What are the solutions of 3x^2 - x+ 7 =0

Jesse should use kilograms to weigh the package for postage.

Jesse should use kilograms to weigh the package for postage. The books and documents in the box would likely weigh more than grams, so a larger unit of measurement is needed. Kilograms are a commonly used metric unit for measuring weight, and they are suitable for weighing the package accurately and determining the postage required.

Answer:

Answer choice A.

Step-by-step explanation:

The y-intercept is the -8 for the g(x) equation. The chart shows that when x=0, y=-4. This is the y-intercept for f(x). -8 is less than -4.

Answer:

Step-by-step explanation:

[tex]\text{x-intercept is for y = 0}\to(x,\ 0)\\\\\text{y-intercept is for x = 0}\to(0,\ y)\\\\f(x):\\\\\text{From the table:}\\\\(0,\ -4)\to\text{y-intercept is -4}\\(16,\ 0)\to\text{x-intercept is 16}[/tex]

[tex]g(x)=4\sqrt{x}-8\to y=4\sqrt{x}-8\\\\\text{x-intercept:}\\\text{put y = 0 to the equation of the function}\\\\4\sqrt{x}-8=0\qquad\text{add 8 to both sides}\\4\sqrt{x}=8\qquad\text{divide both sides by 4}\\\sqrt{x}=2\to x=2^2\\x=4\leftarrow \text{x-intercept}\\\\\text{y-intercept:}\\\text{put x = 0 to the equation of the function}\\\\y=4\sqrt0-8\\y=0-8\\y=-8\leftarrow\text{y-intercept}[/tex]

Answer:

Step-by-step explanation:

The coordinates of the intersection of the line are the solution of the system of equations.

[tex]\underline{+\left\{\begin{array}{ccc}x-y=1\\y-x=1\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad0=2\qquad\bold{FALSE}[/tex]

The system of equations has no solution. Therefore, the lines are parallel (the intersection does not exist).

The area of a full circle would be Area = PI x r^2

The diameter would be the width of the dorr, so the radius would be half that. 34/2 = 17  inches.

Area for a full circle would be 3.14 x 17^2 = 907.46 square inches.

A semi circle is a half circle.

The area would be 907.46 / 2 = 453.73 square inches.

Multiply the area by the cost:

453.73 x 0.95 = 431.04

The answer is C.

Final answer:

To find the cost of the stained glass window, calculate the area of a 34-inch diameter semi-circular window, and then multiply that by the cost per square inch ($0.95). The total cost is approximately $431.17.

Explanation:

To calculate the cost of the stained glass window, we must first find the area of the semi-circular window above the door. Since the width of the door is 34 inches, the diameter of the semi-circle is also 34 inches, which means the radius (r) is half of that, or 17 inches.

Step 1: Calculate the area of the semi-circle
The formula for the area of a circle is A = πr². For a semi-circle, it would be half of that area, so the formula changes to A = (πr²) / 2.
Plugging in the radius, we get A = (3.14 * (17²)) / 2 = (3.14 * 289) / 2 = 453.86 square inches.

Step 2: Calculate the cost of the stained glass
The cost per square inch is $0.95. Multiplying the area by the cost per square inch, we get Total Cost = 453.86 * $0.95 = $431.167, which rounds to $431.17.
The closest cost option given is C. $431.04.

Answer:

[tex]4\sqrt{37} units[/tex] is the perimeter of square ABCD.

Step-by-step explanation:

Coordinates of square ABCD:

A = (3,4), B = (2,-2), C = (-4-1) , D = (-3,5)

Distance formula: [tex](x_1,y_1),(x_2,y_2)[/tex]

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance of AB: A = (3,4), B = (2,-2)

[tex]AB=\sqrt{(2-3)^2+(-2-4)^2}[/tex]

[tex]AB=\sqrt{(-1)^2+(-6)^2}=\sqrt{37} units[/tex]

Given that the ABCD is square, then:

AB = BC = CD = DA

Perimeter of the square ABC = AB +BC + CD + DA

[tex] AB+ AB+ AB+ AB= 4AB=4\sqrt{37} units[/tex]

[tex]4\sqrt{37} units[/tex] is the perimeter of square ABCD.

