Answer:
The given expression is equivalent to 3(2^(3/8))x.
Step-by-step explanation:
The given expression (3 root 8^1/4 x) can be written as:
3√(8^(1/4))x
we know that 2^3 = 8
= 3√(2^(3/4))x
We know that √x = (x)^(1/2)
= 3(2^((3/4)(1/2))x
Powers multiply with each other, 3*1/4*2 = 3/8
= 3(2^(3/8))x
if f(x)= -8x+4, then f^-1(x)=
Answer:
[tex]f^{-1}[/tex](x) = [tex]\frac{4-x}{8}[/tex]
Step-by-step explanation:
let y = f(x) and rearrange making x the subject
y = - 8x + 4 ( add 8x to both sides )
8x + y = 4 ( subtract y from both sides )
8x = 4 - y ( divide both sides by 8 )
x = [tex]\frac{4-y}{8}[/tex]
Change y back into terms of x
[tex]f^{-1}[/tex](x) = [tex]\frac{4-x}{8}[/tex]
Translate the word phrase into a math expression.
15 fewer than the product of 4 and a number.
(Pls help immediately)
Answer:
4x-15 Rate me 5 stars if its correct
Step-by-step explanation:
Answer:
(4 * x) - 15
Step-by-step explanation:
"15 fewer" means "subtract 15" or - 15
"the product of 4 and a number":
Product is another word for "multiply".
A number is generally set as a variable, "x".
The product of 4 and a number means 4 * x, or 4x.
Set the equation:
4x - 15 is your answer.
~
Find the image of A(4, -2) after it is reflected over the line y= 2, then reflected over the line x = 2.
(-8,6)
O (0.-2)
O (0,6)
(-8, -2)
Answer:
(0,6)
Step-by-step explanation:
we have the point
A(4,-2)
step 1
Find the image after it is reflected over the line y= 2
The distance of the point A to the line y=2 is equal to 4 units
so
The rule of the reflection is equal to
(x,y) ------> (x,2+4)
A(4,-2) ---> A'(4,6)
step 2
Find the image after it is reflected over the line x= 2
The distance of the point A' to the line x=2 is equal to 2 units
so
The rule of the reflection is equal to
(x,y) ------> (2-2,y)
A'(4,6) ---> A''(0,6)
Which best explains what determines weather a number is irrational?
Answer:
Step-by-step explanation:
B
What are the right choices
Answer:
(0.1,1.1)
Step-by-step explanation:
we have
[tex]f(x)=3^{x}[/tex]
[tex]g(x)=-log(x)[/tex]
Solve the system of equations by graphing
The solution is the intersection point both graphs
The solution is the point (0.081,1.093)
see the attached figure
Round to the nearest tenth ----> (0.1,1.1)
Given that ƒ(x) = x² + 5x, evaluate ƒ(-2).
-6
-14
7
f(-2) means replace x in the equation with -2, then solve:
-2^2 +5(-2)
Simplify:
4 + -10
Add:
-6
Which parent function is represented by the table?
Answer:
Step-by-step explanation:
Notice that for each unit increase in x, y increases by 1 unit. Thus, the parent function is y = x.
Answer:
f(x)=x
Step-by-step explanation:
We are given with a table, Lets look at the value of x and y
The value of y is constantly increasing and the value of x is also increasing constantly. So it is a table for a linear equation.
the value of x and y are same, so the equation of the line is
y=x
when x=-2 the value of y=-2
when x=1 the value of y=1
Hence , the parent function is [tex]f(x)=x[/tex]
plzzzzz answer guys!!!
Answer:
Sorry if its wrong i hope it helps!
A. 90 degrees
B. 45 degrees
C. 30 degrees
D. 120 degrees
For this case we have by definition, that each of the four internal angles of a square measure 90 degrees.
If we draw the diagonals of the square then the angles are divided by two, that is:
[tex]\frac {90} {2} = 45[/tex]
Thus, angle 3 measures 45 degrees.
[tex]A3 = 45[/tex]
By definition, the sum of the internal angles of a triangle is 180 degrees.
