[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{\frac{7}{2}})\qquad (\stackrel{x_2}{\frac{5}{3}}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(\frac{5}{3}-2)^2 + (1-\frac{7}{2})^2}\implies d=\sqrt{(\frac{-1}{3})^2 + (-\frac{5}{2})^2} \\\\\\ d=\sqrt{\cfrac{1}{9}~~ + ~~\cfrac{25}{4}}\implies d=\sqrt{\cfrac{229}{36}}\implies d=\cfrac{\sqrt{229}}{\sqrt{36}}\implies d=\cfrac{\sqrt{229}}{6}[/tex]
help meeeeee plssss with steps
Answer:
p = 18, q = 0
Step-by-step explanation:
The expression on the left side of the equation is
[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} $}[/tex]
Multiply the denominators to get a common denominator:
[tex]\text{$\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)$}[/tex]
= [tex]\left(\sqrt{5}\right)^2-2^2[/tex] ∵ (a + b)(a - b) = a² - b²
[tex]=5-4\\\\= 1[/tex]
[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} $}\\\\[/tex]
[tex]=\dfrac{\left(\sqrt{5}+2\right)\left(\sqrt{5}+2\right)}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)} + \dfrac{\left(\sqrt{5} - 2\right)\left(\sqrt{5} - 2\right)}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}[/tex]
Since denominator
[tex]\text{$\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)$} = 1,[/tex]
the expression becomes
[tex]=\left(\sqrt{5}+2\right)^2 + \left(\sqrt{5}-2\right)^2\\\\= 5 + 4\sqrt{5} + 4 + 5 - 4\sqrt{5} + 4\\\\[/tex]
[tex]= 10 + 8 = 18[/tex]
Therefore
[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} = p + q\sqrt{5}$}\\\\\\= > \large \text{$ 18 = p + q\sqrt{5}$}[/tex]
Now [tex]\sqrt{5}[/tex] is an irrational number and p = rational so since there is no [tex]\sqrt{5}[/tex] term on the left side, q = 0 and p = 18
After a 70% reduction, you purchase a new clothes dryer on sale for $204. What was the original price of the
clothes dryer?
Answer:$346.8
Step-by-step explanation:
1. X - 70% = 204
Want to get the value of X
2. X + 70% = 204 + 70%
= X = 204 x 1.7
= X = $346.8
Answer:
Original Price = $680
Step-by-step explanation:
Think about what a 70% reduction in price means.
If the original price of an item is $100 then a 70% reduction would mean that it costs 70% less from the original price. This means you would be paying only 30% of the original price
Let the original price be $P
Then the price you pay after 70% reduction is 30% of P
= P x 30/100
= P x 0.3 (30% = 30/100 = 0.3)
= 0.3P
We are given that this sale price = $204
--> 0.3P = 204
Dividing both sides by 0.3 gives us the value for P
0.3P/0/3 = 204/0.3
P = 204/0.3 = 680
So
Original Price = $680
We can double check our computations as follows
If original price = 680, then a reduction of 70% would be a discount of
0.7 x 680 = 476
Price after discount = Original Price - Discount
= 680 - 476 = 204
So our results are consistent
Which graph represents the solution set of the system of inequalities?
The correct graph that represents the solution set of the system of inequalities is in Option(b).
What is Inequality in mathematics?Inequality is a statement of an order relationship (greater than, greater than, or equal to, less than, or less than or equal to) between two integers or algebraic expressions in mathematics.
The given system of inequalities are,
y < -3x - 2
y ≤ x - 2
We have to select the graph that represents the solution set of the system of inequalities.
y < -3x - 2
Let, y = -3x - 2
Now, plot the graph of the line y = -3x - 2 with a Dotted line ( as < is a strict inequality).
y ≤ x - 2
Let, y = x - 2
Now, plot the graph of the line y = x - 2 on the graph.
The area between the two lines of inequalities on the graph represent the solution set.
Upon comparison with the graphs in the options, the correct graph is present in Option(b).
