The line's equation is:
[tex]21x+45y=-6[/tex]To get slope and y-intercept, we have to re arrange this into slope intercept form, that is:
y = mx + b
Where
m is the slope
b is the y-intercept
Let's do this:
[tex]\begin{gathered} 21x+45y=-6 \\ 45y=-21x-6 \\ y=-\frac{21x}{45}-\frac{6}{45} \\ y=-\frac{21}{45}x-\frac{6}{45} \end{gathered}[/tex]So,
The slope is -21/45
y intercept is -6/45
Using Euler's formula, how manyedges does a polyhedron with 20faces and 12 vertices have?? ] edgesEuler's Formula: F + V = E + 2Enter
SOLUTION:
Case: Euler's formula
Given:
Faces= 20
Vertices =12
Euler's formula: F + V = E + 2
Required: To find the number of Edges
Method:
Step 1: Recreate the formula to isolate E
F + V = E + 2
E = F+V - 2
Step 2: Plug in the value of the variables
E = F+V - 2
E= 20 + 12 - 2
E = 30
Step 3:
The value of E is 30
Final answer:
The Polyhedron has 30 edges
-3×+9=-3(2×+3)+3(×-4)+1
The expression we have is:
[tex]-3x+9=-3(2x+3)+3(x-4)+1[/tex]Step 1. To solve for x, we need to first apply the distributive property on the right-hand side of the equation. The distributive property is to multiply the number outside each pair of parenthesis by the terms inside it. We get the following:
[tex]-3x+9=-3\cdot2x-3\cdot3+3\cdot x+3\cdot(-4)+1[/tex]Solving the multiplications on the right-hand side:
[tex]-3x+9=-6x-9+3x-12+1[/tex]Step 2. Combine the like terms.
We start by combining the terms that contain x:
[tex]-3x+9=-3x-9-12+1[/tex]And then, combine the independent terms:
[tex]-3x+9=-3x+4[/tex]Step 3. Add 3x to both sides of the equation:
[tex]-3x+3x+9=4[/tex]On the left side, we get that -3x+3x cancel each other:
[tex]9=4[/tex]As we can see, this is not true, which means that there is no solution for x.
Answer: There is no solution for x.
NO LINKS!! Part 4: Please help me with this Similarity Practice
Answer:
C' = (10, 1)
Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation, followed by a translation of 3 units down.
Step-by-step explanation:
If two triangles are said to be similar, their corresponding angles are congruent and their corresponding sides are in the same ratio.
Given vertices of triangle ABC:
A = (0, 0)B = (1, 4)C = (5, 2)To maintain similarity but not maintain congruence, dilate triangle ABC (since dilation keeps the corresponding angles of both triangles the same).
Given vertex of triangle A'B'C':
B' = (2, 5)If ΔABC is dilated by a scale factor of 2, with the origin as the center of dilation, B' = (2, 8). If the triangle is then translated 3 units down, B' = (2, 5), which matches the given coordinate of point B'.
Therefore, the series of transformations is:
Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation.Translation of 3 units down.Mapping Rule: (x, y) → (2x, 2y - 3)
Therefore, the coordinates of point C' are:
⇒ C' = (2(5), 2(2) -3) = (10, 1)
May I please get help with this for I am confused S to hash by my original and final points of the figure and where I should Rotate it to 270° clockwise
ANSWER:
Point in original figure (2, -3)
Point in final figure (-3, -2)
STEP-BY-STEP EXPLANATION:
The first thing is to determine the original point of the figure on the graph, which would be:
[tex]P(2,-3)[/tex]The rule for 270° counterclockwise rotation is as follows:
[tex](x,y)\rightarrow(y,-x)[/tex]We apply it in this case, and the new point would be:
[tex]P(2,-3)\rightarrow P^{\prime}(-3,-2)[/tex]We represent the result on the graph, as follows
can you explain the steps to letter a which is above the word solution i dont understand them
Given the series:
[tex]1-\frac{1}{3}+\frac{1}{9}-...[/tex]State if the series is convergent or divergent and if convergent, find its sum.
The sequence of terms forms a geometric pattern. Each term is found by multiplying the previous term by a constant number (the common ratio).
