We have that F(x) is the function that determines the absolute value of the cube of the input, then we have that f(x) is:
[tex]f(x)=\lvert x^3\rvert[/tex]Part 1. Evaluate F(5): x = 5
[tex]f(5)=\lvert5^3\rvert=\lvert125\rvert=125[/tex]Part 2. Evaluate F(-7): x = -7
[tex]f(-7)=\lvert-7^3\rvert=\lvert-343\rvert=343[/tex]Part 3. Evaluate F(5)xF(-7)
[tex]f(5)\cdot f(-7)=125\cdot343=42875[/tex]Perform the indicated operation.1.61 kg -200 g1.61 kg - 200 g-9 (Type [whole number or a decimal.)
Answer:
Explanation:
We are asked to subtract 200 g from 1.61 kg. To perform this operation, we first convert kg to grams.
Now,
1 kg = 1000g
therefore,
1.61 kg = 1.61 * 1000 g = 1610 g.
The operation now becomes
1610 g - 200 g
which evaluates to
1610 g - 200 g = 1410 g
Which is our answer!
Find the first three terms and stated term given the geometric sequence, with a1 as the first term. Given termsan=3^n-1, a5
Answer:
First three terms: 1, 3 and 9
Stated term = 81
Explanation:
Given the formula;
[tex]a_n=3^{n-1}[/tex]Let's go ahead and determine the first three terms of the geometric sequence.
For the 1st term;
[tex]\begin{gathered} a_1=3^{1-1} \\ =3^0 \\ =1 \end{gathered}[/tex]For the 2nd term;
[tex]\begin{gathered} a_2=3^{2-1} \\ =3^1 \\ =3 \end{gathered}[/tex]For the 3rd term;
[tex]\begin{gathered} a_3=3^{3-1} \\ =3^2 \\ =9 \end{gathered}[/tex]Let's now find the stated term;
[tex]\begin{gathered} a_5=3^{5-1} \\ =3^4 \\ =81 \end{gathered}[/tex]Lines AB and CD at E. If m∠AEC=x^2+3x and m∠BED=6x+4 ,find m∠CEB.
Explanation
Step 1
when two lines intersect, vertical angles that are equal are formed.Also two angles are Supplementary when they add up to 180 degrees
then
[tex]\begin{gathered} m\measuredangle\text{AEC =}m\measuredangle BED \\ \text{replacing} \\ x^2+3x=6x+4 \end{gathered}[/tex]and
[tex]m\measuredangle\text{AEC}+\text{ m}\measuredangle CEB=180[/tex]Step 2
solve for x,
[tex]\begin{gathered} x^2+3x=6x+4 \\ x^2+3x-6x=+4 \\ x^2+3x-6x-4=0 \\ x^2-3x-4=0 \\ \text{factorize} \\ (x-4)(x+1)=0 \\ it\text{ means} \\ x-4=0 \\ x=4 \\ or \\ x+1=0 \\ x=-1 \end{gathered}[/tex]we just take the positive number, because we are searching for an angle ( angles and distance are always positives)
then
[tex]x=4[/tex]Step 3
replace the value of x in the angle AEC
[tex]\begin{gathered} m\measuredangle AEC=x^2+3x \\ m\measuredangle AEC=4^2+3\cdot4 \\ m\measuredangle AEC=16+12 \\ m\measuredangle AEC=28 \\ \end{gathered}[/tex]replace the value of AEC in equation (2) to find CEB
[tex]\begin{gathered} m\measuredangle\text{AEC}+\text{ m}\measuredangle CEB=180 \\ 28+m\measuredangle CEB=180 \\ \text{subtract 28 in both sides} \\ 28+m\measuredangle CEB-28=180-28 \\ m\measuredangle CEB=152 \end{gathered}[/tex]I hope this helps you.
