Foster recently went on a weekend hiking trip and recorded the elevation changes at several checkpoints. Fosters elevation log can be seen in the table below. If the next checkpoint has a change in final elevation of 148.3 what is the change in elevation

The binomial are factors of the given polynomial function f(x) = x³ + 3x² -16x- 48.

Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number.

We can check whether the given binomials are factors of a given polynomial or not by factorizing the given polynomial.

[tex]f(x) = x^3 + 3x^2 -16x- 48[/tex]

Factoring out x² and 16, we get

[tex]f(x) = x^2(x + 3) -16(x+3)[/tex]

Now, factoring out (x+3), we get

[tex]f(x) = (x + 3)(x^2-16)[/tex]

Using Algebraic identity [tex]a^2-b^2=(a+b)(a-b)[/tex], we get

[tex]f(x) = (x + 3)(x+4)(x-4)[/tex]

So, it is clear that only the (x-4) binomial is a factor of the given polynomial and (x-3) and (x+2) are not.

Therefore, (x-4) is a factor of the given polynomial and (x-3) and (x+2) are not.

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The coordinates of the point on the directed line segment are (7/2,21/4).

What is a line segment?

A line segment is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon.

Here, we have

A line segment with coordinates partitioned in some ratio.

Let's say that the ends of the segment are A and B.

We have to find the coordinates of C.

Coordinates of point A are = (2,9)

Coordinates of point B are = (8,-3)

Considering the point C as (x,y) and the partition ratios as m:n i.e 1:3

By applying the section formula, we get

x = mx₂ + nx₁ /(m+n) ,  y = my₂ + ny₁ /(m+n)

x = 1 × 9 + 3 × 2 / (1+3) , y = 1×(-3) + 3 × 8 / (1+3)

x = 14/4,   y = 21/4

x = 7/2 , y = 21/4

Hence, the coordinates of the point on the directed line segment are (7/2,21/4).

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Change in y when x =2 and  Δx= 0.1 is 2.05 and the differential dy when x= 2 and dx = 0.1 is 2

Δy and dy can be calculates as follows

We already knew that Δy = f( x + Δx ) - f(x) and y = f(x)

so we just need to subtitute the values

Δy = f( x + Δx ) - f(x)

Δy = f( 2 + 0.1 ) - f(2) and back to y = f(x) we can subtitute the f(x) by [tex]5x^{2}[/tex] so,

Δy = [tex]5(2.1)^{2} -5(2)^{2}[/tex]

Δy = 2.05

and for the differential,

dy = f'(x) dx  and we need to know diferential from y=[tex]5x^{2}[/tex] is 10x

so we just subtitutes the values

dy = f'(x) dx

dy = f'(2) (0.1) and back to  diferential from y=[tex]5x^{2}[/tex] is 10x so subtitute the f'(x)

dy = 10(2) (0.1)

dy =  2

hence, change in y, Δy is 2.05 an the diferenyial dy is 2

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The total change in the car's speed during that time is 1500 per hour

The difference is that expressions, which are essentially mathematical "phrases," do not contain an equal sign. Equations have an equal sign and demonstrate that two mathematical expressions are equivalent. An algebraic equation is 2x + b = 14, whereas 2x + b is an algebraic expression.

One of the three main types of algebraic expressions is the monomial expression. Binary Expression Expression of a polynomial.

In the mathematics curriculum and in mathematics in general, algebraic expressions are crucial. Students must be proficient in computations and the manipulation of algebraic expressions in order to advance and perform well in mathematics. They must also be able to read and write expressions.

Given ,

total change in car =300× 2

                              = 1500 per hour

Therefore the total change in the car's speed is 1500 per hour

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The point estimate of the population mean is 30 and margin of error for the confidence interval with lower bound 25 and upper bound 35 is 5.

Point Estimate = Upper bound + Lower bound /2

Point Estimate = 35 + 25 /2

Point Estimate = 60/2

Point Estimate =30

Margin of error = Upper bound − Lower bound /2

Margin of error =  35 -25/2

Margin of error = 10/2

Margin of error =5

Therefore the  point estimate is 30 and the margin of error is 5.

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The solution of the system of equations using substitution is, (2500, 5).

