A boat traveled 140 miles downstream and back. The trip downstream took 7 hours. The trip
back took 70 hours. Find the speed of the boat in still water and the speed of the current.

Answer:

(1 +a + b)(1 - a -b)

Step-by-step explanation:

1 - 2ab - (a² +b²) = 1 - 2ab - a² - b²

                           = 1 - (2ab + a² + b²)

                           = 1 - (a + b)²

                           = 1² - (a +b)²    

Identity: x² - y² = (x + y)(x - y)

                          = (1 + (a+b))(1- [a +b] )

                          = (1 +a + b)(1 - a -b)

Answer: (a) The equation 2x^2 + 4x + 3 = k has real roots if and only if its discriminant, which is 4^2 - 4(2)(3), is nonnegative. The discriminant is equal to 0, so the equation has real roots if and only if k = 3.

(b) For the equation f(x) = kx^2 + kx + 1 to have real roots, its discriminant, which is 1 - 4k, must be nonnegative. This gives us k >= 1/4. The range of values of k for which the equation has real roots is k >= 1/4.

(c) When k = -2, the equation f(x) = -2x^2 - 2x + 1 = 0. Solving this equation using the quadratic formula, we get x = (-1 ± √(1 + 8))/4. So, the roots are x = (-1 ± √(9))/4 = (-1 ± 3)/4 = 1/2, -2.

Answer:

x = 12

y = 11

Step-by-step explanation:

It's a parallelogram, so opposite sides are equal.

4x + 10 = 58

4x = 58 - 10 = 48

x = 48/4 = 12

10y - 6 = 104

10y = 104 + 6 = 110

y = 110/10 = 11

The equation is given as y = 4x - 3 , where the slope is m = 4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The value of term 1 = 1 square

The value of term 2 = 5 suqres

The value of term 3 = 9 squares

So , the increment in the number of squares is 4

Let the first point be P ( 1 , 1 )

Let the second point be Q ( 2 , 5 )

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 5 - 1 ) / ( 2 - 1 )

Slope m = 4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 1 = 4 ( x - 1 )

On simplifying the equation , we get

y - 1 = 4x - 4

Adding 1 on both sides of the equation , we get

y = 4x - 3

Therefore , the value of y is 4x - 3

when x = 1 . y = 4 - 3 = 1

when x = 2 , y = 4 ( 2 ) - 3 = 8 - 3 = 5

Hence , the equation of line is y = 4x - 3

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The volume of the composite shape is

Volume is a measure of three-dimensional space.

A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes as well.

The shape above shows two cuboid joined together.

volume of the base cuboid = lbh

= 6×3×1 = 18ft³

Volume of the second cuboid = lbh

= 4×3×8 = 96 ft³

volume of the composite shape = 18ft³ + 96ft³

= 114 ft³

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S=B+15

15 more than blouse (b)

S representing skirts

According to the table, the values of g(x) are 2 units lower than the corresponding values of f(x).

Translation of functions

When a function is transferred without undergoing any form or rotation changes, it has been "translated." A function may be translated both horizontally and vertically.

According to the question;

The table that illustrates function g(x) is; when the function f(x) is shifted vertically down by 2 units to obtain function g

x = 0, 1, 2, 3

g(x) = -2, 0, 6, 24

By shifting the function f vertically down by 2 units, the function g(x) is produced.

Note that the relationship between the functions g and f is as follows:

g(x) = f(x) -2

Therefore, as seen in the above table, the values of g(x) are 2 units fewer than the corresponding values of f(x).

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Answer:

Rotation

Step-by-step explanation:

Answer: Rotation

Step-by-step explanation:

rotation by 180 degrees is (x,y) => (-x,-y)

Looking at some of the points on A like (-1,-1) we can see B has a point on (1,1) and (-6,-2) B has a point on (6,2) and so on

The diameter of the circle is 22 / 12 units

To find the diameter of the figure, we need to rewrite this in standard form of a equation of a circle.

3x² + 3y² - 7x - 6y - 3 ;

This will be written in (h, k) form which is

3x² + 3y² - 7x - 6y - 3

The coordinate of the center is at (7/6, 1)

The radius of the circle is 11/6 and we can find the diameter of the circle by;

diameter of circle = 2 * radius of circle

diameter = 2 * 11 / 6

diameter = 22 / 12

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200 number of students brought their lunch to school on Thursday.

A Percentage is a number or ratio that can be expressed as a fraction of 100.

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100.

Percentage formula = (Value/Total Value) × 100

P% of Number = X

where X is the required percentage.

