An expression for the given statement is (x²/3)+4.
The given statement is 4 more than the quotient of x squared and 3.
We need to find an expression for the given statement.
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be addition, subtraction, multiplication, or division.
The terms involved in an expression in math are:
Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
According to the question, we get (x²/3)+4.
Therefore, an expression for the given statement is (x²/3)+4.
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#23-6: The pool concession stand made $5,800 in June and $6,300 in July. What is the percent of increase in sales? Round the answer to the nearest tenth.
Answer:
8.6%
Step-by-step explanation:
To find the percent change, you will need to compute the positive difference and then divide the difference by the original (the older amount).
So the positive difference will be obtain by doing larger minus smaller:
6300
- 5800
-----------
500
The older amount was 5800.
So 500/5800 is the answer as a un-reduced fraction.
I'm going to reduce it by dividing top and bottom by 100:
500/5800 = 5/58
5/58 is the answer as a reduced fraction.
5 divided by 58 gives=0.086206897 in the calculator .
Approximately 0.0862 is the answer as a decimal.
To convert this to a percentage, multiply it by a 100:
8.62%
Rounded to the nearest tenths is 8.6%
-------------
So 5800+5800(.0862) should be pretty close to 6300 (not exactly though since we rounded).
5800+5800(.0862)=6299.96 using the calculator.
What is the value of y?
Y + 30°
A. 85°
B. 55
c. 110°
D. 10°
Answer:
B. 55°
Step-by-step explanation:
Note that the total angle measurements of a triangle is = 180°.
Add all the measurements together:
40 + y + 30 + y = 180
Simplify. Combine like terms:
(40 + 30) + (y + y) = 180
70 + 2y = 180
Isolate the y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First subtract, then divide.
Subtract 70 from both sides:
70 (-70) + 2y = 180 (-70)
2y = 180 - 70
2y = 110
Divide 2 from both sides:
(2y)/2 = (110)/2
y = 110/2
y = 55
B. 55° is your answer.
~
Answer: The answer is B, 55 degrees.
Step-by-step explanation:
You substitute 55 into y, making it 55+85, +55, +40, making it 180 degrees. Since all sides in a triangle add up to 180, B is your correct answer.
Hope that helps!
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 36 and 2304, respectively.
Answer:
[tex]a_n=9(4^{n-1})[/tex]
Step-by-step explanation:
we know that
In a Geometric Sequence each term is found by multiplying the previous term by a constant, called the common ratio (r)
In this problem we have
[tex]a_2=36\\ a_5=2,304[/tex]
Remember that
[tex]a_2=a_1(r)[/tex] -----> [tex]36=a_1(r)[/tex] -----> equation A
[tex]a_5=a_4(r)[/tex]
[tex]a_5=a_3(r^{2})[/tex]
[tex]a_5=a_2(r^{3})[/tex]
Substitute the values of a_5 and a_2 and solve for r
[tex]2,304=36(r^{3})[/tex]
[tex]r^{3}=2,304/36[/tex]
[tex]r^{3}=64[/tex]
[tex]r=4[/tex]
Find the value of a_1 in equation A
[tex]36=a_1(4)[/tex]
[tex]a_1=9[/tex]
therefore
The explicit rule for the nth term is
[tex]a_n=a_1(r^{n-1})[/tex]
substitute
[tex]a_n=9(4^{n-1})[/tex]
Answer:
an=9(4^n-1)
Step-by-step explanation:
What is h(10) equal to? h:k→k^2-k
h(10)=[1]
[tex]h(k)=k^2-k\\\\h(10)=(10)^2-10=90[/tex]
28
The elevation at ground level is O feet. An elevator starts 90 feet below ground level.
After traveling for 15 seconds, the elevator is 20 feet below ground level. Which
statement describes the elevator's rate of change in elevation during this 15-second
interval?
A
The elevator traveled upward at a rate of 6 feet per second.
The elevator traveled upward at a rate of 4 feet per second.
B
C
The elevator traveled downward at a rate of 6 feet per second.
D
The elevator traveled downward at a rate of 4 feet per second.
Step-by-step explanation:
If we graph elevation vs time, the rate of change is the slope of the line.
At t = 0, h = -90.
At t = 15, h = -20.
m = (-20 − (-90)) / (15 − 0)
m = 70/15
m = 4.67
The closest answer is B. The elevator traveled upward at a rate of 4 feet per second.
Solve for f(-1).
F(x) = -3x + 3
F(-1) =
F(x) = -3x + 3
replace x in the equation with -1:
F(-1) = -3(-1) + 3
Simplify:
f(-1) = 3+3
f(-1) = 6
Write the equation of the line that passes through the points (0, -6) and (-4, 0).
Show how you arrived at your answer.
What would be the EQUATION? I’m confused. Please help.
Answer:
The slope is -3/2.
Step-by-step explanation:
Hint: slope formula:
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{rise}{run}[/tex]
[tex]\displaystyle \frac{0-(-6)}{(-4)-0}=\frac{6}{-4}=\frac{6\div2}{-4\div2}=\frac{3}{-2}=-\frac{3}{2}[/tex]
[tex]\Large \textnormal{Therefore, the slope is -3/2.}[/tex]
Answer:
y=(-3/2)x+-6
or
y=(-3/2)x-6
Step-by-step explanation:
We are going to use slope-intercept form to find the equation for this line.
y=mx+b is slope-intercept form where m is the slope and b is the y-intercept.
y-intercept means where it crosses the y-axis; the x will be 0 here. Look the question gives us the y-intercept which is -6.
So we already know b which is -6.
y=mx+-6
Instead of finding the slope using the slope formula which you could.
I'm going to plug in the point (-4,0) into y=mx+-6 to find m.
So replace x with -4 and y with 0 giving you:
0=m(-4)+-6
0=-4m-6
Add 6 on both sides:
6=-4m
Divide both sides by -4:
6/-4=m
Reduce the fraction:
-3/2=m
The slope is -3/2.
Again you could use the slope formula which says [tex]m=\frac{y_2-y_1}{x_2-x_1} \text{ where } (x_1,y_1) \text{ and } (x_2,y_2) \text{ are points on the line}[/tex].
This is the same thing as lining the points up vertically and subtracting the points vertically then putting 2nd difference over first difference. Like this:
( 0 , -6)
-( -4 , 0)
---------------
4 -6
The slope is -6/4 which is what we got doing it the other way.
So the equation with m=-3/2 and b=-6 in y=mx+b form is
y=(-3/2)x+-6
or
y=(-3/2)x-6
8. Which expression is equivalent
to 24 + 15?
A 2 X (12 + 7)
B 3 X (8 + 5)
C 5 x (8 + 3)
D 8 X (3 + 7)
Answer:
B
Step-by-step explanation:
Given
24 + 15 ← factor out 3 from each term
= 3(8 + 5)
As a check
24 + 15 = 39 and
3(8 + 5) = 3 × 13 = 39
Hence 24 + 15 = 3(8 + 5) → B
a brokerage firm charges 1 1/4% if its fee on stock purchase was 400$ what was amount of purchase?
let's say the amount purchased was "x", so then that's the 100%.
if we know that 400 is the 1¼% and "x" is the 100%, what is "x"?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 400&1\frac{1}{4} \end{array}\implies \cfrac{x}{400}=\cfrac{100}{1\frac{1}{4}}\implies \cfrac{x}{400}=\cfrac{100}{\frac{1\cdot 4+1}{4}}\implies \cfrac{x}{400}=\cfrac{\frac{100}{1}}{\frac{5}{4}} \\\\\\ \cfrac{x}{400}=\cfrac{\stackrel{20}{~~\begin{matrix} 100 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{1}\cdot \cfrac{4}{~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{x}{400}=80\implies x=32000[/tex]
Last week, a coral reef grew 20.3 mm taller. How much did it grow in meters?
