4) Write the quadratic equation of the following in vertex form: vertex (-1,3) and passes through (1,-5)
I
ULTS
Factor completely
5) 15m2 - 6
6) 2x2 + 5x - 10% - 25
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
4)
If an equation representing a parabola is in vertex form such as
[tex]y\:=a\left(x-k\right)^2+h[/tex]
then its vertex will be at (k, h).
Therefore the equation for a parabola with a vertex at (-1, 3), will have the general form
[tex]y\:=a\left(x+1\right)^2+3[/tex]
If this parabola also passes through the point (1, -5) then we can determine the 'a ' parameter.
[tex]-5\:=a\left(1+1\right)^2+3[/tex]
simplifying the equation
[tex]2^2a+3=-5[/tex]
[tex]4a+3=-5[/tex]
subtract 3 from both sides
[tex]4a+3-3=-5-3[/tex]
[tex]4a=-8[/tex]
Divide both sides by 4
[tex]\frac{4a}{4}=\frac{-8}{4}[/tex]
[tex]a=-2[/tex]
So our equation in vertex form is:
[tex]y\:=-2\left(x+1\right)^2+3[/tex]
5)
Given the expression
[tex]15n^2-6n[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c[/tex]
[tex]=15nn-6n[/tex]
[tex]\mathrm{Rewrite\:}6\mathrm{\:as\:}3\cdot \:2[/tex]
[tex]\mathrm{Rewrite\:}15\mathrm{\:as\:}3\cdot \:5[/tex]
[tex]=3\cdot \:5nn-3\cdot \:2n[/tex]
Factor out the common term 3n
[tex]=3n\left(5n-2\right)[/tex]
6)
Given the expression
[tex]2x^2+5x-10x-25[/tex]
Factor 2x²+5x: x(2x+5)
Factor -10x-25: -5(2x+5)
so the expression becomes
[tex]=x\left(2x+5\right)-5\left(2x+5\right)[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}\left(5+2x\right)[/tex]
Related Questions
Ltd say we're given the quadratic equation x + 2x2 - 4 = -7x + 6
Enter your answers separated by a comma
Answers
Answer:
x=1 ,x= -5
Step-by-step explanation:
x+2x2-4=-7x+6
2x2+x+7x-4-6=0
2x2+8x-10=0
divide through out by 2 to reduce the equation
x2+4x-5=0
by using formula method
x=[-b+\-√b2-4ac]/2a. a=1, b=4 c=-5
x=[-4+\-√4^2-4*1*-5]/2*1
x=[-4+\-√16+20]/2
x=[-4+\-√36]/2
x=[-4+\-6]/2
x=(-4+6)/2 ,x=(-4-6)/2
x=2/2 , x=-10/2
x=1 , x=-5
The number of solutions to the equation are two and Real in nature. The solutions are x = 1 and x = - 5.
We have the following quadratic equation -
x + [tex]2x^{2}[/tex] - 4 = -7x + 6
We have to determine its solutions.
What is the Quadratic formula to find the roots of a quadratic equation ?The Quadratic formula is -
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
According to question, we have -
x + [tex]2x^{2}[/tex] - 4 = -7x + 6
Rearranging the equation -
[tex]2x^{2}[/tex] + x + 7x - 4 - 6 = 0
[tex]2x^{2}[/tex] + 8x - 10 = 0
Using the quadratic formula -
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
[tex]$x=\frac{-8\pm\sqrt{64-(-80)}}{4}$[/tex]
[tex]$x=\frac{-8\pm\sqrt{144}}{4}$[/tex]
[tex]$x=\frac{-8 +12}{4}[/tex] and [tex]$x= \frac{-8-12}{4}[/tex]
x = 1 and x = - 5
Hence, the number of solutions to the equation are two and Real in nature. The solutions are x = 1 and x = - 5.
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Help me pls it’s important
Answers
Answer:
The value of x = -10 if g(x)=0.
i.e.
When x = 0, g(-10)=0
Step-by-step explanation:
From the given graph, it is clear that the graph passes through the x-axis when x = -10.
In other words, the function becomes zero at x = -10.
Thus, the x-intercept x = -10 will determine that:
at x = -10 , g(-10) = 0
Thus, the value of x = -10 if g(x)=0.
i.e.
When x = 0, g(-10)=0
Find the missing number to make a unit rate 6/2=3/?