Answer:

- 3.396

Step-by-step explanation:

Given equation is,

[tex]log_{\frac{3}{4}} 25 = 3x-1[/tex]

By using logarithm property,

[tex]log_ax=\frac{log_bx}{log_ba}[/tex]

We get,

[tex]\frac{log25}{log\frac{3}{4}}=3x-1[/tex]

[tex]\frac{1.39794000867}{-0.124938736608}=3x-1[/tex]

[tex]-11.18900388=3x-1[/tex]

Adding 1 on both sides,

[tex]-10.18900388=3x[/tex]

[tex]\implies x = -\frac{10.18900388}{3}=-3.39633462667\approx -3.396[/tex]

Hence, the approximate value of x is -3.396.

First option is correct.

Answer: They might switch options around but if not...

Option A) -3.396

Check the picture below.

bearing in mind that adjacent angles in a parallelogram are supplementary angles.

Answer:

2

Step-by-step explanation:

So I'm going to use vieta's formula.

Let u and v the zeros of the given quadratic in ax^2+bx+c form.

By vieta's formula:

1) u+v=-b/a

2) uv=c/a

We are also given not by the formula but by this problem:

3) u+v=uv

If we plug 1) and 2) into 3) we get:

-b/a=c/a

Multiply both sides by a:

-b=c

Here we have:

a=3

b=-(3k-2)

c=-(k-6)

So we are solving

-b=c for k:

3k-2=-(k-6)

Distribute:

3k-2=-k+6

Add k on both sides:

4k-2=6

Add 2 on both side:

4k=8

Divide both sides by 4:

k=2

Let's check:

[tex]3x^2-(3k-2)x-(k-6) \text{ with }k=2[/tex]:

[tex]3x^2-(3\cdot 2-2)x-(2-6)[/tex]

[tex]3x^2-4x+4[/tex]

I'm going to solve [tex]3x^2-4x+4=0[/tex] for x using the quadratic formula:

[tex]\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\frac{4\pm \sqrt{(-4)^2-4(3)(4)}}{2(3)}[/tex]

[tex]\frac{4\pm \sqrt{16-16(3)}}{6}[/tex]

[tex]\frac{4\pm \sqrt{16}\sqrt{1-(3)}}{6}[/tex]

[tex]\frac{4\pm 4\sqrt{-2}}{6}[/tex]

[tex]\frac{2\pm 2\sqrt{-2}}{3}[/tex]

[tex]\frac{2\pm 2i\sqrt{2}}{3}[/tex]

Let's see if uv=u+v holds.

[tex]uv=\frac{2+2i\sqrt{2}}{3} \cdot \frac{2-2i\sqrt{2}}{3}[/tex]

Keep in mind you are multiplying conjugates:

[tex]uv=\frac{1}{9}(4-4i^2(2))[/tex]

[tex]uv=\frac{1}{9}(4+4(2))[/tex]

[tex]uv=\frac{12}{9}=\frac{4}{3}[/tex]

Let's see what u+v is now:

[tex]u+v=\frac{2+2i\sqrt{2}}{3}+\frac{2-2i\sqrt{2}}{3}[/tex]

[tex]u+v=\frac{2}{3}+\frac{2}{3}=\frac{4}{3}[/tex]

We have confirmed uv=u+v for k=2.

Answer:

8.  $114

10.  60 stamps

Step-by-step explanation:

8.

Let Dylan have d, Mike have m, and Jeremy have j

3 of them have 171, so we can write:

1. [tex]d + m + j = 171[/tex]

Mike has twice as Dylan, so we can write:

2. m = 2d

Jeremy had three times as Mike, so:

3. j = 3m

We can write equation 3 as m = j/3

Also, if we put this into equation 2, we have:

j/3=2d

d=j/6

Now we have d and m in terms of j. We put it into equation 1 and solve for j:

[tex]\frac{j}{6} + \frac{j}{3} + j = 171\\\frac{3j+6j+18j}{18}=171\\\frac{27j}{18}=171\\27j=18*171\\27j=3078\\j=\frac{3078}{27}\\j=114[/tex]

Jaime has $114

10.

amount of stamps Maddy has is m and amount Simon has is s

Maddy had twice as many stamps as Simon:

m = 2s

Also

After Maddy sold 60 stamps, Sinom had twice as many stamps as Maddy:

s+60=2(m-60)