What is substitution method?

In the "by substitution" method, one of the equations is solved for one of the variables (you choose which one), which is then plugged back into the other equation where the chosen variable is "substituted" for and the second equation is then solved for. The first variable is then back-solved.

The equations are,

d = 200m + 1500             ..(1)

d = 500m                         ..(2)

Substitute d = 500m in equation (1),

500m = 200m + 1500

300m = 1500

      m = 5

Plug m = 5 in equation (2),

d = 500(5) = 2500

Hence, the solution of the system of equations using substitution is, (2500, 5).

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The equation of the parabola as described in the task content is; f (x) = -3 (x - 5)² + 9.

It follows from the task content that the equation of the parabola which has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f (x) = a (x-h)² + k be determined.

Recall that the vertex of a quadratic equations of the given form is defined by the coordinates (h, k).

On this note, the required equation of the parabola by substitution of h and k is;

f (x) = -3 (x - 5)² + 9.

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Answer:

Decimal: 0.08

Fraction: 2/25

Step-by-step explanation:

To convert a percentage to a decimal, we divide the percentage by 100, or move the decimal point to the left 2 times:

8/100 = 0.08

To convert a percentage to a fraction, we need to understand what a percentage is first. A percentage is a "number or ratio expressed as a fraction of 100". This means that percentages are numbers out of 100 (x% = x/100). Therefore, to convert 8% to a fraction, we divide 8 by 100:

8% = 8/100

Next, simplify the fraction

8/100 = 2/25

3)The first angle in the triangle is three times that of the second angle. The second angle is two times that of the third angle. The ratio of angles in the triangle is 6:2:1.

4)The scale of a map measures 1 inch : 1250 miles. If the distance between two cities measures 3 inches on the map. The actual distance between the two cities on the ground is 3750 miles.

5)A sum of 2700 dollars is shared among Eric, Jo and Richard. Jo's share is two times that of Richard's share. Eric's share is three times that of Jo's share. Eric's share is 1800 dollars.

3) Let A,B,C are the angles of a triangle.

Given that, A =3B, B=2C

A = 3B =3(2C) = 6C

B=2C

Thus, A:B:C = 6C: 2C: C = 6:2:1

4) Given, scale of the map is 1 inch : 1250 miles

The distance between two cities is given as 3 inches.

The actual distance between two cities is 3*1250 = 3750 miles.

5) J is Jo's share, E is Eric's share, R is Richard's share

Given that, J=2R, E=3J

E=3J = 3*2R = 6R

E+J+R = 2700

6R + 2R + R = 2700

9R = 2700

R = 300 dollars

Eric's share = 6R = 6(300) = 1800 dollars

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The function f(x) = 12×[tex]5^{x-1}[/tex], x = week number

Given data,

week 1 = 12 visitors

week 2 = 60 visitors

week 3 = 300 visitors

week 4 = 1500 visitors

week 5 = 7500 visitors

The function can be given by :

f(x) = 12×[tex]5^{x-1}[/tex], x = week number

f(1) = 12×[tex]5^{0}[/tex] = 12

f(2) = 12×[tex]5^{1}[/tex] = 60

f(3) = 12×[tex]5^{2}[/tex] = 300

f(4) = 12×[tex]5^{3}[/tex] = 1500

f(5) = 12×[tex]5^{4}[/tex] = 7500

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Answer:

x = 9

Step-by-step explanation:

7x + 18 = 81

     -18     -18

------------------------

7x = 63

÷7    ÷7

-----------

x = 9

I hope this helps!

The translation rule is T<5, 2> and the image of U' is (0,3)

Translation.

The transformation of a shape in a plane that preserves length, which means that the object is transformed without getting its dimensions affected. i.e., it may just be shifted to left/right/up/down is referred as translation.

Given,

The vertices of a rectangle are R(-5, -5), S(-1,-5), T(-1, 1), and U(-5, 1). A translation maps R to the point (0, -3).

Here we need to find the translation rule and the image of U

Here we know the given the vertices of rectangle which are  R(–5, –5), S(–1, –5), T(–1, 1), and  U(–5, 1).

And it is also given that the translation maps R(-5,-5) to the point (0, -3). we have to find the translation rule and the image of U.

