Answer:
[tex]\large\boxed{f(x)=(x+1)^2-4}[/tex]
Step-by-step explanation:
[tex]\text{The vertex form of a quadratic equation}\ f(x)=ax^2+bx+c:\\\\f(x)=a(x-h)^2+k\\\\(h,\ k)-\text{vertex}\\=====================================[/tex]
[tex]\bold{METHOD\ 1:}\\\\\text{convert to the perfect square}\ (a+b)^2=a^2+2ab+b^2\qquad(*)\\\\f(x)=x^2+2x-3=\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-3\\\\f(x)=(x+1)^2-4\\==============================[/tex]
[tex]\bold{METHOD\ 2:}\\\\\text{Use the formulas:}\ h=\dfrac{-b}{2a},\ k=f(k)\\\\f(x)=x^2+2x-3\to a=1,\ b=2,\ c=-3\\\\h=\dfrac{-2}{2(1)}=\dfrac{-2}{2}=-1\\\\k=f(-1)=(-1)^2+2(-1)-3=1-2-3=-4\\\\f(x)=(x-(-1))^2-4=(x+1)^2-4[/tex]
need the answer asap !! #34 !!
Answer:
A) 46 mph
Step-by-step explanation:
Step 1: To find the speed, you need to find the distance and time to travel between Chicago and Cleveland.
Distance = 354 miles
Time = 9: 50 am to 5: 30 pm
Time = 7 hours 40 minutes
Step 2: Convert time to hours
1 hour = 60 minutes
40 minutes = 60/40 = 2/3 hours
Step 3: Find the speed
Speed = Distance/Time
Speed = 354/7 + 2/3
Speed = 1062/23
Speed = 46.17 miles per hour rounded off to 46 mph
Therefore, A is the correct answer.
!!
(0201 LC)
Melissa made some chocolate pudding For every 3 cups of chocolate, she added 7 cups of milk. The ratio of chocolate to milk in Melissa's chocolate pudding is
Answer:
its c
3 : 7
3/7
Step-by-step explanation:
Answer:
3/7
Ratio is explained in sentence: For every 3 cups of chocolate, she added 7 cups of milk.
This is another way to say/show a ratio. It is also said as: 3:7, 3/7, and 3 to 7
The probability of spinning a 7 on a spinner is 0.083. If you spun 250 times, approximately how many times would the spinner land on 7
Answer:
21 times
Step-by-step explanation:
To find out how many times the spinner would land on the 7, take the probability times the number of times spun
250 * .083
20.75
It would land on 7 approximately 21 times
Answer:
The spinner will land on 7 approximately 21 times
Step-by-step explanation:
According to your question. The probability of spinning a 7 on the spinner is 0.083 (8.3%). You spin the spinner 250 times and you would like to know how many times the spinner would land on 7 based on the previous probability. To do this we will need to multiply the probability of the spinner landing on 7 in one spin with the amount of total spins.
[tex]250*0.083 = 20.75[/tex]
As shown above we can see that with a probability of 8.3% on 250 spins, the spinner will land on 7 approximately 21 times.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
In circle A, ∠BAE ≅ ∠DAE.
What is the value of x?
14
17
27
34
Answer:
x=17
Step-by-step explanation:
In circle A, ∠BAE ≅ ∠DAE.
∠BAE = 3x-24
∠DAE = x+10
According to the given condition:
∠BAE ≅ ∠DAE.
3x-24 = x+10
Combine the like terms:
3x-x=10+24
2x=34
Divide both the sides by 2
2x/2 = 34/2
x=17
Therefore the value of x = 17
The correct option is 17....
Answer:
The answer is 17 units on edg
Step-by-step explanation:
Select the correct answer.
Which expression is equivalent to x + y + x + y + 3(y + 5)?
Answer:
Step-by-step explanation:
Remove the brackets.
x + y + x + y + 3y + 15
Collect the like terms
2x + 5y + 15
This should be your answer.
Answer: 2x + 5y + 15
Solve the equation.1/8+c=4/5
Answer:
27/40
Step-by-step explanation:
We want to isolate the variable c. In order to do so, we have to subtract 1/8 from both sides. Then, on the left side, we have c, and on the right side we have 4/5-1/8. The fractions 4/5 and 1/8 do not have a common denominator, so we need to multiply 4/5 by 8/8 and 1/8 by 5/5 in order to reach a common denominator of 40 (5 and 8's least common multiple). Then, we get 32/40-5/40, or 27/40.
