The value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.
We are given the logarithmic functions:
log₄3 = 0.792 ,,, (i), and log₄21 = 2.196 ... (ii),
and we are asked to find the value of the logarithmic function log₄7.
On subtracting (i) from (ii), we get:
log₄21 - log₄3 = 2.196 - 0.792.
Using the quotient law of logarithms, according to which:
logₓa - logₓb = logₓ(a/b), we can write the above equation as:
log₄(21/3) = 1.404,
or, log₄7 = 1.404.
Therefore, the value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.
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Answer:
A.
1.404
Step-by-step explanation:
What is this function written in vertex form? f(x) = (x 2)2 3 f(x) = (x2 2x)2 3 f(x) = (x 1)2 2 f(x) = (x 3)2 2x
The vertex form of the give quadratic equation is f(x) = (x+1)² + 2
Vertex form of an equationThe standard vertex form of a quadratic equation is expressed as
y = a(x -h)² + k
where (h, k) is the vertex
Given the quadratic equation
f(x) = x^2 + 2x + 3
Complete the question
f(x) = (x^2+2x) + 3
f(x) = (x^2+2x+1)-1 + 3
f(x) = (x+1)² + 2
Hence the vertex form of the give quadratic equation is f(x) = (x+1)² + 2
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Of the students at milton middle school, 132 are girls. if 55% of the students are girls, how many total students are there at milton middle school?
Answer:
There are 240 students in the school
Step-by-step explanation:
Givens
55% of the total number of students in a school are girls.
Equation
55/100 * x = 132
Solution
Multiply both sides of the equation by 100
55/100x * 100 = 132 * 100
55x = 13200 Divide by 55
55x/55 = 13200/55
x = 240
The table and the graph below each show a different relationship between the same two variables, x and y.
How much more would the value of y be on the graph than its value in the table when x = 12?
Answer:
240
Step-by-step explanation:
Using the straight line formula; y=mx+c, take two points, for example, (4, 80) and (5, 100)
m=change in y/change in x, so;
m=(100-80)/(5-4)= 20
Take point (4, 80)
80=20×4 + c
80-80=c=0
so y=20x
y=20×12=240
what is
f(-1)=-3x^{2}+7x+4
Step-by-step explanation:
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Which points can be connected to draw a line of symmetry through this diamond?
Drag and drop an answer to the box to complete the statement. please answer asap!
The line is drawn at point A and Point C is a line of symmetry because lines of symmetry make exactly two halves with similar shapes and sizes.
What is a line of symmetry?It is defined as the line which will make exactly two halves with similar shape and size in geometry. For a two-dimensional shape, there is a line of symmetry, and for three-dimensional shapes, there is a plane of symmetry. In other words, if we make a mirror image of the shape around the line of symmetry, we will get exactly the same half portion.
We have given a figure in the picture.
The figure is a quadrilateral(a kite)
As we know, lines of symmetry make exactly two halves with similar shapes and sizes.
IF we draw a line from Point A to Point C we will get two similar and figures in size and shape.
Thus, the line is drawn point A and Point C is a line of symmetry because lines of symmetry make exactly two halves with similar shapes and sizes.
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Answer:
point C
Here is a step-by-step explanation of the statement:
1. Draw a point B and a point C on a piece of paper or a computer screen.
2. Draw a straight line that goes through both point B and point C.
3. Fold the paper along the line you just drew, so that the line is the fold line.
4. Notice that if you were to fold the paper exactly in half along the line, point B would match up with its reflection on the other side of the line, and point C would match up with its reflection on the other side of the line.
5. This means that the line you drew is a line of symmetry, because it divides the paper into two identical halves that can be folded together.
6. Therefore, the statement "A line drawn through point B and point C is a line of symmetry" is true.
is 4+-x equivalent to 4-x
Answer:
Yes
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
4 + -x ==> 4 - x
Example
x = 3; 4 + (-3) = 4-3 =1
If m < 0 and b > 0, the graph of y = mx + b does not pass through which quadrant?
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Answer: Quadrant III
Step-by-step explanation:
The slope is negative and the y-intercept is positive.
