Answer:
Therefore the answer is the fourth option y = f(x) = [tex]x^{2}[/tex] - 8x + 13
Therefore when x = 4 then y = -3 from the equation of parabola and this is the required vertex.
Step-by-step explanation:
i) f(x) = [tex]x^{2}[/tex] + 8x + 19 = [tex](x + 4)^{2}[/tex] + 3. SO the vertex is at (-4, 3)
Therefore the answer is the fourth option y = f(x) = [tex]x^{2}[/tex] - 8x + 13
= ([tex]x^{2}[/tex] - 8x + 16) + 3 = [tex](x-4)^{2}[/tex] - 3
Therefore when x = 4 then y = -3 from the equation of parabola and this is the required vertex.
Final answer:
The function with a vertex at the point (4, -3) is f(x) = x² - 8x + 13. This is concluded by using the vertex formula for a quadratic equation and checking the resulting coordinates against the given options.
Explanation:
The question is asking which of the given functions has a vertex at the point (4, -3). To find the vertex of a quadratic function of the form f(x) = ax² + bx + c, we can use the vertex formula, which is h = -b/(2a) for the x-coordinate, and then plug that back into the equation to find the y-coordinate. In this case, the function with the vertex (4, -3) must have the x-coordinate of the vertex at x = 4. Plugging this into the vertex formula, we get 4 = -b/(2a). We then look for a function where -b/(2a) = 4. The function f(x) = x² - 8x + 13 is the correct one because when we apply the formula -(-8)/(2*1) = 8/2 = 4. To confirm, we substitute x = 4 into the function: (4)² - 8(4) + 13 = 16 - 32 + 13 = -3, which gives us the y-coordinate of the vertex, -3.
evaluate the variable expression when a=-4, b=2, c=-3, and d =4. b-3a/bc^2-d
Answer:
Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is
[tex]\dfrac{b-3a}{bc^{2}-d}=1[/tex]
Step-by-step explanation:
Evaluate:
[tex]\dfrac{b-3a}{bc^{2}-d}[/tex]
When a=-4, b=2, c=-3, and d =4
Solution:
Substitute, a=-4, b=2, c=-3, and d =4 in above expression we get
[tex]\dfrac{b-3a}{bc^{2}-d}=\dfrac{2-3(-4)}{2(-3)^{2}-4}\\\\=\dfrac{2+12}{18-4}\\\\[/tex]
[tex]\dfrac{b-3a}{bc^{2}-d}=\dfrac{14}{14}=1[/tex]
Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is
[tex]\dfrac{b-3a}{bc^{2}-d}=1[/tex]
Under a dilation centered at the origin, the point (-4 , 3) has image at (8 , -6) The dilation is
Answer:
Balanced chemical equations only show formulae, not names. A balancing number, written in normal script, multiplies all the atoms in the substance next to it.
32 loaves of bread total, wheat loaves has 8 more then the rye loaves. How many wheat loaves are there?
