Answer:
[tex]\large\boxed{y=4(x-3)^2+2\ \bold{vertex\ form}}\\\boxed{y=4x^2-24x+38\ \bold{standard\ form}}[/tex]
Step-by-step explanation:
The vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - vertex
We have the vertex at (3, 2) → h = 3 and k = 2.
Substitute:
[tex]y=a(x-3)^2+2[/tex]
The point (4, 6) is on athe parabola. Put the coordinates of this point to the equation:
[tex]6=a(4-3)^2+2[/tex] subtract 2 from both sides
[tex]6-2=a(1)^2+2-2[/tex]
[tex]4=a\to a=4[/tex]
Finally:
[tex]y=4(x-3)^2+2[/tex] vertex form
use (a - b)² = a² - 2ab + b²
[tex]y=4(x^2-6x+9)+2[/tex] use the distributive property
[tex]y=4x^2-24x+36+2[/tex]
[tex]y=4x^2-24x+38[/tex] standard form
Answer:
y=4(x-3)^2+2
Step-by-step explanation:
Hopefully this helps :)
Which polynomial function has a leading coefficient of 3 and roots -4,1, and 2, all with multiplicity 1?
Of(x) = 3(x + 4)(x - 1)(x - 2)
Of(x) = (x - 3)(x + 4)(x-7)(x-2)
Of(x) = (x − 3)(x + 4)(x - 1)(x + 1)(x - 2)
Of(x) = 3(x + 4)(x - 1)(x + 1)(x - 2)
For this case, we can discard options B and C because they do not have coefficients. Also, we discard option D because it has 4 roots given by -4.1, -1,2 each with multiplicity "1".
The multiplicity indicates the number of times a root is repeated.
Then, we have that the correct option is option A, we have a coefficient of "3", in addition to three roots (-4,1,2) with multiplicity "1", because they only repeat once.
Answer:
Option A
Answer: A
Step-by-step explanation:
Find the coordinates of point B that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3.
A. (3, 1)
B. (5,3/4)
C. (10, 5)
D. (6, 2)
ANSWER
The correct answer is B.
EXPLANATION
If the point B(x,y) partitions
[tex]A(x_1,y_1)[/tex]
and
[tex]C(x_2,y_2)[/tex]
in the ratio m:n then, then we have
[tex]x = \frac{mx_2+nx_1}{m + n} [/tex]
and
[tex]y= \frac{my_2+ny_1}{m + n} [/tex]
We want to find the coordinates of the point B(x,y) that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3.
This implies that:
[tex]x = \frac{5 \times 11+3 \times - 5}{5 + 3} [/tex]
[tex] \implies \: x = \frac{55 - 15}{8} [/tex]
[tex] \implies \: x = \frac{40}{8} = 5[/tex]
[tex]y = \frac{5 \times 0 + 3 \times 2}{5 + 3} [/tex]
[tex]y = \frac{0 + 6}{8} [/tex]
[tex]y = \frac{6}{8} = \frac{3}{4} [/tex]
Therefore the coordinates of B are
[tex](5, \frac{3}{4} )[/tex]
Answer:
B. (5,3/4)
Step-by-step explanation:
Since, when a segment having end points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is divided by or partitioned by a point, that lies on the segment, in the ratio of m : n,
Then the coordinates of that points are,
[tex](\frac{mx_2+nx_1}{m+n}, \frac{my_2+my_1}{m+n})[/tex]
Here, point B that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3,
Thus, the coordinates of B are,
[tex](\frac{5\times 11+3\times -5}{5+3}, \frac{5\times 0+3\times 2}{5+3})[/tex]
[tex](\frac{55-15}{8}, \frac{0+6}{8})[/tex]
[tex](\frac{40}{8}, \frac{6}{8})[/tex]
[tex](5, \frac{3}{4})[/tex]
Option 'B' is correct.
What is the following quotient?
sqr root 6 + sqr root 11/ sqr root 5+ sqr root 3
Answer:
[tex]\frac{\sqrt{30}-3\sqrt{2}+\sqrt{55}-\sqrt{33} }{2}[/tex]
Step-by-step explanation:
The given expression is
[tex]\frac{\sqrt{6}+\sqrt{11}}{\sqrt{5}+\sqrt{3} }[/tex]
To solve this quotient, we just have to apply a rationalization, which consists in eliminating every root in the denominator. To do so, we multiply and divide the expression by the opposite binomial of the denominator, as follows
[tex]\frac{\sqrt{6}+\sqrt{11}}{\sqrt{5}+\sqrt{3} }=\frac{\sqrt{5}-\sqrt{3} }{\sqrt{5}-\sqrt{3} }\\\\\frac{(\sqrt{6}+\sqrt{11})(\sqrt{5}-\sqrt{3})}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}\\\\\frac{\sqrt{30}-\sqrt{18}+\sqrt{55}-\sqrt{33} }{5-3}\\ \\\frac{\sqrt{30}-3\sqrt{2}+\sqrt{55}-\sqrt{33} }{2}[/tex]
Therefore, the right answer is the second option.
