Answer:
g(x) = (x-3) ^2 -3
Step-by-step explanation:
f(x) = x^2
To shift down 3 units, subtract 3 ( When we move up, we add)
h(x) = x^2 -3
To shift to the right 3 units, replace x with (x-3). I know it seems backwards, but right is minus and left is plus.
g(x) = (x-3) ^2 -3
Brandon buys a basket of flowers for $7 before tax. The sales tax is 4%. What is the total price Brandon pays for the basket of flowers?
Answer:
$7.28
Step-by-step explanation:
We have been given that Brandon buys a basket of flowers for $7 before tax. The sales tax is 4%.
The total price that Brandon paid for the basket of flowers will be equal to 7 plus 4% of 7.
We can represent this information in an equation as:
[tex]\text{The total price that Brandon paid for the basket of flowers}=7+(\frac{4}{100}\times 7)[/tex]
[tex]\text{The total price that Brandon paid for the basket of flowers}=7+(0.04\times 7)[/tex]
[tex]\text{The total price that Brandon paid for the basket of flowers}=7+0.28[/tex]
[tex]\text{The total price that Brandon paid for the basket of flowers}=7.28[/tex]
Therefore, the total price paid by Brandon for the basket of flowers was $7.28.
Answer:
Total price Brandon pays for the basket of flowers is, $7.28
Step-by-step explanation:
As per the given statement: Brandon buys a basket of flowers for $7 before tax.
Convert this $7 into cents.
1 dollars = 100 cents.
$7 = 700 cents.
It is also given that the sales tax is 4%.
then;
Sales tax = [tex]4\% \times 700 = \frac{4}{100} \times 700 = 4 \times 7 =28 cents[/tex]
Total price Brandon pays = Price of Brandon buys a flower before tax + sales tax price
= 700 + 28 = 728 cents = $7.28
Therefore, the total price Brandon pays for the basket of flowers is, $7.28
A store manager ordered 28 crates of mangoes.There were 36 mangoes in each crate.WHEN the mangoes were delivered, he sold the ripe mangoes and repacked the rest equally into 73 boxes.There were 12 mangoes in each box.How many ripe mangoes were sold?
Answer:
Number of ripe mangoes were sold as 132
Step-by-step explanation:
Let's assume number of rip mangoes were sold as 'x'
A store manager ordered 28 crates of mangoes
Number of crates =28
There were 36 mangoes in each crate
Number of mangoes in each crate=36
Total number of mangoes=( Number of crates)*(Number of mangoes in each crate)
Total number of mangoes is
[tex]=28\times 36[/tex]
[tex]=1008[/tex]
WHEN the mangoes were delivered
he sold the ripe mangoes and repacked the rest equally into 73 boxes
There were 12 mangoes in each box
Total number of mangoes is
[tex]=73\times 12+x[/tex]
[tex]=876+x[/tex]
now, we can set them equal
[tex]1008=876+x[/tex]
[tex]x=132[/tex]
To find the number of ripe mangoes sold, multiply the number of crates by the number of mangoes in each crate. Then, multiply the number of boxes by the number of mangoes in each box. Finally, subtract the number of mangoes repacked into boxes from the total number of mangoes delivered.
To find the number of ripe mangoes sold, we need to determine the total number of mangoes delivered and then subtract the number of mangoes repacked into boxes.
First, we find the total number of mangoes delivered by multiplying the number of crates (28) by the number of mangoes in each crate (36): 28 crates * 36 mangoes/crate = 1008 mangoes
Next, we find the number of mangoes repacked into boxes by multiplying the number of boxes (73) by the number of mangoes in each box (12): 73 boxes * 12 mangoes/box = 876 mangoes
Finally, we subtract the number of mangoes repacked into boxes from the total number of mangoes delivered to find the number of ripe mangoes sold: 1008 mangoes - 876 mangoes = 132 ripe mangoes
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Jenson had 558 game cards. He lost 92 of them in a game and gave 105 game cards to his brother. How many game cards had he left ?
Answer:
After giving 197 cards away, Jenson is left with 361 cards
Step-by-step explanation:
What does the fundamental theorem of algebra state about the equation 2x^2-4x+16=0?