Answers
Answer:
yes
Step-by-step explanation:
Answer:
i think its 6/2=3/1
Step-by-step explanation:
AB= 17 cm and BC= 12.75cm Find DB.
Answers
(-1/3+1/9) • 4^2 +5/8
A.) - 2/9
B.) 32/9
C.) -59/18
D.) 73/18
Answers
Answer:
B
Step-by-step explanation:
1. The main show tank has a radius of 70 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally.) What is the volume of the quarter-sphere shaped tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.
2. The holding tanks are congruent. Each is in the shape of a cylinder that has been cut in half vertically. The bottom of each tank is a curved surface and the top of the pool is a flat surface. What is the volume of both tanks if the radius of tank #1 is 35 feet and the height of tank #2 is 120 feet? You must explain your answer using words, and you must show all work and calculations to receive credit.
3. The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made one sixth of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?
Using the information from #3, answer the following question by filling in the blank: The volume of the original main show tank is ____% of the mock-up of the tank.
Answers
Answer:
1. Volume = 5128.67 ft³
The volume if sphere is given by:
V = (4/3)πr³
If the tank is cut into half vertically, then the volume of sphere becomes.
V = (4/3)πr³ / 2
If the tank is cut into half again horizontally, then the volume of the sphere becomes.
V = (4/3)πr³ / 4
Hence, as the main tank forms a quarter sphere, its Volume is given by:
V = (4/3)πr³ / 4
It is given in the question that the radius is 70 ft.
Substitute that in the given formula:
V = (4/3)π(70)³ / 4
V = 5128.67 ft³
2. Volume of tank = 461,814 ft³
Step-by-step explanation:
Congruent tanks implies that both tanks are of identifical shape, form & dimensions. Congruent means that the tanks have the same radius as well as height. Hence, the heights and radii of tanks #1 and #2 are equal and the same.
Let's list out the information given us:
radius(tank #1) = 35 ft ⇒ radius(tank #2) = 35 ft, height(tank #2) = 120 ft ⇒ height(tank #2) = 120 ft
Volume of cylinder = πr²h
The tanks have been cut into half, as such:
Volume of tank = ½πr²h
Volume of tank = Volume(tank #1) + Volume(tank #2)
Since the tanks are congruent (same dimensions), we have:
⇒ ½πr²h + ½πr²h ⇒ πr²h
Volume of tank = π * 35² * 120 = 147,000 π
Volume of tank = 461,814 ft³
3. 1047.2 ft³
Step-by-step explanation:
The following information is missing:
The main show tank has a radius of 60 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally)
The only dimension needed for the main show tank is its radius. Then the model radius will be 1/6 * 60 = 10 feet
The volume of a sphere is:
V = 4/3 * π * r³
For a quarter sphere it is:
V = 4/3 * π * r³ * 1/4
V = 1/3 * π * r³
For the smaller mock-up tank:
V = 1/3 * π * 10³
V = 1047.2 ft³
What is the slope of the line through the points (3, 7) and (5, 15)?
Answers
Answer:
[tex]m=4[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (3, 7)
Point (5, 15)
Step 2: Find slope m
Substitute [Slope Formula]: [tex]m=\frac{15-7}{5-3}[/tex]Evaluate Subtraction: [tex]m=\frac{8}{2}[/tex]Evaluate Division: [tex]m=4[/tex]Answer:
4
Step-by-step explanation:
cuz
What type of number is v64?
Choose all answers that apply:
A)Whole number
B) Integer
c Rational d) irrational
Answers
The correct answers are A) Whole number, B) Integer, and C) Rational.
The number √64 is equal to 8. It satisfies the condition √64 = 8 because 8 multiplied by itself (8 x 8) equals 64.
Based on the options provided, the correct answers are:
A) Whole number: Yes, √64 is a whole number. Whole numbers are non-negative integers, and 8 is a non-negative integer.
B) Integer: Yes, √64 is an integer. Integers are numbers that can be positive, negative, or zero without any fractional or decimal parts. In this case, 8 is a positive integer.
C) Rational: Yes, √64 is a rational number. Rational numbers can be expressed as a fraction p/q, where p and q are integers, and q is not zero. The square root of 64 can be written as 8/1, which is a fraction where both the numerator and denominator are integers.
