The solution for the given logarithmuc function is x = -1 or x = -4.
What is a logarithmic expression?
A logarithmic equation is one that involves the logarithm of a variable-containing expression. To solve exponential equations, first, determine whether both sides of the equation can be written as powers of the same number.
Property of logarithms: log(a) + log(b) = log(ab)
The given function is
[tex]log_{2}(x+2) + log_{2}(x+3)=1[/tex]
By using the property of logarithms, we get
[tex]log_{2}(x+2) + log_{2}(x+3)=1\\\\log_2{[(x+2)(x+3)]}=1\\\\(x+2)(x+3)=2\\\\x^2+2x+3x+6=2\\\\x^2+5x+6-2=0\\\\x^2+5x+4=0\\\\(x+1)(x+4)=0[/tex]
Simplifying, we get
x = -1 (or) x = -4
Hence, the solution for the given logarithmuc function is x = -1 or x = -4.
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If T is the midpoint of RS and V lies between R and T, which statement must be true?
T is the midpoint of RS and V lies between Rand T is RV+VT =TS
Explain about the midpoint?The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the endpoints, and it is equally distant from both of them. It cuts the section in half.
Divide the measurement of the distance between the two end locations by 2. The middle of that line is located at this separation from either end. Alternately, combine the two endpoint x coordinates and divide by 2. similarly for the y coordinates.
The midpoint rule substitutes the midpoints, mi, of each subinterval for xi in a Remain sum with subintervals of equal width to estimate definite integrals.
T is the midpoint of RS so RT =TS
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T is the midpoint of RS and V lies between Rand T is RV+VT =TS
Explain about the midpoint?In geometry, a line segment's midpoint is referred to as the midpoint. It is both the segment's and the endpoints' centroid, and it is equally far away from each. The portion is halved by it.The distance between the two end points should be divided by two. This distance from either end is where the centre of that line is situated. You may also add the two endpoint x coordinates and divide the result by 2. the same is true for the y coordinates.The midpoint rule uses subintervals of equal width to replace the midpoints, mi, of each subinterval in a Remain sum for xi in order to estimate definite integrals.RT = TS because T is the midpoint of RS.
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pls help
first person gets brainliest
Answer: x = 85° , y =45°
Step-by-step explanation:
x + 95 = 180°
x = 180° - 95°
x = 85°
In a triangle,
50° + x + y = 180°
50° + 85° + y = 180°
135° + y = 180°
y = 45°
From the above given expression
x = 35°
y = 95°
In a straight line, the angle is 180°
given angles are 50° internal angle and 95° external angle
then x + 50° + 95° = 180°
x + 145° = 180°
x = 180° - 145°
x = 35°
so in a triangle total angle is 180°
then 50° + x + y = 180°
50° + 35° + y 180°
y = 180° - 85°
y = 95°
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v+-8=-15 i need help
Answer:
- 7
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
help me with this please
We can use the distance formula to determine the side lengths of DEF.
D (3, -1)
E (7, -4)
F (4, -4)
DE --> √((7 - 3)^2 + (-4 - (-1))^2) = √(4^2 + (-3)^2) = √(16 + 9) = √25 = 5
DF --> √((4 - 3)^2 + (-4 - (-1))^2) = √(1^2 + (-3)^2) = √(1 + 9) = √10 ≈ 3.2
EF --> √((7 - 4)^2 + (-4 - (-4)^2) = √(3^2 + 0^2) = √9 = 3
Notice DEF is congruent to ABC because due to SSS (side-side-side) congruency; DE = AB, DF = AC, EF = BC. Because DEF and ABC are congruent, DEF and ABC must have congruent angles.
angleBAC = angleEDF = 34.7 degrees
angleACB = angleDFE = 108.4 degrees
angleCBA = angleFED = 36.9 degrees
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point Z 1 is (3, 1), Z 2 is (negative 2, negative 5). Point A is at (1, negative 4), B is (5, 5), C is (negative 3, 1), and D is (4, negative 2). A dotted line goes from z 1 to (0, 0), and then down to point z 2. Which point represents z1 + z2?
The sum z1 + z2 gives the point with coordinates (1, - 4), so option A is the correct one.
Which point represents z1 + z2?We know that these two points have the coordinates:
z1 = (3, 1)
z2 = (-2, - 5)
And we want to find the addition of the two points.
