Answer
a. ii and iii
Step-by-step explanation
A monomial is a polynomial with only one term.
A binomial is a polynomial with two terms.
The degree of a polynomial is determined by the highest exponent of the x-variable.
i) 2x² + 2x
type: binomial
degree: 2
ii) 2x²
type: monomial
degree: 2
iii) x²
type: monomial
degree: 2
iv) 2x
type: monomial
degree: 1
Then, choices ii and iii are monomials with degree 2
Solve the systems of equations. List the variables p, q, and r. p-6q+4r = 2
2p+4q-8r=16
p-2q=5
Base on the system, the equation has infinite number of solution.
How to solve system of equation?A system of Equations is when we have two or more linear equations working together.
Therefore, the system of equation can be solved as follows:
p - 6q + 4r = 2
2p + 4q - 8r = 16
p - 2q = 5
Using equation(iii)
p = 5 + 2q
substitute the value of p in equation (i) and equation(ii)
Therefore,
5 + 2q - 6q + 4r = 2
-4q + 4r = -3
2(5 + 2q) + 4q - 8r = 16
10 + 4q + 4q - 8r = 16
8q - 8r = 6
Therefore, combine the new equations to find q and r.
-4q + 4r = -3
8q - 8r = 6
Multiply equation(1) by 2
- 8q + 8r = -6
8q - 8r = 6
add the equations
0 = 0
Therefore, equation have infinite number of solution.
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What is the radius of a circle whose circumference is 207.24 inches ?
The circumference of the circle C = 207.24 inches.
The formula for the circumference of circle is,
[tex]C=2\pi r[/tex]Assume the value of pi be 3.14.
Substitute 207.24 for C in the formula to determine the radius of circle.
[tex]\begin{gathered} 207.24=2\pi r \\ r\approx\frac{207.24}{2\cdot3.14} \\ =33 \end{gathered}[/tex]Thus radius of circle is 33 inches.
in this equation , what is the value of b^2-4ac 2x^2+6x+5=0Note that the general form of a quadratic equation is ax^2+bx+c=0
Answer:
-4
Explanation
Given the standard form of a quadratic equation expressed as ax^2 + bx + c = 0
Comparing to the given equation 2x^2+6x+5=0
ax^2 = 2x^2
a = 2
bx = 6x
b = 6
c = 5
Get b^2 - 4ac
Substitute the values of a, b and c into b^2 - 4ac
b^2 - 4ac
= 6^2 - 4(2)(5)
= 36 - 40
= -4
Hence the value of b^2 - 4ac is -4
Expand the logarithm fully using the properties of logs. Express the final answer interms of log a, and log y.
To solve this problem, we will use these rules
[tex]\begin{gathered} \log ab=\log a+\log b\rightarrow(1) \\ \log a^n=n\log a\rightarrow(2) \end{gathered}[/tex]The given expression is
[tex]\log x^5y[/tex]By using rule (1)
[tex]\log x^5y=\log x^5+\log y[/tex]Use the rule (2) with log x^5
[tex]\log x^5=5\log x[/tex]Then the last answer is
[tex]\log x^5y=5\log x+\log y[/tex]The answer is 5 log x + log y
Additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate. What is the final price after the rebate if an envelope costs $0.35 and a 'forever' postage stamp costs $0.41?
Group of answer choices
$99.99
$10.76
$109.23
$100.75
If additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41,then the cost after all the rebates will be $100.75.
Given that additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41.
We are required to find the cost after all the rebates and envelopes provided.
The cost can be calculated as under:
Cost=109.99-10.00+0.35+0.41
=$100.75
Hence if additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41,then the cost after all the rebates will be $100.75.
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Please help will mark BRAINLIEST
The staff of a restaurant consists of 25 people,
including 8 waiters, 12 waitresses and 5 cooks. For
Mother's Day, a total of 9 people will need to be
selected to work. If the selections are made at
random, determine the probability that 3 waiters, 4
waitresses and 2 cooks will be selected.
