5 Quick algebra 1 questions for 50 points!
Only answer if you know all 5, Tysm! :)
Answers
The equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4
How to determine the equations?When a linear equation is represented as:
Ax + By = C
The slope (m) is:
m = -A/B
When the linear equation is represented as:
y = mx + c
The slope is m
A line perpendicular to a linear equation that has a slope of m would have a slope of -1/m
Using the above highlights, the equations of the lines are:
6. y = -2x + 5; (2, 7)
The slope is:
m = -2
The perpendicular slope is:
n = 1/2
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 1/2(x - 2) + 7
Evaluate
y = 1/2x - 1 + 7
This gives
y = 1/2x + 6
7. y = -5; (11, 15)
The slope is:
m = 0
The perpendicular slope is:
n = 1/0 = undefined
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 15
8. Graph ; (-12, 10)
The slope is:
m = (y2 - y1)/(x2 - x1)
Using the points on the graph, we have:
m = (2 - 3)/(3 - 4)
m = 1
The perpendicular slope is:
n = -1
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = -1(x + 12) + 10
y = -x - 12 + 10
Evaluate
y = -x - 2
9. y = -1/6x + 1; (-2, -9)
The slope is:
m = -1/6
The perpendicular slope is:
n = 6
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 6(x + 2) - 9
Evaluate
y = 6x + 12 - 9
This gives
y = 6x + 3
10. 6x + 2y = 14; (12, 0)
The slope is:
m = -6/2
m = -3
The perpendicular slope is:
n = 1/3
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 1/3(x - 12) + 0
Evaluate
y = 1/3x - 4
Hence, the equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4
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Related Questions
5x-4y=19
x+2=8
Solve simultaneous equation
Answers
Answer:
x = 6, y = 5
Step-by-step explanation:
5x - 4y = 19 -------> equation 1
x + 2 = 8 --------> equation 2
Step 1 : Subtract 2 on both sides in equation 2.
x + 2 - 2 = 8 - 2
x = 6
Step 2 : Substitute the value of x is equation 1.
5 ( 6 ) - 4y = 19
( 5 * 6 ) - 4y = 19
30 - 4y = 10
Step 3 : Subtract 30 on both sides.
30 - 30 - 4y = 10 - 30
- 4y = - 20
Step 4 : Multiply - 1 on both sides.
- 1 * - 4y = - 1 * - 20
4y = 20
Step 5 : Divide 4 on both sides.
4y / 4 = 20 / 4
y = 5
Hence,
x = 6
y = 5
Answer:
x = 5, y = 3/2.
Step-by-step explanation:
5x-4y=19
x+2y =8 Multiply this by 2:
2x + 4y = 16 Adding this to first equation 1:
7x = 35
x = 5
So
5 + 2y = 8
2y = 3
y = 3/2.
Todd is attempting to predict how much money his furniture company will make based on the amount raw materials the company currently has at its disposal. The average profit from the sale of 1 piece of furniture can be expressed 2x-2 as and the average number of pieces of furniture that can be made using the current supply of raw materials can be expressed as 2x-2. What polynomial function can Todd use to calculate the average profit
Answers
Answer:
[tex]4x^{2} -8x+4[/tex]
Step-by-step explanation:
The average profit expression is for 1 piece of furniture
The amount of furniture is another expression
So we have to multiply both expressions to get the total profit.
(2x-2) (2x-2) = 4x^2 - 4x - 4x + 4
= 4x^2 - 8x + 4
Which of the following is a valid probability distribution? Probability distribution A is shown. The probabilities of 1, 2, 3, 4, 5 and 6 are all 0.2. Probability distribution B is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.3; 5 is 0.2; 6 is 0.1. Probability distribution C is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.4; 5 is 0.1; 6 is 0.1. Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Answers
Considering the given probability distributions, distribution D is valid.
When a probability distribution is valid?A probability distribution is valid if:
There are no negative probabilities.The sum of all probabilities is of 1.In this problem, only distribution D has a sum of 1, hence it is the only valid distribution.
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Answer:
Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Step-by-step explanation:
The answer above is correct.
What term in the sequence is the value 107?
Answers
Answer:
17th term
Step-by-step explanation:
Substitute [tex]a_{n}[/tex] with the value 107
107=11+6(n-1)
96=6n-6
102=6n
n=17
17th term !!