We put the first equation in the second and solve for s:

s+60=2(m-60)

s+60=2(2s-60)

s+60=4s-120

180=3s

s=60

THus, m = 2(60) = 120

So maddy had 120 - 60 = 60 more stamps than Simon

Answer:

About 121.25

Step-by-step explanation:

Step 1: Interpret x and y

y is the number of accidents that occur = ?

x is the speed = 60 km/h

Step 2: Substitute value of x in the equation

y=0.0875x² - 10.5x + 436.25

y=0.0875(60)² - `10.5(60) + 436.25

Step 3: Find the value of y

y=0.0875(60)² - `10.5(60) + 436.25

y = 121.25

Therefore, the right answer is the last option which is 'about 121.25.'

!!

Answer:

The unit vector in the opposite direction of u is:

[tex]\vec{u} =-\frac{1}{\sqrt{23}}<-3i-4,\sqrt{2}>[/tex]

Step-by-step explanation:

To find the unit vector suppose u  that points in the opposite direction as v

[tex]\vec{v}=<-3i,-4\sqrt{2}>[/tex]

we use the formula:

[tex]\vec{u} =-\frac{1}{||\vec{v}||}\vec{v}[/tex]

Finding [tex]||\vec{v}||[/tex]

[tex]||\vec{v}|| = \sqrt{x^2+y^2}\\||\vec{v}|| = \sqrt{(3i)^2+(4\sqrt{2}^2} \\||\vec{v}|| = \sqrt{9i^2+(16*2)}\\ i^2 = -1\\||\vec{v}|| = \sqrt{9(-1)+32}\\||\vec{v}|| = \sqrt{-9+32}\\||\vec{v}|| = \sqrt{23}[/tex]

[tex]\vec{u} =-\frac{1}{\sqrt{23}}<-3i,-4\sqrt{2}>[/tex]

The unit vector in the opposite direction of u is:

[tex]\vec{u} =-\frac{1}{\sqrt{23}}<-3i,-4\sqrt{2}>[/tex]

(4x+3y)(4x-3y)

Multiply the two brackets together

4x(4x)(4x-3y)(-3y)(4x)(3y)(-3y)

16x^2-12xy+12xy-9y^2

16x^2-9y^2

Answer is 16x^2-9y^2

[tex]\huge{\boxed{16x^2-9y^2}}[/tex]

Use the FOIL method.

First term in each binomial: [tex]4x*4x=16x^2[/tex]

Outside terms: [tex]4x*-3y=-12xy[/tex]

Inside terms: [tex]3y*4x=12xy[/tex]

Last term in each binomial: [tex]3y*-3y=-9y^2[/tex]

Add these all together. [tex]12xy-12xy+16x^2-9y^2=\boxed{16x^2-9y^2}[/tex]

Answer:

I prefer to express solutions to inequalities using interval notation. Both formats are are important but I think interval notation is easier to understand and represents better the solutions.

For example, if you have the following inequation:

x-2> 1

x>3

Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U  (3, inf) instead of 'x>3 or x<-3' which can be confusing.

Answer:

21/2x^2+4x

Step-by-step explanation:

Answer:

a(8)=12582912

Step-by-step explanation:

The 8th term can be determined by the formula:

an = a1 * r^(n-1)

where

n = the term to be found = 8

a1 = 1st number

r = common ratio

Common ratio can be found by dividing the second term by the first term

= 48/6 = 8

Substitute the values in the formula

a(8) = 6 * 8^(8-1)

a(8) = 6 * 8^7

a(8)= 6*8*8*8*8*8*8*8

a(8) = 6 * 2097152

a(8)=12582912 ....

Therefore the 8th term is 12582912 ....

Answer:

12582912

Step-by-step explanation:

You simply need to start by finding the pattern. Divide the second number by the first (the answer is 8), then divide the third number by the second, so on and so on. You will see the answer is always 8 which means each number is getting multiplied by eight to reach the next term. Finally, multiply the last number in the sequence by your answer (8) until you reach the 8th term.

Answer: The inverse is x/5

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

How I got this answer:

The original function has 5x or 5*x, which reads out "five times x"

We have some unknown number x and we are multiplying it by 5. The inverse function undoes everything the original f(x) function does. Since the opposite of multiplicaiton is division, this means our answer involves dividing by 5.

