Answer:
about 30 more cents.
Step-by-step explanation:
Determine the number of real solutions:
1. y = -x? +2 x + 6
2. y = 2x² - 6x + 5
3. y = x² + 8x + 16
Here is my answer.. correct me if im wrong.
Hi :) I was wondering if you could help, I'm mixed up about this one.
Answer:
the image is sideways
Step-by-step explanation:
Answer:
well buddy see you thinking to hard its right there just relax and look closely
Step-by-step explanation:
2x + y = 15
x = 15 - 2y
is it no solution?
Answer:
It has a solution.
Step-by-step explanation:
Step 1: Rearrange 1st equation into slope-intercept form
2x + y = 15
y = 15 - 2x
Step 2: Rearrange 2nd equation into slope-intercept form
x = 15 - 2y
2y + x = 15
2y = 15 - x
y = 15/2 - x/2
Step 3: Rewrite systems of equations
y = 15 - 2x
y = 15/2 - x/2
Since the two lines are not parallel, they will have a solution.
Is -5/13 a rational number
Answer:
yes -5/13 is a rational number
what is the 4th term of 3n+5
Answer:
17
Step-by-step explanation:
if the sequence is 3n+5
we do 3x4(since we are working out the 4th term) +5
3x4=12 12+5=17
Simplify
6 (2x^2-5)=
x= -3
The value of the expression for x=-3 is 78.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 6(2x²-5).
Here, x=-3
Substitute x=-3 in the expression 6(2x²-5), we get
6(2(-3)²-5)
= 6(18-5)
= 78
Therefore, the value of the expression is 78.
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Ethan sold some watches at $14 each and 20 bookmarks at $1.50 each. Roy sold the same number of watches at $13.50 each and 20 bookmarks at $1.80 each. They collected the same amount of money. How many watches did Ethan sell? Ethan Roy watches 17-114 watches come total Bookmarks 20 × $1.56-30 Bookmarly 20-11-80-36 Same total
[<Answer>] (1):
Heyy there, it's Avery. And I'm here to help! :)
----------------------------------------------------------------------------------------------------------[<The Explanation>]:
Let x= number of watches sold
Ethan= x(14) + (20)(1.50)
Roy = x(13.50) + (20)(1.80)
Since they collected the same amount of money:
14x + (20)(1.50) = 13.50x + (20)(1.80)
Combine like terms:
14x - 13.50x = (20)(1.80) - (20)(1.50)
0.50x = 36 - 30
0.50x = 6
x = 6/0.50
x= 12
Ethan sold 12 watches. And also Roy.
Andddd...We're done! :D
----------------------------------------------------------------------------------------------------------
[<Ending>] <3
Hope this helps and if it's wrong, you can't sue me! :D
Bye! Hope this works for you :)
Have a nice day! - Avery <3
Area of rectangle and traingle
Please helpp
Step-by-step explanation:
\(here \: is \: your \: solution \\ \\ base \: = 4 \: cm \\ \\ height \: = 6 \: cm \\ \\ area \: of \: traingle = (1 \div 2) \times base \times height \\ \\ area \: = (4 \times 6) \div 2 \\ \\ area = 12 \: cm.sq \\ \\ hope \: it \: helps\)
Answer: a
Step-by-step explanation:
which set of shapes are a correct decomposition of a regular hexagon??(
The set of shapes that are a correct decomposition of a regular hexagon are A. Six equilateral triangles
How to decompose a hexagon ?The regular hexagon may be partitioned into a collection of six congruent equilateral triangles through the act of drawing lines that interconnect its vertices with its center.
The rationale behind this phenomenon can be elucidated by the fact that the collective sum of the interior angles of a regular hexagon amounts to 720 degrees. This value is precisely twice the angle measurement of an equilateral triangle. Consequently, it can be deduced that the angle measurement of each of the six equilateral triangles which form the hexagon is 120 degrees.
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Options include:
Six equilateral triangles
Three equilateral triangles and three squares
Six squares
Three equilateral triangles and three rectangles
Please help due in 5 min!!!
who can do math pleaseeeee
Answer/Step-by-step explanation:
1. Reference angle = 37°
Opposite side = 15 ft
Adjacent side = height of tree = x
✅Equation:
Tan 37° = 15/x
Solve:
x*tan 37 = 15
x = 15/tan 37
x = 15/0.75
x = 20
✅Sentence answer: height of the tree = 20 ft
2. Reference angle = 52°
Hypotenuse = 300 m
Opposite side = height of the building = x
✅Equation:
Sin 52° = x/300
Solve:
Sin 52 * 300 = x
0.79 * 300 = x
237 = x
x = 237
✅Sentence answer: height of the building = 237 meters
2. Reference angle = 75°
Hypotenuse = 20 ft
Adjacent side = distance of the building to the base of the ladder = x
✅Equation:
Cos 75 = x/20
Solve:
Cos 75 × 20 = x
0.26 × 20 = x
5.2 = x
x = 5.2
✅Sentence answer: distance of building form the base of the ladder = 5.2 ft
Find the volume of the space inside the right cylinder that is not filled by the right cone below.