Answer: (A) degree of 2; 1 ± i√7
Step-by-step explanation:
Degree of the polynomial designates the number of roots.
x² - 2x + 8
a=1 b=-2 c=8
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(8)}}{2(1)}[/tex]
[tex]=\dfrac{2\pm\sqrt{4-32}}{2}[/tex]
[tex]=\dfrac{2\pm\sqrt{-28}}{2}[/tex]
[tex]=\dfrac{2\pm2i\sqrt{7}}{2}[/tex]
[tex]=\dfrac{2(1\pm\\i\sqrt7)}{2}[/tex]
= 1 ± i√7
The sum of the measures of the interior angles of the polygon below is 1800°
Answer:
False
Step-by-step explanation:
The sum of the interior angles of a regular polygon is (n – 2)180 where n is the number of sides. Since this is a 10 sided figure,
the sum of the interior angles is (10-2)* 180 =1440
What is the distance between the points (–6, –10) and (2, 5)?
Answer:
17
Step-by-step explanation:
To find the distance between two points, we use the formula
d =sqrt( (x2-x1)^2 + (y2-y1)^2)
d= sqrt((2--6)^2+(5--10)^2 )
d= sqrt((2+6)^2+(5+10)^2 )
d = sqrt(8^2 + 15^2)
d = sqrt(64+225)
d =sqrt(289)
d =17
An electric heater uses 3/5 watts power each hour. How man watts power will the heater use in a 1/2 hour
Answer: 3/10 watts
Step-by-step explanation:
3/5 converts to 6/10
6/10 / 2 = 3/10
Answer:
3/10
Step-by-step explanation:
3/5 converts to 6/10
6/10 / 2 = 3/10
Natalie makes 2000 per month she spends 100 on credit card payments and 250 on an auto loan what is her debt to income ratio
The mean and standard deviation for number of robberies in the U.S. from 2000 to 2015 are x̄ = 354,718 and sx = 28,803. The mean and standard deviation for number of assaults in the U.S. for the same time period are ȳ = 774,140 and sy = 44,910. The correlation coefficient is r = 0.84. Find the equation for the least-squares regression line for number of assaults compared with number of robberies. ŷ = 309,552.15 + 1.31x ŷ = 1.31 + 309,552.15x ŷ = 546,641.84 + 0.64x ŷ = 0.64 + 546,641.84x Unable to determine the equation
Answer:
[tex]\hat{y}=309,552.15 + 1.31x[/tex]
Step-by-step explanation:
The equation for the least-squares regression is,
[tex]\hat{y}=a+bx[/tex]
where b is the slope and a is the intercept.
They can be found out by,
[tex]b=r\cdot \dfrac{SD_y}{SD_x},\\\\a=\overline{y}-b\overline{x}[/tex]
where,
r = correlation coefficient = 0.84
[tex]SD_y[/tex] = standard deviation of y = 44,910
[tex]SD_x[/tex] = standard deviation of x = 28,803
[tex]\overline{y}[/tex] = mean of y = 774,140
[tex]\overline{x}[/tex] = mean of x = 354,718
Putting the values,
[tex]b=0.84\cdot \dfrac{44910}{28803}=1.309\approx 1.31[/tex]
[tex]a=774140-(1.31\times 354718)\approx 309,552.15[/tex]
Therefore the equation is,
[tex]\hat{y}=309,552.15 + 1.31x[/tex]
The length of a base of a rectangular prism is 8 inches. The width of the prism is 4 and a half inches, and the height is 3 and a half inches. What is the volume of the prism?
Determine the equation of the hyperbola.
Answer:
A) x²/9 -y²/4 = 1
Step-by-step explanation:
The distance from center to one vertex is half the difference of the distances from a point to either focus. That is, the distance from center to the vertex is 3 on the x-axis, so the x-term is (x/3)² = x²/9.
In the picture, ...
... c² = a² + b²
The problem statement tells us c = √13, so we know c² = 13. Then ...
... b² = c² - a² = 13 -9 = 4
and the y-term is y²/4.
Thus, the equation is ...
... x²/9 - y²/4 = 1
_____
You knew that was the correct choice as soon as you knew the x-term.
Solve for x 13x-7 11x+11
Answer:
answer 7.3
13x-7+11x+11=180
Step-by-step explanation:
Luke's turkey chili recipe calls for 1.5 pounds of ground turkey for every 6 servings. How many servings can he make if he has 5 pounds of ground turkey? Show your work.
Final answer:
Luke can make 20 servings with 5 pounds of ground turkey.
Explanation:
To determine the number of servings Luke can make with 5 pounds of ground turkey, we need to set up a proportion. The recipe calls for 1.5 pounds of ground turkey for every 6 servings. So, we can set up the proportion: 1.5 pounds / 6 servings = 5 pounds / x servings, where x represents the unknown number of servings. To solve for x, we cross multiply: 1.5 pounds * x servings = 5 pounds * 6 servings. Simplifying the equation, we get: 1.5x = 30. Dividing both sides by 1.5, we find that x = 20. Therefore, Luke can make 20 servings with 5 pounds of ground turkey.