So:
[tex]A2 + A3 + 90 = 180\\A2 = 180-90-A3\\A2 = 180-90-45\\A2 = 45[/tex]
Thus, angle 2 measures 45 degrees.
Answer:
45 degrees
Please can someone help.
Answer:
CD = 12.7 cmStep-by-step explanation:
[tex]\text{Use the Pythagorean theorem to calculate the length of the CB:}\\\\CB^2+BA^2=AC^2\\\\CB^2+6^2=12^2\\\\CB^2+36=144\qquad\text{subtract 36 from both sides}\\\\CB^2=108\to CB=\sqrt{108}\\\\CB=\sqrt{36\cdot3}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\CB=\sqrt{36}\cdot\sqrt3\\\\CB=6\sqrt3[/tex]
[tex]\text{Use sine to calculate the length of CD:}\\\\sin\theta=\dfrac{opposite}{hypotenuse}\\\\\theta=55^o\\opposite=6\sqrt3\\hypotenuse=CD\\\\\sin55^o\approx0.8192\qquad(look\ at\ the\ picture)\\\\\text{Substitute:}\\\\0.8192=\dfrac{6\sqrt3}{CD}\\\\0.8192=\dfrac{10.3923}{CD}\qquad\text{multiply both sides by}\ CD\\\\0.8192CD=10.3923\qquad\text{divide both sides by 0.8192}\\\\CD\approx12.7[/tex]
3 + (5 + 7) = (3 + 5) + 7 what property is shown
Answer:
Properties of Real Numbers ...
Step-by-step explanation:
Commutative Property of Multiplication (Numbers) 2 • 10 = 10 • 2
Associative Property of Addition (Numbers) 5 + (6 + 7) = (5 + 6) + 7
Associative Property of Multiplication (Numbers) 6 • (3 • 2) = (6 • 3) • 2
Additive Identity (Numbers) 6 + 0 = 6
The equation demonstrates the Associative Property of Addition, stating that the grouping of numbers being added does not affect the sum.
Explanation:The property shown in the equation 3 + (5 + 7) = (3 + 5) + 7 is the Associative Property of Addition. According to this property, the grouping of numbers being added does not affect the sum. In other words, when adding three or more numbers, it doesn't matter how they are grouped in parentheses.
In this specific equation, we are adding 5 and 7 first, which gives us 12. Then, adding 3 to 12 gives us a sum of 15. On the other side of the equation, we first add 3 and 5 to get 8, and then add 8 to 7 to get the same sum of 15.
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Solve for x. x2 + x - 6 = 0
Answer:
x=2 x = -3
Step-by-step explanation:
x^2 + x - 6 = 0
Factor. What 2 numbers multiply to -6 and add to 1
-2 *3 = -6
-2+3 = -1
(x-2) (x+3) =0
Using the zero product property
x-2 =0 x+3 =0
x=2 x = -3
Estimate the value of 98.5 x 13?
To estimate the value of 98.5 x 13, round the final answer to the hundredths position. In this case, round up to 922.00.
Explanation:To estimate the value of 98.5 x 13, we can use the rounding rule that states if the first digit to be dropped is greater than 5, we round up. In this case, the digit in the thousandths place is greater than 5, so we round up to the hundredths position. Therefore, the estimated value is 922.00.
A rectangular garden has a perimeter of 48 cm and an area of 140 sq. cm. What is the width of this garden? A.) 12 cm B.) 10 cm C.) 10 in. D.) 12 sq. cm.
Perimeter: 2W +2L = 48
Area = L x W = 140
Rewrite the area to solve for L: L = 140/W
Now replace that in the perimeter formula:
2W + 2(140/W) = 48
Divide all terms by 2:
W + 140/W = 24
Divide both sides by W:
140 + w^2 = 24w
Subtract 24w from both sides:
w^2 - 24w + 140 = 0
Factor:
(w-10) (w-14) = 0
Solve for each w for 0:
10-10 - 10 and 14-14 = 0
So the 2 dimensions are 10 and 14 cm.
