The graph represents the projected profits for a
company, y, based on the number of units sold, x.
250
200
150
100
50
0
10 15
20
(25, 200)
25
(30, 150)
30
35
x
If the end-of-year analysis indicates that profits did not
meet expectations, which inequality in vertex form
represents the region containing the results of the
year?
Oy< -2(x+25)² - 200
O y> 2(x-25)² + 200
y> 2(x+25)² - 200
Oy< -2(x-25)² + 200
Answers
The inequality in vertex form represents the region containing the results of the year is y < -2(x - 25)² + 200 option (D) is correct.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
From the graph:
The vertex is:
(25, 200)
The vertex form of the parabola:
y = a(x - h)² + k
y = a(x - 25)² + 200
Plug x = 30 and y = 150
a = --2
y = -2(x - 25)² + 200
The inequality will be:
y < -2(x - 25)² + 200
Thus, the inequality in vertex form represents the region containing the results of the year is y < -2(x - 25)² + 200 option (D) is correct.
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Related Questions
Simplify to the fullest;
[tex]{ \rm{ \frac{dy}{dx} + 2x + 1 = 2 }}[/tex]
Answers
Answer:
[tex]{ \tt{ \frac{dy}{dx} + 2x + 1 = 2 }} \\ \\ { \tt{ \frac{dy}{dx} = - 2x + 1 }} \\ \\ { \tt{dy = ( - 2x + 1) \: dx}} \\ \\ { \tt{ \int dy = \int( - 2x + 1) \: dx}} \\ \\ { \tt{y = - {x}^{2} + x + c}} \\ \\ { \tt{y = - x(x + 1) + c}}[/tex]
Answer:
[tex]y=-x^2+x+\text{C}[/tex]
Step-by-step explanation:
Given equation:
[tex]\dfrac{\text{d}y}{\text{d}x}+2x+1=2[/tex]
[tex]\text{Isolate $\dfrac{\text{d}y}{\text{d}x}$}:[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}+2x+1-2x-1=2-2x-1[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=-2x+1[/tex]
Multiply both sides by dx to get all the terms containing y on the left side, and all the terms containing x on the right side:
[tex]\implies \text{d}y=(-2x+1)\;\text{d}x[/tex]
Integrate both sides:
[tex]\implies \displaystyle \int 1\;\text{d}y=\int(-2x+1)\;\text{d}x[/tex]
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Integrate each term separately:
[tex]\implies \displaystyle \int 1\;\text{d}y=\int -2x\;\text{d}x+\int 1\;\text{d}x[/tex]
Take the constant outside the integral:
[tex]\implies \displaystyle \int 1\;\text{d}y=-2\int x\;\text{d}x+\int 1\;\text{d}x[/tex]
Integrate, using the rules given below:
[tex]\implies y=-2 \cdot \dfrac{1}{1+1}x^{(1+1)}+x+\text{C}[/tex]
[tex]\implies y=-x^2+x+\text{C}[/tex]
Integration rules:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\(where $n$ is any constant value)\end{minipage}}[/tex]
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Please help,, Consider the sequence of steps to solve the equation: 5(x - 3) = 7x2 Step 1 ⇒ 10(x - 3) = 7x Step 2 ⇒ 10x - 30 = 7x Step 3 ⇒ 3x - 30 = 0 Step 4 ⇒ 3x = 30 Step 5 ⇒ x = 10 Identify the property of equality which yields Step 5.
Answers
Summary: The solution to the equation (x - 3)(x + 9) = -27 is x = 0 and x = -6.
The perimeter of the triangle below is 68 units. Find the value of y
Answers
Since we are talking about perimeter add all of the sides together and set them equal to the total creating the equation 68=3y+y-1+4y-3. Combine like terms and you get 68=8y-4. From here you can use inverse operations to solve for the value of y. So add 4 to both sides and you get 72=8y (-4 and +4 cancel out). Finally divide both sides by 8 and you are left with 9=y.
