Step-by-step explanation:
8^x= 64
8²= 64
In logarithmic form,
log(base 8) 64= 2
The equation 8ˣ=64 in logarithmic form is written as log8(64) = x, where x is the exponent to which the base 8 is raised to obtain 64.
The equation 8ˣ=64 in logarithmic form, you have to understand the relationship between exponentials and logarithms. The logarithmic form of the equation is logb(a) = c, which means b to the power of c equals a. Given that 8 squared (8²) equals 64, you can express 8^x=64 as log8(64) = x, which is the logarithmic form of the given exponential equation.
Consider the following quadratic equation. Determine a possible value of b so that the quadratic has two complex solutions. -14 12 -16 14
Answer:
Can you attach the quadratic equation?
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
PLATO user
Evaluate
[32+ (7.6 - 22)] - [30 = (4 + 1)]
Answer:
I got 11.6
Step-by-step explanation:
Hope my answer has helped you in any way!
Find three consecutive numbers such that the sum of one-fourth the first and one-fifth the second is five less than one-seventh the third
Answer:
The numbers are -16,-15 and -14
Step-by-step explanation:
Let
x ----> the first number
x+1 ----> the second number
x+2 ---> the third number
we know that
(1/4)x+(1/5)(x+1)=(1/7)(x+2)-5
Multiply by (4*5*7) both sides
35x+28(x+1)=20(x+2)-140*5
35x+28x+28=20x+40-700
43x=-688
x=-16
so
x+1=16+1=-15
x+2=-16+2=-14
The numbers are -16,-15 and -14
The measure of A is 10° greater than the measure of B. The two angles are complementary. Find the measure of each angle.
The m A is ° and m B is °.
since its complementary, the sum if both angles equals 90 degrees.
you do x+x+10 so you combine like terms to get 2x+10=90
then you subtract 10 to get
2x=80
and divide by 2
x=40
angle a=50 degrees
angle b=40 degrees
Answer:
m < A = 50 degrees, m < B = 40 degrees.
Step-by-step explanation:
Complementary angles sum to 90 degrees, so:
A + B = 90
As A = B + 10:
B + 10 + B = 90
2B = 80
B = 40.
So A = 40 + 10 = 50.
Fixed rate mortgage offer:
Purchase price: $170,000
Down payment ($34K): 20%
Term: 30 years
Interest rate: 4.25%
Property tax (yearly): $1,500
Homeowner’s insurance (yearly): $1,000
Use this example from a fixed-rate mortgage calculator to help you answer the questions. Keep the page open after you complete this question.
According to the calculator, the monthly payment Demarco and Tanya should anticipate paying for principal and interest is
$208.
$877.
$669.
$1,200.
Answer: its C. $669
Step-by-step explanation:
Please helpppp .......
Answer:
It would be (-2,11)
Step-by-step explanation:
I used desmos for this, since it says graphing.
desmos.com/calculator/glijhd4ksg
look at the link to view the graph and solution.
Normally, you would plot points from one line, connect them, then do the same for the other line.
Hope this helps!
When using a graph to find the solution you must look at where the lines intersect. Look at the graph provided below:
As you can see the graph below shows that the two lines intersect at point (-2, 11)
Hope this helped!
~Just a girl in love with Shawn Mendes
5x + 1y + 4z=-1
4x + 6y +9z= -68
9x + 1y + 4z = 27
Select one:
(7,-4, -8)
(-4,-8, 7)
(-8, -7, -4)
(-7,4, -8)
(-7, -4, -8)
Answer:
[7, -4, -8]
Step-by-step explanation:
Just simply plug in each choice into the equations to confirm their authenticities.
