Which statements describe the function ? check all that apply. f(x) has one real zero because it crosses the x-axis once. f(x) has two real zeros because it crosses the x-axis twice. f(x) has real zeros at 1 and –1. f(x) has a real zero at 2.5. f(x) has x-intercepts at (1, 0) and (–1, 0). f(x) crosses the x-axis when x = 1 and x = –1. f(x) has an x-intercept at (2.5, 0).

Answer:

(a) k = 4
(b) y = - 2x + 9

Step-by-step explanation:

x2-x1, y2-y1  
= 3-2, 3-5

= 1,-2
3,3 + 1,-2 = (4,1)

x=4

Type of model best fits the given situation linear.  Since it has a constant of +3 everyday.

What is a linear equation in math?

the membership of the local pta increases by 3 members a day for each day during the month of September.

Since it has a constant of +3 everyday.

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The (f + g)(x) = 15x - 2 is represent the total round trip time.

According to the statement

we have given that the f(x) represents the time it takes a boat to travel upstream and g(x) represents the time it takes a boat to travel downstream.

And we have to find the total round trip time.

So, For this purpose, the given information is:

f(x) = 3x − 10 and g(x) = 12x + 8

And

The total round trip time is represented by the term (f + g)(x)

We know that the

(f + g)(x) = f(x) + g(x)

Substitute the given values in it

So, (f + g)(x) = f(x) + g(x)

(f + g)(x) = (3x - 10) + (12x + 8)

(f + g)(x) = 15x - 2

Hence, The (f + g)(x) = 15x - 2 is represent the total round trip time.

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The new dimensions of the flower bed are 4√2 and 6√2

The dimensions of the initial rectangular flower bed are given as:

Length = 4ft

Width = 6 ft

The area of the new flower bed is twice the area of the old one.

This means that

New Area = Old Area * 2

Substitute the dimensions of the old area in the above equation

New Area = 4 * 6 * 2

Express 2 as √2 * √2

This gives

New Area = 4 * 6 * √2 * √2

Rewrite the above equation as:

New Area = 4√2 * 6√2

The area of a rectangle is

Area = Length * Width

This means that:

Length = 4√2 ft

Width = 6√2 ft

Hence, the new dimensions of the flower bed are 4√2 and 6√2

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Answer: 6x8

Step-by-step explanation:

(4+x)(6+x)=2*24

x^2+10x+24=48

subtract 48 on both sides

x^2+10x-24=0

Solve using the quadratic formula

-10±√(100+96)÷2

simplifies to

-(10±14)÷2 = 2, -12

-12 doesn't work though because the sides can't be negative.

So x=2

To check, add both sides by 2:

2(4x6)=6x8=48

Answer:

Laplace transforms turn a Differential equation into an algebraic, so we can solve easier.

y'= pY-y(0)

y"=p²Y - py(0)- y'(0)

Substituting these in differential equation :

p²Y -py (0)  -y' (0)-6(pY-y(0)) + 13Y

Substituting in the initial conditions given , fact out Y, and get:

Y( p²-6p+13) = -3

Y=-3/ p²-6p+13

now looking this up in a table to Laplace transformation we get:

y=-3/2.e³т sin(2t)

for the last one, find the Laplace of t∧2 . which is 2/p³

pY - y(0)+ 5Y= 2/p³

Y= 2/p³(p+5)

Taking partial fractions:

Y=-2/125(p+5) + 2/125p - 2/25p² + 2/5p³

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Answer:

The integral transform that converts a function of a real variable to a function of a complex variable is called Laplace transform. first we need to substitute y' and y" in differential equation then finding Laplace transformation and at last taking partial fractions.

