The value of x = [tex]\frac{2b-5d}{3c}[/tex] .
What is a equation?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
The given equation is
[tex]5d^{3}=d^{2}(2b-3cx)[/tex]
5[tex]d^{3}= d^{2}2b-3cd^{2}x[/tex]
3c[tex]d^{2}x = d^{2}2b-5d^{3}[/tex]
x = [tex]\frac{d^{2}(2b-5d) }{3cd^{2} }[/tex]
x = [tex]\frac{2b-5d}{3c}[/tex]
Hence, The value of x = [tex]\frac{2b-5d}{3c}[/tex] .
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Marie’s age is 12 less than triple Carl's’s age. When you add Marie's age to Carl’s age, you get 68. How old is Marie and how old is Carl? Show work.
A.) Use x to represent Carl's age. If x is Carl's age, write an expression for Marie's age using Carl's age x.
B.) Write an equation for the situation.
C.) Solve the equation from part a. Show your work. What is Marie's age and Carl's age.
30 Points for answering!
A disco ball is shaped like a sphere with diameter of 60 inches to the nearest square inch what is the surface area of the disco ball
To calculate the surface area of a sphere, you have to use the following formula:
[tex]SA=4\pi r^2[/tex]Where "r" is the radius of the sphere.
We know that the diameter of the sphere is d = 60 inches and that the radius is half the diameter, then the radius can be determined as follows:
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{60}{2} \\ r=30in \end{gathered}[/tex]Once the radius is calculated, you can determine the surface area of the sphere:
[tex]\begin{gathered} SA=4\pi(30^2) \\ SA=4\pi\cdot900 \\ SA=3600\pi\approx11309.73in^2 \end{gathered}[/tex]The surface area of the sphere is 3600π in², expressed as a decimal value, the surface area is equal to 11309.73 in²
Bette used 3 jumbo cans of frosting to frost 105
cupcakes for the cupcake challenge at her school and 5 jumbo cans of frosting to frost an
additional 175 cupcakes. How many jumbo cans of frosting would she need to frost 280
cupcakes?
The jumbo cans of frosting would she need to frost 280 cupcakes is 8 cans.
What is addition?Addition simply means the sum of the numbers that are given.
In this case, Bette used 3 jumbo cans of frosting to frost 105 cupcakes for the cupcake challenge at her school and 5 jumbo cans of frosting to frost an additional 175 cupcakes. This implies that the total cupcakes will be:
= 105 + 175 = 280
In this case, the cans used will be the addition of the cans above. This will be:
= 3 + 5
= 8 cans
This shows the concept of addition.
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Write a quadratic equation to match the relationship given in the table
In order to find the quadratic equation, let's use the standard form of a quadratic equation:
[tex]y=ax^2+bx+c[/tex]Using the point (0, 2) from the table, we have:
[tex]\begin{gathered} 2=a\cdot0^2+b\cdot0+c \\ c=2 \end{gathered}[/tex]Now, using the points (-1, -2) and (1, 22):
[tex]\begin{gathered} -2=a(-1)^2+b(-1)+2 \\ a-b=-4 \\ 22=a(1)^2+b(1)+2 \\ a+b=20 \end{gathered}[/tex]Adding both equations, we can solve for a:
[tex]\begin{gathered} a-b+(a+b)=-4+(20) \\ 2a=16 \\ a=8 \\ a+b=20 \\ 8+b=20 \\ b=12 \end{gathered}[/tex]Therefore the equation is y = 8x² + 12x + 2
How to solve the blank
Answer:
blank = - 3
Step-by-step explanation:
let x represent the blanks , then
[tex]\frac{2}{3}[/tex] ([tex]\frac{9}{5}[/tex] + x) = [tex]\frac{2}{5}[/tex] x + [tex]\frac{2}{5}[/tex]
multiply through by 15 ( the LCM of 3 and 5 ) to clear the fractions
10([tex]\frac{9}{5}[/tex] + x) = 6x + 6 ← distribute parenthesis on left side
[tex]\frac{90}{5}[/tex] + 10x = 6x + 6
18 + 10x = 6x + 6 ( subtract 6x from both sides )
18 + 4x = 6 ( subtract 18 from both sides )
4x = - 12 ( divide both sides by 4 )
x = - 3
A 25-foot ladder is leaning against the side of a house so that the bottom of the ladder is 15 feet from the base of the house. Will the ladder reach a window that is 21.5 feet above the ground?
The ladder will not reach a window that is 21.5 feet above the ground if the length of the ladder is 25 feet.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
From the data:
The right angle triangle can be drawn:
From the diagram:
Applying Pythagoras' theorem:
BC² = AB² + AC²
25² = 15² + AC²
After solving
AC = 20 feet
AC < 21.5 feet
Thus, the ladder will not reach a window that is 21.5 feet above the ground if the length of the ladder is 25 feet.
