Given the following equation:
[tex]3x+15=3\mleft(x+5\mright)[/tex]You must solve for "x" as following:
1. Apply the Distributive property:
[tex]\begin{gathered} 3x+15=(3)(x)+(3)(5) \\ 3x+15=3x+15 \end{gathered}[/tex]2. Observe the equation. You can notice that left side is equal to right side. If you try to solve for "x", you get:
[tex]\begin{gathered} 3x-3x=15-15 \\ 0=0 \end{gathered}[/tex]What is the surface area of the regular pyramid below?A. 648 sq. unitsB. 552 sq. unitsC. 396 sq. unitsD. 522 sq. units
Step 1:
Concept: Calculate the area of each face and add all together to get the surface area of the pyramid.
The regular pyramid below have 4 triangles and a square
Step 2: Apply the area formula to find the area of the 4 triangles and a square.
[tex]\begin{gathered} \text{Area of a triangle = }\frac{Base\text{ x Height}}{2} \\ \text{Area of the square base = Length x Length} \end{gathered}[/tex]Step 3:
Given data for the triangle
Height = 21
Base = 12
[tex]\begin{gathered} Area\text{ of a triangle = }\frac{Base\text{ x Height}}{2} \\ =\text{ }\frac{21\text{ x 12}}{2} \\ =\text{ }\frac{252}{2} \\ =126\text{ sq. units} \\ \text{Area of the four triangles = 4 x 126 = 504 sq. units} \end{gathered}[/tex]Step 4: Find the area of the square
Given data for the square
Length = 12
Area = length x length = 12 x 12 = 144 sq. units
Step 5: Add the area of the four triangles and the square.
Surface area of the regular pyramid = 504 + 144
= 648 sq. units
What is 132% as a decimal?
Step 1: Problem
What is 132% as a decimal?
5Jamal's band learns lots of new songs.The band learns a new song every fourdays. At this rate, how many new songswill the band learn in four weeks?LAsongs
Given that The band learns a new song every four days.
We need to find the number of new songs for four weeks.
We know that one week= 7 days
[tex]1\text{ w}eek\text{ = 7 days }[/tex]Multiply by 4 to find the number of days in four weeks.
[tex]1\times4\text{ w}eek\text{ = 7 }\times4\text{ days }[/tex][tex]4\text{ w}eeks\text{= 28days }[/tex]We need to find the number of new songs that the band learns in 28 days.
Divide 28 by 4 to find the number of songs since the band learns one new song every 4 days.
[tex]\frac{28}{4}=7\text{ songs}[/tex]The band learns 7 songs in four weeks.
Suppose that the functions fand g are defined for all real numbers x as follows.f(x)=x+5g(x)=2x²Write the expressions for (g+f)(x) and (g–f)(x) and evaluate (g.f)(-3).
The expression (g+f)(x) is equal to g(x)+ f(x), (g-f)(x) is equal to g(x) f(x) and the expression (g*f)(-3) is equal to g(-3)*f(-3).
Then, we have
[tex](g+f)(x)=g(x)+f(x)=2x^2+x+5[/tex]Similarly,
[tex](g-f)(x)=g(x)f(x)=2x^2-(x+5)=2x^2-x-5[/tex]And finally,
[tex]\begin{gathered} (g\cdot f)(-3)=g(-3)\cdot f(-3)=2(-3)^2\cdot(-3+5) \\ (g\cdot f)(-3)=2(9)\cdot(2) \\ (g\cdot f)(-3)=36 \end{gathered}[/tex]In summary, the answers are:
[tex]\begin{gathered} (g+f)(x)=2x^2+x+5 \\ (g-f)(x)=2x^2-x-5 \\ (g\cdot f)(-3)=36 \end{gathered}[/tex]Y 3+ 2+ 1+ -4 -3 -2 -1 1 2 3 -1- -2 -3+ -4 47 What is the slope of the line?