½(10p-7q) if p=9 and q=2
Evaluate the expression for p = 9 and q = 2:
[tex]\begin{gathered} \frac{1}{2}(10(9)-7(2)) \\ \frac{1}{2}(90-14) \\ \frac{1}{2}(76)=38 \\ \end{gathered}[/tex]graph the system of inequalties make sure your solution area is clear in your graph. then name a solution point & and a non soultion point
the red line indicates
[tex]y\ge2x-1[/tex]green line indicates
[tex]y<-x+2[/tex]the blue line indicates
[tex]y\ge-4[/tex]to find the solution point in the graph, we need to find the point at which they intersect and this graph, it doesn't have a solution point because all the three points didn't intersect
Simplify: 8z + 5y + 6z + Зу * O 14z + 8y 13y + 9z O 22y 22z
Answer:
14z + 8y
Explanation:
Given the equation 8z + 5y + 6z + Зу
first is to collect the like terms;
8z + 5y + 6z + Зу
= (8z + 6z) + (5y + 3y)
= 14z + 8y
Hence the simplified form is 14z + 8y
Can you help me with this?
Ryan is trying to earn $350 to purchase a new pair of Jordan 1 sneakers. He already has $75 in his bank account and will mow lawns to earn the remainder of the money. If he earns $25 for each lawn mowed, create an equation to determine how many lawns he will need to mow. Let m represent the number of lawns mowed.
Ms. Kirkland is baking muffins. Each batch of muffins uses 1 ½ pounds of flour. How many batches of muffins can she bake with 7 ½ pounds of flour? ______________ batches. (Just the number).
Answer:
5
Step-by-step explanation:
7.5/1.5=5
Answer: The answer is 5
Step-by-step explanation: I have my ways ;>
For a craft project you need 182 inches of ribbon, but it is only sold by the meter. Determine the amount of ribbon, in meters, you need to buy for the project. (1 inch = 2.54 centimeters and 1 centimeter = 0.01 meter)
462
47
12
5
The length of the ribbon used for the craft project is 5 meters.
What is conversion?A conversion factor is a quantity that is multiplied or divided between two different sets of units. In the event that a conversion is necessary, it must be carried out using the proper conversion factor to produce an equivalent value. When translating between inches and feet, 12 inches equals one foot.
To represent the same attribute in a different unit of measurement, employ a unit conversion. Hours can be replaced with minutes, and miles can be replaced with feet, kilometers, or any other unit of measurement when describing distance. Measurements are frequently given in one unit of measurement, like feet, but are required in another, like chains.
Given,
The length of ribbon needed for the craft project = 182 inches
So, the length of the ribbon needs to be in meters.
Thus, we can convert inched to centimeters by
1 inches = 2.54 centimeters
As 1 cm = 0.01 m
So, 1 inch = 2.54 x 0.01 m
1 inch = 0.0254 m
Then for the length of 182 inches,
114 inch = 0.0254 x 182 meters
= 4.6228
≈ 5 meters
Therefore, the length of the ribbon is 5 meters
To learn more about the conversions, visit:
https://brainly.com/question/1560145
#SPJ1
Answer: 5
Step-by-step explanation: i did the test
The angle of the roof on Makenna's dollhouse is 24°. She built a scale model of the dollhousewith a scale ratio of 1 : 4. What is the measure of the angle of the roof of the model?
Note that in scaling objects, the lengths will increase or decrease and the angles will be the same.
From the problem, the angle of the roof on Makenna's doll house is 24 degrees, and the scale model will be 1 : 4
The angle is still equal to 24 degrees.
The answer is B. 24 degrees
The height of the triangle is 3 feet less than twice its base. The area of the triangle is 52 ft2. What is the height of the triangle?
Given:
Base of triangle = b
Height of triangle, h, is 3 feet less than twice its base. This is expressed as:
h = 2b - 3
Area of triangle = 52 ft²
To find the height of the triangle, use the Area of a triangle formula below:
[tex]A=\frac{1}{2}bh[/tex]Thus, we have:
[tex]\begin{gathered} 52=\frac{1}{2}\times b\times(2b-3) \\ \\ 52=\frac{b(2b-3)}{2} \end{gathered}[/tex]Let's solve for the base, b:
[tex]\begin{gathered} 52=\frac{2b^2-3b}{2} \\ \\ Multiply\text{ both sides by 2:} \\ 52\times2=\frac{2b^2-3b}{2}\times2 \\ \\ 104=2b^2-3b \end{gathered}[/tex]Subtract 104 from both sides to equate to zero:
[tex]\begin{gathered} 2b^2-3b-104=104-104 \\ \\ 2b^2-3b-104=0 \end{gathered}[/tex]Factor the quadratic equation:
[tex](2b+13)(b-8)[/tex]Thus, we have:
[tex]\begin{gathered} (2b+13)\text{ = 0} \\ 2b\text{ + 13 = 0} \\ 2b=-13 \\ b=-\frac{13}{2} \\ \\ \\ (b-8)=0 \\ b=8 \end{gathered}[/tex]We have the possible values for b as:
b = - 13/2 and 8
Since the base can't be a negative value, let's take the positive value.
