What is the largest integer that is less than √83-√35?​

The vertex of the parabola is (-1,-1)

What is vertex of parabola?

The vertex of a parabola is the highest point or the lowest point, also known as the maximum or minimum of the parabola. The vertex is the point of intersection of the parabola and its line of symmetry.

The vertex is the maximum or minimum point of a parabola.

The vertex is the point where the parabola changes direction.

Here, the point where the parabola changes it direction is (-1,-1).

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The four terms of the series will be equal to 14,20,26, and 32.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the equation for the series is given as, t(n) = 6n + 8. The series will be formed as,

t(n) = 6n + 8.

t(1) = 6 x 1 + 8 = 6 + 8 = 14

t(2) = 6 x 2 + 8 = 12 + 8 = 20

t(3) = 6 x 3 + 8 =  18 + 8 = 26

t(4) = 6 x 4 + 8 = 24 + 8 = 32

Therefore, the four terms of the series will be equal to 14,20,26, and 32.

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The product of linear factors for f(x) is given as (x + 1)(x² + 4x + 2) for -1 as a zero of the polynomial x³ + 5x² + 6x + 2.

The factor theorem states that;

f(x) is divisible by x - a if and only if f(a) = 0

f(x) is divisible by x + a if and only if f(-a) = 0

in both cases, a and -a are the zeros of the polynomials.

From the question, given that -1 is a zero of

f(x) = x³ + 5x² + 6x + 2, then it is divisible by x + 1 and f(-1) = 0.

Dividing x³ + 5x² + 6x + 2 by x + 1 using the long division will result to another factor x² + 4x + 2 with a remainder of zero. (complete long division is attached as a photo!)

Therefore we can then conclude that (x + 1)(x² + 4x - 2) is the product of linear factors for f(x) = x³ + 5x² + 6x + 2 and -1 as a zero.

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The Least number of baseball cards Isabella could have is 49

To solve the problem, the multiples of seven will be necessary to ascertain the one that will:

multiples of 7: 7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 , 63....

14 is short of 1 when divided by 5 but it is divisible by 2 without remainder

49 is the least number that fall short of 1 card to make it a multiple of 5 and have a remainder one when divided by 2

Hence the answer is 49

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The correlation coefficient when there is a study of bone density on 5 random women is -0.909.

It is the statistical measure of the strength of the linear relationship that's between two variables. The correlation coefficient is calculated by calculating the covariance of the variables and dividing that number by the product of the standard deviations of those variables.

The steps for calculating the correlation coefficient are as follows:

The statistical software was used and the values include

Dependent variable = y

Independent variable = x

It should be noted that linear regression has an equation that is in the form of Y = a + bx. The equation is y = 451.674 - 2.051. This was gotten through the statistical software used.

Sample size = 5

Correlation coefficient = -9.09

In conclusion, the coefficient is -9.09.

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The Linear equation used is x -y = 1; to find the age of Isabelle's age.

What is Linear Equation?

An equation is said to be linear if the maximum power of the variable is consistent Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present. A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason.

Let the age of Ben be x;

Let the age of Amara be y;

According to the question:

It is given that:

Ben is one year younger than Amara. That means we have to form a linear equation such that Amara is one year older than Ben.

So,

We have assumed the Age of Ben is x;

we have assumed the Age of Amara is y;

So, According to the question,

Framing the linear equation,

x -1 =y;

⇒x -y = 1;

Hence, We can find the age of Isabelle using the linear equation: x -y = 1;

where x is ben's age;

where y is Amara's age.

Therefore, The Linear equation used is x -y = 1; to find the age of Isabelle's age.

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Answer:

A:

Answer:65Step-by-step explanation:C^2= A^2 + B^2C^2 = (60)^2 + (25)^2 C^2 = 4225Take the square root of CC = 65

Answer:

2/3 u need to walk to reach the clothing shop

If the dairy farmer wants to mix a 80% protein. The amount of pounds of each that he should use is 80% 280 pounds and 55% 1120 pounds.

