In order to determine the number of thermos, divide by 3 by 2/3, as follow:
[tex]\frac{\frac{3}{1}}{\frac{2}{3}}=\frac{3\cdot3}{1\cdot2}=\frac{9}{2}=4.5[/tex]the previous result means that nalli can make four and one hal thermoses with 3 cups of cocoa powder.
A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a spade?A. 4/13B. 16C. 1/4D. 17
The number of ace in a deck of 52 cards is =4
The number of spade in a deck of 52 cards is = 13.
The number of ace of spade in a deck of 52 cards is =1
The event is non-exclusive hence the probablity can be determined as,
[tex]\begin{gathered} P(A\cup S)=P(A)+P(S)-P(A\cap S) \\ =\frac{4}{52}+\frac{13}{52}-\frac{1}{52} \\ =\frac{16}{52} \\ =\frac{4}{13} \end{gathered}[/tex]Thus, option (A) is correct.
find the inverse of each given function f(x)=4x-12f^-1(x)=______x+______
The original function is f(x) = 4x - 12...
to find the inverse function, we need to solve it for x:
f(x) = 4x - 12
f(x) + 12 = 4x
(f(x) + 12)/ 4 = x
f(x)/4 + 3 = x
if we change now f^-1(x) for x and x for f^-1(x):
x/4 + 3 = f^-1(x)
f^-1(x) = x/4 + 3
f^-1(x) = (1/4)x + 3
Answer:
looking to recieve help with finding the vertex of the parabola.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
f(x) = - 2x² + 4x + 2
Step 02:
y = ax² + bx + c
a = -2
b= 4
c = 2
vertex of the parabola equation
[tex]yv\text{ =- }\frac{b^{2}-4ac}{4a}[/tex][tex]\begin{gathered} yv\text{ = -}\frac{4^2-4\cdot(-2)\cdot(2)}{4\cdot(-2)} \\ yv\text{ = -}\frac{(16+16)_{}}{-8} \end{gathered}[/tex]yv = (- 32) / (- 8)
yv = 4
[tex]xv\text{ = -}\frac{b}{2a}[/tex][tex]\begin{gathered} xv\text{ =- }\frac{4}{2(-2)} \\ xv\text{ = }\frac{-4}{-4} \end{gathered}[/tex]xv = 1
Vertex:
(xv , yv ) = (1 , 4 )
The answer is:
The vertex of the parabola is (1 , 4)
I need help with my math
From the question, we can deduce the answer using indices which deals with power of numbers, e.g
[tex]\frac{5^2.5^3}{5^4}=\frac{5^{2+3}}{5^4}=\frac{5^5}{5^4}=5^{5-4}=5^1=5[/tex]Also, for the next one,
[tex]\frac{9^4.9^6}{9^8}=\frac{9^{4+6}}{9^8}=\frac{9^{10}}{9^8}=9^{10-8}=9^2[/tex]This applies to every other ones provided in the question,
Considering Option D,
[tex]\begin{gathered} \frac{b^{2k}.b^{3k}}{b^{4k}} \\ \text{where k is 2,} \\ \frac{b^{2(2)}.b^{3(2)}}{b^{4(2)}}=\text{ }\frac{b^4.b^6}{b^8}=\frac{b^{4+6}}{b^8}=\frac{b^{10}}{b^8}=b^{10-8}=b^2 \\ \text{Where k=2, Option D is favoured} \end{gathered}[/tex]Since the equation D favours the solution,
Hence, the best option is D.
14. In the isosceles trapezoid shown, GJ = 5, HI = 9, and GI = 8.6. Determine the length of HJ.O A. 4.3B. 5C. 8.6D. 9
In the isosceles trapezoid GJIH the length of HJ is 8.6
It is given that GJIH is the isosceles trapezoid
In an isosceles trapezoid the two non parallel sides are isosceles, that is the angle formed by them and the length of those two sides are equal.
The sides ,
GH = JI
GI and JH are the two diagonals of the trapezoid.
In any isosceles trapezium have equal opposite sides. Therefore diagonals of trapezium are equal.
The length of one of the diagonal GI is 8.6
So the length of another diagonal HJ is lenght of GI = 8.6
Therefore, in the isosceles trapezoid GJIH the length of HJ is 8.6
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Find the area of the shape. 12 m 6 m 11 m 4 m 3. What is the perimeter of the above shape?