A collection of 36 shirts and 42 jackets contains 842 buttons. A collection of 66 shirts and 77 jackets contains 137 buttons. Each shirt has the same number of buttons, and each jacket has the same number of buttons. How many buttons are there in a Fiona's Fashion shirt, and how many buttons are there in a jacket?
Answer:
Step-by-step explanation:
Let x represent the number of buttons on shirts and y represent the number of buttons on jackets.
If 36 shirts and 42 jackets contain 842 buttons. This implies:
36x + 42y = 842 (1)
If 66 shirts and 77 jackets contain 137 buttons. This implies:
66x + 77y = 137 (2)
If you take the first equation: 36x + 42y = 842 and isolate the x, then you will have x = (842 - 42y) / 36
If you substitute x into the second equation:
66((842-42y)/36) + 77y = 137
→ 11(842-42y)/6 + 77y = 137
→ 11(842-42y) + 6(77y) = 137(6)
→ 9262 - 462y + 462y = 822
→ 9262 = 822 which reveals that the equations do not have a solution
A hotel has 150 rooms. The charges for a double room are $270 per night and $150 per night for a single room. On a night when the hotel was completely occupied. Revenues were $33,300. Which pair of equation can be used to determine the number of double room, d and the number of single room,s,in the hotel?
Step-by-step explanation:
Let s be charges for a single room and d be charges for a double room per night.
We are told that a hotel has 150 rooms. We can represent this information as:
[tex]s+d=150...(1)[/tex]
The charges for a double room are $270 per night and $150 per night for a single room. So the charges for s single rooms will be 150s and charges for d double rooms will be 270d.
On a night when the hotel was completely occupied. Revenues were $33,300.
We can represent this information as:
[tex]150s+270d=33,300...(2)[/tex]
Therefore, our desired pair of equations will be:
[tex]s+d=150...(1)[/tex]
[tex]150s+270d=33,300...(2)[/tex]
Answer: First equation: s+d=150; second equation: 150s+270d=33300
Step-by-step explanation: To solve the given problem we need to write two equations, the first one will express that the total number of rooms is the sum of the single rooms an the double rooms. The second equation will include the sum of the total earnings for the single and double rooms:
First equation:
s+d=150 (the single rooms and the double rooms equal 150 rooms)
second equation:
150s+270d=33300 (the sum of the single and double rooms each one of them multiplied by their prices, equals the total revenue)
To solve the equation we isolate s from the first equation:
s=150-d
and we replace it in the second one:
150(150-d)+270d=33300
solving for d:
22500-150d+270d=33300
120d=33300-22500
120d=10800
d=10800/120
d=90.
now we calculate s from the first equation:
s=150-d
s=150-90
s=60.
There are 60 single rooms and 90 double rooms.
Pls help me with this Trig question!
Answer:
s = 65/3 pi
Step-by-step explanation:
The length of the intercepted arc is given by the formula
s =r*theta when theta is given in radians
r = 13
theta = 5 pi/3
Substituting what we know
s = 13 * 5 pi/3
s = 65/3 pi
Since we want an exact answer, we have to leave it in terms of pi and as a fraction
Sweet t purchased a new pair of jeans to wear at the battle of the bands on sale at 40% off.He saved $20 what was his regular price of the jeans
Dan paid $34.30 for a sweater the price included a 40% markup what is the cost of the sweater before the markup
Answer:
$24.5
Step-by-step explanation:
Let x be the cost of sweater before markup.
We are told that Dan paid $34.30 for a sweater the price included a 40% markup. This means x plus 40% of x equals 34.30.
We can represent this information as:
[tex]x+\frac{40}{100}x=34.30[/tex]
[tex]x+0.40x=34.30[/tex]
[tex]1.40x=34.30[/tex]
[tex]x=\frac{34.30}{1.40}[/tex]
[tex]x=24.5[/tex]
Therefore, the cost of sweater before the markup was $24.5.
If you break up the number under the radical in the square root of 36 into two factors that are perfect squares, what are the two factors?
Answer:
6
Step-by-step explanation:
sqrt (36)
Lets break this into parts
sqrt(4 * 9)
sqrt(4) * sqrt(9)
2 * 3
6
MATH HELP WILL UPVOTE!!!