14 isn't a choice so the answer is B. 10 cm.
find the discriminant and the number of real roots for this equation 4x^2+16x+16=0
Final answer:
The discriminant of the equation 4x^2+16x+16=0 is 0, indicating that there is one real, repeated root.
Explanation:
To find the discriminant and the number of real roots for the equation 4x^2+16x+16=0, we first recognize it as a quadratic equation of the form ax^2+bx+c=0. The discriminant of a quadratic equation is given by the formula b^2-4ac. In our equation, a=4, b=16, and c=16. Substituting these values into the formula gives us 16^2 - 4(4)(16), which simplifies to 256 - 256, yielding a discriminant of 0. A discriminant of 0 indicates that there is exactly one real root, which is also a repeated or double root.
Factor completely 3x3 + 12x2 + 18x.
Step-by-step explanation:
solved in the picture....
Answer:
The factored form of the given expression is [tex]3x(x^2+4x+6)[/tex].
Step-by-step explanation:
The given expression is
[tex]3x^3+12x^2+18x[/tex]
we need to find the factored form of the given expression.
Taking GCF common, we get
[tex]3x(x^2+4x+6)[/tex]
If a quadratic expression is defined as [tex]ax^2+bx+c[/tex] and
[tex]b^2-4ac<0[/tex], then the expression can not be factored further.
In the above parentheses the quadratic expression is [tex]x^2+4x+6[/tex],
[tex]b^2-4ac=(4)^2-4(1)(6)=-8<0[/tex]
It means the quadratic expression is [tex]x^2+4x+6[/tex] can not be factored further.
Therefore the factored form of the given expression is [tex]3x(x^2+4x+6)[/tex].
Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
Answer:
150
Step-by-step explanation:
Given that;
Company A offers;
Salary= $ 17000
commission= $100 per tv set
Company B offers;
Salary= $29000
Commission = $ 20 per tv set
Let the number of tv set sold to be= x
To solve this problem, the amount obtained after selling for A option should be equal to B option
Form equations
[tex]17000 +100 x = 29000 + 20x\\\\\\100x-20x= 29000-17000\\\\\\80x=12000\\\\\\x=12000/80 = 150[/tex]
The number of televisions sold for the options to be equal = 150
Answer:
Amara needs to sell 150 televisions to make both options earnings equal.
Step-by-step explanation:
Let the number of television sold be = x
For company A:
Salary is $17,000 plus a $100 commission for each television she sells.
Equation becomes:
[tex]f(x)=17000+100x[/tex]
For company B :
Salary is $29,000 plus a $20 commission for each television she sells.
Equation becomes:
[tex]f(x)=29000+20x[/tex]
So, to calculate how many televisions would Amara need to sell for the options to be equal, we will equal both the equations.
[tex]17000+100x=29000+20x[/tex]
=> [tex]100x-20x=29000-17000[/tex]
=> [tex]80x=12000[/tex]
x = 150
So, Amara needs to sell 150 televisions to make both options earnings equal.
We can check this :
[tex]17000+100(150)=29000+20(150)[/tex]
=> [tex]17000+15000=29000+3000[/tex]
=> [tex]32000=32000[/tex]
What is a point-slope equation of the line with the slope -13 that goes through the point (5,7)?
Answer:
Equation of line: y=3x-18
Step-by-step explanation:
Point: (5,7) and slope=-13
y-7=-13(x-5)
y=-13x+72
How do I do this problem?
Answer:
7x+y=37
Step-by-step explanation:
You basically just add the numbers, So you add 5 and 2 and then you subtract 2 from 3 which is 1 and then you add 21 and 16
what is 1 1/4 + 3 5/8 = when its reduced to lowest term.
Answer:
4 7/8 or 4.875
Step-by-step explanation:
1 1/4 + 3 5/8 = 4 7/8 or 4.875
PLEASE MARK ME AS BRAINLIEST UWU
Hello There!
Your answer is 4[tex]\frac{7}{8}[/tex]
First, I like to always start by adding our whole numbers together so we have 1 and 3 which gives us a sum of 4.
