Determine whether the point (2, 0) is a solution to the system of equations. Explain your reasoning in complete sentences. graph of a line 3 times x plus 2 and the absolute value of x minus 1 plus one. The graphs intersect at the point 0 comma 2
Answers
Answer:
(2,0) is not a solution of the system. The point does not belong to any of the graphs.
Step-by-step explanation:
To easily solve this question, we can graph both equations in a graphing calculator, and verify the intersection point, which is equal to the solution of the system of equations.
Plotting the graphs
y = 3x + 2
g = |x-1| +1
We obtain the intersection point
(0,2)
Solution of the system of equations
Related Questions
Solve for x in the given interval.
sec x= -2√3/3, for π/2 ≤x≤π
Answers
Answer:
b. [tex]x=\frac{5\pi}{6}[/tex]
Step-by-step explanation:
The given function is
[tex]\sec x=-\frac{2\sqrt{3} }{3},\:\:for\:\:\frac{\pi}{2}\le x \le \pi[/tex]
Recall that the reciprocal of the cosine ratio is the secant ratio.
This implies that;
[tex]\frac{1}{\cos x}=-\frac{2\sqrt{3} }{3}[/tex]
[tex]\Rightarrow \cos x=-\frac{3}{2\sqrt{3} }[/tex]
[tex]\Rightarrow \cos x=-\frac{\sqrt{3}}{2}[/tex]
We take the inverse cosine of both sides to obtain;
[tex]x=\cos^{-1}(-\frac{\sqrt{3}}{2})[/tex]
[tex]x=\frac{5\pi}{6}[/tex]
There are two brands of Corn Flakes, Post and Kellogs. Each brand has the same size box. However, because of each brand’s filling procedure, they have different mean weights. The weights of a box of Post Corn Flakes is approximately normal with μ = 64.1 oz and σ = .5 oz while the weight of a box of Kellogs, which is also normally distributed, has μ = 63.9 oz and σ = .4 oz.
A box is selected from each brand and weighed. What is the probability that the Post box will outweigh the Kellogs box?
Answers
Probability of an event is the measure of its chance of occurrence. The probability that the post box will outweigh the Kellogs box is 0.4129 approximately.
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z-score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] standard deviation [tex]\sigma[/tex])
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z-tables, the p-value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
What is the distribution of random variable which is sum of normal distributions?Suppose that a random variable X is formed by [tex]n[/tex] mutually independent and normally distributed random variables such that:
[tex]X_i = N(\mu_i , \sigma^2_i) ; \: i = 1,2, \cdots, n[/tex]
And if
[tex]X = X_1 + X_2 + \cdots + X_n[/tex]
Then, its distribution is given as:
[tex]X \sim N(\mu_1 + \mu_2 + \cdots + \mu_n, \: \: \sigma^2_1 + \sigma^2_2 + \cdots + \sigma^2_n)[/tex]
If, for the given case, we assume two normally distributed random variables as:
X = variable assuming weights of boxes of Post Corn Flakes
Y = variable assuming weights of boxes of Kellogs
Then, as per the given data, we get:
[tex]X \sim N(\mu = 64.1, \sigma = 0.5)\\Y \sim N(\mu = 63.9, \sigma = 0.4)[/tex]
Then, the probability that the Post box will outweigh the Kellogs box can be written as:
[tex]P(X > Y)[/tex]
Or,
[tex]P(X -Y > 0)[/tex]
We need to know about the properties of X-Y.
Also, since [tex]E(aX) = aE(X), Var(aX) = a^2Var(X)[/tex], thus,
[tex]-Y \sim N(-63.9, 0.4)[/tex]
As both are independent(assuming), thus,
[tex]X - Y \sim N(\mu = 64.1 - 63.9, \sigma = 0.5 + 0.4) = N(0.2, 0.9)[/tex]
Using the standard normal distribution, we get the needed probability as:
[tex]P(X -Y > 0) = 1 - P(X - Y \leq 0) \\P(X -Y > 0)= 1- P(Z = \dfrac{(X-Y) - \mu}{\sigma} \leq \dfrac{0 - 0.2}{0.9})\\P(X -Y > 0) \approx 1 - P(Z \leq -0.22)[/tex]
Using the z-tables, the p-value for Z = -0.22 is 0.4129
Thus, [tex]P(X > Y) = P(X - Y > 0) \approx 0.4129[/tex]
Thus, the probability that the post box will outweigh the Kellogs box is 0.4129 approximately.