In order to find the translation rule,

First we have to identify the Horizontal shift for the given point

That is calculated as,

=> 0 - (-5) = 5 unit

Which means R is shifted to 5 units horizontally.

Now, the Vertical shift is calculated as,

=> -3 - (-5) = 2 units

Which means R is shifted to 2 units vertically.

Therefore, the translation rule is < 5, 2 >  

So, the image of U(-5, 1) is calculated as,

=> -5 + 5 = 0

=> 1 + 2 = 3

Therefore, the point of the image U' is (0, 3)

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The value of the y is 18 when x = 5.

Given,

In the question:

If y varies inversely as x

and, y=9 when x =10

To find the value of y when x = 5

Now, According to the question:

Based on the given conditions:

Formulate:

y = k/x

Calculate and substitute y = 9 , x = 10 into y = k/x

9 = k/10

k = 90

To find the equation of the function:

y = 90/x

Calculate and substitution x = 5 into y = 90/x

y = 18

Hence, The value of the y is 18 when x = 5.

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The amount of saline and water in the solution is given as 27.9 cm³ and 282.1 cm³ respectively.

Given that,
A patient is administered 310cm^3 of a saline and water solution that is labeled as 9% saline.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

here,
According to the condition,
Amount of saline = 0.09 × 310 = 27.9
Amount of water = 310 - 27.9 = 282.1

Thus, the amount of saline and water in the solution is given as 27.9 cm³ and 282.1 cm³ respectively.

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Answer:

Step-by-step explanation:

we cant see it so this is not able to answer

The trigonometric equation cos² 2x is equivalent by reduction formulas to the expression 1 - 4 · cos² x + 4 · cos⁴ x.

Herein we find the case of a trigonometric equation involving a double angle that must be reduced into a single one by means of reduction formulas. First, write the trigonometric equation:

cos² 2x

Second, use the trigonometric fundamental formula:

1 - sin² 2x

Third, reduce the double angle by the sine formula for the double angle:

1 - 4 · sin² x · cos² x

Fourth, use again the trigonometric fundamental formula and expand the resulting expression:

1 - 4 · (1 - cos² x) · cos² x

1 - 4 · (cos² x - cos⁴ x)

1 - 4 · cos² x + 4 · cos⁴ x

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Answer:

which statement is true about these eight angles that are formed from parallel lines being cut by a transversal the answer is C

m=y₂-y₁/x₂-x₁ we use this formula for line with slope 4 and y intercept is negative

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Let us consider a equation with slope 4 and a negative y intercept

y=4x-3

In the above equation 4 is the slope and -3 is the y intercept

x    0      1        2      3

y     -3    1        5      9

We have to plot this graph and the graph is given in attachment.

We get to know the slope is 4 by taking any two points (2,5) and (3,9) and applying in formula

m=y₂-y₁/x₂-x₁

Hence m=y₂-y₁/x₂-x₁ we use this formula for line with slope 4 and y intercept is negative

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The run is 9x miles long, while the bike race is 22y miles long.

The distance between two points in mathematics is referred to as the distance. The distance formula, which is simply a derivation of the Pythagorean theorem, which is used to find the length of any one side of a right triangle when you know the lengths of the other two sides, can be used to calculate this distance.

Therefore,

d = vt

where:

d = distance (miles)

v = speed (mph)

t = time (hours)

Let  x = run time

Let  y = bike time

Total time:      x + y = 4

We can create an equation that represents the formula using these variables.

d total = d bike + d run

49 = 9x + 22y

The equation is then only expressed in terms of x or y. We're going to get it in terms of x.

49 = 9x +22(4 - x)

49 = 9x + 88 - 22x

-39 = -13x

3 = x

To determine the distance between each part, enter this value of x into the variables.

run distance = 9x

bike distance = 22(4 - x)

Let x be run time, y be the bicycle race time.

Total time

x+y = 4

Run distance R = 9x

Bicycle race distance  B = 22y

Total distance

9x + 22y = 49

Replace y in the second equation with 4 - x to solve this system.

You'll obtain

y = 1

x = 3

so

R = 9x = 27

B = 22y = 22

Hence, The run is 9x miles long, while the bike race is 22y miles long.

