(75 POINTS PLEASE RESPOND ASAP)
Explain how to solve 4x + ^3 = 7 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.
Answers
Answer:
1.596
Step-by-step explanation:
So you can rewrite log as: [tex]log_{b}a=x = > b^x=a[/tex] So in this case it's already in exponential form which we'll use to rewrite into logarithm form.
[tex]4^{x+3} = 7\\log_47=x+3\\\\\frac{log7}{log4}=x+3\\1.404\approx x+3\\x\approx1.596[/tex]
Answer:
x = -1.596
Explanation:
[tex]\rightarrow \sf 4^{x + 3} = 7[/tex]
take log on both sides
[tex]\rightarrow \sf log(4^{x + 3}) = log(7)[/tex]
[tex]\rightarrow \sf (x + 3)log(4) = log(7)[/tex]
[tex]\rightarrow \sf x + 3= \dfrac{log(7)}{log(4)}[/tex]
[tex]\rightarrow \sf x= \dfrac{log(7)}{log(4)} -3[/tex]
calculate
[tex]\rightarrow \sf x= -1.596322539[/tex]
[tex]\rightarrow \sf x= -1.596 \quad (rounded \ to \ nearest \ thousand)[/tex]
Related Questions
Select the correct answer.
Which function is the inverse of ?
Answers
Answer:
B. [tex]f^{-1}(x) = \frac{x + 3}{9}[/tex]
Step-by-step explanation:
[tex]let \space\ y = f(x)\\\\y = 9x -3\\[/tex]
• Now make x the subject of the equation:
[tex]9x = y + 3\\\\x = \frac{y + 3}{9} \\[/tex]
• Replace x with f⁻¹(x) and y with x:
[tex]f^{-1}(x) = \frac{x + 3}{9}[/tex]
Now evaluate f(x)=2x^4-4x^3-11x^2+3x-6 for x=-2.
F(-2)=
Answers
Answer:
8
Step-by-step explanation:
f(x)=2x^4-4x^3-11x^2+3x-6
f(-2)=2(-2)^4-4(-2)^3-11(-2)^2+3(-2)-6
f(-2)=2(16)-4(-8)-11(4)-6-6
f(-2)=32+32-44-12
f(-2)=64-44-12
f(-2)=20-12
f(-2)=8
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4
Answers
An expression is defined as a set of numbers, variables, and mathematical operations.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression that is equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p are given below,
If the given expression 2.3p – 10.1 = 6.5p – 4 – 0.01 is simplified, then the expression can be written as,
2.3p – 10.1 = 6.5p – 4 – 0.01
2.3p – 10.1 = 6.49p – 4
Thus, Option A is one of the option.
Using the multiplication property of Equality, if we multiply both the sides of the equation by 100, then we will get,
230p – 1010 = 650p – 400 – p
Thus, c is one of the option.
Hence, the correct options are A and C.
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Horizontal lines n and m are intersected by lines q and p. At the intersection of lines q and n, the uppercase right angle is angle 4. At the intersection of lines q and m, the uppercase left angle is angle 1. At the intersection of lines p and n, the bottom left angle is angle 3. At the intersection of lines p and m, the uppercase left angle is angle 2.
If angle 1 is 110°, what would the other angle measures have to be in order for m || n and
q || p?
Angle 2 = °
Angle 3 = °
Angle 4 = °
Answers
The values of the angles based on the information will be:
Angle 2 = 110°Angle 3 = 70°Angle 4 = 70°How to calculate the angles?From the information given, angle 1 is 110° and the horizontal lines n and m are intersected by lines q and p.
In this case, it should be noted that opposite angles are equal. Hence, angle 2 is also 110°.
Angle 3 will be:
= 180° - 110° = 70° (angle on a straight line).
Angle 4 will also be 70° as opposite angle to angle 3.
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5 14/15 on a number line rounded to the nearest whole number or half.
PLEASE HELP ME!!!!! I NEED HELP
Answers
Answer:
Step-by-step explanation:
Here we will show you step-by-step how to get the solution to: "What is 5/14 rounded to the nearest whole number?"
First, we convert the fraction to a decimal number by dividing the numerator by the denominator:
5 / 14 = 0.3
Then, we round to the nearest whole number using the following rules:
If the number to the right of the decimal point is .5 or higher, then add 1 to the left of the decimal point.
