Which inequality represents all values of x for which the product below is defined?
√5x * √x+3
A. x>0
B. x≤-3
C. x≥-3
D. x≥0

The x-intercepts of the parabola are [tex]\( x = -3 \) and \( x = 1 \)[/tex].

To find the x-intercepts of the parabola defined by the equation [tex]\( y = -3x^2 - 6x + 9 \)[/tex], we need to set y=0 and solve for x.

So, we have:

[tex]\[ -3x^2 - 6x + 9 = 0 \][/tex]

Now, let's solve this quadratic equation using the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]where \( a = -3 \), \( b = -6 \), and \( c = 9 \).\[ x = \frac{-(-6) \pm \sqrt{(-6)^2 - 4(-3)(9)}}{2(-3)} \]\[ x = \frac{6 \pm \sqrt{36 + 108}}{-6} \]\[ x = \frac{6 \pm \sqrt{144}}{-6} \][/tex]

[tex]\[ x = \frac{6 \pm 12}{-6} \][/tex]

Now, we have two possible values for x:

1. When [tex]\( x = \frac{6 + 12}{-6} = \frac{18}{-6} = -3 \)[/tex]

2. When [tex]\( x = \frac{6 - 12}{-6} = \frac{-6}{-6} = 1 \)[/tex]

let's say the point dividing JK is say point P, so the JK segment gets split into two pieces, JP and PK

[tex]\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ J(-25,10)\qquad K(5,-20)\qquad \qquad \stackrel{\textit{ratio from J to K}}{7:3} \\\\\\ \cfrac{J~~\begin{matrix} P \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} P \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~K} = \cfrac{7}{3}\implies \cfrac{J}{K} = \cfrac{7}{3}\implies3J=7K\implies 3(-25,10)=7(5,-20)\\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf P=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill\\\\ P=\left(\cfrac{(3\cdot -25)+(7\cdot 5)}{7+3}\quad ,\quad \stackrel{\textit{y-coordinate}}{\cfrac{(3\cdot 10)+(7\cdot -20)}{7+3}}\right) \\\\\\ P=\left( \qquad ,\quad \cfrac{30-140}{10} \right)\implies P=\left(\qquad ,~~\cfrac{-110}{10} \right)\implies P=(\qquad ,\quad -11)[/tex]

Answer:

-11

Step-by-step explanation:

J =(–25, 10)

K=(5, –20)

Point L divides JK into a 7:3 ratio

To find the coordinates of L we will use section formula.

Formula : [tex]x=\frac{mx_2+nx_1}{m+n}[/tex] and [tex]y=\frac{my_2+ny_1}{m+n}[/tex]

m: n = 7: 3

[tex](x_1,y_1)=(-25,10)\\(x_2,y_2)=(5,-20)[/tex]

Substitute the values

[tex]x=\frac{7(5)+3(-25)}{7+3}[/tex] and [tex]y=\frac{7(-20)+3(10)}{7+3}[/tex]

[tex]x=-4[/tex] and [tex]y=-11[/tex]

Hence the y coordinate of L is -11

Answer:

f(n)=8(-3)^(n-1)

The formula which can be used to show the nth term of a geometric sequence where the first term is 8 and the common ratio is - 3 is,

⇒ - 8/3 × (- 3)ⁿ

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

We have to given that;

The first term is, 8

And, the common ratio is –3

Now,

The nth term of a geometric sequence is:

⇒ T (n) = arⁿ⁻¹

Put a = 8 and r = - 3

⇒ T (n) = 8 (- 3)ⁿ⁻¹

⇒ T (n) = - 8/3 × (- 3)ⁿ

Thus, The formula which can be used to show the nth term of a geometric sequence where the first term is 8 and the common ratio is - 3 is,

⇒ - 8/3 × (- 3)ⁿ

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[tex]\text{Hey there!}[/tex]

[tex]\text{The slope formula is:}\dfrac{\bf{y_2\ - y_1}}{\bf{x_2\ - x_1}}[/tex]

[tex]\bf{y_2 = -8}[/tex]

[tex]\bf{y_1=4}[/tex]

[tex]\bf{x_2=-4}[/tex]

[tex]\bf{x_1=0}[/tex]

[tex]\text{Your equation should look like this:}\dfrac{-8 \ - 4}{-4 \ - 0}[/tex]

[tex]\text{Solve the numerator first (the top) then the denominator (the bottom) }[/tex]

[tex]\text{-8 - 4 = -12}[/tex]

