Solve for x 7(x - 9) = 8x - 6

Answer:

The vertices are 4 units to the left and right of the center.

The foci are units to the left and right of the center on the major axis.  

The directrices are vertical lines.

Step-by-step explanation:

The statements 2, 3 and 4 are correct. The ellipse graph shows that the foci are units to the left and vertices are 4 units to the left. The center os the ellipse is not at the origin (0,0) so the statement 1 is not correct. Ellipse is an oval shape with 2 other points known as foci. The foci of the ellipse are at left and right axis marked from the center.

Answer:

3 4 5

Step-by-step explanation:

Answer:

f(x) = 6/x

f'(x) = -6/x²

f'(-2) = -6/4 = -3/2

Final answer:

Using the quadratic formula, the exact solutions of the equation x² + 7x - 4 = 0 are x = (-7 + √65) / 2 and x = (-7 - √65) / 2.

Explanation:

To solve the quadratic equation x2 + 7x − 4 = 0 using the quadratic formula, we first identify the coefficients as a = 1, b = 7, and c = -4. The quadratic formula is x = [tex]\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]. Substituting the values we have:

x = [tex]\frac{-(7) \pm \sqrt{7^2 - 4(1)(-4)}}{2(1)}[/tex]

x = [tex]\frac{-7 \pm \sqrt{49 + 16}} {2}[/tex]

x = (-7 ± √65) / 2

Therefore, the exact solutions for x are x = (-7 + √65) / 2 and x = (-7 - √65) / 2.

The exact solutions of [tex]\(x^2 + 7x - 4 = 0\) are \(x = \frac{-7 + \sqrt{65}}{2}\)[/tex] and [tex]\(x = \frac{-7 - \sqrt{65}}{2}\).[/tex]

To find the exact solutions of the quadratic equation [tex]\( x^2 + 7x - 4 = 0 \)[/tex] using the Quadratic Formula, we start with the standard form of a quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex] and apply the formula:

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

In the equation [tex]\( x^2 + 7x - 4 = 0 \)[/tex], the coefficients are:

[tex]- \( a = 1 \)[/tex]

[tex]- \( b = 7 \)[/tex]

[tex]- \( c = -4 \)[/tex]

Now, substitute these values into the Quadratic Formula:

1. Calculate the discriminant [tex]\[ b^2 - 4ac = 7^2 - 4(1)(-4) = 49 + 16 = 65 \][/tex]

 [tex]\[ b^2 - 4ac = 7^2 - 4(1)(-4) = 49 + 16 = 65 \][/tex]

2. Substitute [tex]\( b \), \( a \)[/tex], and the discriminant into the formula:

[tex]\[ x = \frac{-7 \pm \sqrt{65}}{2(1)} \][/tex]

 [tex]\[ x = \frac{-7 \pm \sqrt{65}}{2} \][/tex]

So, the exact solutions of the equation [tex]\( x^2 + 7x - 4 = 0 \)[/tex] are:

[tex]\[x = \frac{-7 + \sqrt{65}}{2} \quad \text{and} \quad x = \frac{-7 - \sqrt{65}}{2}\][/tex]

Answer:

solution given:

1st expression=27=3×3×3

2nd expression=45=5×3×3

here

common factor =3×3=9

Answer:

4

Step-by-step explanation:

[tex]y=mx+b[/tex]

[tex]m=slope[/tex]

[tex]b=y-intercept[/tex]

[tex]y=4x+3[/tex]

4 is your slope.

Answer: 4

Step-by-step explanation:

Answer:

we need the triangle to answer that...

Step-by-step explanation:

I'm sorry

Radius = 14/2 = 7 inches

Volume = [tex]\pi r^{2} h[/tex] = 3.14 x 7 x 7 x 6 = 923.16 = approx. 923.2 cubic inches

The shown triangle is scalene and right, so the correct options are C and F.

First, we can see that the 3 sides have different measures. So the triangle is Scalene (and we discard options A and E).

We also can see that one of the angle is 90°, which means that we have a right triangle. So option C is correct. (And we discard B and D).

Concluding, we have a scalene right triangle. So the correct options are C and F.

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Answer:

Right and Scalene

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Final answer:

To construct three-dimensional figures from different views, one must employ orthographic drawing techniques, which include selecting a vanishing point and systematically drawing construction lines to create depth.

Explanation:

Constructing three-dimensional figures from different views is a skill often associated with orthographic drawings. This process allows you to visualize an object as if you were viewing it from multiple perspectives, ultimately creating a three-dimensional representation. The steps to follow are quite systematic:

Begin by drawing one face of the cube. Select a suitable vanishing point.

Draw faint construction lines from each corner of the cube face to the vanishing point to establish depth.

Next, draw horizontal and vertical lines for the back face of the cube, ensuring that each corner connects with the corresponding construction line.

