What is the value of p in the equation y2=-4x? p=?
Answer:
the value of p=-1
Step-by-step explanation:
General equation of a parabola is
[tex]y^2= 4p(x)[/tex] where vertex is at (0,0)
now we compare the given equation with general form
[tex]y^2=-4x[/tex]
We have -4 in the place of 4p
[tex]4p=-4[/tex]
Divide both sides by 4
so p = -1
the value of p = -1
What is the radical form of each of the given expressions? 4 1/7 AND 4 7/2 AND 7 1/4 AND 7 1/2 I WILL UPVOTE
from 5x^2-6x+8, subtract 3x^2-2x-4?
Write the ratio 7/8 :14 as a fraction in its simplest form
marathon runner runs26.2 miles at the pace of 6.2 minute per mile round off answer to the nearest minute how long will it take to run marathon
how do you solve:
5x^2 + 25x - 70
3.1 Pull out like factors :
5x2 - 25x - 70 = 5 • (x2 - 5x - 14)
3.2 Factoring x2 - 5x - 14
The first term is, x2 its coefficient is 1 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -14
Step-1 : Multiply the coefficient of the first term by the constant 1 • -14 = -14
Step-2 : Find two factors of -14 whose sum equals the coefficient of the middle term, which is -5 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 2
x2 - 7x + 2x - 14
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-7)
Add up the last 2 terms, pulling out common factors :
2 • (x-7)
Step-5 : Add up the four terms of step 4 :
(x+2) • (x-7)
Which is the desired factorization
4.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
4.2 Solve : 5 = 0
This equation has no solution.
A a non-zero constant never equals zero.
4.3 Solve : x+2 = 0
Subtract 2 from both sides of the equation :
x = -2
4.4 Solve : x-7 = 0
Add 7 to both sides of the equation :
x = 7
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex : 5.1 Find the Vertex of y = x2-5x-14
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.5000
Plugging into the parabola formula 2.5000 for x we can calculate the y -coordinate :
y = 1.0 * 2.50 * 2.50 - 5.0 * 2.50 - 14.0
or y = -20.250
Root plot for : y = x2-5x-14
Axis of Symmetry (dashed) {x}={ 2.50}
Vertex at {x,y} = { 2.50,-20.25}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-2.00, 0.00}
Root 2 at {x,y} = { 7.00, 0.00}
5.2 Solving x2-5x-14 = 0 by Completing The Square .
Add 14 to both side of the equation :
x2-5x = 14
Now the clever bit: Take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4
Add 25/4 to both sides of the equation :
On the right hand side we have :
14 + 25/4 or, (14/1)+(25/4)
The common denominator of the two fractions is 4 Adding (56/4)+(25/4) gives 81/4
So adding to both sides we finally get :
x2-5x+(25/4) = 81/4
Adding 25/4 has completed the left hand side into a perfect square :
x2-5x+(25/4) =
(x-(5/2)) • (x-(5/2)) =
(x-(5/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-5x+(25/4) = 81/4 and
x2-5x+(25/4) = (x-(5/2))2
then, according to the law of transitivity,
(x-(5/2))2 = 81/4
We'll refer to this Equation as Eq. #5.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(5/2))2 is
(x-(5/2))2/2 =
(x-(5/2))1 =
x-(5/2)
Now, applying the Square Root Principle to Eq. #5.2.1 we get:
x-(5/2) = √ 81/4
Add 5/2 to both sides to obtain:
x = 5/2 + √ 81/4
Since a square root has two values, one positive and the other negative
x2 - 5x - 14 = 0
has two solutions:
x = 5/2 + √ 81/4
or
x = 5/2 - √ 81/4
Note that √ 81/4 can be written as
√ 81 / √ 4 which is 9 / 2
5.3 Solving x2-5x-14 = 0 by the Quadratic Formula .
If there is a ratio of 3 to 2 what is the ratio of 3if the total is 30
the product of x and y, in three different ways; the product of the sum and the difference of x and y, using parentheses
PLZZZZZ HELP
Which answer best describes the system of equations shown in the graph?
not enough information
consistent and independent
coincident
inconsistent
Answer:
Option (2) is correct.
The given system of equation is Consistent and independent.