--------

Here is a more algebraic explanation

f(x) = 5x

y = 5x  .... replace f(x) with y

x = 5y

5y = x

y = x/5 .... divide both sides by 5 (to undo the multiplication)

g(x) = x/5 .... replace y with g(x)

here g(x) represents the inverse of f(x)

One useful property of inverses is that f( g(x) ) = g( f(x) ) = x

Answer:

[tex]\sin \frac{3\pi}{2} = -1[/tex]

[tex]\cos\frac{3\pi}{2} =0[/tex]

Step-by-step explanation:

Please refer to the image attached.

Here we have a circle with unit radius. At some angle Ф the radius = 1 , and it is the hypotenuse (shown by green line in the image attached) of the ΔPQR thus formed. As our angle  Ф increases, the hypotenuse gets closer to the positive y axis and at 90°, it overlap the y axis. Hypotenuse (H) and Opposite site (O) becomes same and Adjacent (A) becomes 0.

As our angle move further and reaches 180, the Hypotenuse and adjacent becomes same and overlap negative x axis. As we move further at 270 i.e [tex]\frac{3\pi}{2}[/tex] , the hypotenuse and opposite side overlap on y axis and Adjacent side become 0. However the opposite side becomes negative here .

Our sine ratio says

[tex]\sin \frac{3\pi}{2} =\frac{opposite}{Hypotenuse}[/tex]

[tex]\sin \frac{3\pi}{2} =\frac{-1}{1}[/tex]

[tex]\sin \frac{3\pi}{2} =-1[/tex]

Hence we have our [tex]\sin \frac{3\pi}{2} = -1[/tex]

Now

[tex]\cos\frac{3\pi}{2} =\frac{Adjacent}{Hypotenuse}[/tex]

Adjacent as we discussed is 0 at [tex]\frac{3\pi}{2}[/tex]

[tex]\cos\frac{3\pi}{2} =\frac{0}{1}[/tex]

[tex]\cos\frac{3\pi}{2} =0[/tex]

Answer:

-30

Step-by-step explanation:

-3ab        original equation

-3(-2)(-5) .          plug in numerical values

6(-5) .             -3 times -2 is 6

-30 .         6 times -5 is -30.

Answer:

-30

Step-by-step explanation:

Plug in -2 for a & -5 for b in the expression given:

-3ab = (-3)(-2)(-5)

Multiply across. Note that:

Negative number x negative number = positive number.

Positive number x negative number = negative number.

(-3)(-2)(-5) = (6)(-5) = -30

-30 is your answer.

~

Answer:

The x-intercepts are (4,0) and (-1/3,0).

Step-by-step explanation:

f or any relation/function will intersect the x-axis when y is 0.

Set that's what we will do is set y to 0 and solve for x.

0=3x^2-11x-4

I'm going to attempt to factor.

a=3

b=-11

c=-4

We need to find two numbers that multiply to be ac and add up to be b.

ac=-12=-12(1)

b=-11=-12+1

Let's factor 3x^2-11x-4 by grouping.

3x^2-11x-4

3x^2-12x+1x-4       ; I replaced -11x with -12x+1x

Group the first 2 pairs and group the last two pairs like so:

(3x^2-12x)+(1x-4)

Now factor what you can from each pair:

3x(x-4)+1(x-4)

Now you have two terms, both with the common factor (x-4) so factor it out:

(x-4)(3x+1)

Now let's go back to solving:

3x^2-11x-4=0

This is the same as solving:

(x-4)(3x+1)=0  (because this is just the factored form of the original equation.)

Now this means either x-4=0 or 3x+1=0.

We need to solve both.

x-4=0 can be solved by adding 4 on both sides resulting in x=4.

3x+1=0 requires two steps.

3x+1=0

Subtract 1 on both sides:

3x=-1

Divide both sides by 3:

x=-1/3

The x-intercepts are (4,0) and (-1/3,0).

Answer:

The negative x-intercept is at (-1/3 , 0).

The positive x-intercept is at (4 , 0).

Explanation:

Where does f(x) = 3x2 – 11x – 4 intersect the x-axis?

