[tex]1\frac{1}{6}[/tex] cups of cheese should be used for [tex]\frac{2}{3}[/tex] of the recipe.
Step-by-step explanation:
Given,
Quantity of cheese used in recipe = [tex]1\frac{3}{4}\ cups = \frac{7}{4}\ cups[/tex]
Recipe to made = [tex]\frac{2}{3}[/tex]
Quantity to use in [tex]\frac{2}{3}[/tex] of recipe = [tex]\frac{2}{3}\ of\ quantity\ required\ for\ full\ recipe[/tex]
Quantity to use = [tex]\frac{2}{3}*\frac{7}{4}[/tex]
Quantity to use = [tex]\frac{7}{6} = 1\frac{1}{6}\ cups[/tex]
[tex]1\frac{1}{6}[/tex] cups of cheese should be used for [tex]\frac{2}{3}[/tex] of the recipe.
Keywords: fraction, multiplication
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The graph of which function has a minimum located at (4, –3)?
f(x) = one-halfx2 + 4x – 11
f(x) = –2x2 + 16x – 35
f(x) = one-halfx2 – 4x + 5
f(x) = 2x2 – 16x + 35
Answer:
f(x) = 1/2x^2 – 4x + 5 (the third option)
Step-by-step explanation:
I looked it up on a graphing calculator.
The quadratic function that has a minimum located at (4, -3) is:
[tex]f(x) = (1/2)*x^2 - 4x + 5[/tex]
Which function has a minimum located at (4, -3)?All the options are quadratic functions, so we need to find the one with a leading coefficient positive, which also has a vertex at (4, -3).
The 3 ones with positive leading coefficients are:
[tex]f(x) = (1/2)*x^2 + 4x -11[/tex]
[tex]f(x) = (1/2)*x^2 - 4x + 5[/tex]
[tex]f(x) = 2x^2 - 16x + 35[/tex]
The vertex of the first one is at:
[tex]x = -4/(2*1/2) = -4[/tex]
The x-value of the vertex must be x = 4, so we can discard this.
For the second quadratic function the x-value of the vertex is:
[tex]x = -(-4)/(2*1/2) = 4[/tex]
Then the y-value of the vertex is:
[tex]f(4) = (1/2)*4^2 - 4*4 + 5 = -3[/tex]
Then the vertex is at (4, -3), so this is the correct option.
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Zoe had x dollars on Monday.
Her sister took $4.50 from Zoe on Tuesday.
Zoe's mother gave her $20 on Wednesday.
Zoe spent half of her money on Thursday.
She had $17.80 left in her pocket.
how much did Zoe have on Monday
What is 22,119 rounded on o the nearest hundred
Help please! these questions are really confusing me
Answer:
Figure 1: Option A : [tex]$ \sqrt{\frac{\textbf{3}}{\textbf{2}}} $[/tex] ; [tex]$ \frac{\textbf{1}}{\textbf{2}} $[/tex] ; [tex]$ \sqrt{\textbf{3}}} $[/tex]
Figure 2: Option B: [tex]$ \frac{\sqrt{\textbf{19}}}{\textbf{10}} $[/tex] ; [tex]$ \frac{\textbf{9}}{\textbf{10}} $[/tex] ; [tex]$ \frac{\sqrt{\textbf{19}}}{\textbf{9}} $[/tex]
Figure 3: Option C: [tex]$ \frac{\textbf{4}}{\textbf{5}} $[/tex] ; [tex]$ \frac{\textbf{3}}{\textbf{5}} $[/tex] ; [tex]$ \frac{\textbf{4}}{\textbf{3}} $[/tex]
Step-by-step explanation:
[tex]$ \textbf{Sin A} \hspace{1mm} \textbf{= } \hspace{1mm} \frac{\textbf{opp}}{\textbf{hyp}} $[/tex]
[tex]$ \textbf{Cos A} \hspace{1mm} {\textbf{=} \hspace{1mm} \frac{\textbf{adj}}{\textbf{hyp}} $[/tex]
[tex]$ \textbf{Tan A} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{Sin A}}{\textbf{Cos A}} $[/tex]
We can simply follow these three formulas to solve the problem.