Given:                              y'= pY-y(0)

                                         y"=p²Y - py(0)- y'(0)

Putting y' and y" in differential equation :

                               p²Y -py (0)  -y' (0)-6(pY-y(0)) + 13Y

Substituting in the initial conditions given , fact out Y, and get:

                                 Y( p²-6p+13) = -3

                                                    Y=-3/ p²-6p+13

by Laplace transform we get:

                                  y=-3/2.e³т sin(2t)

for the last one, find the Laplace transform of t∧2 . which is 2/p³

                                  pY - y(0)+ 5Y= 2/p³

                                                     Y= 2/p³(p+5)

Taking partial fractions:

                                Y=-2/125(p+5) + 2/125p - 2/25p² + 2/5p³

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Answer:

6 - 16y

Step-by-step explanation:

2(3 – 8y) = 2 × 3 - 2 × 8y = 6 - 16y

Solving a linear equation, we will see that after 9 days he cuts the last section.

We know that the initial length of the piece of cloth is 20m, and the taylor each day cuts a piece of 2 meters of it.

So, the length as a function on the number of days, is:

L(x) = 20m - 2m*x

Here we just need to solve:

L(x) = 2m

Because the last cut is when the long piece measures 4 meters (in that case he does one cut and has the two final pieces of 2 meters).

Solving that, we get:

20m - 2m*x = 2m

20m - 2m = 2m*x

18m/2m = x = 9

After 9 days he cuts the last section.

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If a diameter intersects a chord of a circle at a perpendicular then the chord is bisected.

The solution to the problem:

A circle's chord is intersected perpendicularly by its diameter, which also passes through the center of the circle. The chord and diameter are perpendicular. Any line that is perpendicular to a chord on the circle and passes through its center divides it. The chord is divided equally by the diameter.

Therefore, the chord is bisected.

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The surface area of the shape is 117.8 km²

From the question, we are to determine the surface area of the figure

The given figure is a cone.

Total surface area of a cone  = Area of circular part + Curved surface area

Total surface area of a cone = πr² + πrl = πr(r + l)

Where r is the radius

and l is the slant height

From the given information,

r = 3 km

l = 9.5 km

The total surface area of the cone = π×3(3+9.5)

The total surface area of the cone = 3π(12.5)

The total surface area of the cone = 117.8 km²

Hence, the surface area of the shape is 117.8 km²

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Answer: B

Step-by-step explanation:

First, find the sum of the bottles, which is 6,235,168,989 which is not an estimate.

Rounding it to the nearest billion, the answer is 6,000,000,000 or B)

Answer: $223,600

Step-by-step explanation:

Since it is $86 per square foot and you're replacing the 2,600 square foot house you would just take 2,600 × 86 and get 223,600 dollars.

Answer:

Yes

Step-by-step explanation:

The given line is an average of the data points.

Answer: 1/2

Step-by-step explanation:

The probabilities must add to 1, so:

[tex]P(x < 9) +P(X=9)+P(X > 9)=1\\\\\frac{1}{6}+P(X=9)+\frac{1}{3}=1\\\\P(X=9)=\boxed{\frac{1}{2}}[/tex]

The option that is true with regard to the following functions is Option B. "The domain g(x) and h(x) include all real number while the domain of i(x) and h(x) are restricted"

Note that this function is indicative of a straight-line. See the attached graph for function 1. Note that it doesn't have any end points. That is, it is Asymptote.

This represents an exponential graph. Just like the function above it doesn't have any end point. It however has an asymptote:

y = 0

This is indicative of logarithm graph. It doesn't have any end but has an asymptote x == 0

Notice that in the mid point there is an end point given as (0, -14). Thus, it is correct to state that the function in Option B is the only one that exhibits end behavior and as such is restricted.

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The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.

According to the statement

we have to find the condition of the expected values in the case of testing of goodness-of-fit test.

So, For this purpose we know that the

The goodness of fit test is of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected.

So, The main condition of the expected value for the goodness of fit test is

For each​ category, the expected frequency is at least 5.

Without this condition the test is not possible, so overall this the main condition related the goodness of fit test.

So, The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.

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Answer:

See attached image

Step-by-step explanation:

Every step holds except for step 5

In mathematics, it deals with numbers of operations according to the statements.

Here,
Step 1 is the result of the distribution of -5 while opening the parenthesis, So, Step 1 holds the distributive property.

