x² + 2x – 1 = 0 in English words.

Answer:

The function g(x) has smallest minimum y-value.

Step-by-step explanation:

The given functions are

[tex]f(x)=4(x-6)^4+1[/tex]

[tex]g(x)=2x^3+28[/tex]

The degree of f(x) is 4 and degree of g(x) is 3.

The value of any number with even power is always greater than 0.

[tex](x-6)^4\geq 0[/tex]

Multiply both sides by 4.

[tex]4(x-6)^4\geq 0[/tex]

Add 1 on both the sides.

[tex]4(x-6)^4+1\geq 0+1[/tex]

[tex]f(x)\geq 1[/tex]

The value of f(x) is always greater than 1, therefore the minimum value of f(x) is 1.

The minimum value of a 3 degree polynomial is -∞. So, the minimum value of g(x) is -∞.

Since -∞ < 1, therefore the function g(x) has smallest minimum y-value.

The function f(x)=4(x-6)^4+1 has the smallest minimum y-value as its minimum value can be directly located at y=1 while g(x)=2x^3+28, being a cubic function, continues infinitely in the negative direction.

In this mathematical problem, we are tasked to determine which of the functions, f(x)=4(x-6)^4+1 or g(x)=2x^3+28, has the smallest minimum y-value. Each of these functions represent distinct types of polynomials which have different properties. The function f(x) is a quartic function that is even, or symmetric around the y-axis, while g(x) is a cubic function.

The minimum value of f(x) can be determined directly by setting the expression (x - 6)^4 to 0, yielding the minimum value 1 because any real number to the power of 4 is always non-negative and the smallest non-negative number is 0. For cubic functions like g(x), they do not have absolute minimum or maximum. They go from negative to positive infinity as x ranges over all real numbers. Therefore, the function f(x)=4(x-6)^4+1 has a smaller minimum y-value.

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Answer:

Option B

Step-by-step explanation:

When two intersecting lines cut each other they form four angles. these two pair of angles are called opposite angles or vertical angles. The vertical angles formed by two intersecting segments are equal.

Thus option B is correct: The vertical Angles Formed By Two Intersecting Segments Are Congruent !

Answer:

B.

Step-by-step explanation:

When you intersect two lines, the angles opposite by the intersection vertex has the same measure. Generally, Those angles are called vertical angles.

In the figure, we have that angle 1 and angle 3 are vertical angles, then both have the same measure. So, the correct option is B) Vertical Angles Formed By Two Intersecting Segments Are Congruent.

Answer:

5:3

5 to 3

3/5

There are three ways to write numbers as ratios

As a ratio:

x:y

As a word sentence:

x to y

As a fraction:

x/y

Answer:

The ratio of carnations to daffodils in three different ways are 5/3, 5:3 and 5 to 3.

Step-by-step explanation:

Given information:

Number of roses = 4

Number of carnations = 5

Number of daffodils = 3

We need to write the ratio of carnations to daffodils in three different ways.

The three different ways to write as ratio are

1. Fraction

[tex]\frac{x}{y}[/tex]

2. Ratio using colon

[tex]x:y[/tex]

3. Word form

x to y

The ratio of carnations to daffodils  is

[tex]\frac{\text{Number of carnations}}{\text{Number of daffodils}}=\frac{5}{3}[/tex]

It can be written as 5:3 and 5 to 3.

Therefore the ratio of carnations to daffodils in three different ways are 5/3, 5:3 and 5 to 3.

Answer

I think its Rational

Step-by-step explanation:

Answer:

Irrational

Step-by-step explanation:

A rational number can be expressed in the form

[tex]\frac{a}{b}[/tex] where a and b are integers

Given

x² = 55 ( take the square root of both sides )

x = ± [tex]\sqrt{55}[/tex] ← irrational

[tex]\sqrt{55}[/tex] cannot be expressed as a rational number

Answer:

Ostrich meat is a "red meat" similar in color and taste to beef. However, it is lower in fat grams per serving compared to chicken and turkey.

Step-by-step explanation:

Hope this helped??!! :3

Answer:

Each of them eat 140 scoops.

