The given equation is expressed as
3x/2 - 4 = 16
The first step is to multiply both sides of the equation by 2. It becomes
3x/2 * 2 - 4 * 2 = 16 * 2
3x - 8 = 32
3x = 32 + 8
3x = 40
x = 40/3
x = 13.33
One bar of candy A and two bars of candy B have 782 calories. Two bars of candy A and one bar of candy B contain 787 calories. Find the caloric content of eachcandy barCandy bar A contains calories and candy bar B contains calories
ANSWER:
Candy bar A: 264 calories
Candy bar B: 259 calories
STEP-BY-STEP EXPLANATION:
Let x be the number of calories in candy bar A and y be the number of calories in candy bar B.
We can establish the following system of equations according to the data of the statement:
[tex]\begin{gathered} x+2y=782\rightarrow x=782-2y \\ \\ 2x+y=787 \end{gathered}[/tex]We substitute the first equation into the second and solve for y, just like this:
[tex]\begin{gathered} 2\cdot(782-2y)+y=787 \\ \\ 1564-4y+y=787 \\ \\ -3y=787-1564 \\ \\ y=\frac{-777}{-3} \\ \\ y=259 \\ \\ \text{ Now, for x:} \\ \\ x=782-2y \\ \\ x=782-2\cdot259 \\ \\ x=782-518 \\ \\ x=264 \end{gathered}[/tex]Therefore:
Candy bar A contains 264 calories and candy bar B contains 259 calories
Given Point A, what is the coordinate for A' after the following transformation has occurred?(x, y) + (x – 5, -y + 2)A (5, 7)
So we have the point A=(5,7) and the following transformation:
[tex](x,y)\rightarrow(x-5,-y+2)[/tex]Transformations take a point as input and return another point that usually is different than the one used as input. Since our input is (5,7) then we just need to replace 5 and 7 in place of x and y on the transformation:
[tex]\begin{gathered} A^{\prime}=(x-5,-y+2)=(5-5,-7+2)=(0,-5) \\ A^{\prime}=(0,-5) \end{gathered}[/tex]Then, the point we are looking for is A'=(0,-5).
1 foot= 12 inches 2 feet= inches
Solution
We are given that
[tex]1\text{ foot = 12 inches}[/tex]To find
[tex]\begin{gathered} \text{2 f}eet\text{ = 2}\times12\text{ inches} \\ \text{2 f}eet\text{ =}24\text{ inches} \end{gathered}[/tex]1. Find the domain and range of f(x) = sqrt(x)2. Find the domain and range of f(x) = 3x + 2
We have the function:
[tex]f(x)=\sqrt[]{x}[/tex]The domain is the set of values of x for which f(x) is defined. In this case, f(x) is defined only for non-negative values of x, so the domain is D:{x≥0}.
The range is the set of values that f(x) can take for the domain in which it is defined. In this case, f(x) will only take non-negative values, so the range can be defined as R: {y≥0}.
For the linear function f(x) = 3x+2, we don't have restrictions for the domain and the the range: both x and y can take any real value, so the domain and range are D: {x: all real numbers} and R: {y: all real numbers}.
Answer:
For the function f(x) = √x, the domain is D:{x≥0} and the range is R: {y≥0}.
For the function f(x) 3x+2, the domain is D: {x: all real numbers} and the range is R: {y: all real numbers}.
