Answer:Given : f(x)=x
4
−3x
2
+4
f(2)=(2)
4
−3(2)
2
+4
=16−12+4=8
This can also be verified by the actual divison
What is the y-intercept in the equation y = 45x + 65?
Answer:
The y intercept is : 65
Step-by-step explanation:
The y intercept is 65 as it is in the form of y=mx+c.
The c is the y intercept, being 65
m(x) = 4x + 15 m(x) needs to be 7 x =
Answer:
x = -2
Step-by-step explanation:
If m(x) = 4x + 15 and m(x) = 7, the we can substitute and get the equation:
4x + 15 = 7
x = -2
If sin A 0.3, cos A = 0.7, sin B = (1/√5)
and cos B: (-1/√5) find the exact value of cos(A - B).
(i know the answer but i want to know how to solve it as well)
The exact value of cos(A - B) is -2√5 /25.
What are Sine and Cosine?In math, the trigonometric functions of an angle are sine and cosine. In the context of a right triangle, the sine and cosine of an acute angle are defined as the ratio of the lengths of the adjacent leg to the hypotenuse, and the sine of the specified angle is the ratio of the opposite leg's length to the hypotenuse's length.The concepts of sine and cosine can be expanded to include any real value in terms of the lengths of particular line segments in a unit circle.The sine and cosine can be extended to any positive or negative value, even complex numbers, according to more recent definitions of the terms, which also represent them as infinite series or as the solutions to specific differential equations.Therefore,
sin A = 0.3
sin B = (1/√5)
cos A = 0.7
cos B = (-1/√5)
cos(A-B) = cos a cos b + sin a sin b
⇒ cos(A-B) = 0.7(-1/√5) + 0.3((1/√5))
⇒ cos(A-B) = -0.7/√5 + 0.3/√5
⇒ cos(A-B) = -0.4/√5
On multiplying, √5 on the numerator and denominator,
⇒ cos(A-B) = -0.4 x √5 / 5
⇒ cos(A-B) = -2√5 /25
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printer a can print a 300 page document in 10 minutes. printer b can print a 400 page document in 8 minutes. Both printers were run until a total of 1000 pages were printed. How many pages did printer b print?
Answer:
625 pages
Step-by-step explanation:
Rate x time of the one printer + the rate x time of the second printer = 1000 pages
t= time
([tex]\frac{300}{10}[/tex] )t +( [tex]\frac{400}{8}[/tex]) t = 1000
30t + 50t = 1000
t(30 + 50) = 1000
80t = 1000 Divide both sides by 80
t = 12.5
It took 12.5 minutes to get this job done with both printers.
Look at printer b
[tex]\frac{400}{8}[/tex] (12.5) = pages
50 x 12.5 = 625 pages
Bethany is building a storage trunk. 5ft long, 4ft height and 2ft wide. how much wood is needed to make the trunk
Answer:
76 square feet of wood.
Explanation:
Bethany is building a storage trunk with the following dimensions:
• Length = 5 ft.
,• Height = 4 ft.
,• Width = 2 ft.
We are to determine how much wood is needed to make the trunk.
The amount of wood that will be needed to make the truck is the surface area of the trunk. The storage trunk is in the shape of a rectangular prism.
The surface area of a rectangular prism is found using the formula below:
[tex]\text{Surface Area=2(LW+LH+WH)}[/tex]Substitute the given dimensions:
[tex]\begin{gathered} \text{Surface Area}=2(5\times2+5\times4+2\times4) \\ =2(10+20+8) \\ =2\times38 \\ =76\; ft^2 \end{gathered}[/tex]Bethany needs 76 square feet of wood to make the trunk.
True or False: The relation {(9,1), (0,1), (9,-3), (-4,12)} is a function.
Given
relation = {(9,1), (0,1), (9,-3), (-4,12)}
Find
Is this a function?
Explanation
A relation is a function only if it relates each element in its domain to only one element in the range.
here , domain 9 has two range value 1 and -3
so it is not a function
Final Answer
Hence , it is false
Answer:
False
Step-by-step explanation:
Definition:
Function is a set of coordinate points where each coordinate points do not have same domains (x-values). If we express mathematically, we can do as [tex]\displaystyle{f=\left \{(x_0,y_0),(x_1,y_1),(x_2,y_2),...,(x_n,y_n)\}\right}[/tex] where [tex]\displaystyle{x_0\neq x_1 \neq x_2\neq \dots \neq x_n}[/tex]Function is also considered to be a relation but not all relations can be functions.
