Hi, can you help me to solve this exercise please, it’s about Function Evaluation & Applications!
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Given
[tex]f(x)=\lvert x\rvert+4[/tex]Part A
[tex]\begin{gathered} we\text{ want to find f(4)} \\ we\text{ only n}eed\text{ to substitute the value of 4 to x in the given function} \\ f(4)=\lvert4\rvert+4 \\ f(4)=4+4_{} \\ f(4)=8 \end{gathered}[/tex]Part B
[tex]\begin{gathered} we\text{ want to evaluate f(-4)} \\ \text{note that the absolute value returns postive values} \\ \text{thus, }\lvert-4\rvert=4 \\ f(-4)=\lvert-4\rvert+4 \\ f(-4)=4+4 \\ f(-4)=8 \end{gathered}[/tex]Part C
[tex]\begin{gathered} To\text{ find f(t), we only n}eed\text{ to replace t with x} \\ f(t)=\lvert t\rvert+4 \end{gathered}[/tex]Related Questions
Brandon's car used 10 gallons to travel 310 miles. At what rate does the car use gas, in miles per gallon?On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
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Given:
At 10 gallons, the car is able to cover 310 miles.
Find: At 1 gallon, the car can travel ____ miles.
Solution:
First, let's fill in the number line with the given values.
To solve for the question mark at 1 gallon, simply divide 310 by 10.
[tex]310\div10=31[/tex]Hence, the car uses gas at 31 miles per gallon.
Enter your solution as an ordered pair, with no spaces and with parentheses. OR the answer could be: Infinitely many OR No Solution
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Given the equation system:
[tex]\begin{gathered} 1)y=4x \\ 2)3x+2y=55 \end{gathered}[/tex]The first step is to replace the first equation in the second equation
[tex]3x+2(4x)=55[/tex]With this, we have a one unknown equation. Now we can calculate the value of x:
[tex]\begin{gathered} 3x+8x=55 \\ 11x=55 \\ \frac{11x}{11}=\frac{55}{11} \\ x=5 \end{gathered}[/tex]Now that we know the value of x, we can determine the value of y, by replacing x=5 in the first equation
[tex]\begin{gathered} y=4x \\ y=4\cdot5 \\ y=20 \end{gathered}[/tex]This system has only one solution and that is (5,20)
why are whole numbers rational numbers?
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Answer:
Step-by-step explanation:
A whole number can be written as a fraction that has a denominator of 1. So, the whole numbers 18, 3, and 234 can be written as the rational numbers 18/1, 3/1, and 234/1.
So, all whole numbers are rational numbers, but not all rational numbers are whole numbers.
Find the mzEFH, given that mzEFG = 50°. F E G . I
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By theorem, we will have that m
m
=> m
=>2m
Then, we replace values and solve:
2m m
So, we have that m
A box contains 6 red pens, 4 blue pens, 8 green pens, and some black pens. Leslie picks a pen and returns it to the box each time. the outcomes are: number of times a red pen is picked: 8number of times a blue pen is picked: 5 number of times a green pen is picked: 14number of times a black pen is picked: 3Question: if the theoretical probability of drawing a black pen is 1/10, how many black pens are in the box?
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We have:
x = total pens
n = number of black pens
so:
[tex]x=6+4+8+n=18+n[/tex]and for black pen:
[tex]\begin{gathered} \frac{1}{10\text{ }}=0.1\text{ (probability)} \\ \text{then} \\ \frac{n}{18+n}=0.1 \\ n=0.1(18+n) \\ n=1.8+0.1n \\ n-0.1n=1.8+0.1n-0.1n \\ 0.9n=1.8 \\ \frac{0.9n}{0.9}=\frac{1.8}{0.9} \\ n=2 \end{gathered}[/tex]answer: 2 black pens
helpppppppppppppppppppppppppppppppppppppp
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Answer:
[tex]\large \text{$f^{-1}(x) = 3x -6$}[/tex]
Graphs attached
Step-by-step explanation:
Your inverse function is correct. So not sure what additional information you need
I am not familiar with the graphing tool you have been provided with. My graph is attached. I used a free online graphing tool
Please can I have the answer for number 12?Thanks a lot
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Given:
length of the piece of string = 3/4 inches
length of the piece that we need = 1/8 inches
The number of smaller piece that we can get from the original piece of string can be calculated using the formula:
[tex]\text{Number }of\text{ smaller piece = }\frac{length\text{ of original piece}}{length\text{ of smaller piece}}[/tex]Applying this formula:
[tex]\begin{gathered} \text{Number of smaller piece = }\frac{3}{4}\div\text{ }\frac{1}{8} \\ \end{gathered}[/tex]If the number of pieces is represented as n:
[tex]n\text{ = }\frac{3}{4}\div\text{ }\frac{1}{8}[/tex]Answer:
A genetic experiment with
peas resulted in one sample of offspring that consisted of 447 green peas and 169 yellow peas.
a. Construct a 90% confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
a. Construct a 90% confidence interval. Express the percentages in decimal form.