Answer:
Step-by-step explanation:
Let the no. Of rye bread = x
Wheat bread = x + 8
The total bread is 32
: x + x + 8 = 32
2x = 32 - 8
2x = 24
x = 24/2
x = 12
No. Of wheat bread = x + 8 = 12+8
No. Of wheat bread = 20
Answer:
Wheat loaves is 20
Step-by-step explanation:
Let wheat loaves be A
And rye loaves be B
A + B = 32
Hence A = B + 8
So, B + B + 8 = 32
2B = 24
B = 12
A = 20
PLEASE ANSWER THIS ASAP
Write an equation in slope intercept form for the line that passes through (4,-1) and is perpendicular to the graph of y=7/2x-3/2
Answer:
The equation of line passes through [tex](4,-1)[/tex] and perpendicular to the graph [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]y=\frac{-2x}{7}+\frac{1}{7}[/tex]
Step-by-step explanation:
Given point is [tex](4,-1)[/tex] and equation of line is [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex]
Let the slope of line that passes through point [tex](4,-1)[/tex] is [tex]m_1[/tex]
And slope of line [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]m_2=\frac{7}{2}[/tex] . As it is in the form of [tex]y=mx+c[/tex]
We know the relation between slope of perpendicular line are given by
[tex]m_1\times m_2=-1\\And\ m_1=\frac{-1}{m_2}[/tex]
So, the slope [tex]m_1=\frac{-1}{\frac{7}{2}}=\frac{-2}{7}[/tex]
Now, we can write the equation of line having point [tex](4,-1)[/tex] and slope [tex]\frac{-2}{7}[/tex]
[tex](y-y_1)=m(x-x_1)\\\\(y-(-1))=\frac{-2}{7}(x-4)\\\\y+1=\frac{-2x}{7}-(\frac{2\times -4}{7})\\ \\y+1=\frac{-2x}{7}+\frac{8}{7}\\\\y=\frac{-2x}{7}+\frac{8}{7}-1\\\\y=\frac{-2x}{7}+\frac{8-7}{7}\\\\y=\frac{-2x}{7}+\frac{1}{7}[/tex]
So, the equation of line passes through [tex](4,-1)[/tex] and perpendicular to the graph [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]y=\frac{-2x}{7}+\frac{1}{7}[/tex]
Simplify the expression 2j+4j+j+7
Answer:
7j+7
Step-by-step explanation:
2j+4j+j+7
combine like terms
7j+7
Sorry I don't really know how to explain it, but you just have to combine terms with the same unit
hemraj made $135 for 9 hours of work. at the same rate, how many hours would he have to work to make $165?
Answer:
11 hrs
Step-by-step explanation:
so he made 135 for 9 hrs.....thats (135/9) = $ 15 an hr
so if he made 165, he would have to work (165/15) = 11 hrs <==
4 2/5 divided by 1 1/5
Will mark brainliest and 15 points
Answer: its going in straight lines
Step-by-step explanation:
The test scores for a math test are displayed in the following box plot. What percent of the students scored at least 75 on the test?
Please show the picture of the box plot otherwise your question is unanswerabe.
What is the remainder when 16,055 is divided by 16? Please i need help
Answer:
16,055/16 = 1003
The remainder would be 7
Step-by-step explanation:
I’m so cunfused! Help please?
Answer:
36
Step-by-step explanation:
To obtain the required number, multiply 27 by the inverse of [tex]\frac{3}{4}[/tex]
The inverse of [tex]\frac{3}{4}[/tex] is [tex]\frac{4}{3}[/tex] ( fraction turned upside down ), thus
[tex]\frac{4}{3}[/tex] × 27 ← divide 3 and 27 by 3
= 4 × 9 = 36
How do you solve -2(x+5)=4
Answer:x = -7
Step-by-step explanation:
-2x-10=4
-2x=14
-x=7
X=-7
Answer:
x = -7Step-by-step explanation:
[tex]-2(x+5)=4\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2\!\!\!\!\diagup(x+5)}{-2\!\!\!\!\diagup}=\dfrac{4\!\!\!\!\diagup^2}{-2\!\!\!\!\diagup_1}\\\\x+5=-2\qquad\text{subtract 5 from both sides}\\\\x+5-5=-2-5\\\\x=-7[/tex]
Tabitha earns $8.50 per hour at her summer job. She wants to save money to buy a tablet that costs $289 plus 6% sales tax. Tabitha has already saved $75. write and solve an inequality that shows how many hours Tabitha will need to work to have enough money to buy the tablet.
Answer:
The Inequality that shows number of hours Tabitha will need to work to have enough money to buy the tablet is [tex]75+8.5x\geq 306.34[/tex].
Tabitha needs to work at least 28 hours to buy the tablet.
Step-by-step explanation:
Amount earn per hour = $8.50
Amount already saved = $75
Cost of tablet = $289
Sales tax = 6%
We to write and solve the inequality number of hours Tabitha will need to work to have enough money to buy the tablet.