As accorded to the relation, it turns out that there are two same domains (x-values) which is 9 from (9,1) and (9,-3). Therefore, this relation doesn’t satisfy the definition of function so it’s not a function.
Please let me know if you have any questions!
1. 3x-4=232. 9-4x=173.6(x-7)=364. 2(x-5)-8= 34
Solving those simple linear equations, by isolating the variable, and combining like terms.
1.3x-4=23
3x -4=23
3x=27
x=9
2) 9-4x=17
-4x =17-9
-4x=8
4x=-8
x=-2
3) 6(x-7)=36 Distributing the factor
6x -42=36
6x=36+42
6x=78
x=13
4) 2(x-5)-8=34 Distributing the factor
2x -10-8=34
2x -18=34
2x=52
x=26
Given vectors a=(3, 2) and b=(-5, 6), find – 3a+2b.Write your answer in component form.-3a + 2b =
Vector a = (3, 2), then;
[tex]-3a=-3(3,2)\text{ = (-9,-6)}[/tex]Also, vector b = (-5, 6), then;
[tex]2b=2(-5,6)=(-10,12)[/tex]Then, -3a + 2b = (-9, -6) + (-10, 12)
[tex]\begin{gathered} -3a+2b=(-9+(-10),-6+12)_{} \\ -3a+2b=(-19,6) \end{gathered}[/tex]The answer is (-19,6)
4. the probability that an engine overheats is 0.12. the probability that an engine leaks oil is .08. (a) if overheating and leaking oil are independent, what is the probability that an engine overheats and leaks oil?
The probability that the engine over heats and leaks is 0.0096
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
Probability is a metric used to express the possibility or chance that a particular event will occur. Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.
Engine leaks oil AND overheats,
hence P(Engine overheats) = P(Engine overheats) X P(Engine leaks oil) = 0.12 X 0.08 = 0.0096
Hence the probability of leaking of engine due to over heating is 0.0096
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What is the equation of the line that passes through the point (-8,6) and has a slope of 1/4
The equation of the line is 4y = x + 32 which passes through the point (-8,6) and has a slope of 1/4.
We have been given the required line that passes through the point (-8,6) and has a slope of 1/4.
What is the slope of the line?The slope of a line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Let the required line would be as
⇒ y - y₁ = m (x - x₁ )
The required line passes through the point (-8,6)
Here x₁ = -8 and y₁ = 6 and m = 1/4
Substituting these inputs into the above equation obtains the line equation.
⇒ y - 6 = 1/4 (x - (-8))
⇒ y - 6 = 1/4 (x + 8)
⇒ 4y - 24 = x + 8
⇒ 4y = x + 8 + 24
⇒ 4y = x + 32
Thus, the equation of the line is 4y = x + 32 which passes through the point (-8,6) and has a slope of 1/4.
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Plssss help due tomorrow!!
Answer:
y = -1/3x +1
Step-by-step explanation:
You want the slope-intercept form equation of the line through the points (-3, 2) and (-9, 4).
SlopeThe slope is given by the formula ...
m = (y2 -y1)/(x2 -x)
m = (4 -2)/(-9 -(-3)) = 2/-6 = -1/3
Y-interceptThe y-intercept is given by the formula ...
b = y1 -m(x1)
b = 2 - (-1/3)(-3) = 1
Slope-intercept equationThe slope-intercept equation of the line is ...
y = mx +b
y = -1/3x +1
I inserted a picture because it was too much to type but this is the 2nd part to my other question, Please answer.
Based on the quantity of the bag of sugar that Jaleel and Angela purchased, and their recipes for brownies, the amount of flour needed by each is:
Angela - 5 cups of flour Jaleel - 6 ²/₃ cups of flourHow much flour is needed?Jaleel and Angela purchased a 20-cup bag of sugar and divided it evenly which means that they each get 10 cups of sugar.
Jaleel's recipe shows that every 1.5 cups of sugar needs a cup of flour. If he had 10 cups of sugar therefore, the amount of flour needed would be:
= Number of cups of sugar / Cups of sugar per cup of flour
= 10 / 1.5
= 6 ²/₃ cups of flour
Angela's recipe is such that every cup of sugar needs 1/2 cups of flour. This means that with 10 cups of sugar, the amount of flour needed is:
= 10 x 1/2
= 5 cups of flour
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Whats the answer to this -11 + 2x
A.-10
B.9
C.-12
D.6
it is known that a certain kind of algae in the dead sea can double in population every 4 days. suppose that the population of algae grows exponentially, beginning now with a population of 3,000,000. (a) how long it will take for the population to quadruple in size? days (b) how long it will take for the population to triple in size? days
Since the algae grow exponentially with doubling time of 4 days, then the population will be quadruple in size in 8 days and will be triple in size in 6.34 days.