If we remove the % sign, we need to express the above formula

P/100 × Number = X

Given:

Total number of students in school = 800

25% students bring their lunch every day.

25% of 800

= [tex]\frac{25}{100} \times 800[/tex]

= 25 × 8

= 200

200 students bring their lunch to school on Thursday.

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Since the corresponding sides are not proportional, we can say that the triangles are not similar

In similar triangles, corresponding sides are always in the same ratio.

Given are two triangles ΔWUV and ΔXZY.

It is given that -

VW = 60     ZY = 48     YX = 40     VU = 50     UW = 40     XZ = 32

For the triangles to be similar, the corresponding sides will be proportional.

WU/XZ = UV/ZY = WV/XY

40/32 = 50/48 = 60/40

1.25 ≠ 1.044 ≠ 1.5

The corresponding sides are not proportional.

Therefore, since the corresponding sides are not proportional, we can say that the triangles are not similar.

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The perimeter of the triangle is 16+8√2 feet.

The perimeter of any two-dimensional figure is defined as the distance around the figure. The formula for a closed shape figure's perimeter is typically equal to the length of the figure's outer line.

The perimeter of a triangle will therefore be equal to the sum of its three sides. Consequently, if a triangle has sides a, b, and c,

Here, a= 8 feet

b=  8 feet

c= 8√2 (length of a leg * √2= 8*√2)

Perimeter= Sum of all three sides of the triangle

Perimeter = a + b + c

Perimeter= 8+ 8 +8√2

Perimeter=  16+8√2 feet.

16+8√2 feet is the perimeter of the triangular garden.

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Answer:

56in.²

Step-by-step explanation:

the given figure can be divided into three parts .

( see attachment)

Finding area of I

Area = 7*4

Area = 28 in.²

Area of II

Area = 5 * (7-3) = 5*4

Area = 20 in.²

Area of III

area = 1/2 * 4*4

area = 8in.²

Total area [ 28 + 20 +8] in.² = 56in.²

Answer:

Both C and D are equations for the two given points.

Step-by-step explanation:

A. Y+2=0.5(x-3)  NO

 (-3,-5):  -5+2 = 0.5(-3-3);   -3 = 0.5(-6);   -3 = -3  YES

 (3,2):     2+2 = 0.5(3-3):   4 = 0.5(0);   4 = 0   NO

B. Y-5=0.5(x-3)  NO

(-3,-5):  -5-5=0.5(-3-3);  -10 = -3   NO

(3,-2):  -2-5=0.5(3-3);   -7 = 0       NO

C. Y+5=0.5(x+3)   YES

(-3,-5):  -5+5=0.5(-3+3);  0 = 0    YES

(3,-2):   -2+5=0.5(3+3);  3 = 3      YES

D. Y=0.5x-3.5   YES

(-3,-5):  -5 = 0.5(-3)-3.5;  -5 = -5 YES

(3,-2):  -2 = 0.5(3)-3.5;  -2 = 1.5 - 3.5   YES

The students divided the number ‘n’ by 3 instead of dividing (n-5) by 3.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: Given, Scott solve the equation Winnie, Texas, working realize they made a mistake identify Scott era wrote an algebraic expression for “5 less than a number n divided by 3” as (n/3) - 5.

We have to find the error made by the students.

5 less than a number n = n - 5

5 less than a number n divided by 3 = (n - 5)/3

Correct expression = (n - 5)/3

Expression written by student = (n/3) - 5

Therefore, the students divided the number ‘n’ by 3 instead of dividing (n-5) by 3.

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What’s the Error? A Scott solve the equation Winnie, Texas, working realize they made a mistake identify Scott era wrote an algebraic expression for “5 less than a number n divided by 3” as (n/3) - 5. What error did the they make?

Answer: If Ken brought 8 liters of water for everyone to share and they drank 5 liters of it, then the remaining amount of water they have is 8 - 5 = 3 liters.

Step-by-step explanation:

Based on the following given inequality; the symbol will be reversed when the variable is isolated

The condition for the symbol of an inequality to be reversed is;

if the variable is isolated and a negative number is used to divide.

The symbols of inequality are;

Greater than >

Less than <

Greater than or equal to ≥

Less than or equal to ≤

Equal to=

–10.5 < 3a

a < -10.5/3

a > -3.5

Yes

b6 ≤ 7

b ≤ 7/6

b ≤ 1.17

No

–4.5c > 9

c > 9/-4.5

c < -2

Yes

–215 ≤ –52d

d ≤ -215 / -52

d ≤ 4.14

No

Hence, the symbol will be reversed when the variable is isolated if the result of the division is negative.

