]

[tex]x=-7 \implies f(-7)=-3(-7)^3-5(-7)^2+(-7)-7=770[/tex]

[tex]x=7 \implies f(7)=-3(7)^3-5(7)^2+(7)-7=-1274[/tex]

[tex]x=-\dfrac{1}{3} \implies f\left(-\dfrac{1}{3}\right)=-3\left(-\dfrac{1}{3}\right)^3-5\left(-\dfrac{1}{3}\right)^2+\left(-\dfrac{1}{3}\right)-7=-\dfrac{70}{9}[/tex]

[tex]x=\dfrac{1}{3} \implies f\left(\dfrac{1}{3}\right)=-3\left(\dfrac{1}{3}\right)^3-5\left(\dfrac{1}{3}\right)^2+\left(\dfrac{1}{3}\right)-7=-\dfrac{22}{3}[/tex]

[tex]x=-\dfrac{7}{3} \implies f\left(-\dfrac{7}{3}\right)=-3\left(-\dfrac{7}{3}\right)^3-5\left(-\dfrac{7}{3}\right)^2+\left(-\dfrac{7}{3}\right)-7=\dfrac{14}{9}[/tex]

[tex]x=\dfrac{7}{3} \implies f\left(\dfrac{7}{3}\right)=-3\left(\dfrac{7}{3}\right)^3-5\left(\dfrac{7}{3}\right)^2+\left(\dfrac{7}{3}\right)-7=-70[/tex]

As f(p/q) ≠ 0, none of the possible rational roots are actual roots of the given polynomial.

The values of x and y are 30 and 80

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

The parallel line and the transversal

The value of y is calculated as

y + 25 = 105 ---- alternate angle theorem

So, we have

y = 80

For x, we have

3x - 15 + 105 = 180 --- coresponding angle

So, we have

3x = 90

Divide

x = 30

Here, we make use of

2x + 54 = 180 --- sum of alternate interior angles

So, we have

2x = 126

Divide

x = 63

This is calculated as

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

So, we have

Slope = (6 - 6)/(5 - 2)

Slope = 0

Hence, the slope is 0

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A reasonable exponent is one that is fractional. For instance, 412 4 1 2 can be used to represent the number 4.

Given,

[tex]$\left(\frac{4 y^2}{5}\right)^2[/tex]

Apply exponent rule: [tex]$\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$[/tex]

[tex]$=\frac{\left(4 y^2\right)^2}{5^2}[/tex]

Simplify [tex]$\left(4 y^2\right)^2: 16 y^4$[/tex]

[tex]$=\frac{16 y^4}{5^2}[/tex]

The we get,

[tex]$& =\frac{16 y^4}{25}[/tex]

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The value of a, b, and c are 1, -2, and 6 respectively.

The y-intercept of this quadratic function is 6.

The axis of symmetry of this quadratic function is 1.

The vertex of this quadratic function is (1, 5).

Mathematically, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry, Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = x² - 2x + 6, we have:

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-2)/2(1)

Axis of symmetry, Xmax = 2/2 = 1.

Vertex (h, k) = (1, 5).

In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).

y-intercept = 6.

Lastly, we would create a table and then graph the quadratic function as follows;

x         y

0         6

2         2

5         11

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Complete Question:

Quadratic Function f(x) = x² - 2x + 6 2.

1. List a, b, and c.

2. Find the axis of symmetry.

3. Find the vertex.

4. What is the y-intercept?

5. Create a table and graph.

The functions are matched as follows -

y = √x ⇒  d. Square root

y = |x| ⇒  g. Absolute value

y = x² ⇒  h. Quadratic

y = 1/x² ⇒  f. Reciprocal Squared

y = 1/x ⇒  b. Reciprocal

y = x³ ⇒  a. Cubic

y = ∛x ⇒  e. Cube root

y = x ⇒  c. Linear

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The first function is given as -

y = √x

Since, this function contains a square root symbol, so it is a square root function.

The second function is given as -

y = |x|

Since, this function contains absolute value symbol, so it is a absolute value function.

The third function is given as -

y = x²

Since, this function contains power of 2 and x is squared, so it is a quadratic function.

