The initial function is:
[tex]f(x)=x^2-10x-24[/tex]And we know that one solution is r=-2
The equation of the line parallel to y = 3x + 8 that passes through the point (4, 5) is
To answer this question, we need to remember that a line is parallel to another one if its slopes are the same. A line parallel to y = 3x + 8 must has a slope, m = 3.
Now, to find the parallel line, we can use the point-slope form of the line equation as follows:
1. The point for which the line passes through is (4, 5):
[tex]y-y_1=m(x-x_1)[/tex]Then, we have:
(4, 5) ---> x1 = 4, y1 = 5
m = 3
[tex]y-5=3(x-4)\Rightarrow y-5=3x-12[/tex]Then
[tex]y=3x-12+5\Rightarrow y=3x-7[/tex]Therefore, the equation of the line parallel to y = 3x + 8 that passes through the point (4, 5) is y = 3x - 7.
Scale the rectangle by finding 3A. What are the vertices of the scaled rectangle
Given A, the matrix that contains the vertices of a rectangle on the plane, calculate 3A as shown below
[tex]3A=3\begin{bmatrix}{1} & {6} & {6} & {1} \\ {1} & {1} & {5} & {5} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}=\begin{bmatrix}{3*1} & {3*6} & {3*6} & {3*1} \\ {3*1} & {3*1} & {3*5} & {3*5} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}=\begin{bmatrix}{3} & {18} & {18} & {3} \\ {3} & {3} & {15} & {15} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}[/tex]Where each column of the 4x2 matrix above represents a vertex of the new rectangle; therefore, the 4 vertices are
(3,3), (18,3), (18,15), (3,15). The second option.2) Elena has some bottles of water that each holds 17 fluid ounces. a) Write an equation that relates the number of bottles of water (b) to the total volume of water (w) in fluid ounces. b) How much water is in 51 bottles? Show your work. c) How many bottles does it take to hold 51 fluid ounces of water? Show your work.
Answer:
(a)
Since each bottle holds 17 fluid ounces, then if b is the number of bottles of water and w is the total volume of water in fluid ounces we can set the following equation:
[tex]w=17b\text{.}[/tex](b)
Now, if b=51,
[tex]w=17\times51=867.[/tex]Therefore, in 51 bottles there are 867 fluid ounces.
(c)
If w=51, solving for b we get:
[tex]\begin{gathered} 51=17b, \\ \frac{51}{17}=b, \\ b=3. \end{gathered}[/tex]
Therefore, it would take 3 bottles to hold 51 fluid ounces.
A sample was done , collecting the data below. Calculate the standard deviation,to one decimal place
By definition, the standard deviation is
[tex]\sigma = \sqrt{\frac{\sum_{i=1}^{n}\left(x_i-\bar{x}\right)^2}{n}}[/tex]It seems hard so let's do it step by step, first, let's find the mean of the data
[tex]\begin{gathered} \bar{x}=\frac{24+29+2+21+9}{5} \\ \\ \bar{x}=17 \end{gathered}[/tex]Now we have the mean value, let's do each value of the set minus the mean value
[tex]\begin{gathered} x_1-\bar{x}=24-17=7 \\ \\ x_2-\bar{x}=29-17=12 \\ \\ x_3-\bar{x}=2-17=-15 \\ \\ x_4-\bar{x}=29-17=4 \\ \\ x_4-\bar{x}=9-17=-8 \end{gathered}[/tex]Now we have the difference between each element and the mean value, let's do the square of all values
[tex]\begin{gathered} (x_1-\bar{x})^2=7^2=49 \\ \\ (x_2-\bar{x})^2=12^2=144 \\ \\ (x_3-\bar{x})^2=(-15)^2=225 \\ \\ (x_4-\bar{x})^2=4^2=16 \\ \\ (x_5-\bar{x})^2=(-8)^2=64 \end{gathered}[/tex]Now we have the square of the difference we sum them
[tex]\begin{gathered} \sum_{i=1}^5\left(x_i-\bar{x}\right)^2=\left(x_1-\bar{x}\right)^2+\left(x_2-\bar{x}\right)^2+\left(x_3-\bar{x}\right)^2+\left(x_4-\bar{x}\right)^2+\left(x_5-\bar{x}\right)^2 \\ \\ \sum_{i=1}^5\left(x_i-\bar{x}\right)^2=49+144+225+16+64 \\ \\ \sum_{i=1}^5\left(x_i-\bar{x}\right)^2=498 \end{gathered}[/tex]Now we have the sum we must divide by the number of elements, in that case, 5 elements
[tex]\frac{\sum_{i=1}^5\left(x_i-\bar{x}\right)^2}{5}=99.6[/tex]Now we take the square root of that value to have the standard deviation!
