Answer:
The solutions are (-2, 0) and (1, 3).
Step-by-step explanation:
Edginuity Sample response: The graph consists of a parabola and a line. The parabola opens down and has a vertex of (0, 4). The line has a slope of 1 and a y-intercept of 2. We want to solve
-x² + 4 = x + 2
Create two curves as follows:
y = -x² +4
and
y = x + 2
By graphing the two curves together, their points of intersection are the solutions.
y = -x² + 4 is a parabola with vertex at (0, 4), and it opens downward.
y = x + 2 is a straight line with slope - 1 and with y-intercept = 2
The points of intersection are (-2, 0) and (1, 3).
Consider quadrilateral MATH with vertices (0,0), (s,O). (s,t) and (O,t). Sarah used the distance formula to prove that MT=AH. What conclusion can be made from Sarah's calculations?
Step-by-step explanation:
You could say that the diagonals are congruent.
2t - 15t is equal to
2t-15t is equal to
Answer:
2 result(s) found
t=2
t=
2
11
=5.500
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*t^2-(15*t-22)=0
Step by step solution :
STEP
1
:
Equation at the end of step 1
2t2 - (15t - 22) = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 2t2-15t+22
The first term is, 2t2 its coefficient is 2 .
The middle term is, -15t its coefficient is -15 .
The last term, "the constant", is +22
Step-1 : Multiply the coefficient of the first term by the constant 2 • 22 = 44
Step-2 : Find two factors of 44 whose sum equals the coefficient of the middle term, which is -15 .
-44 + -1 = -45
-22 + -2 = -24
-11 + -4 = -15 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -11 and -4
2t2 - 11t - 4t - 22
Step-4 : Add up the first 2 terms, pulling out like factors :
t • (2t-11)
Add up the last 2 terms, pulling out common factors :
2 • (2t-11)
Step-5 : Add up the four terms of step 4 :
(t-2) • (2t-11)
Which is the desired factorization
Equation at the end of step
2
:
(2t - 11) • (t - 2) = 0
STEP
3
:
Theory - Roots of a product
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
3.2 Solve : 2t-11 = 0
Add 11 to both sides of the equation :
2t = 11
Divide both sides of the equation by 2:
t = 11/2 = 5.500
Solving a Single Variable Equation:
3.3 Solve : t-2 = 0
Add 2 to both sides of the equation :
t = 2
Supplement : Solving Quadratic Equation Directly
Solving 2t2-15t+22 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
4.1 Find the Vertex of y = 2t2-15t+22
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 2 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,At2+Bt+C,the t -coordinate of the vertex is given by -B/(2A) . In our case the t coordinate is 3.7500
Plugging into the parabola formula 3.7500 for t we can calculate the y -coordinate :
y = 2.0 * 3.75 * 3.75 - 15.0 * 3.75 + 22.0
or y = -6.125-0
Below are the demand and supply equations for overhead projectors in a certain market. In these equations, p represents price, D represents demand, and S represents supply. S = three-fourths p minus 28 D = negative 2 p 131 What is S at the point of equilibrium, to the nearest whole number? a. 12 b. 15 c. 58 d. 67.
For the equilibrium, the value of supply and the value of demand will be equal. Then the value of price (p) is 58.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
The demand and supply equations for overhead projectors in a certain market.
In these equations, p represents price, D represents demand, and S represents supply.
[tex]\rm S = \dfrac{3}{4}p - 28 \\\\D = -2 p + 131[/tex]
For the equilibrium, the value of supply and the value of demand will be equal. Then we have
[tex]\begin{aligned} \dfrac{3}{4}p - 28 &= -2 p + 131\\\\3p- 112 &= -8p + 524\\\\11p &= 636\\\\p &= 57.81818 \approx 58 \end{aligned}[/tex]
More about the linear system link is given below.
https://brainly.com/question/20379472
Answer: B. 15
Step-by-step explanation: edge 2022 i got it right
Jasleen has 6 packs of 8 colored markers to put into party gift bags. She spilts the markers equally among 9 gift bags. What is the minimum amount of markers she can put in each bag?
Your answer is 252.
I hope this helps.