The fourth function is given as -

y = 1/x²

Since, this function contains power of 2, x is squared and the value is reciprocal of x², so it is a reciprocal squared function.

The fifth function is given as -

y = 1/x

Since, this function contains reciprocal value of x, so it is a reciprocal function.

The sixth function is given as -

y = x³

Since, this function contains power of 3 and x is cubed, so it is a cubic function.

The seventh function is given as -

y = ∛x

Since, this function contains a cube root symbol, so it is a cube root function.

The second function is given as -

y = x

Since, this function contains y equal to x, so it is a linear function.

Therefore, all the different functions are identified.

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We can see that the exponential model is better

The main difference between a linear and an exponential function is the way they change as their input variable (usually denoted as x) increases.

In summary, linear functions have a constant rate of change, while exponential functions have an increasing rate of change.

For the linear function;

f(x) = 946(6) + 3349

= 9025

For the exponential function;

g(x) = 3866e^0.138(6)

g(x) = 8848

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Answer:

Below

Step-by-step explanation:

Put '9' where  'n' is and compute

(9)^2 + 6(9) ÷ 3 =

81  +    54 ÷3  =

81  + 18 =   99

Answer:

a

Step-by-step explanation:

Answer:

6)  x = 6

7) x = 4

8) x = 4

9) x = 6

10) x = 6

Step-by-step explanation:

This is based on Dr. Henry Borenson's method of using pawns to explain algebraic equations.  Frankl I find using variables more intuitive

Let each pawn represent an x in the equations

6.
x + 8 = 10 + 4

x = 10 + 4 - 8

x = 14 - 8 = 6

7.  

x + x = 4 + x
2x = 4 + x
2x - x = 4

x = 4

8.

x + x + x + 2 = 7 + 7
3x + 2 = 14

3x = 14 - 2

3x = 12

x = 12/3

x = 4

9.

2x + 4 = x + 10

2x - x = 10 - 4

x = 6

10

3x = x + 10 + 2

3x = x + 12

3x - x = 12

2x = 12

x = 6

The inequality is written as 15x + 70y ≤ 920. Then the region below the line is the solution to inequality.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Serenity is assembling beaded jewelry with no more than 920 beads she presently has in inventory. Bracelets use 15 beads and necklaces use 70 beads.

Let 'x' be the number of bracelets and 'y' be the number of necklaces. Then the inequality is given as,

15x + 70y ≤ 920

The region below the line is the solution to inequality.

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PLEASE GIVE BRAINLIEST!
thank you and have a good day :)

Answer:

20

Step-by-step explanation:

1/5(3+2+5)^2

3+2+5 = 10

10^2 = 100

100/5 = 20

If a rectangular room is 2 meters longer than it is wide, and its perimeter is 24 meters then the  dimensions of the room: 7 meter x 5 meter

Perimeter is a mathematical term, it indicates total outer boundary of a figure, we define it only for two dimensional figures.

Perimeter = Sum of length of the all the sides

Let x be the width of the room in meters.

Then the length of the room is 2 meters longer, which means it is x+2 meters.

In this case, we know that the perimeter is 24 meters.

So we can set up an equation:

Perimeter = 2Length + 2Width

Substituting the values we know:

24 = 2(x+2) + 2x

Simplifying the equation:

24 = 2x + 4 + 2x

24 = 4x + 4

20 = 4x

x = 5

So the width of the room is 5 meters, and the length is x+2 = 7 meters.

Therefore, the dimensions of the room are 7 meters by 5 meters.

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Answer:

The answer is thirty (30)

Part A:

Look at photo

Part B:

After 5 minutes, the altitude of the airplane is 20,500 feet. This means that the airplane has been descending for 5 minutes and has lost an altitude of 10,250 feet.

After 30 minutes, the altitude of the airplane is -29,250 feet. This means that the airplane has been descending for 30 minutes and has lost an altitude of 60,000 feet. The negative value of the altitude indicates that the airplane has landed or is close to landing.

At both 5 minutes and 30 minutes, the airplane is descending. The rate of descent is constant, as represented by the slope of the equation, and is equal to -1025 feet per minute. At 5 minutes, the airplane is still at a high altitude, while at 30 minutes the airplane has landed or is close to landing, as indicated by the negative value of the altitude.