Side note: we are able to multiply by 8/8 and 5/5 because both of those fractions equal 1.
Write an equation (a) in slope intercept form and (b) in standard form for the line passing through (1,9) and perpendicular to 3x+5y=1.
Answer:
[tex]\large\boxed{a)\ y=\dfrac{5}{3}x+\dfrac{22}{3}}\\\boxed{b)\ 5x-3y=-22}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\m-slope\\b-y-intercept\\\\\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\=========================\\\\\text{We have the equation of a line in the standard form.}\\\text{Convert it to the slope-intercept form.}\\\\3x+5y=1\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\5y=-3x+1\qquad\text{divide both sides bvy 5}\\\\y=-\dfrac{3}{5}x+\dfrac{1}{5}\to m_1=-\dfrac{3}{5}[/tex]
[tex]a)\\\\y=m_2x+b\\\\m_1=-\dfrac{3}{5}\to m_2=-\dfrac{1}{-\frac{3}{5}}=\dfrac{5}{3}\\\\\text{Put the value of slope and the coordinates of the given point (1, 9)}\\\text{to the equation of a line:}\\\\9=\dfrac{5}{3}(1)+b\\\\9=\dfrac{5}{3}+b\qquad\text{subtract}\ \dfrac{5}{3}\ \text{from both sides}\\\\\dfrac{27}{3}-\dfrac{5}{3}=b\\\\\dfrac{22}{3}=b\\\\\text{Finally:}\\\\y=\dfrac{5}{3}x+\dfrac{22}{3}[/tex]
[tex]b)\\\\\text{The standard form of an equation of a line:}\\\\Ax+By=C\\\\\text{Convert the equation}\ y=\dfrac{5}{3}x+\dfrac{22}{3}\ \text{to the standard form:}\\\\y=\dfrac{5}{3}x+\dfrac{22}{3}\qquad\text{multiply both sides by 3}\\\\3y=5x+22\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\-5x+3y=22\qquad\text{change the signs}\\\\5x-3y=-22[/tex]
What are the factors of x squared minus 4x minus 5?
Answer:
(x-5) (x+1)
Step-by-step explanation:
x^2 -4x-5
What 2 numbers multiply to -5 and add to -4
-5*1 = -5
-5+1 = -4
(x-5) (x+1)
What is the distance between (8, -3), (4,-7)?
A.- 6
B. 9
C.[tex]\sqrt{35}[/tex]
D.[tex]\sqrt{42}[/tex]
Thank You!
Answer:
[tex]4\sqrt{2}[/tex] which is none of your choices....
Did you mean (8,-3) and (4,-7)?
Step-by-step explanation:
We need to first find the distance between the x's.
Then the distance between the y's.
The distance between the x's is 8-4=4.
The distance between the y's is -3-(-7)=4.
So the distance between two points [tex](x_1,y1)\text{ and }(x_2,y_2)[/tex] is [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex].
So we already found x1-x2 and y1-y2 so now we have:
[tex]\sqrt{(4)^2+(4)^2}[/tex]
[tex]\sqrt{16+16}[/tex]
[tex]\sqrt{2(16)[/tex]
[tex]\sqrt{16}\sqrt{2}[/tex]
[tex]4\sqrt{2}[/tex]
Differentiate x^2/4-x^3
Answer:
x^4 + 8x
-----------------
(4-x^3)^2
Step-by-step explanation:
d /dx (x^2/(4-x^3))
When we differentiate a fraction u/v
df/dx = u/v
= v du/dx-u dv/dx
---------------------------
v^2
we know u = x^2 so du/dx = 2x
v = (4-x^3) so dv/dx = -3x^2
d dx = (4-x^3) (2x)- x^2 ( -3x^2)
-------------------------------------
(4-x^3)^2
Combining terms
(8x-2x^4) --3x^4
-------------------------------------
(4-x^3)^2
8x-2x^4 +3x^4
-------------------------------------
(4-x^3)^2
x^4 + 8x
-------------------------------------
(4-x^3)^2
3x + 7y + 6 = 0 what is the y intercept
Answer:
The y-intercept is located at (0, -6/7)
Step-by-step explanation:
First, we should convert this equation from Standard Form(ax+by+c=0) into Slope-Intercept Form(y = mx+b), with b being the y-value of the y-intercept.
Work:
3x+7y+6=0
First, isolate the variables by subtracting 6 from both sides to keep the equation equal
3x+7y = -6
Next, isolate the y-variable by subtracting 3x from both sides to keep the equation equal
7y = -3x - 6
Then, divide by +7 on both sides to keep the equation equal and to simplify the left side even more, to completely isolate the variable
y = -3x/7 -6/7
The y-intercept is located at (0, -6/7)
Jonathan borrowed $475 at a simple annual interest rate of 2%. How many years will it take him to repay the loan if he wants to pay $38 in interest?
A. 4
B. 5
C. 6
D. 7
Answer:
a
Step-by-step explanation:
rationalize the denomintaors 3square root of 3 - 3 square root of 3
Answer:
Please see attached image
Step-by-step explanation:
An analysis of the expression can be seen in the image below
See attached figure
A chef used one- third of a bag of potatoes for a meal. If the potatoes fed 7 people, what fraction of the bag did each person get?
Answer: 1/21 of the bag
Step-by-step explanation:
If only one person eats the meal they are consuming 1/3 of a bag of potatoes. However if more than one person is eating the potatoes we need to multiply 1/3 by the reciprocal of how many people are eating.
For example:
2 people 1/3*1/2=1/6
3 people 1/3*1/3=1/9
So then we apply this principle for seven people.
7 people 1/3*1/7=1/21
We can check our answer by working backwards
1/21*7=7/21=1/3
So each person got 1/21 of the bag.
If one kilogram equals 2.2 pounds, how many kilograms equal 112 pounds? Round your answer to the nearest hundredth, if necessary.
Answer:
50.91
Step-by-step explanation:
Write a proportion:
1 kg / 2.2 lb = x kg / 112 lb
Cross multiply:
2.2 x = 112
Divide:
x = 50.91
50.91 kg equals 112 pounds.
9 cu yd 113 cu in - 4 cu ft 129 cu in
Answer:
=8 yd³ 22 ft³ 1712 in³
Step-by-step explanation:
To perform the indicated operation we need to convert the given measurements of volume to common units.
1 yd = 3 ft
1 yd³=27ft³
1 ft³=1728 in³
Thus 9 yd³=(27×9)ft³
=243 ft³
113 in³ into ft= 113/1728
9 yd³ 113 in³= 243 113/1728 ft³
4 ft³ 129 in³= 4 129/1728 ft³ = 4 43/576 ft³
Performing the operation given in the equation:
243 113/1728 ft³ - 4 43/576 ft³ = 238 1712/1728 ft³
238 ft³= 8 yd³ 22 ft³ + (1712/1728) × 1728
=8 yd³ 22 ft³ 1712 in³
There are 3,280.84 feet in a kilometer. There are 5,280 feet in a mile. To the nearest hundredth, how many kilometers are in a mile?
Answer:
1.61
Step-by-step explanation:
1 mile × (5280 ft / 1 mile) × (1 kilometer / 3280.84 ft) = 1.61 kilometers
To convert miles to kilometers, divide the number of feet in a mile (5,280) by the number of feet in a kilometer (3,280.84). This calculation reveals that there are approximately 1.61 kilometers in a mile, a conversion factor that facilitates precise and efficient measurement conversions.
The question asks how many kilometers are in a mile, given that there are 3,280.84 feet in a kilometer and 5,280 feet in a mile. To find the answer, you can use the information that 1 kilometer equals 3,280.84 feet. Therefore, to convert feet to kilometers, you divide the number of feet by 3,280.84.
To find how many kilometers are in a mile, you follow these steps:
Start with the conversion factor that 1 mile = 5,280 feet.Since 1 kilometer = 3,280.84 feet, we divide the total feet in a mile by the number of feet in a kilometer to convert miles to kilometers. That calculation would be 5,280 feet / 3,280.84 feet per kilometer = 1.60934 kilometers.
To the nearest hundredth, there are 1.61 kilometers in a mile. This conversion is useful for making quick and accurate estimates between the two units of measurement commonly used in many parts of the world.
If sin x = -1/2, and 270° < x < 360°, what is cos(x - 30°)?
Answer:
x = -30
cos(x - 30) = ½
Step-by-step explanation:
Look at the picture
select the action you would use to solve x-3=12 . then select the property that justifies the action
The x is a placeholder for some currently unknown number. Let's say that number was 10. So we replace x with 10 to get 10-3 = 12. That statement is false because 10-3 is actually 7. What you can do is keep guessing until you get the right answer.
A much better approach is to undo what is happening to x. We have x and we subtract off 3 to get 12. Following this in reverse, we need to add 3 to both sides so that x is isolated.
x-3 = 12
x-3+3 = 12+3
x = 15
Let's replace x with 15 and see if the equation is true
x - 3 = 12
15 - 3 = 12
12 = 12
Sure enough we get the right answer.
The idea of adding 3 to both sides is possible through the additive property of equality (if a = b, then a+c = b+c)
==========================================
In summary, I added 3 to both sides using the additive property of equality. Doing this isolated x to get x = 15.
Square ABCD has side length 4. Determine the
area of the shaded region (use pi as 3).
Answer:
The area of the shaded region is [tex]8\ units^{2}[/tex]
Step-by-step explanation:
step 1
Find the curved area ACD (formed by segment AD, segment DC and the curved segment AC)
we know that
The curved area ACD is equal to the curved area ACB
The curved area ACD is equal to the area of the square minus the area of a quarter of circle
[tex]ACD=b^{2} -\frac{1}{4}\pi b^{2}[/tex]
we have that
[tex]b=4\ units[/tex]
substitute
[tex]ACD=4^{2} -\frac{1}{4}(3)(4)^{2}[/tex]
[tex]ACD=16 -12=4\ units^{2}[/tex]
step 2
Find the area of the shaded region
The area of the shaded region is equal to the area of the square minus two times the curved area ACD
so
[tex]4^{2} -2(4)=16-8=8\ units^{2}[/tex]
Help me please!!! What is the mean of the following data values?
A. 33
B. 27
C. 37
D. 43
Answer:
By mean, find the average. Add them all up and divide by how many numbers are there.
22+37+49+15+92= 215
215/5= 43.
Therefore, the answer is D, 43.
To find the mean, you add up all the values and then divide by the number of values. In this case, the mean is 43, which corresponds to option D.
To find the mean (average) of a set of data values, you sum all the values and then divide by the total number of values. In this case, you have the following data values: 22, 37, 49, 15, and 92.
Mean = (22 + 37 + 49 + 15 + 92) / 5
Mean = (215) / 5
Mean = 43
So, the mean of the given data values is 43.
The correct answer is D. 43.
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the perimeter and area of each figure:
a. A square with a side length of 3.5 inches.
[tex]3.5 \times 3.5 = 12.25 \: for \: are \\ 3.5 \times 4 = 14 \: for \: perimeter[/tex]
Susan Pollack had worked at Carl’s Garage as a receptionist for 22 years when she became permanently disabled. She was 55 years old at the time and had planned to retire at age 60. Her final average salary was $48,600 a year. Her rate of benefits is 2%. What is her annual disability benefit?
A. $26,244
B. $29,001
C. $25,667
D. $22,500
Answer:
it is C
Step-by-step explanation:
Answer:
The is A. Not c
Step-by-step explanation:
Help me plz. Haven’t been able to answer this problem. Even my TEACHER is stumped. (Mark brainliest)
Answer:
K 48 inches
Step-by-step explanation:
First lets determine how big of table cloth we need
The table is 3 ft in diameter which is 36 inches
That means the radius is d/2 = 36/2 = 18 inches
We need to add 5 inches to the radius to hang over the edge
18+5 = 23
We need to add the hem which is 1 inch
23+1 = 24
The radius is 24 inches
The diameter would be 2r = 2*24 = 48 inches
An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
Answer:
im kinda sure the answer is 120 degrees
Step-by-step explanation:
but maybe not
is a number less than 10 the same as the difference of a number and 10?
Answer:
Ten more than x x + 10
Step-by-step explanation:
Answer:
No.
10-x and x-10 are only the same when x=10.
They are not the same because subtraction is not commutative.
Step-by-step explanation:
A number less than 10 is 10-x .
The difference of a number and 10 means x-10.
10-x is not the same as x-10
We can find out when they are the same by solving:
10-x=x-10
Add x on both sides:
10=2x-10
Add 10 on both sides:
20=2x
Divide both sides by 2:
10=x
So they are only the same when x=10.
It is mainly not an identity because subtraction isn't commutative.
Given: angle 2 and angle 4 are vertical. Prove angle 2 congruent to angle 4
Answer:
Refer to pics
Step-by-step explanation:
Vertical angles are two angles which are vertically opposite and have the same measure. Thus, the two angles are to be congruent.
Vertical angles are often formed when two straight lines intersect at a point.
From the given question, the steps to prove that angle 2 and angle 4 are congruent are:
With reference to the sketch attached to this answer;
<AOC + <AOD + <BOC + <BOD = [tex]360^{o}[/tex] (sum of angle at a point)
Thus,
<AOC + <AOD = [tex]180^{o}[/tex] (supplementary angle property)
also,
<BOC + BOD = [tex]180^{o}[/tex] (supplementary angle property)
So that;
<AOD ≅ <BOC (vertically opposite angle property)
Therefore,
<2 and <4 are congruent (vertically opposite angle property)
It can be concluded that vertically opposite angles are equal in measure, thus congruent.
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Y varies directly with x and inversely with the source root of z if y =4 when x=z and z=4 what is y when x=6 and z=9
Answer:
8
I made a couple of assumptions so you might want to make sure I made the right assumptions.
I assumed you meant square root of z; not source of z.
I also assumed you meant x=2 not x=z.
Step-by-step explanation:
y varies directly with means y=k times something where k is a constant.
Inversely means to divide by whatever it says it varies inversely with.
So we have:
[tex]y=k \cdot \frac{x}{\sqrt{z}}[/tex]
We are given y=4 and x=2 and z=4, which means:
[tex]4=k \cdot \frac{2}{\sqrt{4}}[/tex]
[tex]4=k \cdot \frac{2}{2}[/tex]
[tex]4=k(1)[/tex]
[tex]4=k[/tex]
So the constant is k which means the equation for any (x,y,z) is:
[tex]y=4 \cdot \frac{x}{\sqrt{z}}[/tex]
We want to know y when x=6 and y=9:
[tex]y=4 \cdot \frac{6}{\sqrt{9}}[/tex]
[tex]y=4 \cdot \frac{6}{3}[/tex]
[tex]y=4 \cdot 2[/tex]
[tex]y=8[/tex]
Which point on the y-axis lies on the line that passes through
point C and is perpendicular to line AB?
O(-6,0)
O (0, -6)
O (0, 2)
O (2,0)
Answer:
0(0,2)
Step-by-step explanation:
0(0,2)
0(0,-6)
0(2,0)
0(-6,0)
The line perpendicular to the line AB passes through the point (0, 2)
What are perpendicular line?Two geometric objects are perpendicular if their intersection forms right angles at the point of intersection called a foot.
The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂.
Given is a graph of a line, we need to find the which point on the y-axis lies on the line that passes through point C and is perpendicular to line AB,
From the given figure in the question it is observed that the line AB passes through the points (-2, 4) and (2, -8)
The coordinate of point C is, (6, 4)
Obtain the slope of the line AB.
-8-4 / 2+2 = -3
Consider the slope of AB as, m1
m1 = -3
Consider a line which is perpendicular to the line AB passing through the point C.
Assume the slope of the perpendicular line as m2,
The product of the slope of two mutually perpendicular lines is always equal to -1
The equation formed for the slope is as follows: 1/3
Finding the equation of the line,
y-y₁ = m(x-x₁)
3y - x = 6
Therefore, the equation of the perpendicular line is 3y - x = 6
In option 3 it is given that the line perpendicular to AB passes through the point (0, 2)
The equation of the line which is perpendicular to AB is 3y - x = 6
Substitute for in the above equation
3y - (0) = 6
3y = 6
y = 2
From the above calculation it is concluded that the line passes through the point (0, 2).
This implies that option 3 is correct.
Hence, the line perpendicular to the line AB passes through the point (0, 2)
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Solve the equation 5x + (−2) = 6x + 4 using the algebra tiles. What tiles need to be added to both sides to remove the smaller x-coefficient? What tiles need to be added to both sides to remove the constant from the right side of the equation?
Answer:
a) Adding -5x on both sides of the equation to remove the smaller x-coefficient
b) Adding -4 on both sides will remove the constant from the right side of the equation
Step-by-step explanation:
Given equation:
5x + (−2) = 6x + 4
a) What tiles need to be added to both sides to remove the smaller x-coefficient?
Smaller x-coefficient is 5x to remove the smaller x-coefficient
So, Adding -5x on both sides of the equation to remove the smaller x-coefficient
b) What tiles need to be added to both sides to remove the constant from the right side of the equation?
the constant on right side is 4
Adding -4 on both sides will remove the constant from the right side of the equation
Answer:
What tiles need to be added to both sides to remove the smaller x-coefficient?
✔ 5 negative x-tiles
What tiles need to be added to both sides to remove the constant from the right side of the equation?
✔ 4 negative unit tiles
What is the solution?
✔ x = –6