To find the slope we can use the formula so:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]now we can replace the coordinates so:
[tex]m=\frac{-1-0}{-1-5}=\frac{-1}{-6}=\frac{1}{6}[/tex]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
Bob's new machine for work cost him £6700. It will depreciate at 28% each year. After how many years will it be worth less than £1000?
It will be valued less than £1000 after x = -0.8260748 years.
Based on the given conditions, formulate:
6700 × (1 - 28%) = 1000
Calculate the sum or difference:
6700 ×0.72ˣ = 1000
Reduce the greatest common factor on both sides of the equation:
67 × 0.72ˣ = 10
Divide both sides of the equation by the coefficient of variable:
67 × 0.72ˣ / 67 = 10 / 67
Rewrite as fraction:
0.72ˣ = 10 / 67
Convert exponential to logarithm form:
x = log°.₇₂ 10 / 67
Convert decimal to fraction:
x = log°₍₇₂/₁₀₀₎ 10 / 67
After simplifying -
get the result:
x = -0.8260748
Hence , After x = -0.8260748 years will it be worth less than £1000.
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are z^3 and 3z eqivalent expressions? explain
Given the expressions:
[tex]\begin{gathered} z^3 \\ 3z \end{gathered}[/tex]these two expressions are not equivalent, since one is thrice a number and the other is a cubic number. We can see this if we write completely each expression:
[tex]\begin{gathered} z^3=z\cdot z\cdot z \\ 3z=z+z+z \end{gathered}[/tex]thus, the expressions are not equivalent
Find the domaine and range of each relation. Determine if the relation is a function .
D: {-5, -2, 1, 2}
R: {-4, 0, 3}
The relation is a function
Explanation:Given:
5) Ordered pairs on a coordinate plane
To find:
the domain, range, and the type of relation
[tex]\begin{gathered} The\text{ domain is the input of a funcion \lparen x values\rparen} \\ The\text{ range is the output of the function \lparen y values\rparen} \end{gathered}[/tex]To determine the domain and range, we will list the ordered pairs:
(-5, 3), (-2, -4), (1, 0), (2, 3)
The first number in each pair represents the x values (domain), while the 2nd number in each pair represents the y values (range)
The domain: {-5, -2, 1, 2}
The range: {3, -4, 0, 3}
Rearranging and picking one of the repetitions:
The range: {-4, 0, 3}
For a relation to be a function, each input will have only one output.
None of the inputs appears more than once. Hence, each input has only one output. It is a function
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
can you explain to me how to solve this please
To solve the exercise you can use the following properties of exponents and radicals
[tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex][tex]a^ma^n=a^{m+n}[/tex][tex]\frac{a^m}{a^n}=a^{m-n}[/tex]So, you have
[tex]\begin{gathered} \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=\frac{7^{\frac{1}{3}}\cdot7^{\frac{1}{2}}}{\sqrt[6]{7^5}} \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=\frac{7^{\frac{1}{3}+\frac{1}{2}}}{7^{\frac{5}{6}}} \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=\frac{7^{\frac{5}{6}}}{7^{\frac{5}{6}}} \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=7^{\frac{5}{6}-\frac{5}{6}} \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=7^0 \end{gathered}[/tex]By definition
[tex]\begin{gathered} a^0=1 \\ \text{Where a }\ne0 \end{gathered}[/tex]So
[tex]\begin{gathered} \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=7^0 \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=1 \end{gathered}[/tex]Therefore, the correct answer is b. 1.
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:
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.
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.
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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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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just need help solving this ( not graded just a review)
Given
jenny mixed 4kg of mixed nuts containing 16% of peanuts with 12kg of mixed nuts containing 40% of peanuts .
Find
Percent in the new mixture of peanuts
Explanation
we are given 4kg of mixed nuts containing 16% of peanuts
Amount of quantity =
[tex]\frac{percentage}{100}\times totalamount[/tex]so,
[tex]\frac{16}{100}\times4=0.64kg[/tex]and also 12kg of mixed nuts containing 40% of peanuts .
so,
[tex]\frac{40}{100}\times12=4.8kg[/tex]so,total weight
[tex]0.64+4.80=5.44kg[/tex]let total mass pf mixture containing x % peanuts.
so,
[tex]\begin{gathered} \frac{5.44}{16}=\frac{x}{100} \\ 34=x \end{gathered}[/tex]Final Answer
Percent in the new mixture of peanuts = 34%
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.
which expression can be used to find the surface area of the following rectangular prism A 15+10+6B 15+15+15+6 C 6+6+10+10+15+15D 6+10
Answer:
C. 6 + 6 + 10 + 10 + 15 + 15
Explanation:
The surface area of a rectangular prism can be calculated as:
Surface Area = lw + lw + wh + wh + lh +lh
Where l is the length, w is the width, and h is the height.