Figure 1:
Sin A = [tex]$ \frac{6\sqrt{3}}{12} $[/tex] = [tex]$ \frac{\sqrt{3}}{2} $[/tex]
Cos A = [tex]$ \frac{6}{12} = \frac{1}{2} $[/tex]
Tan A = [tex]$ \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}} $[/tex] = [tex]$ \sqrt{3} $[/tex]
Figure 2:
Sin A = [tex]$ \frac{2\sqrt{19}}{20} $[/tex] = [tex]$ \frac{\sqrt{19}}{10} $[/tex]
Cos A = [tex]$ \frac{18}{20} = \frac{9}{10} $[/tex]
Tan A = [tex]$ \frac{\frac{\sqrt{19}}{10}}{\frac{10}{9}} $[/tex] = [tex]$ \frac{\sqrt{19}}{9} $[/tex]
Figure 3:
Sin A = [tex]$ \frac{16}{20} $[/tex] = [tex]$ \frac{4}{5} $[/tex]
Cos A = [tex]$ \frac{12}{20} = \frac{3}{5} $[/tex]
Tan A = [tex]$ \frac{\frac{4}{5}}{\frac{3}{5}} $[/tex] = [tex]$ \frac{4}{3} $[/tex]
Hence, the answer.
Write an expression to represent:
"15 times a number w"
Answer:
15×w
Step-by-step explanation:
15 times w is a number bigger 15 times or added up again and again 15 times:
w+w+w+w+w+w+w+w+w+w+w+w+w+w+w or 15×w
The expression to represent "15 times a number w" is written as 15w. Substituting ½ for w would lead to the multiplication 15 × ½, resulting in 7.5.
Explanation:To represent the phrase "15 times a number w," you would write the algebraic expression 15w. This is accomplished by using the coefficient 15 to indicate that the number w is being multiplied by 15. So, if you were to substitute the value ½ for w into this expression, you would perform the multiplication 15 × ½ to get the result, which simplifies to 7.5.
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The 5th power of what number is equal to 3^15?
3^15 = 14,348,907
Which means...
x^5 = 14,348,907
If we execute [tex]\sqrt[5]{14348907}[/tex] and do the same with x^5 we get...
x = 27
So the 5th power of 27 is equal to 3^15.
⭐ Answered by Hyperrspace (Ace) ⭐
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The fifth power of the number 27 is equal to 3¹⁵.
To find the fifth power of a number that is equal to 3¹⁵, we need to determine what number raised to the power of 5 gives us 3¹⁵.
Let's call the number we are looking for "x." So, we need to solve the equation:
x⁵ = 3¹⁵
To find x, we can take the fifth root of both sides of the equation:
x = (3¹⁵[tex])^{(1/5)[/tex]
x = 3³
x = 27
This means that if we raise 27 to the power of 5 (27⁵), we will get 3¹⁵ (3 raised to the power of 15).
In conclusion, the number we are looking for is 27, as 27^5 is equal to 3¹⁵.
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Identify the x intercept and y intercept of the line 2x-4y=-12
The x-Intercepts of the line 2x - 4y = -12 is -6 and the y-intercept is 3.
To identify the x and y intercepts of the line, we set one variable to zero and solve the equation for the other variable.
For the x-intercept, we set y=0 and solve for x in the equation: 2x - 4(0) = -12, hence x = -6.
For the y-intercept, set x=0 and solve for y in the equation: 2(0) - 4y = -12, hence y = 3.
Therefore, the x-intercept is -6 and the y-intercept is 3
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Use the drawing tools to form the correct answers on the graph. Plot the zeros of this function: f(x) = (x – 1)(x – 7).
The answer is in the graph picture
The zeros of the function f(x) = (x - 1)(x - 7) are 1 and 7
The function is given as:
f(x) = (x - 1)(x - 7)
Set the function to 0.