The probability that 3 waiters, 4 waitresses, and 2 cooks will be selected is 0.085.
The probability that an outcome will be recorded is calculated by dividing the whole possibilities of the desired outcome by the total number of possible outcomes.
Probability = Favourable outcomes / Possible outcomes
The total number of staff in the restaurant is 25.
There are 8 waiters, 12 waitresses, and 5 cooks.
Now, on Mother's Day, a total of 9 people need to be selected.
The combination can be used to find the number number of ways people can be selected.
Therefore,
The number of ways to select 3 waiters, 4 waitresses, and 2 cooks will be:
= ₈C₃ × ₁₂C₄ × ₅C₂
= [ 8! / 3! 5! ] × [ 12! / 4! 8! ] × [ 5! / 2! 3! ]
= [ 8 × 7 × 6 / 3 × 2 ] × [ 12 × 11 × 10 × 9 / 4 × 3 × 2 ] × [ 5 × 4 / 2 ]
= 56 × 495 × 10
= 277200 ways
If there are no restrictions and these 9 people are chosen at random from the 25 available staff, then the number of ways is
₂₅C₁₀ = [ 25! / 10! 15! ]
₂₅C₁₀ = [ 25 × 24 × 23 × 22 × 21 × 20 × 19 × 18 × 17 × 16 / 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 ]
₂₅C₁₀ = 3268760
Therefore, the probability that 3 waiters, 4 waitresses, and 2 cooks will be selected is :
= 277200 / 3268760
= 0.08480279983 = 0.085
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The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set2.7.15, 3, 12, 9, 15, 8, 3, 10 The range is 13(Simplify your answer.)The population mean is 8.4(Simplify your answer. Round to the nearest tenth as needed.)The population variance is(Simplify your answer. Round to the nearest tenth as needed.)The population standard deviation is (Simplify your answer. Round to the nearest tenth as needed)
We have the following data set:
2,7,15,3,12,9,15,8,3,10
The range is the difference between the highest and lowest values in the set, to find the range, order the data set from least to greatest.
2,3,3,7,8,9,10,12,15,15
Then,
[tex]\begin{gathered} \text{Range}=15-2 \\ \text{Range}=13 \end{gathered}[/tex]Mean is represented by the following expression:
[tex]\text{Mean}=\frac{\text{Sum of all data points}}{Number\text{ of data po}ints}[/tex][tex]\text{Mean}=\frac{84}{10}=8.4[/tex]Population variance formula looks like this:
[tex]\begin{gathered} \sigma^2=\frac{\sum^{}_{}(x-\mu)^2}{N} \\ \text{where,} \\ \sigma^2=\text{population variance} \\ \sum ^{}_{}=addition\text{ of} \\ x=\text{each value} \\ \mu=population\text{ mean} \\ N=\text{ number of values in the population} \end{gathered}[/tex]Then, substituting:
[tex]\begin{gathered} \sigma^2=\frac{(2-14)^2+(3-14)^2+\cdots+(15-14)^2}{10} \\ \sigma^2=20.44 \end{gathered}[/tex]For the standard deviation:
[tex]\begin{gathered} s=\sqrt[]{\frac{\sum ^{}_{}(x-\mu)^2}{N}} \\ s=4.521 \end{gathered}[/tex]write the percent as a fraction or a mixed number in simplest form 4.8%
Suppose the function f(x)=30(2)^x gives a beetle population after x weeks.How many beetles will there be after 56 days
Answer:
7,680 beetles
Explanation:
The function that gives the beetle population after x weeks is given below:
[tex]f\mleft(x\mright)=30\mleft(2\mright)^x[/tex]To determine the beetle population after 56 days, first convert 56 days to weeks.
[tex]56\text{ days=}\frac{57}{7}=8\text{ we}eks[/tex]Thus, the beetle population will be:
[tex]\begin{gathered} f(8)=30(2)^8 \\ =30\times256 \\ =7,680 \end{gathered}[/tex]There will be 7,680 beetles after 56 days.