The easiest way is to consider the situation as a geometric sequence. If the population doubles its size in 4 days, then it will be quadruple in:
2 x 4 days = 8 days.
In general, we can use the growth formula:
P(t) = Po . 2^(t/Td)
Where:
P(t) = population at time t
Po = initial population
Td = doubling time
Parameters given:
Td = 4 days
P(t) = 3Po
Plug those parameters into the formula:
3 Po = Po . 2^(t/4)
3 = 2^(t/4)
log 3 = (t/4) log 2
t = 4 . log 3 / log 2 = 6.34 days.
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How do you find average speed from aHow do you find average speed from a distance time graph?\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ distance time graph?
An average speed can be calculated from a distance time graph through the division is change in distance and change in its corresponding time.
What is distance time graph?A distance time graph is a type of graph that show the distance covered by an object with respect to time.
When plotting a distance time graph, the distance is plotted in the y-axis while time is plotted of the X -axis and a suitable scale of used to fill in the observed figures.
Speed is the product of distance travelled by an object with respect to its time. Therefore, an average speed can be calculated through the division is change in distance and change in its corresponding time.
That is ; average speed= ∆speed/∆ time
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For the equation, complete the given ordered pairs.Need help solving the last order pair.
Hello!
First, let's remember:
In an ordered pair, we will have two variables represented as (x, y).
In the first two ordered pairs, the exercise informed the value of x. In the third ordered pair, it informs the value of y. We will solve it in a similar way, look:
[tex]\begin{gathered} 4x-y=7 \\ 4x-7=7 \\ 4x=7+7 \\ 4x=14 \\ x=\frac{14}{4}=\frac{7}{2} \end{gathered}[/tex]Answer:x = 7/2 or also x = 3.5.
Algebraically solve for x: 7/2x-2/x+1=1/4
Step-by-step explanation: Check the photo
Answer:
x = -2
Step-by-step explanation:
7/(2x) - 2/x + 1 = 1/4
7/(2x) - 4/(2x) + 1 = 1/4
(7-4)/(2x) = 1/4 - 1
3/(2x) = 1/4 - 4/4
3/(2x) = - 3/4
3 = (-3/4)(2x)
3 = -6x/4
3*4 = -6x
12 = -6x
12/-6 = x
-2 = x
Check:
7/(2*-2) - 2/-2 + 1 = 1/4
7/-4 + 1 + 1 = 1/4
-7/4 + 2 = 1/4
-7/4 + 8/4 = 1/4
5. suppose waiting time until the next failure of oil pump system is exponentially dis tributed, with mean of 37 hours. the pump is continuously in operation. what is the probability that the system does not fail for 2 days?
The Probability that the system does not fail for 2 days is 0. 053
Given ,
Mean (u) = 37 hours .
Step 1 : Calculate the rate parameter, λ.
λ = 1/ mean
λ = 1/ 37 = 0.02703
Step 2 : Find the probability that the system does not
fall for two days, P ( x[tex]\leq[/tex]2 )
P ( x[tex]\leq[/tex]2 ) .= 1 - e power (lamda(x))
= 1 - e - 2(lamda)
= 1 - e power -2(0. 02703 )
By solving,
P ( x[tex]\leq[/tex]2 ) = 0.05263
P ( x[tex]\leq[/tex]2 ) = 0. 053 [ upto three decimals]
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A number is selected randomly from a container containing all the integers from 10 to 50. Find P(Prime|between 11 and 30).A. 7/10B. 1/2C. 1D. 3/10
Given:
Numbers in the container: All integers from 10 to 50
Let's find P(Prime numbers| numbers between 11 and 30).
Here, we are to find the conditional probability.
Apply the formula:
P(Prime|between 11 and 30) = P(prime numbers and between 11 and 30) ÷ P(numbers between 11 and 30).
Where:
• Prime numbers between 11 and 30 = 11 , 13 , 17 , 19 , 23 , 29 =6 numbers
,• Intergers from 10 to 50 = 41 integers.
To find the probability, we have:
[tex]\begin{gathered} P(Prime|between11and30)=\frac{\frac{6}{41}}{\frac{20}{41}} \\ \\ =\frac{6}{41}\ast\frac{41}{20} \\ \\ =\frac{6}{20} \\ \\ =\frac{3}{10} \end{gathered}[/tex]Therefore, we have:
P(Prime|between 11 and 30) = 3/10.
