Answer:
Step-by-step explanation:
13n=78 /13
n= 6
The ratio of green M & M's to yellow is 2:5
a. If there are only green and yellow M & M's in the bag, what is the smallest number of M & M's possible?
b. If there are 84 total green and yellow M & M's in the bag, how many are green?
c. If red M & M's were added to the bag in part b to get a total of 100, what is the ratio of green to yellow to red in simplest form? (enter ratio as green:yellow:red)
:
:
a. The smallest number of M & M's possible is 14.
b. The number of green is 24.
c. The ratio of green to yellow to red in 6: 15: 25.
How to calculate the value?a. When there are only green and yellow M & M's in the bag, the smallest number of M & M's possible will be:
= (2 × 2) + (2 × 5)
= 4 + 10
= 14
b. If there are 84 total green and yellow M & M's in the bag, the number of green will be:
= 2 / (2 + 5) × 84
= 2/7 × 84
= 24 green
c. If red M & M's were added to the bag in part b to get a total of 100, the ratio of green to yellow to red in simplest form will be:
= Green : Yello : Red
= 24 : 60 : 100
= 6 : 15 : 25
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Given: <1 and <2 are complementary. <1 and <3 are complementary
Prove: 22 = 23
Complete the proof.
Answers:
1st box: [tex]\boldsymbol{90}[/tex]
2nd box: [tex]\boldsymbol{90}[/tex]
3rd box: [tex]\boldsymbol{\text{m}\angle 2 = \text{m}\angle 3}[/tex]
===============================================
Explanation:
Complementary angles form a corner. Note that "complementary" and "corner" both start with "C" to help remember the rule.
By "corner", I refer to a 90 degree angle.
Since [tex]\angle 1\text{ and } \angle 2[/tex] are complementary, we know that [tex]\text{m}\angle 1+\text{m}\angle 2 = 90[/tex] simply by the definition of what it means to be complementary.
---------------
Through similar logic, [tex]\angle 1\text{ and } \angle 3[/tex] are complementary which means [tex]\text{m}\angle 1+\text{m}\angle3 = 90[/tex]
We can then equate the left hand sides (LHS) of both equations since both LHS expressions equal 90. This is an example of the substitution property in action.
That's how we end up with [tex]\text{m}\angle 1+\text{m}\angle 2 = \text{m}\angle 1+\text{m}\angle 3[/tex]
After this point, subtract [tex]\text{m}\angle1[/tex] from both sides to cancel them out. We'll be left with [tex]\text{m}\angle 2 = \text{m}\angle 3[/tex], which concludes with [tex]\angle 2 \cong \angle 3[/tex] to show the two angles are congruent.
Sophia takes guitar lessons at home every Sunday. Her instructor charges $15 to cover home visit costs, and $30 per hour of training. One Sunday, Sophia's mother pays the instructor $75 for the guitar lessons. Select the equation that represents the given situation and find the number of hours of Sophia's lesson.
The equation to represent the situation is y = 15 + 30x.
The number of hours Sophia used for the guitar training after paying 75 dollars is 2 hours.
How to use equation to represent situations?Sophia takes guitar lessons at home every Sunday. Her instructor charges $15 to cover home visit costs, and $30 per hour of training. One Sunday, Sophia's mother pays the instructor $75 for the guitar lessons.
The equation that can be used to represent the given situation is as follows:
let
x = number of hours used for the training
y = total cost
Therefore,
y = 15 + 30x
Now, Sophia's mother spent 75 dollars for her daughters training. Let's find the hours Sophia used.
Therefore,
75 = 15 + 30x
75 - 15 = 30x
60 = 30x
divide both sides by 30
x = 60 / 30
x = 2
Therefore, she used 2 hours for the training.
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a store put dress shirts on sale for 2 for $27.00. How much will
someone pay if they buy 5 shirts?
Answer:
$67.50
Step-by-step explanation:
27(2) = 54
27/2 = 13.5
54+13.5 = 67.5
Answer:
67.5
explanation:
27/2= 13.5
5*13.5= 67.5
can someone please help asap !!!
Answer:
a = -1
b = -9
Step-by-step explanation:
when x = -2 put -2 for x in the equation:
a(3- (-2)) = -2*(-2) + b and then solve
a(3+2) = 4+b
5a = 4+b
then look at the numbers in the box and try for which number this equation will work. when you put a = -1 and b = -9 you will see it is equal on both sides because each side is -5
Luke claims two circles are always isometric because the shape never changes. Is he correct?
