Answer:
(3x - 1)(5x^2 + 2)
Step-by-step explanation:
15x^3 - 5x^2 (the first two terms) have the common factor 5x^2, so that
15x^3 - 5x^2 = (5x^2)(3x - 1).
Likewise, 6x - 2 = 2(3x - 1).
Thus, 15x^3 - 5x^2 +6x-2 can be written as (3x - 1)(5x^2 + 2)
For retirement, Mike invested $2,500 in an account that pays 6% annual interest, compounded quarterly. Find the value of his investment after 10 years.
$2,035.05
$1,609.05
$4,109.05
$4,535.05
Answer:
$4,535.05
Step-by-step explanation:
Final answer:
The correct option is $4,535.05. To find the value of Mike's investment after 10 years with compound interest, use the formula A = P(1 + r/n)^(nt) with the given values. The final value of Mike's investment is $4,535.05.
Explanation:
Mike invested $2,500 in an account with 6% annual interest compounded quarterly. We can use the compound interest formula: A = P(1 + r/n)^(nt) to calculate the value after 10 years.
Here's the calculation: A = $2,500(1 + 0.06/4)^(4*10) = $4,535.05. Therefore, the value of Mike's investment after 10 years is $4,535.05.
Shawna and her best friend Keisha go shopping. The function p(t) = 3x +2x-4x2+ 21 represents how much money each girl spent based on the number of hours they were shopping. If Shawna and Keisha each go shopping for 2 hours, how much money did they spend together?
Answer:
[tex]\$30[/tex]
Step-by-step explanation:
we have
[tex]p(t)=3x+2x-4x^{2}+21[/tex]
Find the amount of money that each girl spent
For t= 2 hours
[tex]p(2)=3(2)+2(2)-4(2)^{2}+21[/tex]
[tex]p(2)=10-16+21[/tex]
[tex]p(2)=\$15[/tex]
Find the amount of money that they spend together
Multiply by 2 the amount of money that each girl spent
[tex](2)\$15=\$30[/tex]
Shawna and Keisha spent $30 together when each of them went shopping for 2 hours.
It seems there might be a typo in the function p(t) you provided. It should be[tex]\( p(t) = 3t + 2t - 4t^2 + 21 \)[/tex], where t represents the number of hours spent shopping.
To find out how much money Shawna and Keisha spent together when each of them went shopping for 2 hours, we need to evaluate the function p(t) at [tex]\( t = 2 \)[/tex] and then add the results.
Let's plug in t=2 into the function p(t):
[tex]\[ p(2) = 3(2) + 2(2) - 4(2)^2 + 21 \][/tex]
[tex]\[ = 6 + 4 - 16 + 21 \][/tex]
[tex]\[ = 10 - 16 + 21 \][/tex]
[tex]\[ = 15 \][/tex]
Multiply by 2 since $15 is for each girl = 2*$15= $30
what is the value of x in this figure?
Answer:
D
Step-by-step explanation:
In a 30-60-90 triangle, if the short leg is x, then the long leg is x√3, and the hypotenuse is 2x.
Here, the hypotenuse is 10. So the short leg is:
10 = 2x
x = 5
If the short leg is 5, then the long leg is 5√3.
The volume, V, of a rectangular prism is determined using the formula, where / is the length, w is the width, and his the
height of the prism. Carltren solves for w and writes the equivalent equation w=
Using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches,
and a length of 3.2 inches?
Answer:
[tex]\large\boxed{width=4.5\ in}[/tex]
Step-by-step explanation:
[tex]V=lwh\qquad\text{divide both sides by}\ lh\\\\\dfrac{V}{lh}=\dfrac{wlh}{lh}\\\\w=\dfrac{V}{lh}\\\\\text{We have}\\\\V=138.24\ in^3\\h=9.6\ in\\l=3.2\ in\\\\\text{Substitute:}\\\\w=\dfrac{138.24}{(3.2)(9.6)}=\dfrac{138.24}{30.72}=4.5\ in[/tex]
The volume of a rectangular prism is calculated using the formula V = lwh, where V is the volume of the prism, l and w are the length and width of the base of the prism, respectively, and h is the height of the prism.