Therefore, the base of the triangle, b = 8 feet
To find the height, substitute b for 8 from the height equation, h=2b-3
Thus,
h = 2b - 3
h = 2(8) - 3
h = 16 - 3
h = 13 feet.
Therefore, the height of the triangle, h = 13 feet
ANSWER:
13 feet
Which sequence of transformations maps polygon ABCD onto polygon WXYZ?
We have to find the transformations that led from polygon ABCD to WXYZ.
As the shapes are not equally oriented, we have to find if one of the transformation is a rotation or a reflection.
We can fin this by looking at the position of corresponding sides. So first, we have to find corresponding sides of the two polygons. The polygon WXYZ has also a scale transformation, so its size is proportional, with a proportion greater than 1 as it is bigger, to the size of ABCD.
Each side in the pre-image has a corresponding side in the image. Each corresponding side in the image will be k times bigger than the side in the pre-image, and this k is the same for the four sides.
We can look at the sides that are parallel to the axis, BC and CD, and see that CD is longer than BC. If we look at WXYZ, YZ is longer than YX.
Then, we can conclude that YZ and CD are corresponding sides as BC and YX.
The scale factor is k = 2 as YZ is twice as long as CD.
Then we can see, by the position of BC and CD respect to YX and YZ that no rotation can convert the pre-image into the image, so the orientation of the image is due to a reflection with axis of symmetry at x = 7.
Then, after the reflection, the image is dilated with a factor k = 2.
Answer:
B. A reflection of polygon ABCD followed by a dilation of the image with a scale factor of 2.
Answer:
B
Step-by-step explanation:
plato
Evaluate 42+5/9r if r= -1/2 42 + 5/9r=
Answer:
41 13/18
Explanation:
Given the expression:
[tex]42+\frac{5}{9}r[/tex]When the value of r is given to be:
[tex]r=-\frac{1}{2}[/tex]We substitute to obtain:
[tex]\begin{gathered} 42+\frac{5}{9}r=42+\frac{5}{9}(-\frac{1}{2}) \\ =42-\frac{5}{18} \end{gathered}[/tex]Next, we take the lowest common multiple of the denominators (1 and 18).
[tex]\begin{gathered} =\frac{756-5}{18} \\ =\frac{751}{18} \\ =41\frac{13}{18} \end{gathered}[/tex]Therefore, when r=-1/2, the value of the expression is:
[tex]41\frac{13}{18}[/tex]Hello i am a senior graduating May i am struggling on algebra on .. if you can please help me with this problem
Answer:
Explanation:
Here, we want to complete the remainder of the table for the given function rule
What this means is that we need to fill in the given y values
To do this, we simply substitute the x values at each point, to get the corresponding y-value
We proceed as follows:
A) At this point , x is-3 , so we substitute -3 for x
Mathematically:
[tex]\begin{gathered} y\text{ = -}\frac{(-3)}{3}\text{ + 2} \\ y\text{ = }\frac{3}{3}\text{ + 2} \\ \\ y\text{ = 1 + 2} \\ y\text{ = 3} \end{gathered}[/tex]B) Here, x is 0
[tex]\begin{gathered} y\text{ = -}\frac{0}{3}\text{ + 2} \\ y\text{ = 0 + 2} \\ y\text{ = 2} \end{gathered}[/tex]C) Here, x is 3
[tex]\begin{gathered} y\text{ = -}\frac{3}{3}\text{ + 2} \\ y\text{ = -1 + 2} \\ y\text{ = 1} \end{gathered}[/tex]D) Here, x is 6
[tex]\begin{gathered} y\text{ = -}\frac{6}{3}\text{ + 2} \\ y\text{ = -2 + 2} \\ y\text{ = 0} \end{gathered}[/tex]At the pediatrician's office, patients are able to draw a toy from the toy bin. The toy bin has 12 puzzles, 16boxes of crayons, and 2 bouncy balls. What is the probability of drawing...a box of crayons?a puzzle?anything but a bouncy ball?(write your answer as a fraction in lowest terms)
SOLUTION
Total outcomes = 12 puzzles + 16 boxes of crayons + 2 bouncy balls = 30.