L s p< (Round to three decimal places as needed.)
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
O
No, the confidence interval includes 0.25, so the true percentage could easily equal 25%
L
O Yes, the confidence interval does not include 0.25, SO the true percentage could not equal 25%
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Using the z-distribution, it is found that:
a. The 90% confidence interval to estimate of the percentage of yellow peas is: (34.04%, 41.58%).
b. The correct option is: Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%.
What is a confidence interval of proportions?The bounds of a confidence interval of proportions is given according to the equation presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the parameters are described as follows:
[tex]\pi[/tex] is the sample proportion.z is the critical value of the distribution.n is the sample size, from which the estimate was builtThe confidence level is of 90%, hence the critical value is z = 1.645, using a z-distribution calculator.
The values of the sample size and of the estimate are given as follows:
[tex]n = 447, \pi = \frac{169}{447} = 0.3781[/tex]
Hence the lower bound of the interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3781 - 1.645\sqrt{\frac{0.3781(0.6219)}{447}} = 0.3404[/tex]
The upper bound is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3781 + 1.645\sqrt{\frac{0.3781(0.6219)}{447}} = 0.4158[/tex]
As a percentage, the interval is given as follows: (34.04%, 41.58%).
The confidence interval does not contain 0.25, hence the true percentage would not be equal to 25%, contradicting the expectation.
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Attached is a photo of my written question, thank you.
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Given:
The function is,
[tex]f(x)=-2x^2-x+3[/tex]Explanation:
Determine the function for f(x + h).
[tex]\begin{gathered} f(x+h)=-2(x+h)^2-(x+h)+3 \\ =-2(x^2+h^2+2xh)-x-h+3 \\ =-2x^2-2h^2-4xh-x-h+3 \end{gathered}[/tex]Determine the value of expression.
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-2x^2-2h^2-4xh-x-h+3-(-2x^2-x+3)}{h} \\ =\frac{-2h^2-4xh-h}{h} \\ =-2h-4x-1 \end{gathered}[/tex]So exprression after simplification is,
-2h - 4x - 1
If cos A = 3/√13 and angle A is not in quadrant I, determine the exact value of sin A.
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To determine the exact value of sin A we get -2/√13
What is determinant?
the determinant is a scalar of value that is a function of to the entries of a square matrix. It is allows characterizing of some properties of to the matrix and the linear map of represented by the matrix.
It is a scalar value which is associated with the square matrix.
Sol-Cos A =3/√13
angle A is not in quadrant I
So angle A is in quadrant IV
Thus,
Sin A =-√(√13)^2-3^2/√13
=-√13-9/√13
=-√4/√13
=-2/√13
Thus the answer is -2/√13.
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What is the average rate of change from f(-1) to f(1)?Type the numerical value for your answer as a whole number, decimal or fractionMake sure answers are completely simplified
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The average rate of change of the function is the average rate at which one quantity is changing with respect to another.
Average rate of change = (y2 - y1)/(x2 - x1)
y represents the output values and it is also called f(x)
x represents the input values
For the given interval,
for f(- 1), x = -1 and f(x) = 8
For f(1), x = 1, f(x) = 4
Average rate of change = (4 - 8)/1 - - 1) = - 4/(1 + 1) = - 4/2
Average rate of change = - 2
You need 30 ounces of chocolate chips to bake some cooldes. You already have 8 ounces of chocolate chips at home. Write an inequality that could beused to find how many ounces of chocolate chips you need to buy.whats the inequality:
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Given:
Amount of chocolate chips needed = 30 ounces
Amount of chocolate you have already = 8 ounces
Let's find the inequality that can be used to find the ounces of chocolate chips you need to buy.
To write the inequality, we have:
8 + x ≥ 30
Where x represents the ounces of chocolate chips you need to buy.