Step 2, states adding like terms across each side, so combining as terms hold,

Step 3, Addition over the equal sign. So it also holds

Step 4, subtraction of 12 over the equal sign. So subtraction of the terms also holds.

Step 5, does not hold because the number 12 gets divided by 8 it is not an associative property.

Thus, Every step holds except for step 5.

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Answer: [tex]\frac{2x\sqrt[4]{y^{2}}}{3}[/tex]

Step-by-step explanation:

[tex]\sqrt[4]{\frac{16}[81}} \sqrt[4]{\frac{x^{11}y^{8}}{x^{7}y^{6}}}\\\\=\frac{2}{3} \sqrt[4]{x^{4}y^{2}}\\\\=\frac{2x\sqrt[4]{y^{2}}}{3}[/tex]

Answer:

y = - 5x² - 10x + 2

Step-by-step explanation:

y = - 5(x + 1)² + 7 ← expand (x + 1)² using FOIL

  = - 5(x² + 2x + 1) + 7 ← distribute parenthesis by - 5

 = - 5x² - 10x - 5 + 7 ← collect like terms

 = -5x² - 10x + 2 ← in standard form

Answer: y = -5x² - 10x + 2

Step-by-step explanation:

Given quadratic function

y = -5 (x + 1)² + 7

Given requirement

Quadratic Standard Form: y = ax² + bx + c

Simplify the exponents

y = -5 (x + 1) (x + 1) + 7

y = -5 (x² + x + x + 1) + 7

y = -5 (x² + 2x + 1) + 7

Expand the parenthesis by distributive property

y = (-5) · x² + (-5) · 2x + (-5) · 1 + 7

y = -5x² + (-10x) + (-5) + 7

y = -5x² - 10x - 5 + 7

Combine like terms

[tex]\Large\boxed{y=-5x^2-10x+2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The x-intercept of the function g(x) = -5(x - 3)^2 is (3, 0) and the vertex of the function g(x) = -5(x - 3)^2 is (3, 0)

The function is given as:

g(x) = -5(x - 3)^2

Set g(x) to 0, to determine the x-intercept.

-5(x - 3)^2 = 0

Divide through by -5

(x - 3)^2 = 0

Take the square root of both sides

x - 3 = 0

Add 3 to both sides

x = 3

Hence, the x-intercept of the function g(x) = -5(x - 3)^2 is (3, 0)

The function is given as:

g(x) = -5(x - 3)^2

A quadratic function is represented as:

g(x) = a(x - h)^2 + k

Where, the vertex is

Vertex = (h, k)

By comparing g(x) = a(x - h)^2 + k and g(x) = -5(x - 3)^2, we have

(h, k) = (3, 0)

Hence, the vertex of the function g(x) = -5(x - 3)^2 is (3, 0)

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The paragraph looks like:

Since AC, MN, and DB intersect at O, ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD.

In the question, we are asked to convert the given proof to the paragraph format, where the proof is already given to us.

The proof given to us is:

Statements________________________Reasons

1. AC, MN, and  DB intersect at O.______1. given

2. ∠AOM ≅ ∠NOC__________________2. vertical angles theorem.

3. ∠MOD ≅ ∠BON__________________3. vertical angles theorem.

4. ∠BON ≅ ∠NOC__________________4. given.

5. ∠AOM ≅ ∠MOD_________________5. transitive property of congruence.

To convert this proof to the paragraph format, we need to translate each statement along with its reason in the paragraph.

Thus, the paragraph looks like:

Since AC, MN, and DB intersect at O, ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD.

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The value of the z score is 1.03.

According to the statement

we have given that the value of mean and standard deviation and we have to find the value of the z score.

So, For this purpose we know that the

Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean.

And the given values are:

mean value = 69 inches

s.d value = 2.8 inches

And the value of x is 71.9 inches.

So, The Z score is

z = x - mean / standard deviation

substitute the values in it then

z = 71.9 - 69 / 2.8

then

z = 2.9 /2.8

z  = 1.03

So, The value of the z score is 1.03.