Next, we just have a fraction of [tex]\frac{1}{4}[/tex] and [tex]\frac{5}{8}[/tex]
We an change our 1/4 to 2/8 because it has a common denominator.
Then, we can add 5/8 together and 2/8 together to get us a sum of 7/8.
Lastly move our whole number over and we have a mixed number of 4 and 7/8
A square parking lot has 6,400 square meters what is the length in meters
Answer:
Length of the square parking plot = 800 m
Step-by-step explanation:
Area of the square parking plot = 6400 Sq. m
side * side = 6400
side * side = 64 * 100 = 8 * 8 * 10 * 10
side =√ (8 * 8 * 10 * 10)
side = 8 * 10 = 80 m
. What's the common difference of the sequence 0, 5, 10, 15, 20, . . . ?
A. d = –5
B. d = 3
C. d = –2
D. d = 5
Answer:
D. d = 5
Step-by-step explanation:
d = d² - d¹
= 5 - 0
= 5
d = d³ - d⁴
= 10 - 5
= 5
d = dⁿ - dⁿ-¹
The common difference of the given sequence will be 5, i.e. option D.
What is Arithmetic progression?Arithmetic progression is the sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. The common difference is the value between each successive number in an arithmetic sequence
i.e. Common difference (d) = Successive term - Previous term
We have,
0, 5, 10, 15, 20, . . .
Here,
a₁ = 0
a₂ = 5
a₃ = 10
a₄ = 15
a₅ = 20
Now,
Find the common difference,
i.e.
Common difference (d) = a₂ - a₁ = 5 - 0 = 5,
Now,
Common difference (d) = a₃ - a₂ = 10 - 5 = 5
Now,
Common difference (d) = a₄ - a₃ = 15 - 10 = 5
Now,
Common difference (d) = a₅ - a₄ = 20 - 15 = 5
Now,
The Common difference is same for all i.e. 5.
Hence, we can say that the common difference of the given sequence will be 5, i.e. option D.
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Rewrite using the distributive property 6(x + 3)
Answer: 6x+18
Step-by-step explanation: Because of the Distributive property, you would multiply the 6 by the’x’ and 3, as they are in the parenthesis.
The distributive property is the ability of one operation to "distribute" over another operation contained inside a set of parenthesis. So, all we (you) need to do is "distribute" the 6 to the x and 3. Observe.
6(x + 3) =
6x + 18 is the rewritten equation using the distributive property.
how long is the arc intersected by a central angle of π/3 radians in a circle with a radius of 6 feet round your answer to the nearest tenth
[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ \cline{1-1} r=6\\ \theta =\frac{\pi }{3} \end{cases}\implies s=6\left( \frac{\pi }{3} \right)\implies s=2\pi \implies \stackrel{\textit{rounded up}}{s=6.3}[/tex]
Answer: [tex]arc\ length=6.3\ ft[/tex]
Step-by-step explanation:
You need to use the following formula for calculate the arc lenght:
[tex]arc\ length=r\theta[/tex]
Where "r" is the radius and [tex]\theta[/tex] is the central angle in radians.
You know that the central angle in radians s:
[tex]\theta=\frac{\pi }{3}[/tex]
And the radius is:
[tex]r=6\ ft[/tex]
Therefore, the final step is to substitute the values into the formula. Then you get:
[tex]arc\ length=(6\ ft)(\frac{\pi }{3})[/tex]
[tex]arc\ length=6.3\ ft[/tex]
the mode and median of a data are18. 24 and18.05respectively. Find the mean of the data
Answer:
20.01
Step-by-step explanation:
The mean of 18, 24 and 18.05 is 20.01.
The factored form of a quadratic equation is y=(2x+1)(x-5), and the standard form is y=2x²-9x-5. Which of the following statements accurately describes the graph of y?
A) The x-intercepts are -1 and 5, and the y-intercept is -5.
B) The x-intercepts are -1/2 and 5, and the y-intercept is -5.
C) The x-intercepts are -1/2 and 5, and the y-intercept is 5.