[tex]\dfrac{-12}{-4 - 0}[/tex]

[tex]-4 - 0=-4[/tex]

[tex]\dfrac{-12}{-4} =\ ?[/tex]

[tex]\dfrac{-12\div-4}{-4\div-4}=\dfrac{3\div1}{1\div1}=3[/tex]

[tex]\boxed{\boxed{\bf{Answer: 3}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

3

Step-by-step explanation:

Slope formula:

   ↓

[tex]\frac{Y_2-Y_1}{X_2-X_1}=\frac{Rise}{Run}[/tex]

[tex]\frac{(-8)-4}{(-4)-0}=\frac{-12}{-4}=\frac{-12\div-4}{-4\div-4}=\frac{3}{1}=3[/tex]

Therefore, the slope is 3 is the correct answer.

It is formed by two rays lie in a plane.

The simplified formula for calculating the monthly lease payment for a car is the sum of the depreciation fee and the finance fee. These are calculated based on the car's initial cost, residual value, and the lease factor.

In the context of car leasing, the simplified formula used to calculate the monthly lease payment is: depreciation fee + finance fee. The depreciation fee is calculated by subtracting the car's expected residual value at the end of the lease from its initial cost (MSRP) and then dividing this by the number of months in the lease. The finance fee is calculated as the sum of the MSRP and the residual value, multiplied by the lease factor or money factor which is essentially the interest rate.

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Answer:

x = 7

x = - 1

Step-by-step explanation:

2(x-3)²-32=0                      Add 32 to both sides

2(x-3)² - 32+32 = 32          Combine

2(x - 3)²  = 32                     Divide by 2

2(x - 3)² /2 = 32/2              Do the division

(x - 3)² = 16                         Take the square root of both sides

sqrt(x - 3)² = sqrt(16)           Do the square root.

x - 3 = +/- 4

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

x - 3 = 4                                Add 3 to both sides

x - 3+3 = 4+3

x = 7

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

x - 3 = - 4                            Add 3 to both sides

x -3 +3 = - 4 + 3                      

x = - 1

Answer:

Standard deviation can be difficult to interpret as a single number on its own. Basically, a small standard deviation means that the values in a statistical data set are close to the mean of the data set, on average, and a large standard deviation means that the values in the data set are farther away from the mean, on average.

Step-by-step explanation:

The standard deviation has the same units as the original data.

Final answer:

The context of a dataset influences its interpretation by providing background information that affects understanding. Different contexts can lead to varying interpretations of the same dataset. Understanding context is essential for accurate data interpretation and decision-making.

Explanation:

Answer:

A pentagon is a 5 sided shape. Angles are very easy to draw. You could figure out the angles by drawing them or using a calculator or probably a math equipment.

Step-by-step explanation:

A pentagon is a 5-sided shape. Angles are very easy to draw. You could figure out the angles by drawing them or using a calculator or probably math equipment.

A pentagon shape is a flat shape or a flat (two-dimensional) 5-sided geometric shape.

In geometry, it is considered as a is a five-sided polygon with five straight sides and five interior angles, which add up to 540°.

A pentagon shape is a plane figure, or a flat (two-dimensional) 5-sided geometric shape.

The measure of each angle of a regular pentagon is given by the below formula. The measure of the central angle a regular pentagon makes a circle, i.e. total measure is 360°.

Hence, a pentagon is a 5-sided shape. Angles are very easy to draw. You could figure out the angles by drawing them or using a calculator or probably math equipment.

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Answer:300 cm2(in the case of rectangle)

Step-by-step explanation:

The question is ambiguous.Something is missing.what is the shape of the object is not told here.

But if you consider it a "rectangle",the angles will be right angles.

area of a rectangle=length×breadth

=20cm×15cm

=300 centimetre2

Answer: square centimeters

Step-by-step explanation:

Hi, the answer to the question is square centimeters.

The lengths of the picture are in centimeters. So, when you calculate the area of the picture that is a triangle you obtain square centimeters.

Mathematically speaking:

20cm x 15 cm =  300 square centimeters

By multiplying the same unit you obtain the square unit.

Feel free to ask for more if it´s necessary or if you did not understand something.

Answer:

B.) 83.7758

Step-by-step explanation:

Answer:

83.75 cubic inches

Step-by-step explanation:

We are given the diameter of a cone 8 inches, and height 5 inches and we are to find the volume of this cone.

(diameter is 8 inches so radius will be 4 inch)

We know that the volume of a cone is given by:

Volume of cone = [tex] \pi r ^ 2 \frac { h } { 3 } [/tex]

Substituting the given values in the above formula:

Volume of cone = [tex] \pi \times 4 ^ 2 \times \frac { 5 } { 3 } [/tex] = 83.75 cubic inches

(diameter is 8 inches so radius will be 4 inches)

Answer:

D. Vertex (1, -25); intercepts x = -4, 6

Step-by-step explanation:

Vertex

x = -b/2a

x = - (-2)/2(1)

x = 2/2

x = 1

y = 1^2 - 2(1) - 24

y = 1 - 2 - 24

y = -25

Vertex (1, -25)

x-intercepts when y = 0

x^2 - 2x - 24 = 0

(x - 6)(x + 4) = 0

x - 6 = 0; x = 6

x + 4 = 0;x = -4

Answer

D. Vertex (1, -25); intercepts x = -4, 6

Answer:

Yes it can be simplified.

Answer: -7 and 13/21

Step-by-step explanation:

(-3 2/7) - (4 1/3)

Least common multiple for the denominator= 21

1. -23/7 - 13/3

2. -69/21 - 91/21 = -160/21

3. -7 13/21

ANSWER

[tex]y = - 2{x}^{2} -28x - 96[/tex]

EXPLANATION

We have that

[tex]x = - 8 \: \: and \: \: x = - 6[/tex]

are the roots of the quadratic function.

This implies that

[tex]x + 8 \: \: and \: \: x + 6[/tex]

are factors of the quadratic function.

The quadratic function will have an equation of the form:

[tex]y = a(x + 8)(x + 6)[/tex]

It was also given that, the vertex of the function is at

[tex](-7, 2)[/tex]

This point must satisfy the equation.

This implies that:

[tex]2= a( - 7 + 8)( - 7+ 6)[/tex]

This implies that,

[tex]2=-a[/tex]

[tex]a = - 2[/tex]

We substitute the value of 'a' to get the equation in factored form as:

[tex]y = - 2(x + 8)(x + 6)[/tex]

We expand the parenthesis to write the equation in standard form.

[tex]y = - 2( {x}^{2} + 6x + 8x + 48)[/tex]

[tex]y = - 2( {x}^{2} + 14x + 48)[/tex]

[tex]y = - 2{x}^{2} -28x - 96[/tex]

Or in vertex form, the equation is

[tex]y = - 2 {(x + 7)}^{2} + 2[/tex]

Answer:

[tex]f(x)=\frac{3}{5}(x+1)^2+4[/tex]

Step-by-step explanation:

The equation of a quadratic function in vertex form is given by:

[tex]f(x)=a(x-h)^2+k[/tex]

Where (h,k) is the vertex.

It was given in the question that the vertex of the parabola is (-1,4).

When we substitute the vertex into the formula we get:

[tex]f(x)=a(x+1)^2+4[/tex]

The parabola also passes through (4,19) hence it must satisfy its equation.

[tex]19=a(4+1)^2+4[/tex]

[tex]19-4=a(5)^2[/tex]

[tex]15=25a[/tex]

We divide both sides by 25 to get:

[tex]a=\frac{15}{25}= \frac{3}{5}[/tex]

Hence the quadratic function is:

[tex]f(x)=\frac{3}{5}(x+1)^2+4[/tex]

Answer:

The answer is B

Step-by-step explanation:

$2.50+$1.95=$27.46

                     -2.50

                       24.69

24.63/1.95

equal $12.80 or 12.8

Answer:

B) 1.95x + 2.50 = 27.46; Isaac traveled 12.8 miles.

Step-by-step explanation:

Answer: 200 x 10

Step-by-step explanation:

√400 x √100 = 40,000  

√40,000 = 200  

The solution is :  The required simplified form is 20 × 10.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

We are given to find the simplified form of the following radical expression :

E = √400x100

We will be using the following property of radicals :

√x = x^1/2

and, √a* b = √a * √b

Therefore, we have

√400 x √100

= √40,000  

now, we get,

√40,000

= √400 x √100

=√20² x √10²  

=20x10

=200

Thus, the required simplified form is 20 × 10.

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Answer:

Third option.

Step-by-step explanation:

You need to cube both sides of the equation. Remember the Power of a power property:

[tex](a^m)^n=a^{mn[/tex]

[tex]\sqrt[3]{162x^cy^5}=3x^2y(\sqrt[3]{6y^d})\\\\(\sqrt[3]{162x^cy^5})^3=(3x^2y(\sqrt[3]{6y^d}))^3\\\\162x^cy^5=27x^6y^36y^d[/tex]

According to the Product of powers property:

[tex](a^m)(a^n)=a^{(m+n)[/tex]

Then. simplifying you get:

[tex]162x^cy^5=162x^6y^{(3+d)}[/tex]

Now you need to compare the exponents. You can observe that the exponent of "x" on the right side is 6,  then the exponent of "x" on the left side must be 6. Therefore:

[tex]c=6[/tex]

You can notice that the exponent of "y" on the left side is 5,  then the exponent of "x" on the left side must be 5 too. Therefore "d" is:

[tex]3+d=5\\d=5-3\\d=2[/tex]

Answer:

An equation to have no solution means that the system of equations do not intersect at all and therefore will not have any solutions. If an equation has indefinite many solutions then the system of equations will have the same line since they are intersecting each other

Step-by-step explanation:

First, you must find the total number of people. Add together 32, 54, 78, 112, and 96 to get 372. Next, add the number of diabetic patients with the number of patients with eye problems (54 + 112 = 166).

Your fraction is now 116/372. Simplify this to get your answer, 29/93 or 0.31.

Answer:

The value of x is 20°

Step-by-step explanation:

we know that

m∠ 9 and m∠ 11 are corresponding angles

If line c is parallel to line d

then

m∠ 9 = m∠ 11

Substitute

6x=120°

x=20°

Answer:

20

Step-by-step explanation:

:))

Answer:

1 solution

Step-by-step explanation:

This is a linear equation and has one solution

6x - 4 = x + 6 ( subtract x from both sides )

5x - 4 = 6 ( add 4 to both sides )

5x = 10 ( divide both sides by 5 )

x = 10 ← only 1 solution

Answer:

2568 kg

Step-by-step explanation:

30816 divided by 24 gives us 1284 or the total number of cartons which can then be multiplied by 2 to give us the weight of the empty cartons.

To find the total mass of the empty cartons, divide the total number of exercise books by the number of exercise books in each carton and then multiply by the difference in mass between a full and empty carton.

To find the total mass of the empty cartons, we need to determine how many cartons there are and the difference in mass between a full carton and an empty carton.

Given that each carton contains 24 exercise books and there are 30816 exercise books in total, we can calculate the number of cartons by dividing the total number of exercise books by 24.

So, there are 1284 cartons in total.

Now, we need to find the difference in mass between a full carton and an empty carton. The difference is 12 kg - 2 kg = 10 kg.

To find the total mass of the empty cartons, we multiply the number of cartons by the mass difference: 1284 cartons * 10 kg/carton = 12840 kg.

Therefore, the total mass of the empty cartons is 12840 kg.

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Answer:

63 % for cats and 37 % for dogs

Step-by-step explanation:

Answer:

The answer I believe is 4.

Step-by-step explanation:

Answer: the answer is 4

Step-by-step explanation:

;)

Answer:

$13.95

Step-by-step explanation:

You need to multiply the 5 notebooks with the costs of each notebook, which gives you the total costs before tax.

Answer:

[tex](2y-1)^{2}[/tex]

Step-by-step explanation:

[tex]4y^{2} -4y+1[/tex]

Sum = -4

Product = 1

Factors = -1 , -1

[tex](2y-1)^{2}[/tex]

Answer:

D.

Step-by-step explanation:

To find this area, we can break it up into two rectangles, one with dimensions of 4x19 and another of 24x11. All we have to do is find the areas of both rectangles and add them together!

Since 4*19=76 and 11*24=264, we get D. 340 square units as our answer.

For this case we have that the area of the figure is given by the sum of the areas of two rectangles. The area of a rectangle is given by:

[tex]A = a * b[/tex]

Where:

a, b: They are the sides of the rectangle

[tex]A_ {1} = 24 * 11\\A_ {1} = 264[/tex]

On the other hand:

[tex]A_{2} = 4 * (4 + 11 + 4) = 4 * 19 = 76[/tex]

Thus, the total area is:

[tex]A_ {t} = 264 + 76\\A_ {t} = 340[/tex]

The total area is 340 square units

Answer:

Option D

Answer:

The output is 23

Step-by-step explanation:

we know that

f(x) ----> is the output

x ----> is the input

we have that

f(x)=3x-1

For x=8 (input)

Find the value of f(x) (output)

f(8)=3(8)-1=23

The output is 23