Let's find the value of the common ratio by dividing any two successive terms, for example:
[tex]r=\frac{-\frac{1}{3}}{1}=-\frac{1}{3}[/tex]The common ratio is greater than -1 and less than 1, so the series is convergent.
Now we find the sum of the infinite series by using the formula:
[tex]S=\frac{t_1}{1-r}[/tex]Where t1 is the first term, that is, t1 = 1.
Substituting:
[tex]S=\frac{1}{1-\left(-\frac{1}{3}\right)}[/tex]Now we add the numbers to the denominator:
[tex]S=\frac{1}{1+\frac{1}{3}}[/tex]We have a sum of an integer and a fraction:
[tex]1+\frac{1}{3}[/tex]To add these numbers, we must get them to have the same denominator, thus:
[tex]1+\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3}[/tex]Operating:
[tex]S=\frac{1}{\frac{4}{3}}[/tex]To divide by a fraction, we multiply by its reciprocal:
[tex]S=1\cdot\frac{3}{4}=\frac{3}{4}[/tex]Part 2: Multiple Choice Must show all work to get full credit.
The correct value of x is -6, as determined by the equation KL + LM = KM. As a result, Option C is correct.
What is an equation and what type is it?Equations are classified into two types: identities and conditional equations. An identity holds true for all variable values. A conditional equation is only true for specific variable values. An equation is formed by joining two expressions with an equals sign ("=").From the given figure,
KL + LM = KM
15 + 2x + 10 = x + 19
2x + 25 = x + 19
x = -6
Therefore, the correct value of x is -6 which is obtained from the given equation KL + LM = KM. So, Option C is correct.
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if the probability of a airplane flight arrives on time is 0.75 find the probability that out of 3 flights ALL arrive on time? and out of 3 flights at least one of them arrives on time?
ANSWER
[tex]P(\text{all}-3)=0.42[/tex]EXPLANATION
We want to find the probability that all 3 flights will arrive on time.
To do that, we have to find the product of the probability that each plane will arrive on time three times.
That is:
[tex]\begin{gathered} P(\text{all}-3)=0.75\cdot0.75\cdot0.75 \\ P(\text{all}-3)=0.42 \end{gathered}[/tex]That is the answer.
step by step on how to solve -887.4 (-0.1) & -6 × 3.3
The numbers have opposite signs, so the result of the multiplication will be negative i.e -19.8.
We are given two mathematical expressions to be solved. An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.
The first expression is solved below :
E1 = -887.4(-0.1)
We need to multiply the two numbers with each other. Both the numbers are negative, so the result of the multiplication will be positive.
E1 = 88.74
The second expression is solved below :
E2 = -6 × 3.3
This is a simple multiplication of two real numbers. The numbers have opposite signs, so the result of the multiplication will be negative.
E2 = -19.8
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4. What is the value of y in the system of equations shown below?
z+y+z=22
y+z=16
z-2=7
Answer:
Step-by-step explanation:
Y = 22 - 2Z
22 - 2Z + Z = 16
22 - Z = 16
Z = 6
Y + Z = 16
Y + 6 = 16
Y = 10
A company surveyed 1200 people. Twice as many females as males. How many each were surveyed
Females: X
Males: Y
X=2Y because "Twice as many females as males"
The total surveyed are:
[tex]x+y=1200[/tex][tex]2y+y=1200[/tex]Then we have:
[tex]3y=1200[/tex][tex]y=\frac{1200}{3}=400[/tex]From the first equation:
[tex]x=1200-y=1200-400=800[/tex]So, males are 400 and females are 800.
90 divided by 5(3x2)-1=
The solution of expression 90 ÷ [5 (3×2) - 1} is,
90 ÷ [5 (3×2) - 1} = 3.10
We have to given that,
An expression to simplify as,
⇒ 90 ÷ [5 (3×2) - 1}
We can simplify the expression as,
⇒ 90 ÷ [5 (3×2) - 1}
⇒ 90 ÷ [5 ×6 - 1]
⇒ 90 ÷ [29]
⇒ 3.10
Therefore, The solution of expression 90 ÷ [5 (3×2) - 1} is,
90 ÷ [5 (3×2) - 1} = 3.10
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Solve: (2,1); m=undefined. Answer has to be in slope intercept form, so y=mx+b. SHOW ALL WORK SO I CAN HAVE A BETTER UNDERSTANDING :)
Answer:
x = 2
Step-by-step explanation:
So this seems kind of a trick question. This is why. The given slope is undefined. That means this is a vertical line. Vertical lines cannot be written in slope-intercept form,
y = mx+b.
