(fog)(x) = 5x² - 15x + 61
Explanation:The given functions are:
f(x) = 5x + 1
g(x) = x² - 3x + 12
(fog)(x) = f(g(x))
This means that we are substituting g(x) into f(x)
(fog)(x) = 5(x² - 3x + 12) + 1
(fog)(x) = 5x² - 15x + 60 + 1
This can be further simplified as:
(fog)(x) = 5x² - 15x + 61
What is the name of the decimal number?7.1seventy-one seven and one hundredthsseven and one tenth seventeen
Answer:
seven and one-tenth.
Explanation:
To name decimal number, we first name the values before the decimal point, in this case, seven
Then, we add an and that corresponds to the decimal point
Finally, we say the number after the decimal point and the place of this number, in this case, one-tenth.
Therefore, the name of the decimal number 7.1 is:
seven and one-tenth.
Give the point-slope form of the equation of the line that is perpendicular to y= -4x/5+10 and contains P(5,6)
You have to write the equation of a line perpendicular to
[tex]y=-\frac{4}{5}x+10[/tex]That crosses the point (5, 6)
A caracteristic of a line permendicular to another one is that its slope pf the perpendicular line is the negative inverse of the slope of the first line.
So for example if you have two lines:
1_ y=mx+b
and
2_ y=nx+c
And both lines are perpendicular, the slope of the second one will be the negative inverse of the slope of the first one, that is:
[tex]n=-\frac{1}{m}[/tex]The slope of the given line is m=-4/5
The negative inverse is
[tex]-(\frac{1}{-\frac{4}{5}})=-(-\frac{5}{4})=\frac{5}{4}[/tex]Now that you know the slope of the perpendicular line, use it along with the given point (5, 6)
in the slope-point formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-6=\frac{5}{4}(x-5) \end{gathered}[/tex]Use the Pythagorean Theorem to find x, in simplest radical form. 20
The Pythagorean theorem states that the sum of the squares of the two sides of a right angle is equal to the square of the hypotenuse (longest side).
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{where }c\text{ is the hypotenuse, and }a\text{ and }b\text{ are the other two sides of a right triangle.} \end{gathered}[/tex]Given: c = 20, a = 8, and b = x. Find x.
[tex]\begin{gathered} a^2+b^2=c^2 \\ (8)^2+(x)^2=(20)^2 \\ 8^2+x^2=20^2^{} \\ 64+x^2=400 \\ x^2=400-64 \\ x^2=336 \\ \sqrt{x^2}=\sqrt[]{336} \\ x=\sqrt[]{16\cdot21} \\ x=4\sqrt{21}\text{ (final answer)} \end{gathered}[/tex]I’m not firmiliar with the sun or difference of cubes (HW assignment)
Given:
[tex]125r^3-216[/tex]Find-: Factor using the formula of the sum or difference of cube.
Sol:
Factoring sum and differences of cubs is:
[tex]\begin{gathered} x^3-y^3=(x-y)(x^2+y^2+xy) \\ \\ x^3+y^3=(x+y)(x^2+y^2-xy) \end{gathered}[/tex]Apply for the given information.
[tex]\begin{gathered} =125r^3-216 \\ \\ =(5r)^3-(6)^3 \end{gathered}[/tex][tex]\begin{gathered} x^3-y^3=(x-y)(x^2+y^2+xy) \\ \\ (5r)^3-(6)^3=(5r-6)((5r)^2+(6)^2+(5r)(6)) \\ \\ =(5r-6)(25r^2+36+30r) \end{gathered}[/tex]Riley read 1 book in 2 months. If she reads at a constant rate, how many books did she read in one month? Give your answer as a whole number or a FRACTION in simplest form.On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
To find out the unit rate
Divide the total books by the total months
so
1/2=0.5 books per month
the answer is 0.5 books per monthIn the double number line
we have
books 0 0.5 1
months 0 1 2
Learn with an example v Sharon has a red ribbon and an indigo ribbon. The red ribbon is 6 1/4 inches long. The indigo ribbon is 6 1/4 inches longer than the red ribbon. How long is the indigo ribbon?
