The ounces of cheese Ellie uses to make tacos is 2
What is a unitary method?
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Calculation :
1 pound = 16 ounces
Total cheese Ellie has = [tex]\frac{2}{8}[/tex] pound
Cheese required to make tacos = [tex]\frac{2}{8}[/tex]×[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{8}[/tex] pounds
Ounces of cheese required to make cheese are [tex]\frac{1}{8}[/tex] × 16 = 2 ounces
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What is equivalent to x^3y^-7
Answer: [tex]\displaystyle\\\frac{x^3}{y^7}[/tex].
Step-by-step explanation:
[tex]\displaystyle\\x^3y^{-7}=\frac{x^3}{y^7} .[/tex]
SinA=√1-x÷√1+X
Find the value of cosA
The value of cos A is √(1 + x²)/ (1 - x²) /√1 + x
Trigonometric ratios
It is important to note that
sin A = opposite/ hypotenuse
cos A = adjacent/ hypotenuse
Then,
opposite = [tex]\sqrt{1} - x[/tex]
Hypotenuse = [tex]\sqrt{1} + x[/tex]
Let's find the adjacent side using the Pythagorean theroem
[tex](\sqrt{1} + x)^2 = (\sqrt{1 -x } )^2 + x^2[/tex]
[tex]1 + x^2 = 1 - x^2 + x^2[/tex]
[tex]x = \sqrt{\frac{1 + x^2}{1 -x^2} }[/tex]
cos A = x/hypotenuse
[tex]cos A = \frac{\sqrt{\frac{1+x^2}{1 -x^2} } }{\sqrt{1} +x}[/tex]
cos A = √(1 + x²)/ (1 - x²) /√1 + x
Thus, the value of cos A is √(1 + x²)/ (1 - x²) /√1 + x
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A plane travels 2,000 kilometers at a speed of 900 kilometers per hour (kph) with no wind. when a tailwind is present, the plane’s speed increases by x kilometers per hour. the time it takes the plane to travel the same distance with the tailwind, t(x), is defined by the function . what is the meaning of the y-intercept for this function? the time it takes the plane to travel without the tailwind the speed of the plane when there is no tailwind present the minimum amount of time it takes the plane to travel 2,000 km the time it takes the plane to travel when the speed is decreased by 900 kph
The meaning of the y-intercept exists in the time required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour (kph) with no wind. [tex]$2 \frac{2}{9}$[/tex] hours required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour with no wind.
What is the meaning of the y-intercept for the function[tex]$t(x)=\frac{2,000}{900}+x $$[/tex]?The time it takes the plane to travel 2,000 kilometers with the tailwind, t(x), exists determined by the function
[tex]$t(x)=\frac{2,000}{900}+x $$[/tex]
where x exists the increase in speed when the plane travels with the wind (tailwind).
The y-intercept exists at x=0, then
[tex]$&t(0)=\frac{2,000}{900}+x \\[/tex]
[tex]$&t(0)=\frac{20}{9}=2 \frac{2}{9}[/tex] hours
[tex]$2 \frac{2}{9}$[/tex] hours required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour with no wind.
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What is the end behavior of the radical function represented by this graph? The graph shows the square root function. The function starts at the point (minus 3, 0) and extends upwards and to the right. Some major points on the graph are (0, 3), (2, 4), and (5, 5). A. As x decreases in value, increases in value. As x increases in value, decreases in value. B. As x decreases in value, increases in value. As x increases in value, increases in value. C. As x decreases in value, decreases in value. As x increases in value, increases in value. D. As x decreases in value, decreases in value. As x increases in value, decreases in value.
The option that describes the end behavior of the graph of the square root function with coordinates (-3, 0), (0, 3), (2, 4), and (5, 5), is the option;
C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.
Which method can be used to find the end behavior of the graph?The given coordinates on the graph are;
(-3, 0), (0, 3), (2, 4), and (5, 5)
The coordinates of the starting point of the graph = (-3, 0)
Shape of the graph = Extends from point (-3, 0), upwards and to the right
Therefore;
As the x-value increases, the y-value increases and vice versa, with, x increasing faster than y.
However, given that the graph is for a square root function, the correct option is option C;
C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.
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Match each quadratic function given in factored form
with its equivalent standard form listed on the left.
