Answer:
1) [tex]y=x^2+2[/tex]
2) [tex]y=x^2-4[/tex]
3) [tex]y=x^2[/tex]
4) [tex]y=x^2+6x+14[/tex]
Step-by-step explanation:
Question 1
Given points: (-2, 6) (-1, 3) (0, 2) (1, 3)
This is likely to be a quadratic equation with a vertex of (0, 2) since the points (-1, 3) and (1, 3) are symmetrical about x = 0
Vertex form of quadratic equation: [tex]y=a(x-h)^2+k[/tex]
(where (h, k) is the vertex)
[tex]\implies y=a(x-0)^2+2[/tex]
[tex]\implies y=ax^2+2[/tex]
To find a, input one of the points into the equation:
[tex](1, 3)\implies a(1)^2+2=3\implies a=1[/tex]
Therefore, the equation of the graph is [tex]y=x^2+2[/tex]
Question 2
If the parabola intersects the x-axis at (-2, 0) and (2, 0) then
[tex]y=a(x+2)(x-2)[/tex]
We are told that the y-intercepts if (0, -4). Input this into the equation to find a:
[tex]\implies a(0+2)(0-2)=-4[/tex]
[tex]\implies -4a=-4[/tex]
[tex]\implies a=1[/tex]
Therefore,
[tex]\implies y=(x+2)(x-2)[/tex]
[tex]\implies y=x^2-4[/tex]
Question 3
Given points: (-2, 4) (-1, 1) (0, 0) (1, 1)
This is likely to be a quadratic equation with a vertex of (0, 0) since the points (-1, 1) and (1, 1) are symmetrical about x = 0
Vertex form of quadratic equation: [tex]y=a(x-h)^2+k[/tex]
(where (h, k) is the vertex)
[tex]\implies y=a(x-0)^2+0[/tex]
[tex]\implies y=ax^2[/tex]
To find a, input one of the points into the equation:
[tex](-2,4)\implies a(-2)^2=4\implies a=1[/tex]
Therefore, the equation of the graph is [tex]y=x^2[/tex]
Question 4
[tex]f(x) = x^2 + 5[/tex]
If we wish to move the function to the left by 3 units, we substitute x for [tex]x+3[/tex]:
[tex]\begin{aligned}\implies f(x+3) & =(x+3)^2+5\\ & = x^2+6x+9+5\\ & = x^2+6x+14\end{aligned}[/tex]
[tex]\implies y=(x+3)^2+5[/tex]
20 g of copper was heated from 25°C to 80°C. How much energy was used to heat Cu? (Specific heat capacity of Cu is 0.385 J/g °C)
114°
Explanation:
ΔE = mcΔT
ΔE = 5(0.38)(80 - 20)
ΔE = 1.9(60)
ΔE = 114°
Solva.
3
ba
a+b=21
1
a = 37
0 = 20
a = 20
b = 11
1
o = 12
b = 9
b = 15
b = 16
10.
4
The values of a and b in the sytem of equation are 12 and 9 respectively.
How to find the variables(a and b) in the sytem of equation?b = 3 / 4 a
a + b = 21
Therefore, let's substitute b in equation(ii)
a + b = 21
a + 3 / 4 a = 21
4a + 3a / 4 = 21
7a / 4 = 21
cross multiply
7a = 21 × 4
7a = 84
divide both sides by 7
a = 84 / 7
a = 12
b = 3 / 4 a
b = 3 / 4 × 12
b = 36 / 4
b = 9
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i dont know what to do for tis
Answer:
is this by any chance about simultaneous equations? If so,
Step-by-step explanation:
Step 1 is telling us to decide on whether x and y should be the unknown. For instance, you want x to be the unknown, so u solve for x.
Step 2 is telling us to write equations with x and y.
For example,
7x + 5y = 12
7x - 2y = 9
This may not be accurate but it is an equation.
Step 4 is telling us to check whether the solution is accurate or not. For instance, we say 7 is x. so we substitude 7 into the original equation to see whether the answer we found is correct.
For step 5, im not really sure.
hope this helps though???
The angles X, of a tree blowing from the vertical, are distributed
according to the probability distribution shown.
What is the probability that the tree's angle, from the vertical, will
be greater than 4 degrees?