D) Irrational: No, √64 is not an irrational number. Irrational numbers cannot be expressed as fractions and have an infinite non-repeating decimal expansion. However, √64 is a terminating decimal, as it equals 8, which means it is not an irrational number.
Therefore, the correct answers are A) Whole number, B) Integer, and C) Rational.
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65 effing points, will mark brainliest! here we go again
Jeremy has heard a lot of people in the club talking about tackling a 950-foot rock formation. Jeremy has set a limit that they won’t climb anything that takes longer than 7 hours, so they have enough time to travel to and from the place. Will it be possible to climb a 950-foot rock formation within Jeremy’s time constraint? Explain why or why not.
Answers
Answer:
No
Step-by-step explanation:
The amount of minutes to climb up 1 foot of height would take around 2 to 3 minutes. if you divide 950 with 2, you get 475 which would be the time in minutes it takes to climb, if we convert 475 minutes to hours, it would be an estimate of 7.92 hours. So as we see they would need an extra 92 minutes to climb the full 950 feet. If you were able to climb it at an average rate of 135.7 ft/hr, you could make it.
(this was someone elses explanation)
Where is the midpoint of AB if A(6,4) and B(5,-2)?
A (11,2)
B) (11,6)
C) (5.5,3)
D (5.5,1)
Answers
Answer:
Midpoint={5.5,1}
Step-by-step explanation:
M={x1+x2/2,y1+y2/2}
M={6+5/2,-2+4/2}
M={11/2,2/2}
M={5.5,1}
A class is selling smoothie tickets to raise money. It costs $700 for a bulk order of smoothies. If they charge $4.50 per smoothie ticket, what is the maximum amount of smoothie tickets they need to sell to raise at least $1,600?
A. 185 tickets
B. 200 tickets
C. 215 tickets
D. 250 tickets
Answers
Answer:
Step-by-step explanation:
Ok look, you gonna laern something’s so basically you can not be a man of a man who is a man of a man and he killed you he was the one he saw him kill him he said it would be a good day he is not the only person who he was killed him in electric he didn’t know what he saw and killed a good man he said was he killed a man he was a good father he said ihe on my way to the hospital was at my moms for my first time here in a good day with him I was with green light blue red white white yellow blue blue orange green yellow blue blue green green orange yellow yellow orange orange brown white yellow yellow white yellow orange yellow yellow green yellow blue blue i was the yellow orange orange yellow orange green yellow blue blue white white blue green green among us
E
Which transformation of the parent square root function will result in the given domain and range? domain : [2,∞) range : [3,∞)
Answers
Answer:
B. g(x) = (x - 2)^(1/2) + 3Step-by-step explanation:
This is B
(x - 2) is not negative and defined when x≥0g(x) gets minimum value of 3 at minimum value of x = 2By what percent would the area of the rectangle change if the width of the rectangle is increased by 50% and the length is increased by the same number of units?
Answers
Answer:
. i think it's wrong
If you have 3 sticks of length 2 cm, 3 cm and 5 cm. What kind of triangle these sticks would form? Justify your answer.
Answers
Answer:
Scalene triangle (As the definition says)
Complete the flow proof
Answers
Answer:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. ∠V ≅ ∠Y [tex]{}[/tex] Given
2. [tex]\overline {WZ}[/tex] bisects ∠VWY [tex]{}[/tex] Given
3. ∠VWZ = ∠YWZ [tex]{}[/tex] Definition of bisection of angle
4. [tex]\overline {WZ}[/tex] ≅ [tex]\overline {ZW}[/tex] [tex]{}[/tex] Reflexive property
5. ΔWVZ ≅ ΔWYZ [tex]{}[/tex] Angle-Angle-Side congruency postulate
6. [tex]\overline {VZ}[/tex] ≅ [tex]\overline {YZ}[/tex] [tex]{}[/tex] CPCTC postulate
Step-by-step explanation:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. ∠V ≅ ∠Y [tex]{}[/tex] Given
2. [tex]\overline {WZ}[/tex] bisects ∠VWY [tex]{}[/tex] Given
3. Given that ∠VWY is bisected by [tex]\overline {WZ}[/tex], therefore ∠VWY is split into two equal angles, ∠VWZ and ∠YWZ, from which we have ∠VWZ = ∠YWZ [tex]{}[/tex] by the definition of bisection of angle ∠WXY by [tex]\overline{WZ}[/tex]
4. By reflexive property, a line is congruent to itself, therefore, [tex]\overline {WZ}[/tex] ≅ [tex]\overline {ZW}[/tex]
5. Given that two adjacent angles and a side adjacent to the two angles in ΔWVZ are congruent to the corresponding two adjacent angles and adjacent side in ΔWYZ, ΔWVZ is congruent to ΔWYZ by the Angle-Angle-Side (AAS) congruency postulate
6. Given that ΔWVZ ≅ ΔWYZ, and side [tex]\overline {VZ}[/tex] of ΔWVZ is the corresponding side to side [tex]\overline {YZ}[/tex] of ΔWYZ, therefore, [tex]\overline {VZ}[/tex] is congruent to [tex]\overline {YZ}[/tex] by the Congruent Parts of Congruent Triangle are Congruent (CPCTC) postulate.
