We have to find the range of the function f(x).
The definition of f(x) is:
[tex]f(x)=2^x-10[/tex]The domain of this function is defined as: D: {-1, 0, 1, 2, 3}, which represents all the integers from -1 to 3.
Then, we have to find the range by applying the function to each of the elements of the domain:
[tex]f(-1)=2^{-1}-10=\frac{1}{2}-10=-9.5[/tex][tex]f(0)=2^0-10=1-10=-9[/tex][tex]f(1)=2^1-10=2-10=-8[/tex][tex]f(2)=2^2-10=4-10=-6[/tex][tex]f(3)=2^3-10=8-10=-2[/tex]Then, the range of f(x) is R: {-9.5, -9, -8, -6, -2}.
Answer:
The options that apply from the list are -9, -6 and -2. [Options c, d and e]
What is the exact value of cosine of the quantity pi over 3 question mark
We are required to find the value of the cosine of pi over 3.
The cosine of an angle is a ratio of the side adjacent to the angle to the hypothenuse side
Our approach is to first plot a triangle that will help us give values to this side and get our ratio.
Fortunately, pi over 3 is a special angle as we will see.
We can convert it to degrees via the formula:
[tex]\frac{\pi}{3}\times\frac{180^o}{\pi}=60^o[/tex]Recall that the sum of angles in an equilateral triangle of sides' ratio 2:2:2 is 180 degrees and each angle is 60 degrees.
We can find side o through Pythagoras Theorem as:
[tex]o=\sqrt[]{2^2-1^2}=\sqrt[]{4-1}=\sqrt[]{3}[/tex]The cosine of the angle is a ratio of the adjacent side, o and hypothenuse, 2.
[tex]\cos 60^o=\cos \frac{\pi}{3}=\frac{\text{adj}}{\text{hyp}}=\frac{1}{2}[/tex]OPTION B
please i need your help i will appreciate it
The value of c is 5/2 that satisfy the conclusions of the mean value theorem.
Given Function:
f(x) = x^2-3x+3 on interval [1,4].
The Mean Value Theorem states that for a continuous and differentiable function f(x)=x^2-3x+3 on the interval [1,4] there exists such number c from the interval [1,4] that [tex]f'(c)=\frac{f(4)-f(1)}{4-1}[/tex].
f(4) = 4^2-3*4+3
= 16-12+3
= 4+3
= 7
f(1)=1^2-3*1+3
= 1-3+3
= 1
f'(c) = 2c -3
2c-3 = 7 - 1 / 4 - 1
2c - 3 = 6/3
2c -3 = 2
2c = 5
c = 5/2
Therefore the value of c = 5/2 that satisfy the conclusions of the mean value theorem.
Learn more about the mean value theorem here:
https://brainly.com/question/1581272
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what is 2/3 times 3/8
Mutiply both fractions:
[tex]\frac{2}{3}\times\frac{3}{8}[/tex][tex]\frac{2\times3}{3\times8}=\frac{6}{24}[/tex]Simplify by 6.
[tex]\frac{1}{4}[/tex]Answer:
Do the multiplication straight across 2 times 3= 6. 3times 8= 24 so 6/24 or 1/4
A student is taking a test in which items of type A are worth 8 points and items of type B are worth 12 points. It takes 3 min to complete each item of type A and 6 min to complete each item of type B. The total time allowed is 60 min and Anna answers exactly 16 questions. How many questions of each type did she complete? Assuming that all her answers were correct, what was her score? She completed questions of type A.
Type A questions are worth 8 points each.
Type B questions are worth 12 points each.
it takes 3 minutes to answer a Type A question
it takes 6 minutes to answer a Type B question.
total time allowed = 60 minutes
She answered a total of 16 questions.
let
number of question answer on type A = x
number of question answered on type B = y
Therefore,
3x + 6y = 60
x + y = 16
then,
[tex]\begin{gathered} 3x+6y=60 \\ x+y=16 \\ x=16-y \\ 3(16-y)+6y=60 \\ 48-3y+6y=60 \\ 3y=60-48 \\ 3y=12 \\ y=\frac{12}{3} \\ y=4 \\ x=16-4 \\ x=12 \end{gathered}[/tex]She answered 12 questions on type A and 4 questions on type B.
If all her answer is correct her score can be computed below
[tex]undefined[/tex]identify the terms, like terms, coefficients and constants 2c - 2b + c + 3 + b - 4
1) In this expression, we have
1.1 ) Terms: We have 6 terms in total.