[tex]\begin{gathered} \text{Probability = }\frac{required\text{ outcome}}{\text{total outcome}} \\ \\ \text{probability of drawing a box of crayons = }\frac{16}{30}=\text{ }\frac{8}{15} \end{gathered}[/tex][tex]\text{Probability of drawing a puzzle = }\frac{12}{30}\text{ = }\frac{2}{5}[/tex]Probability of anything but bouncy ball means the probability of drawing out a box of crayons or probability of drawing out a puzzle.
[tex]\begin{gathered} \text{This becomes = }\frac{8}{15}+\frac{2}{5} \\ \\ =\text{ }\frac{8+6}{15}\text{ = }\frac{14}{15} \\ \end{gathered}[/tex]A number is multiplied by 6 and the product is added to 4 the sum is equal to the product of 2 and 17 find the number
A number = x
Is multiplied by 6 = 6x
And the product is added to 4 = 6x + 4
The sum is equal to the product of 2 and 17 ; 6x + 4 = 2 * 17
Solve for x
6x + 4 = 2 * 17
Combine like terms
6x = 34 - 4
6x = 30
Divide both sides by 6
6x/6 = 30/6
x = 5
Answer:
5, hope this helped my love have a good rest of your day ^^
Step-by-step explanation:
the product of 2 and 17 is 34
34 - 4 is 30
30 devided by 6 is 5
therefore, by working backwords we can figure out that this math riddle would be equal to 5 ^^
Further analysis finds that the correlation coefficient for this data is negative 0.792 which they may is a good description of what the scatter plot and correlation coefficient indicate
Jc, this is the correct answer:
As you can see in the scatter plot, the more time one of the physical trainer's client exercises, the less weight he or she has. However, we don't have any evidence that the cause of this is exclusively the time of exercise, more likely there would be other reasons or factors involved.
In consequence, the right answer is D.
(6x 2 +3x 3 +7x)−(x+3× 2 +2x 3
Given
[tex](6x^2+3x^3+7x)-(x+3x^2+2x^3\text{)}[/tex]To solve this question, let's observe the following steps
Step 1: Remove the parentheses (Brackets). So that we will obtain=>
[tex]6x^2+3x^3+7x-x-3x^2-2x^3[/tex]The next step is to collect like terms
[tex]3x^3\text{ }-2x^3\text{ + }6x^2-3x^2\text{ +}7x\text{ - x}[/tex]Then we will proceed to simplify further
[tex]x^3+3x^2\text{ + 6x}[/tex]Simplity the expression:4b+9b
Since both variables are equal (b) we can add them:
[tex]4b+9b[/tex][tex]13b[/tex]Use the image below to describe at least three different ratios, written In simplest form. Indude at least one part-to-part ratio and one part-to-whole ratio.
Par
In the figure shown we notice that there are 15 blue squares and 10 white squares. The ratio between them is 15 to 10, this is equivalent to a ratio 3 to 2.
Therefore, there are 3 blue squares for each 2 squares, this can be written as:
[tex]3\colon2[/tex]Find the slope of the line graft below. I found the coordinates but I am unsure of the formula.
Answer;
[tex]m\text{ = -}\frac{4}{3}[/tex]Explanation;
Here, we want to find the slope of the given line
To do this, we are going to use the slope of a line formula
Mathematically, to use this, we need the coordinates of two points that lie on the given line
We have these already marked in red
Identifying the points, we have them as (0,1) and (3,-3)
Now, we write the formula to use and substitute the coordinates of the points as appropriate
We have this as:
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ (x_1,y_1)\text{ = (0,1)} \\ (x_2,y_2)\text{ = (3,-3)} \\ \\ m\text{ = }\frac{-3-1}{3-0}\text{ = }\frac{-4}{3} \end{gathered}[/tex]
Jeans are marked up 150% at Antoinette's Boutique. Today they are all on sale, 20% off the usual retail. If the wholesale price of jeans is $20, how much do they sell for today?
