A 3-digit numeral is formed by selecting digits at random from 2,4,6,7 without repetition. Find the probability that the number is formed greater than 600. P(greater than 600)

Answer:

(4x -1  ) ( x  +5  )

Step-by-step explanation:

4x2 + 19x-5

(4x   ) ( x    )

We need to get -5    The factors are -1 and 5  and 1 and -5

4*5 = 20  

so the 5 will be on the outside  We do this because we have +19 on the inside

(4x -1  ) ( x  +5  )

Lets check

FOIL

4x^2 +20x -x -5 = 4x^2 +19x-5  

Answer:

The factors are (4x-1)(x+5).

Step-by-step explanation:

4x^2+19x-5

Break the middle term:

First multiply the coefficient of first term by the constant.

4*5=20

Now find any two numbers whose product = 20 and whose sum is equal to the middle term.

20*1 = 20

20-1 = 19

Now break the middle term:

4x^2+20x-x-5

Now group the first two terms and last two terms:

(4x^2+20x)-(x+5)

Now take the common from each group.

4x(x+5)-1(x+5)

(4x-1)(x+5).

Thus the factors are (4x-1)(x+5).....

Answer: It’s D

5x

25x can still be simplified all the way down to 5x

(D) 5x Is the correct answer

Answer: Each kid would receive 13 pieces of candy

Step-by-step explanation: Since Carlene has 104 pieces of candy and she wants to distribute them evenly to 8 kids she would have to do division and divide 104 with 8 which equals to 13 which means 13 pieces of candy are going to each kid.

Answer: Our required equation would be

[tex]\dfrac{\text{Number of pieces of candy}}{\text{Number of kids}}[/tex]

and each kid would get 13 pieces of candy.

Step-by-step explanation:

Since we have given that

Number of pieces of candy left over from halloween = 104

Number of kids in which she would like to distribute = 8

As every student get pieces of candy evenly.

So, Number of pieces of candy each kid would get is given by

[tex]\dfrac{\text{Number of pieces of candy}}{\text{Number of kids}}\\\\=\dfrac{104}{8}\\\\=13[/tex]

Hence, our required equation would be

[tex]\dfrac{\text{Number of pieces of candy}}{\text{Number of kids}}[/tex]

and each kid would get 13 pieces of candy.

Answer:

True

Step-by-step explanation:

The prefix "co" means together, and the base "linear" means line. Therefore co-linear means together on a line

Answer:

12.53

Step-by-step explanation:

x = x₂ - x₁ = -6 - 0   = -6

y = y₂ - y₁ =  7 - (-4) = 11

We can use the Pythagorean theorem to calculate the distance.

z² = (-6)² + 11² = 36 + 121 = 157

z = √157 ≈ 12.53

The distance between the two points is 12.53.

Answer:

a)The equation is $35l-$215

b)Amount = $695

c)They will loose $215.

Step-by-step explanation:

From the question you should understand that;

The equation that relates the fund raised and number of lawns aerated during a day is;

Let number of lawns aerated that day be l

The cost to aerate one lawn per day is $35

Cost to rent the aeration machine is $215

a)The equation is ;

[tex]=(l*35)-215[/tex]

=  $35l-$215

b)Money raised

number of lawns,l=26

Substitute in the equation

Amount=$35l-$215

=$(35×26)-$215

=$910-$215=$695

c)If the team were unable to aerate due to weather condition, they will incur a loss to to renting of the aeration machine.They will lose $215.This can be avoided by not renting the aeration machine when the weather conditions seems unfavorable for working.

The answer is option "D. Figure U"

Answer:

60

Step-by-step explanation:

Answer:

$10.

Step-by-step explanation:

Let x represent the original cost of bag of cat food.

We have been given that a pet store owner set the price of a bag of cat food at 50% above the cost. So the cost of cat food would be x plus 50% of x.

[tex]x+\frac{50}{100}*x\rightarrow x+0.5x=1.5x[/tex]

We are further told that the price was reduced by 20%, when it did not sell. So price of cat food after reduction would be [tex]1.5x[/tex] minus 20 percent of [tex]1.5x[/tex].

