If QR = 9 and ST = 13 calculate LM.

Answer: 0

Step-by-step explanation:

The given equation: [tex]6a^2+5a+4=3[/tex]

Subtract 3 from both the sides, we get

[tex]6a^2+5a+1=0[/tex]

Now , we can split 5a as 2a+3a and [tex]2a\times 3a = 6a^2[/tex]

So, [tex]6a^2+5a+1=0\Rightarrow\ 6a^2+2a+3a+1=0[/tex]

[tex]\Rightarrow\ 2a(3a+1)+(3a+1)=0\\\\\Rightarrow\ (3a+1)(2a+1)=0\\\\\Rightarrow\ (3a+1)=0\text{ or }(2a+1)=0\\\\\Rightarrow\ a=-\dfrac{1}{3}\text{ or }a=-\dfrac{1}{2}[/tex]

At [tex]a=-\dfrac{1}{3}[/tex]

[tex]2a+1=2(-\dfrac{1}{3})+1=-\dfrac{2}{3}+1=\dfrac{-2+3}{3}=\dfrac{1}3{}[/tex]

At [tex]a=-\dfrac{1}{2}[/tex]

[tex]2a+1=2(-\dfrac{1}{2})+1=-1+1=0[/tex]

Since, [tex]0< \dfrac{1}{3}[/tex]

Hence, the possible value of 2a+1 is 0.

Answer:

inverse = ( log(x+4) + log(4) ) / (2log(4)), or

c. y = ( log_4(x+4) + 1 ) / 2

Step-by-step explanation:

Find inverse of

y = 4^(-6x+5) / 4^(-8x+6)   - 4

Exchange x and y and solve for y.

1. exchange x, y

x = 4^(-6y+5) / 4^(-8y+6)   - 4

2. solve for y

x = 4^(-6y+5) / 4^(-8y+6)   - 4

transpose

x+4 = 4^(-6y+5) / 4^(-8y+6)

using the law of exponents

x+4 = 4^( (-6y+5) - (-8y+6) )

simplify

x+4 = 4^( 2y - 1 )

take log on both sides

log(x+4) = log(4^( 2y - 1 ))

apply power property of logarithm

log(x+4) = (2y-1) log(4)

Transpose

2y - 1  = log(x+4) / log(4)

transpose

2y = log(x+4) / log(4) + 1 = ( log(x+4) + log(4) ) / log(4)

y = ( log(x+4) + log(4) ) / (2log(4))

Note: if we take log to the base 4, then log_4(4) =1, which simplifies the answer to

y = ( log_4(x+4) + 1 ) / 2

which corresponds to the third answer.

Answer:

The correct option is;

As x → ∞ f(x) → -∞, and  as x → -∞ f(x) →∞

Step-by-step explanation:

The values given are;

x,      f(x)

-4,     18

-3,     9

-2,     6

-1,      3

0,      0

1,      -3

2,     -6

3,     -9

4,     -18

Based on the table, as the magnitude of x increases in the positive direction,  the magnitude of f(x) increases in the negative direction

Therefore, the correct option that best predicts the end behavior of the graph of f(x) is As x → ∞ f(x) → -∞, and  as x → -∞ f(x) →∞.

Answer:No solution

Step-by-step explanation:An absolute value equation cannot equal a negative number

Answer:

9th term geometric sequence (a9) = 1 / 256

Step-by-step explanation:

Given:

Geometric sequence 1,1/2,1/2²

First term (a) = 1

Common ratio (r) = A2 / A1 = (1/2) / 1 = 1/2

Number of term (n) = 9

Find:

9th term geometric sequence (a9)

Computation:

[tex]an = ar^{n-1}[/tex]

a9 = ar⁹⁻¹

a9 = (1)(1/2)⁸

a9 = (1/2)⁸

a9 = 1/256

9th term geometric sequence (a9) = 1 / 256

Answer: 1,300 students went on the trip

Step-by-step explanation: So we know that 65% filled the seats so let's turn that into a fraction.  [tex]\frac{65}{100}[/tex] . Now we know that there are 2,000 seats in total so let's put that into a fraction. [tex]\frac{x}{2,000}[/tex]  The x represents the students that went on the trip.

               [tex]\frac{65}{100} = \frac{x}{2,000}[/tex]  we have to cross multiply

   65(2,000) = 100 (x)

    130,000   =  100 (x)          

    130,000   ÷  100                            

        1,300    =   x          So now we know that 1,300 went to the trip students

Answer:

[tex] Area = 2,031ft^2 [/tex]

Total weight of gravel on the roof = [tex] 24,372 pounds [/tex]

Step-by-step Explanation:

The area Adams planned to cover with gravel can be divided into 3 rectangles as shown in the diagram attached.

