Factor completely x3 + 8x2 − 3x − 24. (x − 8)(x2 − 3) (x + 8)(x2 + 3) (x − 8)(x2 + 3) (x + 8)(x2 − 3)

Answer:

The shortest altitude is 6.72 cm

Step-by-step explanation:

Given that the side lengths are

24 cm, 25 cm, 7 cm

The area of a triangle =

[tex]A = \sqrt{s \cdot (s-a)\cdot (s-b)\cdot (s-c)}[/tex]

Where;

s = Half the perimeter = (24 + 25 +  7)/2 = 28

A = √((28×(28 - 24)×(28 - 25)×(28 - 7)) = 84 cm²

We note that 84/7 = 12

Therefore, the triangle is a right triangle with hypotenuse = 25, and legs, 24 and 7, the height of the triangle = 7

To find the shortest altitude, we utilize the formula for the area of the triangle A = 1/2 base × Altitude

Altitude  = A/(1/2 ×base)

Therefore, the altitude is inversely proportional to the base, and to reduce the altitude, we increase the base as follows;

We set the base to 25 cm to get;

Area of the triangle A =  1/2 × base × Altitude

84 = 1/2 × 25 × Altitude

Altitude = 84/(1/2 × 25) = 6.72 cm

The shortest altitude = 6.72 cm.

Answer:

Step-by-step explanation:

JK = JO = 4

MN = NO = 6   ⇒  LM = 18 - 6 = 12

KL = LM = 12

NJ = NO + OJ = 6 + 4 = 10

JL = JK  + KL = 4 + 12 = 16

LN = 18

P = NJ + JL + LN = 10 + 16 + 18 = 44

Answer:

63°

Step-by-step explanation:

complement means that the two angles add to 90°

90 - 27 = 63°

Answer:

Step-by-step explanation:

complement angles have sum of angles=90°

∠AOC=27

∠BOC=90-27=63°

Answer:

267x

Step-by-step explanation:

Multiplication  means times

267 * x

267x

Answer:

267x

when you multiply a number by a variable, you can combine the terms if there is no coefficient for the variable.

Answer:

On-time Buses: 75%

Running late Buses: 13.46%

Step-by-step explanation:

Part 1: Solve for the probability of Jerry owning an "on-time" bus

Of the 48 buses that run on time, Jerry owns 36 of them. Therefore, the probability of a bus running on time being owned by Jerry will be solved with the ratio of 36 buses to 48 buses.

Part 2: Solve for the probability of Jerry owning a "running late" bus

Of the 52 buses that run late, Jerry owns 7 of them. Therefore, the probability of a bus running late & being owned by Jerry will be solved with the ratio of 7 buses to 52 buses.

Answer:

x = 10

Step-by-step explanation:

5x - 6 = 44

Add 6 on both sides of the equation.

5x = 50

Divide by 5 on both sides of the equation.

x = 10

So, the value of x is equal to 10

Answer:

x=10

Step-by-step explanation:

5x-6=44

grouping constants and numbers with coefficient of x we get

5x=44+6

5x=50

5x/5=50/5

x=10

Its $2.99 because 6.94-3.95=2.99 so $2.99

Answer:

$2.99

Step-by-step explanation:

To find the value of the drawing tablet, we can use the known total cost and the cost of the pencils.  Let's build an equation, where x represents the cost of the drawing tablet:

x + 3.95 = 6.94

Now let's solve the equation for x to find the cost of the tablet.

x + 3.95 = 6.94

x + 3.95 - 3.95 = 6.94 - 3.95

x = 2.99

So the cost of the drawing tablet is $2.99.

Cheers.

Answer:

x=-106/37

y=70/37

Step-by-step explanation:

I chose to set up the problem as a matrix to solve here.

(Another way to do this would be to isolate one variable in one of the equations, substitute it into the other equation, solve for that, and then plug it back in to get the final variable.)

My work is in the attachment. Lmk if you have any questions.