[tex]1.5x-(\frac{20}{100}\times 1.5x)[/tex]

[tex]1.5x-(0.20\times 1.5x)[/tex]

[tex]1.5x-(0.3x)[/tex]

[tex]1.2x[/tex]

Since price after reduction was $12, so we will equate [tex]1.2x[/tex] with 12 as:

[tex]1.2x=12[/tex]

[tex]\frac{1.2x}{1.2}=\frac{12}{1.2}[/tex]

[tex]x=10[/tex]

Therefore, the original cost of cat food was $10.

Check the picture below.

bear in mind that, horizonta lines are just y = "some constant", and vertical lines are x = "some constant".

Answer: 7

Step-by-step explanation: Since there are no 0’s, just count the number of digits. There are 7.

Answer:

[tex]\sqrt[3]{x} -3[/tex]: The parent graph will move 3 units down.

[tex]\sqrt[3]{x-3}[/tex]: The parent graph will move 3 units right.

Step-by-step explanation:

The parent function [tex]\sqrt[3]{x}[/tex] looks like the first image attached.

Using knowledge of transformations, numbers outside the radical move the graph up or down (vertically). A positive number moves the graph up; a negative number moves the graph down.

Numbers inside the radical move the graph left or right (horizontally). A positive number moves the graph left; a negative number moves the graph right.

In the first transformation [tex]\sqrt[3]{x} -3[/tex] the number is outside of the radical, meaning that the graph will move vertically. The 3 is negative, so the graph will move 3 units down.

The first transformation moves the parent graph 3 units down.

In the second transformation [tex]\sqrt[3]{x-3}[/tex] the number is inside the radical so the graph will move horizontally. The 3 is negative so the graph will move 3 units to the right.

The second transformation moves the parent graph 3 units right.

The attached images show:

Answer:

AB = 3

Step-by-step explanation:

Since AB is a perpendicular bisector then Δ is isosceles and AD = AC, that is

4x - 1 = 2x + 3 ( subtract 2x from both sides )

2x - 1 = 3 ( add 1 to both sides )

2x = 4 ( divide both sides by 2 )

x = 2

Hence AB = x + 1 = 2 + 1 = 3

Answer:

AB=3

Step-by-step explanation:

Answer:

7033/10000

Step-by-step explanation:

You get his answer by times it by 1000 so the decimal point is out of the number

Answer:

E and F.

Step-by-step explanation:

Let the side opposite the smallest angle have a measurement of x (this is the shortest side).

The hypotenuse is twice the shorter side so the hypotenuses would be 2x in this case.

The long leg is square root of 3 times the short side or sqrt(3)x in this case.

So the ratio of long leg to short leg is [tex]\frac{\sqrt{3}x}{x}=sqrt(3):1[/tex]

and

the ratio of short leg to long leg is [tex]\frac{x}{\sqrt{3}x}=1:sqrt(3)[/tex].

The answer is not A that division is equivalent to 1:1.

B same reason as A.

C is not right because 1:sqrt(2) is not the same as 1:sqrt(3)

I bolded the reason in C so you can see why I said that.

You can also put these in your calculator and compare the decimals like so:

D gives us 0.816 approximately while  sqrt(3)/1 gives 1.73 and 1/sqrt(3) gives 0.58 approximately. 0.816 is neither one of those.

How about E?  1:sqrt(3) is exactly what one of our ratios say.

How about F?  sqrt(3)/3=0.58 so this is what one of our ratios is equivalent to.

So E and F are your answers.

The only correct options are: E. [tex]\(1 : \sqrt{3}\)[/tex] and F. [tex]\(\sqrt{3} : 3\)[/tex].

To determine the correct ratios between the lengths of the legs of a [tex]\(30^\circ\)-\(60^\circ\)-\(90^\circ\)[/tex] triangle, we first recall the properties of such a triangle:

Step 1: In a [tex]\(30^\circ\)-\(60^\circ\)-\(90^\circ\)[/tex] triangle, the side lengths are in the ratio [tex]\(1:\sqrt{3}:2\)[/tex], where:

The shortest leg (opposite the [tex]\(30^\circ\)[/tex] angle) has length (1).

The longer leg (opposite the [tex]\(60^\circ\)[/tex] angle) has length [tex]\(\sqrt{3}\)[/tex].

The hypotenuse has length (2).

Step 2: Identify the correct ratio between the legs:

The ratio of the shortest leg to the longer leg is [tex]\(1:\sqrt{3}\)[/tex].

