Theorem is a statement that can be proved or that is proven to be true.
Option A is a theorem because it is proven that the area of two congruent figures are equal.
Option B is a theorem because the area of a square is the square of the length of its side.
[tex]\begin{gathered} A_{square}=l\times l \\ A_{square}=l^2 \end{gathered}[/tex]Option C is a theorem because the area of a rectangle is the product of its base and height.
[tex]\begin{gathered} A_{rec\tan gle}=b\times h \\ A_{rec\tan gle}=bh \end{gathered}[/tex]Thus, A, B and C are CORRECT
Kamal drew a scale drawing of a theater. He used the scale 6 inches = 10 feet. What scale factor does the drawing use?Simplify your answer and write it as a ratio, using a colon.
Given:
Kamal drew a scale drawing of a theater.
He used the scale 6 inches = 10 feet.
The scale factor will take the form:
[tex]inches\colon feet=x\colon y[/tex]Where (x) is the number of inches that corresponding to the number of feet (y)
So, x = 6, y = 10
So, the scale factor =
[tex]inches\colon feet=6\colon10[/tex]Simplifying the ratio, so the answer will be:
[tex]inches\colon feet=3\colon5[/tex]Which of the following is the graph of y = |3+x|?
3. Given AB with coordinates A(-4,5) and B(12,13). Find the horizontal distance and the vertical
distance from A to B, stated in that order.
The required distance would be 17.88 units coordinates A(-4,5) and B(12,13) and the horizontal distance is 16 units and the vertical distance is 8 units from A to B which are determined by the graphing method.
What is the distance between two points?The distance between two points is defined as the length of the line segment between two places representing their distance.
Given AB with coordinates A(-4,5) and B(12,13).
The formula of the distance between two points is A(x₁, y₁) and B(x₂, y₂) is given by: d (A, B) = √ (x₂ – x₁)² + (y₂ – y₁) ².
x₁ = -4, y₁ = 5
x₂ = 12, y₂ = 13
distance = √ (12 – (-4))² + (13 – 5)²
distance = √ (12 + 4)² + (8)²
distance = √ (16)² + (8)²
distance = √ (256 + 64)
distance = √320
distance = 17.88 units
The horizontal distance is 16 units and the vertical distance is 8 units from A to B which are determined by the graphing method.
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It takes 6 slices of bread, 9 oz of cheese, and 2 oz of butter tomake three grilled-cheese sandwiches. What is the cost per sandwichif bread (18 slices) costs $1.90, 1 lb of cheese costs $2.49, and1/2 lb of butter costs $1.29?a. $.78b. $4.87c. $2.12d. $1.62
Step 1: Write the equivalence of each unit
[tex]\begin{gathered} 1lb\Rightarrow16\text{ oz} \\ 1\text{ lb of cheese }\Rightarrow\text{ 16 oz of che}ese \\ \frac{1}{2}\text{ lb of butter }\Rightarrow\text{ 8 oz of butter} \end{gathered}[/tex]Step 2: Calculate the cost of producing 3 grilled-cheese sandwiches
[tex]\begin{gathered} 18\text{ slices of bread cost \$1.90} \\ 1\text{ slice will cost x} \\ \Rightarrow x=\frac{1.90}{18} \\ 6\text{ slices of bread will cost=}\frac{1.90}{18}\times6=\text{ \$0.63} \end{gathered}[/tex][tex]\begin{gathered} 1\text{ lb of cheese cost \$2.49 } \\ \text{ Since 1 lb is equal to 16 oz} \\ 16\text{ oz of cheese cost \$2.49} \\ 1\text{ oz of cheese will cost \$x} \\ \Rightarrow\text{ \$x=}\frac{2.49}{16}\text{ } \\ 9\text{ oz will cost }\Rightarrow\text{ }\frac{2.49}{16}\times9=\text{ \$1.40} \end{gathered}[/tex][tex]\begin{gathered} \frac{1}{2}\text{ lb of butter cost \$1.29} \\ \text{ This implies } \\ 8\text{ oz of butter will cost \$1.29} \\ 1\text{ oz of butter will cost \$x} \\ \Rightarrow\text{ \$x =}\frac{1.29}{8} \\ 2\text{ oz will then cost =}\frac{1.29}{8}\times2=\text{ \$0.32} \\ \end{gathered}[/tex]From the above calculations we can calculate the cost of producing three grilled-cheese sandwiches as
[tex]0.63+1.40+0.32=\text{ \$2.35}[/tex]Thus, the cost per sandwich is given as
[tex]\frac{2.35}{3}=\text{ \$0.78}[/tex]Hence, the cost per sandwich is $0.78
Option A is the right answer
In right triangle ABC, C is the right angle. Which of the following is cos B if sin A = 0.4
Answer:
Given that,
In right triangle ABC, C is the right angle.
sin A=0.4
To find cos B,
we get the triangle as,
we know that,
Hypotenuse of the triangle is AB
For the angle A, opposite side is CB
For the angle B, adjacent side is CB
From the definition of sine and cosine we get,
[tex]\sin A=\frac{CB}{AB}[/tex]Also,
[tex]\cos B=\frac{CB}{AB}[/tex]Comparing both we get,
[tex]\sin A=\cos B[/tex]It is given that sinA=0.4
Hence we get, cosB=0.4
Answer is: 0.4
when Ibuprofen is given for fever to children 6 months of age up to 2 years, the usual dose is 5 milligrams (m) per kilogram (kg)of body weight when the fever is under 102.5 degrees Fahrenheit how much medicine would be usual dose for a 18 month old weighing 20 poundsRound your answer to the nearest milligram
dose: 5 milligrams (m) per kilogram (kg)
1 pound= 0.5kg
20 pounds= 10kg
[tex]5\text{ m/kg }\cdot10\operatorname{kg}=50m[/tex]the usual dose for a 18 month old weighing 20 pounds is 50 miligrams
If an absolute value expression is greater than a negative number, there is no solution. O True O False
Absolute value inequalities are defined by the following properties:
[tex]\begin{gathered} |x|a\rightarrow x<-b,or,x>b \end{gathered}[/tex]Notice that when the absolute value expression is greater than real numbers, the solution is defined.
Therefore, the given statement is false because there's a solution in such a case.I need help please!!! I need the answer please!!
Right and solve any quality which can be used to determine v , The number of visits Nolan can make to his first free movie ticket.
Answer:
20 + 2.5v ≥ 40
v ≥ 8
Step-by-step explanation:
Nolan receives:
- fixed value: 20
- vari
how to solve a given fraction by multiplying the denominators, not by factoring
In the picture there is a problem which is incomplete. There are two terms with the numerator and denominator. The fraction is [tex]\frac{a-b}{2a^{2}-ab-3b^{2} } -\frac{a+b}{2a^{2}-5ab+3b^{2}}=0[/tex]
Given that,
In the picture there is a problem which is incomplete.
We have to complete the fractions by solving.
There are two terms with the numerator and denominator.
There are only variable not numbers.
We have,
=[tex]\frac{a-b}{2a^{2}-ab-3b^{2} } -\frac{a+b}{2a^{2}-5ab+3b^{2}}[/tex]
We have to take an LCM.
[tex]\frac{(a-b)(2a^{2}-ab-3b^{2})- (a+b)(2a^{2}-5ab+3b^{2})}{(2a^{2}-ab-3b^{2})(2a^{2}-5ab+3b^{2})}[/tex]
Now,
Just take the numerator term and solve it
[tex](a-b)(2a^{2}-ab-3b^{2})- (a+b)(2a^{2}-5ab+3b^{2})[/tex]
Separate each term with multiplication
a(2a²-ab-3b²)-b(2a²-ab-3b²)-a(2a²-5ab+3b²)-b(2a²-5ab+3b²)
Multiply the terms
2a³-a²b-3ab²-2a²b+ab²+3b³-2a³+5a²b-3ab²-2a²b+5ab²-3b³
Arrange the terms to get calculation easy
2a³-2a³-a²b-2a²b+5a²b-2a²b-3ab²+ab²-3ab²+5ab²+3b³-3b³
Subtract the terms
2a³-2a³=0
-a²b-2a²b+5a²b-2a²b=-5a²b+5a²b=0
-3ab²+ab²-3ab²+5ab²=-6ab²+6ab²=0
3b³-3b³=0
Now, We get the numerator as 0.
So, If numerator is 0 then the whole term is 0.
Because, any term divides by 0 is 0.
Therefore, The fraction is [tex]\frac{a-b}{2a^{2}-ab-3b^{2} } -\frac{a+b}{2a^{2}-5ab+3b^{2}}=0[/tex]
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Solve the following for 'x'x+1+3 2= xO A. -1O B. 3O c. 3OD. 1
Step 1: "braking" fractions
[tex]\begin{gathered} \frac{x}{3}+\frac{x+1}{2}=x \\ \frac{x+1}{2}=\frac{x}{2}+\frac{1}{2} \end{gathered}[/tex]We replace the second in the original equation:
[tex]\frac{x}{3}+\frac{x}{2}+\frac{1}{2}=x[/tex]Step 2: rearraging the equation (the terms with x on one side, numbers on the other)
[tex]\begin{gathered} \frac{x}{3}+\frac{x}{2}+\frac{1}{2}=x \\ \frac{x}{3}+\frac{x}{2}=x-\frac{1}{2} \\ \frac{x}{3}+\frac{x}{2}-x=-\frac{1}{2} \end{gathered}[/tex]Step 3: adding fractions
Since
[tex]\begin{gathered} \frac{1}{3}+\frac{1}{2}-1=\frac{1}{3}+\frac{1}{2}-\frac{1}{1} \\ =(\frac{1}{3}+\frac{1}{2})-\frac{1}{1} \\ \end{gathered}[/tex]We know that
[tex]\begin{gathered} (\frac{1}{3}+\frac{1}{2})=\frac{1\cdot2+1\cdot3}{3\cdot2} \\ =\frac{2+3}{6} \\ =\frac{5}{6} \end{gathered}[/tex]Replacing it:
[tex]\begin{gathered} (\frac{1}{3}+\frac{1}{2})-\frac{1}{1}=\frac{5}{6}-\frac{1}{1} \\ =\frac{5\cdot1-6\cdot1}{6\cdot1} \\ =\frac{5-6}{6} \\ =-\frac{1}{6} \end{gathered}[/tex]Then
[tex]\begin{gathered} \frac{x}{3}+\frac{x}{2}-x=-\frac{1}{2} \\ -\frac{1}{6}x=-\frac{1}{2} \end{gathered}[/tex]Step 4: finding x
[tex]\begin{gathered} -\frac{1}{6}x=-\frac{1}{2} \\ \frac{1}{6}x=\frac{1}{2} \\ 6\cdot\frac{1}{6}x=6\cdot\frac{1}{2} \\ x=3 \end{gathered}[/tex]Answer: C.x=3help help help pleaseeeee!!!!!!
a) The linear equation that models the price-sales relationship for toy is C(x) = -500x +5500
b) The forecast calls for 2250 sales at a $6.50 pricing.
Define slope.The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.
A line's equation is represented by:
y = mx +b
, where
The slope, or m, represents the rate of change.
The value of y at x = 0 is represented by the y-intercept or b.
Item a:
In this issue:
Two points are (6, 2500) and (8, 1500).
The slope is calculated by dividing the change in y by the change in x, so:
m = [tex]\frac{1500-2500}{8-6}[/tex]
m = [tex]\frac{-1000}{2}[/tex]
m = -500
Thus,
y = -500x +b
Point (6,2500) indicates that, which we utilize to find b, is true when.
y = -500x +b
2500 = -500(6) + b
b = 5500
Thus
y = -500x + 5500
Item b:
When x = 6.5, sales are y, so:
y = -500(6.5) + 5500
y = 2250
The forecast calls for 2250 sales at a $6.50 pricing.
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The general equation of a horizontal line is?
Solution
Explanation:
The equation of a horizontal line passing through a point (a, b) is y = b, where 'b' is constant because in the equation y = mx + b, where 'b' is the y-intercept, there is no change in the value of y on the horizontal line and the slope is zero, therefore, the equation of a horizontal line is y = b.
Answer:
The general equation of a horizontal line is y = b where b is constant.
The volume of this triangular prism is 20,580 cubic millimeters. What is the value of p?
We have that the formula of the volume of the triangular prism is:
[tex]V=A\cdot h[/tex]Where A is the area of the base and h is the height. Then we can write the volume like this:
[tex]\begin{gathered} A=\frac{p\cdot b}{2} \\ \Rightarrow V=(\frac{p\cdot b}{2})\cdot h=\frac{p\cdot b\cdot h}{2} \end{gathered}[/tex]now, if b=20, h=42 and V=20580, then we substitute and solve for p:
[tex]\begin{gathered} V=\frac{p\cdot b\cdot h}{2} \\ \Rightarrow20580=\frac{p\cdot20\cdot42}{2}=420\cdot p \\ \Rightarrow p=\frac{20580}{420}=49 \\ p=49 \end{gathered}[/tex]therefore, the value of p is 49 milimeters
Graph the exponential function.G(x)=(1/3)^xPlot five point on the graph of the function.
Graph the function:
[tex]G(x)=(\frac{1}{3})^x[/tex]We'll use the following values of x: {-2, -1, 0, 1, 2}.
Substituting:
[tex]G(-2)=(\frac{1}{3})^{-2}=3^2=9[/tex][tex]G(-1)=(\frac{1}{3})^{-1}=3^1=3[/tex][tex]G(0)=(\frac{1}{3})^0=1[/tex][tex]G(1)=(\frac{1}{3})^1=0.333[/tex][tex]G(2)=(\frac{1}{3})^2=0.111[/tex]The graph of the function is shown below:
Please help I don't understand how to do this. I am stuck
For this exercise, you will demonstrate the tests to show that y=x^19-8x^7+7x^4 is neither an even function nor an odd function.
A) When you apply the test for evenness and simplify the resulting equation, you get
y=
B) When you apply the test for oddness and simplify the resulting equation, you get
y=
The given equation is proved that y=x¹⁹-8x⁷+7x⁴ is neither an even nor an odd function.
Given the equation is y=x¹⁹-8x⁷+7x⁴
Replace x and -x and check to see if the resultant equation matches the
original equation to see whether the function is even
Write the original equation into a function first by swapping y for f(x).
f(x) = x¹⁹-8x⁷+7x⁴
now, replace x with -x
f(-x) = (-x)¹⁹-8(-x)⁷+7(-x)⁴
f(-x) = -x¹⁹+8x⁷+7x⁴
now check whether f(x) = f(-x)
since f(x)≠f(-x), the function is not even.
If you want to determine whether a function is odd, you should check to see if f(-x) = -f (x). The function is odd if the two equations are the same.
-f(x) = -(x¹⁹-8x⁷+7x⁴)
-f(x) = -x¹⁹+8x⁷-7x⁴
now check whether f(-x) = -f(x)
since f(-x)≠-f(x), the function is not odd.
hence the equation is neither an even nor an odd function.
Therefore, the equation is proved that it is neither even nor odd.
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mrs. Baker phone 25 shells on the beach she brought 2/5 of the shells to our classroom how many shells did she bring to her classroom
Given that Mrs. Baker phone 25 shells on the beach, and the brought 2/5 of the shells to class.
[tex]\begin{gathered} \text{total T = 25} \\ \text{fraction brought to class }f(C)=\frac{2}{5} \end{gathered}[/tex]The number of shells she bring to class will be the product of the fraction and the total;
[tex]\begin{gathered} n(C)=f(C)\times T \\ n(C)=\frac{2}{5}\times25 \\ n(C)=10 \end{gathered}[/tex]Therefore, the number of shells she bring to class is;
[tex]10[/tex]How much money to feed to 20 people if two pizzas are $12 and 3 people will eat 1 pizza?
The question is in the image. Need help with #8
SOLUTION
The graph is a function
The domain is all real numbers apart from 0 given by the interval
(-∞,0) ∪ (0,∞)
The Range of the function is all positive numbers given by the interval
(0,∞)
The function is increasing on the interval
(-∞,0)
The function is decreasing on the interval
(0,∞)
9. Connect Mr. Douglas works at thecomputer store four days a week from10:15 A.M. until 4:45 P.M. How many hoursdoes Mr. Douglas work in four weeks?First find the differencebetween 10:15 AM. andnoon and then between noonand 4:45 P.M.
From 10:15 a.m. to 12:00 p.m. there are 1:45 hours. From 12:00 p.m. to 4:45 p.m. there are 4:45 hours therefore, each day Mr. Douglas works
[tex]1\colon45+4\colon45=6\colon30[/tex]hours.
Now, each week, Mr. Douglas works 4 days therefore, in one week, he works:
[tex]4\times6\colon30[/tex]hours. Simplifying the above resut we get:
[tex]26\text{ hours.}[/tex]Finally, in four weeks Mr.Douglas works:
[tex]26\times4\text{ hours=104 hours.}[/tex]Answer:
[tex]104\text{ hours.}[/tex]Find the distance
d(P1.P₂) between
the given points P1
and P2.
P1 = (0,0)
P2 = (6,5)
Simplify your answer, use radicals as needed.
The distance between the two points P1 and P2 is d = √61.
What is the distance?Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage. Length is measured in distance. For instance, the length of a road is its distance. The most popular units of measurement for distance in the metric system are millimeters, centimeters, meters, and kilometers.So, the distance between points P1 and P2:
Where, P1 = (0,0) and P2 = (6,5).The distance formula: d = √(x₂-x₁)²+(y₂-y₁)²Now, substitute the values in the formula as follows:
d = √(x₂-x₁)²+(y₂-y₁)²d = √(6-0)²+(5-0)²d = √36+25d = √61Therefore, the distance between the two points P1 and P2 is d = √61.
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When completing a composition translation (more then one translation) we move from right to left?
if you do this I will name my future kid after you
We have to determine wheter the line segments MN and RS are parallel, perpendicular or neither. To do this we will find the slope of each of this segments; the slope is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For the line segment MN we have M(-2,2) and N(1,-3), then
[tex]\begin{gathered} m_1=\frac{-3-2}{1-(-2)} \\ =\frac{-5}{3} \end{gathered}[/tex]For the line segment RS we have R(-2,1) and (3,4), then
[tex]\begin{gathered} m_2=\frac{4-1}{3-(-2)} \\ =\frac{3}{5} \end{gathered}[/tex]Now that we have the slopes of each lines segments we have to remember two theorems.
T1. Two lines are parallel if and only if
[tex]m_1=m_2[/tex]T2. Two lines are perpendicular if and only if
[tex]m_1m_2=-1[/tex]Once we know this theorems we can answer the question.
First, we notice that the slopes of this segments are not equal so we can conlcude that they are not parallel.
Let's see if they are perpendicular, to do this we multiply the slopes
[tex]\begin{gathered} m_1m_2=(-\frac{5}{3})(\frac{3}{5}) \\ =-\frac{15}{15} \\ =-1 \end{gathered}[/tex]Since the result of their multiplication is -1 we conclude that this lines segments are perpendicular.
Erica wants to build the birdhouse shown. She bought a 29-inch by 45-inch sheet of plywood. Does Erica have enough wood to make the birdhouse? Explain. Find the area of the base and the sides. A(base) = 7x7 = 49 A(sides) = 7x11 = 77 Find the total area. th Total Area = 2x +4x)= 98+=in?
We can divide our birdhouse in 4 rectangles and 2 squares. Each rectangle has measure
and eac square has measure
Then, the total area of our birdhouse is
[tex]\text{Total area=2}\times49+4\times77[/tex]which gives
[tex]\begin{gathered} \text{Total area=98+}308 \\ \end{gathered}[/tex]the birdhouse has an area:
[tex]\text{Total area=}406in^2[/tex]Now, sinde Erica buy a plywood with dimensions 29x45 in^2, she has
[tex]29\times45=1305in^2[/tex]By comparing both numbers, we can see that she have enough wood to make the birdhouse because 1305 in^2 is greater than 406 in^2.
simplify both questions and give full explanation please
Answer:
First question: 1/x^-7
Second question:
x^7
Step-by-step explanation:
To divide these problems (same variable base and exponents) subtract the exponents.
To get rid of a negative on the exponent, "push" the term across the fraction bar. Passing over the fraction bar changes the sign of the exponent. There are math reasons for this, its not random. But thats how it works. (Has to do with an exponent of -1 which will give you the reciprocal of your base).
Also, to multiply terms with the same base, add the exponents.
see image.
What percent of last semesters college cost was spent on books
Okay, here we have this:
Considering the provided information, we obtain the following equation:
Which characteristic of the line that passes through the points (6,10) and (12,2)..
SOLUTION:
Let us find the slope of the line:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]Where x1 = 6, x2 = 12, y1 = 10 and y2 = 2
[tex]\begin{gathered} m\text{ = }\frac{2-10}{12-6} \\ m\text{ = }\frac{-8}{6}\text{ = -}\frac{4}{3} \\ \\ \end{gathered}[/tex]The slope of the given line is -4/3
Find the distance between (5, -7) and (-2,-4)
Answer: 7.62
Step-by-step explanation:
The cost of creating a software program is $5000. Every extra feature added to the software costs $100. Thetotal charge of the software with x extra features is given by the function f(x) = 100x + 5000. How will the graphof this function change if the basic cost is raised to $5200 and the cost of each extra feature is increased to$120?
The original function is:
[tex]f(x)=100x+5000[/tex]Which means that it has a slope of 100, and a starting point of 5000.
As we can see on the image above, the first point is (0,5000), which is the starting point of the function. The second point is (2, 5200), which means that for a 2 unit increase on the features, we got 200 increase on the price, leading to a slope of 100.
If we change the basic cost to 5200, the starting point of the function will increase by 200 units, if we change the slope to 120, then for every feature we add, the cost will increase faster. In summary, the cost of the program will be higher to start, and it will also increase faster. This is illustrated in the image below:
[tex]g(x)=120x+5200[/tex]In green we have the new function, and in red we have the old one. We can see that the new one increases faster, and is always above the old one.
in one hour thirty two cars pass through a particular intersection at the same rate how long would it take for 96 cars to pass through the intersection
In one hour number of cars pass a pparticular intersection is 32.
The number of hours to pass 96 cars is three times the hours to pass the 32 cars.
Determine the number of hours to pass 96 cars from a particular intersection.
[tex]3\cdot1=3[/tex]Answer: 3 hours