Step-by-step explanation:

Let x be the amount eaten by each of them,

Given,

The initial ice cream Masha has =  200 scoops

Final ice cream Masha has = ( 200 - x ) scoops

while the initial ice cream Liz has = 180 scoops,

Final ice cream Liz has = (180-x) scoops,

According to the question,

[tex]\frac{200-x}{180-x}=\frac{3}{2}[/tex]

[tex]400-2x=540-3x[/tex] ( by cross multiplication )

[tex]-2x=140-3x[/tex]       ( Subtracting 400 on both sides )

[tex]x=140[/tex]  ( adding 3x on both sides )

Hence, each of them eat 140 scoops.

Answer: 140 scoops.

Hope this helped!

Answer:

The numbers are    44 (greater) and 16 (  smaler)

Step-by-step explanation:

4x+11x =60

15x = 60

x=4

4*4=16

11*4=44    

44+16 = 60

4/11 =0.363636......

16/44= 0.363636......

Answer:

B

Step-by-step explanation:

Using the rule of exponents

[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]

Given

f(x) = [tex]16^{x}[/tex], then when x = [tex]\frac{1}{2}[/tex]

f([tex]\frac{1}{2}[/tex] ) = [tex]16^{\frac{1}{2} }[/tex] = [tex]\sqrt[2]{16}[/tex] = 4

Answer:

The x intercept is 6

Step-by-step explanation:

To find the x intercept, set y =0 and solve for x

y= 1/2 x-3​

0 = 1/2x -3

Add 3 to each side

0+3 = 1/2 x-3+3

3 =1/2x

Multiply each side by 2

2*3 =1/2x*2

6 =x

The x intercept is 6

Answer:

what ever it said above

Step-by-step explanation:

Answer:

0.6625 in²

Step-by-step explanation:

The surface area of this figure will be the area of the base added to area of the triangles

Area of the 4 triangles

Area of a triangle is given by ;

[tex]A=\frac{1}{2} *b*h[/tex]

where b is the base length and h is the height of the triangle

Area of 1 triangle

Given base length as 0.25 inches and height is 1.2 inches.

[tex]A=\frac{1}{2} *0.25*1.2=0.15\\[/tex]

Area of all 4 triangles

- multiply the area of one triangle by 4

- 0.15*4=0.6 in²

Area of the base

The base is a square of length 0.25 inches

Area of a square=length×length

[tex]A=l*l\\A=0.25*0.25=0.0625in^{2}[/tex]

Total surface area

Total surface area= Area of the triangles + Area of the base

[tex]=0.6+0.0625=0.6625in^{2}[/tex]

Answer:

Numbers less than 1/9.

Step-by-step explanation:

We are given a number [tex]a[/tex] and that it is less than -3.

That is [tex]a<-3[/tex].

What is the range of possibles for [tex]\frac{1}{a^2}[/tex]?

So if [tex]a<-3[/tex] then [tex]a^2>9[/tex].

*I knew to flip inequality here because if I square any number less than -3 it was going have a value bigger than 9.

If [tex]a^2>9[/tex], then [tex]\frac{1}{a^2}<\frac{1}{9}[/tex].

*When taking reciprocal flip the inequality.

Let's do a test:

Let's see if we pick a number less than -3 that we get a result that is less than 1/9 after we find the reciprocal of the square of the number we choose.

Let's pick -4.

-4 is less than -3

Square -4, you get 16  and 16>9.

The reciprocal of 16 is 1/16 and 1/16<1/9.

So 1/16 is a number less than 1/9.

Final answer:

The range of possible values for 1/a squared is all positive numbers greater than 0.

Explanation:

The range of possible values of 1/a squared can be determined by considering the range of values for a. Since a is a number less than -3, it means that a is a negative number less than -3. To find the range of possible values for 1/a squared, we need to consider the range of possible values for a squared. Since a squared is the square of a negative number, it will always be positive. Therefore, the range of possible values for 1/a squared is all positive numbers greater than 0.

A horizontal line test on the inverse of a function yields the same results as a vertical line test on the function itself, and the conclusion is the same as in paragraph two.

A vertical line test looks for one or more intersections with a specified set of relations.  We can conclude that the relation is a function if there is only one intersection with the relation at ANY point in its domain.  If a VERTICAL line intersects the function several times, it is not a function.

Here, we see that the vertical line test on the depicted relation produces just one intersection at any point in the domain of the relation, hence we infer that the graph depicts a function.

A function's inverse is a reflection of the function about the y=x line.  The outcome is the same as swapping the x and y axes.