Now, let's analyze the given options:

A. [tex]\(\sqrt{2} : \sqrt{2}\)[/tex]: This ratio simplifies to (1:1), which is incorrect for a [tex]\(30^\circ\)-\(60^\circ\)-\(90^\circ\)[/tex] triangle.

B. [tex]\(\sqrt{3} : \sqrt{3}\)[/tex]: This ratio simplifies to (1:1), which is incorrect for a [tex](30^\circ\)-\(60^\circ\)-\(90^\circ\)[/tex] triangle.

C. [tex]\(1 : \sqrt{2}\)[/tex]: This does not match the ratio [tex]\(1 : \sqrt{3}\)[/tex].

D. [tex]\(\sqrt{2} : \sqrt{3}\)[/tex]: This does not match the ratio [tex]\(1 : \sqrt{3}\)[/tex].

E. [tex]\(1 : \sqrt{3}\)[/tex]: This matches the correct ratio [tex]\(1 : \sqrt{3}\)[/tex].

F. [tex]\(\sqrt{3} : 3\)[/tex]: This does not match the ratio [tex]\(1 : \sqrt{3}\)[/tex].

Thus, the only correct options are: E. [tex]\(1 : \sqrt{3}\)[/tex] and F. [tex]\(\sqrt{3} : 3\)[/tex]

Answer:

25

Step-by-step explanation:

Since she predicts that 80% of the invited people come, she needs to invite a number greater than 20, so that 80% of that number is 20.

Let the number of invited people be x.

80% of x must be 20.

80% * x = 20

0.8x = 20

Divide both sides by 0.8

x = 25

Answer: She should invite 25 people.

Check: Let's find 20% of 25. If it is 20, then 25 is correct.

80% of 25 = 0.8 * 25 = 20

Since 80% of 25 is 20, the answer, 25, is correct.

Answer:

80/100=.80

.80x=20

x=25

Step-by-step explanation:

Answer:

he correct answer is 4.

Step-by-step explanation:

Answer:

The correct answer is 20.

Step-by-step explanation:

Can I get brainliest?

Answer:

The answer is C) 13.

Step-by-step explanation:

To find the hypotenuse (longest side) of a right triangle, you need to use the Pythagorean Theorem. The formula for the hypotenuse is a^2 + b^2 = c^2.

5^2 (five squared) equals 25, and 12^2 (twelve squared) equals 144.

25 + 144 = 169

Next, find the square root of 169. It is 13. 13 is the length of the hypotenuse.

I hope this helped! :)

In the right triangle ABC, the length of the AC is equal to [tex]13[/tex] units.

" Right triangle is defined as a triangle with one of the interior angles with measure equals to [tex]90[/tex] degrees."

Formula used

Pythagoras theorem,

(Hypotenuse)² = ( adjacent side)² + (opposite side)²

According to the question,

In the right triangle ABC,

Adjacent side 'BC' [tex]= 12[/tex] units

Opposite side 'AB' [tex]= 5[/tex] units

'AC' represents the hypotenuse of the right triangle

Substitute the value in the Pythagoras theorem we get,

[tex]AC^{2} = BC^{2} +AB^{2} \\\\\implies AC^{2} = 12^{2} + 5^{2} \\\\\implies AC^{2} = 144 + 25\\\\\implies AC = \sqrt{169} \\\\\implies AC =13units[/tex]

Hence, Option(C) is the correct answer.

Learn more about the right triangle here

https://brainly.com/question/6322314

#SPJ2

Step-by-step explanation:

the triangle is obtuse...has an angle greater than 90deg

also it is scalene...all 3 sides are different length

The triangle is a scalene and obtuse triangle

A scalene triangle is a type of triangle with three different length sides and three interior angles that add up to 180 degrees. Scalene triangles have no equal of parallel sides , hence there is no line of symmetry. The interior angles of a scalene triangle can be acute , right or obtuse angles.