To solve the exercise you can use a rule of three.
Let us first find the usual price of jeans:
[tex]\begin{gathered} \text{ \$20}\rightarrow100\text{\%}\Rightarrow\text{ wholesale price of jeans} \\ \text{ \$x}\rightarrow150\text{\%}\Rightarrow\text{ usual sale price of jeans} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{150\text{\%}\cdot\text{ \$20}}{100\text{ \%}} \\ x=\frac{150\cdot\text{\$20}}{100} \\ x=\text{\$}\frac{150\cdot\text{20}}{100} \\ x=\text{\$}\frac{3000}{100} \\ x=\text{\$}30 \end{gathered}[/tex]Then, the usual price of the jeans is $30.
Now, let us find the discounted price of the jeans
[tex]\begin{gathered} \text{ \$30}\rightarrow100\text{\%} \\ \text{ \$x}\rightarrow80\text{\%} \\ \text{ Because now the jeans have a 20\% discount, that is} \\ 100\text{\%}-20\text{\%}=80\text{\%} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{80\text{\%}\cdot\text{ \$30}}{100\text{ \%}} \\ x=\frac{80\cdot\text{ \$30}}{100} \\ x=\text{ \$}\frac{80\cdot\text{30}}{100} \\ x=\text{ \$}\frac{240\text{0}}{100} \\ x=\text{\$}24 \end{gathered}[/tex]Therefore, today the jeans sell for $24.
Find the values of x, y, and ..m x =30020VOm 4y =m 2 =64°Po
A biologist just discovered a new strain of bacteria that helps defend thehuman body against the flu virus. He puts 75 cells in a petri dish, theygrow at rate of 20% per hour. How many hours will it take to create aneffective dosage of 1,750 cells? *O About 17 hoursAbout 14 hoursO About 28 hoursAbout 20 hours
Given:
Rate = 20%
Here let's use the exponential growth function to find the number of hours.
ou are making identical door prizes for a charity event. You want to use all of the following items.
54 packages of peanuts
81 fruit bars
18 CDs
You can make at most
door prizes. Each door prize would have
packages of peanuts
fruit bars, and CDs
Putting the important informations, we want to use all items and divide them into equal groups in a way that we get the most prizes.
We we want a factor that is common to the three quantities, 54, 81 and 18, and is the greatest of them.
This is a question of Greatest Common Factor or Greatest Common Divisor (different names, same thing).
To calculate it, we have to find all the common factors of theses numbers.
One way to do that is to look for numbers that can divide all of them.
The numbers are 54, 81 and 18. As we can see the three numbers are divisable by 3:
[tex]\begin{gathered} \frac{54}{3}=18 \\ \frac{81}{3}=27 \\ \frac{18}{3}=6 \end{gathered}[/tex]So, we now that 3 is a common factor. Let's note it to use later on.
Now have got 18, 27 and 6. We can see that, again, all of them are divisable by 3:
[tex]\begin{gathered} \frac{18}{3}=6 \\ \frac{27}{3}=9 \\ \frac{6}{3}=2 \end{gathered}[/tex]And let's note the "3" again to use later on.
The numbers now are 6, 9 and 2. 2 is only divisable by 2, but 9 isn't, so we don't have any more common factors.
In the end, we have the factor 3 and 3, which makes 3*3 = 9. Thus, 9 is the Greates Common Factor of 54, 81 and 18 and it divides them into 6, 9 and 2.
These are the answers we are looking for, because now we know that the most groups we can divide the items into is 9 and each group will have 6, 9 and 2 of those items.
So the phrase of the answer is:
"You can make at most 9 door prizes. Each door prize would have 6 packages of peanuts, 9 fruit bars, and 2 CDs."