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Using it's concept, the probability that a student plays basketball or soccer is given as follows:

B. 7/10.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

P(A or B) is the probability that a student plays basketball or soccer, hence, from the Venn diagram:

Hence the probability P(A or B), that is, the probability that a student plays basketball or soccer, is given as follows:

p = 7/10.

Which means that option B is correct.

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Answer:

A perfect cube monomial must have three identical root , such that the product of the roots equal the perfect square monomial . The coefficient of the monomial must be divisible by 3 . Any monomial can be a perfect cube root .

Step-by-step explanation:

1.)1000=10 cube

2.) 729=9 cube

3.) 512=8 cube

4.) 343=7 cube

5.) 216=6 cube

6.) 125=5 cube

7.) 64=4 cube

8.) 27=3 cube

9.) 8=2cube

10.) 1=1 cube

An equation in standard form for a hyperbola with center (0, 0), vertex (-5, 0), and focus (-6, 0) is given by y²/25 - x²/9 = 1.

An equation can be defined as a mathematical expression which is used to show and indicate that two (2) or more numerical quantities are equal.

Mathematically, the equation of a hyperbola in standard form is given by:

[tex]\frac{(y\;-\;k)^2}{a^2} - \frac{(x\;-\;h)^2}{b^2} = 1[/tex]

Given the following data:

Center (h, k) = (0, 0)

Vertex (h+a, k) = (-5, 0)

Foci, F = (h+c, k) = (-6, 0) and F' = (6, 0)

Also, we can logically deduce that the value of a and c are -5 and -6 respectively.

For the value of b, we would apply Pythagorean's theorem:

c² = a² + b²

b² = c² - a²

b² = (-6)² - (-5)²

b² = 36 - 25

b² = 9.

b = √9

b = 3.

Substituting the given parameters into the equation of a hyperbola in standard form, we have;

[tex]\frac{(y\;-\;k)^2}{a^2} - \frac{(x\;-\;h)^2}{b^2} = 1\\\\\frac{(y\;-\;0)^2}{-5^2} - \frac{(x\;-\;0)^2}{3^2} = 1\\\\\frac{y^2}{-5^2} - \frac{x^2}{3^2} = 1\\\\\frac{y^2}{25} - \frac{x^2}{9} = 1[/tex]

y²/25 - x²/9 = 1.

In conclusion, we can logically deduce that an equation in standard form for a hyperbola with center (0, 0), vertex (-5, 0), and focus (-6, 0) is given by y²/25 - x²/9 = 1.

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Answer:

-20

Step-by-step explanation:

He went back 20 and not forward 20.  Everyone would want a penalty if you got to go forward.

Answer:

Step-by-step explanation:

Answer:

i think no 3 hasexactly one 0

The difference of the x-coordinate of point A and the x-coordinate of point B is 0

The coordinate of a point on an xy-plane is written in the form (x, y). The given figures are circles A and B where the circle A is greater than circle B.

The position of the dots in both sides are positioned at the centre and as such the coordinate point at the centre of both circle will be the origin (0, 0)

According to the question, we are to find the difference of the x-coordinate of point A and the x-coordinate of point B

x-coordinate of pint A = 0

x-coordinate of point B = 0

Take the difference

Difference = 0 - 0

Difference = 0

Hence the difference of the x-coordinate of point A and the x-coordinate of point B is 0

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The altitude of the trapezoid, based on the given parameters is 5 units

From the question, we have the following parameters about the trapezoid

Base length 1 of the trapezoid = 6

Base length 2 of the trapezoid = 10

Area of the trapezoid = 40

Altitude of the trapezoid = h

The area of the trapezoid is calculated using

Area = 0.5 * (Sum of the two base lengths) * Altitude of the trapezoid

Substitute the given parameters in the above formula

40 = 0.5 * (6 + 10) * h

Evaluate the sum of 6 ad 10 (do not approximate)

40 = 0.5 * (16) * h

Evaluate the product of 0.5 and 16 (do not approximate)

40 = 8 * h

Divide both sides by 8 (do not approximate)

h = 5

Hence, the altitude of the trapezoid, based on the given parameters is 5 units

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Answer:

5 units

Step-by-step explanation: