Mr. Martin and his son are planning a fishing trip to Alaska. The rates of two companies are shown.

Wild Fishing Inc.
Round Trip Flight $200 / Daily Rate $25
Fisherman's Service
Round Trip Flight $150 / Daily Rate $30

Part A : Which company offers a better deal for a three day trip for Mr. Martin and his son? What will be the cost?
Part B : Which company would charge $700 for 6 days for both of them?
Part C : Write an expression to represent the cost of the trip for Mr. Martin and his son for each company.

Answer:

12x-183

Step-by-step explanation:

2(4x+3)+3(x-63)+x

8x+6+3x-189+x

12x+6-189

12x-183

Answer:

The Proof is given below.

Step-by-step explanation:

Given:

M is the Mid Point of HS and GT

To Prove:

Δ GMH ≅ Δ TMS

Proof:

In  Δ GMH and Δ TMS

M is the Mid Point of HS and GT ........{Given}  

     GM ≅ MT               ....……….{ M is the Mid Point of GT }

     HM ≅ SM               …………..{ M is the Mid Point of HS }

∠ GMH ≅ ∠ TMS         ....……….{ Vertical opposite angles are equal}

Δ GMH ≅ Δ TMS         ..........….{ By Side-Angle-Side test}  ...Proved

Answer:

Part 1) The slope is [tex]m=25[/tex] (the cost of the gym is $25 per month)

Part 2) The y-intercept is the point (0,-100) see the explanation

Part 3) [tex]y=25x-100[/tex], After 14 months the cost is [tex]\$250[/tex]

Step-by-step explanation:

Part 1) What is the slope of the line

Let

x ---> the number of months

y ---> the total cost in dollars

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

From the graph take two points

(0,-100) and (4,0)

substitute the values in the formula

[tex]m=\frac{0+100}{4-0}[/tex]

[tex]m=\frac{100}{4}[/tex]

[tex]m=25[/tex]

Remember that the slope is equal to the unit rate of the linear equation

That means ----> the cost of the gym is $25 per month

Part 2) What is the y-intercept of the line

we know that

The y-intercept is the value of y when the value of x is equal to zero

Looking at the graph the y-intercept is the point (0,-100)

In context this problem, the y-intercept represent the rebate of $100 that the gym was offering for sign up for a full year      

Part 3) What is the linear equation for the line in this situation? What is the cost of the gym membership after 14 months

we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept      

we have

[tex]m=25[/tex]

[tex]b=-100[/tex]

substitute the values

[tex]y=25x-100[/tex]

For x=14 months

substitute

[tex]y=25(14)-100[/tex]

[tex]y=350-100=\$250[/tex]

Answer:

b, d, and e

Step-by-step explanation:

The analysis, the following statements are true:

The line goes through the origin.

The line is sloping upward.

The x-intercept is 0.

The equation of the line using the point-slope form of a linear equation:

Point-slope form: y - y₁ = m(x - x₁),

where (x₁, y₁) is a point on the line, and m is the slope.

Given:

Point (x₁, y₁) = (-4, -3)

Slope (m) = 3/4

Substitute these values into the point-slope form:

y - (-3) = (3/4)(x - (-4))

y + 3 = (3/4)(x + 4)

Now, let's simplify this equation:

y + 3 = (3/4)x + 3

y = (3/4)x

This is the equation of the line.

Now, let's evaluate the statements:

The line is horizontal. (False)

The slope of the line is 3/4, which means it has a positive slope and is sloping upward.

The line goes through the origin. (True)

The line does not pass through the origin (0, 0) because its y-intercept is 3.

The point (3, 4) lies on the line. (False)

Let's substitute the coordinates (3, 4) into the equation:

y = (3/4)x

4 = (3/4)(3)

4 = 9/4

Since 4 ≠ 9/4, the point (3, 4) does not lie on the line.

The line is sloping upward. (True)

The slope is positive (3/4), so the line is indeed sloping upward.

The x-intercept is 0. (False)

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

0 = (3/4)x

x = 0

This shows that the x-intercept is 0.

Based on the analysis, the following statements are true:

The line is sloping upward.

The x-intercept is 0.

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Answer:

0.6

Step-by-step explanation:

it is right

The proportion of laptop prices that are between 624 dollars and 768 dollars would be: 0.3907 or 39.07%.

To determine the proportion of laptop prices that are betwee the specified prices, we would ge the z scores in the following way:

624 dollars

Z1 = (624 - 750) / 60 = -2.1

768 dollars

Z2 = (768 - 750) / 60 = 0.3

Now, if we use the standard distribution table, we would arrive at;

P(-2.1 < Z < 0.3) ≈ 0.3907

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Answer:

b $80

Step-by-step explanation:

Interest = Principal x Interest Rate x Time

$40 = P x 0.1 x 5

$40 = 0.5 P

Dividing the equation by 0.5 we get;

P = $40 / 0.5

P = $80

Answer:

x > 5

Step-by-step explanation:

Given

9x - 2 > 43 ( add 2 to both sides )

9x > 45 ( divide both sides by 9 )

x > 5

The solution to the inequality (9x - 2 > 43) is (x > 5).

To solve the inequality (9x - 2 > 43), follow these steps:

1. Add 2 to both sides of the inequality to isolate the term with x on one side:

[tex]\[ 9x - 2 + 2 > 43 + 2 \] \[ 9x > 45 \][/tex]

2. Divide both sides of the inequality by 9 to solve for x:

[tex]\[ \frac{9x}{9} > \frac{45}{9} \] \[ x > 5 \][/tex]

This means that any value of x greater than 5 will satisfy the original inequality. The solution set is all real numbers greater than 5.

No, Sam is not correct. Cosine and sine are not always equal for congruent angles.

No, Sam is not correct. Congruent angles have the same measure, but cosine and sine are not always equal for congruent angles. Cosine measures the ratio of the adjacent side to the hypotenuse in a right triangle, while sine measures the ratio of the opposite side to the hypotenuse. These ratios are not the same in most cases, so cos X will not equal sin Y for congruent angles.

Answer:

11 minutes.

Step-by-step explanation:

To print 500 pages the first printer takes 20 minutes.

Then in one minute it can print [tex]\frac{500}{20} = 25[/tex] pages.

Again, to print 500 pages the first printer takes 25 minutes.

Then in one minute it can print [tex]\frac{500}{25} = 20[/tex] pages.

So, working together both the printer will print (20 + 25) = 45 pages in 1 minute.

Therefore, they will print 500 pages in [tex]\frac{500}{45} = 11.11[/tex] minutes ≈ 11 minutes. (Answer)

Answer:

The Value of tan x is the option E.

[tex]\tan x=\dfrac{4}{3}[/tex]

Step-by-step explanation:

Given:

[tex]\textrm{Opposite side to angle x}= 8[/tex]

[tex]\textrm{Adjacent side to angle x}= 6[/tex]

To Find:

[tex]\\tan x=?[/tex]

Solution:

In a Right Triangle Tangent Identity is

[tex]\tan x= \dfrac{\textrm{side opposite to angle x}}{\textrm{side adjacent to angle x}}[/tex]

Substituting the values we get

[tex]\tan x= \dfrac{8}{6}=\dfrac{4}{3}[/tex]

The Value of tan x is the option E.

[tex]\tan x=\dfrac{4}{3}[/tex]

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

we have

[tex]\frac{2}{5}(x-4)=2x[/tex]

Solve for x

Multiply by 5 both sides

[tex]2(x-4)=10x[/tex]

Divide by 2 both sides

[tex]x-4=5x[/tex]

Subtract x both sides

[tex]x-4-x=5x-x[/tex]

[tex]-4=4x[/tex]

Divide by 4 both sides

[tex]x=-1[/tex]

Answer:

18

Step-by-step explanation:

(5+1)3=5*3+1*3=15+3=18

Answer:

A

Step-by-step explanation:

In the figure shown, ABC is a right triangle with side lengths a, b, and c, and CD is an altitude to side AB. This altitude divides the triangle into two right triangles ADC and BDC. In these triangles,

So,

[tex]\triangle ABC\sim \triangle CBD\sim \triangle ACD[/tex]

1. From the similarity [tex]\triangle ABC\sim \triangle CBD,[/tex] you have

[tex]\dfrac{AB}{BC}=\dfrac{BC}{BD}\\ \\\dfrac{c}{a}=\dfrac{a}{s}[/tex]

2. From the similarity [tex]\triangle ABC\sim \triangle ACD,[/tex] you have

[tex]\dfrac{AB}{AC}=\dfrac{AC}{AD}\\ \\\dfrac{c}{b}=\dfrac{b}{r}[/tex]

Hence, option A is true

Final answer:

The correct proportions for the right triangle ABC with altitude CD are c/a = b/r and c/b = a/s, derived from the similarity of the triangles ACD and CBD with triangle ABC.(Option c)

Explanation:

In the given right triangle ABC with altitude CD, we can apply similarity properties to find the true proportions related to the side lengths labeled a, b, and c, and the segments of the altitude, labeled h, r, and s. To solve the problem, we can consider the two right triangles ACD and CBD created by drawing altitude CD. Since these triangles are similar to ABC, their corresponding side ratios will be equal.

Applying the similarity of triangles (Theorem 22), two sets of proportions become evident:

These proportions come from setting the sides of the smaller triangles against the hypotenuse c of the larger triangle ABC and using corresponding sides of similar triangles. Thus, the correct answer is that the true proportions are c/a = b/r and c/b = a/s, which match option C) in the question.

The measure of the hypotenuse is 25.0 units

Step-by-step explanation:

Let us revise how to find the length of the hypotenuse in a right Δ

∵ The legs of a right triangle measure 7 units and 24 units

∴ x = 7 units and y = 24 units

∵ [tex]z=\sqrt{x^{2}+y^{2}}[/tex]

- Substitute the values of x and y in the rule to find z

∵ [tex]z=\sqrt{(7)^{2}+(24)^{2}}[/tex]

∴ [tex]z=\sqrt{49+576}[/tex]

∴ [tex]z=\sqrt{625}[/tex]

∴ z = 25 units

∵ z is the hypotenuse

∴ The measure of the hypotenuse = 25 units

The measure of the hypotenuse is 25.0 units

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Answer:

Range [tex]\rightarrow[/tex] all real numbers less than or equal to 0 [tex]\rightarrow[/tex] ( - ∞ , 0 ]

Step-by-step explanation:

For visual understanding a graph of the  function is attached with the answer.

For example: x has a range of ( - ∞ , + ∞ ) but |x| has a range of [ 0 , + ∞ ). Similarly range of |x + 1| is [ 0 , + ∞ ).

For example: Range of |x| is [ 0 , + ∞ ) but range of -|x| is ( - ∞ , 0 ]. Similarly range of -|x + 1| is ( - ∞ , 0 ]

Therefore the range of f(x) = -2|x + 1| will be ( - ∞ , 0 ].

(NOTE : [a,b] means all the numbers between 'a' and 'b' including 'a' and 'b'.

(a,b) means all the numbers between 'a' and 'b' excluding 'a' and 'b'.

(a,b] means all the numbers between 'a' and 'b' including only 'b' not 'a'.

[a,b) means all the numbers between 'a' and 'b' including only 'a' not 'b'.

{a,b} means only 'a' and 'b'.

{a,b] or (a,b} doesn't mean anything. )

Answer:

B

Step-by-step explanation:

all real numbers less than or equal to 0

Answer:

m∠CEB is 55°

Step-by-step explanation:

Since ∠ADE = 55°, and ∠ADE is half of ∠ADC because ED bisects ∠ADC. Bisect means to cut in half.

∠ADC = 110° because it is double of ∠ADE.

Since AB║CD and AD║BC, the two sets of parallel lines means this shape is a parallelogram. In parallelograms, opposite angles have equal measures.

∠ADC = ∠CBE = 110°

All quadrilaterals have a sum of angles 360°. Since ∠DCB = ∠BAD and we know two of these other angles are each 110°:

360° - 2(110°) = 2(∠DCB)

∠DCB = 140°/2

∠DCB = ∠BAD = 70°

∠DCB was bisected by EC, which makes each divided part half.

∠DCE = ∠BCE = (1/2)(∠DCB)

∠DCE = ∠BCE = (1/2)(70°)

∠DCE = ∠BCE = 35°

All triangles' angles sum to 180°.

In ΔBCE, ∠BCE = 35° and ∠CBE = 110°.

∠CEB = 180° - (∠BCE + ∠CBE)

∠CEB = 180° - (35° + 110°)

∠CEB = 55°

Therefore m∠CEB is 55°.

For this case we must find the solution set of the following inequalities:

[tex]x> -5[/tex]

The solution is given by all values of x greater than -5.

[tex]x <5[/tex]

The solution is given by all values of x greater than -5.

Then, the solution set is given by all real numbers.

Answer:

The solution is given by all real numbers.

Option C

The solution set for the given conditions corresponds to all real numbers between and inclusive of -5 and 5.