This nonparametric test requires at least ordinal level data. Its purpose is to find out if there is any difference between two sets of related observations and it is used if the assumptions required for the paired t-test cannot be met. Which test is it?
a. ANOVA
b. Rank correlation
c. Kruskal-Wallis
d. None of the above
Answer: Rank correlation
Step-by-step explanation:
hope it helps
If a car travels 400 miles in 4 hours how fast is it going?
Answer:
100 miles per hour
Step-by-step explanation:
Answer:
100 miles in 1 hour
Step-by-step explanation:
all you have to do is divied 400 and 4
HELP HAVING BAD DAY A line passes through the points A(–1, 7) and B(1, 3). a Find the slope of the line.
Answer:
the slope is -2
Step-by-step explanation:
if you move the x by 2, you would see a decrease in the y by 4. 2/-4 = -2.
Determine the slope from the following order pairs:
(5, 7) (6,3)
Answer:
Step-by-step explanation:
(3-7)/(6-5)= -4/1= -4
is number 1 a function??
Answer:
yes
Step-by-step explanation:
From a hot-air balloon, Daniel measures a 33^{\circ} ∘ angle of depression to a landmark that’s 1579 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.
Check the picture below.
Make sure your calculator is in Degree mode.
5 in
5 in
4.3 in
14 in
5 in
Can you help me find out the surface area
Answer:
219.6
Step-by-step explanation:
i used omnicalculator
a pet store donated 50 pounds of food for adult dogs , puppies and cats to an animal shelter. 19 and 3/4 pounds was adult dog food and 19 7/8 was puppy food. how many pounds of cat food did the store donate?
Answer: 10 3/8
Step-by-step explanation:
= 50 - 19 3/4 - 19 7/8
= 10 3/8
solve for x 5x= -20
Answer:
Today: Monday, 12 October 2020
Hour: 09.13 WIB (in Indonesian)
_________________________
5x = -20
x = -20/5
× = -4
Answer:
x = -4
Step-by-step explanation:
5x = -20
x = -20/5
x = -4
I hope this helped!
Fill the blanks:
Given: MOL~ REY
Answer:
1. <R
2. <E
3. <L
4. RE
5. YE
6. 5
could someone please help draw this math problem for me ?? i need help!
PLS HELP ME
Aisha divides 15 meter of ribbon into 2 equal pieces.
What is the length of each piece of ribbon?
Enter your answer as a fraction in simplest form by filling in the boxes.
⊆⊇ m
⊂⊃
Answer:
7.5 meters
Step-by-step explanation:
14/2=7 16/2=8 so you go halfway for 15
Divide the total length by 2
Length of ribbon=15m
Half:-
15/27.5mLarge cheese pizzas cost $5 each and large pepperoni pizzas cost $6 each. The expression 5c+6p models the total cost of large cheese pizzas (c) and large pepperoni pizzas (p). What does each part of the expression represent in the context of the situation? Drag the correct description to each part of the expression.
Answer: 5c represents the cost of 'c' large cheese pizzas and 6p represents the cost of 'p' large pepperoni pizzas.
Step-by-step explanation:
Given: Large cheese pizzas cost $5 each and large pepperoni pizzas cost $6 each.
The expression 5c+6p models the total cost of large cheese pizzas.
here c represents Number of large cheese pizzas and p represents number of large pepperoni pizzas such that
5c represents the cost of 'c' large cheese pizzas and 6p represents the cost of 'p' large pepperoni pizzas.
[Total cost = Cost of each item x Number of items ]
find the number of bounded and unbounded regions that 4 lines in general position divide a plane into. then find the number of regions for 5 through 10 lines. organize the information in a chart. (ALL THE BLANK SPOTS IN THE ATTACHMENT ARE WHAT I AM CONFUSED ON) please help I have till friday to finish!