To find the slope of the line, we will follow the steps given below:
Step 1: select two points on the graph
(0, -1) and (4,2)
Step 2: Apply the slope formula:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]=>
[tex]\text{slope}=\frac{2-(-1)}{4-0}=\frac{2+1}{4}=\frac{3}{4}[/tex]The slope of the graph is:
[tex]\frac{3}{4}[/tex]Use the following function for questions # 1 - # 5:f(x) =x?- 14x + 44#1: Find the X value of the turning point.
The given function is
f(x) = x^2 - 14x + 44
To find the turning point, we would differentiate the function, equate the derivative to zero and solve for x. We have
f'(x) = 2x - 14
Equating it to zero, we have
2x - 14 = 0
2x = 14
x = 14/2
x = 7
The value of x of the turnng point is 7
find the smallest non negative value for x in degrees that makes the equation cot (x) = √3 true.
Given:
cot (x) = √3
To find the smallest non-negative value for x in degrees:
So, we get
[tex]\begin{gathered} \cot x=\sqrt{3} \\ \cot x=\cot (30^{\circ}) \\ x=30^{\circ} \end{gathered}[/tex]Hence, the answer is,
[tex]x=30^{\circ}[/tex]The price of a train ticket consists of an initial fee of $5 plus a fee of $2.75 per stop. Julia has $21 and would like to travel 50 kilometers. She wants to know the largest number of stops she can afford to buy on a ticketLet S represent the number of stops that Julia buys.1) Which inequality describes this scenario?A. 5+2.75•S ≤ 21 B. 5+2.75•S ≥ 21 C. 5+2.75•S ≤ 50 D. 5+2.75•S ≥ 502) What is the largest number of stops that Julia can afford?
Let's begin by listing out the information given to us:
Initial fee = $5
Fee per stop = $2.75
Amount with Julia = $21
What is the highest number of stops she can make?
S = the number of stops Julia bought
Julia pays the initial fee of $5. We subtract this from the $21, we have
$ (21 - 5) = $16
Julia has $16 left to buy her stops. She cannot spend beyond the amount of money with her (altogether $21). She spends lesser than or equal to $21 (≤ $21)
The inequality that describes this scenario is given by:
initial fee + fee per stop * number of stops ≤ 21
5 + 2.75 * S ≤ 21
Hence, option A is the correct answer
What is the largest number of stops that Julia can afford?
This is gotten by dividing the amount left after subtracting the initial fee by the fee per stop
n = 16/2.75 = 5.82 = 5 stops (rounding downwards)
We round downwards because the number of stops must be a whole number and it must be lesser than or equal to $21 altogether
The number of adults living in homes on a randomly selected city block is described by the following probability distribution. Number of adults, x1 ,2,3,4 or moreProbability, P(x) 0.250.500.15??? What is the probability that 4 or more adults reside at a randomly selected home?(A) 0.10(B) 0.15 (C) 0.25(D) 0.50 (E) 0.90
The answer is letter A. 0.1
because the probability = 1
So Probability of select 4 adults = 1 - 0.25 - 0.5 - 0.15
= 0.1
9. At last Friday's soccer game there were a total of 673 fans in attendance, including students and non-students.Let x represent the number of students, and y represent non-students. Which of the following statements couldrepresent the number of fans in attendance. Select all that apply.a. x + y = 673b. 335 and 138c. 335 and 338d. x=y - 673e. y = -x + 673f. 273 and 400
The answer is A
From the question:
Total fans in attendence = 673
x = number of students
y= non - students
Total of fans in attendance =
x + y= 673
2) Given that XY || AC, what is YC if BX = 10, BA = 15, and BY = 8?A) 4 B) 6 C)8D)12
We can see that triangles ABC and AXY are congruent
This means that
[tex]\frac{AX}{BX}=\frac{YC}{BY}[/tex]Now, we know that BX=10, BY=8 and BA=AX+BX, hence AX=BA-BX, we have
[tex]\frac{BA-BX}{10}=\frac{YC}{8}[/tex]now, since BA-BX=15-10, BA-BX=5, it yields,
[tex]\frac{5}{10}=\frac{YC}{8}[/tex]Now, we need to isolate YC, this is given by
[tex]YC=8(\frac{5}{10})[/tex]Since
[tex]\frac{5}{10}=\frac{5\cdot1}{5\cdot2}=\frac{1}{2}[/tex]we have that
[tex]\begin{gathered} YC=8(\frac{1}{2}) \\ YC=\frac{8}{2} \\ YC=4 \end{gathered}[/tex]hence, the answer is YC=4, which corresponds to A).
