Answer:
-36 + 27j
Step-by-step explanation:
−9(4 − 3j)
Distribute
-9 * 4 -9 * (-3j)
-36 + 27j
Answer:
27j - 36.
Step-by-step explanation:
−9(4 − 3j)
= -9 * 4 - 9 * (-3j)
= -36 + 27j
= 27j - 36
Hope this helps!
Intro to Exponential Equations
Answer:
d.) 36
Step-by-step explanation:
f(x) = 4.[tex]3^{x}[/tex]
f(2) = 4 × 3² = 4 × 9 = 36
The farmer loaded 2/5 of the boxes onto the truck. He needed to load 345 more boxes of tomatoes onto the truck. How many boxes of tomatoes de he have to load altogether?
Answer:
575 boxes
Step-by-step explanation:
Let the total number of boxes = x
The farmer already loaded [tex]\dfrac25[/tex] of the boxes onto the truck.
Therefore, the remainder [tex]=1-\dfrac25=\dfrac35[/tex]
Since he needed to load 345 more boxes of tomatoes onto the truck.
[tex]\dfrac35 \times x =345\\3x=345\times5\\x=(345\times5) \div 3\\x=575[/tex]
The farmer had 575 boxes of tomatoes to load altogether.
Please help me, tysm if you do :)
The length of a rectangle is 2 cm less than three times the width. The perimeter of the rectangle is 92 cm. Find the dimensions of the rectangle. A. 11, 31 cm
B. 12, 34 cm
C. 12, 38 cm
D. 13, 37 cm
Answer:
B.12.32
Step-by-step explanation:
Let y be the widht of this triangle and x the length of itFrom the first information we can write :
3y-x=2
from the second one :
2y+2x= 92
so our equation are :
3y-x=22y+2x= 92Multiply the first one by 2 then add it to the second one to get rid of x :
6y-2x= 42y+2x+6y-2x= 92+4 8y = 96 y= 12 replace y by 12 to calculate the value of x x= 34two cars are traveling down the highway with the same speed if the first car increases its speed by 1km/hr and the other car decreases its speed by 10km/hr,then the first car will cover the same distance in 2hrs as the second car in 3 hrs, what is the speed of the cars
Answer:
Their speed is 32 km/h.
Step-by-step explanation:
Since they're at the same speed, we can assign a variable to their speed called "x". When the first car increases its speed by 1 km/h, its new speed is "x + 1", while the other car decreases its speed by 10 km/h, so its new speed is "x - 10". The distance's formula can be expressed as below:
[tex]\text{distance} = \text{speed}*\text{time}\\[/tex]
With the modifications to their speed, the distance the first car covers in 2 h and the distance the second car covers in 3 h is shown below:
[tex]\text{distance}_{car1} = (x + 1)*2 \\\text{distance}_{car1} = 2*x + 2[/tex]
[tex]\text{distance}_{car2} = \text{speed}*\text{time}\\\text{distance}_{car2} = (x - 10)*3\\\text{distance}_{car2} = 3*x - 30[/tex]
Since the distance covered by them must be the same, we can find the value of x that makes the expressions equal.
[tex]2*x + 2 = 3*x - 30\\2*x - 3*x = -30 -2\\-x = -32\\x = 32[/tex]
Their speed is 32 km/h.
I need help with this question please help
Answer:
6, 10, 8 is the correct answer.
Step-by-step explanation:
Given that, the recursive function:
[tex]a_n=a_{n-1}-(a_{n-2}-4)[/tex]
6th term, [tex]a_{6} =0[/tex]
5th term, [tex]a_{5} =-2[/tex]
To find:
First three terms of the sequence = ?
Solution:
Putting n = 6 in the recursive function:
[tex]a_6=a_{5}-(a_{4}-4)\\\Rightarrow 0=-2-(a_{4}-4)\\\Rightarrow 2=-(a_{4}-4)\\\Rightarrow -2=(a_{4}-4)\\\Rightarrow -2+4=a_{4}\\\Rightarrow a_{4}=2[/tex]
Putting n = 5 in the recursive function:
[tex]a_5=a_{4}-(a_{3}-4)\\\Rightarrow -2=2-(a_{3}-4)\\\Rightarrow -2-2=-(a_{3}-4)\\\Rightarrow 4=(a_{3}-4)\\\Rightarrow a_{3}=8[/tex]
Putting n = 4 in the recursive function:
[tex]a_4=a_{3}-(a_{2}-4)\\\Rightarrow 2=8-(a_{2}-4)\\\Rightarrow 2-8=-(a_{2}-4)\\\Rightarrow 6=(a_{2}-4)\\\Rightarrow a_{2}=10[/tex]
Putting n = 3 in the recursive function:
[tex]a_3=a_{2}-(a_{1}-4)\\\Rightarrow 8=10-(a_{1}-4)\\\Rightarrow 8-10=-(a_{1}-4)\\\Rightarrow -2=-(a_{1}-4)\\\Rightarrow 2=a_{1}-4\\\Rightarrow a_{1}=4+2\\\Rightarrow a_{1}=6[/tex]
So, first, second and third terms are 6, 10, 8.
in the function y+3=(1/3x)^2, what effect does the number 1/3 have on the graph, as compared to the graph of y=x^2
Answer:
I think the answer is it stretches the graph horizontally by a factor of 3.
Step-by-step explanation:
Answer: it stretches the graph horizontally by a factor of 3
Step-by-step explanation: I got it correct on a-pex
Anyone please help me
Answer:
(a) 6
(b) 14
Step-by-step explanation:
Answer: (a) 6
(b) 14
Step-by-step explanation:
Let a represent the unknown digit for Chinese --> 70 + a
Let b represent the unknown digit for Mathematics --> 80 + b
Total scores ÷ Total number of tests = Average
[tex]\dfrac{78 + (70 + a) + (80 + b) + 62}{4}=76\\\\\\\dfrac{290 + a + b}{4}=76\\\\\\290 + a + b=304\\\\\\a+b=14[/tex]
The two digits must add up to 14.
The only options are: (9,5), (8,6), (7,7), (6,8), and (5,9),
Mathematics - Chinese
(9, 5) 89 - 75 = 14 LARGEST Difference
(8, 6) 88 - 76 = 12
(7, 7) 87 - 77 = 10
(6, 8) 86 - 78 = 8
(5, 9) 85 - 79 = 6 SMALLEST Difference
What is the solution for x in the given equation? sgrt9x+7+sgrt2x=7
Round $535 998 to the nearest HUNDRED
Answer: 536,000
Step-by-step explanation:
Answer:
536 000
Step-by-step explanation:
because it izz what it izz
show that the straight line x+y does not intersect the curve x^2-8x+y^2-12y+6=0 if k^2-20k+8>0
The width of a rectangle is 38 centimeters. The perimeter is at least 692 centimeters. Write an inequality that represents all possible values for the length of the rectangle. Then solve the inequality.
Answer:
See bolded / underlined / italicized below -
Step-by-step explanation:
This is a great question!
If x were the length of this rectangle, then we could conclude the following,
2( 38 ) + 2( x ) > 692,
As you can see there is a greater than sign present, as the perimeter is at least 692 centimeters. In this case the perimeter is given to be at least 692 centimeters, but can also be calculated through double the width and double the length together. And of course we are given the width to be 38 cm -
2( 38 ) + 2x > 692,
76 + 2x > 692,
2x > 616,
x > 308
Solution = Length should be at least 308 cm
( The attachment below is not drawn to scale )
A chord cuts off a 120 degree arc. If the radius of the circle is 26 inches, find the
chord length
Answer:
26sqrt(3)
Step-by-step explanation:
You end up with two 30-60-90 triangles.
26/2 = 13
2 * 13 * sqrt(3) = 26sqrt(3)
Which of these systems of linear equations has no solution?
2 x + 8 y = 15. 4 x + 16 y = 30.
2 x minus y = 18. 4 x + 2 y = 38.
4 x + 7 y = 17. 8 x minus 14 y = 36.
4 x minus 3 y = 16. 8 x minus 6 y = 34.
Answer:
4 x minus 3 y = 16. 8 x minus 6 y = 34 has no solution
Step-by-step explanation:
Examine the system
2 x + 8 y = 15
4 x + 16 y = 30
We see that these equations are identical except for a factor of 2, and thus recognize that this system has infinitely many solutions.
Next, look at the system
2 x minus y = 18
4 x + 2 y = 38
If we divide the second equation by 2, we get the system
2x - y = 18
2x + y = 19
Combining these two equations, we get 4x = 37, which has a solution.
Third, analyze the system
4 x + 7 y = 17 => 8x + 14y = 34
8 x minus 14 y = 36 => 8x - 14y = 36, or 16x = 70, which has a solution
Finally, analyze the system
4 x minus 3 y = 16 => -8x + 6y = -32
8 x minus 6 y = 34 => 8x - 6y = 34
If we combine these two equations, we get 0 + 0 = 2, which is, of course, impossible. This system has no solution.
Answer:
4 x minus 3 y = 16. 8 x minus 6 y = 34 has no solution. the 4th option.
Step-by-step explanation:
The solution for the following system of linear equation 3m-2n=13 is (2,-1) true or false
Answer:
Not True
Step-by-step explanation:
>_<
[tex]\text{To find your answer, plug in the values to the equation and solve:}\\\\3(2)-2(-1)=13\\\\\text{Solve:}\\\\3(2)-2(-1)=13\\\\6+2=13\\\\8=13\\\\\text{8 does not equal 13, therefore making the equation FALSE}\\\\\boxed{\text{False}}[/tex]
can I get help with this question. I need to find the value of x
Step-by-step explanation:
sides of 2 triangles are proportional
x/12=28/21
x=16
=======================================================
Explanation:
The diagonal pieces are 28 and 21. They pair up to get the fraction 28/21
The horizontal pieces are x and 12, in the same order from left to right. The order is important (so things pair up properly). We get the fraction x/12
-------
Set the two fractions equal to each other and solve for x
28/21 = x/12
28*12 = 21*x .... cross multiply
336 = 21x
21x = 336
x = 336/21 .... divide both sides by 21
x = 16
Which graph represents the solution set of the system of linear inequalities below?
Answer:
C
Step-by-step explanation:
First you find which line is which.
The one with 5x in it is the steepest one, and we have to be above it due to the >.
The one with 2x in it is the least steep, and we have to be below it due to the <.
Graph C satisfies both these restrictions.
please help i will give out brainliest
Answer:
6, 0, 10
b
Step-by-step explanation:
The price (p), in cents, of a sweet is directly proportional to the mass (m) of the
sweet.
When the sweet cost 55 cents, the mass is 220 g. Find
(a) the equation connecting p and m.
(b) the mass, in grams, of a sweet which cost 540 cents,
(c) the cost of a sweet in cents, with a mass of 115 g
Jennifer had $80 to spend on herself. She spent 1/5 of the money on a sandwhich, 1/6 for a ticket to a museum, and 1/2 of it on a book. How much money does Jennifer have left over?
Answer:
$10.67
Step-by-step explanation:
Jennifer has a total amount of $80 to buy what she needs
1/5 of the money is spent on sandwich
= 1/5×80
= $16
The amount spent on sandwich is $16
1/6 of the money is spent on tickets to a museum
= 1/6×80
= 0.166×80
= $13.33
The amount spent on tickets is $13.33
1/2 of the money is spent on a book
= 1/2×80
= 0.5×80
= $40
The amount spent on a book is $40
Therefore, to calculate the amount left on her we add the total money spent and subtract it from the original amount of money that she has to spend
= $80-$16+$13.33+$40
= $80-$69.33
= $10.67
Hence the amount of money left on Jennifer is $10.67
Find the equation of the given parabola in vertex and standard form. Describe in words all transformations that have been applied to the graph of y=x^2 to obtain the given graph of the transformed function
Answer: [tex]a)\ \text{Vertex}:y=-\dfrac{3}{2}(x+1)^2+6[/tex]
[tex]b)\ \text{Standard}:y=-\dfrac{3}{2}x^2-3x=\dfrac{9}{2}[/tex]
c) Transformations: reflection over the x-axis,
vertical stretch by a factor of 3/2,
horizontal shift 1 unit to the left,
vertical shift 6 units up
Step-by-step explanation:
Intercept form: y = a(x - p)(x - q)
Vertex form: y = a(x - h)² + k
Standard form: y = ax² + bx + c
We can see that the new vertex is (-1, 6). Use the Intercept form to find the vertical stretch: y = a(x - p)(x - q) where p, q are the intercepts.
p = -3, q = 1, (x, y) = (-1, 6)
a(-1 + 3)(-1 -1) = 6
a (2)(-2) = 6
a = -6/4
a = -3/2
a) Input a = -3/2 and vertex (h, k) = (-1, 6) into the Vertex form to get:
[tex]y=-\dfrac{3}{2}(x+1)^2+6[/tex]
b) Input a = -3/2 into the Intercept form and expand to get the Standard form:
[tex]y=-\dfrac{3}{2}(x+3)(x-1)\\\\\\y=-\dfrac{3}{2}(x^2+2x-3)\\\\\\y=-\dfrac{3}{2}x^2-3x+\dfrac{9}{2}[/tex]
c) Use the Vertex form to identify the transformations:
[tex]y=-\dfrac{3}{2}(x+1)^2+6[/tex]
a is negative: reflection over the x-axis|a| = 3/2: vertical stretch by a factor of 3/2h = -1: horizontal shift left 1 unitk = +6: vertical shift up 6 unitsIf both nappes of a right circular cone are intersected by a plane that does not
pass through the vertex of the cone, the resulting curve will be an)
Answer:
Hyperbola
Step-by-step explanation:
When the two napes of a cone are intersected by a plane, the resulting curve is that of the two branches of a hyperbola. See attached image.
Can someone please help me I really need help please help me
Answer:
18.87 square cm.
Step-by-step explanation:
The area of the rectangle will be (4 + 4) * 4, since the length of the rectangle would be the diameter of the circle, and the width of the rectangle would be the radius. (4 + 4) * 4 = 8 * 4 = 32 square cm.
Then, we can calculate the area of the semicircle. The area of a circle is pi * r^2, so the area of a semicircle will be half of that. pi * (4^2) / 2 = pi * 16 / 2 = 8pi. 8 * 3.14159265 = 25.1327412 square cm.
The shaded area of the middle of the shape will then be 32 - 25.1327412 = 6.8672588 square cm.
The two triangles will have the same area. Their bases will be 14 minus the diameter of the circle, then divide that by 2 to get each separate base. 14 - 8 = 6 / 2 = 3. The heights of the triangles will be the radius of the circle, or 4 cm.
1/2 * 3 * 4 = 1/2 * 12 = 12/2 = 6. That is the area of one triangle, so the area of both triangles would be 6 * 2 = 12 square cm.
6.8672588 + 12 = 18.8672588, or 18.87 square cm.
Hope this helps!
Answer:
(44 - 8(pi)) cm^2 Exact area
18,9 cm^2 Approximate area
Step-by-step explanation:
The shaded area is the area of the trapezoid minus the area of the semicircle.
area of trapezoid = (b1 + b2)h/2
area of semicircle = (pi)(r^2)/2
The triangles at both sides are right triangles. Each of the horizontal legs has length (14 cm - 8 cm)/2 = 3 cm. Each of the vertical legs is congruent to the radius of the semicircle.
b1 = lower base = 14 cm
b2 = upper base = 14 cm - 3 cm - 3 cm = 8 cm
shaded area = (b1 + b2)h/2 - (pi)(r^2)/2
= (14 cm + 8 cm)(4 cm)/2 - (pi)(4 cm)^2 / 2
= 44 cm^2 - 8(pi) cm^2
= (44 - 8(pi)) cm^2 Exact area
= 18.9 cm^2 Approximate area
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Penelope has $1,459.75 in her bank account. To pay her bills, she writes 4 checks in the amounts of $200.25, $359.45, $125, and $299.35. Then she deposits $375 into her account. Penelope’s account balance after she pays her bills and makes the deposit is $ .
Answer:
$850.7
Step-by-step explanation:
Penelope has $1459.75 in her account.
She pays different amount that are given above.
i.e.
=1459.75-200.25-359.45-125-299.35
=475.7
Then she deposit $375
Now,
=475.7+375
=850.7
So, She has $850.7 in her account after she pays her bills and makes deposits.
Answer:
$805.7 OwO
Step-by-step explanation:
A school contains 357 boys and 323 girls.
If a student is chosen at random, what is the probability that is a girl?
Correct your answer to 2 decimal places.
Answer:
19/40
Step-by-step explanation:
just divide the number of girls by the total number of students.
323/680 = 19/40 or 0.48
John couldn't recall the Serial number on his expensive bicycle. He remembered that
there were 6 different digits, none used more than once, but couldn't remember what
digits were used. He decided to write down all of the possible 6 digit numbers from 0 to 9. How many different possibilities will he have to create?
Answer:
151,200
Step-by-step explanation:
The possible set of numbers will be 151200
What is permutation?A permutation is an arrangement of objects in a definite order.
Given that, John want to find his bicycle's number, so he decided to write down all the possible 6-digit numbers from 0 to 9.
Here, we will use permutation to find the possible numbers,
Formula =
ⁿPₓ = n! / (n-x)!
Therefore,
¹⁰P₆ = 10! / (10-6)!
= 10! / 4!
= 10 × 9 × 8 × 7 × 6 × 5 = 151200
Hence, the possible set of numbers will be 151200
Learn more about permutation, click;
https://brainly.com/question/1216161
#SPJ2
The perimeter of a rectangular field that measures 2 feet by 18 inches is _________ ft. A. 40 B. 7 C. 84 D. 6
Answer:
B. 7
Step-by-step explanation:
Complete the table for different values of X in the polynomial expression -7x^2+32x+240. Then, determine the optimal price that the taco truck should sell it’s tacos for. Assume whole dollar amounts for the tacos.
Answer:
$6
Step-by-step explanation:
Tico’s taco truck is trying to determine the best price at which to sell tacos, the only item on the menu, to maximize profits. The taco trucks owner decided to adjust the price per taco and record data on the number of tacos sold each day with each new price. When the taco truck charges $4 for a taco, it sells an average of 60 tacos in one day. With every $1 increase in the price of a taco, the number of tacos sold per day decreases by 7.
The owner can calculate the daily revenue using the polynomial expression (-7x²+32x+240),
where x is the number of $1 increases in the taco price. In this activity, you’ll interpret and manipulate this expression and the scenario it represents.
x is number of $1 increments above the initial price of $4. (x=0 means a price of $4, x=1 means a price of $5, etc.)
The revenue is -7x²+32x+240. The average number of tacos sold is the revenue divided by the price.
For example, if x = 0, then the taco price is $4, the revenue is $240, and the number of tacos sold is 60.
If x = 1, then the taco price is $5, the revenue is $265, and the number of tacos sold is 53.
Each time x increases by 1, the number of tacos sold decreases by 7.
Continuing:
[tex]\left[\begin{array}{cccc}Value\ of\ x&Taco\ Price\ (\$)&Average\ Number\ of\ Tacos\ Sold&Daily\ Revenue\ (\$)\\0&4&60&240\\1&5&53&265\\2&6&46&276\\3&7&39&273\\4&8&32&256\\5&9&25&225\\6&10&18&180\end{array}\right][/tex]
The optimal price is $6. At this price, the revenue is a maximum at $276.
Help me asap i really need this
Answer:
3
Step-by-step explanation:
6/2
I hope this is right :)
y = 5x + 2 3x = –y + 10 What is the solution to the system of equations
Answer:
x = 1 , y = 7
Step-by-step explanation:
Solve the following system:
{y = 5 x + 2 | (equation 1)
3 x = 10 - y | (equation 2)
Express the system in standard form:
{-(5 x) + y = 2 | (equation 1)
3 x + y = 10 | (equation 2)
Add 3/5 × (equation 1) to equation 2:
{-(5 x) + y = 2 | (equation 1)
0 x+(8 y)/5 = 56/5 | (equation 2)
Multiply equation 2 by 5/8:
{-(5 x) + y = 2 | (equation 1)
0 x+y = 7 | (equation 2)
Subtract equation 2 from equation 1:
{-(5 x)+0 y = -5 | (equation 1)
0 x+y = 7 | (equation 2)
Divide equation 1 by -5:
{x+0 y = 1 | (equation 1)
0 x+y = 7 | (equation 2)
Collect results:
Answer: {x = 1 , y = 7
Answer:
D) (1,7)
Step-by-step explanation:
just took the test
solve this...question
Answer: 5. P = (-4, 6) R = (-4, -4)
6. (a) a = 4, b = 3 (b) BC = 8 (c) B = (3, 4)
7. (a) m = 4, n = 6 (b) PQ = (-2, 6) (c) SR = (2, -6)
Step-by-step explanation:
5. The distance from Q (4, 0) to A (0, 3) is 4 left and up 3.
So the distance from A to P is 4 left (0 - 4) and up 3 (3 + 3)
--> P = (-4, 6)
Similarly, the distance from Q (4, 0) to B (0, -2) is 4 left and down 2.
So the distance from A to P is 4 left (0 - 4) and down 2 (-2 - 2)
--> P = (-4, -4)
6. Follow the same steps as #5 (above) to get the following coordinates:
A = (-3, 4) B = (3, 4)
D = (-3,-4) C = (3, -4)
a) a = 4, b = 3
b) BC = 2(4) = 8
c) B = (3,4)
7. Follow the same steps as #5 (above) to get the following coordinates:
P = (-4, 6) Q = (0, 6)
S = (0, -6) R = (4, -6)
a) m = 4, n = 6
b) midpoint PQ = (-2, 6)
c) midpoint SR = (2, -6)