Solution:
Let the number of hours she need to work be 'x'.
First we will find the total amount required to buy tablet.
Amount of sales tax = [tex]\frac{6}{100}\times289 = \$17.34[/tex]
Now Total cost to buy tablet will be equal to sum of Cost of tablet and Amount of sales tax.
framing in equation form we get;
Total cost to buy tablet = [tex]289+17.34 = \$306.34[/tex]
Now we can say that;
Amount already saved plus Amount earn per hour multiplied by Amount earn per hour should be greater than or equal to Total cost to buy tablet.
framing in equation form we get;
[tex]75+8.5x\geq 306.34[/tex]
hence The Inequality that shows number of hours Tabitha will need to work to have enough money to buy the tablet is [tex]75+8.5x\geq 306.34[/tex].
On solving the above Inequality we get;
First we will subtract both side by 75 we get;
[tex]75+8.5x-75\geq 306.34-75\\\\8.5x\geq 231.34[/tex]
Dividing both side by 8.5 we get;
[tex]\frac{8.5x}{8.5}\geq \frac{231.34}{8.5}\\\\x\geq 27.21[/tex]
Hence Tabitha needs to work at least 28 hours to buy the tablet.
Word Problem: You are traveling to your aunt's house that is 239 miles away. If you are currently twice as far from home as you are from your aunt's, how far have you traveled?
Answer:
119.5
Step-by-step explanation:
find the discriminant 7x^2-5x+1=0
Answer:
Therefore,
[tex]Discriminant=-3[/tex]
Step-by-step explanation:
Given:
[tex]7x^{2}-5x+1=0[/tex]
To Find:
Discriminant = ?
Solution:
For a Quadratic Equation ax²+bx+c=0
The Discriminant is given as
[tex]Discriminant=b^{2}-4ac[/tex]
On comparing we get
[tex]a=7\\b=-5\\c=1[/tex]
Substituting the values we get
[tex]Discriminant=(-5)^{2}-4\times 7\times 1\\Discriminant=25-28\\Discriminant=-3[/tex]
Therefore,
[tex]Discriminant=-3[/tex]
What is the solution to the system of equations?
(3x+2y = 39
(5x-y=13
O (4,7)
O (7,4)
O (12,5)
(5, 12)
Answer:
X = 5
Y= 12
Step-by-step explanation:
3x + 2y = 39 —> (1)
5x - y = 13 —> (2)
Multiply (2) with 2
10x - 2y = 26 —> (b)
(1) + (b)
This will eliminate the y factor, leaving:
13x = 65
Therefore, x = 65/14
X= 5. Put this value of 5 in equation 1, which gives;
15 + 2y = 39
2y = 39-25
2y = 24
Y = 12
Answer:
x=5
y = 12
Step-by-step explanation:
3x + 2y = 39
2y = 39 - 3x
y = (39 - 3x) / 2
5x - y = 13
5x - ((39 - 3x) / 2) = 13
5x - 39/2 + 3/2x = 13
5x + 3/2x = 13 + 39/2
13/2x = 65/2
x = 65/2 * 2/13
x = 65/13
x = 5
y = (39 - 3x) / 2
y = (39 - 3*5) / 2
y = (39 - 15) / 2
y = 24/2
y = 12
What is the measure of angle x, in degrees, in the figure shown? A triangle with angle measure 60 degrees and 53 degrees. The third angle has an unknown measure, x degrees.
Answer: x = 67
Step-by-step explanation:
60+53+x = 180
The degrees of a triangle always equal 180
113+x = 180
Subtract the 113 from the 180
x= 67
Answer:113
explanation: hope it helps☺
How dose 4x+7=19. Work
Answer:
3
Step-by-step explanation:
4x+7=19
4x=19-7
4x=12
x=12/4
x=3
20 POINTS FOR REAL please answer
The data on the graph show the foot lengths and forearm lengths for a group of people. The line of best fit for the data is shown. Use the equation of the line of best fit to predict the length of a person’s forearm if the length of their foot is 8 inches.