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of sides of the triangle are

The measure of side AB = 11.9

The measure of side BC = 7

The measure of side AC = 6

And , the measure of ∠ABC = 132°

So , the sides of the triangle are having different lengths so it can be classified as a scalene triangle

And , the angle is obtuse , so it is also an obtuse triangle

Hence , the triangle is scalene

To learn more about scalene triangle click :

https://brainly.com/question/10651823

#SPJ7

Answer:

(g-f)(3) = 23

Step-by-step explanation:

f(x) = 4-x^2

g(x) = 6x

we need to find g-f(3)

Put the value of x = 3 in g(x) and f(x) and subtract f(x) from g(x) i.e

(g-f)(3) = g(3) - f(3)

(g-f)(3) = 6(3) - {4-(3)^2}

(g-f) (3)=18-(4-9)

(g-f)(3) = 18-(-5)

(g-f)(3) = 18+5

(g-f)(3) = 23

so, (g-f)(3) = 23

Answer:

23

Step-by-step explanation:

(g-f)(3)=g(3)-f(3)

So we need to find g(3) and f(3). Then subtract.

g(3)=6(3)=18.

f(3)=4-(3)^2=4-9=-5.

(g-f)(3)=g(3)-f(3)=18-(-5)=18+5=23

For this case we have that the equation of a line of the slope-intersection form is given by:[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut-off point with the y axis

To find the slope we look for two points through which the line passes:

We have to:

[tex](x1, y1) :( 1,2)\\(x2, y2): (- 1, -4)[/tex]

Thus, the slope is:

[tex]m = \frac {-4-2} {- 1-1} = \frac {-6} {- 2} = 3[/tex]

We have then:

[tex]y = 3x + b[/tex]

Substituting a point in the equation to find b:

[tex]2 = 3 (1) + b\\2 = 3 + b\\b = 2-3\\b = -1[/tex]

Finally, the equation is:[tex]y = 3x-1[/tex]

Answer:

Option D

The equation of a circle is written as (x-h)^2 + (y-k)^2 = r^2

Where the center point of the circle is (h,k) and r is the radius.

In the given equation 16 = r^2

To find r take the square root of both sides:

r = √16

r = 4

The answer is A.

Answer: OPTION A.

Step-by-step explanation:

The equation of a circle in center-radius form  is:

[tex](x - h)^2 + (y- k)^2 = r^2[/tex]

Where the center is at the point (h,k) and "r" is the radius.

Then, given the equation of the circle:

[tex](x - 3)^2 + (y + 1)^2 = 16[/tex]

You can idenfity that:

[tex]r^2=16[/tex]

Therefore, in order to find the radius, you need to solve for "r".

Then, this is:

[tex]r=\sqrt{16}\\\\r=4[/tex]

Answer:

The first one

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{b}{8}[/tex]

Multiply both sides by 8

8 × tan30° = b, that is

b = 8tan30°

Answer:

b = (8)tan(30o)

Step-by-step explanation:

Answer:

[tex]f(x) = - 5 {(x - 1)}^{2} [/tex]

Step-by-step explanation:

The given parent function is:

[tex]f(x) = {x}^{2} [/tex]

If we shift to the right by 1 unit, the function becomes:

[tex]f(x) = {(x - 1)}^{2} [/tex]

If we stretch by a factor of 5, the function becomes,

[tex]f(x) =5 {(x - 1)}^{2} [/tex]

Finally reflecting over the x-axis gives:

[tex]f(x) = - 5 {(x - 1)}^{2} [/tex]

Answer:

f'''(x)=-5(x-1)^2

Step-by-step explanation:

Given:

f(x)= x^2

Shifting 1 unit to right means subtracting 1 from the function i.e

f(x-1)=(x-1)^2

f'(x)=(x-1)^2

now vertically stretching above f'(x)  by a factor of 5:

5f'(x)=5(x-1)^2

f''(x)=5(x-1)^2

finally reflecting above f'''(x) over the x-axis:

-f''(x)=-5(x-1)^2

f'''(x)=-5(x-1)^2 !