A giant pie is created in an attempt to break a world record for baking. The pie is shown below:What is the area of the slice of pie that was cut, rounded to the nearest hundredth? 78.13 ft2 82.43 ft2 86.31 ft2 91.98 ft2
step 1
Find out the area of the complete pie
[tex]A=pi*r^2[/tex]r=30/2=15 ft ----> the radius is half the diameter
substitute
[tex]\begin{gathered} A=pi*15^2 \\ A=225pi\text{ ft}^2 \end{gathered}[/tex]Remember that the area of a complete circle, subtends a central angle of 360 degrees
so
Applying proportion
Find out the area for a central angle of 42 degrees
[tex]\begin{gathered} \frac{225pi}{360^o}=\frac{x}{42^o} \\ \\ x=\frac{225p\imaginaryI}{360^{o}}*42^o \\ \\ x=26.25pi \\ x=26.25*3.14 \\ x=82.43\text{ ft}^2 \end{gathered}[/tex]The answer is 82.43 ft27. The distance y (miles) that an athlete training for a marathon is from home after x(hours) is shown in the figure to the right.Distance from Homea. What is the y-intercept as an ordered pair?30b. Find the slope of this line. (Be aware of the scale)200Distance (miles)(1, 10)10C. What is the equation of this linear segment?0 0.5 1.0 1.5 2.0 2.5 3.0Time (hours)
The last one! Synthetic division please explain how to do this!!
The given expression is:
[tex](x^3+5x^2-18)\div(x-3)[/tex]This can be solved using the synthetic division as shown below
Therefore, the quotient = x² + 8x + 24
The remainder = 54
To confirm the remainder, substitute if f(54) = 0
f(x) = x³ + 5x^2
Question 12Which equation contains a perfect square trinomial?O x2 - 6x + 72 = 0O x2 + 2x - 4 = 0O2? + 14x + 49 = 0O x2 – 5x + 64 = 0
A perfect square trinomial has a general structure which is
[tex]a^2\pm2ab+b^2[/tex]The one that meets this structure is
[tex]x^2+14x+49[/tex]We know it because it can be re written as
[tex]x^2+2\cdot7\cdot x+7^2[/tex]Which shows in a more explicit way the estructure of a perfect square trinomial. The right answer is c
1. Do you the following side lengths form a right triangle?2. Which measurement is closest to the value of X in centimeters?
Answer:
Part 1:
Yes, the side lengths form a right triangle.
Part 2:
Option d 37.1 cm
Explanation:
We need to use the pythagorean theorem.
In part 1, if the 3 side lengths are a right triangle, then, they must verify:
[tex]7.5^2=4.5^2+6^2[/tex]By the theorem. Then:
[tex]\begin{gathered} 7.5^2=56.25 \\ 4.5^2+6^2=20.25+36=56.25 \end{gathered}[/tex]They're equal, then the lengths correspond to a right triangle.
For part 2, we need to use again the theorem. In this case:
[tex]\begin{gathered} 12^2+x^2=39^2 \\ x=\sqrt{1521-144} \\ x=\sqrt{1377} \\ x\approx37.1cm \end{gathered}[/tex]A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 91 m long and 68 m wide. What is the length of a training track running around the field? (Use the value 3.14 for I, and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
Concept:
To figure out the length of the running track, we will use the following steps below
Step 1:
Calculate the length of the round the two semicircles
[tex]\begin{gathered} perimeter\text{ of semi circle=}\pi r \\ r=\frac{68m}{2}=34m \end{gathered}[/tex]By substituting the values in the formula above, we will have
[tex]\begin{gathered} Perimeter\text{ of semicircle=}\pi r \\ Perimeter\text{ of semicircle=3.14}\times34m \\ Perimeter\text{ of semicircle=106.76m} \end{gathered}[/tex]Step 2:
The image below will be used to calculate the length round the training track
Hence,
To calculate the length of the track we will have
[tex]\begin{gathered} Length\text{ of track=AB+arc BD+DC+arc AC} \\ AB=91m \\ arcBD=106.76m \\ arcAC=106.76m \\ DC=91m \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \begin{equation*} Length\text{ of track=AB+arc BD+DC+arc AC} \end{equation*} \\ Length\text{ of track=91+106.76+91m+106.76} \\ Length\text{ of track=395.52m} \\ Length\text{ of track=395.52m} \end{gathered}[/tex]Hence,
The final answer = 395.52m
A cylindrical barrel has a radius of 1.2 feet and a height of 4 feet. Find the volume of the barrel.
