Wendy was asked to write an equation and solve this problem. Dylan bought a box of markers. He used 14 markers and had 18 that he didn’t use. How many markers were in the box? Wendy’s work is shown below. Steps Wendy’s Work Step 1 m minus 14 = 18 Step 2 m minus 14 minus 14 = 18 minus 14 Step 3 m = 4 In which step, if any, did Wendy first make a mistake in her work? step 1 step 2 step 3 no mistake
Answers
Answer: STEP 2
Step-by-step explanation: I took the quiz i am pretty positive
plz mark me as the brainliest
Answer:
step 2 or b
Step-by-step explanation:
Related Questions
does anyone know the answer with process
Answers
Answer:
a) ab(5a + 15b - 2ab)
b) (5a + 9b)(5a - b)
Step-by-step explanation:
When you are factoring, you will factor out "common factors", which are numbers/variables that are shared by all terms within the given expression.
A "term" is a standalone group of either number, variable, exponents, or a mix of them.
a) 5a²b + 15ab² - 2a²b²
For question a, note that they all have the variables a & b, but that they do not all share the same factors.
Factors of:
5: 1 , 5
15: 1 , 3 , 5 , 15
2: 1 , 2
In this case, factor out one a and one b:
ab(5a + 15b - 2ab) is your answer.
~
b) 25a² - 81b²
You can find perfect squares. Note that it is a² - b², which means that it will factor as such:
(a² - b²) = (a + b)(a - b)
(25a² - 81b²) = (5a + 9b)(5a - b)
(5a + 9b)(5a - b) is your answer.
~
In your own words, write a verbal expression for the following algebraic expression.
18p
Answers
Step-by-step explanation:
18p is a multiplication expression in itself.
It could be written as 18 x p. I am confused on what you mean as 'verbal' so i'm gonna take a wild guess and say word form.
eighteen times p???
Sorry if it's wrong.
What is it? Could someone draw these coordinates
Answers
The coordinates are simple. Hope you understand this and you can draw it out.
What is the probability of rolling a number less than 4 and then rolling a prime number
Answers
Answer:
1/6
Step-by-step explanation:
What is the slope of the line that passes through the points (-4,-1) and (-2,-5)?
Answers
Step-by-step explanation:
m= (-5+1)/(-2+4)
m= -4/2
m= -2
Consider function f.
Which statement is true about function f?
A.
The function is continuous.
B.
As x approaches positive infinity, approaches positive infinity.
C.
The function is increasing over its entire domain.
D.
The domain is all real numbers.
Answers
Answer:
Step-by-step explanation:
Check for continuity by evaluating 2^x and -x^2 - 4x + 1 at the break point x = 0: 2^0 is 1 and -x^2 - 4x + 1 is also 1, so these two functions approach the same value as x approaches 0.
Now do the same thing with
-x^2 - 4x + 1 and (1/2)x + 3 at x = 2; the first comes out to -11 and the second to 4. Thus, this function is not continuous at x = 2.
We must reject statement A.
Statement B: as x increases without bound, (1/2)x + 3 also increases without bound. This statement is true.
Statement C: False, because the quadratic -x^2 - 4x + 1 has a maximum at
x = -b/[2a], or x = -(-4)/[-2], or x = -2
Statement D: True: there are no limitations on the values of the input, x.
The statement B is as x approaches positive infinity f(x) approaches positive infinity is true
What is the definition of the limit?A point or level beyond which something does not or may not extend or pass.
We have to check for continuity by evaluating \(2^x\) and \(-x^2 - 4x + 1\)
at the break point x = 0
\(2^0\)is 1 and \(-x^2 - 4x + 1\) is also 1,
So these two functions approach the same value as x approaches 0.
Now do the same thing with
\(-x^2 - 4x + 1\)and \((1/2)x + 3\) at x = 2;
The first comes out to -11 and the second to 4.
Thus, this function is not continuous at x = 2.
