Answer:
step 2 is wrong
Step-by-step explanation:
4 multiply by 2x = 8x4 multiply by -4 = -16CORRECT STEP4(2x - 4) = 8 + 2x + 88x - 16 = 8 + 2x + 88x - 16 = 2x + 16 6x = 32x = 32/6 = 5 ( approximately )Here, The work of a student to solve the equation :
[tex]4(2x - 4) = 8 + 2x + 8[/tex]
The steps for calculating the value of x are :
Step 1: [tex]4(2x - 4) = 8 + 2x + 8[/tex]
Step 2: [tex]6x - 8 = 16 + 2x[/tex]
Step 3: [tex]6x - 2x = 16 + 8[/tex]
Step 4: [tex]4x = 24[/tex]
Step 5: [tex]x = 6[/tex]
Step 2 is incorrect, as the student instead of multiplying, adds the number as:
[tex]4(2x - 4) = 8 + 2x + 8[/tex]
Here, the correct step is:
[tex]\boxed{\bold{8x - 16 = 16 + 2x}}[/tex]
[tex]6 x = 32[/tex]
[tex]x = 5.33[/tex]
So, the error is in STEP 2 and the correct option is (B).
A man has 16 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.50, how many dimes and how many quarters does he have?
Let d = number of dimes, q = number of quarters.
Step one:
A man has 16 coins in his pocket, all of which are dimes and quarters.
Set up the first equation for the number of dimes and quarters. Help PLS
Answer: 10 dimes and 6 quarters, see below for the equations.
Step-by-step explanation:
We know how much a dime is worth and how much a quarter is worth, and they give us the total number of coins and the total number of change.
This equation shows the total number of coins:
d + q = 16
This equation shows the worth of these coins:
0.10d + 0.25q = 2.5
Now, we can graph these equations. See attached. The point of intersection, where the lines cross, is our solution. In the graph, d = x and q = y.
This point is (10, 6) meaning he has 10 dimes and 6 quarters in his pocket.
Claire got 17 out of 20 questions correct on her vocabulary quiz. What percent of the questions did she get wrong?
The percentage of the questions she got wrong is 15%
What is a Percentage?
Percentage is a number or ratio by dividing the value by the total value and then multiplying the result by 100.
How to determine this
Out of 20 questions, Claire got 17 questions
i.e the questions she got right = 17
The questions she got wrong = 20 - 17 = 3
To get the percentage she got wrong
= 3/20 *100%
= 300/20%
= 15%
Therefore, the percentage she got wrong is 15%
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what type of number is 15/10
Answer:
The number 15/10 is a fraction, specifically a rational number. It can be expressed as the quotient of two integers, where 15 is the numerator and 10 is the denominator. In this case, the fraction is equivalent to 1.5, which is a decimal representation of the rational number.
Step-by-step explanation:
Answer:
Fraction, 15/10 is written out as 15 Over 10
Chantel is deciding which of two similar wallets she will buy. Both are rectangular, but she wants the one that will best fit in her purse. The larger wallet is 18 centimeters long and the smaller one is 10 centimeters long. What is the area of the larger wallet if the area of the smaller one is 60 square centimeters?
The requried area of the larger wallet is 194.4 square centimeters.
Since the two wallets are similar, their corresponding sides are proportional. Let x be the width of the smaller wallet, then the width of the larger wallet is 18/10 times x, or 9/5 times x. Therefore, the dimensions of the larger wallet are 9/5 times the dimensions of the smaller wallet.
The area of the smaller wallet is x times 10 (length times width), or 10x square centimeters. We are given that this area is 60 square centimeters, so:
10x = 60
x = 6
Therefore, the width of the smaller wallet is 6 centimeters. The width of the larger wallet is 9/5 times 6, or 10.8 centimeters. The length of the larger wallet is 18 centimeters.
The area of the larger wallet is 10.8 times 18, or 194.4 square centimeters. Therefore, the area of the larger wallet is 194.4 square centimeters.
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Question 20 of 42
Which of the following is a type of data that is likely to be normally
distributed?
A. The weights of all the 5-year-olds in the United States
B. The outcomes of a fair die rolled 100 times
C. The number of students in a class who get a perfect score on a
test
D. The number of students in a class who get a B on a test
Answer: Option B, the outcomes of a fair die rolled 100 times, is likely to be normally distributed.
Step-by-step explanation:
Answer: Option B, The outcomes of a fair die rolled 100 times
Step-by-step explanation:
that would most likely be normally distributed.
hope it helped! Good luck!!! :)
Each triangle in the quilting square pattern shows has a base and height of 2 inches how much fabric is needed to create one quilting square
Answer:
The amount of fabric needed to create one quilting square is 8 inches.