So, we have:
f(x) = (x - 1)(x - 7) = 0
This gives
(x - 1)(x - 7) = 0
Split
(x - 1) = 0 or (x - 7) = 0
Remove brackets
x - 1 = 0 or x - 7 = 0
Solve for x
x = 1 or x = 7
Hence, the zeros of the function are 1 and 7
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A triangle with a height of 12
inches has an area of 42 square
inches. How long is the base of
the triangle? (need help) need it asap
The area of a triangle is 1/2*base*height
So make your equation: 1/2*b*12=42
6*b=42
b=7
So the base is 7 inches long
Hope that helped!
Polynomial equation when zeros are -4, -2, 1, 4
Step-by-step explanation:
Given,
The zeros of the polynomial are - 4, - 2, 1 and 4
To find, the polynomial equation = ?
We know that,
The polynomial equation = (x - A)(x - B)(x - C)(x - D)
= (x + 4)(x + 2)(x - 1)(x - 4)
= [(x + 4)(x - 4)] [(x + 2)(x - 1)]
= ([tex]x^{2}-16[/tex])([tex]x^2-x+2x-2[/tex])
= ([tex]x^{2}-16[/tex])([tex]x^2+x-2[/tex])
= [tex]x^{4}+x^{3}-2x^{2}-16x^{2}-16x+32[/tex]
= [tex]x^{4}+x^{3}-18x^{2}-16x+32[/tex]
Thus, the required poynomial equation is [tex]x^{4}+x^{3}-18x^{2}-16x+32[/tex].
The following examples illustrate the inverse property of multiplication. Study the examples, then choose the statement that best describes the property.
1
5
• 5 = 1
√2 (
1
√2
) = 1
Inverse property of multiplication: For all real numbers except , a • = 1.
Answer:
[tex]\text{Inverse property of multiplication: For all real numbers except }0,\text{ }a\cdot 1/a=1[/tex]
Explanation:
These are the examples given to illustrate the inverse property of multiplication:
[tex]1/5\cdot 5=1\\\\ \sqrt{2}\cdot (1/\sqrt{2})=1[/tex]
And you must complete the statement to describe the property.
Inverse property of multiplication: For all real numbers except __, a • __ = 1.In the first example, 1/5 and 5 are reciprocal numbers of each other, also known as multiplicative inverses. And the example is showing that the product of 1/5 and its reciprocal is 1.
In the second example, [tex]\sqrt{2}\text{ and }(1/\sqrt{2})[/tex] are reciprocal of each other. Again, the example is showing that the product of those a number at its reciprocal is 1.
That is a general property, that can be written as:
[tex]a\cdot 1/a=1[/tex]
That property is satisfied by any number except 0, because the reciprocal of [tex]0[/tex] , i.e. [tex]1/0[/tex] is not defined.
Then, the statemen is:
[tex]\text{For all real numbers except }0,\text{ }a\cdot 1/a=1[/tex]
The statement that best describes the inverse property of multiplication is: Inverse property of multiplication: For all real numbers except 0, a * a⁻¹ = 1.
This means that if you multiply a number by its reciprocal, you will always get 1.
The examples you provided illustrate this property nicely:
5 * 1/5 = 1
√2 * 1/√2 = 1
Note that the inverse property of multiplication does not hold for the number 0, because the reciprocal of 0 is undefined.
Here is another example of the inverse property of multiplication:
3 * 1/3 = 1
You can check any other real number and its reciprocal, and you will always find that the product is 1.
The inverse property of multiplication is a useful property in mathematics, and it is used in many different areas, such as algebra, calculus, and physics.
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Translate the following sentence into an equation. The sum of twice a number x and 13 is two less than three times x.
Question 20 options:
a)
2x + 13 = 3x – 2
b)
2(x + 13) + 3x – 2
c)
2x + 13 = 2 – 3x
d)
2x + 13 = 3(x – 2)
Answer:
2x + 13 = 3x - 2
Step-by-step explanation:
This should be the answer
Answer:
its 2
Step-by-step explanation:
What is 15x when x=4
Answer:
60
Step-by-step explanation:
15*4=60
The 15x when x = 5 will be 60.
What is the arithmetic operator?
Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Given,
x = 4
Now,
15x is nothing but we need to multiply 15 with x
So,
15x = 15 × 4
15x = 60
Hence,The 15x when x = 5 will be 60.
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Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points (4,5), (-6,-6), and (-14,2), respectively. The epicenter of an earthquake is determined to be 10 units from X, 5 units from Y, and 13 units from Z. Where on the coordinate plane is the epicenter located?
Find the coordinates of the epicenter.
Answer:
(-2, -3)
Step-by-step explanation:
A careful graph shows the point (-2, -3) is at the intersection of the circles whose radii are the given distances from the receiving stations.
_____
The simultaneous equations for the circles can be solved algebraically.
The epicenter is 10 units from X, so lies on the circle ...
(x -4)^2 +(y -5)^2 = 10^2
x^2 -8x +16 +y^2 -10y +25 = 100
x^2 +y^2 -8x -10y = 59
__
The epicenter is 5 units from Y, so lies on the circle ...
(x +6)^2 +(y +6)^2 = 5^2
x^2 +12x +36 +y^2 +12y +36 = 25
x^2 +y^2 +12x +12y = -47
__
The epicenter is 13 units from Z, so lies on the circle ...
(x +14)^2 +(y -2)^2 = 13^2
x^2 +28x +196 +y^2 -4y +4 = 169
x^2 +y^2 +28x -4y = -31
__
Subtracting the second equation from each of the other two, we get ...
(x^2 +y^2 -8x -10y) -(x^2 +y^2 +12x +12y) = (59) -(-47)
-20x -22y = 106 . . . . eq1 -eq2
(x^2 +y^2 +28x -4y) -(x^2 +y^2 +12x +12y) = (-31) -(-47)
16x -16y = 16 . . . . . . . .eq3 -eq2
These simultaneous linear equations can be solved a variety of ways. We might use substitution:
x = y+1 . . . . . from eq3 -eq2 divided by 16
10(y +1) +11y = -53 . . . . . from eq1 -eq2 divided by -2
21y = -63 . . . . . . . . . . . . simplify, subtract 10
y = -3
x = y+1 = -2
The epicenter is located at (x, y) = (-2, -3).
I need help on this please can someone help me with this
Answer:
C. 11
Step-by-step explanation:
First, find the value of "x" by solving the first equation. You need to move every other number to the other side of "x". When you move a number, you have to do the opposite operation to both sides.
5x + 6 = 10 The opposite of +6 is -6.
5x + 6 - 6 = 10 - 6 Subtract 6 from both sides
5x = 10 - 6 The "6" on the left cancelled out. Simplify the right side
5x = 4 The opposite of multiply by 5 is divide by 5
5x/5 = 4/5 Divide both sides by 5
x = 4/5 Value of "x"
Substitute the value of "x", which is 4/5, in the "x" for the second equation.
10x + 3
= 10(4/5) + 3 Multiply 10 and 4/5
= [tex]\frac{10*4}{5}[/tex] + 3 Combine into the numerator
= [tex]\frac{40}{5}[/tex] + 3 Divide the top by the bottom
= 8 + 3 Add
= 11 Value of second equation
Therefore the value of 10x + 3 is 11.
PLEASE HURRY!!! THANK YOU
1. There were 88 birds in the tree and then b of the birds flew away. Write an expression that shows how many birds are in the tree now.
2. Brice had $73 and then he earned d more dollars. Write an expression that shows how much money he has now.
3. Kurt's car gets 23 miles to a gallon of gasoline. He filled up his car's gas tank with g gallons. Write an expression that shows how far Kurt can drive on a tank of gasoline.
The product of t and three is 13.5
Answer: t = 4.5
Step-by-step explanation: 13.5/3 = 4.5
Answer:
T = 4.5
Step-by-step explanation:
The way to solve this is simple.
You just have to divide 13.5 by 3
and then you get the answer of 4.5!
Hope this helped!
~Oreo!!
Consider the enlargement of a triangle that has a scale factor of 7.5.
A small triangle has a base of 5 centimeters and height of 2 centimeters. A larger triangle has a base of b and height of a.