AC=16
BD=17
9514 1404 393
Answer:
D. 640 m³
Step-by-step explanation:
The height CD of the cone is found using the Pythagorean theorem.
BC² + CD² = BD²
8² + CD² = 17²
CD = √(289 -64) = 15
The volume of the cylinder is ...
V = πr²h
The volume of the cone is ...
V = 1/3πr²h
So, the portion of the cylinder not occupied by the cone is ...
V = (πr²h) -(1/3πr²h) = (2/3)πr²h
V = 2/3(π)(8 m)²(15 m) = 640π m² . . . . . matches choice D
the perimeter of a semicircle protractor is 14.8cm,find it's radius
The radius of the semicircle protractor is approximately 4.693 cm.
Given,Perimeter of a semicircle protractor = 14.8 cm.
To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.
Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =\((1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693\) cm.
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A sector with central angle theta is cut froma circle of radius 10 inches and the edges of the secotr are brought toegether to ormnr a cone find the amgnitude of theta such that thte volume of the conbe is a maximum
So, the maximum volume of the cone is approximately 1047.19 cubic inches.
The volume of a cone is given by the formula V = (1/3) * pi * r^2 * h, where r is the radius of the base and h is the height of the cone. In this case, the height of the cone is the radius of the circle, which is 10 inches, and the radius of the base is half the length of the circumference of the sector, which is (theta/360) * 2 * pi * 10 inches.
We want to find the value of theta that maximizes the volume of the cone. We can do this by taking the derivative of the volume formula with respect to theta, setting it equal to 0, and solving for theta.
V = (1/3) * pi * r^2 * h
= (1/3) * pi * ((theta/360) * 2 * pi * 10)^2 * 10
= (1/3) * pi * (theta/36)^2 * 100
dV/dtheta = (2/3) * pi * (theta/36) * (100/36)
= (2/3) * pi * theta/36
Setting dV/dtheta = 0 and solving for theta, we get theta = 0.
Since the magnitude of theta must be positive, the maximum volume occurs when theta = 0, which means that the entire circle is used to form the cone. The maximum volume of the cone is then
V = (1/3) * pi * r^2 * h
= (1/3) * pi * (10)^2 * 10
= (1/3) * pi * 100 * 10
= (1/3) * pi * 1000
= approximately 1047.19 cubic inches
So, the maximum volume of the cone is approximately 1047.19 cubic inches.
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We want to find the value of theta that maximizes the volume of the cone. We can do this by taking the derivative of the volume formula with respect to theta, setting it equal to 0, and solving for theta.
V = (1/3) * pi * r^2 * h
= (1/3) * pi * ((theta/360) * 2 * pi * 10)^2 * 10
= (1/3) * pi * (theta/36)^2 * 100
dV/dtheta = (2/3) * pi * (theta/36) * (100/36)
= (2/3) * pi * theta/36
Setting dV/dtheta = 0 and solving for theta, we get theta = 0.
Since the magnitude of theta must be positive, the maximum volume occurs when theta = 0, which means that the entire circle is used to form the cone. The maximum volume of the cone is then
V = (1/3) * pi * r^2 * h
= (1/3) * pi * (10)^2 * 10
= (1/3) * pi * 100 * 10
= (1/3) * pi * 1000
= approximately 1047.19 cubic inches
So, the maximum volume of the cone is approximately 1047.19 cubic inches.
The population of a city increases by 0.5% per year. If this year's population is 374,000, what will next year's population be, to the nearest individual?
Answer: the answer is actually 375870
Step-by-step explanation:
The population of the city in the next year will be 375870.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the population of a city increases by 0.5% per year. If this year's population is 374,000.
The population of the city next year will be calculated as,
Population = 374000 x 1.005
Population = 375870
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Please help with this exercise:
Consider the vectors v1, v2, v3 in R2 (sketched in the
accompanying figure). Vectors v1 and v2 are parallel.