We would have 3 rectangles. See the attachment below to check out how we arrive at the dimensions of the 3 rectangles.

Area of rectangle = L*W

Area to be covered by gravel = area of rectangle 1 + area of rectangle 2 + area of rectangle 3

Area to be covered with gravel = [tex] (30*17) + (13*9) + (52*27) [/tex]

[tex] Area = (30*17) + (13*9) + (52*27) = 2,031ft^2 [/tex]

Total weight of gravel on the roof = 12 pounds per square foot multiplied by total area of the roof to be covered = [tex] 12 * 2031 = 24,372 pounds [/tex]

Answer:

2031 and 16925

Step-by-step explanation:

Answer:

27/2 units^3

Step-by-step explanation:

Formula for volume: l * w * h   or   a * h  because l * w = area.

27/5 ( which is area ) * 5/2 ( the height ) = 27/2

i hope this helps

The volume of the following rectangular prism is 27/2 units^3

We know that the rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The volume of a rectangular prism = Length X Width X Height

We are given the dimensions as Length = 5/2

Area = 27/5

Here a * h  because l * w = area.

Volume = Length X Width X Height

= area X Width

= 27/5 x 5/2

= 27/2

The volume is 27/2 units^3.

Learn more about a rectangular prism;

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Answer:

9.48*

Step-by-step explanation:

This is a right triangle. The formula for solving the Hypotenuse, or the longest side of the right triangle is A^2 + B^2 = C^2. If we put the numbers from the problem into the formula this is what we get :

3^2 + 9^2 = C^2

9 + 81 = C^2

90 = C^2

9.48 = C

* This is rounded, the exact number is closer to 9.486832980505138. Your class should tell you what to round to.

Answer:

The answer would be A. 3√10 blocks

Step-by-step explanation:

I have had this question and its 3√10 blocks.
Hope this helps you other people :))

Answer:

False roots are x = -1 or x = 5/2 or x = 3/2

Step-by-step explanation:

Solve for x:

4 x^3 - 12 x^2 - x + 15 = 0

The left hand side factors into a product with three terms:

(x + 1) (2 x - 5) (2 x - 3) = 0

Split into three equations:

x + 1 = 0 or 2 x - 5 = 0 or 2 x - 3 = 0

Subtract 1 from both sides:

x = -1 or 2 x - 5 = 0 or 2 x - 3 = 0

Add 5 to both sides:

x = -1 or 2 x = 5 or 2 x - 3 = 0

Divide both sides by 2:

x = -1 or x = 5/2 or 2 x - 3 = 0

Add 3 to both sides:

x = -1 or x = 5/2 or 2 x = 3

Divide both sides by 2:

Answer:  x = -1 or x = 5/2 or x = 3/2

Answer:

False

Step-by-step explanation:

f(x) = 4x³ - 12x² - x + 15

Set output to 0.

Factor the function.

0 = (x + 1)(2x - 3)(2x - 5)

Set factors equal to 0.

x + 1 = 0

x = -1

2x - 3 = 0

2x = 3

x = 3/2

2x - 5 = 0

2x = 5

x = 5/2

4 is not a lower bound for the zeros of the function.

Answer:

$14,580

Step-by-step explanation:

To start off, 10% of 20,000-one easy way to do this is to multiply 20,000 by 0.1, which is 10% in decimal form

-In doing that, you get 2,000

-Now the question says that the value is depreciated which means it goes down in value, so subtract 2,000 from 20,000 to 18,000

-the value of the car after one year is now $18,000

Now, let's move to the second year.  This time find 10% of 18,000

-multiply 18,000 by 0.1 to get 1,800

-since the value is depreciating, or becoming less, we will subtract 1,800 from 18,000 to get 16,200

-the value of the car after two years is now $16,200

Finally, let's look at the value of the car after three years.  Only this time, we will now find 10% of 16,200

-multiply 16,200 by 0.1 to get 1,620

-since value is being depreciated, or lessened, we will once again be subtracting.  Subtract 1,620 from 16,200 to get 14,580

Therefore, the value of the car after three years is now $14,580.

Answer:

Hey there!

First, we want to find the radius of the circle, which equals the length of line segment AC.

Length of line segment AC, which we can find with the distance formula: [tex]\sqrt{25\\[/tex], which is equal to 5.