An ice sculpture is melting because of heat. Assuming its height changes by negative 2 over 25 m every hour, what will be the change in the height after 5 hours? negative 2 over 5 meter negative 2 over 125 meter 2 over 125 meter 2 over 5 meter
Answers
Answer:
[tex] \frac{ - 2}{25} \times 5[/tex]
first you multiply 2 by 5. Then you get 10 over 25. Then you simplify it. What is the common factor of both 10 and 25? Is it 2? No 2 is a factor of 10 but not 25. It's 5. After you get the common factor you divide both numbers by it. So 10/5 would be 2. 25 divide by 5 would be 5. And the negative sign remains
-2/25 x 5/1 = -10/25 = -2/5
hope this helps :}
Juan invested $100 in a savings account the earns 5% annually. The value, A, of the investment can be calculated using the equation A=p(1+r) with and exponent of t, where p is the investment in dollars, r is the interest rate, and t is the time of years. What amount will be in the savings account in two years?
Answers
Answer:
$110.25
Step-by-step explanation:
Step one:
given
principal= $100
rate= 5%
time = 2 years
Required
The final amount
Step two:
The compound interest formula is
[tex]A=p(1+r)^t[/tex]
substituting we have
[tex]A=100(1+0.05)^2\\\\A=100(1.05)^2\\\\A=100*1.1025\\\\A=110.25\\\\[/tex]
The final amount is $110.25
Pls tell me the answer
Answers
Answer:
1/4
Step-by-step explanation:
You began membership in a new health and fitness club which has access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, w, as a function of time, t, over an eight-week period.
Time (weeks)
0
1
2
3
4
5
6
7
8
Weight (lb)
150
144
143
141
140
137
137
132
129
If you lost 13 pounds in the first five weeks, what is the average rate of change of weight with respect to time over the first five weeks of the program?
a.
+0.38 pounds per week
b.
-0.38 pounds per week
c.
+2.6 pounds per week
d.
-2.6 pounds per week
Answers
Answer:
d
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Just took the test
Element X decays radioactively with a half life of 13 minutes. If there are 830 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 20 grams?
Answers
Answer:
26.92 min
if I'm not wrong!
1. The zeros of a quadratic relation are 3 and The second differences are positive
a) Will the optimal value be a maximum or minimum? Justify your answer.
Answers
Answer:
The optimal, vertex, value will be a minimum
Step-by-step explanation:
The given zeros of the quadratic relation are 3 and 3
The sign of the second differences of the quadratic relation = Positive
Whereby the two zeros are the same as x = 3, we have that the point 3 is the optimal value or vertex (the repeated point in the graph of the quadratic relation) of the quadratic relation
Whereby, the table of values for the quadratic relation from which the second difference is found starts from x = 3, we have;
To the right of the coordinate points of the zeros of the quadratic relation, the positive second difference in y-values gives as x increases, y increases which gives a positive slope
By the nature of the quadratic graph, the slope of the line to the left of the coordinate point of the zeros of the quadratic relation will be of opposite sign (or negative). The quadratic relation is cup shaped and the zeros, therefore, the optimal value will be a minimum of the quadratic relation
HELP PLSS
Solve the equation 17−(3x+5)=3x−6
Answers
Answer:
x = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
17 - (3x + 5) = 3x - 6
Step 2: Solve for x
Distribute negative: 17 - 3x - 5 = 3x - 6Add 3x on both sides: 17 - 5 = 6x - 6Combine like terms: 12 = 6x - 6Isolate x term: 18 = 6xIsolate x: 3 = xRewrite: x = 3Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 17 - (3(3) + 5) = 3(3) - 6Multiply: 17 - (9 + 5) = 9 - 6Add: 17 - 14 = 9 - 6Subtract: 3 = 3Here we see that 3 does indeed equal 3.
