10. Seven more than the quotient of a number b
and 45 is greater than 5.

Answer:

P(x) = 0.7 [tex]x^{4}[/tex] - 4.9x³ + 5.6x² + 11.2x

Step-by-step explanation:

given a polynomial with roots x = a and x = b , then the factors are

(x - a) and (x - b)

If x = a is of multiplicity 2 then factor is (x - a)²

the polynomial is then the product of the factors

p(x) = a(x - a)(x - b) ← a is a multiplier

give x = 4 is a root with multiplicity 2 then (x - 4)² is the factor

x = 0 has factor (x - 0) , that is x

x = - 1 has factor (x - (- 1)) , that is (x + 1)

the polynomial is then the product of the factors

P(x) = ax(x + 1)(x - 4)² ← expand squared factor using FOIL

       = ax(x + 1)(x² - 8x + 16)

       = a(x² + x)(x² - 8x + 16) ← distribute

       = a([tex]x^{4}[/tex] - 8x³ + 16x² + x³ - 8x² + 16x)

      = a([tex]x^{4}[/tex] - 7x³ + 8x² + 16x)

to find a substitute (5, 21 ) into P(x)

21 = a([tex]5^{4}[/tex] - 7(5)³ + 8(5)² + 16(5))

21 = a(625 - 875 + 200 + 80)

21 = 30a ( divide both sides by 30 )

0.7 = a

then

P(x) = 0.7([tex]x^{4}[/tex] - 7x³ + 8x² + 16x) ← distribute parenthesis

P(x) = 0.7[tex]x^{4}[/tex] - 4.9x³ + 5.6x² + 11.2x

The number of 3 / 16 yards pieces that can be cut from 3 / 4 yard of ribbon is 4.

The actual length of the ribbon is 3 / 4 yards.

He wants to cut 3 / 16 yards pieces from the actual length of the ribbon.

Therefore, the number of 3 / 16 yard that can be cut from 3 / 4 yard of ribbon can be calculated as follows;

number of pieces of ribbon = 3 / 4 ÷ 3 / 16

number of pieces of ribbon = 3 / 4 × 16 / 3

number of pieces of ribbon =  48 / 12

Therefore,

number of pieces of ribbon =  4 yards

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Answer: its 18,0000

Step-by-step explanation: Be smart  2x9= 18+ three 0,s?

The horizontal asymptote is y = [tex]\frac{9}{4}[/tex].

Let f(x) = [tex]\frac{9x^{3}-5x-9}{4x^{3}-9x+4}[/tex]

Line y = L is a horizontal asymptote of the function y=f(x), if either [tex]\lim_{x \to \infty} f(x) = L[/tex] or, [tex]\lim_{x \to -\infty} f(x) =L[/tex] and L is finite.

We will calculate limits :

[tex]\lim_{x \to \infty}(\frac{9x^{3}-5x-9}{4x^{3}-9x+4}) = \frac{9}{4}[/tex]

[tex]\lim_{x \to -\infty}(\frac{9x^{3}-5x-9}{4x^{3}-9x+4}) = \frac{9}{4}[/tex]

Hence, horizontal asymptote is y = [tex]\frac{9}{4}[/tex].

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The probability that the sample proportion will differ from the population proportion by more than 3% is 0.8948

The requirement to solve the probability between z-values is to know that the probability between the z-values is the difference between the probability of the greatest z-value and the lowest z-value.

In this case, the sample proportion:

= ✓[p(1 - p)/n]

= ✓(0.13 × 0.87)/329

= 0.01854.

The probability will be:

P(-0.03 / 0.01854) < z < (0.03 / 0.01854)

P(-1.62 < z < 1.62)

Looking at the z table, the probability is 0.08948

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Using an inequality to represent the problem, Chang must run at least an additional 9 miles or greater than 9 miles

In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

To find the number of additional miles he will run, let's set the unknown number equals t

12 + t > 21

t > 21 - 12

t >9

Chang will need to run at least 9 miles

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Answer: Marks bakery

Step-by-step explanation:

divide 450 by 3 = 150 loaves of bread Ann baked per day

divide 560 by 4= 140 loaves of bread Mark bakes per day

Thus Marks bakery bakes bread at a faster rate.