The tiles on the left contain functions written using function notations. Match each function with its input
Answer:
Part 1) h(g)=-4+g ----> the input is g
Part 2) f(h)=-h-7 -----> the input is h
Part 3) g(f)=-2f -----> the input is f
Step-by-step explanation:
Part 1) we have
h(g)=-4+g
we know that
The input is the independent variable and the output is the dependent variable
so
the output is h(g) or 4+g
the input is the variable g
Part 2) we have
f(h)=-h-7
we know that
The input is the independent variable and the output is the dependent variable
so
the output is f(h) or h-7
the input is the variable h
Part 3) we have
g(f)=-2f
we know that
The input is the independent variable and the output is the dependent variable
so
the output is g(f) or 2f
the input is the variable f
Answer: Questions are in different places than other people screen.
h(g) = -4+g - The input is G
g(f) = 2f - The input is F
f(h) = h - 7 - The input is H
Step-by-step explanation:
Just put tha answer in nd get a good grade :)
select the quadratic function with a graph that has the following features
x-intercept at (8,0)
y-intercept at (0,-32)
maximum value at (6,4)
axis of symmetry at x=6
A. f() = 1/2 x2 +6 - 32
B.f() = -x2 + 12x -32
C.f() = 1/2 x2 + 6x -16
D f() = -x2 + 12x -6
Answer:
Option B [tex]f(x)=-x^{2}+12x-32[/tex]
Step-by-step explanation:
we know that
For the given values, the quadratic function is a vertical parabola open downward (vertex is a maximum)
The equation in vertex form is equal to
[tex]f(x)=a(x-h)^{2} +k[/tex]
where
(h,k) is the vertex
a is a coefficient
we have
(h,k)=(6,4)
so
[tex]f(x)=a(x-6)^{2} +4[/tex]
Find the value of a
For x=8, y=0 -----> the y-intercept
substitute
[tex]0=a(8-6)^{2} +4[/tex]
[tex]0=a(2)^{2} +4[/tex]
[tex]0=4a +4[/tex]
[tex]a=-1[/tex]
substitute
[tex]f(x)=-(x-6)^{2} +4[/tex]
Convert to standard form
[tex]f(x)=-(x^{2}-12x+36) +4[/tex]
[tex]f(x)=-x^{2}+12x-36+4[/tex]
[tex]f(x)=-x^{2}+12x-32[/tex]
The graph in the attached figure
What is the y-value in the solution to this system of linear equations?
4x + 5y = −12
-2x + 3y = −16
A.)−4
B.)−2
c.)2
D.)5
Answer:
Option A.)−4
Step-by-step explanation:
we have
4x+5y=-12 -----> equation A
-2x+3y=-16 -----> equation B
Solve the system of equations by elimination
Multiply the equation B by 2
2*(-2x+3y)=-16*2
-4x+6y=-32 -----> equation C
Adds equation A and equation C
4x+5y=-12
-4x+6y=-32
-----------------
5y+6y=-12-32
11y=-44
y=-4
Answer with Step-by-step explanation:
We are given a system of linear equations:
4x + 5y = −12
-2x + 3y = −16
Multiply second equation by 2 and add it to first equation.
4x+5y-4x+6y= -12-32
⇒ 11y= -44
Dividing both sides by 11
⇒ y= -4
Hence, the y-value in the solution to the system of linear equations
4x + 5y = −12
-2x + 3y = −16 is:
A.)−4
Rewrite the following radical expression in rational exponent form.
[tex]( \sqrt{x)} ^5[/tex]
Answer:
Step-by-step explanation:
note that the square root of any number can be expressed as the number raised to a [tex]\frac{1}{2}[/tex] power
i.e √a = [tex]a^{\frac{1}{2} }[/tex]
Applying this to our expression
[tex](\sqrt{x} )^{5}[/tex]
= [tex]x^{\frac{1}{2} * 5 }[/tex]
= [tex]x^{\frac{5}{2}}[/tex]
The Answer Is...
x^5/2
[tex]x^ \frac{5}{2}[/tex]
What is the scale factor of the dilation?
- Convert 4444 to base 10
Answer:
4444₁₀
Step-by-step explanation:
4×10³=4000 (that's 10 to the power of 3)
4×10²=400
4×10¹=40
4×10⁰=4
4000+400+40+4=4444
Evaluate B2 for B = 9.
B^2 for B = 9 means squaring the value of 9, resulting in 9^2, which equals 81. Therefore, B^2 for B = 9 is 81.
To evaluate B^2 for B = 9, you simply substitute the value of B into the expression and then perform the calculation. Here's how it's done:
B^2 means "B squared," which is equivalent to multiplying B by itself. So, for B = 9, we have:
[tex]\(B^2 = 9^2 = 9 \times 9\)[/tex]
Now, calculate the product:
[tex]\(9 \times 9 = 81\)[/tex]
So, B^2 for B = 9 is equal to 81.