Vertical lines have the equation "x = anumber" It literally cannot be written in the form y=mx+b.
The point given is (2,1) this is in the form (x,y) so x is 2 and y is 1. We are interested in the x.
x is 2 is written as:
x = 2 This is the equation of the lines through (2,1) with m=undefined.
Help mee pleasee!!
thank you <3
The linear equation y = -500x + 5000 models the price-sales relationship for the toy and the daily sales of the toy would be $1250 if the price is set at $7.50.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The line must pass through points (6, 2000) and (8,1000) which is given in the question.
We have to determine the slope of the line :
m = (y₂ - y₁)/(x₂ -x₁ )
m = (1000 - 2000)/(8 - 6)
m = -1000/2
m = -500
This represents new assistants per year
So with through points (6, 2000) and (8,1000), the equation becomes
y - 2000 = -500(x -6)
y = -500x + 3000 + 2000
y = -500x + 5000
Using this equation to predict the daily sales of the toy if the price is set at $7.50.
Assume that the ratio of change in price to change in daily sales is constant and let x be the price of the toy and y be the number of sales.
Substitute the value of x = 7.50
y = -500(7.50) + 5000
y = -56000 + 294000
y = 1250
Hence, the daily sales of the toy would be $1250 if the price is set at $7.50.
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helppppppppppppppppppppppppp
Answer:
No
Step-by-step explanation:
V/3 is -35, which is smaller than 5
Use the standard normal distribution to find the probability P(z < –2.08)
P(z < -2.08) = 0.018763
Explanations:From the standard normal distribution table, we can check the probability given any z-score
Therefore, checking P(z < -2.08) from the standard normal distribution:
P(z < -2.08) = 0.018763
What is the value of X?What is the value of the radius In circle O?
Answer
x = 4.5 units
Radius = 29 units
Explanation
The center of the circle is point O.
So, any line drawn from that point O to any point on the circumference of the circle is the radius of the circle and will therefore have the same length.
Therefore, OC = OD
OC = 6x + 2
OD = 10x - 16
6x + 2 = 10x - 16
Rewriting this
10x - 16 = 6x + 2
10x - 6x = 2 + 16
4x = 18
Divide both sides by 4
(4x/4) = (18/4)
x = 4.5 units
Then, we can now calculate the radius of the circle now
Radius = OC = OD
= 6x + 2 or 10x - 16
= 6(4.5) + 2 or 10(4.5) - 16
= 27 + 2 or 45 - 16
= 29 units.
Hope this Helps!!!
how do I write a function that describes the given transformation
1) Considering that this is our parent function:
[tex]f(x)=2^x[/tex]2) Then let's visualize what happens when we transform it to :
[tex]g(x)=2^{x-3}+1[/tex]3) So now let's reflect that across the y-axis, and vertically shrink that by 1/3:
Elsie has just finished polishing some of her antique penny collection. She has twelve pennies, each with a different date. To store her coins she has purchased many plain black bags, and wishes to put the same number of coins in each bag. She has no restriction on the number of bags she can use. In how many possible ways can she store her coins
The possible ways Elsie (combinations) can store her 12 coins in the bags she purchased is 6 ways
What is a combination in mathematics?A combination is the number of possible arrangements.
The number of coins = 12 coins
The number of black bags = Many
Number of coins per bag = The same number of coins
Required;
The number of ways Elsie can store her coins
Solution;
The ways the coins can be stored is given by the factors of 12 which are; 1, 2, 3, 4, 6, and 12
The coins can therefore be stored as follows;
1 coin per bag to give 1 × 12 = 12 bags of coins2 coins per bag to give 12 ÷ 2 = 6 bagsShared into 3 coins each to give 12 ÷ 3 = 4 bags 4 coins to give 12 ÷ 4 = 3 bags6 coins each to give 12 ÷ 6 = 2 bags12 coins in each bag to give 12 ÷ 1 = 1 bagsThe possible number of ways Elsie can store the coins is 6 ways
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The measure of an angle is 28.5°. What is the measure of its complementary angle?
