Answer:
x = 4
Step-by-step explanation:
8(x - [tex]\frac{5}{2}[/tex] ) = 3x ← distribute the parenthesis by 8
8x - 20 = 3x ( subtract 3x from both sides )
5x - 20 = 0 ( add 20 to both sides )
5x = 20 ( divide both sides by 5 )
x = 4
Given the points A(-5,-5) and B(7, 1), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 1:5, but not necessary In that order, give two possible coordinates of point P. Graph segment AB and P in the coordinate plane.
The two coordinates on the segment AB due to internal division are (5,0) and (-3,-4).
What is internal division?
When a point P divides the line joining the two points and the potint P lies in between the two coordinates then the division is internal division. If the point lies outside of the given coordinates then the division is known as external division.
The division is internally because point P lies on the line as given in the question.
The formula for the internal division is as follows:
[tex]X=\frac{mx_1+nx_2}{m+n}\\Y=\frac{my_1+ny_2}{m+n}[/tex]
Since points are A(-5,-5) and B(7,1) hence, [tex]x_1=-5,x_2=7,y_1=-5,y_2=1[/tex] and ratio is 1:5 then [tex]m=1,n=5[/tex].
Substute all value to obtain the coordinates.
[tex]X_1=\frac{1(-5)+5(7)}{1+5}\\X_1=5\\Y_1=\frac{1(-5)+5(1)}{1+5}\\Y_1=0[/tex]
Hence, the first cordinate is (5,0).
As given in the question that the ratio in not necessarily in the order of 1:5 so, consider the ratio is 5:1.
Now, m=5 and n=1.
Again substitute all values in to find the new coordinate.
[tex]X_2=\frac{5(-5)+1(7)}{5+1}\\X_2=-3\\Y_2=\frac{5(-5)+1(1)}{5+1}\\Y_2=-4[/tex]
Hence, another coordinate is (-3,-4).
Hence, the two coordinates on the segment AB due to internal division are (5,0) and (-3,-4).
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Write each as an algebraic expression.
10) the product of 10 and a number n
12) the difference of 19 and a number n
14) The product of 7 and the sum of × and 2
15) The difference of 11 and the quotient of x and 3
11) the sum of a number n and 5
13) a number n squared
Answer:
10) 10n
12) 19-n
14) 7(x+2)
15) x/3 -11
11) n+5
13) n^2
Step-by-step explanation:
product = multiply
difference= subtract
sum = add
quotient = divide
Answer:
lo siento soy nuevo en este aplicación ay mis sierras disculpas
Select all triangles congruent to triangle 4.
Answer:
1, 2, 4, 5
Step-by-step explanation:
You want triangles congruent to triangle 4.
CongruenceIn this exercise, we can determine congruence using SSS congruence: the lengths of the sides in congruent triangles will match. (The order of appearance of the side lengths as you go around the triangle is irrelevant.)
Triangle 4The lengths of the sides are ...
diagonal of 4×2 rectangle5 grid squaresdiagonal of 4×3 rectangleLooking at the other triangles, we see side lengths of ...
Triangle 1All side lengths match: congruent to 4.
Triangle 2All side lengths match: congruent to 4.
Triangle 3One side is 6 grid squares: not congruent.
Triangle 5All side lengths match: congruent to 4.
Triangle 6One side is 6 grid squares: not congruent.
Triangle 7One side is the diagonal of a 3×2 rectangle: not congruent.
Triangle 8One side is the diagonal of a 4×1 rectangle: not congruent.
__
Additional comment
Triangles 3 and 6 are congruent to each other, but not to triangle 4.
< GRADES / 2022 RATIOS AND PROPORTIONS UNIT TEST Q21
21
What percent represents the shaded part of the hundredths grid shown?
Answer: A) 0.05%
Step-by-step explanation: Converting the shaded area of the hundredths grid to a fraction would be 5/100 (or 1/20 simplified). Then convert 5/100 to a percentage by calculating 5 ÷ 100, which is 0.005%, therefor the answer is A.
find the salary of a person who is paid $3,800.00 per month
Answer:45600
Step-by-step explanation: 3800x12
Use a quadratic equation to find two real numbers with a sum of 31 and a product of 210?