As a result, a horizontal line test on the inverse of a function yields the same results as a vertical line test on the function itself, and the conclusion is the same as in paragraph two.

For such more question on function

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Answer:

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================[/tex]

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\==========================[/tex]

[tex]\text{We have the equation of a line:}\ y=2x-7\to m_1=2.\\\\\text{The slope of a parallel line:}\ m_2=m_1=2.\\\\\text{We have the equation:}\\\\y=2x+b\\\\\text{Put the coordinates of the point (5, -1) o the equation:}\\\\-1=2(5)+b\\-1=10+b\qquad\tex\text{subtract 10 from both sides}\\-11=b\to b=-11\\\\\text{Finally:}\\\\y=2x-11[/tex]

the correct answer is B) (-5, 7), which represents the center point of the circle.

The equation of a circle in standard form is given by:

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

Where:

- (h, k) is the center of the circle

- r is the radius of the circle

Comparing this standard form to the given equation [tex]\( (x + 5)^2 + (y - 7)^2 = 36 \)[/tex], we can identify the center and radius of the circle.

For the given equation:

- Center of the circle: (-5, 7) because the term [tex]\( (x + 5)^2 \)[/tex] means the x-coordinate of the center is -5, and the term [tex]\( (y - 7)^2 \)[/tex]means the y-coordinate of the center is 7.

- Radius of the circle: [tex]\( r = \sqrt{36} = 6 \)[/tex] because the equation is already in the form [tex]\( r^2 = 36 \), so \( r = 6 \).[/tex]

So, the correct answer is B) (-5, 7), which represents the center point of the circle.

Answer:

x = -0.683 (3dp)

x = -7.317 (3dp)

Step-by-step explanation:

Step 1: Apply the quadratic formula

(-b±([tex]\sqrt{b^{2}-4ac}[/tex])) / 2a

a = 1 (x²)

b = 8 (8x)

c = 5 (5)

(-8±([tex]\sqrt{8^{2}-4 x 1 x 5}[/tex])) / 2 x 1

Step 2: Simplify

(-8±([tex]\sqrt{44}[/tex])) / 2

Step 3: Solve

You need to replace the ± with first a + and then a -.

(-8+([tex]\sqrt{44}[/tex])) / 2 = -0.683 (3dp) = x

(-8-([tex]\sqrt{44}[/tex])) / 2 = -7.317 (3dp) = x

Hope this helps!

Answer:

Yep your correct, 3 east 5 north.

Step-by-step explanation:

He first walks 6 east and 2 north

He then walks 3 west and 3 north

East and west are opposites so 6-3=3 east (not west because he walked more blocks east than west)

North and north are the same so 2+3=5 north

PLEASE GIVE BRAINLIEST

Answer:

[tex]\large\boxed{x=-8\pm5\sqrt2}[/tex]

Step-by-step explanation:

[tex](x-2)^2+12(x+2)-14=0\\\\\text{Substitute}\ (x+2)=t:\\\\t^2+12t-14=0\qquad\text{add 14 to both sides}\\\\t^2+2(t)(6)=14\qquad\text{add}\ 6^2=36\ \text{to both sides}\\\\\underbrace{t^2+2(t)(6)+6^2}=14+36\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(t+6)^2=50\Rightarrow t+6=\pm\sqrt{50}\qquad\text{subtract 6 from both sides}\\\\t=-6\pm\sqrt{25\cdot2}\\\\t=-6\pm5\sqrt2[/tex]

[tex]\text{we're going back to substitution}\\\\x+2=-6\pm5\sqrt2\qquad\text{subtract 2 from both sides}\\\\x=-8\pm5\sqrt2[/tex]

Answer:

Look at pic.

Step-by-step explanation:

Hope this helps!

Using the quadratic formula, the roots of the equation 2x^2 - 3x + 8 = 0 are found to be complex numbers. The roots are: x = 3/4 ± sqrt(-55) / 4.

The subject of this question is the solution to the quadratic equation using the quadratic formula. The quadratic formula is used to find the roots of a quadratic equation, which is an equation of the form ax^2 + bx + c = 0.

The quadratic formula is given by: x = [-b ± sqrt(b^2 - 4ac)] / (2a)

For your equation, 2x^2 - 3x + 8 = 0, the values are a = 2, b = -3 and c = 8.