When the measure of an angle is 28.5° then the angle measure of its complementary angle will be 61.5°.
What is complementary angle?They are referred to as complementary angles when the sum of two angles is 90 degrees. For instance, the angles of 30 degrees and 60 degrees complement one another.
If we know the measurement of one angle, we can easily find the unknown angle because the sum of complementary angles equals 90 degrees.
As an illustration, if one of the two angles is 45 degrees, then the formula is:
x + 45 = 90
x = 90 - 45 = 45°.
If 2 complementary angles adds up to 90°
So the complementary angle of 28.5° is
90° - 28.5° = 61.5°
Thus, the angle measure of its complementary angle will be 61.5°.
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A model for the potential through the heart (between sinoatrial node and atrioventricular node) for an individual is…. Where P(v) is the new voltage (in millivolts) after 1 second given a previous voltage v and u is a positive constant called the updating potential. A. Calculate, including units, the value of P(100): ______ mV B. Find the average rate of change in P on the interval [30, 120] (the answer will contain u). = __________ D. The system is said to be in equilibrium at a value for v for which P(v) = v. For what range of values or u does this system have an equilibrium? (Use interval notation) __________
The model is given in the question.
a. The value of P(100) is
[tex]P(100)=0.7\times100=70mV[/tex]b. The average rate of change in P on the interval [30,120] is
[tex]A=\frac{P(120)-P(30)}{120-30}=\frac{0.7\times120-(0.7\times30+u)}{90}[/tex][tex]A=\frac{84-21-u}{90}=\frac{63-u}{90}[/tex]c. The graph of P (v) is represented the linear function.
Yes it represents a linear function.
Line RQ is a perendicular bisector to line PS at Q between P and A. By which of the five congruence statements HL, AAS, ASA, SAS, SSS, can you immediatley conclude that triangle PQR is congruent toe triangle SQR
Figure it out ur self
can someone pls help with this problem?
Answer:
(6√13)/13
Step-by-step explanation:
You want the exact value of cot(arcsin(√13/7)).
Trig ratiosThe relevant trig ratios are ...
Sin = Opposite/Hypotenuse
Tan = Opposite/Adjacent
Cot = 1/Tan = Adjacent/Opposite
Pythagorean theoremThe Pythagorean theorem can be used to find the side adjacent to the angle whose sine is √13/7. Using the sine ratio, we can take the opposite side to be √13, and the hypotenuse to be 7. Then the adjacent side is ...
adjacent² +opposite² = hypotenuse²
adjacent² +(√13)² = 7²
adjacent² = 49 -13 = 36
adjacent = √36 = 6
CotangentThen the cotangent of the angle is ...
cot(arcsin(√13/7)) = adjacent/opposite = 6/√13
cot = (6√13)/13
Three cards are drawn with replacement from a standard deck of 52 cards. Find the the probability that the first card will be a spade, the second card will be a red card, and the third card will be a face card. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Given:
The total cards is: 52
Number of spade cards: 13
Number of red cards: 26
Number of face cards: 12
Therefore,
[tex]P(\text{spade)}=\frac{13}{52}=\frac{1}{4}[/tex][tex]P(red)=\frac{26}{52}=\frac{1}{2}[/tex][tex]P(\text{face)}=\frac{12}{52}=\frac{3}{13}[/tex]The probability that the first card will be a spade, the second card will be a red card, and the third card will be a face card is given by:
[tex]P(spade\text{ and red and face)=P(spade)}\cdot P(red)\cdot P(face)[/tex]Substitute:
[tex]=\frac{1}{4}\cdot\frac{1}{2}\cdot\frac{3}{13}=\frac{1\cdot1\cdot3}{4\cdot2\cdot13}=\frac{3}{104}[/tex]Answer: 3/104
MODELING WITH MATHEMATICS The top of the slide is 12 feet from the ground and has an angle of depression of 53°.What is the length of the slide? Round your answer to the nearest whole number.12 ft53AThe slide is aboutfeet long.
