We have that Linda's mean speed is 54 miles per hour. Since the total trip is 378 miles, we have the following rule of three:
[tex]\begin{gathered} 54\text{miles}\rightarrow1h \\ 378\text{miles}\rightarrow x \end{gathered}[/tex]therefore, we have:
[tex]\begin{gathered} x=\frac{378\cdot1}{54}=7 \\ x=7 \end{gathered}[/tex]Finally, we have that Linda should expect to drive 7 hours.
The sides of an L-shaped figure meet all the right angles
ANSWER:
24 ft²
STEP-BY-STEP EXPLANATION:
To determine the area of the figure, we must divide the L-shaped figure into two rectangles just like this:
We calculate the area of each rectangle and the sum of both areas would be the area of the L-shaped figure, in the following way:
[tex]\begin{gathered} A_1=L\cdot W=6\cdot2=12\text{ ft}^2 \\ \\ A_2=L\cdot W=3\cdot4=12\text{ ft}^2 \\ \\ \text{ Therefore:} \\ \\ A_t=A_1+A_2=12+12 \\ \\ A_t=24\text{ ft}^2 \end{gathered}[/tex]The area of the L-shaped figure is equal to 24 ft².
State the domain of the function.{-2,0, 1, 2, 3, 4){-4,0, 1, 2, 6){0, 1,2,3)(-2,4)
D= {-2,0,1, 2,3,4}
1) Considering that the Domain is the set of entries of a function, on the x-axis, and examining that graph we can state
- The lowest value for that is given by x=-2
- The highest value for that is x= 4
- The points (-2,-4) (0,0), (1,1), (2,2), (3,1) and (4,6)
2) So, we can write the set, the Domain, after examining the options as:
D= {-2,0,1, 2,3,4}
Notice that we're considering the x-coordinates
3) So the answer is D= {-2,0,1, 2,3,4}
MP is the perpendicular bisector of the side AC of the triangle ABC, in which AB = AC. prove that angle APB = 2 angle B
We have the following:
[tex]\begin{gathered} \frac{a}{\sin now,[tex]\begin{gathered}According to projections through the year 2030, the population y of the given state in year x is approximated byState A: - 5x + y = 11,700State B: - 144x + y = 9,000where x = 0 corresponds to the year 2000 and y is in thousands. In what year do the two states have the same population?The two states will have the same population in the year
The x variable represents the year in question. The year 2000 is represented by x = 0, 2001 would be repreented by x = 1, and so on.
The year in which both states would have the same population can be determined by the value of x which satisfies both equations.
We would now solve these system of equations as follows;
[tex]\begin{gathered} -5x+y=11700---(1) \\ -144x+y=9000---(2) \\ \text{Subtract equation (2) from equation (1);} \\ -5x-\lbrack-144x\rbrack=11700-9000 \\ -5x+144x=2700 \\ 139x=2700 \\ \text{Divide both sides by 139} \\ x=19.4244 \\ x\approx19\text{ (rounded to the nearest whole number)} \end{gathered}[/tex]Note that x = 19 represents the year 2019
ANSWER:
The two states will have the same population in the year 2019
Find the lateral surface area of thiscylinder. Round to the nearest tenth.8ft4ftLSA = [ ? ] ft2—
Solution
Step 1:
Write the lateral surface area or curved surface area of a cylinder:
[tex]Lateral\text{ surface area = 2}\pi rh[/tex]Step 2:
Write the given data
Height h = 8ft
Radius r = 4 ft
Step 3:
Substitute in the formula to find the lateral surface area.
[tex]\begin{gathered} Lateral\text{ surface area = 2}\pi rh \\ =\text{ 2 }\times\text{ 3.142 }\times\text{ 4 }\times\text{ 8} \\ =\text{ 201.1 ft}^2 \end{gathered}[/tex]Final answer
201.1
Which of the following represents the set of possible rational roots for thepolynomial shown below?2x3 + 5x2 - 8x - 20 = 0oa{=}, +2, +1, +2, +3, +3 + 1}O B. {+1, +2, +4, +5, +10, 20}O a {, +1, +2 +3 +4, + 3, +10, +20)02 (1.1,2,3,4,5,10,20)
We will have that the set of rational roots for the expression will be:
[tex]\mleft\lbrace\pm\frac{1}{2},\pm1,\pm2,\pm\frac{5}{2},\pm4,\pm5,\pm10,\pm20\mright\rbrace[/tex][Option C].
