Solve this equation for x. Round your answer to the nearest hundredth. 0.75=logx
Answers
Answer:
Step-by-step explanation:
[tex]10^.^7^5=10^l^o^g^(^x^)\\=10^.^7^5=x\\=10^\frac{3}{4}=\sqrt[4]{10^3} =\sqrt[4]{1000} =5.6=x[/tex]
To solve the equation 0.75 = log(x), we exponentiate both sides with base 10, resulting in x = 10^0.75. The calculated value of x to the nearest hundredth is approximately 5.62.
Explanation:To solve the equation 0.75 = log(x), we need to understand that the logarithm function here is the common logarithm, which means it has a base of 10. The equation essentially states that 10 raised to the power of 0.75 equals x. To find x, we simply need to perform the inverse operation of taking the logarithm, which in this case is exponentiation.
We use the fact that if logb(a) = c, then bc = a, where b is the base, a is the result, and c is the exponent. Therefore, we can rewrite our original equation as:
x = 100.75
Using a calculator, we can find that:
x ≈ 5.62
This is the value of x, rounded to the nearest hundredth, as the question requested.
Related Questions
A car is traveling at a rate of 99 kilometers per hour. What is the car's rate in meters per second? How many meters will the car travel in 10 seconds? Do not
round your answers.
Answers
Answer:
27.5 m/s
275 m
Step-by-step explanation:
99 km/hr × (1000 m / km) × (1 hr / 3600 s) = 27.5 m/s
Distance = rate × time
d = 27.5 m/s × 10 s
d = 275 m
Nora divided 315 cans equally among 26 cartons and had 3 cans left over. How many cans were in each carton? 100 EASY POINTS AND MARK BRAINLIEST!! ANSWER ASAP
Answers
Answer:
12 cans with 3 left over
Step-by-step explanation:
It's pretty simple.
You already know you have 3 left over so all you have to do is 315 divided by 26.
315 ÷ 26 ≈ 12.12 but since you already know you have 3 left over, the answer would be 12.
Answer:
12 cans per carton
Step-by-step explanation:
Subtract the remainder of cans to the total amount.
315 - 3 = 312
Divide by the number of cartons.
312 / 36 = 12 cans per carton
Best of Luck!
Which statements are always true regarding the diagram?
Select three options.
m25+ m23 = m24
m23 + m24+ m25 = 180°
m25+ m26 =180°
m 2 + m
3 = m_6
m 2 + m 3 + m25 = 180°
Answers
Answer:
C) m∠5 + m∠6 =180°
D) m∠2 + m∠3 = m∠6
E) m∠2 + m∠3 + m∠5 = 180°
Step-by-step explanation:
TRUST ME! JUST TOOK MY QUIZ ON E2020
The correct equations are:
m∠2 + m∠3 + m∠5 = 180°
m∠2 + m∠5 = m∠4
m∠5 + m∠6 = 180°
m∠2 + m∠3 = m∠6
Equation
Equation is an expression used to show the relationship between two or more numbers and variables.
From the diagram:
m∠2 + m∠3 + m∠5 = 180° (sum of angles in a triangle)
But:
m∠3 + m∠4 = 180° (angle in a straight line)
m∠2 + m∠3 + m∠5 = m∠3 + m∠4
m∠2 + m∠5 = m∠4
Also:
m∠5 + m∠6 = 180° (angle in a straight line)
But:
m∠2 + m∠3 + m∠5 = 180
m∠2 + m∠3 + m∠5 = m∠5 + m∠6
m∠2 + m∠3 = m∠6
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What is the solution to the system of equations graphed below?
y = x-2
y= 4X-5
Answers
Answer:
(1,-1)
That is the ordered pair where they cross.
Step-by-step explanation:
The solution of the system is where the pair of lines there cross at.
The intersection is in the fourth quadrant there so your guess should definitely be of the form (positive, negative).
Only one choice is that and it is B.
It really does look like they cross at (1,-1).
To describe how to get from the origin to the intersection, I would say you would need to travel right 1 unit and down 1 unit.
We can even plug in our pair into both equations and see if it works.
y=x-2
y=4x-5
So if we plug in (1,-1) and assuming it is a solution, then both equations will give us the same thing on both sides. Let's try it:
y=x-2
-1=1-2
-1=-1
That's the same thing on both sides.
y=4x-5
-1=4(1)-5
-1=4-5
-1=-1
Again that is the same thing on both sides.
(1,-1) is indeed our solution.