We substitute these values into the quadratic formula:

x = [3 ± sqrt((-3)^2 - 4*2*8)] / (2*2)

After carrying out the operations, we obtain:

x = [3 ± sqrt(9 - 64)] / 4

The term inside the square root is negative, meaning that the roots of the equation are complex numbers:

x = [3 ± sqrt(-55)] / 4

The answer to the equation is: x = 3/4 ± sqrt(-55) / 4

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Answer:

$13.00

Step-by-step explanation:

so you multiply $5.50 by 2.25 gallons

5.50

x 2.25 =

      2750+1100+1100= 12.3750

then you round it off which will make your answer $12.38

then to find out how much it will be with the taxes you add $12.38 and .072 to it to make the total for the ice cream $13.00

Answer:

5

Step-by-step explanation:

Let's just pretend the 6 numbers are: a,b,c,d,e,f.

Then (a+b+c+d+e+f)/6 =4 (given by first statement.)

Let's pretend the average of 2 numbers is 2 means they are talking about the a and b.

So (a+b)/2=2.

Now we want to find (c+d+e+f)/4 as requested by their question.

So first step multiply both sides of our first equation by 6 giving us:

a+b+c+d+e+f=24

So the second step multiply both sides of our second equation by 2 giving us:

a+b=4.

Now if a+b+c+d+e+f=24 and a+b=4, then c+d+e+f=20 since 20+4=24.

So the average of the four numbers c,d,e, and f is 20/4=5.

Answer: I think its $37.84625 according to the working shown :)

Step-by-step explanation:

cost of paper= $5.79, hence 2 is 2 x 5.79= 11.58

pens= $9.25

paperclips= $2.29

calendar= $12.50

Total= 11.58+9.25+2.29+12.50= 35.62

6.25% sales tax on total purchase= 6.25/100 x 35.62= $2.22625

Adding the sales tax: 35.62+2.22625‬= $37.84625‬‬

Answer:

$37.84625

Step-by-step explanation:

(5.79*2)+9.25+2.29+12.50=35.62

tax: 6.25% of total cost:

6.25/100 * 35.62=2.22625

total cost + tax

35.62+2.22625=37.84625

If there was a graphical representation, I would be happy to assist you.

Simplified form of expression is,

⇒ - 3√3

We have to given that,

An expression is,

⇒ 2√27 + √12 - 3√3 - 2√12

We can simplify it as,

⇒ 2√27 + √12 - 3√3 - 2√12

⇒ 2 √9×3 + √3×4 - 3√3 - 2√3×4

⇒ 2 × 3 √3 - 2√3 - 3√3 - 2 × 2√3

⇒ 6√3 - 2√3 - 3√3 - 4√3

⇒ - 3√3

Therefore, Simplified form of expression is,

⇒ - 3√3

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Final answer:

The expression simplifies to 4sqrt(3) after breaking down the square roots of 27 and 12 into 3√(3) and 2√(3), respectively, and combining like terms.

Explanation:

To simplify the expression 2√(27) + √(12) - 3√(3) - 2√(12), we should first simplify √(27) and √(12) individually.

Square root of 27 can be written as √(9*3). Since 9 is a perfect square, we get 3√(3). Similarly, √(12) can be simplified to √(4*3). As 4 is a perfect square, this simplifies to 2√(3).

Now, substituting back into the original expression, we get 2(3√(3)) + 2√(3) - 3√(3) - 2(2√(3)), which simplifies to 6√(3) + 2√(3) - 3√(3) - 4√(3).

Combining like terms, we obtain 6√(3) - 2√(3), which simplifies further to 4√(3).

Therefore, the simplified form of the original expression is 4√(3).

Answer:

The perimeter can be found by calculating lengths of sides using distance formula and then adding up the lengths

Step-by-step explanation:

If the vertices of a quadrilateral are known in the coordinate plane, the vertices can be used to determine the lengths of sides of quadrilateral. The distance formula is used for calculating the distance between two vertices which is the length of the side

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

after calculating all the lengths of four sides using their vertices, they can be summed up to find the perimeter ..

Answer:

10.000

Step-by-step explanation:

10^4 is equal to 10,000.

10^4 to the second power means that you have too add 4 zeros to the end of the number.

Since 10 already has a 0, you would add 3 more.

Therefore, the answer would be 10,000.

10^4 is the same as saying 10 x 10 x 10 x 10, which is equal to 10 000.