The given sets are {x | x > -5} U {x | x < 5}, which represents the union of numbers greater than -5 and numbers less than 5. Considering both conditions, the solution set encompasses all real numbers in between these two values, inclusive of -5 and 5. Therefore, the correct solution is All real numbers.

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Answer:

[tex]x=5[/tex]

Step-by-step explanation:

The complete question is

m ∠ A = 100 - x

m ∠ B = 80 + x

m ∠ C = 110 - 3x

m ∠ D = 75 + 2x

Quadrilateral ABCD is a parallelogram if both pairs of opposite angles are equal. Prove that Quadrilateral ABCD is a parallelogram by finding the value of x.

Options

A) x = 5

B) x = 7

C) x = 10

D) x = 15/2

we know that

In a parallelogram, opposite angles are parallel and consecutive angles are supplementary

so

m ∠ A=m ∠ C

m ∠ B=m ∠ D

m ∠ A+m ∠ B=180°

m ∠ B+m ∠ C=180°

step 1

Find the value of x

we know that

m ∠ A=m ∠ C

substitute the given values

[tex](100-x)^o=(110-3x)^o[/tex]

solve for x

Group terms

[tex]3x-x=110-100[/tex]

Combine like terms

[tex]2x=10[/tex]

[tex]x=5[/tex]

step 2

Verify the measure of the angles

[tex]m\angle A=100-5=95^o[/tex]

[tex]m\angle B=80+5=85^o[/tex]

[tex]m\angle C=110-3(5)=95^o[/tex]

[tex]m\angle D=75+2(5)=85^o[/tex]

therefore

[tex]m\angle A=m\angle C[/tex] ---> is ok

[tex]m\angle B=m\angle D[/tex] ---> is ok

[tex]m\angle A+m\angle B=180^o[/tex] ---> is ok

[tex]m\angle B+m\angle C=180^o[/tex] ---> is ok

Final answer:

The equation of a line perpendicular to y=2/3x-6 has a slope of -3/2. The general form of the equation is y = -3/2x + b, where b is the y-intercept.

Explanation:

The student has asked for an equation of a line that is perpendicular to the line given by y=2/3x-6. For two lines to be perpendicular, the product of their slopes must be -1. Since the slope (m₁) of the given line is 2/3, the slope of the line perpendicular to it (m₂) must satisfy the equation m₁×m₂ = -1. Therefore, m₂ must be -3/2 (since (2/3)×(-3/2) = -1).

An equation of a straight line can be represented by y = mx + b, where m is the slope and b is the y-intercept. To find an equation of a line perpendicular to y=2/3x-6, we can use the slope m₂ = -3/2. The general form of the equation of the line we are seeking would then be y = -3/2x + b, where b is the y-intercept that can be determined based on a specific point the line passes through.

Answer:

7

Step-by-step explanation:

The point is reflected over the x-axis so we just need to look at the y-value.

The distance between the two points will be twice the y-value.

|3.5 * 2| = 7

A descending sort would list the data from tallest to shortest in the height field of a database about trees.

The kind of sort that would list the data from tallest to shortest in the height field of a database about trees is a descending sort. This sort arranges the data in reverse order, with the tallest tree at the top and the shortest tree at the bottom. To perform a descending sort in a database, you can use the ORDER BY clause with the DESC keyword in the SQL query.

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Answer:

6

Step-by-step explanation:

Answer:

[tex]5280 \: feet \: = 1 \: mile \\ \\ = > 1 \: mile \: = 5280 \: feet \\ \\ = > 3.5 \: miles \: = \: 3.5 \times 5280 \: feet \\ \\ = > 3.5 \: miles \: = \: 18480 \: feet[/tex]

9514 1404 393

Answer:

  8 inches, 13 inches, 19 inches

Step-by-step explanation:

Let's identify the side lengths (shortest to longest) as a, b, c. Then we have ...

  a + b + c = 40 . . . . . . perimeter

  2c -a = 30

  2a +2b +c = 61

__

Subtracting the third equation from twice the first gives ...

  2(a +b +c) -(2a +2b +c) = 2(40) -(61)

  c = 19 . . . . .  simplify

Using this in the second equation, we have ...

  2(19) -a = 30

  38 -30 = a = 8 . . . . add a-30

Then the first equation reveals b:

  8 + b + 19 = 40

  b = 40 -27 = 13

The side lengths are 8 in, 13 in, and 19 in.