Both the graph and the verification told us that.
Answer:
1, -1
Step-by-step explanation:
A.P.E.X 2021
(30 points)
When graphed, the three lines y = -x + 2, y = 2x − 1, and y = x − 2 intersect in such a way that they form a triangle.
What are the coordinates of the three vertices of this triangle?
A.
(2, 0), (0, 2), and (-1, -3)
B.
(0, 2), (2, 0), and (1, -1)
C.
(1, 1), (2, 0), and (-1, -3)
D.
(1, 1), (0, 2), and (-1, -3)
E.
(2, 0), (1, -1), and (-1, -3)
Answers
The vertices of the triangle are the points where any pair of lines intersect.
We start by setting up the system
[tex]\begin{cases}y=-x+2\\y=2x-1 \end{cases} \iff -x+2=2x-1 \iff 3x=3 \iff x=1[/tex]
Using one of the two equations we can derive the correspondent y value:
[tex]f(x)=-x+2 \implies f(1)=-1+2 = 1[/tex]
So, one vertex is (1, 1)
We choose the other two pairs of lines to find the other vertices:
[tex]\begin{cases}y=-x+2\\y=x-2 \end{cases} \iff -x+2=x-2 \iff x=2 \implies y = 0[/tex]
[tex]\begin{cases}y=x-2\\y=2x-1 \end{cases} \iff x-2=2x-1 \iff x=-1 \implies y=-3[/tex]
So, the three vertices are (1, 1), (2, 0), (-1, -3).
Answer:
(1, 1), (2, 0), and (-1, -3)
Step-by-step explanation:
I got right on the test.
The area of a rectangle is (X - 5x² + 3x - 15), and the width of the rectangle is (x2 + 3). If area = length x width, what is the
length of the rectangle?
x + 5
x - 15
x + 15
x-5
Answers
Answer:
Step-by-step explanation:
Area of rectangle = x³-5x²+3x-15
Width of rectangle = x²+3
Length of rectangle= ?
We will apply the formula:
Area= length* width
Hence we know the area and width.
x³-5x²+3x-15/x²+3 = length
By dividing the terms we get (x-5).
Thus the correct option is x-5....
Use the quadratic expression 25x2−y2 to answer the questions.
A: Which statement describes the correct method to factor the quadratic expression?
B: What are the factors of the quadratic expression?
Select one answer for question A, and select two answers for question B.
A: This quadratic expression can be factored by using the perfect square trinomial pattern.
A: This quadratic expression can be factored by finding the correct pair of binomial factors.
A: This quadratic expression can be factored by using the difference of squares pattern.
B: (5x+y)
B: (x+5y)
B: (5x+5y)
B: (x−5y)
B: (5x−y)
B: (5x+5y)
Answers
Answer:
Part A)
This quadratic expression can be factored by using the difference of squares pattern.
Part B) (5x+y) and (5x-y)
Step-by-step explanation:
Given:
25x^2-y^2
above polynomial can be factorize by using difference of squares formula
a2-b2=(a+b)(a-b)
25x^2-y^2= (5x-y)(5x+y)
so for part A)
correct option is This quadratic expression can be factored by using the difference of squares pattern.
Part B)
As factored above in part A,
the factors of given polynomial 25x^2-y^2 are (5x+y)(5x-y)
so for part B) correct options are (5x+y) and (5x-y) !
1. A plane flew 3,200 miles in 5 hours.
How fast was it flying?
Use the formula d = rt.
Answers
Answer:
640 miles per hour.
Step-by-step explanation:
I calculated this by 3200/5
Is this appropriate?
Can anyone show me how to do this or do it for me ill give brainlist
Answers
Answer: x^2-6x-8
Step-by-step explanation:
Step 1 : Factor - x^3-11x^2+22x+40: (x-5)(x^2-6x-8)/(x-5)
Step 2 : Divide, which should give you x^2-6x-8
A box contains five slips of paper. Each slip has one of the number 4, 6, 7, 8, or 9 written on it and all numbers are used. The first player reaches into the box and draws two slips and adds the two numbers. If the sum is even, the player wins. If the sum is odd, the player loses.
a. What is the probability that the player wins?
b. Does the probability change if the two numbers are multiplied? Explain.
Answers
6+4= 10
6+8= 14
8+4= 12
These are all even so as long as they get one of these combinations they will win
b. All three combinations still work when multiplied
6*4=24
6*8=48
8*4= 32
The probability that a player wins the game by adding the numbers from the slips drawn from the box is 40%. If the rule changes and the player multiplies the numbers instead of adding them, the winning probability increases to 70%.
Explanation:
The game consists of drawing two numbers from the box and verifying whether their sum or product is even or odd. In Mathematics, for the sum to be even, both numbers must be odd or both must be even. If we check, we have 2 odd numbers (7, 9) and 3 even numbers (4, 6, 8). The combinations for even sum could be odd-odd or even-even. The total successful events would be 1 (odd-odd) + 3 (even-even) = 4 out of total 10 possible events (5C2), which gives us the probability of the player winning the game as 4/10 or 40%
Now, whether the probability changes when we multiply instead of adding: Yes, it does! In Mathematics, an even number results when multiplying any number by an even number, regardless of whether the other number is odd or even. Therefore, since 3 out of 5 numbers are even, the probability that the player wins if they multiply the two numbers they select instead of adding them is greater, confirmed by calculating combinations again and we find 7 out of 10 possible events yield an even product, therefore probability is 70%, which is greater than that of adding them.
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The graph of f(t) = 5•2^t shows the value of a rare coin in year t What is the
meaning of the yintercept?
Answers
Answer:
D.
Step-by-step explanation:
The y-intercept is where the graph crosses the y-axis.
It crosses the y-axis at (0,5).
The graph is of f(t)=5*2^t where t is the number of years and the value of f(t) is the value of that coin after t years.
So we have (0,5) is on the graph of f which means f(0)=5.
f(0)=5 means at t=0 years the value of the coin is $5.
As per the y-intercept of a function, when the coin was purchased, the value of it was $5.
What is the y-intercept of a function?"The y-intercepts are points where the graph of a function crosses or touches the y-axis of the Cartesian Plane. "
The given function is
[tex]f(t)=5(2^{t})[/tex]
As per the graph of the given function, it starts from the point (0, 5).
Hence, it cuts the y-axis at point (0, 5).
Therefore, at the time of purchasing the coin, the value of the coin was at $5.
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What is the range of the function on the graph?
Answers
Find the solution(s) to 2x2 – 5x – 3 = 0.
Answers
Answer:
x = - [tex]\frac{1}{2}[/tex], x = 3
Step-by-step explanation:
Given
2x² - 5x - 3 = 0 ← in standard form
Consider the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 3 = - 6 and sum = - 5
The factors are - 6 and + 1
Use these factors to split the x- term
2x² - 6x + x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(x - 3) + 1 (x - 3) = 0 ← factor out (x - 3) from each term
(x - 3)(2x + 1) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
x - 3 = 0 ⇒ x = 3
Which number line best shows how to solve -6 - (-8)?
Answers
Answer:
-6 - (-8) = 2.
Your number line might have a bubble at 2. Or it may show movement 8 units to the right of -6. Whatever it is, you should end up at the value of 2.
Step-by-step explanation:
We don't see a number line, but I can still show how to solve.
-6 - (-8) is the same as doing negative six plus negative one times negative 8. Or in number terms it would look like:
-6 + (- 1(- 8))
In the order of operations -- PEMDAS -- we do parenthesis first.
- 1( - 8) = 8, so we simplify by plugging this value back into the equation:
-6 + 8
-6 + 8 is the same as 8 - 6.
8 - 6 = 2
Your answer is 2.
What is the value of D?
Answers
Answer:
80
Step-by-step explanation:
If there is any cyclic quadrilateral, which is a quadrilateral inscribed inside a circle, there is one simple property that is
the opposite angles add upto 180.
Thus we can say
96 + c = 180
and
d + 100 = 180
Since we need d, we use 2nd equation:
d + 100 = 180
d = 180 - 100
d = 80
For the function y=-3+ cos (x + 4)], what is the minimum value?
Answers
Answer:
-4 is the mimumum of y=-3+cos(x+4)
Step-by-step explanation:
The minimum value of y=cos(x) is -1.
The minimum value of y=cos(x+4) is still -1; the +4 inside the cosine function only affected the horizontal shift.
The minimum value of y=-3+cos(x+4) is -3-1 which is -4. This brought the graph down 3 units so if the minimum was previously -1 and it got brought down 3 units then it's new minimum is -4.
What would be a common mistake when solving this problem? 3(x-3) <3
Answers
Answer:
Incorrectly distributing the 3 and (x-3).
Step-by-step explanation:
A common mistake when solving 3(x-3) <3 would be incorrectly distributing the 3 and (x-3).
