Answer:
p(x) = 5(x + 3)² - 45
Step-by-step explanation:
Sandra wrote the function as p(x) = 30x + 5x².
So, this is a formula of a parabola, and this we have to convert into vertex form.
Now, rearranging the function we get
p(x) = 5(x² + 6x)
⇒ p(x) = 5(x² + 6x + 9) - 45
⇒ p(x) = 5(x + 3)² - 45
So, this is the vertex form and the vertex of the parabola is (-3,-45).
We know the formula of a parabola having vertex at (m,n) and axis parallel to positive y-axis is given by
(x - m)² = 4a(y - n)
⇒ [tex]y = \frac{1}{4a} (x - m)^{2} + n[/tex] (Answer)
Ronny read for 2.75 hours yesterday. His older brother read for 1.18 hours and his younger brother read for 0.43 hours.
How much longer did Ronny read than his two brothers combined?
1.14 hours
1.57 hours
1.61 hours
2.32 hours
£150in the ratio of 4:1
Answer:
£120:£30
Step-by-step explanation:
A ratio of 4:1 is also a ratio of 4x:x, as long as x is not equal to 0.
4x + x = 150
5x = 150
x = 30
4x = 4(30) = 120
4:1 = 120:30
Answer: £120:£30
A bean plant grows at a constant rate for a month. After 10 days, the plant is
35 centimeters tall. After 20 days, the plant is 55 centimeters tall.
Which equation models the height of the plant, y, after x days?
A. y+35 = 2(x+10)
B. y - 35 = 2(x - 10)
C. y - 10 = 2(x - 35)
D. y - 35 = 1/2 (x - 10)
Answer:
B. y - 35 = 2(x - 10)
Step-by-step explanation:
The height of the plant, y, after x days could be modeled by the equation
y-y0=k(x-xo) (1),where y0 was the initial height at 'x0'th. day, and k is the constant of proportionality.From equation (1), k could be evaluated as follows:k=(y-y0)/(x-x0) From the problem statement, we may determine k by plugging in the given values, e.g. y0= 35, x0=10, y=55, x=20.Thus,k=(55-35)/(20-10)=2Therefore, the model equation becomesy-35=2(x-10)Answer:
the answer is B
Step-by-step explanation:
Which of the following shapes is the cross-section for a cone
A.triangle
B.square
C.circle
D.pentagon
Final answer:
The correct shape for the cross-section of a cone, when cut perpendicularly to its axis, is a circle. This is known as a conic section. The correct option is C.
Explanation:
The student asked which shape represents the cross-section for a cone. The cross-sectional shape of a cone depends on the angle at which it is cut. If a cone is cut by a plane perpendicular to its axis (the center line from the tip to the base), the cross-section is a circle. Therefore, the correct shape for the cross-section of a cone, when cut perpendicularly to its axis, is a circle.
Julio tenía 2/3 de una tablilla de chocolate en el recreo comió 1/5 que fracción de la tablilla le queda?
Answer:
7/15 de la tablilla de chocolate le va a quedar.
Step-by-step explanation:
2/3 se converte en 10/15
y 1/5 se converte en 3/15
Entonces le va a quedar 10/15-3/15 = 7/15 de la tablilla de chocolate.
Answer:
2/3 - 1/5 = 7/15
Step-by-step explanation:
tienes que obtener denominadores iguales para restar las fracciones para obtener una respuesta. El denominador que tiene 3 y 5 igual es 15. así que tienes que multiplicar 3 por 5 y 5 por 3 y todo lo que hagas abajo deberías hacerlo al number de arriba.
the total heigh of bill mary and rob is 180 cm bob is twice as tall as bill and mary is 28 cm taller than bill how tall is rob
Answer:
Rob is 76 cm tall.
Step-by-step explanation:
Let b = height of bill.
Let m = height of Mary.
Let r = height of Rob.
"the total heigh of bill mary and rob is 180 cm"
b + m + r = 180 Equation 1
"bob* is twice as tall as bill"
*I think you meant Rob is twice as tall as Bill.
r = 2b
"mary is 28 cm taller than bill"
m = b + 28
Substitue r = 2b and m = b + 28 into Equation 1.
b + b + 28 + 2b = 180
4b + 28 = 180
4b = 152
b = 38
r = 2b
r = 2(38) = 76
Rob is 76 cm tall.
Rob height is 76cm.
Given that,
Total height of Bill, Mary and Rob is 180cm.Rob is twice tall as Bill.Mary is 28cm taller than Bill.We need to find the height of Rob.According to the given data, computation of the data are as follows,
Let Bill height be X, then Rob height is 2X and Mary height is X + 28.
So, X + 2X + X + 28 = 180cm
4X = 180 - 28
X = 152 [tex]\div[/tex] 4
X = 38
Hence, Bill height = X = 38cm
Rob height = 2X = 76cm
Mary height = X + 28 = 66cm
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what is the total cost of a sweatshirt if the regular price is $42 and the sales tax is 5 1/2
Answer:
$44.31
Step-by-step explanation:
Regular Price = $42
Sales Tax Rate = 5 1/2% or 5.5%
The total cost would be the regular price PLUS the sales tax. We find the sales tax by finding 42's 5.5%.
First, converting percentage to decimal (dividing by 100):
5.5% = 5.5/100 = 0.055
Now finding 5.5% of $42:
42 * 0.055 = $2.31
Now, the total price is the SUM of regular and this sales tax:
Total Price = 42 + 2.31 = $44.31
Y=-3 write in the general form of equation
Answer:
y + 3 = 0Step-by-step explanation:
The general form of an equation of a line:
Ax + By + C = 0
We have
y = -3 add 3 to both sides
y + 3 = -3 + 3
y + 3 = 0
where A = 0, B = 1, C = 3
Answer this please, thank you !
Answer:
m∠ADC=55°
Step-by-step explanation:
step 1
Find the value of x
we know that
m∠CDE+m∠EDF=180° ----> by supplementary angles (form a linear pair)
substitute the given values
[tex](2x+1)\°+(x-7)\°=180\°[/tex]
solve for x
[tex]2x+x=180+6[/tex]
[tex]3x=186[/tex]
[tex]x=62[/tex]
step 2
Find the measure of angle ∠ADC
we know that
m∠ADC=m∠EDF ----> by vertical angles
m∠EDF=(x-7)°
substitute the value of x
m∠EDF=(62-7)°=55°
therefore
m∠ADC=55°
Danielle has $6.65 worth of change in nickels and dimes. If she has 5 times as many nickels as dimes, how many of each type of coin does she have?
Answer:
95 nickels 19 dimes
Step-by-step explanation:
d=dimes
5d=nickels
0.05(5d) + 0.10(d) = 6.65
0.25d + 0.10d = 6.65
0.35d=6.65
Divide by 0.35
d= 19 (19 coins)
19 dimes =$1.9
6.65-1.9= $4.75
Nickels=$4.75
4.75/0.05 = 95 coins
19*5=95
114 coins in total
19*0.10 = 1.9
95*0.05=4.74
4.75+1.9= 6.65
Answer:
There are 19 dimes and 95 nickels
Step-by-step explanation:
Represent the numbers of nickels and dimes by n and d. Then n = 5d.
The value of the nickels is $0.05n and that of the dimes is $0.10d. Together these two amounts come to $6.65:
$0.05n + $0.10d = $6.65.
But n = 5d.
Substituting 5d for n, we get:
$0.05(5d) + $0.10d = $6.65
Combining the two terms on the left, we get:
0.25d + 0.10d = 6.65, or
0.35d = 6.65.
Solving for d, we get d = 6.65/0.35, or d = 19. Since n = 5d, n = 5(19) = 95.
There are 19 dimes and 95 nickels.
Simplify 34x+13xy+12y
Answer:
Step-by-step explanation:
47x+12y
Factoring a Linear Binomial:
Please include steps:
18+ 6v
Answer:
6(3 + v)
Step-by-step explanation:
Given
18 + 6v ← factor out 6 from each term
= 6(3 + v) ← in factored form
solve the equation y=11.3x + 13.8 estimates the amount that businesses will spend, in billion of dollars on a certain business technology where x is the number of years after 2000 for what years will the spending be more than $59 billion where spending will be more than $59 billion more than blank years after 2000
Answer:
Spending will be more than $59 billion more than 4 years after 2000.
Step-by-step explanation:
Given:
[tex]y=11.3x + 13.8[/tex]
x is the number of years.
Business spending is $59 billion.
Hence we can say that y = $59.
Now Substituting the value of y in above equation we will find the value of x in number of years.
[tex]11.3x+13.8=59\\11.3x=59-13.8\\ 11.3x= 45.2\\\\x=\frac{45.2}{11.3} = 4 years.[/tex]
Hence we can say that,
After 4 years after 2000 the spending will be more than $59 billion.
or
Spending will be more than $59 billion more than 4 years after 2000.
The equation demonstrates that the spending will exceed $59 billion more than 4 years after 2000.