Area of the given shape is obtained as,
[tex]\begin{gathered} A=(12\times6)+(11-6)\times4 \\ A=72+(5\times4) \\ A=72+20 \\ A=92m^2 \end{gathered}[/tex]Perimeter of the shape is simply the addition of all the sides
i.e.
[tex]\begin{gathered} P=12+11+4+6 \\ P=23+10 \\ P=33m \end{gathered}[/tex]A customer wants to leave a 15% tip. The bill was $35. How much should the customer leave as a tip?
The customer wants to leave 15% tip, if the bill is $35, then the tip is
[tex]=15\text{ \% of 35}[/tex][tex]=\frac{15}{100}\times\text{ \$35}[/tex][tex]=\text{ \$5.25}[/tex]Therefore, the customer should leave $5.25 as a tip.
please help me with these questions (lesson 2.06 and below)
we have the function
[tex]H(x)=-2\sqrt[3]{x}+1[/tex]For each value of x, substitute in the given function to obtain the value of H(x)
so
For x=-8
substitute
[tex]\begin{gathered} H(x)=-2\sqrt[3]{-8}+1 \\ H(x)=-2(-2)+1 \\ H(x)=5 \end{gathered}[/tex]For x=0
[tex]\begin{gathered} H(x)=-2\sqrt[3]{0}+1 \\ H(x)=-2(0)+1 \\ H(x)=1 \end{gathered}[/tex]For x=1
[tex]\begin{gathered} H(x)=-2\sqrt[3]{1}+1 \\ H(x)=-2(1)+1 \\ H(x)=-1 \end{gathered}[/tex]choose the correct value on each side of the equation.
Answer:
442.12
Expalanation:
Given the expression
458.13 + y = 900.25
We are to look for the value of y
Subtract 458.13 from bith sides of the equation:
458.13 + y - 458.13 = 900.25 - 458.13
y = 442.12
Hence the correct value is 442.12
.13 from bith sides of the equation:
458.13 + y - 458.13 = 900.25 - 458.13
Which graph shows the solution to the equation (see the attached photo)
Given: An equation
[tex]4^{x-3}=8[/tex]Required: To draw the graph of the solution of the equation.
Explanation: The given equation is-
[tex]4^{x-3}=8[/tex]Solving,
[tex]\begin{gathered} (2^2)^{x-3}=2^3 \\ 2^{2x-6}=2^3 \end{gathered}[/tex]Now since the base on both sides are the same hence the exponents must also be equal i.e.,
[tex]\begin{gathered} 2x-6=3 \\ 2x=9 \\ \Rightarrow x=\frac{9}{2} \end{gathered}[/tex]Hence the graph of the equation can be drawn by taking the equations
[tex]\begin{gathered} y=4^{x-3} \\ y=8 \end{gathered}[/tex]Hence the graph is
Final Answer: Option C is correct.
the difference of a number and 6 is the same as 5 times the sum of the number and 2. what is the number? a. -4 b. -2 c. -1d. 1
Let x represent the number.
the difference of a number and 6. This would be expressed as
x - 6
5 times the sum of the number and 2. This would be expressed as
5(x + 2)
Since both expressions are the same, it means that
x - 6 = 5(x + 2)
We would open the bracket on the right hand side by multiplying each term inside the bracket by the term outside the bracket. It becomes
x - 6 = 5x + 10
5x - x = - 6 - 10
4x = - 16
x = - 16/4
x = - 4
The correct option is A
1) What is the value of u? A) 32° B) 34 C) 36° D) 68°
Triangle XYZ is an isosceles triangle, then ∠Z and ∠X (also called u) measure the same.
The addition of the internal angles of a triangle is equal to 180°:
∠X + ∠Y + ∠Z = 180°
Replacing with ∠X = ∠Z = u, and ∠Y = 112°:
u + 112° + u = 180°
2u + 112° = 180°
2u = 180° - 112°
2u = 68°
u = 68°/2
u = 34°
how do we do thios one i askled btainly they got it wrong asnwer its two parts
Use synthetic division to find the result when x³ + 3x² - 6x + 20 is divided by
x + 5.
Answer:
[tex]x^{2} + 8x + 34 + \frac{190}{x-5}[/tex]
Step-by-step explanation:
if the scale on a map is inches/miles equal 2/10, how would the folding lengths be represented 15feet.
We will have the following:
First, we know that 1 miles has 5280 feet, so 10 miles will have 52800 feet.