To add them, we just need to add the correspondent coordinates:
(3, 1) + (-2, -5) = (3 - 2, 1 - 5) = (1, - 4)
That point is the sum of z1 and z2, and we know that it is the point A, so point A is the correct option.
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Determine which of the lines if any are parallel or perpendicular
Answer:
Parallel: Lines a and b
Perpendicular: none
Step-by-step explanation:
Both lines a and b have a slope of 1/3.
This means they are parallel, so they'll never intersect.
Perpendicular lines form a right angle, and none seem to do see here.
round to the nearest ten thousand
a.12,456
b.60,792
c.93,245
As per the rule of round off, the nearest ten thousand to the numbers are
a.12,456 = 10,000
b.60,792 = 60,000
c.93,245 = 90,000
Round off
Round off defines a change a number into an approximation having fewer significant digits.
Given,
Here we need to round off the following numbers to the nearest ten thousand.
a.12,456
b.60,792
c.93,245
a. 12,456
If you rounded to the nearest ten thousands place. The 1 in the ten thousands place rounds down to 1, or stays the same, because the digit to the right in the thousands place is 2.
If the digit to the right is less than 5 we round toward 0.
Therefore, 12,456 was rounded down toward zero to 10,000
b. 60,792
If you rounded to the nearest ten thousands place. The 6 in the ten thousands place rounds down to 6, or stays the same, because the digit to the right in the thousands place is 0.
So, if the digit to the right is less than 5 we round toward 0.
Then 60,792 was rounded down toward zero to 60,000
c. 93, 245
Similar to the previous one, if rounded to the nearest ten thousands place. The 9 in the ten thousands place rounds down to 9, or stays the same, because the digit to the right in the thousands place is 3.
When the digit to the right is less than 5 we round toward 0.
93245 was rounded down toward zero to 90,000
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At an elevation of 1221.4 feet, Lake Mead will hold 28,945,000 acre-feet of water. Which number is the best estimate of this amount of water?
The estimate of the amount 28,945,000 is 3 × 10⁷
What is an estimate of a value?An estimate is a rough or approximate calculation or judgement value.
The question is with regards to the scientific notation which is of the form a × 10ᵇ, where absolute a is of a value 1 ≤ a < 10
The scientific notation form of a number is found as follows;
The decimal point on the number is moved from its position to the point such that the number of non zero numbers to the left of the decimal point is 1
The number b is the number of places to which the decimal point is moved.
b is positive when the decimal point is moved to the left
b is negative when the decimal point in the number is moved to the right
b is zero when the decimal point is not moved
The scientific notation number formed, a × 10ᵇ, which is read as a times 10 raised to the power b.
The zeros in the tail to the right of the decimal point are removed
The number 28,945,000 in scientific notation is 2.8945 × 10⁷
The number part of the scientific notation is approximated to the next higher whole number, as follows;
The first digit to the right of the decimal point is 8 which is larger than 5, therefore the 2 is increased to 3
The approximated number is therefore;
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What is the angle measure of YLA?
Measure of angle YLA in the given figure is 32°.
Given,
∠LYA = 21°
∠GLA = 32°
A is the incentre of the ΔPQR.
Therefore,
∠YLA = ∠GLA
∠LYA = ∠GYA
=> ∠YLA = 32
Hence, Measure of angle YLA in the given figure is 32°.
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If m∠A is 50°, can you conclude that Line u and Line v are parallel? If so, provide a justification.
Answer:
yes, because 130 + 50 = 180 .
Step-by-step explanation:
If the degrees on the inside adds up to 180 then the lines are parallel.
Please help need answer now!!!!!! Pleaseee
Keaton knows that the slope of a certain line is m = -8/5. Does he have enough information to write the equation of the line? Explain. A. Yes the y intercept of this equation must be (0,0) so you can write the equation with only the slope value B. yes if you know the value of the slope, then you can guess the location of the y intercept and write the equation C. No, to write the equation of a line do you need to know both the Slope and one ordered pair that lies on the line D. No you don’t need to know the slope of a line to write its equation 
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 )
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
To obtain either equation we require to know both the slope and one ordered pair that lies on the line.
Type the correct answer in the box. Use numerals instead of words. For this item, a non-integer answer should be entered as a fraction using / as the fraction bar. Simplify the numerical expression. The expression has a value equal to
[tex] \frac{2}3 \: \div {2}^{4} + ( \frac{3}{4} + \frac{1}{6} ) \: \div \frac{1}{3} [/tex]
After solving thie expression using BODMAS rule we get the result equal to [tex]\frac{67}{24}[/tex].