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x^2=49 which numbers are solutions to the equation
So we need to solve the following equation for x:
[tex]x^2=49[/tex]We can apply a square root to both sides but it is important to remember the following property. For any given number a we have:
[tex]\sqrt[]{a^2}=\lvert a\rvert[/tex]Which means that:
[tex]\sqrt[]{a^2}=a\text{ and }\sqrt[]{a^2}=-a[/tex]So for our case we have:
[tex]\begin{gathered} \sqrt[]{x^2}=\sqrt{49} \\ \lvert x\rvert=7 \\ x=7\text{ and }x=-7 \end{gathered}[/tex]Then the solutions are 7 and -7.
building a is 881 ft tall and contains 66 stories. building b contains 103 stories. if the two buildings have the same number of feet per floor approximately the height of building b. what is the approximate height of building b?
Answer:
approximately 1,375 feet
Step-by-step explanation:
Set up and solve this proportion:
[tex] \frac{881}{66} = \frac{h}{103} [/tex]
[tex]66h = 90743[/tex]
[tex]h = 1375[/tex]
So the height of building b is about 1,375 feet.
Which mapping diagram is not a function?
Mapping diagram (D) is not a function.
What is a function?A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. Four broad categories can be used to classify different types of functions. Dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.So, an option which is not a function:
According to the given image, we can easily point out that option (D) is not a function.As the f(x) has two mirror images g(x) which is not possible, and hence option (D) is not a function.Therefore, mapping diagram (D) is not a function.
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what is the measure of a
Answer:
Measure of Angle A is 100°
Step-by-step explanation:
The sum of interior angles of a polygon is given by the formula :
(n-2)×180 (where n is the number of sides)
n = 6
(6-2)×180 =
4 × 180 = 720
So :
A + B + C + D + E + F = 720
Substitute values given in diagram (angle d is 90 as the little square indicates a right angle) (Calling angle a as x) :
x + 135 + 115 + 90 + 110 + 170 = 720
Simplify :
x + 620 = 720
Subtract 620 from both sides :
x = 720 - 620
x = 100
Measure of Angle A is 100°
Hope this helped and have a good day
PLEASE HELP!!! PLEASE HURRY!!!
Answer:
C.
Step-by-step explanation:
as M is right over the middle of LN, this is an isoceles triangle (both legs are equally long).
so, we need to calculate only one leg and then double it fit both legs.
we get e.g. LM via Pythagoras.
LM is the Hypotenuse of the right-angled triangle with half of LN and the height to M being the legs.
so,
LM² = height² + (LN/2)² = 3² + 6² = 9 + 36 = 45
LM = sqrt(45) = 6.708203932... units
the perimeter is the sum of all 3 sides :
LN + LM + MN = LN + 2×LM = 12 + 2×sqrt(45) =
= 25.41640786... units
A designer builds a model of a bicycle. The finished model is exactly the same shape as the original, but smaller. The scale factor is 2:7. (a) Find the ratio of the height of the model to the height of the original. (b) Find the ratio of the surface area of the model to the surface area of the original. (c) Find the ratio of the volume of the model to the volume of the original. Write these ratios in the format m:n.
Given
Scale Factor of 2:7
When the scale factor is a:b
Recall the following
[tex]\begin{gathered} \text{The ratio of the sides is} \\ a:b \\ \; \\ \text{The ratio of the area is} \\ a^2:b^2 \\ \; \\ \text{The ratio of the volume is} \\ a^3:b^3 \end{gathered}[/tex]Given that the ratio is is 2:7 then we have the following
[tex]\begin{gathered} \text{The ratio of the height of the model to the height of the original is} \\ 2:7 \\ \; \\ \text{The ratio of the surface area of the model to the surface area of the original is} \\ 2^2:7^2\Longrightarrow4:49 \\ \; \\ \text{The ratio of the volume of the model to the volume of the original is} \\ 2^3:7^3\Longrightarrow8:343 \end{gathered}[/tex][tex]undefined[/tex]
I need answer on this graphing va substitution.Problem 7 I tried to solve it but not sure that’s correct
Given the system of equations:
[tex]\begin{gathered} 2x+9y=27 \\ x-3y=-24 \end{gathered}[/tex]To solve it by substitution, follow the steps below.