0.1
0.7
0.9
1
Using the uniform distribution, it is found that there is a 0.9 probability that the tree's angle, from the vertical, will be greater than 4 degrees.
What is the uniform probability distribution?It is a distribution with two bounds, a and b, in which each outcome is equally as likely.
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
In this problem, the bounds are a = 3 and b = 13, hence:
[tex]P(X > 4) = \frac{13 - 4}{13 - 3} = 0.9[/tex]
There is a 0.9 probability that the tree's angle, from the vertical, will be greater than 4 degrees.
More can be learned about the uniform distribution at https://brainly.com/question/13889040
Answer:
There is a 0.9 probability that the tree's angle, from the vertical, will be greater than 4 degrees.
Step-by-step explanation:
just took the test :D
Find the number that makes the ratio equivalent to 4:8.
:64
Answer:
4:8 = 32:64
Step-by-step explanation:
4:8 = x:64
256=8x
32 = x
BRAINLIEST? TY!
Write an equation for the line that passes through (−8.5,11) and (5,−2.5)
y = -x + 2.5
slope formula:
[tex]\sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]
find slope:
[tex]\rightarrow \sf \dfrac{-2.5-11}{5-(-8.5)}[/tex]
[tex]\rightarrow \sf \dfrac{-13.5}{13.5}[/tex]
[tex]\rightarrow \sf -1[/tex]
equation formula:
[tex]\sf y_1-y = m(x_1-x)[/tex]
find equation:
[tex]\hookrightarrow \sf y-11=-1(x-(-8.5)[/tex]
[tex]\hookrightarrow \sf y-11=-x-8.5[/tex]
[tex]\hookrightarrow \sf y=-x-8.5+11[/tex]
[tex]\hookrightarrow \sf y=-x+2.5[/tex]
Slope:-
m=-2.5-11/5+8.5m=-13.5/13.5m=-1Equation in point slope form
y-11=-1(x+8.5)y-11=-x-8.5y=-x+2.5
Answer 1-3 please. Thank you.
Answer:
If we look at this spinner, we first need to find out how many letters there are in total.
There are 12 letters in total.
1.
For this question, they want us to find the probability of getting the letter 'R'.
We need to find how many letter 'R's there are.
There are 2 lettered 'R', out of the 12 letters.
So the probability of getting the letter 'R' is 2/12 which simplifies to 1/6.
2.
For this question, they want us to find the probability of getting the letter 'L'.
We need to find how many letter 'L's there are.
There are 3 lettered 'L's, out of the 12 letters.
So the probability of selecting the letter 'L' is 3/12 which simplifies to 1/4.
3.
For this question, they want us to find the probability of getting the letter 'B'.
We need to find how many letter 'B's there are.
There are 0 lettered 'B's, out of the 12 letters.
Therefore the probability of selecting the letter 'B' is impossible.
4.
For this question, they want us to find out which letter has the most likely chance of getting landed on.
In order to find this, we need to find one letter that is repeated a lot in this spinner, that way it is more likelier of getting that letter.
Let's look at each individual letter keeping the letters we've found so far to the side.
P(Z) = 4/12, which simplifies to 1/3.
P(S) = 1/12, which is already in simplest form.
P(F) = 2/12, which simplifies to 1/6.
Now let's compare all the probabilities for selecting each letter.
P(R) = 1/6
P(L) = 1/4
P(B) = impossible ← immediately eliminate this choice
P(Z) = 1/3
P(S) = 1/12
P(F) = 1/6
Now out of all of these probabilities, we can infer that the chances of getting the letter 'Z' is the most likeliest.
Please help with my homework. I will give a brainlist out. Only solve 27 please.
Now
Base×Height=8517H=85H=85/17H=5ftLast month Kim trained 3 times as many dogs as cats. If the total number of cats and dogs she trained last month is 28, how many cats did Kim train?
1. Draw a model 2. Write an equation and solve.
2nd Question: How many more dogs than cats did Kim train?
1. Draw a model 2. Write an equation and solve.
Answer:
1. 7
2. 14
Step-by-step explanation:
Check the attachment.
What number has 6 tens and 1
more one than tens?
Answer:
17
Step-by-step explanation:
billy took a 3/4 mile hike in the woods. if the stopped every 1/4 of a mile to drink from his water bottle, how many times did the top?