The function d(h)=50+45h represents the distance a family traveled, in miles, h hours after they stopped for lunch. What does the value 45 represent in this situation?
The family drove 45 miles after they stopped for lunch.
Before lunch, the family traveled at a speed of 45 mph.
After lunch, the family traveled at a speed of 45 mph.
The family drove 45 miles before they stopped for lunch.
Answer:
After lunch, the family traveled at a speed of 45 mph is the only solution that makes sense when simplifying d(h)=50+45H
Step-by-step explanation:
Answer: After lunch the family drove 45 miles per hr. HOPE THIS HELPS!
Daryl earns $8 per hour working after school. He needs at least $352 for a stereo system. Write and solve an inequality to find the number of hours h Daryl must work to reach his goal.
Answer:
Step-by-step explanation:
First you need to divide by the amount he needs by the amount he gets, 352 divided by 8. That equals 44, so he will need to work 44 hours to reach his goal.
I need help. I have tried doing this question and none of the answers were right. Please help me.
Which ordered pairs lie on the graph of the exponential function f(x)=− 3 (x−1) +2 ? Select each correct answer.
A. (4,−25)
B. (1, 1)
C. (−1, 2)
D. (0, 0)
Answer:
A and B
Step-by-step explanation:
assuming the function should be
- [tex]3^{x-1}[/tex] + 2, then
A
substitute the x value into f(x) and check the validity of the y- value
f(4) = - [tex]3^{3}[/tex] + 2 = - 27 + 2 = - 25 ← agrees with y value
(4, - 25) lies on the graph
B f(1) = - [tex]3^{0}[/tex] + 2 = - 1 + 2 = 1 ← agrees with y value
(1, 1) lies on the graph
C
f(- 1) = - [tex]3^{-2}[/tex] + 2 = - [tex]\frac{1}{9}[/tex] + 2 ≠ 2
(- 1, 2) does not lie on the graph
D
f(0) = [tex]3^{-1}[/tex] + 2 = - [tex]\frac{1}{3}[/tex] + 2 ≠ 0
(0, 0) does not lie on the graph
Fluffy's tail was 1/3 of a meter long. Fireballs tail is 1/4 of a meter long . How much longer is fluffy's than Fireballs tail?
Answer:1/12
Step-by-step explanation:1/3-1/4=1/12
Select the correct answer. Given: AD = CF BC = DE Prove: AB = EF Statement Reason 1. AD = CF given 2. AD = AB + BC + CD CF = CD + DE + EF segment addition 3. AB + BC + CD = CD + DE + EF Transitive Property of Equality 4. AB + BC = DE + EF 5. BC = DE given 6. AB = EF Subtraction Property of Equality What is the reason for the fourth statement in this proof? A. definition of collinear points B. segment addition C. Subtraction Property of Equality D. Substitution Property of Equality
Answer:
Step-by-step explanation: The answer is D- Substitution Property of Equality. I just did the test and it was right.
Answer:
C. Subtraction property of equality.
Step-by-step explanation:
Given AD= CF
And BC=DE
To prove that AB=EF
Proof:
1.Statement: AD=CF
Reason: Given in question.
2. Statement: AD= AB+BC+ CD, CF= CD+DE+EF
Reason: Segment addition property because AB,BC,and CD are the segments of AB and CD,DE and DE are segments of CF.
3. Statement: AB+BC+CD=CD+DE+EF
Reason: Transitive property of equality
Transitive property: If ab=bc and bc=ca
Then , ab=ca
4.Statement: AB+BC= DE+EF
Reason: By using subtraction property of equality.
5. Statement:BC=DE
Reason: Given in question.
6. Statement: AB=EF
Reason: when we put BC=DE . Then we get AB+DE=DE+EF. By using subtraction property of equality .
Hence proved .
HELP PLEASE!! which of the following represents a function?
please explain too i don’t understand this.
Answer:
A is a function because if draw a line right down the middle no other dots will intercept
Step-by-step explanation:
A function is where one input has only one out put
As you can tell in the table(c) -3 is repeated that's what makes it not a function.same for B since there are more than one inputs it's not a function
Hope this helps!
If A varies inversely as the square of B, what is the effect on B if A is multiplied by 3? Please explain.