We must reject statement A.
for B we have as x increases without bound,
\((1/2)x + 3\)
also increases without bound.
Therefore the statement B is true statement.
Statement C is False,
because the quadratic\(-x^2 - 4x + 1\) has a maximum at
\(x = -b/[2a],\)
\(x = -(-4)/[-2],\)
\(x=-2\)
There are no limitations on the values of the input, x.
D is also false negative number are in real numbers.
Therefore,the statement B is as x approaches positive infinity f(x) approaches positive infinity is true
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You work sixteen hours a week at Walmart. You earn $7.35 an hour. Your family is going on a trip to New York this Christmas. It costs $3692.00. Your parents told you that you have to pay for half of the trip with your own money. How many weeks must you work to earn enough to pay for the trip?
Answers
Answer: 16 weeks rounded up.
Step-by-step explanation: If you have to pay for half of the trip. And you make $7.35/hr. And you work 16 hours per week.
$3692/2 = $1846
$1846/$7.35 per hour = 251.16 hours
251.16 hours/16 hours per week = 15.6975 weeks
aaaaaaaawwaaaaaaaaaaaaaaaa
if you answer some of them ill appreciate it ( you don't have to answer all of them )
Answers
Answer:
1) 23, 3, 13
2) 7, 13, 18
3) 9, 6, 77
4) 39, 8, 46
5) 13, 1, 32
6) 45, 9, 54
7) 14, 45, 30
8) 25, 10, 39
Step-by-step explanation:
Left to Right
a) use definition 2 to find an expression for the area under the curve y=x^3 from 0 to 1 as a limit.(b) the following formula for the sum of the cubes of the first n integers is proved in Appendix E. useit to evaluate the limit in part (a).1^3 + 2^3 +3^3+.....n^3 = [n(n+1)/2]^2Definition 2: The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating.
Answers
The area A of the region S that lies under the graph of the continuous function f is \(\frac{1}{4}\).
(a)
\(A =\) \(\int\limits^A_b {f(x)} \, dx\)
= \(\lim_{n \to \infty}\)∑ f(xi) Δ x
a = 0, b = 1 → Δ x = \(\frac{1-0}{n}\) = \(\frac{1}{n}\)
x₀ = 0, x₁ = \(\frac{1}{n}\) , x₂ = \(\frac{2}{n}\), x₃ = \(\frac{3}{n}\), ..., xi = \(\frac{i}{n}\)
f(x) = \(x^{3}\)
f(xi) = \([\frac{i}{n} ]^{3}\) = \(\frac{i^{3} }{n^{3} }\)
Then,
A = \(\lim_{n \to \infty}\) ∑(\(\frac{i^{3} }{n^{3} }\)) * \(\frac{1}{n}\)
(b)
A = \(\lim_{n \to \infty}\) [\(\frac{1}{n}\) * ∑ \(\frac{i^{3} }{n^{3} }\) ]
= \(\lim_{n \to \infty}\) [\(\frac{1}{n}\) * \(\frac{1}{n^{3} }\) ∑ \(i^{3}\)]
= \(\lim_{n \to \infty}\) [\(\frac{1}{n^{4} }\) * [\(\frac{n(n+1)}{2}\)]^2]
= \(\lim_{n \to \infty}\) [\(\frac{1}{n^{4} }\) * \(\frac{n^{2}(n+1)^{2} }{4}\)]
= \(\lim_{n \to \infty}\) \(\frac{(n+1)^{2} }{4n^{2} }\)
= \(\frac{1}{4}\) * \(\lim_{n \to \infty}\) \((\frac{n+1}{n} )^{2}\)
= \(\frac{1}{4}\) * \(1^{2}\)
A = \(\frac{1}{4}\)
Therefore the area A of the region is \(\frac{1}{4}\).
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a 95 confidence interval for p1-p2 is (-0.185, -0.093). explain how the confidence interval provides the same information as the significance test in part a
Answers
We can conclude that the difference between p1 and p2 is statistically significant at the 5% level of significance.