I only need part bb) A foam protector is covered with PVC material to make it waterproof. Find the total surface area of a protector which is covered by PVCmaterial.
Assuming all the parts are covered, inluding the internal part, we have to find the surface area of the whole protector.
So, let's list which areas we need:
- We need the lateral areas of the external parts, which are 4 rectangles.
- We need the top and bottom areas, which are both area of squares minus the area of the cicle of the hole.
- We need the interior aread, which is the same as the lateral area of a cylinder.
For the external part, we only need the dimensions of each rectangle. since they have the same length and the other sides are the sides of the squares, they are all the same.
The area of each of them is:
[tex]A_{\text{rectangle}}=300mm\cdot1.8m=0.3m\cdot1.8m=0.54m^2[/tex]Since we have 4, the total exterior lateral area is:
[tex]A_{\text{lateral}}=4\cdot0.54m^2=2.16m^2[/tex]For the top and bottom, both are the same, a square of 300 mm x 300 mm with a hole of 150 mm diameter.
First, let's get all to meters: 0.3 m x 0.3 m and 0.15 m diameter. The radius of the circle is half the diameter, so:
[tex]r=\frac{0.15m}{2}=0.075m[/tex]The area of a circle given its radius is:
[tex]A=\pi r^2[/tex]So, the area of both the top and bottom is the area of the square minus the area of the circle and double all of this:
[tex]\begin{gathered} A_{\text{top/ottom}}=2((0.3m)^2-\pi(0.075m)^2) \\ A_{\text{top/ottom}}=2(0.09m^2-0.005625\pi m^2) \\ A_{\text{top/ottom}}=2(0.09-0.005625\pi)m^2 \end{gathered}[/tex]We deal with π later on.
For the lateral area of the cylinder, we can remember that it is the same as the area of a rectangle with on dimension being the length of the cylinder and the other being the circumference of the top/bottom.
the circumference of a circle is:
[tex]C=2\pi r[/tex]The radius is the same as the hole, and the length is 1.8m, so the lateral area of the cylinder is:
[tex]\begin{gathered} A_{\text{cylinder}}=1.8m\cdot2\pi(0.075m) \\ A_{\text{cylinder}}=(1.8\cdot0.15\pi)m^2 \\ A_{\text{cylinder}}=(0.27\pi)m^2 \end{gathered}[/tex]So, the total surface area is the sum of all of these:
[tex]A=2.16m^2+2(0.09-0.005625\pi)m^2+(0.27\pi)m^2[/tex]Now, we just need to evaluate:
[tex]\begin{gathered} A=2.16m^2+2\cdot0.072328\ldots m^2+0.848230\ldots m^2 \\ A=2.16m^2+0.144657\ldots m^2+0.848230\ldots m^2 \\ A=3.152887\ldots m^2 \\ A\approx3.15m^2 \end{gathered}[/tex]So, the lateral area is approximately 3.15 m².
The triangles formed by two ladders leaning against a wall are similar. How long is the shorter ladder?
To solve this problem we must use proportions
[tex]\begin{gathered} \text{ }\frac{x}{8}\text{ = }\frac{42}{24} \\ \text{ x = }\frac{8\text{ x 42}}{24} \\ \text{ x = }\frac{336}{24} \\ \text{ x = 14} \end{gathered}[/tex]The length of the shortest ladder is 14.
letter B is the correct answer.