Learn more about standard normal distribution here:
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The probability that a randomly selected Post box outweighs a Kellogg's box is approximately 50%.
To find the probability that the Post box will outweigh the Kellogg's box, we need to calculate the difference in weights between the two brands and then determine the probability that this difference is positive.
Let X be the weight of a box of Post Corn Flakes and Y be the weight of a box of Kellogg's Corn Flakes.
We are given that:
- For Post Corn Flakes, X ~ N(μ = 64.1, σ = 0.5)
- For Kellogg's Corn Flakes, Y ~ N(μ = 63.9, σ = 0.4)
We want to find P(X > Y), which is the probability that a randomly selected box of Post Corn Flakes weighs more than a randomly selected box of Kellogg's Corn Flakes.
Now, let Z = X - Y. We are interested in finding P(Z > 0).
The mean and standard deviation of Z can be calculated as follows:
- Mean of Z: μ_Z = μ_X - μ_Y = 64.1 - 63.9 = 0.2 oz
- Standard deviation of Z: σ_Z =[tex]sqrt(σ_X^2 + σ_Y^2) = sqrt(0.5^2 + 0.4^2)= sqrt(0.25 + 0.16)= sqrt(0.41) = 0.64 oz[/tex]
Now, we standardize Z:
Z = (X - Y - μ_Z) / σ_Z
Therefore,
P(Z > 0) = P((X - Y - μ_Z) / σ_Z > 0)
= P((X - Y) > μ_Z)
= P((X - Y) > 0.2)
Now we look up the z-score corresponding to Z = 0.2:
z = (0.2 - μ_Z) / σ_Z
= (0.2 - 0.2) / 0.64
= 0
The probability that Z is greater than 0 is equal to the probability that the standardized Z-score is greater than 0, which is 0.5.
Therefore, the probability that the Post box will outweigh the Kellogg's box is 0.5 or 50%.
If Seven cookies are shared equally by four people how many cookies will each person get
Answers
Final answer:
Each person will get 1 cookie and there will be 3 cookies leftover.
Explanation:
In this scenario, we have 7 cookies that are being shared equally among 4 people. To find out how many cookies each person will get, we divide the total number of cookies by the number of people.
So, 7 cookies divided by 4 people = 1.75 cookies per person.
Since we can't divide a cookie into fractions, each person will get 1 cookie and there will be 3 cookies leftover.
One angle of a triangle measures 60°. The other two angles are in a ratio of 7:17. What are the measures of those two angles?
Answers
Answer:
35° and 85°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Since one angle = 60° then the sum of the other 2 angles = 120°
Sum the parts of the ratio 7 + 17 = 24 parts, hence
[tex]\frac{120}{24}[/tex] = 5° ← value of 1 pat of the ratio, hence
7 parts = 7 × 5° = 35°
17 parts = 17 × 5° = 85°
note that 60° + 35° + 85° = 180°
Which line contains the point (2, 1)?
a)4x-y=7
b)2x+5y=4
c)7x-y=15
d)x+5y=21
Answers
4(2)-(1)=7
7=7
Two numbers total 14 ,and their differences is 12 .find two numbers
Answers
Answer:
12+2 =14
Step-by-step explanation:
Answer: 1 and 13.
Step-by-step explanation: Because of the total, we know that the first number has to be less than 5, but greater than 0. to start in the median, let's use 3.
3+12 = 15.
That won't work, so let's try 2.
2+12 = 14.
There's the answer.
Estimate the limit, if it exists.
Answers
Answer:
0
Step-by-step explanation:
The given limit is
[tex]\lim_{x \to \infty} \frac{x^2+x-22}{4x^3- 13}[/tex]
Divide both the numerator and the denominator by the highest power of x in the denominator.
