For this case we must solve the following equation:
[tex]\frac {5} {6} x = \frac {10} {3}[/tex]
Multiplying by "6" on both sides of the equation we have:
[tex]5x = \frac {10 * 6} {3}\\5x = \frac {60} {3}\\5x = 20[/tex]
Dividing between 5 on both sides of the equation we have:
[tex]x = \frac {20} {5}\\x = 4[/tex]
So, the solution is [tex]x = 4[/tex]
Answer:
Option D
Answer: LAST OPTION.
Step-by-step explanation:
In order to solve for the variable "x" from the expression [tex]\frac{5}{6}x=\frac{10}{3}[/tex], you need to follow these steps:
1) You need to multiply both sides of the equation by 3:
[tex]3(\frac{5}{6}x)=(\frac{10}{3})(3)\\\\\frac{15}{6}x=10[/tex]
2) You need to multiply both sides of the equation by 6:
[tex](6)(\frac{15}{6}x)=(10)(6)\\\\15x=60[/tex]
3) Finally, you can divide both sides of the equation by 15:
[tex]\frac{15x}{15}=\frac{60}{15}\\\\x=4[/tex]
What factor is used to convert feet per minute into miles per hour?
To convert feet per minute into miles per hour, use the conversion factor of 5280 feet in 1 mile and 60 minutes in 1 hour. Divide the given value by 5280 to get the number of miles, then divide the result by 60 to convert minutes to hours.
Explanation:To convert feet per minute into miles per hour, you need to use the conversion factor of 5280 feet in 1 mile and 60 minutes in 1 hour. Here's the step-by-step calculation:
First, determine the number of miles in the given feet per minute by dividing the given value by 5280.Next, divide the result by 60 to convert minutes to hours.The final result will be the given value in feet per minute converted to miles per hour.For example, if you have a speed of 300 feet per minute:
300 feet per minute / 5280 feet per mile = 0.056818 miles per minute.0.056818 miles per minute / 60 minutes per hour = 0.000947 miles per hour.Therefore, 300 feet per minute is equal to 0.000947 miles per hour.Learn more about Unit Conversion here:https://brainly.com/question/19420601
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What is the solution of log2 (3x - 7) = 3?
4
5
Answer:
x = 5
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
[tex]log_{2}[/tex](3x - 7) = 3, then
3x - 7 = 2³ = 8 ( add 7 to both sides )
3x = 15 ( divide both sides by 3 )
x = 5
The required solution of logarithmic expression log2 (3x - 7) = 3 is x = 5. Option B is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
To solve for x in the equation log2 (3x - 7) = 3, we first use the definition of a logarithm to change the logarithmic form to the exponential form.
log2 (3x - 7) = 3
2³ = 3x - 7
Next, we solve for x by adding 7 to both sides of the equation:
8 + 7= 3x - 7 + 7
15 = 3x
Finally, we divide both sides of the equation by 3:
x = 5
So, the solution of log2 (3x - 7) = 3 is x = 5.
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To the nearest hundredth of a centimeter, what is the length of a leg of the triangle?
[1] cm
84.6 cm
Answer:
The length of a leg of the triangle = 59.83 cm
Step-by-step explanation:
Points to remember
If a right angled triangle with angles 45°, 45° and 90° then the sides are in ratio 1 : 1 : √2
It is given a right angled triangle with 45°, 45° and 90° and hypotenuse = 84.6 cm
To find the length of a leg
Let 'x' be the length of each leg,
From the figure we can write,
1: 1 : √2 = x : x : 84.6
Therefore x = 84.6/√2
= 59.83 cm
Therefore the length of a leg of the triangle = 59.83 cm
ANSWER
59.82
EXPLANATION
The given right angle is an isosceles right triangle.
Let the length of a leg be x cm.
Then by the Pythagoras Theorem,
[tex] {x}^{2} + {x}^{2} = 84.6 ^{2} [/tex]
[tex]2 {x}^{2} = 7157.16[/tex]
Divide both sides by 2.
[tex]{x}^{2} = \frac{7157.16}{2} [/tex]
[tex]{x}^{2} = 3578.58[/tex]
Take positive square root of both sides to get,
[tex]x = 59.82123369[/tex]
Hence the length of a leg is 59.82 to the nearest hundredth.
716,773 rounded to the nearest thousand
Answer: 717,000
Step-by-step explanation:
716,773 rounded to the nearest thousand is 717000 because the 7 is closer to 10 than it is to 0
Hello There!