So, replacing l by 3, w by 2, and h by 5, we get:
Surface Area = 3(2) + 3(2) + 2(5) + 2(5) + 3(5) + 3(5)
Surface Area = 6 + 6 + 10 + 10 + 15 + 15
Therefore, the expression that can be used to find the surface area is:
Surface Area = 6 + 6 + 10 + 10 + 15 + 15
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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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!!!
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
155 divided by 12 step-by-step explanation
Answer:
Step-by-step explanation:
Step 1:
Start by setting it up with the divisor 12 on the left side and the dividend 155 on the right side like this:
1 2 ⟌ 1 5 5
Step 2:
The divisor (12) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top:
0
1 2 ⟌ 1 5 5
Step 3:
Multiply the divisor by the result in the previous step (12 x 0 = 0) and write that answer below the dividend.
0
1 2 ⟌ 1 5 5
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.
0
1 2 ⟌ 1 5 5
- 0
1
Step 5:
Move down the 2nd digit of the dividend (5) like this:
0
1 2 ⟌ 1 5 5
- 0
1 5
Step 6:
The divisor (12) goes into the bottom number (15), 1 time(s). Therefore, put 1 on top:
0 1
1 2 ⟌ 1 5 5
- 0
1 5
Step 7:
Multiply the divisor by the result in the previous step (12 x 1 = 12) and write that answer at the bottom:
0 1
1 2 ⟌ 1 5 5
- 0
1 5
1 2
Step 8:
Subtract the result in the previous step from the number written above it. (15 - 12 = 3) and write the answer at the bottom.
0 1
1 2 ⟌ 1 5 5
- 0
1 5
- 1 2
3
Step 9:
Move down the last digit of the dividend (5) like this:
0 1
1 2 ⟌ 1 5 5
- 0
1 5
- 1 2
3 5
Step 10:
The divisor (12) goes into the bottom number (35), 2 time(s). Therefore put 2 on top:
0 1 2
1 2 ⟌ 1 5 5
- 0
1 5
- 1 2
3 5
Step 11:
Multiply the divisor by the result in the previous step (12 x 2 = 24) and write the answer at the bottom:
0 1 2
1 2 ⟌ 1 5 5
- 0
1 5
- 1 2
3 5
2 4
Step 12:
Subtract the result in the previous step from the number written above it. (35 - 24 = 11) and write the answer at the bottom.
0 1 2
1 2 ⟌ 1 5 5
- 0
1 5
- 1 2
3 5
- 2 4
1 1
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 155 divided by 12 calculated using Long Division is:12
11 Remainder
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]Which set represents a Pythagorean triple? 27,38,42. 33,44,55. 35,38,42. 68,72,81
The sets that represents a Pythagorean triple is 33,44,55.
How to represent Pythagorean triple?Pythagorean triple is used to find the side of a right angle triangle.
The Pythagoras theorem is represented as follows;
c² = a² + b²
where
c is the hypotenuse sidea and b are the other legs of the right triangle.Therefore, the Pythagorean triple must follow the principle : c² = a² + b²
Hence,
33² + 44² = 55²
1089 + 1936 = 3025
Therefore, the Pythagorean triple is 33,44,55.
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Base= 5.4 cm, Height= 2 cm. Find the area of the triangle. A.21.6 cm2 B. 10.8 cm2 C. 7.4 cm2 D. 5.4 cm2
Step 1
Given;
[tex]\begin{gathered} width=5.4cm \\ length=2cm \end{gathered}[/tex]Required; To find the area of the triangle
Step 2
State the area of a triangle
[tex]\begin{gathered} A=\frac{1}{2}\text{ base x height} \\ A=\frac{1}{2}\times5.4\times2 \\ A=5.4cm^2 \end{gathered}[/tex]Answer;
[tex]Area=5.4cm^2[/tex]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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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
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]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%.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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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
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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what is the total number of digits required in numbering the pages of a book, if the books has 1150 pages?
help me please
thank you
Answer:
Domain: [tex](-\infty, \infty)[/tex]
Range: [tex][0, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