Therefore, the inequality that could be used to fid how many ounces of chocolate chips needed is:
8 + x ≥ 30
ANSWER:
8 + x ≥ 30
Evalue each expression for the given value(s) of the variable(s)exponents
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Any number raised to the power of zero equals 1, then
[tex]r^0s^{-2}=1\cdot s^{-2}=s^{-2}[/tex]then, we need to substitute the value 10 in the variable s. It yields,
[tex]s^{-2}=\frac{1}{s^2}\Rightarrow\frac{1}{10^2}=\frac{1}{100}[/tex]Then, the answer is
[tex]r^0s^{-2}=\frac{1}{s^2}\Rightarrow\frac{1}{100}[/tex]that is, 1 / 100.
Help pleas Which statement best completes the diagram.
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The statement which best completes the cause and effect diagram is that: A. British leaders limit the ability of colonists to expand westward.
What is a cause and effect graphic organizer?A cause and effect graphic organizer is also referred to as cause and effect diagram and it can be defined as a type of chart which highlights and shows the relationship between two things, phenomenon, or events in which an occurrence of one (cause) typically leads to the occurrence of another (effect).
During the late 18th to mid 19th centuries, the United States of America began to grow westward and this led to the emigration of Native American tribes who had in this geographical region for thousands of years before the arrival of European colonists.
Consequently, conflict developed between them which was known as "The French and Indian War" and this caused British leaders to limit the ability of many European colonists to continue expanding westward.
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Complete Question:
Which statement best completes the diagram?
A. British leaders limit the ability of colonists to expand westward.
B. British merchants refuse to buy raw materials from the colonies.
C. British military forces are ordered to leave North America.
D. British leaders end policies that strictly controlled the colonies.
1) K thinks of a number, then doubles the number ,and then multiplies the result by 3 . If her final number is 65 more than her original number, then what was her original number?
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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The original number is 13.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 2x = 4 is an equation.
We have,
Let the number be K.
K thinks of a number, then doubles the number, and then multiplies the result by 3.
This can be written as:
(2 x k) = 2k ____(1)
3 x (2k) = 6k ____(2)
If her final number is 65 more than her original number can be written as:
6k = 65 + k _____(3)
From (3) we get,
6k = 65 + k
Subtract k on both sides.
6k - k = 65 + k - k
5k = 65
Divide both sides by 5.
5k / 5 = 65 / 5
k = 13
Thus,
The original number is 13.
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riangle QRS has vertices Q(8, −4), R(−1, 2), and S(3, 7). What are the coordinates of vertex Q after the triangle is reflected across the y-axiriangle QRS has vertices Q(8, −4), R(−1, 2), and S(3, 7). What are the coordinates of vertex Q after the triangle is reflected across the y-axi
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Martin and Isabelle go bowling. Each game costs $10, and they split that cost. Martin has his own bowling shoes, but Isabelle pays $3 to rent shoes.Which graph shows a proportional relationship? Explain why.
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We have the following:
Martin's graph is good and correct, although it is not totally straight, but the relationship that it keeps is totally proportional.
On the other hand, Isabelle's graph, although it is totally straight, is wrong, because she must start from 3, which is the rental value of the shoes, and her graph starts at 0, therefore it is wrong, despite of which shows a proportional relationship.
Therefore the correct answer is Martin's graph.
Answer:
Step-by-step explanation:
To find the area of a shape region:Find the area of the entire region:Fimd the area of the unshaded region(s)Subtract the area of the unshape region from the area of the entire region
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IN order to find the area of the shaded region, proceed as follow:
calculate the area of the right triangle:
A = b·h/2
A = (21 yd)(34 yd)/2 = 357 yd²
next, calculate the area of the circle:
A' = π r²
A' = (3.1415)(7 yd)² = 153.93 yd²
next, subtract the area of the circle to the area of the rectangle:
AT = A - A' = 357 yd² - 153.93 yd²
AT = 203.07 yd²
Hence, the area of the shaded region is 203.07 yd²
1a. 100 foot-long rope is cut into 3 pieces.The first piece of rope is 3 times as long asthe second piece of rope. The third piece istwice as long as the first piece of rope.What is the length of the longest piece ofrope?