A hook in an office storage closet can hold no more than 6 pounds. An order of jumbo paperclips weighs 2 pounds and an
order of packing tape weighs 3 pounds. If x is the number of orders of paperclips and y is the number of orders of packing
tape, which graph represents how many of each order could be put in a bag hanging from the hook?
Answers
Answer:
The first graph represents how many of each order could be put in a bag hanging from the hook ⇒ 1st
Step-by-step explanation:
* Lets explain how to solve the problem
- The order of jumbo paperclips weighs 2 pounds
- x is the number of orders of paperclips
∴ The weight of the paperclips order is 2 × x = 2x
- The order of packing tape weighs 3 pounds
- y is the number of orders of packing tape
∴ The weight of the tape order is 3 × y = 3y
- The weight of the total order is 2x + 3y
- The hook can hold no more than 6 pounds
∴ 2x + 3y ≤ 6
- Lets find the graph which represent this inequality
∵ The equation of any line is y = mx + c, where m is the slope of the
line and c is the y-intercept
- The y-intercept means substitute x in the equation by 0
- The x- intercept means substitute y in the equation by 0
∵ The inequality is 2x - 3y ≤ 6
∵ The equation of the line is 2x + 3y = 6
- Subtract 2x from both sides
∴ 3y = 6 - 2x
- Divide both sides by 3
∴ y = 6/3 - 2/3 x
∴ y = 2 - 2/3 x
- Find the y-intercept
∵ x = 0
∴ y = 2
∴ The line intersect the y-axis at point (0 , 2)
- Find the x-intercept
∵ y = 0
∴ 0 = 2 - 2/3 x
- Add 2/3 x to both sides
∴ 2/3 x = 2
- Multiply both sides by 3
∴ 2 x = 6 ⇒ divide both sides by 2
∴ x = 3
∴ The line intersect the x-axis at point (3 , 0)
- From the figure the first and the second figures have the same
x-intercept and y-intercept
∵ The inequality is 2x + 3y ≤ 6
- The sign ≤ means the line is sold and the shading is under the line
∴ The first figure is the answer
* The first graph represents how many of each order could be put in a
bag hanging from the hook
Answer:
Option A.
Step-by-step explanation:
Let x is the number of orders of paperclips and y is the number of orders of packing tape.
An order of jumbo paperclips weighs 2 pounds and an order of packing tape weighs 3 pounds.
Total weight = [tex]2x+3y[/tex]
A hook in an office storage closet can hold no more than 6 pounds. It means total weight must be less than or equal to 6 pounds.
[tex]2x+3y\leq 6[/tex]
The related equation is
[tex]2x+3y=6[/tex]
Substitute x=0 in the above equation.
[tex]2(0)+3y=6[/tex]
[tex]3y=6[/tex]
[tex]y=2[/tex]
The y-intercept is 2.
Substitute y=0 in the above equation.
[tex]2x+3(0)=6[/tex]
[tex]2x=6[/tex]
[tex]x=3[/tex]
The x-intercept is 3.
Check the inequality by (0,0).
[tex]2(0)+3(0)\leq 6[/tex]
[tex]0\leq 6[/tex]
This statement is true, it means (0,0) is included in the shaded region.
The sign of inequity is "≤" it means the related line is a solid line and shaded region lie below the line.
Therefore, the correct option is A.
Parallelogram FGHJ was dilated and translated to form
similar parallelogram F'G'H'J'.
What is the scale factor of the dilation?
Answers
Answer: The required scale factor of the dilation is 4.
Step-by-step explanation: Given that the parallelogram FGHJ was dilated and translated to form similar parallelogram F'G'H'J'.
We are to find the scale factor of the dilation.
From the graph, we note that
JH = 2 units and J'H' = 8 units.
We know that
[tex]\textup{Scale factor of dilation}=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the correponding side of the original figure}}.[/tex]
Therefore, the scale factor of the given dilation is
[tex]S=\dfrac{J'H'}{JH}\\\\\\\Rightarrow S=\dfrac{8}{2}\\\\\Rightarrow S=4.[/tex]
Thus, the required scale factor of the dilation is 4.
Answer:
4 on edge
Step-by-step explanation:
Can u help me solve this
Answers
Explanation:
Rewrite the left side in terms of sine and cosine, then rearrange.