Answer:
0.0203 meters
Step-by-step explanation:
If a coral reef grew 20.3 mm taller, it grew 0.0203 meters taller.
20.3 mm = 0.0203 meters
The coral reef grew by 20.3 millimeters last week, which is equivalent to 0.0203 meters. This is calculated by dividing the millimeters by 1000, as there are 1000 millimeters in a meter.
Explanation:The amount of growth in the coral reef's height can be converted from millimeters to meters by using the conversion ratio of 1 meter being equal to 1000 millimeters. So, to find out how much the coral reef grew in meters, we would take the growth in millimeters (20.3 mm) and divide by 1000.
The calculation would be like this: 20.3 mm / 1000 = 0.0203 meters.
So, the coral reef grew by 0.0203 meters last week.
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what is a line of symmetry
Answer:
A line where you put it in the middle of the shape and see if it's symmetrical or the same. You fold the shape and if one side matches to other, that is symmetrical. That is the line of symmetry.
A line of symmetry divides a figure into two parts such that each part is the mirror image of the other. In other words, if we flip one side of the figure over the line of symmetry, it should match up exactly with the other side.
Let event A = You buy a new umbrella on Friday. Which event is most likely to
be independent of A?
Answer:
B. You had a math test on Thursday
Step-by-step explanation:
B is most likely the answer because you would have a math test regardless of the weather. Teachers do stuff like that. Also I just took this quiz on APEX.
1200 people visited a museum. 240 of the visitors were children. what percent of the visitors were children?
Answer:
20 percent
Step-by-step explanation:
To find the percentage that were children, we take the number of children over the total and multiply by 100%
There are 240 children and 1200 total people
240/1200 * 100%
.2*100%
20%
Answer:
20 Percent.
Step-by-step explanation:
240:1200*100 =
(240*100):1200 =
24000:1200 = 20
Explain the effect of c on the graph of y=f(x) for the function y=f(x)+c ?
Answer:
Shifts it up c units.
Step-by-step explanation:
The '+ c' will move the whole graph upwards c units.
By translation of axis, the effect of c on the graph of y=f(x) for the function y=f(x)+c is it shifts up the curve by c units.
What is the effect of c on the graph of y=f(x) for the function y=f(x)+c ?The translation of axis on any curve y = f(x) is the shifting of the graph by a definite unit from the original equation or curve.
If the curve is given as y = f(x) ± a, then for +a , it shifts the curve on the graph upwards on y axis by a units and for -a, it shifts the curve on the graph downwards on y axis by a units.
The given function is y = f(x) and thus for the graph y = f(x) + c, from the principle of translation of axis, it shifts the curve upwards on y-axis by c units.
Therefore, by translation of axis, the effect of c on the graph of y=f(x) for the function y=f(x)+c is it shifts up the curve by c units.
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Which choice is equivalent to the expression below?
Square root of -17
A.-3sqr of 3i
B.-sqr of 27
C.-3sqr of 3
D.3sqr of 3
E.3i sqr of 3
Answer:
d
Step-by-step explanation:
3×3×3 is 27 so that's the answer
Angelo has a credit score of 726. According to the following table, his credit rating
is considered to be which of these?
A.Good
B.Fair
C.Poor
D.Excellent
Answer is A
Answer:
A. good
Step-by-step explanation:
it is in the range of 660-749.
Answer:
"Good"
Step-by-step explanation:
"Good" is appropriate, because the score 726 is between 660 and 749.
What is the change that occurs to the parent function f(x) = x^2 given the function f(x) = 2(x + 2)^2 + 1.
The graph is compressed by a factor of 2, moves 2 units to the right, and 1 unit up.
The graph is compressed by a factor of 2, moves 2 units to the left, and 1 unit up.
The graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up.
The graph is stretched by a factor of 2, moves 2 units to the right, and 1 unit up.