Group of answer choices
Yes - an isometry preserves shape.
Yes - all circles are similar.
No - the center may be located on a difference coordinate.
No - an isometry preserves both size and shape.
Luke asserts that since the shape is constant, two circles are always isometric. he is wrong. No, an isometry keeps the size and shape intact.
Given that,
Luke asserts that since the shape is constant, two circles are always isometric.
We have to say is he accurate.
The answer is
No, an isometry keeps the size and shape intact.
Because a shape-preserving transformation (movement) in the plane or in space is called an isometric transformation (or isometry). The isometric transformations include translation, rotation, and combinations thereof, such as the glide, which combines a translation with a reflection.
Therefore, Luke asserts that since the shape is constant, two circles are always isometric. he is wrong. No, an isometry keeps the size and shape intact.
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Gordon is 5 years older than Krutika. David is 6 years younger than Krutika. If the total of their ages is 86, how old is the eldest of them?
Answer:
Step-by-step explanation:
Well let Krutica’s age = x
K = x, G = x+5, D = x-6
K+G+D = 86
x + x+5 + x-6 = 86
3x = 87
x = 29
Gordon is the eldest of the few:
29 or x+5=
34 years old
Answer: Gordon is 34 years old
Which is the equation in slope-intercept form
for the graph of the line shown?
F. y=-3x - 2
G. y=-3x + 2
H. y = 3x - 2
I. y = 3x + 2
Please help me!
If f(x) = -8m + 3 and g(x) = -8m^2 + m - 5, what is (f times g)x?
A.) 64m^3 - 16m^2 + 43m - 15
B.) 64m^3 +43m - 15
C.) 64m^3 - 32m^2 + 43m - 15
D.) -16m^2 + 43m - 15
Answer: Choice C
[tex]64m^3-32m^2+43m-15[/tex]
==================================================
Explanation:
Multiply out the expressions using the distribution rule as shown below.
[tex](-8m+3)(-8m^2+m-5)\\\\n(-8m^2+m-5) \ \ \text{ ... see note1}\\\\-8m^2n+mn-5n\\\\-8m^2( n )+m( n )-5( n )\\\\-8m^2( -8m+3 )+m( -8m+3 )-5( -8m+3 ) \ \ \text{ ... see note2}\\\\( 64m^3-24m^2 )+( -8m^2+3m )+( 40m-15 )\\\\64m^3+(-24m^2-8m^2)+(3m+40m)-15 \\\\64m^3-32m^2+43m-15 \\\\[/tex]
I used the tool WolframAlpha to confirm the answer is correct. GeoGebra is another free tool that offers similar capabilities.
Footnotes:
Note1: I let n = -8m+3, and replaced -8m+3 with n. That way the distribution on the next step could happen.Note2: I plugged in n = -8m+3. After which distribution happens 3 more times.Which of the following is equal to ?
The given expression, [tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}[/tex] is equal to [tex]\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex].
What are Exponents?
The exponent of a number indicates how many times to multiply the number.For example, three to the power of two is represented as, [tex]3^{2}[/tex]. Here, 3 is the base number and 2 is the exponent. Also, [tex]3^{2} =3 \times 3[/tex].What are the Laws of Exponents?
There are major seven Laws of Exponents as follows:
Product Rule of Exponents: [tex]a^{m} \times a^{n} =a^{m+n}[/tex]Quotient Rule of Exponents: [tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex]Power of a Power Rule: [tex](a^{m} )^{n} =a^{m \times n}[/tex]Product of a Power Rule: [tex]a^{m} \times b^{m} =(ab)^{m}[/tex]Power of a Quotient Rule: [tex]\frac{a^{m} }{b^{m} } =(\frac{a}{b})^{m}[/tex]Zero Power Rule: [tex]a^{0} =1[/tex]Negative Exponent Rule: [tex]a^{-m} =\frac{1}{a^{m}}[/tex]From the given question, we have the expression, [tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}[/tex] -----(1)
Here, we can use the power of a power rule to simplify the expression.