Finally, outline the shape of the cube with darker lines to make it distinct.

With practice, you'll develop the ability to 'see' the three dimensions in the drawing. Visualizing three-dimensional figures can also be enhanced by using models or multiple photographs, as not all details can be captured from a single angle. Three-point perspective, where vanishing points are placed above and below the horizon line, can also aid in this visualization process.

Answer:

[tex]P(X<29.1)=P(\frac{X-\mu}{\sigma}<\frac{29.1-\mu}{\sigma})=P(Z<\frac{29.1-29}{0.1})=P(z<1)[/tex]

And we can find this probability using the normal standard distribution, excel or a calculator and we got:

[tex] P(z<1) =0.8413[/tex]

And if we convert this into percent we got 84.13% rounded to the nearest percent would be:

84%

Step-by-step explanation:

Let X the random variable that represent the circumferences of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(29,0.1)[/tex]  

Where [tex]\mu=29[/tex] and [tex]\sigma=0.1[/tex]

We are interested on this probability

[tex]P(X<29.1)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X<29.1)=P(\frac{X-\mu}{\sigma}<\frac{29.1-\mu}{\sigma})=P(Z<\frac{29.1-29}{0.1})=P(z<1)[/tex]

And we can find this probability using the normal standard distribution, excel or a calculator and we got:

[tex] P(z<1) =0.8413[/tex]

And if we convert this into percent we got 84.13% rounded to the nearest percent would be:

84%

Answer:

13.1%

Step-by-step explanation:

Answer:

-32

Step-by-step explanation:

Subtract 6 to get next term.

Answer:

-32

Step-by-step explanation:

I'm saying this is the answer because if you look at the pattern of numbers, it keeps decreasing by 6. If you continue this sequence, you will find that you will just have to follow the same pattern of decreasing by 6. This will lead you to get -32 as your next number in your arithmetic sequence.

(Hope this helped you)

Answer:

14

Step-by-step explanation:

-2x^3 - 2x^2 - 4x-2

Let x = -2

-2 (-2)^3 - 2 (-2)^2 -4(-2) -2

Exponents first

-2 (-8) -2 (4) -4(-2) -2

Then multiply

16 -8 +8 -2

Then add and subtract

14

Final answer:

The dimensions of the poster are 15 inches in length and 12 inches in width.

Explanation:

The area of a wall covered by a rectangular poster is 180 square inches, and the length is 1.25 times longer than the width. To determine the dimensions of the poster, we will let the width be w inches. Therefore, the length would be 1.25w inches. The area of a rectangle is given by the formula length × width. Substituting our expressions for length and width into the formula for area gives us the equation 1.25w × w = 180. Simplifying this equation will help us find the value of w.

1.25w^2 = 180
w^2 = 180 / 1.25
w^2 = 144
w = √144
w = 12 inches (width)

Now that we have the width, we can find the length:
Length = 1.25 × 12 = 15 inches

The dimensions of the poster are:

Length: 15 inches

Width: 12 inches

Answer:

3/8 (D)

Step-by-step explanation:

15 11th grader's favorite class is science. There are a total of 40 11th graders. That makes the probability 15/40 = 3/8 = D

Answer:

34

Step-by-step explanation:

First, we need to find 8% of 1,575. To do so we have to divide 8 by 100, then multiply the quotient by 1,575.

8% ⇒ 0.08

1,575 × 0.08 = 126

Now add the 8% increase to the original cost.

1,575 + 126 = 1,701

Option 1: $1,701.

I hope this helps :)

Look at the attached picture

Hope it will be helpful to you.

Answer:

x = 109

Step-by-step explanation:

[tex](x + 12) \degree + 59 \degree = 180 \degree \\ (sum \: of \: exterior \: angles \: on \: same \: side \: \\ of \: transversal) \\ (x + 71) \degree = 180 \degree \\ x + 71 = 180 \\ x = 180 - 71 \\ \purple{ \bold{ x = 109}}[/tex]

Answer:

B

Step-by-step explanation:

Answer:

denominator > numerator

Step-by-step explanation:

The degrees can be found in the "power" that they have.

The denominator has a degree of a power of 2 (3x²). The numerator has a degree of only 1 (5x). Therefore, by degrees, the denominator is greater than the numerator.

~

Answer:

Any graph with the same slope but with different y intercepts is parallel to that. For example in y = mx + b form the equation will be

y = 4x - 15

So, some equations that will be parallel

y = 4x

y = 4x - 16

y = 4x +3

Hoped this helped ya :)

Answer:

y=4x-5

Step-by-step explanation:

First step is to turn the given equation into slope intercept form y=mx+b.