716,772 rounded to the nearest thousand would be 717,000
772 is closer to 717,000 than 716,000
What is the simplified form expression 2(x-5)?
Answer:
2x-10
Step-by-step explanation:
original equation: 2(×-5)
distributive property: 2(x) 2(-5) =2x-10
Answer:
2x-10
2(x-5)
2*x=2x
2*5=10
How many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is not allowed?
Answer:
2520
Step-by-step explanation:
7×6×5×4×3 = 2520
Imagine □□□□□
For the 1st □, there are 7 choices
For the 2nd □, there are 6 choices (since 1 out of the 7 numbers is already used)
For the 3rd □, there are 5 choices (since 2 out of the 7 numbers are used)
And so on...
The total number of 5-digit numbers that can be formed with the digits 1 to 7, without repetition, is 2520.
Explanation:Your question pertains to the concept of permutations - the number of ways items can be arranged without repetition. In this case, you are considering how many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 without repeating any digit.
A helpful way to think about this is to think of the 5 places for our 5-digit number (i.e., _ _ _ _ _). For the first position, you have 7 choices (the digits 1 to 7) to choose from. Once you have chosen a digit, you are left with 6 choices for the second position, 5 for the third position, 4 for the fourth, and finally 3 for the fifth. So, the total number of 5-digit numbers you can form is 7 × 6 × 5 × 4 × 3 = 2520.
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What is the answer to this question
Estimate the x-coordinates at which the relative maxima and relative minima occur for the function.
f(x) = 3x3 + 9x2 – 1
ANSWER
Relative minimum occurs at x=0
Relative maximum occurs at x=-2
EXPLANATION
The given function is;
[tex]f(x) = 3 {x}^{3} + 9 {x}^{2} - 1[/tex]
We take the first derivative to get:
[tex]f'(x) = 9 {x}^{2} + 18x[/tex]
At turning point f'(x)=0
[tex] 9 {x}^{2} + 18x = 0[/tex]
[tex] 9x(x + 2) = 0[/tex]
[tex]x = 0 \: or \: x = - 2[/tex]
We take the second derivative to get
[tex]f''(x) = 18x + 18
[/tex]
[tex]f''(0) = 18(0) + 18 = 18 \: > \: 0[/tex]
Relative minimum occurs at x=0
[tex]f''( - 2) = 18( - 2)+ 18 = - 18 \: < \: 0[/tex]
Relative maximum occurs at x=-2
Answer:
Relative minimum occurs at x=0
Relative maximum occurs at x=-2
Step-by-step explanation:
What is the output of the following function for x 1? F(x)=-x^3-2x^2+7x-10
Answer:
-6
Step-by-step explanation:
Let x =1
F(x)=-x^3-2x^2+7x-10
F(1) = - (1)^3 -2(1)^2 +7(1) -10
= -1 -2 +7-10
= -3+7-10
=-6
The output of the given function F(x)=-x^3-2x^2+7x-10 when x equals 1 is -6. We substituted x=1 into each term to calculate this.
Explanation:The given function is F(x)=-x^3-2x^2+7x-10. To find the output of the function when x equals 1, you substitute '1' in place of 'x' in the equation. So let's calculate:
For -x^3, substituting x=1, we get: -1^3 = -1For -2x^2, substituting x=1, we get: -2*(1^2) = -2For 7x, substituting x=1, we get: 7*1 = 7Lastly, -10 remains the same as there's no x to substituteNow, add all the results together: -1 - 2 + 7 - 10 = -6. Therefore, when x equals 1, the output of the function F(x) is -6.
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What is the pattern in the values as the exponents increase?
Answer:
Option D is correct.
Step-by-step explanation:
We need to find the pattern in the values as the exponents increase.
First value is 1/3
if we multiply 3 with 1/3 i.e. 1/3*3 we get 1
The next value is 1 in the table.
Now, if we multiply 1 with 3 i.e. 1*3 we get 3
The next value is 3 in the table.
Now, if we multiply 3 with 3 i.e 3*3 we get 9
So, the next value is 9 in the table.
So, if we multiply 3 with the previous value we get the next value in the table.
Hence Option D multiply the previous value by 3 is correct.
What is f(3) for the quadratic function
f(x)=2x2 + x – 12?