Answer:
The amount of fabric needed to create one quilting square is 8 inches.
Step-by-step explanation:
Given the unit circle what is the value of y PLEASE HELP
Answer: √35/6
Step-by-step explanation:
see image for explanation
A quantity shrinks at a continuous rate of
per year. Its effective growth rate is
per year.
Answer:
Based on the information provided, there seems to be a discrepancy between the given information about the quantity shrinking at a continuous rate and the requested information about its effective growth rate. If a quantity is shrinking continuously, it is not experiencing growth, and therefore there is no effective growth rate. Nonetheless, assuming that the requested information was about the effective shrinkage rate of the quantity per year, this information can be extracted from the given information that "A quantity shrinks at a continuous rate of 33% per year." The effective shrinkage rate of the quantity can be calculated as follows:
Let r be the continuous shrinkage rate of the quantity
The effective shrinkage rate of the quantity is given by the expression (1 - r).
From the given information , r = 33% = 0.33.
Therefore, the effective shrinkage rate of the quantity is (1 - r) = (1 - 0.33) = 0.67 or 67% per year.
Note that if the phrase "effective growth rate" was a mistake, and the original intent was to ask for the shrinkage rate, then the above calculation gives the answer. Otherwise, further clarification is needed.
You may be interested in visiting A quantity's size after t years is given by A(t) =...
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Step-by-step explanation:
The question refers to the concept of continuous growth or shrinkage, and the effective growth rate in a financial context. Despite missing figures, assuming a quantity shrinks at a continuous rate of 3% and its effective growth rate is 2%, it implies a net shrinkage is 1% annually.
Explanation:The question pertains to the subject of compound interest in finance, but it appears that some of the figures and percentages are missing. However, generally speaking, continuous growth or shrinkage refers to the rate at which a quantity increases or decreases for a specific period of time. The effective growth rate is a term in finance that is used to compare the annual interest rates between financial products that have different compounding terms. For instance, if a quantity shrinks at a continuous rate of 3% per year, and its effective growth rate is 2% per year, it means that net shrinkage is 1% per year.
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Subtract t⁴-3t²+7 from 5t³-9.
Answer:
t⁴+5t³-3t²-2
Step-by-step explanation:
You can't subtract a variable with a different exponent:
Example:
CAN'T BE SUBTRACTED - 3x²-3x⁴
CAN BE SUBTRACTED - 4x²-2x²=2x²
[tex]\sf -t^{4}+5t^{3} +3t^{2} -16.[/tex]
Step-by-step explanation:1. Write the expression.[tex]\sf (5t^{3} -9)-(t^{4}-3t^{2} +7 )[/tex]
2. Remove the parenthesis.Beware of the terms of the right hand side parenthesis, as we'll have to change the symbol of all of them because of the minus (-) symbol infront of the parenthesis.
[tex]\sf 5t^{3} -9-t^{4}+3t^{2} -7[/tex]
3. Work with like terms.Like terms are terms that contain the same variables and can be added and subtracted simply. For example, 7x and 2x are like terms, because they are both expressed in terms of x. However, 7x and x² are not like terms, because one os expressed in terms of x and the ither in terms of x².
• Note: All natural numbers not being multiplied by any variables are like terms.
So now let's identify those like terms:
From this expression: [tex]\sf 5t^{3} -9-t^{4}+3t^{2} -7[/tex]
Only -9 and -7 are like terms. And, since -9-7= -16, the resulting expression should be the following:
[tex]\sf 5t^{3} -t^{4}+3t^{2} -16[/tex]
4. Order the terms correctly.So even though the last expression is the answer to this problem, we can polish it a little bit by ordering the terms. In math and other exact sciences, terms are normally ordered alphabetically and from greatest to least of it's the same variable with different exponents. Therefore, the final answer is:
[tex]\sf -t^{4}+5t^{3} +3t^{2} -16.[/tex]
What is the value of c in the equation?
15.3 = StartFraction c Over 2.1 EndFraction
13.2
17.4
32.13
321.3
Answer:
32.13
Step-by-step explanation:
The value of c in the equation 15.3 = c/2.1 is 32.13. To solve for c, you can cross-multiply and simplify the equation to c = 15.3 x 2.1 = 32.13.
The solution to the equation "the quotient of a number and 8 is 16" is 128. To solve for the number, you can multiply both sides by 8 to get "the number is 16 x 8 = 128."