The complete question is:

Suppose you have entered a 49?-mile biathlon that consists of a run and a bicycle race. During your? run, your average velocity is 9 miles per? hour, and during

Suppose you have entered a 49?-mile biathlon that consists of a run and a bicycle race. During your? run, your average velocity is 9 miles per? hour, and during your bicycle? race, your average velocity is 22 miles per hour. You finish the race in 4 hours. What is the distance of the? run? What is the distance of the bicycle? race?

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Answer:

C

Step-by-step explanation:

the directrix and focus are equidistant from the vertex

vertex = (0, 1 ) and focus = (0, - 2 ) then directrix is a horizontal line above the vertex with equation

y = 4

the focus and directrix are equidistant from any point (x, y ) on the curve.

using the distance formula

[tex]\sqrt{x-0)^2+(y-(-2))^2}[/tex] = | y - 4 |

[tex]\sqrt{x^2+(y+2)^2}[/tex] = | y - 4 | ( squaring both sides )

x² + (y + 2)² = (y - 4)²

x² + y² + 4y + 4 = y² - 8y + 16 ( subtract y² from both sides )

x² + 4y + 4 = - 8y + 16 ( add 8y to both sides )

x² + 12y + 4 = 16 ( subtract x² + 4 from both sides )

12y = - x² + 12 ( divide through by 12 )

y = - [tex]\frac{1}{12}[/tex] x² + 1

Answer: Y = -[tex]\frac{1}{12}[/tex][tex]x^{2}[/tex] + 1

Step-by-step explanation: Correct on Edmentum

By using CPCTC theorem ∆ ADC congruence ∆ BCD.

According to CPCTC, which stands for "corresponding parts of congruent triangles are congruent," if two or more triangles are congruent, their corresponding angles and sides must also be congruent.

Corresponding parts of Congruent triangles is the abbreviation for this phrase. According to the CPCT theorem, if two or more congruent triangles are selected, their corresponding sides and angles are also selected as congruent.

AD = BC and angle ADC = angle BCD

we have to prove AC = BD

Let's see ∆ ADC and ∆ BCD

Given AD = BC

angle ADC = angle BCD

CD = CD

from S - A - S, we get

∆ ADC congruence ∆ BCD

Therefore, by using CPCTC theorem ∆ADC congruence ∆BCD.

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Answer:

Where is it

Step-by-step explanation:

we are here to help you

Answer:

x=([tex]\sqrt{41}[/tex]+7)/4, (-[tex]\sqrt{41}[/tex]+7)/4

Step-by-step explanation:

2x²+1=7x

2x²-7x+1=7x-7x

2x²-7x+1=0

2(x²-7x/2+1/2)=0

x²-7x/2+1/2=0

x²-7x/2+8/16=0

x²-7x/2+49/16-41/16=0

(x-7/4)^2-41/16=0

(x-7/4)^2-41/16+41/16=0+41/16

(x-7/4)^2=41/16

x-7/4=[tex]\sqrt{41}[/tex]/4    x-7/4=-[tex]\sqrt{41}[/tex]/4

x=[tex]\sqrt{41}[/tex]/4+7/4    x=-[tex]\sqrt{41}[/tex]/4+7/4

x=([tex]\sqrt{41}[/tex]+7)/4, (-[tex]\sqrt{41}[/tex]+7)/4

Answer:

8.  x = 9

9.  x = 9

10. x = 36

11.  x = 8

Step-by-step explanation:

Question 8

As the base of the triangle has been bisected, set the expressions either side of the perpendicular bisector equal to each other and solve for x:

[tex]\implies 5x-15=2x+12[/tex]

[tex]\implies 5x-15-2x=2x+12-2x[/tex]

[tex]\implies 3x-15=12[/tex]

[tex]\implies 3x-15+15=12+15[/tex]

[tex]\implies 3x=27[/tex]

[tex]\implies \dfrac{3x}{3}=\dfrac{27}{3}[/tex]

[tex]\implies x=9[/tex]

Question 9

As the base of the triangle has been bisected, set the expressions either side of the perpendicular bisector equal to each other and solve for x:

[tex]\implies 8x-63=4x-27[/tex]