Emma younger brother and sister went on a carnival ride that has two separate circular track ana's brother rode in a blue car that traveled a total distance of 220 around the track and a sister Road in a green car that travels to total distance of 126 feet around the track and drew of the ride
1. The distances of 220 feet and 126 feet are the circumferences of the two circles. We can see the circumference as a kind of 'perimeter' for a circle.
2. The radius of the circle of Ana's brother in the blue car is as follows:
a. We have that the circumference of a circle is given by the formula:
[tex]C=2\cdot\pi\cdot r[/tex]Then, we need to solve this equation for r. We have that pi = 3.14, and C = 220 feet. Then, we have:
[tex]220=2\cdot\pi\cdot r\Rightarrow r=\frac{220}{2\pi}\Rightarrow r=\frac{220}{2\cdot3.14}\Rightarrow r=35.0318[/tex]Rounding to the nearest tenth, we have that the radius is RB = 35.0 feet (or 35 feet).
3. We can apply the same procedure to find the radius of the circle made by Ana's sister in the green car (she traveled 126 feet).
[tex]126=2\cdot\pi\cdot r\Rightarrow r=\frac{126}{2\cdot3.14}\Rightarrow r=20.0637[/tex]Rounding to the nearest tenth, we have that the radius is RG = 20.1 feet.
4. The difference in the radii of the circles is the difference between the two ones already obtained. Then, we have:
[tex]d=rB-rG=35.0-20.1\Rightarrow d=14.9[/tex]Therefore, the difference is 14.9 feet.
(2x² + 7x - 15) + (x + 5)
We are given the below expression
[tex]\begin{gathered} (4x^2\text{ + x + 1) + (x - 2)} \\ \text{First, open the parentheses} \\ 4x^2\text{ + x + 1 + x - 2} \\ \text{Collect the like terms} \\ 4x^2\text{ + x + x + 1 - 2} \\ 4x^2\text{ + 2x - 1} \end{gathered}[/tex]From the quadratic function generated, we will be solving for x using the general formula
[tex]\begin{gathered} ax^2\text{ + bx + c = 0} \\ 4x^2\text{ + 2x - 1= 0} \\ \text{let a = 4, b= 2 and c = -1} \\ \text{The general quadratic formula is written as} \\ x\text{ = -b }\pm\text{ }\frac{\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ \text{Substitute the above values into the formula} \\ x\text{ = -(2) }\pm\text{ }\frac{\sqrt[]{2^2\text{ - 4 x 4(-1)}}}{2\text{ x 4}} \\ x\text{ = -2 }\pm\text{ }\frac{\sqrt[]{4\text{ -4(-4)}}}{2\text{ x 4}} \\ x\text{ = -2 }\pm\text{ }\frac{\sqrt[]{4\text{ + 16}}}{8} \\ x\text{ = -2 }\pm\text{ }\frac{\sqrt[]{20}}{8} \\ \sqrt[]{20}\text{ = }\sqrt[]{4}\text{ x }\sqrt[]{5} \\ \sqrt[]{20\text{ }}\text{ = 2}\sqrt[]{5} \\ \text{Hence,} \\ x\text{ = -2 + }\frac{2\sqrt[]{5}}{8}\text{ OR -2 - }\frac{2\sqrt[]{5}}{8} \\ x\text{ = 0.3090 or x = -0.8075} \end{gathered}[/tex]the sum of the first and the third term of a GP is 10 if the first term is 2 find :(a)the common ratio (b)the 6th term
(a)the common ratio = 2
(b)the 6th term = 64
How to find the common ratio and 6th term ?