Rewrite the formula to find the width of the base of the prism if the volume, length of the base, and height of the prism are already known
Answer:
The width of the base = the volume ÷ (length × height)
w = V/lh
Step-by-step explanation:
* Lets take about how to re-arrange any formula
- The formula of the volume of the rectangular prism is:
V = lwh, where l is the length of the base , w is the width of the
base and h is the height of the prism
- To find the formula of the width from the formula of the volume,
we must isolate the width in one side and all other dimensions in
other side
∵ V = lwh ⇒ divide both sides by l and h
∵ V/(lh) = (lwh)/(lh) ⇒ cancel lh up with lh down
∴ V/(lh) = w
∴ w = V/(lh)
∴ w = V ÷ (lh)
* The width of the base = the volume ÷ (length × height)
Answer:
Width=[tex]\frac{Volume}{(Length)*(height)}[/tex]
Step-by-step explanation:
You only have to clear the start of the formula:
V=L*W*H
Since lenght and height are multiplying the width of the base you have to clear them and take them to the other side of the equation dividing:
[tex]\frac{V}{l*h}[/tex]
So you can calculate the width of the base by dividing the volume between the product of the Height times the length.
Solve 2x^2 - 7x - 15 = 0.
a, (3/2,-5)
b (-3/2,5)
c ()
For this case we must solve the following quadratic equation:
[tex]2x ^ 2 -7x -15 = 0[/tex]
We must apply the following formula:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
We have to:
[tex]a = 2\\b = -7\\c = -15[/tex]
Substituting we have:
[tex]x = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (2) (- 15)}} {2 (2)}\\x = \frac {7 \pm \sqrt {49 + 120}} {4}\\x = \frac {7 \pm \sqrt {169}} {4}\\x = \frac {7 \pm13} {4}[/tex]
Thus, the solutions are:
[tex]x_ {1} = \frac {7 + 13} {4} = \frac {20} {4} = 5\\x_ {2} = \frac {7-13} {4} = \frac {-6} {4} = - \frac {3} {2}[/tex]
ANswer:
[tex]x_ {1} = 5\\x_ {2} = - \frac {3} {2}[/tex]
Answer:
{-3/2, 5} would be the right choice
Which of the following best describes the volume of a solid
Answer:
Option B
Step-by-step explanation:
we know that
The volume of a solid is the amount of space occupied by a solid object. The volume of solid is expressed as cubic units.
therefore
It is the amount of three -dimensional space inside the solid
Answer:
B. It is the amount of three-dimensional space inside the solid.
Step-by-step explanation:
Volume is defined as the amount of three-dimensional space enclosed by a close surface. Volume is the product of the three dimensions of a body. The SI unit of volume is m³.
eg. Volume of cube = a³
Volume of cuboid = L×B×H
Volume of sphere = [tex]\frac{4}{3}\pi r^3[/tex]
Volume of cylinder = πr²h
Volume of cone = [tex]\frac{1}{3}\pi r^2h[/tex]
list all the factors of 96
[tex]\text{Hey there!}[/tex]
[tex]\text{1(96) = 96}[/tex]
[tex]\text{2(48) = 96}[/tex]
[tex]\text{4(24) = 96}[/tex]
[tex]\text{6(16) = 96}[/tex]
[tex]\text{8(12) = 96}[/tex]
[tex]\text{The factors of 96 are: 1, 2, 3, 4, 6,8, 12, 16, 24, 32, 48, 96}[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Select the correct answer from each drop-down menu. Desiree is given an aptitude test with 50 multiple-choice questions. For every correct answer, Desiree will get 3 points. For every wrong answer, 1 point will be deducted. For every question unanswered, 0.5 point is deducted. Desiree did not leave any question unanswered and gets 110 points on the test. If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is and the equation will have .