Step 1: Solve one linear equation for x in terms of y.
Let's choose the second equation. To solve it for x, add 3y to each side of the equations.
[tex]\begin{gathered} x-3y=-24 \\ x-3y+3y=-24+3y \\ x=-24+3y \end{gathered}[/tex]Step 2: Substitute the expression found for x in the first equation.
[tex]\begin{gathered} 2x+9y=27 \\ 2\cdot(-24+3y)+9y=27 \\ -48+6y+9y=27 \\ -48+15y=27 \end{gathered}[/tex]Step 3: Isolate y in the equation found in step 2.
To do it, first, add 48 to both sides.
[tex]\begin{gathered} -48+15y=27 \\ -48+15y+48=27+48 \\ 15y=75 \end{gathered}[/tex]Then, divide both sides by 15.
[tex]\begin{gathered} \frac{15y}{15}=\frac{75}{15} \\ y=5 \end{gathered}[/tex]Step 4: Substitute y by 5 in the relation found in step 1 to find x.
[tex]\begin{gathered} x=-24+3y \\ x=-24+3\cdot5 \\ x=-24+15 \\ x=-9 \end{gathered}[/tex]Answer:
x = -9
y = 5
or (-9, 5)
Also, you can graph the lines by choosing two points from each equation, according to the picture below.
Over the last three evenings, Karen received a total of 130 phone calls at the call center. The second evening, she received 4 times as many calls as the third evening. The first evening, she received 10 more calls than the third evening. How many phone calls did she receive each evening?
3 answers for this problem.
CORRECT ANSWERS ONLY
If the second evening, she received 4 times as many calls as the third evening. The first evening, she received 10 more calls than the third evening. The number of phone calls did she receive each evening is: 30, 80, 20.
Number of phones receivedLet x , y, z represents the 1st , 2nd, and 3rd evenings respectively
X + Y + Z = 130
Y = 4Z
X = z+10
Substituting the second and third equations into the first:
z+10 + 4z + z = 130
Combine like terms
6z + 10 = 130
Subtract 10 from both sides
6z +10 -10 = 130 -10
6z =130 -10
6z =120
Divide both side by 6z
z = 120/6
z = 20
Solving for y
y = 4z
y = 4×20
y = 80
Solving for x
x = z+10
x = 20 +10
x = 30
Check:
x + y + z =130
30 +80 + 20 =130
Therefore they each received 30 phones, 80 phones and 20 phones.
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if graph of g(x)is the graph of the parent function f(x)=x translated 3 units upward,then the y-intercept of the function g(x) is __
Answer: (0,3)
Step-by-step explanation:
The y-intercept for f(x)=x would be (0,0). Therefore, if we translate it up by three to get g(x), then the y coordinate would go up by 3, resulting in (0,3).
is 3 13/28 bigger than 3 17/20
Answer: 3 17/20 is bigger than 3 13/28
Step-by-step explanation:
2 ways:
1) Turn the fractions into decimal form.
13/28 = 0.464
0.464 + 3 = 3.464
17/20 = 0.85
0.85 + 3 = 3.85
2) Check which one is bigger
3.85 is bigger than 3.464 because the tenth place is bigger than the second number.
Second way:
1) Remove the 3s.
Both equations have three, so you could remove both sides three
3 13/28 ? 3 17/20
13/28 ? 17/20
2) Multiply both bottom expressions by itself.
(The numbers that its multiplying equals to 1. When multiplying a number by 1, it stays the same.)
13/28 * 20/20 = 260/560
17/20 * 28/28 = 476/560
3) Compare the fractions
260/560 ? 476/560
260/560 < 476/560
The number in the fraction is bigger
Answer:
No, 3 ¹³/₂₈ is smaller than 3 ¹⁷/₂₀.
Step-by-step explanation:
Convert both mixed numbers into improper fractions:
[tex]\implies 3 \frac{13}{28}=\dfrac{3 \times 28+13}{28}=\dfrac{97}{28}[/tex]
[tex]\implies 3 \frac{17}{20}=\dfrac{3 \times 20+17}{20}=\dfrac{77}{20}[/tex]
The lowest common multiple of 28 and 20 is 140.