A geometric progression, which is another name for a geometric sequence, is a series of non-zero numbers .In a G.P each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratioA geometric progression is given by a, ar, a[tex]r^{2}[/tex], a[tex]r^{3}[/tex],....Here, the common ratio = r
the first term = a = 2
(a)the common ratio
[tex]a +ar^{2} = 10\\\\2(1+r^{2} ) = 10\\\\(1+r^{2} ) = 5\\\\r^{2} =4\\\\r = 2[/tex]
The common ratio (r) = 2
(b)the 6th term
[tex]a_{n}=ar^{n-1} \\\\a_{6}=ar^{6-1} \\\\a_{6} =2(2^{5} )\\\\a_{6}=64[/tex]
Thus ,the 6th term = 64
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Evaluate.
(a − 2b)^3 when a = −2 and b = −1/2
Answer:
the answer is 1
Step-by-step explanation:
(a-2b)^3
(-2-2*-1/2)^3
(-2+1)^3
(-1)^3
=1
I need help pls pls pls
Help I don’t understand!!
Farm c is Marc's farm it have 60 % of purple flowers
To find percentage :
In Farm B it shows that 0.6 are purple flowers .
0.6 is 6 of 10 it is 60 %.
And other farms have 11/20 that is 55% in Farm A
For Farm C only 40 %.
Percentage :
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".Although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.The formula used to calculate percentage is: (value/total value)×100%.If you are required to convert a decimal number like 0.57 to a percentage, you simply multiply it by 100. That is, 0.57 x 100 = 57. Therefore, 0.57 as a percentage equals 57%.To find 10% of a number means dividing by 10 because 10 goes into 100 ten times. Therefore, to find 20% of a number, divide by 5 because 20 goes into 100 five times.To learn more about PERCENTAGE refer :
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help meeeeeeeeeeeeeeeeeeeeeee
thank you
In the linear graph, the value of x such that f(x) = -3 is -2.
How to find coordinates in a linear graph?A linear graph is a straight line or straight graph which is drawn on a plane connecting the points on x and y coordinates.
Therefore, a linear graph is represented in the form of a straight line.
It shows the relationship between variables x and y.
x is the horizontal variables while y is the vertical variables.
Therefore, the graph of the given function is f(x).
Let's use the graph to find x such that f(x) = - 3
f(x) is the y coordinates of the linear graph.
Let's find x when f(x) = -3
Therefore,
x = - 2
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Match the corresponding graph with the number. Note:a number can have multiple graphs.
(6) A function is increasing when the y-value increases as the x-value increases.
The domain is the set of allowable x-values
The following graphs increases over their entire domain:
B, E, I, J, N, G
(7) A function is said to be decreasing when the y-value decreases as the x-values increase.
The following graphs decreases over their entire domain:
A, F
One letter tile is selected and the spinner is spun. What is the probability that both will be avowel?P (vowel) Tile:P (vowel) Spinner:Multiply fractions - probability that both will be a vowel
SOLUTION:
Step 1:
To find the probability of picking a vowel from G, B, E and A.
A and E are the vowels here,
[tex]P\text{ (vowel) Tile : }\frac{2}{4}\text{ = }\frac{1}{2}[/tex]Step 2:
To find the probability that the spinner showed a vowel from A, B and C.
A is the only vowel here,
[tex]P\text{ (vowel) Spinner: }\frac{1}{3}[/tex]Step 3:
To find the probability that both will be a vowel:
[tex]\begin{gathered} P\text{ (vowel) Tile X P (vowel) spinner} \\ \frac{1}{2}\text{ x }\frac{1}{3} \\ \\ \frac{1}{6} \end{gathered}[/tex]CONCLUSION:
The probability that both will be a vowel is 1/6
Find the quotient. 1/5 divided by (-5/7)
The most appropriate choice for fraction will be given by -
The correct quotient for this division is [tex]-\frac{7}{25}[/tex]
What is a fraction?
Suppose there is a collection of objects and a part of collection has been taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.
The upper part of fraction is called numerator and the lower part of fraction is called denominator.
We can do addition, subtraction, multiplication and division on fractions.
Here,
The calculation for division of two fractions has been shown below.