The equation that represents the given situation is 3x - (50 - x) - 0.5(50 - x) = 110. This equation is derived from the fact that Desiree gets 3 points for each correct answer, 1 point deducted for each wrong answer, and 0.5 point deducted for each unanswered question.
Explanation:The equation that represents the given situation is 3x - (50 - x) - 0.5(50 - x) = 110.
This eqUation is derived from the fact that Desiree gets 3 points for each correct answer, 1 point deducted for each wrong answer, and 0.5 point deducted for each unanswered question.
By solving the equation, you can find the value of x, which represents the number of questions Desiree answered correctly.
Solve.
1/3s – 6 < 24
{s | s < 6}
{s | s < 10}
{s | s < 54}
{s | s < 90}
The answer is:
The fourth option,
{s | s <90}
Why?Solving inequalities involves almost the same process of solving equalities for variable isolation.
We are given the inequality:
[tex]\frac{1}{3}s-6<24[/tex]
So, solving we have:
[tex]\frac{1}{3}s-6<24\\\\\frac{1}{3}s-6+6<24+6\\\\\frac{1}{3}s<30\\\\\frac{1}{3}s*3<30*3\\\\s<90[/tex]
Hence, we have that the correct option is the fourth option:
{s | s <90}
Have a nice day!
Answer:
{s | s < 90} D is the correct answer
Step-by-step explanation:
It is.
Write 2,929.874 in
word form
What is the answer to 4 plus 4
The answer to 4+4 is 8
4+4=8
4) Which equation represents a line parallel to the line y = 5x - 6?
A) y = 2x + 5
(B) y = 5x-2
C) y=-x-5
D) y=-2x-5
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 5x - 6 is in this form with slope m = 5
• Parallel lines have equal slopes
y = 5x - 2 is the only line with a slope of 5 → B
Parallel lines have the same slope. As the slope of the original line is 5, the line y = 5x - 2 represents a line parallel to the original line y = 5x - 6.
Explanation:When two lines are parallel, their slopes are equal. Using this fact, we can identify which equation represents a line parallel to the line y = 5x - 6 by comparing their slopes. The slope of the given line is 5, as it's the coefficient before x in the equation y = mx + b, where m is the slope.
Looking at the provided options:
A) y = 2x + 5, this is not parallel as the slope is 2, not 5. (B) y = 5x-2, it's parallel as the slope is 5, which matches the slope of the original line.C) y=-x-5, this is not parallel as the slope is -1, not 5. D) y=-2x-5, this is also, not parallel as the slope is -2, not 5. Learn more about Parallel lines here:https://brainly.com/question/29762825
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Which of these points lies on the line described by the equation below?
y-3 = 5(x-9)
O A. (3,9)
O B. (9,3)
O C. (-9, -3)
O D. (-3, -9)
Answer:
The answer should be: B. (9,3)
Answer: B. (9,3)
Step-by-step explanation:
To solve this problem, we start organizing the equation to the Slope intercept form:
[tex]y=5(x-9)+3[/tex]
[tex]y=5x-45+3[/tex]
[tex]y=5x-42[/tex]
Where 5 is the positive slope of the line, and -42 is the y-axis intercept. knowing the y-intercept, we may infer that choices C or D are incorrect, because values must be lower than -42. Thus, we replace the x value of choices A and B to verify which one applies:
Choice A
[tex]y=5(3)-42[/tex]
[tex]y=-27[/tex]
[tex]27\neq 9[/tex]
Choice B
[tex]y=5(9)-42[/tex]
[tex]y=3[/tex] Correct!
Solve angle ABC by using the measurements angle ABC = 90°, angle BAC = 40°, and a = 10. Round measures of sides to the
nearest tenth and measures of angles to the nearest degree.