Identify the domain and range for the given relation. Indicate whether the relation is a function or not andexplain
Given :
Domain is:
[tex]D\colon\mleft\lbrace0,-1,1\mright\rbrace[/tex]Range is:
[tex]R\colon\mleft\lbrace0,1,2\mright\rbrace[/tex]Here is one output for one input.
How many gallons are equivalent to 12 quarts?
Given:
The objective is to convert 12 quarts into gallons.
In general,
[tex]1\text{ gallon=4}quart[/tex]12 quarts can be converted to gallons by,
[tex]\begin{gathered} x=\frac{12}{4} \\ x=3\text{ quarts} \end{gathered}[/tex]Hence, 12 quarts is 3 gallons.
graph the line represented by the equation 2x + 3y = 8
Given the equation
2x + 3y = 8
The given equation represents a line
It is required at minimum two points to graph the line
So, assume two value for x and find y using the given equation
When x = -2
2 * -2 + 3y = 8
-4 + 3y = 8
3y = 8 + 4
3y = 12
y = 12/3 = 4
so, the point (-2 , 4) lie on the line
And assume x = 4
so, 2 * 4 + 3y = 8
8 + 3y = 8
3y = 0
y = 0
So, the point (4 , 0) lie on the line
so, the line is passing through the points (-2 , 4) and ( 4 , 0)
By connecting the points and extending the line we will get the graph of 2x + 3y = 8
See the following image;
help me asap please!!! no explanation just the process and answer
To find out the determinant, multiply in cross
so
(3)*(-2)-(5)*(-7)=-6+35=29
therefore
the answer is 29
3 2 1 -3-2- 1 2 3 2 -3 Domain: (-3,3] Range: [-2, 2] Domain: (-2, 2] Range: [-3,3] Domain: (-2,-3) Range: (2,3) Domain: {-2, -1, 0, 1, 2} Range: {-3, -2, - 1, 0, 1, 2, 3} None of the above NON
The domain is [ -2, 2]
and the range is [-3, 3]
hi I need help ;]]] ❄️❄️❄️
The order from least to greatest is -4.7,-4,-31/8, [tex]-3\frac{1}{8}[/tex]
What is Fraction?A fraction represents a part of a whole.
The given integers are -31/8,-4.7, -4 and -3 1/8
Now let us simplify the fraction values
-31/8=-3.875
-4.7
-4 and
[tex]-3\frac{1}{8}[/tex]=-24+1/8=-23/8=-2.875
As there is a negative sign, the smallest number with negative sign will be greatest and largest number with negative sign is smaller.
So -4.7,-4, -3.875, -2.875
-4.7,-4,-31/8, [tex]-3\frac{1}{8}[/tex]
Hence the order from least to greatest is -4.7,-4,-31/8, [tex]-3\frac{1}{8}[/tex]
To learn more on Fractions click:
https://brainly.com/question/10354322
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(a) Does f (x) have a horizontal asymptote? If so, what is it?(b) Does f (x) have any vertical asymptotes? If so, what are they?
a) Horizontal asymptotes are horizontal lines that the graph of a function approaches but never touches. To find the horizontal asymptote, we would apply one of the rules which states that
If the degree of the of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x axis of the graph. It occurs at y = 0
The degree is the largest exponent in the function. Looking at the given function, the degree of the numerator is 2 while the degree of the denominator is 3. Thus,
there is a horizontal asymptote at y = 0
b) The vertical asymptotes are vertical lines which correspond to the zeros of the denominator of rational functions. It is equal to the values of x that make the denominator to be zero. Looking at the given function, (x + 1) cancels out in the numerator and denominator. We are left with (x - 4) and (x + 5). We would equate both terms to zero and solve for x. These values of x would make the denominator to be equal to zero. We have
x - 4 = 0
x = 4
x + 5 = 0
x = - 5
Thus,
there are vertical asymptotes at x = - 5 and x = 4
What is an equation of the line parallel to the line on the graph that passes through (2,25)?