The power of a power rule is of the form, [tex](a^{m} )^{n} =a^{m \times n}[/tex]
Solving expression (1) using the power of a power rule, we get
[tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}=\frac{(x^{2} y^{3})^{-2 \times 3} }{(x^{6} y^{3} z)^{2 \times 3} }\\\implies [\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}=\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex]
Therefore, the given expression is equal to [tex]\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex]
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HELP!!!!!!! LOTS OF POINTS
Answer:
1) 1 A. Yes B. Because the change in x and y is constant
2) 2 A. No B. Although the change in y is
constant, the change in x is not
3) 5. A. No B.Because the change in y is not constant
4) 4,5 A. yes B.Because the change in x and constant
Step-by-step explanation:
19) For which value of s is the value of the expression s + 6 ÷s greatest?
A. 1
B. 2
C. 3
D. 4
The correct option A. 1, is the value of the variable 's' for which the solution of the expression is greatest .
Define the meaning of the greatest value?whenever one value exceeds another. We employ the "greater than" symbol. as in: 9 > 6.For the given question,
The expression is-
(s + 6) ÷ s
Use the options;
A : s = 1
= (s + 6) ÷ s
= (1 + 6) ÷ 1
= 7
B : s = 2
= (s + 6) ÷ s
= (2 + 6) ÷ 2
= 4
C : s = 3
= (s + 6) ÷ s
= (3 + 6) ÷ 3
= 3
D : s = 4
= (s + 6) ÷ 4
= (4 + 6) ÷ 4
= 2.5
Thus, the value of the variable 's' for which the solution of the expression is greatest is 1.
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21a5b³-14a³b² +63a²b
———————————-
7ab
Answer:
[tex]3a^4b^2-2a^2b+9a[/tex]
Step-by-step explanation:
Because multiplication is the inverse of division, we're able to split this fraction into three separate fractions, which will simplify nicely at the end:
[tex]\frac{21a^5b^3}{7ab}; \frac{-14a^3b^2}{7ab}; \frac{63a^2b}{7ab}[/tex]
We can start by simplifying each fraction since 21, -14, and 63 are all divisible by 7:
[tex]\frac{3a^5b^3}{ab}; \frac{-2a^3b^2}{ab}; \frac{63a^2b}{ab}[/tex]
Finally, when dividing quotients with exponents, we subtract the exponents and we put all of our answers back together since everything was multiplied by each other at the beginning of the problem:
[tex]3a^4b^2-2a^2b+9a[/tex]
Nathaniel invested $2,900 in an account paying an interest rate of 5.4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 11 years?
Answer:
$5252.53============================
GivenInvested amount P = $2900,Annual interest rate r = 5.4% = 0.054,Time t = 11 years,Compound number = continuous.Find the balance after 11 yearsUse equation for continuous compound:
[tex]P(t) = P_0e^{tr}[/tex],where P(t) - final amount, P₀ - initial amount, t - time, r - interest ratePlug in the values and calculate:
[tex]P(11) = 2900e^{11*0.054}=5252.53 \ rounded[/tex]Answer:
$5,252.53 (nearest cent)
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amount.P = Principal amount.e = Euler's number (constant).r = Annual interest rate (in decimal form).t = Time (in years).Given values:
P = $2,900r = 5.4% = 0.054t = 11 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=2900 \cdot e^{(0.054 \cdot 11)}[/tex]
[tex]\implies \sf A=2900 \cdot e^{0.594}[/tex]
[tex]\implies \sf A=2900 \cdot 1.81121882[/tex]
[tex]\implies \sf A=5252.53457...[/tex]
Therefore, assuming no deposits or withdrawals are made, the amount of money in the account after 11 years would be $5,252.53 (nearest cent).
Sarah mailed her computer to Store B for repairs. Her bill was:
Initial Repair Cost = $1,350
Sales Tax of 7 percent = $94.50
Total Cost of Computer Repair = $1,444.50
Shipping = 2 percent of Total Cost
What is the cost to ship this computer from Store B?
$
Answer: $28.89
Step-by-step explanation: 2% of 1,444.50 is $28.89
Arnulfo deposited $55 into a savings account. According to the rule of 72, what interest rate will cause his money to double in approximately 23 years?.
Interest rate will cause his money to double in approximately 23 years is 3.13%.
Given:
Arnulfo deposited $55 into a savings account and interest is in semi annually.