Therefore, multiply the numerator and denominator of each improper fraction by the same number to make both denominators 140:
[tex]\implies \dfrac{97 \times 5}{28 \times 5}=\dfrac{485}{140}[/tex]
[tex]\implies \dfrac{77 \times 7}{20 \times 7}=\dfrac{539}{140}[/tex]
Therefore, as 539 > 485:
[tex]\implies \dfrac{539}{140} > \dfrac{485}{140}[/tex]
[tex]\implies \dfrac{77}{20} > \dfrac{97}{28}[/tex]
[tex]\implies 3 \frac{17}{20} > 3 \frac{13}{28}[/tex]
Therefore, 3 ¹³/₂₈ is smaller than 3 ¹⁷/₂₀.
Find the equation of a line that contains the points (-2, 2) and (-6,-5). Write the equation in slope-intercept form, usingfractions when required
Explanation
Lets first find the slope:
[tex]m=\frac{2-(-5)}{-2-(-6)}=\frac{2+5}{-2+6}=\frac{7}{4}[/tex]Now let's use the point-slope formula:
[tex]\begin{gathered} y-2=\frac{7}{4}(x-(-2)) \\ y-2=\frac{7}{4}(x+2) \\ y-2=\frac{7}{4}x+\frac{7}{2} \\ y=\frac{7}{4}x+\frac{7}{2}+2 \\ y=\frac{7}{4}x+\frac{7}{2}+\frac{4}{2} \\ y=\frac{7}{4}x+\frac{11}{2} \end{gathered}[/tex]Answer
[tex]y=\frac{7}{4}x+\frac{11}{2}[/tex]round 286 to the nearest ten with explanations
Answer:290
Step-by-step explanation:
first look at the ones place it is greater than 4 so round up
286 to the nearest tenth is 290.
What is a place value?Place value, which is related to a digit's location in a number, is the amount that each digit is worth.
Given:
The number is 286.
The digit in tenth place is 6.
And the number 6 is greater than the number 4.
And 6 > 4.
So, the number will round off to the nearest tenth.
6 becomes zero.
And the number left to 6 will increase by 1.
That means 8 + 1 = 9.
So,
286 to the nearest tenth is 290.
Therefore, 290 is the nearest ten of the required number.
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The temperature has been dropping 2 degrees Celsius per hour since midnight. If the temperature is 13 degrees at midnight, what is the temperature at 3:00AM?
If the temperature is 13 degrees at midnight, then the temperature will be 6 degrees at 3:00 AM.
Temperature at midnight = 13 °
Temperature drop per hour = 2 °
We need to find the temperature at 3:00 AM
Number of hours till then = 3 hours.
Temperature drop will be calculated by using multiplication.
Temperature drop = 2 × 3 = 6°
Temperature ate 3:00 AM = 12 - 6 = 6°
Therefore, we get that, if the temperature is 13 degrees at midnight, then the temperature will be 6 degrees at 3:00 AM.
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Help me with this question within 1-5 minutes please
Answer:
[tex]-12w + x[/tex]
Step-by-step explanation:
question:
[tex]-3w - 3x - 7w + 4x - 2w[/tex]
first you add all the 'w' together.
(-3)+(-7)+(-2) = -10+(-2)=-12
so, [tex]-12w - 3x + 4x[/tex]
second you add all the 'x' together
(-3)+(4) = 1
so, [tex]-12w+1x[/tex]
then simplify:
[tex]-12w + x[/tex] <--answer
hope this helps!
EASY POINTS - CORRECT ANSWER = BRAINLIEST
The animals at a safari park include gorillas, buffalo and wallabies. There are 24 more buffalo than there are gorillas. There are 7 times as many wallabies as there are gorillas. There are the same number of buffalo as there are wallabies. How many gorillas are there at the safari park?