Sarah needs 3 feet of fabric for a project she is working on, but the store only sells the fabric in meters. One meter of fabric costs $1.20. How much will the fabric cost?
Answer:
$1.10
Step-by-step explanation:
1 ft = 0.3048 m
3 ft = 3 * 1 ft = 3 * 0.3048 m = 0.9144 m
$1.20/m * 0.9144 m = $1.09728
Answer: $1.10
Answer:
$ 1.08
Step-by-step explanation:
1 feet = 12 inches
so, 3 feet = 12 x 3 = 36 inches
1 metre = 40 inches
Cost of 1 m of fabric = $ 1.20
cost of 40 inches of fabric = $ 1.20
Cost of 1 inch of fabric = $ 1.20 / 40 = $ 0.03
Cost of 36 inches of fabric = $ 0.03 x 36 = $ 1.08
Thus, the cost pf 3 feet fabric is $ 1.08
2. Janice is buying paint to paint her new apartment. The store sells paint in one-gallon cans. How accurate does her estimate need to be for the amount of paint needed?
3. A city planner is measuring the distance of one city block. Which unit of measure should she use: 1 mile, 1 meter, inch?
When estimating the amount of paint needed, Janice should strive for an accurate estimate to avoid running out of paint or wasting excess. Factors to consider include the size of the apartment, the type of paint, and the need for multiple coats.
Explanation:When estimating the amount of paint needed, Janice should strive for an accurate estimate to avoid running out of paint or wasting excess. Since the store sells paint in one-gallon cans, it is best to estimate in whole gallons. However, if Janice wants a more precise estimate, she can consider the following factors:
The size of the apartment: She can measure the walls and ceiling to calculate the surface area that needs to be painted.The type of paint: Different surfaces require different amounts of paint. For example, a textured wall may require more paint than a smooth wall.Multiple coats: If Janice plans to apply multiple coats of paint, she should account for the extra paint needed.By considering these factors and making an accurate estimate, Janice can ensure that she buys the right amount of paint for her new apartment.
What is the third quartile of {6, 9, 16, 11, 12, 16, 5, 14, 5}
The answer is 9.5
You tube is awesome for explaining this
Find a fraction that is equivalent to 1.5 over 9 with a whole number in both numerator and the denominator
Answer: [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
We need to remember that equivalent fractions are defined as fractions whose numerators and denominator are different but both fractions represent the same value.
To find an equivalent fraction, we must multiply the numerator and the denominator by the same number (Which must be a nonzero whole number).
In this case, to find a fraction equivalent to [tex]\frac{1.5}{9}[/tex], with a whole number in both numerator and the denominator, we can multiply the numerator and the denominator by 2. Then you get:
[tex]\frac{1.5*2}{9*2}=\frac{3}{18}[/tex]
Reducing the fraction, you get:
[tex]=\frac{1}{6}[/tex]
the simplified whole number fraction equivalent is 1/6.
To find a fraction equivalent to 1.5 over 9 with a whole number in both the numerator and the denominator, first convert the decimal in the numerator to a fraction by expressing it as 1.5 or 15/10. Then, you can write the original fraction as (15/10)/9 which simplifies to 15/90 by multiplying the numerator and the denominator by 10. Finally, you simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 15 in this case. Thus, the simplified whole number fraction equivalent is 1/6.
Two race cars,car x an y,are at the starting point of a two km track at the same time.car x and car y make one lap every 60 s and every 80 sec respectively.
How long, in minutes, will it take for the faster car to be 5 laps ahead of the slower car?
To find the time for Car X to be 5 laps ahead of Car Y, we calculate the difference in laps completed per minute (0.25 laps) and divide the target difference (5 laps) by this rate, which gives us 20 minutes.
Explanation:The question asks how long it will take for Car X to be 5 laps ahead of Car Y if Car X makes one lap every 60 seconds and Car Y every 80 seconds. To solve this, we need to find the difference in laps completed by the two cars over time, until Car X is 5 laps ahead. Since Car X is the faster car, it takes one lap less time than Car Y to complete a lap.