2c -2b +c +3 + b -4 Combining like terms we can rewrite them as
c -b -1
1.2) Like terms are the ones that share the same variable
2c, c
-2b, b
1.3) Coefficients the numbers that multiply the variables
2c - 2b + c + 3 + b - 4
So we have:
2, -2, 1
1.4) The constants. Simply put in this case, the numbers that do not vary
-4 and 3
-15-3r=6r+3c Solve for r.
Answer:
[tex]r=\frac{-c-5}{3}[/tex]Explanation:
We want to solve for r in the equation below;
[tex]-15-3r=6r+3c[/tex]We need to move all terms of r to one side and divide both sides by the coefficient of r.
firstly subtract 6r from both sides;
[tex]\begin{gathered} -15-3r-6r=6r-6r+3c \\ -15-9r=3c \end{gathered}[/tex]then add 15 to both sides;
[tex]\begin{gathered} -15+15-9r=3c+15 \\ -9r=3(c+5) \end{gathered}[/tex]divide both sides by -9;
[tex]\begin{gathered} \frac{-9r}{-9}=\frac{3(c+5)}{-9} \\ r=\frac{-(c+5)}{3} \\ r=\frac{-c-5}{3} \end{gathered}[/tex]Therefore;
[tex]r=\frac{-c-5}{3}[/tex]Solve the following inequality. Write the solution set in interval notation
Given:
Inequality is
[tex]5(x-3)<2(3x-1)[/tex]To find:
The solution set of the given inequality:
Explanation:
[tex]\begin{gathered} 5(x-3)<2(3x-1) \\ 5x-15<6x-2 \\ 5x-6x<15-2 \\ -x<13 \\ x>-13 \end{gathered}[/tex]Therefore the solution set is
[tex](-13,\hat{\infty)}[/tex]Final answer:
The solution set is
[tex](-13,\infty)[/tex]Use the system of equations below to solve for z.7x+3y+2z-4w=184w+5x-3y-2z=6-2w-3x+y+z=-52z+3w+4y-8x=11253
Equations:
[tex]\begin{gathered} 7x+3y+2z-4w=18\text{ \lparen1\rparen} \\ 5x-3y-2z+4w=6\text{ \lparen2\rparen} \\ -3x+y+z-2w=-5\text{ \lparen3\rparen} \\ -8x+4y+2z+3w=11\text{ \lparen4\rparen} \end{gathered}[/tex]Sum (1)+ (2):
[tex]\begin{gathered} 7x+3y+2z-4w=18\text{ }\operatorname{\lparen}\text{1}\operatorname{\rparen} \\ + \\ 5x-3y-2z+4w=6\text{ }\operatorname{\lparen}\text{2}\operatorname{\rparen} \\ 5x+7x+3y-3y+2z-2z-4w+4w=18+6 \\ 12x=24 \\ x=\frac{24}{12}=2 \end{gathered}[/tex]x=2
Now, we are going to sum (3)*2+(2).
[tex]\begin{gathered} 5x-3y-2z+4w=6\text{ }\operatorname{\lparen}\text{2}\operatorname{\rparen} \\ + \\ 2*(-3x+y+z-2w)=-5*2\text{ }\operatorname{\lparen}\text{3}\operatorname{\rparen} \\ 5x-6x-3y+2y-2z+2z+4w-4w=6-10 \\ -x-y=-4 \\ -2-y=-4 \\ y=-2+4=2 \end{gathered}[/tex]y=2.
Replacing y and x in (4) and (3):
[tex]\begin{gathered} -3(2)+2+z-2w=-5\text{ }\operatorname{\lparen}\text{3}\operatorname{\rparen} \\ -8(2)+4(2)+2z+3w=11\text{ }\operatorname{\lparen}\text{4}\operatorname{\rparen} \end{gathered}[/tex][tex]\begin{gathered} -6+2+z-2w=-5 \\ z-2w=-5+6-2 \\ z-2w=-1\text{ \lparen5\rparen} \end{gathered}[/tex][tex]\begin{gathered} -16+8+2z+3w=11 \\ 2z+3w=11+16-8 \\ 2z+3w=19\text{ \lparen6\rparen} \end{gathered}[/tex]Isolating w in (5) ans replacing in (6):
[tex]\begin{gathered} 2w=-1-z \\ w=\frac{-1-z}{2} \end{gathered}[/tex][tex]\begin{gathered} 2z+3(\frac{-1-z}{2})=19 \\ \frac{4z-3-3z}{2}=19 \\ z-3=19*2 \\ z=38-3=35 \end{gathered}[/tex]Answer: z=35.