This means that it is impossible for both x and y to be negative, and thus it does not pass through Quadrant III
write √a^8a^3 as an algebraic expression using a rational exponent
Answer:
A
Step-by-step explanation:
I assume that the whole expression a⁸a³ is under the square root.
then remember 2 things :
1. when multiplying the same base variable (or constant) the result is that single base variable (or constant) to the power of the sum of the exponents.
e.g. x³x² = x⁵ because
x×x×x × x×x = x×x×x×x×x = x⁵
2. a square root as exponent is 1/2.
a cubic root is 1/3 and so on.
therefore
sqrt(a⁸a³) = sqrt(a¹¹) = a^11/2
b) Another sequence is defined using this term-to-term rule, Un+1 = kun + r where k and rare constants. Given that u₁ = 37, U₂= 188 and u3 = 943, find the value of k and the value of r. b ) Another sequence is defined using this term - to - term rule , Un + 1 = kun + r where k and rare constants . Given that u₁ = 37 , U₂ = 188 and u3 = 943 , find the value of k and the value of r .
The values of k and r are given by 5 and 3 respectively.
Here in this problem it is given that,
General formula for the sequence is given by,
[tex]U_{n+1}=kU_n+r[/tex]
First term of the sequence, [tex]U_1=37[/tex]
Second term,
[tex]U_2=188[/tex]
[tex]U_{1+1}=188[/tex], rearranging
[tex]kU_1+r=188[/tex], applying general formula
[tex]37k+r=188[/tex]..........(1)
Third term,
[tex]U_3=943[/tex]
[tex]U_{2+1}=943[/tex], rearranging
[tex]kU_2+r=943[/tex], applying general formula
[tex]188k+r=943[/tex]..........(2)
Now (2) - (1) we get,
188k+r-37k-r = 943-188
151k = 755
k = 755/151 = 5
Hence the value of k is 5.
Substituting the value of k in (1) we get,
37*5+r = 188
185+r = 188
r = 188-185 = 3
Thus the value of r is 3.
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One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?
$\begin{align*}
&-x^2 + 18x + 81 \\
&3x^2 - 6x + 9 \\
&8x^2 - 32x + 32 \\
&25x^2 - 30x - 9 \\
&x^2 - 14x + 196
\end{align*}$
Answer:
Step-by-step explanation:
The quadratic expression having repeated root is 8x² - 32x + 32.
What are Quadratic Expressions?Quadratic expressions are polynomial expressions of second degree.
The general form of a quadratic expression is ax² + b x + c.
We have to find the root of each quadratic expression.
-x² + 18x + 81 = 0x² - 18x - 81 = 0
Discriminant = [tex]\sqrt{(-18)^2-(4*-81)}[/tex] = [tex]\sqrt{648}[/tex]
x = (18 + √648) / 2 or x = (18 - √648) / 2
Distinct roots
3x² - 6x + 9x² - 2x + 3
Discriminant = [tex]\sqrt{(-2)^{2}-(4*3) }[/tex] = [tex]\sqrt{-8}[/tex]
x = (2 + [tex]\sqrt{-8}[/tex]) / 2 or x = (2 - [tex]\sqrt{-8}[/tex]) / 2
Distinct roots
8x² - 32x + 32
x² - 4x + 4Discriminant = [tex]\sqrt{(-4)^{2}-(4*4) }[/tex] = 0
x = (4 + 0)/ 2 or x = (4 - 0) / 2
x = 2 or x = 2
Repeated roots
Hence the quadratic expression having repeated roots is 8x² - 32x + 32.
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Find the value of the lettered angle b
Answer:
60°Step-by-step explanation:
30 is an opposite angle (2 angles of 30°)
sum of all angles = 360°
360 - 90 -30 - 150 - 30 = 60°
check
60 + 30 + 150 + 30 + 90 = 360°
the answer is good
Answer:
b = 60
Step-by-step explanation:
A straight line is 180 degrees
30+90+b = 180
Combine like terms
120 +b = 180
b =180-120
b = 60
What is the measure of \angle x∠xangle, x?
Angles are not necessarily drawn to scale.
Answer:
Step-by-step explanation:
Comment
x and 133 sit on the the same straight line with MO in common. Therefore they are supplementary which means that the add to 180o.
Equation
x + 133 = 180
Solution
Subtract 133 from both sides
x + 133 = 180
x + 133 - 133 = 180 - 133
x = 47 degrees.