Answer:

yes, if the labor takes 150 minutes (or 2h 30 minutes)

Step-by-step explanation:

m + 350 = 2m + 200

2m - m = 350 - 200

m = 150

If they observes a blood sample with a compound microscope that has a 10x ocular lens and a 40x objective lens. The larger that the blood cells appear under the microscope is: 400x.

Given data:

Blood sample has:

10x ocular lens

40x objective lens

Using this formula to determine how large the blood cells appear

Blood cells = ocular lens × objective lens

Let plug in the formula

Blood cells =  10x × 40x

Blood cells = 400x or 400 times larger

Therefore the blood cells appear 400 times larger.

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400 times larger

Answer:

  336, 504

Step-by-step explanation:

You want the next two numbers in the sequence beginning 6, 24, 60, 120, 210, ....

When attempting to identify a sequence it is often useful to look at the differences between terms, then at the differences of those, and so on. If The differences at some level are constant, that level tells you the degree of the polynomial that will describe the sequence. If they have a common ratio, then the sequence will be based on an exponential function.

1st differences: 18, 36, 60, 90

2nd differences: 18, 24, 30

3rd differences: 6, 6 . . . . . . . . constant, indicating a cubic function

We can go to the trouble to write four equations in the four coefficients of the cubic describing this sequence, or we can let suitable technology find it for us. The attachment shows a graphing calculator solution for the coefficients. The 10^-14 value for the 'd' coefficient is effectively 0. This value is due to the inexact representation of numbers in the floating point arithmetic used by the calculator.

The equation of the n-th term a[n] is ...

  a[n] = n³ +3n² +2n

The next two terms are ...

  a[6] = 336

  a[7] = 540

__

Additional comment

The equations for the coefficients of y = ax³ +bx² +cx +d will use the given sequence values and x values of 1..4. Here they are:

  6 = a·1 +b·1 +c·1 +d

  24 = a·8 +b·4 +c·2 +d

  60 = a·27 +b·9 +c·3 +d

  120 = a·64 +b·16 +c·4 +d

The second attachment shows a calculator solution for these four equations. (a, b, c, d) = (1, 3, 2, 0)

Answer:

Step-by-step explanation

so basically you need to see what m<I equals and do the same for the rest of them and you should get your answer and that would be let me see and m<k= -44 degrees and m<I and J= -10 degrees and there you have if this is not right i tried have the same step and ask another person

The rate at which the tip of the woman's shadow is moving, found by making use of the relationships between similar triangle and differentiation is 10 ft/s

Similar triangles are triangle in which all three sides of one proportional to three sides of the other triangle

Height of the woman = 6 ft.

The speed with which the woman walks towards the streetlight = 8 ft/s
The length of the shadow of the woman

Height of the street light = 30 ft.

Let a represent the horizontal distance from the woman to the street light, and let b represent the horizontal distance from the woman to the tip of her shadow, from the similar triangles formed by the shadow, we have;

[tex]\dfrac{30}{x+y} =\dfrac{6}{y}[/tex]
Which gives;

[tex]y = \dfrac{x}{4}[/tex]

The length of the tip of the woman's shadow to the street light, l, in terms of x is therefore;

[tex]l =x + y = x + \dfrac{x}{4} = \dfrac{5\cdot x}{4}[/tex]

[tex]\dfrac{dx}{dt} = 8[/tex]

Therefore, dx = 8·dt

x(t) = 8·t

Writing the function for the l in terms of time t gives;

[tex]l = \dfrac{5\cdot x}{4}[/tex]

[tex]l = \dfrac{5\times 8\cdot t}{4} = \dfrac{40\cdot t}{4} = 10\cdot t[/tex]

The speed at which the tip of the shadow is moving,

[tex]\dfrac{dl}{dt} = \dfrac{d}{dt} \left (10\cdot t ) = 10[/tex]

The speed of the shadow dl/dx = 10 ft./s

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well, the reduction in value is £12500 - £11625 = £875.

if we take 12500 to be the 100%, what is 875 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 12500 & 100\\ 875& x \end{array} \implies \cfrac{12500}{875}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{100}{7}=\cfrac{100}{x}\implies 100x=700\implies x=\cfrac{700}{100}\implies x=7[/tex]

Answer: El porcentaje de reducción exacto es de: 7%, con esto el precio de descuento es de €875.