How many solutions x, y does the system
xv1 + yv2 = v3
have? Argue geometrically.
Answer:
sorryyyyyy dont knowwwwwwww
since vectors v1 and v2 are parallel, the system xv1 + yv2 = v3 will have infinitely many solutions regardless of the specific values of v1, v2, and v3.
Geometrically, this is due to the fact that v1 and v2 span the same direction in space, so any combination of x and y will still lie on the same line or in the same direction.
Since vectors v1 and v2 are parallel, they lie on the same line or are scalar multiples of each other. Let's analyze the possible cases geometrically:
1. **Vectors v1 and v2 are collinear (lie on the same line):**
In this case, any combination of x and y that satisfy the equation \(xv1 + yv2 = v3\) will lie on the same line as v1 and v2. This means there are infinitely many solutions for x and y.
2. **Vectors v1 and v2 are scalar multiples of each other:**
If v1 and v2 are scalar multiples of each other, then they represent the same direction in space. In this case, any combination of x and y that satisfy the equation will give a vector that lies on this line (spanned by v1 and v2), which is also the direction of v3. Hence, again there are infinitely many solutions.
3. **Vectors v1 and v2 are not collinear but have different directions:**
This scenario is not possible because you stated that v1 and v2 are parallel. If they have different directions, they would not be parallel.
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(a) From Latoya's results, compute the experimental probability of rolling a 1 or 6.
(b)Assuming that the cube is fair, compute the theoretical probability of rolling a 1 or 6.
(c)Assuming that the cube is fair, choose the statement below that is true.
A. The experimental and theoretical probabilities must always be equal.
B. As the number of rolls increases, we expect the experimental and theoretical probabilities to
become closer, though they might not be equal.
C. As the number of rolls increases, we expect the experimental and theoretical probabilities to
become farther apart.
(a) To compute the experimental probability of rolling a 1 or 6 from Latoya's results, we need to determine the number of times a 1 or 6 was rolled and divide it by the total number of rolls Latoya made.
Let's assume that Latoya rolled the dice 100 times and obtained 20 1's and 10 6's. The total number of successful outcomes (rolling a 1 or 6) is 20 + 10 = 30.
Therefore, the experimental probability of rolling a 1 or 6 is 30/100 = 0.3 or 30%.
(b) Assuming the cube is fair, the theoretical probability of rolling a 1 or 6 can be determined by considering the favorable outcomes (rolling a 1 or 6) divided by the total possible outcomes (rolling any number from 1 to 6).
Since there are two favorable outcomes (1 and 6) out of six possible outcomes (1, 2, 3, 4, 5, 6), the theoretical probability is 2/6 = 1/3 or approximately 0.3333.
(c) The correct statement is B. As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. This is due to the law of large numbers, which states that as more trials are conducted, the experimental probability tends to converge towards the theoretical probability. However, it is not necessary for them to be exactly equal. Random variations can cause some discrepancy, but with a larger number of rolls, the experimental probability should approach the theoretical probability more closely.
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Need help with proofs, anyone know how?
Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.
What is a perpendicular bisector?In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.
This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.
Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;
MS ≅ QSNS ≅ RSMN ≅ QN ∠NMS and ∠NQSΔMNS ≅ ΔQNSRead more on perpendicular bisectors here: brainly.com/question/19154899
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Complete Question:
The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS
We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.
NS and NS
NS and RS
MS and RS
MS and QS
A physical education teacher wanted to know the effects of various activity levels on body composition. She surveyed her physical education classes and categorized 30 students into five activity levels based on the amount of daily exercise in which the students participated: inactive, semiactive, normal, active, and very active. She measured percent body fat values using skinfold calipers on all subjects with the following results.
Inactive Semiactive Normal Active Very Active
30.2 29.4 22.9 17.6 10.9
29.6 17.6 25.4 13.4 13.7
35.2 26.4 19.6 20.3 12.8
19.1 25.3 18.7 19.6 14.7
26.3 22.5 21.8 15.1 9.3
22.4 28.6 24.9 10.7 12.7
Required:
a. What is the independent variable in this study? What is the dependent variable?
b. What are the means and standard deviations for each group?
c. Does a significant difference exist among any of the groups?
