The curve that passes through the point (1,1) with a given slope is a line.
1. The equation of a line can be determined using the point-slope form of the equation, which is y - y1 = m(x - x1).
2. For the given point (1,1) and slope, the equation of the line is y - 1 = m(x - 1).
3. Substituting the given slope m for the equation, we get y - 1 = m(x - 1).
4. Simplifying the equation, we get y = mx - m + 1.
5. The equation of the line can also be written in the general form of the equation of a line, which is y = mx + b.
6. Substituting the given slope m and the y-intercept b = -m + 1, the equation of the line can be written as y = mx - m + 1.
7. The slope of the line can be determined by calculating the rise (change in y-coordinate) over the run (change in x-coordinate).
8. For the given point (1,1) and another point (x2, y2), the slope can be calculated using the formula m = (y2 - y1)/(x2 - x1).
9. For example, if the second point has coordinates (3, 4), the slope of the line can be calculated as m = (4 - 1)/(3 - 1) = 3/2.
10. The equation of the line can then be determined using the point-slope form of the equation, which is y - y1 = m(x
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Given the function y= x2 + 10x +16=0
What are the x-intercepts of the function?
Answer:
(0,-8) and (0,-2)
Step-by-step explanation:
Factorize: x² + 10x + 16 = 0
You'll get: (x + 8)(x + 2) = 0
The roots are x = -8 and x = -2
So the curves intercepts the x-axis at (0,-8) and (0,-2)
Answer:
(-2,0) and (-8, 0)
Step-by-step explanation:
Factor the function:
(x + 2)(x+8) = 0
x = -2, -8
x intercepts are when y=0
Coordinates are:
(-2,0) and (-8, 0)
What is the solution to this equation? x over 5 equals 25
Answer: 5
Step-by-step explanation:
Because 5x5=25
Please be right
Need help asap
Answer: 3.51
Step-by-step explanation:
Answer: The tip was 3.50$
Step-by-step explanation: Since the tip is 20% you would times the given amount by 20 then divide it by 100.
20 x 17.53 / 100 = 3.506
We're rounding to the nearest cent, so that would be 3.50.
answers for number 21 and 24 questions
How many solutions over the complex number system does this polynomial have 7x^5-33x^4-4x^2+3x+52=0.
The number of solutions over the complex number system to the given polynomial is 5 .
The complex number is fundamentally the mix of a real number and a nonexistent/imaginary number. The complex number is given by a+ib, where a is defined as the real number and ib = imaginary number. Additionally, a,b has a place with real numbers and i = √-1.
Consequently, a complex number is a straightforward portrayal of expansion of two numbers, i.e., real number and a imaginary number. One piece of it is simply genuine and the other part is absolutely nonexistent.
Now, the given polynomial is 7x⁵ - 33x⁴ -4x²+3x+52=0.
We know very well that for complex number, its number of solution is decided by the degree of the polynomial. Degree is defined as the highest exponent of variables present in polynomial. Highest exponent present in polynomial is 5.
Hence, number of solutions are 5.
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What is the value of the expression below when x= 6 x^2+10x+3
Answer: 99
Step-by-step explanation:
substitute 6 in to the x in the equation
[tex]6^{2} +10(6)+3[/tex]
36+60+3
96+3
99
Answer:
99
Step-by-step explanation:
(6)^2 +10(6)+3
6^2=6*6=36
10*6=60
36+60+3
99
Which theorem shows triangle ATC is congruent to triangle BTD?
The theorem to shows triangle ATC is congruent to triangle BTD will be ''SAS'' theorem.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle ATC is congruent to triangle BTD.
Now,
In the figure, we get;
⇒ AT = TB (Side)
⇒ AC = BD (Side)
⇒ ∠ATC = ∠DTB = 90° (Vertically opposite angle)
Thus, By using SAS theorem the triangle ATC is congruent to triangle BTD.
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a study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. it was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 2 days with an approximately normal distribution. (a) find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places.
The required probability that their hospital stay is from 5 to 6 days is 3.31%.
What is normal distribution?An normal distribution is a sort of ceaseless likelihood dissemination wherein most information guides bunch to the center of the reach, while the rest tighten evenly toward one or the other limit. The center of the reach is otherwise called the mean of the distribution.
