Step-by-step explanation:
Let the required number be x.
[tex] \therefore \: 3x + 6 = 21 \\ [/tex]
In which step did Cyrus make an error?
7 7 (x - 1)² = 12
(x - 1)2 = 36 Step 1
I-1= 6
Step 2
I=7
Step 3
Answer:
In step 2 Cyrus make an error.
Step-by-step explanation:
Given : Expression [tex]\frac{1}{3}(x-1)^2=12[/tex]
To find : In which step did Cyrus make an error?
Solution :
Expression [tex]\frac{1}{3}(x-1)^2=12[/tex]
Step 1 - [tex](x-1)^2=36[/tex]
Step 2 - [tex]x-1=6[/tex]
Step 3 - [tex]x=7[/tex]
There is a mistake in step 2,
As we are taking root both side so RHS value is +6 and -6.
So that there are two solutions of the equation.
Correct steps are,
Step 2 - [tex]x-1=6,-6[/tex]
Step 3 - [tex]x=7,-5[/tex]
Therefore, In step 2 Cyrus make an error.
Answer is step 2
Step-by-step explanation:
Solve for t
T+20.04=14.3
Answer:
T= -5.74
Step-by-step explanation:
A line passes through the points (1,4) and (3,-4). Which is the equation of the line
Answer: y=-4x+8
Step-by-step explanation:
Find 20% of 40. A. 8 B. 2 C. 0.5
Answer:
A)8
Step-by-step explanation:
10 percentage is 4 (to get this you have to do 40/10)
so 20 percentage is 8 (4*2)
Answer: 8
Multiply 20%×40 and get 8
Simplify the expression.
Which equation is equivalent to f(x) = -3(x-2)2 + 14?
The given function f(x) = -3(x-2)^2 + 14 is a quadratic equation shown in vertex form. To find an equivalent equation in standard form or solve for its roots, one can expand and simplify or use the quadratic formula with the appropriate coefficients.
The equation f(x) = -3(x-2)^2 + 14 is a quadratic equation in vertex form. In standard form, a quadratic equation is represented as at^2 + bt + c = 0. To express f(x) in this standard form, we simply need to expand the squared term and simplify. The given equation already shows that the parabola has been reflected vertically due to the negative sign before the coefficient of the squared term, and it is shifted 2 units to the right and 14 units up from the origin.
Transformations of the independent variable such as multiplying by a constant or adding a number, like in f(2x) or f(-2x), will affect the graph of the quadratic function. They result in horizontal scaling or reflection, while transformations like f{-2(x+1)} involve horizontal shifting.
To solve a quadratic equation that is set equal to zero, we can use the quadratic formula, which employs the coefficients a, b, and c. As an example, for a quadratic equation with constants a = 4.90, b = 14.3, and c = -20.0, the roots can be found through this formula.
An angle whose measure is –405° is in standard position. In what quadrant does the terminal side of the angle fall? Quadrant I Quadrant II Quadrant III Quadrant IV
Answer:
(D)Quadrant IV
Step-by-step explanation:
Given the angle -405
[tex]-405^0=-360^0-45^0\\-45^0=-45^0+360=315^0[/tex]
Angle 315 degrees is in Quadrant IV [tex](270\leq x\leq 360)[/tex], therefore:
Angle -405 degrees is in Quadrant IV.
Answer: its DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
The area of each of the bases will be m2.
The area of the right and left lateral faces will be m2.
The area of the front and back lateral faces will be m2.
The lateral area of the prism will be m2.
The surface area of the prism is 22 m2.