The quadratic equation whose sum of two real roots is 31 and product is 210 will be [tex]x^{2} -31x+210 = 0[/tex].
According to the question,
We have the following information:
The sum of roots of a quadratic equation = 31
The product of roots of a quadratic equation = 210
We know that the standard form of the quadratic equation is given as follows:
[tex]ax^{2} +bx+c = 0[/tex]
Now, the sum of roots is -b/a and the product of roots is c/a.
So, we have the following expressions:
-b/a = 31
b = -31 and a = 1
c/a = 210
c = 210 and a = 1
So, the equation will be:
[tex]x^{2} -31x+210 = 0[/tex]
Hence, the quadratic equation whose sum of two real roots is 31 and product is 210 will be [tex]x^{2} -31x+210 = 0[/tex].
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In this problem we determine the first time after 10 o'clock at which the minute hand and the hour hand of a clock point in the exact same direction ( meaning when they are " on top of" each other). See if you can find the time on your own before reading the following steps. ( Assume that both hands move continously. For example, from 10 o'clock to 11 o'clock, the hour hand smoothly and gradually moves from pointing at the 10 to pointing at the 11.)
a) Let m be the number of mintues after 10 o'clock at which the minuet hand and hour hand are pointing in the same direction. In terms of m, trhough what fraction of hte entire face of the clock has the minute hand traveled during the m minutes after 10 o'clock?
b) In terms of m, what fraction of hte distance from 10 to 11 has the hour hand traveled during the m minutes after 10 o'clock?
c) Trough what farction of the entire clock's face doe sthe hour hand travel during the m minutes after 10 o'clock?
d) At what exact time do the minute hand and hour hand point in the same direction?
( GIVE BRAINLIST IF CORRECT AND ANSWER!! )
Answer:
a) 1:25 b) 2:06 c) 5:00 d) 4:10
Step-by-step explanation:
Which expression is equal to 14y−17+512y+6 , expressed in simplest form?
Answer:
526y-11
Step-by-step explanation:
14y-17+512y+6=526y-11
Answer:
Option (C)
Step-by-step explanation:
To simplify an expression, we can combine like terms. For this expression, there are two pairs of like terms, one-fourth y and five-twelfths y, and the constants negative seventeen and six.
To combine the fractions, we can find the least common denominator, twelve, so we can rewrite the fraction as three-twelfths.
Now combine the like terms to get eight-twelfths y minus eleven, which simplifies to two-thirds y minus eleven.
Please help me out don’t answer if you don’t know I would really appreciate it ;)
What is the simplified version of each expression? Assume all variables are positive
Answer:
A) 3
B) 2[tex]\sqrt{6}[/tex]
C) 3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
A
3x3 = 9
B
24 = 2x2x2x3 We can pull out a pair of 2 and are left with 6
C
18 = 2x3x3 We can pull out a pair of 3 and are left with 2
Does y vary directly with x? If it does, what is an equation for the direct variation?
The variable y varies directly with x and the variation equation is (b) y = -1/2x
How to determine the equation of the variation?The graph represents the given parameter
On the graph, we can see that:
The values of x are divided by -2 to get y
This means that the graph represents a direct variation
Recall that we stated that:
The values of x are divided by -2 to get y
This means that the constant of variation is -1/2
The direct variation equation is represented as:
y = kx
Where k represents the constant of variation i.e. k = -1/2
Substitute the known values in the above equation So, we have the following equation
y = -1/2x
Hence, the equation of variation is y = -1/2x
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A pirate ship found a treasure chest that contained 127 gold coins and 253 silver coins. If there are 38 pirates on the ship and they split the coins evenly, how many coins did they collect?
A. 10
B. 11
C. 380
D. 418
The number of coins that the pirates collect is A. 10.
How to calculate the value?From the information, the pirate ship found a treasure chest that contained 127 gold coins and 253 silver coins and there are 38 pirates on the ship.
The number of coins that way person will get will be:
=>Total coins / Number of pirates
= (253 + 127) / 38
= 380 / 38
= 10
Each person gets 10 coins.
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Find the perimeter of triangle ABC. Round your answer to two decimal places.
Check the picture below.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-7}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{-8}) ~\hfill AB=\sqrt{(~~ 3- (-7)~~)^2 + (~~ -8- 2~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 10)^2 + ( -10)^2} \implies \boxed{AB=\sqrt{ 200 }}[/tex]
[tex]B(\stackrel{x_1}{3}~,~\stackrel{y_1}{-8})\qquad C(\stackrel{x_2}{-4}~,~\stackrel{y_2}{-9}) ~\hfill BC=\sqrt{(~~ -4- 3~~)^2 + (~~ -9- (-8)~~)^2} \\\\\\ ~\hfill BC=\sqrt{( -7)^2 + ( -1)^2} \implies \boxed{BC=\sqrt{ 50 }} \\\\\\ C(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-9})\qquad A(\stackrel{x_2}{-7}~,~\stackrel{y_2}{2}) ~\hfill CA=\sqrt{(~~ -7- (-4)~~)^2 + (~~ 2- (-9)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -3)^2 + (11)^2} \implies \boxed{CA=\sqrt{ 130 }} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{\LARGE perimeter}}{\sqrt{200}~~ + ~~\sqrt{50}~~ + ~~\sqrt{130}} ~~ \approx ~~ \text{\LARGE 32.61}[/tex]
Gary and Kathy's restaurant bill comes to $35.50. They are planning to tip the waiter 20%. How much money will they pay including the tip?
Answer: $42.60
Step-by-step explanation:
divide $35.50 by 5 and then add the quotient ---> $7.10, to $35.50, which equals $42.60.
This is part B to my last question
The y-intercept of the graph of the function g(n) represents the height of the flower.
We are given:
A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, after n days.
g(n) = 10(1.02)^n
which is an exponential function.
We need to find what the y-intercept of the graph of the function g(n) represents.
We have the exponential function;
g(n) = 10(1.02)^n
where,
x-coordinate of the graph represents the number of days.
y-coordinate of the graph represents the height of the flower.
Thus, the y-intercept of the graph of the function g(n) represents the height of the flower.
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I need help please!!
the slope of the given point is m=2/17
Jerry has 4 1/2 cup of strawberry he use 3/4 cup of a strawberry to make a breakfast smoothie he wants to use the remaining strawberry to make pancakes if he takes 1 1/4 cup of strawberries to make one pancake how many pancake can he make.
Jerry will able to make 3 pancakes if he has 4 1/2 cup of strawberry from which he make use of 3/4 strawberry to make breakfast smoothie and he need 1 1/4 cup of strawberries to make one pancake.
Total strawberry Jerry has = 4 1/2 cup = 9/2 cups
Strawberry used to make smoothies = 3/4 cup
Remaining strawberries
= 9/2 - 3/4
= (18-3)/4 = 15/4
To make one pancake, Jerry needs = 1 1/4 cup = 5/4 cup
Number of pancakes Jerry can make = 15/4/5/4 = 3 pancakes
Hence, the number of pancakes, Jerry can make is 3
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What translation is made from f(x) → f(x) + 6? sliding it up reflection across the y-axis rotation around the origin reflection across the x-axis
The translation made from f(x) → f(x) + 6 is sliding it up
what is translation in geometry?A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction.
A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.
Any translation in a Euclidean space is an isometry.
the translation made from f(x) → f(x) + 6 involves moving the graph up 6 units
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The pharmacists milkweed concoction didn’t work. It only gave the queen split ends. However, the queen, in a rare kind hearted moment, agreed to let the pharmacist try again. This time he has decided to combine a mixture 50% sorghum with a mixture containing 75% sorghum to create a 10 ounce mixture containing 60% sorghum. How many ounces of the 50% mixture should the pharmacist use?
The ounces of the 50% mixture that the pharmacist should use is 6 ounce.
How to calculate the ounces?From the information, we need two equations to solve this problem.
equation 1:
x + y = 10
equation 2:
.5x + .75y = 10(.6)
set y = 10 - x
.5x + .75(10-x) = 6
.5x + 7.5 - .75x = 6
.5x -.75x = 6 - 7.5
-.25x = -1.5
Divide
x = -1.5/-.25
x = 6
Therefore, 6 ounce of the 50% sorghum are required.
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help please!!! asap!
Answer:
The registration fee is $28
Step-by-step explanation:
5,600/100=56 which is 1% of 5,600.
56/2=28 which is 0.5% of 5,600.
;)
Answer: $28
Step-by-step explanation:
you calculate what 0.5 percent is of 5,600 :)
Kenya went to the convenience store to buy some snacks. She spent a total of $12. 00 on soda and candy. The soda cost $3. 00 and each candy bar cost $1. 50. If kenya bought one soda, how many candy bars did kenya buy?.
The number of candy bar that she bought is 6
The total amount that she spend for soda and candy= $12
The cost of one soda = $3
The cost of one candy bar = $1.50
Number of soda that she bought = 1
Consider the number of candy bar that she bought as x
Then the equation will be
3×1 + 1.50 × x = 12
Multiply the terms
3 + 1.50x = 12
Move 3 to right hand side of the equation
1.50x = 12 - 3
1.50x = 9
Move 1.50 to the right hand side of the equation
x = 9 / 1.50
x = 6
Hence, the number of candy bar that she bought is 6
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
A, B, E
Step-by-step explanation:
You want three true statements describing the circle whose equation is ...
x² + y² – 2x – 8 = 0
GraphA graphing calculator can plot this equation for you. The result is attached.
We see that ...
The radius of the circle is 3 units.The center of the circle lies on the x-axis.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.__
Additional comment
The standard form equation of a circle is ...
(x -h)² +(y -k)² = r² . . . . . center (h, k), radius r
Rearranging the given equation to this form, we have ...
(x -1)² +y² = 8 +1 = 9 . . . . . . . . r²=9 ⇒ r=3
This means the center is (1, 0), and the radius is 3. The point (1, 0) is on the x-axis.
The circle with equation x² + y² = 9 is centered at the origin and has radius 3.
−2 1/4×(−1 1/3)[tex]−2 1/4×(−1 1/3)[/tex]
The value after multiplying the given mixed fractions is 7/6 .
In the question ,
it is given that ,
the two mixed fraction are given as [tex]-2\frac{1}{4}[/tex] and [tex]-1\frac{1}{3}[/tex] ,
we need to find their value after multiplication .
we first convert the mixed fractions into improper fraction ,
So ,
[tex]-2\frac{1}{4}[/tex] = (-2×4+1)/4 = (-8+1)/4 = -7/4
and
[tex]-1\frac{1}{3}[/tex] = (-1×3+1)/3 = (-3+1)/3 = -2/3
So , the product of -7/4 and -2/3 is written as
= -7/4 × -2/3
= (-7 × -2)/(4 × 3)
= 14/12
after simplifying ,
= 7/6
Therefore , The value after multiplying the given mixed fractions is 7/6 .
The given question is incomplete , the complete question is
Find the value after multiplying the given mixed fraction [tex]-2\frac{1}{4} \times -1\frac{1}{3}[/tex] .
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What did the king krum call the royal math and science teacher
Answer: HISFAVORITESUBJECTS
Step-by-step explanation:
A group consisting of 42 aggressive zombies triples in size every hour. Which equation matches the number of zombies after 2 hours?
The equation that matches the number of zombies after 2 hours is z = 42 × 3².
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, a group consisting of 42 aggressive zombies triples in size every hour.
Let the number of zombies be z.
Therefore, the equation that matches the number of zombies after 2 hours will be:
= 42 × 3^n
= 42 × 3²
= 42 × 9
= 378 zombies
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For each of the six plots, identify the strength of the relationship (e.g. weak, moderate, or strong) in the data and whether fitting a linear model would be reasonable. a. strong relationship, a linear model would NOT be reasonable b. strong relationship, a linear model would NOT be reasonable c. strong relationship, a linear model would be reasonable d. weak relationship, a linear model would be reasonable e. weak relationship, a linear model would NOT be reasonablelX f. moderate relationship, a linear model would be reasonable
The strength and relationships of the given data is verified as reasonable.
Given,
Determine the degree of the link (weak, moderate, or strong) in each of the six plots and if it is reasonable to fit a linear model to the data.
(a) There is a moderate relationship in the data. A linear model should not be reasonable.
→ From the plot here, it is clear that the data is following a quadratic trend, so a linear model should not be reasonable. On the other hand, it is also clear that the data is scattered more than a little around the approximate quadratic trend line, so there is a moderate relationship in the data.
(b) There is a strong relationship in the data. A linear model should be reasonable.
→ From the plot here, it is clear that the data is following a linear trend, so a linear model should be reasonable. On the other hand, it is also clear that the data is scattered almost a little around the approximate linear trend line, so there is a strong relationship in the data.
(c) There is a weak relationship in the data. A linear model should not be reasonable.
→ From the plot here, it is clear that the data is not following any trend, so a linear model should not be reasonable. On the other hand, it is also clear that the data is scattered everywhere, so there is a weak relationship in the data.
(d) There is a moderate relationship in the data. A linear model should not be reasonable.
→ From the plot here, it is clear that the data is following a quadratic trend, so a linear model should not be reasonable. On the other hand, it is also clear that the data is scattered more than a little around the approximate quadratic trend line, so there is a moderate relationship in the data.
(e) There is a strong relationship in the data. A linear model should be reasonable.
→ From the plot here, it is clear that the data is following a linear trend, so a linear model should be reasonable. On the other hand, it is also clear that the data is scattered almost a little around the approximate linear trend line, so there is a strong relationship in the data.
(f) There is a weak relationship in the data. A linear model should not be reasonable.
→ From the plot here, it is clear that the data is not following any trend, so a linear model should not be reasonable. On the other hand, it is also clear that the data is scattered everywhere, so there is a weak relationship in the data.
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What is the constant rate of change in this equation? Write only the number as your answer y=5x + 12
Answer:
The slope (constant rate of change) is 5.
Find the equation of the parabola with the given x-intercepts and point on the graph. Use y = a(x-p)(x-q).
1. x-int: (-2,0) , (5,0)
P (3,6)
Answer:
Below
Step-by-step explanation:
a(x-p)(x-q) p = -2 q = 5
a ( x- - 2)(x - 5) sub in the values of the point given (3,6) to calculate 'a'
6 = a (3+2)(3-5)
a = -6 /10 = - 3/5
y = -3/5 (x+2)(x-5)
Answer:
[tex]\textsf{Intercept form}: \quad y=-\dfrac{3}{5}(x+2)(x-5)[/tex]
[tex]\textsf{Standard form}: \quad y=-\dfrac{3}{5}x^2+\dfrac{9}{5}x+6[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
If the x-intercepts are (-2, 0) and (5, 0) then:
p = -2q = 5Substitute the values of p and q into the formula:
[tex]\implies y=a(x-(-2))(x-5)[/tex]
[tex]\implies y=a(x+2)(x-5)[/tex]
To find a, substitute the given point on the curve P (3, 6) into the equation:
[tex]\implies 6=a(3+2)(3-5)[/tex]
[tex]\implies 6=a(5)(-2)[/tex]
[tex]\implies 6=-10a[/tex]
[tex]\implies a=\dfrac{6}{-10}[/tex]
[tex]\implies a=-\dfrac{3}{5}[/tex]
Substitute the found value of a into the equation:
[tex]\implies y=-\dfrac{3}{5}(x+2)(x-5)[/tex]
Expand to write the equation in standard form:
[tex]\implies y=-\dfrac{3}{5}(x^2-3x-10)[/tex]
[tex]\implies y=-\dfrac{3}{5}x^2+\dfrac{9}{5}x+6[/tex]
The amount of chlorine needed to treat a wimming
pool i directly proportional to the volume of the pool
The constant of proportionality for the relationship is 0.002.
We are provided that amount of chlorine needed is directly proportional to the volume of the pool .
So we can formulate the relation as
C = kV ... (1) ( where C = amount of chlorine ,
k = constant of proportionality
V = volume of the pool )
the sample ratio of chlorine to the the volume of pool , we have :
5 : 2500
10 : 5000
15 : 7500
So taking the first sample value and putting it in eqn (1)
we get
5 = k (2500)
therefore,
k = 5/ 2500
k = 0.002
So the constant of proportionality will be 0.002
Similarly if we take the other values also the constant of proportionality will remain the same.
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Daniela bakes 36 cookies and gives 2 cookies to her friends
anwser: she has 34 cookies left
9. If XYZ LMN, what is the length of XZ?
The two triangles are congruent.
So, their corresponding sides will be equal.
So, 2x+5 = 5x-19
3x = 24
x = 8 cm.
So, XZ = 2*8+5 = 21 cm