Answer:
[tex](x,y)=(3,-7)[/tex]
Step-by-step explanation:
[tex]x-y=10 \implies 2x-2y=20 \\ \\ (3x+2y)+(2x-2y)=-5+20 \implies 5x=15 \implies x=3 \\ \\ \therefore 3-y=10 \implies y=-7 \\ \\ \therefore (x,y)=(3,-7)[/tex].
Answer: y=-25
Step-by-step explanation:
3(y+10)-2y=5
3y+30-2y=5
y+30=5
y=5-30
Question 2
For the equation, x² - 16x + 4 = 0 answer the following questions:
5 pts
On solving the provided question, we can say that the equation, x² - 16x + 4 = 0 => ( x - 12)(x + 2) = 0 => x = 12, -2
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
the equation,
x² - 16x + 4 = 0
( x - 12)(x + 2) = 0
x = 12, -2
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which relationship would most likey have no correlation?
A the number of pizzas ordered, and the the total price of the bill
B The number of miles driven, and the number of gallons of gas in the car
C a person’s height and the person’s shoe size
D a person’s age, and the adress aof the person
Answer:
D
Step-by-step explanation:
Age and adress have quite less. In common
Answer:
A
Step-by-step explanation:
the number of pizzaordered
Box A contains only green and purple counters.
Box B contains only green, purple and orange counters.
Juan picks one counter from box A and one counter from box B.
How many possible ways are there for Juan to pick exactly one purple counter.
There are 2 possible ways for Juan to pick exactly one purple counter.
What is the multiplication principle of countingThe multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.
We have two tasks from the question which are:
picking one purple counter from Box A and picking one purple counter from Box B.
To find the number of ways to pick one purple counter from Box A, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).
where n is the total number of counters in the box and r is the number of purple counters in the box.
we know that there are only green and purple counters in Box A, and since Juan wants to pick one purple counter, we can assume that there is one purple counter in the box.
so, the number of ways to pick one purple counter from Box A = 1.
Similarly, to find the number of ways to pick one purple counter from Box B
we know that there are green, purple and orange counters in Box B, and since Juan wants to pick one purple counter, we can assume that there are two purple counters in the box.
so, the number of ways to pick one purple counter from Box B = ²C₁ = 2.
Now, using the multiplication principle, we can find the total number of ways for Juan to pick exactly one purple counter:
1 x 2 = 2
Therefore, there are 2 possible ways for Juan to pick exactly one purple counter using the multiplication principle of counting
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In the triangle ABC side a = 8 angle C = 90 angle B = 50, what is the measure of side b?
(picture of triangle is purely for labeling, use angles and side lengths specified in the problem)
The measure of the side b in the right triangle ABC is 8 units.
How to find the side of a right triangle?A right triangle is a triangle with one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees. The triangle ABC is a right angle triangle because it has one angle as 90 degrees.
Therefore, the side b can be found using trigonometric ratios.
Hence,
tan 45° = opposite / adjacent
tan 45° = b / a
tan 45° = b / 8
cross multiply
b = 8 tan 45°
b = 8 × 1
b = 8
Therefore,
length of b = 8 units.
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i don’t not know how to solve. i need the complete answer please
Part (a)
[tex]D(1)=\frac{1000}{\sqrt{1}}-1=999 \\ \\ D(4)=\frac{1000}{\sqrt{4}}-1=499 \\ \\ \frac{D(4)-D(1)}{4-1}=\frac{499-999}{4-1}=\boxed{-\frac{500}{3}}[/tex]
Part (b)
[tex]D(100)=\frac{1000}{\sqrt{100}}-1=99 \\ \\ \frac{D(100)-D(4)}{100-4}=\frac{99-499}{100-4}=\boxed{-\frac{25}{6}}[/tex]
At a restaurant, your total bill is $81.95 . You wish to give a tip of 15% of the total bill. What is the amount of the tip? Round your answer to the nearest cent
Answer:
Step-by-step explanation:
Find 15 percent of 81.95 and add it to that.
The answer is 94.24 rounded.
pls help look on the images
You graph >7 with an open dot to the right.
The inequalities ≤ and ≥ would have a closed dot on the number line.
a > 3 is matched to the statement; "you must be older than 13 to play in the basketball league".
s < 3.5 is matched to the statement; "To use one stamp, your domestic letter must be under 3.5 ounces".
t ≥ 48 is matched to the statement; "You must be at least 48 inches tall to ride on the rollercoaster".
What are inequality signsInequality signs are mathematical symbols used to indicate that one quantity is greater than, less than, or equal to another quantity. These inequality signs includes:
Less than: <Greater than: >Less than or equal to: ≤Greater than or equal to: ≥These symbols are used in mathematical expressions and equations to compare values and express relationships between them.
Therefore, with a good understanding of inequality signs we conclude that:
On a graph, > 7 is with an open dot to the right.
Only the inequalities ≤ and ≥ would have a closed dot on the number line.
a > 3 is matched to the statement; "you must be older than 13 to play in the basketball league".
s < 3.5 is matched to the statement; "To use one stamp, your domestic letter must be under 3.5 ounces".
t ≥ 48 is matched to the statement; "You must be at least 48 inches tall to ride on the rollercoaster".
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The ratio of 50 hours to 30 hours
The ratio of 50 hours to 30 hours is 1.33 hours.
What is ratio ?
ratio can be defined as the given value divided by the total value, called as the ratio.
Given ,
To find the ratio of 50 hours to 30 hours
let ratio of x to y is x/ y
similarly,
ratio = 50/30
ratio = 5/3
ratio = 1.33 hours.
in terms of minutes it is = (5/3) * 60
number of minutes = 100 minutes
so the ratio of 50 hours to 30 hours in terms of minutes = 100 minutes
Hence, The ratio of 50 hours to 30 hours is 1.33 hours.
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Amy's sister is 7 years less than twice Amy's age, a. The sum of Amy's age and her sister's age is 41. Which equation represents this relationship?
1. a + (7 - 2a) = 41
2. a + (2a - 7) = 41
3. 2a - 7 = 41
4. a = 2a - 7
Answer:
The relationship between Amy's age, a, and her sister's age is that her sister is 7 years less than twice Amy's age. To represent this relationship, we can use the equation:
2a - 7 = sister's age
This equation shows that the sister's age is equal to twice Amy's age minus 7.
Alternatively, we can use the equation:
a + (2a - 7) = 41
This equation shows that the sum of Amy's age and her sister's age is 41.
The correct equation is number 2. a + (2a - 7) = 41
12. Joel was given instructions to observe, measure and grade this sprinkler (see Figure 1). Holes need
to be spaced 15mm apart, but the company can accept a 1mm allowance either way. Joel left his notes
highlighting sections A and B. Examine Figure 1 and tell what you think your measurements of sections
A and B would be (don't use a ruler). Explain why you gave the answers you did. (3 points)
Length of A:
Explanation:
I
mm
+2
B
Length of B:
mm
Figure 1
The sprinkler's holes have to be 15mm apart and can have a 1mm allowance that space B is bigger than space A, and the notes in space B say "+2" while space A says "-3".
How to calculate length?If you have the area A and width w , its length w is determined as h = A/w . If you have the perimeter P and width w , its length can be found with h = P/2−w . If you have the diagonal d and width w , it's length is h = √(d²−w²)Each rectangular shape is characterized by two dimensions, its length, and width. The longer side of the rectangle is known as the length and the shorter side is known as the width.To calculate the length and width of a rectangle first, calculate the value of width 'w' by using the area of rectangle formula that is, 'w = A/l'. Then substitute the value of width in the formula of the perimeter of a rectangle and simplify the value of length 'l', that is, P = 2 (l + A/I)To learn more about length refers to:
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Sara is considering ordering a large pizza from two different shops. Pizza
4 U charges $14 plus $1.25 per topping. John's Pizza charges $10 plus
$1.50 per topping. Which inequality could be solved to find the number of
toppings that makes Pizza 4 U less expensive than John's Pizza?
Answer:
C
Step-by-step explanation:
Let x = number of toppings.
Pizza 4 U price:
14 + 1.25x
John's Pizza price:
10 + 1.5x
We want Pizza 4 U to be less expensive.
Pizza 4 U price < John's Pizza price
14 + 1.25x < 10 + 1.5x
-0.25x < -4
0.25x > 4
Answer: C
Answer:
C) 0.25x > 4
Step-by-step explanation:
Define the variable:
Let x be the number of pizza toppings.If Pizza 4 U charges $14 plus $1.25 per topping:
14 + 1.25xIf John's Pizza charges $10 plus $1.50 per topping:
10 + 1.5xIf Pizza 4 U is less than John's Pizza:
⇒ 14 + 1.25x < 10 + 1.5x
⇒ 4 + 1.25x < 1.5x
⇒ 4 < 0.25x
⇒ 0.25x > 4
Therefore, the inequality that could be solved to find the number of
toppings that makes Pizza 4 U less expensive than John's Pizza is:
C) 0.25x > 4Graph the equations of the lines to check that they are parallel.
