Answer:
3
[tex]d\in R,\hspace{5}d\neq 0[/tex]
Step-by-step explanation:
You can solve for any variable. From the first equation, let's solve for c :
[tex]\frac{c+1}{d} =5\\\\c+1=5d\\\\c=5d-1[/tex]
Now, replace the value of c into the other equation:
[tex]\frac{30d}{2c+2} \\\\\frac{30d}{2(5d-1)+2} \\[/tex]
Using distributive property
[tex]\frac{30d}{10d-2+2} =\frac{30d}{10d} =3[/tex]
However, keep in mind that this is true for:
[tex]d\in R,\hspace{5}d\neq 0[/tex]
Help me cuh what are the period and vertical shift of the cosecant function below?
Answer:
Period: 2pi vertical shift: 2 units up
Step-by-step explanation:
Answer:
D. period: 4pi; vertical shift: 2 units up
Step-by-step explanation:
Just did the test right now hope this helps some of yall :)
how to do this question plz answer
Answer: 28
Step-by-step explanation:
The shape is grouped into 4 identical parallelograms.
Thus, as the combined area of the figure is 308, you can divide 308/4 to get 77. Thus, each parallelogram has an area of 77.
Then, divide 14/2 to get that the height of each parallelogram is 7.
The area of a parallelogram is l*w. Thus, because l = 7, each parallelogram has a width of 11 because 77/7 = 11.
Then, simply add 11+11+6 to get y.
Hope this helps <3
If (ax+b)(bx+a)=26x^2+ Box(x) +26, where a, b, and Box are distinct integers, what is the minimum possible value of Box, the coefficient of x?
Question in latex: If $(ax+b)(bx+a)=26x^2+\Box\cdot x+26$, where $a$, $b$, and $\Box$ are distinct integers, what is the minimum possible value of $\Box$, the coefficient of $x$?
Answer:
16.59
Step-by-step explanation:
Given:
[tex](ax+b)(bx+a)=26x^2+\Box\cdot x+26[/tex]
Expanding the left hand side, we have:
[tex](ax+b)(bx+a)=abx^2+a^2x+b^2x+ab\\=abx^2+(a^2+b^2)x+ab\\=26x^2+\Box\cdot x+26\\ab=26 \implies b=\frac{26}{a}[/tex]
Therefore:
[tex]a^2+b^2=a^2+\dfrac{26}{a} =\dfrac{a^3+26}{a}[/tex]
To find the minimum value, we take the derivative and solve for its critical point.
[tex]\frac{d}{da} (\frac{a^3+26}{a})=\frac{2a^3-26}{a^2}\\$Setting the derivative equal to zero, we have:\\2a^3-26=0\\2a^3=26\\a^3=13\\a=\sqrt[3]{13}[/tex]
Recall that:
[tex]\Box=a^2+b^2=\dfrac{(\sqrt[3]{13}) ^3+26}{\sqrt[3]{13}}\\=\dfrac{13+26}{\sqrt[3]{13}}\\\\\Box=16.59[/tex]
The minimum possible value of the coefficient of x is 16.59.
Answer:
173
Step-by-step explanation:
For sympliciy let the box equal y.
Expanding the left side we get (a*x+b)(b*x+a) = (a*b*(x)^2 + (a^2 + b^2)x + a*b). Hence we have that (a*b*(x)^2 + (a^2 + b^2)x + a*b) = 26*(x)^2 + x*y + 26. Scince the coefficients of like terms in our equation must be equal, ab=26. Hence (a,b) = (1,26),(26,1),(-1,-26),(-26,-1),(2,13),(13,2),(-2,-13),(-13,-2). Since a^2 + b^2 = y we can see that the only 2 values of y are 677 and 173 (by simply plug in the values of (a,b)), taking the smaller of the two our answer is [173].
Matt invested $1500 into a stock of his choice. After two years, he had received
$400 in dividends. He sold the stock and received a total of $1600. What is Matt's
rate of return on investment?
For this question, the time given confuses me. I know the rate of return is just total return divided by divided by investment, Assuming that Matt received the $400 in dividends as cash payouts, and they weren't reinvested into buying shares of the stock, then his total return over two years was $500, Now, if Matt's dividends were reinvested into the stock - and if you have a 401(k) or IRA, that's what usually happens - then his ROI would have been only 6% because he only made a profit of $100 on an investment of $1500. Note: In the real world, in current market conditions, Matt probably would have got about a 5% return on a good stock, and Bella would have received about 0.05% on a savings account.
hope this helped you ;)
Matt probably would have got about a 5% return on a good stock.
How to find the rate of return?The rate of return is just the total return divided by investment.
Consider that Matt received the $400 in dividends as cash payouts, and they weren't reinvested into buying shares of the stock, then his total return over two years was $500.
Now, if Matt's dividends were reinvested into the stock then his ROI would have been only 6% because he only made a profit of $100 on an investment of $1500.
In the real, current market conditions, Matt probably would have got about a 5% return on a good stock, and Bella would have received about 0.05% on a savings account.
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Help please ASAP :) please give answers to both questions
Answer:
2 cm
10 cm
Step-by-step explanation:
14/7 = 2
This helps to find because area of rectangle = bh or base times height.
A = 1/2 bh
30 = 1/2 b 6
30 = 3b
b = 10
Answer:
b = 2 cm
b = 10 cm
Step-by-step explanation:
Area of a Rectangle: A = lw
Area of a Triangle: A = 1/2bh
We are given area and length, so simply plug it in:
14 = 7w
w = 2 cm
We are given area and height, so simply plug it in:
30 = 1/2(6)(b)
30 = 3b
b = 10 cm
HELPPP DO NOT LOOK IT UP PLS
the question is 1/2 of 5 =
Answer:
2.5
Step-by-step explanation:
1/2x5=?
5/2=?
2.5=?
Answer:
[tex]\boxed{2.5}[/tex]
Step-by-step explanation:
=> [tex]\frac{1}{2} of 5[/tex]
The word "of" means "to multiply"
=> [tex]\frac{1}{2} * 5[/tex]
=> [tex]\frac{1*5}{2}[/tex]
=> [tex]\frac{5}{2}[/tex]
=> 2.5
Please help me if you can thanks
Step-by-step explanation:
a, 3
b,
draw lines through the corresponding corners of each shape These lines will cross at the centre of enlargement O
Perform the indicated operation (25m2 - 20m + 4) ÷ (5m - 2)
Hey there! :)
Answer:
5m - 2.
Step-by-step explanation:
We can use long division to divide the two expressions:
5m - 2
5m - 2 | 25m² - 20m + 4
25m² - 10m
-
0m² - 10m + 4
-10m + 4
-
0
The quotient of this operation is 5m - 2.
Square all the integers from 1 to 10 inclusive. Then, round each number to the nearest hundred. Finally, sum the numbers. What do you get?
Answer:
22.467
Step-by-step explanation:
Hello,
You just have to do the computation in XL or using a calculator, and round each number to the nearest hundred
x sqrt(x)
1 1
2 1.414
3 1.732
4 2
5 2.236
6 2.449
7 2.646
8 2.828
9 3
10 3.162
and do the sum which is 22.467
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
300
Step-by-step explanation:
First let's square all the integers from 1 to 10 inclusive. We get:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100.
Rounding to the nearest hundred, we get that 1, 4, 9, 16, 36, and 49 all round to 0 and 64, 81, and 100 round to 100.
Therefore, we obtain
0+0+0+0+0+0+0+100+100+100,
or 300.
which of the following shows the polynomial below written in descending order?
Answer:
A
Step-by-step explanation:
Descending order is where the monomials of a polynomial are arranged in decreasing exponent order so the answer is A.
Answer:
the answer is option a because all the expression in option a is written descending power form.
• How can you tell that a point on the graph is a maximum, a minimum, or neither?
Answer:
If it is on the maximum, then the y-value of the point cannot be any higher and still be on the graph of the function. If it is on the minimum, the the y-value of the point cannot be any lower and still be on the graph of the function. If it isn't either the maximum or the minimum, it is neither.
Adding to "undo" subtraction and subtracting to "undo" addition are both examples of using inverse operations to solve equations. Think of another pair of inverse operations in mathematics. How do these inverse operations "undo" each other?
Answer:
see below
Step-by-step explanation:
Multiplication and division are also inverse operations
15 * 10 = 150
150 ÷10 = 15
Divide 150 by 10 and we get 15 back
The division undoes the multiplication
This also works in reverse
150 ÷ 10 = 15
15*10 =150
The multiplication undoes the division
The numbers $1,$ $2,$ $\dots,$ $10$ are to be entered into the 10 boxes shown below, so that each number is used exactly once: \[P = (\square + \square + \square + \square + \square)(\square + \square + \square + \square + \square).\]What is the maximum value of $P$? What is the minimum value of $P$?
Answer:
Maximum = 756
Minimum = 600
Step-by-step explanation:
A square is a shape that has the large areas of a defined perimeter out of available rectangles. It implies they want the two parentheses to be as similar in value. as a result, to establish the maximum value of P.
And to establish the minimum value, to have the greatest difference for them. 1 + 2 + 3 ... +10=55, which wasn't even but which can be split as similarly as possible into 27 and 28 which have a product of 756. In this question it can be done in a variety of ways, one of which is:
(1 + 3 + 5 + 8 + 10) × (2 + 4 + 6 + 7 + 9) = 756
At the very least, the biggest difference can be created if one term is made of the smallest numbers, while the other full of the highest, or:
(1 + 2 + 3 + 4 + 5) × (6 + 7 + 8 + 9 + 10)=600
which equation has roots of 3plus or minus sqare rt 2?
Answer:
Option D is correct.
The equation with roots 3 plus or minus square root 2 is x² - 6x + 7
Step-by-step explanation:
The roots of the unknown equation are
3 ± √2, that is, (3 + √2) and (3 - √2)
The equation can then be reconstructed by writing these roots as the solutions of the quadratic equation
x = (3 + √2) or x = (3 - √2)
The equation is this
[x - (3 + √2)] × [x - (3 - √2)]
(x - 3 - √2) × (x - 3 + √2)
x(x - 3 + √2) - 3(x - 3 + √2) - √2(x - 3 + √2)
= x² - 3x + x√2 - 3x + 9 - 3√2 - x√2 + 3√2 - 2
Collecting like terms
= x² - 3x - 3x + x√2 - x√2 - 3√2 + 3√2 + 9 - 2
= x² - 6x + 7
Hope this Helps!!!
The sum of digits in two-digit number is 13. If the place values of the digits are reversed, the new number is 27 more than the original number. Find the original number.
Answer: 58
Step-by-step explanation:
The sum of the two digit number is 13. On reversing its digits the new number is 27 more than the original number find the number?
Let's set up a system with two variables: x = tens place of our answer, y = units place of our answer.
Digit sum of a two digit number is 6:
x+y=13
Reverse the digits and you get 27 more than the original value:
10y+x=10x+y+27
Now let's solve:
y=13-x
10(13-x)+x=10x+(13-x)+27
130-10x+x=130x-10x + 27
130-9x=9x+40
-90=18x
x=5
y=13-5
y=8
So our original number was 58. Sum of digits is 13. Swap the order of the digits to make 85, and you have a number 27 more than the original number.
The value of original number is, 58.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The sum of digits in two-digit number is 13.
And, If the place values of the digits are reversed, the new number is 27 more than the original number.
Now, Let the one's place digit is y and the ten's place is x of the original number.
Then, We get;
⇒ x + y = 13 .. (i)
And, If the place values of the digits are reversed, the new number is 27 more than the original number.
So, We get;
⇒ 10y + x = 27 + 10x + y
⇒ 10y - y + x - 10x = 27
⇒ 9y - 9x = 27
⇒ y - x = 3
⇒ y = x + 3 ... (ii)
Substitute the value of y from (ii) in (i), we get;
⇒ x + y = 13
⇒ x + x + 3 = 13
⇒ 2x = 13 - 3
⇒ 2x= 10
⇒ x = 5
And, From (ii);
⇒ y = x + 3
⇒ y = 5 + 3
⇒ y = 8
Thus, The original number is,
⇒ 10x + y = 10 × 5 + 8
= 50 + 8
= 58
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Find the total surface area of this triangular prism...
Answer:
144 cm^2
Step-by-step explanation:
8x6+4x10+4x8+4x6
48+40+32+24
80+40+24
120+24
144
Help please on linear math
Answer:
D
Step-by-step explanation:
[tex]y=\frac{-9x-5}{-8}[/tex]
factoring out a negative[tex]y=\frac{9x+5}{8}[/tex]
Answer:
[tex] \frac{5}{8} [/tex]Option D is the correct option.
Step-by-step explanation:
Given that
9x - 8y = 0
finding y-intercept
put x = 0 , we get
9(0) - 8y + 5 = 0
Calculate the product
-8y + 5 = 0
Move the constant to L.H.S and change its sign
-8y = 0 - 5
Calculate the difference
-8y = -5
divide both sides of the equation by -8
-8y/-8 = -5/-8
Calculate
y = 5/8
Hope this helps...
Good luck on your assignment...
At which root does the graph of f(x) = (x + 4) 6(x + 7)5 cross the x-axis?
-7
4
4
07
Answer:
-7 and -4
Step-by-step explanation:
The graph of the function f(x) = (x + 4)⁶ (x + 7)⁵ cross the X axis at x = -4 and x = -7.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given is a function,
f(x) = (x + 4)⁶ (x + 7)⁵
When the function cross the X axis, the value of the function will be 0.
Let f(x) = 0
(x + 4)⁶ (x + 7)⁵ = 0
This implies that, either x + 4 = 0 or x + 7 = 0
x + 4 = 0 ⇒ x = -4
x + 7 = 0 ⇒ x = -7
Hence the roots are -4 and -7 where the function crosses the X axis.
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WILL GIVE BRAINLIEST THANKS AND 5 STARS... PLZ HELP
Answer:
507x223 is greater than 530 x 200
914x385 is less than 900 x 400
Which of the following functions is graphed below?
8
84
4.
24
-8
2
4
8
8
12
-2
4
-6+
-87
Answer:
Step-by-step explanation:-
-
-8239910.76
19. Solve for g: 5 / 8 = 12 / g
Answer:
19.2Solution,
[tex] \frac{5}{8} = \frac{12}{g} \\ or \: 5 \times g = 12 \times 8 \: ( \: cross \: multiplication) \\ or \: 5g = 96 \\ or \: g = \frac{96}{5} \\ g = 19.2[/tex]
Hope this helps..
Good luck on your assignment...
Answer:
Step-by-step explanation:
5/8=12/g
*8 *8
5=12*8/g
*g *g
5g=12*8=96
:5 :5
g=96/5
g=19.2
The planet mercury is approximately 6*10^7 miles from the sun. The distance between the sun and mars is approximately 2*10^8 miles. About how many times farther from the sun is mars than mercury.
Answer:
Around 10/3 or 3.33 times farther.
Step-by-step explanation:
We simply divide the larger distance by the smaller distance to find our ratio:
2(10⁸)/6(10⁷)
10/3
*Remember when you divide exponents, you subtract them
Helppp!!!! please!!!
Answer: B. rectangular pyramid
Point L is located at (4, -3) and M is located at (-8, 5). Find the y value of the point that lies halfway between L and M.
Answer:
y = 1
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[ [tex]\frac{1}{2}[/tex] (x₁ + x₂ ), [tex]\frac{1}{2}[/tex] (y₁ + y₂ ) ]
Here (x₁, y₁ ) = (4, - 3) and (x₂, y₂ ) = (- 8, 5), thus the y value of midpoint is
y = [tex]\frac{1}{2}[/tex] (- 3 + 5) = 0.5 × 2 = 1
In circle C. r = 32 units.
What is the area of circle C?
A
32īt units?
c
641 units?
256TI units
1024Tt units?
Answer:
1024 pi
Step-by-step explanation:
r = 32 units.
Area = pi * r^2
Area = 3.14 * 32^2
Area = 1024 * pi
Tt = pi??
Please help me with this. Attention all smart people!!!
Answer: CPCTC
Step-by-step explanation:
because in the step before that it was proved that the triangles were congruent and CPCTC is used after they are proved congruent.
By CPCT [Corresponding Part of congruent Triangle]
<h=<j
hope i helped
-lvr
question 1: 5 1/8 is 2/3 of what number?
question 2: what fraction of 9 3/8 is 4 3/8?
Answer:
1) [tex]7 \frac{11}{16} [/tex]
2) [tex] \frac{7}{15} [/tex]
Step-by-step explanation:
1) Let's convert the mixed fraction into a improper fraction.
[tex]5\frac{1}{8} \\ = \frac{5(8) + 1}{8} \\ = \frac{41}{8} [/tex]
Let the number be x.
[tex] \frac{2}{3} x = \frac{41}{8} \\ x = \frac{41}{8} \div \frac{2}{3} \\ x = \frac{41}{8} \times \frac{3}{2} \\ x = \frac{123}{6} \\ x = 7 \frac{11}{16} [/tex]
2)[tex]4 \frac{3}{8} = \frac{35}{8} [/tex]
[tex]9 \frac{3}{8} = \frac{75}{8} [/tex]
[tex]4 \frac{3}{8} \div 9 \frac{3}{8} \\ = \frac{35}{8} \div \frac{75}{8} \\ = \frac{35}{8} \times \frac{8}{75} \\ = \frac{7}{15} [/tex]
What is the ratio of the Volume of the smaller pyramid to the larger pyramid
which shape is a parallelogram?
Answer:
A,C,and D are parralelograms
The parallelogram are shapes with figures having opposite sides which are parallel
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The sum of angles of a parallelogram is 360°
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the parallelogram be represented as ABCD
Now , from the figure 1
a)
The figure is having opposite sides are parallel
where AB = CD
And , BC = AD
So , it is a parallelogram
b)
The figure does not have any sides parallel
So , it is not a parallelogram
c)
The shape is having 2 sides as parallel
And , AB = CD
So , it is a parallelogram
d)
The shape is having 2 sides as parallel
And , AB = CD
So , it is a parallelogram
Hence , the parallelogram is solved
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