ANSWER:
D. 3/10
please help me , and can you explain what i shluld study to understand this
x = 12° and y = 7° are the value of linear angles.
What is linear pair of angles?
When two lines meet at a single point, a pair of linear angles is created. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair's angles add up to 180° in all cases.8x° = 96°
x = 96/8
x = 12°
8x° = 11y + 19
8 * 12° = 11y + 19
96 = 11y + 19
11y = 96 - 19
11y = 77
y = 77/11
y = 7°
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Josiah skateboards from his house to school 3 miles away. It takes him 36 minutes. If Josiah's speed, in miles per minute, is constant, what is the constant of proportionality? Type the number that represents the constant of proportionality in the box below.
13
Step-by-step explanation:
i said 36 divide by 3 is 13
a+b=0
What does b equal
Answer: D) -a
Step-by-step explanation:
a+b=0 , add -a for both side
- a + a + b = 0 - a
we cancel (- a + a) and we get
b = 0 - a => b = -a
Answer:
option d -a
if you take a to the opposite side of the equal mark it's sign is going to change since it's positive it's going to be negative on the other side 0 -a = -a
baam answer
The perimeter of a rectangle is to be between 140 and 220 inches. FindThe range of values for its length when its width is 20 inches
The lower value of the perimeter is 140 inches .
Width of the rectangle is 20 inches .
The length of the rectangle is calculated as ,
[tex]\begin{gathered} \text{Perimeter = 2 ( Length + width )} \\ 140=\text{ 2 ( Length + }20\text{ )} \end{gathered}[/tex]Rearranging the terms ,
[tex]\begin{gathered} \text{Length + 20 = }\frac{140}{2} \\ \text{Length + 20 = 70} \\ \text{Length = 50 inches} \end{gathered}[/tex]The higher value of perimeter is 220 inches .
Width of the rectangle is 20 inches .
The length is calculated as,
[tex]\begin{gathered} \text{Perimeter = 2 ( Length + width )} \\ 220=\text{ 2 ( Length + }20\text{ )} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{Length + 20 = 110} \\ \text{Length = 110 - 20} \\ \text{Length = 90 inches} \end{gathered}[/tex]Thus the range of values for the length of the given rectangle are 50 and 90 .
Home NaviarStudent and Parent...Grades and Attenda...If DE is parallel to PQ and DE is parallel to XY,which statement must be true?A. PQ and XY are perpeAdicular lines.B. PQ and XY are parallel lines.C. PQ and XY are skew lines.D. PQ and XY are oblique lines.
The line DE is parallel to line PQ and line DE is parallel to XY.
If any one line is parallel to any other line and any of one line (from two parallel line) is parallel to third line then all three line are parallel to each other.
So line PQ, line XY and line DE all three parallel to each other.
Option B is correct.
Question 1
Order from smallest to largest by selecting the dropdown beside each option. Mark the smallest with number 1.
• Number of pennies in a stack that is 1 ft high [Select]
• Number of books in a stack that is 1 ft high [Select]
• Number of dollar bills in a stack that is 1 ft high [Select]
• Number of slices of bread in a stack that is 1 ft high [Select]
.
Question 2
The order from smallest to largest is a book, bread, penny, bills
In decreasing size, they are a book, a loaf of bread, a penny, and a bill.
The following details must be taken into account;
The least number of books was thought to be necessary to reach one foot, followed by bread and then pennies.Finally, there should be bills.We can infer from the facts above that the smallest to largest items are books, bread, pennies, and cash.
Hence, The order from smallest to largest is a book, bread, penny, bills.
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Write the coordinates of the vertices after a reflection over the y-axis
The most appropriate choice for reflection will be given by-
After reflection over y-axis, coordinate of K will become K' (6, -1)
After reflection over y-axis, coordinate of L will become L' (0, -1)
After reflection over y-axis, coordinate of M will become M' (0, -2)
After reflection over y-axis, coordinate of J will become J' (6, -2)
What is reflection?
Reflection of a figure about a line is a transformation in which a mirror image of the figure can be obtained over the line.
The line is called the line of reflection.
Here,
After reflection over the y - axis, sign of x coordinate will be same.
Coordinate of K = (-6, -1)
After reflection over y-axis, coordinate of K will become K' (6, -1)
Coordinate of L = (0, -1)
After reflection over y-axis, coordinate of L will become L' (0, -1)
Coordinate of M = (0, -2)
After reflection over y-axis, coordinate of M will become M' (0, -2)
Coordinate of J = (-6, -2)
After reflection over y-axis, coordinate of J will become J' (6, -2)
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imagine that a long stretch of single-strand dna has 30% adenine, 25% thiamine, 15th% cytosine, and 30% guanine. what is the probability of randomly drawing 10 adenine in a row in a sample of 10 randomly chosen nucleotides? explaination
In a sample of 10 nucleotides, the likelihood of drawing 10 consecutive adenines at random is 0.000006.