Area Original = 1
2
(5)(2) = 5 cm2
What is the area of the enlarged triangle? cm2
Answer: ✔ 281.25
Step-by-step explanation:
Answer:
281.25
Step-by-step explanation:
It is correct E d g e n u i t y
6v+13b=377
4v+9b=259
Answer:
v = 13
b = 23
Step-by-step explanation:
To solve this system of equations, we can negate one equation and add it to other to cancel out one variable.
Looking at v and b, the coefficients are 6, 4 and 13, 9, respectively.
It would be easier to use the LCM of 6 and 4
[tex]E_1 : 6v + 13b = 377\\E_2: 4v + 9b = 259\\\\4E_1 + (- 6)E_2:\\24v + 52b = 1508\\-24v - 54b=-1554\\\\0v -2b = -46\\-2b = -46\\b = 23\\\\4v + 9(23) = 259\\4v + 207 = 259\\4v = 52\\v = 13\\\\6(13) + 13(23)\\78 + 299\\377[/tex]
72% of the students in Math 6th at AZVA are currently passing mastering their lessons. If 324 students are currently mastering their Math lessions, how many students are in Math 6th?
a) Use a percent equation OR set up a proportion that will use to solve the problem.
b) Solve the problem. Show your work.
Answer:
Step-by-step explanation:
72% of the students in math 6 = 324
let x represent the students in math 6
turn ur percent to a decimal
0.72x = 324
x = 324 / 0.72
x = 450 students <===
Answer:
its 233.28
Step-by-step explanation:
cuz i took a test and this was the right answer
56∙9÷14∙ 1/3
help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help
Answer:
Result = 12
Step-by-step explanation:
Fractions
Fractions are the general expression for rational numbers, defined as
[tex]\displaystyle \frac{a}{b}, \ b\neq 0[/tex]
Where a and b are integer numbers. Some operations with fractions have special rules than those with integers. The product of two or more fractions is
[tex]\displaystyle \frac{x}{y}\cdot \frac{w}{z}\cdot \frac{r}{s}=\frac{xwr}{yzs}[/tex]
We'll use that rule to operate the numbers given in the question:
[tex]\displaystyle 56\cdot \frac{9}{14}\cdot \frac{1}{3}=\frac{504}{42}[/tex]
The fraction can be simplified to an integer by dividing it
[tex]\displaystyle \frac{504}{42}=12[/tex]
Answer:The Answer is 12.
Step-by-step explanation:
When going through a step by step problem you always wanna go from the left to right.(Unless you have parentheses)
56*9=504
504/14=36
36*1/3=12
There for, you answer is 12.
Hope this helped you. Remember Stay Positive!
Morse code is a way to transmit text using a series of dots or dashes. The Morse Code for "Add" is shown. What fraction of the shapes are dots in the Morse code for "Add"
Add in Morse code is :
.—..-..
There are 8 total symbols, 5 of them are dots.
The fraction would be 5/8 are dots.
Answer:
[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
The Morse Code for Add is:
.__.._..
There are 5 dots and 3 dashes, so there are 8 figures in total. The fraction is 5 divided by the total number of symbols, which is 8. So the answer is [tex]\frac{5}{8}[/tex]
A pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length h ft is to be built. If fencing costs $ 4 divided by ft for the legs and $ 16 divided by ft for the hypotenuse, write the total cost C of construction as a function of h.
Answer:
[tex]\frac{8h}{\sqrt{2}} + 16h[/tex]
Step-by-step explanation:
First we need to compute the side length as a function of h
So x be the side length of the right isosceles triangle, in Pythagorean formula we have
[tex]x^2 + x^2 = h^2[/tex]
[tex]2x^2 = h^2[/tex]
[tex]x = \frac{h}{\sqrt{2}}[/tex]
The cost for the legs is
[tex]C_l = 4*2x = \frac{8h}{\sqrt{2}}[/tex]
The cost for the hypotenuse is
[tex]C_h = 16h[/tex]
So the total cost in term of h is
[tex]C = C_l + C_h = \frac{8h}{\sqrt{2}} + 16h[/tex]
The total cost C of construction as a function of h is C = 16 / h + 8√2 / h
The pen is in the shape of an isosceles right angle. This means one of the
angle is 90 degrees and 2 sides of the triangle are equal and the base angles
are equal too.