ANSWER:
18.1 ft³
STEP-BY-STEP EXPLANATION:
Given:
Radius (r) = 1.2 ft
Height (h) = 4 ft
We can determine the volume of the cylindrical barrel using the following formula:
[tex]V=\pi\cdot r^2\cdot h[/tex]We substitute each value and calculate the volume, like this:
[tex]\begin{gathered} V=\left(3.14\right)\left(1.2^2\right)\left(4\right) \\ \\ V=18.1\text{ ft}^3 \end{gathered}[/tex]The volume of the barrel is 18.1 ft³
in a table that shows no exact solutions, how do you know if there are any solutions? How can you find an approximate solution?
If we have a quadratic equation described in a table and it does not show the exact solution (roots) of the equation, we can look if, with the values of x or the independent variable sorted, we have a change of sign.
This indicates that there is a root between those two values of x.
For example:
x = 2 --> f(x) = -3
x = 3 --> f(x) = 4
We can see that from x=2 to x=3, we have a sign change. Then we know that, because of the continuity of the quadratic function, we must have a value between x=2 and x=3 for which f(x)=0. This is an application of the Intermediate Value Theorem.
We can then approximate the value of the root x=r as the average between x=2 and x=3. This is the bisection method to find roots of functions. In this case, it would give a result r=2.5.
There are other methods (Newton-Raphson or False position, for example), but this bisection method is the simplest approximation.
What is the slope-intercept form of a line? What two specific pieces of information do you need to write an equation of a line in slope-intercept form? Explain/discuss how you would find those two pieces of information if you were only given two points on the line. Use the points (-3,1) and (3,-5) to illustrate this process.
The slope-intercept form of a line is:
y = ax + b
In which a is the slope and b is the y-intercept, which is the value of y when x = 0.
To write an equation in this form, we need the slope and the y-intercept.
Using two points, we find the slope a dividing the change in y by the change in x. Then, having a, we can replace one of these points into the equation, to find the intercept b.
In this question:
We have points (-3,1) and (3,-5)
Finding the slope:
Change in y: -5 - 1 = -6
Change in x: 3 - (-3) = 3 + 3 = 6
Slope: a = -6/6 = -1
So
y = -x + b
Using the point (-3,1), we have that when x = -3, y = 1. So
1 = -(-3) + b
1 = 3 + b
3 + b = 1
b = 1 - 3
b = -2
The equation is:
y = -x - 2
Financial statements use the formula working C=current Assets - current Liabilities. The formula can be written in symbols as C=A-L. Solve the formula for A.
Given that C = A - L
To solve for A, add L to both sides of the equation
C + L = A - L + L
C + L = A
=>A = C + L
Circle B is a transformation of Circle A. Describe the transformations that show why Circle A is similar to Circle B. YA 12 Circle B is the result of dilating Circle A with A as the center of dilation and using a scale factor of . then translating the image 12 units down. 10 8 6 A А Circle B is the result of dilating Circle A with A as the center of dilation and using a scale factor of then reflecting the image in the y-axis. 4 N -2 0 -2 2 4 6 8 10 12 x -4 Circle B is the result of dilating Circle A with A as the center of dilation and using a scale factor of, then translating the image 12 units down. -6 B -8 -10 -12 Circle B is the result of dilating Circle A with A as the center of dilation and using a scale factor of then rotating the image 180°.
The two circles, A and B have different diameters. The diiameter of circle A is 5 units while the diameter of circle B is 4 units. This means that circle B is smaller than circle A. This means that there is a dilation and it is a reduction. Thus, we can say that B is 4/5 * A
4/5 * 5 = 4
The image was then translated 12 units down. The correct option is the third one
Write the inequality in slope - intercept form. 2x+y<13
Answer:
Step-by-step explanation:
recall the formula for slope-intercept y=mx+b
given: 2x + y < 13
put in the equal sign but remember it's less than
2x + y = 13
y = -2x +13
now it's in slope-intercept form :)
Translate each graph as specified below.(a) The graph of =yfx is shown. Translate it to get the graph of =y+fx2.(b) The graph of =ygx is shown. Translate it to get the graph of =yg−x5.