A graph is labeled as Foot Length versus Forearm Length. The horizontal axis is labeled as Length of Foot left parenthesis inches right parenthesis and the vertical axis is labeled as Length of Forearm left parenthesis inches right parenthesis. The values on the horizontal axis range from 0 to 15 in increments of 1 and the values on the vertical axis range from 0 to 15 in increments of 1. Several points are scattered throughout the graph and a line is shown which passes between these points and the equation of the line is labeled as y equals 1 decimal point 1 1 x minus 0 decimal point 8 3.
A.
8.88 inches
B.
6.94 inches
C.
9.16 inches
D.
8.05 inches
Answer:
Option D.
8.05 inches
Step-by-step explanation:
Let
x ----> Length of Foot in inches
y ----> Length of Forearm in inches
we have
[tex]y=1.11x-0.83[/tex]
For x=8 in
substitute the value of x in the linear equation and solve for y
[tex]y=1.11(8)-0.83=8.05\ in[/tex]
write the expression in the standard form a+bi (showing all work)
(2-i)^3
[tex]2-11i \text{ is the standard form of given expression }[/tex]
Solution:
The standard form of complex number is: a + bi
where a is the real part and bi is the imaginary part
Given expression is:
[tex](2-i)^3[/tex]
Expand the above expression using algebraic identity
[tex](a-b)^3=a^3-b^3-3ab(a-b)[/tex]
[tex]\text{For } (2-i)^3 \text{ we get, a = 2 and b = i}[/tex]
Thus on expanding using the above algebraic identity we get,
[tex](2-i)^3=(2)^3-(i)^3-3(2)(i)(2-i)[/tex]
Simplify the above expression
[tex](2-i)^3=8 -i^3-6i(2-i)\\\\(2-i)^3=8 -i^3-12i+6i^2[/tex]
We know that,
[tex]i^2 = -1\\\\i^3 = -i[/tex]
Substituting in above simplified expression, we get,
[tex](2-i)^3=8-(-i)-12i+6(-1)\\\\(2-i)^3=8 + i -12i -6\\\\\text{Combine the like terms }\\\\(2-i)^3=8 - 6 + i -12i\\\\(2-i)^3=2-11i[/tex]
Thus the given expression is expressed in standard form
When one end of a seesaw is 9 inches above the ground and the other one is 21 inches above the ground how far are the ends above the ground when the seesaw is level
Answer:
15
Count down from 21 and count up from 9 till you have the same number.
21 9
20 10
19 11
18 12
17 13
16 14
15 15
Now they are the same height.
Step-by-step explanation:
When a seesaw is level, the height of both ends above the ground is the average of the heights when one end is lifted. In this case, both ends are 15 inches above the ground when the seesaw is level.
Explanation:The question is asking for the height of the ends of a seesaw when it is in a level or balanced position. A seesaw balances when it is level, and both ends are at the same height. Considering the given details, one end is 9 inches and the other is 21 inches above ground, when they switch positions due to the seesaw's pendulum-like movement. But when the seesaw is level, both ends are at the same height. Therefore, the height of both ends of the seesaw when it is level is the average of 9 inches and 21 inches. You calculate this average by adding the two given distances and dividing by 2. So:
((9 inches + 21 inches) / 2) = 15 inches
So, when the seesaw is level, both ends are 15 inches above the ground.
Learn more about seesaw here:https://brainly.com/question/21623981
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Your neighbor has decided to enlarge his garden. The garden is rectangular with width 6 feet and length 15 feet. The new garden will be similar to the original one, but will have a length of 35 feet. Find the perimeter of the original garden and the enlarged garden.
Answer:
Original garden: 42 feet
Enlarged garden: 98 feet
Step-by-step explanation:
Perimeter = length (2) + width (2)
Original perimeter:
P = 15(2) + 6(2)
P = 30 + 12
P = 42 feet
In this problem, similar is proportional, so the new garden will be proportional to the old one.
