Answer:
see below
Step-by-step explanation:
2/3 ÷ 4
We use copy dot flip
The flip means make a reciprocal of the second number
2/3 * 1/4
Multiply the numerators
2*1 = 2
Multiply the denominators
3*4 =12
Put the numerator over the denominator
2/12
Simplify
1/6
To use equivalent fractions to find the quotient of \( \frac{2}{3} \) ÷ 4, follow these steps:
### Step 1: Understand the Operation
Division of fractions can be thought of as multiplying by the reciprocal. The reciprocal of a number a is simply \( \frac{1}{a} \).
### Step 2: Find the Reciprocal of the Divisor
The divisor here is the whole number 4. Its reciprocal is \( \frac{1}{4} \).
### Step 3: Multiply the Dividend by the Reciprocal of the Divisor
Instead of dividing \( \frac{2}{3} \) by 4, you can multiply \( \frac{2}{3} \) by \( \frac{1}{4} \).
### Step 4: Perform the Multiplication
Now, multiply the two fractions:
\[ \frac{2}{3} \times \frac{1}{4} = \frac{2 \cdot 1}{3 \cdot 4} \]
This results in a new fraction:
\[ \frac{2}{12} \]
### Step 5: Simplify the Resulting Fraction
Finally, you need to simplify the fraction to its simplest form. To do that, find the greatest common factor (GCF) of the numerator and the denominator and divide both by this number.
For \( \frac{2}{12} \), the greatest common factor is 2. So we divide both the numerator and the denominator by 2:
\[ \frac{2 \div 2}{12 \div 2} = \frac{1}{6} \]
### Conclusion
Therefore, the quotient of \( \frac{2}{3} \) ÷ 4 is \( \frac{1}{6} \). This is the simplest form of the fraction you obtain when \( \frac{2}{3} \) is divided by 4.
The equation tan(x- pi/3) is equal to _____.
Answer:
D
Step-by-step explanation:
we can use the formula of tan(A-B) to solve this equation .
The formula is
[tex]tan(A-B)= \frac{tanA-tanB}{1+tanA.tanB}[/tex]
In our question , A is x and B is [tex]\frac{\pi }{3}[/tex]
so when we apply these in the question we get
[tex]tan(x-\frac{\pi }{3} )=\frac{tanx-tan\frac{\pi }{3} }{1+tanx.tan\frac{\pi }{3} }[/tex]
Now since [tex]tan\frac{\pi }{3} = \sqrt{3}[/tex]
we get
[tex]tan(x-\frac{\pi }{3} )=\frac{tanx-\sqrt{3} }{1+\sqrt{3} tanx.} }[/tex]
so correct option is
D
Can you help me with this question please? I will reward 20 points for best answer.
* You don't have to solve the problem for me, I just want to know the formula and how to solve it.
"When the fundraiser began, 600 people wanted to purchase the dance troupe’s T-shirts at $12 per T-shirt, but as the group increased the price of their T-shirts, they noticed a fall in the demand. For every $1 increase in price, the demand fell by 50 shirts. The dance troupe’s initial supply was short by 210 T-shirts which corresponded to an initial price of $9.75. For every $1 increase in price, they ordered 40 more T-shirts. Write a system of linear equations to represent both the demand and supply for the T-shirts. Let q represent the quantity of T-shirts and p represent the price."
Answer:
Demand: q = -50p + 1200
Supply: q = 40p
Step-by-step explanation:
First let's define our variables.
q = quantity of T-shirts
p = price
We know that when p = 12, q = 600. When p increases by 1, q decreases by 50. So this is a line with slope -50 that passes through the point (12, 600). Using point-slope form to write the equation:
q - 600 = -50 (p - 12)
Converting to slope-intercept form:
q - 600 = -50p + 600
q = -50p + 1200
Similarly, we know that when p = 9.75, q = 600 - 210 = 390. When p increases by 1, q increases by 40. So this is a line with slope 40 that passes through the point (9.75, 390). Using point-slope form to write the equation:
q - 390 = 40 (p - 9.75)
Converting to slope-intercept form:
q - 390 = 40p - 390
q = 40p
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.
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
#SPJ3
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
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
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]
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.
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.
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.
Use the properties of exponents to rewrite the expression.
(-3yz)(-3yz)(-3yz)(-3yz)
Answer:
Answer is 81y^4z^4
Step-by-step explanation:
The expression is (-3yz) (-3yz) (-3yz) (-3yz).
Since all the four terms have power 1:
(-3yz)^1 (-3yz)^1 (-3yz)^1 (-3yz)^1
We know that we can add the powers if the terms have same base
So,
=(-3yz)^1+1+1+1
=(-3yz)^4
=(-3)^4(y)^4(z)^4.
If the power is an even number than the negative sign changes into positive sign.
=3^4y^4z^4
=81y^4z^4
Thus the answer is 81y^4z^4....
In the first term, 5 is a . In the second term, (3y + 13) is a . In the third term, -1 is a .
The complete statements of the expression are
In the first term, 5 is a coefficientIn the second term, (3y+ 13) is a factorIn the third term, -1 is a constantHow to complete the statements in the expression
From the question, we have the following parameters that can be used in our computation:
5x - 8(3y + 13) - 1
Consider an expression
Ax + b
Where x is the variable, we have
A is a coefficientA is a factorb is a constantUsing the above as a guide, we have the following:
In the first term, 5 is a coefficient
In the second term, (3y+ 13) is a factor
In the third term, -1 is a constant
Question
Use the given expression to complete the statements.
5x– 8(3y + 13) – 1
In the first term, 5 is a _____
In the second term, (3y+ 13) is a ______
In the third term, -1 is a ______
Which steps will verify that is a rectangle
Answer:
1) Are there 4 right angles? (90° angles)
2) Are there 2 sets of parallel lines?