See graphs below
Explanation:[tex]\begin{gathered} a)\text{ y = f(x)} \\ f(x)\text{ + 2 is a translation of 2 units upward} \\ To\text{ get }y\text{ = f(x )+ 2, we will assign values to x and add 2 to its y coordinates in order to get } \\ \text{the coordinates of the new one} \end{gathered}[/tex]let x = -2, -1, 0, 1, 2
on the original
when x = -2, y = -3
new y coordinate = -3 + 2 = -1
when x = -1, y = 0.5
new y -coordinate = 0.5 + 2 = 2.5
when x = 0, y = 1
new y coordinate = 1 + 2 = 3
when x = 1, y = 1.5
new y oordinate = 1.5 +2 = 3.5
when x = 2, y = 5
new y-coordinate = 5 + 2 = 7
plotting the new points against x:
b) y = g(x)
y = g(x - 5)
subtract 5 from the x coordinate of the previous line
We will assign values for x, in order to get values of y
let x = 0, 1, 3
when x = 0, y = 0
new x coordinate = 0 - 5 = -5
when x = 1, y = 4
new x coordinate = 1 - 5 = -4
when x = 3, y = 7
new x coordinate = 3 - 5 = -2
plotting the points on the graph:
Ezra has a square brick patio. He wants to reduce the width by 6 feet and increase the length by 6 feet.Let xrepresent the length of one side of the square patio Write expressions for the length and width of the new patio. Then find the area of the new patio if the original patio measures 13 feet by 13 feet.
Explanation:
Ezra has a square brick patio where x represents the length of one side of this square patio:
And hee wants to reduce the width by 6 feet, and increase the length by 6 feet.
The new width is x-6,
The new length is x+6.
[tex]\begin{gathered} Expressions\text{ for the length and the width of the new patio:} \\ l=x+6 \\ w=x-6 \end{gathered}[/tex]Then, we need to find the area of the new patio:
[tex]A=lw[/tex]We multiply the length by the width. The area is:
[tex]lw=(x+6)(x-6)[/tex]And finally, if the original measure of the sides is x=13 ft, the area of the new patio is:
[tex]\begin{gathered} (x+6)(x-6) \\ \downarrow \\ (13+6)(13-6) \\ \downarrow \\ (19)(7) \\ \downarrow \\ 133 \end{gathered}[/tex]Since it represents the area the units are square feet:
133 square feet.
These results are shown in option B.
Answer:
[tex]lw=(x+6)(x-6);133\text{ square feet}[/tex](4a²b) ?Simplify:(2a3b4)32a5710AB.4ab63с225510D4ab53
We would apply the following laws of exponents
(x^y)^z = x^(yz)
a^c * a^d = a^(c + d)
a^c / a^d = a^(c - d)
The given expression is
(4a^2b)^2/(2a^3b^4)^3
By applying the first law above, it becomes
[4^2a^(2*2)b^2]/[2^3a^(3*3)b^(4*3)]
= [16a^4b^2]/[8a^9b^12]
by applying the second and third laws, we have
16/8 * a^(4 - 9) * b^(2 - 12)
= 2a^-5b^-10
Also, x^-1 = 1/x
Thus, the final expression would be
2/a^5b^10
Option C is correct
Which statement regarding the association shown could explain the relationship?A. class size appears to have little effect on test scores.B. schools is more affluent areas have larger class sizes, which is associated with higher test scores.C. schools in more affluent areas have smaller class sizes, which is associated with higher test scores. D. schools in less affluent areas have smaller class sizes, which is associated with lower test scores.
plss help Solve for y.