Protein I 80% = x pounds

Protein II 55% = 1400 - x pounds

Mixture 60% = 1400

Hence,

80% x + 55% ( 1400 - x ) = 60% × 1400

80 x + 55 ( 1400 - x ) = 84000

80 x + 77000 - 55 x = 84000

Combine like terms

80 x - 55 x = 84000 - -77000

25 x = 7000

Divide both side by 25x

x= 7000/25

x =280 pounds ( Protein I)

Protein II

1400 - x pounds

1400 -280

=  1120 pounds

Therefore the farmer should use 280 pounds and 1120 pounds.

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The initial population of the bacterial population at time t = 0, can be found to be 1,406.25.

The size of the bacterial population after 3 hours is 720,000.

The doubling period of the bacterial population is said to be 20 minutes. The number of doubling periods in 120 minutes is:

= 120 / 20

= 6 doubling periods

The initial population is:

= Population at 120 minutes / 2 ^ number of doubling periods

= 90,000 / 2⁶

= 1,406.25

The bacterial population at 3 hours is:

= Bacterial population at t = 0 x 2 ^ number of doubling periods in 3 hours

= 1,406.25 x 2 ^ (180 minutes in 3 hours / 20)

= 1,406.25 x 2⁹

= 720,000

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Answer:

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

Multiply the second equation by 9 and subtract from the first one:

Answer:

[tex]\left(\; \boxed{1}\:,\boxed{-1}\;\right)\; \textsf{and}\;\left(\; \boxed{7}\:,\boxed{-1}\;\right)[/tex]

Step-by-step explanation:

Given system of conics:

[tex]\begin{cases}(x-4)^2+(y+1)^2=9\\\\\dfrac{(x-4)^2}{9}+\dfrac{(y+1)^2}{81}=1\end{aligned}[/tex]

Multiply the second equation by 81:

[tex]\implies \dfrac{81(x-4)^2}{9}+\dfrac{81(y+1)^2}{81}=81[/tex]

[tex]\implies 9(x-4)^2+(y+1)^2=81[/tex]

Rearrange to make (y + 1)² the subject:

[tex]\implies (y+1)^2=81-9(x-4)^2[/tex]

Substitute into the first equation and simplify:

[tex]\implies (x-4)^2+81-9(x-4)^2=9[/tex]

[tex]\implies -8(x-4)^2=-72[/tex]

[tex]\implies (x-4)^2=9[/tex]

Solve for x:

[tex]\implies \sqrt{ (x-4)^2}=\sqrt{9}[/tex]

[tex]\implies x-4=\pm3[/tex]

[tex]\implies x=4\pm3[/tex]

[tex]\implies x=1, 7[/tex]

Substitute the found values of x into the first equation and solve for y:

[tex]\begin{aligned}x=1 \implies (1-4)^2+(y+1)^2&=9\\(-3)^2+(y+1)^2&=9\\9+(y+1)^2&=9\\(y+1)^2&=0\\y+1&=0\\y&=-1\end{aligned}[/tex]

[tex]\begin{aligned}x=7 \implies (7-4)^2+(y+1)^2&=9\\(3)^2+(y+1)^2&=9\\9+(y+1)^2&=9\\(y+1)^2&=0\\y+1&=0\\y&=-1\end{aligned}[/tex]

Therefore, the solution to the given system of conics is:

Answer:

$4.90

Step-by-step explanation:

He already has $13.70 (7.40+6.30) saved up so you have to subtract that from 18.60 to find the total Ace needs to save up.

18.60-13.70=4.90

To check your answer, you can add 7.40, 6.30, and 4.90 and see if you get a total of 18.60.

