⟨A = 7•x + 40° and ⟨B = 3•x + 112°
From a possible diagram of the question, ⟨A = ⟨B, which gives;
x = 18°⟨A = 166°How can the value of x and the measure of ⟨A be found?Given;
⟨A = 7•x + 40°
⟨B = 3•x + 112°
In the diagram from a similar question posted online, we have;
⟨A and ⟨B are corresponding anglesCorresponding angles formed by parallel lines having a common transversal are congruent, therefore;
⟨A and ⟨B are congruentWhich gives;
⟨A = ⟨B7•x + 40° = 3•x + 112°
7•x - 3•x = 112° - 40° = 72°
7•x - 3•x = 4•x = 72°
x = 72° ÷ 4 = 18°
Therefore;
x = 18°Which gives;
⟨A = 7•x + 40°
⟨A = 7 × 18 + 40° = 166°
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Answer:d
Step-by-step explanation:
khan
Which function is the inverse of f(x) = 2x + 3?
05²¹(x) = -1/2 x 1/2
s^²(x) = { x = 1/
2
O f¹(x) = -2x + 3
O f¹(x)=2x+3
Answer: Option 2
Step-by-step explanation:
Let f(y)=x.
[tex]x=2y+3\\\\x-3=2y\\\\y=\frac{1}{2}x-\frac{3}{2}\\\\f^{-1}(x)=\frac{1}{2}x-\frac{3}{2}[/tex]
The inverse of the function is,
⇒ f ⁻¹(x) = 1/2 (x - 3)
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = 2x + 3
Now,
We can find the inverse of function as;
⇒ f (x) = 2x + 3
Put y = f (x);
⇒ y = 2x + 3
Solve for x;
⇒ y - 3 = 2x
⇒ x = 1/2 (y - 3)
⇒ f ⁻¹(x) = 1/2 (x - 3)
Thus, The inverse of the function is,
⇒ f ⁻¹(x) = 1/2 (x - 3)
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olives and pineapple pizza delivered two large pizzas cut into eight slices each. james and his sister both ate 5/8 of the pizza together. how many slices are left?
If a baseball is a sphere with a radius of 3.75 cm, what is the surface area of the baseball? use π = 3.14. a. 176.6 cm² b. 725.8 cm² c. 60.5 cm² d. 181.46 cm²
The surface area of the baseball is 176.6 cm² b.
What is meant by surface area?As a refresher, the surface area of an object is the sum of the areas of all of its faces or the exterior surfaces of its three dimensions. It is calculated in square units.The base, top, and lateral surfaces (sides) of the object's surface are added together to get the object's overall surface area. This is calculated in square units and done using several area formulas.A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.To find the surface area of the baseball:
r=3.75
[tex]A=4\pi r^{2}[/tex]
[tex]A=4*\pi *3.75^{2}[/tex]
A=176.6 cm² b.
The surface area of the baseball is 176.6 cm² b.
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Seven is not an example of _____.
an expression
a term
a variable
a constant
Answer:
a variable.
Seven is a number and cannot be a variable.
Find the maclaurin series for f(x) using the definition of a maclaurin series. [assume that f has a power series expansion. do not show that rn(x) → 0. ] f(x) = e−6x
The equation of [tex]f(x) = e^{-6x}[/tex] by maclaurin series is [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex].
The maclaurin series for f(x) is defined by the following formula:
[tex]f(x) = \sum_{i=0}^{\infty} \frac{f^{(i)} (0)}{i!} .x^{i}[/tex]--------------(1)
Where [tex]f^{i}[/tex] is the i - th derivative of the function
If f(x) = [tex]e^{-6x}[/tex], then the formula of the i - th derivative of the function is:
[tex]f^{i} =(-6)^{i} .e^{-6x}[/tex]----------------------(2)
Then,
[tex]f^{i}(0) = (-6)^{i}[/tex]
Lastly, the equation of the trascendental function by Maclaurin series is: [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6)^{i}.x^{i} }{i!} \\f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex]---------------(3)
Hence,
The equation of [tex]f(x) = e^{-6x}[/tex] by maclaurin series is [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex].
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how do i get the method on how to solve this x+5(-2)-1
Answer:
I forgot the name but I can show you how to do it lol
Step-by-step explanation:
x+5(-2)-1
x-10-1 we multiplied 5 and -2
x-11
x=11
how I did the last one is there is a non-existent 0 with an equal sign like my teacher says so we added 11 to both sides.