Answer:
∠ACB==50°
b=15.6 units
c=11.9 units
Step-by-step explanation:
step 1
Find the measure of angle BCA
we know that
The sum of the interior angles of a triangle must be equal to 180 degrees
∠ABC+∠BAC+∠ACB=180°
substitute the given values
90°+40°+∠ACB=180°
∠ACB=180°-130°=50°
step 2
Find the measure of side b
Applying the law of sines
a/sin(∠BAC)=b/sin(∠ABC)
substitute the given values
10/sin(40°)=b/sin(90°)
b=10/sin(40°)
b=15.6 units
step 3
Find the measure of side c
Applying the law of sines
c/sin(∠ACB)=a/sin(∠BAC)
substitute the given values
c/sin(50°)=10/sin(40°)
c=[10/sin(40°)]*sin(50°)
c=11.9 units
ANSWER:
C=11.9
ABC=90 deg.
BAC=40 deg.
A=10
Which values represent the independent variable?
(-2, 4), (3,-2), (1, 0), (5,5)
A. {-2,3, 1,5)
B. (4, -2,0,5)
C. (-2,4,3, -2)
D. (-2,-1,0,5)
someone please help
A company manufactures its product at a cost of $0.50 per item and sells it for $0.85 per item daily overhead is $600 how many items must be manufactured each day in order for the company to break even
so the company has an overhead of $600, usually that involves premises leasing and industrial equipment for the manufacturing of the product, that's cost. The cost to make each item is 50 cents, so if the company produces "x" items, their cost is 0.5x total.
so our cost equation C(x) = 0.5x + 600 <---- items' cost plus overhead.
the company sells the product for 85 cents, so if they sell "x" items, their total revenue or income will be 0.85x.
so our revenue equation is simply R(x) = 0.85x.
as you already know, the break-even point is when.... well, you break even, no losses but no gains either, how much you take in is the same amount that you shelled out, namely R(x) = C(x).
[tex]\bf \stackrel{R(x)}{0.85x}=\stackrel{C(x)}{0.5x+600}\implies 0.35x=600\implies x=\cfrac{600}{0.35} \\\\\\ x\approx 1714.285714285714\implies \stackrel{\textit{rounded up}}{x=1714}[/tex]
What value of x is in the solution set of 4x - 12 s 16 + 8x?
-10
-9
-8
-7
Answer:
-7
Step-by-step explanation:
4x-12=16+8x
-12-16=8x-4x
-28÷4=x
x=-7
Answer:
-7 :)
Step-by-step explanation:
factorise 21x^2-14y^2
Answer:
[tex]\large\boxed{21x^4-14y^2=7(3x^4-2y^2)=7(x^2\sqrt3-y\sqrt2)(x^2\sqrt3+y\sqrt2)}[/tex]
Step-by-step explanation:
[tex]21x^4-14y^2=7(3x^4-2y^2)\\\\=7\bigg((\sqrt3)^2x^{2\cdot2}-(\sqrt2)^2y^2\bigg)\qquad\text{use}\ (a^n)^m=a^{nm}\ \text{and}\ (ab)^n=a^nb^n\\\\=7\bigg((x^2\sqrt3)^2-(y\sqrt2)^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=7(x^2\sqrt3-y\sqrt2)(x^2\sqrt3+y\sqrt2)[/tex]
On the April 3 billing date, Michaelle Chappell had a balance due of $ 1495.39 on her credit card. From April 3 through May 2, Michaelle charged an additional $ 305.34 and made a payment of $ 800.
a) Find the finance charge on May 3, using the previous balance method. Assume that the interest rate is 1.8 % per month.
b) Find the new balance on May 3.
a) Finance Charge ≈ $18.01 the interest rate is 1.8 % per month.
b) The finance charge is approximately $18.01, and the new balance is approximately $1018.74.
To calculate the finance charge using the previous balance method, we'll need to follow these steps:
a) Find the finance charge on May 3:
Calculate the average daily balance for the billing period.
