a linear combination can be:
(a + b)*(4x + 15y) = a*12 + b*15
How to solve the given system of equations:Here we have the system of equations:
(2/3)*x + (5/2)*y = 15
4x + 15y = 12
To solve the system of equations, we first need to isolate one of the variables in one of the equations, I will isolate x on the second equation.
4x = 12 - 15y
x = (12 - 15y)/4
Now we can replace that in the other equation:
(2/3)*x + (5/2)*y = 15
(2/3)* (12 - 15y)/4 + (5/2)*y = 15
Now we can solve that for y.
2 - (10/4)*y + (5/2)*y = 15
2 = 15
That is a false equation, then we conclude that the system of linear equations has no solutions.
This means that the two lines are parallel lines, then a linear combination can be:
(a + b)*(4x + 15y) = a*12 + b*15
Where a and b are two real numbers.
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Answer:Your answer is
There are no solutions.
Step-by-step explanation:Brainliest Please?
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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check ple im not sure its right
Answer:
8
Step-by-step explanation:
You are correct The distance from -6 to 2 is 8.
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 x. A. 11√6/2 B. 22 C. 33 D. 11√3/2
Answer:
B
Step-by-step explanation:
using the tangent ratio on the triangle on the right and the exact value
tan60° = [tex]\sqrt{3}[/tex] , then letting the altitude be h
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{11\sqrt{6} }{h}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by h )
11[tex]\sqrt{6}[/tex] = h × [tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
11[tex]\sqrt{2}[/tex] = h
using the sine ratio in the triangle on the left and the exact value
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{x}[/tex] = [tex]\frac{11\sqrt{2} }{x}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
[tex]\sqrt{2}[/tex] × x = 22[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
x = 22
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.
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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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
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.
What is the answer to the question: 9 to the second power times 13
Answer:
1053
Step-by-step explanation:
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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Alvin and Bala had 26 stickers. Alvin had 8 more stickers than Bala. How many
stickers did Bala have?
Answer:
Bala has 5 stickers
( please mark me as brainliest )
Step-by-step explanation:
total stickers = 26
= 26/2
=13
stickers Alvin had more = 8
=13 + 8
= 21
= 26 - 21
= 5
.. . Bala has 5 stickersHelp 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.
Which expression is equivalent to x^2 + 5x - 6? Explain how.
(1) (x + 3) (x - 2)
(2) (x + 2) (x - 3)
(3) (x - 6) (x + 1)
(4) (x + 6) (x - 1)
Answer:
(4) (x + 6)(x - 1)
Step-by-step explanation:
Hello!Given expression
[tex]x { }^{2} + 5x - 6[/tex]
Find numbers when they are multiplied gives 6 and when they are added which gives 5.
Thus, these numbers are -1 & 6.
[tex]x {}^{2} + 6x - x - 6 \\ x(x + 6) - 1(x + 6) \\ (x + 6) \: \: (x -1 )[/tex]
Can also check the multiplied values of these two values.
Hope it helps!
Answer:
(4)
Step-by-step explanation:
Determine two multiples which when multiplied gives - 6(the last term in the equation), when added, gives +5 (the middle term in the equation).
Multiples are: +6 and -1
input the two multiples in place of the middle term (+5x)
=x^2+6x-1x-6
Collect like terms
=x(x+6)-1((x+6)
Answer= (x+6)(x-1)
Confirm answer above:
Open bracket
x(x-1)+6(x-1)
x^2-x+6x-6
x^2+5x-6 (initial equation).
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
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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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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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]
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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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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How do I solve this question.
Hello, the solution of the geometry problem is in this photo.
AOC = 136°
BOC = 44°
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]
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?
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.
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
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]
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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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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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
Find the surface area of the composite figure.
5 cm
6 cm
20 cm
4 cm
5 cm 4 cm
SA =
12 cm
-6 cm
[?] cm²
Answer:
[tex]644cm^2[/tex]
Step-by-step explanation:
First we'll work out the surface area of the pink figure.
That's the area of the two 5 by 6 rectangles on the top and bottom, plus the area of the two 5 by 20 and two 6 by 20 rectangles on the sides.
However, we note that the purple figure is blocking out a 6 by 12 section on the pink figure, so we'll need to subtract this.
The above works out to [tex]2\times(30+100+120)-72=428 cm^2[/tex].
Then we'll work out the surface area of the purple figure.
This will be the area of the two 4 by 6 rectangles at the top and bottom, plus the area of the two 4 by 12 and one 6 by 12 rectangles on the sides. Note that there's only one 6 by 12 rectangle because the other face is joined to the pink figure, so it's blocked out.
That's [tex]2\times(24+48)+72=216cm^2[/tex].
So the total surface area is [tex]428+216=644cm^2[/tex].