Answer:

C

Step-by-step explanation:

note that (f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 10x + 7 - (x² - 7x) ← distribute parenthesis by - 1

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

= - x² + 17x + 7 → C

Final answer:

To find (f - g)(x), you need to subtract the function g(x) from the function f(x). The answer is -x^2 + 17x + 7.

Explanation:

To find (f - g)(x), we need to subtract the function g(x) from the function f(x).

Given f(x) = 10x + 7 and g(x) = x^2 - 7x, we substitute these values into (f - g)(x):

(f - g)(x) = f(x) - g(x) = (10x + 7) - (x^2 - 7x)

Expanding and simplifying, we get (f - g)(x) = -x^2 + 17x + 7.

Answer:

(0-4)/(1-k)= -2

-4/(1-k)= -2

-2(1-k)= -4

-2 +2k = -4

2k = -2

k = -1

(-1, 4)

y - 4 = -2( x + 1)

y - 4 = -2x - 2

y = -2x + 2

Answer:

70s-10       s=7

Step-by-step explanation:

first you want to multiply 7 * 10 which will give you 70 s -10 then you want to divide the 70 by 10 and you will get seven as your answer

Answer:

Step-by-step explanation:

7(10s-10)

= 70s - 70

A. Part 1- The scale factor from BC to FG is 7/13 . Since this ratio is less than 1, it indicates a contraction.

B. Part 2- The length of side EF is 221/182

C. Part 3- The exact area of EFGH is 7213127/33124​  square inches.

Let's solve each part step by step:

A. Part 1:

To find the scale factor from BC to FG, we need to find the ratio of the lengths of the corresponding sides of the similar quadrilaterals.

Given:

Diagonal AC (in quadrilateral ABCD) has length 7.

Diagonal EG (in quadrilateral EFGH) has length 13.

Using the fact that the diagonals of similar quadrilaterals are proportional, we have:

BC/ FG​ = AC/ EG

Substituting the given values:

BC/ FG​ = 7/13

So, the scale factor from BC to FG is 7/13 . Since this ratio is less than 1, it indicates a contraction.

B. Part 2:

Given side AB has a length of 17/26 . To find the length of side EF, we use the scale factor found in Part 1.

If the scale factor from BC to FG is 7/13 , then the length of side EF can be found using the proportion:

EF/ AB​ = FG/ BC

Substituting the given values:

EF=7/13×17/ 26

Solving for EF:

EF= 13/ 7​ × 17/ 26 = 221/ 182

So, the length of side EF is 221/182

​C. Part 3:

If the area of quadrilateral ABCD is 147 square inches, and the scale factor is 7/13 , the area of quadrilateral EFGH can be found using the scale factor squared.

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.

So,

( EF/AB )^2 =( 7/13 )^2

( 221/ 182)^2 =( 7/13 )^2

Solving for ( 221/ 182 )^2 :

( 221/182 )^2 = 48841/ 33124

Now, if the area of ABCD is 147 square inches, then the area of EFGH would be:

147× 48841/ 33124 = 7213127 /33124

So, the exact area of EFGH is 7213127/33124​  square inches.

Answer:

The coordinates of a point are a pair of numbers that define its exact location on a two dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y axis. The coordinates of a given point represent how far along each axis the point is located.

Step-by-step explanation:

The location of solutions in the coordinate plane is described using a Cartesian coordinate system, involving movements either vertically (upward or downward) or horizontally (to the right or left) from the origin, represented by coordinates (x, y).

The location of the solutions in the coordinate plane can be described using a Cartesian coordinate system. This system is based on two perpendicular lines, the x-axis (horizontal) and the y-axis (vertical), intersecting at the origin (0,0). When we are looking at solutions on this grid, we can describe their positions in relation to the origin.

If a solution moves vertically upward from the origin, its y-coordinate increases while the x-coordinate remains the same.

Moving vertically downward means the y-coordinate decreases.

Horizontally to the right, the x-coordinate increases from the origin.

Horizontally to the left, the x-coordinate decreases.

The point at which the solution lies can be described by a pair of numbers, or coordinates, such as (x, y), where x is the position along the horizontal axis and y is the position along the vertical axis.

Answer:1 2/3

Step-by-step explanation:

2/3+1/3+2/3=5/3=1 2/3

Step-by-step explanation: If you take a look at the right side of the equation, a 3 is being added to our variable x.

If you were going to solve this equation, you must subtract 3 from the right side and the left side to isolate our variable.

You would end up with 4 = x.