Answer
x = 47
Simplify each expression
3+8b+4+7b-3
Answer:
9. 15b + 4
10. 4y + 6
11. 15r+72
12. 130n + 20
Step-by-step explanation:
9. Combine Like terms
10. Combine Like terms
11. Distribute the 8 into (r + 9) then combine like terms
12. Distribute 10 into (3n + 2 + 10n) then combine like terms
Answer:
[tex]\mathsf {9) 15b + 4}\\\mathsf {10) 4y + 6}\\\mathsf {11) 15r + 72}\\\mathsf {12) 130n + 20}[/tex]
Step-by-step explanation:
[tex]\textsf {Question 9}[/tex]
[tex]\mathsf {3 + 8b + 4 + 7b - 3}[/tex]
[tex]\mathsf {8b + 7b + 4 + 3 - 3}[/tex]
[tex]\mathsf {15b + 4}[/tex]
[tex]\textsf {Question 10}[/tex]
[tex]\mathsf {8 + 7y - 3y + 2 - 4}[/tex]
[tex]\mathsf {7y - 3y + 8 + 2 - 4}[/tex]
[tex]\mathsf {4y + 6}[/tex]
[tex]\textsf {Question 11}[/tex]
[tex]\mathsf {8(r + 9) + 7r}[/tex]
[tex]\mathsf {8r + 8(9) + 7r}[/tex]
[tex]\mathsf {8r + 7r + 72}[/tex]
[tex]\mathsf {15r + 72}[/tex]
[tex]\textsf {Question 12}[/tex]
[tex]\mathsf {10(3n + 2 + 10n)}[/tex]
[tex]\mathsf {10(13n + 2)}[/tex]
[tex]\mathsf {10(13n) + 10(2)}[/tex]
[tex]\mathsf {130n + 20}[/tex]
State true or false. (i) Cube of any odd number is even. F (ii) A perfect cube does not end with two zeros.T (iii) If square of a number ends with 5, then its cube ends with 25. F (iv) There is no perfect cube which ends with 8. F (v) The cube of a two digit number may be a three digit number. F (vi) The cube of a two digit number may have seven or more digits. (vii) The cube of a single digit number may be a single digit number. T
Give reasons why
i. Cube of any odd number is even. False
ii. A perfect cube does not end with two zeros. True
iii. If square of a number ends with 5, then its cube ends with 25. False
iv. There is no perfect cube which ends with 8. False
v. The cube of a two digit number may be a three digit number. False
vi. The cube of a two digit number may have seven or more digits. False
vii. The cube of a single digit number may be a single digit number. True
Reasons
i. Cube of any odd number is even. This statement is false because the cube of odd numbers are also odd
ii. A perfect cube does not end with two zeros. This statement is True because the cube of a two digit number cannot be a 3 digit number and therefore cannot end with two zeros.
iii. If square of a number ends with 5, then its cube ends with 25. This statement is False
Using the illustration
35^2 = 35 x 35= 1225 , its square ends with 5
35^3= 35 x 35 x 35= 42875 which ends with 75
iv. There is no perfect cube which ends with 8. This statement is False.
Using the illustration, the cube of 2 is given thus
2 * 2 * 2 = 8
The cube of 2 ends with 8
v. The cube of a two digit number may be a three digit number. This statement is False.
Using the illustration, 10 is a two digit number
10 * 10 * 10 = 1000
The cube of 10 which is a two digit number is not a three digit number and same applies to all two digit numbers
vi The cube of a two digit number may have seven or more digits. This statement is False because the cube of a two digit number can only be a four digit number.
vii. The cube of a single digit number may be a single digit number. This statement is True because the cube of a single digit number can be a single, two or three digit number.
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A website sells a dress at £20 and shoes at £25. The website has an offer: Buy a dress and shoes together and get 1 3 off the price. There is also a shipping and handling charge of £4 added at the end, after any discount. If Ruth buys both a dress and shoes, how much will she actually pay?
£36
20+25=45 Take away 13 and it's 32. 32+4 (the shipping charge) is 36. So Ruth pays 36 pounds.
Factor this expression completely 9x^2 - 72x + 8
The solution for the given equation will be x=7.8873 and x=0.112699.