Explanation:To solve the problem, we first need to set the equation y = 11.3x + 13.8 to greater than 59, as we are trying to find out when the spending will be more than $59 billion. The equation will therefore be, 11.3x + 13.8 > 59.
Then, we subtract 13.8 from both sides of the equation to isolate the term with x, resulting in 11.3x > 45.2.
Finally, we divide each side by 11.3 to solve for x, which will give us x > 4. Consequently, the spending will be more than $59 billion more than 4 years after 2000.
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The student council is selling Candy bars to earn money towards their budget for the school dance explain why the number of candy bars is the independent variable
Answer:
the number of candy bars they have is not affected by the other factors like the budget or the student council
Final answer:
The number of candy bars is the independent variable because it can be manipulated or changed by the student council to affect the amount of money they earn.
Explanation:
The number of candy bars is considered the independent variable in this scenario. The independent variable is the one that is manipulated or changed in an experiment, and its value does not depend on any other variable.
In this case, the student council is selling candy bars to earn money for their budget, and the number of candy bars they sell is the variable that they have control over.
By increasing or decreasing the number of candy bars sold, they can affect the amount of money they earn for their budget.
Solve for x. Round your answer to the nearest hundredth.
13.48x − 200 < 256.12
Answer:
x<33.84
Step-by-step explanation:
13.48x - 200 < 256.12
13.48x - 200 + 200 < 256.12 + 200
13.48x < 456.12
13.48x / 13.48 < 456.12 / 13.48
x < 33.84
Answer:
b
Step-by-step explanation:
declan ran 500 meters in 5 minutes . calculate the unit rate
Answer:
100 meters in 1 minute
Step-by-step explanation:
500/5=100
To find the unit rate of a question, divide.
500 / 5 = 100
100 meters per minute.
______
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A basketball arena can hold approximately 7,000 people. Fans bought 5,134 tickets before the game. About how many more seats are left to fill before the game.
There are about 1866 seats left to fill before the game.
Step-by-step explanation:
Number of people hold be basketball arena = 7000
Tickets bought by fans = 5134
Seats left to fill = Total capacity of arena - tickets bought by fans
Seats left to fill = [tex]7000-5134[/tex]
Seats left to fill = 1866
There are about 1866 seats left to fill before the game.
Keywords: subtraction
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Using the Pythagorean theorem:
L = √(15^2 - 9^2)
L = √(225 - 81)
L = √144
L = 12
The answer is 12'
8. Which equation has no solution?
A.
-5+8x - 9=3(x+3)
B.
-216-3x) = -12 +6x
C. 6-213-2x) = -413-x)
D.
-(4x +9) = 2x - 3(2x+3)
Answer:
Step-by-step explanation:
-5+8x-9=3(x+3)
8x-14=3x+9
8x-3x-14=9
5x-14=9
5x=9+14
5x=23
x=23/5
----------------------
-216-3x=-12+6x
-216-3x-6x=-12
-216-9x=-12
9x=-216-(-12)
9x=-216+12
9x=-204
x=-204/9
x=-68/3
------------------
6-213-2x=-413-x
-207-2x=-413-x
-207-2x-(-x)=-413
-207-2x+x=-413
-207-x=-413
x=-207-(-413)
x=-207+413
x=206
------------------------
-(4x+9)=2x-3(2x+3)
-4x-9=2x-6x-9
-4x-9=-4x-9
Infinitely many solutions.
is jonia high risk? explain why
Answer:
Step-by-step explanation:
The Waist to Hip Ratio (WHR) is a ratio commonly expressed as a decimal that has been shown to be a good predictor of possible cardiovascular problems in both men and women. If Jonia has a WHR greater than 1, she is at “high risk” for cardiovascular problems.
−4 1/3÷−2 3/5 please help need a 100
Answer:
1 2/3
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Exact Form:
5/3
Decimal Form:
1.6
Mixed Number Form:
1 2/3
Answer:
-4 1/3 divided by -2 3/5 equals 5/3
The amount y in cups of flour is proportional to the number x of eggs in a recipe. The recipe calls for 7 cups of flour for every 5 eggs
A: write and equation that represents the situation
B: interpret the slope
C: how many eggs are included when the recipe uses 14 cups of flour
Answer:
A. y=3/2x
B. y=3/2x
C. 18
Step-by-step explanation:
Mrs. Battle is designing a brick walkway to install in her front yard.
How many square feet of bricks will be needed for the walkway?