Answer:
The graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up.
Step-by-step explanation:
The base of the quadratic function is
[tex]f(x) = {x}^{2} [/tex]
We can transform this function to look narrower or wider.
Looking narrower is termed a stretch.
This happens when a>1
Looking wider is termed a compression.
This happens when 0<a<1
We can also
[tex]g(x) = a {(x + h)}^{2} + k[/tex]
+h moves the parent graph to the left by h units
-h moves the parent graph to the left by h units.
+ k moves the parent function up by k units
- k moves the parent function down by k units.
The change that occurs to
[tex]f(x) = {x}^{2} [/tex]
given
[tex]f(x) = 2( {x + 2)}^{2} + 1[/tex]
is that, the graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up
Therefore the last choice is the correct answer.
John walked 9 5/8 mile at an average speed of 1 3/4 mile per hour how long did it take John to walk this distance
so, we know his average speed is 1¾ of a mile in 1 hour, so how long is it to cover 9⅝ miles then?
[tex]\bf \begin{array}{ccll} miles&hour\\ \cline{1-2} 1\frac{3}{4}&1\\\\ 9\frac{5}{8}&x \end{array}\implies \cfrac{~~1\frac{3}{4}~~}{9\frac{5}{8}}=\cfrac{1}{x}\implies \cfrac{~~\frac{1\cdot 4+3}{4}~~}{\frac{9\cdot 8+5}{8}}=\cfrac{1}{x}\implies \cfrac{~~\frac{7}{4}~~}{\frac{77}{8}}=\cfrac{1}{x}[/tex]
[tex]\bf \cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{11}{~~\begin{matrix} 77 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}} =\cfrac{1}{x}\implies \cfrac{2}{11}=\cfrac{1}{x}\implies 2x=11\implies x=\cfrac{11}{2}\implies x=5\frac{1}{2}[/tex]
The required time is 5.5 hours.
Simple linear equation:Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1.
It is given that,
Speed=[tex]1\frac{3}{4}[/tex] mile per hour.
Distane:=[tex]9\frac{5}{8}[/tex] mile
[tex]Time=\frac{Distance}{Speed}[/tex]
Now, substituting the given values into the above formula we get,
[tex]T=\frac{\frac{77}{8} }{\frac{7}{4} }\\ =\frac{77\times4}{8\times 7} \\=\frac{11}{2}\\ T=5.5 hour[/tex]
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A distance of 150 km was covered by a motorcyclist traveling at an average speed of 75 km/h, by a bus at 60 km/h, a truck at 50 km/h, and a bicyclist at 20 km/h. How much time did each require to travel the entire distance? Explain why speed and the time needed to travel 150 km are inversely proportional quantities?
I need to know how to explain the last sentence.
Answer:
Motorcyclist: 2 hours
Bus: 2.5 hours
Truck: 3 hours
Bicyclist: 7.5 hours
Step-by-step explanation:
The equation of line CD is y = -2x - 2. What is the equation of a line parallel to line CD in slope-intercept form that contains point (4,5)?
Answer:
y=-2x+13
Step-by-step explanation:
Slope-intercept form of a line is y=mx+b where m is slope and b is y-intercept.
The slope of y=-2x-2 is -2 since m=-2.
A line that is parallel to the given line is going to have the same slope.
So we already know the equation we are looking for should be in the form y=-2x+b.
We just to need to find b.
We can use the given point on our line do that.
5=-2(4)+b
5=-8+b
8+5=b
13=b
So the equation is y=-2x+13.
Answer:
y = -2x+13
Step-by-step explanation:
The slope of the original line is -2 so you take that and plug it in with the points (4,5) in point slope form to get y-5 = -2(x-4), then you simplify to get y-5 = -2x+8 then y = -2x+13
Which is the end point of a ray
Answer:
Point S is the endpoint of a ray.