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
Find the Solution for
9x²−72x+8=0
using the Quadratic Formula where
a = 9, b = -72, and c = 8
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{(-72)\pm\sqrt{(-72)^2-4(9)(8)}}{2(9)}[/tex]
x= [tex]\dfrac{72\pm4896}{\sqrt{18}}[/tex]
The discriminant b2−4ac>0
so, there are two real roots. After solving for plus and then minus we will get two values as follows.
x=7.8873
x=0.112699
Therefore the solution for the given equation will be x=7.8873 and x=0.112699.
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What is the value of y? 17.5ft 12.5ft 11.6ft 16.5ft
Answer:
y = 16.5 ft
Step-by-step explanation:
• in the right triangle BCD :
cos(∠BCD) = 8/14
________
• In the right triangle ABC :
cos(∠BCA) = 14/(8+y)
________
Since ∠BCD and ∠BCA are the same one
then
cos(∠BCD) = cos(∠BCA)
Therefore
[tex]\frac{8}{14} =\frac{14}{y+8}[/tex]
[tex]\Longleftrightarrow 8(y+8)=14^2[/tex]
[tex]\Longleftrightarrow 8y+64=196[/tex]
[tex]\Longleftrightarrow 8y=196-64[/tex]
[tex]\Longleftrightarrow 8y=132[/tex]
[tex]\Longleftrightarrow y=\frac{132}{8}[/tex]
[tex]\Longleftrightarrow y=16.5[/tex]
A table of data is given.
x f(x)
-2 71
-1 13
0 3
1 0.6
2 0.1
Which exponential model best represents the data?
Of(x) = 3(1.2)^x
Of(x) = 2(0.3)^x
Of(x) = 2(3)^x
Of(x)=3(0.2)^x
Answer:
The choice D.
[tex]f(x) = 3 {(0.2)}^{x} [/tex]
Answer:
D
Step-by-step explanation:
Order of elimination:
1. the graph is going down exponentially. This means that the base is less than 1.
A and C are eliminated.
2. When x is equal to 0, f(x) = 3.
Substitute x for 0, and you'll find out that the only one possible is D.
which one is it? I will give you twenty points, if you will answer
Answer:
A fraction equivalent to [tex]\frac{1}{2}[/tex] on the number line is [tex]\frac{3}{6}[/tex].
Drag the dot to [tex]\frac{3}{6}[/tex] on the number line.
Step-by-step explanation:
3 is half of 6. To check if this is correct multiply [tex]\frac{1}{2}[/tex] and 3.
[tex]\frac{1}{2}*3=\frac{3}{6}[/tex]
Hope this helps!
If not, I am sorry.
All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample to make a statistical inference about the mean of the normally distributed population from which it was drawn? m e = startfraction z times s over startroot n endroot endfraction.
Sonam says that the 20th figure in this pattern has 400 small triangles. do you agree? explain your thinking.
Answer:
No. There should be 210 small triangles
Step-by-step explanation:
The number of small triangles in these figures forms a sequence
Fig No Small Triangles
1 1
2 3 (1+2)
3 6 (1+2+3)
So the nth figure should have 1+2+3+.....+(n-1)+ n
1+2+3+.....+(n-1)+ n = [tex]\frac{n (n-1)}{2}[/tex]
So for 20th figure, n = 20 and number of small triangles = 20 x 21 /2 = 420/2 = 210
Help anyone? Simple problem
Answer:x>7
Step-by-step explanation:
Its saying a nuber greater than 7 and 3 plus 8 would be 11
What value of n makes the equation true?
-1/5n+7=2
n=
[tex] \frac{ - n}{5} + 7 = 2 \\ \\ \frac{ - n + 35}{5} = 2 \\ \\ - n + 35 = 10 \\ \\ - n = 10 - 35 \\ \\ - n = - 25[/tex]
cancel (-) sign both sides ,
[tex]n = 25.[/tex]
What is the missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x? 1. The distributive property: 4x – 12 + 4 < 10 + 6x 2. Combine like terms: 4x – 8 < 10 + 6x 3. The addition property of inequality: 4x < 18 + 6x 4. The subtraction property of inequality: –2x < 18 5. The division property of inequality: ________ x < –9 x > –9 x < x is less than or equal to negative StartFraction 1 Over 9 EndFraction. x > –x is greater than or equal to negative StartFraction 1 Over 9 EndFraction.