Let R be the length of the red ribon and let I be the length of the indigo ribbon. We have that the red ribbon is 6 1/4 inches long, then:
[tex]R=6\frac{1}{4}=\frac{25}{4}[/tex]Then, the indigo ribbon is 6 1/4 inches longer than the red ribbon. Then we have:
[tex]I=R+6\frac{1}{4}[/tex]therefore:
[tex]I=\frac{25}{4}+\frac{25}{4}=\frac{50}{4}=\frac{25}{2}=12\frac{1}{2}[/tex]finally, we have that the indigo ribbon is 12 1/2 inches long
Convert 253 inches to yards using dimensional analysis.
As given by the question
There are given that the 253 inches
Now,
To convert the inches to yards, multiply the value in inches by the conversion factor 0.0277777787.
So,
[tex]253\times0.0277777787=7.0277778.[/tex]Hence, the value of the given inches is 7.0278 yards.
Hi, I’m really confused with this question and I’m not sure how to solve it!
SOLUTION
The figure below would help in answering the question
Let's get the slopes of the line for company G and company H
Slope m is given as
[tex]m=\frac{rise}{run}[/tex]For company G, we have slope as
[tex]m=\frac{5}{1}=5[/tex]For Company H, we have
[tex]m=\frac{4}{1}=4[/tex]From the graph
Cab fare for 1 mile with company G is $7
Cab fare for 10 miles with company H is?
To get this we need to get the equation of the line H
From
[tex]\begin{gathered} y=mx+b \\ where\text{ m is slope and b is the y-intercept, we have } \\ y=4x+2 \end{gathered}[/tex]Now substituting x for 10 in the equation, we have
[tex]\begin{gathered} y=4x+2 \\ y=4(10)+2 \\ y=40+2 \\ y=42 \end{gathered}[/tex]Hence the cab fare for 10 miles with Company H is $42
The rate charge per mile by Company G is the slope we got as 5.
Hence the answer is $5 per mile
The rate charge per mile by Company H is the slope we got as 4.
Hence the answer is $4 per mile
Just give me the answer please, my device is at 10%
Solve for x
We can use sine
[tex]\begin{gathered} \sin 48^0=\frac{x}{17} \\ \text{Cross multiply} \\ x=17\times\sin 48^0 \\ x\text{ =17}\times0.7431448 \\ x=12.6\text{ } \end{gathered}[/tex](If there is more than one answer, use the "or" button.)Round your answer(s) to the nearest hundredth.A ball is thrown from a height of 141 feet with an initial downward velocity of 21 ft/s. The ball's height h (in feet) after t seconds is given by the following.h = 141 - 21t - 16t ^ 2How long after the ball is thrown does it hit the ground?
Solution:
Given:
[tex]h=141-21t-16t^2[/tex]To get the time the ball hit the ground, it hits the ground when the height is zero.
Hence,
[tex]\begin{gathered} At\text{ h = 0;} \\ h=141-21t-16t^2 \\ 0=141-21t-16t^2 \\ 141-21t-16t^2=0 \\ 16t^2+21t-141=0 \end{gathered}[/tex]To solve for t, we use the quadratic formula.
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{where;} \\ a=16,b=21,c=-141 \\ t=\frac{-21\pm\sqrt[]{21^2-(4\times16\times-141)}}{2\times16} \\ t=\frac{-21\pm\sqrt[]{441+9024}}{32} \\ t=\frac{-21\pm\sqrt[]{9465}}{32} \\ t=\frac{-21\pm97.288}{32} \\ t_1=\frac{-21+97.288}{32}=\frac{76.288}{32}=2.384\approx2.38 \\ t_2=\frac{-21-97.288}{32}=\frac{-118.288}{32}=-3.6965\approx-3.70 \end{gathered}[/tex]
Since time can't be a negative value, we pick the positive value of t.
Therefore, to the nearest hundredth, it takes 2.38 seconds for the ball to hit the ground.