Step-by-step explanation:
coincident : When two lines overlap each other. then they are coincident lines.Inconsistent: When there is no solution for the given system of equations then the system is called "inconsistent". Consistent : When there is one or infinitely many solutions for the given system of equations is called "consistent".Independent : When each equation of the system gives new information Otherwise they are called Dependent. like x + y = 2 and 2x + 2y =4 this shows one equation is multiple of other hence, dependent.Now consider the given graph,
Since, they intersect at a unique point. Hence, they are consistent.
Also the two given equations are independent of each other .Thus, independent also.
Thus, the given system of equation is Consistent and independent.
Thus, option (2) is correct.
The temperature, in degrees fahrenheit (°
f., decreased at a constant rate from 0°f to -25 °f in 5 hours. by how many degrees did the temperature decrease per hour?
The temperature decreased at a constant rate of 5 degrees Fahrenheit per hour.
Explanation:The question is asking for the rate at which the temperature is decreasing per hour. The temperature started at 0oF and decreased to -25oF. That's a total change in temperature of 25oF (since we're counting how much it dropped below 0o). This change happened over the course of 5 hours. Therefore, to find the rate of change, we divide the total change (25 degrees) by the total time (5 hours). This gives us 5oF per hour. So, the temperature decreased at a rate of 5oF per hour.
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Which test point holds true for y − 2x ≤ 1?
(0, 2)
(-2, 4)
(1, 4)
(5, 0)
Answer:idek tbh
Step-by-step explanation:
Sheila deposited $1,050.00 into a saving account at her local bank. if the interest rate is 1.5%, then how much will he have after 18 months (round your answer to the nearest cent)?
Suppose the function shown below was expressed in standard form, y=ax^2+bx+c. What is the value of a? the graph shows a parabola facing downward with a vertex of (1,4) and the x intercepts are (3,0) and (-1,0) with a y intercept of (0,3)
...?
This is the graph they are referring to
Why do we use decimals in everyday life
compute the following linear combinations. 4(-2,3)-2(6,-7) ...?
Answer:
Step-by-step explanation:
alright lets get started.
the linear combination is given by :
[tex]4(-2,3)-2(6,-7)[/tex]
foiling 4 and 2 into the parenthesis
[tex](4*-2, 4*3)+(-2*6,-2*-7)[/tex]
[tex](-8, 12)+(-12,14)[/tex]
Combinig x and y terms together
[tex](-8-12, 12+14)[/tex]
[tex](-20,26)[/tex] : answer
Hope it will help. :)
some one factor 5x^2+23x+26
5*x^2-23*x-(-26)=0
1. x = 2
2. x = 13/5 = 2.600(-1,5),(0,6),(-1,7),(2,9) what is the domain range and is it a function ?
A souvenir maker wants to create a scale model of the Empire State Building. The Empire State Building is 1,472 feet tall and has a base with dimensions 286 ft by 286 ft. If the model is 6 in. tall, what are the approximate dimensions of its base in inches? (Round your answer to the nearest tenth of an inch.)
A) 1.2 in. by 1.2 in.
B) 1 in. by 1 in.
C) 0.2 in. by 0.2 in.
D) 2.3 in. by 2.3 in.
Twice a number decreased by 44 is 6 times the sum of the number and 3 times the number. find the number
A retailer charges a flat handling fee of $5.00, plus $0.75 per quarter pound, to ship an item. Bailey pays $9.50 to have an item shipped from the retailer. What is the weight of the item? 1.50 pounds
Answer:
1.50 pounds
Step-by-step explanation:
Given : A retailer charges a flat handling fee of $5.00, plus $0.75 per quarter pound, to ship an item.
Bailey pays $9.50 to have an item shipped from the retailer.
To Find: What is the weight of the item?
Solution:
He paid total amount = $9.50
A flat handling fee = $5.00
Amount he paid without handling fee = $9.50-$5.00
=$4.50
Now we are supposed to find what is the weight of an item that costs $4.50
So, we are given that it costs $0.75 per quarter pound, to ship an item.
So, cost of 1 pound = [tex]\frac{0.75}{\frac{1}{4}}=3[/tex]
So, it cost $3 for 1 pound
So, weight of an item that costs $1 = [tex]\frac{1}{3}[/tex]
So, weight of an item that costs $4.50=[tex]\frac{1}{3}\times 4.50[/tex]
=1.50 pounds
Hence the weight of the item is 1.50 pounds.