Check: 7.40+6.30+4.90=18.60

Answer: 4.014e+9 square inches

Answer:

Selling price = RS 3150

Loss percent = 10%

Step-by-step explanation:

1 quintal = 100kg

Cost price = 35*100

= RS 3500

Loss = RS 350

Selling price = RS 3500-350

Selling price = RS 3500-350 =RS 3150

Loss percent = Loss *100%

Cost Price

= 0.1 *100

= 10%

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The axis of symmetry of the parabola, having the equation, f(x) = 3·(x - 5)² + 1 is the line x = h = 5

A parabola is the locus of a point that moves such that the distance of the point from a fixed point is the same as the distance of the moving point from a fixed line.

The graph of a parabola has the shape of an open umbrella

The given equation for the parabola is; f(x) = 3·(x - 5)² + 1

The equation is given in the vertex form, f(x) = a·(x - h)² + k, where;

(h, k) = The vertex of the parabola

The axis of symmetry of a parabola, which is the line that divides the parabola in two, passes through the vertex of the parabola

Comparing the equation, f(x) = 3·(x - 5)² + 1, to the vertex form of a parabola,  gives;

a = 3

(h, k) = (5, 1) (The vertex of the parabola)

Which gives; h = 5

The equation of the axis of symmetry is therefore the line, x = h = 5

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An equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6 is y=x/2-5.

Given that, an equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

We know that, the slope of a line parallel to given line is m1=m2.

Here, x−2y=6

⇒ 2y=x-6

⇒ y=x/2-3

So, slope = 1/2

The slope of a line parallel to the given line = 1/2

Now, put m=1/2 and (x, y)=(-6, -8) in y=mx+c and solve for c

-8=1/2(-6)+c

⇒ c=-8+3

⇒ c=-5

Thus, y=x/2-5

Therefore, an equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6 is y=x/2-5.

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The explanation is above

Answer:

THE CORRECT ANSWER IS 1.9824 x 10^7

Step-by-step explanation:

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Part A Write an inequality to represent the possible lengths of time

the tent can be rented

[tex]6.11\leq h\leq 11.66[/tex]

Part B. Using your inequality in Part A, what is one possible length of

time the tent could be rented

[tex]6hr 6min\leq h\leq 11hr39min[/tex]

The definition of a linear inequality

The inequality symbol is used to compare two mathematical expressions in what are referred to as linear inequalities. The expression could be both numerical and algebraic, or it could just be one.

What does a linear inequality in mathematics look like?

What Is an Example of Linear Inequality? An example is the linear inequality x - 5 > 3x - 10. The LHS is obviously greater than the RHS because the greater than symbol is being utilized in this inequality. After being resolved, the inequality appears as follows: 2x 5 x (5/2).

Given That

45h+225 is total cost in dollars for renting tent and parents are willing to spend between $500 and $750 for the tent.

Part A

[tex]500\leq 45h+225\leq 750\\500-225\leq 45h+225-225\leq 750-225\\275\leq 45h\leq 525\\\frac{275}{45} \leq h\leq \frac{525}{45} \\6.11\leq h\leq 11.66[/tex]

Part B

[tex]6.11hr\leq h\leq 11.66hr[/tex]

6.11 hr = 366 minute approx.

11.66 hr = 699 minute approx.

[tex]6hr 6min\leq h\leq 11hr39min[/tex]

Hence this is the answer

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When a six sided dice through with the coin all the possible outcomes  are as follows

H-1 H-2 H-3 H-4 H-5 H-6

T-1 T-2 T-3 T-4 T-5 T-6

Probability that she gets an outcome of tails and 2 = 1 / 12

Isabelle flips a fair coin and rells a fair six-sided dice.

Coin has two face H or T

Dice has six face hat is 1, 2, 3, 4, 5, 6  

When a six sided dice through with the coin all the possible outcomes  are as follows

H-1 H-2 H-3 H-4 H-5 H-6

T-1 T-2 T-3 T-4 T-5 T-6

So there are total 12 outcomes possible when a six sided dice through with the coin.