Answer:

[tex]\huge\boxed{\left\{\begin{array}{ccc}x=-\dfrac{106}{37}\\y=\dfrac{70}{37}\end{array}\right}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}5x-3y=-20&\text{multiply both sides by 5}\\4x+5y=-2&\text{multiply both sides by 3}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}25x-15y=-100\\12x+15y=-6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad37x=-106\qquad\text{divide both sides by 37}\\.\qquad\boxed{x=-\dfrac{106}{37}}[/tex]

[tex]\text{Substitute it to the first equation}\\\\5\left(-\dfrac{106}{37}\right)-3y=-20\\\\-\dfrac{530}{37}-3y=-20\qquad\text{multiply both sides by (-37)}\\\\(-37\!\!\!\!\!\diagup)\left(-\dfrac{530}{37\!\!\!\!\!\diagup}\right)-(-37)(3y)=(-37)(-20)\\\\530+111y=740\qquad\text{subtract 530 from both sides}\\\\111y=210\qquad\text{divide both sides by 111}\\\\y=\dfrac{210}{111}\\\\y=\dfrac{210:3}{111:3}\\\\\boxed{y=\dfrac{70}{37}}[/tex]

Answer:

increasing

Step-by-step explanation:

a function is increasing when y increases as x increases

Since the graph goes up as x increases, the function f(x) is increases between -2 and -1

Answer:

7.834 × 10^-8

Step-by-step explanation:

= 7.834 × 10^-8

(scientific notation)

= 7.834e-8

(scientific e notation)

= 78.34 × 10^-9

(engineering notation)

(billionth; prefix nano- (n))

= 0.00000007834

(real number)

^ means the number after is exponent.

Answer:

-3

Step-by-step explanation:

-7+4=-3

The absolute value of -3 is 3

The negative sign in front of the absolute value bracket makes it -3

Answer:

y=5sec(3x) +6

y=-3tan(x+2pi)

y=-10cot(x/2-2pi)

y=-1/2cos(5x/6+pi)

y =-1/3sin(x/3)

y = 2/3csc(x/4)+6

The functions in increasing order of their periods are given below.

y=5sec(3x) +6

y=-3tan(x+2pi)

y=-10cot(x/2-2pi)

y=-1/2cos(5x/6+pi)

y =-1/3sin(x/3)

y = 2/3csc(x/4)+6

As y = 2/3csc(x/4)+6 gives a high value than the other, it is considered the highest.

Ascending order way going up from small value to excessive cost and textual content from A to Z. Descending order manner arranging the numbers from largest to smallest and textual content from Z to A. while the names are arranged for a list, then it is usually arranged in A to Z order, alphabetically.

Steps to find the Period of a Function

Learn more about functions here: https://brainly.com/question/2833285

#SPJ2

A is vowel.

first condition prevents any vowels, thus there will be no A at all

Answer:

64 mph

Step-by-step explanation:

Given that:

Speed for the first 3 hours = 52 mph

Average speed for 4 hours = 55 mph

To find:

Speed for the next hour = ?

Solution:

Formula for average speed is given as:

[tex]Average\ Speed = \dfrac{Total\ Distance}{Total \ Time \ Taken}[/tex]

Formula for Distance:

[tex]Distance =Speed \times Time[/tex]

Distance traveled in first 3 hours:

[tex]Distance =52\times 3 = 156\ miles[/tex]

Let the speed for the next hour = u mph

Distance traveled in 1 hour = [tex]u \times 1 = u\ miles[/tex]

Total distance traveled = (156 + u) miles

Total time = 4 hours

Average Speed = 55 mph

Putting the values in formula:

[tex]55 = \dfrac{156+u}{4}\\\Rightarrow 220 = 156+u\\\Rightarrow \bold{u = 64\ mph }[/tex]

So, the answer is: 64 mph

Answer:

358 and remainder of 3

Step-by-step explanation:

1. Divide it like any other problem

Hope this helps

Answer:

Step-by-step explanation: Given that a civil servant own a car is 1/6.

A) The Pr. that each own a car = Pr of each multiplied by the other.

Pr = 1/6 ×1/6

P = 1/36

B) Pr that only one owns a car

= 1/6 × (1-1/6) + 1/6 × (1-1/6)

= 1/6 × 5/6 + 5/6 × 1/6

= 5/36 + 5/36

= 10/36

= 5/18

Answer:

[tex]-40c^{2} d^{2} -32cd[/tex]

Step-by-step explanation:

-20c³ is the expression which is equivalent to (-5cd⁻⁴)(2cd²)².

To simplify the given expression, (-5cd⁻⁴)(2cd²)², we can apply the power of a product rule, which states that (ab)² is equal to a²b².

Let's break down the expression step by step:

(-5cd⁻⁴)(2cd²)²

First, let's square the expression (2cd²)²:

(2cd²)² = (2)²(c)²(d²)² = 4c²d⁴

Now, we substitute this result back into the original expression:

(-5cd⁻⁴)(4c²d⁴)

To simplify further, we can multiply the coefficients and combine the variables:

(-5)(4) = -20

(c)(c²) = c³

(d⁻⁴)(d⁴) = 1

Putting it all together, the expression (-5cd⁻⁴)(2cd²)² simplifies to -20c³.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ2

Answer:

44

Step-by-step explanation:

base = 3- -5 = 8

height = 8 - -3 = 11

1/2 bh

1/2(8)(11) = 44

Answer:

Following are the answer to this question:

Step-by-step explanation:

Some of the information is missing which is defined in the attached file, and the solution to this question can be defined as follows:    

When the point AC ≅ BC point is in the equal distance from point A and Point B then Point A is perpendicular and the bisector point is in equally distant from the endpoints of that intersects points.

please find the attachment of the full question:

Answer:

If segment AC ≅ segment BC, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.

