According to the product rule of logarithms, the given equation is written as, log₄(x² + 13x + 40) = 1
Product rule of logarithm
Basically, the product rule states that the sum of two logarithms is equal to the product of the logarithms.
And it is the first law and it can be represented as;
logₐ(x) + logₐ(y) = logₐ(xy)
Given,
Here we have the logarithmic equation log 4(x+8) + log 4(x+5) = 1
And we have to rewrite the equation.
Here we have the logarithmic equation,
=> log₄(x+8) + log₄(x+5) = 1
By using the product property of logarithms,
We have to rewrite the equation as,
=> log₄(x+8)(x+5) = 1
Now, we have to expand (x+8)(x+3) using the FOIL Method.
Then we get,
=> log₄(x² + 5x + 8x + 40) = 1
=> log₄(x² + 13x + 40) = 1
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kims music files takes up 7 gigs of space on her hard drive. about how many bytes is that how many bits is that?
Select all symmetries that apply
Subtract. (−4x − 1) – (6x – 5)
Answer:
-10x+4
Step-by-step explanation:
distribute the minus
-4x-1-6x+5
-10x+4
hopes this helps please mark brainliest
Find the unknown term in the geometric proportion 8 : 2 :: x : 6
Arithmetic proportions are those whose means are not equal and are called discrete arithmetic proportions. On the contrary, if the means of the arithmetic proportion are equal, it is called continuous.
[tex]\bf\large{\underline{\fcolorbox{blue}{aqua}{Problem:}}}[/tex]
[tex] \sf8 : 2 :: x : 6[/tex]
Since the unknown term is an extreme and as we have seen, it is equal to the product of the means divided by the other extremes, we will have:
[tex]\boxed{\: x = \frac{8 \times6}{2} = \frac{48}{2} = 24 }[/tex]
Therefore, the resulting geometric proportion would be:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red\longmapsto \sf \orange{8 : 24 :: 6}[/tex]
|||
Solving a word problem on proportions using a unit rate
Ali made $306 for 17 hours of work.
At the same rate, how many hours would he have to work to make $126?
Express the sample proportion as a percent:
Out of 1150 insurance applicants, 837 have no citations on their driving record.
%
Answer:
837/1150=0.727
Or 73%
Step-by-step explanation:
The sum of $5400 was borrowed from a bank
at the rate of 10% per annum for 3 years. How much would the simple interest payable would be?
(A) $1800
(B) $540
(C) $1620
(D) $486
The simple interest on $5400 at a rate of 10% per annum for 3 years is $ 1620
Simple interest:The interest on a loan at a fixed rate per annum. The formula used for simple interest is given by
Simple interest (I) = ptr
Where p = principal amount
t = time period
r = rate of interest per year.
Here we have
The sum of $5400 was borrowed from a bank at a rate of 10% per annum for 3 years
Find the simple interest that can be payable
From above observations
Principal amount, P = $5400
Rate of interest = 10% = 10/100 = 0.1
Time period, t = 3 years
The simple interest that can be payable = $5400(3)(0.1) = $ 1620
Therefore,
The simple interest on $5400 at a rate of 10% per annum for 3 years is $ 1620
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The inequality x ≤ -2 would represent the values {-1, -2, -3}.
False
True
Answer:
False
Step-by-step explanation:
x ≤ - 2
the symbol ≤ ( less than or equal to ) means that x can equal - 2 and any values to the left of - 2 on the number line.
- 1 is to the right of - 2 and - 3 is to the left , so
the values represented are - 2, - 3
Usman graphs a proportional relationship. Leandro graphs a line that passes through the origin. What do you know about the y-intercept of each student’s graph? Explain your answer.
If the graph is passes through the origin then there is no y - intercept on the graph.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Usman graphs a proportional relationship.
And, Leandro graphs a line that passes through the origin.
Now,
Since, Leandro graphs a line that passes through the origin.
That's mean the graph has no any y - intercept.
Thus, If the graph is passes through the origin then there is no y - intercept on the graph.
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calculate the sizes of angles marked with letters in the following diagrams, giving reasons for your answers
Which is the solution to the system of equations?
y = 1/8x −1
−5x + 4y = −13
A. (0,−1)
B. (8,0)
C. (1,−7/8)
D. (2,−3/4)
The solution to the system of equations y = 1/8x −1 and −5x + 4y = −13 is (2, −3/4). Option D is correct.
We are given:
y = 1/8 x − 1 ..............equation i.
− 5x + 4y = − 13 ..............equation ii.