[tex]\sigma=\sqrt{99.6}=9.979[/tex]We write it using only one decimal the result would be
[tex]\sigma=9.9[/tex]With no rounding.
Final answer:
[tex]\sigma=9.9[/tex]ctice 3.4.PS-19 Use the expression 6.5u - (10 =2) + 13 to answer 9–10. 9. Which part of the expression represents a quotient? Describe its parts. 10. Which part of the expression represents a product of two factors? Describe its p 9. The part of the expression that represents a quotient is (10=2). (Use the operation symbols in the math palette as needed. Do not simplify.) In this quotient, 6 is the dividend and 5U is the divisor
10 is the dividend while 2 is the divisor
Here, from the part that represents the quotient, we want to get the divisor and the dividend
From the question, the part that represents a quotient is given as;
[tex]\frac{10}{2}[/tex]Now, when we speak of the dividend, we mean the numerator of the fraction, and when we talk of the divisor, we are talking about the denominator
In simpler terms, what we want to divide is the dividend while what we are dividing with is the divisor
With respect to the given question, 10 is the dividend while 2 is the divisor
a bakery must pay the 8% sales tax on this week total sales of $2,050. How much sales tax will the bakery pay to the state for this week?
It must pay 8% of $2050 which is $2050*8% = $164
Given:• PQRS is a rectangle.• mZ1 = 50°PeNSRWhat is mZ2?130°85°70°65°
We can start answering this having that a rectangle is a parallelogram. The diagonals of a parallelogram bisect each other. Therefore, we have that the sides Q to the point where the diagonals intersect each other of the rectangle is congruent to R to this point. Then, we have two congruent sides.
The angles opposite to these sides are congruent too. They have the same measure. Since we have a triangle, and the sum of the internal angles of a triangle is equal to 180, we can say that:
[tex]m\angle1+2\cdot m\angle2=180[/tex]Then, we have:
[tex]50+2\cdot m\angle2=180[/tex]Subtracting 50 from both sides of the equation, and then dividing this equation by 2, we have:
[tex]50-50+2\cdot m\angle2_{}=180-50\Rightarrow2\cdot m\angle2=130[/tex][tex]2\cdot\frac{m\angle2}{2}=\frac{130}{2}\Rightarrow m\angle2=65[/tex]Therefore, the measure of angle 2 (m<2) is equal to 65 (degrees) (last option).
By visual inspection, determine the best-fitting regression model for thescatterplot.
From visual inspection it is clear that the best fitting regression model for this scatterplot is linear.
In the graph we can clearly see that the points form an almost straight line with a negative slope.
Now we know that a straight line has an equation of y = mx + c
The regression equation will be Y = aX + b which is a linear equation.
The mathematical figure known as a scatter plot, also known as a scatter graph, scatter chart, scattergram, a scatter diagram, uses Cartesian coordinates to display values in typically two variables for a set of data.
One more variable can be shown if a points are color, shape, and size coded. The data are represented as a set of points, where each point's position on the horizontal axis is determined by the value of one variable, and its position on the vertical axis by the value of the other variable.
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A blimp provides aerial television views of a tennis game. The television camera sights the stadium at 14° angle of depression. The altitude of the blimp is 300m . What is the line-of sight distance from the television camera to the base of the stadium ? Round to the nearest hundred meters.
Notice that with the information given, we can make a simple schematics of a right angle triangle for which we know an acute angle, a leg, and are asked to find the other leg of the triangle (or the hypotenuse, since the word "line of sight is not used properly in the text of the problem). The schematics is shown below:
The other leg of the right triangle is pictured in red in the image, if it is what the problem is asking (LINE OF SIGHT DISTANCE, which is always understood as a horizontal reference).
So we can use the tangent function to solve this case, as shown below
[tex]\begin{gathered} \tan (14\circ)=\frac{300}{d} \\ d=\frac{300}{\tan (14)}\approx1203.23 \end{gathered}[/tex]which tells us that the horizontal distance between camera and end of the field is approximately 1203.23 meters.