F -3
G 3
H 6
I. 9
Answer:
f(3) = 9
Step-by-step explanation:
Wherever you see an x on the right, put a 3 in for that x
f(x) = 2x^2 + x - 12
f(3) = 2*(3)^2 + 3 - 12
f(3) = 2*9 + 3 - 12
f(3) = 18 + 3 - 12
f(3) = 9
if you shift the linear parent function, f(x)=x, up 13 units, what is the equation of the new function?
Answer:
f(x) = x + 13
Step-by-step explanation:
Given f(x) then f(x) + c represents a vertical translation
• If c > 0 then vertical shift up ↑ of c units
• If c < 0 then vertical shift down ↓ of c units
here c = + 13, hence
f(x) = x + 13
Answer plz ASAP!!!!!!!
Let the base = x
Then the height would be 2x ( twice the length of the base.
Now using the given formula you get:
25 = 1/2 * 2x *x
Multiply 2x by 1/2:
1/2 * 2x = 2x/2
25 = 2x/2 * x
2x/2 = 1x, now you have:
25 = x *x
Multiply x by x:
25 = x^2
Take the square root of both sides:
x = √25
x = 5
which of the following equations is of a parabola with a vertex at (1,2)
answer choices
1. y=(x-1)^2 - 2
2 . y=(x-1)^ 2 + 2
3 . y=(x+1)^2 - 2
4 . y=(x+1)^2 + 2
ANSWER
The choice is correct.
[tex]y = {(x -1)}^{2} + 2[/tex]
EXPLANATION
The equation of a parabola in vertex form is given by:
[tex]y = a {(x -h)}^{2} + k[/tex]
where (h,k) is vertex of the parabola and 'a' is the leading coefficient of the parabola.
From the given options, the leading coefficient must be a=1.
We also have the vertex of the parabola at (1,2). This implies that h=1 and k=2.
We substitute these values into the formula to get,
[tex]y = {(x -1)}^{2} + 2[/tex]
The second option is correct.
what is the sum of -36 4/9 - (10 2/9) - (18 2/9)
let's firstly convert the mixed fractions to improper fractions and then add them up.
[tex]\bf \stackrel{mixed}{36\frac{4}{9}}\implies \cfrac{36\cdot 9+4}{9}\implies \stackrel{improper}{\cfrac{329}{9}} \\\\\\ \stackrel{mixed}{10\frac{2}{9}}\implies \cfrac{10\cdot 9+2}{9}\implies \stackrel{improper}{\cfrac{92}{9}}~\hfill \stackrel{mixed}{18\frac{2}{9}}\implies \cfrac{18\cdot 9+2}{9}\implies \stackrel{improper}{\cfrac{164}{9}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf -\cfrac{329}{9}-\cfrac{92}{9}-\cfrac{164}{9}\implies \stackrel{\textit{using the LCD of 9}}{\cfrac{-329-92-164}{9}}\implies -\cfrac{585}{9}\implies -65[/tex]
1. On delivery, eggs should be rejected if:
A. There is only one USDA inspection stamp on each carton
B. The shells of the eggs have cracks in them
c. The shells vary in color
D. The eggs are odorless
When eggs are delivered, if one notices that B. The shells of the eggs have cracks in them, the eggs should be rejected.
Eggs that have cracks in them can be potentially dangerous to people because microorganisms like bacteria can enter through those cracks and either spoil the egg or make it harmful for consumption.
It is therefore best that an egg that has a crack, be rejected upon delivery.
Other options are incorrect because:
One USDA inspection stamp is good enough proof that the eggs are good Shell color has no effect on whether an egg is bad or not Eggs are supposed to be odorlessIn conclusion, if an egg has a crack in it upon delivery, it should be rejected.
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what is the y-interceptof the line shown?
Answer:
y- intercept = 4
Step-by-step explanation:
The y- intercept is the value of the y- coordinate where the line crosses the y- axis.
Here the y- intercept = 4 or (0, 4) ← coordinates of point
Answer:
( 0 , 4 )
Step-by-step explanation:
The y - intercept of the line is where the line hit's or crosses the y - axis and in the case since the line goes through 4 on the y - axis
An unknown number x is at most 10. Which graph best represents all the values of x? Number line graph with closed circle on 10 and shading to the right. Number line graph with open circle on 10 and shading to the right. Number line graph with open circle on 10 and shading to the left. Number line graph with closed circle on 10 and shading to the left.
Answer:
Step-by-step explanation:
The question does say at most 10. That includes 10. So the circle on 10 should indicate it is closed or fully filled in.
The shading should go left. It should indicate less than 10.