−2y+5=−11
Responses
y = 8
y, = 8
y = 3
y, = 3
y=−3
y equals negative 3
y=−8
y equals negative 8
Responses
y = 8
y, = 8
y = 3
y, = 3
y=−3
y equals negative 3
y=−8
y equals negative
2) A scuba diver descends to a location that is -12 1/3 m relative to sea level. He then descends another 8 1/4 M. What is the scuba divers final location relative to sea level.
NUMBERS ONLY
Answer: -20 7/12
Step-by-step explanation: Hope this helps!
An open topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 30 cm by 40 cm and folding up the sides. Determine the dimensions of the squares that must be cut to create a box with volume of 2448cm^3.
Let's start by drawing the situation:
According to this, one of the dimensions of the box is 40-2x. The other one is 30-2x and the last one, that we could say it's the height, is x.
The volume of a box is given by the product of the three dimensions:
[tex]\begin{gathered} V=(40-2x)\cdot(30-2x)\cdot x \\ V=(1200-80x-60x+4x^2)\cdot x \\ V=1200x-140x^2+4x^3 \end{gathered}[/tex]Use the given value of the volume to find x:
[tex]\begin{gathered} 2448=1200x-140x^2+4x^3 \\ 4x^3-140x^2+1200x-2448=0 \end{gathered}[/tex]Factoring this expression we have that:
[tex]\begin{gathered} 4(x-3)(x^2-32x+204)=0 \\ x-3=0 \\ x=3 \end{gathered}[/tex]One of the possible dimensions of the square is 3. Now, solve the quadratic expression (third factor) to find the other 2 options:
[tex]\begin{gathered} x^2-32x+204=0 \\ x=\frac{-(-32)\pm\sqrt[]{(-32)^2-4(1\cdot204)}}{2\cdot1} \\ x=\frac{32\pm\sqrt[]{1024-816}}{2} \\ x=\frac{32\pm\sqrt[]{208}}{2} \\ x1=\frac{32+\sqrt[]{208}}{2} \\ x2=\frac{32-\sqrt[]{208}}{2} \end{gathered}[/tex]It means that the squares can have 3 different dimensions, which are:
[tex]3,\frac{32+\sqrt[]{208}}{2},\frac{32-\sqrt[]{208}}{2}[/tex]Nevertheless, the second possible option is not coherent since it's value is close to 23 and the dimensions of the cardboard are 30 and 40. It means that the possible dimensions are 3 and (32-sqrt(208))/2.
10.{(0,8), (1, 2), (3, 7), (5,9), (3, 6)}
the image is downloading, please don't close the session
if 2/3n = -12 what is tbe vLue of n=
If 2/3n = -12
This can be re-written as
2n/3 = -12
Multiply both sides of the equation by 3 to eliminate the fraction on the left hand side
2n = -36
Divide both sides of the equation by 2 (to eliminate the 2 and isolate the n)
n = -18
Solve for y.y+3/9=4/5
As per given by the question,
There are given that;
[tex]\frac{y-3}{9}=\frac{4}{5}[/tex]Now,
Solve the given equation for the value of y.
So,
The given equation can be written as,
[tex]\frac{y-3}{9}-\frac{4}{5}=0[/tex]Then,
[tex]\begin{gathered} \frac{5(y-3)-36}{45}=0 \\ 5y-15-36=0 \\ 5y-51=0 \\ 5y=51 \end{gathered}[/tex]So,
[tex]y=\frac{51}{5}[/tex]Hence, the value of y is;
[tex]\frac{51}{5}[/tex]In circle U m ∠TUs=107. Solve for x if m TS = (3x+39). If necessary round your answer to the nearest tenth
Answer:
x=22.7
Explanation:
In the circle:
• m∠TUS=107°
,• The measure of arc TS = (3x+39)°
In a circle:
Therefore:
[tex]\begin{gathered} m\widehat{TS}=m\angle TUS \\ \implies3x+39=107\degree \end{gathered}[/tex]We solve the equation for x:
[tex]\begin{gathered} \text{ Subtract 39 from both sides} \\ 3x+39-39=107-39 \\ 3x=68 \\ \text{ Divide both sides by 3} \\ \frac{3x}{3}=\frac{68}{3} \\ x\approx22.7\degree \end{gathered}[/tex]The value of x is 22.7 (correct to the nearest tenth).
