Answer:
y = [tex]\frac{1}{4}[/tex] x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
4x + y = 7 ( subtract 4x from both sides )
y = - 4x + 7 ← in slope- intercept form
with slope m = - 4
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex] , then
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute )- 4, 5 ) into the partial equation
5 = - 1 + c ⇒ c = 5 + 1 = 6
y = [tex]\frac{1}{4}[/tex] x + 6 ← equation of perpendicular line
you have 600 feet of fencing to enclose a rectangular plot that borders a river if you do not fence the side along the river
45,000 square feet is the largest area that can be enclosed.
What is rectangle?
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.The largest area will always be a square.
600/4=150 feet on each side but one side is not needed
put this 150 feet not needed with the opposite 150 feet to get 300 feet
you have a rectangle 150 by 300 by 150 by the river
= 150 * 300 = 45,000 square feet
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The complete question is -
You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and the width of the plot that will maximize the area. What is the largest area that can be enclosed?
George was solving the equation (2x-1)(x+3)=4 and he got the solution x=1/2 and x=-3. Jeffrey came along and said, "You made a big mistake! You set each factor equal to zero, but it's not equal to zero, it's equal to 4. So you have to set each factor equal to 4 and then solve." Who is correct? Show George and Jeffrey how to solve this equation. To be sure that you are correct, check your solutions.
The solution to the system of equation is -7/2 and 1
Solving linear equationAn algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as the addition, subtraction, division and multiplication.
Given the quadratic equation below;
(2x-1)(x+3)=4
Expand
2x^2+6x-x-3 = 4
2x^2+5x-3-4=0
2x^2+5x-7=0
2x^2-2x+7x-7=0
2x(x-1)+7(x-1) = 0
2x+7 = 0 and x - 1 = 0
x = -7/2 and x = 1
Hence the solution to the system of equation is -7/2 and 1
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. The oxygen saturation of a lake is found by dividing the
amount of dissolved oxygen the lake water currently has
per liter by the dissolved oxygen capacity per liter of the
water, and then converting that number into a percent.
If the lake currently has 6.4 milligrams of dissolved oxy-
gen per liter of water and the dissolved oxygen capacity
is 9.5 milligrams per liter, what is the oxygen saturation
level of the lake, to the nearest percent?
A. 64%
B. 67%
C. 70%
D. 89%
E. 95%
Answer:
70% i think
Step-by-step explanation:
2. State what additional information is required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate
The additional information required to prove the SSS Triangle Congruence Postulate is UT = T F
How to state the additional information required?The congruence postulate is given as:
SSS Triangle Congruence Postulate
The above means that the three sides of the triangles are congruent.
From the figure, the following side lengths are said to be congruent
UV and FV
TV and TV
For the congruence postulate of the triangle to be SSS Triangle Congruence Postulate, then the third corresponding sides must be congruent
This is represented as:
UT = T F
Hence, the additional information required to prove the SSS Triangle Congruence Postulate is UT = T F
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Damian is building a display case to hold
75 model cars. The case will have fewer
than 10 shelves, and each shelf will hold
no more than 15 cars. If Damian wants
each shelf to have the same number of
cars, how many shelves should he put in
the display case?
The cost of 5 gallons of gasoline is $20. Write an equation to show the relationship between the cost, c, and the gallons of gasoline, g. Enter your equation AND your work or explanation in the box provided.
An equation to show the relationship between the cost, c, and the gallons of gasoline, g is; c = 4g
How to interpret a Linear Equation?
The general form of a linear equation in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
We are told that the cost of 5 gallons of gasoline is $20. Thus, the cost of one gallon of gasoline = 20/5 = $4 per gallons
Therefore if he cost is c, and the gallons of gasoline is denoted by g, then the formula to find the cost with these letters is;
c = 4g
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Ed needed to extend the string on his kite. The current string was seven and three fourths feet. He cut a piece of string that measured 8.5 feet and added it to the existing string. What is the new length of the string?
The new length of the string that Ed have now is 16.25 feet.
What is a fraction ?Fraction is some part of a total quantity.
Ed has a kite and a string of length[tex]7\frac{3}{4}[/tex] feet which is = [tex]\frac{31}{4}[/tex] feet.
He wants to extend the sting length so he added another 8.5 feet which is
= [tex]\frac{17}{2}[/tex] feet.
∴ The total length of the string will become
(31/4) + (17/2) feet.
= (31 + 34)/4 feet.
= 65/4 feet.
= 16.25 feet.
So, after he extended his string it has a length of 16.25 feet.
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Answer:
To find the new length of the string, we need to add the length of the new piece of string to the existing length.