Which values represent solutions to cosine (startfraction pi over 4 endfraction minus x) = startfraction startroot 2 endroot over 2 endfraction sine x, where x is an element of [0, 2pi)?
The given trigonometric function consists of trigonometric values of common angles.
The values that represent the solution to [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex], x ∈ [0, 2·π) are; [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].
What are trigonometric functions?Trigonometric functions are real functions in mathematics that connect an angle of a right-angled triangle to ratios of two side lengths. They are widely utilized in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.The given function is: [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex]
Where; x ∈ [0, 2·π).
We have; cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B).
[tex]cos(\frac{\pi }{4} )=\frac{\sqrt{2} }{2}, sin(\frac{\pi }{4} )=\frac{\sqrt{2} }{2}[/tex]Which gives:
[tex]cos(\frac{\pi }{4}-x )=\frac{\sqrt{2} }{2}. cosx+\frac{\sqrt{2} }{2}.sinx[/tex]So, we obtain:
[tex]\frac{\sqrt{2} }{2} .cosx=\frac{\sqrt{2} }{2}.sinx-\frac{\sqrt{2} }{2} .sinx=0\\cosx=0\\cos\frac{\pi }{2} =0[/tex]
Therefore, the possible solutions (x-values) to cos x = 0 are:
[tex]0[/tex] ≤ [tex]\frac{n.\pi }{2}[/tex] ≤ [tex]2.\pi[/tex]
Where, n = 1, 3, 5, .., x ∈ [0, 2·π)
We get: [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].
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Find the volume of the cylinder shown using the formula in the box below. Round your answer to the nearest tenth. Show your work
Answer: 1960.2 cm
Step-by-step explanation:
v = πr^2h
v = π7.4^2(11.4)
= π54.76(11.4)
= 171.9464(11.4)
= 1960.2
The volume of the cylinder rounded to the nearest tenth is 1,960.2 cubic cm
What is the volume of the cylinder?Volume of the cylinder = πr²h
Where,
r = radius = 7.4 cm
h = height = 11.4 cm
π = 3.14
So,
Volume of the cylinder = πr²h
= 3.14 × 7.4² × 11.4
= 3.14 × 54.76 × 11.4
= 1,960.18896
Approximately to the nearest tenth
= 1,960.2 cubic cm
Therefore, 1,960.2 cubic cm is the volume of the cylinder with radius 7.4 cm and height 12.4 cm
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Help please I need this asap
Answer:
It is a little hard to see. I think that it is 10.
Step-by-step explanation:
They break even where the two lines intersect. If you look at the bottom of the graph and find 10 and then trace that straight up, I think that is where I see the lines crossing.
check ple im not sure its right
Answer:
8
Step-by-step explanation:
You are correct The distance from -6 to 2 is 8.
1/?
Which number produces a rational number when Multiplied 1/5
Answer:
-2/3
Step-by-step explanation:
A rational number is a number that can be expressed as a fraction so when you add 2 fractions it’s a rational number
help solve math problem
Answer:
(c) x < -5.170
Step-by-step explanation:
The given function is an exponential function with a decay factor of 0.5 and a y-intercept of 0.5^2 = 0.25. It will be larger for more negative x-values.
EstimateWe know that 2^3 = 8, so (1/2)^-3 = 8. This means the exponent of 0.5 in the given inequality will be more negative than -3:
x +2 < -3
x < -5 . . . . . . . . subtract 2
The only answer choice in this range is ...
x < -5.170
Exact solutionTaking the logarithm of both sides of the inequality, we have ...
(x +2)log(0.5) > log(9)
x +2 < log(9)/log(0.5) . . . . . . log(0.5) < 0, so the inequality reverses
x < log(9)/log(0.5) -2 . . . . . . subtract 2
x < (0.95424251)/(-0.30103000) -2 = -3.1699250 -2
x < -5.1699250 ≈ -5.170
Let the domain of discourse s be people. let a be statisticians and let b be people who bathe regularly. in set notation, what is the sentence all statisticians bathe regularly.
If set A shows the statistians and B shows the person who bath regularly then the notation which shows that all statistians bath regularly is A∩B.
Given that A shows the statistians and B shows the person who bath regularly.
We are required to show the sentence that "All statistians bath regularly"in set notation.
We know that set is a collection of things, place,anything which can be measured or denoted as something else.
"∪" shows union means when we put this sign between two sets then the resulting set will contain all the elements of both the sets.
"∩" shows intersection means when we put this sign between two sets then the resulting set will contain all the common elements of both the sets.
Since A represents statistians and B represents people who bath regularly and we require statistians who bath regularly is A∩B.
Hence if A shows the statistians and B shows the person who bath regularly then the notation which shows that all statistians bath regularly is A∩B.
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A 3D electron microscope magnifies objects 1 000 000 times. A water molecule has a diameter of
[tex]2 \times {10}^{ - 10} [/tex]
m.
How large will it appear in the microscope?
give your answer in milimetres.
The diameter of the water molecule is 2 * 10^-4 m or 0.2 mm.
What is a microscope?The term microscope refers to a device that is capable of increasing the size of an object. If the object is quite large, then it can be seen with the unaided eye.
Microscopes are very important in the sphere of scientific research as it was very instrumental in the study of cells and in the process of examination of other samples. There are several kinds of microscopes hay could be used for several purposes such as;
Electron microscopeCompound microscopeScanning electron microscope Light microscope etc.Each of these microscopes have a unique instance in which they could be utilized.
Given that the diameter of water is about 2 * 10^-10 m, a magnification by 1 000 000 times gives a diameter of 2 * 10^-4 m or 0.2 mm.
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The half life of a substance is defined as the time required for the substance to decrease by half. If the weight of a substance begins at 128 grams, and the half life is 7 years, what will be the weight of the substance after 28 years?
the weight of the substance after 28 years is 8 grams.
How to determine the amountWe have that the half life of a substance is defined as the time required for the substance to decrease by half
The formula for calculating the half - life of a material is given as;
[tex]N(t) = N0 (\frac{1}{2} )^\frac{t}{t^\frac{1}{2} }[/tex]
Where
N(t) is final amountNo is the initial amount = 128 gramst1/2 is the half life = 7 yearst is the time elapsed = 28 yearsSubstitute into the formula
N(t) = 128 × (0. 5) ^28/ 7
N (t) = 128 × ( 0. 5) ^ 4
N(t) = 128 × 0. 0625
N(t) = 8 grams
Thus, the weight of the substance after 28 years is 8 grams.
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How do I solve this question.
Hello, the solution of the geometry problem is in this photo.
AOC = 136°
BOC = 44°
Which of the following equations is the translation 2 units down of the graph of y = |x |?
a.) y = | x - 2|
b.) y = | x + 2|
c.) y = | x | + 2
d.) y = | x | - 2
Answer:
d
Step-by-step explanation:
up and down is outside of the x stuff so its c or d
and c is moving it up
d is moving it down
Answer:
d) y = | x | - 2
Step-by-step explanation:
In order to translate a graph downward 2 units ,we subtract 2 from the original function.
therefore,
If the Original function is y = |x|
Then the Function of the translated graph is y = | x | - 2
Three divers went scuba diving in the ocean for a couple of hours. The table shows how much oxygen they had left in their oxygen tanks.
Diver Oxygen (liters)
Alexis seventy nine over eighth
Dante 9.3
Sofia nine and eight over fifteenth
Place the divers in order from least to greatest based on the number of liters left in their oxygen tank.
Sofia, Dante, Alexis
Alexis, Sofia, Dante
Dante, Alexis, Sofia
Dante, Sofia, Alexis
The divers in order from least to greatest based on the number of liters left in their oxygen tank will be Alexis, Dante, and Sofia. The correct answer is B.
What is ascending order?In mathematics, placing numbers in ascending order refers to doing so from least to largest from left to right. When numbers are arranged in ascending order, they are done so from least to largest.
Given that three divers went scuba diving in the ocean for a couple of hours. The table for the oxygen requirement is given below:-
Diver Oxygen (liters)
Alexis Seventy nine over eighth
Dante 9.3
Sofia Nine and eight over fifteenth
The Numbers are:-
Alexis ( Seventy nine over eighth) = 79 / 9 = 8.78
Dante = 9.3
Sofia ( Nine and eight over fifteenth ) = 9(9/15} = 9.6
The arrangement from least to highest will be Alexis, Dante, and Sofia.