According to question:We have,
mean(a) = 7.37, standard deviation(S) = 2
Using formula
[tex]Z = \frac{x-a}{S}[/tex]
Then,
P( hospital stay is from 5 to 6 days)
P(5[tex]\leq[/tex]x[tex]\leq[/tex]6) = P[tex](\frac{5-7.37}{2}\leq z\leq \frac{6-7.37}{2})[/tex] = P(-3.16 ≤ z ≤-1.827 )
⇒P(z≤-1.827) - P(z≤-3.16)
⇒ 0.034 - 0.001 = 0.331 = 3.31%
Theus, probability is 3.31%
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qlqn peut m'aider pr les coordonnées
Answer: something
Step-by-step explanation: you are welcome
the sales tax rate is 7.25% in California, then how much would you pay in Los
Angeles for a pair of shoes that cost $39.00?
Answer:
The sales tax in California is 7.25%, which means that for every dollar you spend, you need to pay an additional 7.25 cents in sales tax. So if you buy a pair of shoes that costs $39.00, you would need to pay an additional $2.84 in sales tax (39 x 0.0725 = 2.84). This means that the total cost of the shoes would be $41.84 (39 + 2.84 = 41.84).
Step-by-step explanation:
Answer:
41.83
Step-by-step explanation:
39 x .0725 = 2.83 Tax rounded to the nearest cent
2.83 + 39 = 41.83
a certain field is a rectangle with a perimeter of feet. the length is feet more than the width. find the width and length of the rectangular field.
The length and width of the rectangular field is 316 ft and 133 ft respectively.
An algebraic equation is a mathematical statement that equalises two expressions. A variable, coefficients, and constants are common components of an algebraic equation. Also look into Algebraic Expressions. Equality is represented by equations or the equal sign.
It is balanced because both sides are equal in value. To avoid making an error that throws the equation out of balance, ensure that any change on one side is reciprocated on the other.
Given,
perimeter of rectangular field = 898 ft
let width be 'x'
then,
length = x+183
The perimeter of a rectangle is,
[tex]P = 2(length + width)\\\\898 = 2( ( x + 183 ) + x )\\\\898 = 2(2x+183)\\\\898 = 4x + 366\\\\4x = 898 - 366\\\\4x = 532\\\\x=\frac{532}{4}\\\\x=133[/tex]
Thus, the width is 133 ft and length is (133+183)=316 ft.
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Your question is incomplete, here is the complete question.
A certain field is a rectangle with a perimeter of 898 ft. The length is 183 ft more then the width. Find the width and length of the rectangular field?
Which triangle involves altitudes?
Answer:
The isosceles triangle altitude bisects the angle of the vertex and bisects the base. It should be noted that an isosceles triangle is a triangle with two congruent sides and so, the altitude bisects the base and vertex.
the fox population in a certain region has an annual growth rate of 9% per year. in the year 2012, there were 20,700 foxes counted in the area. what is the fox population predicted to be in the year 2019? round to the nearest fox.
37,840 is the fox population predicted to be in the year 2019.
What is a growth rate?
The country, territory, or geographic area's yearly average rate of change in population size over a certain time period. It expresses the proportion, usually multiplied by 100, between the annual growth in population size and the total population for that year.
Here, we have
A growth rate of 9% per year means that at the end of each year, the population is 1.09 times what it was at the start of the year.
We keep this up for t years, starting with an initial population of 20,700, and get
P(n) = 20,700 (1.09)ⁿ
n = years since 2012, when the population was 20,700
For the year 2019,
n = 2019 - 2012 = 7
P(7) = 20,700 (1.09)⁷ ≅ 37,840
Hence, 37,840 is the fox population predicted to be in the year 2019.
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which equation can be solved by using this system of equations? startlayout enlarged left-brace 1st row y = 3 x superscript 5 baseline minus 5 x cubed
By using the concept of equation, it can be calculated that-
The equation can be solved by using this system of equations
[tex]3x^5-5x^3+2x^2-10x+4=4x^4+6x^3-11[/tex]
What is equation?
At first it is important to know about algebraic expressions.
Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
Here the system of equation are-
[tex]3x^5-5x^3+2x^2-10x+4=0\\4x^4+6x^3-11=0[/tex]
So the equation can be solved by using this system of equations
[tex]3x^5-5x^3+2x^2-10x+4=4x^4+6x^3-11[/tex]
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Complete Question
Which equation can be solved by using this system of equations?
[tex]3x^5-5x^3+2x^2-10x+4=0\\4x^4+6x^3-11=0[/tex]
Sheila is making accessories for the soccer team. She uses 722.56 inches of fabric on headbands for 28 players and 4 coaches. She also uses 241.64 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Answer:
27.72 inches of fabric
Step-by-step explanation:
28+3=31
Fabric used on each player:
559.24÷31=18.04
271.04÷28=9.68
PLEASE HELP!!! QUICKLY!! 20 points!!!