The equation of the line that is parallel to y = 1/5(x + 4) is y = 1/5x + 37/5 or y = 1/5(x + 37). The graph is shown below.
How to Write the Equations of Parallel Lines?Recall that when two lines are parallel to each other, they will have the same slope (m), and each can be expressed in slope-intercept form as y = mx + b.
Given the line, y = 1/5(x + 4), which can be rewritten as y = 1/5x + 4/5, the slope (m) = 1/5.
Substitute m = 1/5 and (x, y) = (3, 8) into y = mx + b:
8 = 1/5(3) + b
8 = 3/5 + b
8 - 3/5 = b
37/5 = b
b = 37/5
To write the equation of the parallel line, substitute m = 1/5 and b = 37/5 into y = mx + b:
y = 1/5x + 37/5
The graph of the lines are shown below.
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Pedro wanted to know the height of the school gym. He measured the shadow from the gym on the
ground to be 40 feet and measured his own shadow to be 10 feet. Pedro is 5.5 feet tall. Find the height
of the gym. Show all work necessary to justify your answer.
Answer: We can use the relationship between the height of an object, the length of its shadow, and the length of the shadow of a person known to be a certain height, to find the height of the gym.
The relationship can be represented using the following proportion:
gym height / shadow of gym = Pedro's height / shadow of Pedro
We can set up the proportion and cross-multiply to get:
gym height * shadow of Pedro = Pedro's height * shadow of gym
We know that Pedro's height is 5.5 feet and his shadow is 10 feet, and the shadow of the gym is 40 feet, so we can substitute these values into the proportion and solve for the gym height:
gym height * 10 = 5.5 * 40
gym height = (5.5 * 40) / 10
gym height = 22 feet
So, the height of the school gym is 22 feet.
Step-by-step explanation:
A cup of coffee has temperature 98°C and takes 45 minutes to cool to 60°C in a room with temperature 19°C. Use Newton's law of cooling to find what the temperature of the coffee will be after t minutes. (Round your value for k to three decimal places.)
(b)
What is the average temperature of the coffee during the first forty-five minutes? (Round your answer to one decimal place.)
Answer:
Part A: [tex]T(t)=79e^{-0.015t}+19[/tex]
Part B: [tex]76.4^\circ \text{C}[/tex]
Step-by-step explanation:
Newton's law of cooling can be modeled with the general equation [tex]\displaystyle \frac{dT}{dt}=-k(T-T_a)[/tex] with solution [tex]\displaystyle T(t)=(T_o-T_a)e^{-kt}+T_a[/tex] for cooling. [tex]T(t)[/tex] represents the temperature of the coffee after [tex]t=45[/tex] minutes given the initial temperature [tex]T_o=98^\circ \text{C}[/tex] and room/air temperature of [tex]T_a=19^\circ \text{C}[/tex] with constant [tex]k[/tex].
Part A: Temperature of coffee after "t" minutes
[tex]T(t)=(T_o-T_a)e^{-kt}+T_a\\T(45)=(98-19)e^{-45k}+19\\60=79e^{-45k}+19\\41=79e^{-45k}\\\frac{41}{79}=e^{-45k}\\\ln(\frac{41}{79}) =-45k\\k\approx0.015\\T(t)=79e^{-0.015t}+19[/tex]
Part B: Average temperature of coffee after 45 minutes
[tex]\displaystyle T_{avg}=\frac{1}{b-a} \int\limits^b_a {T(t)} \, dt\\\\=\frac{1}{45-0}\int\limits^{45}_0 {(79e^{-0.015t}+19)} \, dt\\\\=\frac{1}{45}\biggr(\frac{79}{-0.015}e^{-0.015t}+19t\biggr)\biggr|_0^{45}\\ \\=\frac{1}{45}\biggr(\biggr(\frac{79}{-0.015}e^{-0.015(45)}+19(45)\biggr)+\frac{79}{0.015}\biggr)\\ \\\approx 76.4^\circ \text{C}[/tex]
Simplify the expression 4•3+4•x
Answer:
12+4x
Step-by-step explanation:
multiply 3 by 4 and get 12.
then you multiply 4 by x and get 4x.
You then end up with 12+4x or 4x+12
Find the quotient. If possible, rename the quotient as a mixed number. Select the answer that is in simplest form. 2/5 ÷ 2/8
A. 1 2/5
B. 2 1/5
C. 1 3/5
option c. 1 3/5
2/5 ÷ 2/8
= 2/5 × 8/2
= 8/5
= 1 3/5
Hence, option c. 1 3/5
During a football practice andre attempted 32 field goals and was successful on 75 % of them. How many successful field goals did he make ?
Answer:24
Step-by-step explanation:
75 percent *32
= (75/100)*32
= (75*32)/100
= 2400/100 = 24
Now we have: 75 percent of 32 = 24
how do i do this help please
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
As we know, exterior angle of a triangle is equal to sum of the two internal angles that are not in linear pair with it (or opposite to that angle)
So, by using this property :
[tex]\qquad \sf \dashrightarrow \: 4x + 80 \degree = 2x\degree + 108\degree[/tex]
[tex]\qquad \sf \dashrightarrow \: 4x - 2x \degree = 108\degree - 80\degree[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x \degree = 28\degree [/tex]
[tex]\qquad \sf \dashrightarrow \: x = (28 \div 2)\degree [/tex]
[tex]\qquad \sf \dashrightarrow \: x = 14\degree [/tex]
Angle Q is equal to :
[tex]\qquad \sf \dashrightarrow \: 2x [/tex]
[tex]\qquad \sf \dashrightarrow \: 2 \times 14 \degree[/tex]
[tex]\qquad \sf \dashrightarrow \: 28 \degree[/tex]
Solve for y: y + 17 = 35 -52 52 -18 18
Answer:
18
Step-by-step explanation:
y+17=35
y=18
Anyone know kokushibo (Mitchikatsu Tsugikuni)?
Answer: YESS
Step-by-step explanation: HOW DO WE HAVE THE SAME NAME? AND KOKUSHIBO IS THE UPPER MOON 1 DEMON I HAVE HIM AS MY PFP
Answer: Upper Moon 1
The second to strongest demon (technically third from Tanjiro.) Is the twin brother of Yoriichi.
Which expression is equivalent to
O
1
125
ܝܐܐܗ ܝ
125
05
(5-2)(5-¹) ₂
Answer:
[tex](125)[/tex]
(5-2)(5_-1)2
A cyclist is riding a bicycle whose wheels have a diameter of 2.1 feet. Suppose the wheels turn at a rate of 260 revolutions per minute.
(a) Find the angular speed of the wheels in radians per minute.
(b) Find the speed of the cyclist in feet per minute.
a) The angular speed is 1633 rad/min.
b) The speed is 1715 feet per minute.
What is the angular speed?We know that the angular speed would have to do with the speed with the object would move through a circular path. Let us note that in this case we have that the wheels turn at a rate of 260 revolutions per minute.
Now;
1 rev/min = 6.28 rad/min
260 revolutions per minute = 260 * 6.28/1
= 1633 rad/min
Given that;
v = rω
v = linear speed
r = radius
ω = angular speed
v = 1.05 feet * 1633 rad/min
v = 1715 feet per minute.
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Maddox has 123 black-and-white photos and 174 color photos. He wants to place them on photo pages that have 9 photo holders per page. Can he fill the pages without any photos left over? Explain.
The pages of the photo holder, given the number of pictures that Maddox has, can be filled without any photos left over.
How to find the number of pages ?To find out if Maddox will be able to fill up the pages of the photo holders without there being any leftovers, you need to first find the total number of photos that Maddox has.
The total is:
= 123 black-and-white photos + 174 color photos
= 297 photos
Each photo holder holds 9 pictures so the number of pages needed is:
= 297 / 9
= 33 pages
This shows that no photo will be left over.
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Ill give brainliest to who answers.
Answer:
Triangle NML
Step-by-step explanation:
Use the corresponding angles in the order they are stated and do the same for the other side. N corresponds to N on the other triangle. P corresponds to M on the other triangle, and Q corresponds to L on the other triangle. Now just say it as Triangle NML
If you still have any questions don't hesitate to ask!
in the notation “s(x)=...,” what does “s(x)” represent
The statement s(x) means that s is a function of x
How to interpret the function notationFrom the question, we have the following parameters that can be used in our computation:
s(x)
The above is a function notation
Generally, the expression f(x) means that f is a function of x
When f is replaced with s, we have
s is a function of x
Hence, the meaning is that "s is a function of x"
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How many solutions can be found for the system of linear equations represented on the graph?
