Answer:
221
Step-by-step explanation:
Interest goes up 5 dollar each year
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
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 value of n makes the equation true?
(2x9y") (4x²,10)-8x^11,20
=
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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Lorena solved the equation 5k – 3(2k – ) – 9 = 0. Her steps are below.
5k – 6k + 2 – 9 = 0
–k – 7 = 0
–k = 7
k = 1/7
Analyze Lorena’s work to determine which statements are correct. Check all that apply.
Answer: K= -9
Step-by-step explanation:
5k−3(2k)−9=0
Multiply 3 and 2 to get 6.
5k−6k−9=0
Combine 5k and −6k to get −k.
−k−9=0
Add 9 to both sides. Anything plus zero gives itself.
−k=9
Multiply both sides by −1.
k=−9
(Hope this helps)
The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an elephant weighs 2400 pounds on Planet A, find the elephant's weight on Planet B.
The weight of the elephant on planet B given the ratio of the weights on planet A an B is 72 pounds.
What is the weight of the elephant on Planet B?Ratio is used to compare two or more quantities together. It shows the number of times that one quantity is contained in another quantity. In this question, the weight of the elephant on Planet B is 100/3 times that of Planet A.
In order to determine the weight of the elephant on Planet B, multiply the ratio of the weight in planet B by the weight in Planet A and divide by the ratio of weight in planet A.
Weight in Planet B = (3 x 2400) / 100 = 72 pounds
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5. Each term in the second row is deter- mined by the function y=2x-1. 2 4 5 3 7 9 What number belongs in the shaded box? X y 1 1 3 5 12
Answer:
23
Step-by-step explanation:
12 * 2= 24
24-1= 23
is it f(2)=10 ? I don’t get number 2.
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.
in what quadrant l ll lll lv does the point 8,-9 lie?
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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Evaluate the expression,g(m - 9) +5 if g = -4 and m = 3
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]For the function f(x)=x2−9, find
(a) f(x+h),
(b) f(x+h)−f(x), and
(c) f(x+h)−f(x) h
(a) f(x+h)=
The value of f(x+h) is x² + 2xh + h² - 9, the value of f(x+h)−f(x) is 2xh + h², and the value of (f(x+h)−f(x))/h is 2x + h.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The function:
f(x) = x² - 9
(a) f(x + h)
f(x + h) = (x + h)² - 9
f(x + h) = x² + 2xh + h² - 9
(b) f(x+h)−f(x)
= x² + 2xh + h² - 9 - (x² - 9)
f(x+h)−f(x) = 2xh + h²
(c) (f(x+h)−f(x))/h
= (2xh + h²)/h
= 2x + h
Thus, the value of f(x+h) is x² + 2xh + h² - 9, the value of f(x+h)−f(x) is 2xh + h², and the value of (f(x+h)−f(x))/h is 2x + h.
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1 2 3 5 9 Find a number between and 10 Write your answer as an improper fraction and as a mixed number
In finding a number between 9/8 and 10/8, we can use the average of these two.
We can ensure that this number lies between this two.
[tex]Ave=\frac{1}{2}(a+b)[/tex]where a and b are the two numbers
So we have :
[tex]\begin{gathered} Ave=\frac{1}{2}\times(\frac{9}{8}+\frac{10}{8}) \\ =\frac{9}{16}+\frac{10}{16} \\ =\frac{19}{16} \end{gathered}[/tex]Therefore, one number that lies between 9/8 and 10/8 is :
[tex]\begin{gathered} \frac{19}{16} \\ or \\ 1\frac{3}{16} \end{gathered}[/tex]x + y = 12 x - y = 2
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!
Given the example below, the zero product rule is exhibited correctly
because it take the factored form of the quadratic and sets equal to zeros
and solves.
x²+4x-21-
(x+7)(x-3)=0
x+7=0 or x-3=0
x=-7
x=3
True or false
The statement is true. This is an example of Factorization being correct as it takes the factors of the quadratic equation set them equal to 0 and then calculates the value of x.
In the given question, an example of factorization is taken for the equation x²+4x-21 which is factorized using the Middle-Term split rule. We have to find out if the example is conducted correctly.
Factorization is the rule to factorize an equation such that its factors if multiplied together form the equation itself.
We will verify the factorization, for equation x²+4x-21
=> x² + 4x - 21
=> x² + 7x -3x -21
=> x(x + 7) -3(x + 7)
=> (x + 7)(x - 3) = 0
=> x = -7, x = 3
Hence, the statement is True.
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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?
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°.
12. (01.02)
Which function below is the inverse of f(x) = x² - 9?
FOR EQUATION INVERSES IT MEANS ... x and y swap positions.
[tex]x = (f(x))^{2} - 9 \\ (f(x))^{2} = x + 9 \\ \sqrt{(f(x))^{2} } = \sqrt{x + 9} \\ f(x) = \sqrt{x + 9} [/tex]
ATTACHED IS THE SOLUTION.
Please tell me the answer and how you got the answer (AKA How you solved it) And the first person to give me the correct answer gets marked (Due In 3.5 Minutes)
• Thanks
Step-by-step explanation:
the range is the interval or set of all valid y (functional result) values.
we see that y goes continuously through every value between +5 (we see no y values bigger than that) and -5 (we see no y values lower than that).
the filled dots also tell us that the end points would be included (if this would be a necessary information - it is not, because the curve reaches +5 and -5 also in between).
so, the range is
-5 <= y <= +5
An object oscillates as it moves along the
x-axis. Its displacement varies with time
according to the equation
x = 4 sin(pi(t)+ pi/2)
where t = time in seconds and
x = displacement in meters
What is the displacement between t = 0
and t = 1 second?
[?] meters
It is found that the displacement between t= 0 and t = 1 second is of 0.536 m.
The equation of motion is given by:
x(t) = 4 sin(πt + π/2)
The displacement between t= 0 and t = 1 second is given by:
d = x(1) - x(0)
Hence,
position of the object when t = 1
x(1) = 4sin(π(1) + 1 (π/2))
= 4 sin (π + π/2)
= 4 sin (3π/2)
= 4 x √3/2
= 2√3
= 3.464
position of the object when t = 0
x(0) = 4sin(π(0) + (π/2))
= 4 sin (0 + π/2)
= 4 x 1
= 4
Then,
d = x(1) - x(0)
= 4 - 3.464
= 0.536(approx)
Therefore, the displacement of the object between t = 0 and t = 1 is 0.536.
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Use the graph below which shows the profit y in thousands of dollars of a company in a given year t where t represents the number of years since 1980 find the linear function y where y depends on t the number of years since 1980 Y=_
First we need to find the slope by using two points
(15,190)=(t1,y1)
(25,170)=(t2,y2)
[tex]m=\frac{y_2-y_1}{t_2-t_1}=\frac{170-190}{25-15}=\frac{-20}{10}=-2[/tex]Then we calculate the y-intercept
[tex]190=-2(15)+b[/tex]we isolate the b
[tex]b=190+30=220[/tex]The equation is
[tex]y=-2t+220[/tex]
What is the length of segment KL? Round the answer to
the nearest tenth of a units.
K=(-4,-6) L =(5,1)
Answer:
d ≈ 11.40
Step-by-step explanation:
K: (-4, -6); L: (5, 1)
(x₁, y₁) (x₂, y₂)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(5 - (-4))² + (1 - (-6))²
d = √(5 + 4)² + (1 + 6)²
d = √(9)² + (7)²
d = √81 + 49
d = √130 ≈ 11.40
I hope this helps!
HURRY On a coordinate plane, a curve goes through (negative 6, 0), has a maximum at (negative 5, 500), decreases to (negative 2.5, negative 450), increases through (0, negative 50), increases again through (1, 0), and then goes through (2, 400).
The real solutions to the equation 3x5 + 25x4 + 26x3 – 82x2 + 76x = 48 are shown on the graph. What are the nonreal solutions?
StartFraction 1 + i StartRoot 5 EndRoot Over 3 EndFraction, StartFraction 1 minus i StartRoot 5 EndRoot Over 3 EndFraction.
StartFraction negative 1 + i StartRoot 5 EndRoot Over 3 EndFraction, StartFraction negative 1 minus i StartRoot 5 EndRoot Over 3 EndFraction.
StartFraction negative 1 + StartRoot 5 EndRoot Over 3 EndFraction, StartFraction negative 1 minus StartRoot 5 EndRoot Over 3 EndFraction.
StartFraction 1 + StartRoot 5 EndRoot Over 3 EndFraction, StartFraction 1 minus StartRoot 5 EndRoot Over 3 EndFraction.
The non-real solutions of the polynomial expression are x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3
How to determine the non-real solutions?The equation of the polynomial expression is given as:
3x5 + 25x4 + 26x3 – 82x2 + 76x = 48
Rewrite the equation as
3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48 = 0
The points on the graph are given as
(-6, 0), (-5, 500), (-2.5, -450), (0, - 50), (1, 0), (2, 400).
Write out the x-intercepts
(-6, 0) and (1, 0)
This means that
Real solution = -6
Real solution = 1
Rewrite the above as
x = -6 and x = 1
So, we have
x + 6 = 0 and x - 1 = 0
Multiply
(x + 6)(x - 1) = 0
The next step is to divide the polynomial equation 3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48 = 0 by (x + 6)(x - 1) = 0
This is represented as
3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48/(x + 6)(x - 1)
Using a graphing calculator, we have
3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48/(x + 6)(x - 1) = 3x^3 + 10x^2 - 6x + 8
So, we have
3x^3 + 10x^2 - 6x + 8
Factorize
(x + 4)(3x^2 - 2x + 2)
Next, we determine the solution of the quadratic expression 3x^2 - 2x + 2 using a quadratic formula
So, we have
x = (-b ± √(b² - 4ac))/2a
This gives
x = (2 ± √((-2)² - 4 * 3 * 2))/2 * 3
So, we have
x = (2 ± √-20)/6
This gives
x = (2 ± 4√-5)/6
Divide
x = (1 ± 2√-5)/3
Split
x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3
So, the conclusion is that
Using the polynomial expression, the non-real solutions are x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3
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Given: f (x) = 2x² − 3x+5 and g(x)=x-4, find (f+g)(x) * help
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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18x-3y=-15
-6x+y=5
Solve by substitution
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]
identify the maxima and minima and intervals on which the function is decreasing and increasing
Solution
From the given graph,
The maxima is
[tex](1,-1)[/tex]The minima isThe inetrev
[tex](7,-19)[/tex]aterval inwh which the function is increasing is
[tex](-\infty,1)\cup(7,\infty)[/tex]dec
[tex](1,7)[/tex]I need help I’m confused and stuck
Answer:
Step-by-step explanation:
x = -A x 2/7 + 10
Answer:
-3.5 (or -3.50); each cup of coffee is $3.50
Step-by-step explanation:
the slope of the function is what is in front of the x
that is
-3.50 or just -3.5
this means that each cup of coffee is $3.50
Find a formula for the exponential function passing through the points (-1,5/4) and (3,320).
[tex]{\Large \begin{array}{llll} y = ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=-1\\ y=\frac{5}{4} \end{cases}\implies \cfrac{5}{4}=ab^{-1}\implies \cfrac{5}{4}=\cfrac{a}{b} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} x=3\\ y = 320 \end{cases}\implies 320=ab^3\implies 320=ab^{4-1}\implies 320=ab^4 b^{-1} \\\\\\ 320=ab^4\cdot \cfrac{1}{b}\implies \stackrel{\textit{substituting from the previous equation}}{320=\cfrac{a}{b}b^4\implies 320=\cfrac{5}{4}b^4}\implies 320\cdot \cfrac{4}{5}=b^4 \\\\\\ 256=b^4\implies \sqrt[4]{256}=b\implies \boxed{4=b} \\\\\\ \cfrac{5}{4}=\cfrac{a}{b}\implies \cfrac{5}{4}=\cfrac{a}{4}\implies \boxed{5=a}~\hfill {\Large \begin{array}{llll} y =5(4)^x \end{array}}[/tex]
Suppose the top of the minute hand of a clock is 2 in. From the center of the clock. For the duration, determine the distance traveled by the tip of the minute hand (30 minutes)
yes
yes
yes
yes
yes
yes
no
Please help I’ll mark you as brainliest if correct !
For the given 14 digit credit card, the value of first letter A is found as 4.
What is defined as the arithmetic progression?An arithmetic progression (AP) is a succession in which the differences between each successive term are the same. In this type of progression, it is possible to derive a formula for the AP's nth term.For the given question;
The formula for finding the sun of nth terms of the AP are-
Sn = n/2(a + l)
Where, Sn is the sum of all termsn is the total number of AP.a is the initial term.l is the last term.From the given 14 digits credit card, consider initial 3 letters.
A,_, 8
The sum of three consecutive numbers is 18.
Thus, applying Sum formula of AP
Sn = n/2(a + l)
n = 3Sn = 18a = Al = 3Put the values;
18 = 3/2(A + 8)
Simplifying;
3A + 24 = 36
A = 12/3
A = 4
Thus, the value of the first digit of the credit card is found as 4.
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The measure of the vertex angle of an isosceles triangle is three times the measure of a base angle. Find the number of degrees in the measure of the vertex angle.
We will label the base angles of the triangle as "x".
[tex]\text{Base angle=x}[/tex]Since the vertex angle is 3 times the measure of the base angle, the vertex angle will be equal to 3x:
[tex]\text{Vertex angle =3x}[/tex]The following image represent the angles in the isosceles triangle:
Now we use the following property of triangles:
The sum of all of the internal angles in a triangle must be equal to 180°.
Thus, we add the angles and equal them to 180°
[tex]3x+x+x=180[/tex]We combine the terms on the left:
[tex]5x=180[/tex]And divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{180}{5} \\ x=36 \end{gathered}[/tex]And since x=36, the vertex angle will be:
[tex]\text{vertex angle = 3x = 3(36)=108\degree}[/tex]answer: 108°
1. How much does it cost to use a yard of ribbon?
#9 satin ribbon
Cost $4.99 per roll
100 yards per roll
Step-by-step explanation:
You will want to divide the cost of $4.99 by 100, this will give you the cost per yard.
Answer:
$4.99 / 100 = $0.0499
About 5 cents per yard.
Please give thanks, 5 stars, and brainliest answer :)
a figure is dilated by a scale factor of 3, if the origin is the center of dilation, what is the new vertex, a', if the old vertex was located. at A(3,4)?
A figure is dilated by a scale factor of 3 if the origin is the center of dilation, What is the new vertex, a', if the old vertex was located. at A(3,4)?
_______________________________________
Please, give me some minutes to take over your question
__________________________________________
Simplify to the fullest;
[tex]{ \rm{ \frac{dy}{dx} + 2x + 1 = 2 }}[/tex]
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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