In summary, when you substitute B = 9 into the expression B^2, you get 9^2, which equals 81. Therefore, B^2 for B = 9 is 81.
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Kyra and her twin sister share shoes. In there closet they have four pairs of Sandals,five pairs of tennis shoes, and three pairs of boots. What is the probability that kyra selects a pair of sandals, put them on and then her sister selects a pair of tennis shoes?
Answer:
Step-by-step explanation:
The total number of shoes they share is
4 + 5 + 3 = 12
Kyra: 4/12 = 0.333333
Tennis Shoes: There are now 11 shoes. 5/11 = 0.46
The probability that Kyra selects a pair of sandals and her sister selects a pair of tennis shoes is 3/20.
Explanation:To find the probability that Kyra selects a pair of sandals and her sister selects a pair of tennis shoes, we need to determine the total number of possible outcomes and the number of favorable outcomes.
There are 4 pairs of sandals, 5 pairs of tennis shoes, and 3 pairs of boots in the closet. Assuming Kyra selects a pair of sandals first, she has 4 options. After Kyra selects the sandals, there will be 3 pairs of sandals left.
Since the sandals are chosen without replacement, her sister will have 5 options for the pair of tennis shoes. The total number of possible outcomes is the product of the options for each step: 4 * 5 = 20.
Therefore, the probability that Kyra selects a pair of sandals and her sister selects a pair of tennis shoes is 3/20.
The total cost of Anja’s trip to the dentist was $628.35. She paid a flat fee of $89.95 which included the checkup and cleaning and then had 4 cavities filled, each of which cost the same amount. Which shows the correct equation and value of x, the cost of each cavity filling?
Answer:
89.95 + 4x =628.35
x = 134.60
Step-by-step explanation:
The trip to the dentist had a flat fee plus 4 cavities for a total cost of 628.35
fee + 4 * cost of cavity = 628.35
Let x = the cost of each cavity
89.95 + 4x =628.35
Subtract 89.95 from each side
89.95-89.95 + 4x =628.35-89.95
4x =538.40
Divide each side by 4
4x/4 =538.40/4
x =134.60
What is the area of rectangle ABCD?
Answer:
18 square units
Step-by-step explanation:
you multiply the base by the hight after graphing the square.
EMERGENCY!! 30 POINTS!!
Jasmine and Carlotta are sisters, and each have their own savings. Tog
movies. Each girl has to pay back an equal amount Carlotta also owes
change in Carlotta's savings after she repays her brother?
A. -28= 2 + (-6)
B. 28- 2 + (-6)
C. -28 2+(-6)
D. -28 = 2-(-6)
You would need to divide the money by 2 ( both sisters) to get the equal amount they each need to pay. Then include the extra amount Carlotta owes.
The correct equation would be -28 ÷ 2- (-6)
Answer:
a
Step-by-step explanation:
complete the fact family 3+6=9
Answer:
The rest is 6+3=9 , 9-6=3 , 9-3=6.
I need help with PLATO Course Texas Algebra II, Semester A do you think you can help me with the answers?
What is the converse of the following true conditional? If the converse is true, rewrite the statements as a biconditional. If either is false, give a counterexample.
If two lines are parallel, they do not intersect.
Select one:
a. If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.
b. If two lines do not intersect, they are parallel. One statement is false. If two lines are parallel, they may intersect twice.
c. If two lines do not intersect, they are parallel. Both statements are true. Two lines are parallel if (and only if) they do not intersect.
d. If two lines do not intersect, they are not parallel. Both statements are true. Two lines are not parallel if (and only if) they do not intersect.
Answer: A
Step-by-step explanation: The converse of a conditional is when the two statements switch spots, for example:
Conditional: If someone like ice cream, they have brown hair
Converse: If someone has brown hair, they like ice cream
The converse of our given conditional would be:
If two lines do not intersect, they are parallel
This eliminates Option D
Next, the converse is false.
Skew lines (example attached) do not intersect and are also not parallel, meaning if two lines do not intersect, they could be either parallel or skew.
This eliminates Option C and B, leaving us with Option A
We want to find the converse statement to one given statement and see if it is true.
We will see that the correct option is a:
If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.