If the original length was 15 and the new length is 35, then 15 would have had to have been multiplied by 2 1/3. That means you need to multiply 6 by 2 1/3, which is 14. That means the dimensions of the enlarged yard is 14 (width) × 35 (length).
Enlarged perimeter
P = 35(2) + 14(2)
P = 70 + 28
P = 98 feet
Final answer:
The perimeter of the original rectangular garden is 42 feet, and the perimeter of the enlarged garden, which is similar in proportion to the original, is 98 feet.
Explanation:
The original garden has a width of 6 feet and a length of 15 feet. The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, the perimeter of the original garden is 2(6 feet + 15 feet) = 2(21 feet) = 42 feet.
Since the new garden is similar to the original one, and its length is 35 feet, it means that the width will also increase in the same proportion. The original length to width ratio is 15:6 which simplifies to 5:2. Applying this ratio to the new length of 35 feet will give us the new width:
35 feet / 5 = 7 feet (per unit of the ratio)
7 feet * 2 = 14 feet (new width)
The perimeter of the enlarged garden is then 2(14 feet + 35 feet) = 2(49 feet) = 98 feet. So, the perimeter of the original garden is 42 feet and the perimeter of the enlarged garden is 98 feet.
At present, a man is 5 times older than his daughter. In 7 years, the man is 3 times as old as his daughter. What are their present ages?
The present age of father is 35 and daughter is 7.
Step-by-step explanation:
Let,
Age of father = x
Age of daughter = y
According to given statement;
A man is 5 times older than his daughter.
x = 5y Eqn 1
In 7 years, the man is 3 times as old as his daughter.
x+7 = 3(y+7)
[tex]x+7=3y+21\\x=3y+21-7\\x=3y+14\ \ \ Eqn\ 2[/tex]
Putting value of x from Eqn 2 in Eqn 1
[tex]3y+14=5y\\14=5y-3y\\14=2y\\2y=14[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{14}{2}\\y=7[/tex]
Putting y=7 in Eqn 1
[tex]x=5(7)\\x=35[/tex]
The present age of father is 35 and daughter is 7.
Keywords: linear equation, substitution method
Learn more about substitution method at:
brainly.com/question/8929610brainly.com/question/8908016#LearnwithBrainly
Final answer:
The present ages of the man and his daughter are 35 years and 7 years, respectively.
Explanation:
The question asks us to find the current ages of a man and his daughter, given that the man is currently five times older than his daughter and that after 7 years, he will be three times as old as her. To solve this, we can set up two equations based on the information provided:
Let D be the daughter's current age, the man's current age is 5D (since he is five times older).In 7 years, the daughter's age will be D+7 and the man's age will be 5D+7. At that time, the man will be three times as old as his daughter, so we have 5D+7 = 3(D+7).Now, we solve the equation from step 2 to find the daughter's age:
5D + 7 = 3(D + 7)5D + 7 = 3D + 215D - 3D = 21 - 72D = 14D = 7So, the daughter is currently 7 years old. To find the man's age, we multiply the daughter's age by 5:
Man's age = 5 x 7 = 35 years old
Therefore, the man is currently 35 years old and the daughter is 7 years old.
What is the complete factorization of 64x2 - 48x + 9?
O A. (8x - 3)(8x+3)
B. (8x - 3)2
OC. 4(4x - 3)2
D. 4(4x - 3)(4x+3)
Please helppp
Answer:
B) (8x-3)²
Step-by-step explanation:
64x2 - 48x + 9= (8x)² - 2*8x*3 + 3²
Compare with a² - 2ab +b² = (a-b)²; a = 8x and b =3
=(8x-3)²
A school charges $4.99 per child, $6.00 per adult, and $2.50 per baby, to go see the school play. How much money would they collect if 12 kids, 25 adults, and 6 babies came to see the play?