The inequality 4(x – 3) + 4 < 10 + 6x is solved as x > -9. Then the variable x is greater than the negative 9. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
The inequality equation is given below.
4(x – 3) + 4 < 10 + 6x
Then the steps of solving are given below.
1. The distributive property: 4x – 12 + 4 < 10 + 6x
2. Combine like terms: 4x – 8 < 10 + 6x
3. The addition property of inequality: 4x < 18 + 6x
4. The subtraction property of inequality: –2x < 18
5. The division property of inequality: x > –9
Then x is greater than the negative 9.
Then the correct option is B.
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Solve the following equation, and check your solution. Be sure to show all work in order to receive full credit.
Solve -17 + n/5 = 33.
Answer:
n = 250
See solution and check blow.
Step-by-step explanation:
Solution:
-17 + n/5 = 33
Add 17 to both sides.
-17 + 17 + n/5 = 33 + 17
n/5 = 50
Multiply both sides by 5.
n/5 × 5 = 50 × 5
n = 250
Check:
-17 + n/5 = 33
Since we found out that n = 250, substitute 250 for n in the equation.
-17 + 250/5 = 33
Simplify the left side. Divide 250 by 5.
-17 + 50 = 33
Add on the left side.
33 = 33
Since 33 = 33 is a true statement, the solution n = 250 is correct.
f(x) = x + 6 , find the ordered pair when x = -2.
(-2,4)
(2,-4)
(-2,-4)
(2,4)
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option A, (-2, 4)}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{f(x) = x + 6}[/tex]
Find: [tex]\textsf{f(-2)}[/tex]
Solution: We need to plug in the value -2 into every variable x that we have in the expression and simplify to get the solution.
Plug in the values
[tex]\textsf{f(x) = x + 6}[/tex][tex]\textsf{f(-2) = -2 + 6}[/tex]Simplify
[tex]\textsf{f(-2) = -2 + 6}[/tex][tex]\textsf{f(-2) = 4}[/tex]Therefore, the ordered pair that would match would have a x-coordinate of -2 and a y-coordinate of 4 producing (-2, 4) which matches option A.
The product of 2 more than 3 times a number and 6 less than 4 times the number (z)
Answer:
[tex]12z^{2} -10z -12[/tex]
Step-by-step explanation:
Let the number be z
2 more than 3 times z ==> 3z + 2
6 less than 4 times z ==> 4z - 6
Product of the above two is
[tex](3z + 2) (4z - 6) \\= (3z)(4z) + (3z)(-6) + (4z)(2) + (2)(-6)\\= 12z^{2} -18z + 8z - 12\\= 12z^{2} -10z -12[/tex]
Brandon is a running back for his local high school football team. In the last game, he carried the ball 8 times. In the first 5 carries, he gained 6 yards, 12 yards, and 4 yards before losing 2 yards and then losing additional yards. His last 7 carries combined for yards. What was his total net yardage for the game?
Using it's concept, it is found that Brandon's net yardage for the game was of 26.
How to find the net yardage?The total net yardage is the sum of all the yardage they gain, that is, the positive gains are added with a plus signal, while the negative gains are added with a negative signal.
Hence, his net yardage, considering that he gained 20 yards on his last 7 carries, is given by:
6 + 20 = 26.
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Find the solution:
3x + 2y = 12
-2x + 3y = 5
Answer:
x = 3
y = 2
Step-by-step explanation:
3x + 2y = 12
-2x + 3y = 5 to find the solution we will use elimination method and for that, multiply second equation with 3 and the first equation with 2
2 * 3x + 2y = 12
6x + 4y = 24
3 * -2x + 3y = 5
-6x + 9y = 15 now find the sum of both equation:
6x + 4y -6x + 9y = 24 + 15 add like terms
13y = 39 divide both sides by 13
y = 3 now that we found the value of y we can use this to calculate the value of x
3x + 2y = 12 replace y with 3
3x + 2*2 = 12
3x + 4 = 12 subtract 4 from both sides
3x = 9 divide both sides by 3
x = 3
0.33632287 to 3sf please
Answer:
.
Step-by-step explanation:
