Answer:
y=0.25x+3
Step-by-step explanation:
use desmos graphing calculator and put the coordinates into a table
What is the distance between point p and q
- P(-5,7) Q(6,7)
The distance between the two points P(-5, 7) and Q(6, 7) is 11 units.
What is the distance formula?The distance formula between two points (x₁, y₁) and (x₂, y₂) is,
D = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].
Two points are given P(-5, 7) and Q(6, 7).
∴ D = [tex]\sqrt{(6 + 5)^2 + (7 - 7)^2[/tex].
D = [tex]\sqrt{(11)^2[/tex].
D = 11 units.
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Is the sum of 3.04 and √20 rational or irrational? Explain.
Answer:
Irrational
Step-by-step explanation:
A rational number can be expressed as p/q where p and q are integers
3.04 is rational since it can be expressed as 304/100
√20 is not rational. √20 = √(4·5) = √4·√5 = 2√5
While 2 is a rational number, √5 is irrational since 5 is a prime number and square roots of primes are not rational
An irrational number multiplied by a rational number is irrational so √20 is irrational
An irrational number added to a rational number results in an irrational number.
So 3.04 + √20 is irrational
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What mixed number is equivalent to 21 ÷ 4?
Answer:
Step-by-step explanation:
5 1/4
Answer:là
5
với số dư
1
.
5
1
4
Step-by-step explanation:
The perimeter of a triangle is 58 cm. The triangle is isosceles, but if its base were lengthened by 4 cm and each leg were shortened by 7 cm, then it would be equilateral. Find the base of the original
triangle.
A. 12 cm
B. 11 cm
C. 23 cm
D. 16 cm
The base of the original triangle is 12 centimetres.
How to find the base of the original triangle?A triangle is a polygon with three sides. The perimeter of a triangle is 58 cm. The triangle is isosceles.
An isosceles triangle is a triangle with 2 sides equal to each other and two angles equal to each other.
Therefore, let's find the base of the original triangle when the base were lengthened by 4 cm and each leg were shortened by 7 cm,
Hence,
let
x = length of legs
y = length of the base
Therefore,
2x + y = 58
Hence,
y + 4 = x - 7
x - y = 11
2x + y = 58
x - y = 11
3x = 69
x = 69 / 3
x = 23
-y = 11 - 23
-y = -12
y = 12
Therefore,
base of the original triangle = 12 cm
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Factor the expression.
- 20a-35
The positive GCF of -20a and -35 is 5. Complete each equation with an expression or integer factor.
5x -4a=-20a
5× - 7 = - 35
The expression with 5 factored out is
Answer:
5(-4a -7) = -20a -35
Step-by-step explanation:
Your redecorating your bedroom, and you want to put in a dressing table. The wall where you want to put it measures 4.7m. There is also a cupboard door on this wall, which takes up 410mm. The dressing table you like is 123cm wide. Once you've bought the dressing table , how much space on the wall, do you have left, not including the cupboard doors? I need this working out in metres please.
Answer:
3.06 meters
Step-by-step explanation:
The first thing you want to do, since we are working with different units here, is find out how many centimeters make a meter... and so on.
1cm = 0.01m
1mm = 0.001m
123cm = 1.23m (Dressing table)
410mm = 0.41m (Cupboard door)
Now all we need to do is subtract.
We can add the two numbers together or (If you prefer) subtract separately.
1.23 + 0.41 = 1.64
Now subtract that number from the measurement of the wall:
4.7 - 1.64 = 3.06
The amount of space left is 3.06m.
my teacher is asking what is 4 cubed and the options are [tex]3^{3}[/tex] , [tex]3^{3}[/tex] > 12 , [tex]4^{3}[/tex] , and 3-4 please help !
Adante begins to evaluate the expression 3 1/3x5 1/4using the steps below.
3 1/3 x5 1/4
(3 1/3x(5+1/4)
(3 1/(3+1/3)(1/4)
Step-by-step explanation:
Here you are the answer.
Solve for x and the missing measures given QS = 34 and TS = 3x + 2
Answer:
x = 5
TS = 17
QT = 17
Step-by-step explanation:
The tick marks show us that line segment QT is equal to TS.
QS = QT + TS and QT and TS are the same length
34 = 2(3x + 2) Distribute the 2
34 = 6x + 4 Subtract 4 from both sides
30 = 6x Divide both sides by 6
5 = x
Substitute in 5 for x
3x + 2
3(5) + 2
15 + 2 = 17
TS is 17
QT is 17
Every day, Garrett's burrito stand uses 1 7/10 bags of tortillas. How many days will 8 1/2 bags of tortillas last?
Answer: 5 days.
Step-by-step explanation: To solve this problem, we first need to convert 1 7/10 bags of tortillas to a decimal number. We can do this by dividing the numerator of the fraction (7) by the denominator (10) and adding the result to the whole number (1) to get 1 + 7/10 = 1.7 bags of tortillas.
Next, we can divide the number of bags of tortillas that Garrett's burrito stand uses per day (1.7 bags) into the total number of bags of tortillas that are available (8.5 bags) to find out how many days the tortillas will last: 8.5 bags / 1.7 bags/day = 5 days
Therefore, the 8 1/2 bags of tortillas will last for 5 days.
[3x (4.6÷2)] +14.1 =
Answer:
21
Step-by-step explanation:
PEMDAS : Parenthesis, Exponent, Multiplication/Division, Addition/Subtraction.
First, we want to deal with the parenthesis within the parenthesis.
(4.6/2) = 2.3
Rewrite it into the equation.
[3 * 2.3] + 14.1 = ?
Now, do the work in the parenthesis again.
[6.9] + 14.1 = ?
There isn't anymore parenthesis, exponents, or multiplication/division, so we move onto addition now and add both terms.
6.9 + 14.1 = 21
? = 21
The answer is 21.
help meee please for a lot of points it gotta be to answer choices
Answer:
B and D
Step-by-step explanation: I got it right
The length of a rectangle is 8 inches more than it’s width. It’s area is 308 square inches. The length is?
Answer:38.5
Step-by-step explanation:
308/8 =38.5
Answer: 8ft
Step-by-step explanation:
the length of the room is 8fr
You are a construction worker who is laying down concrete drainage pipes. Each pipe is 5 feet long and 3 inches thick, and has an outside diameter of 6.5 feet. You lay down 4 drainage pipes end to end.
At any given time, what is the volume of water that passes through the 4 drainage pipes at half capacity? Round the answer to the nearest tenth of a cubic foot.
141.3
165.8
282.6
306.6
565.2
Answer:
Volume = 282.6 ft.²
Step-by-step explanation:
Volume: V = πr²h
Step 1: The answer needs to be in cubic feet, so convert all units to feet
1. 3 ft./12 in. = 0.25 ft.
Step 2: Subtract 0.5 ft from 6.5 ft to find the actual diameter of the pipe that the water will be passing through
2. 6.5 ft. - 0.5 ft. = 6 ft.
Step 3: Plug 3 ft. (radius), 3.14 for π, and 5 ft for h
3. V = (3.14)(3 ft.)²(5 ft.)
Step 4: Solve for the V (volume)
4. V = (3.14)(9 ft.)(5 ft.) → V = (28.26)(5) → V = (28.26)(5) → V = 141.3 ft.²
Step 5: Divide 141.3 by 2, since we want half the capacity
5. 141.3 ft.²/2 = 70.65 ft.²
Step 6: Multiply 70.65 by 4 since we want the total volume of water passing through four pipes
6. 70.65 ft.² ∙ 4 = 282.6 ft.²
Which ordered pairs in the form (x, y) are solutions to the equation
7x−5y=28?
Select each correct answer.
Responses
(7, 9)
Begin ordered pair 7 comma 9 end ordered pair
(4, 10)
Begin ordered pair4 comma 10 end ordered pair
(−1, −7)
Begin ordered pair negative 1 comma negative 7 end ordered pair
(−6, −14)
The ordered pair (-1, -7) is the solution to the equation 7x - 5y = 28.
Define solutions of linear equations.The collection of variable values in linear equations that yields all feasible solutions is referred to as the solution of a linear equation. In order to describe real-world issues, linear equations contain unknown values in the form of one or more variables. The collection of values for each variable in a system of linear equations is referred to as the solution set.
Consider the equation,
7x - 5y = 28
Now put the values from options, the pair values at which LHS = RHS that will be the solution to the equation.
Put x = 77, y = 9 in the equation
7(7) -5(9)
= 49 - 45
= 4
This is not a solution.
Put x =4, y= 10
7(4) - 5(10)= 28 - 50
= -32
This is not a solution.
Put x= -1, y = -7
7(-1) - 5 (-7)
= -7 + 35
= 28
So, this is the solution to the equation as LHS = RHS
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Answer:
C. the ordered pair (1.5, 10)
Step-by-step explanation:
Graph the equation.
y
=
−
4
(
x
+
2
)
2
−
1
y=−4(x+2)
2
−
Answer:
see instructions
Step-by-step explanation:
1. (x + 2) = 0 gives us x = -2 = x coordinate of vertex; and
the -1 at the end gives us the y coordinate.
Move the vertex of the parabola to the point (-2,-1)
2. The -4 in front of the (x+2)² gives the direction and stretch of the parabola. FROM the Vertex, position the other point Down 4 and Right 1 (at (1,-5)).
HELP ME OUT OMG THANKS
Answer: r = 12
Step-by-step explanation:
11 - 23 = 12
YOUR SO WELCOME!!! :D
Four consecutive even integers have a sum of 332. What is the least of these integer
Answer: 80
Step-by-step explanation:
set the 4 numbers to be x,x+2,x+4,x+6
They add up to 332 so the equation would be
x+(x+2)+(x+4)+(x+6)=332
4x=320
x=80
the rest of the numbers are 82,84,86
smallest is 80
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50 points
Answer: D
Step-by-step explanation:
The parent function abs(x) is a V, similar to graph B.
When it is multiplied by a negative number then it reflects across the Y axis, and if the number is greater than 1, then the graph is horizontally compressed (like you're squishing the sides together, closer to each other). If the number is less than 1, either decimals or a fraction, then it is stretched (like you are pulling the sides away from each other and they are getting wider).
In this case you are multiplying abs(x) by 4, which is greater than 1 so it is compressed by a factor of 4, and then multiplying it by a negative, which reflects it across the y axis.
In a certain board game, players spin a spinner to determine how many spaces they advance. The odds in favor of advancing five spaces are 3/10. Find the probability of advancing five spaces.
(b)Ravi has a box of candies with different flavors. He will randomly choose one piece of candy. The probability that he chooses a strawberry-flavored piece is 6/19. What are the odds against him choosing a strawberry-flavored piece?
The probability of advancing five spaces is 3/13 and the odds against is 13 : 6
How to determine the probability and the odds?The board game
From the question, we have the odds to be
Odds in favour = 3/10
This can be rewritten as
Odds in favour = 3 : 10
For an odd represented as a : b, the probability is
Probability = a/a + b
Using the above as a guide, we have
Probability = 3/13
The box of candies
From the question, we have the probability to be
Probability = 6/19
For a probability represented as a/b, the odds against is
Odds = b - a : a
Using the above as a guide, we have
Odds = 19 - 6: 6
Evaluate
Odds = 13 : 6
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Old Navy had $940 worth of orders for shirts. The prices for the shirts were categorized by style: $10 for tank tops, $14 for graphic tees, and $22 for polos. The number of polos ordered was one more than half the number of graphic tees, and the number of graphic tees ordered was eight less than twice the number of tank tops. Determine the number of each type of shirt ordered.
The number of each type of shirt ordered are as follows;
number of graphic tees = 29number of tanks tops = 19number of polos = 15How to find the number of each type of shirt ordered?Old Navy had $940 worth of orders for shirts.
The prices for the shirts were categorized by style: $10 for tank tops, $14 for graphic tees, and $22 for polos.
The number of polos ordered was one more than half the number of graphic tees, and the number of graphic tees ordered was eight less than twice the number of tank tops.
let
x = number of graphic tees
Hence,
number of polos = 1 + 1 / 2 x
Number of tank tops = 1 / 2 x + 4
Therefore, the total
14x + 10(1 / 2 x + 4) + 22(1 + 1 / 2 x) = 940
14x + 5x + 40 + 22 + 11x = 940
30x + 62 = 940
30x = 878
x = 29.266667
x = 29
number of polos = 1 + 1 / 2 (29) ≈ 15
Number of tank tops = 1 / 2 (29) + 4 ≈ 19
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When loaded with bricks, a lorry has a mass of 11600 kg. If the mass of the bricks is three times that of the empty lorry, find the mass of the bricks.
Answer:
8700kg
Step-by-step explanation:
b = mass of bricks
l = mass of lorry
b+l = total mass = 11600kg
b = 3l ==> l = b/3
substitute: b + b/3 = 11600
multiply every term by 3 to get rid of denominator: 3b + b = 34800
simplify and solve: 4b = 34800 ==> b = 8700
check: l = 8700/3 = 2900
2900 + 8700 = 11600? YES
During a test, 3 out of 100 cars selected at random were found to be defective. Use this ratio to estimate the number of defective cars if 1,500 cars are tested.
There are 45 defective cars if 1,500 cars are tested.
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities.
Given that;
During a test, 3 out of 100 cars selected at random were found to be defective.
Now,
Since, During a test, 3 out of 100 cars selected at random were found to be defective.
Let number of defective cars if 1,500 cars are tested = x
So, By definition of ratio, we get;
⇒ 3 / 100 = x / 1,500
Solve for x as;
⇒ 3 × 1500 / 100 = x
⇒ 3 × 15 = x
⇒ x = 45
Thus, There are 45 defective cars if 1,500 cars are tested.
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y=9.44x+84.182
is this function a good model for the data
Answer:
Step-by-step explanation:
443
solve 3x+1=-5 by graphing. then find the x- and y-intercepts
The graph of the equation is shown below
The x-intercept is -2
The y-intercept is undefined
Graph of linear equations and determining the interceptsFrom the question, we are to solve the equation by graphing and determine the x- and y-intercepts
The given equation is
3x + 1 = -5
To determine the x-intercepts, we will solve the equation
3x + 1 =-5
3x = -5 - 1
3x = -6
Divide both sides by 3
x = -2
Since, y is not defined in the equation, the y-intercept is undefined
The graph of the equation is shown below.
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17. Write 2 numbers that are less than -1000?
Answer: -1001, -1002
Step-by-step explanation:
Dr. Hill charges $30 for a tutoring session, plus $0.25 per problem.
Write an equation to represent the problem.
Then, determine how many problems he helped with if he charged $47.75
What angles are linear pairs? Check all that apply.
Answer:
show the choices please.
Step-by-step explanation:
30+ w =150 what does w equal?
If 3(x + 5) + 2 = 5, what is the value of x?
Answer:
-4
Step-by-step explanation:
3x+15+2=5
3x=-15-2+5
3x=-12
x=-12/3
x=-4
Answer:
x=-4
Step-by-step explanation:
Given:
[tex]3(x+5)+2=5[/tex]
To find:
The value of x.
Explanation:
It is given that,
[tex]3(x+5)+2=5[/tex]
That implies,
[tex]3(x+5)+2=5\\3x+15+2=5\\3x+17=5\\3x=5-17\\3x=-12\\x=-\frac{12}{3} \\x=-4[/tex]
Hence, the value of x is -4.