3) Are there 2 sets of congruent lines?
4) Are there a set of congruent diagonals?
~
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]
582.5 divided by 2.5
Answer:
You'll get your answer as : 233
Use the law of sines to find the value of a.
Law of sines:
What is the best approximation of the value of a?
2.4 cm
2.7 cm
3.0 cm
3.3 cm
Answer:
3.0 cm
Step-by-step explanation:
The Law of Sines states the relationship between the sides and the angles of non-right (oblique) triangles.
In the given triangle,the following relation holds;
[tex]\frac{4.7}{sin(95)}=\frac{a}{sin(40)}\\\\a=\frac{4.7}{sin(95)}*sin(40)\\\\a=3.03[/tex]
Answer:
Option C. a = 3.0 cm
Step-by-step explanation:
We have to find the value of a from the given triangle ABC.
By applying sine rule in ΔABC
[tex]\frac{sin95}{4.7}=\frac{sin40}{a}[/tex]
Now we cross multiply in the given equation.
a(sin95°) = 4.7(sin40°)
a(0.9962) = 4.7(0.6428)
a = [tex]\frac{4.7(0.6428)}{0.9962}[/tex]
a = 3.03 cm ≈ 3.0 cm
Therefore, a = 3.0cm Option C. will be the answer.
The sum of two angles measures is 95 degrees. Angle 2 is 40 degrees smaller than 2 times angle 1. What are the measures of the two angles in degrees?
Answer:
<1 = 45
<2 = 50
Step-by-step explanation:
Let <1 = x
Let <2 = y
=============
x + y = 95
y = 2*x - 40
=============
I think the easiest way to do this is to substitute the second or bottom equation into the top equation. Substitute for y
x + 2x - 40 = 95 Combine like terms on the left.
3x - 40 = 95 Add 40 to both sides.
3x -40+40 = 95+40 Combine
3x = 135 Divide by 3
x = 45
=================
Now use the top equation to solve for y
x + y = 95
45 + y = 95 Subtract 45 from both sides.
45 - 45 + y = 95 -45 Combine
y = 50
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
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
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]
A cylinder has a base diameter of 16 inches and a height of 18inches. What is the volume in cubic inches, of the nearest tenths place ?
Answer:
3619.11 cubic inches
Step-by-step explanation:
volume of a cylinder is [tex]V=\pi r^2h[/tex]
diameter is 16 in, so radius (r) is 8 in
plug in values: [tex]V=\pi 8^2(18) = 3619.11[/tex] cubic inches
The volume of a cylinder with a diameter of 16 inches and a height of 18 inches is calculated using the formula V = πr²h, which results in approximately 3617.3 cubic inches when rounded to the nearest tenths place.
To calculate the volume of a cylinder, we use the formula V = πr²h. Given that the diameter of the cylinder is 16 inches, which means its radius (r) is half of that, 8 inches. The height (h) of the cylinder is given as 18 inches. To find the volume, first square the radius, then multiply by π (approximated as 3.14 for this purpose), and then by the height.
So, the calculation looks like this:
Therefore, the volume of the cylinder, rounded to the nearest tenth place, is 3617.3 cubic inches.
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.
A triangle has two congruent sides that measure 8.7 cm and 12.3 cm. Which could be the measure of the third side
Answer:
Option C. 15 cm
Step-by-step explanation:
The correct question is
A triangle has two sides that measure 8.7 cm and 12.3 cm. Which could be the measure of the third side?
A. 2.6 cm
B. 3.6 cm
C. 15 cm
D. 21 cm
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Analyze two cases
Let
x ----> the length of the third side
First case
x+8.7 > 12.3
x>12.3-8.7
x> 3.6 cm
Second case
12.3+8.7 > x
21 > x
Rewrite
x < 21 cm
Please help me out!!!
Answer:
8
Step-by-step explanation:
Use the Pythagorean theorem.
a^2 + 6^2 = 10^2
a^2 + 36 = 100
a^2 = 64
a = 8
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]
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
Divide in simplest form
Well, you can’t really divide a fraction because it is already a division problem. So we have to do the opposite.
9/4 divided by3/16
Leave the first fraction alone
Change the division sign into a multiplication sign.
Then switch the denominator and numerator of the second fraction, this new fraction is called a reciprocal.
Now multiply the numerators together and the denominators together and simplify.
You get: 144/12
Simplified the answer is : 12
Carrie made 127 brownies and packed 13 in each box. How many boxes are
packed and how many brownies are left over?
9 boxes and brownies left over
Answer:
9 boxes are packed and 10 brownies are left over.
Step-by-step explanation:
Carrie made 127 brownies and packed 13 in each box.
The number of boxes packed are; [tex]\frac{127}{13}[/tex] = 9[tex]\frac{10}{13}[/tex]
Which means that 9 boxes were packed and 10 brownies were left over.
42 base X + 53 base X = 125 base X
[tex]42_x+53_x=125_x\\4\cdot x^1+2\cdot x^0+5\cdot x^1+3\cdot x^0=1\cdot x^2+2\cdot x^1+5\cdot x^0\\4x+2+5x+3=x^2+2x+5\\x^2-7x=0\\x(x-7)=0\\x=0 \vee x=7[/tex]
There is no numeral system with base 0, so [tex]x=7[/tex].
g(x) = x3 + 6x2 + 12x + 8
Determine the function’s value when x = −1.
Answer:
g(-1) = 1
Step-by-step explanation:
Synthetic division is by far the fastest way to evaluate this function at x = -1. Set up synth. div. as follows:
-1 ) 1 6 12 8
-1 -5 -7
----------------------
1 5 7 1
since the remainder is 1, g(-1) = 1