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Answer:
No, because the ladder will only reach 20 feet high
Step-by-step explanation:
I go it right on my quiz :]
slope of p=
slope of q=
slope of r=
slope of m=
*PLEASE HELP*
Find the nth term of this quadratic sequence
2, 8, 18, 32, 50,
Step-by-step explanation:
+6,+10,+14,+18
+4+4+4
therefore quadratic 4/period function=2
[tex]y = 2{x}^{2} + bx + c[/tex]
y=2 x=1
[tex] 0 = b + c[/tex]
y=8 x=2
8=8+2b+c
0=2b+c
y=18 x=3
0=3b+c
therefore
the equation is 2x^2=y
12:36=21 :
Fill in the blank I don't understand it ?
Answer:
63
Step-by-step explanation:
12:36
36/12=3
21(3)=63
What is the difference between the values of |-
10 and 19 ?
Answer: 9
Step-by-step explanation:
the value of -10 is 10 and the value of 19 is 19 s0 19 - 10
1.8.7 Check Your Understanding
Amala is copying XY.
After drawing an arc with the compass from the first point of the construction, the next step is [DROP DOWN 1].
Drop Down 1
Y
pick a point on the arc that will be the second endpoint of the new segment
Select a Value
adjust the compass width to equal the length of XY
use a straightedge to draw a line segment from the new points
pick a point on the arc that will be the second endpoint of the new segment
The next step after drawing an arc with the compass from the first point of the construction will be, to pick a point on the arc that will be the second endpoint of the new segment. (a)
To copy a line we have to follow a few steps of the procedure.
The steps are;
Adjust the compass width to equal the length of XY.Draw an arc with the compass from the first point of the construction.Pick a point on the arc that will be the second endpoint of the new segment. Use a straightedge to draw a line segment from the new points.The newly constructed line is exactly equal to the given line.To know more about the construction of copied structure visit,
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y=2 and x=-10 what is the value of k the constant
Answer:
- 164/4+50y/3+ify=0
Step-by-step explanation:
hope it helps
Will give brainlest:)
Answer:
1/9
Step-by-step explanation:
-1/9 + 2/9
Since the denominator is the same, we can add the numerators
(-1+2)/9 = 1/9
Lin knows that angle A is congruent to angle D. She claims that triangles ABC and DEF
must be similar. Convince Lin that the triangles are not similar.
If p and q vary inversely and p is 5 when q is 4, determine q when p is equal to 10.
If p and q vary inversely and p is 5 when q is 4, the value of q when p is equal to 10 is 2.
What is an inverse variation?An inverse variation can be defined as a type of proportionality which shows the relationship that exist between two (2) distinct variables, wherein, as the value of one variable increases, the value of the other variable decreases and vice-versa.
Mathematically, an inverse variation can be modeled or represented by this expression:
p ∝ 1/q
p = k/q
Where:
p and q are the variables.k represents the constant of proportionality.
Next, we would determine the constant of proportionality (k) by substituting the value of the given variable as follows:
k = pq
k = 5(4)
k = 20
Now, we can determine the value of q:
q = k/p
q = 20/10
q = 2.
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PLEASE HELP FAST PLEASE
Given:BC=AD and BC||AD Prove: BEC=DEA
Answer: ad bc is the answer
Step-by-step explanation:
Here is a linear equation: y = 2/3x + 1 Are (6, 5) and (9, 8) solutions to the equation? Explain or show your reasoning.
A linear equation is a mathematical form of a line segment the point (6,5) satisfies the equation y = 2/3x + 1 so it is the solution of the equation but (9,8) is not the solution.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given linear equation, y = 2/3x + 1
To be a point of its solution the point must satisfy the given equation.
Substitute (6,5)
5 = (2/3)6 + 1
5 = 2(2) + 1 = 5
Therefore, the (6,5) is the solution of the equation.
Substitute,(9,8)
(2/3)9 + 1 = 7
8 ≠ 7
So,(9,8) is not the solution of the equation.
Hence "A linear equation is a mathematical form of a line segment the point (6,5) satisfies the equation y = 2/3x + 1 so it is the solution of the equation but (9,8) is not the solution".