First, we find out how many laps Car X completes more than Car Y in one minute:
Laps per minute for Car X: 1 lap/60 seconds = 1/60 laps per second * 60 seconds = 1 lapLaps per minute for Car Y: 1 lap/80 seconds = 1/80 laps per seconds * 60 seconds = 0.75 lapsThe difference in the number of laps per minute is 1 lap - 0.75 laps = 0.25 laps per minute for Car X compared to Car Y.
Next, we calculate the time it will take for Car X to be 5 laps ahead:
5 laps / 0.25 laps per minute = 20 minutesTherefore, it will take 20 minutes for Car X to be 5 laps ahead of Car Y.
please help me . Is the roped off area triangle ABC, a right triangle ?
yes a right triangle is and angle that is a angle at 90 degrees. A quick method if you don't ha protractor to measure is to measure the angle on a piece of paper like a posted note or note card since all the angles are 90 on them then see if they match up.
Answer:
Yes
Step-by-step explanation:
It is a right angle because it is 90 degrees.
Also,you can tell its a right angle because the variables a, b, and c
represent the Pythagorean Theorem which is used for finding missing lengths of a right triangle.
I didnt see the part at the bottom but the explanation for that would be
50+40> 30 True 40 squared + 30 squared= 50 squared
50+30> 40 True or 1600+900=2500
40+30> 50 True 2500=2500
triangle EFG in which segment EF measures 3 units and segment FG measures 5 units
In ΔEFG, is it possible for segment GE to measure 6 units?
Answer:
Yes
Step-by-step explanation:
It can be 6 units. The rule relating to the sides of the triangle is that you should be able to add two sides and get a length that is longer than the third side. You usually add the lower two numbers because it basically says that it will work for all sides but, if you're still in doubt you just have to compare the numbers.
For Example
3+5 is greater than 6
5+6 is greater than 3
6+3 is greater than 5.
All of these makes sense so 6 can be a possible answer.
In triangle EFG, it is not possible for segment GE to measure 6 units.
Explanation:No, it is not possible for segment GE to measure 6 units in triangle EFG.
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Since segment EF measures 3 units and segment FG measures 5 units, the sum of these two sides is 8 units, which is less than 6 units. Therefore, segment GE cannot be 6 units long in triangle EFG.
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HELP ASAP PLEASE!!!!!!!!!!!!!!!
20p!!!ill mark you as brain please help!!! hurry
Answer:
[tex]\boxed{\text{1172 in}^{2}}[/tex]
Step-by-step explanation:
SA = SA(prism) + SA(cylinder) – 2SA(cylinder base)
1. Surface area of rectangular prism
The formula for the surface area of a rectangular prism is
S = 2(lw + lh + wh)
Data:
l = 16 in
w = 11 in
h = 11 in
Calculations:
2(Top + Bottom) = 2lw = 2 × 16 × 11 = 352 in²
2(Front + Back) = 2lh = 2 × 16 × 11 = 352 in²
2(Left + Right) = 2wh = 2 × 11 × 11 = 242 in²
Total area = 946 in²
2. Surface area of cylinder
A = A(top) + A (base) + A(side) = 2A(base) + A(side)
Data:
d = 8 in
h = 9 in
Calculations:
r = ½d = ½ × 8 = 4 in
[tex]\begin{array}{rcl}SA & = & 2\pi r^{2}+ 2\pi rh \\& = & 2 \times 3. 14\times 4^{2} +2\times 3. 14 \times 4\times 9\\& = & 6.28\times 16 + 226.08\\& = & 100.48 + 226.08\\& = & 326.56 \text{ in}^{2}\\\end{array}[/tex]
3. Excluded area
Excluded area = 2A(base) = 100.48 in²
4. Total area
[tex]A = 946 + 326.56 - 100.48 \approx \boxed{\textbf{1172 in}^{2}}[/tex]
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
x - 4y = -22
x- y=-10
Enter the correct answer.
DONE
Answer:
{-6,4}
Step-by-step explanation:
Given
x-4y=-22 Eqn 1
x-y=-10 Eqn 2
Subtracting both equations:
The left hand side of equation 2 will be subtracted from left hand side of eqn 1 and the right side of equation 2 will be subtracted from right hand side of eqn 1.