If the number to the right of the decimal point is less than .5, then leave the number to the left of the decimal point as is and remove the digit to the right of the decimal point.
.4 is less than .5. Thus, we leave the number to the left of the decimal point as is and remove the digit to the right of the decimal point.
5/14 rounded to the nearest whole number is therefore:
0
According to the property
below?
√30
OA. 25
OB. -√5
O C. 5
OD. -5
OE. √5
Vo = √ which choice is equivalent to the quotient
4
Answers
Answer:
√30/6 = √5
The correct answer would be E
The value of the expression √30/√6 is √5, option E is correct.
What is Number system?A number system is defined as a system of writing to express numbers.
The given property is √a/√b = √(a/b)
Now we have to find the equivalent to the quotient √30/√6
By the given property let us plug in a as 30 and b as 6
√30/√6
= √(30/6)
When we simplify the fraction inside the root we get 5
= √5
Hence, the value of the expression √30/√6 is √5, option E is correct.
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Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$350 and $400.
[ ? ]%
Answers
Construct a truth table for the following symbolic statement.
Use the type of truth table where each variable or operator in the given expression has its own column. Fill in the rows of the truth table one at a time.
Answers
The truth table is completed for each column as T T F F T T T
What is a truth table?A truth table is a mathematical table which shows all the truth values of a given combination of logic statements.
Analysis:
The truth table is shown in the attached file
in the attached file, the first two columns were given,
The third column is the negation of p, and P is true(T) which means its negation is false(F).
The fourth column is the negation of Q, which means Q is true(T) so its negation is false(F).
In the fifth column, negation P is implies negation Q. The truth table for implication, is only false if Q is false, else it is True.
Same as in the sixth column.
The last column is bi-implication, the truth table for this only true, if both statements are false or both are true else, it is false.
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The cost of the fruit is given by the function y=3x+1, where x is the number of fruits and y is the total cost. Find the range of the function.
Answers
is 4+-x equivalent to 4-x
Answers
Answer:
Yes
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
4 + -x ==> 4 - x
Example
x = 3; 4 + (-3) = 4-3 =1
Find the missing length A. 80
B. 15
C. 64
D. 60
Answers
Answer:
the answer is C.64
Step-by-step explanation:
Answer:
the answer is C
Step-by-step explanation:
because the
I need help solving this
Answers
Answer: y = -x + 5
Step-by-step explanation:
A slope-intercept equation is in the form y = mx + b where m is the slope and b is the y-intercept. Since we are given the slope, we will plug it in with the point they gave us, and solve for b.
y = mx + b
(1) = (-1)(4) + b
1 = -4 + b
5 = b
Lastly, we will write our equation by substituting m with -1 and b with 5.
y = mx + b
y = -1x + 5 or y = -x + 5
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Shapes A and B are similar.
a) Calculate the scale factor from shape A to
shape B.
b) Find the value of r.
Give each answer as an integer or as a fraction in
its simplest form.
5 cm
11 cm
A
20 cm
3 cm
rcm
B
12 cm
Not drawn accurately
Answers
The scale factor from A to B is 5/3 and the value of r is 33/5
The scale factor from A to BFrom the figure, we have the following corresponding sides
A : B = 5 : 3
Express as fraction
B/A = 3/5
This means that, the scale factor from A to B is 5/3
The value of rFrom the figure, we have the following corresponding sides
A : B = 11 : r
Express as fraction
B/A = r/11
Recall that:
B/A = 3/5
So, we have:
3/5 = r/11
Multiply by 11
r = 33/5
Hence, the value of r is 33/5
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This year, a small business had a total revenue of $44,100. If this is 26% more than their total revenue the previous year, what was their total revenue the previous year?
Answers
Answer:
look at the picture .
Step-by-step explanation:
look at the picture .