The negative x-intercept is at (-1/3 , 0).

The positive x-intercept is at (4 , 0).

Set f(x) equal to zero so

3x2 – 11x – 4 = 0

Plug in a. b, and c into the quadratic formula

and get 2 solutions:

1/3 and -4

take the opposite signs and put it in the x intercepts

Answer:

angle B

Step-by-step explanation:

Answer:

100,000 dollars.

Step-by-step explanation:

One grand = 1,000$

Multiply.

100 × 1,000

=100,000$

Answer:

Option A.) 1.30

Step-by-step explanation:

we know that

The secant of x is 1 divided by the cosine of x:

so

sec(40°)=1/cos(40°)

using a calculator

sec(40°)=1.30

Answer:

A.) 1.30

Step-by-step explanation:

If the cosine value is 40*, the secant value to the hundredths degree is 1.30.

sec(40°)=1.30

Answer:

f. sqrt 7 meters

Step-by-step explanation:

we use Pythagoras' theorem here,

let the unknown side be x,

therefore,

=> 3² + x² = 4²

=> x² = 16 - 9

=> x = √7 m

Answer:

f. sqrt 7 meters

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem to solve.  We know the hypotenuse is 4 and one leg is 3.  We want to solve for the other leg.

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

Substituting into the equation

3^2 + b^2 = 4^2

9+b^2 = 16

Subtracting 9 from each side

9-9+b^2 = 16-9

b^2 =7

Taking the square root of each side

sqrt(b^2) = sqrt(7)

b = sqrt(7) meters

Answer:

0.5 or 1/2

Step-by-step explanation:

Let A be the event that the number cube is 3 or odd as 3 is also an odd number. So the event space will be:

{1,3,5}

The total number of outcomes are 6 as in:

{1,2,3,4,5,6}

So the probability of tossing 3 or odd number will be:

P(A) = n(A) / n(S)

= 3/6

=1/2

Hence the probability in fraction form is 1/2 and in decimal form is 0.5 ..

Answer:

600g chopped tomatoes

450ml of stock

225ml of red wine

Step-by-step explanation:

Times them all by 0.75

Answer:

15%

Step-by-step explanation:

Answer:

580

Step-by-step explanation:

Let's translate this word for word.

87 is 15% of what number

87 = 15% times x

87=.15 times x

[tex]87=.15 \cdot x[/tex]

Divide both sides by .15

[tex]\frac{87}{.15}=\frac{.15x}{.15}[/tex]

Cancel out the common factor of .15 on the right; that is .15/.15=1.

[tex]580=x[/tex]

580 is the number

Answer:

580

Step-by-step explanation:

Alright. Translate that into math, and you get:

87=15/100x

multiply both sides by x

8700/15=x

x=8700/15

x=580

Check:

580*15/100

58*15/10

870/10

87

BINGO!

Answer:

Length of larger piece: 7 m

Total length of carpet is: 19 m

Step-by-step explanation:

Let the smaller piece have length x.

Let the larger piece have length y.

"The length of the smaller piece is 5 meters greater than the length of the larger piece."

x = y + 5

"If the length of the smaller piece is 12 meters"

x = 12

x = y + 5

12 = y + 5

7 = y

y = 7

The larger piece has length 7 meters.

The total length of the carpet is x + y = 12 m + 7 m = 19 m

To find the length of the larger piece of carpet, use the equation x + 5 = 12, and solve for x. Substitute the total length of the carpet for x in the formula to find the length of the larger piece.

The problem involves finding the length of the larger piece of carpet when the length of the smaller piece and the total length of the carpet are known. Let's assume the length of the larger piece is x meters. According to the problem, the length of the smaller piece is 5 meters greater than the length of the larger piece, so the length of the smaller piece can be represented as x + 5 meters. The total length of the carpet is the sum of the lengths of the smaller and larger pieces, so we can create the equation: x + (x + 5) = total length. Given that the length of the smaller piece is 12 meters, we can substitute x + 5 with 12 in the equation and solve for x:

x + (x + 5) = total length

x + x + 5 = total length

2x + 5 = total length

2x = total length - 5

x = (total length - 5) / 2

Now we have the formula to calculate the length of the larger piece. Simply substitute the total length of the carpet into the formula to find the length of the larger piece.

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