The equation of the perpendicular line as required is; y = 2x -3.
What is the equation of the perpendicular line?Since the line in discuss is perpendicular to the given line whose slope is; -1/2. It therefore follows that the slope of the line to be determined is;
m = -1/(-1/2) = 2.
The equation of the required line can therefore be written as;
2 = (y-7)/(x-2)
2x -4 = y -7
Hence, y = 2x -3 is the equation of the line.
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5x-4y=19
x+2=8
Solve simultaneous equation
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.
What term in the sequence is the value 107?
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!
Jackson has a gift card for $120 to use at a department store. he wants to purchase 2 shirts and 3 pairs of pants with his gift card. if x represents the cost of the shirts and y represents the cost of the pants, what are the domain and range of this relationship?
0 ≤ x ≤ 60
The range of this relationship can be defined as,0 ≤ y ≤ 40
Definition of Domain and Range
The set of all the possible input values for which the provided function is defined is termed as the domain of that function.
The set of all the possible values that a given function can generate as an output is termed as the range of that function.
Forming the Relation
It is given that,
Jackson wants to purchase 2 shirts and 3 pairs of pants with his gift cardx represents the cost of the shirts and y represents the cost of the pantsThe limit of the gift card = $120Thus, the relation formed is given by,
[tex]2x + 3y \leq 120[/tex]
Domain and Range of the Given Relation
We have,
[tex]2x + 3y \leq 120[/tex]
⇒ [tex]2x \leq 120[/tex]
⇒ [tex]x\leq60[/tex]
Thus, the domain is given by,
⇒ [tex]0\leq x\leq 60[/tex]
Similarly,
[tex]3y\leq 120[/tex]
⇒ [tex]y\leq 40[/tex]
Thus, the range is given by,
⇒ [tex]0\leq y\leq 40[/tex]
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determine intervals when the graph is concave up or concave down
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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What is the solution of √x+ 12 =
= x?
O x = -3
O x = 4
O x = -3 or x = 4
Ono solution
PLEASE HELP
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
Solve the following equation:
(d - 3) tan 37°
17
Give your answer to 1 d.p.
-
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)
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]
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
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
[tex] \bf \huge x {}^{2} + 5 = 6[/tex]
solve for x :
[tex] \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]
[tex] \tiny \textsf{Song recommendations \:? }~ [/tex]
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]
i am not able to solve this problem
Answer:
C
Step-by-step explanation:
you know the drill
what is the slope of the line shown below
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.
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.
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.
PLEASE I NEED THIS
SO MANY POINTS
The speed of Sali is 18.75 km/hr.
Given,
Total distance travelled by Jane and Sali =63 km.
The total time is taken by Jane=3.5 hours.
Sali started to cycle 4 minutes after Jane started to cycle [tex]=\frac{4}{60}=\frac{1}{15}[/tex] hours.
What is the formula to find speed?The formula to find speed is [tex]Speed=\frac{Distance}{Time} \ km/hr[/tex].
The speed of Jane[tex]=\frac{63}{3.5}=18 \ km/hr[/tex].
Let the speed of Sali be [tex]x \ km/hr[/tex].
Sali caught up with Jane when they had both cycled 30 km.
Thus, [tex]\frac{30}{18}-\frac{30}{x}=\frac{1}{15}[/tex]
[tex]\implies \ \frac{30x-540}{18x} =\frac{1}{15}[/tex]
[tex]\implies \ 15(30x-540)=18x[/tex]
[tex]\implies \ 5(30x-540)=6x[/tex]
[tex]\implies \ 150x-2700=6x[/tex]
[tex]\implies \ 144x=2700\implies \ x=18.75[/tex]
Therefore, the speed of Sali is 18.75 km/hr.
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If −1 is a zero of the polynomial p(x)=ax^3−x^2+x+4, find the value of a.
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
Geometry question I’m confused with this help
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
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.
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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How many 50c make up $200
Answer:
40. 50c goes into 200 40 times
X=
Help mea please thank u :)
The value of x is the length GH, which is determined as 6.
Value of xThe value of x is the length GH and can be calculated from Pythagoras theorem.
|OG|² = |OS|² + |SG|²
|OG|² = 9² + 12²
|OG|² = 225
|OG| = √225
|OG| = 15
x + H = |OG|
where;
H is radius of the circle = 9x + 9 = 15
x = 15 - 9
x = 6
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a circular field was fenced using 66 posts placed two metres apart what is the area of the field in square metres
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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PROBLABILITY!!!
(I added the picture needed)
1.Create a sample space and find the product of each combination. What is the probability that a person wins the game? Express your answer as a fraction in lowest terms and as a percent rounded to the nearest tenth.
(answer to this one is 9/28 and 32.1%)
2. You realize a short time into the carnival that you don’t have enough prizes to last the entire event. You call your teacher, and she suggests that you change the winning number so that a participant will win only 25% of the time. What number will that be? Support your answer.
3. Participants achieving a winning score of 36 or higher in four consecutive attempts will receive a large prize! What is the probability of this occurring?
4. After changing the game rules, participants and the crowd are disappointed when the first five games yield scores of 12, 18, 30, 28, and 24. What statement can you recommend the teacher posts to reassure everyone that the game is fair?
The probability that a person wins the game is 32.1%
How to illustrate the probability?Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.
Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:
= 24 + 4 = 28
The frequency table will be such that 28 or more has a relative frequency of 9. Therefore, the probability that a person wins the game will be:
= 9/28 = 32.1%
When you win 25% of the time, this illustrates that the number of products picked will be:
= 25% × 28
= 7 products.
The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:
= 1/6⁴
= 1/1296
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Help fast. i really need help fast
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
five times Linda’s age is 85
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
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
what’s the sun of -6 4/5 and 6 4/5
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]
Given that
5,6,-2,4,8,1,1,1,1,1
• find the mean
mode
median
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
Please help I’ve tried to answer this 3 times and I keep getting it wrong
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]----------------------------
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!
[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]
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
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:
which of the following statements must be true abut this diagram. check all that apply
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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Easy! 40 PTS!!! Log Functions
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