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Answer:

showed below

Explanation:

you can start by plotting a dot at (2,0), since the line must go through that point. Since m, the slope, is -2, you can re-write this into a fraction to make it easier, looking like this: -2/1. Slope in general can be written as “rise over run” or “rise/run”, so the numerator is how far you go up on the graph, while the denominator is how far you go over. In this case, the slope is negative, so instead of up and right, the line goes down and right. From (2,0) you would go down by 2, and right by one. At that point you polar another dot. That point is (3,-2). From there, you can take a straight edge and line it up with the two dots and draw your line. It looks like what is in the picture.

The possible value of angle X, to the nearest degree is 78°.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in ΔXYZ, x = 300 cm, z = 290 cm and ∠Z=109°.

Here, sinX/x=sinZ/z

sinX/300 = sin109°/290

sinX/300 = 0.9455/290

sinX/300 = 0.00326

sinX=0.00326×300

sinX=0.978

∠X=78°

Therefore, the possible value of ∠X, to the nearest degree is 78°.

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Answer: 0.48

Step-by-step explanation:

So the question is asking for the probability of the spinner not  landing on "C" within the 125 tries. So, we can see there are 4 possibilities:

Now, we add up how many times it landed on these 4 possibilities, which is 15 + 12 + 18 + 15 = 60.

To calculate the possibility, we divide the selected possibilities by the total amount of possibilites, which is [tex]\frac{60}{125\\}[/tex], which is equal to 0.48

The probability can you expect the spinner to not land on C is,

⇒ 0.48.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Now, the question is asking for the probability of the spinner not landing on "C" within the 125 tries.

So, we can see there are 4 possibilities:

A , A

A , B

B , A

B , B

Now, we add up how many times it landed on these 4 possibilities, which is,

⇒ 15 + 12 + 18 + 15 = 60.

Thus, To calculate the possibility, we divide the selected possibilities by the total amount of possibilities, which is;

⇒ 60 / 125

⇒ 0.48

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The value of h(x) = 0 gives x=5.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the b. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

h(x) = -x + 5

So, for h(x)= 0 we have

-x + 5= 0

now, solving for x

-x = -5

x= 5

Thus, the value of x is 5.

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If the sample met these conditions, then it is possible to construct a confidence interval for the proportion of all homes in the city that have a television.

In order to construct a confidence interval, the sample must meet the following conditions:

The sample must be randomly selected from the population, large enough to ensure a normal distribution, and the population must be normally distributed. If these conditions are met, then a confidence interval can be constructed to provide an estimate of the proportion of homes that have a television.

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Answer:

The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²vvvThe diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²v

Step-by-step explanation:

its E and A

Answer:

The solutions to the inequality are B, E, and F: 25, 36, and 9.

Step-by-step explanation:

The solutions to the inequality √x < 10 are the values of x that make the inequality true when plugged in. To find these values, we can square both sides of the inequality:

√x < 10

x < 10^2 = 100

So, the values of x that make the inequality true are those that are less than 100. The options that satisfy this condition are:

A. 100 (not a solution)

B. 25 (solution)

C. -100 (not a solution)

D. 105 (not a solution)

E. 36 (solution)

F. 9 (solution)

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -1}{2}~~~ ,~~~ \cfrac{ y +5}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(1~~,~~3)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -1 }{2}=1\implies x-1=2\implies \boxed{x=3} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +5 }{2}=3\implies y+5=6\implies \boxed{y=1}[/tex]

The percent change in the price is  -6.67

The percentage change will be given by the formula:

Percent change = 100%*(new price - old price)/old price

We know that:

old price = 15 pounds.

new price = 14 pounds

Replacing that we will get:

percent change = 100%*(14 - 15)/15 = -6.67%

The price is 6.67% smaller.

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Answer:

Step-by-step explanation:

Sally has 20 water bottles he gives 10 to jerry, then final count of water bottles that Sally has is 10.

What is the addition?

The addition is the process of adding two or more numbers together to get their sum. Addition in math is a primary arithmetic operation, used for calculating the total of two or more numbers. For example, 7 + 7 = 14.

We have given,

sally has 20 water bottles he gives 10 to jerry how many does sally have left?

Sally originally had 20 water bottles.

When she gives 10 water bottles to Jerry, she will have 20 - 10 = 10 water bottles left.

Therefore, the final count of water bottles that Sally has is 10.

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