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The school store has 2000 pencils in stock and sells an average of 50 pencils per day. The manager reorders when the the number of pencils in stock is 950 let d= the number of days
we make a equation depending of the days
[tex]T=2000-50d[/tex]Where T is the total of pencils
In this equation we are going to subtract 50 pencils for each day from the original 2000
to know the days where are 950 pencils we replace the total by 950 and solve d
[tex]\begin{gathered} 950=2000-50d \\ 50d=2000-950 \\ 50d=1050 \\ d=\frac{1050}{50} \\ \\ d=21 \end{gathered}[/tex]the number of days is 21
In a game
of ice hockey, the hockey puck took 0.6 second to travel 66 feet to the goal line. Determine the
the average speed of the puck in feet per second.
Answer:
The average speed of the puck is 110 ft per second.
Step-by-step explanation:
Using the d = st formula to find distance when given the speed and time, you can rewrite it to be s = d/t.
When you substitute the values in, you get s = 66/0.6, which is 110.
Hope this helps.
P.S. Mark as brainliest!
the question is in the image
For the given opens down parabola, ordered pair of the vertex (h, k) = (1, -4) , the maximum value of the parabola is y = -4.
As given,
Graph of parabola shows it open down parabola.
Vertex is the highest point on the graph of parabola.
it is known as the maximum value.
Let (h, k) be the vertex of the given parabola.
From the graph value of the vertex is equal to :
(h ,k)=(1, -4)
h represents the x-coordinate.
k represents the y-coordinate.
y-coordinate represents the maximum value of the parabola.
y =-4 is the maximum value.
Therefore, for the given opens down parabola, ordered pair of the vertex (h, k) = (1, -4) , the maximum value of the parabola is y = -4.
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I just want the answer :)
Answers ↓
angle 1 → 90°
angle 2→ 44°
angle 3 → 90°
angle 4 → 46°
I hope this helps u
Mark says, '81 is a square number. Therefore, 810 is a square number.'
Is Mark correct? Explain your answer.
Answer:
mark is right
Step-by-step explanation:
3+5x5 =13
Answer:
Mark is not correct , becouse squared number Is number which can be after "=" when you times same numbers for example: 4*4=16 so 16 is squared number,is this make sense?
NEEED HELPPP ASAPPPPPP
The inverse of the function → f(x) = [tex]\sqrt{11x+12}[/tex] is
f⁻¹(x) = (x² - 12)/11
We have -
y = f(x) = [tex]\sqrt{11x+12}[/tex]
We have to find its inverse function.
What is the procedure to find inverse of function ?Inverse of a function can be calculated by following the steps mentioned below -
Step 1 - Replace 'y' with 'x' and vice - versa.
Step 2 - Rewrite the equation by solving for 'y'.
Step 3 - Replace 'y' with f⁻¹(x).
According to the question -
y = f(x) = [tex]\sqrt{11x+12}[/tex]
x = [tex]\sqrt{11y+12}[/tex]
x² = 11y + 12
x² - 12 = 11y
y = (x² - 12)/11
f⁻¹(x) = (x² - 12)/11
Therefore, the inverse of the function → f(x) = [tex]\sqrt{11x+12}[/tex] is
f⁻¹(x) = (x² - 12)/11
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a dietician is planning a snack package of fruit and nuts. each ounce of fruit will supply zero units of protein, 3 units of carbohydrates, 2 units of fat and will contain 20 calories each. each ounce of nuts will supply 3 units of protein, 2 units of carbohydrates and 4 units of fat, and will contain 50 calories. Every package must provide at least 9 units of protein, at least 18 carbohydrates, and no more than 22 units of fat. Find the number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least amount of calories. What is the least number of calories?
ANSWER ASAP PLEASE
The number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least amount of calories is
3 ounces of nut5 ounces of fruitThe least number of calorie is 250 calories
How to find the number of ounces of fruit and number of ounces of nuts with the least amount of calories.given data
1. each ounce of fruit will supply zero units of protein, 3 units of carbohydrates, 2 units of fat and will contain 20 calories
2. each ounce of nuts will supply 3 units of protein, 2 units of carbohydrates and 4 units of fat, and will contain 50 calories
3. Every package must provide at least 9 units of protein, at least 18 carbohydrates, and no more than 22 units of fat
To get at least 9 units of protein, we take at least 3 ounces of nut
3 ounces of nut will give 3 times each unit, and they are as follows
3 * 3 = 9 units of protein2 * 3 = 6 units of carbohydrates4 * 3 = 12 units of fat50 * 3 = 150 caloriesAnother restriction is no more than 22 units of fat and we have 12 already remaining 10 units of fat
fruits has lesser calories hence we use it to get the required fats
10 units of fat ÷ 2 units of fat in fruit = 5
5 ounces of fruit will give 5 times each unit, and they are as follows
5 * 3 = 15 units of carbohydrates5 * 2 = 10 units of fat 5 * 20 = 100 caloriesCombining 3 ounces of nut and 5 ounces of fruit will give
9 + 0= 9 units of protein6 + 15 = 21 units of carbohydrates12 + 10 = 22 units of fat150 + 100 = 250 caloriesAbove maintains the requirements stated in the question with the minimal calorie
the required calorie is 250
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For a given week, Tammy's Coffee House has available 1584 ounces of A grade coffee and 1536 ounces of B grade coffee. These are blended into 1-pound
packages as follows: an economy blend that contains 3 ounces of A grade coffee and 8 ounces of B grade coffee, and a superior blend that contains 9 ounces of
A grade coffee and 3 ounces of B grade coffee. (The remainder of each blend is made of filler ingredients.) There is a $3 profit on each economy blend package
sold and a $2 profit on each superior blend package sold. Assuming that the coffee house is able to sell as many blends as it makes, how many packages of
each blend should it make to maximize its profit for the week?