Step-by-step explanation:
A ray is a line with a single endpoint (or point of origin) that extends infinitely in one direction. Point S is the endpoint for rays SR, SU, and ST.
The ray's endpoint is Point S.
Given is a figure of an angle S being divided into two angles by the ray SU,
We need to find the endpoint of the ray,
So,
A ray's endpoint is the singular location where the ray comes to an end.
A ray is a line that emanates from an initial point known as the endpoint or origin and travels endlessly in one direction.
A ray, as opposed to a line segment, has no set length and travels in one direction indefinitely.
A ray's terminus, which is also its beginning point, is typically identified as a single point in space.
A ray is a line that has a single terminus (or point of origin) and travels in a single direction indefinitely.
The intersection of rays SR, SU, and ST is at point S.
Hence the ray's endpoint is Point S.
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how do you find the vertex of this equation: y = 6x-x2
Answer:
(3,9)
Step-by-step explanation:
This is a quadratic equation.
A quadratic in standard form is [tex]y=ax^2+bx+c[/tex].
If we compare [tex]y=ax^2+bx+c[/tex] to [tex]y=6x-x^2[/tex], we see there [tex]c=0,b=6,a=-1[/tex].
Now to find the vertex, we first find the x-coordinate of the vertex which is:
[tex]\frac{-b}{2a}[/tex].
So now plug in our values:
[tex]\frac{-6}{2(-1)}=\frac{-6}{-2}=3[/tex]
So the corresponding y-coordinate can be found by the equation that relates x to y: [tex]y=6x-x^2[/tex].
So we are plugging in 3 where we see x: [tex]y=6(3)-3^2=18-9=9[/tex].
So the vertex is (3,9).
Find the midpoint of the segment between the points (15,−9) and (−2,−18)
Answer:
(13/2, -27/2)
Step-by-step explanation:
The midpoint is found by using
midpoint = (x1+x2)/2, (y1+y2)/2
= (15+-2)/2, (-9+-18)/2
=13/2, -27/2
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. x2 +6x +8 = 0
Answer:
Step-by-step explanation:
The roots are very clear on the graph. I have left them unlabeled so that you can put the two points in.
The points are (-4,0) and (-2,0)
The graph was done on desmos which you can look up. The box in the upper left corner was filled with
y = x^2 + 6x + 8
Ellie wants to change her password which is ELLIE9 but with same letters and number. In how
many ways she can do that?
P = 256
P = 150
P = 200
P = 179
[tex]\dfrac{6!}{2!2!}-1=\dfrac{3\cdot4\cdot5\cdot6}{2}-1=180-1=179[/tex]
The number of passwords she can create is an illustration of permutations.
The number of ways to create the password is 179
The password is given as: ELLIE9
The number of characters in the password is:
[tex]n = 6[/tex]
L and E are repeated twice.
So, we have
[tex]L = 2[/tex]
[tex]E = 2[/tex]
The number of new passwords to create is then calculated as:
[tex]Passwords = \frac{n!}{L!E!} - 1[/tex] --- 1 represents the current password
This gives
[tex]Passwords = \frac{6!}{2!2!} - 1[/tex]
Expand
[tex]Passwords = \frac{6 \times 5 \times 4 \times 3 \times 2!}{2! \times 2 \times 1} - 1[/tex]
[tex]Passwords = \frac{6 \times 5 \times 4 \times 3 }{2 \times 1} - 1[/tex]
Simplify
[tex]Passwords = 180 - 1[/tex]
Subtract
[tex]Passwords = 179[/tex]
Hence, the number of ways to create the password is 179
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Nick is solving the equation 3x2=20−7x with the quadratic formula.
Which values could he use for a, b, and c?
a = 3, b = −7 , c = 20
a = 3, b = 7, c = −20
a = 3, b = −20 , c = 7
a = 3, b = 20, c = −7
Answer: Second option.