To translate the sentence "the quotient of a number and 8 is 16" into an equation, you can use "x" to represent the number and write x/8 = 16.
Answer:
c or a
Step-by-step explanation:
i thing a
Please help !!!!!!!!!!!!!!!!!!!!!!
2) The way the coordinates show the given scale factor is that the ratio of both x and y coordinates to the mapped coordinate before dilation are all equal.
3) The coordinates after dilation are: (5.4, 27)
How to use scale factor dilation?2) The coordinates transformed points after dilation are completed as:
B(2, 4) → B'(3, 6)
K(4, -4) → K'(6, -6)
N(-6, 0) →N'(-9, 0)
The scale factor is same because using the ratio of the x coordinates gives:
3/2 = 1.5
6/4 = 1.5
-9/-6 = 1.5
3) The point W of the vertex of the polygon has coordinates as (2, 10)
Thus, if dilated by a scale factor of 2.7, we have the new coordinates as:
(2*2.7, 10*2.7) = (5.4, 27)
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URGENT! Can someone please help?
a. The missing values of the logarithm expression is log₃(40).
b. The missing values of the logarithm expression is log₅(8).
c. The missing values of the logarithm expression is log₂(1/25).
What is the missing of the logarithm expression?The missing values of the logarithm expression is calculated as follows;
(a). log₃5 + log₃8, the expression is simplified as follows;
log₃5 + log₃8 = log₃(5 x 8) = log₃(40)
(b). The log expression is simplified as;
log₅3 - log₅X = log₅3/8
log₅X = log₅8
X = 8
(c). The log expression is simplified as;
-2log₂5 = log₂Y
log₂5⁻² = log₂Y
5⁻² = Y
1/25 = Y
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What types of polynomials do you think could factor using the relationship made
in the previous question?
If a is replaced with an x, and b is replaced with a 2, how would the equation
look, and what does it mean?
Create your own replacement of a and b and explain how your equations would
look and what would it mean?
The relationship in the previous question involves the difference of squares pattern, which applies to polynomials of the form:
a^2 - b^2
where a and b are any real numbers.
If we replace a with x and b with 2, the equation would look like:
x^2 - 2^2 = (x + 2)(x - 2)
This means that any polynomial of the form x^2 - 4 can be factored using the difference of squares pattern.
As for creating our own replacement of a and b, let's say we replace a with y and b with 3. Then the equation would look like:
y^2 - 3^2 = (y + 3)(y - 3)
This means that any polynomial of the form y^2 - 9 can be factored using the difference of squares pattern.
Amelia gathered data about the heights of students at her school. Based on the displays, what inferences can you make about each sample?
Amelia can make inferences by using
The range of heightsThe shape/mean of the distributionThe presence of outliers, etc.What is the inferences about?Inferences from data on student heights include range determination based on minimum and maximum values, indicating greater variability with a larger range.
The average height of students can be determined using measures like mean, median, and mode. The distribution's shape can be determined by the histogram or box plot, indicating how the heights are distributed. inferences can be made by the use of height samples to gain insight into school population.
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5a-3b=7b find the ratio of a:b
(i need answers quick)
The ratio of a:b in 5a-3b=7b is 4:5.
We know that,
A ratio is an ordered pair of numbers a and b, written as a/b where b does not equal 0. A proportion is an equation in which two ratios are equal to each other. For example, if there are 2 boys and 6 girls, you can write the ratio as: 1 : 3 (for every boy there are 3 girls).
Ratios compare two numbers obtained by dividing. If one data point (A) is compared to another data point (B), it is expressed as A/B. It means that we are partitioning information A from information B. For example, if A is five and B is 10, your ratio would be 5/10, or 1/2.
For above information,
5a - 3b = 7b
5a = 7b- 3b
5a= 4b
So, a/b= 4/5
a:b is 4:5
Thus, the ratio of a:b in 5a-3b=7b is 4:5.
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Let p be the constant function p (z) = 1,000,000,000. Let q be the exponential function q (2) = 10
The product of the two functions is (pq) (z) = 10ª-2, where a is a constant. What is the value of a?
C2023 Illuminate Education, Inc.
P
C
[tex]\large \boxed{\mathrm{10}}[/tex]
The constant function p has a fixed output of one billion, while the exponential function q has a base of two and an output of 10. As the input increases by one, the output of q doubles. For example, q(3) = 20 and q(4) = 40. The rate of growth of q is much faster than p. In fact, q will eventually surpass p for large enough inputs. This demonstrates the power of exponential growth and highlights the importance of understanding the functions used in equations and models.