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To solve the exercise, it is easier to make a drawing, like this
So, you have
[tex]\begin{gathered} z=3y \\ y=y \\ x=2z \\ z+y+x=100 \end{gathered}[/tex]Now solving
[tex]\begin{gathered} x=2z \\ x=2(3y) \\ x=6y \end{gathered}[/tex][tex]\begin{gathered} z+y+x=100 \\ 3y+y+6y=100 \\ 10y=100 \\ \frac{10y}{10}=\frac{100}{10} \\ y=10\text{ ft} \end{gathered}[/tex][tex]\begin{gathered} x=6y \\ x=6(10) \\ x=60\text{ ft} \end{gathered}[/tex][tex]\begin{gathered} z=3y \\ z=3(10) \\ z=30\text{ ft} \end{gathered}[/tex]Therefore, the length of the longest piece is 60ft.
Find a function of the form y = A; A * sin(kx) + C or y = A * cos(kx) + C whose graph matches this one:I don’t understand how my answer is wrong
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Recall that the graph of the cosine function is:
Now, notice that the given graph is the above graph but with a midline
[tex]y=1,[/tex]and amplitude equal to 4. The frequency is also different.
Therefore, the equation of the function given in the graph is:
[tex]y=4cos(\frac{\pi}{5}x)+1.[/tex]Answer: [tex]y=4cos(\frac{\pi x}{5})+1.[/tex]Triangle Inequality TheoremDetermine if a triangle can be formed with the given lengths. If so, classify the triangle by its angle.YESorNO
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Given:-
[tex]7,20,12[/tex]To find:-
Wheather the given sides form a valid triangle.
So now let,
[tex]A=7,B=20,C=12[/tex]To check we use the condition,
[tex]A+B>C,B+C>A,C+A>B[/tex]Substituting the values we get,
[tex]7+20>12,20+12>7,12+7>20[/tex]In the above condition 12+7>20 is wrong.
So the condition fails and the given sides doesnt form a triangle.
6. Line 1 passes through the points (1,4) and (-2,5). Line 2 passes through the points (1,0) and (0,3). What is true about Line 1 and Line 2? (2 points) (A) (B) They are perpendicular. They are parallel. They both decrease. They both increase. (C) (D)
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First, calculate the slope (m) of both lines.
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Line 1:
Point 1 = (x1,y1) = (1,4)
Point 2 = (x2,y2) = (-2,5)
Replacing:
[tex]m=\frac{5-4}{-2-1}=\frac{1}{-3}=-\frac{1}{3}[/tex]Line 2:
Point 1 = (x1,y1) = (1,0)
Point 2 = (x2,y2) = (0,3)
[tex]m=\frac{3-0}{0-1}=\frac{3}{-1}=-3[/tex]Lines to be parallel must have the same slope, and to be perpendicular, they must have negative reciprocal slope.
None of the slopes are equal or negative reciprocal. SO, A and B are false-
Now, for the increase/ decrease
We can see that both lines have a negative slope, so they both decrease.
Correct option: C
J is the midpoint of CT if CJ=5x-3 and JT=2x+21 find CT
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Since J is the midpoint of the CT segment, then:
[tex]\begin{gathered} CJ=JT \\ 5x-3=2x+21 \end{gathered}[/tex]Now, you can solve the equation for x:
[tex]\begin{gathered} 5x-3=2x+21 \\ \text{ Add 3 from both sides of the equation} \\ 5x-3+3=2x+21+3 \\ 5x=2x+24 \\ \text{ Subtract 2x from both sides of the equation} \\ 5x-2x=2x+24-2x \\ 3x=24 \\ \text{ Divide by 3 from both sides of the equation} \\ \frac{3x}{3}=\frac{24}{3} \\ x=8 \end{gathered}[/tex]Replace the value of x into the equation for segment CJ or segment JT to find out what its measure is. For example in the equation of the segment CJ:
[tex]\begin{gathered} CJ=5x-3 \\ x=8 \\ CJ=5(8)-3 \\ CJ=40-3 \\ CJ=37 \end{gathered}[/tex]Finally, you have
[tex]\begin{gathered} CJ=37 \\ CJ=JT \\ 37=JT \\ \text{ Then} \\ CT=CJ+JT \\ CT=37+37 \\ CT=74 \end{gathered}[/tex]Therefore, the measure of the segment CT is 74.