Average Daily Balance = (Total of daily balances) / (Number of days in the billing period)
Determine the number of days in the billing period (from April 3 to May 2). There are 30 days in this billing period.
Find the daily balances by considering the transactions during the billing period:
Daily balance from April 3 to May 2 = Previous balance on April 3 + Charges during the period - Payments during the period
Daily balance from April 3 to May 2 = $1495.39 + $305.34 - $800
Calculate the average daily balance:
Average Daily Balance = (Total of daily balances) / (Number of days in the billing period)
Average Daily Balance = [(1495.39 + 305.34 - 800) * 30] / 30
Average Daily Balance = $1000.73
Calculate the finance charge using the previous balance method:
Finance Charge = (Average Daily Balance) * (Monthly Interest Rate)
Finance Charge = $1000.73 * (0.018) [0.018 is the monthly interest rate as a decimal]
Finance Charge ≈ $18.01
b) Find the new balance on May 3:
New Balance = Previous balance + Charges during the period - Payments during the period + Finance Charge
New Balance = $1495.39 + $305.34 - $800 + $18.01
New Balance ≈ $1018.74
So, on May 3, the finance charge is approximately $18.01, and the new balance is approximately $1018.74.
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Final answer:
The finance charge on May 3 using the previous balance method is $26.92, assuming a monthly interest rate of 1.8%. The new balance on May 3, after adding the finance charge, additional charges, and subtracting the payment, is $1027.65.
Explanation:
To calculate the finance charge using the previous balance method, we take the balance due on the April 3 billing date, which was $1495.39, and apply the monthly interest rate of 1.8%. The charge is computed as follows:
Finance Charge = Previous Balance × Monthly Interest Rate
Finance Charge = $1495.39 × 0.018
Finance Charge = $26.91702
Since financial amounts are usually rounded to cents, the finance charge would be $26.92.
To find the new balance on May 3, we will take the previous balance and add the finance charge and any additional charges, then subtract any payments made. This looks like:
New Balance = Previous Balance + Finance Charge + Additional Charges - Payments
New Balance = $1495.39 + $26.92 + $305.34 - $800
New Balance = $1027.65
Therefore, the new balance on May 3 is $1027.65.
An object is translated by (x + 4, y - 2). If one point in the image has the coordinates (5, -3), what would be the coordinates of its pre-image? (9, -5) (1, -5) (9, -1) (1, -1)
Answer:
(1,-1)
Step-by-step explanation:
A translation of (x,y) ⟶ (x + 4, y – 2) means that the coordinates of the pre-image have moved four units to the right and two units down.
To get the coordinates of the pre-image rom the image, we must reverse the procedure.
That is, we must go two units up and four units to the left.
The coordinates of Point P' are (5, -3), so those of P must have been (1, -1).
Answer:
(1,-1) is the answer
Step-by-step explanation:
Hope this helps
Please help with this
Answer:
16/9
Step-by-step explanation:
Step 1 : {Apply exponent rule}
Step 2: repeat
the equation for the circle below is x ^2 + y^2 = 100. what is the length of the circles radius?
Answer: 10 units.
Step-by-step explanation:
The equation of the circle in Center-radius form is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where the center is (h,k) and "r" is the radius.
The equation of the circle given is:
[tex]x ^2 + y^2 = 100[/tex]
You can observe that is written in Center-radius form.
Then, you can identify that:
[tex]r^2=100[/tex]
Knowing this, you need to solve for "r" to find the lenght of the radius.
This is:
[tex]r=\sqrt{100}\\\\r=10[/tex]
Therefore, the lenght of the radius is 10 units.
At the movie theatre, child admission is $5.20 and adult admission is $8.60 . On Thursday, twice as many adult tickets as child tickets were sold, for a total sales of $868.00 . How many child tickets were sold that day?