Help yalllll question is in the pic
Answers
Step-by-Step Solution:
=> f(x) = 5x - 1
=> g(x) = 2x^2 + 1
=> Find value of (f * g)(-3)
First Substitute x as -3 in f(x) and g(x) :-
f(x) = 5x - 1
f(-3) = 5(-3) - 1
f(-3) = -15 - 1
=> f(-3) = -16
g(x) = 2x^2 + 1
g(-3) = 2(-3^2) + 1
g(-3) = 2(9) + 1
g(-3) = 18 + 1
=> g(-3) = 19
Now Multiply f(-3) with g(-3) :-
= f(-3) * g(-3)
= -16 * 19
=> -304
Therefore, (f * g)(-3) = -304
what is the solution to this equation? 8(e)^2x+1=4
Answers
Answer:
Exact Form:
x=3/8e^2
Decimal Form:
x=0.05075073…
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
A triangle has the dimensions shown. The perimeter of the triangle would be represented by which type of expression?
linear expression
quadratic expression
exponential expression
rational expression
Answers
The third side is a linear expression , Option A is the right answer.
The missing diagram is attached with the figure.
What is a Triangle ?A triangle is a polygon with three sides , three vertices , three angles .
It is given that the side of the triangle as 3x+1 , 5x-2 , y
Perimeter is given as 10x-1
Perimeter = 3x+1 +5x-2 + y = 10x-1
8x -1 +y = 10x -1
y = 2x
which is a linear expression.
Therefore the third side is a linear expression , Option A is the right answer.
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can you help me solve this question
Answers
Answer: Coordinates: (1,3) length RS: 3 length RT: 2 ST: 3.6
Step-by-step explanation:
a^2+b^2=c^2
3^2+2^2=c^2
9+4=c^2
13=c^2
3.6=c
What two numbers differ by 46. (29,17,38,71,35,63,24)
Answers
Answer: 63 and 17 differ by 46.
Step-by-step explanation:
63-17=46
Subtraction is what you do when trying to find the difference of something.
pls help asap!!!!
Which number best represents the slope of the graphed line?
Answers
Answer:
C: 1/2
Step-by-step explanation:
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: C. \cfrac{1}{2}[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \textsf{Slope of line - } [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{rise}{run} [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{0 - ( - 4)}{8 - 0} [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{ 4}{8 } [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{ 1}{2} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) after t seconds is given by the following.
Answers
A quadratic equation is in the form of ax²+bx+c. The time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The complete question is:
A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) after 7 seconds is given by the following, h=2+31t-16t². Find all values of t for which the ball's height is 16 feet. Round your answer(s) to the nearest hundredth.
The time at which the height of the ball is 16 feet can be found by,
h = 2 + 31t - 16t²
16 = 2 + 31t - 16t²
16 - 2 - 31t + 16t² = 0
16t² - 31t + 14 = 0
[tex]t = \dfrac{-(-31)\pm \sqrt{(-31)^2-4(16)(14)}}{2(16)}\\\\[/tex]
t = 0.717 , 1.221
Hence, the time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.
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8x3+70÷7-7
tell accordingly the correct answer will be marked as brainliest
Answers
U have to solve it by order of operation ( u start solving from right to left)
Order of operation in this case:
- ➗or✖️
- ➕or➖
So we can see that 70 divided by 7 is first so we solve it and it will give us 10.
Then we solve 8x3 which is 24, so now we have 24 +70+10-7, so the FINAL ANSWER IS 27
Answer:
27
Step-by-step explanation:
When solving complicated equations like this, we need to remember the order of operations (PEMDAS), which is the order that we solve an equation
P arentheses
E xponents
M ultiplication
D ivision
A ddition
S ubtraction
now, here's the thing: we actually to multiplication/division at the same time, and the same thing with addition/subtraction
(as in, adding -4 is the same thing as subtracting 4, so we can't truly make a distinction between the two)
so, when we have multiple instances of multiplication/division , we solve left to right
(and then the same thing for addition/subtraction)
8 × 3 + 70 ÷ 7 - 7
so, we first need to multiply 8 by 3
8 × 3 = 24
next, we move to the right:
and we divide 70 by 7
70 ÷ 7 = 10
let's rewrite our equation:
(24) + (10) - 7
24 + 10 - 7 = 27
so, the answer to this expression is 27
hope this helps!! have a lovely day :)
need help asap!!! ill give brainliest for right answer!
A rectangular pyramid has a height of 6 units and a volume of 40 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?
A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
Answers
Answer:
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct
Got it right one the test! <3
A four-person committee is chosen from a group of eight boys and six girls.
If students are chosen at random, what is the probability that the committee consists of all boys?
•4/1001
• 15/1001
•10/143
•133/143
Answers
Answer:
The answer is 10/143
Step-by-step explanation:
Identify the Property of Equality that is used in each statement.
