Answer: (1,3,5) & (2,2)
Step-by-step explanation:
During the worst periods of hyperinflation in a certain country, the price of food increase at a rate of 10% per month. State whether this increases was linear or exponential. If your food bill was 100 in one month during this period, what was it three months later?
Answer:
The increase was exponential
After three months his expense was: $133.1
Step-by-step explanation:
The increase was exponential, because if we call x the initial price, then after the first month the new price p is:
[tex]p = x (1 + \frac{10\%}{100\%})\\\\p=x(1+0.1)[/tex]
After the second month, the new price is 10% of the price of the previous month, that is:
[tex]p = [x (1 + 0.1)](1 + 0.1)\\\\p = x (1 + 0.1) ^ 2[/tex]
After month n, the price is:
[tex]p = x (1 + 0.1) ^ n[/tex]
Note that the equation has the form of an exponential growth function, where x is the initial price and n is the number of months elapsed.
In this case [tex]x = 100[/tex] and [tex]n = 3[/tex]. So:
[tex]p = 100 (1 + 0.1) ^ 3\\\\p=\$133.1[/tex]
plz help me plz plz plz
Answer:
195
Step-by-step explanation:
9 times 10 is 90 and 7 times 15 is 105
so 105+90=195
Answer:
195 cm
Step-by-step explanation:
The area of ABCD is 195 cm.
Multiply the sides together:
9 ⋅ 10 = 90
7 ⋅ 15 = 105
Add them together:
105 + 90 = 195
Therefore, the area of ABCD is 195 cm.
The first diagram shows an equilateral triangle and a
square with the same side length S. Find the area of the
triangle Ar in terms of the area of the square As
Answer:
Ar = ¼√3 As
Step-by-step explanation:
Area of an equilateral triangle is:
Ar = ¼√3 s²
Area of a square is:
As = s²
Substituting:
Ar = ¼√3 As
What is the range of the given function?
{(-2, 0), (-4,-3), (2, -9), (0,5), (-5, 7)}
{x|x = -5, -4,-2, 0, 2)
{yly = -9, -3, 0,5,7)
{x|x= -9,-5, 4, -3, -2, 0,2 5,7}
{yly = -9, -5, -4 -3 -2,0, 2, 5, 7}
Step-by-step explanation:
range is all the y values
{y|y=-9, -3, 0, 5, 7}
The range of a function are all the ys included in the graph. In this case that would be:
(-2, 0), (-4,-3), (2, -9), (0,5), (-5, 7)
Remember to order it from least to greatest:
{yly = -9, -3, 0,5,7}
Hope this helped!
~Just a girl in love with Shawn Mendes
Which product is equivalent to 25x2 – 16?
Answer:
The correct answer would be 34
Step-by-step explanation:
When solving an expression, we would first solve the operator with the highest precedence. In mathematics, there are four basic operators. Addition, subtraction, multiplication and division. The precedence of Division and multiplication is higher than the precedence of Addition and subtraction. So by solving this with the precedence, we would first solve the multiplication operator which is 25 * 2, it will give 50, then we will subtract 16 from it like 50-16, which will give us 34.
Answer:
(5x+4)(5x-4)
Step-by-step explanation:
The product expression can be obtained by factorizing the expression 25x²-16 provided in the question.
The expression is a difference of two squares whose factors are generally
(a-b)(a+b)
√25x² is 5x
√16 is 4
Therefore the product required is (5x+4)(5x-4)
25x²-16 is equivalent to (5x+4)(5x-4)
Given the following coordinates complete the reflection transformation. A(−5,0) B(−3,3) C(−3,0) Transformation: Complete the double reflection over the lines x=−2 followed by x=1. A"( , ) B"( , ) C"( , )
Answer:
A''(1,-1) B''(3,2) C''(3,2)
Step-by-step explanation:
A(−5,0) B(−3,3) C(−3,0)
reflection over x=-2
Perpendicular distance between points y-coordinates of points (A, B and C) and y=-1 are 3,1 and 1
after reflections, the perpendicular distance will be 6,2,2, and the points will be at
A'(1,0) B'(−1,3) C'(−1,0)
again reflection over x=1
Perpendicular distance between points y-coordinates of points (A', B' and C') and y=1 are 0,2,2
after reflections, the perpendicular distance will be 0,4,4 and the points will be at
A''(1,-1) B''(3,2) C''(3,2)!
Three vertices of a square are (–1, 2), (2, 2), and (2, –1).
What is the fourth vertex of the square?
(–1, –1)
(–1, –2)
(2, 1)
(5, 1)
Question 5
Three vertices of a square are (–1, 2), (2, 2), and (2, –1).
What is the fourth vertex of the square?
(–1, –1)
(–1, –2)
(2, 1)
(5, 1)
Answer:
(-1,-1)
Step-by-step explanation:The square needs to be all side with the same value when you graph the vertices on x-y plot, you obtain (x is the dot that correspond a vertice and y the forth vertice )
x 2 | x
1 |
|
-2 -1 | 1 2
y -1| x
-2 |
If you draw a line between vertices the value it will be 2 + (-1) so the forth vertice has to be (-1,-1)
The function whose graph is shown below has the following characteristics.
•Two relative minima
•Two relative maxima
○True
○False
Answer with explanation:
A function is said to attain maximum in the interval , if you consider any two points on the curve suppose (a,b) and (c,d)
if , c>a
Then , f(d) > f(a).
A function is said to attain minimum in the interval,
if ,c>a
Then,f(d)< f(a).
A function can have more than one relative Maximum and more than one relative Minimum.
The function whose graph is given here has following Characteristics
•Two relative minima
•Two relative maxima
is True .
If f(x) = 5x, what is f^-1(x)?
o f^-1(x) = -5x
o f^-1(x)= -1/5x
o f^-1(x) = 1/5x
o f^-1(x) = 5x
Answer:
Third choice
Step-by-step explanation:
They are asking us to find the inverse of y=5x. To do this you just switch x and y and then remake y the subject of the equation (solve for y.)
y=5x
x=5y (I switch x and y)
x/5=y ( I divided both sides by 5)
Then you just replace y with the f^-1(x) thing
f^-1(x)=x/5
or
f^-1(x)=1/5x
If f(x) = 5x, then the inverse of the function, f⁻¹(x) is x/5.
Given that :
f(x) = 5x
Let y = f(x).
So, y = 5x
Now, interchange the values for x and y.
Then,
x = 5y
Now, solve for y.
Divide both sides of the equation by 5.
x/5 = y
So, the inverse of the function is x/5.
Hence f⁻¹(x) = x/5.
To learn more about Inverse Functions, click here :
https://brainly.com/question/29141206
#SPJ7
Find the value of y.
Answer:
The answer should be the last one.
Step-by-step explanation:
Answer:
=2√2 the fourth choice.
Step-by-step explanation:
We can use the Pythagoras theorem to calculate the value of y.
a²+b²=c²
a=1
b=y
c=3
Therefore substituting for the values in the theorem above we get:
1²+y²=3²
Leave y on one side.
y²=3²-1²
y²=9-1
y²=8
y=±2√2 in surd form.
Since we expressing length, a scalar quantity, we take the modulus of our answer. Thus y=2√2
A box can hold 24 crayons. How many boxes must be used to put all of Mr.Syed's 98 crayons into boxes?
Answer:
5 boxes
Step-by-step explanation:
Given:
Total crayons : 98
Capacity of each box : 24
Number of boxes of 24 crayons needed to hold 98 crayons,
= 98 ÷ 24
= 4.08 boxes.
However since we cannot have 0.08 of a box, we must round this up to the next larger whole number of boxes.
4.08 rounded up to next whole number = 5
Hence he will need 5 boxes to hold all 98 crayons
Solve (x + 2<5) n (x-7>-6).
{x11
{x1x < 3 or x> 1)
{all real numbers)
For this case we must solve [tex]x + 2 <5[/tex]intersected with [tex]x-7> -6[/tex]
So, we have:
[tex]x + 2 <5\\x <5-2\\x <3[/tex]
The solutions are given by all strict minor numbers to 3.
[tex]x-7> -6\\x> -6 + 7\\x> 1[/tex]
The solutions are given by all the major strict numbers to 1.
If we intersect the solutions of both equations we have [tex]x <3[/tex] ∩ [tex]x> 1[/tex].
The intersection is given by [tex]1 <x <3[/tex]
Answer:
The solution interval is (1,3)
What are the coordinates of point C on the directed segment from A (-8,4) to B (10,2) that partitions the segment such that AC:CB is 2:1?
To find the coordinates of point C, divide the x- and y-coordinates of AB in the ratio 2:1.
Explanation:To find the coordinates of point C, we can use the concept of dividing a line segment in a given ratio. Given that AC:CB is 2:1, we can divide the x- and y-coordinates of the line segment AB in the same ratio.
The x-coordinate of point C is calculated by dividing the difference between the x-coordinates of points A and B by the sum of the ratio (2+1).
The y-coordinate of point C is calculated by dividing the difference between the y-coordinates of points A and B by the sum of the ratio (2+1).
Therefore, the coordinates of point C are (-2, 3).
Learn more about Coordinates here:https://brainly.com/question/30227780
#SPJ12
The correct option is d. [tex]\((4, 0)\)[/tex]. The coordinates of point [tex]\(C\)[/tex] are [tex]\((4, 0)\)[/tex].
To find the coordinates of point [tex]\(C\)[/tex] that partitions the segment [tex]\(AB\)[/tex] in the ratio [tex]\(AC:CB = 2:1\)[/tex], we use the section formula. Given points [tex]\(A(x_1, y_1)\)[/tex] and [tex]\(B(x_2, y_2)\)[/tex] with a ratio [tex]\(m:n\)[/tex], the coordinates [tex]\((x, y)\)[/tex] of the point dividing the segment in the ratio [tex]\(m:n\)[/tex] are given by:
[tex]\[x = \frac{mx_2 + nx_1}{m + n}, \quad y = \frac{my_2 + ny_1}{m + n}\][/tex]
For this problem:
- [tex]\(A(-8, 4)\)[/tex]
- [tex]\(B(10, -2)\)[/tex]
- Ratio [tex]\(m:n = 2:1\)[/tex]
Plugging in the values:
[tex]\[x = \frac{2 \cdot 10 + 1 \cdot (-8)}{2 + 1} = \frac{20 - 8}{3} = \frac{12}{3} = 4\][/tex]
[tex]\[y = \frac{2 \cdot (-2) + 1 \cdot 4}{2 + 1} = \frac{-4 + 4}{3} = \frac{0}{3} = 0\][/tex]
Thus, the coordinates of point [tex]\(C\)[/tex] are [tex]\((4, 0)\)[/tex].
The complete question is:
What are the coordinates of point C on the directed segment from A(−8,4) to B(10,−2) that partitions the segment such that AC:CB is 2:1 ?
A. (1,1)
B. (−2,2)
C. (2,−2)
D. (4,0)
PLEASE HELP
A rectangular pyramid has a height of 6 units and a volume of 40 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?
A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
Answer:
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct
Step-by-step explanation:
step 1
Find the area of the base of the rectangular pyramid
we know that
The volume of the rectangular pyramid is equal to
[tex]V=\frac{1}{3}BH[/tex]
where
B is the area of the base
H is the height of the pyramid
we have
[tex]V=40\ units^{3}[/tex]
[tex]H=6\ units[/tex]
substitute and solve for B
[tex]40=\frac{1}{3}B(6)[/tex]
[tex]120=B(6)[/tex]
[tex]B=120/6=20\ units^{2}[/tex]
step 2
Find the volume of the rectangular prism with the same base area and height
we know that
The volume of the rectangular prism is equal to
[tex]V=BH[/tex]
we have
[tex]B=20\ units^{2}[/tex]
[tex]H=6\ units[/tex]
substitute
[tex]V=(20)(6)=120\ units^{3}[/tex]
therefore
The rectangular prism has a volume that is three times the size of the given rectangular pyramid. Shannon is correct
Answer:
C
Step-by-step explanation:
Got it right one the test! <3
What is the distance between the points (2, 8) and (-7, -4) in the coordinate plane?
The distance between the points (2, 8) and (-7, -4) is 15 units.
Using the distance formula derived from the Pythagorean theorem, the distance between the points (2, 8) and (-7, -4) is found to be 15 units.
The distance between two points in the coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. For points (2, 8) and (-7, -4), the distance can be calculated as follows:
Subtract the x-coordinates: 2 - (-7) = 9.Subtract the y-coordinates: 8 - (-4) = 12.Square each result: 92 = 81 and 122 = 144.Add the squares together: 81 + 144 = 225.Take the square root of the sum: \\sqrt{225}\ = 15.Therefore, the distance between the points (2, 8) and (-7, -4) is 15 units.
What value of b will cause the system to have an infinite
number of solutions?
у= 6x –b
—3х + 1/2y=-3
a) 2
b) 4
c)6
d)8
Answer:
Option C) b=6
Step-by-step explanation:
we know that
If two linear equations of a system of equations have an infinite of solutions, then both equations are identical
we have
[tex]y=6x-b[/tex] -----> equation A
[tex]-3x+(1/2)y=-3[/tex]
Multiply by 2 both sides
[tex]-6x+y=-6[/tex]
Adds 6x both sides
[tex]y=6x-6[/tex] ------> equation B
equate equation A and equation B
[tex]6x-b=6x-6[/tex]
solve for b
[tex]b=6[/tex]
solve 2/5+1/4+7/10= in simplest form
Answer:
1.35 or 27/20
Step-by-step explanation:
(2/5) + (1/4) + (7/10)
= 0.4 + 0.25 + 0.7
= 1.35 or 27/20
which equation represents the data in the table? check all that apply
Answer:
[tex]y-6=-\frac{5}{4}(x+2)[/tex]
[tex]y-1=-\frac{5}{4}(x-2)[/tex]
[tex]y-3.5=-1.25x[/tex]
Step-by-step explanation:
step 1
Find the slope of the linear equation
with the points (-2,6) and (2,1)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{1-6}{2+2}[/tex]
[tex]m=-\frac{5}{4}[/tex]
step 2
Find the equation of the line into point slope form
The equation of the line in slope point form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{5}{4}[/tex]
1) with the point (-2,6)
substitute
[tex]y-6=-\frac{5}{4}(x+2)[/tex]
2) with the point (2,1)
substitute
[tex]y-1=-\frac{5}{4}(x-2)[/tex]
3) with the point (0,3.5)
substitute
[tex]y-3.5=-\frac{5}{4}(x-0)[/tex]
[tex]y-3.5=-\frac{5}{4}x[/tex] -------> [tex]y-3.5=-1.25x[/tex]
Answer:
A, D, E
Step-by-step explanation:
One triangle has the hypotenuse of 26 and the shortest side is 10, what is the other side?
a. 22
b. 25
c. 24
d. 23
Answer:
C. 24
Step-by-step explanation:
In a right triangle, the sum of the squares of the two legs of the triangle is equivalent to the square of the hypotenuse.
a²+b²=c²
a=10
b=?
c=26
Let us substitute with the values given in the question.
10²+b²=26²
100+b²=676
b²=676-100
b²=576
b=√576
=24
The other leg of the triangle is 24 units long.
Answer: option c.
Step-by-step explanation:
You need to use the Pythagorean Theorem. This is:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse and "b" and "c" are legs of the triangle.
In this case you know that:
[tex]a=26\\b=10[/tex]
Then, you need to substitute values into [tex]a^2=b^2+c^2[/tex] and then solve for "c".
So, this is:
[tex]26^2=10^2+c^2\\\\26^2-10^2=c^2\\\\576=c^2\\\\\sqrt{576}=c\\\\c=24[/tex]
why does 7 9/7 = 8 2/7?
Firstly see what they are in mixed fraction form:
[tex]7 \frac{9}{7} = \frac{58}{7} [/tex]
therefore, 7 9/7 is equal to 58/7
[tex]8 \frac{2}{7} = \frac{58}{7} [/tex]
Prove that the diagonals of a rectangle bisect each other.
The midpoint of AC is _____
Answer:
answer is a,b
Step-by-step explanation:
I have answered ur question
The mid-point of AC is (a, b). So, option D is correct. In a rectangle, the two diagonals bisect each other at their mid-point.
How to prove that the diagonals of a rectangle bisect each other?Find the mid-points of both the diagonals of the rectangleMid-point = ((x1+x2)/2, (y1+y2)/2)If the midpoints of both the diagonals are the same then they are said to bisect each other. If they are not the same, then they are not bisecting each other.Calculation:The given rectangle is ABCD
Its vertices have coordinates as
A - (0, 0)
B - (0, 2a)
C - (2a, 2b)
D - (2a, 0)
The diagonals are AC and BD.
Finding their mid-points:
Mid-point of the diagonal AC = ((0 + 2a)/2 , (0 + 2b)/2)
⇒ (2a/2, 2b/2)
⇒ (a, b) ... (1)
Mid-point of the diagonal BD = ((0 + 2a)/2, (2a+0)/2)
⇒ (2a/2, 2b/2)
⇒ (a, b) ...(2)
From (1) and (2), the midpoints of both the diagonals are equal. So, the diagonals of the rectangle ABCD bisect each other.
Hence, proved.
Therefore, the mid-point of the diagonal AC is (a, b).
Learn more about the diagonals of a rectangle here:
https://brainly.com/question/17117320
#SPJ2
drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. solve for x and match the solutions
The solutions to the linear equations in variable x and unknown constant [tex]\alpha[/tex] are [tex]\frac{-\alpha}{6}[/tex], [tex]\frac{3}{\alpha}[/tex] and [tex]\frac{-6}{\alpha}[/tex].
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
We are given linear equations in variable x with an unknown constant [tex]\alpha[/tex] and we have to solve for x.
[tex]4 = \frac{6}\alpha}x + 5\\\\\frac{6}{\alpha}x = - 1\\\\x = \frac{-\alpha}{6}[/tex].
[tex]7 + 2\alpha{x} = 13.\\\\2\alpha{x} = 6.\\\\x = \frac{3}{\alpha}[/tex]
[tex]-\alpha{x} - 20 = -14.\\\\-\alpha{x} = 6.\\\\x = \frac{-6}{\alpha}[/tex]
learn more about linear equations here :
https://brainly.com/question/11897796
#SPJ5
Find the value of x in the picture please
Answer:
Option B. The value of x is 20
Step-by-step explanation:
we know that
The intersecting chords theorem states that the products of the lengths of the line segments on each chord are equal.
so
In this problem
[tex](x)(x-11)=(x-8)(x-5)\\x^{2}-11x=x^{2}-5x-8x+40\\-11x=-13x+40\\2x=40\\x=20[/tex]
Match the expression with its name.
10x2 – 5x + 10
quadratic trinomial
cubic monomial
not a polynomial
fourth-degree binomial
Answer:
[tex]\large\boxed{10x^2-5x+10\ -\ \bold{quadratic\ trinomial}}[/tex]
Step-by-step explanation:
[tex]\text{quadratic trinomial}\ -\ ax^2+bx+c\\\\\text{cubic monomial}\ -\ ax^3\\\\\text{not a polynomial}\ -\ \dfrac{a}{x}\\\\\text{fourth-degree binomial}\ -\ ax^4+bx[/tex]
[tex]10x^2-5x+10\\\\\text{the highest power of variable (x) is 2}\to \boxed{x^2}\ \to\ \bold{quadratic}\\\\\text{polynomial has 3 terms}\ \to\ \boxed{10x^2,\ -5x,\ 10}\ \to\ \bold{trinomial}[/tex]
what is equivalent to 10/10^3/4
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\\\ ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{10}{10^{\frac{3}{4}}}\implies \cfrac{10^1}{10^{\frac{3}{4}}}\implies \cfrac{10^{\frac{4}{4}}}{10^{\frac{3}{4}}}\implies 10^{\frac{4}{4}}\cdot 10^{-\frac{3}{4}}\implies 10^{\frac{4}{4}-\frac{3}{4}}\implies 10^{\frac{1}{4}}\implies \sqrt[4]{10}[/tex]
Which table contains the vertex of the graph represented by y=x^2-6x+4?
A
x y
-2 20
0 4
2 -4
4 -4
B
x y
-1 11
1 -1
3 -5
6 4
C
x y
-3 31
-1 12
0 4
2 12
D
x y
0 5
2 7
3 5
5 7
Answer:
Table B
Vertex is (3,-5)
Step-by-step explanation:
We are given with an equation of a parabola [tex]y=x^2-6x+4[/tex]
Let is convert it into standard form of a parabola
[tex]y=x^2-6x+4[/tex]
adding and subtracting 9 in the right hand side of the =
[tex]y=x^2-6x+9-9+4[/tex]
[tex]y=x^2-2\times 3\times x+ 3^2-9+4[/tex]
the first three terms of the right hand side forms the expression of square of difference
[tex]a^2-2 \times a \times b+b^2 = (a-b)^2[/tex]
Hence
[tex]y=(x-3)^2-5[/tex]
adding 5 on both sides we get
[tex](y+5)=(x-3)^2[/tex]
Comparing it with the standard equation of a parabola
[tex]X^2=4\times \frac{1}{4} \times Y[/tex]
where [tex]X=x-3[/tex] and [tex]Y=y+5[/tex]
The vertex of [tex]X^2=4\times \frac{1}{4} \times Y[/tex] will be (0,0)
and thus vertex of
[tex](y+5)=(x-3)^2[/tex] will be (3,-5)
Hence the Table B is our right answer
19. x² + x = 6
the graf
Factors:
Solution(s):
For this case we must factor the following equation:
[tex]x ^ 2 + x-6 = 0[/tex]
We must find two numbers that, when multiplied, obtain -6 and when summed, obtain +1. These numbers are: +3 and -2
So, we have to:
[tex](x + 3) (x-2) = 0[/tex]
The roots are:
[tex]x_ {1} = - 3\\x_ {2} = 2[/tex]
ANswer:
[tex](x + 3) (x-2) = 0[/tex]
Find the formula for (f + g)(x) and simplify your answer.
f(x) = 3x and g(x) =
[tex] \sqrt{x - 4} [/tex]
[tex](f+g)(x)=3x+\sqrt{x-4}[/tex]
Complete the table for the given rule y=6x-4
Answer:
1 = 2
3 = 14
10 = 56
Step-by-step explanation:
y = 6x - 4
y = 6 - 4
y = 18 - 4
y = 60 - 4
Step-by-step explanation:
In first there is 2
ln second there is 14
ln third there is 56
I hope this is right answer!
convert -3 degree to farenheit
Answer:
26.6 degrees
Step-by-step explanation:
Use the converting formula:
(-3°C × 9/5) + 32 = 26.6°F
-3 degrees to Fahrenheit would be 26.6
The formula is attached in the image below
-3 × 1.8 = -5.4
-5.4 + 32 = 26.6