The resale value V, in thousands of dollars, of a boat is a function of the number of years since the start of 2011, and the formula isV = 10.5 - 1.1t.(a) Calculate V(3).________thousand dollarsExplain in practical terms what your answer means.This means that the resale value of the boat will be______thousand dollars at the start of the year_______(b) In what year will the resale value be 6.1 thousand dollars?______(c) Solve for t in the formula above to obtain a formula expressing t as a function of V. t=______(d) In what year will the resale value be 2.8 thousand dollars?_______
Answer
a) V (3) = 7.2 thousand dollars.
In practical terms, the resale value of the boat will be 7.2 thousand dollars at the start of the year 2014.
b) t = 4years.
The resale value will be 6.1 thousand dollars in the year 2015.
c) t = 9.545 - 0.909V
d) t = 7 years.
7 years after the start of 2011 = 2018.
Explanation
We are given that the resale value (V), in thousands of dollar, of a boat is given as
V = 10.5 - 1.1t
where t = number of years since the start of 2011.
a) We are told to calculate V(3).
V = 10.5 - 1.1t
t = 3
V = 10.5 - 1.1 (3)
V = 10.5 - 3.3
V = 7.2 thousand dollars.
In practical terms, the resale value of the boat will be 7.2 thousand dollars at the start of the year 2014.
b) In what year will the resale value be 6.1 thousand dollars.
V = 10.5 - 1.1t
what is t when V = 6.1
6.1 = 10.5 - 1.1t
1.1t = 10.5 - 6.1
1.1t = 4.4
Divide both sides by 1.1
(1.1t/1.1) = (4.4/1.1)
t = 4 years.
4 years afther the start of 2011 = 2015.
c) We are asked to solve for t and obtain a formula expressing t as a function of V.
V = 10.5 - 1.1t
1.1t = 10.5 - V
Divide through by 1.1
[tex]\begin{gathered} \frac{1.1t}{1.1}=\frac{10.5}{1.1}-\frac{V}{1.1} \\ t=9.545-\frac{V}{1.1} \\ t=9.545-0.909V \end{gathered}[/tex]t, expressed in terms of V, is t = 9.545 - 0.909V
d) We are now asked to calculate in what year will the resale value be 2.8 thousand dollars.
t = 9.545 - 0.909V
t = 9.545 - 0.909 (2.8)
t = 9.545 - 2.545
t = 7 years.
7 years after the start of 2011 = 2018.
Hope this Helps!!!
Solve triangle EFG with the given parts.f = 17.78, F = 27.3°, G = 102.1°
STEP - BY - STEP EXPLANATION
What to find?
g, E and e
Given:
Step 1
Find the measure of side g using the sine ratio.
[tex]\begin{gathered} \frac{sinF}{f}=\frac{sinG}{g} \\ \\ \frac{sin27.3}{17.78}=\frac{sin102.1}{g} \\ \\ gsin27.3=17.78sin102.1 \\ \\ g=\frac{17.78sin102.1}{sin27.3} \\ \\ g\approx37.9 \end{gathered}[/tex]Step 2
Find angle E.
[tex]E+F+G=180(sum\text{ of interior angle in a triangle\rparen}[/tex][tex]\begin{gathered} E+27.3+102.1=180 \\ \\ E=180-102.1-27.3 \\ \\ E=50.6° \end{gathered}[/tex]Step 3
Find side e using the sine ratio.