What is BODMAS?To solve arithmetic expressions of several operators, the BODMAS rule is a mathematics is a technique. We will solve an equation with several operators with the use of BODMAS. It provides the decoding of the mathematical phrase in the proper sequence.
B= Bracket
O= Of
D= Divide
M= Multiply
A= Addition
S= Subtraction
To solve this numerical expression,
[tex]\frac{2}{3}[/tex] ÷ 2⁴ + ([tex]\frac{3}{4}[/tex] + [tex]\frac{1}{6}[/tex]) ÷ [tex]\frac{1}{3}[/tex]
Use BODMAS method
[tex]\frac{2}{3}[/tex] ÷ 16 + ([tex]\frac{9+2}{12}[/tex]) ÷ [tex]\frac{1}{3}[/tex]
[tex]\frac{2}{3}[/tex] ÷ 16 + ([tex]\frac{11}{12}[/tex]) ÷ [tex]\frac{1}{3}[/tex]
[tex]\frac{2}{3}[/tex] × [tex]\frac{1}{16}[/tex] + ([tex]\frac{11}{12}[/tex]) × 3
[tex]\frac{1}{24}[/tex] + [tex]\frac{33}{12}[/tex]
[tex]\frac{67}{24}[/tex]
The expression has a value equal to [tex]\frac{67}{24}[/tex].
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Simplify log7 (x) - 2
Answer:
x log (7) -2
Step-by-step explanation:
Help me please!!!!!!!!!!!!
Answer:
1. 2,772
2.1,071
3.4,641
4. 36,610
5. 4,096
6. 36,270
7. 2,403
8. 3,320
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Solve the equations for x and match the solutions.
The solution to each of the equations are matched together as:
1. 4 = 6/a*x + 5 → x = -a/6
2. 7 + 2ax = 13 → x = 3/a
3. -ax - 20 = -14 → x = -6/a
How to Solve an Equation?To solve an equation, apply the properties of equality in order to isolate the variable solved for to one side of the equation, which gives us the solution to the problem.
1. 4 = 6/a*x + 5
4 = 6x/a + 5
Combine like terms
-6x/a = -4 + 5
-6x/a = 1
-6x/a(a) = 1(a) [multiplication property of equality]
-6x = a
-6x/-6 = a/-6 [division property of equality]
x = -a/6
2. 7 + 2ax = 13
2ax = 13 - 7
2ax = 6
Divide both sides of the equation by 2a
x = 6/2a
x = 3/a
3. -ax - 20 = -14
-ax = -14 + 20
-ax = 6
x = 6/-a
x = -6/a
Therefore, the solutions are:
1. x = -a/6
2. x = 3/a
3. x = -6/a
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Kim spent $65 dollars on a new computer but she gave away $10 dollars to her friend Samantha.How many dollars does Kim have left to buy her new computer.
Answer:
Step-by-step explanation:Le quedo +10$
Ya que
-65 y le regalaron +10
2(x-7)² = 32? What are the solutions
Answer:
lmfa you answer my questions i recently posted ill answer yours.
Step-by-step explanation:
please tho
The correct solution is x=(+11 , +3)
Step-by-step solution:
2(x-7)²=32
⇒2(x-7)(x-7)=32
⇒(x-7)(x-7)=(32/2)
⇒(x-7)(x-7)=16
⇒(x-7)²=16
⇒[tex](x-7)=\sqrt{16}[/tex]
⇒(x-7) = ±4
⇒(x-7) = +4 or ⇒(x-7) = -4
⇒x = +4+7 or ⇒x = -4+7
⇒x = +11 or ⇒x = +3
Therefore, the correct solution is x = (+11 , +3)
What is an equation of the line that passes through the points (4, 8)(4,8) and (4, 3)(4,3)?
Answer:
x=4
Step-by-step explanation:
x=4 would go through 4,3 and 4,8 as 4 is a vertical line
A family has a $42,000 annual salary. Can they afford an $85,000 house with a $65,000 mortgage requiring payments of $720 per month, including principal, interest, taxes, and insurance?
Yes! they can afford an $85,000 house with a $65,000 mortgage requiring payments of $720 per month.
What is in a mortgage?
Principal, interest, taxes, and insurance make up the majority of mortgage payments. Your outstanding loan balance is reduced by the amount of the principal part. Borrowing money has a cost, which is interest.
Given data:
Annual Salary =$42,000
Cost =$85,000
Mortgage = $65000
Monthly Payment = $720
First Criterian : - Never Spend more than 2.5 times of your Annual Income.
2.5 * 42,000
= 105,000
it can be afforded.
Second Criterian : - Monthly Payment should not exceed Weekly Income
Monthly Payment = 720
Weekly earnings = 42000 / 52 weeks = 807
it can afforded.
Third Criterian : - monthly payment should not exceed 28% of monthly earnings.
Monthly payment = 720
Monthly earnings = 42,000 / 12 = 3500
28% * 3500
= 980
it can be afforded.
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Solve the system by substitution
4x+y=42
y=x+7
(7, 14)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Left to Right
Equality Properties
Algebra I
Solving systems of equations using substitution/elimination
Step-by-step explanation:
Step 1: Define Systems
4x + y = 42
y = x + 7
Step 2: Solve for x
Substitution
Substitute in y: 4x + (x + 7) = 42
Combine like terms: 5x + 7 = 42
Isolate x term: 5x = 35
Isolate x: x = 7
Step 3: Solve for y
Define equation: y = x + 7
Substitute in x: y = 7 + 7
Add: y = 14
What are th roots of 3x^2+10=4x
The roots of the Quadratic Equation are
(2 + i√26)/3 and (2 - i√26)/3
Given, a quadratic equation i.e. 3x² + 10 = 4x
On simplifying, we get
3x² - 4x + 10 = 0
while checking the discriminant of the given quadratic equation, we get
D = b² - 4ac
D = (-4)² - 4(3)(10)
D = 16 -120
D = -104
i.e. D < 0.
So, the quadratic equation has imaginary roots
On applying quadratic formula, we get
x = (4 ± √(-104))/6
x = (4 ± i2√26)/6
x = (2 ± i√26)/3
Hence, the roots of the Quadratic Equation are
(2 + i√26)/3 and (2 - i√26)/3
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Based on the graph above, determine the amplitude, midline, and period of the function
Amplitude:?
Period:?
Midline: y=?
The amplitude, midline and period of the function are 3 units, 4units and 5 units respectively
How to determine the amplitude, midline, and period of the function based on the graph?
The amplitude is half the full height of the periodic function. That is:
Amplitude = (maximum - minimum)/2
Check the image attached, the maximum and minimum are labeled max and min respectively
Amplitude = (-1 - (-7))/2 = 6/2 = 3 units
The midline is the middle of the periodic graph or halfway between the minimum and maximum of the graph
Midline = (maximum + minimum)/2
Midline = (-1 + (-7))/2 = -8/2 = -4 units
The period is the distance between two peaks or (maximums) on the graph.
Period = 1-(-4) = 5 units
Therefore, the amplitude, midline and period are 3 units, 4units and 5 units respectively
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Country S has 12,345,000 residents who tested positive for COVID-19. What is the largest place value of the numeric part of this quantity?
The largest place value of the numeric part of this quantity is 10 million.
What exactly is a place value in mathematics?Our entire number system is built around place value. This is the system in which the value of a number is determined by the position of its digits. The numbers 42,316 and 61,432 differ because the digits are in different positions.
Every digit in a number has a place value in mathematics. Place value is the value represented by a digit in a number based on its position in the number. For example, 7 hundreds or 700 is the place value of 7 in 3,743. The place value of 7 in 7,432 is, however, 7 thousands or 7,000.
In the number, 12,345,000, the highest place value is 1 and it denotes 10 million.
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Which equations represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4, -2)? Select two
options.
Oy=-¾x+1
V 3x - 4y = -4
O 4x - 3y = -3
Oy-2=-¾(x-4)
Oy+2=¾(x+4)
Mark this and return
Save and Exit
Next
Submit
Answer:
Step-by-step explanation:
5
The equation of line passes through the point (-4, -2) will be;
⇒ 3x - 4y = - 4
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (-4, -2).
And, The parallel line is,
⇒ 3x - 4y = 7
⇒ y = 3/4x - 7/4
Now,
Since, The equation of line passes through the point (- 4, -2).
So, We need to find the slope of the line.
Since, The slope of the parallel line is same.
Hence, Slope of the line is,
⇒ y = 3/4x - 7/4
m = dy/dx = 3/4
m = 3/4
Thus, The equation of line with slope 3/4 is,
⇒ y - (-2) = 3/4 (x - (-4))
⇒ y + 2 = 3/4 (x + 4)
⇒ y + 2 = 3/4x + 3
⇒ y = 3/4x + 3 - 2
⇒ y = 3/4x + 1
⇒ 4y = 3x + 4
⇒ 3x - 4y = - 4
Therefore, The equation of line passes through the point (-4, -2) will be;
⇒ 3x - 4y = - 4
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Find the zeros of the function algebraically. (Enter your answers as a comma-separated list.)
f(x) = -25x^4 + 9x²
X =
The zeros of the function algebraically, by using these values we get, {x = -3/5, x = 3/5}
What are the zeros of the function algebraically?
The zeros of a function are the points at which the function's value is zero. These are obtained algebraically by setting the function to zero and solving the quadratic.
We have,
f(x) = -25x⁴ + 9x²
= (25 • (x⁴)) - 32x²
= (5)²x⁴ - (3)²x²
= 25x⁴ - 9x²
= x² • (25x²- 9)
25x² - 9
A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
25 is the square of 5
9 is the square of 3
x² is the square of x¹
Factorization is (5x + 3) • (5x - 3)
x² * (5x+3) * (5x-3)
x = -3/5, x = 3/5
Hence, the zeros of the function algebraically, by using these values we get, {x = -3/5, x = 3/5}
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Solve the system of equations 2x + 5y = -9 and 3x + 4y = 4 by combining the
equations.
try
(2x
(3x
+ 5y =-9)
+ 4y = 4)
2x +5y = -9
3x +4y= 4
0x0y=
Answer:
You do it as solving by substitution.So first make x the subject of the formula in eqn1
substitute eqn1 into eqn two and solve After getting y substitute in the equation* and get x
The value of x and y in the system of equations are 8 and -5 respectively.
Given,
2x + 5y = -9
3x + 4y = 4
Now,
To solve the system of equation,
Let us make the coefficient of x same in both the equations to eliminate x.
2x +5y = -9
3x + 4y = 4
Multiply equation 1 with 3 and equation 2 with 2.
6x + 15y = -27
6x + 8y = 8
Now subtract both the equations,
7y = -35
y = -5
Now substitute y in equation,
2x + 5(-5) = -9
2x - 25 = -9
x = 8
Thus the system of equation solutions are x = 8 and y = -5.
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If d = 2, evaluate 6d.
Answer:
12
Step-by-step explanation:
1) Substitute d into the question
We can see that the question says that is d is 2 what would 6d be.
Another way of writing 6d would be 6 x d
If we put d into the equation we would be left with 6 x 2
2) Solve
6 x 2 = 12
Hope this helps, have a great day!!
Answer:
12
Step-by-step explanation:
6d=6(2)
6*2=12
HOPE IT HELPS
What is the range (spread) of the following set of numbers: [38, 39, 39, 40, 40, 40, 41, 41, 41,
42, 43, 44] *
06
07
12
44
Answer:
44 i think <333
Step-by-step explanation:
ndicate in standard form the equation of the line passing through the given point and having the given slope, in the equation box below. D(5, –2) m = 2/5
Answer:
x - y = 3
Step-by-step explanation:
Answer:
2x - 5y = 20
Step-by-step explanation:
Standard form should look like:
Ax + By = C
and the numbers A,B, and C have to be whole numbers (actually integers, because negative is okay too except A has to be positive)
You have been given a point and the slope. There is a shortcut, fill-in-the-blank equation called point-slope that you can just fill in a point and the slope. Then we can change that equation into standard form.
Point-slope equation:
y - Y = m(x - X)
Fill in (5, -2), which is the (X, Y). 5 in place of X and -2 in place of Y. Fill in 2/5 for the m which is slope.
y - Y = m(x - X)
y - -2 = 2/5(x - 5)
simplify, and distribute.
y + 2 = 2/5x - 2
Multiply through by 5 to get rid of the fraction.
5y + 10 = 2x - 10
Subtract 10.
5y = 2x -20
Subtract 2x.
5y - 2x = -20
Rearrange the terms.
-2x + 5y = -20
Multiply through by -1 (because that A has to be positive)
2x - 5y = 20
The equation in standard form is:
2x - 5y = 20
gabriel is bored and starts writing his name over and over again on his paper. what is the 1000th letter?
Answer:
'e'
Step-by-step explanation:
number of letter in his name: 7
number of times his name is written at the 1000th letter
= 1000/7 = 142 R 6
since there is a remainder of 6 letters after the previous complete set of his name, therefore the 1000th letter is the 6th letter of his name, and that is e