Always double check your work:
3(9)+(9)-1+4(9)-3=68
27+8+33=68
68=68
can somebody help me with this problem in mathematics.
Answers
Answer:
Hachem saves $875.
Step-by-step explanation:
$2,500 - 35% = $1,625
$2,500 - $1,625 = $875
Solve each step of this problem
Answers
The cost is given as
[tex]10+0.5x[/tex]Where x is the number of hours
The y-intercept is obtained from the graph as shown below
The value of the y-intercept is obtained to be 10
The y-intercept represents the value represents the fixed cost.
The slope of the cost is obtained from the cost function to be 0.5.
The slope represents the change in cost with respresent to time (hour).
Hence,
lank 1: 10
Blank 2: The fixed cost
Blank 3: 0.5
Blank 4: Change in cost or charge with respect to time used in hours
Blank 5:
[tex]C=10+0.5h[/tex]Answer:
donde están lo calisado los continentes
Blood types: The blood type O negative is called the "universal donor" type, because it is the only blood type that may safely be transfused into any person.
Therefore, when someone needs a transfusion in an emergency and their blood type cannot be determined, they are given type O negative blood. For this
reason, donors with this blood type are crucial to blood banks. Unfortunately, this blood type is fairly rare; according to the Red Cross, only 7% of U.S. residents
have type O negative blood. Assume that a blood bank has recruited 19 donors. Round the answers to four decimal places.
a) what is the probability that three or more of them have type O negative blood?
b) what is the probability that fewer than four of them have type O negative blood?
c) It (would/wouldn’t) be unusual if none of the donors had type O negative blood since the probability is __?
Answers
a) It is 0.1275 times more probability that fewer than five of them have type o negative blood.
b) The probability that less than five of them are type o negative blood types is 0.9933.
c) 0.2708 probability that there are no donors who have type O negative blood. It would not be odd to have no type o negative donors because this likelihood is higher than 0.05.
There are only two outcomes that can occur for any individual. Type o negative blood is either present or absent. Any other person has no effect on a person's likelihood of having type O negative blood. To answer this question, we thus employ the binomial probability distribution.
Binomial probability distributionThe probability of precisely x successes on n repeated trials is known as a binomial probability, and X can only have two possible outcomes.
P(X=x)= [tex]C_{n,x.P^{x}.(1-P)^{n-x} }[/tex]
Additionally, p is the probability that X will occur.
A whopping 7% of Americans have type o negative blood.This means that P=0.07
18 donors.This mean that n = 18
the probability that three or more of them have type o negative bloodEither less than three have, or at least three do. The sum of the probabilities of these events is 1. So
P(X<3) + P(X≥3)=1
We want P(X≥3)
So,
P(X≥3) = 1-P(X<3)
In which
P(X< 3)= P(X = 0)+P(X = 1)+P(X = 2) = 0.2708 + 0.3669 +0.2348 = 0.8725
P(X≥3) = 1-P(X<3) = 1- 0.8725=0.1275
It's 0.1275 times more likely that fewer than five of them have type O negative blood.
The probability that fewer than five of them have type o negative bloodP ( x < 5 )= P(X=0)+P(X=1)+P(X=3)+P(X=3)+P(X=4)
P(X=x)= [tex]C_{n,x.P^{x}.(1-P)^{n-x} }[/tex]
P(X=0)= [tex]C_{18,0(0.07)^{0}.(0.93)^{18} }= 0.2708[/tex]
P(X=1)= [tex]C_{18,1(0.07)^{1}.(0.93)^{17} }= 0.3669[/tex]
P(X=2)= [tex]C_{18,2(0.07)^{2}.(0.93)^{16} }= 0.2348[/tex]
P(X=3)= [tex]C_{18,3(0.07)^{3}.(0.93)^{15} }= 0.0942[/tex]
P(X=4))= [tex]C_{18,4(0.07)^{4}.(0.93)^{14} }= 0.0266[/tex]
P(X < 5)=P(X=0)+P(X=1)+P(X=3)+P(X=3)+P(X=4)
0.2708+0.3669+0.2348+0.0942+0.0266=0.9933
Would it be unusual f none of the donors had type o negative bloodP(X=0)= [tex]C_{18,0(0.07)^{0}.(0.93)^{18} }= 0.2708[/tex]
Probability of having no type O negative blood donors is 0.2708. It would not be odd to have no type o negative donors because this likelihood is higher than 0.05.
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11) BUSINESS Julian makes and sells wallets. He estimates that his income can be modeled by
y = 16x130, where x is the number of wallets he sells. He estimates that his costs to make
the wallets can be modeled by y = 8x + 150. How many wallets does Julian need to make in
order to break even?
Answers
The number of wallets does Julian need to make in order to break even are 35.
What are linear equation?X 1, ldots, and x n are the variables, and display style b, a 1, ldots, and a n are the coefficients. In mathematics, a linear equation is an equation that can be written as x 1, ldots, and x n + a n + b = 0. Ax + By = C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y). frequently actual numbers. The first-degree equations are linear equations. The following is the equation for a straight line. Ax+by+c = 0, where a and b are both zeros, is the conventional form of a linear equation.
In order to "break even," his earnings and expenses have to be equal. The number of wallets (x) is represented in both equations. Simply put, you have to work out the equations in the system.
Both the given equation are equal to y
So,
16x - 130 = 8x + 150
16x - 8x = 150 + 130
x = 280/8
x = 35
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odd even or neitheer
how many mistakes i have explain it to me
Answers
Answer:
neitheroddoddevenevenneitherevenevenStep-by-step explanation:
You want to classify a number of functions as even, odd, or neither.
Even FunctionAn even function has a graph that is symmetrical about the y-axis. It has the characteristic that ...
f(x) = f(-x)
A polynomial function will be an even function if it consists entirely of even-degree terms. (A constant is degree zero, hence even degree.) A rational function will be an even function if it can be reduced to the ratio of even functions.
Odd FunctionAn odd function has a graph that is symmetrical about the origin. It has the characteristic that ...
f(x) = -f(-x)
A polynomial function will be an odd function if it consists entirely of odd-degree terms. A rational function will be an odd function if it reduces to the ratio of an even and an odd function.
NeitherA function is neither even nor odd if it does not have one of the symmetries mentioned above. A polynomial consisting of a mix of even- and odd-degree terms will be neither even nor odd.
1. (x³+4x²)/(7x²+1)This is the ratio of a "neither" function to an even function. It is neither even nor odd.
2. (2x⁴+8x³)/(x³+4x²)The ratio can be reduced to ...
[tex]\dfrac{2x^4+8x^3}{x^3+4x^2}=\dfrac{2x^3(x+4)}{x^2(x+4)}=2x[/tex]
This consists only of an odd-degree term. It is an odd function.
3. x³/(7x²+1)This is the ratio of an odd function to an even function. It is an odd function.
4. (4x²+7)/(7x⁸+3x²)This is the ratio of two even functions. It is an even function.
5. (2x³+8x²)/(x³+4x²)As in problem 2, the function can be reduced:
[tex]\dfrac{2x^3+8x^2}{x^3+4x^2}=\dfrac{2(x^3+4x^2)}{x^3+4x^2}=2[/tex]
It is an even (degree 0) function.
6. (x²-4)/(x-2)This is the ratio of an even function to a "neither" function. It is neither even nor odd.
The function reduces to x+2, which is neither even nor odd.
7. 1/(x²+9x⁶)This is the ratio of two even functions. It is an even function.
8. (4x³+2x)/(7x⁵+3x³)This is the ratio of two odd functions. It can be reduced to the ratio of two even functions, so it is an even function.
[tex]\dfrac{4x^3+2x}{7x^5+3x^3}=\dfrac{2x(2x^2+1)}{x^3(7x^2+3)}=\dfrac{4x^2+2}{7x^4+3x^2}[/tex]
36 muffins and uses 4 cups of almonds. What is the unit rate of muffins per cup of almonds that he is using?
Answers
The unit rate of muffins per cup of almonds that the baker is for every 9 muffins, he uses 1 cup of almonds.
What is the unit rate?The unit rate is the ratio of a variable against another variable.
The unit rate explains the quantity relationship between the number of muffins produced and the cups of almonds used by the baker.
For this situation, a cup of almonds can make 9 muffins.
The total number of muffins made = 36
The total number of cups of almonds used = 4
The ratio of muffins to cups of almonds = 36:4 or 9:1
The unit rate of muffins per cup = 9 (36/4)
Thus, the baker is producing 9 muffins per cup of almonds used.
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x + y = 12 x - y = 2
Answers
Answer:
x = 7
y = 5
(7, 5)
Step-by-step explanation:
From the way, this question looks I'm going to assume substitution.
x + y = 12
x - y = 2
------------------
2x = 14
÷2 ÷2
-------------
x = 7
x + y = 12
7 + y = 12
-7 -7
-------------------
y = 5
I hope this helps!
18x-3y=-15
-6x+y=5
Solve by substitution
Answers
Answer:
consistent system with equation [tex]y=6x+5[/tex]
Step-by-step explanation:
[tex]18x-3y=-15[/tex], [tex]-6x+y=5[/tex]
To solve by substitution, we have to isolate a variable in one of the equations. I will isolate y in the second equation.
[tex]-6x+y=5[/tex]
+6x +6x
[tex]y=6x+5[/tex]
Next, substitute this y value for y in the first equation:
[tex]18x-3y=-15[/tex]
[tex]18x-3(6x+5)=-15[/tex]
and distribute.
[tex]18x-18x-15=-15[/tex]
[tex]-15=-15[/tex]
We are left with an equality of constants. This means that the system of equations is actually just one equation, meaning it has an infinite number of solvable points (this is sometimes called consistent). And, its equation is just what we solved for in the first step:
[tex]y=6x+5[/tex]
A B C D Given that ABCD and AD - CB, how can you prove that A ABD ACDB? (G.6)(1 point) O A. Side-Side-Angle (SSA) O B. Angle-Side-Angle (ASA) C. Side-Side-Side (SSS) O D. Side-Angle-Side (SAS)
Answers
Answer
Option C is correct.
Side-Side-Side (SSS)
Explanation
The key to proving that two triangles are similar or congruent is to prove that three of either side lengths or angles are congrunet, similar or the same.
For the figure given, we have already been told that
Side AB = Side CD
Side AD = Side CB
Since the two triangles share a similar side in BD, we can complete this by saying
Side BD = Side BD
Side AB = Side CD
Side AD = Side CB
Side BD = Side BD
So, three of the sides of the triangles are equal or congruent.
Hope this Helps!!!
What value of n makes the equation true?
(2x9y") (4x²,10)-8x^11,20
=
Answers
In the equation [tex](2x^{9} y^{n})(4x^{2}y^{10}) = (8x^{11}y^{20})[/tex] value of n = 10
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.
[tex](2x^{9} y^{n})(4x^{2}y^{10}) = (8x^{11}y^{20})[/tex]
exponents multiplied with the same base: am * an = a{m + n}
On the powers of x, use the Rule of Multiplying Exponents.
⇒ x⁹ * x² = x⁹⁺² = x¹¹
The powers of y operate similarly.
⇒ [tex]y^{n} * y^{10} = y^{n + 10} = y^{20}[/tex]
Since y¹⁰⁺¹⁰ = y²⁰
Therefore in the given equation, the value of n = 10
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Find values for the variables so that the following matrices are equal.
Answers
Given:
[tex]\begin{bmatrix}{x} & {7y} \\ {z} & {20}\end{bmatrix}=\begin{bmatrix}{4} & {21} \\ {4} & {20}\end{bmatrix}[/tex]Let's find the values of the variables so that the matrices are equal.
To find the values of the variables, divide the values of the result by the corresponding values of the main matrix.
We have:
• x = 4
• 7y = 21
Divide both sides by 7:
7y/7 = 21/7
y = 3
• z = 4
[tex]\begin{gathered} \begin{bmatrix}{x=4} & {7y=21} \\ {z=4} & {20}\end{bmatrix} \\ \\ \begin{bmatrix}{4} & {7(3)} \\ {4} & {20}\end{bmatrix} \end{gathered}[/tex]Therefore, we have:
• x = 4
,• y = 3
,• z = 4
ANSWER:
• x = 4
,• y = 3
,• z = 4
What are the solutions to x2 + 8x + 7 = 0?
x = –8 and x = –7
x = –7 and x = –1
x = 1 and x = 7
x = 7 and x = 8
Answers
The solutions for the quadratic equation x² + 8x + 7 = 0 is option B x = -7 and x = -1
Given,
The quadratic equation : x² + 8x + 7 = 0
We have to find the solutions for this quadratic equation using the quadratic formula.
Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Here,
a = 1, b = 8 and c = 7
Now,
[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
= [tex]\frac{-8(+-)\sqrt{8^{2} -4(1)(7)} }{2(1)}[/tex]
= [tex]\frac{-8(+-)\sqrt{64-28} }{2}[/tex]
= (-8±√36)/2
= (-8±6)/2
Now,
Solve for
(-8 + 6) / 2 = -2/2 = -1
Solve for
(-8 - 6) / 2 = -14/2 = -7
That is,
The solutions for the quadratic equation x² + 8x + 7 = 0 is x = -1 and x = -7
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Three friends went together to pick apples. They picked a total of 5 1/2 baskets of apples. If each person took home an equal amount of the baskets how many baskets did each person get?
Answers
The most appropriate choice for fraction will be given by -
Each person get [tex]1\frac{5}{6}[/tex] baskets of apples.
What is fraction?
Suppose there is a whole collection of objects and some parts of the objects are taken from the whole collection. Fraction represents those parts which are taken. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
Here,
Number of person = 3
Total baskets of apple picked = [tex]5\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex] baskets
Number of baskets each person got =
[tex]\frac{11}{2} \div 3\\\frac{11}{2} \times \frac{1}{3}\\\frac{11}{6}\\1\frac{5}{6}[/tex]
Each person got [tex]1\frac{5}{6}[/tex] baskets of apples
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a container holds 2300 ounces fruit punch. A factory places the fruit punch into 32-ounce bottles. How man full Bottles of fruit punch can the factory produce?
Answers
A container holds 2300 ounces fruit punch. A factory places the fruit punch into 32-ounce bottles, factory can produce 71 full bottles.
What is an ounce?The uncia, an ancient Roman unit of measurement, is the source of the ounce (/ans/), any of numerous possible measures of mass, weight, or volume.
Although it is frequently used outside of the Anglosphere, it is predominantly employed in the United States to measure packaged foods and food portions, postal items, the areal density of fabric and paper, boxing gloves, and other items.
Although the avoirdupois ounce is the standard unit of mass for most applications, the actual weight of precious metals like gold, silver, platinum, palladium, rhodium, etc. is measured in "troy ounces," which are equal to 31.1034768 g.
'Ounce' is also used in the following other contexts: A unit of measure for force is the ounce-force. A unit of volume is the fluid ounce.A multitude of distinct ounces measuring mass or volume have been employed historically by various trades at various times and in various countries.Solving the question,
[tex]\frac{2300}{32} = 71.875[/tex]
Thus, we can say that a factory can produce 71 full bottles.
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◆ Rewrite the fractions as sixths. 1/2 + 1/3= _/6 + _/6
Answers
Answer: 1/2 + 1/3 = 3/6 + 2/6
Step-by-step explanation: you multiply 1/2 by 3/3 (1 x 3 and 2 x 3), which gives you 3/6, and then multiply 1/3 by 2/2 (1 x 2 and 3 x 2), which gives you 2/6.
hope this helps! :)
state where the function is continuous, discontuous and the type of discontinuity for each
Answers
For x = 2
[tex]\lim _{x->2^-}(\frac{x}{x-2})=-\infty[/tex][tex]\begin{gathered} \lim _{x->2^+}(6)=6 \\ \end{gathered}[/tex]Since:
[tex]\lim _{x->2^+}f(x)\ne\lim _{x->2^-}f(x)[/tex]The function is discontinuous at x = 2. Besides since the function has a vertical asymptote on one of the sides, we can conclude it is a infinite discontinuity.
For x = 6:
[tex]\lim _{x->6^-}6=6[/tex][tex]\lim _{x->6^+}\frac{x-2}{x^2-6x+8}=\lim _{x->6^+}\frac{x-2}{(x-2)(x-4)}=\lim _{x->6^+}\frac{1}{x-4}=\frac{1}{2}[/tex]Since:
[tex]\lim _{x->6^+}f(x)\ne\lim _{x->6^-}f(x)[/tex]The function is discontinuous at x = 6, at this point the function has a jump discontinuity
Enter values to complete the table below.
Answers
The slope of the equation, represented by the value of y/x for the given values of x and y, is 3/1, 3/1, 3.
What does slope in mathematics mean?The slope of a line can be used to gauge how steep it is. Slope is theoretically determined as "rise over run" (change in y divided by change in x).
The slope is the ratio of the rise in height between two points to the fall in elevation between those same two points.
The x and y values are provided.
The equation's slope is shown by the ratio y/x.
if y = -3 and x = -1,
y/x = 3/1
if y = 3 and x = 1
y/x = 3/1
if y = 6 and x = 2
y/x = 6/2 = 3
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is it f(2)=10 ? I don’t get number 2.
Answers
10
Step-by-step explanation:
f(2)=
3(2)+4
3x2+4
using PEMDAS multiplication comes first
6+4
=10
Answer:
f(2) = 10 and f(3) = 13
Step-by-step explanation:
In this context f(2) means "what is y when x equals 2?" How about when x = 3? So we plug the values into the equation and solve for f(x) - which is basically what we called "y" in algebra.
Given: f (x) = 2x² − 3x+5 and g(x)=x-4, find (f+g)(x) * help
Answers
The value of (f+g)(x) is c(x) = 2x² + (-2)x + 1.
How can we add linear functions?
Addition of two individual functions, a(x) and b(x); linearly, results in the formation of the functional addition, c(x) of the two functions, such as
c(x) = a(x) + b(x) = (a+b)(x) – (i)
Domain of a quadratic equation:
The domain of a quadratic function f(x) is the set of x-values for which the function is defined, and the range is the set of all the output values, as is the case with any function (values of f). Any x is a valid input for quadratic functions because their domain is typically the entire real line. Generally, for a quadratic equation the domain goes from (-∞ ,∞ ).
Given, f(x)= 2x² - 3x + 5 and g(x)= x - 4
Let, y = c(x) denote the value of the function (f+g)(x).
Here, following available literature,
c(x) = (f+g)(x) = f(x) + g(x) [Using (i)]
c(x) = (2x² - 3x + 5)+(x - 4) = 2x² - 3x + 5 + x - 4 = 2x² + (-2)x + 1
Therefore, y = c(x) = 2x² + (-2)x + 1 is the value of (f+g)(x).
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Evaluate the expression,g(m - 9) +5 if g = -4 and m = 3
Answers
To find the answer you substitute in the expression the g by -4 and the m by 3, as follow:
[tex]-4(3-9)+5[/tex]To evaluate:
1. Make operations in parenthesis:
[tex]=-4(-6)+5[/tex]2. Multiplication
[tex]=24+5[/tex]3. Addition:
[tex]=29[/tex]Can you please answer
Answers
From the given picture we can see
A right triangle DEC, where
The side opposite to angle C, ED has a length of 12 feet
The hypotenuse DC has length x feet
To find the value of x, we will use the sine ratio
[tex]\begin{gathered} \sin 70=\frac{opposite}{\text{hypotenuse}} \\ \sin 70=\frac{DE}{DC} \end{gathered}[/tex]Since the opposite side DE = 12
Since the hypotenuse DC = x
Rectangle ABCD is transformed into rectangle EFGH. Choose all the correct statements about the transformation below. CHOOSE ALL STATEMENTS THAT ARE CORRECT.
A. Rectangle ABCD is similar to rectangle EFGH
B. The scale factor of the dilation is 0.4
C. Rectangle ABCD is congruent to rectangle EFGH
D. The dilation is an enlargement
E. The dilation is a reduction
F. The scale factor of the dilation is 2.5
Answers
The correct options are,
A. Rectangle ABCD is similar to rectangle EFGH.
D. The dilation is an enlargement.
F. The scale factor of the dilation is 2.5.
The similarity criteria of rectangles are that their corresponding sides should be proportional to each other. The ratio of their corresponding length is equal to L = 25÷10, which gives L=2.5, and the ratio of their corresponding width is equal to W = 15÷6, which gives w = 2.5. Hence, both rectangles are similar.
The dilation is an enlargement because the size of the rectangle is increased by a scale factor of 2.5.
The scale factor of the dilation is the ratio of the sides, which is equal to 2.5.
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What is the entire set of people for a study?
census
population
sample
survey
Answers
Answer: The population
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in what quadrant l ll lll lv does the point 8,-9 lie?
Answers
The point lie in Quadrant IV (8 , -9).
Quadrant in coordinate geometry is divided into four parts which is called Quadrants.
Quadrants I (x, y)Quadrants II (-x, y)Quadrants III (-x, -y)Quadrants IV (x, -y)And, To find the in which quadrant does point (8, -9) lie ?
Now According to the above explanation is that:
We have, Point is (8, -9)
Thus, we can clearly see that
This point is lie in Quadrant IV (8 , -9).
Hence, The point lie in Quadrant IV (8 , -9).
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Consider the incomplete paragraph proof.
Given: P is a point on the perpendicular bisector, l, of MN.
Prove: PM = PN
Line l is a perpendicular bisector of line segment M N. It intersects line segment M N at point Q. Line l also contains point P.
Because of the unique line postulate, we can draw unique line segment PM. Using the definition of reflection, PM can be reflected over line l. By the definition of reflection, point P is the image of itself and point N is the image of ________. Because reflections preserve length, PM = PN.
Answers
From the unique line postulate, we can draw unique line segment PM and as we are given that P is a point on the perpendicular bisector I of MN, the proof below has shown that using the definition of reflection, point P is the image of itself and point N is the image of point M
How to Interpret the Perpendicular Bisector?We are given :
Point P is a point on the perpendicular bisector, l, of MN.
Now, we want to prove that PM = PN
A Reflection in transformation can be defined as the transformation in which the figure is the mirror image of the other figure. This means that every point is a mirror reflection of itself .
With the aid of the definition of reflection, we can form the statement that point P is the image of itself , and point N is the image of M .
The line l which is the perpendicular bisector of MN acts as a Line of symmetry or axis of reflection.
Finally, when talking about transformations, it is common knowledge that reflections preserve length which means that the required proof PM = PN will hold true
Therefore, we will conclude that point N is the image of M .
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f(x) = (x + 3)² - 2x² ; x = -12
Answers
I attached a photo to answer you question. Hope this helps!
Hello? Can someone help me with this please?The coffee preferences of 100 people were recorded in a survey.What proportion of the circle (in degrees) is represented by the espresso segment?
Answers
Recall that a whole circle is equal to 360°.
Espresso accounts for 5 out of 100 people surveyed.
Therefore,
[tex]\begin{gathered} 360\degree\times\frac{5}{100} \\ =360\degree\times0.05 \\ =18\degree \end{gathered}[/tex]The proportion of the circle that is represented by the espresso segment is 18°.