The confidence interval and significance test in part A both provide similar information. The significance test in part A tests if the difference between p1 and p2 is statistically significant, while the confidence interval provides an estimated range of values for the true difference between p1 and p2 with a certain degree of confidence (95% in this case).A confidence interval is a range of values that we believe will include a population parameter with a specified level of confidence.
It can be computed to estimate the population mean or the difference between two population means, such as p1 and p2.In contrast, a significance test assesses whether the difference between two population proportions is statistically significant.
The test calculates a p-value, which is the likelihood of obtaining the observed difference between two proportions, assuming the null hypothesis (that there is no difference between the two proportions) is true. A p-value less than the level of significance (usually 0.05) indicates that the difference between the two proportions is statistically significant, while a p-value greater than the level of significance indicates that the difference is not statistically significant.
Both the confidence interval and the significance test inform us about the difference between two population proportions. The confidence interval provides a range of plausible values for the difference, while the significance test tells us whether the difference is statistically significant or not. In this particular case, since the confidence interval does not contain zero,
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birth statistics include statistics on both live births and fetal deaths. True or false
Answers
True. Birth statistics typically include data on both live births and fetal deaths.
Fetal deaths refer to the loss of a pregnancy before the fetus is delivered and can be classified as either early or late fetal deaths, depending on the gestational age at the time of the loss. While the focus of birth statistics is often on live births, tracking fetal deaths is important for monitoring the health of pregnant women and identifying potential risks or problems with pregnancy. In the United States, fetal death statistics are typically collected by state health departments and reported to the National Vital Statistics System. These statistics provide important information for researchers, healthcare providers, and policymakers working to improve maternal and fetal health outcomes.
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Select all correct answers. one solution to a quadratic equation is . what is true about any remaining solutions? there are at least two more real solutions. there are no other real solutions. there is exactly one complex solution. there are two or more complex solutions. there are no complex solutions. there is exactly one more real solution.
Answers
There is exactly one more real solution or there is exactly one more complex solution
Given,
One solution to a quadratic equation is x = -5/3
We have to find the correct statements from the given ones;
A polynomial of degree two is a quadratic equation.
This implies that a polynomial has two solutions.
We already have an answer to the query, which is a true root.
Then, the additional response that we lack can appear in the form of two responses.
It may be a real root or a complicated root, depending on the situation.
The following is the response to this query:
There is exactly one more real solution or there is exactly one more complex solution
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A closed rectangular container with a square base no top is to have a volume of 2400 cubic centimeters. It costs three times as much per square centimeter for the bottom as it does for the sides. Use calculus to find the dimensions of the container of least cost.
Answers
The dimensions of the rectangle are length = 13.38 cm, width = 13.38 cm and height = 13.4 cm.
Given that,
A closed rectangular container must have a volume of 2400 cubic centimeters and a square base without a top. The bottom is three times more expensive per square centimeter than the sides.
We have to calculate the size of the container with the lowest cost.
We know that,
Volume V = 2400 cm³
Let us take the base of the square length as x and height is h
Volume of the rectangle is length × width ×height
Length and width are same x and height is h
Then,
x × x × h = 2400
h = \(\frac{2400}{x^2}\)
Area of the sides \(A_s\)= length ×height = hx + hx + hx + hx = 4(\(\frac{2400}{x^2}\))x = \(\frac{9600}{x}\)
Let cost is $1 for 1 cm²
Cost of the sides \(C_s\) = \(\frac{9600}{x}\) × 1 = \(\frac{9600}{x}\)
Area of the top and bottom is area of square \(A_t\) = x² + x² = 2x²
Cost of the sides \(C_t\) = 2x²
Total cost = \(C_s +C_t\)
C = \(\frac{9600}{x}\) + 2x²
By differentiating on both the sides
\(\frac{dC}{dx}\) = 4x - \(\frac{9600}{x^2}\)
Taking \(\frac{dC}{dx}\) = 0
0 = 4x - \(\frac{9600}{x^2}\)
4x = \(\frac{9600}{x^2}\)
4x³ = 9600
x³ = \(\frac{9600}{4}\)
x³ = 2400
Taking cube root on both the sides,
x = 13.38 cm
Then h = \(\frac{2400}{x^2}\) = \(\frac{2400}{(13.38)^2}\) = \(\frac{2400}{179.02}\) = 13.4 cm
Therefore, The dimensions of the rectangle are length = 13.38 cm, width = 13.38 cm and height = 13.4 cm.