The FAA now figures the average checked bag to weigh 30 pounds. This is up from a previous figureof 23 pounds. Find the amount of increase and the percent of increase, to the nearest wholepercent.
As given by the question
There are given that the average checked bag to weighs 30 pounds.
Now,
From the question
The increasing amount is:
[tex]30-23=7[/tex]Then,
The percent of increasing is:
[tex]\begin{gathered} \frac{30-23}{23}\times100=\frac{7}{23}\times100 \\ =30.43 \end{gathered}[/tex]Hence, the increasing amount is 7 and the percent of the increasing amount is 30%.
which rules describe the pattern shown in the table? Select all that apply.Number of Bracelets 1. 2. 3. 4. 5Number of Beads. 16 32 48 64. 801. The number of beads is 16 times the number of bracelets.2. The number of beads is 15 more than the number of bracelets3. Each bracelet has 32 beads4. Each bracelet has 16 beads 5. The number of bracelets is equal to the number of beads.
As per given by the question.
There are given that a table of number of bracelets and numbers of beads.
Now,
According to the table,
In first option, the numbers of beads is 16 times the number of bracelets.
That means,
The number of bracelet is 1, the their 16 times greater the beads.
hence, the option first is described the pattern.
Now,
For the second option,
The number of beads is 15 more than the the number of bracelets.
So,
There are no any conclusion of option second match with the given table.
Hence, the option second is does not described the pattern.
Now,
For the option third.
Then,
According to the given table, there are different different numbers of beacelets and their different different beads. But in option third, there are given that each bracelets has 32 beads.
Hence, the option third is does not match with pattern.
Now,
For the option fourth;
The option fourth is "Each bracelets has 16 beads".
Then,
The option third is,"Each bracelets has 32 beads".
According to the given table, in all type of bracelets, atleast 16 beads are present. that means;
For 1 bracelets, there are 16 beads, for 2 bracelets, there are 32 beads(16+16), and for bracelets 3, there are 48 beads(16+16+16) so on.
Hence, the option fourth is described the pattern.
Now,
For the option fifth;
The option fourth is "the numbers of bracelets is equal to the number of beads".
Then,
According to the table, this statement is incorrect.
Hence, the option fourth also dose note described the pattern.
Then,
The option first and option fourth is described the pattern.
NO LINKS!! Please assist me with this problem.
Answer:
(x -h)² +(y -k)² = r²r(h, k)Step-by-step explanation:
You are being asked for the equation of a circle, and a description of what it is.
Points equidistantThe distance equation tells you that the distance of (x, y) from (h, k) is ...
d = √((x -h)² +(y -k)²)
If this distance is r, the radical can be removed, and we can write the equation as ...
(x -h)² +(y -k)² = r² . . . . formula for P(x, y)
DescriptionThis is a circle of radius r, with a center at (x, y) = (h, k).
The equation of a circle of radius r with center at (x, y) = (x -h)² +(y -k)² = r².
Given that, P(x, y) is a distance r>0 from a fixed point C(h, k).
What is a circle equation?The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.
The standard equation of a circle with center at (x1,y1) and radius r is (x-x1)²+(y-y1)²=r²
Using distance formula,
The distance between (x, y) from (h, k) is
d = √((x -h)² +(y -k)²)
If this distance is r, then we get
(x -h)² +(y -k)² = r²
Hence, the equation of a circle of radius r with center at (x, y) = (x -h)² +(y -k)² = r².
To learn more about an equation of a circle visit:
https://brainly.com/question/23799314.
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