-f(*) = (x + 2)(x - 6)
f(x) = (x - 4)(x + 3)
f(x) = (x - 12)(x 1)
f(x) = (x -3)(x + 4)
The standard form of the given quadratic equation in factored form is
(x+2) (x-6) = x²-4x-12
(x-4) (x+3) = x²-x-12
(x-12) (X+1) = x²-11x-12
(x-3) (x+4) = x²+x-12
what are quadratic equations?
A quadratic function can be defined as a function having the highest degree 2. The standard form of a quadratic function is ax²+bx+c where a and b are not equal to zero
To convert a factored quadratic function into the standard form, we first need to open the brackets by multiplying the integers. Then carry out addition or subtraction operations to obtain the equation.
f(x) = (x+2) (x-6)
x²+2x-6x-12
x²-4x-12
similarly, the standard form of equations 2,3 and 4 are :
(x²-x-12)
(x²-11x-12)
(x²+x-12)
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Answer:
B, D, A, C
Step-by-step explanation:
f(x) = (x + 2)(x – 6)
✔ B
f(x) = (x – 4)(x + 3)
✔ D
f(x) = (x – 12)(x + 1)
✔ A
f(x) = (x – 3)(x + 4)
✔ C
PLS HELP IM STUCK PLS
Answer:
-4
Step-by-step explanation:
We are going to substitute 0 in for x and solve for y.
-2(0)+ 8y = -32 Anything times zero is zero
0 + 8 y = -32 Anything plus zero is itself.
8y = -32 Divide both sides by 8
y = -4
Find the area in square units of ABC△ plotted below.
Answer:
71
Step-by-step explanation:
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y,z)=x2 y2 z2; 3x 4y−3z=34
The extremum of f(x,y) is subject to the given constraint, There is a global minimum (x,y,z.) (4,2,-8).
An instance of a constraint is the fact that there are only so many hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. one which restricts, limits, or regulates; a test.
A constraint is something that limits or controls what you may do. Their decision to abandon the ride turned into made due to economic constraints. Water shortages in the location could be the main constraint on development. Synonyms: limit, drawback, scale back, rein more Synonyms of constraint.
predicament or restriction. repression of herbal emotions and impulses: to exercise constraint. unnatural restraint in manner, communique, and many others.; embarrassment. Something that constrains.
By lagranier multi plur
of = hog
(2x, is, 22>= 25-47
8x=42
10x + 2 = 42
2
28
2x=4, 4= 2
=2
722 (4)
(4.9,2) = (4.2-8)
(4,2-8)= 84
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20 points and I will mark brainlyist to the first right answer.
Answer:
Step-by-step explanation:
Movie A: 267 students
Movie B: 217 students
Movie C: 233 students
Movie D: 183 students
I dont know this one
Answer:
10, 8
Step-by-step explanation:
l + w = 18
l*w = 80
8 and 10 works
Name the rule for this sequence.
27, 21, 15, 9, 3,...
A) divide the previous term by 0.06
B) divide the previous term by 0.6
C) add 6 from the previous term
D) subtract 6 from the previous term
Answer:
D) subtract 6 from the previous term
Step-by-step explanation:
27-6=21, 21-6=15, 15-6=9, and 9-6=3
о
О A. y< x
у>4
О B. y< x
y<4
( C. y> x
у>4
о D. y> x
y<4
-5
5
5
Answer:
b
Step-by-step explanation:
B
Find the sum of the convergent series. (round your answer to four decimal places. ) [infinity] (sin(9))n n = 1
The sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31
For given question,
We have been given a series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]
[tex]\sum_{n=1}^{\infty}~(sin(1))^n=sin(1)+(sin(1))^2+...+(sin(1))^n[/tex]
We need to find the sum of given convergent series.
Given series is a geometric series with ratio r = sin(1)
The first term of the given geometric series is [tex]a_1=sin(1)[/tex]
So, the sum is,
= [tex]\frac{a_1}{1-r}[/tex]
= sin(1) / [1 - sin(1)]
This means, the series converges to sin(1) / [1 - sin(1)]
[tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]
= [tex]\frac{sin(1)}{1-sin(1)}[/tex]
= [tex]\frac{0.8415}{1-0.8415}[/tex]
= [tex]\frac{0.8415}{0.1585}[/tex]
= 5.31
Therefore, the sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31
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An athlete trains for 80 min each day for as many days as possible. Write an equation that relates the number of days d that the athlete spends training when the athlete trains for 400min.
80d = 400 is the equation that relates the number of days d that an athlete spends training when the athlete trains for 400 min given that athlete trains for 80 min each day for as many days as possible. This can be obtained by converting the given statements into algebraic equation.