The result of the expression (-3/10) + -9 × 9/10 is -42/5

The expression is

(-3/10) + -9 × 9/10

The expression is the mathematical statement that consist of different variables, numbers and the mathematical operators.

The expression is

(-3/10) + -9 × 9/10

Here we have to do the suitable arithmetic operations

First do the multiplication in the given expression

= (-3/10) + (-9×9)/10

= (-3/10) + -81/10

Add the terms in the expression

Here the denominator of the both term is equal so we just need to add the numerators

= (-3 + -81) / 10

= (-3 - 81) / 10

= -84 / 10

Divide both numerator and denominator by 2

= -42/5

Hence, the result of the expression (-3/10) + -9 × 9/10 = -42/5

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y + 2 = 5/2 (x - 6) ; 5x-2y=34 ; y=5/2x-17 is the equations of the line that goes through the point (6,-2) and is perpendicular to the line y+2=-2/5(x-10), Hence the correct options are B, C and F.

The standard forms of the equation of a line are:

Slope-intercept form:

y = mx + c

Where m indicates the slope of the line and c is the y-intercept

Intercept form:

x/a + y/b = 1

General form of the equation of the straight line, i.e. Ax+By+C = 0

x/(-C/A) + y/(-C/B) = 1

where a = -C/A and b = – C/B

Normal form:

The equation of the line whose length of the normal from the origin is p and the angle made by the normal with the positive x-axis is given by α is given by:

x cos α+y sin α = p

Given,

Point = (6,-2) = (x2,y2)

Equation of line = y+2=-2/5(x-10)

General equation of the line = y - y1 = m ( x-x1 )

After comparing we get,

Slope of the given line = -2/5

As we know both the lines are perpendicular to each other so, product of their slopes must be equal to -1.

m1 × m2 = -1

-2/5 × m2 = -1

We get m2 = 5/2

So the equation of the line having slope  5/2 and passing through  (6,-2) is:

y - y2 = m2 ( x-x2 )

y -(-2) = 5/2 (x - 6)

y + 2 = 5/2 (x - 6)

Hence, we get equation of the line as y + 2 = 5/2 (x - 6) .

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The function f(x) = -3(x + 2)² + 1 has it's vertex as (-2, 1) and an axis of symmetry x = -2

The graph of a quadratic function is called a parabola and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph. You can think of like an endpoint of a parabola.

In the given function;

f(x) = -3(x + 2)² + 1

Kindly find the attached graph of the function below

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The cost to rent chair is $1.5  and table is $8.5  .

In the question ,

it is given that

the cost to rent 12 chairs and 2 tables [tex]=[/tex] $35

and the cost to rent 3 chairs and 5 tables  [tex]=[/tex] $47

let the cost for 1 chair ne "c"

and let the cost for 1 table = "t"

So , according to the question ,

the equations are

12c + 2t = 35      ....equation(1)

3c + 5t = 47         ....equation (2)

On multiply equation (2) by 4 and then subtracting equation (1) from it ,

we get

(12c + 20t) - (12c + 2t) = 188 - 35

12c + 20t - 12c -2t = 153

18t = 153

t = 153/18

t = 8.5

and 12c + 2(8.5) = 35

12c + 17 = 35

12c = 18

c = 18/12

c = 1.5

Therefore , The cost to rent chair is $1.5  and table is $8.5  .

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Answer:

5x-9=26

Step-by-step explanation:

5x=35

5 5

x = 7

mark me on brainliest please follow me to

Answer:

x = 7

Step-by-step explanation:

When five times a number is decreased by 9 ​, the result is 26 . What is the​ number?