The equation for a circle, is: [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h, k) is the center of the circle, and r is the radius.

Although I don't know the center of the circle, I can tell you that it is either choice B or D, because the radius, 5, squared, is 25.

Hope this helps :) (And let me know if you edit the question)

Answer:  The equation of the circle is (x+1)²+(y+1)² = 25

Step-by-step explanation:  Use the Pythagorean Theorem to calculate the length of the radius from the coordinates given for the triangle location:  A(-1,-2), B(-1,1) and C(3,1)  The sides of the triangle are AB=3, BC=4, AC=5.

Use the equation for a circle: ( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.

As the directions specify, the radius is AC, so it makes sense to use the coordinates of A (-1,-2) as the center.  h is -1, k is -2  The radius 5, squared becomes 25.

Substituting those values, we have (x -[-1])² + (y -[-2])² = 25 .

When substituted for h, the -(-1) becomes +1 and the -(-2) for k becomes +2.

We end up with the equation for the circle as specified:

(x+1)²+(y+1)² = 25

A graph of the circle is attached. I still need to learn how to define line segments; the radius is only the segment of the line between the center (-1,-2) and (1,3)

Work Shown:

sin(angle) = opposite/hypotenuse

sin(35) = 10/x

x*sin(35) = 10

x = 10/sin(35)

x = 17.434467956211 make sure your calculator is in degree mode

x = 17.4

Answer:

[tex]\boxed{17.4}[/tex]

Step-by-step explanation:

sin [tex]\theta[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

sin (35) = [tex]\frac{10}{x}[/tex]

x = [tex]\frac{10}{sin(35)}[/tex]

x = 17.4344679562...

x ≈ 17.4

Answer:

m∠B = 60°

b = 26 units

c = 30 units

Step-by-step explanation:

In a right triangle ACB,

By applying Sine rule,

[tex]\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{SinC}{c}[/tex]

m∠A = 30°, m∠C = 90°

m∠A + m∠B + m∠C = 180°

30° + m∠B + 90° = 180°

m∠B = 180° - 120°

m∠B = 60°

Therefore, [tex]\frac{\text{Sin30}}{15}=\frac{\text{Sin90}}{c}=\frac{\text{Sin60}}{b}[/tex]

[tex]\frac{1}{30}=\frac{\text{Sin90}}{c}=\frac{\text{Sin60}}{b}[/tex]

[tex]\frac{1}{30} =\frac{1}{c}=\frac{\frac{\sqrt{3}}{2}}{b}[/tex]

[tex]\frac{1}{30}=\frac{1}{c}=\frac{\sqrt{3}}{2b}[/tex]

[tex]\frac{1}{30} =\frac{1}{c}[/tex] ⇒ c = 30 units

[tex]\frac{1}{30}=\frac{\sqrt{3}}{2b}[/tex]

b = 15√3

b = 25.98

b ≈ 26 units

Answer:

C. Same is not an orange belt and Kate is not a red belt.

Step-by-step explanation:

The negation for the statement is Sam is not an orange belt or Kate is not a red belt.

The negation of a conjunction is equivalent to the disjunction of the negation of the statements making up the conjunction. To negate an “and” statement, negate each part and change the “and” to “or”.

Given statement:

Sam is an orange belt and Kate is a red belt.

Now, to make the negation we have to consider the rule "To negate an “and” statement, negate each part and change the “and” to “or”."

So, the negation statement would be

Sam is not an orange belt or Kate is not a red belt.

Learn more about  De Morgan's laws here:

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Answer:

{-1, 3, 7, 11, 15}

Step-by-step explanation:

we just substitute the set of even numbers in the function f(x) given to get our corresponding set of odds numbers

for 0

2(0)-1=0-1=-1

for 2

2(2)-1=4-1=3

for 4

2(4)-1=8-1=7

for 6

2(6)-1=12-1=11

for 8

2(8)-1=16-1=15

Answer:

-8 < x < -2

start number line at -10 and end it at 0

draw an open circle* over the dash indicating -8 and -2

connect the open circles

*open circle because it is less than and greater than, not less than or equal to and greater than or equal to

Answer:

-8<x<-2

Step-by-step explanation:

yw luv :D

as the exterior angle is known

sum of that angle and f angle = 180

142 + f = 180

f = 180 - 142

f = 38

Answer:

38

Step-by-step explanation:

Hope this helps you :)

Answer:

d

Step-by-step explanation:

Answer: E definition of midpoint

Step-by-step explanation:

Correct on Plato

Answer:

[tex]\boxed{Option \ C}[/tex]

Step-by-step explanation:

[tex]Sin \ Y = \frac{Opposite }{Hypotenuse } = \frac{XZ}{XY}[/tex]

[tex]Cos \ Y = \frac{Adjacent}{Hypotenuse} = \frac{YZ}{XY}[/tex]

[tex]Tan Y = \frac{opposite}{adjacent} = \frac{XZ}{ZY}[/tex]

Answer:

[tex]\boxed{\mathrm{C}}[/tex]

Step-by-step explanation:

sin [tex]\theta[/tex] = Opposite/Hypotenuse

sin (Y) = [tex]\frac{XZ}{XY}[/tex]

cos [tex]\theta[/tex] = Adjacent/Hypotenuse

cos (Y) = [tex]\frac{YZ}{XY}[/tex]

tan [tex]\theta[/tex] = Opposite/Adjacent

tan (Y) = [tex]\frac{XZ}{YZ}[/tex]

Answer:

B. The horizontal cross-sections of the prisms at the same height have the same area.

Step-by-step explanation:

Notice that the cone and the pyramid have the same volume. This is important.

This follows the Cavalieri's principle that, for the case of 3 dimensions, as the present case, it states, roughly, that if we have two bodies like the cone and the pyramid, and if we have parallel planes crossing each section, and we always have the same area, these two bodies have the same volume.

In this case, both, cone and pyramid have the same volume, then (reciprocally):

B. The horizontal cross-sections of the prisms at the same height have the same area.

Answer:

B. The horizontal cross-sections of the prisms at the same height have the same area.

Step-by-step explanation:

ap333x

Answer:

7 is the least.

Step-by-step explanation:

Their are 12 balls, and 6 of them are red. if you are to pick every single ball except the red ones, you cut the number of balls in half, and are left with 6 red balls, and 6 balls picked. Your next pick must be a red ball, making 7 picks.

Answer: 320 students

Step-by-step explanation:

From the question, we are informed that a school counselor surveyed 90 randomly selected students about thé langages they speak and thé students surveyed 16 speak more than one langage fluently. This means that 16/90 speak more than one language.

When 1800 students are surveyed, the number of students that can be expected to speak more than one langage fluently will be:

= 16/90 × 1800

= 16 × 20

= 320 students

Answer:

a. 25%

b. 55%

c. 35%

Hope it helps you and pls mark as brainliest : )

Answer: It represents that 2 will be divided into 3 equal parts.

Step-by-step explanation:

The given fraction : [tex]\dfrac{2}{3}[/tex]

here, Numerator = 2

Denominator = 3

It represents that 2 will be divided into 3 equal parts.

(x+2) + x + (x+4) = 2(1/2) + 2(x+3)

They are equal to each other and the rectangle has 2x more perimeter

The triangle would be divided in half from that rectangle.

Answer:

V > -15

Step-by-step explanation:

[tex]\frac{V}{3} +12>7\\\\\frac{V}{3}>-5\\\\V>-15[/tex]

Answer:

V > -15

Step-by-step explanation:

V/3 + 12 > 7

V/3 > -5

V > -15

Answer: x ≥  -5

Step-by-step explanation:

First, let's see how the function f(x) = IxI works:

if x ≥ 0, IxI = x

if x ≤ 0, IxI = -x

Notice that for 0, I0I = 0.

Ok, we want that:

|x+5| = x+5

Notice that this is equivalent to:

IxI = x

This means that  |x+5| = x+5 is only true when:

(x + 5) ≥ 0

from this we can find the possible values of x:

we can subtract 5 to both sides and get:

(x + 5) -5 ≥ 0 - 5

x ≥  -5

So the graph in the number line will be a black dot in x = -5, and all the right region shaded.

something like:

-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4__ ...

Answer:

1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x ← is in slope- intercept form

with slope m = 1

Answer:

1

Step-by-step explanation:

Answer:

It takes Carrie and James an hour and a half to finish the job.

Step-by-step explanation:

assuming they have to inspect ONE case of watches.

Carrie can inspect 1/5 case in one hour.

James can inspect 1/3 case in one hour.

Carrie worked alone for 1 hour, so she finished 1/5 of a case.

She leaves 4/5 case to finish.

She had lunch.

After that, Carrie and James worked together for x hours to finish the job.

When they work together, the finish 1/5+1/3 = 8/15 case per hour.

So time to finisher the remaining case

Time = 4/5 / (8/15)

= 4/5 * 15/8

= 3/2 hours

= an hour and a half.