[tex](x-4y)-(x-y)=-22-(-10)\\x-4y-x+y=-22+10\\-4y+y=-12\\-3y=-12\\\frac{-3y}{-3}=\frac{-12}{-3}\\ y=4[/tex]
Putting y=4 in eqn 2
[tex]x-4=-10\\x=-10+4\\x=-6\\So,\\Solution Set = \{-6,4\}[/tex]
Answer:
{x, y} = {-6, 4}
Step-by-step explanation:
It is given that,
x - 4y = -22 ------(1)
x - y= -10 -------(2)
To ind the value of x and y
subtract eq(2) from eq(1)
x - 4y = -22 ------(1)
x - y= -10 -------(2)
0 -3y = -12
3y = 12
y = 12/3 = 4
Substitute the value of y in eq (1)
x - 4y = -22 ------(1)
x - (4*4) = -22
x - 16 = -22
x = -22 +16 = -6
Therefore {x, y} = {-6, 4}
Use the X method to find the solutions of
6x2 + 2x – 20 = 0.
x =
x =
Step-by-step explanation:
1..take 2 common from given equation.
2.. then factories the obtained equation.
3.. separate the equation as
3x-5=0 and X+2=0
Answer:
x=-2
and
x=5/3
Step-by-step explanation:
i just did it on edg
A triangle has an area of 38.4 cm2. The
height of the triangle is 12.8 centimeters.
What is the length of the base of the
triangle?
Answer:
6cm
Step-by-step explanation:
[tex]A = \frac{h_b b}{2}[/tex]
[tex]38.4 = \frac{12.8_b b}{2}[/tex]
[tex]b = 2\frac{A}{h_b}[/tex]
[tex]b = 2\frac{38.4}{12.8}[/tex] = 6
The total space enclosed by the three boundaries of the triangle is called the area of the triangle.
The length of the base of the triangle is 6 cm.
GivenA triangle has an area of 38.4 cm2.
The height of the triangle is 12.8 centimeters.
What is the area of the triangle?The total surface or space enclosed by the three boundaries of the triangle is called the area of the triangle.
The formula to calculate the area of the triangle is given by;
[tex]\rm Area \ of \ the \ rectangle = \dfrac{1}{2} \times Base \times Height\\\\[/tex]
Substitute all the values in the formula;
[tex]\rm Area \ of \ the \ triangle= \dfrac{1}{2} \times Base \times Height\\\\\rm 38.4 = \dfrac{1}{2} \times Base \times 12.8\\\\ Base = \dfrac{38.4 \times 2}{12.8}\\\\Base = 3 \times 2\\\\Base = 6 \ cm[/tex]
Hence, the length of the base of the triangle is 6 cm.
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What is the volume and surface area of a right cylinder with a height of 8 and a base diameter of 10?
Answer: Volume is 628.32
Surface Area is 408.41
Step-by-step explanation:
The formula for the surface area is A=2 π r h + 2πr*r
The formula for Volume is V=πr*rh
Good luck!
(08.03)
Given the geometric sequence where a1 = 4 and the common ratio is 3, what is the domain for n?
Answer:
Domain of a geometric or arithmetic sequence is the counting numbers unless otherwise noted.
Answer: Set of Natural numbers.
Step-by-step explanation:
We know that the domain of a function is the set of all values for x for which the function must be defined.
The domain of the geometric sequence is always the set of natural numbers , since each term has a particular position in the sequence according to an order which can only represent by natural numbers.
Hence, the domain for the given geometric sequence = Set of natural numbers.
Solve the equation.
8 – 2x = -8х + 14
A) x= -1
B) x= -3/5
C) x= 3/5
D) x= 1
Answer:
x = 1 is correct
Step-by-step explanation:
[tex]8 - 2x = - 8x + 14[/tex]
[tex]8x-2x + 8 = - 8x + 8x + 14 - 8[/tex]
[tex]6x = 6[/tex]
[tex]x = 1 [/tex]
What is this answer ?
Answer:
Step-by-step explanation:
A isn't. You have that right. A sinusoidal wave is one that creates a sine curve.
Absolute value curves look sort of like a spear head.
What are the zeros of the quadratic function f(x) = 6x2 + 12x – 7?
Answer:
-6 ± √78\6 [0.47196014..., -2.47196014... = x]
Step-by-step explanation:
The roots [zeros] are the x-values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.
Answer:
x = 1 + √74/6 or x = 1 - √74/6
Step-by-step explanation:
Points to remember
Zeros of a quadratic equation ax² + bx + c = 0
x = [-b ± √(b² - 4ac)]/2a
To find the zeros of given quadratic equation
It is given that,
6x² +12x - 7 = 0
Here a = 6, b = -12 and c = -7
x = [-b ± √(b² - 4ac)]/2a
= [-12 ± √(12² - 4*6*(-7))]/2*6
= [12 ± √(144 +168 )]/12
= [12 ± √312]/12
= [12 ± 2√74]/12
= 1 ± √74/6
x = 1 + √74/6 and x = 1 - √74/6
URGENT HELP PLEASE HELP ME!!!!!!!!!))
Shari rolls a pair of dice, numbered 1 to 6, 64 times. How many times can she expect to roll an odd number?
Answer:
About 30
Step-by-step explanation:
1ST: see how many odd numbers are in 1-6 (which is 3)
2nd: Divide 64 by 3 (when rounded it equals around 30)
The volume of the sphere is 500/3 π cubic units. What is the value of the radius, x? 4 units 5 units 8 units 10 units
Answer:
The radius of the sphere is 5 units
Step-by-step explanation:
The volume of the sphere with radius r is given by the formula;
[tex]volume=\frac{4}{3}*\pi*r^{3}[/tex]
The volume of the sphere is given as; 500/3 π cubic units
We substitute this value into the formula and solve for r;
[tex]\frac{500}{3}\pi=\frac{4}{3}*\pi*r^{3}\\\\r^{3}=\frac{500}{4}\\\\r=\sqrt[3]{125}=5[/tex]
Answer:
The correct answer is second option
The radius of sphere = 5 units
Step-by-step explanation:
Points to remember
Volume of sphere = (4/3)πx³
Where 'x' is the radius of sphere.
To find the radius of sphere
We have volume is 500/3 π cubic units
(4/3)πx³ = 500/3 π
x³ = (500/3) * (3/4)
= 500/4 = 125
x = ³√125
x = 5 units
The correct answer is second option
The radius of sphere = 5 units
There are 162 people waiting in line to ride a roller coaster when the line closes for the day. Each roller coaster car holds 12 people. After loading c cars on the roller coaster, there are 6 people still in line. Write an equation to represent the number of cars, c, that have been loaded on the roller coaster. Solve the equation to find the number of cars on the roller coaster.
Answer:
13 Cars Have Been Loaded, Equation: 12x + 6 = 162
Step-by-step explanation:
If a car holds 12 people, and there are 162 people waiting divide 162 by 12. This gives you 13.5, which means that 13 total cars have been loaded, while .5 or 6 are left waiting on the line. So 13!
Answer:
162
Step-by-step explanation:
ADD EMMM UPPP GIRLLLLLGET IT TOGETHER
When 30% of a number is added to the number, the result is 130.
Answer:
100
Step-by-step explanation:
100% of a number + 30% of a number is 130% of a number.
This means 130 = 1.3x.
Now we simplify:
130=1.3x
/1.3 /1.3
100=x
x=100
Therefore, the number is 100.
The unknown number is 100.
Given that, 30% of a number is added to the number, the result is 130.
What is a percentage?The term "percentage" was adapted from the Latin word "per centum", which means "by the hundred". Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of the whole is always taken as 100.
Let the unknown number be x.
30% of x+x=130
⇒0.3x+x=130
⇒1.3x=130
⇒x=100
Therefore, the unknown number is 100.