Answer:
The area of each of the bases will be m2 answer; (1)(3)=3
The area of the right and left lateral faces will be m2. answer; (1)(2)=2
The area of the front and back lateral faces will be m2. answer; (2)(3)=6
The lateral area of the prism will be m2. answer ; 16
Step-by-step explanation:
Area of each bases = 3 m²
Area of the right and left lateral faces = 2 m²
Area of the front and back lateral faces = 6 m²
Lateral area = 16 m²
Surface area of the rectangular prism = 22 m²
What is the lateral Area of a Rectangular Prism?Lateral area = 2(l + w)h
What is the Surface Area of a Rectangular Prism?Surfacea area = 2(wl+hl+hw)
We are given a rectangular prism that has the following dimensions:
Length (l) = 1 m
Width (w) = 3 m
Height (h) = 2 m
Area of each bases = l × w = 1 × 3 = 3 m²
Area of the right and left lateral faces = 1 × 2 = 2 m²
Area of the front and back lateral faces = 2 × 3 = 6 m²
Lateral area of the rectangular prism = 2(l + w)h = 2(1 + 3)2 = 16 m²
Surface area of the rectangular prism = 2(wl+hl+hw) = 2(3 × 1 + 2 × 1 + 2 × 3) = 22 m²
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Mari needs to rent a storage unit. She needs to determine the volume of the storage unit to decide if the storage unit is big enough to hold her things. If the storage unit is 8 feet high , what is the volume of the storage unit?
Answer:
D. 176
Step-by-step explanation:
segment the shape into two rectangles
(4 + 2) * (5 - 2) * 8 = 144
(2) * (2) * 8 = 32
144 + 32 = 176
100 points!!!
Multi-Step Equations with Distributive Property
Answer:
An example below
Step-by-step explanation:
5(4a + 7(a + 2b))
First simply the inside bracket using distributive property:
7(a + 2b)
7(a) + 7(2b)
7a + 14b
5(4a + 7a + 14b)
5(11a + 14b)
Use distributive property again
5(11a) + 5(14b)
55a + 70b
Answer:
x= -2
Step-by-step explanation:
An example could be
10 ( x+2) + 3(x+4) = 6(x+3)
Distribute
10x+20 +3x+12 = 6x+18
Combine like terms
13x +32 = 6x+18
Subtract 6x from each side
13x-6x +32 = 6x-6x+18
7x +32 = 18
Subtract 32 from each side
7x +32-32 = 18-32
7x =-14
Divide by 7
7x/7 = -14/7
x = -2
Write a expression to represent the perimeter of the following triangle. 3k+5. 2k+16 4k+15
Answer:
P = 9k + 36
Step-by-step explanation:
Assuming these are the following sides
3k+5. 2k+16 4k+15
To find the perimeter we add the sides
P = 3k+5+ 2k+16+ 4k+15
Combine like terms
P = 9k + 36
hurry plzzzzz!!!!!!!!!!!!! Find the height of a square pyramid that has a volume of 75 cubic feet and a base length of 5 feet. A:5 feet B:9 feet C:25 feet D:45 feet
Answer:
B
Step-by-step explanation:
The volume of a square pyramid can be found using:
v=1/3 bh
Where b is the area of the base, and h is the height
First, let's find the area of the base
a=l*l
We know the length is 5, so we can substitute it in
a=5*5
a=25
Now we know b(area), is 25, and we know the volume is 75, so we can substitute them in
v=1/3 bh
75=1/3(25)h
Divide both sides by 1/3, or multiply both sides by the reciprocal, 3/1
225=25h
Divide both sides by 25
h=9
So, the height is 9 feet , or choice B
Solve this question: Can you make 100 by interspersing any number of pluses and minuses within the string of digits 9 8 7 6 5 4 3 2 1? You can’t change the order of the digits! So what’s the least number of pluses and minuses needed to make 100? For instance, 98 - 7 - 6 + 54 - 32 shows one way of interspersing pluses and minuses, but since it equals 107, it’s not a solution.