Solution:
From the given figure;
[tex]\begin{gathered} Opposite=12\text{ feet} \\ Hypotenuse=length\text{ of slide} \\ \theta=53\degree \end{gathered}[/tex]Applying SOHCAHTOA
[tex]\begin{gathered} \sin\theta=\frac{Opposite}{Hypotenuse} \\ \sin53\degree=\frac{12}{Hypotenuse} \\ Hypotenuse=\frac{12}{\sin53\degree} \\ Hypotenuse=15.02562=15\text{ feet \lparen nearest whole number\rparen} \end{gathered}[/tex]Hence, the slide is about 15 feet long
Use the Factor Theorem to find the zeros of f(x) = x³+4x² - 4x - 16 given that (x - 2) is afactor of the polynomial.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given polynomial function
[tex]f(x)=x^3+4x^2-4x-16[/tex]STEP 2: Apply the factor theorem
A polynomial function f(x) has a factor (x-a) if and only if f(a) = 0, this means that (x-2) will be a factor if and only if f(2)=0.
By checking,
[tex]\begin{gathered} f(2)=2^3+4(2^2)-4(2)-16 \\ f(2)=8+16-8-16=0 \end{gathered}[/tex]Hence, (x-2) is a factor and the first zero is 2
STEP 3: We divide the polynomial by its factor to get the quotient expression
[tex]\frac{x^3+4x^2-4x-16}{(x-2)}=x^2+6x+8[/tex]STEP 4: we find out the factors of the quotient
If f(a) is zero, this means that a must be a factor of 16
The factors of 16 are 1,2,4,8,16
[tex]\begin{gathered} x^2+6x+8=(x+4)(x+2) \\ f(-4)=(-4^2)+6(-4)+8=16-24+8=0 \\ f(-2)=(-2)^2+6(-2)+8=4-12+8=0 \end{gathered}[/tex]Hence, (x+4) and (x+2) are also factors of the polynomial.
Therefore, the zeroes of the given function are:
[tex]2,-4,-2[/tex]Be Allison has been to the large muffin sale table Chris wants to pay more signs
By proportion, Chris should mix 8/3 parts of the red paint in 2 fluid ounces of blue paint.
Purple paint is made using a combination of red paint and blue paint.
Now Allison made purple paint by mixing 3 parts red [aint and 4 parts blue paint.
Therefore, the ratio for the purple paint is :
= 4 parts blue paint / 3 red paint
Chris has 2 fluid ounces of blue paint.
Let the amount of red paint Chirs have to be x.
Then the proportion should be equal.
So,
4 / 3 = x / 2
By cross multiplication,
4 × 2 = 3 × x
8 = 3x
Dividing each side by 3,
x = 8/3
Chirs should mix 8/3 parts of the red paint with blue paint.
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6 1/9to a mixed number is?
Answer: It's already a mixed number; if your talking about improper fractions it is 55/9
Step-by-step explanation:
6x9+1
6x9=54+1=55/9
Answer:
55/9
Step-by-step explanation:
Because 9 x 6 is 55 then + 1 is 55
A dinner plate has 25.12 inches of metal around it's edge. What is the radius of the plate?
Assuming your teacher wants you to use 3.14 for pi, then,
C = circumference = perimeter around the circle
C = 2*pi*r
r = C/(2*pi)
r = (25.12)/(2*3.14)
r = 4 inches is the radius
The radius of the circle is 4 inches
What is a Circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the centre for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
Given data ,
Let the circumference of the circle be = A
Now , Circumference A = 25.12 inches
The circumference of circle = 2πr
π = 3.14
Substituting the values in the equation , we get
2πr = 25.12
Divide by π on both sides , we get
2r = 8
Divide by 2 on both sides , we get
r = 4 inches
Therefore , the value of r is 4 inches
Hence , The radius of the circle is 4 inches
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A group of 6 students was asked, "How many hours did you watch television last week?" Here are their responses.
4, 19, 7, 15, 13, 4
Find the mean number of hours for these students.
If necessary, round your answer to the nearest tenth.
Answer:
10.3
Step-by-step explanation:
To calculate the mean we need to:
(4 + 19 + 7 + 15 + 13 + 4)/6
10.33333,...
Round to nearest tenth: 10.3
multiple fractions (reduce to lowest terms or tenths)61/2×41/4
Answer:
312.6
Explanation:
Given the expression
61/2 * 41/4
Multiply both numerator and denominator
= 61/2 * 41/4
= (61*41)/(2*4)
= 2501/8
= 312.625
To nearest tenth 61/2 * 41/4 = 312.6