y=4x+17
ExplanationStep 1
2 equations of lines are parallel if the slope is the same, so
a) find the slope of the graphed line
the slope of a line can by calculated by using
[tex]\begin{gathered} slope=\frac{change\text{ in y }}{change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1} \\ where \\ P1(x_1,y_1) \\ and \\ P2(x_2,y_2) \\ are\text{ 2 points from the line} \end{gathered}[/tex]so
pick up 2 points from the the line and let
[tex]\begin{gathered} P1(0,10) \\ P2(10,50) \end{gathered}[/tex]replace and evaluate
[tex]\begin{gathered} slope=\frac{change\text{\imaginaryI ny}}{change\text{\imaginaryI nx}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ slope=\frac{50-10}{10-0}=\frac{40}{10}=4 \end{gathered}[/tex]hence, the slope of the line is 4
Step 2
now, using the slope and a point we can find the equation of the line
use the point-slope formula, it says
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where\text{ m is the slope} \\ (x_1,y_1)\text{ is a point from the line} \end{gathered}[/tex]so
a)let
[tex]\begin{gathered} P1(2,25) \\ sloipe=4 \end{gathered}[/tex]b) now ,replace and solve for y
[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ y-25=4(x-2) \\ y-25=4x-8 \\ add\text{ 25 in both sides} \\ y-25+25=4x-8+25 \\ y=4x+17 \end{gathered}[/tex]so, the answer is
y=4x+17
I
Circle the value that correctly converts 6.5 cm in inches.26 in0.26 in2.6 in260 in
2.6 inches (third option)
Explanation:Given:
To convert 6.5cm to another unit
To find:
The value of 6.5 cm inches
To determine the value in inches, we need to do a conversion from cm to inches
1 inch = 2.54 cm
let 6.5 cm in inches = y
6.5cm = y
2.54cm = 1 inch
crossmultiply:
[tex]\begin{gathered} 6.5(1)\text{ = y\lparen2.54\rparen} \\ 6.5\text{ = 2.54y} \\ divide\text{ both sides by 2.54y:} \\ \frac{6.5}{2.54}\text{ = y} \\ y\text{ = 2.559} \end{gathered}[/tex]To the nearest tenth, y = 2.6
Hence, the value of 6.5cm in inches is 2.6 inches (third option)
Which number is not equal to 225%?its is exercise number 5
To do this, you can first convert the percentage form to its decimal form, like this
[tex]225\text{\%}=\frac{225}{100}=2.25[/tex]Now, you can convert the numbers that are possible answers into their decimal form, like this
Option A.
[tex]2\frac{1}{4}=\frac{2\cdot8+1}{4}=\frac{8+1}{4}=\frac{9}{4}=2.25[/tex]Option B.
[tex]\frac{9}{4}=2.25[/tex]Option C.
[tex]\frac{50}{40}=\frac{5\cdot10}{4\cdot10}=\frac{5}{4}=1.25[/tex]Option D.
[tex]\frac{45}{20}=\frac{9\cdot5}{4\cdot5}=\frac{9}{4}=2.25[/tex]Therefore, the number that is not equal to 225% is 50/40 and the correct answer is C. 50/40.