Leah drank
2 thirds of
liter of water Monday before going jogging. She drank
3
fourths
liter of water after her jog. How much water did Leah drink altogether? Write your answer as a mixed number. ( kinda got confused on this)
Answer:
17/12=1 5/12
Step-by-step explanation:
the addition of 2/3+3/4=17/12=~1 5/12
HELP MEEEE PLEASEEE, SOMEONE...
Answer:
1/7 chance of happening
(Hi!, I hope you found this helpful. Please tell me if you disagree with my answer. Have a great day:)
Would this improve my skills or just give me the answer
Step-by-step explanation:
Ummm i think you should try your best cause thats how you improve
Explain how the distance formula can prove Pythagoras' Theorem. In your
explanation use the Pythagoras Theorem and how the distance formula can be used
with a right triangle when only given the hypotenuse.
Answer:
Given a triangle ABC, Pythagoras' Theorem shows that:
[tex]c^2=a^2+b^2[/tex]
Thus,
[tex]c = \sqrt{a^2+b^2}[/tex]
The distance formula, gives an equivalent expression based on two points at the end of the hypotenuse for a triangle.
[tex]d^2 = (x_{2} -x_{1})^2 + (y_{2} -y_{1})^2[/tex]
[tex]d = \sqrt{(x_{2}-x_{1})^2 + (y_{2} -y_{1})^2 }[/tex]
Therefore when given the hypotenuse with endpoints at
[tex](x_{1}, y_{1}) and {(x_{2}, y_{2})[/tex]
We know that the third point of the right triangle will be at
[tex](x_{2}, y_{1})[/tex]
and that the two side lengths will be defined by the absolute values of:
[tex](x_{2} - x_{1}) = a[/tex]
[tex](y_{2} - y_{1}) = b[/tex]
GIVEAWAY!! QUICK QUESTION!!!
Mr. Segura told Ms. Chang that the coefficient of kk is 11. What would you tell one of your classmates that the coefficient of -k−k is? Type the number, don't write it out!
Answer:
-2
Step-by-step explanation:
Given :
An example of a coefficient ⇒ '11' in 11kkSolving :
The coefficient is the part that precedes the variable(s)Therefore, on solving -k - k⇒ -2k⇒ -2 is the coefficientAnswer:
-2
Step-by-step explanation:
Given expression: -k - k
Combine like terms and simplify:
⇒ -k - k
⇒ -(k + k)
⇒ -(2k) = -2k
Determining the constant:
The constant of the term MUST be an integer. It CANNOT be a variable. In this case, the only constant that is a cooeficient of k is -2.
Thus, the cooeficient of -k−k is -2.
A banner is made of a square and a semicircle. The square has side lengths of 26 inches. One side of the square is also the diameter of the semicircle. What is the total area of the banner? Use 3.14 for π.
Answer:
941.33 in^2.
Step-by-step explanation:
The area of a semicircle = 1/2 area of circle = 1/2 * 3.14 * radius^2.
The radius = 1/2 * 26 = 13 in.
Total area = area of square + area of semicirccle
= 26^2 + 1/2 * 3.14 * 13^2
= 676 + 265.33
= 941.33 in^2.
A vacant rectangular lot is being turned into a community vegetable garden with a uniform path around it. area of the lot is represented by 4x^2 40x - 44 where x is the width of the path in meters. Find the wisdom the path surrounding the garden.
By factorizing the expression, 4x² + 40x - 44, the width of the path (x) is calculated as: 11 meters.
How to Factorize an Expression?To factorize an expression, such as 4x² + 40x - 44, we need to determine the two factors that will give us -176 when multiplied, and also give us 40 when added.
To find the width of the path, x, we need to factorize 4x² + 40x - 44, using the two factors, 4 and -44.
4x² - 44x + 4x - 44
(4x² - 44x) + (4x - 44)
4x(x - 11) + 4(x - 11)
(x - 11)(4x + 4) = 0
x = 11 or x = -4/4 = -1
The value of the width of the path, x, cannot be negative. Therefore, the width of the path would be: 11 meters.
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#SPJ1
anyone knows the answer?!
Answer:
The third option
Step-by-step explanation:
the lowest point on function 1 is -7
the lowest point on function 2 is -9
7. Which expressions represent the total area of the
large rectangle? Select all that apply.
A. 6(m+n
B. 6n + m
С. 6n + 6т
D. Omn
E. (n + m)6
Answer:
D.
Step-by-step explanation:
Not for sure sorry but i think its D or A so so sorry
45% of the children in a school have a dog, 30% have a cat, and 18% have a dog and a cat. What percent of those who have a dog also have a cat
The percentage of the children that have dog or cat is = 57%
Calculation of percentage of childrenThe percentage of children that have a dog = 45%
The percentage of children that have a cat = 30%
The percentage of children that have dog and cat= 18%
Therefore the percentage of children that have dog or cat = (45 + 30) - 18
= 75 - 18
= 57%
Therefore, the percentage of the children that have dog or cat is = 57%
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7. For a party, Allison orders 15 pizzas. Some of the pizzas are pepperoni and cheese and cost $11.50 each. The rest of the pizzas are deluxe and cost $15.25 each. The total cost for the pizzas including a $5 delivery charge is $200. How many of the pizzas are deluxe?
Answer:
6 deluxe pizzas
Step-by-step explanation:
200-5=195
195 is the total cost of pizzas
195=11.50x+15.25y
y=−0.75x+12.79
(the y intercept and slope are rounded)
x is reg. pizzas. y is deluxe
x+y=15
y=-x+15
if you plot both y=-x+15 and y=-0.75+12.79 you get coordinates that round to 9,6
9 pizzas
6 deluxe pizzas.
The points P (4, 1) and Q (-2, 4) are
reflected in line y = 3. Find the co-ordinates
of P', the image of P and Q', the image of
Q.
Step-by-step explanation:
hope it will help you
thank you
Answer:
Step-by-step explanation:
The line y = 3 is a horizontal line.
In order for us to reflect these two points, we need to draw our horizontal line and graph those points on the coordinate plane. Then you count the number of points that your original coordinates are away from the horizontal line. Once you have got that down, you count the same number on the other side (over line) and then plot and label your new coordinates.*View the attached graph*
Hope this helps!
A shop keeper sold 7 3/4 kg, 2 1/2 kg and 3 3/5 kg of sugar to three customers in a day. Find the total weight of sugar on that day?
Pls it is urgent
Answer:
13.85kg
Step-by-step explanation:
7 3/4=7.75
2 1/2=2.5
3 3/5=3.6
7.75+2.5+3.6
=13.85kg
If a gas tank and hold 25 gallons how many gallons does it contain when it is 2/5 full
Please help i really need help with this one
9.
about 5/7 of the earth's surface is covered with water.
about 88 957 440 km squared is land. in km², about how
much of the earth's surface is covered with water?
What is the area of the figure triangle sides 3, 4, 8
Answer:
Area of a triangle = (base x height) / 2
if the base is 3 and height is 4
Area = (3x4)/2 = 6 sq units
if the base is 4 and height is 8
Area = (4x8)/2 = 16 sq units
if base is 3 and height is 8
Area = (3x8)/2 = 12 sq units
Milan is drawing a triangle. One side has a length of 9 cm, and another side has a length of 6 units. What could be the length of the third side?
3 cm
7 cm
15 cm
18 cm
Answer: 7 cm
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP *67 points*
If it didn't have that piece cut out on the bottom, it would be a rectangle that's 9cm wide and 5cm high. Its area would be 9x5= 45 cm².
But that piece is cut out of the bottom. The cut-out piece is 3cm wide and 3cm high, so its area is 3x3= 9 cm².
9 cm² have been cut out of the 45 cm² of the complete big rectangle. So the remaining area of the figure is 45 - 9 = 36 cm² .
Kelly's monthly profit for selling candles is represented by the function P (x) = 7.5x - 200, where x represents the number of candles sold. Complete each table
Profit is selling price minus cost price, we assumed that the number of candles sold is 100, then the profit is $550
Note: The question is not complete
Cost and Selling priceGiven Data
From the expression we can see the followingcost per candle = $7.5Number of candles sold for the month = xTotal cost of candles purchased for the month = $200We have the expression
P (x) = 7.5x - 200
Assuming the number of candles sold is x = 100
P (100) = 7.5*100 - 200
P (100) = 750 - 200
P (100) = $550
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