divide and Simplify 7/5 ÷7/9
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What we have is a fractional division, this is following expression
[tex]\frac{(\frac{7}{5})}{(\frac{7}{9})}[/tex]For this procedure, it says to multiply the top and bottom ends to get the numerator, and the middle numbers to get the denominator
[tex]\frac{7\cdot9}{7\cdot5}=\frac{9}{5}[/tex]In conclusion after splitting and simplifying this, the answer is 9/5
ratio problems that I am struggling with
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7 out of every 500 Americans are aged 13-17 years generation are vegetarian
Thus the ratio of the vegetarian is 7 : 500
In a group of 350,
Let x be the number of people who are vegetarian
So, the ratio out of 350 who are vegetarian are : x : 350
SInce the ratio is same so:
[tex]\begin{gathered} 7\text{ : 500=x:250} \\ \frac{7}{500}=\frac{x}{250} \\ \text{ Simplify for x,} \\ x=\frac{7}{500}\times250 \\ x=\frac{7}{2} \\ x=3.5 \\ x\approx4 \end{gathered}[/tex]So, the number of people who are vegetarian out of 350 people is 4 people
Please help me don't understand
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Answer:
x=13
Step-by-step explanation:
50+3x=89
89-50=3x
39=3x
13=x
find the area of the circle with a circumference of 30π. write your solution in terms of π
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we know that
the circumference of a circle is giving by
[tex]C=2\pi r[/tex]we have
C=30pi
substitute
[tex]\begin{gathered} 30\pi=2\pi r \\ \text{simplify} \\ r=\frac{30}{2} \\ r=15\text{ units} \end{gathered}[/tex]Find the area of the circle
[tex]A=\pi r^2[/tex]substitute the value of r
[tex]\begin{gathered} A=\pi(15^2) \\ A=225\pi\text{ unit\textasciicircum{}2} \end{gathered}[/tex]the area is 225π square unitsWrite an exponential expression: Let 10 be the base and an even number between 1 and 10 be the exponent.
Then write the exponential expression in expanded form and standard form.
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The exponential expression as required to be chosen is; 10⁴.
The expanded form of the expression is; 10 × 10 × 10 × 10.
The standard form of the expression is; 10,000.
Exponential expressions in expanded form and Standard form.It follows from the task content that the exponential expression is to be written in expanded and standard form.
Since the exponential expression must have 10 as the base and an even number between 1 and 10 as the exponent.
An example of such exponential expression is therefore;
10⁴.
Hence, to write the expression in expanded form; it is written as a product of factors as follows;
10 × 10 × 10 × 10
Also, the expression can be written in standard form as the result of the multiplication above;
= 10,000.
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Please help with this question
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The average velocities of the stone are: i) 12.96 m / s, ii) 13.20 m / s, iii) 13.20 m / s, iv) 13 m / s. The instantaneous velocity is approximately equal to 13 meters per second.
How to find the average velocity and the instantaneous velocity of a stone
The average velocity (u), in meters per second, is the change in the height (h), in meters, divided by the change in time (t), in seconds. And the instantaneous velocity (v), in meters per second, is equal to the average velocity when the change in time tends to zero.
a) Then, the average velocities are determined below:
Case i)
u = [f(1.05) - f(1)] / (1.05 - 1)
u = (18.748 - 18.1) / 0.05
u = 12.96 m / s
Case ii)
u = [f(1.01) - f(1)] / (1.01 - 1)
u = (18.232 - 18.1) / 0.01
u = 13.20 m / s
Case iii)
u = [f(1.005) - f(1)] / (1.005 - 1)
u = (18.166 - 18.1) / 0.005
u = 13.20 m / s
Case iv)
u = [f(1.001) - f(1)] / (1.001 - 1)
u = (18.113 - 18.1) / 0.001
u = 13 m / s
The fourth option offers the best estimation for the instantaneous velocity at t = 1 s. Then, the instantaneous velocity is approximately equal to 13 meters per second.
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a line with a slope of 1/3 and containing the point (-4,7)
Answers
An equation of line with a slope of 1/3 and containing the point (-4,7) is
y = 1/3 x + 25/7
In this question, we have been given
slope (m) = 1/3
and a point (-4, 7)
We need to find an equation of a line with a slope of 1/3 and containing the point (-4,7)
Using the formula for the slope-point form of equation of line,
y - y1 = m(x - x1)
y - 7 = 1/3(x + 4)
y - 7 = (1/3)x + 4/3
y = (1/3)x + 4/3 + 7
y = 1/3 x + 25/7
Therefore, an equation of line with a slope of 1/3 and containing the point (-4,7) is y = 1/3 x + 25/7
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