If x=2, then 2x = 4.
5= 3a; therefore, 3a = 5.
If T=4, then 5T + 7 equals 27.
If 9 = 4x and 4x = m, then 9 = m.
Answers
Step-by-step explanation:
x = 2. 2(x) = 2(2). 2x= 4. Multiplication Property of Equality (if you have two equals sides and then multiply them by the same quantity both sides will remain equal)
5=3a therefore 3a = 5. Symmetric Property if a=b then b=a
T = 4 => 5T = 20 (Multiplication Property of Equality) => 5T + 7 = 27 (Addition Property of Equality. basically if two sides are equal and you add the same quantity they will remain equal)
Last one is transitive property which states. if a=b and b=c then a=c so in this case a would be 9, b would be 4x and c would be m
The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete two rotations every minute.
Write a sine model, y = asin(bt) + k, for the hight (in feet) of the end of one blade as a function of time t (in seconds). assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.
Options are displayed in the picture
Answers
Answer:
D: y= 10sin([tex]\frac{\pi }{15}t[/tex]) + 30
Step-by-step explanation:
30 feet above the ground is the k value.
10 feet long is how long the blades reach up and down which is also known as the amplitude.
The rest is given in all answers.
Evaluate:
2/3 + 4/5 x 7/5 - 8/3
Answers
Step-by-step explanation:
please mark me as brainlest
Answer:
-0.88
Explanation:
2/3 + 4/5 x 7/5 - 8/3
2/3 + 28/25 - 8/3
2/3 - 8/3 + 28/25
-6/3 + 28/25
-2 + 28/25
-50/25 + 28/25
-22/25
-0.88
Consider a quadrilateral with vertices A(2,2) , B(2,5) , C(7,2), and D(7,5). What is the shape and area of quadrilateral ABCD
Answers
Answer:
Shape is rectangle
Area of rectangle = length * width
= 5 * 3
= 15 units²
Which choice is equivalent to the expression below?
450
OA. 45²
OB. 0
OC. 45
O D. 1
Answers
Answer:
D is the answer because according to the law any number which has 0 at their power is equal to 1.
The correct value of this expression is 1. Letter D
We know that a power is the multiplication of equal factors - according to the exponent. That is, we just multiply the sentence by itself with the value given by the exponent.
Therefore, any number raised to the power of zero will be 1.
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I. Answer each question. Write the letter of the correct answer in your paper.
Read and analyze the following problems carefully. Then, write your answer on a separate sheet of paper.
_____1. In a given circle, the radius is 9 cm. What is its diameter?
A. 18 m
B.18 cm
C. 4.5 m
D. 4.5 cm
_____2. Which of the following is the formula in solving for the area of a circle?
A. A= 2πr
B. A= πr2
C. A= πd
D. A=2 πr2
_____3. The diameter of a circle is8 cm, what is its area?
A.50.24 cm2
B.200.96 cm2
C.25.12 cm2
D.100.48 cm2
_____4. What is the radius of a circle if the area is 36m2?
A. 0.339 m
B. 3.39 m
C. 33.9 m
D. 339m
_____5. What is the area of a circle if the radius is 5m?
A. 15. 7 m2
B. 31.4 m2
C. 78.5 m2
D. 157 m2
Answers
1) B) 18 cm
Radius (r) = 9 cm
Diameter (d) = 2r = 9 * 2 = 18 cm
2) B) A = πr^2
3) A) 50.24 cm^2
Diameter (d) = 8 cm
Radius (r) = d/2 = 8/2 = 4 cm
Area (A) = πr^2
Therefore,
= πr^2
= 3.14 * 4 * 4
= 3.14 * 16
=> 50.24
Area (A) = 50.24 cm^2
4) B) 3.39 m
Area (A) = πr^2 = 36 m^2
Therefore,
πr^2 = 36
3.14 * (r^2) = 36
r^2 = 36/3.14
r^2 = 3600/314
r^2 = 11.46
r = √11.46
=> r = 3.39
Radius (r) = 3.39 m
5) C) 78.5 m^2
Radius (r) = 5 m
Area (A) = πr^2
Therefore,
= πr^2
= 3.14 * 5 * 5
= 3.14 * 25
=> 78.5
Area (A) = 78.5 m^2