Find the required equation for the given question:Here in the question it is given that,
Athlete trains for 80 min each day,that is each day the athlete spends 80 min.
We have to assume the variable d the number of days the athlete spends training.Finally we have to find an equation that relates the number of days d that the athlete spends training when the athlete trains for 400 min.So we can write that,
400 min is the time spent by the athlete
400 min = number of days × time spent by the athlete in one day
400 min = d × 80
⇒ 80d = 400
Hence 80d = 400 is the equation that relates the number of days d that an athlete spends training when the athlete trains for 400 min given that athlete trains for 80 min each day for as many days as possible.
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Ujarak has 100mL t of a strong toothpaste with a 1.1% concentration of sodium fluoride. They have a weaker toothpaste with a 0.3% concentration of sodium fluoride.
What volume, in milliliters, of the weaker toothpaste would Ujarak need to add to the strong toothpaste to create a blend with a 0.8% concentration of sodium fluoride?
The volume of the 0.3% concentration of sodium fluoride required to mix with 100mL of a strong toothpaste with a 1.1% concentration of sodium fluoride to create a blend with a 0.8% concentration of sodium fluoride is 60 mL.
What are mixtures?Mixtures refers to substances which are composed of two or more substances physically combined together.
The 1.1% concentration of sodium fluoride will form a mixture with the 0.3% concentration sodium fluoride.
Let the volume of the 0.3 % concentration toothpaste required be x.
Final volume of toothpaste = (100 + x) mL
Amount of mixture = 0.8 * (100 + x)
100 ml * 1.1 + x * 0.3 = 0.8 * (100 + x)
solving for x
110 + 0.3x = 80 + 0.8x
110 - 80 = 0.8x - 0.3x
30 = 0.5x
x = 60
Therefore, 60 mL of the 0.3% concentration of sodium fluoride is required.
In conclusion, the volume of the weaker solution of the sodium fluoride solution required is obtained from the method of mixtures.
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Determine the area between the curves by integrating over the x-axis or y-axis.
x=y^2
x=-|y|+12
When [tex]y\ge0[/tex] (above and on the [tex]x[/tex]-axis), we have [tex]|y|=y[/tex]. The parabola [tex]x=y^2[/tex] intersects with [tex]x=-|y|+12[/tex] in this region when
[tex]y^2 = -y + 12 \implies y^2 + y - 12 = (y-3)(y+4) = 0 \implies y=3[/tex]
On the other hand, when [tex]y<0[/tex] (below the [tex]x[/tex]-axis, we have [tex]|y|=-y[/tex], and so the curves intersect when
[tex]y^2 = -(-y) + 12 \implies y^2 - y - 12 = (y - 4)(y+3) = 0 \implies y=-3[/tex]
The area between the curves is then given by the definite integral,
[tex]\displaystyle \int_{-3}^3 (-|y| + 12) - y^2 \, dy[/tex]
The integrand is symmetric about the [tex]x[/tex]-axis, so the integral is equivalent to
[tex]\displaystyle 2\int_0^3 12 - y - y^2 \, dy = 2 \left(12y - \frac{y^2}2 - \frac{y^3}3\right)\bigg|_0^3 = \boxed{45}[/tex]
Find the largest 4-digit number which is a perfect square.
Answer:
To find the biggest 4-digit number which is a perfect square, we have to take the square of biggest 2-digit number. ∴ The biggest 4-digit number which is a perfect square = 9801.
Step-by-step explanation:
mark as brainlest answerAnswer:
9801
Step-by-step explanation:
well we know 100 squared is the first 5 digit square number so it must be 99 squared, which is 9801
Of all the numbers whose difference is 10, find the two that have the minimum product
Answer: -9
Step-by-step explanation: You might think that the smallest two numbers are 11 and 1 but there are negative numbers. 1 - (-9) is equal to 10. 1 x (-9) is -9.
Helppppppp show the steps to your answer
The numeric value of the expression -a² - 2bc - |c| for a = -3, b = -5 and c = 2 is of 9.
How to find the numeric value of an expression?The numeric value of an expression is found replacing each letter by it's attributed value.
In this problem, the expression is:
-a² - 2bc - |c|
The attributed values are:
a = -3, b = -5 and c = 2
Hence the numeric value will be given by:
-a² - 2bc - |c| = -(-3)² - 2(-5)(2) - |2| = -(9) + 20 - 2 = -9 + 18 = 9.