Hope it helps!
What is the diameter of this circle if the circumference is 30 inches?
Answers
Answer:
d≈9.55
Step-by-step explanation:
the answer is 9.55 inches
Answer:
diameter = 9.55 in
Step-by-step explanation:
Circumference = pi x diameter so re-arrange
circumference / pi = diameter
30 / pi = diameter
9.55 in = diameter
Use the drawing tool(s) to form the correct answer on the provided number line.
Evaluate the following expression when a = 5 and b = 1. Then, plot the resulting value on the provided number line.
12+[2-(4·a²)] ÷ 7+b
Answers
Answer:
1
Step-by-step explanation:
12+[2-(4 × a²)] ÷ 7+b
= 12+[2-(4 × 5²)] ÷ 7+ 1
= 12+[2-(4 × 25)] ÷ 7+ 1
= 12 + (2 - 100)÷ 7 + 1
= 12 - 98 ÷ 7 + 1
= 12 - 14 + 1
= 1
Answer:
-1
Step-by-step explanation:
a circular field was fenced using 66 posts placed two metres apart what is the area of the field in square metres
Answers
Answer:
1386m cubic
Step-by-step explanation:
hope it helps.in case of any other question, you can count on me.good day.
The area of the circular field in square meters will be equal to, 1386 m².
What is the area?An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass a compact figure's surface. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.
As per the given information in the question,
Total number of posts = 66
Distance between two posts = 2 meters
Then, the circumference of the area will be,
= 66 × 2 = 132 meters
Now, let's find the radius of the circle,
C = 2πr
132 = 2 × 3.14 × r
r = 132/(2 × 3.14)
r = 21.01 m
Use the formula for the area of the circle:
A = πr²
A = 3.14 × (21.01)²
A = 441.420 × 3.14
A = 1386 m²
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what is the slope of the line shown below
Answers
Answer:
A. -3
Step-by-step explanation:
Use slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
Use the points given, (-1, 6) and (2,-3)
[tex]\frac{-3-6}{2+1}=\frac{-9}{3}[/tex]
Simplify the answer.
[tex]\frac{-9}{3}=-3[/tex]
The slope of the line is -3.
Hope this helps!
If not, I am sorry.
Please help I’ve tried to answer this 3 times and I keep getting it wrong
Answers
Answer:
[tex] \boxed{\bf A. \: x - 2}[/tex]
Step-by-step explanation:
[tex] \sf ( x + 1)^2-9/ x + 4 [/tex]
First, we need to factor the expressions that are not already factored.
[tex] \sf ( x - 2) ( x + 4) / x + 4 [/tex]Now, let's Cancel out x+4 in both numerator and denominator.
[tex] \sf x - 2 [/tex]----------------------------
[tex] \bf \huge x {}^{2} + 5 = 6[/tex]
solve for x :
[tex] \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]
[tex] \tiny \textsf{Song recommendations \:? }~ [/tex]
Answers
Given :
x² + 5 = 6Subtract 5 from each side :
x² + 5 - 5 = 6 - 5x² = 1Take the root on each side :
√x² = √1x = ±1Hence, the values of x are :
[tex]\fbox {x = 1}[/tex][tex]\fbox {x = -1}[/tex][tex]x^2+5=6\\x^2=1\\x=1 \vee x=-1[/tex]
(y^3-2)(y^2+11) what is the answer
Answers
Answer:
[tex]y^{5}[/tex] + 11y³ - 2y² - 22
Step-by-step explanation:
(y³ - 2)(y² + 11)
each term in the second factor is multiplied by each term in the first factor.
y³(y² + 11) - 2(y² + 11) ← distribute both parenthesis
= [tex]y^{5}[/tex] + 11y³ - 2y² - 22
which of the following statements must be true abut this diagram. check all that apply
Answers
The options w > x, w > y, and x + y = w are correct because the sum of the two interior angles is equal to the exterior angle.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
From the figure,
The interior angle of a triangle is w
w > x (true)
w > y (true)
x + y = w (sum of the two interior angles is equal to the exterior angle)
Thus, the options w > x, w > y, and x + y = w are correct because the sum of the two interior angles is equal to the exterior angle.
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Solve the following equation:
(d - 3) tan 37°
17
Give your answer to 1 d.p.
-
Answers
Answer: 25.6
Step-by-step explanation:
[tex](d-3) \tan 37^{\circ}=17\\\\d-7=\frac{17}{\tan 37^{\circ}}\\\\d=\frac{17}{\tan 37^{\circ}}+3 \approx \boxed{25.6}[/tex]
In the following exercises, multiply the binomials. Use any method.
249. (6p + 5)(p + 1)
Answers
Answer:
Hence the expression [tex]$$(6p+5)(p+1)=6p^2+11p+5$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (6p+5)(p+1).We have to multiply the given expression.Multiply the (6p+5) by 1 , multiply the (6p+5) by p then add like terms.[tex]$$\frac{\begin{matrix}{} & {} & 6p & + & 5 \\ \times & {} & p & + & 1 \\ \end{matrix}}[/tex]
_____________
[tex]{\frac{\begin{matrix}{} & {} & 6p & + & 5 \\ 6{{p}^2} & + & 5p & {} & {} \\ \end{matrix}}{\begin{matrix}6{{p}^2} & + & 11p & + & 5 \\ \end{matrix}}}$$[/tex]
i am not able to solve this problem
Answers
Answer:
C
Step-by-step explanation:
you know the drill
A coordinate grid showing Number of Classes on the horizontal x-axis and Total Cost in dollars on the vertical y-axis with 2 lines. The first line passes through (0, 10) and a point at (4, 32). The second line passes through (0, 0) and a point at (2, 15).
Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. What is the system of equations representing these costs?
y = 5.5x and y = 7.5x + 10
y = 7.5x and y = 5.5x
y = 7.5x and y = 5.5x + 10
y = 7.5x + 10 and y = 5.5x + 10
Answers
The system of equations representing these costs are; y = 7.5x and y = 5.5x + 10
How to find the equation of a line?The slope of the first line is;
m = (y2 - y1)/(x2 - x1)
m = (32 - 10)/(4 - 0)
m = 5.5
Now, the first coordinate has a y-intercept of 10. Thus, the equation here for the cost is; y = mx + c = 5.5x + 10
The slope of the second line is;
m = (y2 - y1)/(x2 - x1)
m = (15 - 0)/(2 - 0)
m = 7.5
Now, the first coordinate has a y-intercept of 0. Thus, the equation here for the cost is; y = mx + c = 7.5x + 0 = 7.5x
Thus, the system of equations representing these costs are;
y = 7.5x and y = 5.5x + 10
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Answer:
y = 7.5x and y = 5.5x + 10
Step-by-step explanation:
Geometry question I’m confused with this help
Answers
Answer: ∠PQR = 130°
Step-by-step explanation:
The word bisects means that angle PQS and SQR are equal to each other.
3x + 5 = 2x + 25
3x = 20
x = 20
Now, we will plug this value back in and solve for angle PQR. There are three ways we could do this.
[1]
(3x + 5) + (2x + 25)
(3(20) + 5) + (2(20) + 25)
(60 + 5) + (40 + 25)
(65) + (65)
130 degrees
[2]
(3x + 5) * 2
(3(20) + 5) * 2
(65) * 2
130 degrees
[3]
(2x + 25) * 2
(2(20) + 25) * 2
(65) * 2
130 degrees
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
Kindly help!
Answers
[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]
★ Radius of first sphere [tex]\sf r_{1}[/tex] = 6cm.
★ Radius of second sphere [tex]\sf r_{2}[/tex] = 8cm.
★ Radius of third sphere [tex]\sf r_{3}[/tex] = 10cm.
[tex] {\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}[/tex]
★ The radius of the resulting sphere formed.
[tex] {\large{\textsf{\textbf{\underline{\underline{Formula \: used :}}}}}}[/tex]
[tex]\star \: \tt Volume \: of \: sphere = {\underline{\boxed{\sf{\red{ \dfrac{ 4}{3}\pi {r}^{3} }}}}}[/tex]
[tex] {\large{\textsf{\textbf{\underline{\underline{Concept :}}}}}}[/tex]
★ As, three spheres are melted to from one new sphere. Therefore, volume of three old sphere is equal to volume of new sphere.
i.e, Volume of first sphere + volume of second sphere + volume of third sphere = Volume of new sphere.
[tex] {\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]
Let,
The radius of resulting sphere be [tex]R[/tex]
According to the question,
• Volume of first sphere + volume of second sphere + volume of third sphere = Volume of new sphere.
[tex] \longrightarrow \sf \dfrac{4}{3} \pi {(r_{1})}^{3} + \dfrac{4}{3} \pi {(r_{2})}^{3} + \dfrac{4}{3} \pi {(r_{3})}^{3} = \dfrac{4}{3} \pi {(R)}^{3} [/tex]
• here
☆[tex]\: \sf r_{1}[/tex] = 6cm
☆[tex]\: \sf r_{2}[/tex] = 8cm
☆[tex]\: \sf r_{3}[/tex] = 10cm
Putting the values,
[tex] \longrightarrow \sf \dfrac{4}{3} \pi {(6)}^{3} + \dfrac{4}{3} \pi {(8)}^{3} + \dfrac{4}{3} \pi {(10)}^{3} = \dfrac{4}{3} \pi {(R)}^{3} [/tex]
Taking " [tex]\dfrac{4}{3} \pi [/tex]" common,
[tex] \longrightarrow \sf \dfrac{4}{3} \pi \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = \dfrac{4}{3} \pi {(R)}^{3} [/tex]
[tex]\longrightarrow \sf \cancel{ \dfrac{4}{3} \pi} \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = \cancel{ \dfrac{4}{3} \pi } {(R)}^{3} [/tex]
[tex]\longrightarrow \sf \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = {(R)}^{3} [/tex]
[tex]\longrightarrow \sf \bigg[ 216 +512 + 1000 \bigg] = {(R)}^{3} [/tex]
[tex]\longrightarrow \sf 1728 = {(R)}^{3} [/tex]
[tex]\longrightarrow \sf \sqrt[3]{1728} = R[/tex]
[tex]\longrightarrow \sf \sqrt[3]{ 12 \times 12 \times 12 } = R[/tex]
[tex]\longrightarrow \sf \sqrt[3]{ {(12)}^{3} } = R[/tex]
[tex]\longrightarrow \sf R = \red{12 \: cm} [/tex]
Therefore,
Radius of the resulting sphere is 12cm.
[tex]{\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}[/tex]
★ Figure in attachment.
[tex]{\underline{\rule{290pt}{2pt}}}[/tex]
Help fast. i really need help fast
Answers
Answer: 80 miles
Step-by-step explanation:
- 400/5 = 80
- so 80 is 1/5 of 400
hope this helps :)
Answer:
80 miles
Step-by-step explanation:
The whole journey is 400 miles, so we say that he traveled x miles, where x equals 400.
if we multiple 1/5 by x miles, then we will get how much he travels
1/5*x = 1/5*(400), since x = 400, so you can replace x with 400
1/5*x=1/5*400=400/5=80 miles
Identify the axis of symmetry the function graphed below.
Answers
Answer: A. X = -1
Step-by-step explanation:
An axis of symmetry is the line that divides the object into two equal halves, creating a mirror-like reflection. Only at x = -1 will that occur.
If −1 is a zero of the polynomial p(x)=ax^3−x^2+x+4, find the value of a.
Answers
Answer:
a = 2
Step-by-step explanation:
given x = - 1 is a zero then f(- 1) = 0 , that is
a(- 1)³ - (- 1)² - 1 + 4 = 0
- a - 1 - 1 + 4 = 0
- a + 2 = 0 ( subtract 2 from both sides )
- a = - 2 ( multiply both sides by - 1 )
a = 2
Easy! 40 PTS!!! Log Functions
Answers
Answer:
C
Step-by-step explanation:
When x is negative 1/2 ^x becomes 1 / ( 1/2 ^x) meaning it is quite large as x becomes more negative
when x = 0 the value is 1
as x increases from 0 to + inf the value becomes smaller...but never negative
the only graph that fits is C
What is the solution of √x+ 12 =
= x?
O x = -3
O x = 4
O x = -3 or x = 4
Ono solution
PLEASE HELP
Answers
Answer:
x₁ = 4
(x₂ = -3)
Step-by-step explanation:
√(x + 12) = x
x + 12 = x²
x² - x - 12 = 0
Δ = 49
x = (1 ±√Δ)/2
x₁ = 4
x₂ = -3
the right solution is 4 this can be seen by inserting the solutions found in the starting equation
what’s the sun of -6 4/5 and 6 4/5
Answers
Answer:
the answer is 0.