The length of your step is 34 inches (in.). If you walk 10,000 steps in a day, how many feet (ft.) will you walk? ?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
step length = 34 inches
walking = 10000 steps
Step 02:
feet to inches
1 feet = 12 inches
1 step --------------- 34 inches
10000 steps ------- x
1 * x = 10000 * 34
x = 340000
340000 inches * ( 1 feet / 12 inches)
28333.33 feet
The answer is:
You will walk 28333.33 feet .
geometry, please give answer i know how to I think I did the steps wrong
We get that
[tex]\begin{gathered} m\angle1+m\angle4=180\rightarrow \\ 10x+2+5x+13=180 \\ 15x+15=180 \\ 15x=165 \\ x=\frac{165}{15}=11\rightarrow \\ m\angle1=10\cdot11+2=112 \end{gathered}[/tex]Name the type of angle relationship. If no relationship exists, write "none. a. <1 and < 8 b. < 2 and < 3 C. < 5 and <7 d. < 2 and < 7 e. <1 and < 3 f. < 5 and <8
Answers:
a. ∠1 and ∠8: Alternate exterior Angles.
b. ∠2 and ∠3: None
c. ∠5 and ∠7: Corresponding angles.
d. ∠2 and ∠7: Alternate interior angles.
e. ∠1 and ∠3: Corresponding angles
f. ∠5 and ∠8: None
Explanation:
a. ∠1 and ∠8: Alternate exterior Angles. They are externals, on opposite sides, and they are formed by the transversal of two lines.
b. ∠2 and ∠3: None
c. ∠5 and ∠7: Corresponding angles. One is internal and the other is external and they are on the same side of the transversal.
d. ∠2 and ∠7: Alternate interior angles. They are interior, on opposite sides, and they are formed by the transversal of two lines.
e. ∠1 and ∠3: Corresponding angles. One is internal and the other is external and they are on the same side of the transversal.
f. ∠5 and ∠8: None
25 mice were involved in a biology experiment involving exposure to chemicals found in ciggarette smoke. developed at least tumor, 9 suffered re[iratory failure, and 4 suffered from tumors and had respiratory failure. A) how many only got tumors? B) how many didn't get a tumor? C) how many suffered from at least one of these effects?
Explanation:
The total number of mice for the experiment is
[tex]Universalset=25[/tex]How to know how many mice didn't have a tumor?
Identify the total mice who did not have any effects or the effects did not include a tumor.
The number of mice that had respiratory failur is
[tex]n(R)=9[/tex]Based on this, it can be concluded 9 mice did not have a tumor,
Hence,
The number of mice that didnt have a tumor is 9
To figure out the number that got only tutmor, we will consider the number that has both tumors and respiratory failure
[tex]n(T\cap R)=4[/tex]The number that developed tumors is given below as
[tex]n(T)=15[/tex]Hence,
The number that got
Construct an isosceles right triangle.
Take into account that an isosceles triangle has two sides with equal lengthd and two internal angles with the same measure.
Then, for instance, you have the following triangle:
As you can notice, you have two angles with the same measure and two sides with the same lengths.
A transformation is a nonrigid transformation if it does not preserve what? Can you name anonrigid transformation? What is the rule for the nonrigid transformation?Nonrigid transformationRule (x,y) →
A transformation is nonrigid transformation if it does not preserve the structure of the original object.
An example of a nonrigid transformation is the dilation, and its general rule is:
[tex]D_k(x,y)=(kx,ky)[/tex]where 'k' is the scale factor
Graph the line with slope -3/4 passing through the point (4,3)
The graph is displayed after the explanation
Explanation:The slope is rise/run = -3/4
The line passes through (4, 3)
The run is 4, we add 4 to the x-coordinate
The rise is -3, we add -3 to the y-coordinate
We have:
(4 + 4, 3 - 3) = (8, 0)
We use (4, 3) and (8, 0) to graph the line
The graph is shown below:
Find the midpoint M of the line segment joining the points C=(8,7) and D= (4,-5)
Explanation
We are told to find the midpoint of the line segment. To do so, we will use the formula:
[tex]midpoint=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}[/tex]In our case
[tex]\begin{gathered} x_1=8,y_1=7 \\ x_2=4,y_2=-5 \end{gathered}[/tex]Substituting the values above
[tex]\begin{gathered} Midpoint=\frac{8+4}{2},\frac{7-5}{2} \\ \\ Midpoint=\frac{12}{2},\frac{2}{2} \\ \\ Midpoint=(6,1) \end{gathered}[/tex]Thus, the midpoint is (6,1)
A sample has mean 97 and standard deviation 12.Part: 0/2Part 1 of 2(a) What value is 2.5 standard deviations above the mean?The value that is 2.5 standard deviations above the mean is
The value that is 2.5 standard deviations above the mean is 127
Marie requires 2 gallons of paint to cover an area of 400 square feet. Identify the graph that shows the relationship between the quantity of paint and the area covered and the parent function that best describes it. Then use the graph to estimate how many gallons of paint Marie requires to paint an area of 2,400 square feet.