For 23 years the interest payments will be = 23*2
= 46
Interest rate = 2*72 / 46
= 144/46
= 72/23
= 3.13%
Therefore Interest rate will cause his money to double in approximately 23 years is 3.13%.
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Find the area of the floor of a square room in square metres of which each side is 800 cm
Answer:
A = 64 m²
Step-by-step explanation:
Step 1: What is the question asking
A = ? m²Step 2: What is known
sides = 800 cmStep 3: Conversion
convert 800 cm to metersKilo, Hecto, Deca, Base, Deci, Centi, Milli800 cm = 8 mStep 4: Answer the question/solve for the area
Area of a square = s²A = s² = 8² = 64 m²Anyone ?. Need help
Step-by-step explanation:
it is a parallelogram.
that means both pairs of opposite sides are parallel and the sides of each pair are equally long.
the sum of all internal angles is 360°.
the opposing angles are equal.
and therefore neighboring angles are complementary angles (or a linear pair) : together they have 180°.
so,
76 = 4x - 8
84 = 4x
x = 21
-3z + 8 + 76 = 180
-3z + 84 = 180
-3z = 96
z = -32
-3z + 8 = -6y - 10
-3×-32 + 8 = -6y - 10
96 + 8 = -6y - 10
104 = -6y - 10
114 = -6y
y = -19
Marie ran 842.4 meters in 12
minutes. How many
did she run?
A. 70.2
B. 70
C. 60.2
D. 72
meters/minute
Answer:
A. 70.2
Step-by-step explanation:
solve your equation step-by-step.
842.412=x1
Step 1: Cross-multiply.
842.412=x1
(842.4)*(1)=x*(12)
842.4=12x
Step 2: Flip the equation.
12x=842.4
Step 3: Divide both sides by 12.
12x12=842.412
x=70.2
Hope this helps! :D
Please mark Brainliest!!!
Someone please help me with this problem, thank uuu
Answer:
B
Step-by-step explanation:
(Simplify your answer.)Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other. x-8 f(x) = 4x + 8 and g(x) = 4
Answer:
x, x, yes==========================
Givenf(x) = 4x + 8,g(x) = (x - 8)/4.To find f(g(x)), g(f(x)),Determine if f and g are inverse functions.Solutionf(g(x)) = 4(x - 8)/4 + 8 = x - 8 + 8 = xg(f(x)) = (4x - 8 + 8)/4 = 4x/4 = xSince both composite functions result in same value of x, they are inverses of each other.Isaac works at a deli. He made a 30-cup batch of potato salad, and now he is filling 2.5-cup
to-go containers to sell to customers.
Write an equation that shows how the number of cups of potato salad remaining,y, depends
on the number of to-go containers Isaac has filled, x.
y =
Help
The equation y = 30 - x shows the number of cups of potato salad remaining, and its solution is y = 27.5.
Isaac made a 30-cup batch of potato salad, and now he is filling 2.5-cup
to-go containers to sell to customers.
Let y represent the number of cups of potato salad remaining,
And x represents the number of to-go containers Isaac has filled,
As per the given situation, we can write the equation as:
y = 30 - x ....(i)
Substitute the value of x = 2.5 in the above equation,
y = 30 - 2.5
y = 27.5
Thus, the equation y = 30 - x shows the number of cups of potato salad remaining, and its solution is y = 27.5.
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Evaluate the expression −(4)power2− (−2)power4
Answer:
-32
Step-by-step explanation:
-(4)^2 - -2^4 = -16 - 16 = -32
Draw a square and it diagonals. Guess the measures of these angles.
All angles of a square are 90° regardless of the length of its sides. However, all sides must be the same length.
What is a square?A square is a term to refer to a geometric figure that is characterized by the following characteristics:
Has four sidesIt has four 90° anglesAll its sides have the same lengthOne key to identifying a square and the value of its angles is to add them together. The sum of the angles of any geometric figure must result in 360°.
90° + 90° + 90° + 90° = 360°Additionally, if we mark the diagonals of a square we must take into account that these angles will have a different value. To find this value we must divide the angle in half, because these diagonals divide the figure into two parts.
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differentiative
2x-3
2x+1
The differential equation is 8x-4 when the equation is (2x-3)(2x+1).
Given that,
The equation is (2x-3)(2x+1)
We have to find the differentiative equation.
