Answer:
-45
Explanation:
-14 + (-31)
= -14 - 31
= -45
T
A metal worker traced a triangular piece of sheet metal on a coordinate plane, as shown. The un
represent inches. What is the length of the longest side of the metal triangle? Approximate the length
of the longest side to the nearest tenth of an inch using a calculator
The length of the longest side of the metal triangle is 7.8 inches
What is a triangle called ?A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same. Triangles can be divided into three groups based on the lengths of their sides, and these groups are as follows: Scalene. Isosceles. Equilateral. Interior angles in triangles all add up to 180°, 180°, 180°, etc. A triangle's angles are equal to the sum of the angles at each of its three vertices. Three diagonals must meet at three different locations to form a triangle. There are five possible arrangements of three diagonals.
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Find the height of the tree if the tree's shadow is 13 feet and the stick person's height is 5.2 feet, and the stick person's shadow is 4 feet.?
Answer: 16.9 feet.
Step-by-step explanation:
The person's shadow is 1.3 times its shadow, which was found by dividing 5.2 by 4. Once we have the proportion, we can multiply the tree's shadow by 1.3 and get 16.9 feet.
Complete the table below by writing the symbols for the cation and anion that make up each ionic compound. The first row has been completed for you.
The cations and Anions for the given compounds are;
1) CuS: Cation; Cu²⁺ and Anion: Su²⁻
2) (NH₄)₂O; Cation; NH₄⁺ and Anion: O²⁻
3)Mn₃(PO₄)₂; Cation; Mn²⁺ and Anion: PO₄³⁻
4) VBr₅; Cation; V⁵⁺ and Anion: Br⁻
How to Identify Anions and Cations?Cations are defined as Positively charged ions that are formed by loss of electrons by an atom. In a cation, number of electrons are less than number of protons.
Anions are defined as Negatively charged ions that are formed by gaining of electron by an atom. In anions, number of electrons are more than the number of protons.
Thus;
1) CuS
Cation; Cu²⁺
Anion: Su²⁻
2) (NH₄)₂O
Cation; NH₄⁺
Anion: O²⁻
3) Mn₃(PO₄)₂
Cation; Mn²⁺
Anion: PO₄³⁻
4) VBr₅
Cation; V⁵⁺
Anion: Br⁻
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200 lottery tickets are sold for $6 each. The person with the single winning ticket will get $90. What is the expected value for a ticket in this lottery?
The probability of winning is 1/200.
The probability of losing is 199/200.
The gain of winning is
($90 - $6) that is $90 of the winning ticket minus the $6 ticket cost.
The loss of lossing is -$6 that is a player loses $6 for the ticket.
The expected value therefore is calculated as
[tex]\begin{gathered} E(X)=(90-6)(\frac{1}{200})+(-6)(\frac{199}{200}) \\ E(X)=(84)(\frac{1}{200})+(-6)(\frac{199}{200}) \\ E(X)=0.42-5.97 \\ E(X)=-5.55 \end{gathered}[/tex]Therefore, the expected value for a ticket in this lotter is -$5.55 or an average loss of $5.55.
+3Which of the following is the function f(x) if f'(x) =
f(x) = 8(x -3) (option C)
Explanation:
[tex]f^{-1}(x)\text{ = }\frac{x}{8}+3[/tex]let y = inverse of f(x)
[tex]y\text{ = }\frac{x}{8}+\text{ 3}[/tex]Interchange x and y:
[tex]\begin{gathered} x=\text{ }\frac{y}{8}+\text{ 3} \\ mu\text{ltiply through by 8:} \\ 8(x)\text{ = 8}(\frac{y}{8})+\text{ 3(8)} \\ 8x\text{ = y + 24} \end{gathered}[/tex][tex]\begin{gathered} \text{make y the suject of by subtracting 24 to both sides} \\ 8x\text{ - 24 = y} \\ y\text{ = 8(x - 3) (option C)} \\ f(x)\text{ = 8(x - 3) (option C)} \end{gathered}[/tex]Question 1 of 5
Drag each tile to the correct location on the table. Not all tiles will be used.
Match each quadratic function with the attributes of its graph.
A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices. For instance, the points A, B, C, D, and E in the aforementioned figures are vertices.
Vertex form the equation again.Fill in the square for 2 x ² + 8 x + 7.
To continue, tap...
2 ( x + 2 ) 2 − 1 Set y to the newly created right side.
y = 2 ( x + 2 ) 2 − 1
Find the values of a, h, and k using the vertex form, y = a (x h ) 2 + k. a = 2 h = 2 k = 1
Find the (h,k) vertex. ( 2, 1 ) .
2 x ² + 8 x - 7
Discover the initial derivative.
4 x + 8
Solve the problem 4 x + 8 = 0 by setting the first derivative to 0.
To continue, tap... x = − 2
Locate the values at which the derivative is ambiguous.
All real numbers fall under the expression's domain, with the exception of cases where it is undefined. In this instance, the phrase is defined even if there is no real number.
At each x value where the derivative is 0 or undefined, evaluate 2 x 2 + 8 x 7.
( − 2 , − 15 ).
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The function y=f(x)y=f(x) is graphed below. Plot a line segment connecting the points on ff where x=-6x=−6 and x=2.x=2. Use the line segment to determine the average rate of change of the function f(x)f(x) on the interval -6\le x \le 2.−6≤x≤2.
The average rate of change of the function f(x) on the interval−6≤x≤2 is -0.5
This is further explained below.
What is the average rate?Generally, The average rate of reaction is referred to as the change in concentration of any of the reactants or any of the products per unit of time during a specific period of time. This change may occur at any point throughout the reaction.
A single rate is applicable to property that is located in more than one place and that is calculated by weighting the separate rates that are calculated for each location.
In conclusion, The average rate of change on x e(a, b)
[tex]\begin{aligned}m &=\frac{f(b)-f(a)}{b-a} \\\\m &=\frac{f(2)-f(-6)}{2-(-6)} \\\\&=\frac{2-(-(-6))}{8}=\frac{6}{2} \\\\=-0.5\\\\\end{aligned}[/tex]
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Three glasses of milk and 4 snack bars have a total of 80 carbohydrates (carbs), and 4 glasses of milk and 3 snack bars have a total of 81 carbs. Determine how many carbs are in one glass of milk and in one snack bar.
Let m be a glass of milk and s be a snack bar.
3 glasses of milk and 4 snack bars have a total of 80 carbohydrates. So, the expression is,
[tex]3m+4s=80\ldots..(1)[/tex]4 glasses of milk and 3 snack bars have a total of 81 carbs.
[tex]4m+3s=81\ldots\ldots.(2)[/tex]The above equation can be rewritten as,
[tex]\begin{gathered} 4m=81-3s \\ m=\frac{81-3s}{4}\ldots..(3) \end{gathered}[/tex]Put equ (3) in (1) to find s.
[tex]\begin{gathered} 3\times(\frac{81-3s}{4})+4s=80 \\ \frac{243-9s}{4}+4s=80 \\ \frac{243-9s+16s}{4}=80 \\ 243-9s+16s=320 \\ 7s=77 \\ s=11 \end{gathered}[/tex]Now, put 11 for s in equ (1) to find m.
[tex]\begin{gathered} 3m+4\times11=80 \\ 3m+44=80 \\ 3m=36 \\ m=12 \end{gathered}[/tex]So, there are
Kaylee obtains a loan with simple interest to buy a car that costs $8,500. If Kaylee pays $1,020 in interest during the four-year term of the loan, what was the rate of simple interest?A.0.03%B.3%C.8.3%D.12%
Answer : r = 3%
[tex]\begin{gathered} I\text{ = }\frac{P\text{ X R X T}}{100} \\ \text{Where I = interest, P = principal, R = rate, and T= time} \\ I\text{ = \$1,020} \\ P\text{ = \$8,500} \\ T\text{ = 4} \\ 1020\text{ = }\frac{8500\text{ x r x 4}}{100} \\ 1020\text{ x 100 = 8500 x 4 x r} \\ r\text{ = }\frac{8500\text{ x 4}}{1020\text{ x 100}} \\ r\text{ =}\frac{34000}{102000} \\ r\text{ = }0.333 \\ r\text{ = }3^{} \\ r\text{ = 3\%} \end{gathered}[/tex]Question 2 of 3 Which decimal is equivalent to ( 8 × 3 ) ( 1 10 × 1 10 ) ?
The expression's decimal is equivalent to (B) 0.24.
What do we mean by decimal numbers? A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of whole and partially whole quantities. One of the number types in algebra that has a whole number and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.So, ( 8 × 3 ) ( 1/10 × 1/10 ):
Solve as follows:
(8 x 3) x (1/10 × 1/10)24 x 1/10024/1000.24Therefore, the expression's decimal is equivalent to (B) 0.24.
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The correct question is given below;
Which of the following decimals is equivalent to (8 x 3) (1/10 × 1/10)
A. 0.024
B. 0.24
C. 2.4
D. 24.0
Table 1 shows two variables m and n that are related by an equation n ab^m where a and b are constantBelow shows table 1:m : 1 2 3 4 5n : 24 48 96 192 384a) plot the graph of log10 n against m by using a scale of 2 cm to 1 unit on the x-axis and 2cm to 1.2 unit on the y-axisb) hence, find the value of a and b
Answer
a) The plotted graph is shown in the Explanation below.
b) a = 12, b = 2
Explanation
n = a(b^m)
Taking the logarithm of both sides
log n = log [a(b^m)]
log n = log a + log (b^m)
log n = log a + m log b
So, to first plot the graph, we know we need to rewrite this equation to match the equation of a straight line. Equation of a straight line is
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
log n = (log b) m + log a
y = mx + b
y-axis = log n
slope = log b
x-axis = m
intercept = log a
So, we need to plot log n (on the y-axis) against m (on the x-axis)
m | n | log n
1 | 24 | 1.38
2 | 48 | 1.68
3 | 96 | 1.98
4 | 192 | 2.28
5 | 384 | 2.58
The values for log n are then plotted against the corresponding value of m
The image is presented below.
From the graph, we can easily see that
Intercept = 1
To obtain the slope, for a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
Using the two farthest points,
(x₁, y₁) and (x₂, y₂) = (1, 1.38) and (5, 2.58)
[tex]\begin{gathered} Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1} \\ \text{Slope = }\frac{2.58-1.38}{5-1}=\frac{1.2}{4}=0.3 \end{gathered}[/tex]b) Intercept = log a = 1.08
a = log⁻¹ (1.08) = 12
Slope = log b = 0.3
b = log⁻¹ (0.3) = 1.995 = 2
n = 12 (2^m)
We can test this by putting values of m in the expression looking to get n
when m = 1,
n = 12 (2^1)
n = 12 (2) = 24
when m = 5
n = 12 (2^5)
n = 12 (32) = 384
So, our model works!!!
Hope this Helps!!!
The following table shows a proportional relationshipbetween w and z.w2182.455819Write an equation to describe the relationship betweenwand z.
As it is a proportional relationship then this relationship can be described by a line. To find the equation of the line that passes through the points shown in the table, you can first find the slope and then use the point-slope formula.
maths lit inflation g11I from South Africa we use Rands
It is given that the price of the box increases from R17.99 to R19.99.
It is required to find the inflation rate for the period.
Recall the formula for the Inflation Rate:
[tex]\frac{\text{ Current price}-\text{ Initial price}}{\text{ Initial price}}\times100\%[/tex]Substitute the given prices:
[tex]\frac{19.99-17.99}{17.99}\times100\%=\frac{2}{17.99}\times100\%=\frac{200}{17.99}\%\approx11.1\%[/tex]The answer is about 11.1%.Pls tell me the answer it is due in 20 min pls pls pls
I WILL GIVE YOU A TONE OF BRAINLY POINTS AND FIRST ONE TO AMSWER GETS BRAINLYIEST
Answer:
100 is the number
Step-by-step explanation:
For this equation, it may be helpful to replace words with symbols.
The question is:
if 6% of x is the same as 5% of 120, then what is x?
The comma splits the sentence into two parts
if 6% of x is the same as 5% of 120 is the main focus, and the second part requires you to find x.
In the question "if 6% of x is the same as 5% of 120"
the word "of" can be replaced with " * ", and the words "is the same as" can be replaced with "=". The if can be dropped
The question becomes:
6% * x = 5% * 120
This equation can be easily solved.
6% = 0.06
5% = 0.05
So,
0.06x=0.05*120
0.06 x = 6
x = 6 / 0.06
x = 100
Heather, Tom, and Kareem have a total of $86 in their wallets. Heather has $9 less than Kareem. Tom has 3 times what Kareem has. How much does each have?
Answer: Heather: $10, Kareem: $19, Tom: $57
Step-by-step explanation:
How do yu solve -8w times -w
The result of the expression -8w times -w is [tex]8w^{2}[/tex]
The expression is -8w times -w
Expressions is the mathematical statements that have a minimum of two terms containing numbers or variables, connected by an operator in between. The operator maybe addition, subtraction, division or multiplication.
Here the expression is -8w times -w
Here -8w times -w means, we have to multiply the -8w by -w
Therefore the expression is
-8w × -w
We know when we multiply the a negative number by negative number the result will be positive number
-8w × -w = [tex]8w^{2}[/tex]
Hence, the result of the expression -8w times -w is [tex]8w^{2}[/tex]
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Solve for x.5/6x = 15
The answer is 18
You first multiply both sides by 6 which will make 15, now 90
then divide both sides by 5 so that will make 90, 18 thus x=18 is correct
what is the total number of digits required in numbering the pages of a book, if the books has 1150 pages?
Which of these transactions types INCREASE how much you owe the credit card company? (Choose 4)
1. Balance Transfers
2. Purchases
3. Interest Charged
4. Cash Advances
5. Payments
This figure is a right triangular prism. The sides of its triangular bases are each 5 cm and the height of the triangular base is approximately 4.3 cm. The length of the prism between the bases is 8 cm. What is the approximate surface area of this prism?
The approximate surface area of the right triangular prism is 141.5 cm².
How to find surface area of a triangular prism?The surface area of a triangular prism can be found as follows;
surface area of a triangular prism = (perimeter × length) + (2 × base area)
Therefore,
perimeter of the triangular base = 5 + 5 + 5
perimeter of the triangular base = 15 cm
length = 8 cm
The base area = 1 / 2 bh
where,
b = baseh = heightThe base area = 1 / 2 × 4.3 × 5
The base area = 1 / 2 × 21.5
The base area = 10.75 cm²
Hence,
surface area of a triangular prism = (15 × 8) + 2(10.75)
surface area of a triangular prism = 21.5 + 120
surface area of a triangular prism = 141.5 cm²
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Answer:
Step-by-step explanation:
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Find the distance between point A and point c
Answer:
Option C: Square root of 74
Step-by-step explanation:
Use the distance formula
which function is used to find y, the remaining balance after x number of payments have been made?
Given data:
The first point on the graph is (0,20,000).
The second point on the graph is (40,0).
The equattion of the line is,
(y-20,000)/(x-0)=(0-20,000)/(40-0)
(y-20,000)/(x)=-500
y-20,000=-500x
y=-500x+20,000
Thus, the equation of the line is y=-500x+20,000
WILL GIVE BRAINLYEST 200 POINTS!!!1
The range will be impacted by A. The range will increase by 12.
What is a range?A range simply means the difference between the highest and the lowest number.
Highest number = 34
Lowest number = 15
Range = 34 - 15 = 19
When the highest number is 46, the range will be:
= Highest number - Lowest number
= 46 - 15
= 31
The difference will be:
= 31 - 19
= 12
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Answer:
The range will be impacted by A. The range will increase by 12.What is a range?A range simply means the difference between the highest and the lowest number.Highest number = 34Lowest number = 15Range = 34 - 15 = 19When the highest number is 46, the range will be:= Highest number - Lowest number= 46 - 15= 31The difference will be:= 31 - 19= 12
Step-by-step explanation:
Ms. Wood has a class of 18 students. She can spend 20 dollars on each student to buy math supplies for the year. She first buys all of her students calculators, which costs a total of 155.88 . After buying the calculators, how much does she have left to spend on each student?
The change after buying the calculators is $204.12
How to calculate the change gotten after purchasing the calculators ?Ms. Wood has a class of 18 students
She wants to spend $20 on each of her students
The total money she can spend can be calculated as follows
= 18 × 20
= 360
She buys the calculators for her students, everything costs $155.88
The money she has left to spend can be calculated as follows
= 360 - 155.88
= 204.12
Hence she has $204.12 left as the change she can spend on her students
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A population of values has a normal distribution with μ=62.9 and σ=25.8. You intend to draw a random sample of size n=22.
In a population of values having a normal distribution with (μ = 62.9) and (σ = 25.8), and we intend to draw a random sample of size (n = 22),
(i) The probability that a single randomly selected value is less than 45.3 [P(X < 45.3) is 0.2476
(ii) The probability that a sample of size (n = 22) is randomly selected with a mean less than 45.3 [P(M < 45.3)] is (0.0007)
As per the question statement, a population of values has a normal distribution with (μ = 62.9) and (σ = 25.8) and we intend to draw a random sample of size (n = 22).
We are required to calculate:
(i) The probability that a single randomly selected value is less than 45.3 [P(X < 45.3)
(ii) The probability that a sample of size (n = 242) is randomly selected less than 45.3 [P(M < 45.3)].
Let us assume that, a random variable "X" follows normal distribution with mean (μ = 62.9), standard deviation (σ = 25.8) and a sample size of (n = 22).
(i) The probability that a single randomly selected value is less than 45.3 [P(X < 45.3) is,
P (X < 45.3) = P[{(X - μ)/σ} < {(45.3 - 62.9)/25.8}]
= [P{Z < (-0.6822)}]
=0.247556247343...[Using Excel Function "NORMSDIST (-0.6822)]
≈ 0.2476
(ii) The probability that a sample of size (n = 22) is randomly selected with a mean less than 45.3 [P(M < 45.3)] is,
P(M < 45.3) = P[{(M - μ)/(σ/√n)} < {(45.3 - 62.9)/25.8/√22)}]
= P[{(M - μ)/(σ/√n)} < {(45.3 - 62.9)/5.5006}]
=P[Z < (-3.19965)]
= (0.000687972836)...[Using Excel Function "NORMSDIST (-1.49)]
≈ 0.0007
Probability: Probability is the branch of mathematics concerning numerical descriptions about the extent to which an event is likely to occur, or how likely it is that, a proposition is true, and is measured by the ratio of the favorable cases to the whole number of cases possible.Sample: In statistics, quality assurance, and survey methodology, sampling is a logical selection of a subset (a statistical sample) of individuals from within a larger statistical population to estimate characteristics of the whole population.To learn more about Samples and Probability, click on the link below.
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Identify the information given to you in the application problem below. Use thatinformation to answer the questions that follow on Practical Domain and PracticalRange.Round your answers to two decimal places as needed.The cost to fill your motor home's propane tank is determined by the functionC(9) = 3.37g where C is the output (cost in $) and g is the input (gallons of gas).The propane tank can hold a maximum of 17 gallonsIdentify the practical domain of this function by filling in the blanks below.Minimum Gallons Purchased 59 s Maximum Gallons PurchasedPractical Domain:
Solution:
The cost to fill the propane tank is modeled by the function;
[tex]\begin{gathered} C(g)=3.37g \\ \\ \text{ Where }C=cost(\text{ \$})\text{ and }g=gallon\text{ \lparen of gas\rparen} \end{gathered}[/tex]The practical domain of this function is;
[tex]0\leq g\leq17[/tex]Hence, the range of this function is;
[tex]\begin{gathered} \text{ Minimum cost:} \\ C(0)=3.37(0) \\ \\ C(0)=0 \\ \\ Maximum\text{ cost:} \\ C(17)=3.37(17) \\ \\ C(17)=57.29 \end{gathered}[/tex]Thus, the practical range is;
[tex]0\leq C(g)\leq57.29[/tex]Kathleen begins working and at age 32 she invests $6000.00 into a retirement account that pays an APR of 6.4% compounded monthly. She expects to retire at age 65. What will be the size of Kathleen’s total interest when she retires?
Simple interest is the cost of borrowing money without accounting for the effects of compounding.12672 is the size of Kathleen’s total interest when she retires.
What is Simple Interest?Simple interest is the cost of borrowing money without accounting for the effects of compounding.
Given that Kathleen begins working and at age 32 she invests $6000.00 into a retirement account that pays an APR of 6.4% compounded monthly. She expects to retire at age 65.
Let us calculate the age or time
65-32 =33 years
A=P(1+rt)
A= Final Amount
P=Principle amount=6000
r = rate of interest=6.4%
t is time =33 years
Substitute these values in Formula.
Convert 6.4% to decimal number by dividing with 100.
A=6000(1+0.064(33))
A=6000(1+2.112)
A=6000(3.112)
A=18672
The final Amount she got is 18,672.
To find the interest amount we have to substitute initial amount from final amount.
18672-6000
=12672
Hence 12672 is the size of Kathleen’s total interest when she retires.
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9.) The line plot shows the number of pounds of fish eaten by each dolphin at the zoo. Fish Eaten by Dolphins (pounds) XXX X х x x 16 20 24 28 32 36 Which stem and leaf plot best represents the data in the line plot? Fish Eaten by Dolphins (pounds) Fish Eaten by Dolphins (pounds) Stem Leaf Stem Leaf 1 889 1 2 3 88 0026 1113 3 KEY 2|0 - 20 pounds KEY 2|0 - 20 pounds Fish Eaten by Dolphins (pounds) Fish Eaten by Dolphin (pounds) Stem Leaf Stem Leaf 1 D 7 78 015 0003 89 0 26 2 3 KEY = 20 pounds 2|0 - 20 pounds
C
1) Writing down the data gathered from that :
lbs number of fishes
18 2
19 1
20 1
26 1
31 3
34 1
2) Examining the steam and plot graphs we can state that the best represents those collected data is the option C
Note how many times those data are enlisted, and you can conclude that. On the left the tens and on the right the units, just like the "key" displays.
3) Hence, the answer is C
rosa has 3 3/4 pounds of dough. she use 3/4 of a pound for one medium of loaf of bread. how many medium loaves of brrad could be me from rosa's dough?2 3/16353 9/16
The number of pounds of doughs available is given as:
[tex]3\frac{3}{4}[/tex]The fraction of a pound used for one medium is given as:
[tex]\frac{3}{4}[/tex]The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $1400, which was tobe divided equally among the members going. Prior to the trip, 5 members decided not to go. If thecost per person increased by $14, how many people went on the expedition?
originally, the cost was to be divided among all members
[tex]\frac{1400}{m}=x[/tex]Where m is the number of members and x was the cost per person originally
When 5 people decided not to go, x was increased $14 and m decreased 5...
[tex]\frac{1400}{m-5}=x+14[/tex]Now, we have two equations that we need to solve...
[tex]\frac{1400}{m}=x,\: \frac{1400}{m-5}=x+14[/tex][tex]\begin{gathered} \frac{1400}{m}=x \\ - \\ \underline{\frac{1400}{m-5}=x+14} \\ \frac{1400}{m}-\frac{1400}{m-5}=x-\mleft(x+14\mright) \end{gathered}[/tex]if we subtract the two expressions, we get the above
Now, we simplify...
[tex]\begin{gathered} \frac{1400}{m}-\frac{1400}{m-5}=x-\mleft(x+14\mright) \\ -\frac{7000}{m\left(m-5\right)}=-14 \end{gathered}[/tex]Now, we solve for m
[tex]\begin{gathered} -\frac{7000}{m\left(m-5\right)}=-14 \\ -\frac{7000}{m\left(m-5\right)}m\mleft(m-5\mright)=-14m\mleft(m-5\mright) \\ -7000=-14m\mleft(m-5\mright) \\ -7000=-14m^2+70m \\ -14m^2+70m=-7000 \\ -14m^2+70m+7000=-7000+7000 \\ -14m^2+70m+7000=0 \\ m_{1,\: 2}=\frac{-70\pm\sqrt{70^2-4\left(-14\right)\cdot\:7000}}{2\left(-14\right)} \\ m_{1,\: 2}=\frac{-70\pm\:630}{2\left(-14\right)} \\ m_1=\frac{-70+630}{2\left(-14\right)},\: m_2=\frac{-70-630}{2\left(-14\right)} \\ m1=-20,\: m2=25 \end{gathered}[/tex]we obtain that m=25, meaning there are 25 members, so 25-5=20, this is, 20 people went to the expedition