Answer:

Step-by-step explanation:

Part A:

x  |  y  |  Equation

0  | 30,750 | y = -1025*0 + 30,750

5  | 27,250 | y = -1025*5 + 30,750

8  | 23,750 | y = -1025*8 + 30,750

10 | 20,250 | y = -1025*10 + 30,750

30 | -20,250 | y = -1025*30 + 30,750

Part B:

After 5 minutes, the altitude is 27,250 feet. This means that the airplane has been descending steadily for 5 minutes and is now at a lower altitude than when it started.

After 30 minutes, the altitude is -20,250 feet. This means that the airplane has been descending steadily for 30 minutes and is now much lower than when it started. The airplane is close to the ground and about to land.

Answer:

860,000.

Step-by-step explanation:

If the sales in 2022 were up 75% from 800,000, the sales in 2022 would be 800,000 + (800,000 * 75%) = 800,000 + 600,000 = 1,400,000.

To find the sales for 2021, we'll have to use the average annual growth rate to find the sales in between 2012 and 2022.

Let's assume that the sales grew linearly, so the average annual growth rate would be (1,400,000 - 800,000) / (2022 - 2012) = 600,000 / 10 = 60,000.

The sales in 2021 would then be 800,000 + 60,000 = 860,000.

Answer:

151.37

Step-by-step explanation:

Answer:

151.372868 but rounded is 151.37

Step-by-step explanation:

1863.4/12.31=151.372868 rounded is 151.37

300.5 ml of antihistamine is needed for a 100​-pound person to take in a​ week

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

1 day = 24 hours

1 week = 7 days = 24 hours per day * 7 days = 168 hours

A typical dose for a 100​-pound person is 22 mg every six hours. Hence for one week:

Dosage in one week = (22 mg per 6 hours) * 168 hours = 616 mg

Antihistamine also comes in a liquid form with a concentration of 12.3 ​mg/ 6 mL. For 616 mg:

Amount of antihistamine = 616 mg / (12.3 ​mg/ 6 mL) = 300.5 ml

300.5 ml of antihistamine is needed

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Answer:

Step-by-step explanation:

Evaluate the expression 10 - 2x for the x-values given below.

a. x = 2 \quad b. x = \frac {1}{2}\quad c. x = -2

a.x=2b.x=

2

1

​

a.x=-2

Answer:

The new slope is 2,

New y-intercept is - 7

Line is flatter since slope has reduced

Step-by-step explanation:

The value of x is 11.78.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

In a figure, the four angles sum must equal 360.

Now,

The four angles are:

6x + 7, 5x + 13, 12x + 9, and 73

Solve for x.

6x + 7 + 5x + 13 + 12x + 9 + 73 = 360

23x + 89 = 360

23x = 360 - 89

23x = 271

x = 11.78

Thus,

x is 11.78.

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Complete question:

In the figure measurement angle 1 is 6x + 7°, measurement angle 2 equals 5x + 13°, and measurement angle 3 equals 12x + 9° and measurement angle 4 equals 73°.

What is the value of x?

Answer: Balu originally had 40 sweets.

Step-by-step explanation:

Let x be the number of sweets Balu originally had.

After Amal gives one third of his sweets to Balu, Balu's number of sweets becomes x + (1/3)x = (4/3)x.

After Balu gives one third of his sweets to Chandran, Chandran's number of sweets becomes 40 + (1/3)(4/3)x = 40 + (1/3)x.

After Chandran gives one third of his sweets to Amal, Amal's number of sweets becomes (2/3)x + (1/3)(40 +(1/3)x) = (2/3)x + (1/3)x + 40/3 = (5/3)x + 40/3.

Since all three of them now have the same number of sweets, we can set the number of sweets each of them has equal:

(4/3)x = (5/3)x + 40/3.

Now, we will isolate x by rearranging the equation. Subtracting (5/3)x from both sides, we get:

(4/3)x - (5/3)x = 40/3

Simplifying the left side:

-x/3 = 40/3

Dividing both sides by -1/3:

x = 40

Thus, Balu originally had 40 sweets.