∴ x = 3 is the solution to the equation.
Answer:
x = 3
Step-by-step explanation:
17 - 1(3x + 5) = 3x - 6
17 − 3 − 5 = 3x − 6
12 - 3x = 3x - 6 subtract five
-3x + 12 = 3x - 6 rearrange terms
-3x = 3x - 18 subtract twelve
-6x = 18 subtract negative three
divide by negative six
x = 3
Find the perimeter of the figure
Answers
Answer:
142
Step-by-step explanation:
Ok explanation
we know the sides 9, 11, 38, and 13.
there are 2 missing sides we need to find
so the first one whic is the longer one is we know that the 38 is already 1 part of it but not the whole thing. We know the 9 is part of the 38 since it connects. So that gives us that side of 47.
Now for the shrter side, we know 1 part of it is 13 And the other part is 11. So we Add them up and get 24
Now the sides are 9, 11, 38, 13, 47, and 24
We add them up and get 142
Answer:
142 mi
Step-by-step explanation:
Top = 9 +38 = 47
Right Side = 13
Bottom Right = 38
11 + 9 = 20
Left Side = 24
47 + 13 +38 + 20 + 24 = 142
Cameron invests $1000. He has a choice of two schemes:
Scheme A offers $25 every year.
Scheme B offers 2% interest compounded annually.
Over what periods of investment (in whole years) is scheme A better than scheme B?
Answers
Answer: 2 year
Step-by-step explanation: After 3 years scheme B would be 80$ while Scheme A would be 75$
can someone please help me
Answers
Answer:
X<2
Step-by-step explanation:
- signs will be cancelled after taking common.
then 6 is subtracted from 18 and we get 12.
then 12 is divided by 6 and we get 2.
the inequality sign will remain the same.
Answer:
Inequality Notation: x < 2See screenshot belowI hope this helps!
7 divided by 276 is what? I am terrible at division
Answers
Answer:
39.4285714286
Step-by-step explanation:
Hope this helps and have a great day!!!
To go to school each day, Myra walks 20 yards due south to the bank then 48 yards east.
Answers
Answer: 68
Step-by-step explanation:
Isabella wants to purchase a new refrigerator. When she applies for an installment loan at the appliance store, her loan application is turned down. What consumer law says that a lender must give her the reason, in writing, that she was denied the loan?
Answers
Answer:
fair credit billing act
HELP FAST!! WILL GIVEV BRAINLIEST
Answers
Answer:
-2, -4, -1.5
Step-by-step explanation:
-6x+10>16
-6x>6
x<-1
(anything less than -1)
Answer:-4, -2, -1.5
Step-by-step explanation: First, simplify the equation. You should get -6x+10>16
Then, substitute the values into the place of x. If they are greater than 16, they are solutions. -4, -2, and -1.5 work. Hope this helps you!
What is the slope of the following line? 4x+2y=12 *
4
8
-2
-4
Answers
Answer:
4
Step-by-step explanation:
because if change to slope intercept form: y = mx+b
4=m
m=slope
Answer: Slope = -4.000/2.000 = -2.000
x-intercept = 285/2 = 142.50000
y-intercept = 285/1 = 285.00000
Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
4*x+2*y-(12*48-2-4)=0
STEP
1
:
Pulling out like terms
1.1 Pull out like factors :
4x + 2y - 570 = 2 • (2x + y - 285)
Equation at the end of step
1
:
STEP
2
:
Equations which are never true:
2.1 Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Equation of a Straight Line
2.2 Solve 2x+y-285 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2x+y-285 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 285/1 so this line "cuts" the y axis at y=285.00000
y-intercept = 285/1 = 285.00000
Calculate the X-Intercept :
When y = 0 the value of x is 285/2 Our line therefore "cuts" the x axis at x=142.50000
x-intercept = 285/2 = 142.50000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 285.000 and for x=2.000, the value of y is 281.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 281.000 - 285.000 = -4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -4.000/2.000 = -2.000
Geometric figure: Straight Line
Slope = -4.000/2.000 = -2.000
x-intercept = 285/2 = 142.50000
y-intercept = 285/1 = 285.00000