Step-by-step explanation:
When you are adding two of the same numbers together, and one of them is positive while the other is negative, they cancel each other out.
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathsf{-6 \dfrac{4}{5} + 6 \dfrac{4}{5}}[/tex]
[tex]\mathsf{= \dfrac{-6 \times 5 + 4}{5}+ \dfrac{6 \times 5 + 4}{5}}[/tex]
[tex]\mathsf{= \dfrac{-30 + 4}{5}+ \dfrac{30 + 4}{5}}[/tex]
[tex]\mathsf{= \dfrac{-34}{5} + \dfrac{34}{5}}[/tex]
[tex]\mathsf{= 0}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{0}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
determine intervals when the graph is concave up or concave down
Answers
The graph is concave has two curved part as follows;
The graph is concave up between;(0, 1), and (1, 0)The graph is concave down between; (0, 1), and (-a, 2)How can the direction of concavity be found?The direction the concave part of the graph faces is given as follows;
The graph is concave up when the concave part faces up
It is concave down when the concave part faces down
From the given diagram, we have;
The graph is concave up between;
(0, 1), and (1, 0)
The graph is concave down between; (0, 1), and (-a, 2)
Where a is in the range; 1 < a < 2
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Cai invests £2500 in an account that pays 3.55% simple interest interest per year. He takes out his money after 2.75years. what is the value of the investment when he takes out the investment
Answers
Answer:
So now,
you know the formula for simple interest is P×R×T divided by a hundred?
So 2500 times 3.55 times 2.75 divided by 100
Which statements accurately describe the function f(x) = 3(18)"? Select three options.
The domain is all real numbers.
The range is y> 3.
The initial value is 3.
The initial value is 9.
The simplified base is 3√2.
Answers
The initial value of the function f(x) = 3(18)ˣ is 3. The domain of the function is all real numbers and the range is y > 0
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the function f(x) = 3(18)ˣ, hence:
The initial value of the function f(x) = 3(18)ˣ is 3. The domain of the function is all real numbers and the range is y > 0
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Triangle not drawn to scale
Given: m&A=40°,m&B=88°,a=15cm. Then b
= _?__cm to the nearest hundredth
Answers
Answer:
b = 23.3
Step-by-step explanation:
First, we need to determine whether this is a right or non-right triangle.
We know that the sum of all the angles in a triangle must add up to 180, so we can add angles A and B and subtract the sum from 180:
[tex]180-(40+88)=180-128=52[/tex]
The 52 indicates that it is a non-right triangle, so we must rely on either the law of sines or law of cosines to find the measure of b.
Given that we have angle A and its resulting side, a, along with angle B, we can use the law of sines:
[tex]\frac{sin A}{a}=\frac{sin B}{b}[/tex]
[tex]\frac{sin 40}{15}=\frac{sin 88}{b}\\ \\ 15*sin 88=b * sin 40\\\\b=\frac{b*sin 40}{sin 88}\\ \\b=23.3216=23.3[/tex]
How many 50c make up $200
Answers
Answer:
40. 50c goes into 200 40 times
Given that
5,6,-2,4,8,1,1,1,1,1
• find the mean
mode
median
Answers
Answer:
mean: 2.6, mode: 1, median: 1
Step-by-step explanation:
The mean is essentially the average of the data set which can be defined as: [tex]\frac{\text{sum of data set}}{\text{amount of data in data set}}[/tex]. So adding all the values together you get: [tex]26[/tex]. and counting all the numbers in the data set you find the data set has 10 numbers. This gives you the equation: [tex]\frac{26}{10} = 2.6[/tex] which is the mean
To find the mode, you find which number occurs most frequently, this is of course 1, which can really be determined by just looking at the data set for a second. all the other numbers only occur once, while 1 is in the data set 5 times. So 5 is the mode
To find the median you sort the data, from min to max, and then find the middle number. Sorting the data set gives you. -2, 1, 1, 1, 1, 1, 4, 5, 6, 8. Since this data set has an even amount of numbers, there is not going to be an exact middle. If you go the "middle" which is the 5th and 6th number, you add these two numbers and divide the sum by 2. This gives you: (1+1)/2 = 1 So the median is 1