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Find the missing length indicated.
The missing length indicated on the right triangle is 120 units
How to determine the missing length?To start with:
The missing length in the right triangle can be represented with the variable x
Next, we have the following equivalent ratio from the given triangle
64 : x = x : 289 - 64
Express the ratio as a fraction
64/x = x/(289 - 64)
Evaluate the difference on the right-hand side
64/x = x/225
Cross multiply in the above equation
x * x = 64 * 225
This gives
x^2 = 64 * 225
Take the square root of x^2 (do not approximate)
x = 64 * 225
Take the square root of 64 and 225 (do not approximate)
x = 64 * 225
Evaluate the product of 8 and 5
x = 120
Based on the given parameters, the missing length indicated on the right triangle is 120 units
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In the regular pentagon below, if AP = 4 m and BC = 10 m, find it's area.
First symmetrically cut the pentagon to get 5 pieces. (So that you will get the idea that this polygon is divided into 5 triangles)
Then find the area of one of the triangles:
Area of Triangle = [tex]\frac{1}{2} bh[/tex]
A = [tex]\frac{1}{2}[/tex] × 4 × 10
A = 20 m²
To find the area of the whole pentagon shape:
A = 20 × 5 = 100 m²
Hope it helps!
1 + 7x = 5x + 25 solve for X
Answer:
x = 12
Step-by-step explanation:
1 + 7x = 5x + 25 ( subtract 5x from both sides )
1 + 2x = 25 ( subtract 1 from both sides )
2x = 24 ( divide both sides by 2 )
x = 12
Answer:
12
Step-by-step explanation:
Start by subtracting both sides by 5x:
[tex]1+7x-5x=25\\1+2x=25[/tex]
Subtract 1 from both sides
[tex]2x=24[/tex]
Divide both sides by 2
[tex]x=12[/tex]
Check[tex]1+7(12)=5(12)+25\\1+84=60+25\\85=85[/tex]
Therefore x = 12
6;15; x; 45;....... is a quadratic number pattern (sequence). Determine the value of x.
Solving a system of equations, we conclude that the value of x is 28.
How to determine the value of x?
Here we have the quadratic number pattern:
6, 15, x, 45, ...
First, we have that:
15 - 6 = 9
So 9 is the first difference.
Then we will have:
x = 15 + 9 + a
(where a is the second difference, constant of the sequence).
And:
45 = x + 9 + a + a
Then we have a system of equations:
x = 15 + 9 + a
45 = x + 9 + a + a
We can isolate a on the first equation:
a = x - 24
We can replace that in the other equation:
45 = x + 9 + 2a
45 = x + 9 + 2*(x - 24)
Now we can solve that for x:
45 - 9 = x + 2*(x - 24)
36 = 3x - 48
36 + 48 = 3x
84 = 3x
84/3 = x = 28
The value of x is 28.
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julianna wrote -16+ x = -8 on the board.Do not solve.Tell how you would simplify julianna's expression?
Answer:
x = 8
Step-by-step explanation:
→ Add 16 to both sides
x = 8
The correct solution for the given expression [tex]-16+x = -8 \\[/tex] is [tex]x[/tex] is equal to [tex]8[/tex].
Given expression:
[tex]-16+x =- 8 \\[/tex]
To solve for [tex]x[/tex], Rearrange the equation or isolate [tex]x[/tex] terms on one side of the expression.
Add [tex]8[/tex] on both side of the equation:
[tex]-16+x+8=-8+8[/tex]
Simplify:
[tex]x-8 = 0[/tex]
Isolate [tex]x[/tex] on one side:
[tex]x= 8[/tex]
The correct value of [tex]x[/tex] is [tex]8[/tex].
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What is the volume of a square pyramid that is 8 feet tall with base edges of 3 feet?
8 ft
3 ft
3 ft
4a. In a cookie mix, we find no-bake cookies, vanilla cookies, and cinnamon cookies in a ratio of 2 2 2 If a bag of the mix contains 40 no-bake cookies, how many vanilla cookies are there? please help
Answer:
40 vanilla cookies
Step-by-step explanation:
Lets say that
N = No-bake cookies
V = Vanilla cookies
C = Cinnamon cookies
If the ratio is 2 : 2 : 2
And there are 40 no-bake cookies
It would be 40 vanilla cookies and 40 cinnamon cookies because the ratio is all the same
( N : V : C )
( 40 : 40 : 40 )
Hope this helps (๑ > ᴗ <)وxx
( I am so sorry if this is wrong!!)