Step-by-step explanation:

Answer:

39.35 sec

Step-by-step explanation:

Given that:

The winning time is represented by the function:

T = 46.97 - 0.099x

Where x = year ; x = 0 corresponding to 1920

According to the formula, what was the winning time in 1997?

first find the value of x;

x = 1997 - 1920 = 77 years

Nowing plugging the value of x in the function :

T = 46.97 - 0.099(77)

T = 46.97 - 7.623

T = 39.347 seconds

T = 39.35 s

===================================================

Explanation:

The only given number here is the 20 degree angle. So we'll start with that. This is an inscribed angle, which doubles to 2*20 = 40, and this is the measure of the arc the inscribed angle cuts off (inscribed angle theorem). Consequently, it means that central angle b is also 40 degrees.

With b = 40, we can see that c = 180-b = 180-40 = 140. This is because b+c = 180 as the two angles are supplementary.

Answer:

140 degrees

Step-by-step explanation:

If the given angle is 20 degrees then the other unknown angle would also be 20 degrees because this triangle is an isosceles triangle. 20+20+20=180 proving the triangle sum theorem.

[tex](x-9)^2=15\\x-9=\sqrt{15} \vee x-9=-\sqrt{15}\\x=9+\sqrt{15} \vee x=9-\sqrt{15}[/tex]

Answer:

Rushmont

Step-by-step explanation:

Trenton can be ruled out due to its constant increase rate of 1.5. Rushmont can be ruled out because it goes from an increase rate of ~1.8 to an increase rate of 1.4 to an increase rate of 1.3 (exponential decay, not growth, so possibly...). Springville has a rate of ~1.9, then 1.475, then 1.3, also exponential decay. However, y\ =\ x\frac{38}{10}-185 goes through all of springville's points (or close to it), so Rushmont must be the answer.

The town that has growth that follows an exponential model is Town B, Rushmont where the population increases or decreases at a consistent rate over time.

In this case, analyze the population data from the three towns to determine which one exhibits exponential growth.

Let's go through each option briefly:

A. Springville:

B. Rushmont:

C. Trenton:

Based on the analysis above, the town that shows growth following an exponential model is Rushmont (B). It exhibits a consistent increase in population over time, suggesting exponential growth.

Learn more about population models here:

https://brainly.com/question/32701660

#SPJ4

Answer:

Kyra=15 points

Liam=20 points

30 points=y=4/3x+5

Step-by-step explanation:

I graphed each equation and point on the graph given

HOPE THIS HELPS!!! :)

PLEASE CORRECT ME IF IM WRONG

Answer:

A

Step-by-step explanation:

Looking for the graph which

crosses the x- axis at x = - 1 ( x- intercept )

crosses the y- axis at y = - 3 ( y- intercept )

has a minimum value of - 4 at x = 1, that is vertex = (1, - 4) and minimum U

The required graph is A

The graph A should match the description.

learn more about the graph here: https://brainly.com/question/19661552

Answer:

sqrt(30)+sqrt(50) = 12.5482933869171364     which is between   m and n    12 and 13

Answer:

The value = 1

Step-by-step explanation:

Here in this question, we are interested in calculating the product of the trigonometric identities given.

To adequately calculate this correctly, we shall need to express the trigonometric identities in their normal division form which is as follows ;

Mathematically;

cotA = 1/tanA

let’s leave sin A

sec A = 1/cos A

So inputing the values of the following, we have ;

1/tan A * sin A * 1/cos A

This can be written as;

1/tan A * sin A/cos A

Mathematically; sinA/cos A = tan A

making that substitution, we have;

1/tan A * tan A

= tan A/tan A = 1

Answer:

3900

Step-by-step explanation:

since its to the nearest 100th we use the common rule that if the number is greater than half way then we round up otherwise if it is less then we round down. In the number 3867, 867 is greater than 850 so we round up. It becomes 3900 then.

Answer:

Step-by-step explanation:

c - 10  ≥  15 =

c  ≥ = 15 + 10

c  ≥ = 25

c  = 26 ( or numbers above 26)