Answer:
10, 15, 21, 28, and 36
Step-by-step explanation:
The rule is the number of line which is n. (n-2)*(n-1) divided by 2
The slope of that line through the origin that divides the region bounded is 1.0315
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
here, we have,
given that,
y = 5x - 3x2
5x - 3x2 = 0
x(5 - 3x) = 0
x = 0 , x = 5/3
Area under y = 5x - 3x2 is A = [0 to 5/3] 5x - 3x2 dx
A = [0 to 5/3] 5x2/2 - 3x3/3
A = [0 to 5/3] 5x2/2 - x3
A = 5(5/3)2/2 - (5/3)3 = 125/54
line passing through origin is in the form of y = mx
==> mx = 5x - 3x2
==> 3x2 + mx - 5x = 0
==> 3x2 + x(m -5) = 0
=> x(3x + (m -5)) = 0
==> x = 0 , x = (5 -m)/3
Area under y = 5x - 3x2 and y = mx is (125/54)/2 = 125/108
==> ?[0 to (5 -m)/3] 5x - 3x2 -mx dx = 125/108
==> ?[0 to (5 -m)/3] (5 - m)x - 3x2 dx = 125/108
==> [0 to (5 -m)/3] (5 - m)x2/2 - x3 = 125/108
==> (5 - m)[(5 -m)/3]2/2 - ((5 -m)/3)3 = 125/108
==> (5 -m)3/18 - (5 -m)3/27 = 125/108
==> (5 -m)3/54 = 125/108
==> (5 -m)3 = 125/2
==> (5 -m) = 3.9685
==> m = 5 - 3.9685
==> m = 1.0315
Hence slope of line = 1.0315
To learn more about slope
brainly.com/question/3605446
#SPJ3
The complete question is given below
There is a line through the origin that divides the region bounded by the parabola y=5x−3x^2 and the x-axis into two regions with equal area. What is the slope of that line?
a toy store sells assorted bags of marbles sold in small or large bags the table show the number of each color of marble in the small bag the manager of the store wants to mantain the same ratio of each color of the marble in the large bag as in the small bag
if each marble cost 20 green marble how much does the large bag cost
10$
Hope this helped!
please help me with this....!!!!!!!!
Answers:
5x^2 + 2 = 4x has no real solutions3x^2 + 24x = -48 has exactly one real solution3(x+5)^2 = -2 has no real solutions4x^2 - 16x = 0 has two real solutions======================================================
Explanation:
We can use the discriminant formula to determine how many (and what type of) roots we have. The term "root" is another word for "solution" or "x intercept". It's the x value that makes y = 0.
Any quadratic is of the form ax^2 + bx + c = 0
The discriminant formula is
d = b^2 - 4ac
which is found underneath the square root in the quadratic formula.
Here are the three possible outcomes
d > 0: we get two different real number solutionsd = 0: we have exactly one real number solutiond < 0: there are no real number solutions (the two solutions are complex or imaginary numbers).With all that in mind, let's find the discriminant of the first equation on the very left.
First we need to get it into standard form ax^2+bx+c = 0
5x^2 + 2 = 4x
5x^2 - 4x + 2 = 0
We see that
a = 5b = -4c = 2Computing the discriminant gets us...
d = b^2 - 4ac
d = (-4)^2 - 4(5)(2)
d = 16 - 40
d = -24
The actual discriminant value itself doesn't matter. All we care about is whether its positive, zero, or negative.
In this case, we get a negative discriminant. So this equation goes to the "no real solutions" column.
-------------------------
Let's move onto the next quadratic
3x^2 + 24x = -48
3x^2 + 24x + 48 = 0
a = 3, b = 24, c = 48
d = b^2 - 4ac
d = 24^2 - 4(3)(48)
d = 0
The discriminant of zero means this equation goes into the "exactly one real solution" category.
-------------------------
For the next equation, we don't need to use the discriminant formula here.
Notice that the right hand side is negative, but the left side is never negative because 3 is positive and (x+5)^2 is never negative. There is no way to have 3(x+5)^2 be negative if we let x be a real number only.
The equation 3(x+5)^2 = -2 goes into "no real solutions" pile.
-------------------------
For the last equation, we have
a = 4, b = -16, c = 0
So,
d = b^2 - 4ac
d = (-16)^2 - 4(4)(0)
d = 256
The result is a positive number, so we have two different solutions.
The discriminant is a perfect square which means we not only have real number solutions, but those solutions are rational numbers. This only works when a,b,c are rational as well.
Solve the absolute value equation.
(7n+9)+11=3
The solution set is
Somebody please help with these multi-step equation(s)
Answer:
h = -1
Step-by-step explanation:
-( 4+h) = 3h
Distribute the minus sign
-4 -h = 3h
Add 4 to each side
-4-h+h = 3h+h
-4 = 4h
Divide each side by 4
-4/4 = 4h/4
-1 = h
Find the area for this square
Answer:
361
Step-by-step explanation:
Multiply length x width to find area. 19 x 19 = 361
If a van traveled 240 miles in 4 hours, how far could the van travel in 5 hours?
Answer: i think 300
Step-by-step explanation: i divided 240 by 4 and got 60 then multiplied 60X5=300
Answer:
300 miles in five hours.
Step-by-step explanation:
speed = distance/time
distance = speed*time
240/4=60
d= 60*5
d=300 miles in five hours.
Word explanation:
You can use the formula, speed=distance/time to find the speed which is 60 mph. Now use the formula for distance which is distance= speed*time. The answer would be 300 miles in five hours.
Point hh is located at (4,-2)(4,−2) on the coordinate plane. point hh is reflected over the yy-axis to create point h'h ′ . point h'h ′ is then reflected over the xx-axis to create point h''h ′′ . what ordered pair describes the location of h''?h ′′ ?
Answer:
(-4,2)
Step-by-step explanation:
Notice that the xx-coordinate and the yy-coordinatechange sign when HH is reflected over the yy-axis and then reflected over the xx-axis.
Answer:
The correct ans is (4,-2)
Step-by-step explanation:
Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
Answer: 64.0
Step-by-step explanation:
PLEASE HELP
an artist is constructing a piece of art in the shape of rectangle. The artist wants to use string to tightly tie each vertex of rectangle to the other three vertices. The rectangle is 12.0 feet wide and 7.0 feet long. how much string should the artist use? round your answer to the nearest tenth of a foot
feet of string:
Answer:
An artist use 51.9 feet of string for constructing a piece of art in the shape of rectangle
Step-by-step explanation:
Here an artist is constructing a piece of art in the shape of rectangle having length 12 feet & width of 7 feet
Since the artist wants to use string to tightly tie each vertex of rectangle to the other three vertices. Hence one string will tie in a diagonal way
Hence total length of string will be
Total length = Perimeter of rectangle + length of diagonal
Perimeter of rectangle = 2( length + width ) = 2 ( 12 + 7 ) = 2 x 19 = 38 feet
Length of diagonal given by Pythagoras theorem
[tex]\mathrm{Length = { \left( { a }^{ 2 } + { b }^{ 2 } \right) }^{ 0.5 } = { \left( { 12 }^{ 2 } + { 7 }^{ 2 } \right) }^{ 0.5 } = 13.89244\:\:feet}[/tex]
Hence
Total length = Perimeter of rectangle + length of diagonal
Total length = 38 feet + 13.89244 feet = 51.9 feet
Hence an artist use 51.9 feet of string for constructing a piece of art in the shape of rectangle
It takes 33 minutes to walk to the pool from her house. If she rides her bike it takes her 1/3 of that time. Natasha leaves her house for the pool at 3:12. If she is riding her bike, what time will she arrive? _:_
Answer:
Natasha will arrive at 3:23
Step-by-step explanation:
(1/3)*33= 11
3:12+11= 3:23
Pls answer the question attached.
I WILL MARK U BRAINLIST
Answer:
The original price of the toaster is 2000
Step-by-step explanation:
Given: Toaster price = 2240
VAT = 12%
VAT amount = ?(I'll include this one)
Assume the original price be x.
Let the original price be x
Then, x + 12% of x = 2240
x+12/100x x = 2240
100x+12x/ 100= 2240
112x/100=2240
112x = 2240 x 100 ⇒ 224000
x = 224000/112
x = 2000.
So, the original price of toaster = Rs. 2000.
The VAT amount = 2240 - 2000 ⇒ Rs. 240.
The VAT amount is Rs. 240.
What is -3/8 times (-1/7)?