Probability: The probability of an occurrence is defined as the ratio between the number of favorable outcomes to a certain event and the entire number of potential outcomes.
The following calculation shows the likelihood of picking 10 consecutive adenines at random from a sample of 10 nucleotides:
According to the information provided, there are 10 adenines and a likelihood of 0.30 that DNA contains them. n = 10 and p = 0.30
Therefore, Probability = (0.30)10 = 0.000006
The likelihood of randomly selecting 10 consecutive adenines from a sample of 10 nucleotides is calculated by multiplying the likelihood that DNA contains adenines by 10 times.
Therefore, The probability of picking 10 consecutive adenines at random from a sample of 10 nucleotides is 0.000006.
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does anyone know the answer?
ΔXYZ ≅ ΔUTV
The two angles of the non-included side of the triangle are congruent to the two sides and non-included sides of the second triangle, according to the AAS theorem.
What exactly is the AAS theorem?The AAS theorem is an angel, angle side theorem that states that two angles on any side of a triangle that are congruent to two angles on another triangle are said to be congruent.The triangles are congruent if two pairs of corresponding angles and the side between them are known to be congruent. This is known as the angle-side-angle shortcut. Angle-angle-side (AAS) is another shortcut in which two pairs of angles and the non-included side are known to be congruent.To learn more about congruent triangles refer to :
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The radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder with water. The radius of the cone's base is 5 centimeters, and its height is 10 centimeters
The number of times one needs to use completely filled cone to completely fill the cylinder with water is...
The number of times one needs to use completely filled cone to completely fill the cylinder with water is 24
What is volume of cone and cylinder?The volume of cylinder is equal to the product of the area of the circular base and the height of the cylinder.
Given that radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters.
The radius of the cone's base is 5 centimeters, and its height is 10 centimeters.
The volume of cylinder is πr²h
For a volume of cone it is 1⁄3πr²h.
So volume of cylinder = 22/7×(10)2×20=3.142×100×20
=6284
volume of cone it is 1⁄3πr²h=1/3×3.142×(5)^2×10=261.16
Number of times one needs to use the completely filled cone to completely fill the cylinder with water =
= Volume of cylinder/Volume of cone
6284 / 261.16 = 24
Hence the number of times one needs to use completely filled cone to completely fill the cylinder with water is 24
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Describe how the equations for an ellipse, circle, hyperbola and parabola differ from one another. Include an example of each in your description.
See explanation below
Explanation:An ellipse has a standard equation formula written as:
[tex]\frac{(x^{}-h)^2}{a^2}+^{}\frac{(y-k)^2}{b^2}\text{ = 1}[/tex]When the sign between the x^2 and y^2 terms is positive, then it is a ellipse
[tex]\begin{gathered} \text{example of an ellipse:} \\ \frac{(x-3)^2}{9}\text{ + }\frac{(y\text{ - 8})^2}{25}\text{ = 1} \end{gathered}[/tex]An hyperbola has a standard equation written as:
[tex]\frac{(x^{}-h)^2}{a^2}-^{}\frac{(y-k)^2}{b^2}\text{ = 1}[/tex]when the sign between the parenthesis of x^2 and y^2 terms is minus, then it is an hyperbola
[tex]\begin{gathered} \text{example of a hyperbola:} \\ \frac{x^2}{64}\text{ - }\frac{y\text{ }^2}{49}\text{ = 1} \end{gathered}[/tex]A circle has a general formula written as:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where vertex = (h, k)} \\ r\text{ = radius} \end{gathered}[/tex]The terms x^2 and y^2 are not divided by a constant. Also the left side of the equation represents the square of the radius
[tex]\begin{gathered} An\text{ example of a circle} \\ (x-1)^2+(y-3)^2\text{ = }10 \end{gathered}[/tex]Parabola has a vertex form of equation written as:
[tex]\begin{gathered} y=a(x-h)^2+\text{ k} \\ \text{where a = constant} \end{gathered}[/tex][tex]\begin{gathered} An\text{ example:} \\ y\text{ = 2(x - 1})^2\text{ + }3 \end{gathered}[/tex]Here, we only have term x^2, no y^2. y has an exponent of 1. Also a constant of a