[tex]\implies 8x-63-4x=4x-27-4x[/tex]

[tex]\implies 4x-63=-27[/tex]

[tex]\implies 4x-63+63=-27+63[/tex]

[tex]\implies 4x=36[/tex]

[tex]\implies \dfrac{4x}{4}=\dfrac{36}{4}[/tex]

[tex]\implies x=9[/tex]

Question 10

Angles on a straight line sum to 180°.  Therefore, as the other angle on the line is a right angle, equate the given expression to 90° and solve for x:

[tex]\implies (3x-18)^{\circ}=90^{\circ}[/tex]

[tex]\implies 3x-18=90[/tex]

[tex]\implies 3x-18+18=90+18[/tex]

[tex]\implies 3x=108[/tex]

[tex]\implies \dfrac{3x}{3}=\dfrac{108}{3}[/tex]

[tex]\implies x=36[/tex]

Question 11

Interior angles of a triangle sum to 180°.  Therefore, equate the sum of the given angles to 180° and solve for x:

[tex]\implies 90^{\circ}+(3x)^{\circ}+(8x+2)^{\circ}=180^{\circ}[/tex]

[tex]\implies 90+3x+8x+2=180[/tex]

[tex]\implies 11x+92=180[/tex]

[tex]\implies 11x+92-92=180-92[/tex]

[tex]\implies 11x=88[/tex]

[tex]\implies \dfrac{11x}{11}=\dfrac{88}{11}[/tex]

[tex]\implies x=8[/tex]

Answer:

  57 cm²

Step-by-step explanation:

You have a composite figure and you want to find its area.

There are several ways you can decompose the given figure. Three of them are shown in the attachments. The missing dimensions are found by realizing that the sum of the right-side dimensions is equal to the left-side dimension, and the sum of the bottom-side dimensions is equal to the top dimension.

Extending the vertical boundary line divides the figure into a left rectangle that is 7 cm high and 7 cm wide, and a right rectangle that is 2 cm high and 4 cm wide. This is shown in the first attachment.

The area of each rectangle is the product of its height and width, and the total area is the sum of these:

  Area = (height)×(width) . . . . . area formula for one rectangle

  Area = (7 cm)(7 cm) +(2 cm)(4 cm) = 49 cm² +8 cm² = 57 cm²

Extending the horizontal boundary line divides the figure into a top rectangle 2 cm high and 11 cm wide, and a bottom rectangle 5 cm high and 7 cm wide. This is shown in the second attachment. The total area is ...

  Area = (2 cm)(11 cm) +(5 cm)(7 cm) = 22 cm² +35 cm² = 57 cm²

A line can be drawn corner-to-corner to divide the figure into two trapezoids. This is shown in the third attachment.

The upper right trapezoid has bases 11 cm and 4 cm, and height 2 cm.

The lower left trapezoid has bases 7 cm and 5 cm, and height 7 cm.

The area of a trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

Then the total area is ...

  Area = 1/2(11 cm +4 cm)(2 cm) +1/2(7 cm +5 cm)(7 cm) = 15 cm² +42 cm²

  Area = 57 cm²

The rectangle that encloses the entire figure is 7 cm high and 11 cm wide, so has an area of ...

  A = HW = (7 cm)(11 cm) = 77 cm²

From that area, the lower right corner space is cut out. It has dimensions 5 cm high by 4 cm wide, so an area of (5 cm)(4 cm) = 20 cm².

The area of the figure itself is the difference between the area of the bounding rectangle and the area of the cut-out space at lower right:

  Area = 77 cm² -20 cm² = 57 cm²

The area of the figure in the picture is 57 cm².

Answer:

u= 3

Step-by-step explanation:

Isolate a square root on the left hand side

Original equation

    √5u-10-√2u-1 = 0

    Isolate

    √5u-10 = √2u-1+0

Eliminate the radical on the left hand side

Raise both sides to the second power(√5u-10)2 = (√2u-1)2 After squaring

5u-10 = 2u-1

Solve the linear equation

Rearranged equation

     3u  -9 = 0

    Add  9  to both sides

     3u  = 9

    Divide both sides by 3

    A possible solution is :

    u = 3