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Express the limit lim Σ (2 sin² (2πæ;*) +5) Aæ; over [1, 8] as an integral. n→ [infinity] i=1
Provide a, b and f(x) in the expression ∫_a^b▒〖f(x)dx〗f(x)
a = 1 0, b = 8 [infinity], f(x) =
Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using geometry. ∫_0^10▒|8x-6|dx
Find the average value fave of f(x) = x7 between -1 and 1, then find a number c in [-1,1] where f(c) = fave.
fave =
C =
Answers
(a) The given limit can be expressed as an integral: ∫₁⁸ (2 sin²(2πx) + 5) dx.
To express the given limit as an integral, we have:
lim(n→∞) Σ(2 sin²(2πæ;*) + 5) Δæ;
i=1
This can be rewritten as the sum:
lim(n→∞) [2 sin²(2π(1/n)) + 5 + 2 sin²(2π(2/n)) + 5 + ... + 2 sin²(2π(n/n)) + 5] Δæ;
As n approaches infinity, this sum approaches an integral:
∫₁⁸ (2 sin²(2πx) + 5) dx.
So, the limit can be expressed as the integral ∫₁⁸ (2 sin²(2πx) + 5) dx.
(b) The integral ∫₀¹₀ |8x - 6| dx represents the area of a region bounded by the x-axis and the graph of |8x - 6|.
To find the area represented by the integral ∫₀¹₀ |8x - 6| dx, we consider the graph of |8x - 6|. This function has two parts: one where 8x - 6 is positive, and the other where it is negative. The integral evaluates the area between the graph and the x-axis.
The region bounded by |8x - 6| and the x-axis is a trapezoid with two equal legs and a height of 6/8 = 3/4. The bases of the trapezoid are the intervals where 8x - 6 changes sign: [0.75, 1.25] and [1.25, 1.75].
To find the area, we calculate the area of the two triangles formed by the bases and subtract it from the area of the rectangle with height 3/4 and width 0.5: Area = (0.5)(3/4) - 2(0.5)(1/4)
= 3/8 - 1/4
= 1/8.
Therefore, the integral ∫₀¹₀ |8x - 6| dx represents an area of 1/8.
(c) The average value of f(x) = x⁷ between -1 and 1 is fave = 2/9. There is no number c in [-1, 1] where f(c) = fave.
The average value of a function f(x) over an interval [a, b] is given by:
fave = (1/(b - a)) ∫[a,b] f(x) dx.
For f(x) = x⁷ over the interval [-1, 1], we have:
fave = (1/(1 - (-1))) ∫[-1,1] x⁷ dx
= (1/2) ∫[-1,1] x⁷ dx
= (1/2) [x⁸/8]_[-1,1]
= (1/2) [(1/8) - (1/8)]
= 0.
The average value of f(x) = x⁷ over the interval [-1, 1] is 0.
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p + 5 = 15 help meeeeeeeeeeeeee
Answers
Answer:
p=10
Step-by-step explanation:
subtract 5 on both sides and you'll get p=10 :]
good at math & need points? help!!
Answers
Answer:
D
Step-by-step explanation:
In the problem 12.4 + 4.7, what is the Divisor?
Answers
Answer:4.7
Step-by-step explanation:
Select the correct answer.