Answer:
98-76+54+3+21=100
1 Plus3 MinusesStep-by-step explanation:
Possible Variants are:
[tex]98 - 76 + 54 + 3 + 21 = 100\\9 - 8 + 76 + 54 - 32 + 1 = 100\\98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100\\98 - 7 - 6 - 5 - 4 + 3 + 21 = 100\\9 - 8 + 76 - 5 + 4 + 3 + 21 = 100\\98 - 7 + 6 + 5 + 4 - 3 - 2 - 1 = 100\\98 + 7 - 6 + 5 - 4 + 3 - 2 - 1 = 100[/tex]
[tex]98 + 7 - 6 + 5 - 4 - 3 + 2 + 1 = 100\\98 - 7 + 6 + 5 - 4 + 3 - 2 + 1 = 100\\98 - 7 + 6 - 5 + 4 + 3 + 2 - 1 = 100\\98 + 7 - 6 - 5 + 4 + 3 - 2 + 1 = 100\\98 - 7 - 6 + 5 + 4 + 3 + 2 + 1 = 100\\9 + 8 + 76 + 5 + 4 - 3 + 2 - 1 = 100\\9 + 8 + 76 + 5 - 4 + 3 + 2 + 1 = 100\\9 - 8 + 7 + 65 - 4 + 32 - 1 = 100\\[/tex]
From:
98-76+54+3+21=100
The least number of plus and minuses needed to make 100 are 1 and 3 respectively.
The least number of pluses and minuses needed to arrange the numbers 9 8 7 6 5 4 3 2 1 to equal 100 is four. A valid combination resulting in 100 is 98 - 7 + 65 + 43 - 21 which uses two minuses and two pluses.
Explanation:Your question asks how many pluses and minuses can be inserted in the string 9 8 7 6 5 4 3 2 1 without altering its order to make 100. An interesting mathematical challenge problem indeed!
Remember, this question pertains to arithmetic operations of addition (+) and subtraction (-). A possible solution can be 98 - 7 + 65 + 43 - 21. This results in 100 with four total operations interspersed (two minuses and two pluses).
By using the arithmetic operations strategically, the least number of pluses and minuses (total four) you need to yield 100 is produced. Hence, this combination of digits and operators achieve the intended sum balancing positive and negative values.
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Use the information to write an equation with variables on both sides. Let x represent Kim’s age.
Bob is 4 years older than twice Kim’s age.
Paul is 1 year younger than 3 times Kim's age.
Bob and Paul are the same age.
Which equation can be used to determine Kim’s age, x, from the information about Bob and Paul?
4x + 2 = 3x + 1
4x + 2 = 3x + (–1)
2x + 4 = 3x + 1
2x + 4 = 3x + (–1)
Hey! I hope this helps!
Answer:2x + 4 = 3x+ (-1)
Option D)
Step-by-step explanation:We are given the following in the question:
Let x represent Kim's age
"Bob is 4 years older than twice Kim's age"
Thus, Bob's age =
4 + 2x years
"Paul is 1 year younger than 3 times Kim's age."
Thus. Paul's age is
(3x - 1) years
If Bob's age and Paul's age is equal, we can write:
2x + 4 = 3x + (-1)
Thus, the required expression is
2x + 4 = 3x + (-1)Option D)
Option D! 2x + 4 = 3x + (-1)The equation can be used to determine Kim’s age will be 2x + 4 = 3x + (–1). Then the correct option is D.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Use the information to write an equation with variables on both sides. Let x represent Kim’s age.
Bob is 4 years older than twice Kim’s age. Then the age of the Bob will be in terms of x.
B = 2x + 4
Paul is 1 year younger than 3 times Kim's age. Then the age of the Paul will be in terms of x.
P = 3x – 1
Bob and Paul are the same age.
B = P
Put the value of B and P, then we have the equation will be
2x + 4 = 3x – 1
2x + 4 = 3x + (–1)
Then the correct option is D.
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Find the unknown side of the triangle below
A. 4cm
B. 3cm
C. 9cm
D. 19cm
Answer:
C - 9 cm
Step-by-step explanation:
We can use the Pythagorean theorem to figure out the missing side length, in this case, X.
The Pythagorean theorem states: a^2 + b^2 = c^2, with c being the hypotenuse. We have the side length of the hypotenuse which is 15, and we have another side length of 12. Let's put these back in our equation:
a^2 + 12^2 = 15^2;
If we simplify the squares by simply doing them: a^2 + 144 = 225;
Now let's subtract 144 from both sides to isolate the variable, a:
a^2 = 81;
Now we square both sides to find a:
a = 9
The missing side length is 9 cm.