A infinitely many solutions
B no solution
C one solution
D two solutions
Because there is only one intercept on the graph, the system of equations has a single solution.
How many solutions does the system has?
When we have a system of equations, we can solve it graphically by graphing both equations on the same coordinate axis, and find the points where the graphs intercept.
Each one of these intercepts is a solution of the system of equations.
Here we can see that the system of equations is graphed, and there is a single intercept at the point (1, 3)
So the system has a single solution.
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DUE SOON! PLEASE HELP AND SHOW WORK SO I KNOW HOW TO GET THE ANSWER FOR NEXT TIME!!
BEEN STUCK ON THIS FOREVER
QUESTION DOWN BELOW!
Answer:
To solve this problem, we need to use the concept of scale factor. The scale factor tells us how much larger or smaller an image is compared to the original image. In this case, the scale factor is 7/6, which means that the new image will be 7/6 times larger than the original image.
We can use the scale factor to find the dimensions of the new image. To do this, we simply multiply the dimensions of the original image by the scale factor.
Original dimensions: 24 cm x 12 cm
New dimensions: (24 cm x 7/6) x (12 cm x 7/6) = 28 cm x 14 cm
So, the dimensions of the photograph after it is sent through the photocopier are length 28 cm and width 14 cm.
Therefore, the correct answer is length 28 cm, width 14 cm.
A small business produces oak chairs and walnut chairs. The business can make at most 40 chairs per week. Materials cost $100 per oak chair and $150 per walnut chair. The business has a budget of $4500 per week for materials. Each oak chair sells for $400 and each walnut chair for $500. How many of each type of
chair should the business make each week to maximize income?
The most money an individual is allowed to earn in accordance with the law is known as their maximum wage, also referred to as their wage ceiling.
The inequality be [tex]I=400 x+500y[/tex].
What is meant by maximize income?A maximum wage, often known as a wage ceiling, is the maximum amount of money an individual is permitted to make under the law.
The amount of money, property, and other transfers of value obtained over a predetermined period of time in return for services or goods are often referred to as "income." Income is defined in accordance with the context in which the word is employed; there is no single, universal definition.
Let x be the oak chairs produced
y be the walnut chairs produced
[tex]$$x+y \leq 20 \\ \\100 x+150 y \leq 2400 \\ \\x \geq 0 \\ \\y \geq 0 \\ \\ I=400 x+500 y\end{array}\right.$$[/tex]
The inequality be [tex]I=400 x+500y[/tex].
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Consider a circle with centre O and chords AB and CD.chord AB = Chord CD . Prove that arc AB = arc CD
The proof that arc AB = arc CD is shown below
How to prove that arc AB = arc CD Given a circle with center O and chords AB and CD,
Such that AB = CD.
Considering a point P on arc AB and a point Q on arc CD
Such that AP = BP and CQ = DQ
Since OP = OQ and P and Q are on arcs AB and CD respectively,
It follows that angle POQ is equal to half the central angle of the circle that subtends the same arc as chord AB.
Similarly, arc AB is equal to the central angle of the circle that subtends arc CD.
Therefore:
POQ i= 1/2 * central angle of the circle and
Arc CD subtends twice the central angle as POQ.
Since the central angles subtended by arc AB and arc CD are equal, it follows that the arcs themselves are equal, i.e., AB = CD.
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Please help and show work, I've tried but can't figure it out.
(PICTURE INCLUDED)
Tim and Jan started at the same spot. Tim went 8 miles east and 15 miles north. Jan went 5 miles west and 12 miles north. How far apart are they? Round your answer to the nearest tenth.
Answer:
21.4 miles apart
Step-by-step explanation:
David calculations were wrong since the distance he measure were how far apart they both were together from the home and not from eachother.
simply just draw a line from the End point Jan is from Tim, you can see that it forms a third triangle to which you can use Pythagoras to figure the distance apart.
David already calculated the length of the two other sides being 13 and 17 so:
13^2 + 17^2 = c^2
458 = c^2
c = squareroot of 458
c = 21.4
therefore the distance between Jan and Tim was actually 21.4 miles