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We ahve the slope m = 1/2 and the point (-2, 1). Substitute:

[tex]y-1=\dfrac{1}{2}(x-(-2))[/tex]

[tex]y-1=\dfrac{1}{2}(x+2)[/tex] - point-slope form

Covert to the slope-intercept form (y = mx + b):

[tex]y-1=\dfrac{1}{2}(x+2)[/tex]          use the distributive property

[tex]y-1=\dfrac{1}{2}x+1[/tex]          add 1 to both sides

[tex]y=\dfrac{1}{2}x+2[/tex]   - slope-intercept form

Convert to the standard form (Ax + By = C):

[tex]y=\dfrac{1}{2}x+2[/tex]     multiply both sides by 2

[tex]2y=x+4[/tex]        subtract x from both sides

[tex]-x+2y=4[/tex]         change the signs

[tex]x-2y=-4[/tex]   -  standard form

Convert to the general form (Ax+By+C=0):

[tex]x-2y=-4[/tex]        add 4 to both sides

[tex]x-2y+4=0[/tex]   - general form

f(x) = 2x + 7 and f(x) = -1

Replace f(x) with -1:

-1 = 2x +7

Subtract 7 from both sides:

-8 = 2x

Divide both sides by 2:

x = -8 /2

x = -4

Answer:

[tex]h= 116.616[/tex]

Step-by-step explanation:

we have

[tex]h= 105sin (0.0698(90+1)) + 105[/tex]

step 1

Solve (90+1)

[tex]h= 105sin (0.0698(91)) + 105[/tex]

step 2

Solve 0.0698(91)

[tex]h= 105sin (6.3518) + 105[/tex]

step 3

Solve sin (6.3518)

[tex]h= 105(0.11063) + 105[/tex]

step 4

Solve 105(0.11063)

[tex]h= 11.616 + 105[/tex]

step 5

Solve 11.616 + 105

[tex]h= 116.616[/tex]

Answer:

There are infinite numbers that added or multiplied will give the same answer. But, if the require this two numbers to be the same, then we need to solve the following equation to see what we found out:

x + y = x * y

Given that we want the numbers to be equal, then y=x.

x + x = x * x

2x = x^2

x^2 - 2x = 0

x(x-2) = 0

We find that NOT only x=2 meets this requirement but also x=0.

Therefore, there is another number that when added, multiplied or squared gives the same result. The other number is zero!

We can prove it:

0 × 0 = 0

0 + 0 = 0

Answer:

The ordered pair of P'=(-8.75, 5.25)

Step-by-step explanation:

To get the ordered pair of point P' you simply have to multiply the coordinates of P by scale factor of 7/4

P:(-5,3)

P'(x,y)= (-5* 7/4, 3*7/4)

P'(x,y) = (-35/4 , 21/4)

P'(x,y) = (-8.75, 5.25)..

Thus the ordered pair of P'=(-8.75, 5.25)....

Answer:

(−5.25, −3.5)

Step-by-step explanation:

Answer:

Possibility 1: [tex]\frac{(x+1)(x+1)}{(x-4)(x+5)}[/tex]

Possibility 2: [tex]\frac{(x+1)(x+3)(x-3)}{x(x-4)(x+5)}[/tex]

Possibility 3: [tex]\frac{-4(x-4)(x+1)}{-4(x-4)(x-4)}[/tex]

There are infinitely many more possibilities.

Step-by-step explanation:

So we are looking for a fraction in terms of x.

We have a horizontal asymptote so that means the degree of the top has to equal to degree of the bottom. It is also at y=1 which means the coefficient of the leading term on top and bottom must be the same (but not zero) since the same number divided by the same number is 1.  

Now we also have a vertical asymptote at x=4 which means we need a factor of x-4 on bottom.

So there is a lot of possibilities. Here are a few:

Possibility 1: [tex]\frac{(x+1)(x+1)}{(x-4)(x+5)}[/tex]

You have the degrees are the same on top and bottom and the leading coefficients are the same.  You also have that factor of (x-4) on bottom.

Possibility 2: [tex]\frac{(x+1)(x+3)(x-3)}{x(x-4)(x+5)}[/tex]

Possibility 3: [tex]\frac{-4(x-4)(x+1)}{-4(x-4)(x-4)}[/tex]

Now a factor of (x-4) can be canceled here but you still have a factor of (x-4) left on bottom so you still have the vertical asymptote. You also still have the same leading coefficient on top and bottom (-4 in this case) and the same degree.

Answer:

x = 40

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Consider the triangle on the left and calculate the third angle

Subtract the sum of the 2 angles from 180

third angle = 180° - (75 + 50)° = 180° - 125° = 55°

Consider the triangle on the right

The third angle = 55° ( vertical angles )

Subtract the sum of the 2 angles from 180

x = 180 - (55 + 85) = 180 - 140 = 40