The correct options are given below:-
Sofia, Dante, Alexis
Alexis, Dante, and Sofia.
Dante, Alexis, Sofia
Dante, Sofia, Alexis
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Answer:
Dante, Alexis and Sofia
Step-by-step explanation:
please tell me if I'm wrong but I'm positive its Dante, Alexis and Sofia
What is the slope of the linear equation that has the values shown in the table? Show your work
Slope can be found from two points using the equation [tex]\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex].
Take any two points to substitute in. In this example, I'll use the first two points, (-4, 15), and (-2, 9). Put these into the equation and you'll get
[tex]\frac{(9-15)}{(-2-(-4))}[/tex]. Simplify further to get [tex]\frac{-6}{2}[/tex]. Divide this and you'll get the slope, -3!
hope this helps!
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
x ≤ -2
Step-by-step explanation:
3(x + 2) ≤ 5(-2 - x)
Distribute on both sides.
3x + 6 ≤ -10 - 5x
Add 5x to both sides.
8x + 6 ≤ -10
Subtract 6 from both sides.
8x ≤ -16
Divide both sides by 8.
x ≤ -2
Answer:
[tex]\textsf{D. }x\leq-2[/tex]
Step-by-step explanation:
Given inequality: [tex]3(x+2)\leq5(-2-x)[/tex]
Step 1: Distribute [tex]3[/tex] and [tex]5[/tex] through the parentheses.
[tex]\implies 3(x)+3(2)\leq5(-2)+5(-x)[/tex]
[tex]\implies 3x+6\leq-10-5x[/tex]
Step 2: Subtract [tex]6[/tex] from both sides.
[tex]\implies 3x+6-6\leq-10-6-5x[/tex]
[tex]\implies 3x\leq-16-5x[/tex]
Step 3: Add [tex]5x[/tex] to both sides.
[tex]\implies 3x+5x\leq-16-5x+5x[/tex]
[tex]\implies 8x\leq-16[/tex]
Step 4: Divide both sides by [tex]8[/tex].
[tex]\implies \dfrac{8x}{8}\leq\dfrac{-16}{8}[/tex]
[tex]\implies x\leq-2[/tex]
if AB = 3 centimeters and AC = 2 centimeters, what is the largest possible perimeter, in centimeters, of isosceles triangle ABC?
Answer:
8
Step-by-step explanation:
AB is 3 cm and AC is 2 cm, and since triangle ABC is an isosceles triangle, BC can either be 3 cm or 2 cm. We want the longest perimeter possible, so make BC 3 cm, and add the side lengths to find the perimeter.
P = 3 + 3 + 2 = 8.
someone help me out pleaseee
Answer:
[tex] \frac{29}{18} = 1 \frac{11}{18} [/tex]
Step-by-step explanation:
To solve this question, we definitely need to make w the subject.
[tex]w - \frac{5}{6} = \frac{7}{9} \\ w - \frac{5}{6} + \frac{5}{6} = \frac{7}{9} + \frac{5}{6} \\ w = \frac{29}{18} \\ = 1 \frac{11}{18} [/tex]
Evaluate 5(14 – 23) + 8 ÷ 2. (1 point) 26 34 44 56
Answer:
-41
Step-by-step explanation:
5(14-23)+8 ÷ 2
=5(-9)+4
=-45+4
=-41
The solution of the given expression 5(14-23)+8 ÷ 2 is -41.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Example; 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
Simplification usually involves making the expression simple and easy to use later.
WE have given an expression as;
5(14-23)+8 ÷ 2
Solve the bracket then division;
=5(-9) + 4
=-45+4
=-41
Therefore, the solution of the given expression is -41.
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How many faces, edges and vertices does the shape below have?
Faces:
Edges:
Vertices:
the number of faces, edges and vertices the shape below has is 4, 4 and 6 respectively.
How to determine the numberIt is important to note that according to Euler’s formula for any convex polyhedron, the number of Faces (F) and vertices (V) added together is exactly two more than the number of edges (E).
It is mathematically written as;
Face + vertices = 2 + edges
F + V = 2 + E
From the figure given, we can see that it is a kite
Number of vertices = 4
Number of faces = 4
2 + edges = faces + vertices
2 + edges = 4 + 4
2 + edges = 8
Edges = 8 - 2
Edges = 6
Thus, the number of faces, edges and vertices the shape below has is 4, 4 and 6 respectively.
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PLEASE help me, im really struggling on this.
The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Let x represent the number of pounds of bananas sold and y represent the grapes sold, hence:
x + y = 52 (1)
Also:
x + 2.25y = 72 (2)
The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72
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Please Help!
The total arm and blade of a windshield wiper is 9 in. long and rotates back and forth through an angle of 92 degrees. The shaded region in the figure is the portion of the windshield cleaned by the 7-in. wiper blade. What is the area of the region cleaned?
answer with the last three decimal places
The area of the region cleaned by the 7-in wiper blade with the angle subtended being 92⁰ as described in the task content is; 39.32in².
What is the area cleaned by the 7-in wiper blade?According to the task content, it follows that the wiper blade is 7-in long and subtends an angle of 92°.
Consequently, the area swept by the blade in discuss can be determined by the Area of sector formula and hence, is;
Area = (92/360) × (22/7) × 7².
Area = 39.32 in².
Ultimately, it follows from the solving steps above that the area of the region cleaned by the 7-in wiper blade with the angle subtended being, 92⁰ is; Area = 39.32 in².
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What do you get when you combine the following numbers? -4-4-4-4
Answer:
-16
Step-by-step explanation:
you just add all of them together
A casino offers the following game: you draw one card from a standard 52-card deck. If you draw a jack, you win $1.25. If you draw a queen, you win $3.25. If you draw a king, you win $4.5 dollars. If you draw any ace except the ace of spades, you win $6.5. If you draw the ace of spades, you win $7.75. The entry fee to play this game is $1.75. Compute the expected value of this gamble (include the entry fee in your expected value).
Let [tex]W[/tex] be the random variable for the winnings from playing the game once.
• There are 4 jacks in the deck, so you draw a jack with probability 4/52 = 1/13. In this case you "win" $1.25 - $1.75 = -$0.50.
• There are 4 queens, with draw probability 4/52 = 1/13 and winnings $3.25 - $1.75 = $1.50.
• There are 4 kings, with draw probability 4/52 = 1/13 and winnings $4.50 - $1.75 = $2.75.
• There are 4 aces, and 3 of these are not of the spade suit, so the probability of drawing any of these is 3/52 and you win $6.50 - $1.75 = $4.75.
• There is only 1 ace of spaces, with draw probability 1/52 and winnings $7.75 - $1.75 = $6.00.
• Adding these up, it follows that the probability of drawing any other card is 1 - (1/13 + 1/13 + 3/52 + 1/52) = 10/13, in which you have the privilege of "winning" -$1.75.
So, the probability mass function for [tex]W[/tex] is
[tex]\mathrm{Pr}(W=w) = \begin{cases} \dfrac1{13} & \text{if } w \in \{-\$0.50, \$1.50, \$2.75\} \\\\ \dfrac3{52} & \text{if } w = \$4.75 \\\\ \dfrac1{52} & \text{if } w = \$6.00 \\\\ \dfrac{10}{13} & \text{if } w = -\$1.75 \\\\ 0 & \text{otherwise} \end{cases}[/tex]
The expected winnings from playing one round of this game are
[tex]\Bbb E[W] = \displaystyle \sum_w w\,\mathrm{Pr}(W=w)[/tex]
[tex]\Bbb E[W] = \dfrac{-\$0.50 + \$1.50 + \$2.75}{13} + \dfrac{3\cdot\$4.75}{52} + \dfrac{\$6.00}{52} + \dfrac{10\cdot(-\$1.75)}{13}[/tex]
[tex]\Bbb E[W] \approx \boxed{-\$0.67}[/tex]
What is the answer to the question: 9 to the second power times 13
Answer:
1053
Step-by-step explanation:
Rashon walked 10 miles in 4 hours. if he walked the same distance every hour, how far did he walk in one hour? write your answer in feet if 1 mile equals 5280 feet.
Answer:
Step-by-step explanation:
Miles per hour: [tex]\frac{10miles}{4hrs} = 2.5\frac{miles}{hour}[/tex]
Feet per hour:
[tex]2.5\frac{miles}{hours} (\frac{5280ft}{1mile} )[/tex]
[tex]=13,200\frac{ft\\}{hr}[/tex]