[tex]\begin{gathered} \frac{sinE}{e}=\frac{sinF}{f} \\ \\ \frac{sin50.6}{e}=\frac{sin27.3}{17.78} \\ \\ esin27.3=17.78sin50.6 \\ \\ e=\frac{17.78sin50.6}{sin27.3} \\ \\ e\approx29.96 \end{gathered}[/tex]ANSWER
g=37.9
E=50.6°
e = 29.96
Given a regular octagon and a regular nonagon, which one has the greater interior angle?(Type your answer as the name of the polygon)
Answer:
Nonagon
Explanation:
Each of the interior angles of a polygon is calculated using the formula:
[tex]\frac{180^0\mleft(n-2\mright)}{n}[/tex]An Octagon has 8 sides, therefore:
[tex]\begin{gathered} Each\; \text{Interior Angle=}\frac{180^0(8-2)}{\square} \\ =\frac{180\times6}{8} \\ =\frac{1080^0}{8} \\ =135^0 \end{gathered}[/tex]A Nonagon has 9 sides, therefore:
[tex]\begin{gathered} Each\; I\text{nterior Angle=}\frac{180^0(9-2)}{9} \\ =\frac{180\times7}{9} \\ =\frac{1260^0}{9} \\ =140^0 \end{gathered}[/tex]Therefore, the nonagon has a greater interior angle.
What is the value of x in the proportion2 1/4 = 1 1/2_________x = 3 3/5A. 2 2/5B. 5 2/5C. 8 1/10D. 12 3/20
First, we transform the mixed fractions
[tex]\begin{gathered} 2\frac{1}{4}=2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4} \\ 1\frac{1}{2}=1+\frac{1}{2}=\frac{2}{2}+\frac{1}{2}=\frac{3}{2} \\ 3\frac{3}{5}=3+\frac{3}{5}=\frac{15}{5}+\frac{3}{5}=\frac{18}{5} \end{gathered}[/tex]Then, we use cross multiplication
[tex]\begin{gathered} \frac{\frac{9}{4}}{x}=\frac{9}{4}\times\frac{1}{x}=\frac{9}{4x} \\ \frac{\frac{5}{2}}{\frac{18}{5}}=\frac{3}{2}\times\frac{5}{18}=\frac{15}{36} \end{gathered}[/tex]so, we have
[tex]\frac{9}{4x}=\frac{15}{36}[/tex]Finally, we solve for x, we multiply x on both sides
[tex]\begin{gathered} \frac{9}{4x}x=\frac{15}{36}x \\ \frac{15}{36}x=\frac{9}{4} \\ x=\frac{\frac{9}{4}}{\frac{15}{36}} \\ x=\frac{9}{4}\times\frac{36}{15} \\ x=\frac{9\times9\times4}{15\times4} \\ x=\frac{81}{15} \\ x=\frac{27}{5} \end{gathered}[/tex]Since 27/5 = 5+2/5.Then,
[tex]x=5\frac{2}{5}[/tex]Then the answer is the second one.
9km 87 m equals
option A = 9.087km
option B= 90.87km
option c = 0.9087km
option D= 908.7km
option e= none of these
please don't give wrong answer
The half life of titanium - 44 , a radioactive isotope, is 63 years. If a substance starts out with 1000 kg of titanium- 44( round all the answers to the nearest hundredth of a kilogram or year) A) how much titanium- 44 will remain after 441 years ? B) how long will it be before there is only 1 kg of titanium- 44 ?
a)
Every 63 years, the amount of titanium halves.
441 years later means how many halving?
441/63 = 7 halving
We start off with 1000 and do 7 halving to get the amount of Titanium-44 after 441 years.
[tex]\begin{gathered} 1000(\frac{1}{2})^7 \\ =7.8125 \end{gathered}[/tex]after 441 years, the amount of titanium remaining would be 7.8125 kg
b)
Let's find the point where the remaining titanium would be 1 kg.
That would be:
[tex]1=1000(\frac{1}{2})^t[/tex]t is the time we are looking for. We can solve this using Ln(natural log):
[tex]\begin{gathered} 1=1000(\frac{1}{2})^t \\ 0.001=\frac{1}{2}^t \\ ln(0.001)=\ln (\frac{1}{2}^t) \\ \\ t=\frac{\ln (0.001)}{\ln (\frac{1}{2})} \\ t=9.965 \end{gathered}[/tex]There is basically 9.965 halving. That would make the years approximately:
9.965 * 63 (half life) = 627.795 years (approx)
Mr. McFall uses 2% cups of peanuts for every 1/2 cup of chocolate chips in a mixture. Enter the number of cups of peanuts for every 1 cup of chocolate chips. Remember to reduce.
To solve this problem I'll use proportions.
2 1/8 cups ------------------------ 1/2 cup of chocolate.
x ----------------------- 1 cup od chocolate chips
x = (1*2 1/8) / 1/2
x = 17/8 / 2
x = 4 % cups of peanuts
rectangle rstw has diagonals RT and SW that intersect at Z. If RZ= 5x+8 and SW= 11x-3 find the value of x.
Answer:
19
Explanation:
We know that the diagonals of a rectangle are always equal, therefore RT = SW.
So if RZ = 5x + 8 and SW = 11x - 3, lets's go ahead and find x as shown below;
[tex]\begin{gathered} 2(5x+8)=11x-3 \\ 10x+16=11x-3 \\ 16+3=11x-10x \\ 19=x \\ \therefore x=19 \end{gathered}[/tex]If the area of the rectangle is 4836 square feet find the length of the rectangle
Solution
- Let the length of the rectangle be x
- Let the width of the rectangle be y.
- Thus, we can interpret the lines of the question as follows:
[tex]\begin{gathered} \text{ The length is 30 less than 6 times the width can be written as} \\ x=6y-30\text{ (Equation 1)} \\ \\ \text{The area of the rectangle is 4836. This is written as:} \\ xy=4836\text{ (Equation 2)} \end{gathered}[/tex]- Now, let us solve these two equations simultaneously.
- We shall proceed by solving the system of equations graphically.
- Wherever the graphs of Equation 1 and Equation 2 intersect represents the solution to the system of equations
- The plot of the equations is given below
- Observe that the graphs cross at two points. The first point is positive and the other, negative.
- Since we cannot have negative lengths (x) or width (y), we can discard the negative coordinates.
- Thus, the length (x) and width (y) are given below:
[tex]\begin{gathered} \text{length(x)}=156 \\ \text{width(y)}=31 \end{gathered}[/tex]Final Answer
The length of the rectangle is 156 feet
Mr. Hanes places the names of four of his students, Joe, Sofia, Hayden, and Bonita, on slips of paper. From these, he intends to randomly select two students to represent his class at the robotics convention. He draws the name of the first student, sets it aside, then draws the name of the second student. Whats the probability he draws he draws Sofia then joe?
Given:
Total student = 4
Joe, Sofia, Hayden, and Bonita.
Find-:
Probability he draws Sofia then Joe.
Explanation-:
Probability: Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
The formula of probability:
[tex]P(A)=\frac{\text{ Number of favorable outcomes to A}}{\text{ Total number of possible outcomes}}[/tex]For Sofia.
Total number of possible outcomes = 4
Favorable outcomes for Sofia = 1
So probability for Sofia :
[tex]P(S)=\frac{1}{4}[/tex]After the first student set it aside.
For Joe.
Total number of possible outcomes = 3
A favorable outcome for Joe = 1
So probability for Joe.
[tex]P(J)=\frac{1}{3}[/tex]So probability for Sofia then joe is:
[tex]\begin{gathered} P=\frac{1}{4}\times\frac{1}{3} \\ \\ P=\frac{1}{12} \end{gathered}[/tex]
we need to seat 200 people. A table holds 8 people How Many tables do we need ?