Convert the polar equation r=3 to a Cartesian equation.x^2+y^2=√3x^2+y^2=3x^2+y^2=9
For the given equation:
[tex]\begin{gathered} \text{Polar form: } \\ r=3 \\ \\ \text{Cartesian form:} \\ x^2+y^2=3^2 \\ x^2+y^2=9 \end{gathered}[/tex]Please help me and explain to me these questions step by step. Thank youQuestion 8: Use simple interest
Given:
Amount Nicole borrowed = $1100
Annual interest rate = 7%
Duration = 6 months
Let the amount of interest be x
The amount after t years can be calculated using the formula:
[tex]\text{Amount = }P(1\text{ }+\text{ rt)}[/tex]The interest that she would pay can be calculated using the formula:
[tex]\text{Interest = Amount - Principal}[/tex]The amount after 6 months is:
[tex]\begin{gathered} \text{Amount = 1100(1 + 007 }\times\frac{6}{12}) \\ =\text{ 1138.5} \end{gathered}[/tex]Hence, the interest:
[tex]\begin{gathered} \text{Interest = 1138.5 - 1100} \\ =\text{ 38.5} \end{gathered}[/tex]Answer: $38.5
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In a test of a sex-selection technique, results consisted of 284 female babies and 15 male babies. Based on this result, what is the probability of a female being born to
a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?
The probability that a female will be born using this technique is approximately
(Type an integer or decimal rounded to three decimal places as needed.)
Does the technique appear effective in improving the likelihood of having a female baby?
O No
O Yes
The probability of the girl being born to a couple is 0.949. Yes, it is effective in increasing the likelihood that the baby will be a girl as the number of girls is more than the number of boys.
What is probability?
Probability means possibility. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Given
In a test of sex-selection technique, results consisted of 284 female babies and 15 baby boys.
Total children = 284 + 15 = 299
The probability of the girl being born to a couple will be
[tex]P = \frac{284}{299}[/tex]
P = 0.9498
Thus, the probability of the girl being born to a couple is 0.9498.
Yes, it is effective in increasing the likelihood that the baby will be a girl as the number of girls is more than the number of boys.
To learn more about the probability link is given below.
brainly.com/question/795909
#SPJ1
i inserted a picture of the questions 19 and 20 that i need help with.
WE are given that 9 tickets have a total cost of $94.50. To determine the price for each ticket we must find the quotient between the total amount spent and the number of tickets, like this:
[tex]\frac{94.50}{9}[/tex]Solving the operations we get:
[tex]\frac{94.50}{9}=10.5[/tex]Therefore, each ticket has a price of $10.50
consider the line y=2/5x. What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answer:
- 5/2
Step-by-step explanation:
If the slope of a line is m then the slope of the perpendicular line is -1/m
The slope of y = 2/5 x is 2/5
Slope of perpendicular line = - 5/2
65+ (blank) =180
11x + (blank)=180
11x =
x =
Answer:
sorry if this is wrong
I just answered it according to the question you gave not the pic
Step-by-step explanation:
x = 65
11x + x = 180
12x = 180
x = 180 ÷ 12
= 15
Which statements about the graph of the exponential function f(x) are TRUE?The x-intercept is 1.The y-intercept is 3.The asymptote is y = -3The range is all real numbers greater than -3The domain is all real numbers.f(x) is positive for all x-values greater than 1As x increases, f(x) approaches, but never reaches, -3.
1 The x-intercept is the value of x where the graph intersects the x-axis. The graph crosses the x-axis at x = 1. This statement is true.
2 The y-intercept is the value of y where the graph intersects the y-axis. The graph crosses the y-axis at y = -2. This statement is false.
3 The horizontal asymptote is the value of y to which the graph approaches but never reaches. This value seems to be y = -3, thus this statement is true.
4 The range is the set of values of y where the function exists. The graph exists only for values of y greater than -3. This statement is true.
5 We can give x any real value and the function exists, i.e., any vertical line would eventually intersect the graph. This statement is true.
To find the domain of a function when we are given the graph, we use the vertical line test. This consists of drawing an imaginary vertical line throughout the x-axis. If the line intersects the graph, that value of x is part of the domain.
This imaginary exercise gives us the centainty that there is no value of x that won't intercept the graph, thus the domain is the set of all the real values.
6 We can see the graph is positive exactly when the function has its x-intercept, thus This statement is true.
7 As x increases, y goes to infinity. The value of -3 is not a number where f(x) approaches when x increases, but when x decreases. This statement is false.