Answer:
a. The independent variable is the activity level
The dependent variable is the body composition (the percentage of body fat in the values)
b. The mean and standard deviation are;
(Mean, Standard deviation)
Inactive(27.13, 5.8), Semiactive(24.97, 4.367), Normal(22.217, 2.73), Active(16.12, 3.73), Very Active (12.35, 1.95)
c. Yes
Between Semiactive and Active, Semiactive and Very Active, Normal and Very Active, Normal and Active, Active and Inactive, and Inactive and Very Active
Step-by-step explanation:
a. The independent variable is the activity level
The dependent variable is the body composition (the percentage of body fat in the values)
b. The given data are presented as follows;
Inactive \({}\) Semiactive Normal Active Very Active
30.2 \({}\) 29.4 22.9 17.6 10.9
29.6 \({}\) 17.6 25.4 13.4 13.7
35.2 \({}\) 26.4 19.6 20.3 12.8
19.1 \({}\) 25.3 18.7 19.6 14.7
26.3 \({}\) 22.5 21.8 15.1 9.3
22.4 \({}\) 28.6 24.9 10.7 12.7
Bymaking use of Microsoft Excel, we have;
Inactive \({}\) Semiactive Normal Active Very Active
Mean 27.13 \({}\) 24.97 22.217 16.12 12.35
Standard Deviation 5.8 \({}\) \({}\) 4.367 2.73 3.73 1.95
c. Yes
\(t=\dfrac{(\bar{x}_{1}-\bar{x}_{2}) }{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}\)
The degrees of freedom = n - 1 = 6 - 1 = 5
The critical t = 2.5706
Therefore, we have;
The test statistic for Inactive and semi active ≈ 0.72875
The test statistic for Semiactive Normal ≈ 1.309
The test statistic for Inactive and Normal ≈ 1.8773
The test statistic for Semiactive and Active ≈ 3.775 (Significant)
The test statistic for Semiactive and Very Active ≈ 6.464 (Significant)
The test statistic for Normal and Very Active ≈ 7.204 (Significant)
The test statistic for Normal and Active ≈ 3.231 (Significant)
The test statistic for Active and Inactive ≈ 3.91 (Significant)
The test statistic for Active and Very Active ≈ 2.194
The test statistic for Inactive and Very Active ≈ 5.92 (Significant)
Where the test statistic is larger than the critical 't' the statistic is significant
Surveying A triangular parcel of ground has sides of lengths 725 feet, 650 feet, and 575 feet. Find the measure of the largest angle.
cos⁻¹ ( 7/23) is the measure of the largest angle.
What is known as a triangle?
The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point.
The triangle's three angles add up to a total of 180 degrees.
The lengths are given as a = 725 feet, b = 650 feet, and c = 575 feet.
Since, we know the fact that angle opposite to largest side is greatest. Hence, the largest angle would be opposite to side a.
Now, use the law of cosine
cosA = b² + c² - a²/2bc
On substituting the values, we get
cosA = (650)² + ( 575 )² - ( 725)²/2*650*575
= 422500 + 330625 - 525625/747500
= 227500/747500
= 7/23
A = cos⁻¹ ( 7/23)
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Janet needs to paint the walls of a room shaped like a
rectangular prism. The room
has a length of 10 ft., a width of 15 ft, and a height of 8 ft. How much paint does she need to cover the
To solve this problem, we will use the formula of rectangular prism surface area.
The formula is:
A=2(wl+hl+hw)
A is the area, w is the width, l is the length, and h is the height.
So we will put in all the numbers.
A=2((15)(10)+(8)(10)+(8)(15))
Multiple all the numbers inside:
A=2(150+80+120)
Add all the numbers inside:
A=2(350)
Multiply:
A=700ft^2
Hope this helped!
explain why the graph would look like the line y=x if you graph it
The graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.
How to explain the informationBoth the numerator and denominator of f(x) = x(x+5)(x+3) / (x+3)(x+5) cancel out the factors (x+3) and (x+5), giving us a simplified expression for the function, f(x) = x.
A line with a slope of 1 passes through the origin in an upward direction. When we examine the graph of y=x, which is a straight line passing through the origin with a slope of 1, it becomes apparent that adding 1 to x also adds 1 to y.
Since the simplified expression is merely f(x) = x, we can deduce that the graph of this function follows a linear path passing through the origin with a slope of 1.
In conclusion, the graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.
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Graph the line with slope 3 passing through the point (5, 3)
A graph of the line with slope 3 passing through the point (5, 3) is shown in the image attached below.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (5, 3) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 3 = 3(x - 5)
y = 3x - 15 + 3
y = 3x - 12
In conclusion, we would use an online graphing calculator to plot the equation y = 3x - 12 as shown in the graph attached below.