[tex]=\lim_{x \to \infty} \frac{\frac{x^2}{x^3}+\frac{x}{x^3}-\frac{22}{x^3}}{\frac{4x^3}{x^3}- \frac{13}{x^3}}[/tex]
This simplifies to;
[tex]=\lim_{x \to \infty} \frac{\frac{1}{x}+\frac{1}{x^2}-\frac{22}{x^3}}{4- \frac{13}{x^3}}[/tex]
As [tex]x\to \infty, \frac{c}{x^n} \to 0[/tex]
[tex]=\lim_{x \to \infty} \frac{0+0-0}{4- 0}=0[/tex]
The limit is zero
Melinda spent 4 Hours Reviewing for Her Midterm exams. She spent 1/4 Of The Time studying for social studies.How Many Hours Did she spend on social studies
Answers
Answer:
1 hour
Step-by-step explanation:
1/4 of 4 is 1
Answer:one hour
Step-by-step explanation:
2x+3x+4x=180
9x=180
x=20
how did they get 20, am i missing something
Answers
➷ We'll work from here:
9x = 180
To isolate x, you would need to divide both sides by 9
x = 180/9
Solve:
x = 20
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer: ❤️Hello!❤️ x = 20
Step-by-step explanation: Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*x+3*x+4*x-(180)=0
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
9x - 180 = 9 • (x - 20)
Step 2 :
Equations which are never true :
2.1 Solve : 9 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
2.2 Solve : x-20 = 0
Add 20 to both sides of the equation :
x = 20
If 5 bags of apples weigh 12 1/7 pounds, how many pounds would you expect 1 bag of apples to weigh?
Answers
Answer:
2 and 3/7 pounds
Step-by-step explanation:
Convert the mixed number to an improper fraction
12 1/7 becomes 85/7
This represents 5 bags, so divide it by 5 to see what one bag should weigh...
(85/7)/5 becomes (85/7)/(5/1)
which becomes
(85/7)*(1/5) (division is the same as multiplying by the reciprocal)
85/35
17/7 (reduce the fraction by factoring out a 5 from top and bottom)
2 and 3/7 pounds
The length of a rectangular field is 7 m less than 4 times the width. The perimeter is 136m ?. Find the width and the length of the rectangle
Answers
➷ The perimeter is the total of all the lengths / widths
The lengths can be represented by 4x - 7
The width can be represented by x
2 times the length + 2 times the width would equal the perimeter
2(x) + 2(4x - 7) = 136
Simplify:
2x + 8x - 14 = 136
10x - 14 = 136
Add 14 to both sides:
10x = 150
Divide both sides by 10:
x = 15
The width is equal to 15m
The length is 4(15) - 7 = 53m
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
write an explicit formula formula for the sequence 2, 8, 14, 20, 26,...
a. a_n= 2n-2
b. a_n= 2n+2
c. a_n=4n+2
d. a_n = 6n-4
Answers
Answer:
d. a_n = 6n - 4.
Step-by-step explanation:
The common difference (d) is 8-2 = 14-8 = 20-14 = 26-20 = 6.
This is an Arithmetic Sequence with the first term (a1) is 2.
The general form of the explicit formula is a_n = a1 + d(n - 1) so this sequence has the formula:
a_n = 2 + 6(n - 1)
a_n = 2 + 6n - 6
a_n = 6n - 4.
The sequence is an illustration of an arithmetic sequence.
The explicit formula is: (d) [tex]a_n = 6n - 4[/tex]
We have:
[tex]a_1 = 2[/tex] -- the first term
Next, we calculate the common difference (d)
[tex]d = a_2 - a_1[/tex]
So, we have:
[tex]d = 8 -2[/tex]
[tex]d = 6[/tex]
The explicit formula is calculated using:
[tex]a_n = a_1 + (n - 1)d[/tex]
So, we have:
[tex]a_n =2 + (n - 1) \times 6[/tex]
Open bracket
[tex]a_n = 2 + 6n - 6[/tex]
Collect like terms
[tex]a_n = 6n - 6 + 2[/tex]
[tex]a_n = 6n - 4[/tex]
Hence, the explicit formula is: (d) [tex]a_n = 6n - 4[/tex]
Read more about arithmetic sequence at:
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?2300 is invested in 4 years at 5% per year simple interest work out the total interest
Answers
Answer:
460
Step-by-step explanation:
I=P x r x t
P is the principal amount, $2300.00.
r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.
t is the time involved, 4....year(s) time periods.