good morning I really need help with numbers 3 and 4
a) 6 x 18 = 108
b) 8 x 74 = 592
Explanations:According to the distributive property:
a (b + c) = ab + ac
Let us do each of the exercises 3 and 4 using the distributive property:
3) 6 x 18
Step 1: Write 18 as 10 + 8
18 = 10 + 8
6 x 18 = 6 ( 10 + 8)
Step 2: Apply the distributive property
6 ( 10 + 8) = (6 x 10) + (6x8)
Step 3: Multiply each of the terms
60 + 48
Step 4: Add the two together
108
Therefore, 6 x 18 = 108
4) 8 x 74
Step 1: Write 74 as 70 + 4
74 = 70 + 4
8 x 74 = 8 ( 70 + 4)
Step 2: Apply the distributive property
8 ( 70 + 4) = (8 x 70) + (8x4)
Step 3: Multiply each of the terms
560 + 32
Step 4: Add the two together
592
Therefore, 8 x 74 = 592
12x+18 rewrite using distributive property
we have
12x+18
REmember that
12=(2^2)*(3)
18=(2)*(3^2)
substitute
(2^2)*(3)x+(2)*(3^2)
Factor (2)*(3)=6
6(2x+3)
therefore
the answer is
6(2x+3)the radius of a circle is 4 centimeters. what is the diameter? give the exact answer in simplest form
we have that
the diameter is two times the radius
so
in this problem
D=2r
D=2(4)=8 cm
diameter is 8 cmA __ is a polynomial with one term.
Answer:
Monomial
Step-by-step explanation:
A polynomial that consists of exactly one term is called monomial.
Examples are 3, 10x², xy,...
So the answer is: Monomial
An empty swimming pool needs to be filled to the top. The pool is shaped like a cylinder with a diameter of 9 m and a depth of 1.1 m. Suppose water is pumped into the pool at a rate of 13 m^3 per hour. How many hours will it take to fill the empty pool?
Use the value 3.14 for pi, and round your answer to the nearest hour. Do not round any intermediate computations.
Answer:
πr2h
volume of cylinder
3.14×3×3×1.1=31.086m^3
1hour=13m^3
31.086m^3
divide 31.086÷13=2.3912hours
Express the function graphed on the axes below as a piecewise function.108642-10-8-6-4-22416810-4-6-8-10
Answer:
[tex]f(x)=\begin{cases}2x+3,x\le-4 \\ 2x-12,x>2\end{cases}[/tex]Explanation:
The equation of the line to the left is 2x + 3 and we see that it only exists for x <= -4.
The equation of the line to the right is 2x - 12 and we see that it only exists for x > 2.
Therefore, we can write
f(x) = 2x + 3 for x < = -4
f(x) = 2x -12 for x > 2
Or in the notation of piecewise function, the above can be written consicely as
[tex]f(x)=\begin{cases}2x+3,x\le-4 \\ 2x-12,x>2\end{cases}[/tex]
which is our answer!
Select all of the following that are statistical questions A. What is the price of the orangeB. What is the weight of an orange C. What is the average price of an orange D. What is the average weight of an orange grown in the U.S.A E. What percent of oranges grocery stores were grown in the USAThere is more than one answerPlease help no wrong answers please
Take into account that a statistical question refers to situation which data set are involved. Then, you can consider as statistical questions:
What is the average price of an orange
average takes into account the price of more than one orange.
What is the average weight of an orange grown in U.S.A
What percent of oranges grocery stores were grown in the USA
8) Suppose y varies inversely as x, if y = 7 when x = 6then find y when x = -21.
Suppose y varies inversely as x, if y = 7 when x = 6
then find y when x = -21.
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form
y*x=k
where
k is the constant of proportionality
step 1
Find the value of k
we have
y=7, x=6
k=7*6
k=42
the equation is
y*x=42
step 2
For x=-21
substitute
y*(-21)=42
y=42/(-21)
y=-2You flip a coin and roll a die. The table shows the sample space.12 3 4 5 6Heads(H) H-1 H-2 H-3 H-4H-5H-6Tails(T) T-1 T-2 T-3 T-4 T-5 T-6What is the probability of getting a head or a tail and anven number?Answer as a reduced fraction in the form ab.
You flip a coin and roll a die. The table shows the sample space.
1
2 3 4 5 6
Heads(H) H-1 H-2 H-3 H-4H-5H-6
Tails(T) T-1 T-2 T-3 T-4 T-5 T-6
What is the probability of getting a head or a tail and an
even number?
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
In this problem
the size of the sample space is (6+6+6)=18
the size of the event space is equal to (6+6+3)=15
REmember that an even number are (2,4 and 6)
so
the probability is equal to
P=15/18
simplify
P=5/6
therefore
the answer is5/6