Using pythagora's theorem
Therefore,
x² + x² = h²
2x² = h²
x² = h² / 2
x = √h²/ √2 = h/√2
cost of the legs = 4 / h/√2 + 4 / h /√2 = 8√2 / h
cost of the hypotenuse = 16 / h
Total cost = 16 / h + 8√2 / h
C = 16 / h + 8√2 / h
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length of a rectangle is 4 more than its breadth.represent in the form equation
Answer:
L = B + 4
Step-by-step explanation:
Let the breadth be B
Let the length be L
But from the question, we were told that the length is 4 more than the breadth. This is expressed as
L = B + 4
Help please I really need it
Answer:
X-Intercept is -45. (Answer would be (-45,0))
Step-by-step explanation:
You can use Desmos which is a graphing calculator to figure out the answer. Plug the equation into Desmos and it will show you a line and where the x-intercept is. And boom, you got your answer.
What is 4x4 i need to know
Answer: 16
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
4x4 is 4 groups of four.
You can visibly show this by doing four lines of four dots.
••••
••••
••••
••••
count those dots, you get 16
QUESTION 4 of 10: Your restaurant purchases 1,625 bottles of Chablis per year. The annual increase of purchases has been 6%. If this
increase continues for 5 years, what will be your average increase in bottles purchased per year over that time?
a) 110 bottles
b) 190 bottles
c) 260 bottles
d) 400 bottles
Answer:
A - 110
Step-by-step explanation:
So if it is 6% increase you would times the number by 1.06. So you would do this like 5 times:
1,625 x 1.06 = 1722.5
1722.5 x 1.06 = 1825.85
1825.85 x 1.06 = 1935,401
1935.401 x 1.06 = 2051,52506
2051.52506 x 1.06 = 2174,6165636
Now you have the total number of bottles after 5 years, you would find the increase which is 2174.6165636 - 1,625 ≈ 550. 550 / 5 = 110
A
⭐ Answered by Foxzy0⭐
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The average increase in bottles purchased per year over that time is c) 110 bottles.
What is percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is generally denoted using the percent sign ''%''.
Now it is given that,
Number of bottles purchased per year, a = 1,625
Percentage increase per year, r = 6% = 0.06
Total time period, n = 5 years
Since, the equation of a exponential growth function is given as,
y = a(1 +r)ⁿ
⇒ y = 1625(1 +0.06)⁵
⇒ y = 1625(1.06)⁵
⇒ y = 1625*1.338
⇒ y = 2,175
Therefore, average increase in bottles purchased per year over that time = (2175 - 1625) / 5
= 550 / 5
= 110 bottles
Thus, the average increase in bottles purchased per year over that time is c) 110 bottles.
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Which is the value of this expression when a = 5 and k = negative 2? (3^2 a^-3)(3 a^-4)^-2
Answer: C 25/9
Step-by-step explanation:
Find the output, yyy, when the input, xxx, is 555.
y = 5x-3y=5x−3
The output y is [tex]y=22[/tex]
Explanation:
The expression is [tex]y=5 x-3[/tex]
We need to determine the output y, when the value of input is x is 5.
That is, substituting [tex]x=5[/tex] in [tex]y=5 x-3[/tex], we get,
[tex]y=5(5)-3[/tex]
Multiplying the value within the bracket, we have,
[tex]y=25-3[/tex]
Subtracting the terms, we get,
[tex]y=22[/tex]
Thus, the value of output y is [tex]y=22[/tex]
Lisa purchased a concert ticket on a website. The original price of the ticket was $85. She used a coupon code to receive a 20% discount. The website applied a 10% service fee to the discounted price. Lisa's ticket was less than the original price by what percent?
Answer:
10%
Step-by-step explanation:
The original price of the ticket was $85 and she had a discount of 20%. Since the website applied a 10% service fee to her discount price, then Lisa'a ticket would be 10% less than the original price.