Which of the expressions are equivalent to the one below? Check all thatapply.3. (2 + 6) + 4.5A. (6+2): 3+ 4.5B. 3.2 + 3.6+4.5O C.3.2 + (6 + 4): 5D. 5·4+3.(6+2
We have
[tex]3\cdot(2+6)+4\cdot5=44[/tex]For the other expressions
[tex](6+2)\cdot3+4\cdot5=44[/tex][tex]3\cdot2+3\cdot6+4\cdot5=44[/tex][tex]3\cdot2+(6+4)\cdot5=56[/tex][tex]5\cdot4+3\cdot(6+2)=44[/tex]As we can see the expressions that are equivalent are A, B, and D.
ANSWER
A, B, and D.
The shorter sides of a rectangle measure 4 inches eachand one of its diagonals measures 8 inches. Which ofthe following is the measure of one of its longer sides?
Lets draw a picture of the rectangle:
From our figure, we can note that triangle ABC is a right triangle, so we can apply Pythagorean theorem, that is
[tex]4^2+x^2=8^2[/tex]which gives
[tex]16+x^2=64[/tex]If we move 16 to the right hand side, we get
[tex]\begin{gathered} x^2=64-16 \\ x^2=48 \end{gathered}[/tex]Then, x is given by
[tex]x=\sqrt[]{48}[/tex]since 48 = 16 x 3, we get
[tex]\begin{gathered} x=\sqrt[]{16\times3} \\ x=\sqrt[]{16}\times\sqrt[]{3} \\ x=4\sqrt[]{3} \end{gathered}[/tex]therefore, the answer is
[tex]x=4\sqrt[]{3}[/tex]which is the measure of the longer side.
14. (04.06 LC)The first four terms of a sequence are shown below:8, 5, 2, -1Which of the following functions best defines this sequence? (5 points)f(1) = 8, f(n + 1) = f(n) + 5; forn 21f(1) = 8, f(n + 1) = f(n) - 5; for n 2 1f(1) = 8, f(n + 1) = f(n) - 3; for n 2 1f(1) = 8, f(n + 1) = f(n) + 3; forna 1
Given
The sequence, 8, 5, 2, -1.
To find: Which of the following functions best defines this sequence?
a) f(1) = 8, f(n + 1) = f(n) + 5; for n=1,2,3,4,...
b) f(1) = 8, f(n + 1) = f(n) - 5; for n=1,2,3,4,...
c) f(1) = 8, f(n + 1) = f(n) - 3; for n=1,2,3,4,...
d) f(1) = 8, f(n + 1) = f(n) + 3; for n=1,2,3,4,...
Explanation:
It is given that,
The first four terms of a sequence is, 8, 5, 2, -1.
Since,
[tex]\begin{gathered} 5-8=-3 \\ 2-5=-3 \end{gathered}[/tex]Then, the above sequence is an arithmetic sequence.
That implies,
[tex]\begin{gathered} f(n)=f(1)+(n-1)d \\ =8+(n-1)(-3) \end{gathered}[/tex]Therefore, for n=1,2.
[tex]\begin{gathered} f(1)=8 \\ f(2)=8+(2-1)(-3) \\ =8-3 \\ =f(1)-3 \end{gathered}[/tex]Then,
[tex]f(n+1)=f(n)-3[/tex]Final result: Hence, the answer is option c).
1. Rectangular Prism: a. The measures: 1 =5, w = 7, h = 8 .. b. The measures: h =7, w = 7,1 = 7. C. W = 3.6, I = 4.2, h = 8.3
Volume of rectangular prism = Length x width x height = lwh
Part a
l=5, w=7, h=8
Volume = 5 x 7 x 8
=280 cm^3
Part b
l=7, w=7, h=7
Volume = 7 x 7 x 7
Volume = 343cm^3
Part c
l=4.2, w=3.6, h=8.3
Volume= 125.496 cm^3
Part A: Write g(x) as a transformation of f(x).Part B: Write h(x) as a transformation of f(x).Part C: Write m(x) as a transformation of f(x)
ANSWERS
• g(x) = f(x) - 2
,• h(x) = -f(x)
,• m(x) = f(x) + 7
EXPLANATION
The values on the table of function g(x) are all 2 less than the values of f(x). Therefore g(x) = f(x) - 2.
The values of function h(x) are all the opposite of the values of f(x). Therefore h(x) = -f(x).
The values of function m(x) are all 7 more than the values of f(x). Therefore m(x) = f(x) + 7.