In the case that the problem is asking for the slant distance between the camera and the end of the field, we need to find the HYPOTENUSE of the right angle triangle (pictured in orange in the image above), and in such case we use the sine function as shown below:
[tex]\begin{gathered} \sin (14)=\frac{300}{\text{hyp}} \\ \text{hyp}=\frac{300}{\sin (14)}\approx1240.07 \end{gathered}[/tex]Which tells us that the slant distance between camera and the end of the field is about 1240.7 meters
From the drawing you sent, it looks more like the teacher may be asking for the slant distance. So please use the second answer : 1240.7 meters.
Please remind you teacher that the standard use of "line of sight" is to represent the horizontal line from which the angle of elevation or angle of depression is measured. So it is not appropriate to use the term in the context it has been used.
Caitlin read a book. She started reading at 9:45 a.m. and ended at 10:37 a.m. How did How many minutes did Caitlin read?
To calculate the number of minutes, we have to convert the hours to minutes or we can calculate the difference between the starting and ending times to a fixed hour.
In this case, we will use the second approach.
We will use 10:00 am as the fixed hour.
Then, if she started reading at 9:45 am, 15 minutes had passed until 10 am.
If she ended reading at 10:37 am, 37 minutes passed from 10 am.
Then, we can add the two segments:
[tex]T=15+37=52\min [/tex]Answer: she read 52 minutes.
5) A bird, flying 25 feet above the sea, spotted a fish swimming 7 feet below the surface. How far did the bird need to go to catch the fish?
The bird is flying 25 feet above sea surface and the fish is swimming 7 feet below sea surface:
Distance is equal to:
[tex]25-(-7)=25+7=32[/tex]The bird will have to dive 32feet to catch the fish.
In the circle below, if AD is a diameter, and the chord BC = 48, find the length of the segment BP.
Solution
- The length BP is the half of length BC.
- The Diameter is AD and it divides the chord into two equal parts.
- Thus, BP is half of BC. This means that
[tex]\begin{gathered} BP=\frac{BC}{2} \\ \\ BP=\frac{48}{2}=24 \end{gathered}[/tex]Final Answer
BP = 24
Samant coria 5 awz D X 3y + 2x25 26-27 +32=8 -2xtily - 29-12 267-37 +32-21 x+4y + 3xl 5x+7-28=-34 -X134+32=2
Given data:
The first given equation is x-3y+2z=5.
The second given equation is 2x-4y+3z=8.
Third equation is -2x+4y-2z =-12.
Add second and third equations.
[tex]\begin{gathered} (2x-4y+3z)+(-2x+4y-2z)=8-12 \\ z=-4 \end{gathered}[/tex]Substitute -4 for z in first and second equations.
[tex]\begin{gathered} x-3y=13 \\ x=13+3y \\ 2x-4y=20 \\ 2(13+3y)-4y=20 \\ 26+2y=20 \\ 2y=-6 \\ y=-3 \end{gathered}[/tex]The value of x is,
[tex]\begin{gathered} x-3(-3)+2(-4)=5 \\ x=4 \end{gathered}[/tex]Thus, the value of x is 4, the value of y is -3, and the value of z is -4.
A plater holds 24 strawbers,2 aplles,16 oranges.What fraction of all the fruits are strawberiias?Fracion of apples?Fraction of oranges?
The fraction for strawberries, apples, and oranges is 12/21, 1/21, and 8/21 respectively.
What are fractions?A fraction depicts a portion of an entire. This entire could be a location or a group of things. The Latin word "fraction," which means "to break," is where the word "fraction" comes from. In mathematics, a fraction is represented by a numerical value that designates a portion of an entire. The numerator displays how many pieces the whole has been divided into. It is positioned at the top of the fraction, beneath the fractional bar is the denominator.
Given,
Number of strawberries = 24
Number of apples = 2
Number of oranges = 16
So, the total number of fruits is given as
= 24 + 2 + 16
= 42
The fraction for strawberries = 24/42
=12/21
The fraction for apples = 2/42
= 1/21
The fraction for oranges = 16/42
=8/21
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A chicken soup recipe calls for 15 cups of chicken stock. How much is this in quarts?Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer
Recall the conversion
1 quarts = 4 cup
Given that there is 15 cups, multiply it by the ratior of quarts to cup, making sure that the cup is in the denominator
[tex]\begin{gathered} 15\text{ cups}\times\frac{1\text{ quarts}}{4\text{ cups}} \\ =15\cancel{\text{cups}}\times\frac{1\text{ quarts}}{4\cancel{\text{cups}}} \\ =\frac{15\times1\text{ quarts}}{4} \\ =\frac{15\text{ quarts}}{4} \\ =3\text{ }\frac{3}{4}\text{ quarts} \end{gathered}[/tex]Therefore, 15 cups is equivalent to 3 and 3/4 quarts.