5x - 9 = 26

add 9 to both sides:

5x - 9 + 9 = 26 + 9

5x =35

divide both sides by 5:

5x/5 =35/5

x = 7

well now, let's recall the remainder theorem, check your textbook since we know you're Da Bomb and love to check that theorem.

well, we know a factor is (x-2) for the polynomial f(x), that means that f(2) =  0, so let's use that

[tex]f(x)=x^3+x^2-5ax+2a^2\hspace{5em}\stackrel{\textit{a factor of f(x)}}{(x-2)}\qquad thus\qquad f(2)=0 \\\\\\ 0=(2)^3+(2)^2-5a(2)+2a^2\implies 0=8+4-10a+2a^2 \\\\\\ 0=2a^2-10a+12\implies 0=2(a^2-5a+6) \\\\\\ 0=a^2-5a+6\implies 0=(a-2)(a-3)\implies a= \begin{cases} 2\\ 3 \end{cases}[/tex]

Answer: The skis cost $117.60.

Step-by-step explanation:

A pair of skis costing $210 is 30% off.

30% of $210 is $147

Then two weeks later, it will be 20% off THAT price.

20% of $147 is $117.60

Therefore, $117.60 is the clearence price of the skis. Hope this helps!

Answer:

A, C, D, E

Step-by-step explanation:

17 is a positive whole number

All whole numbers are integers and rational

Natural numbers are numbers that are positive whole numbers

It is real since you don't have any negative roots

The graph of this proportional relationship would look like this: A line passes through the point (0, 0) and continues through the point (14, 7).

In Mathematics, a graph simply refers a type of chart that is typically used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points passing through the origin (0, 0) because as the values on the x-coordinate (x-axis) increases or decreases, the values on the y-coordinate (y-axis) increases or decreases simultaneously.

By critically observing graph of this proportional relationship (see attachment), we can logically deduce that it passes through both points (0, 0) and (14, 7).

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The number of quadrilaterals that can be formed with the vertices of a regular pentagon is given by:

5.

The number of vertices for each polygon is given as follows:

Hence, to build the quadrilaterals, four vertices are taken from the set of five vertices of the pentagon.

The formula to be used is given as follows:

The order of the vertices is not relevant, hence the combination formula is used, given as follows:

[tex]C_{n,x} = \frac{n!}{x!(n - x)!}[/tex]

Which gives the number of different combinations of x elements from a set of n elements.

Hence, in the context of this problem, the number of quadrilaterals is obtained as follows:

[tex]C_{5,4} = \frac{5!}{4!1!} = 5[/tex]

The problem asks for how many quadrilaterals can be formed with the vertices of a regular pentagon.

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The statement which must be true given the premise that; T is the midpoint of RS and V lies between R and T is; Choice A; RV + VT = TS.

It follows from the task content that the answer choice which represents a true statement regarding the given description be identified.

Since it is given that T is the midpoint of RS, it follows that;

RT = TS.

Also, it is given that point V lies between R and T; it therefore obviously follows that the equation which is true about RV and VT is;

RV + VT = RT.

Therefore, since segments RT and TS are equal;

It follows from the substitution property of equality that;

RV + VT = TS.

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An equation modeling the population, p, of Ohio given the year, t is,

p = 0.04t + 10.98.

What is population?

The term "population" refers to all citizens who are either permanently residing in a country or who are just passing through. This indicator reveals how many people typically reside in a certain area. Growth rates are the population changes that occur each year as a result of births, deaths, and net migration.

Given: In the year 2000, the population of Ohio was 11.03 million people. By the year 2017 the population of Ohio was 11.66 million people.

From this we get, two points (0, 11.03) and (17, 11.66).

First to find the slope using the above two points.

[tex]m=\frac{11.66 - 11.03}{17-0} = \frac{0.63}{17} = 0.04[/tex]

Now to find the equation,

Consider,

p - 11.66 = 0.04(t - 17)

p - 11.66 = 0.04t - 0.68

          p = 0.04t - 0.68 + 11.66

          p = 0.04t + 10.98

Therefore, the equation modeling the population, p, of Ohio given the year, t is, p = 0.04t + 10.98

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Answer:

c is ur answer

I hope it's help◉‿◉

Answer:

the answer of this question is:

1q+17r+10