-1/64 has what value
Answer:
If you're looking for the absolute value, its 1/64
Step-by-step explanation:
The absolute value is the distance a number is from 0.
1/64 is 1/64th away from 0/64
So, the answer would be 1/64
I hope this helped you! :)
helpp me plz respond
Hector paid $68 for a taxi ride. This driver has a sign above his mirror that recommends a 20% tip. Estimate the amount the driver expects to be tipped to the nearest dollar.
Answer:
Answer:
The answer is 14
Step-by-step explanation:
IT IS NOT 82 I JUST TOOK THE TEST AND IT WAS WRONG...THE ANSWER IS 14!
The driver expects to be tipped approximately $14.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Hector paid $68 for a taxi ride. This driver has a sign above his mirror that recommends a 20% tip.
The amount recieved as a tip is given as -
20% of 68
20/100 x 68
13.6
Therefore, the driver expects to be tipped approximately $14.
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An artist makes a scale drawing of a building he likes. The building is 90 feet tall and 45 feet wide.If this picture is 3 feet wide how tall will this picture be?
Answer:
The Building's tall and wide ratio is 90 : 45 = 2 : 1
now the wide is 3, let's say that tall is a.
2 / 1 = a / 3
a = 2 x 3
a = 6
So the picture will be 6 feet tall.
a right prism has a square base, a surface area of 512 inches squared, and a height of 12 inches. Find the length of the square base
Answer:
8 inches
Step-by-step explanation:
Surface area of a prism is:
S = 2A + Ph
where A is the area of the base, P is the perimeter of the base, and h is the height of the prism.
The base is a square, so A = s² and P = 4s:
S = 2s² + 4sh
Given that S = 512 and h = 12:
512 = 2s² + 4s(12)
512 = 2s² + 48s
256 = s² + 24s
0 = s² + 24s - 256
0 = (s + 32) (s - 8)
s = -32, s = 8
Since s must be positive, s = 8 inches.
Follow below steps;
To find the length of the square base of the right prism:
First, calculate the lateral surface area: 512 in² = 4s * 12 where s is the side length of the square base.
Then, solve for s: 512 = 48s, s = 512 / 48 = 10.67 in.
Therefore, the length of the square base is 10.67 inches.
Write a function for p(x), the profit from selling x necklaces.
The revenue from selling x necklaces is r(x) = 10x. The cost of buying x necklaces is c(x) = 4x + 15. The profit from selling x necklaces is p(x) = r(x) – c(x)
ANSWER
[tex]p(x) = 6x - 15[/tex]
EXPLANATION
The revenue from selling x necklaces is
[tex]r(x) = 10x[/tex]
The cost of buying x necklaces is
[tex]c(x) = 4x + 15[/tex]
The profit from selling x necklaces is
[tex]p(x) = r(x) - c(x)[/tex]
We substitute the functions to get;
[tex]p(x) = 10x- (4x + 15)[/tex]
[tex]p(x) = 10x- 4x - 15[/tex]
[tex]p(x) = 6x - 15[/tex]
Therefore the function for the profit is
[tex]p(x) = 6x - 15[/tex]
2x + 3y = 17
5x + 6y = 32
Usibg method if elimination
Answer:
Solution (-2, 7)
Step-by-step explanation:
2x + 3y = 17 (1)
5x + 6y = 32 (2)
Using elimination method
Multiply (-2) to the equation (1)
-4x - 6y = -34
Now you have 2 new equations
-4x - 6y = -34
5x + 6y = 32
----------------------------Add
x = -2
Substitute x = -2 into 2x + 3y = 17
2(-2) + 3y = 17
- 4 + 3y = 17
3y = 21
y = 7
Solution (-2, 7)
Final answer:
The solution to the system of equations 2x + 3y = 17 and 5x + 6y = 32 using the elimination method is x = -2 and y = 7.
Explanation:
To solve the system of equations using the method of elimination, we manipulate the equations to make the coefficients of either x or y the same, and then subtract one equation from the other to eliminate that variable. Let's consider the given equations:
2x + 3y = 17 (Equation 1)
5x + 6y = 32 (Equation 2)
We can see that the coefficients of y are in the ratio of 3:6 or 1:2. To use elimination, we want the coefficients to match, so we can multiply Equation 1 by 2:
(2)(2x) + (2)(3y) = (2)(17)
4x + 6y = 34 (New Equation 1)
Now we can subtract the new Equation 1 from Equation 2:
(5x + 6y) - (4x + 6y) = 32 - 34
5x - 4x + 6y - 6y = -2
x = -2
Now that we have a value for x, we can substitute it back into one of the original equations to solve for y. Let's substitute x into Equation 1:
2(-2) + 3y = 17
-4 + 3y = 17
3y = 17 + 4
3y = 21
y = 7
The solution to the system of equations is x = -2 and y = 7.