We will use the substitution method to solve the given equation.
substitute the value of y from equation i in equation ii, and we will get;
− 5x + 4(1/8 x − 1) = − 13
− 5x + 1/2 x − 4 = − 13
(-10 + 1) / 2 x = -13 + 4
-9/2 x = -9
x = -9 * 2 / -9
x = 2
Put the value of x in equation i, we will get;
y = 1/8 *2 − 1
y = 1/4 - 1
y = 1 - 4 / 4
y = -3 / 4
So, the value of x = 2 and the value of y = -3 / 4.
Thus, the solution to the system of equations y = 1/8x −1 and −5x + 4y = −13 is (2, −3/4). Option D is correct.
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5x−3y=−3
Step 1 of 2 : Determine the slope and the y-intercept (entered as an ordered pair) of the equation above. Reduce all fractions to lowest terms.
The slope of the function 5x − 3y = −3 is 5/3 and the y-intercept of the function 5x − 3y = −3 is 1.
First, let us understand the slope intercept form;
The slope intercept form is simply a way of writing a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are obvious.
We know that the slope intercept form of a line is y = mx + c where m is the slope of the line and b is the y-intercept of the line.
We are given;
5x − 3y = −3
- 3y = -5x - 3
3y = 5x + 3
y = 5/3 x + 1
Compare with y = mx + c, we will get;
m = 5/3
b = 1
So, the slope is 5/3 and the y-intercept is 1.
Thus, the slope of the function y = 2 + 34x is 5/3 and the y-intercept of the function y = 2 + 34x is 1.
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Find the value of the linear correlation coefficient r. Round your answer to 3 decimal places if necessary.
(1 , 6) , (3 , 4) , (5 , 2)
The value of the linear correlation coefficient r is of:
m = -1.
What is a linear function?A linear equation is a special function that has the format of the equation given as follows:
y = mx + b.
The coefficients of the equation y = mx + b are given as follows:
m is the slope, representing the rate of change of y relative to x, which is also the correlation coefficient of the linear function.b is the y-intercept, representing the value of y when x = 0.In this problem, the points of the function are listed as follows:
(1 , 6) , (3 , 4) and (5 , 2)
From these three points, we can gather that when x increases by 2, y decays by 2, hence the slope of the linear function is given as follows:
m = -2/2 = -1.
Meaning that the linear correlation coefficient r of the linear function is of r = -1.
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If the graph is reflected over the x-axis, what is the
domain of the function?
Answer:
When the function is to be reflected over the x and y-axis, we write it as a reflection of a function over x = y, so it is divided into two parts or two cases y = x and y = − x. When the graph of function is reflected over y = x, then we will swap the coordinates of the x and y-axis with each other while their signs remain the same.
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the estimated value of each expression with its position on the number line.
From the number line √90-√40 match with D, [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] match with C, 2√27 -√48 match with E and [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] match with A.
In the given question we have to match the each expession with its position on the number line.
The given first expression is √90-√40.
We firstly simplifying the expression.
√90-√40=√9×10-√4×10
√90-√40=3√10-2√10
Taking common [tex]\sqrt{10}[/tex] on both side
√90-√40=√10(3-2)
√90-√40=√10
√90-√40=3.16
From the number line √90-√40 match with D.
The given second expression is [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex].
We firstly simplifying the expression.
We can write it as
[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\frac{\sqrt{5\times7}-\sqrt{6\times7}}{\sqrt{5}-\sqrt{6}}[/tex]
Taking common √7 on both side
[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\frac{\sqrt{7}(\sqrt{5}-\sqrt{6})}{\sqrt{5}-\sqrt{6}}[/tex]
[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\sqrt{7}[/tex]
[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] = 2.65
From the number line [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] match with C.
The given third expression is 2√27 -√48.
We firstly simplifying the expression.
We can write it as
2√27 -√48=2√3×9 -√16×3
2√27 -√48=2×3√3 -4√3
2√27 -√48=6√3 -4√3
Taking √3 common on both side, we get
2√27 -√48=√3(6 -4)
2√27 -√48=2√3
2√27 -√48=2×1.71
2√27 -√48=3.42
From the number line 2√27 -√48 match with E.
The given fourth expression is [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex].
We firstly simplifying the expression.
We can write it as
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{\sqrt{9\times6}-\sqrt{4\times6}}{\sqrt{2\times9}-\sqrt{2\times4}}[/tex]
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{3\sqrt{6}-2\sqrt{6}}{3\sqrt{2}-2\sqrt{2}}[/tex]
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{\sqrt{6}(3-2)}{\sqrt{2}(3-2)}[/tex]
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\sqrt\frac{6}{2}[/tex]
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] =√3
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] = 1.71
From the number line [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] match with A.
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Answer: d,c,e,
ur welcomee!
Find the y-intercept and x-intercept of the following linear equation.
x+4y=4
Enter the coordinates to plot points on the graph.
