The triangle mid-segments will be the two opposite or adjacent sides of a triangle.
What is the triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angle of triangle = 180
A line connecting the midpoints of two of a triangle's sides is known as the midsegment. There are always three midsegments in a triangle. The midsegment between any two sides of a triangle is parallel to and half the length of the third side, according to the Triangle Midsegment Theorem, often known as the midsegment theorem.
A midsegment of a triangle is a line segment that joins the midpoints or center of two opposite or adjacent sides of a triangle.
Hence The triangle mid-segments will be the two opposite or adjacent sides of a triangle.
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Complete question:
Define the triangle mid segments.
A small fair charges different admission for adults and children; it charges $2.75 for adults, and $0.25 for children.
On a certain day, the total revenue is $6,962.50 and the fair admits 4900 people.
How many
adults and children were admitted?
Answer: Let's call the number of adults admitted "A" and the number of children admitted "C". We know that:
A + C = 4900 (total number of people admitted)
And the total revenue is:
2.75A + 0.25C = $6,962.50
We can use the first equation to solve for one of the variables in terms of the other:
C = 4900 - A
Substitute this expression for C into the second equation:
2.75A + 0.25(4900 - A) = $6,962.50
Expand and simplify the right side:
2.75A + 1225 - 0.25A = $6,962.50
2.5A = 5737.5
Solve for A:
A = 2298
So there were 2298 adults and 4900 - 2298 = 2602 children admitted.
Step-by-step explanation:
A medical study is conducted to determine which migraine treatment, A or B, provides faster relief. The study uses 10 volunteers who claim to suffer from migraines. Half of the volunteers are randomly assigned to use treatment A when they experience their first migraine. The other half are assigned to use treatment B. Then, after no treatment for one month, the treatments are reversed. The volunteers each record the amount of time it takes, in minutes, to experience relief from their migraine under each treatment. The data are displayed in the table. A 3-column table with 10 rows. Column 1 is labeled volunteer with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Column 2 is labeled Treatment A with entries 10, 13, 13, 9, 13, 12, 14, 10, 8, 7. Column 3 is labeled Treatment B with entries 19, 18, 19, 15, 20, 16, 16, 16, 13, 17. What is the mean difference (A – B) and the standard deviation of the differences?
I think that it could be b but I'm not 100 percent sure
After two weeks on a diet Raymond weighed 180 pounds, which was 90% of his original weight. What was Raymond’s original weight?
Answer:
Step-by-step explanation:
Explain how you can use a table or graph to find the y-intercept.
The y-intercept is calculated using a table or a graph by substituting x = 0.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The y-intercept value is calculated when the x-coordinate is zero.
Now,
Example:
(0, 3), (0. 5), (0, 7) are all y-intercepts of the graph.
Thus,
The y-intercept is calculated when x = 0.
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Lexi MUST spend $100 and get 100 animals. $15 for 1 dog, $1 for 1 cat, and 25 cents for each mice.
thank you to whoever helps <33
A manufacturer can produce printer paper at a cost of $2 per ream. The paper has been
selling for $5 per ream, and at that price, consumers have been buying 4,000 reams a month.
The manufacturer is planning to raise the price of the paper and estimates that for each $1
increase in the price, 400 fewer reams will be sold each month. Express the manufacturer’s
monthly profit as a function of the price at which the reams are sold.
Answer:
Let x be the price per ream in dollars. Then, the manufacturer's profit per ream sold is (x - $2).
The manufacturer estimates that for each $1 increase in the price, 400 fewer reams will be sold each month. Thus, the number of reams sold can be expressed as 4000 - 400(x - $5) reams per month.
The manufacturer's total monthly profit is given by the product of the number of reams sold and the profit per ream, so it can be expressed as:
P(x) = (4000 - 400(x - $5)) * (x - $2)
So the monthly profit as a function of the price per ream is:
P(x) = 4000x - 8000 - 400x^2 + 2000x + 8000
This is a quadratic equation and its maximum value can be found using techniques from algebra or calculus.
Step-by-step explanation:
ABOVE
3 over 5 meters =. centimeters
Answer:
60
Step-by-step explanation:
3/5 = 0.6 meters = 60 cm
What is the range of the function shown on the graph above?
From the graph the range of the function is obtained as option 1: -5 ≤ y ≤ 8.
What is the range of data?
The range of data is defined as a measure of the difference between the maximum value of data and the minimum value of data.
From the graph, the following observations are made -
The endpoints of the graph have closed circles this means that, the endpoints are inclusive of the range.
For closed circles the inequality symbols used is (≤,≥).
The y-axis values suggests the range of the function.
The minimum y-axis value in the fourth quadrant is -5.
The maximum y-axis value in the first quadrant is 8.
The range of the function is [-5 , 8]
Therefore, the range is found to be -5 ≤ y ≤ 8.
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Q9 PLEASE HELP ASAP I ONLY HAVE 5 MIN
Answer: y=5x+2
Step-by-step explanation: I answered this question already, I believe.
The solution is in the attachment!!
If f(x) = x² + 3x - 5, find the value of f(3).
Hey there!
[tex]\huge\textbf{Assuming:}[/tex]
[tex]\mathsf{f(x) = x^2 + 3x - 5}[/tex]
[tex]\mathsf{f(x) = 3^2 + 3(3) - 5}[/tex]
[tex]\mathsf{f(x) = 3 \times 3 + 9 - 5}[/tex]
[tex]\mathsf{f(x) = 9 + 9 - 5}[/tex]
[tex]\mathsf{f(x) = 18 - 5}[/tex]
[tex]\mathsf{f(x) = 13}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\mathsf{f(x) = 13}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Info on the graph with needing the slopes:
PLEASE HELP I REALLY AM STRUGGLING WITH THIS
I added photos of both graphs to be looked at
Using this formula, the tax on 9701 will be 970 + 0.12(9701 − 9700) = 970 + 0.12(1) = $. . This means that your tax only goes up 12 cents instead of almost $200. The graphs show these two scenarios. The correct scenario is shown on Graph 1. The incorrect scenario is shown on Graph 2.
What is the slope of the first piece of the tax function? (Graph 1)
I got y=1x+0 but I don't know if I am correct.
What is the slope of the second piece of the tax function? (Graph 2)
What do these slopes tell us??
The slope for the first piece of the tax function is given as follows:
0.1.
The slope for the second piece of the tax function is given as follows:
0.2.
It tells that for smaller salaries, the tax rate is of 10%, while for salaries on a second range, the tax rate is of 20%.
How to obtain the slope of a linear function?The slope of a linear function represents the rate of change of the output variable relative to the input variable.
For the first piece, when x increases by 5000, the output increases by 500, hence the slope m is given as follows:
m = 500/5000
m = 0.1.
For the second piece, when x increases by 5000, the output increases by 1000, hence the slope m is given as follows:
m = 1000/5000
m = 0.2.
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Draw 2 isosceles triangles ABC and DEF where AC=BC and DF=EF
The conclusions reached in steps 4 and 5 are invalid. This is a flawed argument for the existence of isosceles triangles.
An isosceles triangle contains what?An isosceles triangle has two equal sides and two equal angles as a result. The term comes from the Greek words iso (same) and skelos (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.
Each step is valid, but the conclusion is not. At the end of step 4,
here are a series of isometric maps that lead A to D and C to F, as claimed..
After the final rotation in Step 5, the sequence of isometries takes B to E and C to F —but here’s the hitch—there is no reason why it should still take A to D, in fact it can’t take A to D unless the rotation angle is zero.
If the rotation angle in Step 5 is zero, then the isometries take [A,B,C] to [D,E,F] and the two triangles are indeed similar
But this requires the dilation in Step 2 to have made A′B′ congruent to DE , in other words, it requires assuming the triangles are similar before performing any of of the transformations.
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Question:
This is an invalid proof that all isosceles triangles are similar. Explain which step is invalid and why. 1. Draw 2 isosceles triangles ABC and DEF where AC = BC and DF = EF. 2. Dilate triangle ABC to a new triangle A'B'C' using center C and scale factor DF/AC so that A'C= BC - DF = EF. 3. Translate by directed line segment CF to take A'B'C' to a new triangle A" B" F. Since translation preserves distance, A"F = A'C=DF and B" F = BC = EF. 4. Since A"F=DF, we can rotate using center F to take A" to D. 5. Since B" F = EF, we can rotate using center F to take B" to E. 6. We have now established a sequence of dilations, translations, and rotations that takes A to D, B to E, and C to F, so the triangles are similar.
Please solve for in this equation
Answer:
x = 4 rounded to the nearest whole number (actually 4.0801)
Step-by-step explanation:
The triangle formed by the sides of length 0.9x, 2.8x and 12 form a right triangle with the side of length 12 as they hypotenuse
By the Pythagorean theorem
c² = a² + b² where c = hypotenuse, a and b being the other two sides
Plugging in values we get
12² = (0.9x)² + (2.8x)²
144 = 0.81x² + 7.84x² = 8.65x²
Switching sides:
8.65x²= 144
x² = 144/8.65 = 16.6473
x = √16.6473= 4.0801
Rounded to the nearest integer, x = 4
Which of the following situations represent direct variation?
y = -5x
2y = x
y/x = 12
x/y = 4
All the equations are direct variation equations
How to determine the equations of direct variationA relationship between two variables is said to be a direct variation if one of the variables is proportional to the other, meaning that their ratio is always constant.
Using the above as a guide, we have the following:
y = -5x:
Direct variation
Constant of variation = -5
2y = x
Direct variation
Constant of variation = 1/2
y/x = 12
Direct variation
Constant of variation = 12
x/y = 4
Direct variation
Constant of variation = 1/4
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HELPP WITH ALL 4 OF THESE ? PLEASE!! each is worth 10 points!!
Answer: 1.+900
2. -24
3. -5
4. +10
Step-by-step explanation:
Three girls download a total of 36 songs on their iPods. Jane downloaded twice as many as Inez and since Tracy wanted to have the most, she downloaded one more than Jane did. How many songs did each girl download
Answer:
they each download 36 songs
Find the perimeter of the figure.
Answer:
30
Step-by-step explanation:
Add all the sides and you get 30.
Hope this helps! Pls give brainliest!
Answer:
30
Step-by-step explanation:
6+9.5+6.5+4+4 = 30
Apply
14. The table shows the record high temperature, in degrees
Fahrenheit (°F) or degrees Celsius (°C), of certain states. The
formula F = 1.8C + 32 can be used to convert between degrees
Celsius and degrees Fahrenheit. What is the difference, in
degrees Celsius, between Nevada's record high temperature
and Alaska's record high temperature? Round to the nearest
tenth.
State
Alaska
Florida
Nevada
Texas
Record High
Temperature
38°C
109°F
125°F
49°C
Nolan shoveled driveways over the weekend. He made a total of $82. If he earned the same amount of money on both days, how much money did he make on Saturday alone?
Answer: $41
Step-by-step explanation: $82 all total. 2 days. 82/2=41. He made $41 on Saturday
Demarco and Tanya have received information about three separate mortgage offers. In two or three paragraphs, describe your recommendation for the best financial choice in their situation. Evaluate each of the three offers, compare and contrast their effectiveness, and explain the offer that works best. As you explain your answer, support it using reasons and evidence from the calculations you made based on the information provided in this guide for Analyzing Mortgage Options. pls try to be original
Best Mortgage Option 3 because this mortgage option offers a lower interest rate.
Why Option 3 was recommendedAfter reviewing all three mortgage options available to Demarco and Tanya, I would recommend that they choose option 3. This option offers a lower interest rate compared to the other two options and a longer loan term, which means that their monthly payments will be lower and more manageable for their budget. Additionally, option 3 offers a fixed interest rate, which provides them with more stability and predictability in their mortgage payments, as opposed to options 1 and 2 that offer adjustable interest rates.
Option 1 has the highest interest rate and the shortest loan term, making their monthly payments the highest of all three options. Option 2 offers a slightly lower interest rate, but it still higher compared to option 3, and has a shorter loan term compared to option 3, making their monthly payments still relatively high.
In conclusion, the best financial choice for Demarco and Tanya would be option 3. Its lower interest rate, longer loan term, and fixed interest rate make it the most affordable and stable option for them in the long run.
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If a figure is dilated by a factor of 3, the sides of the pre-image will be _ of the image's sides.
A. one-ninth the size
B. one-third the size
C. nine times the size
D. three times the size
A volleyball is bumped straight up, from 3 m above the ground, with a velocity of 14 meters per second. When does the ball hit the ground?
The equation for the balls height (in meters) is h=-5t^2+14t+3 where t is time in seconds.
(Please let me know if I did it wrong, and explain please)
The function table representing the numerical values is given below.
What is a function?An function in mathematics defines a relationship between one variable (the independent variable, x) and another variable (the dependent variable, y). Example -
y = f{x} = ax + b
Given is a function as -
h = -5t² + 14t + 3
We can write the complete table as -
time {sec} height {m}
-2 - 5 x 4 + 14 x - 2 + 3 = - 45
-1 - 5 x 1 + 14 x - 1 + 3 = - 16
-0 - 5 x 0 + 14 x 0 + 3 = 3
1 - 5 x 1 + 14 x 1 + 3 = 12
2 - 5 x 4 + 14 x 2 + 3 = 11
3 - 5 x 9 + 14 x 3 + 3 = 0
4 - 5 x 16 + 14 x 4 + 3 = - 21
-5 - 5 x 25 + 14 x 5 + 3 = - 52
Therefore, the function table representing the numerical values is given above.
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Divide. (54t2−81t)÷(9t)
Answer:
The answer is 6t-9. This can be calculated by dividing the numerator (54t2−81t) by the denominator (9t). This gives 6t-9.
Step-by-step explanation:
Answer:
81t2+16
Step-by-step explanation:
(9t-4)(-9t-4) : Equation
Distribute parentheses using:(a + b)(c + d) = ac + ad + bc + bd.
Where : a=9t, b=-4, c=-9t, d=-4.
This leads to 9t(-9t) +9t (-4) -4- (9t) -4 (-4).
Now we have to Apply minus-plus rule.
Where: -(-a)=a.+(-a)=-a
-9t.9t - 9t.4 + 4.9t = 4.4
=81t2+16
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When you arrive at the family reunion, Uncle Ignacio has already eaten 9 mini hot dogs. He continues to eat them at a rate of 4 hot dogs per minute. y = 4x + 9 models this situation. Make a graph of this situation.
Answer:
Step-by-step explanation:
y=mx + b where b= y intercept(when x=0) and m= slope(rise/run)
so there is a slope of 4 and a y intercept of 9
so starting from 9, you go up 4, and to the right 1. and that just repeats till you're satisfied.
Laura is the fund raising manager for a local charity she is ordering caps for an upcoming charity walk. The company that makes the caps chargers $6 per cap plus a $25 shipping fee . Laura had buaght of $1000 WhT is the greatest number of caps she can buy?
the maximum number of caps she can order is 162.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, Laura is the fundraising manager for a local charity she is ordering caps for an upcoming charity walk.
Let "x" be the number of caps she ordered.
Since, manufacturing cost for a cap = $6
shipping charges for the lot = $25
Thus,
Total price she paid for x caps = 6*x + 25
Since she had only 1000$
So,
6x + 25 ≤ 1000
6x ≤ 975
x ≤ 975/6
x ≤ 162.5
therefore, the maximum number of caps she can order is 162.
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Given a2 = 6 and a5 = –384 of a geometric sequence, what is the recursive equation for the nth term?
an = –4(an – 1), a1 = –1.5
an = –4(an – 1), a1 = 1.5
an = 4(an – 1), a1 = –1.5
an = 4(an – 1), a1 = 1.5
Answer:
[tex]a_n = (-4)^{n - 1}; a_1 = -1.5[/tex]
Step-by-step explanation:
[tex] a_1 = a_1 [/tex]
[tex] a_2 = a_1 \times r [/tex]
[tex] a_3 = a_1 \times r^2 [/tex]
[tex] a_4 = a_1 \times r^3 [/tex]
[tex] a_5 = a_1 \times r^4 [/tex]
[tex] a_1 \times r = 6 [/tex]
[tex] a_1 \times r^4 = -384 [/tex]
[tex] r = \dfrac{6}{a_1} [/tex]
[tex] a_1 \times (\dfrac{6}{a_1})^4 = -384 [/tex]
[tex] r = \dfrac{6}{a_1} [/tex]
[tex] \dfrac{1296}{a_1}^3} = -384 [/tex]
[tex] r = \dfrac{6}{a_1} [/tex]
[tex] \dfrac{1}{a_1}^3} = -\dfrac{384}{1296} [/tex]
[tex] r = \dfrac{6}{a_1} [/tex]
[tex] a_1^3 = -\dfrac{27}{8} [/tex]
[tex] r = \dfrac{6}{a_1} [/tex]
[tex] a_1 = -1.5 [/tex]
[tex] r = \dfrac{6}{-1.5} [/tex]
[tex] a_1 = -1.5 [/tex]
[tex] r = -4 [/tex]
[tex] a_1 = -1.5 [/tex]
[tex]a_n = (-4)^{n - 1}; a_1 = -1.5[/tex]
According to this diagram, what is sin 28°?
28°
OA. 17
15
OB.
B. 15
8
O C. 17
D. 15
OE
F.
8
15
8
17-
15
62°
90°
00
8
Answer:
sin 28 = 8 /17
Step-by-step explanation:
Since this is a right triangle, we can use trig functions.
sin theta = opp side / hypotenuse
sin 28 = 8 /17
U= (1,2,3,4,5,6,7,8,9)
A=(1,2,5,6)
B=(2,3,4,6,7)
C=(5,6,7,8
Find (B’ n A) u c
Answer:
[tex](B'\cap A)\cup C=\{1,5,6,7,8\}[/tex]
Step-by-step explanation:
[tex]B'=\{1,5,8,9\}[/tex]
[tex](B'\cap A)=\{1,5\}[/tex]
[tex](B'\cap A)\cup C=\{1,5,6,7,8\}[/tex]
The complement of a set, notated with a prime symbol ('), are all other elements that are not in that set.
The intersection of two sets, notated by [tex]\cap[/tex], are just the elements that are contained in both sets.
The union of two sets, notated by [tex]\cup[/tex], are all the elements that are contained in both sets (any duplicates are not included).
Mario has 5 gallons of paint. He uses 1/4 gallon to paint a door. He uses 3/8 gallon to paint a wall. How much paint does Mario have left?
3) Decide if each of the following statements are true or false. If true, give a mathematical explanation. If false, give a counterexample.
a) If a quadrilateral is a square, then it is a rectangle.
b) If a quadrilateral has a pair of parallel sides, then it must have a pair of opposite
sides that are congruent.
c) If the diagonals of a quadrilateral are perpendicular to each other, then the
quadrilateral is a rhombus.
d) If a quadrilateral has one right angle, then all of its angles must be right angles.
e) Write the converse of each of the statements in a)–d) above. Which is true?
f) Write the contrapositive of each of the statements in a)-d) above. Which is true?
The required statements are true or false, are below in the solution part.
What is a square?A square is defined as a polygon that has four sides and is a closed, two-dimensional (2D) object. A square has equal and parallel sides on all four sides.
a) True. If a quadrilateral is a square, then it has four equal sides and four right angles. By definition, a rectangle also has four right angles, so a square is also a rectangle.
b) False. A counterexample is a parallelogram, which has a pair of parallel sides but does not have a pair of opposite sides that are congruent.
c) False. A counterexample is a rectangle, which has perpendicular diagonals but is not a rhombus, which is defined as a quadrilateral with four equal sides.
d) False. A counterexample is an isosceles trapezoid, which has one right angle but not all angles are right angles.
e) Converse of a) - If a quadrilateral is a rectangle, then it is a square. This is false, as there are rectangles that are not squares.
The converse of b) - If a quadrilateral has a pair of opposite sides that are congruent, then it must have a pair of parallel sides. This is true.
The converse of c) - If a quadrilateral is a rhombus, then its diagonals are perpendicular to each other. This is true.
The converse of d) - If all angles of a quadrilateral are right angles, then it has one right angle. This is false, as a square has four right angles but only one of them can be considered "one right angle".
f) Contrapositive of a) - If a quadrilateral is not a square, then it is not a rectangle. This is true.
The contrapositive of b) - If a quadrilateral does not have a pair of parallel sides, then it does not have a pair of opposite sides that are congruent. This is true.
The contrapositive of c) - If a quadrilateral's diagonals are not perpendicular to each other, then it is not a rhombus. This is true.
The contrapositive of d) - If a quadrilateral does not have one right angle, then all of its angles must not be right angles. This is true.
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