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Which functions C(x) represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month
Answer:
The answer in the procedure
Step-by-step explanation:
Let
x ----> the number of gigabytes used in a month
C(x)------> the monthly cost in dollars
step 1
For the interval ----> [0,2]
[tex]0\leq x\leq 2[/tex]
[tex]C(x)=15[/tex]
step 2
For the interval ---->(2,6]
[tex]2< x\leq 6[/tex]
Find the equation of the line
Find the slope
we have
[tex](2,20),(6,40)[/tex]
[tex]m=(40-20)/(6-2)=5[/tex]
The equation of the line in to point slope form is equal to
[tex]y-20=5(x-2)\\ y=5x-10+20\\ y=5x+10[/tex]
therefore
[tex]C(x)=5x+10[/tex]
step 3
For the interval ----> (6,∞]
[tex]x> 6[/tex]
[tex]C(x)=50[/tex]
Answer:
C(x)=[tex]15, 0\leq x\leq 2[/tex]
[tex]5x+10, 2<x\leq 6[/tex]
[tex]50, [/tex] 6<x≤∞
Step-by-step explanation:
C(x) represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month
Lets find C(x) on each interval (for every line graph)
first interval 0 to 2
the value of y is 15 on the interval 0 to 2
Its horizontal line . So equation is c(x)=the constant y value
[tex]C(x)= 15, 0\leq x\leq 2[/tex]
Second interval 2 to 6
Pick two points to get the equation of that line
(3,25) and (6,40)
[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{40-25}{6-3} =5[/tex]
Equation of the line is using m=5 and (3,25)
[tex]y-y1=m(x-x1)[/tex]
[tex]y-25=5(x-3)[/tex]
[tex]y-25=5x-15[/tex]
[tex]y=5x+10[/tex]
[tex]C(x)= 5x+10, 2<x\leq 6[/tex]
Now we look at the third interval
6 to infinity
For the third graph , the value of y is 50 (constant)
It is a horizontal line
So [tex]C(x)= 50, [/tex] 6<x≤∞
We got three equations for C(x)
C(x) is a piecewise function
C(x)=[tex]15, 0\leq x\leq 2[/tex]
[tex]5x+10, 2<x\leq 6[/tex]
[tex]50, [/tex] 6<x≤∞
Someone plz help me
Answer:
Step-by-step explanation:
Write the explanation x-4
If it’s Wrong then please send an invitation of me to be a friend so that I can help you with update updated answers on brainly
Every evening jenna empties her pockects and puts her change in a jar. one week she had 38 coins, all of them dimes and quarters. when she added them up she had a total of 6.95Every evening jenna empties her pockects and puts her change in a jar. one week she had 38 coins, all of them dimes and quarters. when she added them up she had a total of 6.95
Answer:
17 dimes, 21 quarters
Step-by-step explanation:
I suppose you want to know how many dimes and quarters she had in her jar.
Let's say x = dimes and y = quarters.
We can make the following 2 equations:
1) x + y = 38 (number of coins in the jar)
2) 10x + 25y = 695 (a number of dimes plus a number of quarters sum up to 695 cents)
From 1), we can isolate y: y = 38 - x, and place that value in the second equation:
10x + 25y = 695
10x + 25 (38 - x) = 695
10x + 950 - 25x = 695, then we subtract 950 on both sides and simplify
-15x = -255
x = 17
So, Jenna had 17 dimes.
y = 38 - x, so y = 38 - 17 = 21
And she had 21 quarters.
Eileen purchased 3.4 pounds of apples at the total cost of $19.72. If she purchases 6.2 pounds of apples at this store, how much would it cost?
Answer:
$35.96
Step-by-step explanation:
19.72 divided by 3.4 = 5.8
5.8*6.2 =35.96
What is the prime factorization of 440?
2 3 · 5 · 9
2 3 · 3 2 · 5
2 · 4 · 5 · 11
2 3 · 5 · 11
Answer:
I would say the correct answer is 2^3 • 5 • 11
Step-by-step explanation:
To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
Let's start by dividing 440 by 2
440 ÷ 2 = 220 - No remainder! 2 is one of the factors!
220 ÷ 2 = 110 - No remainder! 2 is one of the factors!
110 ÷ 2 = 55 - No remainder! 2 is one of the factors!
55 ÷ 2 = 27.5 - There is a remainder. We can't divide by 2 even anymore. Let's try the next prime number
55 ÷ 3 = 18.3333 - This has a remainder. 3 is not a factor.
55 ÷ 5 = 11 - No remainder! 5 is one of the factors!
11 ÷ 5 = 2.2 -There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
11 ÷ 7 = 1.5714 - This has a remainder. 7 is not a factor.
11 ÷ 11 = 1 - No remainder! 11 is one of the factors!
If we put all of it together we have the factors 2 x 2 x 2 x 5 x 11 = 440. It can also be written in exponential form as 2^3 x 5^1 x 11^1.
here is also the factor tree method : -
describe how the graph of the function is related to the graph of f(x)= x^2. g(x)=x^2-5
Answer:
Translation down 5 units.
Step-by-step explanation:
The - 5 results in a shift of the whole graph down 5 units.
Each value of g(x) is 5 units less f(x).
Answer:
a. Translate down 5 units
Step-by-step explanation:
f(x)= [tex]x^{2}[/tex]g(x)=[tex]x^{2}[/tex] -5So g(x) is the transformed function of f(x)
In this situation, only the parameter c affect the f(x) vertically to have g(x), if:
c > 0 function is translate upc < 0 the function is translate upHere, c= -5
So the function is Translate down 5 units
Hope it will find you well.