Solve for y:6y -4 = 3y +2
1) Solving for y, the following expression
6y -4 = 3y +2 Add 4 to both sides
6y = 3y +2+4
6y = 3y +6 Subtract 3y from both sides
6y -3y = 6
3y = 6 Divide both sides by 3
y= 2
S={2}
2) So the solution for this is y=2
Convert 1 in^3 into cm^3 using the measurement conversion 1 inch= 2.54 cm. Round yo two decimals.
A cubic inch is the same an inch to the third power.
[tex]in^3=in\times in\times in[/tex]If we use our measurement conversion
[tex]1in=2.54\operatorname{cm}[/tex]In our previous equation, we have
[tex]in\times in\times in=2.54\operatorname{cm}\times2.54\operatorname{cm}\times2.54\operatorname{cm}[/tex]Solving this product, we have
[tex]2.54\operatorname{cm}\times2.54\operatorname{cm}\times2.54\operatorname{cm}=16.387064cm^3[/tex]Then, this is our answer.
[tex]1in^3=16.387064cm^3[/tex]What is the approximate length of the radius of a circle with a circumference of 63 inches?A. 4 inchesB. 8 inchesC.10 inchesD. 20 inches
The formula for the circumference of a circle given it's radius is :
C = 2πr
Reversely, the formula for the radius given it's circumference is :
r = C/2π
From the given problem, the circumference is 63 inches,
Solve for the radius using π = 3.14
r = 63/(2 x 3.14)
r = 10.03 inches
So the answer is Choice C. 10 inches
i need help with math
1. false= 3 and 5 are corresponding angles
2. false= 7 and 10 are same side exterior angles
3. true
3. true
8. Find the center of the circle that can be circumscribed about the triangle.y-4-262-224
The labelled triangle is shown below
The required center is the point where the perpendicular bisectors meet. It is called the circumcenter. We would find it by applying the midpoint method. The midpoint formula is expressed as
midpoint, M(x, y) = (x1 + x2)/2, (y1 + y2)/2
For AB,
x1 = - 4, y1 = 0
x2 = 4, y2 = 0
Midpoint = (- 4 + 4)/2, (0 + 0)/2 = (0, 0)
For AC,
x1 = - 4, y1 = 0
x2 = 0, y2 = 4
Midpoint = (- 4 + 0)/2, (0 + 4)/2 = (- 2, 2)
For BC,
x1 = 4, y1 = 0
x2 = 0, y2 = 4
Midpoint = (4 + 0)/2, (0 + 4)/2 = (2, 2)
We woulf find the slope of AC
Slope, m = (y2 - y1)/(x2 - x1) = (4 - 0)/(0 - - 4) = 4/(0 + 4) = 4/4
m = 1
Slope of the line per
Sherman counted up all his hockey player cards and realized he had 200. He recently purchased a book to organize them that holds 20 cards on a page. If he puts 2 pages in a section, how many sections will he have in his book? Select the expression that represents the problem above. a) 200 = 20 = 2 b) 200 x 20 x 2 c) 200 20 x 2 d) 200 x 20 = 2
The total number of hockey cards is 200
The number of cards on a page is 20.
The number of pages in a section is 2.
Let there are x number of sections in a book. So number of cards on the x sections should be equal to total number of cards.
Determine the number of cards on the sections.
[tex]20\times2\times x[/tex]
The total number of hocker card is equal to 200. So equation is,
[tex]200=20\times2\times x[/tex]What is the solution to the inequality 2-2x > -20
To determine the solution for the given inequality, you have to solve it for x:
[tex]2-2x>-20[/tex]First, pass 2 to the right side of the inequality by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 2-2-2x>-20-2 \\ -2x>-22 \end{gathered}[/tex]Next, note that the x-term is multiplied by "-2", to reach the value of x you have to cancel the said multiplication. For this, you have to divide both sides of the expression by "-2"
Now, keep in mind, that when you divide or multiply an inequality by a negative number, the direction of the inequality gets inversed. This means that the symbol "greater than, >" will tur into the symbol "less than. <":
[tex]\begin{gathered} -\frac{2x}{-2}<-\frac{22}{-2} \\ x<11 \end{gathered}[/tex]The solution for this inequality will be the values of x less than 11, symbolically: x < 11
Write the expression without a negative exponent.1/a^-4
Explanation
We are given the expression below:
[tex]\frac{1}{a^{-4}}[/tex]We are required to rewrite the expression without a negative exponent.