Answer:
y intercept: 1
X intercept: 4
Step-by-step explanation:
to find y intercept we set x to 0
0+4y=4
/4. /4
y=1
y intercept is 1
Now for x intercept we set y to 0
x+4(0)=4
x=4
X intercept is 4
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Ordered 0.5mg/ kg and supplied 10 mg/ml and weighs 40 kg how many mls do you give
As per the given relation between ordered mg to kg and supplied mg to ml then weighs 40kg is equal to 2ml.
As given in the question,
Relation between mg to kg as per the ordered is given by ,
0.5 mg / kg
⇒ For 1 kg = 0.5 mg
Relation between mg to ml as per the supplied is given by ,
10 mg / ml
⇒ 1 ml = 10 mg
Now for 40 kg weighs the relation is given by,
1 kg = 0.5 mg
⇒ 40 kg = ( 40 × 0.5) mg
⇒ 40 kg = 20 mg ___(1)
And
1 ml = 10 mg
⇒ ( 2 × 1) ml = ( 2 × 10 ) mg
⇒ 2ml = 20mg ____(2)
From (1) and (2) we get ,
For 40 kg weighs we need 2ml.
Therefore, As per the given relation between ordered mg to kg and supplied mg to ml then weighs 40kg is equal to 2ml.
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Identify the change in the parent function that will produce the related function shown as a dashed line. f(x) = x
An orchard has 440 orange trees. The number of rows exceeds the number of trees per row by 2. How many trees are there in each row?
Given the number of trees in the orchard, the number of trees in each row is 20 trees.
How to find the number of trees?Assuming that the number of rows is represented as x, the number of trees would be 2 less than the number of rows which makes it:
= x - 2
The number of trees is:
x ( x - 2) = 440
x² - 2x - 440 = 0
Solving for r can then be done quadratically which gives us:
x = (2 ± √(2² - 4(1) (- 440)) / 2 (1)
= 22, and -20
The number of rows in the orchard cannot be negative so the number of rows is 22.
The number of trees is therefore:
= Number of rows - 2
= 22 - 2
= 20 trees
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Point E is added to the given figure so that point E lies on segment BD exactly halfway between points B and D. Which statement correctly compares the angle measures?
Answer:
there is no picture but m∠EBD = m∠EBD would be one of the best one as a guess to what the photo might be
Step-by-step explanation:
Point E is added to the given figure so that point E lies on segment BD and it is exactly halfway between points B and D
what is the equation of the line shown below
A y=-2/3x+1
B y=2/3x-1
C y=2x-1
D y=6x=4
The equation of the line is option (C) y = 2x - 1
First we have to choose two points
The first point = (1, 1)
The second point = (2, 3)
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
Slope of the line = (3-1) / (2-1)
= 2 / 1
= 2
From the graph line is intersecting on y axis at y = -1
The slope intercept form of the line
y = mx + b
where m is the slope of the line
b is the y intercept
Substitute the values
y = 2x - 1
Hence, the equation of the line is option (C) y = 2x - 1
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The radius of a circle is 33 cm. What is the area of the circle? Give your answer to 1 d.p.
The area of the circle with radius 33 cm is 3419.5 square centimeters.
According to the question,
We have the following information:
Radius of the circle = 33 cm
We know that the following formula is used to find the area of the circle:
Area of the circle = π[tex]r^{2}[/tex] where r is the radius of the circle
There are two approximate values of π which are 22/7 and 3.14. In this case, we will use the value of π as 3.14.
So, we have the following expression:
Area of the circle = 3.14*33*33
Area of the circle = 3419.46 square centimeters
Rounding it off to one decimal point:
3419.5 square centimeters
Hence, the area of the circle with radius 33 cm is 3419.5 square centimeters.
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Aldo is saving money to buy a game. the game cost $18, and so far he has saved one-third of this cost. How much money has Aldo saved
Answer: c=54
Step-by-step explanation:
8. Why can a² + 100 not be factored using difference of squares? please help!!!
Answer:
the sum of squares kasi yan
Explanation:
first find the squareroot of a² and 100
the squareroot of a²=a
because a×a=a²
the squareroot of 100=10
because 10×10=100
second factor
(a + 10)² or (a + 10)(a + 10)
Which of the following number sentences is true? A. 5+3 x 22 = 256 C. 5+3 x 22 = 32 B. 5+3 x 22 = 180 D. 5+3 x 2² = 17
The sentence which is true is 5+3×2²=17. The correct option is D.
Given the sentences is 5+3×22=256, 5+3×22=32, 5+3×22=180 and 5+3×2²=17.
We want to choose the sentence which is true.
An operator is a wildcard symbol used to indicate a mathematical operation that results in one or more mathematical objects leading to another similar object.