Josh will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $59 and costs an extra $0.08 per mile driven. The second plan has an initial fee of $52 and costs an extra $0.13 per mile driven.
For what amount of driving do the two plans cost the same?
______ miles
What is the cost when the two plans cost the same?
$______
Answer:
140 Miles
$70.2
Step-by-step explanation:
1. Set up an equation
In this case, the equation would be [tex]59 +0.08x=52+0.13x[/tex]
In this equation, x = miles
2. Simplify
You need to subtract 0.08x from the left side and 52 from the right side.
This will give you a number that is equal to an x value.
[tex]7=0.05x[/tex]
3. Divide
Divide 0.05 from both sides. This will give you X=140. Since x=miles,
You would need to drive 140 miles to make the two sides equal.
4. Find the cost.
Plug the 140 in for the x on one side. You only need to do this to one
side because both of the sides are equal.
59 + (0.08 x 140) = $70.2
How do you find slope with x1 and y1?
The slope of the line passes through two points is (y2-y1)/ (x2- x1).
Slope of a line:
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Here we have to find the slope of a line that passes through two points.
Data given:
Point 1 = (x1, y1)
Point 2 = (x2, y2)
The general formula to find the slope of a line:
Slope(m) = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are two points on the line.
Therefore the slope is (y2-y1)/ (x2 - x1).
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What is the angular radius 0 of the first dark ring for a point source being imaged by this telescope?
The angular radius θ of the first dark ring for a point source being imaged by this telescope is 4.00 × 10^-5 degrees
The value of λ = 550 nanometer
The value of D = 0.96 m
We have to find the angular radius theta
The equation will be
sin θ = 1.22λ / D
Substitute the values in the equation
sin θ = 1.22 × (550 × 10^-9) / 0.96
Multiply the term in the numerator
sin θ = 6.71 × 10^-7 / 0.96
Divide the numbers
sin θ = 6.98 × 10^-7
θ = sin^-1 (6.98 × 10^-7)
θ = 4.00 × 10^-5
Therefore, the value of θ is 4.00 × 10^-5 degrees
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What are the two equations of a line?
The two equations of a line are 1) Two point form
2)Slope-intercept form
Two-point form: The equation of a line passing through the two points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex]. The slope of the two-point form is [tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
The equation is [tex]y-x_{1}=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } (x-x_{1})[/tex]
Slope-intercept form: The slope-intercept form is [tex]y=mx+c[/tex]. Here m represents the slope of the line and c represents the y-intercept of the line.
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outside of johnny's home there is a grassy area about 40' x 100' that he mows regularly. beyond that grassy area is a wooded area and taller grass where his kids play hide and seek. johnny mows around the trees, but less frequently than the rest of the yard, and then he has several outbuildings in the wooded area as well. the whole area that has been described is enclosed by a fence. beyond the fence is an area that he does not maintain, and he keeps his collection of exotic marijuana plants hidden in the tall grass in this area. the curtilage of johnny's home is best identified as
Therefore, the space inside the fence serves as the best indicator of Johnny's home's perimeter.
What is perimeter?A perimeter is a closed path that surrounds, encircles, or outlines a two-dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is its circumference. Perimeter calculations have many applications in the real world.
Here,
the grassy area = 40' x 100'
He has numerous outbuildings in the forested area as well, and he mows the area surrounding the trees less regularly than the rest of the yard. A fence completely encloses the area that has been described. He maintains his collection of exotic marijuana plants hidden in the long grass in the area outside the fence, which is an area he does not maintain.
Therefore, the space inside the fence serves as the best indicator of Johnny's home's perimeter.
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Find the volume of this prism with height of 9 width if 6 length of 12
Answer:
SA = 124 cm².
V = 72 cm³
Step-by-step explanation:
25 POINTS!! Brainiest and EXTRA POINTS!! Someone please help me with both problems ASAP!!
First triangle: 20,22, and 18(please solve for All letters includes: X,Y, and Z)
Second triangle: 50,29, and 26
Third Triangle: 55,90, and 50(please solve for All letters includes: X,Y, and Z)
Also, please show your work so I will understand how to do it properly.
The required measure of the angle x is given as 117.38°.
A triangle is given with a measure of.
a = 50, b = 55 and c = 90ft
The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
Apply cosine formula,
c² = a² + b² -2abcosx
Substitute the value in the above expression,
90² = 50² + 55² - 2×50×55×cosx
cosx = -0.46
x = cos⁻¹[-0.46]
x = 117.38°
Hence, as a result, the measure of the angle x is 117.38°.