Given:
x = 2 gallons of paint
y = 400 square feet of area
The graph representing the given point (x,y) = (2, 400) is number 4: linear 12 gallons.
Then, to estimate how many gallons of paint Marie requires to paint an area of 2,400 square feet.
We locate the point y = 2400 and find the corresponding x value. This is:
x = 12
Answer:
* the graph is the fourth one
* 12 gallons
How do I match these polynomial and what are the correct matches?!
Add the polynomials:
[tex](-4x^2-3x+6)+(6x^2-2x+1)[/tex]Removing the parentheses:
[tex]-4x^2-3x+6+6x^2-2x+1[/tex]Collecting like terms:
[tex]2x^2-5x+7[/tex]Find the opposite of:
[tex]2x^2+x-7[/tex]We change the signs of all terms:
[tex]-2x^2-x+7[/tex]Subtract:
[tex](-4x^2+2x-1)-(-2x^2+3x+6)[/tex]Remove the parentheses, but the last one requires changing the signs of the second polynomial (find the opposite):
[tex]-4x^2+2x-1+2x^2-3x-6[/tex]Collecting like terms:
[tex]-2x^2-x-7[/tex]find the value of x then find the measure of both angles
According to the given graph, the angles are linear pairs because they are on a straight angle, so the must sum 180°. Having said that, we express the following.-
[tex](4x+20)+(x-10)=180[/tex]We reduce like terms
[tex]5x+10=180[/tex]Then, we subtract 10 on each side.
[tex]\begin{gathered} 5x+10-10=180-10 \\ 5x=170 \end{gathered}[/tex]At last, we divide the equation by 5.
[tex]\begin{gathered} \frac{5x}{5}=\frac{170}{5} \\ x=34 \end{gathered}[/tex]We use this value to find the angles.
[tex]\begin{gathered} 4x+20=4(34)+20=136+20=156 \\ x-10=34-10=24 \end{gathered}[/tex]Therefore, x is equal to 34, and the angles are 156° and 24°.4(2x + 3) = 3x + 3 + 2x
We operate as follows:
[tex]4(2x+3)=3x+3+2x\Rightarrow8x+12=5x+3[/tex][tex]\Rightarrow3x=-9\Rightarrow x=-3[/tex]The value of x is -3.
Sorry if it's a little blurryAlso this worksheet is about simplify
Write four different equation with -3 as solution.
5x + 20 = 5 subtract 20 both sides
5x = 5 - 20
5x = -15 divide by 5 both sides
x = -15/5
x = -3
3x - 6 = -3x - 24 add 3x both sides
3x + 3x - 6 = - 24
6x - 6 = -24 add 6 both sides
6x = -24 + 6
6x = -18 divide by 6 both sides
x = -18/6
x = -3
1/3 x + 10 = 9 subtract 10 both sides
1/3 x = 9 -10
1/3 x = - 1 multiply by 3 both sides
x = -1(3)
x = -3
x + 23 = 20 subtract 23 both sides
x = 20 - 23
x = -3
In all previous procedures you constructed the equation by taking into account that x=-3, that is the key to determine the expressions left side and right side. For example in the last procedure for x + 23 = 20, you know that -3 plus 20 is equal to 20.
A passcode to enter a building is a sequence of 4 single digit numbers (0-9), and repeated digits aren'tallowed.Suppose someone doesn't know the passcode and randomly guesses a sequence of 4 digits.What is the probability that they guess the correct sequence?
ANSWER
0.0001984
EXPLANATION
There are 10 possible values for each digit of the passcode to enter the building.
These include: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
So, there are:10 x 10 x 10 x 10 = 10^4 = 10,000 total possible passcodes.
For no repeat passcode
We have: 10 x 9x 8 x7 = 5040 total possible passcodes without repetition.