On a number line, point S is at -2, and point T is at 7. Point R is the midpoint of
ST
¯
. Where does point R lie on the number line?
A.
-2.5
B.
4.5
C.
-4.5
D.
2.5
Answers
Answer:
D
Step-by-step explanation:
to find the midpoint of ST , calculate the average of the 2 values
R = (- 2 + 7) ÷ 2 = 5 ÷ 2 = 2.5
Answer:
2.5
Step-by-step explanation:
suppose your coworker proposes the following summary statement for the article: an economist/yougov national poll was conducted july 27-30, 2019 to see what proportion of americans approve of the way donald trump is handling his job as president. the poll was conducted online. the margin of sampling error for overall results is plus or minus 2.5 percentage points. there are two pieces of information missing in this statement for you to be able to approve it. what is the missing information?
Answers
The missing information is the sample size and the actual proportion of Americans who approve of the way Donald Trump is handling his job as president.
To approve the summary statement, we need to know the sample size and the proportion of Americans who approve of Donald Trump's job performance. These two pieces of information are crucial for understanding the validity and representativeness of the poll results.
The sample size refers to the number of participants in the poll, which affects the precision and reliability of the findings. Without knowing the sample size, it is difficult to assess the statistical significance of the results.
Similarly, the actual proportion of Americans who approve of Donald Trump's job as president is essential to determine the accuracy of the poll. It provides a baseline against which the poll results can be compared. Without this information, it is impossible to evaluate the significance and reliability of the reported proportions.
To fully evaluate and approve the summary statement, we need to know the sample size and the actual proportion of Americans who approve of Donald Trump's job as president. These missing pieces of information are crucial for understanding the representativeness and reliability of the poll results.
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Polynomial x²-6y²-xy-5x-5y+6 was factored into (x+ay+b)(x+cy-2) for constants a, b and c. Find the value of a+bc
Answers
Answer:
We know that the polynomial:
x²- 6y²- xy - 5x - 5y + 6
is rewritten as:
(x+ay+b)(x+cy-2)
First, lets expand the above expression:
x^2 + x*(cy) + x*(-2) + (ay)*x + (ay)*(cy) + (ay)*(-2) + b*x + b*(cy) - 2*b
Now we can simplify this to get:
x² + c*(xy) - 2*x + a*(xy) + ac*y² - 2a*y + b*x + bc*y - 2b
now let's group together the terms with the same variables:
x² + (c + a)*(xy) + (b - 2)*x + (bc - 2a)*y + ac*y² - 2b
And that must be equal to:
x²- 6y²- xy - 5x - 5y + 6
notice that equations are equal if and only if all the correspondent factors are equal.
notice that in both cases, the factor that multiplies the x² term is 1.
for the y² term we will have:
a*c = -6
for the xy term we will have
c + a = -1
for the x term we will have
b - 2 = - 5
for the y term we will have
bc - 2a = -5
for the constant term, we will have:
-2b = 6
Then we have a lot of equations, rewriting these we have:
a*c = -6
c + a = -1
b - 2 = -5
bc - 2a = -5
-2b = 6
From the fourth equation, b - 2 = -5
we can get:
b = -5 + 2 = -3
b = -3
notice that for the last equation:
-2b = 6
b = 6/-2 = -3
we have the same solution
Then we can replace the value of b in the above equations to get:
a*c = -6
c + a = -1
-3*c - 2a = -5
Now, we need to isolate one of the variables in one of the equations.
For example, we can isolate c in the second one to get:
c = -1 - a
now we can replace that in other equation, for example the third one:
-3*(-1 - a) - 2a = -5
now we can solve that for a.