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There are 4 bottles of vitamins in
each box of vitamins. Each bottle of vitamins has
20 vitamins. If the clinic wants to have a supply of 400
vitamins how many more boxes should it order
Answer:
the clinic needs 20 more bottles of vitamins to have a supply of 400 vitamins.
Step-by-step explanation:
400 divided by 20 = 20.
Brainliest for whoever gets this correct! What is the sum of the rational expressions below?
Answer:
second option
Step-by-step explanation:
x / x - 1 + 3x / x + 2
= x(x + 2) / (x - 1)(x + 2) + 3x(x - 1) / (x - 1)(x + 2)
= (x² + 2x) / (x² + x - 2) + (3x² - 3x) / (x² + x - 2)
= (4x² - x) / (x² + x - 2)
The length of a rectangle is 4 inches longer than it is wide. If the area is 32 square inches, what are the dimensions of the rectangle?
Answer:
width = 4in
length = 8in
Step-by-step explanation:
A = LxW = 32
L = W + 4
W(W+4) = 32
W² + 4W - 32 = 0
(W + 8)(W - 4) = 0
W ≠ -8 (dimensions cannot be negative)
W = 4in
L = W+4 = 4+4 = 8in
Identify the Vertex. Let g be a translation 2 units up, followed by a reflection in the x-axis and a vertical stretch by a factor of 4 of the graph of. (Show Work)
The g graph exhibits a four-fold vertical stretch.
The graph of f (x)=\(x^{2}\) is translated up to two units, then reflected in the X-axis.
The rule for g.
Identify the vertex
The g graph exhibits a four-fold vertical stretch.
=> g = 4f(x) (x)
an X-axis reflection
=> g = - 4f(x) (x)
(X-axis reflection of (X, Y) is (x , - y)
a conversion two units higher
=> g = -4f(x) + 2
f(x) = x²
=> g = - 4x² + 2
Vertex is at ( 2, 0)
What is a vertical stretch?
When a base graph is multiplied by a particular factor larger than 1, vertical stretch happens. As a consequence, the graph is stretched outward while keeping the input values (or x). We anticipate that the y values in a function's graph will be further away from the x-axis when it is vertically extended.
How to vertically stretch a function?
When given a function’s graph, we can vertically stretch it by pulling the curve outwards based on the given scale factor. Here are some things to remember when we vertically stretch functions:
Ensure that the values for x remain the same, so the base of the curve will not change.
This means that when applying vertical stretches on a base graph, its x-intercepts will remain the same.
Take note of the new critical points, such as the new maximum point of the graph.
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64% is less than or greater than or equal to 13/20
Question 1 of 10
Which expressions are equivalent to the one below? Check all that apply.
log 2-log 4
A. log(¹)
B. log 1
C. log(2) + log(¹)
D. log 2
"The correct option is C." The only expression that is equivalent to log 2 - log 4 is option C: log(2) + log(¹).
The expression "log 2 - log 4" can be simplified using logarithmic properties. Specifically, the property states that "log(a) - log(b) = log(a/b)." Applying this property to the given expression, we have "log 2 - log 4 = log(2/4) = log(1/2) = -log(2)."
The expression log 2 - log 4 can be simplified using logarithmic properties. Let's analyze each option:
A. log(¹): This expression is not equivalent to log 2 - log 4. The logarithm of 1 is 0, but it does not cancel out the terms log 2 and log 4.
B. log 1: This expression is equivalent to 0, but it does not cancel out the terms log 2 and log 4.
C. log(2) + log(¹): This expression is equivalent to log 2 + 0, which simplifies to just log 2. It is not equivalent to log 2 - log 4.
D. log 2: This expression is not equivalent to log 2 - log 4. It represents the logarithm of 2, but it does not account for the subtraction of log 4.
Option C, "log(2) + log(¹)," again uses an exponentiation notation without an exponent and is not a valid mathematical expression.
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Andrew is preheating his oven before using it to bake. The initial temperature of the oven is 65° and the temperature will increase at a rate of 10° per minute after being turned on. What is the temperature of the oven 15 minutes after being turned on? What is the temperature of the oven t minutes after being turned on?
Answer:
see belwo
Step-by-step explanation:
65
increase 10/min
in 15min it'll increase 150
so 65+150 =215
over t mins it'll be 65+10*t
Answer: 215°
t = minutes after being turned on
If the oven temperature increases by 10 per minute, and the initial temperature is 65, this can be represented as:
65 + 10t
After 15 minutes:
65 + 10(15)
65 + 150
215°
If x = temperature of the oven, the temperature of the oven t minutes after being turned on is:
65 + 10t = x