D) The x-intercepts are 1 and -5, and the y-intercept is -5.
Answer:
B) The x-intercepts are -1/2 and 5,and the y-intercept is -5.Step-by-step explanation:
The intercept form of a quadratic equation y = ax² + bx + c:
[tex]y=a(x-p)(x-q)[/tex]
[tex]\text{x-intercepts:}\ p\ \text{and}\ q\\\\\text{y-intercept}:\ a(-p)(-q)[/tex]
We have the equation:
[tex]y=2x^2-9x-5=(2x+1)(x-5)[/tex]
[tex]2x+1=2\left(x+\dfrac{1}{2}\right)\to y=2\left(x+\dfrac{1}{2}\right)(x-5)[/tex]
[tex]y=2\bigg(x-\left(-\dfrac{1}{2}\right)\bigg)(x-5)[/tex]
Therefore
[tex]a=2\\\\x-intercepts:\ p=-\dfrac{1}{2}\ \text{and}\ q=5\\\\\text{y-intercept:}\ (2)\left(-\dfrac{1}{2}\right)(5)=-5[/tex]
The x-intercepts are -1/2 and 5, and the y-intercept is -5.
Explanation:The factored form of a quadratic equation is y=(2x+1)(x-5). To find the x-intercepts, we set y=0 and solve for x. Therefore:
Setting y=0, we have (2x+1)(x-5)=0.Using the zero-product property, we have 2x+1=0 or x-5=0.Solving for x, we get x=-1/2 and x=5.The y-intercept is found by setting x=0 and solving for y. So:
Setting x=0, we have y=(2(0)+1)(0-5).Simplifying, we get y=1(-5)=-5.Therefore, the correct statement is:
The x-intercepts are -1/2 and 5, and the y-intercept is -5.
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Give two different decimals that round to 5.24 when rounding to the nearest hundredths.
ANSWER
5.2387 and 5.2437
EXPLANATION
To round a decimal to the nearest hundredth means we should round to two decimal places.
To round to two decimal places we consider the third decimal place.
When we round 5.2387 to the nearest hundredth, we obtain 5.24 because the third decimal place is greater than or equal to 5 so we round up.
When we round 5.2437 to the nearest hundredth, we get 5.24 because the third decimal place less than 5 so we round off.
In fact there are infinitely many decimals that will round to 5.24 when rounding to the nearest hundredth.
12. Two sides of a triangle have lengths 5 and 12. What must be true about the length of the third side?
less than 12
less than 7
less than 21
less than 17
Answer:
less than 17
Step-by-step explanation:
For any triangle, the sum of any two sides of a triangle has to be greater than the third side. So, the only answer that works is less than 17
The third side will be greater than 7 cm but less than 17 cm.
Option D is correct
What is a triangle?In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.
According to the question
Length of two sides of a triangle is 5 cm and 12 cm
Sum of there two sides = 5 + 12 = 17 cm
Difference of there two sides = 12 - 5 = 7 cm
The third side will be greater than 7 cm but less than 17 cm.
Option D is correct
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Jamarcus has twenty-one coins is his piggy bank, all of which are either dimes or quarters. If Jamarcus has $4.20 in total, how many of each coin does he have?
Answer:
16 quarters 2 dimes
Step-by-step explanation:
16 quarters is 4 dollars
2 dimes is 20 cents
Step-by-step explanation:
If D is number of dimes and Q is number of quarters:
D + Q = 21
10D + 25Q = 420
Solve the system of equations through either substitution or elimination.
10D + 25(21 - D) = 420
10D + 525 - 25D = 420
105 = 15D
D = 7
Q = 14
There are 7 dimes and 14 quarters.
use log4 3~0.7925 and log 4 = 1 to approximate the value of the expression log4 768
Answer:
Step-by-step explanation:
We need to find the value of log4(768).
768 can be written as 3*256
which further can be simplified to 3*4^4
so using the log property log(AB)=log A+ log B
we can write
log4(768) = log4(3)+log4(4^4)
=0.7925+4log4(4)
=0.7925+4
=4.7925