The goal is to isolate y: first subtract 8x from both sides and to completely simplify the equation divide by -2 on both sides:

8x-2y=30

-2y=-8x+30

y= -8/-2x + 30/-2

y=4x-15

** when adding a negative, it's the same as subtracting, so I just changed it

Now you have your equation, we want to focus on the slope. If two equations have the same slope, they won't ever intersect bc they grow at the the same rate.

Use this equation: y=4x+b and bc you're trying to find the equation of another line, pick an ordered pair (it doesn't matter what it is) and plug it into x and y to solve for b (the y-intercept) in order to fulfill y=mx+b

I'm using (2,3):

3=4(2)+b

3=8+b

-5=b

Now you have b, plug it back into y=4x+b (omit the coordinates you put in) and you'll get:

y=4x-5 as your answer

Answer:

15 containers

Step-by-step explanation:

If the circus sells an average of 28,200 grams of peanuts you can expect that it would be close to that number again, it is equal to 28.2 kilograms. Since it only ships in 2 kilogram containers then you would want to buy 15 of them since 15*2=30, which is above what we need.

Answer:

15 I think

Step-by-step explanation:

The area of a circle with a diameter of 5 feet is calculated using the formula A = πr². Halving the diameter to find the radius, then squaring it, multiplying by π (approximated as 3.14), and rounding to the nearest tenth, gives an area of 19.6 ft².

The student's question involves finding the area of a circle with a given diameter where the circle is the table's top designed by Cory. To find the area, one must use the formula A = πr², where A is the area, π (pi) represents the mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Since the diameter of the table is 5 feet, the radius will be half of that, which is 2.5 feet. Plugging this into the formula, we get A = π(2.5²) or A = π(6.25). Assuming π as 3.14, we approximate the area to 19.6 ft² after rounding to the nearest tenth.

Final answer:

To find the area of Cory's circular table with a 5-foot diameter, we calculate the radius as half the diameter (2.5 feet) and use the area formula A = πr² to get approximately 19.6 square feet when using 3.14 for pi.

Explanation:

The question asks us to find the area of a circular table that Cory designs, which seats 8 people and has a diameter of 5 feet. To calculate the area of a circle, we use the formula A = πr², where 'A' is the area, 'π' (pi) is a mathematical constant approximately equal to 3.14, and 'r' is the radius of the circle.

First, we need to find the radius, which is half of the diameter, hence the radius is 5 feet / 2 = 2.5 feet. Using the formula, the area in terms of pi is A = π(2.5 ft)². When we approximate π as 3.14, the area rounded to the nearest tenth in square feet is 3.14 * (2.5 ft)² = 19.625 ft², which can be rounded to 19.6 ft².

Answer:

Step-by-step explanation:

The regular price, r of the ingredients before the discount is $40.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number. So the percentage actually means a part per 100.

Percentage is usually denoted by the symbol '%'.

Amount spent by Matias' stepmother to buy the ingredients for huevos rancheros = $28

This is the discounted price after a 30% off discount.

Let the regular price be x.

x - (30% of x ) = 28

x - (0.3 x) = 28

0.7x = 28

x = 28 / 0.7

x = 40

Hence the original price of the items is $40.

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The value of b in the given equation is 2.

An exponential function in mathematics can be defined as a mathematical function is in form f (x) = aˣ, where “x” is the variable and where “a” is known as a constant which is also known as the base of the function and it should always be greater than the value zero.

Given is graph, we need to determine the value of b in the y = bˣ,

Here as we can see, that the curve has a base at -2,

Therefore the equation of the graph will be y = 2⁻ˣ

Hence, the value of b in the given equation is 2.

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Answer:

No, the distance from (0, 0) to (2, √6) is not 3 units.

Step-by-step explanation:

In the figure attached, the problem is shown clearly.

Distance formula:

√[(x2 - x1)² + (y2 - y1)²]

Distance between (0, 0) and (3, 0)

√[(3 - 0)² + (0 - 0)²] = 3

Then, a point lies on the circle shown if the distance between it and center is 3.

Distance between (0, 0) and (2, √6)

√[(2 - 0)² + (√6 - 0)²] = √[4 + 6] = √10 ≠ 3

Answer:

The facility will be adequate for the task.

Step-by-step explanation:

You require space to service 65 vehicles at any one time and each vehicle requires 300 ft² of space. This means, the 65 vehicles will require space of:

65 * 300 = 19500 ft²

A facility measuring 165 ft. by 130 ft is being considered. The area of the facility is:

165 * 130 = 21450 ft²

Since the space of the facility is larger than the space needed for the 65 vehicles, the facility will be adequate for the task.

Answer:

yes!

Step-by-step explanation:

Answer:

67/1 or about 67% of a book per month

Step-by-step explanation:

P(8) = [tex]\frac{12}{50}[/tex] = [tex]\frac{24}{100}[/tex] = 24%