Louie is building a scale model of an airplane, using a scale of 2 inches =
25 feet. If the airplane is 155 feet long, what is the length of the model?
Answer:
The length of the model is 12.4.
Step-by-step explanation:
2in=25ft
x=155ft
155/25=6.2
2*6.2=12.4
1. How much greater is -20x^2+5x+17 than -19x^2+20x+18
Answer: ?^2-15x-1
2. How much greater is -20x^7+10x^6-5x+15 than 13x^7+14x^5-4x^4-11x^2-17
Please help me 30 points. iMathmatics works, but my parents took my phone and its an app and i'm using a computer at the moment...
Answer:
1. -x²-15x-1
2. -33x⁷+10x⁶-14x⁵+4x⁴+11x²-5x+32
Step-by-step explanation:
-20x^2+5x+17 - (-19x^2+20x+18)
-20x² + 19x² + 5x - 20x + 17 - 18
-x² - 15x - 1
-20x^7+10x^6-5x+15 - (13x^7+14x^5-4x^4-11x^2-17)
-20x⁷ - 13x⁷ + 10x⁶ - 14x⁵ + 4x⁴ + 11x² - 5x + 15 + 17
-33x⁷ + 10x⁶ - 14x⁵ + 4x⁴ + 11x² - 5x + 32
Answer:
1. -x^2 - 15x - 1
2. -33x^7 + 10x^6 - 14x^5 + 4x^4 + 11x^2 - 5x + 32
Step-by-step explanation:
Problem 1.
How much greater is -20x^2 + 5x + 17 than -19x^2 + 20x + 18
Problem 1. Solution:
Subtract the second polynomial from the first polynomial.
-20x^2 + 5x + 17 - (-19x^2 + 20x + 18) =
To simplify the parentheses, think of the negative sign left of the parentheses as the number -1, and distribute it using the distributive property.
= -20x^2 + 5x + 17 -1(-19x^2 + 20x + 18)
We multiply -1 by each term in the parentheses.
= -20x^2 + 5x + 17 + 19x^2 - 20x - 18
Now we combine like terms. First, group each set of like terms together.
= -20x^2 + 19x^2 + 5x - 20x + 17 - 18
Now combine like terms.
= -x^2 - 15x - 1
Answer to Problem 1.: -x^2 - 15x - 1
Problem 2.
How much greater is -20x^7 + 10x^6 - 5x + 15 than 13x^7 + 14x^5 -4x^4 -11x^2 - 17
Problem 2. Solution:
Subtract the second polynomial from the first polynomial.
-20x^7 + 10x^6 - 5x + 15 - (13x^7 + 14x^5 - 4x^4 - 11x^2 - 17) =
To simplify the parentheses, think of the negative sign left of the parentheses as the number -1, and distribute it using the distributive property.
= -20x^7 + 10x^6 - 5x + 15 -1(13x^7 + 14x^5 - 4x^4 - 11x^2 - 17)
We multiply -1 by each term in the parentheses.
= -20x^7 + 10x^6 - 5x + 15 - 13x^7 - 14x^5 + 4x^4 + 11x^2 + 17
Now we combine like terms. First, group each set of like terms together.
= -20x^7 - 13x^7 + 10x^6 - 14x^5 + 4x^4 + 11x^2 - 5x + 15 + 17
Now combine like terms.
= -33x^7 + 10x^6 - 14x^5 + 4x^4 + 11x^2 - 5x + 32
Answer to Problem 2.: -33x^7 + 10x^6 - 14x^5 + 4x^4 + 11x^2 - 5x + 32
How to find the spread in math???
Answer:
interquartile range
range
variance
These are all different ways to find the spread
The spread in math refers to measures like the range, standard deviation, and variance, which estimate the variability within a dataset. The standard deviation and variance provide insights into the dispersion of data points around the mean, while the range shows the overall spread between the highest and lowest values.