The current string length is 7 and 3/4 feet. This can be written as a mixed number, 7 + 3/4 = 7 3/4.
The new piece of string measures 8.5 feet.
To add these two lengths, we can convert the mixed number to an improper fraction and then add the fractions together.
7 3/4 can be converted to an improper fraction as (7 * 4 + 3) / 4 = 31/4.
Now we can add the fractions:
31/4 + 8.5 = (31/4) + (8.5 * 4/4) = 31/4 + 34/4 = 65/4
To simplify the fraction, we can divide the numerator (65) by the denominator (4) to get the whole number part and the remainder.
65 ÷ 4 = 16 remainder 1
So the new length of the string is 16 1/4 feet.
Therefore, the new length of the string is 16 and 1/4 feet.
Step-by-step explanation:
Evaluate.
2/5 exponent 2
Answer: 4/25
Step-by-step explanation:
[tex](\frac{2}{5}) ^2=\frac{2}{5}\times\frac{2}{5}=\large\boxed{\frac{4}{25} }[/tex]
Raheem made a down payment of $250.00 at a local store for an HDTV that cost $880.00 with tax included. He arranged to make 8 equal monthly payments to the store to finish paying for the HDTV. Given that he paid no additional fees, how much was Raheem's monthly payment?
Raheem's monthly payment given that he paid no additional fees is $78.75
How to find Raheem's monthly paymentMonthly payment refers to the amount of money paid by a person every month over a period of time.
Total cost of HDTV = $880.00Down payment = $250.00Number of months to make equal payment = 8Amount remaining after down payment = Total cost of HDTV - Down payment
= $880.00 - $250.00
= $630.00
Amount to pay each month = Amount remaining after down payment / Number of months to make equal payment
= $630.00 / 8
= $78.75
In conclusion, the amount Raheem will pay monthly for a period of 8 months if he paid no additional fees is $78.75
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Which is different? Find “both” answers
Find AC+CB .
Find BC-AC .
Find AB .
Find CA+BC .
The "different" answer is {Blank} The "same" answer is {Blank}.
The different answer is 4 and the same answer is 10.
the possibility that experimental results are due to chance, or some factor other than the experimental variable, is measured by the blank
The possibility that experimental results are due to chance, or some factor other than the experimental variable, is measured by the Probability Value.
What is Probability value?Probability value, also called P-value, is defined as:
Under the premise that the null hypothesis is true, the p-value is the likelihood that test findings will be at least as extreme as the result actually observed.
Now,
According to the definition of probability value, the probability that experimental results are due to chance or some factor, can only be measured by probability value as it fits the context most appropriately.To learn more about probability value, refer to the link: https://brainly.com/question/25638875
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Solve for x and write your answer in simplest form.
x-3(2/3x+3)=3(-3/2x+1)-3/2x
Answer:
x= -6
Step-by-step explanation:
[tex]x-3(\frac{2}{3}x+3)=3(\frac{-3}{2}+1)-\frac{3}{2}\\\\x-2x-9=\frac{-9}{2}+3-\frac{3}{2}\\\\clear fraction\\\\2x-4x-18=-9+6-3\\\\-2x-18=-6\\\\-2x=12\\\\x=-6[/tex]
heidi was able to walk 2/3 of a mile in 12 minutes how far could heidi walk in 1 hour
Heidi is able to walk 10/3 miles in 1 hour (60 min).
What is described as unitary method?It is a method for determining the value of a single unit by subtracting the value of multiple units and subtracting the value of multiple units from of the value of a single unit.
The value of many items is given in the unitary method, and we must either determine the worth of more or fewer items. To do so, we must first determine the value of one item by division and then determine the value of more as well as fewer items by multiplication.Now, for the given question;
It takes Heidi 12 minutes to walk 2/3 miles.
Applying the unitary method.
Then, for in 1 minutes Heidi will walk = 2/(3×12).
For walking in 1 hour or 60 min = (2×60)/(3×12).
Further simplifying;
In 1 hour = 10/3 miles.
Therefore, Heidi would be be able to walk 10/3 miles in 1 hour.
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There are 26 kids who have either black or red pencils.
15 of them have red
21 of them have black
How many kids have both
Answer:
this doesn't make sense cuz 15 have red 21 have black and that's 36 kids but the title says there is 21 kids in all ?
Step-by-step explanation:
Can anyone pleases solve this?
By rationalization and algebra properties, the irrational expression 7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2) is equivalent to the integer 1.
How to simplify a subtraction of irrational fractions
In this question we find a composite irrational expression formed by a irrational fraction being subtracted by other two irrational fraction. Eliminating the irrational denominators by transforming it into rational numbers is an important step for this question, this can be done by means of rationalization, along with algebra properties.
The complete procedure of this exercise is shown below:
7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2)
[7√3 · (√10 - √3)] / [(√10 + √3) · (√10 - √3)] - [2√5 · (√6 - √5)] / [(√6 + √5) · (√6 - √5)] - [3√2 · (√15 - 3√2)] / [(√15 + 3√2) · (√15 - 3√2)]
(7√30 - 21) / 7 - (2√30 - 10) - (3√30 - 18) / (- 3)
(7√30 - 21) / 7 + (10 - 2√30) + (3√30 - 18) / 3
(7√30 - 21 + 70 - 14√30) / 7 + (3√30 - 18) / 3
(49 - 7√30) / 7 + (3√30 - 18) / 3
(147 - 21√30 + 21√30 - 126) / 21
21 / 21
1
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Which algebraic expression represents each verbal expression?
a. the product of five and a number, decreased by eleven
b. the sum of a number and five less than eleven
c. five times a number fewer than eleven
d. the quantity of a number minus eleven, multiplied by five
Answer:
A) 5n − 11
B) 11 − (n + 5)
C) 11 − 5n
D) 5(n − 11)
Your Welcome ;)
The required verbal algebraic expressions are given as ,
(a) 5x - 11 (b) (x + 5) - 11
(c) 5x - 11 (d) (x - 11)×5
What is an algebraic expression?The algebraic expression consists of constants and variables. eg x, y, z etc.
Here,
Let the number x,
a. The product of five and a number, decreased by eleven
⇒ 5x - 11
b. The sum of a number and five less than eleven
⇒ (x + 5) - 11
c. Five times a number fewer than eleven
⇒5x - 11
d. The quantity of a number minus eleven, multiplied by five
⇒(x - 11)×5
Thus, the required expression is shown above
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Vishal came up with an answer of 41 square units for the area of this square.
How long is each side of the tilted square?
_____ units
The length of each side of the given tilted square is √41 units.
What is the length of the side of the square?
The formula to find the area of a square is;
Area = x²
Where x is the side length of the square.
Thus;
x = √41
Now, since all sides of a square are always equal, we can easily say that the length of each side of the given tilted square is √41 units.
Thus, our conclusion is that the length of each side of the given tilted square is √41 units.
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1. Then a survey of 30 students and it was found that 17 of them have a cat, based on these results, guess how many students out of 300 students in the school have cats?
2. If one out of 12 students in a school shares their locker, how many students share their locker in a school with 456 students?
3. Sabrine runs 2 km in 30 minutes. At this rate, what would you run in 90 minutes? And at what rate did she run each hour?
Answer:
The answer is 47.5 because in my math exam i got 47.5 in 50
a sailmaker is designing a mainsail for a newly constructed sailboat. the mainsail foot is 13 feet long, the luff is 10 feet long, and the luff makes a 52° angle at the head with the leach.
So, Part A:
By employing the sines law,
SinA/10 = SinB/13SinA/10 = Sin50/13A = 36.10C = 180-(180-36.10)C = 93.90So,
Sin36.10 / a = Sin50/ b = Sin93.90/cSin36.10 / 10 = Sin50/ 13 = Sin93.90/cc = Sin93.90 × 13 ÷ Sin50c = 16.93 ftNow, Part B:
Area of the mainsail:
= 1/2 × abSinC= 1/2 × 10 × 13 × Sin93.90= 64.85Therefore, the answers to both parts are:
(A) The mainsail foot is 13 feet long, the luff is 10 feet long, the leach is 6.93 feet long, and the mainsail area is 64.85 ft².(B) The mainsail foot is 13 feet long, the luff is 10 feet long, and the luff forms a 50° angle with the leach at the head, requiring the length of the leach and the area of the mainsail.Know more about sines law here:
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The complete question is given below:
A sailmaker is designing a mainsail for a newly constructed sailboat. The mainsail foot is 13 feet long, the luff is 10 feet long, and the luff makes a 50° angle at the head with the leach.
Part A: Determine the length of the leach.
Part B: Find the area of the mainsail.
PLS HELP :) 50 POINTS!!!
Find the distance between the two points on the graph.
Answer:
[tex]3 \sqrt{5} [/tex]
Step-by-step explanation:
See attached for details. Basically finding the distance between 2 points requires creating a right angle triangle. And we are looking for the hypotenuse.
The pythagorean theorem is used.
Is ✓225 + ✓196 a rational or irrational number?
Answer:
yes
Step-by-step explanation:
√225 + √196
15 + 14
29
29 can be written as 29/1 thus 29 is a rational number
Please answer these two questions!
Answer:
The answer to your first question would be B. The answer to the second is C.
Step-by-step explanation:
Hope it helps! =D
Math with a key 6 page 15 task 8 pl. For tomorrow
The value of the expressions will be:
1. -13.
2. 4
3. -9
4. 27
5. 0
How to calculate the value?It should be noted that this is an expression. In this case:
minus × minus = plus
plus × minus = minus
1. (-15) - (-2)
= -15 + 2
= -13
2. (-3( - (-7)
= -3 + 7
= 4
3. 4 - 13
= -9
4. 5 - (-22)
= 5 + 22
= 27
5. (-15) - (-15)
= -15 + 15.
= 0
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Find the values of a and b that complete the mapping diagram.
Value of a and b that completes the mapping diagram will be a=0 and b=1
• Mapping diagram simply means a function that has a special type of relation where the elements of the domain are paired with that of the range.
• Mapping diagram consists of two parallel columns, the first column depicts the domain of the function whereas the second column depicts the range.
• Lines are drawn from first column to second column i.e. from domain to range, to represent the relation between 2 elements.
• Mapping is quite similar to making a flowchart, showing input and output values.
• Point to be noted that every mapping is a relation but every relation is not a mapping.
Value of a and b that completes the mapping diagram will be a=0 and b=1
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Answer: A = 0, and B = 1.
Step-by-step explanation: I put 0, and 1, and it was the perfect answer.
4x100+7x10+6x1+6x(1/10)+3x(1/100)+7x(1/1000)
Please help
Two ways to group 26 students
You are swimming each 25-yard length of a swimming pool 3 seconds
faster than your personal best. What integer represents your change in
time of your personal best after 200 yards?
24 seconds faster time of your personal best after 200 yards.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Suppose the number of laps = m
According to the question, each lap of 25 yards is covered 3 seconds faster than the previous one, so the series become
x , x-3 , x-6 , x-9, ............................
25 * m = 200
m = 200/25
m = 8
As m is the number of laps, and each lap is 3 second faster.
So 8 laps will be 8*3 = 24 seconds faster.
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lindsay bedford works at the baseball cap shop. she is paid $6.50 per hour plus $0.45 for each cap she embroiders. how many caps must she embroider to earn at least $85 in an 8-hour day? group of answer choices
Answer:
Step-by-step explanation:
74 caps
The inside of a flashlight surrounding the bulb is shaped like a parabola in which the base of the bulb represents the vertex and the top of the bulb represents the focus. Which of the following standard equations represents the parabola in which the base of the bulb is at (1, 5) and top of the bulb is at (1, 1)?
The equation of the parabola that models the situation is given by:
(x - 1)² = -16(y - 5).
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
(x - h)² = 4p(y - k).
The focus is located at point (h, k + p).
For this problem, to find the values of the parameters h and k, we have that:
The base is the vertex.The base is at (1,5).Hence:
h = 1, k = 5.
And:
(x - 1)² = 4p(y - 5).
For the focus, and subsequently to find parameter p, we have that:
The top is the focus.The top is at (1,1).Hence:
k + p = 1.
5 + p = 1
p = -4.
Then the equation of the parabola that models this situation is given by:
(x - 1)² = 4p(y - 5).
(x - 1)² = 4(-4)(y - 5).
(x - 1)² = -16(y - 5).
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find the sum and express it in it's lowest terms 3/11 + 2/3=
Answer:
[tex]\frac{31}{33}[/tex]
Step-by-step explanation:
You need a common denominator to add. The smallest number that is divisible by both 11 and 3 is 33. Rewrite both fractions with a denominator of 33
[tex]\frac{3}{11}[/tex] x [tex]\frac{3}{3}[/tex] [tex]\frac{3}{3}[/tex] is just another name for 1. We are making an equivalent fraction. Multiple 3 x3 for the top and 11 x 3 for the bottom to get:
[tex]\frac{9}{33}[/tex]
Do the same for [tex]\frac{2}{3}[/tex]
[tex]\frac{2}{3}[/tex] x [tex]\frac{11}{11}[/tex] [tex]\frac{11}{11}[/tex] is just another name for 1. We are making an equivalent fraction. Multiple 2 x 11 for the top and 3 x 11 for the bottom to get:
[tex]\frac{22}{33}[/tex]
Now add these two fractions together:
[tex]\frac{9}{33}[/tex] + [tex]\frac{22}{33}[/tex] = [tex]\frac{31}{33}[/tex]