A general statement is written as:
If P then Q.
Where P and Q are two given propositions.
The converse statement to the above shown is:
If Q then P.
For this question, we have the statement:
If two line are parallel, they do not intersect.
Then we can write the converse statement as:
If two lines do not intersect, they are parallel.
Which is false, in 3-dimensions we can have two non-parallel lines that don't intersect each other (parallel lines must not intersect and also live on the same plane).
Then the correct option is the first one:
a: If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.
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Which of the following is NOT a possible value of the correlation coefficient?
A. negative 0.9
B. zero
C. positive 0.15
D. positive 1.5
E. negative .05
Answer:
positive 1.5
Step-by-step explanation:
by definition, the possible values for correlation coefficients are
-1 ≤ correlation coefficient ≤ 1
+1.5 lies outside this range and hence is not valid.
The correlation coefficient measures the strength and direction of a linear relationship between two variables, ranging from -1 to +1. Therefore, a value of positive 1.5, as listed in option D, is not a possible value for a correlation coefficient.
Explanation:In mathematics, particularly in statistics, a correlation coefficient is a measure of the strength and direction of the linear relationship between two variables on a scatterplot. The value of a correlation coefficient ranges from -1 to +1. A correlation coefficient of +1 indicates a perfect positive linear relationship, a correlation coefficient of -1 indicates a perfect negative linear relationship, and a correlation coefficient of 0 indicates no linear relationship.
Therefore, the answer to the question is: D. positive 1.5. This is not a possible value for a correlation coefficient because it lies outside the acceptable range of -1 to +1.
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what is the rang for the equation y=2x-3
Answer:
The range for the equation is all real numbers.
Step-by-step explanation:
The range of an equation is the set of y-values that you can get by plugging in all possible x-values.
Another way to put it is, when you graph the equation, whatever y-values the line produces, is its range.
Graphing y=2x-3, you can see it is a graph with a positive slope that extends from negative infinity y-value to positive infinity x-value.
midpoint of the line segment (-1,5) (-8,-4)
Answer:
(- [tex]\frac{9}{2}[/tex], [tex]\frac{1}{2}[/tex] )
Step-by-step explanation:
Using the midpoint formula
Given 2 points (x₁, y₁ ) and (x₂, y₂ ), then midpoint is
([tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex])
with (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (- 8, - 4), then midpoint
= ([tex]\frac{-1-8}{2}[/tex], [tex]\frac{5-4}{2}[/tex] )
= ( - [tex]\frac{9}{2}[/tex], [tex]\frac{1}{2}[/tex] )
Answer:-4.5,0.5
Step-by-step explanation:midpoint =x1+x2/2, y1+y2/2
-1+-8/2=x,-4+5/2=y
-9/2=x,1/2=y
-4.5=x, 0.5=y
What is the value of n in the equation 0=18+128n^2?
Answer:
[tex]\large\boxed{\text{no soltion in the set of real numbers}}\\\boxed{n=-\dfrac{3}{8}i\ \vee\ n=\dfrac{3}{8}i\ \text{in the set of complex numbers}}[/tex]
Step-by-step explanation:
[tex]18+128n^2=0\qquad\text{subtract 18 from both sides}\\\\128n^2=-18\qquad\text{divide both sides by 128}\\\\n^2=-\dfrac{18}{128}\\\\n^2=-\dfrac{18:2}{128:2}\\\\n^2=-\dfrac{9}{64}<0\to\bold{ no\ solution\ in\ the\ set\ of\ real\ numbers}\\\\\bold{In\ the\ set\ of\ Complex\ numbers}\\\\i=\sqrt{-1}\\\\n^2=-\dfrac{9}{64}\to n=\pm\sqrt{-\dfrac{9}{64}}\\\\n=\pm\sqrt{\dfrac{9}{64}\cdot(-1)}\\\\n=\pm\sqrt{\dfrac{9}{64}}\cdot\sqrt{-1}\\\\n=\pm\dfrac{\sqrt9}{\sqrt{64}}i\\\\n=\pm\dfrac{3}{8}i[/tex]
Find the equation in slope-intercept form of a line with slope –2 and y-intercept 4.