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Write the equation of the given line in slope-intercept form.
Answer:
y=7/2x+1
Step-by-step explanation:
Remember this formula
Y=mx+b
m=slope
b=y-intercept
If an equation is balanced properly both sides of the equation must have the same number of.
Both sides of an equation must contain the same number of atoms in order for it to be properly balanced.
An element is balanced if it has the same amount of atoms on both sides of the equation. The equation is balanced if all the components are in balance. Equal numbers and types of each atom appear on both sides of balanced chemical equations. A balanced equation must have coefficients that are the simplest whole number ratio. Chemical reactions always conserve mass.
When the quantity of each type of atom is the same on both sides of the reaction, a chemical equation is considered to be balanced. A chemical equation should have the same number of atoms on both sides. The number of atoms for each element is conserved during a chemical reaction, despite the possibility that reactant molecules may change during the process (producing distinct molecules of product).
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Correct Question:
If an equation is balanced properly both sides of the equation must have the same number of _________________.
8.
Find the value of the missing side.
64°
X
Write the trig equation to solve for x.
11
[tex]\tan 64^{\circ}=\frac{x}{11} \implies x=11 \tan 64^{\circ}[/tex]
Can a gerund be used in place of an infinitive if yes explain through examples?
Gerund can be used in place of infinitive depends on the sentence as this is a subjective.
Some of the sentence only use infinitive.Some of the sentences use both without change in the meaning.Some of the sentences used by both but by change in the meaning.Explanation:
Gerund can be used in place of infinitive in the sentence.
Infinitive is the basic form of verb without any change in the original form of word.Example : She likes to dance.Gerund : in simple explanation verbs ends with ing.Gerund is a verb form act as a noun.Gerund is a noun being either the subject or the object of the given sentence.Example : I like studyingThey are interchangeable or not depends on the sentence.This is a subjective.Some of the sentence only use infinitive.Some of the sentences use both without change in the meaning.Some of the sentences used by both but by change in the meaning.Therefore, gerund and infinitive are interchangeable or not depends on the sentence.
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At a school recess, there needs to be a ratio of 2 adults for every 24 children on the playground. The double number line represents the number of adults and children on the playground at recess. How many adults are needed if there are 72 children?.
help me pls i have the mind of a 6th grader lol
The equation used to find the answer is 26 -14 -6 =
what is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation.
number of flowers picked by the girl = 14
number of flowers already with her = 6
number of flowers picked by her grand mother = 26
so her grandmother picked 26 - 14 - 6 flowers more than her. so then equation becomes 26 -14 -6 = ?
In conclusion, the equation that best describes the above is 26 -14 -6 = ?
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Safia bakes cakes. The dimensions of the oven tray are 600mm x 500mm. A cake tin is 25 cm in diameter.
Safia can fit 4 cakes on the oven tray at one time
Firstly, We need to change the measurements from mm to cm
600mm x 0.1cm/1mm = 60cm
500mm x 0.1cm/1mm = 50cm
Area of the Tray (rectangular) = 60cm * 50cm = 3,000cm²
Area of the cake tin (circular) = π r²
r = d/2 = 25/2 = 12.5cm
Area of the cake tin = 3.14 * (12.5cm)²
Area of the cake tin = 3.14 * 156.25cm²
Area of the cake tin = 490.625cm²
Area of the tray ÷ Area of the cake tin = number of cake tins that fit
3,000cm² ÷ 490.625cm² = 6.11 or 6 cake tins.
thus, We can conclude that she can fit 6 cakes in the oven at once.
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(complete question)
Safia bakes cakes. The dimensions of the oven tray are 600mm x 500mm. A cake tin is 25 cm in diameter. How many cake tins can Safia fit on the oven tray at one time?
PLEASE HELP IM STUCK ON THIS ONE
Triangle GHJ is congruent to triangle EKI by using ASA congruence theorem.
The given triangle are GHJ and EKI.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Consider ΔGHJ and ΔEKI
∠H = ∠K (Given in figure)JK=HI (Given in figure)∠EIK = ∠GJH (Given in figure)IK=JK+IJ (segment addition postulate JK=HI, add IJ to the equivalents)HJ=HI+IJ (segment addition postulate JK=HI, add IJ to the equivalents)IK=HI+IJ (substitution property)HJ=IK (transitive property)ΔGHJ ≅ ΔEKI (By ASA congruence theorem)Hence, proved triangle GHJ is congruent to triangle EKI by using ASA congruence theorem.
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