Probability of guessing correct sequence
Since there is only 1 correct sequence of 4 digits passcode (without repetition) to enter the building
[tex]\begin{gathered} Prob\text{ = }\frac{1}{5040} \\ Prob\text{ = 0.0001984} \end{gathered}[/tex]Hence, the probability that they guess the correct sequence is 0.0001984
The following triangles are scaled copies of each other. What is the scale factor? The scale factor is? What is the length of x? What is the length of y?
If we divide corresponding sides, we can obtain the scale factor:
24/6 = 4
Lenght of x
x/8 =4
Solve for x
x=4 (8)
x= 32
Lenght of y:
36/y=4
Solve for y
36/4=y
9=y
a haunted house found that it number of Halloween weekend customers can be modeled by
You have the following equation for the number N of halloween weekend customers in terms of the entrance price p (in dollars).
Consider that for each dollar p, there are 15 halloween weekend customers less. That is the meaning of the factor -15 in the given function for N(p). As p increases, the term -15p is lower and lower, which means that N is lower.
A line passes through (4,3) and (8,6). Another line has a slope of -3/4. The two lines are parallel. *1 pointTrueFalse
ANSWER
False
EXPLANATION
The formula for the slope of a line that passes through points (x1, y1) and (x2, y2) is:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]The slope of the first line is:
[tex]m=\frac{3-6}{4-8}=\frac{-3}{-4}=\frac{3}{4}[/tex]The other line has a negative slope, so the lines are not parallel.
Please help us in figuring out this math problem so that we can move onto the next one thank you very much
All numbers in scientific notation or standard form are written in the form
[tex]m\cdot10^n[/tex]where m is a number between 1 and 10 and the exponent n is a positive or negative integer.
To convert 64500 into scientific notation, follow these steps:
1. Move the decimal 4 times to left in the number so that the resulting number, m = 6.45, is greater than or equal to 1 but less than 10
2. Since we moved the decimal to the left the exponent n is positive
n = 4
3. Write in the scientific notation form, m × 10^n
= 6.45 × 10^4
ExpenseYearty costor rateGasInsurance$425.00$400,00$110.00$100.00What is the cost permile over the course ofa year for a $20,000 carthat depreciates 20%,with costs shown in thetable, and that hasbeen driven for 10,000miles?OilRegistrationDepreciation20%A $1.10 per mileB, SA. 10 per mileD. $0.50 per mileC. $0.25 per mile
First, we will find 20% of the cost of the car which is $20,000.
Thus, we have:
[tex]\begin{gathered} 20\text{\% of 20,000} \\ \Rightarrow\frac{20}{100}\times20000 \\ \Rightarrow\text{ \$4000} \end{gathered}[/tex]Adding the $4000 to the other expenses provided in the table:
[tex]4000+425+400+110+100=\text{ \$5035}[/tex]To get the cost per mile, we are going to divide the total cost of $5035 by the number of mies, 10,000.
Thus, we have:
[tex]\frac{5035}{10000}=\text{ \$0.50 per mile}[/tex]Hence, the correct option is Option D
Michael rented a truck for one day. There was a base fee of $20.99, and there was an additional charge of 85 cents for each mile driven. Michael had to pay$134.89 when he returned the truck. For how many miles did he drive the truck?
Let the number of miles Michael drove the truck be m.
Then, the cost of the drive is given by the expression,
[tex]20.99+0.85m[/tex]The actual cost is given as $134.89
Hence, we must have that
[tex]\begin{gathered} 20.99+0.85m=134.89 \\ \text{ Subtracting 20.99 from both sides we have} \\ 0.85m=113.9 \\ \text{ Dividing both sides by 0.85 we have} \\ m=\frac{113.9}{0.85}=134 \end{gathered}[/tex]Thus the number of miles is 134 miles
can you help me please? what is the area of this arrow?
Given
Graph
Procedure
Let's calculate the area of the figure as the sum of the area of the rectangle plus the area of the triangle.
Let's first calculate the area of the rectangle.
[tex]\begin{gathered} A_r=lw \\ A_r=10\cdot4 \\ A_r=40 \end{gathered}[/tex]Now let's calculate the area of the triangle.
[tex]\begin{gathered} A_t=\frac{1}{2}\cdot b\cdot h \\ A_t=\frac{1}{2}\cdot7\cdot6 \\ A_t=21 \end{gathered}[/tex]The total area would be
[tex]\begin{gathered} A_T=A_t+A_r \\ A_T=40+21 \\ A_T=61 \end{gathered}[/tex]The area of the arrow would be 61 sq in