Then we will calculate how 15 feet would be represented:
[tex]x=\frac{2in\cdot15ft}{52800ft}\Rightarrow x=\frac{1}{1760}in\Rightarrow x\approx0.000568in[/tex]So, approximately 0.000568 inches would represent 15 feet.
One number is 22 more than another. Their product is – 121.Step 1 of 2: Set up an equation to solve the given word problem. Let x be the smaller number.Answer# KeypadKeyboard ShortcutsO x + x + 22 = - 121O x(22x) = - 121O x(x + 22)- 121O x(x – 22)- 121
Let it be:
• x: The smaller number.
,• x + 22: The larger number.
The product of both numbers is:
[tex]x(x+22)[/tex]Since the product of both numbers is -121, we can write:
[tex]x(x+22)=-121[/tex]The word 'is' is represented by the symbol =.
Therefore, the equation to solve the given word problem is:
[tex]x(x+22)=-121[/tex]Step 2To find the numbers, we solve the previous equation.
[tex]\begin{gathered} x(x+22)=-121 \\ \text{ Apply the distributive property on the left side} \\ x\cdot x+22\cdot x=-121 \\ x^2+22x=-121 \\ \text{ Add }121\text{ from both sides} \\ x^2+22x+121=-121+121 \\ x^2+22x+121=0 \end{gathered}[/tex]Now, we can factor the expression on the left side using the perfect square trinomial rule.
[tex]a^2+2ab+b^2=(a+b)^2[/tex]Then, we have:
[tex]\begin{gathered} x^2+22x+121=0 \\ x^2+2\cdot11\cdot x+11^2=0 \\ (x+11)^2=0 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{(x+11)^2}=\sqrt[]{0} \\ x+11=0 \\ \text{ Subtract 11 from both sides} \\ x+11-11=0-11 \\ x=-11 \end{gathered}[/tex]Finally, we find the another number.
[tex]\begin{gathered} x+22=-11+22 \\ x+22=11 \end{gathered}[/tex]Therefore, the numbers are -11 and 11.
what is 388 divided by 6
Answer:
64.666666666666666666666666... or 64 2/3 or sixty-four and two thirds
Plane a flies 4375 miles in the same amount of time
Given the following:
plane A flies 4375 miles
plane B flies 4550 miles
plane B is flying 35 mph more than plan A.
We are should find the amount of time it takes each plane to atravel their respective distances.
The time equation is:
4375 = 4550
x x + 35
Lets cross multipy
4375(x + 35) = x(4550)
4375x + 153125 = 4550x
153125 = 4550x - 4375x
153125 = 175x
175x = 153125
x = 153125/175
x = 875
x is the speed of plane A
Speed of plane B = 875 + 35 = 910
The amount of time plane A will use is = 4375/875 = 5
The amount of time plane B will use is = 4550/910 = 5
Which of the following is equal to 11.4 9? A. (11 x 9) + (0.4 9) B. (11 + 9) + (0.4 +9) C. (11 x 9) * (0.4 * 9) D. (11 + 9) * (0.4 +9)
Answer
Option A is correct.
(11.4 × 9) = (11 × 9) + (0.4 × 9) = 102.6
Step-by-step Explanation
The best way to explain this is to examine the options one at a time to examine the one that is the most correct.
We want to know which of the options is equal to (11.4 × 9).
11.4 × 9 = 102.6
The options are
A. (11 × 9) + (0.4 × 9)
11 × 9 = 99
0.4 × 9 = 3.6
(11 × 9) + (0.4 × 9) = 99 + 3.6 = 102.6
B. (11 + 9) + (0.4 + 9)
11 + 9 = 20
0.4 + 9 = 9.4
(11 + 9) + (0.4 + 9) = 20 + 9.4 = 29.4
C. (11 × 9) × (0.4 × 9)
11 × 9 = 99
0.4 × 9 = 3.6
(11 × 9) × (0.4 × 9) = 99 × 3.6 = 356.4
D. (11 + 9) × (0.4 + 9)
11 + 9 = 20
0.4 + 9 = 3.6
(11 + 9) × (0.4 + 9) = 20 × 3.6 = 72
Since only option A gives the same answer as the expression in the question, option A is the only correct option.
Hope this Helps!!!
which equation had a graph that is a parabola with vertex at (-1,-1)
After solving all the equations, we can conclude that equation (D) [y = (x + 1)² - 1] had a graph that is a parabola with vertex (-1, -1).