Answer:
10 or 1b
Step-by-step explanation:
Name 2 other categories of data you could use to better understand the physical fitness levels of these students.
Two other categories of data that could be used to better understand the physical fitness levels of students are:
Body composition data:
Cardiovascular fitness data:
We have,
Two other categories of data that could be used to better understand the physical fitness levels of students are:
Body composition data:
This data can include measurements such as body mass index (BMI), body fat percentage, and waist circumference.
By collecting body composition data for students, we can better understand their overall physical health and identify potential risk factors for chronic diseases related to physical fitness.
Cardiovascular fitness data:
This data can include measurements such as resting heart rate, maximal oxygen uptake (VO2 max), and cardiovascular endurance test results.
By collecting cardiovascular fitness data for students, we can better understand their cardiovascular health and fitness levels, as well as identify potential risk factors for heart disease and other related conditions.
Thus,
Two other categories of data that could be used to better understand the physical fitness levels of students are:
Body composition data:
Cardiovascular fitness data:
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∠1 and ∠2 are vertical angles. ∠2 has a measure of 31°.
What is the measure of ∠1?
Enter your answer in the box.
The measure of <1 is 31°.
What are vertical angles?Two angles are said to be vertical angles when they are formed by two straight lines intersecting at a point. This produces a series of angles of which some are vertical, thus they have equal measure.
In the information given in the question, it was given that <1 and <2 are vertical angles. This implies that they have equal measure, such that;
<2 = 31° (given)
So that;
<1 = <2 = 31°
Thus,
<1 = 31°
Therefore, it can be concluded that the measure of <1 is 31°.
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geometry please help
A graph of triangle CAT is shown below.
A graph of triangle C'A'T, the image of ΔCAT after a reflection in the x-axis is shown below.
ΔC'A'T represents a rigid motion because the pre-image and the image are congruent.
What is a reflection over the x-axis?In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.
Next, we would apply a reflection over or across the x-axis;
(x, y) → (x, -y)
C (-1, 2) → (-1, -(2)) = C' (-1, -2)
A (-1, 4) → (-1, -(4)) = A' (-1, -4)
T (3, 2) → (3, -(2)) = T' (3, -2)
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Line ac and df are parallel they are cut by transversal Hj with your partner find the seven unknown angle measures in the diagram explain your reasoning. What do you notice about the angles with vertex B and the angles with vertex E
The measure of the unknown angles in the parallel lines AC and DF with transversal HJ are as follow,
m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.
Two lines AC and DF are parallel to each other in the attached figure
Transversal HJ cut lines AC and DF at point B and E respectively.
Measure of ∠ABE = 63°.
Using the result based on corresponding angles, alternate interior angles , and vertically opposite angles of a parallel lines we get,
Measure of ∠ABE ≅ Measure of ∠DEH ( corresponding angles)
⇒Measure of ∠DEH = 63°
Measure of ∠ABE ≅ Measure of ∠BEF ( alternate interior angles)
⇒Measure of ∠BEF = 63°
Measure of ∠ABE ≅ Measure of ∠CBJ ( vertically opposite angles)
⇒Measure of ∠CBJ = 63°
Using the result of linear pair angles,
Measure of ∠ABE + Measure of ∠CBE = 180°
⇒ Measure of ∠CBE = 180° -63°
⇒ Measure of ∠CBE = 117°
Measure of ∠CBE ≅ Measure of ∠FEH ( corresponding angles)
⇒Measure of ∠FEH = 117°
Measure of ∠CBE ≅ Measure of ∠BED ( alternate interior angles)
⇒Measure of ∠BED = 117°
Measure of ∠CBE ≅ Measure of ∠ABJ ( vertically opposite angles)
⇒Measure of ∠ABJ = 117°
Therefore, the measure of the seven unknown angles formed in the parallel line are given by m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.
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The above question is incomplete, the complete question is:
Lines AC and DF are parallel. They are cut by transversal HJ with your partner find the seven unknown angle measures in the diagram explain your reasoning. What do you notice about the angles with vertex B and the angles with vertex E.
In the attached figure.
20x-12 factor out gcf in order to rewrite expression
Financial aid letters show your aid and costs of attendance for
one year
O four years
the entire time you plan on attending
a semester
Financial aid letters display aid and attendance costs for one year only. Some schools offer a financial aid letter for four years of undergrad, aiding in budget planning for the program.
What is the Financial aid?A few schools may give a budgetary help letter that ventures aid and costs for all four a long time of an undergrad program. This could offer assistance understudies arrange and budget for their whole undergrad instruction.