Question 10 options:
a)
y = -2x
b)
y = 4x -2
c)
y = -2x+4
d)
y = 2x-4
Answer:
c)
Step-by-step explanation:
-2 is the slope so that y equals -2x and the y intercept is positive 4 so that the equation is y=-2x+4
Answer:
c) y = -2x+4
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
Substituting in
y = -2x +4
I need help with this within the next /0 mins sum1 plz help
Answer: Second option.
Step-by-step explanation:
Given the function f(x), which is:
[tex]f(x)=x[/tex]
And given the function g(x), which is:
[tex]g(x)=2[/tex]
You need to substiute the function [tex]g(x)=2[/tex] into the function [tex]f(x)=x[/tex] in order to find [tex](fog)(x)[/tex].
Therefore, through this procedure, you get this answer:
[tex](fog)(x)=(2)[/tex]
[tex](fog)(x)=2[/tex]
You can observe that this matches with the second option.
For this case we have the following functions:
[tex]f (x) = x\\g (x) = 2[/tex]
We must find [tex](f_ {0} g) (x).[/tex]
By definition of composite functions we have to:
[tex](f_ {0} g) (x) = f (g (x))[/tex]
We substitute g (x) into f (x), then we have:
[tex]f (g (x)) = 2[/tex]
Answer:
[tex]f (g (x)) = 2[/tex]
Option B
Which graph represents the function p(x) = |x – 1|?
Answer:
The last one
Step-by-step explanation:
Your equation is p(x) = |x - 1|
The function equation can be represented by f(x) = a|x - h| + k
To find the vertex, you have to find (h,k)
In the equation p(x) = |x - 1|, 1 is h [since its (+h,k) not (-h,k)]
k is 0 since there is no +k after |x-1|.
So, your vertex will be at (1,0)
Thus, the answer is the last graph.
[I also graphed it on a graphing calculator so you can check. :) ]
The vertex will be at (1, 0).
Functions of graphs
The given equation is p(x) = |x - 1|
The function equation can be defined by f(x) = a|x - h| + k
To calculate the vertex, you have to identify (h, k)
In the given equation p(x) = |x - 1|, 1 exists h
[since its (+h, k) not (-h, k)]
k exists 0 since there does not exist +k after |x-1|.
So, the vertex will be at (1, 0).
Therefore, the graph represents the function p(x) = |x – 1| is option (d).
To learn more about the functions of graphs
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Which of the following shows the correct graph and solution of the system
y=-4x+2 and y + 2x = 0?
solution = (1.-2)
solution =(-1.-2)
solution
(-1.2)
solution - (1.-2)
Answer:
solution = (1.-2)
Step-by-step explanation:
put x= 1 and y = -2 in this system : y=-4x+2 and y + 2x = 0
you have : - 2 = - 4(1)+2 and -2 +2(1)=0
-2=-2 and 0=0 .....right
The required solution of the given system of equations is (1, -2), and a graph of the solution has been shown.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
y=-4x+2 - - - -(1)
y + 2x = 0 - - - (2)
Equating equations,
-4x +2 = -2x
x = 1
Put x = -2 in equation 1
y = -4(1) + 2
y = -2
Thus, the required solution of the given system of equations is (1, -2).
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Which is the simplified form of the expression 3(7/5x + 4) - 2(3/2 - 5/4x)
Answer:
Step-by-step explanation:
I think you meant 3([7/5]x + 4) - 2(3/2 - [5/4]x). If that's the case, then identify the LCD: It is 20. Multiply both [7/5]x + 4 and 3/2 - [5/4]x by 20 and then divide the resulting expression by 20:
3(28x + 80) - 2(30 - 25x)
------------------------------------
20
Next, perform the indicated multiplication:
84x + 240 - 60 + 50x
----------------------------------
20
This simplifies to:
34x + 180 17x + 9
---------------- = ----------------
20 10
Next time, please share the answer choices.
Answer:
67x/10 + 9
Step-by-step explanation:
Simplify 7/5x to 7x/5
3(7x/5 + 4) -2(3/2 - 5/4x)
Simplify 5/4x to 5x/4
3(7x/5 + 4) -2(3/2 - 5x/4)
Expand
21x/5 + 12 - 3 + 5x/2
Collect like terms
(21x/5 + 5x/2) + (12 - 3)
Simplify
67x/10 + 9