Step-by-step explanation:
200 calories come from fat, out of 5000 calories total. We can find the percentage with a proportion:
200 / 5000 = x / 100
x = 4
4% of the total calories come from fat.
Which line segment is a chord of o Pin the diagram below?
A. RS
B. PQ
C. QR
D. ST
C or QR
Step-by-step explanation:
Analyze the graph which inequality represents the graph
For this case, we must find two points that belong to the line and thus find the slope.
We have:
[tex](x1, y1) :( 1,1)\\(x2, y2) :(0,4)[/tex]
We found the slope:
[tex]m = \frac {y2-y1} {x2-x1} = \frac {4-1} {0-1} = \frac {3} {- 1} = - 3[/tex]
It is also observed that the cut-off point with the y-axis is 4.
In this way, we discard options A and B.
We evaluate option C:
[tex]y> -3x + 4[/tex]
We substitute the point (0,0) that belongs to the shaded region and verify the inequality:
[tex]0> -3 (0) +4\\0> 4[/tex]
It is not fulfilled!
Thus, the correct option is option D.
ANswer:
Option D
Answer:
For this case, we must find two points that belong to the line and thus find the slope.
We have:
We found the slope:
It is also observed that the cut-off point with the y-axis is 4.
In this way, we discard options A and B.
We evaluate option C:
We substitute the point (0,0) that belongs to the shaded region and verify the inequality:
It is not fulfilled!
Thus, the correct option is option D.
ANswer:
Option D
What is the difference of the two polynomials (9x^2+8x)-(2x^2+3x)
Answer:
7x² + 5x
Step-by-step explanation:
Given
(9x² + 8x) - (2x² + 3x) ← distribute parenthesis, second by - 1
= 9x² + 8x - 2x² - 3x ← collect like terms
= (9x² - 2x² ) + (8x - 3x)
= 7x² + 5x
Distribute the negative sign:
[tex](9x^2+8x)-(2x^2+3x)=9x^2+8x-2x^2-3x[/tex]
Gather like terms:
[tex]9x^2+8x-2x^2-3x = (9x^2-2x^2) + (8x-3x) = 7x^2+5x[/tex]
Which description from the list below accurately describes the relationship between
Answer
Congruent by dilation
Step-by-step explanation:
They are not the same size, nor have the same area and are not currently congruent because they are different sizes.
Answer:
D. Congruent after dilation.Step-by-step explanation:
From the figures, you can observe that the triangles don't have the same size or area, that means they cannot be congruent.
However, if we dilate the first triangle by a scale factor of 2, then both triangles will be congruent, because 5 x 2 = 10, 4 x 2 = 8 and 3 x 2 = 6.
Therefore, the right answer is D. Because if you dilate the first triangle, both would be congruent. Also, because they don't have the same area, size, and they aren't congruent.
Sally has 6 red flags, 4 green flags, and 2 white flags. How many 12-flag signals can she run up a flag pole?
[tex]\dfrac{12!}{6!4!2!}=\dfrac{7\cdot8\cdot9\cdot10\cdot11\cdot12}{2\cdot3\cdot4\cdot2}=13860[/tex]
If f (x) = 3(x+5) + 4/x what is f(a+2)?
Answer:
f(a+2)= 3((a+2)+5) +4/(a+2)
Step-by-step explanation:
Since X was exchanged for a+2, you have to set a+2 as x in the problem.
Answer:
[tex]\large\boxed{f(a+2)=3(a+7)+\dfrac{4}{a+2}}[/tex]
Step-by-step explanation:
[tex]f(x)=3(x+5)+\dfrac{4}{x}\\\\f(a+2)-\text{put x = a + 2 to the equation of f(x):}\\\\f(a+2)=3\bigg((a+2)+5\bigg)+\dfrac{4}{a+2}=3(a+2+5)+\dfrac{4}{a+2}\\\\f(a+2)=3(a+7)+\dfrac{4}{a+2}[/tex]
A cylinder has a height of 16cm and a radius of 5cm. A cone has a height of 12cm and a radius of 4cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of ‘pi’.)
Radius of cylinder = 5cm
Radius of cone = 4cm
Answer:
1055.04
Step-by-step explanation:
Cylinder
h = 16 cm
r = 5 cm
Volume = ?
Formula
V=pi * r^2 * h
Solution
V = pi r^2*h
V = 3.14 * 5*5*16
V = 1256 cm^3
Cone
h = 12 cm
r = 4 cm
Formula
V = (1/3) pi r * r * h
Solution
V = (1/3) 3.14 * 4 * 4 * 12
V = (1/3) 602.88
V = 200.96
Answer
Volume of unoccupied region = Cylinder - Cone
Volume of unoccupied region = 1256 - 200.96
Volume of unoccupied region = 1055.04
You will have to round it to the number of digits required.
To convert 10 kilometers to meters, you would use the ratio 1000 meter/1 kilometer
A. True
B. False
Answer:
True
Step-by-step explanation:
Since 1 km is 1000 metres that is the correct ratio to use
1 : 1000
( × 10 to get 10 km )
10 : 10000
Answer:
Step-by-step explanation:
Let's actually do the work:
10 km 1000 m
--------- * --------------- = 10^4 m
1 1 km
Answer: TRUE
Another engineer is tiling a new building. A square tile is cut along one of its diagonals to form two triangles with two congruent angles. What are the measurements of the interior angles of the triangles? Explain how you calculated them.
Answer:
The measurements of the interior angles of the triangles are 45°-90°-45°
Step-by-step explanation:
we know that
A square is a quadrilateral with 4 equal sides and 4 interior angles of 90 degrees
The diagonal of a square bisect the square into two congruent isosceles right triangles
The two congruent legs of each isosceles right triangle is equal to the length side of the square
The measure of the base's angles of each isosceles right triangle is equal to 45 degrees, because the diagonal bisect the right angle of the square
therefore
The measurements of the interior angles of the triangles are 45°-90°-45°
Answer:
Sample Explanation:
Since the triangle shares an angle with the original square, the triangle has a right angle. Since the triangle has two angles that are congruent, the equation for the measures of all three angles is 90 + 2x = 180, and I found that x = 45. The angles in the triangle are 90°, 45°, and 45°.
Step-by-step explanation:
Finding Unknown Angle Measures Assignment
Finding Unknown Measurements
Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of bottles she needs to sell to earn $100.
1.25x + 1.49 = 100
What error did Barbara make in writing the equation?
Answer:
Since she is selling 1.49 per iced tea bottle, and 1.25 per water bottle, and she only consitered how many water bottles she would sell, and not iced tea bottle, the awnser would be: "Barbara's equation did not consider the number of iced tea drinks."
or
the equation did not account for the number of iced tea drinks.
it should be:
let x = number of water drinks.
let y = number of ice tea drinks.
1.25x + 1.49y = 100
If y* 4x+1 were changed to y = 2x + 6, how would the graph of the new line
compare with the first one?
The new line with the equation y = 2x + 6 will be less steep than the original line y = 4x + 1 due to its lower slope, and will start higher on the y-axis with a y-intercept of 6 compared to the original line's y-intercept of 1.
When comparing the graph of the equation y = 4x + 1 with the new graph of the equation y = 2x + 6, there are two main features to consider: slope and y-intercept. For the original line, the slope is 4, meaning that for every one unit increase in x, y increases by 4 units.
The y-intercept, where the line crosses the y-axis, is at (0,1). On the other hand, the new line has a slope of 2, which indicates a less steep incline; for every one unit increase in x, y increases by only 2 units. Additionally, the y-intercept of this new line is at (0,6), which is higher on the y-axis as compared to the original line.
Kali runs 10 laps around a track each day. each lap around the is 400 meters. how many days will it take kali to run a total of 12 kilometers.
Answer:
3 days
Step-by-step explanation:
First multiply 10 by 400 to find how many meters she runs each day.
10*400 = 4,000
1 kilometer = 1,000 meters
Now convert the meters to kilometers
To convert it to kilometers you divide 4,000 by 1,000, which equals 4 kilometers.
So she runs 4 kilometers each day.
Now divide 12 by 4 to find out how many days it will take to run 12 kilometers.
12/4 = 3 days
If f(c)=0, which of the following statements must be true?
___________________________________________
○A. The point (-c, 0) lies on the graph of f(x)
○B. The point (0, c) lies on the graph of f(x)
○C. x-c is a factor of f(x)
○D. x+c divides evenly into f(x)
Answer:
C.
Step-by-step explanation:
If f(c)=0 then (c,0) is on the graph.
In general, if f(a)=b then (a,b) is on the graph.
By factor theorem if f(c)=0 then x-c is a factor.
If x-c is a factor then x-c will divide f(x) evenly. We know this because the remainder will be 0 because we know x-c is a factor of f.
The only choice that I have said in this whole thing that is true is C.
Answer: The correct option is
(C) x-c is a factor of f(x).
Step-by-step explanation: Given that for a function f(x), f(c) = 0.
We are to select the true statement from the given options.
We have the factor theorem as follows :
Factor theorem : If p(a) = 0 for a polynomial function p(x), then (x-a) is a factor of p(x).
According to the given information, we have
f(c) = 0.
Therefore, (x-c) is a factor of f(x).
Thus, (C) is the correct option.
A circle has a central angle measuring 10 radians that intersects an arc of length 33 cm. What is the length of the radius of
the circle? Round your answer to the nearest whole cm. Use 3.14 for
11 cm
15 cm
22 cm
41 cm
Answer:
it 15cm im sure of it tell me if you get it right
Answer:
15 cmStep-by-step explanation:
The central angle for this problem is:
[tex]\frac{7 \pi}{10}rad \approx 2.2 rad[/tex]
To solve this problem, we have to use an expression that relates, central angle, arc length and radius, which is:
[tex]s=\theta r[/tex]
So, we isolate the radius and solve:
[tex]r=\frac{s}{\theta}=\frac{33cm}{2.2rad}=15cm[/tex]
Therefore, the right answer is the second option.
Suppose y varies directly with x. If y = -4 when x = 8, what is the equation of direct variation?
Complete the steps to write the equation of direct variation.
1. Start with the equation of direct variation y = kx.
2. Substitute in the given values for x and y to get
3. Solve fork to get
4. Write the direct variation equation with the value found for k. The equation is
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that }~~ \begin{cases} y=-4\\ x=8 \end{cases}\implies -4=k(8)\implies \cfrac{-4}{8}=k\implies -\cfrac{1}{2}=k \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{1}{2}x~\hfill[/tex]
Answer:
k = -1/2
y= -1/2x
Step-by-step explanation:
y = kx
We know y = -4 and x=8
-4 = k*8
Divide each side by 9
-4/8 = 8k/8
-1/2 =k
y= -1/2x
i need help step by step
0=x²-7x +10
Answer:
x=2 or x=5
Step-by-step explanation:
0−(x^2−7x+10)
=x^2−7x+10−(x^2−7x+10)
−x^2+7x−10=0
(−x+2)(x−5)=0
−x+2=0 or x−5=0
x=2 or x=5
Answer:
x = 2 or x = 5
Step-by-step explanation:
Several ways to do this.. but i'll use completing the square:
x²-7x +10 = 0
x²-7x = -10 (take the x coefficient , divide that by two and then square the result and add it back to both sides)
x² - 7x + ( -7/2 )² = -10 + ( -7/2 )² (simply the left side using the property (a + b)² = a² + 2ab + b² )
[x + (-7/2)]² = -10 + ( -7/2 )²
[x - (7/2)]² = -10 + ( 49/4 )
[x - (7/2)]² = 9/4
x - (7/2) = ±√(9/4)
x - (7/2) = ±(3/2)
x = (7/2) ± (3/2)
x = 2 or x = 5
C-(-8) = 5 + 2C
What is the answer?
Answer:
C=3
Step-by-step explanation:
C-(-8) = 5 + 2C
C+8 = 5+2C
Subtract C from each side
C-C+8 = 5+2C-C
8 = 5+C
Subtract 5 from each side
8-5 = 5-5+C
3 =C
Answer:
The correct answer is C=3.
Step-by-step explanation:
To solve this problem, we should first eliminate the parentheses on the left side of the equation. To do this, we must recognize that there is subtraction of a negative number, which is the same as adding a positive number. This gives us:
C + 8 = 5 + 2C
Next, we should move all of the variable C's to one side of the equation and move all of the constants (the number terms) to the other side. To do this, we should subtract C from both sides of the equation (to cancel out the C on the left side, moving them to the right) and subtract 5 from both sides (to cancel out the 5 on the right side and move all of the constant terms to the left).
C - C + 8 - 5 = 5 - 5 + 2C - C
If we recognize which terms cancel, we get:
8 - 5 = 2C - C
When we combine like terms through subtraction on both sides, we get:
3 = C
Therefore, the answer is that C = 3.
Hope this helps!
Calculate (Round two decimal places for final answer): 650 mL = _______________ oz.
Answer:
6.5
Step-by-step explanation:
For this case we must perform a conversion of milliliters to ounces.
By definition we have to:
1 US liquid ounce equals 29.5735 milliliters. Then, making a rule of three:
1 oz. ---------> 29.5735 milliliters
x -------------------> 650 milliliters
Where "x" represents the number of oz equivalent to 650 mL.
[tex]x = \frac {650 * 1} {29.5735}\\x = 21.9791[/tex]
Thus, 650 mL equals 21.9791 oz.
Answer:
650 mL equals 21.9791 oz.
Plz convert 5/10 into a simplified fraction and a decimal.
Step-by-step explanation:
[tex]\dfrac{5}{10}=\dfrac{5:5}{10:5}=\dfrac{1}{2}\\\\\dfrac{5}{10}=0.5[/tex]
Select the correct answer from each drop-down menu. If u = <-4, 8> and v = <-7, 5>, v − 5u = and ||v − 5u|| ≈ .
Answer:
v-5u = <13,-35>
||v − 5u|| = 37.33
Step-by-step explanation:
If u = <-4, 8> and v = <-7, 5>
a) v-5u
Multiply u with 5 and then subtract from v
v-5u = <-7,5>-5<-4,8)>
v-5u = <-7,5> - <-20,40>
v-5u = <-7+20,5-40>
v-5u = <13,-35>
b) ||v − 5u||
We already have found v-5u=<13,-35>
Now, we will find ||v − 5u|| = [tex]\sqrt{(v)^2+(u)^2}[/tex]
||v − 5u|| = [tex]\sqrt{(13)^2+(-35)^2}[/tex]
||v − 5u|| = [tex]\sqrt{169+1225}[/tex]
||v − 5u|| = [tex]\sqrt{1394}[/tex]
||v − 5u|| = 37.33
By multiplying vector 'u' by the scalar 5 and subtracting it from 'v', we derive the resultant vector <13,-35>. The magnitude of this vector is approximately 37.36 units.
Explanation:The question involves vector operations, specifically the subtraction of a scalar multiple of a vector from another vector. Let's break down the process. First, multiply vector 'u' by the scalar 5, resulting in: 5u = <5*(-4),5*8> = <-20,40>. Next, subtract this new vector from 'v': v - 5u = <-7,5> - <-20,40> = <(-7)-(-20), 5-40> = <13,-35>. That's the result for v-5u.
To find the magnitude of a vector, we use the formula ||v||= sqrt(x^2 + y^2). So ||v - 5u|| = sqrt((13)^2 + (-35)^2) = sqrt(169 + 1225) = sqrt(1394) ≈ 37.36.
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Which phrase best descubes the translation from the graph y = (x - 5)2 + 7 to the graph of y = (x + 1)2 - 2?
6 units left and 9 units down
6 units nght and 9 units down
6 units left and 9 units up
6 units right and 9 units up
Answer:
"6 units left and 9 units down"
Step-by-step explanation:
Suppose a function is given in this form:
[tex]y=(x-a)^2+b[/tex]
This is the parent function y = x^2
translated a units right (left if there was a + before a)translated b units up (down if there was a - before b)Now, to go from [tex]y=(x-5)^2+7[/tex] to [tex]y= (x+1)^2-2[/tex] , we can see that:
first function is 5 units right and 2nd one is 1 unit left, so there is a horizontal translation of 6 units leftfirst function is 7 units above and 2nd one is 2 units down, so there is a vertical translation of 9 units downThus, "6 units left and 9 units down" is the transformation(translation).
RST= XYZ. If RT = 10, XY = 18, and YZ = 12, what is XZ?
Answer:
A. 10
Step-by-step explanation:
RT = XZ
With this being stated, XZ also has to be 10.
I am joyous to assist you anytime.
what is the equation of the following line? (7,2) (0,0)
Let m = slope
m = (0-2)/(0-7)
m = -2/-7
m = 2/7
y - 0 = (2/7)(x - 0)
y = (2/7)x
Did you follow?
The equation of the line for the given coordinates [tex](7,2) , \ (0,0)[/tex] is equal to [tex]y= \frac{2}{7}x[/tex].
What is equation?"Equation is defined as the relation between the variables using the sign of equality."
Formula used
Slope [tex]'m' = \frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]
Equation of line passing through a point
[tex]y- y_{1} = m (x- x_{1})[/tex]
According to the question,
Given coordinates,
[tex](x_{1} ,y_{1}) = (7,2)\\\\(x_{2} ,y_{2}) = (0,0)[/tex]
Substitute the value in the formula to get slope,
[tex]m = \frac{0-2}{0-7}[/tex]
[tex]= \frac{2}{7}[/tex]
Substitute the value in the formula to get equation of the line,
[tex]y-2= \frac{2}{7} (x-7)\\\\\implies y-2 = \frac{2}{7}x -2\\ \\\implies y = \frac{2}{7}x[/tex]
Hence, the equation of the line for the given coordinates [tex](7,2) , \ (0,0)[/tex] is equal to [tex]y= \frac{2}{7}x[/tex].
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Which graph represents a geometric sequence?
Geometric sequence--
The sequence is said to be geometric if each of the term of the sequence is obtained by multiplying the preceding term of the sequence by a fixed constant.
This fixed constant is known as a common ratio and is denoted by r.
i.e. the sequence is given by:
a,ar,ar²,ar³,.....
The graph which represents the geometric sequence is attached to the answer.
Since the table of values are as follows:
x y
1 1
2 2
3 4
4 8
i.e. the sequence 1,2,4,8
form a geometric sequence.
Since the common ratio of the sequence is: 2 with first term as: 1
(first term is: 1
second term is: 1×2=2
Third term is: 2×2=4
and fourth term is: 4×2=8 )
Answer:
It's B. Second Graph.
Step-by-step explanation:
Solve log525 = x 2 1/2 -2
Answer:
x = 1/2
Step-by-step explanation:
The equation in correct format is:
[tex]log_{5}(25)=x[/tex]
We have to solve this logarithmic equation to find the value of x. This can be done by using the rules of logarithm i.e the power rule and same base rule shown below:
[tex]log(a)^{b}=b \times log(a)\\\\log_{a}(a)=1[/tex]
Using these rules on our equation, we get:
[tex]log_{5}(25)=x\\\\log_{5}(5^{\frac{1}{2} })=x\\\\ \frac{1}{2} log_{5}(5)=x\\\\ \frac{1}{2} (1)=x\\\\ x=\frac{1}{2}[/tex]
Thus the value of x would be 1/2
Answer:
x = 2Step-by-step:
Log5 (25)= xWrite in exponential form
Log5 (5^2)= xSimplify the expression
2= xSwap sides
x = 2
Your beginning food inventory was 26,000. You have purchased an additional 24,000 and have accepted 12,000 in transfers from other locations. In total, you sold 39,000 worth of foodfor the same time period. Your ending inventory is 29,000. What is your gross profit margin percentage
?
Answer
130,000
Hope it helps!
The gross profit margin calculates as 15.38% for the given business scenario, calculated with the values provided in the sales, purchases, inventory, and transfers.
Explanation:The subject of this question is gross profit margin in a business, which can be calculated using certain financial figures and simple arithmetic. We start by determining the cost of goods sold (COGS), which includes the beginning inventory, any additional purchases, and transfers from other locations, subtracted by the ending inventory. Using your figures, we get the following calculation: $26,000 (beginning inventory) + $24,000 (purchases) + $12,000 (transfers) - $29,000 (ending inventory) = $33,000 (COGS).
Next, we subtract the cost of goods sold from the total sales to determine the gross profit: $39,000 (total sales) - $33,000 (COGS) = $6,000 (gross profit).
Finally, to find the gross profit margin percentage, we divide the gross profit by total sales, and then multiply by 100, which gives us: $6,000/$39,000 * 100 = 15.38%.So, your gross profit margin percentage is 15.38%.
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5. There are 396 persons in a theater. If the ratio of women to men is 2:3, and the ratio of men to
children is 1:2, how many men are in the theater?
Answer:
The number of men = 108
Step-by-step explanation:
Total person = 396
ratio of women to men = 2:3
ratio of men to children = 1:2=2:4=3:6
Women = 2
Men = 3
Children = 6
Hence,
women+men+children = 2+3+6 = 11
Now finding out the percentage of each
Women = 2/11 * 396
= 792/11
=72
Men = 3/11 * 396
=1188/11
=108
Children = 6/11 *396
=2376/11
=216
Thus the number of men = 108 ....
VW is parallel to YZ in the map below.
Answer:
3/4=x/9
Step-by-step explanation:
I think we use the side slitter theorem for this case so x/9 pair together and 3/4 also.
This mathematics question from a high school student is about geometric relationships in a three-dimensional coordinate system, with details specifically on parallel lines, vector addition, and a Weissenberg diagram relevant to crystallography.
Explanation:The question on which assistance is sought pertains to geometric concepts, specifically those related to parallel lines and coordinates in a plane or space. In this context, VW being parallel to YZ implies that these lines are in the same geometric plane and maintain a constant distance from each other. Given that the z-axis is horizontal, the x-axis points backward, and the y-axis points upward, we are discussing a three-dimensional Cartesian coordinate system.
Understanding the Weissenberg diagram involves knowledge of crystallography and rotation-oscillation methods. The passage also explains that the vector w lies in the y'z' plane indicating that the vector has no x-component, as mentioned by Wx' = 0. When solving problems like these, it's important to follow vector addition rules and define your axis system correctly, as in the statement that defines +x to be eastward and +y to be northward, which is related to navigation and mapping conventions.
Figures from MIT OCW suggest that the concept of 'contour lines' and their relationship to topographical features such as valleys and ridges is also being examined.
20 POINTS! WILL GIVE BRAINLIEST!
Bryce had a $25 gift card to use on songs and games at an online media store. Songs cost $2 each and games cost $5 each. Bryce spent all the money on the gift card to download 8 items. Solve the system to determine how many games he purchased. Let s represent the number of songs and g represent the number of games.
s + g = 8
2s + 5g = 25
Bryce purchased _____ games.
Answer:
Bryce purchased 3 games.
Step-by-step explanation:
To find the number of songs and games that Bryce downloaded, we need to solve the following system of equations:
s + g = 8
2s + 5g = 25
We know that:
s + g = 8 → 2s + 2g = 16 → 2s = 16 -2g
2s + 5g = 25 → 16 - 2g + 5g = 25
→3g = 25 - 16
→3g = 9
→ g = 3
Therefore, bryce downloaded 3 games and 5 songs!
Answer: 3
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Which figure can be transformed into figure P by a translation 2 units to the right followed by a reflection across the x-axis?
Answer:
Figure M
Step-by-step explanation:
Figure P has vertices at points (-2,4), (-2,8), (-6,8) and (-6,6).
Consider figure M with vertices (-4,-4), (-4,-8), (-8,-8) and (-8,-6).
1. Translate figure M 2 units to the right. This translation has the rule:
(x,y)→(x+2,y),
so
(-4,-4)→(-2,-4);(-4,-8)→(-2,-8);(-8,-8)→(-6,-8);(-8,-6)→(-6,-6).2. Reflect the translation image figure M across the x-axis according to the rule
(x,y)→(x,-y)
Thus,
(-2,-4)→(-2,4);(-2,-8)→(-2,8);(-6,-8)→(-6,8);(-6,-6)→(-6,6).