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the form of the equation of the vertical parabola:
y = a(x - h)² + kWhere h and k are the vertexes.Now, calculate each equation as follows:
(A) y = (x - 1)² + 1
Vertex: (1, 1)Then, the wrong answer.(B) y = (x - 1)² - 1
Vertex: (1, -1)Then, the wrong answer.(C) y = (x + 1)² + 1
Vertex: (1, 1)Then, the wrong answer.(D) y = (x + 1)² - 1
Vertex: (-1, -1)Then, this is the correct option.Therefore, after solving all the equations, we can conclude that equation (D) [y = (x + 1)² - 1] had a graph that is a parabola with vertex (-1, -1).
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Complete question:
Which equation has a graph that is a parabola with a vertex at (–1, –1)?
A.y = (x – 1)2 + 1
B.y = (x – 1)2 – 1
C.y = (x + 1)2 + 1
D.y = (x + 1)2 – 1
At what point do they intersect Round to 2 decimal places.
Solution
See attached graph below
The intersection point of the graph is ( - 0.72 , 0.37 )
The functions f(x) and g(x) are shown on the graph.f(x) = |x|What is g(x)?A. g(x)=Ix-5lB. g(x) = Ixl-5C. g(x) = lxl+ 5D. g(x)= |x+5|
Notice that the graph of g(x) is shifted 5 units to the left, then, the function that represents g(x) is:
[tex]g(x)=|x+5|[/tex]SORRY IF ITS IN THE WRONG SECTION I NEED THE ANSWER. NO LINKS OR REPORT. What makes a source effective? Select the two correct answers (1 point) A. it leads you to another source B. it adds to your understanding of a topic C. it is interesting to you D. it is presented in a written format E. it is accurate
Answer:
B and E
Step-by-step explanation:
Hope this helps!
Which trig equation should be used to solve for x?
Solution:
To find the appropiate trigonometric formula.
we know that,
for the right angle triangle, we have that,
[tex]\sin \theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]The side opposite to the right angle is hypotenuse, the side opposite to the angle theta is opposite side and the other side is adjacent side.
Also we have,
[tex]\cos \theta=\frac{adjacent\text{ side}}{hypotenuse}[/tex][tex]\tan \theta=\frac{opposite\text{ side}}{adjacent\text{ side}}[/tex]Using this we get,
[tex]\sin 37\degree=\frac{x}{12}[/tex]Answer is:
[tex]\sin 37\degree=\frac{x}{12}[/tex]What volume in cubic centimeters of the box below ? Do not include units in your answer.5cm4cm3cm
Given,
The length of the box is 4 cm.
The breadth of the box is 3 cm.
The height of the box is 5 cm.
Required
The volume of the box.
The volume of the cube is calculated as,
[tex]Volume=length\times breadth\times height[/tex]Substituting the values then,
[tex]\begin{gathered} Volume=5\times4\times3 \\ =20\times3 \\ =60\text{ cm}^3 \end{gathered}[/tex]Hence, the volume of the cube is 60 cm^3.
WRITE THE RULE FOR THE TRANSLATION. A (X 1.x C D DI D
The rectangle is moved 6 units to the left and 3 units down.
So, the rule of translation will be:
This is the result:
(x - 6, y - 3)
In this chart, can you please figure out how the Medians AY, BZ, and CX are created by? and can find out how the Altitudes AE, BF, and CD are created by as well?
you are going to set up a stereo system by purchasing separate components. In your price range, you find five different receivers, eight different compact disc players, and 12 different speaker systems. If you want one of each of these components, how many different stereo systems are possible ?
5 receivers
8 compact disc players
12 speaker systems
if we want one of each the possible stereo systems is 5 because is the least amount available
if we try to make the sixth we dont have other receiver
help with this question
ok
When f(x) = 3, from the graph we obtain that x = 1 or only 1
A tub drains water at a rate of 3 gallons a minute. Which equation shows the relationship between g, the number of gallons of water drained from the tub and m, the number of minutes the tub has been draining water?
Okay, here we have this:
Considering the provided information, we are going to identify the requested equation, so we obtain the following:
Based on the information given, we obtain the following function:
Number of Gallons Drained=3*Minutes Elapsed
g=3m
Finally we get that the equation is: g=3m, where g represents the number of gallons drained, and m the number of minutes elapsed.