[tex](1+\tan^2{A})+(1+\dfrac{1}{\tan^2{A}})=\dfrac{1}{\sin^2{A}-\sin^4{A}}\\\\(1+\dfrac{\sin^2{A}}{\cos^2{A}})+(1+\dfrac{\cos^2{A}}{\sin^2{A}})=\\\\\dfrac{\sin^2{A}+\cos^2{A}}{\cos^2{A}}+\dfrac{\sin^2{A}+\cos^2{A}}{\sin^2{A}}=\\\\\dfrac{1}{\cos^2{A}}+\dfrac{1}{\sin^2{A}}=\\\\\dfrac{\sin^2{A}+\cos^2{A}}{(\sin^2{A})(\cos^2{A})}=\\\\\dfrac{1}{(\sin^2{A})(1-\sin^2{A})}=\dfrac{1}{\sin^2{A}-\sin^4{A}} \qquad\text{Q.E.D.}[/tex]
what is the inverse of f(x)= 1/9 x+2
Answers
Answer:
[tex]\large\boxed{f^{-1}(x)=9x-18}[/tex]
Step-by-step explanation:
[tex]f(x)=\dfrac{1}{9}x+2\to y=\dfrac{1}{9}x+2\\\\\text{exchange x to y and vice versa}\\\\x=\dfrac{1}{9}y+2\\\\\text{solve for y}\\\\\dfrac{1}{9}y+2=x\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{9}y=x-2\qquad\text{multiply both sides by 9}\\\\9\!\!\!\!\diagup^1\cdot\dfrac{1}{9\!\!\!\!\diagup_1}y=9x-(9)(2)\\\\y=9x-18[/tex]
What is the value of sec
in the triangle below?
41 ft
9 ft
40 ft
Answers
Answer:
C
Step-by-step explanation:
[tex] \sec( \alpha ) = \frac{1}{ \cos( \alpha ) } \\ \\ \sec( \alpha ) = \frac{1}{ \frac{ad}{hip} } \\ \\ \sec( \alpha ) = \frac{hip}{ad} \\ \\ \sec( \alpha ) = \frac{41}{40} [/tex]
The value of the secθ is 41/40.
What is trigonometry?Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.
For the given situation,
The diagram shows the right-angled triangle.
The sides of the right-angled triangle are
Hypotenuse side = 41 ft
Opposite side = 9 ft
Adjacent side = 40 ft
The value of secθ is
[tex]sec \theta =\frac{1}{cos \theta}[/tex]
where, [tex]cos \theta =\frac{adjacent}{hypotenuse}[/tex]
⇒ [tex]sec \theta =\frac{hypotenuse}{adjacent}[/tex]
⇒ [tex]sec \theta =\frac{41}{40}[/tex]
Hence we can conclude that the value of the secθ is 41/40.
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Jason deposits $5 into his savings account twice a week for 6 weeks. How much money will he have saved after 6 weeks?
Let s stand for the amount of money saved.
Equation:
How much money did he save?
Show your work.
First person who answers gets to be followed and marked brainliest.
Answers
Answer:
$60
The equation is x(5(2))=s or x(10)=s when x = number of weeks
Step-by-step explanation:
For 6 weeks, all you have to do is plug in the 6 where the x is.
6(5(2)) = s
6(10) = s
60 = s
or
6(10) = s
60 = s
the measure of 5 of the interior angles of a hexagon are 110, 120, 90, 140, and 125. what is the measure of the smallest exterior angle?
A) 40
B) 45
C) 30
D) 35
Answers
Answer:
A) 40
Step-by-step explanation:
The sum of the interior angles of a regular polygon is:
[tex](n - 2) \times 180[/tex]
For a hexagon, we put n=6
[tex](6 - 2) \times 180 = 4 \times 180 = 720[/tex]
Let x be the 6th interior angle, then
[tex]x + 110 + 120 + 90 + 140 + 125 = 720[/tex]
[tex]x + 585 = 720[/tex]
[tex]x = 720 - 585 = 135[/tex]
The largest interior angle is 140°
Therefore the least exterior angle will be:
[tex]180 - 140 = 40[/tex]
The correct choice is A
Consider the function.
f(x) = 2*x+12
What is the y-intercept of f(x)?
Answers
the question is already in slope intercept form.
The y-intercept is 12.
y=mx+b whereas m=slope, and b=y-intercept.
hope this helped!
The function is linear function of a form,
[tex]f(x)=ax+b[/tex]
Which always intersects point,
[tex]P(x, n)[/tex]
Or in this case,
[tex]f(x)=2x+12[/tex]
The point is therefore,
[tex]P(x,y)\Longrightarrow\boxed{P(x, 12)}[/tex]
The y-intercept is 12.