Understanding Measures of Spread in Mathematics
To find the spread in math, we consider several different statistics that measure variability or dispersion within a set of data. There are three common measures of spread:
Range: The difference between the highest and lowest values in a dataset. It gives a quick sense of the overall spread but doesn't account for how data is distributed within that range.Standard Deviation: It quantifies the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation can be calculated differently for a sample or a population.Variance: The square of the standard deviation. While we often report standard deviation rather than variance, both measure the spread in the same way. Variance is particularly important because it's additive, allowing the comparison of variances from different sets of data.An alternative measure, the Interquartile Range (IQR), measures the spread within the middle 50 percent of data and can be estimated from a box plot. When examining distributions like scores in a class, comparing the observed distribution to a theoretical one such as the normal distribution can reveal insights into the probabilities surrounding different ranges of scores.
To perform these calculations accurately, tools such as graphing calculators, statistical software, and probability tables can be used. These resources help to visualize data (e.g., creating a box plot) and calculate statistical values, offering a clear view of the data's distribution and spread.
The more you take, the more you leave behind. What am I?
brainliest for right answer
Answer:
Footsteps
Step-by-step explanation:
Answer:
Footsteps.
Step-by-step explanation:
You walk more and more and eventually those footsteps from previous are left behind.
(My dad told me this as a moral lesson when I was young.)
P.S
Have a Amazing Day!
Faker/Tosrel
The diagram below shows scalene triangle JKL. Triangle J K L. Side L K extends to point H to form exterior angle J K H. Which is true about the diagram? Select two options. Measure of angle J K H + measure of angle J K L = 180 degrees Measure of angle J K L + measure of angle J L K + measure of angle K J L = 180 degrees Measure of angle J K H = measure of angle J L K Measure of angle J K L + measure of angle J L K = 90 degrees Measure of angle K J L = measure of angle K L J
Answer:
Step-by-step explanation:
Measure of angle J K H + measure of angle J K L = 180 degreesTrue.
Measure of angle J K L + measure of angle J L K + measure of angle K J L = 180 degreesTrue. The sum of all interior angles = 180
Measure of angle J K H = measure of angle J L K =Can't tell from info given.
Measure of angle J K L + measure of angle J L K = 90 degreesCan't tell from info given.
Measure of angle K J L = measure of angle K L JCan't tell from info given.
Answer:
A and B or the first two
Step-by-step explanation:
what she saying is true so that means that it is A and B
what is the volume of the prism
Answer:
the answer is 18
Step-by-step explanation:
What are the solutions to the quadratics equation 2x+ + 6x – 20 = 1
A model for consumers' response to advertising is given by the equation N(a)=2000+500 ln (a) Where N(a) is the number of units sold, a is the amount spent on advertising, in thousands of dollars, & a≥1.
How many units are sold when $1000 is spent on advertising?
Answer:
Therefore 2000 units are sold when $1000 is spent on advertising.
Step-by-step explanation:
Given that,
The equation of a model for consumer's response to advertising is
N(a)=2000+500 ln(a)
where a is the amount spent on advertising, in thousand of dollars and a≥1,N(a) is the amount of units sold.
$1000 is spent on advertising.
Since a is in thousand of dollars.
∴a=1
Now plug a=1 in the given model
N(a)=2000+500 ln(1)
⇒N(a)=2000+500×0 [ ∵ln(1)=0 ]
⇒N(a) = 2000
Therefore 2000 units are sold when $1000 is spent on advertising.
What is the mean of the values in the stem-and-leaf plot?
Enter your answer in the box.
Key: 2|5 means 25
A stem-and-leaf plot with a stem value of 1 with a leaf value of 2, 3, 5, a stem value of 2 with a leaf value of 8 and 8, a stem value of 3 with a leaf value of 0, and a stem value of 4 with a leaf value of 2.
Answer:
mean = 24
Step-by-step explanation:
In a stem-and-leaf plot, each leaf represents a number or piece of data.
Each the leaf will only show the last digit of the number, and the stem will have the rest.
Examples:
stem value of 1 with a leaf value of 2 = 12
a stem value of 3 with a leaf value of 0 = 30
So, this is your plot:
Stems| Leaves
1 | 2 3 5
2 | 8 8
3 | 0
4 | 2
Your data is 12, 13, 15, 28, 28, 30, 42.