This can be achieved thus:
[tex]\begin{gathered} \frac{1}{a^{-4}} \\ We\text{ }know\text{ }from\text{ }indices\text{ }that\text{ }a^{-x}=\frac{1}{a^x} \\ \therefore\frac{1}{a^{-4}}=1\div a^{-4}=1\div\frac{1}{a^4} \\ =1\times\frac{a^4}{1}=a^4 \end{gathered}[/tex]Hence, the answer is a⁴.
find the absolute extrema for the function on the given internal
Given the function;
[tex]f(x)=-3x^2-24x+3[/tex]The first derivative of the function is;
[tex]f^{\prime}(x)=-6x-24[/tex]At critical points;
[tex]\begin{gathered} -6x-24=0 \\ -6x=24 \\ x=\frac{24}{-6} \\ x=-4 \end{gathered}[/tex]Thus, the f(x) at x=-4 is;
[tex]\begin{gathered} f(-4)=-3(-4)^2-24(-4)+3 \\ f(-4)=-48+96+3 \\ f(-4)=51 \end{gathered}[/tex]Thus, the absolute maxima on the given point is;
[tex](-4,51)[/tex]The absolute minima on the given points is;
[tex](4,-141)[/tex]Find each of the following products by first using division and then multiplication each will be a while number answer
so
[tex]\begin{gathered} \frac{11}{4}\text{ x 8=11 x 2=22 by multiplication} \\ \end{gathered}[/tex]now by division, we can write
[tex]\frac{11}{4}\text{ }\div\frac{1}{8}=22\text{ }[/tex]when we divide by a fraction, we multiply by its reciprocal
3(4x+3)-12how do you simplify
By following the order of operations, we need to evaluate first the multiplication of 3 and (4x+3) by using the distributive property.
[tex]\begin{gathered} 3(4x+3)-12\text{ (given)} \\ \\ \text{apply the distributive property} \\ =(3\cdot4x+3\cdot3)-12 \\ =12x+9-12 \end{gathered}[/tex]After that, combine like terms, we see from the previous solution that 12x has no other like terms, and it will remain as is. 9 and 12 however are both constant, and should be simplified
[tex]\begin{gathered} 12x+9-12 \\ =12x-3 \end{gathered}[/tex]Therefore, 3(4x+3) - 12, when simplified is 12x - 3.
The area of this rectangle is 15ft^2. Write and equation and solve it to find y
The Area of a rectangle can be calculated by using the formula:
[tex]A=L\times W[/tex]Where A is the area, L is the length and W is the width.
By replacing the given values, your equation will be:
[tex]15ft^2=y\times3ft[/tex]Do the next steps to find the value of y:
[tex]\begin{gathered} \text{Divide both sides by 3 ft} \\ \frac{15ft^2}{3ft}=y\times\frac{3ft}{3ft}\text{ } \\ \text{Simplify and reorder terms} \\ 5ft=y \\ y=5ft \end{gathered}[/tex]Thus, the value of y is 5 ft.
Help please I want to know how to solve this not just the answer!!
Answer:
20 overtime hours
Step-by-step explanation:
overtime starts at 40 hours anything after that would be considered overtime
Given: The base of the pyramid is a regular pentagon.13 ft5 ftWhat is the lateral area of the pyramid?O 100108.3O 150O162.5
The Solution.
The lateral area of the given pyramid is the total area of the 5 triangular faces of the pyramid.
So, we have
[tex]\text{Lateral Area of the pyramid = 5(}\frac{1}{2}bh)[/tex]In this case,
[tex]b=5\text{ ft, h=13 ft}[/tex]Substituting these values in the formula above, we get
[tex]\text{Lateral Area of the pyramid = 5}\times\frac{1}{2}\times5\times13[/tex][tex]\text{Lateral Area of the pyramid = }\frac{25\times13}{2}=\frac{325}{2}=162.5ft^2[/tex]Hence, the correct answer is 162.5 square feet (option 4).
I WILL GIVE BRAINLIEST. NO LINKSA cliff is 80 feet above the sea. From the cliff the angle of depression to a boat is 35 degrees. How far is the boat from the base of the cliff? Round your answer to one decimal place.
Solution
For this case we can create the following diagram:
For this case we want to find the value of x and we can use the following property:
[tex]\tan 35=\frac{80}{x}[/tex]And solving we got:
[tex]x=\frac{80}{\tan 35}=114.25[/tex]