Answer:
If A is multiplied by 3, B will be reduced by a factor [tex]\frac{1}{\sqrt{3}}[/tex]
Step-by-step explanation:
Writing the inverse proportionality relationship and expressing the dependence of B on A leads to the following:
[tex]A = \frac{1}{B^2}\implies |B| = \frac{1}{\sqrt{A}}\\B'=\frac{1}{\sqrt{3A}}= \frac{1}{\sqrt{3}}\frac{1}{\sqrt{A}}=\frac{1}{\sqrt{3}}|B|[/tex]
In words, if A triples, B will decrease by a factor [tex]\frac{1}{\sqrt{3}}[/tex], or, in other words, the square of B will decrease to one third of its previous value.
After a birthday party 1/3 of the cake was left if the cake was shared equally between 4 people what fraction did each person revive
Line m contains (6,8) and (-1,2). Line n contains (-1,5) and (5,y). What is the value of y if line m is perpendicular to line n
Answer:
y=-37
Step-by-step explanation:
A perpendicular line has a negative reciprocal slope to the original line. We will use the slope formula to find the slope of line m, then take the negative reciprocal for the slope of line n which will reveal the value of y.
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute [tex]x_1=6\\y_1=8[/tex] and [tex]x_2=-1\\y_2=2[/tex]
[tex]m=\frac{2-8}{-1-6}[/tex]
[tex]m=\frac{2-8}{-1-6}=\frac{-6}{-7} =\frac{6}{7}[/tex]
[tex]m\neq \frac{6}{7}[/tex] for line n because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is [tex]m=-\frac{7}{6}[/tex].
We will substitute [tex]m=-\frac{7}{6}[/tex] into the slope formula to find line n's coordinate value y. We will also substitute [tex]x_1=-1\\y_1=5[/tex] and [tex]x_2=5\\y_2=y[/tex] .
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]-\frac{7}{6}=\frac{y-5}{5-(-1)}[/tex]
[tex]-\frac{7}{6}=\frac{y-5}{6)}[/tex]
[tex]6(-\frac{7}{6})=y-5[/tex]
[tex]-42+5=y-5+5[/tex]
[tex]-37=y[/tex]
The value of y that makes Line n perpendicular to Line m is 59/6. This is found by first calculating the slope of Line m and then finding the negative reciprocal (since perpendicular lines have negative reciprocal slopes), and using this new slope to solve for y in Line n.
Explanation:To solve this problem, we first need to understand that the slopes of two perpendicular lines are negative reciprocals of each other. This means that if Line m has a slope of a, then Line n will have a slope of -1/a.
First, let's find the slope of line m which contains the points (6,8) and (-1,2). The formula for slope is (y2-y1)/(x2-x1). This gives us (2-8)/(-1-6) = -6/-7 = 6/7.
Because line n is perpendicular to line m, its slope will be the negative reciprocal of 6/7, which is -7/6. We can then use this slope and the point (-1,5) to find the value of y when x=5 on line n. We use the equation y-y1 = m(x-x1), and substitute the values in: y - 5 = -7/6 * (5 - (-1)), which simplifies to y = -7 + 5 + 35/6 = 29/6 + 30/6 = 59/6.
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Please help: Quadratic Formula Question
Answer:
1. b=-7
2. c= -10
Step-by-step explanation:
The standard form for the quadratic function is
ax^2 +bx+c
so we need to rewrite the function to be in this form
2x^2 -10 = 7x
Subtract 7x from each side
2x^2 -7x-10 = 7x-7x
2x^2 -7x-10 = 0
a =2, b= -7 c=-10
Given the equation y − 3 = fraction 1 over 2 (x + 6) in point-slope form, identify the equation of the same line in standard form.
Answer: x - 2y = -12
Step-by-step explanation:
[tex]y - 3 = \dfrac{1}{2} (x+6)\\2(y - 3) = (2)\dfrac{1}{2}(x + 6)\\2y - 6 = x + 6\\\underline{-x +6}\quad\underline{-x + 6}\\-x + 2y = 12\\-1(-x + 2y = 12)\\x - 2y = -12[/tex]
ANSWER:
-1/2x + y = 6
ABOUT POINT SLOPE FORM:
y - Y1 = m (x - X1)Y1 & X1 is a point on the linem represents the slopeThis form allows you to identify the slope & the point on the lineABOUT STANDARD FORM:
Ax + By = CA & B & C are integersA &B are both non - zeroThis form is good to use when wanting to find the x & y intercepts of a liney - 3 = 1/2 (x + 6)
y - 3 = 1/2x + 3
+ 3 + 3
y = 1/2x + 6
-1/2x -1/2x
-1/2x + y = 6
I'm not sure if my answer is correct... But please tell me if it's correct or incorrect! Thank you! :)