Answer:
The number of child tickets = 39
Step-by-step explanation:
It is given that,child admission is $5.20 and adult admission is $8.60
Total sales = $868.00
To find the number of child tickets
Le 'x' be the number of children then number of adults = 2x
(x * 5.20) + (2x * 8.60) = 868
5.2x + 17.2x = 868
22.4x = 868
x = 868/22.4
= 38.75 ≈ 39
Therefore the number of child tickets = 39
Select the correct answer.
Which phrase best describes the word definition in an axiomatic system?
A. the accepted meaning of a term
B.
the statement of an axiom
c.
an accepted fact that is not proven
D.
a fact proven by using logic
Reset
Next
Answer:
d
Step-by-step explanation:
In an axiomatic system, the definition is 'the accepted meaning of a term'. An axiom is an accepted unproven fact. A fact proven by using logic is a theorem.
Explanation:In an axiomatic system, the phrase that best describes the 'definition' would be option A - 'the accepted meaning of a term.' An axiomatic system is a sort of framework within mathematics where definitions, axioms, and propositions work together. A definition in this context offers the precise description or meaning of a term used within that mathematical system.
An axiom (option B) would most accurately be described as an accepted fact that is not proven, but instead accepted as truth within an axiomatic system (option C). A fact proven by using logic, on the other hand, would be a theorem (option D).
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How to solve for y and simplify
-3y = -6/5
-3y(5) = (-6/5)(5)
-15y = -6
y = -6/-15
y = 6/15
y = 2/5
find the equation of a line in point slope form with a slope of 3 going through the point (4,-6)?
Answer:
Equation of line: y=3x-18
Step-by-step explanation:
Point: (4,-6) and slope = 3
[tex]y+6=3(x-4)[/tex]
y=3x-18
Answer:
y + 6 = 3(x - 4)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = 3 and (a, b) = (4, - 6), hence
y - (- 6) = 3(x - 4), that is
y + 6 = 3(x - 4) ← in point- slope form
what relationship is used to find the slope of a line?
Answer:
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
Step-by-step explanation:
slope formula
Answer:
[tex]\frac{rise}{run}[/tex]
Step-by-step explanation:
The slope of a line is calculated by dividing the rise by the run.
In the attached example, the rise is 1 and the run is 2, so the slope is 1/2. The rise is the distance the line goes up. The run is the distance the line goes to the right for each (rise) units. The line below goes up 1 and right 2 over and over again.
Gary is selling paperback and hardcover books at a yard
sale. He charges $2 for each paperback. He earned $10
in sales of hardcover books. He earned $20 selling books
at the yard sale. How many paperbacks did he sell?
Answer:
Gary sold 5 paperback books
Step-by-step explanation:
each book is equal to $2 and $10 were made in Hardcover
So that only leaves us with ten unaccounted dollars
5x=10
Each book or (x) in this case is two dollars
so it will come out to be five books
for any real number b, square root b^2=
Answer:
IbI
Step-by-step explanation:
The square root of [tex]\( b^2 \)[/tex] is [tex]\( b \),[/tex] as the square root of any positive number is its positive root.
The square root of [tex]\( b^2 \)[/tex] can be calculated step by step as follows:
Step 1:
Understand the concept.
The square root of a number is a value that, when multiplied by itself, gives the original number. For any real number [tex]\( b \), \( b^2 \)[/tex] represents [tex]\( b \)[/tex]multiplied by itself.
Step 2:
Apply the square root property.
The square root of [tex]\( b^2 \)[/tex] is [tex]\( b \)[/tex] because [tex]\( b \times b = b^2 \).[/tex] The square root of any positive number is its positive root.
Step 3:
Interpret the result.
Since the square root of [tex]\( b^2 \)[/tex] is [tex]\( b \),[/tex] regardless of the value of \( b \), the square root of [tex]\( b^2 \)[/tex] is simply [tex]\( b \)[/tex] . This property holds true for any real number [tex]\( b \).[/tex]
So, the square root of [tex]\( b^2 \)[/tex] is [tex]\( b \).[/tex]