Without graphing, determine the range of the function f(x) = 4|x+6|-5 over
the interval [-10,5].

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]

a quadratic equation is an equation with a degree of 2.

well, is not 2x + x + 3 for sure, and is not 3x³ + 2x + 2 either, that one is a cubic, 3rd degree.

well, one would think is 0x² - 4x + 7, however 0x² is really 0, anything times 0 is 0, so the deceptive equation is really -4x + 7, which is not a quadratic.

5x² - 4x + 5 on the other hand is.

To find the slope and y-intercept of the equation -y = -0.9x + 4, multiply both sides by -1 to get y = 0.9x - 4, revealing a slope of 0.9 and a y-intercept of -4.

To find the slope and y-intercept of the graph -y = -0.9x + 4, we first need to rewrite the equation in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

By multiplying both sides of the equation by -1, we get y = 0.9x - 4. Here, it's clear that the slope (m) is 0.9 and the y-intercept (b) is -4.

This means that for every increase of 1 on the horizontal axis (x), there is a rise of 0.9 on the vertical axis (y). Additionally, the point where the line intersects the y-axis is at y = -4.

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:

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:

Ay=3 over 2 or y=-2 over 3

Step-by-step explanation:

the quadratic formula: y={-b±√(b²-4ac)}/2a

In the equation 6y²-5y-6= 0, a=6, b=-5, c= -6

Substituting for the values in the formula we get:

{-(-5)±√[(-5²)-4(6)(-6)}/2(6)

{5±√169}12

={5±13}/12

(5+13)/12=3/2 or (5-13)/12= -2/3

Answer:

[tex]y=\frac{3}{2}[/tex] or [tex]y=-\frac{2}{3}[/tex]

Step-by-step explanation:

We have the expression

[tex]6y^2-5y-6 = 0[/tex]

For an equation of the form [tex]ay^2 +by +c[/tex]  the quadratic formula is

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

In this case

[tex]a = 6\\b= -5\\c =-6[/tex]

[tex]y=\frac{-(-5) \± \sqrt{(-5)^2 -4(6)(-6)}}{2(6)}[/tex]

[tex]y_1=\frac{3}{2}[/tex]

[tex]y_2=-\frac{2}{3}[/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:

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:

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:

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:

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:

Step-by-step explanation:

A graph shows that only the points listed above are within the doubly-shaded area. Points on the boundary line are not solutions, since the inequalities do not include the "or equal to" case.

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:

(2x)^2-(5)^2

Step-by-step explanation:

Answer:

43091.3 or 43181.81(81 repeated)

Step-by-step explanation:

There are two answers because it depends on the method you use. You can get the second answer by plugging 95 into the equation gram*0.0022=pound or gram=(pound/0.0022). When you insert the 95, you get 43181.81(81 repeated).You can find the first answer by just looking it up on the conversion chart on google.

Answer:

43091.275 Grams

Step-by-step explanation:

95 pounds is equal to 43091.275 grams.

Multiply the mass value by 453.592

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]

It is formed by two rays lie in a plane.

[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.

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

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]

Answer:

1/150 is greater than 1/200. A general rule is that the larger the denominator is, the smaller the fraction.

The bigger fraction is,

⇒ 1 / 150

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

Two numbers are,

⇒ 1/150

⇒ 1/200

Since, We know that;

⇒ 1 / 150 = 0.0067

⇒ 1 / 200 = 0.005

Hence, The bigger fraction is,

⇒ 1 / 150

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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:

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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Answer:

[tex]\large\boxed{1.\ \dfrac{1}{x}=5+2\sqrt6}\\\boxed{2.\ \dfrac{x-1}{x}=-4-2\sqrt6}\\\boxed{3.\ \dfrac{x+1}{x}=6+2\sqrt6}[/tex]

Step-by-step explanation:

[tex]x=5-2\sqrt6\\\\1.\\\\\dfrac{1}{x}=\dfrac{1}{5-2\sqrt6}=\dfrac{1}{5-2\sqrt6}\cdot\dfrac{5+2\sqrt6}{5+2\sqrt6}\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\dfrac{5+2\sqrt6}{5^2-(2\sqrt6)^2}=\dfrac{5+2\sqrt6}{25-2^2(\sqrt6)^2}=\dfrac{5+2\sqrt6}{25-(4)(6)}=\dfrac{5+2\sqrt6}{25-24}\\\\=\dfrac{5+2\sqrt6}{1}=5+2\sqrt6\\\\2.\\\\\dfrac{x-1}{x}=\dfrac{x}{x}-\dfrac{1}{x}=1-\dfrac{1}{x}\\\\\text{use the value of}\ \dfrac{1}{x}\ \text{from 1.}\\\\\dfrac{x-1}{x}=1-(5+2\sqrt6)=1-5-2\sqrt6=-4-2\sqrt6[/tex]

[tex]3.\\\\\dfrac{x+1}{x}=\dfrac{x}{x}+\dfrac{1}{x}=1+\dfrac{1}{x}\\\\\text{use the value of}\ \dfrac{1}{x}\ \text{from 1.}\\\\\dfrac{x+1}{x}=1+5+2\sqrt6=6+2\sqrt6[/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:

(3x + 5)(4x - 7)

Step-by-step explanation:

The most common factors of 35 are 5 and 7. The 12 is a nuisance.

We could try 6 and 2 or 3 and 4 or even 12 and 1. You just have to juggle a bit to get the difference to be - x.  

I'm going to try 3 and 4 first with 5 and 7. The numbers you get for the middle term have to be quite close.

(3x     5)(4x      7) Oops. It's going to come out first try.

Now you need to get the middle term come to - 1

(3x   -  5)(4x  +    7)

Just to make it slightly harder, I'll do it the wrong way first.

-5*4x + 3x*7 = - 20x + 21x = x That is close. Only the signs are incorrect.

So try again.

(3x + 5)(4x - 7)

20x - 21x = - x

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: 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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