Note that the ALEKS graphing calculator can be used to make computations easier.
Economy blend:
Superior blend:
package(s)
package(s)
X
S
There is a requirement of 176 packets of economy blend and 96 packets of a superior blend to make maximum profit for the week.
Using the given data, calculate the x number of packages of the economy blend as well as the y number of packages of the superior mix.
3x + 11y =1584
6x + 4y = 1440
From the graph of these two equations, three extreme points are deduced: (240,0), (0,144), and (176,96).
The maximum (2x +4y) is the goal function.
Determine the aim function's value at all these extreme points,
The objective function value for (240,0) is 2 × 240 = 480
The objective function value for (0,144) is 4 × 144 = 576
The value of the objective function for (176,96) is 2 × 176 + 4 × 96 = 736
∴ The optimal point is (176,96) where x = 176 and y = 96.
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explain which of the following is better to but
someone help me with the last two problems
Here is the completed table:
x /AM/
14 16
3 13
11 33
10 40
What are the values?/AM/ + /AC/ = /AC/
(x + 2) + (3x - 9) = 6x - 21
4x - 7 = 6x - 21
6x - 4x = 21 - 7
2x = 28
x = 28 / 2
x = 14
/AM/ = 14 + 2 = 16
/AM/ + /MW/ = /AW/
(2X + 7) + (3x - 4) = 18
5x + 3 = 18
5x = 18 - 3
5x = 15
x = 15/5
x = 3
/AM/ = (2 X 3) + 7 =
= 6 + 7 = 13
x + x + x + x = 44
4x = 44
x = 44 / 4
x = 11
/AM/ = 11 x 3 = 33
/AG/ + /GM/ = /AM/
2(x + 10) = 3x + 10
2x + 20 = 3x + 10
20 - 10 = 3x - 2x
10 = x
/AM/ = (3 x 10) + 10
= 30 + 10
= 40
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X
x=-4y
The slope is -4, and
the y-intercept is O.
The description of the error in finding the slope and y-intercept, of the graph of the equation is given by the option:
To be in slope-intercept form, the equation needs to be solved for y, not x
The equation in slope-intercept form is, [tex]\displaystyle{y = -\frac{1}{4} \cdot x[/tex]
What is the slope-intercept form of a straight-line equation?The slope-intercept form of the equation of a straight line is an equation of the form, y = m·x + c
The slope-intercept form of a straight-line equation is of the form, y = m·x + c, where:
m = The slope of the equation
c = The y-intercept
The given equation is x = -4·y
The given equation is not in the slope and intercept form given that the subject of the equation is x, rather than y
The error is therefore, in making x, the subject of the equation rather than y, that is the equation needs to be solved for y, not x
The correction of the error is performed as follows:
x = -4·y
-4·y = x
[tex]\displaystyle{y = \frac{x}{-4} = -\frac{1}{4} \cdot x[/tex]
Which gives: [tex]\displaystyle{y = -\frac{1}{4} \cdot x[/tex]
The slope of the graph of the equation is [tex]-\frac{1}{4}[/tex], the y-intercept, c, is 0
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3) Speedy Car Rental charges a flat fee of 30$ plus $.15 for each mile
a) write an equation for the cost as a function of the number of miles driven.
b) how much would the cost be if you drove 80 miles?
Answer:
a) C(m) = flat rate + rate per mile
b) $42
Step-by-step explanation:
a) C(m) = flat rate + rate per mile*No. of miles => 30+.15x
b) 30+.15*80 = 42
Set up a system of equations and solve using substitution or elimination. You must show all work You have 258 coins in a jar. They are a combination of dimes and quarters. If the money in the jar equals $36.75, how many of each type of coin is there?
Answer:
185 dimes and 73 quarters
Step-by-step explanation:
q + d = 258
25(q) + 10(d) = 3675