Add up all these numbers and divide by the number of leaves.
Sum of data = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168
Number of leaves = 7
168 ÷ 7 = 24
∴ The mean is the values in the stem-and-leaf plot is 24.
Situation A
Maria opened a new savings
account with an initial deposit of
$100. She deposits $75 into this
savings account every
two-weeks. What equation can
be used to represent Maria's
account balance, a, after she has
completed d deposits?
The equation a = 100 + 75d represents Maria's account balance.
Step-by-step explanation:
Given that,
Maria opened a new savings account with an initial deposit of $100.She deposits $75 into this savings account every two-weeks.You need to find the equation to represent Maria's account balance, a after she has completed d deposits.
Let 'd' be the number of deposits Maria made after the initial deposit.Let 'a' be the total account balance after 'd' deposits.Therefore, the equation for the total account balance can be framed as the sum of the initial deposit and amount deposited after that.
To find the amount that was deposited after the initial deposit :
⇒ $75 × number of times Maria deposited.
⇒ 75 × d
The equation is written as,
⇒ a = 100 + 75d
Hence the equation a = 100 + 75d represents Maria's account balance.
Araceli had 61 pennies and then lost 12. Now she wants to buy a treat that costs 4 sevenths of the pennies she has left. How many pennies does the treat cost?
The treat would cost 7 cents of your 49
Evaluate the geometric series. Please help me out!!!
Answer:
- 1364
Step-by-step explanation:
The n th term of a geometric series is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
4[tex](-2)^{n-1}[/tex] ← is an n th term
with a = 4 and r = - 2
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a(r^{n}-1) }{r-1}[/tex], thus
[tex]S_{10}[/tex] = [tex]\frac{4((-2)^{10}-1) }{-2-1}[/tex]
= [tex]\frac{4(1024-1)}{-2-1}[/tex]
= [tex]\frac{4(1023)}{-3}[/tex]
= [tex]\frac{4092}{-3}[/tex]
= - 1364
Mr. Thomas cooked 45 hamburgers and hot dogs at a cookout. He cooked three
fewer than twice as many hot dogs as hamburgers. How many hamburgers and
hot dogs were cooked?
Answer:
There are 90 hamburgers and 87 hot dogs
Step-by-step explanation:
What is the domain of this exponential function?
Answer:
Domain = x E R
Step-by-step explanation:
Since an exponential function has no restriction on the "x" value, its domain can range from anywhere on the plane of "x."
Adelina started painting at 2:32. She finished before 3:00. Use digital form to write a time she could
have finished painting
She could have finished painting at
Answer:
2:35
2:47
2:53 etc
Step-by-step explanation:
Since she started or commenced painting at exactly 2:32 and finished painting before 3:00 ,
She could have finished painting 3 minutes later which is 2:35
She could have finished painting 15 minutes later ,which is 2:47
She could have finished painting 21 minutes later which is 2:53 etc
Just make sure you don't write anything that exceeds 3:00 which is about 28 minutes from the time she commenced painting.
The seven students in a sewing
class equally share the cost of
fabric and other supplies. Last
month, each student paid ($167.94
+ $21.41) / 7. This month, each
student paid ($77.23 + $ 6.49) / 7.
Without doing any calculations, in
which month did each student pay
more?
Answer:
Last month
Step-by-step explanation:
Just look at the numbers.
The first number is (167.94 + 21.41) / 7 and the second number is (77.23 + 6.49) / 7. We see that they both have the denominator of 7, so we can just focus on comparing the numerators.
Look at 167.94 + 21.41. Clearly, 167.94 is bigger than 77.23 from the second number. We also see that 21.41 is clearly bigger than 6.49. If both numbers of the first number are bigger than both numbers from the second number, we know that the sum of the first two numbers will be bigger than the second sum.
Thus, the bigger the numerator, the bigger the amount paid, even including the dividing 7 at the end.
Thus, last month, the students had to pay more.
Hope this helps!
Answer:
Last
Step-by-step explanation:
Values being added are greater in last month as compared to this month