Calculus differentiates the process of locating a function's derivatives. A derivative is the pace at which one function changes in relation to another. Sir Isaac Newton set the foundations for the laws of differential calculus. Numerous scientific disciplines make use of the limits and derivatives ideas. The essential ideas of calculus are differentiation and integration.
Differentiation is the rate at which one quantity changes in relation to another.
Take the equation
(2x-3)(2x+1)
We can do in two ways
1st way
Multiply
4x²+2x-6x-3
Subtraction
4x²-4x-3
Differentiation
8x-4
The equation is 8x-4.
2nd way
We have a formula in differentiation that is
u.v=uv'+vu'
Take u as 2x-3 and v as 2x+1
(2x-3)(2)+(2x+1)(2)
4x-6+4x+2
8x-4
Therefore, The differential equation is 8x-4 when the equation is (2x-3)(2x+1).
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Are the lines parallel? y=-3x+2 and 3x+y=6
A. Yes, they have the same slope and a different y intercept
B. No they are not parallell
Answer:
A. Yes, they have the same slope and a different y-intercept.
Step-by-step explanation:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
Rearrange 3x + y = 6 to y = mx + c form.
y = -3x + 6
Parallel lines have the same slope.
Since slope of both lines is -3, the lines are parallel.
A, B, C, D, E, F, G and H form a cuboid. AB = 6.7cm, BC = 2.3cm, and CG = 8.1cm. Find ED rounded to 1DP.
According to the Pythagoras theorem, the value of ED is 8.4 cm
Pythagoras theorem:
Pythagoras theorem defines that the right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Given,
A, B, C, D, E, F, G and H form a cuboid.
AB = 6.7cm, BC = 2.3cm, and CG = 8.1cm.
Now, we need to find the value of Ed and round off it into 1 decimal place.
Here we have the cuboid with the edges named as A, B, C, D, E, F, G and H.
Now, we have to use the value of BC and CG to find the value of hypotenuse of BG.
Because, BG and ED are opposite to each other.
Which means both have the same hypotenuse value.
So, according to the Pythagoras theorem,
=> BG² = BC² + CG²
=> BG² = (2.3)² + (8.1)²
=> BG² = 5.29 + 65.61
=> BG² = 70.9
So, the value of BG is 8.42.
Therefore, the value of ED is 8.4 When we round off this into one decimal place.
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b) Simplify 18x³y³ + 2x³y
The GCF: 2x³y
answer: 2x³y2x³y(9y³+1)
I will mark brainliest!! help much needed >_<
Find the missing value so that the line passing through the 2 points has the given slope.
(-20, y) and (-11, 15); slope: 0
a. 15
b. -13
c. 11
The missing value of that makes the line that passes the given points have a slope of 0 is determined as: a. 15.
What is the Slope of a Line?The slope (m) is defined as the rise of a line over its run. The formula for finding the slope (m) of a line is given as:
Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
Given the points (-20, y) and (-11, 15) has a slope (m) of 0. Therefore, let:
(-20, y) = [tex](x_1, y_1)[/tex]
(-11, 15) = [tex](x_2, y_2)[/tex]
m = 0
Substitute the values into the slope formula:
0 = (15 - y) / (-11 -(-20))
0 = (15 - y) / 9
Multiply both sides by 9
0 = 15 - y
0 + y = 15 - y + y
y = 15
The answer is: a. 15.
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please help with the geometry homework
The triangle RSY is congruent to triangle TSX which is triangle RSY ≅ triangle TSX as side SX ≅ side SY and side XR ≅ side YT.
First, let us understand the SAS congruency theorem:
This one denotes Side - Angle - Side and it means that if 2 sides and one angle of a triangle are equal to the corresponding 2 sides and one angle of another triangle, then they are both congruent.
We are given:
SR and ST are straight lines.
side SX ≅ side SY
side XR ≅ side YT
So,
side SR ≅ side ST
In triangle RSY and triangle TSX;
side SR ≅ side ST (above proved)
∠RSY ≅ ∠TSX (Common)
side SY ≅ side SX (Given)
So, triangle RSY ≅ triangle TSX by SAS congruency theorem.
Thus, the triangle RSY is congruent to triangle TSX which is triangle RSY ≅ triangle TSX as side SX ≅ side SY and side XR ≅ side YT.
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