Answer:
$224.88
Step-by-step explanation:
4.99×12= 59.88 for kids
6×25=150 for adults
2.50×6=15 for babies
59.88+150+15= $224.88 collected in total
Is 16.275 greater then 16.28
Answer:
no
Step-by-step explanation:
16.28 can also be written 16.280 (you could add as many zeros to the end as you want its still the same number)
280 is bigger than 275
95-a (b+c) when a=9, b= 3, and c = 7.4
Answer:
95-9 (3+7)
95-9 (10)
86 (10)
= 8600
Step-by-step explanation:
how many solutions does the system of inequalities graphed below have?
A. 0
B. 1
C. 2
D. infinitely many
Answer:
A 0
Step-by-step explanation:
because the lines are a paraell and they don't touch
A solution is a point that is in both shaded regions at the same time. This is impossible due to the fact the regions do not overlap. This is like saying there is a number larger than 1 and this same number is less than -1 at the same time. This is why there are no solutions to this system of inequalities.
You can also write an equation for equivalent ratios. The equation at the right can be used to find the actual length x of the sculpture room in the museum. Complete the equation and explain what each part represents
The equation relates the scale drawing of the sculpture room to its actual dimensions using equivalent ratios. By setting the actual length corresponding to 6 cm on the drawing to 30 m, we can solve for the unknown actual length, which is 6 meters. So, the actual length of the sculpture room in the museum is 6 meters.
Completing the equation:
The equation in the image is missing a part: it should be:
1 cm : 5 m = x cm : 30 m
Explanation of the equation:
1 cm: This represents the length of the sculpture room on the scale drawing, as indicated by the scale 1 cm : 5 m.
5 m: This represents the actual length corresponding to every 1 cm on the scale drawing.
x cm: This is the unknown variable we're trying to solve for. It represents the actual length of the sculpture room in the museum.
30 m: This is a constant value, chosen because we want to find the length corresponding to 6 cm on the scale drawing (since the sculpture room in the drawing is 6 cm long).
What each part represents:
The colon (:) separates the two equivalent ratios.
The first ratio (1 cm : 5 m) represents the scale factor, which is the conversion factor between the scale drawing and the actual museum dimensions. It tells us that every 1 cm on the drawing corresponds to an actual length of 5 m.
The second ratio (x cm : 30 m) represents the unknown ratio we want to solve for. It relates the unknown actual length (x cm) to the desired actual length of 30 m (corresponding to 6 cm on the drawing).
Solving for x:
To solve for x, we can cross-multiply the two ratios:
(1 cm) * (30 m) = (5 m) * (x cm)
Simplifying the equation, we get:
30 m = 5x cm
Finally, dividing both sides by 5, we get:
x = 6 m
Therefore, the actual length of the sculpture room in the museum is 6 meters.
The sum of three consecutive even numbers is 84. What is the smallest of the three numbers?
Answer: 26
Step-by-step explanation: In this problem we have 3 consecutive even numbers whose sum is 84 and it asks us to find the smallest number.
Consecutive even numbers can be represented as x, x + 2, and x + 4.
Since the sum of these is 84, our equation reads
x + (x + 2) + (x + 4) = 84.
Simplifying on the left we get 3x + 6 = 84.
Subtract 6 from both sides and we have 3x = 78.
Divide both sides by 3 and x = 26.
So our smallest number is 26.
To find the smallest of three consecutive even numbers that sum up to 84, we set up an equation and solve for 'x', where 'x', 'x+2', and 'x+4' represent the numbers. Solving this gives us the smallest number, which is 26.
Explanation:Finding the Smallest of Three Consecutive Even NumbersIf the sum of three consecutive even numbers is 84, we can find the smallest number by setting up an equation. Let's denote the smallest even number as 'x'. The next consecutive even number would be 'x + 2', and the one after that would be 'x + 4'. The sum of these three numbers should equal 84:
x + (x + 2) + (x + 4) = 84
Simplifying this equation, we get:
3x + 6 = 84
Subtracting 6 from both sides, we have:
3x = 78
Now, dividing both sides by 3 gives us:
x = 26
Therefore, the smallest of the three consecutive even numbers is 26.