In a few cases, Financial aid letters may show aid and costs for a single semester, instead of the complete scholarly year. This could be valuable for understudies who are as it were going to part-time or who got to take a semester off.
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Please help with this simple question (Large reward)
Answer:
H
Step-by-step explanation:
Firstly, G and J cannot be the answers because the beginning numbers are too big. If you look at the fractions, you can see 2 and 7/8 because 2 is the smallest of all of them. Now the answer is between F and H.
In F, the second number is 3 and 1/2.
In H, the second number is 3 and 1/4.
If you want to make it an improper fraction to visualize better, it would be 7/2 and 12/4=6/2. Or you can just compare to see which is smaller, 1/2 or 1/4. In this case, 3 and 1/4 is smaller. Therefore the answer is H.
What is the equation of the line shown in this graph?
Answer:
The equation is y=-3
Step-by-step explanation:
The line is horizontal, cutting across the y-axis, which means it will be a y= line. The point it hits the y-axis is -3, so it is y=-3.
a 110 minute meeting should have a 10 minute break in the middle of two equal parts. How long after the meeting start should the break begin
Answer: 24 minutes and 30 seconds after the meeting as started
Step-by-step explanation:
110 minutes into 2 equal parts = 55 minutes in each section.
In the middle of 55 minutes = subtract the 10 minutes for a break from the 55 minutes that leaves you with 45 minutes. 24 minutes and 30 seconds before and after the 10 minute break.
Total session minutes - 110
Two equal parts of session: 55 minutes in each session
10 minute break in each session: 55-10 =45.
24 minutes and 30 seconds + 10 min break (in middle) + 24 minutes and 30 seconds
After 50 minutes the break will start.
The metting is 110 minutes long. According to the Question the metting have 'a'(only one) break of 10 minutes in between of two equal parts of metting.
so, duration of metting without the break=100 minutes
duration of each part=50 minutes
Now, the break should be after First part which is of 50 minutes.
=> The break should 50 minutes after the starting of metting.
prove the identity tan3x-tanx =2sinxsec3x
Solve the following for θ, in radians, where 0≤θ<2π.
2cos2(θ)−8cos(θ)−1=0
Select all that apply:
1.07
1.69
4.59
2.49
2
2.33
Answer:correct answers 1.69
4.59
Step-by-step explanation:
We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
2u^2 - 8u - 1 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 2, b = -8, and c = -1. Substituting these values, we get:
u = (8 ± sqrt(8^2 - 4(2)(-1))) / 2(2)
u = (8 ± sqrt(72)) / 4
u = 2 ± sqrt(18)
Therefore, either:
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and do all 3. :) (Do the one highlighted)
(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions.
Which of the following is not an exponential function?To determine which option is not an exponential function, we will apply general equation of an exponential function.
f(x) = aⁿ
where;
a is the base of the functionn is the exponentSo from the given options;
(³/₅)ˣ is an exponential function, because ³/₅ is the base while x is the exponent.
4ˣ is an exponential function, because 4 is the base while x is the exponent.
(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions, so there is no one base.
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Select all of the figures that show axis symmetry.
Answer: All of them
Step-by-step explanation:
All of them can be divided into two equal halves.
The figures that show axis symmetry are 1, 2, and 3.
What is the axis of symmetry?The axis of symmetry is a line, plane, or other axis that divides a geometric figure into two mirror-image halves that are congruent to each other.
A figure has axis symmetry if it looks the same after being rotated around an axis.
Out of the given figures, the ones that have axis symmetry are:
Sphere (has infinite axis symmetry)Cone (has rotational symmetry around its central axis)Cylinder (has rotational symmetry around its central axis)The figures that do not have axis symmetry are:
Cube (has only point symmetry)Rectangular cone (has no rotational symmetry)So, the figures that show axis symmetry are 1, 2, and 3.
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Which equation represents a direct variation?
Oy - 4x = 8
Oy + 2 = 7x
Oy - 3x = 0
O y = 5x - 2
Answer:
The equation that represents a direct variation is y = 5x - 2.
In a direct variation, one variable is proportional to the other variable, which means that as one variable increases or decreases, the other variable also increases or decreases in direct proportion. The general form of an equation that represents direct variation is y = kx, where k is a constant of proportionality.
In this case, the equation y = 5x - 2 is in the form of y = kx, where k = 5. This means that as x increases or decreases, y will also increase or decrease proportionally, with a constant rate of change of 5. Therefore, this equation represents a direct variation.