Answer:
Step-by-step explanation:
The first thing you need to do, is find the total amount of gorillas.
to do this, you are going to use the equation:
24 + g = 7g
Both sides are equal, since the wallabies and the buffalo are equal. This makes the equation true.
you subtract g from 7g, and you should get:
24= 6g
Divide by six:
4 = g
That is the # of gorillas.
Now, if you add 24 + 4
You get the # of buffalo.
Which is: 28
Since the buffalo and wallabies are the same, the # of wallabies is also 28.
if you want to check, multiply 4x7 to get the amount of wallabies.
Pls help need asap!thx
Answer:
(0,7]
Step-by-step explanation:
It is an open circle at 0 and a closed circle at 7.
What is the range of this quadratic function
The range of the equation of the function given as y = x^2 + 4x + 7 is y >= 3
How to determine the range?The equation of the function is given as
y = x^2 + 4x + 7
Differentiate the function with respect to x
So, we have
y' = 2x + 4
Set the differentiated function to 0
So, we have
2x + 4 = 0
This gives
2x = -4
Divide by 2
x = -2
Substitute x = -2 in the equation y = x^2 + 4x + 7
So, we have
y = (-2)^2 - 4 x 2 + 7
Evaluate
y = 3
The leading coefficient is positive
This means that the vertex is a minimum
So, we have the range to be
y >= 3
Hence, the range is y >= 3
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Elena is traveling to visit her grandparents who live 125 miles away.
a. Elena stops for lunch 2/3 of the way. How far has Elena traveled?
b. Elena enters the city where her grandmother lives after 110 miles. Is she more or less than 9/10 of the way there?
PLS PLS PLS HELPP
a . After stopping for lunch Elena has travelled 50 miles.
b . She is less than 9 / 10 to her grand mother's location after travelling for 110 miles.
How to find the number of miles she travelled?She is traveling to visit her grandparents who live 125 miles away.
a.
She stops for lunch 2/3 of the way.
The distance she has travelled after she stopped for lunch can be calculated as follows:
distance in miles = 2 / 5 × 125
distance in miles = 2 × 25
distance in miles = 50 miles
b.
She enters the city where her grandmother lives after 110 miles.
Hence,
9 / 10 × 125 = 1125 / 10 = 112.5 miles
Therefore, she is less than 9 / 10 of her way there.
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A Sony LCD TV has a selling price of $925 and a 62% markup on selling price. What is the dollar markup and what is the cost?
Answer
Selling price = $ 925
Mark percentage = 62%
[tex]\begin{gathered} \text{Let's x represent Cost price i.e C. P=x} \\ \text{Selling price =C P +profit} \\ Profit\text{ =}\frac{\text{62x}}{100} \\ \\ S\text{. P =x+}\frac{\text{62x}}{100} \\ S\text{. P=x+0.62x} \\ S\mathrm{}P=1.62x \\ \therefore1.62x=925 \\ \end{gathered}[/tex][tex]\begin{gathered} \therefore1.62x=925 \\ \text{Divide both sides by 1.62} \\ \therefore\frac{1.62x}{1.62}=\frac{925}{1.62} \\ \\ x=570.99 \end{gathered}[/tex]The cost price is 570.
i am needing help with this
Side BC is opposite to angle BAC, in the picture.
Answer: Angle BAC - first option
Mr. Michael’s class sold fruit cups for $1.55 each and Mr. Lee’s class sold bottles of sports drink for $1.09 each. Together, the classes sold 97 items and earned $120.45 for their school.
Question 1
Let x represent the number of fruit cups sold and let y represent the number of bottles of sports drinks sold.
Write and solve a system of equations that models the problem.
Enter your answers in the boxes to correctly complete each equation.
Question 1
Let x represent the number of fruit cups sold and let y represent the number of bottles of sports drinks sold.
Write and solve a system of equations that models the problem.
Enter your answers in the boxes to correctly complete each equation.
= 120.45
= 97
Question 2
How much money did Mr. Michael's class earn?
Enter your answer in the box.
$
Question 3
How much money did Mr. Lee's class earn?
Enter your answer in the box.
$
Answer:
Question 1:
x + y = 97
$1.55x + $1.09y = $120.45
Question 2:
32
Question 3:
65
Step-by-step explanation:
phew, way to long to explain why. A brainliest would be nice :)
The cross section (with units in inches) of a parabolic spotlight can be modeled by the equation x=1/20y^2
How far is the bulb from the vertex of the cross section?
The bulb is 5 inches far from the vertex of the cross section.
What is cross section of a parabola?A portion of the right cone known as a parabola is one that runs parallel to the generating line on one side of the conic figure.
The standard equation for a parabola is typically expressed as y² = 4ax if the directrix is parallel to the y-axis, and y² = 4ax if the parabola is in the negative quadrants. The conventional equation of a parabola is x² = 4ax if the parabola is sideways, or if the directrix is parallel to the x-axis. If the parabola is in the negative quadrants, the equation is x² = 4ax.
Given, The equation x = 1/20y² can be used to model the cross section of a parabolic spotlight (with units in inches).
We must determine the distance between the bulb and the cross section's vertex.
Equation x = 1/20y² is alternatively denoted by the expression y² = 20x.
Now, comparing the equation to the parabola's conventional form, y²=4ax
So, 4a=20
a=5
Consequently, a=5 represents the distance from the cross section's vertex to the bulb.
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what is a possible value for the missing term of the geometric sequence? 43____2107
Answer:
150
Step-by-step explanation:
The distance an object travels is determined by how fast it goes and for how long it moves. If an object's speed
remains constant, the formula is d=rt, where d is the distance, r is the speed, and t is the time.
If you drive at 50 miles per hour for 5 hours, how far will you have traveled?
a. 200 miles
b. 10 miles
c. 250 miles
d.300 miles
Answer:
c. 250 miles
Step-by-step explanation:
[tex]d=(50)(5)=250[/tex]
Moving waves can be described either as a function of time or as a function of
a. amplitude.
b. frequency.
c. speed.
d. position.
Moving waves can be described either as a function of time or as a function of position
What is a wave?A wave is a dynamic disturbance of one or more quantities that propagates in physics, mathematics, and related sciences. When waves oscillate frequently around an equilibrium value at a certain frequency, they are said to be periodic.
In a medium, a wave is a disturbance or variation that gradually transfers energy from one point to another. It can be an elastic deformation or a change in pressure, electric or magnetic strength, electric potential, or temperature.
It should be noted that it can be a function of the position as well as the time.
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Pls help
Find the surface area of the cylinder.
In the picture there is a cylinder with height 5 inches and diameter 4 inches. The surface area of cylinder is 87.62.
Given that,
In the picture there is a cylinder with height 5 inches and diameter 4 inches.
The surface area of a cylinder is the area that is enclosed by the flat bases and the curving surface of the cylinder. The cylinder's total surface area includes the area of the curving surface as well as the areas of the two circle-shaped bases of the cylinder.
The surface area of cylinder is 2πr²+2πrh
r is radius which is diameter/2
r=4/2=2
h is 5
Surface area of cylinder= 2πr²+2πrh
=2π×2²+2π×2×5
=8π+20π
=28π
=28×3.14
=87.92
Therefore, the surface area of cylinder is 87.62.
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QUESTION 3After surgery a patient was put on a restricted diet. In the first 2 days after surgery the patient was only allowed to consume•800 Cal/day. In the following 3 days the patient was allowed to consume 1100 Cal/day. In the final 4 days at the hospital thepatient was allowed to consume 1500 Cal/day.a) What was the average energy per day consumed? Round answer to the one if necessary.b) What is the unit symbol for the answer?
Given the patient consumption rate on his diet:
[tex]\begin{gathered} 1-2\text{days}=\text{ 800 Cal/day} \\ 2-3\text{days}=1100\text{ Cal/day} \\ 3\text{ -4days=1500 Cal/day} \end{gathered}[/tex](a) Average energy per day consumed will be since the number of days = 4
[tex]\begin{gathered} =\frac{800+1100+1500}{4} \\ =\frac{3400}{4} \\ =850\text{ Cal} \end{gathered}[/tex]The average energy per day consumed = 850 Cal(b) The unit symbol for the answer = calorie