So, t is 4....year time periods.
To find the simple interest, we multiply 2300 × 0.05 × 4 to get that:
The interest is: $460.00
Elmer body skateboard ramp for his son he wants to surprise him with it so he wants to wrap the ramp with special paper what is the minimum amount of wrapping paper he will need to wrap the ramp.
Answers
Answer:
480 feet
Step-by-step explanation:
The trail is 2982 miles long.It begins in city A and ends in city B.Manfred has hiked 2/7 of the trail before.How many miles has he hikes?
Answers
Answer:
852
Step-by-step explanation:
Solve the equation. Round to the nearest hundredth. Show work.
[tex]4^{-5x-7} = 6^{2x-1}[/tex]
Answers
Answer:
[tex]x=-0.75[/tex]
Step-by-step explanation:
The given equation is
[tex]4^{-5x-7}=6^{2x-1}[/tex]
We take logarithm of both sides to base 10.
[tex]\log(4^{-5x-7})=\log(6^{2x-1})[/tex]
[tex](-5x-7)\log(4)=(2x-1)\log(6)[/tex]
We expand the brackets to get;
[tex]-5x\log(4)-7\log(4)=2x\log(6)-\log(6)[/tex]
Group similar terms;
[tex]-7\log(4)+\log(6)=2x\log(6)+5x\log(4)[/tex]
[tex]-7\log(4)+\log(6)=(2\log(6)+5\log(4))x[/tex]
[tex]\frac{-7\log(4)+\log(6)}{(2\log(6)+5\log(4))}=x[/tex]
[tex]x=-0.752478[/tex]
To the nearest hundredth.
[tex]x=-0.75[/tex]
Plz help me..
WILL GIVE BRAINLIEST
Answers
Answer:
B, 3x - 5
Step-by-step explanation:
Factor by grouping to get (3x - 5)(2x + 3).
Factor 6x2−x−15
6x2−x−15
=(3x−5)(2x+3)
Answer:
(3x−5)(2x+3)
HELPPPPP ... Question 18
Answers
Answer:
Part a) The volume of the prism Q is two times the volume of the prism P
Part b) The volume of the prism Q is two times the volume of the prism P
Step-by-step explanation:
Part 18) we know that
The volume of a rectangular prism is equal to
[tex]V=Bh[/tex]
where
B is the area of the base
h is the height of the prism
a) Suppose the bases of the prisms have the same area, but the height of prism Q is twice the height of prism P. How do the volumes compare?
Volume of prism Q
[tex]VQ=B(2h)=2(Bh)[/tex]
Volume of prism P
[tex]VP=Bh[/tex]
Compare
[tex]VQ=2VP[/tex]
so
The volume of the prism Q is two times the volume of the prism P
b) Suppose the area of the base of prism Q is twice the area of the base of prism P. How do the volumes compare?
Volume of prism Q
[tex]VQ=(2B)h=2(Bh)[/tex]
Volume of prism P
[tex]VP=Bh[/tex]
Compare
[tex]VQ=2VP[/tex]
The volume of the prism Q is two times the volume of the prism P
Write the augmented matrix for each system of equations.
9x-4y-5z=9
7x+4y-4z=-1
6x-6y+z=5
Answers
Answer:
a. [tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]
Step-by-step explanation:
The given system of equation is
[tex]9x-4y-5z=9[/tex]
[tex]7x+4y-4z=-1[/tex]
[tex]6x-6y+z=-5[/tex]
The coefficient matrix is :
[tex]\left[\begin{array}{ccc}9&-4&-5\\7&4&-4\\6&-6&1\end{array}\right][/tex]
The constant matrix is
[tex]\left[\begin{array}{c}9\\-1\\-5\end{array}\right][/tex]
The augmented matrix is obtained by combining the coefficient matrix and the constant matrix.
[tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]
The correct choice is A
Example 5 suppose that f(0) = −8 and f '(x) ≤ 9 for all values of x. how large can f(3) possibly be? solution we are given that f is differentiable (and therefore continuous) everywhere. in particular, we can apply the mean value theorem on the interval [0, 3] . there exists a number c such that f(3) − f(0) = f '(c) − 0 so f(3) = f(0) + f '(c) = −8 + f '(c). we are given that f '(x) ≤ 9 for all x, so in particular we know that f '(c) ≤ . multiplying both sides of this inequality by 3, we have 3f '(c) ≤ , so f(3) = −8 + f '(c) ≤ −8 + = . the largest possible value for f(3) is .
Answers
[tex]f'(x)[/tex] exists and is bounded for all [tex]x[/tex]. We're told that [tex]f(0)=-8[/tex]. Consider the interval [0, 3]. The mean value theorem says that there is some [tex]c\in(0,3)[/tex] such that
[tex]f'(c)=\dfrac{f(3)-f(0)}{3-0}[/tex]
Since [tex]f'(x)\le9[/tex], we have
[tex]\dfrac{f(3)+8}3\le9\implies f(3)\le19[/tex]
so 19 is the largest possible value.
Given a differentiable function with f(0) = -8 and f'(x) ≤ 9 for all x, we use the Mean Value Theorem to find that f(3), at its largest, can be 1.
Explanation:In this mathematics problem, we are given that f is a differentiable function with f(0) = -8 and its derivative f'(x) ≤ 9 for all x. We aim to calculate the possible maximum value of f(3). To do this, we apply the Mean Value Theorem for the interval [0, 3]. By this theorem, there exists a number 'c' in this interval such that the derivative at that point is equal to the slope of the secant line through the points (0, f(0)) and (3, f(3)). Thus, we get the equation: f(3) - f(0) = f'(c). Rearranging this, we get f(3) = f(0) + f'(c). Substituting the given values, f(3) = -8 + f'(c).
Since we know f'(x) ≤ 9 for all x, this means f'(c) ≤ 9 as well. Replacing this in the equation we get f(3) ≤ -8 + 9 = 1. Hence, the largest possible value for f(3) is 1.
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Solve using proper methods. Show work. (25 POINTS)
Initially a tank contains 10,000 liters of liquid at the time t = 0 minutes a tap is opened, a liquid then follows out of the tank. The volume of the liquid V liters, which remains in the tank after t minutes is given by V = 10,000(0.933)^t
a) Find the value of V after 5 minutes.
b) Find how long, to the nearest second, it takes for half of the initial amount of liquid to follow out of the tank.
c) The tank is regarded as effectively empty when 95% of the liquid has flowed out. Show that it takes almost three quarters of an hour for this to happen.
d) (i) Find the value of 10,000 - V when t = 0.001 minutes
(ii) Hence or otherwise, estimate the initial flow rate of the liquid. Give your answer in liters per minute, correct to two significant figures.
Answers
Answer:
a) 7069.82 Liters
b) 600 seconds
c) Shown below
d) (i) 0.6935 liters (ii) Since 0.6935 liters in 0.001 minute, so 693.5 liters per minute is as estimate (in liters per minute)
Step-by-step explanation:
a)
We simply put 5 into t of the equation and get the value of V. So:
[tex]V=10,000(0.933)^t\\V=10,000(0.933)^5\\V=7069.82[/tex]
So after 5 minutes the amount remaining is 7069.82 Liters
b)
half of the initial amount is half of 10,000 which is 5000. So we substitute 5000 into V and solve for t using logarithms.
Note: [tex]ln(a^b)=blna[/tex]
Thus, we have:
[tex]V=10,000(0.933)^t\\5000=10,000(0.933)^t\\0.5=(0.933)^t\\ln(0.5)=ln((0.933)^t)\\ln(0.5)=tln(0.933)\\t=\frac{ln(0.5)}{ln(0.933)}\\t=9.99[/tex]
Thus, t = 9.9949 minutes.
To get answer in seconds, we multiply by 60. Thus 9.9949*60= 600 seconds
c)
95% empty means 5% remaining. 5% of 10,000 = 0.05 * 10,000 = 500. We plug in 500 into V and solve for t as the previous step. Shown below:
[tex]V=10,000(0.933)^t\\500=10,000(0.933)^t\\0.05=0.933^t\\ln(0.05)=ln(0.933^t)\\ln(0.05)=tln(0.933)\\t=\frac{ln(0.05)}{ln(0.933)}\\t=43.1972[/tex]
So it takes around 43.1972 minutes to empty 95%. Since three-quarters of an hour is [tex](\frac{3}{4})(60)=45[/tex] minutes, we have shown that the time it takes (43.1972 minutes) is very close to three-quarters of an hour.
d)
We plug in 0.001 into t and find V. Then we subtract that value from 10,000. This is just finding how much water has been removed in 0.001 minutes. Let's do this:
[tex]V=10,000(0.933)^t\\V=10,000(0.933)^{0.001}\\V=9999.3065\\Now\\10,000 - 9999.3065 = 0.6935[/tex]
So, 0.6935 liters
PLEASE HELP 15 POINTS Sphere A is similar to sphere B.
If the radius of sphere A is 3 times the radius of sphere B, then the volume of sphere A is____ times the volume of sphere B.
3
6
9
27
81
Answers
Answer:
27
Step-by-step explanation:
We figure out the scale factor first, which is the number of times one radius is of the other. We call the scale factor, k.
To get how many times larger is the volume of similar spheres, we will need to cube the scale factor.
Since it is given that radius of Sphere A is 3 times that of Sphere B, we can say that the scale factor (k) = 3. Hence, the volume of Sphere A would be k^3 times the volume of Sphere B.
So, [tex]k^3\\=(3)^3\\=27[/tex]
Hence, the volume of sphere A is 27 times the volume of sphere B.
An experiment consists of rolling a die, flipping a coin, and spinning a spinner divided into 4 equal regions. The number of elements in the sample space of this experiment is
12
3
6
48
Answers
Answer:
48
Step-by-step explanation:
There are 3 events that are taking place.
Rolling a die which has 6 possible outcomes.
Flipping a coin which has 2 possible outcomes.
Spinning a spinner which has 4 possible outcomes.
Since the outcome of each event is independent of the other, the total possible outcomes will be equal to the product of outcomes of each event.
i.e.
Total outcomes = 6 x 2 x 4 = 48
The sample space of the experiment contains all the possible outcomes. so the number of elements in the sample space of this experiment will be 48
Answer:
The correct answer option is 48.
Step-by-step explanation:
Here in this experiment, three events are taking place that include rolling a die, flipping a coin and spinning a spinner.
The possible outcomes of each of these events are:
Rolling a die - 6
Flipping a coin - 2
Spinning a spinner - 4
Therefore, we can find the number of elements in the sample space of this environment by multiplying their possible outcomes.
Number of elements = 6 × 2 × 4 = 48
9 minutes left to finish this!! I need help!
Joey is 17 years older than his sister Pat. In 6 years, Joey will be 7 more than twice Pat’s age then. How old are Joey and Pat today?
Answers
Answer:
p = 4
j = 21
Step-by-step explanation:
Joey = j
Pat = p
j = p + 17
(j+6) = 2*(p + 6) + 7 Simplify this. Remove the brackets.
j + 6 = 2p + 12 + 7 combine like terms
j + 6 = 2p + 19 Subtract 6 from both sides
j +6-6 = 2p +19-6
j = 2p + 13
================
Equation j = 2p + 13 and j = p + 17
2p + 13 = p + 17 Subtract p from both sides
2p-p+13 =p-p + 17
p + 13 = 17 Subtract 13 from both sides
p = 17-13
p = 4
============
j = p + 17
j = 4 + 17
j = 21
Answer:
Joey is 21; Pat is 4
Step-by-step explanation:
The problem statement supports two equations in Joey's age (j) and Pat's age (p):
j - p = 17
(j +6) -2(p +6) = 7
Subtracting the second equation from the first, we have ...
(j -p) -((j +6) -2(p +6)) = (17) -(7)
p +6 = 10 . . . . . simplify
p = 4 . . . . . . . . . subtract 6
J = 17 +4 = 21
Joey is 21; Pat is 4.
A picture measuring 4" high by 6" wide is to be enlarged so that the width is now 9”. How tall will the picture be?
Answers
The original width was 6 inches, the new width is 9 inches.
Divide the new width by the original width to find the scale factor:
9/6 = 1.5
Now multiply the original height by the scale factor to find the new height:
4 x 1.5 = 6 inches.
Water boils at 100 degree, C. This is 400 percent more than my room's temperature. What is my room's temperature?
Answers
Your room temperature is 25°C.
Step-by-step explanation:
hope this helps!
I need help on #20 please
Answers
Answer:
P = 10x³ + 4x² + 8x + 6
Step-by-step explanation:
The perimeter of a rectangle is twice the sum of length and width.
P = 2(L+W) = 2((x³ +2x² -6x +12) +(4x³ +10x -9))
= 2(5x³ +2x² +4x +3) . . . . collect terms inside parentheses
P = 10x³ +4x² +8x +6
The volume of a rectangle or prism is 72 m? the prism is 2 cm wide and the 4 cm high what is the length of the prism
Answers
Answer:
9 cmStep-by-step explanation:
The formula of a volume of a rectangle prism:
[tex]V=lwh[/tex]
l - length
w - width
h - height
We have V = 72 cm³, w = 2 cm and h = 4 cm. Substitute:
[tex](2)(4)l=72[/tex]
[tex]8l=72[/tex] divide both sides by 8
[tex]l=9\ cm[/tex]
A cab charges $1.75 for the flat fee and $0.25 for each mile. Write and solve an inequality to determine how many miles Eddie can travel if he has $15 to spend.
Answers
Answer:
I think it's 53 miles
Step-by-step explanation:
After flat fee of $1.75 leaves him $13.25. Then use the remainder to calculate miles. Each dollar allows 4 miles × 13 = 52+1=53
The inequality is:
[tex]1.75+0.25x\leq 15[/tex]
The solution of the inequality is:
[tex]x\leq 53[/tex]
Step-by-step explanation:Let Eddie could travel x miles.
It is given that:
A cab charges $1.75 for the flat fee and $0.25 for each mile.
This means that the fee charged by Eddie if he travels x miles excluding the flat fee is:
$ 0.25x
Total amount the cab will charge Eddie is:
1.75+0.25x
Also, it is given that:
He has only $ 15 to spend this means that he can spend no more than 15 on riding in a cab.
Hence, the inequality is given by:
[tex]1.75+0.25x\leq 15[/tex]
Now on solving the inequality i.e. finding the possible values of x from the inequality.
We subtract both side of the inequality by 1.75 to obtain:
[tex]0.25x\leq 13.25[/tex]
Now on dividing both side of the inequality by 0.25 we get:
[tex]x\leq 53[/tex]
Hence, Eddie could travel less than or equal to 53 miles .
Find three consecutive even integers that sum up to -72.
Answers
Answer:
-26, -24 and -22Step-by-step explanation:
[tex]n,\ n+2,\ n+4-\text{three consecutive even integers}\\\\\text{The equation:}\\\\n+(n+2)+(n+4)=-72\\\\n+n+2+n+4=-72\qquad\text{combine like terms}\\\\3n+6=-72\qquad\text{subtract 6 from both sides}\\\\3n+6-6=-72-6\\\\3n=-78\qquad\text{divide both sides by 3}\\\\\dfrac{3n}{3}=-\dfrac{78}{3}\\\\n=-26\\\\n+2=-26+2=-24\\\\n+4=-26+4=-22[/tex]