A 130
B 122
C 94
D 80
Answer:
B 122
Step-by-step explanation:
just thinking ur her
-5s=21.5 how do solve it
Answer:
s=-4.1
Step-by-step explanation:
you just need to divide by -5 of each item
so we have -5s/-5=21.5/-5
s=-4.1
How many solutions does the system of equations below have?
y= 3x + 4
y+ 6 = 3x
Answer:
0.
Step-by-step explanation:
If you take these two equations to a graphing calculator, you'll find that they are parallel. I. E. they don't intercept.
A solution to a system of equations is when they intercept, so if they don't intercept, that means no solution.
Answer: No solution
Step-by-step explanation:
Which similarity postulate or theorem can be used to verify that the two triangles shown below are similar?
Answer:
SAS Theorem
Step-by-step explanation:
It would be the SAS theorem because you know 2 sides that have an angle in common on both triangles.
Graph the solution of the inequality.
Answer:
[tex]\displaystyle -16 < x[/tex]
Step-by-step explanation:
[tex]\displaystyle -4[\frac{x}{-4}] < 4[-4] → x > -16[/tex]
Whenever you divide\multiply by a negative, you reverse the inequality symbol.
** The above answer is written in reverse, which is the exact same result.
≥, ≤ → Solid Circle [●]
>, < → Blank Circle [○]
I am joyous to assist you anytime.
what is 1/6 ÷ -2/9 please
Answer:0.0009
Step-by-step explanation:
Answer:
1/6+−2/9=−1/18
Step-by-step explanation:
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
(16×33)+(−29×22)=?
Complete the multiplication and the equation becomes
318+−418=?
The two fractions now have like denominators so you can add the numerators.
Then:
3+−418=−118
This fraction cannot be reduced.
Therefore:
16+−29=−118
Evaluate. 2^−2⋅(12⋅3)−5^3 Enter your answer in the box.
Answer:
-116
Step-by-step explanation:
Answer:
-116
Step-by-step explanation:
2^-2=1/2^2=1/4
5^3=5*5*5=125
12*3=36
-------------------------
1/4(36)-125
9-125=-116
I NEED HELP PLS THIS IS DUE IN 3 HOURS
Factor the following trinomials. (Hint: Solve the equations first.)
x^2−2x−2
and
Factor the following trinomials. (Hint: Solve the equations first.)
x2−6x+4
(these are 2 different problems pls HELP!)
Answer:
Part 1) [tex]x^{2} -2x-2=(x-1-\sqrt{3})(x-1+\sqrt{3})[/tex]
Part 2) [tex]x^{2} -6x+4=(x-3-\sqrt{5})(x-3+\sqrt{5})[/tex]
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
Part 1)
in this problem we have
[tex]x^{2} -2x-2=0[/tex]
so
[tex]a=1\\b=-2\\c=-2[/tex]
substitute in the formula
[tex]x=\frac{-(-2)(+/-)\sqrt{-2^{2}-4(1)(-2)}} {2(1)}\\\\x=\frac{2(+/-)\sqrt{12}} {2}\\\\x=\frac{2(+/-)2\sqrt{3}} {2}\\\\x_1=\frac{2(+)2\sqrt{3}} {2}=1+\sqrt{3}\\\\x_2=\frac{2(-)2\sqrt{3}} {2}=1-\sqrt{3}[/tex]
therefore
[tex]x^{2} -2x-2=(x-(1+\sqrt{3}))(x-(1-\sqrt{3}))[/tex]
[tex]x^{2} -2x-2=(x-1-\sqrt{3})(x-1+\sqrt{3})[/tex]
Part 2)
in this problem we have
[tex]x^{2} -6x+4=0[/tex]
so
[tex]a=1\\b=-6\\c=4[/tex]
substitute in the formula
[tex]x=\frac{-(-6)(+/-)\sqrt{-6^{2}-4(1)(4)}} {2(1)}[/tex]
[tex]x=\frac{6(+/-)\sqrt{20}} {2}[/tex]
[tex]x=\frac{6(+/-)2\sqrt{5}} {2}[/tex]
[tex]x_1=\frac{6(+)2\sqrt{5}}{2}=3+\sqrt{5}[/tex]
[tex]x_2=\frac{6(-)2\sqrt{5}}{2}=3-\sqrt{5}[/tex]
therefore
[tex]x^{2} -6x+4=(x-(3+\sqrt{5}))(x-(3-\sqrt{5}))[/tex]
[tex]x^{2} -6x+4=(x-3-\sqrt{5})(x-3+\sqrt{5})[/tex]