I need help figuring out if what I got is rigjt
The figure in the picture shows 3 squares that form a right triangle. Each side of the triangle is determined by one side of the squares.
The only information we know is the area of two of the squares. The area of a square is calculated as the square of one of its sides
[tex]A=a^2[/tex]So to determine the side lengths of the squares, we can calculate the square root of the given areas:
[tex]\begin{gathered} A=a^2 \\ a=\sqrt[]{A} \end{gathered}[/tex]For one of the squares, the area is 64m², you can determine the side length as follows:
[tex]\begin{gathered} a=\sqrt[]{64} \\ a=8 \end{gathered}[/tex]For the square with an area 225m², the side length can be calculated as follows:
[tex]\begin{gathered} a=\sqrt[]{225} \\ a=15 \end{gathered}[/tex]Now, to determine the third side of the triangle, we have to apply the Pythagorean theorem. This theorem states that the square of the hypothenuse (c) of a right triangle is equal to the sum of the squares of its sides (a and b), it can be expressed as follows:
[tex]c^2=a^2+b^2[/tex]If we know two sides of the triangle, we can determine the length of the third one. In this case, the missing side is the hypothenuse (c), to calculate it you have to add the squares of the sides and then apply the square root:
[tex]\begin{gathered} c^2=225+64 \\ c=\sqrt[]{225+64} \\ c=\sqrt[]{289} \\ c=17 \end{gathered}[/tex]So the triangle's sides have the following lengths: 8, 15 and, 17
Now that we know the side lengths we can calculate the perimeter of the triangle. The perimeter of any shape is calculated by adding its sides:
[tex]\begin{gathered} P=8+15+17 \\ P=40m \end{gathered}[/tex]the circle below is centered at the point (2,-1 ) and had a radius of length 3 what is its equation
The standard equation for a circle is
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{where} \\ a=2 \\ b=-1 \\ r=\text{radius}=3 \\ (x-2)^2+(y-(-1))^2=3^2 \\ (x-2)^2+(y+1)^2=3^2 \\ \end{gathered}[/tex]Simplity 9 - [x - (7+ x)]
First we resolve the part between the square brackets:
[tex]\lbrack x-(7+x)\rbrack=(x-7-x)=0x-7=-7[/tex]Then:
[tex]9-\lbrack x-(7+x)\rbrack=9-(-7)[/tex]Then you apply the opperation with the symbols knowin that:
[tex](+)(+)=+[/tex][tex](+)(-)=-[/tex][tex](-)(-)=+[/tex]And the final answer is:
[tex]9+7=16[/tex]In a scale drawing of a rectangularswimming pool, the scale is 2 inch: 4feet. Find the perimeter and area ofthe swimming pool.15 in.3.5 in.
The given scale is
[tex]2in\colon4ft[/tex]This means each two inches of the scale represents 4 feet of the actual size (or each inch is equivalent to two feet).
So, if the dimensions of the scale are 15 inches by 3.5 inches, then the actual dimensions would be 30 feet by 7 feet.
The perimeter would be
[tex]P=2(w+l)=2(30+7)=2(37)=74ft[/tex]The area would be
[tex]A=w\cdot l=30.7=210ft^2[/tex]Therefore, the perimeter is 74 feet, and the area is 210 square feet.Three friends rented a kayak. It cost $4 per hour per person to rent the kayak, plus $2 for each life jacket, and $3 to park the car. It cost $57 in all. How many hours did they spend kayaking? Write an equation and solve.
Answer:
13 hours
Step-by-step explanation:
Let y = the total cost
let x = hours
y = 4x + 5 5 = the one time fee of the jacket and the parking
57 = 4x + 5 Subtract 5 from both sides
52 = 4x Divide both sides by 4
13 = x
A length of 48 ft. gave Malama an area
of 96 sq. ft. What other length would
give her the same area (96 sq. ft.)?
4
I don’t know how to find the value of x. Geometry is so confusing too me, i can never understand it no matter how many times i re-read my instructions.
The value of x = 40°
Explanation:To solve for x, we will use an illustration:
When two lines intersect, the angles opposite each other are vertical angles. Vertical angles are equal.