Find the missing side lengths. Leave your answers as radicals in simplest form.
The missing side length of the right triangle are as follows;
v = 1 units
u = 2 units
How to find side of a right triangle?A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.
Therefore,
tan 60 = opposite / adjacent
tan 60 = √3 / v
cross multiply
v = √3 / tan 6-
v = √3 / √3
v = 1
Hence,
sin 60 = opposite / hypotenuse
sin 60 = √3 / u
cross multiply
u = √3 / sin 60
u = √3 × 2 / √3
u = 2√3 / √3
u = 2
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GEOMETRY STUFF!! PLSS HELPP, NEED ANSWERS AND SOLUTIONS RN!!
Applying the angle bisector and triangle proportionality theorem, the solutions are:
16. x = 1/2 or x = 4
17. x = 5
18. x = −1 or x = 6.
What is the Angle Bisector Theorem?The angle bisector theorem states that when a line segment divides one of the angles of a triangle into two halves, it also divides the triangle to form segments that are proportional to each other.
16. 3x/(x - 1) = (x + 4)/(x - 2) [triangle proportionality theorem]
Cross multiply
(x - 1)(x + 4) = 3x(x - 2)
x² + 3x - 4 = 3x² - 6x
x² - 3x² + 3x - 4 + 6x = 0
-2x² + 9x - 4 = 0
Factorize -2x² + 9x - 4
(−2x + 1)(x − 4)
-2x = -1
x = 1/2
or
x = 4
17. (2x + 2)/(x + 3) = (4x - 2)/(2x + 2)
(2x + 2)(2x + 2) = (4x - 2)(x + 3)
4x² + 8x + 4 = 4x² + 10x - 6
Combine like terms
4x² - 4x² + 8x - 10x = -4 - 6
-2x = -10
x = -10/-2
x = 5
18. (2x + 3)/(x + 4) = x/(x - 2) [angle bisector theorem]
Cross multiply
(2x + 3)(x - 2) = x(x + 4)
Expand
2x² - x - 6 = x² + 4x
2x² - x - 6 - x² - 4x = 0
x² - 5x - 6 = 0
Factorize x² - 5x - 6 = 0
(x+1)(x−6) = 0
x = −1 or x = 6
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Can someone help me with these two problems and show work please !!
Answer:
13. Two real solutions.
14. No real solutions.
Step-by-step explanation:
Given quadratic equations:
13. [tex]x^2+7x+10=0[/tex]
14. [tex]4x^2-3x+4=0[/tex]
[tex]{\large \textsf{Quadratic Formula: }} x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]
What is the discriminant?
The discriminant (Δ) is b² - 4ac, which is under the square root in the quadratic formula. It is used to determine the number of real solutions (roots) of a quadratic:
When b² - 4ac > 0, the quadratic has two real solutions.When b² - 4ac = 0, the quadratic has one real solution.When b² - 4ac < 0, the quadratic has no real (complex) solutions.13. x² + 7x + 10 = 0
[tex]\implies a=\textsf{1},b=\textsf{7},c=\textsf{10}[/tex]
Find the discriminant value.
[tex]\implies \Delta = b^2 - 4ac[/tex]
[tex]\implies \Delta=(7)^2 - 4(1)(10)[/tex]
[tex]\implies \Delta=49 - 40[/tex]
[tex]\implies \Delta=9[/tex]
As [tex]9[/tex] > 0, this quadratic has two real solutions.
14. 4x² - 3x + 4 = 0
[tex]\implies a=\textsf{4},b=\textsf{-3},c=\textsf{4}[/tex]
Find the discriminant value.
[tex]\implies \Delta = b^2 - 4ac[/tex]
[tex]\implies \Delta = (-3)^2 - 4(4)(4)[/tex]
[tex]\implies \Delta = 9 - 64[/tex]
[tex]\implies \Delta = -55[/tex]
As [tex]-55[/tex] < 0, this quadratic has no real solutions.
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A train traveled 1/5 of the distance between two cities in ¾ hour. at this rate, how many hours will it take the train to travel the entire distance between these two cities?
Answer:
3 3/4 hour
Step-by-step explanation:
(3/4) ÷ (1/5) = (3*5) / (4*1)
= 15/4 hour
15/4 = 12/4 + 3/4 = 3 + 3/4 hour
= 3 3/4 hour