Probability that she gets an outcome of tails and 2 = event occur / total number of events = 1 / 12

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The average change in the otter's position each minute is -24.5 ft per minute and the otter goes deeper.

What is average change?

The ratio of "change in the function values" to "change in the interval endpoints" is referred to as the average rate of change of a function f(x) over an interval [a, b].

Here, we have

Sea level changes by -73.5 ft in 3 minutes

So, we apply the average change formula, and we get

= -73.5/3

= - 24.5 ft per minute

And the otter goes deeper because - 24.5 < 0

Hence, the average change in the otter's position each minute is -24.5 ft per minute and the otter goes deeper.

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Answer: going to take a wild guess and say figure 2 or figure 4 is correct but I'm going with figure 2

Step-by-step explanation:

Answer: Figure 4

Step-by-step explanation:

I got it right on Edmentum

Answer:

38.8333333

sorry if it's wrong.

Answer:

3???

Step-by-step explanation:

Answer:

m∠1 = 26°

Step-by-step explanation:

Interior angles of a triangle sum to 180°, not 360°.

Therefore, the correct calculations to find the measure of angle 1 are:

[tex]\boxed{\begin{aligned}115^{\circ}+39^{\circ}+m \angle 1 &=180^{\circ}\\\\154^{\circ}+m \angle1 & = 180^{\circ}\\\\m \angle1 & = 26^{\circ}\end{aligned}}[/tex]

Answer:

Step-by-step explanation:

The Horizontal asymptote of y = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.

Hope this helps!

Have a great day!!

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{5}}} \implies \cfrac{-1 +2}{2} \implies \cfrac{ 1 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{1 }{ 2 }}(x-\stackrel{x_1}{5}) \implies y +2 = \cfrac{1 }{ 2 } ( x -5) \\\\\\ y+2=\cfrac{1 }{ 2 }x-\cfrac{5 }{ 2 }\implies y=\cfrac{1 }{ 2 }x-\cfrac{5 }{ 2 }-2\implies {\Large \begin{array}{llll} y=\cfrac{1 }{ 2 }x-\cfrac{9}{2} \end{array}}[/tex]

Answer:

y=1/2x-9/2

Step-by-step explanation:

First you want to find the slope by doing -2-(-1)/5-7

Therefore the slope is 1/2

Next you want to add in any set of points, either (5, -2) or (7, -1)

Substitute the x- point in place of x and the y in place of y in y=1/2x+b

Once you do this you should get -2=1/2(5)+b

You should get -2=2 1/2+b

Then subtract 2 1/2 from -2

You should get -4 1/2

Once you have the slope and y- intercept you can put together your problem

y=1/2x-4 1/2

don't forget to convert, y=1/2x-9/2

Hope this helps  

Check the picture below.

Answer:

x > -2

Step-by-step explanation:

3x - 10 < 4x - 8

Collect like terms

3x - 4x < 10 - 8

-1x < 2

Divide both sides by -1

-1x/-1 < 2/-1

x > -2

Answer:

y = 12x + 35

95 pages

Step-by-step explanation:

Let y represent the total number of pages

Let x represent the total number of months

x = 5 (months)

so..

y = 12(5) + 35

y = 60 + 35

y = 95

He earned $71.5 if he earn $11 /hr. I worked for 6 and a half hrs yesterday.

An hour (symbol: h; also abbreviated as hr) is a measure of time that is traditionally thought of as one-fourth of a day and that, according to science, lasts between 3,599 and 3,601 seconds, depending on how quickly the Earth rotates. There are 24 hours in a day and 60 minutes in an hour. 60 minutes is one of the 24 equally spaced out segments of a day.

Given,

Earns $11/hr

Worked for 6 hours and 30 minutes

Multiplying:

$11 × 6.5 hours

$ 71.5

He earned $71.5 if he earn $11 /hr. I worked for 6 and a half hrs yesterday.

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