3 + 3a - 2a = -5
3 + (3 - 2)a = -5
3 + a = -5
a = -5 - 3 = -8
a = -8
now we can use the equation "c = -1 - a" to find the value of c:
c = -1 -(-8) = -1 + 8 = 7
c = 7
then we have:
b = -3
a = -8
c = 7
then:
a + b*c = -8 + (-3)*7 = -8 - 21 = -29
Select the number in each drop down list that will create a list in descending order. (greatest to least)
12.33
12.034
12.003
12.301
Answers
12.33
12.301
12.034
12.003
What is the equation of a line that is parallel to the line 2x + 5y = 10 and passes through the point (-5, 1)? Check all
that apply.
Oy=-x-1
2x + 5y = -5
Oy=-x-3
2x + 5y = -15
y - 1=-2/5(x+ 5)
Answers
Answer:
A: y = -2/5x - 1
B: 2x + 5y = -5
E: y - 1 = -2/5(x+5)
Step-by-step explanation:
I only got 2 out of 3 answers, but the ones listed above should be correct :) Hope this helps! :D
The equation of the line is 2x + 5y = -5.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line that is parallel to the line 2x + 5y = 10 will have the same slope as the given line, which is -2/5.
Using the point-slope form of the equation of a line, we can find the equation of the line passing through the point (-5, 1) with slope -2/5:
y - 1 = (-2/5)(x + 5)
Multiplying both sides by 5.
5y - 5 = -2x - 10
Adding 10 to both sides.
2x + 5y = -5
Now,
2x + 5y = -5
This can be written as,
5y = -2x -5
y = (-2/5)x - 1
Thus,
The equation of the line is 2x + 5y = -5.
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Mrs. morales wrote a test with 13 questions covering spelling and vocabulary. spelling questions (x) are worth 5 points and vocabulary questions (y) are worth 10 points. the maximum number of points possible on the test is 100.
part 1 out of 4
write an equation in slope-intercept form to represent the number of questions on the test.
Answers
The equation in slope-intercept form representing the number of questions on the test is y = 5x + 10.
To write the equation in slope-intercept form, we need to determine the relationship between the number of spelling questions (x) and the number of vocabulary questions (y) on the test.
Given that spelling questions are worth 5 points and vocabulary questions are worth 10 points, we can express the total number of points on the test as 5x + 10y. Since the maximum number of points on the test is 100, we have the equation 5x + 10y = 100.
To write the equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept, we rearrange the equation. First, we divide both sides of the equation by 10 to simplify: x + 2y = 20.
Next, we isolate y by subtracting x from both sides: 2y = -x + 20. Finally, we divide both sides by 2 to solve for y: y = -0.5x + 10.
Therefore, the equation in slope-intercept form representing the number of questions on the test is y = 5x + 10.
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Can someone help on this? Thank you;)
Answers
Answer:
B 4^18
Step-by-step explanation:
Multiply the exponents.
(4^-3)^-6 = 4^(-3 × -6) = 4^18
Answer: B 4^18
Answer:
4^18
Step-by-step explanation:
When an exponent is outside of a bracket that also has an exponent, then you must multiply the exponents to receive your answer. Since you are multiplying -3 by -6, you will get a positive product of 18. So the answer is 4^18
if you have 8 pices of bow tie and your 9 friends have ten times as many as you. how many does yall have in total?
Answers
Step-by-step explanation:
If they have 10 times more that is 8 × 10 = 80
if each person has 80 then you would do 80 × 9 = 720
then including your 8 it would be 729
if it's just 80 total with the 9 friends then it would be 88, the wording of the question is tricky
72*10=720
Have a good day
Write the equation of the line that passes through
the points (-1, 2) and (6, 3) in slope-intercept form,
step 1: choose (x1, y1). (6.3) 7
step 2: x2 = 9.6
y2 = 0
Answers
The equation of the line that passes through the points (-1, 2) and (6, 3) in slope-intercept form is y = (1/7)x + 15/7.
To find the equation of a line that passes through the points (-1, 2) and (6, 3) in slope-intercept form, follow these steps:
Step 1: Find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the first point (-1, 2) as (x1, y1) and the second point (6, 3) as (x2, y2).
m = (3 - 2) / (6 - (-1))
m = 1 / 7
Step 2: Substitute the slope (m) and one of the given points (x1, y1) into the slope-intercept form of the equation of a line:
y = mx + b
Using (-1, 2) as (x1, y1), we have:
2 = (1/7)(-1) + b
Step 3: Solve for b by simplifying the equation:
2 = -1/7 + b
To isolate b, add 1/7 to both sides:
2 + 1/7 = b
Multiplying the whole number 2 by 7 to get a common denominator, we have:
14/7 + 1/7 = b
15/7 = b
Step 4: Substitute the value of b back into the slope-intercept form equation:
y = (1/7)x + 15/7
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flo and carl each must read a 500-page book. flo reads one page every minute. carl reads one page every 50 seconds. flo starts reading at 1:00, and carl starts reading at 1:30. when will carl catch up to flo? a) using t as the number of minutes after 1:30, set up an equation with the number of pages flo has read on the left side and the number of pages carl has read on the right side. then solve the problem.
Answers
Carl will catch up with Flo after 150 minutes, that is, at 4
To solve this problem, we need to find out when Carl will catch up to Flo in terms of the number of pages read.
Let's first find out how many pages Flo will have read after a certain number of minutes, denoted as 't'. Since Flo reads one page every minute, the number of pages Flo will have read after 't' minutes can be calculated as t.
Next, let's find out how many pages Carl will have read after 't' minutes. Since Carl reads one page every 50 seconds, we need to convert minutes to seconds. There are 60 seconds in a minute, so 50 seconds is equivalent to 50/60 or 5/6 minutes. The number of pages Carl will have read after 't' minutes can be calculated as (5/6)t.
Now, let's set up an equation to represent the situation. We know that Carl starts reading 30 minutes after Flo, so we need to account for this time difference. The number of pages Flo has read after 't' minutes is t, and the number of pages Carl has read after 't' minutes is (5/6)(t + 30).
So, the equation becomes t = (5/6)(t + 30).
To solve this equation, we can multiply both sides by 6 to eliminate the fraction: 6t = 5(t + 30).
Expanding the right side of the equation gives us: 6t = 5t + 150.
Simplifying further, we have t = 150.
Therefore, Carl will catch up to Flo after 150 minutes.
Learn more about the least common multiple: https://brainly.com/question/10749076
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What kind of triangle is this please help me find the relationship and value please.
Answers
Answer: x=14°
Step-by-step explanation:
All angles of a triangle added together is 180°. So we can add the angles together.
7x-11+5x-2+2x-3=180 [combine like terms]
14x-16=180 [add both sides by 16]
14x=196 [divide both sides by 14]
x=14
Therefore, x=14°.
Half of the sum of 3x and 4
Answers
Answer:
1.5x + 2
Step-by-step explanation:
(3x + 4)/2 = 1.5x + 2
Which equation represents circle C?
Answers
Answer:
The equation of the circle is
(x + 4)^2 + (y-1)^2 = 162
Step-by-step explanation:
Here, we want to give the correct equation of the circle.
The center of the circle is (-4,1)
Now the other parameter we need to show the equation of the circle is the radius of the circle and this can be obtained from the distance between the circle center and a point on the circumference.
We use the distance formula to calculate this.
So the distance we want to calculate is the distance between;
(-4,1) and (5,-8)
using the distance formula, we have
d = √(x2-x1)^2 + (y2-y1)^2
Substituting these values, we have;
d = √(5 + 4)^2 + (-8-1)^2
d = √(9^2 + 9^2)
d = √(162)
d = 9 √2 units
The formula for the equation of a circle is
(x-h)^2 + (y-k)^2 = r^2
where (h,k) are coordinates of the center which is (-4,1) in this question
The way of the circle is thus,
(x-(-4)^2 + (y-1)^2 = {9√(2)}^2
(x + 4)^2 + (y-1)^2 = 162