Kyah, this is the solution to the exercise:
People = 200
Capacity of each table = 8 people
In consequence, we need:
Number of tables = People/Capacity of each table
Replacing by the values we know:
Number of tables = 200/8
Number of tables = 25
please try to answer quickly my brainly app keeps crashing
From the figure, the radius of the sphere is:
[tex]r=1\text{ in}[/tex]The volume of the sphere is given by the formula:
[tex]V=\frac{4}{3}\pi r³[/tex]Using the value of the radius:
[tex]\begin{gathered} V=\frac{4}{3}\pi(1)³ \\ \\ \therefore V=\frac{4\pi}{3}\text{ in^^b3} \end{gathered}[/tex]Approximating to the nearest cubic inch:
[tex]\therefore V\approx4\text{ in^^b3}[/tex]ther
I need answers to 6a and 6b. This is for my homework :,)
The system of equations has 3 cases
1. y = ax + b, y = ax + c
Since the coefficient of x and y are the same, and the y-intercepts are different, then
The two lines are parallel
2. y = ax + b, y = dx + c
Since the 2 lines have different coefficients of x, then
The two lines are intersected
3. y = ax + b, y = ax + b
Since the two lines have equal coefficients of x and equal y-intercepted, then
The two lines are coincide (same line)
6. a)
Since the system of equations is
[tex]\begin{gathered} y=2x+3 \\ y=12x-2 \end{gathered}[/tex]The coefficients of x not equal
Then from case 2 above
The two lines are intersected
6.b
Since the system of equations is
[tex]\begin{gathered} y=13x+2 \\ y=13x-2 \end{gathered}[/tex]The coefficients of x are equal
The y-interceptes not equal
Then from case 1 above
The two lines are parallel
I need help with this problem.
Using tangent function:
[tex]\begin{gathered} \tan (\theta)=\frac{opposite}{adjacent} \\ \tan (T)=\frac{16}{32}=\frac{1}{2}=0.5 \end{gathered}[/tex]Determine the missing coordinates in the ordered pair (-1,?) so that it will satisfy the given equation
we have the equation
2x-3y=4
Remember that
if the ordered pair is a solution of the given equation, then the ordered pair must satisfy the given equation
we have the ordered pair (-1,a)
substitute the given coordinates in the equation
2(-1)-3(a)=4
-2-3a=4
solve for a
3a=-2-4
3a=-6
a=-2
therefore
the missing coordinate is -2
use properties of operations to write an equivalent expression. will sand image
Use properties of operations to write equivalent expressions
WRITING EQUIVALENT EXPRESSIONS USING PROPERTIES
Commutative Property of Addition :
When adding, changing the order of the numbers does not change the sum. ...
Commutative Property of Multiplication : ...
Associative Property of Addition : ...
Associative Property of Multiplication : ...
Distributive Property :
2.8 w + 5.6
= 2.8 ( w + 2 ) ----------- OPTION B
What’s the correct Answer answer asap for brainlist please
Answer:
A. accuracy
Step-by-step explanation:
precise means to be accurate
estimate the product by rounding to the nearest ten: 28×51×76
To estimate each number by rounding it to the nearest ten, we will look at the unit digit,
If it is less than 5, then we replace it by 0 and keep the ten-digit as it
If it is 5 or more, then we will replace it by 0 and add the ten-digit by 1
Let us do that with every number
28, the unit digit is 8 which is greater than 5, then replace it by 0 and add 2 by 1
28 rounded to 30
51, the unit digit is 1 which is less than 5, then replace it by 0
51 rounded to 50
76, the unit digit is 6 which is greater than 5, then replace it by 0 and add 7 by 1
76 rounded to 80
Now let us multiply them
[tex]28\times51\times76=30\times50\times80=120,000[/tex]The product of the given numbers is 120,000
What are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x² + x - 12?
Answer:
All the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12 are 3/4 and -4/5.
College students are offered a 6% discount on a textbook that sells for
$32.50. If the sales tax is 6%, find the cost of the textbook including the sales
tax.
32.383 is the cost of the textbook including the sales tax.
How does sales tax work?
Government-imposed consumption taxes on the purchase of goods and services are known as sales taxes. A typical sales tax is imposed at the moment of sale, paid for by the shop, and then given to the government.The original price of the textbook = $32.50
Also, the discount percentage = 6%
Thus, the price of the textbook after discount = 32.50 - 6 % of 32.50
= 32.50 - 6 * 3250/100
= 32.50 - 1.95
= 30.55
Now, the sales tax = 6 %
Hence, the cost of the textbook including sales tax
= 30.55 + 6 % of 30.55
= 30.55 + 6 * 30.55/100
= 30.55 + 1.833
= 32.383
Learn more about sales tax
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