The angles marked in magenta are equal.
The angle by the right in magenta colour will also be 52°.
The sum of angles in a triangle = 180°
x° + 52° + 88° = 180°
x + 140 = 180
subtract 140 from both sides:
x + 140 - 140 = 180 - 140
x = 40°
fine one value of x for which f(x) = 4 and find f(0)look at the graph below
To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:
As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:
As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4
[tex]f(-4)=4[/tex]Our final answer will be x = -4
b)
Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph
As we can see it touches the graphic at y = 2, hence, f(0) = 2
[tex]f(0)=2[/tex]To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:
As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:
As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4
[tex]f(-4)=4[/tex]Our final answer will be x = -4
b)
Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph
As we can see it touches the graphic at y = 2, hence, f(0) = 2
[tex]f(0)=2[/tex]Can u guys simplify this?
(2x^-3y^5)^2*(x^7y^-11)
A) What is the perimeter of the regular hexagon shown above?B) What is the area of the regular hexagon shown above?(see attached image)
Remember that
A regular hexagon can be divided into 6 equilateral triangles
the measure of each interior angle in a regular hexagon is 120 degrees
so
see the attached figure to better undesrtand the problem
each equilateral triangle has three equal sides
the length of each side is given and is 12 units
Part A) Perimeter
the perimeter is equal to
P=6(12)=72 units
Part B
Find the area
Find the height of each equilateral triangle
we have
tan(60)=h/6
Remember that
[tex]\tan (60^o)=\sqrt[]{3}[/tex]therefore
[tex]h=6\sqrt[]{3}[/tex]the area of the polygon is
[tex]A=6\cdot\lbrack\frac{1}{2}\cdot(6\sqrt[]{3})\cdot(12)\rbrack[/tex][tex]A=216\sqrt[]{3}[/tex]alternate way to find out the value of happlying Pythagorean Theorem
12^2=6^2+h^2
h^2=12^2-6^2
h^2=108
h=6√3 units
A diver starts out at 342 feet below the surface (or – 342 feet). She then swims upward 237 feet.Use a signed number to represent the diver's current depth.
Given:
A diver starts at 342 feet below the surface, which means -342 feet.
Now, she swims 237 feet upward.
It shows that she is moving in a positive direction.
So, the current depth of diver is,
[tex]-342+237=-105[/tex]The depth is -105 feet, which shows that the diver is still 105 feet below the surface.
Yesterday, Diane had c baseball cards. Today, she gave 6 away. Using c, write and expression for the number of cards Diane has left.
Answer:
The expression is c-6. She gave away 6 cards so subtract 6 from the original number which is c.
Find the volume round to the nearest 10th necessary. Use three. 144 pi and a calculator to get your answers.
The diameter of the cylinder is 24 mm.
Therefore, the radius is given by:
[tex]\frac{24}{2}=12mm[/tex]The height of the cylinder is given as 5 mm.
The formula for the volume V of a cylinder with radius r and height h is given by:
[tex]V=\pi r^2h[/tex]Substitute r = 12mm and h = 5 mm into the formula for volume:
[tex]V=\pi\left(12\right)^2\left(5\right)\approx2261.9[/tex]Therefore, the volume of the cylinder is approximately 2261.9 mm².
.
solve for r 2r + 7 = 4r - 13
2r + 7 = 4r - 13
subtract 4 from both-side of the equation
2r - 4r + 7 = 4r - 4r - 13
-2r + 7 = -13
subtract 7 from both-side of the equation
-2r + 7 = -13 - 7
-2r = -20
divide both-side of the equation by -2
r = 10
2x - 6(x-3) ≥ 5
solve for x.
Answer:
It’s siu
Step-by-step explanation:
Answer:x≤4.6
Step-by-step explanation: 2x-6(x-3)≥5. 1).combine the like terms. 2x+x=3x & -6+-3=-9. 2). isolate the "x". 3x-9≥5. 3x≥14. 3). divide both sides by your coefficient. 3x≥14/ 3
x≥4.6
4) flip your sign. x≤4.6