Combine the radicals -2/13 + 19/13
Answer:
17/13
Step-by-step explanation:
Answer:
Step-by-step explanation:
" / " indicates "division" and should not be used in this context.
If you meant: -2 square root 13 plus 19 square root 13, the simplest result would be 17 square root 13.
Note that if you click on the "omega" symbol (below), a menu of symbols will appear, including the square root symbol √.
Then: -2√13 + 19√13 = 17√13.
What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4?
For this case we have that by definition, the Greatest Common Factor (GCF) is the largest factor that 2 numbers have in common.
So, we have the following expressions:
[tex]42a ^ 5b ^ 3\\35a ^ 3b ^ 4\\42ab ^ 4[/tex]
We look for the positive integers that divide to 35 and 42 without leaving residue:
42: 1,2,3,6,7,14,21
35: 1,5,7
Thus, the GCF of 42 and 35 is 7
Then, the GCF of the three expressions is:
[tex]7ab ^ 3[/tex]
Answer:
[tex]7ab ^ 3[/tex]
Answer:
A) 7ab^3
Step-by-step explanation:
EDG2021
GEOMETRY Please help me!!!!
Answer:
The correct answer is first option
512 cubic mm
Step-by-step explanation:
Points to remember
Volume of hexagonal pyramid = Base area * height
To find the volume of hexagonal pyramid
It is given that, base area = 64 square mm and
height = 8 mm
Volume = Base area * Height
= 64 * 8
= 512 cubic mm
Therefore the correct answer is first option
512 cubic mm
1.2 Puzzle Time
Why Did The Muffler Quit The Car Business?
Write the letter of each answer in the box containing the exercise number
Find the value of the variable which satisfies the equation,
1. 4a - 5 = 11
2. 16 = 17 - 1
Answers
E
-7
3. 8 =
-2
4, 647=9
T.1
5. 12c + 6c = 36
L
6
6. 14x + 11x + 10 = 85
7. 19w - 13 - 6w = -39
E. 2
in
T
8. -4(2n – 5) = -28
9. 85 + 3(12 – 73) = 49
10. -18 = 15z - 9(22 – 2)
H. -2
Solve an equation to find the number.
11. The difference of six times a number and 7 is -49,
W. 12
T. -52
12. Negative sixteen plus the quotient of a number and
-4 is –3.
13. The sum of two times a number and 11 is -7,
U.
-9
14. The total cost for a week at camp is $220. You have
$140. You earn $16 for every item you sell in a
fundraiser. How many items do you need to sell to
pay for a week at camp?
Answer:
B is le answer
Step-by-step explanation:
To find the values of the variables in each equation, isolate the variable on one side by performing operations. The solutions for the variables are 4, -1, 2, 6, no solution, and 10.8 for the respective equations.
Explanation:To find the value of the variable in each equation, we need to isolate the variable on one side of the equation. Let's solve each equation step by step:
4a - 5 = 11
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Solve the following system of equations using the substitution method.
-X + 9y = -5
x - 5y = 1
Answer: x=8.5 y=1.5
Step-by-step explanation:
Use the second problem and get X by itself. X= 5y+1. Now plug that equation into the 1st equation.
-(5y+1) +9y =-5.
-5y-1+9y=-5.
-5y+9y= 1+5
4y= 6
Y=1.5
Now that you know what is the value of Y you can plug that into any equation.
5(1.5) +1
7.5+1
X=8.5
For this case we have the following system of equations:
[tex]-x + 9y = -5\\x-5y = 1[/tex]
We clear "x" from the second equation and replace it in the first:
[tex]x = 1 + 5y[/tex]
Substituting in the first equation:
[tex]- (1 + 5y) + 9y = -5\\-1-5y + 9y = -5[/tex]
We have similar terms:
[tex]-1 + 4y = -5[/tex]
Adding 1 to both sides of the equation:
[tex]4y = -5 + 1\\4y = -4\\y = \frac {-4} {4}\\y = -1[/tex]
We look for the value of "x":
[tex]x = 1 + 5 (-1)\\x = 1-5\\x = -4[/tex]
Answer:
[tex](x, y): (- 4, -1)[/tex]