Step-by-step explanation:
Given a Quadratic equation in the form:
[tex]ax^2+bx+c=0[/tex]
It can be solve with the Quadratic formula. This is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]
In this case, given the Quadratic equation:
[tex]3x^2=20-7x[/tex]
You can rewrite it in the form [tex]ax^2+bx+c=0[/tex]:
- Subtract 20 from both sides of the equation:
[tex]3x^2-20=20-7x-20\\\\3x^2-20=-7x[/tex]
- Add [tex]7x[/tex] to both sides of the equation:
[tex]3x^2-20+7x=-7x+7x\\\\3x^2+7x-20=0[/tex]
Therefore, you can identify that:
[tex]a=3\\b=7\\c=-20[/tex]
Answer:
option B. a=3, b=7, c=-20
I just took the test :)
Step-by-step explanation:
Subtract (3x2 + 2x - 9) - (6x2 - 16). Write your answer as a polynomial
Answer:
The answer is -3x^2+2x+7 ....
Step-by-step explanation:
(3x2 + 2x - 9) - (6x2 - 16)
Open the parenthesis
Keep in mind that when you will open the parenthesis the signs of 2nd bracket will be multiplied by negative sign
3x^2+2x-9-6x^2+16
Arrange the terms:
3x^2-6x^2+2x+16-9
Solve the like terms:
= -3x^2+2x+7
Thus the answer is -3x^2+2x+7 ....
= (3x²+2x-9) - (6x²-16)
= 3x² + 2x - 9 - 6x² +16
= -3x² +2x + 7
While opening the brackets, make sure you change the signs accordingly. If there is a "-" sign outside the bracket then while opening the brackets, terms inside change their signs, which means "+" becomes "-" and vice versa.
What is the value of -4 squared +(5-2)(-6)
-------
I need help ASAP!!!
-4^2= 16
anytime you have a negative number squared it results in the positive version
ex. -4×-4 equals -16, except it should be positive instead of negative.
now 16+-10×-6
-10×-6=60
16+60=76
Please vote my answer brainliest. thanks!
In ABC, O is the centroid of the triangle and AO is 12.7 m. Find the length of OY and AY.
Answer:
[tex]\boxed{OY = 6.35 m} \\\boxed{AY=19.05 m}[/tex]
Step-by-step explanation:
The centroid of a triangle always cuts a triangle perfectly at 2/3.
What I mean by this is that the line that touches the tip of the triangle and touches the median of the base is cut into one third and its other part is cut into two thirds of the whole segment. This segment is AY.
Knowing this, I can tell that OY is 1/3 of the length of AO, which is given to be 12.7 m.
To find OY, make an equation where AO and OY add up to AY.
[tex]12.7+\frac{1}{3} x=x[/tex]The variable x represents the length of AY, and 1/3x represents the length of OY (because it is one-third of AY).
Solve the equation by subtracting 1/3x from both sides.
[tex]12.7=\frac{2}{3} x[/tex]Divide both sides by 2/3.
[tex]x=19.05[/tex]Now we know the length of AY (x). To find the length of OY substitute this value of x into 1/3x, which represents OY.
[tex]\frac{1}{3} (19.05)[/tex]
This gives us 6.35, which is the length of OY.
The final answers are:
OY = 6.35 mAY = 19.05 mWhat is sqrt12x^8/sqrt3x^2 in simplest form
[tex]\bf \cfrac{\sqrt{12x^8}}{\sqrt{3x^2}}~~ \begin{cases} 12=&2\cdot 2\cdot 3\\ &2^2\cdot 3\\ x^8=&x^{4\cdot 2}\\ &(x^4)^2 \end{cases}\implies \cfrac{\sqrt{2^2\cdot 3(x^4)^2}}{\sqrt{3x^2}}\implies \cfrac{2\stackrel{x^2}{~~\begin{matrix} x^4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} ~~\begin{matrix} \sqrt{3} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ ~~\begin{matrix} \sqrt{3} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 2x^2[/tex]
Answer:
2x^3 (C on edge)
Step-by-step explanation: