Answer:
y = 20
Step-by-step explanation:
Given y varies jointly as x and z then the equation relating them is
y = kxz ← k is the constant of variation
To find k use the condition y = 5 when x = 3 and z = 4
5 = k × 3 × 4 = 12k ( divide both sides by 12 )
[tex]\frac{5}{12}[/tex] = k
y = [tex]\frac{5}{12}[/tex] xz ← equation of variation
When x = 6 and z = 8 , then
y = [tex]\frac{5}{12}[/tex] × 6 × 8 = [tex]\frac{5}{12}[/tex] × 48 = 5 × 4 = 20
Which line is perpendicular to the line x =
į
?
O A. X = -2y
B. y = - 2x
O
C. X = -2
O
D. y = 2
Solve for x 2(x - 2)² = (2x - 1)(x - 3)
answer please
Answer:
X = 5
Step-by-step explanation:
Answer: x = 5
Step-by-step explanation:
Solve for x given the equation 2(x - 2)² = (2x - 1)(x - 3).
Simplify the equation.
2(x - 2)(x - 2) = (2x - 1)(x - 3)
2(x² - 4x + 4) = (2x² - 7x + 3)
2x² - 8x + 8 = 2x² - 7x + 3
Solve for x.
2x² - 8x + 8 = 2x² - 7x + 3
-8 - 8
2x² - 8x = 2x² - 7x - 5
+8x + 8x
2x² = 2x² + x - 5
-x - x
2x² - x = 2x² - 5
-2x² - 2x²
- x = - 5
- 5 ÷ - 1 = 5
x is equal to 5.
A worker on an assembly line packed 156 boxes in 3 hours. At this rate, how many boxes would the worker pack in 7 hours?
Answer:
364
Step-by-step explanation:
156/3 = 52 boxes/hour
52 boxes x 7 hours = 364
Given side AB in triangle ABC has length x, what is the length of side AC?
The length of the side AC is 2x and this can be determined by using the sine function which is an important trigonometric function.
Given :
Given side AB in triangle ABC has length x.
The trigonometric function can be used to determine the length of the side AC. Sine function can be used to determine the length of AC.
The sine function is the ratio of the opposite side to the hypotenuse. The sine function is given by:
[tex]\rm sin\theta = \dfrac{Opposite }{Hypotenuse}[/tex]
Now, put the known values in the above equation.
[tex]\rm sin30^\circ = \dfrac{x}{AC}[/tex]
[tex]\rm \dfrac{1}{2}=\dfrac{x}{AC}[/tex]
AC = 2x
So, the correct option is D).
For more information, refer to the link given below:
https://brainly.com/question/21286835
Is 70.61 a rational or irrational number?
Answer:
70.61 is a rational number
Step-by-step explanation:
This is because a rational number is either:
A whole number, like 70, whole number.
Is a terminating decimal, such as the one above 70.61, (A terminating decimal is a decimal that doesn't repeat.
And or has a pattern, or a recurring decimal, like 7.478478..., it repeats the decimal over and over, thus, rational.
Hope this helped you, have a great day.
a boy is y years old now .how old was he 10 years ago
Answer:
Hi there the answer is y-10
Simplify the given equation
5x+2(x-3)=2x-1
A) 7x-3=-2x-1
B) 7x-6=-2x+2
C) 7x-6=-2x-2
Answer: B) 7x-6=-2x+2
Step-by-step explanation:
On Tuesday, I worked $t 1$ hours and earned $3t-3$ dollars per hour. My friend Andrew worked $3t-5$ hours but only earned $t 2$ dollars an hour. At the end of the day, I had earned two dollars more than he had. What is the value of $t$
If I earned $2 more than Andrew at the end of the day, then the value of t is [tex]1\frac{2}{3}[/tex]
Number of hours that I used to work = 1 hour
My hourly pay = $3t - 3
My total pay at the end of the day = Number of hours x hourly pay
My total pay at the end of the day = 1 (3t - 3)
My total pay at the end of the day = $ 3t - 3
Number of hours that Andrew used to work = 3t -5 hour
Andrew's hourly pay = $2
Andrew's total pay at the end of the day = Number of hours x hourly pay
Andrew's total pay at the end of the day = 2 (3t - 5)
Andrew's total pay at the end of the day = $ 6t - 10
At the end of the day, I earned $2 more than Andrew
My total pay = Andrew's total pay + 2
3t - 3 = 6t - 10 + 2
6t - 3t = -3 +10 - 2
3t = 5
t = 5/3
[tex]t = 1\frac{2}{3}[/tex]
If I earned $2 more than Andrew at the end of the day, then the value of t is [tex]1\frac{2}{3}[/tex]
Learn more here: https://brainly.com/question/25765213
First rewrite the expression by combining like terms 1/2(13x+5x-6-8x+14)=1/2
Answer:
1/2(10x+8)
Step-by-step explanation:
Combine like terms
13x+5x+(-8x) and -6+14
What are the roots of the equation x²+2x+17=0 in simplest a+bi form?
Answer:
-1 ±4i
Step-by-step explanation:
The quadratic can be written in vertex form as ...
x² +2x +17 = 0
(x² +2x +1) +16 = 0 . . . . . . . . identify the part that can be a perfect square
(x +1)² = -16 . . . . . . . . . . . . subtract 16
x +1 = ±√(-16) = ±4i . . . . take the square root
x = -1 ±4i . . . . . . . . . . . subtract 1
The roots of the equation are x = -1-4i and x = -1+4i.
_____
Additional comment
It can be worthwhile to remember the form of a perfect square trinomial:
(x +a)² = x² +2ax +a²
If you know the coefficient of x, you can use half of it as the constant in each binomial factor.
In the above, we had 2a=2, so a=1 and a²=1. The constant 17 then is resolved into two parts: one part (1) is used to "complete the square" and the other part (16) is the y-coordinate of the vertex. It is used to find the "radical" portion of the roots.
The roots of the equation [tex]x^2 + 2x + 17 = 0[/tex] are [tex]x = -1 +4i[/tex] and [tex]x = -1 - 4i[/tex].
To find the roots of the equation [tex]x^2 + 2x + 17 = 0[/tex] in simplest a + bi form, we can use the quadratic formula.
The quadratic formula states that for an equation in the form[tex]ax^2 + bx + c = 0[/tex], the roots can be found using the formula:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
We have a = 1, b = 2, and c = 17.
Substituting these values into the quadratic formula, we get:
[tex]x = \frac{-2 \pm \sqrt{4 - 68}}{2}[/tex]
[tex]x = \frac{-2 \pm \sqrt{-64}}{2}[/tex]
[tex]x = \frac{-2 \pm \sqrt{64i^2}}{2}[/tex]
[tex]x = \frac{-2 \pm 8i}{2}[/tex]
[tex]x = -1 \pm 4i[/tex]
So, [tex]x = -1 +4i[/tex] and [tex]x=-1-4i[/tex] are roots.
To learn more on Quadratic equation click:
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I need help! Show all the work, step by step.
Answer:
z = [tex]\frac{4x}{3y}[/tex]
Step-by-step explanation:
x = [tex]\frac{3yz}{4}[/tex] ( multiply both sides by 4 to clear the fraction )
4x = 3yz ( isolate z by dividing both sides by 3y )
[tex]\frac{4x}{3y}[/tex] = z
PLEASE HELP
In Triangle WXY, angle X is equal to angle Y, WX is equal to 9x-11, XY is equal 4 points
to 4x+1, and WY is equal to 7x-3, find x and the measure of each side
Answer:
x = 4WX = WY = 25XY = 17Step-by-step explanation:
The triangle is isosceles with side WX equal to side WY:
WX = WY
9x -11 = 7x -3
2x = 8 . . . . . add 11-7x
x = 4
Then the side measures are ...
WX = WY = 7(4) -3 = 28 -3 = 25
XY = 4(4) +1 = 16 +1 = 17
4x+5y=20 need help solving x and y intercept plotting
Answer:
(Hope this helps can I pls have brainlist (crown)☺️)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x To find the y-intercept, substitute in 0 for x and solve for y.
Slope: [tex]m=-\frac{4}{5}[/tex]
x-intercept(s): ( 5 , 0 )
y-intercept(s): ( 0 , 4 )
PLEASE HELP EMERGENCY what is the solution to the equation ^3 square root 2x+5 =5
Answer:
60
Step-by-step explanation:
[tex] \sqrt[3]{2x + 5} = 5 \\ (\sqrt[3]{2x + 5} = 5) ^{3} \\ 2x + 5 = 125 \\ 2x = 120 \\ x = 60[/tex]
Sara poured 3/4 of the juice from a 2 liter bottle while serving guest party.
How much juice, in liters, is still left in the bottle
Answer:The juice left in bottle is 0.5 litre
Step-by-step explanation:Sara poured 3/4 of the juice from a 2 liter bottle while serving guests at a party how many Juice in liters is still left in the bottle. 2.
1/2divided by 4/9 and its answer write it in a mixed fraction
Answer:
1 1/8
Step-by-step explanation:
1/2 ÷ 4/9
= 1/2 × 9/4
= 9/8
= 1 1/8
Answer:
[tex]1\frac{1}{8}[/tex]
Step-by-step explanation:
hope this helps have a good rest of night :)❤
His grandmother is sick, so Hassan is making a pot of bean soup to bring for dinner. The recipe calls for equal amounts of 3 kinds of beans: kidney, pinto, and black. In all, Hassan uses 2 1/4 cups of beans in the soup.
Use an equation to find the amount of each kind of bean Hassan uses in the soup.
Answer:
0.75 cup
Step-by-step explanation:
K + p + b = 2 1/4
K = p = b
Sence all beans are equal we can divide 2 1/4 by 3
2 1/4 / 3 = 3/4
If a sea turtle traveled 2.8 miles at
top speed in 2 hours, how far
did it travel in one hour?
Answer: 1.4 mph
Step-by-step explanation: It traveled 2.8/2 mph or 1.4 mph.
Would appreciate brainly <3
Answer:
It will travel 1.6 mile
Step-by-step explanation:
please help me answer this question!
Answer:
equation: y = -5/4xslope: -5/4point: (0, 0)Step-by-step explanation:
The slope is found using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (0 -5)/(0 -(-4)) = -5/4
slope = -5/4
The second point can be used to keep it simple.
point: (0, 0)
Point-slope equation:
y -0 = -5/4(x -0)
y = -5/4x . . . . . . . simplified
two friends A and b invest some money in a buisness in the ratio 13:12. they make a profit of 542600. How much should b receive as profit if the profit is proportional to the investment
Answer:
Step-by-step explanation:
I need some help please. I don't understand this. :)
Answer:
i dont know sorry
Step-by-step explanation:
pls ask someone else thanks have a nice day
Find the 66th term of the arithmetic sequence -10, 7, 24, ...−10,7,24,...
Answer:
a(66) = -10 + 17(65) = 1095
Step-by-step explanation:
We know that this is an arithmetic sequence. Subtracting -10 from 7 results in 17; subtracting 7 from 24 also results in 17. Thus, the common difference, d, is 17. The first term is -10.
The general form of an arithmetic sequence is a(n) = a(1) + d(n - 1).
Substituting -10 for a(1) and 17 for d, we get:
a(n) = -10 + 17(n - 1)
Now let n = 66: a(66) = -10 + 17(66 - 1), or a(66) = -10 + 17(65) = 1095
The width of a rectangle measures (10p + 6) centimeters, and its length
measures (2p – 10) centimeters. Which expression represents the
perimeter, in centimeters, of the rectangle?
-
Answer:
24p-8
Step-by-step explanation:
Perimeter just means add up all the sides
(10p+6)+(2p-10)+(10p+6)+(2p-10)
= 24p-8
Help! I give brainlest. Problem is in Image
Answer:
65
Step-by-step explanation:
let's place 9 in place of p and 4 in place of q. I will use a star in place of that symbol for the sake of my convenience having to look for it, apologies.
[tex]9 \star 4 = 9^2-4^2 = 81-16 = 65[/tex]
Answer:
65
Step-by-step explanation:
9^2-4^2=65
The bottom of a ladder rests on the ground and the top of the ladder rests against a wall. The ladder forms a 63° angle with the ground and the top of the ladder is positioned 12 meters up the wall. Which is the exact measure of the ladder in meters?
Answer:
the one you picked was right.
Step-by-step explanation:
if 63° was the angle and the 12 was the side then "x" will be one the bottom. then you flip the fraction meaning 1/sin63° and x/12 and then multiply 12 on both sides. you will be left with x = 12/sin63°. sorry if that doesn't make sense
Write two expressions for the perimeter of the figure.
Answer:
(a) 5 + 7 + 6x + 8x + 6
(b) 18 + 14x
Step-by-step explanation:
Find the area of the figure below, formed from a triangle and a parallelogram
Answer:
32 square millimeters
Step-by-step explanation:
Parallelogram area formula => B x h
Base = 6 mm
Height = 4 mm
Area = 24 mm^2
Triangle area formula B x h x 1/2
Base = 8 mm
Height = 2 mm
Area = 8 mm^2
Total area = 24 + 8 = 32 mm^2
The total surface area of the figure consists of a parallelogram and a triangle is 32 square millimeters so option (C) will be correct.
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area.
If we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.
As per the given parallelogram and a triangle,
The bigger side of parallelogram = 6 + 2 = 8mm
Smaller side = 6mm
The perpendicular distance between the sides of the parallelogram = 4mm
The base of the triangle = 2mm
Height of triangle = 4 mm
Therefore, the complete area ⇒
(1/2)[8 + 6)×4 + (1/2)×2×4 = 32 mm²
Hence "The total surface area of the figure consists of a parallelogram and a triangle is 32 square millimeters".
To learn more about surface area,
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What is the least common denominator for 5 and 16
Answer: 80
Step-by-step explanation:
16, 32, 48, 64, 80
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 75, 80
Write 63 as the product of prime factors
HOW AM I WRONG???
Answer:
It says in ascending order, and I don't think exponents will work.
Step-by-step explanation:
I think the correct answer would be 3 x 3 x 7, or 3² x 7
The only mistake that I can see is that it is not in ascending order.
-Chetan K
Answer:
3*3*7 or 3^2*7
Step-by-step explanation:
Do you need to have the exponent of 2?
If not, then write it as 3*3*7 or 3^2*7
Write the inequality for the situation. Penny has 7 dollars. Fred has fewer dollars than Penny. Left F=Fred
Answer:
7 > F
Step-by-step explanation:
Penny has 7 dollars. Fred has fewer dollars than Penny. Left F=Fred
7. Fred has fewer dollars than Penny. Left F=Fred
7 > Left F=Fred
7 > F
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