The first option is 5+3×22=256.
Solve the LHS, we get
5+3×22=5+66
5+3×22=71.
The first option 5+3×22≠256.
The second option is 5+3×22=32.
Solve the LHS, we get
5+3×22=5+66
5+3×22=71.
The second option 5+3×22≠32.
The third option is 5+3×22=180.
Solve the LHS, we get
5+3×22=5+66
5+3×22=71.
The third option 5+3×22≠180.
The fourth option is 5+3×2²=17.
Solve the LHS, we get
5+3×2²=5+3×4
5+3×2²=5+12
5+3×2²=17.
The fourth option 5+3×2²=17.
Hence, the sentence which is true from the given sentences is 5+3×2²=17.
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need help with algebra
The values of x that make the equation true are approximately 5.7 and -0.7 .
The given equation is :
[tex]\frac{x+1}{x} = \frac{2}{x-4}[/tex]
Using cross multiplication this can be written as:
or, ( x + 1 ) ( x - 4 ) = 2 x
or, x² + x - 4x - 4 = 2x
Putting all the like terms together.
or, x² + x - 4x -2x - 4 = 0
or, x² - 5x - 4 = 0
Now we will use the quadratic formula to find the values of x :
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }[/tex]
or, [tex]{\displaystyle x={\frac {5\pm {\sqrt {(-5)^{2}-4(1)(-4)}}}{2(1)}}\ \ }[/tex]
or, [tex]x = \frac{5+\sqrt{41}}{2} , \frac{5-\sqrt{41}}{2}[/tex]
or, x ≈ 5.7 , -0.7
The roots or zeros of the expression, which are also on the left side of the equation, are used to indicate the values of x that satisfy the equation.
There can only be two possible solutions to a quadratic problem. One argues that if there is only one remedy, there are many different causes of the problem. There are only four possibilities: one real double root, two complex solutions that appear to be complex conjugates of one another, two real solutions, or two real solutions if each of the coefficients has a real value.
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I'll mark as brainlist!
Answer: A & D
Step-by-step explanation: Multiply length times width
l x w = a
Two humitos cout $1500. Complete a table to show the con for 3, 7, and 13 borrins at fest rate
Next, find the cost for a single burrito in each case. What do you notice about the values in this
be
Answer:
I would say the answer is 1500/3/7/13
Step-by-step explanation:
con for 3,7,13 find it divife it by 1500 cost of burrito
Can someone please find the area of the shape below thank you!
Answer:
43 cm^2
Step-by-step explanation:
Area of the triangle:
A = (1/2) x base x height
A = (1/2) x (2 cm + 4 cm) x 7 cm
A = (1/2) x (6 cm) x 7 cm
A = (1/2) x 42 cm^2
A = 21 cm^2
The area of the triangle is 21 cm^2
Area of the rectangle:
A = length x width
A = 11 cm x 2 cm
A = 22 cm^2
The area of the rectangle is 22 cm^2
Area of the figure = Area of the triangle + Area of the rectangle
Area of the figure = 21 cm^2 + 22 cm^2
Area of the figure = 43 cm^2
Fill in the missing statement/reason for the following proof:
The missing statement and the reason of LN bisects ∠MLO, LM≅LO are given and ∠OLN≅∠MLO is because of definition of angle bisector, LN≅LN is because it is common to both the angles ∠LNO AND ∠LNM, LO≅LM is because ΔLNO and ΔLNM both are congruent.
Given that:
LN bisects ∠MLO and LM≅LO
Prove that: ΔLMN ≅ ΔLON
In order to prove ASA congruence between the triangles we need two angles to be congruent to each other. When we look at the figure, we see that ∠LNO ≅ ∠LNM is a common angle in both the triangles.
Hence, using this we will prove that the triangles are congruent by ASA congruence rule.
In ΔLON and ΔLMN
Side ON ≅ Side MN
∠LNO ≅ ∠LNM ( ∵ common angle)
∠ONL ≅ ∠MNL (∵ Given as LN is the angle bisector of ∠MLO)
⇒ ΔLMN ≅ ΔLON ( By ASA congruence theorem).
Statement 1: LN bisects ∠MLO
Reason: Given.
Statement 2: LM≅LO
Reason: Given.
Statement 3: ∠OLN≅∠MLO
Reason: Definition of angle bisector.
Definition of angle bisector: An angle bisector is defined as a line segment that bisects one of the vertex angles of a triangle.
Statement 4: LN≅LN
Reason: Common to both the angles ∠LNO AND ∠LNM and also these angles are 90° because angle made by angle bisector is always 90°.
Statement 5: LO≅LM
Reason: ΔLNO and ΔLNM both are congruent.
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