[tex]\frac{1}{5} \div -\frac{5}{7}\\\frac{1}{5} \times -\frac{7}{5}\\-\frac{7}{25}[/tex]
The correct quotient for this division is [tex]-\frac{7}{25}[/tex]
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For homework Rio is listing some examples of real numbers in a diagram natural 6 whole -1 integer 0 rational .5 Which number did Rio Place incorrectly?
Whole numbers are similar to natural(non-negative, non-fractional). The only difference is that it includes the 0.
In this question, Rio placed -1 as an example of whole number. Since -1 is negative, it is not a whole number, so this the number which Rio placed incorrectly.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Jesse played two days of golf. On the second day, he got a score of 6 below par, or-6. His total score for the two days was O above par, or 0. Define a variable. Then write and solve an equation to find the score Jesse got on the first day. Show your work.
Answer
If Jesse's score on the first day is x
The equation that represents what is described in the question is
x - 6 = 0
x = +6 (6 above par)
Jesse's score on the first day = +6 (6 above par)
Explanation
Let Jesse's score on the first day be x
Jesse's score on the second day = -6 (6 below par)
His total score for the two days was 0
So, the sum of his scores for the two days can be written as
x + (-6)
And that is equal to 0
x + (-6) = 0
x - 6 = 0
We can then solve this to obtain x; Jesse's score on the first day
x - 6 = 0
Add 6 to both sides
x - 6 + 6 = 0 + 6
x = +6 (6 above par)
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For a recent year, the mean fare to fly from Charlotte, North Carolina, to Chicago, Illinois, on a discount ticket was $267. A random sample of 13 round-trip discount fares on this route last month shows:
$321 $286 $290 $330 $310 $250 $270 $280 $299 $265 $291 $275 $281
1. What is the decision rule? (Round your answer to 3 decimal places.)
2. Compute the value of the test statistic. (Round your answer to 3 decimal places.)
1. The decision rule is:
t < 2.681: do not reject the null hypothesis.t > 2.681: reject the null hypothesis.2. The test statistic is: t = 3.42.
What are the hypothesis tested and the decision rule?At the null hypothesis, it is tested if there is not enough evidence that the mean ticket price has increased from $267, that is:
[tex]H_0: \mu \leq 267[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the mean ticket price has increased from $267, that is:
[tex]H_1: > 267[/tex]
For the decision rule, we need to consider that:
It is a right-tailed test, as we are testing if the mean is greater than a value.The t-distribution is used, as we have the standard deviation for the sample but not for the population.Due to the sample size of 13, there are 12 degrees of freedom.The critical value for the test is given by:
t* = 2.681.
Hence the rule is:
t < 2.681: do not reject the null hypothesis.t > 2.681: reject the null hypothesis.What is the test statistic?The test statistic is given by the following equation:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which the parameters are defined as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.Using a calculator from the given sample, and considering the values tested at the hypothesis, the values of the parameters are:
[tex]\overline{x} = 288.3, \mu = 267, s = 22.46, n = 13[/tex]
Hence the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{288.3 - 267}{\frac{22.46}{\sqrt{13}}}[/tex]
t = 3.42.
What is the missing information?The problems asks if the sample gives enough evidence to conclude if the mean ticket price has increased with a significance level of 0.01.
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Question 1 of 44Chico is considering taking out a 14-year loan with monthly payments of $185at an APR of 2.7%, compounded monthly, and this equates to a loan of$25,857.12. Assuming that Chico's monthly payment and the length of theloan remain fixed, which of these is a correct statement?A. If the interest rate were 2.9%, the amount of the loan that Chico isconsidering would be more than $25,857.12B. If the interest rate were 3.1%, the amount of the loan that Chico isconsidering would be more than $25,857.12C. If the interest rate were 2.5%, the amount of the loan that Chico isconsidering would be less than $25857.12.D. If the interest rate were 3.3% the amount of the loan that Chico isconsidering would be less than $25.857.12
We have a loan with a period of 14 years, monthly payments of $185 and an APR of 2.7% compounded monthly.
That equates to a loan of $25,857.12.
We have to check the statements:
A. In the case that the interest rate was higher (2.9% instead of 2.7%), the amount of the loan with the same period and payments should be lower.
This is because, for the same amount of the loan, we should be paying a higher monthly amount if the interest rate is higher.
NOTE: for an interest rate of 2.9%, the amount of the loan would be $25,519.54.
Then, this statement is false.
B. In this case, we increase the rate even more (to 3.1%), so the amount of the loan would be even lower than in case A.
NOTE: it would be $25,188.05.
This statement is false.
C. In this case, the interest rate is less than 2.7%, so the amount of the loan would be higher ($ 26,200.91).
This statement is false.
D. In this case, the interest rate is higher than 2.7%, so the amount of the loan will be less.
This statement is
Two equivalent numbers of 55%
Answer: 0.55 and 55/100
Step-by-step explanation:
Solve for B
A=4B+ 7C
B=
Answer: B=A-7C
Step-by-step explanation:
a=4b+7c a-7c=B
Refer to the diagram to the right.(a)Write an equation for the diagram to the right.b. Find the sum.C. Describe the sum in terms of the distance from the first addend. Explain.d. What integers do the arrows represent?
(a)An equation for the diagram is:
[tex]-5+(-4)=-9[/tex](b)The sum is -9.
(c)The sum (-9) is 4 units away from the first addend (that is, -5).
(d)The arrows represent the integers -5 and -9.
Marie is saving money to buy a prom dress that costs 225$. She already has 85$ and makes 20$ per day. Babysitting after school . Write & solve an inequality to determine how many days marie need to babysit in order to have enough money for the dress.
Given,
Total money needed = 225
Money already Marie has = 85
Marie per day Income = 20
Let it take x days for Marie to have enough money to buy the prom dress.
We can say:
Total Money = Money Marie already has + per day income
Using the given information, we can craft an inequality shown below:
[tex]85+20x\geq225[/tex]This means "85 already have plus 20 per day will need to be atleast 225".
Now, we can do algebra and solve for x. Steps are shown below:
[tex]\begin{gathered} 85+20x\geq225 \\ 20x\geq225-85 \\ 20x\geq140 \\ x\geq\frac{140}{20} \\ x\geq7 \end{gathered}[/tex]Thus, Marie needs 7 days more to have enough money to buy the prom dress.
mr peel started 7 meters away from the motion detector and 2 seconds later he was 3 meters away from the motion detector. find the average rate of changed or slope in meters per second
He started at 7 meters away, so if after 2 seconds now he is 3 meters away, then he move:
[tex]7-3=4[/tex]So he move 4 meters in 2 seconds so to find the rate we divide the meters into the tiem so:
[tex]r=\frac{4}{2}=2[/tex]What is the volume of this cone? Use I 3.14 and round your answer to the nearest hundredth. LI cubic inches
The volume of a cone is given by
[tex]V\text{ = }\frac{1}{3}\pi\text{ r}^2\text{ h }[/tex]Diameter = 34 in
radius = 34/2 = 17 in
Height = 17in
[tex]\begin{gathered} V\text{ = }\frac{1}{3}\text{ x 3.14 x 17 x 17 x17} \\ V\text{ =5142.27 inches} \end{gathered}[/tex]what is another way to write to 72-(-25)?A.72+ 25B.-72-25C.72-25D.-72-(-25)what is the value of -27-8?A.-35B.-19C.19D.35How much is 37 +13A.-50B.-29C.29D.51What is the solution to 40+(-11)?A.-51B.-29C.29D.50What is the value of -31 +30?A.-61B.-1C.1D.61Am sorry to bother you is there any way you can help me I didn't know if I was supposed to send this for people helps
So, basically, we need to simply the expression given to us.
The given expression is:
72 - (-25)
From the laws guiding signs, we know that:
- * - = +
Therefore, the expression becomes:
72 + 25
That is another way of writing the expression