Hope this helps.
r3t40
PG¯¯¯¯¯¯¯¯=9 in. The radius of the circle is 41 inches. Find the length of CT¯¯¯¯¯¯¯.
A. 40
B. 9
C. 80
D. not enough information
Answers
See the attached picture for the solution.
Answer:
Option: C is the correct answer.
C. 80
Step-by-step explanation:
PG=9 in. The radius of the circle is 41 inches.
We know that the side CT is given by:
CT=CS+ST
The side CS is calculated by using the Pythagorean Theorem in ΔCSP
i.e.
[tex]CP^2=CS^2+SP^2\\\\i.e.\\\\[/tex]
as CP is the radius of the circle
and SP=PG=9 in.
i.e.
[tex]41^2=9^2+CS^2\\\\i.e.\\\\1681=81+CS^2\\\\i.e.\\\\CS^2=1681-81\\\\i.e.\\\\CS^2=1600\\\\i.e.\\\\CS=40\ units[/tex]
and
similarly in right angled triangle ΔPST
we have:
[tex]TP^2=ST^2+PS^2\\\\i.e.\\\\41^2=9^2+ST^2\\\\i.e.\\\\ST=40\ units[/tex]
Hence,
[tex]CT=CS+ST\\\\i.e.\\\\CT=40+40\\\\i.e.\\\\CT=80\ in.[/tex]
Which set of side lengths is a Pythagorean triple?
1)1,3, 10
2)4,5,9
3)9, 40, 41
4)16, 30, 44
Answers
[tex]\huge{\boxed{\text{3) \bf{9, 40, 41}}}}[/tex]
A Pythagorean triple is a set of three numbers where [tex]a^2 + b^2 = c^2[/tex].
Trying 1:
[tex]1^2+3^2=10^2[/tex]
[tex]1+9=100[/tex]
[tex]10=100[/tex]
Incorrect.
Trying 2:
[tex]4^2+5^2=9^2[/tex]
[tex]16+25=81[/tex]
[tex]41=81[/tex]
Incorrect.
Trying 3:
[tex]9^2+40^2=41^2[/tex]
[tex]81+1600=1681[/tex]
[tex]1681=1681[/tex]
Correct!
Trying 4: (unnecessary, but practice is good)
[tex]16^2+30^2=44^2[/tex]
[tex]256+900=1936[/tex]
[tex]1156=1936[/tex]
Incorrect.
Complete the equation ....
URGENT NEED HELP ON THIS PROBLEM ASAP!!!
Answers
Answer:
h(x) = 7 * (9/7) ^x
Step-by-step explanation:
h(x) = a b^x
When x=0 h(x) = 7
7 = a * b^0
7 = a *1
7 =a
Rewriting the equation
h(x) = 7 b^x
Let x=1
9 = 7 * b^1
9 = 7 * b
Divide each side by 7
9/7 =7b/7
9/7 =b
h(x) = 7 * (9/7) ^x
• Which of the following equations represents a line that is perpendicular to
y = --4x+9 and passes through the point, (4, 5)?
A. y = -4x+4
B. y = 1/4x+5
C. y = 1/4x+4
D. y = 1/4x+6
Answers
Answer:
C
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 = - 4x + 9 ← is in slope- intercept form
with slope m = - 4
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex], hence
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line
To find c substitute (4, 5) into the partial equation
5 = 1 + c ⇒ c = 5 - 1 = 4
y = [tex]\frac{1}{4}[/tex] x + 4 ← equation of perpendicular line → C
Describe how (2^3)(2^-4) can be simplified.
Answers
Answer:
2^ (-1)
1/2
Step-by-step explanation:
Add the exponents which have common bases.
3 + (-4) = -1
2^ (-1)
1 / 2
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Answer:
The simplified form of the provided expression is [tex]2^{-1}\ or\ \frac{1}{2}[/tex]
Step-by-step explanation:
Consider the provided expression:
[tex](2^3)(2^{-4})[/tex]
Use the product rule of exponent:
[tex]a^m \cdot a^n=a^{m+n}[/tex]
Now use the above formula to simplify the provided expression.
[tex](2^3)(2^{-4})=2^{3+(-4)}[/tex]
[tex](2^3)(2^{-4})=2^{3-4}[/tex]
[tex](2^3)(2^{-4})=2^{-1}[/tex]
Hence, the simplified form of the provided expression is [tex]2^{-1}\ or\ \frac{1}{2}[/tex]