Answer:
1.50 pounds
Step-by-step explanation:
el de arriba lo dijo
Given the mapping diagram, DAYS (month), below, DAYS (July) = _____
Answer:
July has 31 days.
Step-by-step explanation:
The diagram shows that april has 30 days along with June, while May and July have 31 days.
A rectangle is drawn with perimeter 75 cm. The length is 13 more than the width. What is the length?
The perimeter of the rectangle is 75 cm, then the length of the rectangle will be equal to 25.25 cm.
What is the perimeter?A shape's perimeter is the whole distance encircling it. It is the perimeter or length of the contour of any geometric two-dimensional shape. The circumference of several figures could be comparable based on the measurements.
As per the information provided by the question,
The perimeter of the rectangle = 75 cm
Let the width of the rectangle is w.
Then, length (l) is 13 more than,
l = w + 13 (i)
As per the formula of the perimeter of a rectangle,
[tex]P=2(l+w)[/tex]
75 = 2(w + 13 + w)
75 = 4w + 26
4w = 49
w = 12.25 cm
Substitute w = 12.25 cm in equation (i)
l = 12.25 + 13
l = 25.25 cm.
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15 less than 4 times a number is 9 find the number
A family has two cars. the first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 25 miles per gallon of gas. during one particular week, the two cars went a combined total of 775 miles, for a total gas consumption of 35 gallons. how many gallons were consumed by each of the two cars that week?
A building casts a 50-foot shadow. Alex is 5 feet tall and casts a 6-foot shadow. Approximately how tall is the building?
A.24 ft
B.42 ft
C.60 ft
D.50 ft
Answer:
Option B: 42 feet is the answer.
Step-by-step explanation:
The length of the shadow of the building is = 50 feet
Let the height of the building be = L
Height of Alex = 5 feet
Length of Alex's shadow = 6 feet
Now we will equate the ratios.
[tex]\frac{5}{6}= \frac{L}{50}[/tex]
[tex]6L=250[/tex]
[tex]L=250/6[/tex]
L = 41.67 ≈ 42 feet
So, the height of the building is approx 42 feet.
If the length of one of the legs of a right triangle is 10 and the length of the other leg is 24 what is the length of the hypotenuse
Answer:
the hypotenuse is probably 26
Step-by-step explanation:
find the square root of 1.69? show work ...?
The value of the square root of the number 1.69 would be 1.3.
Used the concept of the square root of a number that states that,
The square root of a number is the number that, when multiplied by itself, gives the original number.
Given that the number is,
The square root of 1.69.
Now simplify the number as
The square root of 1.69.
It can be written as,
√1.69
√(1.3)²
= 1.3
Therefore, √1.69 = 1.3
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The range of which function includes -4?
A. y=sqrt(x)-5
B. y=sqrt(x)+5
C. y=sqrt(x+5)
D. y=sqrt(x-5)
Answer: The correct answer is A.
Step-by-step explanation:
Range is defined as the set of 'y' values for which the function is defined.
The graph of [tex]y=\sqrt{x}[/tex] passes through the origin and lies in the first quadrant and in the shape of half parabola. The image is attached below.
The alteration in the 'x' term will transform the graph in the x-direction. In order to find the range we will consider the y-values only. So, we can neglect option C and D.
When we add some constant 'C' in the function, then the graph will shift upward by C-units.
When we subtract some constant 'C' in the function, then the graph will shift downward by C-units.
Therefore, the graph of [tex]y=\sqrt{x}-5[/tex] starts with the point (0,-5) and hence, the graph will lie above this point. The image of the graph is attached below.
As, the range of the function is [tex]y\in {-5,\infty}[/tex], it means that -4 is also included in this range.
Hence, the correct option is A.
The correct option where the range includes -4 is y = sqrt(x) - 5. Other options do not produce negative values in their ranges. Hence, Option A is the correct answer.
To determine which function's range includes -4, we will analyze each option:
Option A: y = sqrt(x) - 5Based on the above analysis, the correct answer is Option A: y = sqrt(x) - 5.
Write the equation of the line that passes through (7,-4) and (-1,2) in slope-intercept form
To make lemonade, kate uses 1 cup of lemon juice and 2 cups sugar. if she makes a larger amount of lemonade with 10 cups of sugar, how many cups of lemon juice does she need?
Kate uses 1 cup of lemon juice and 2 cups of sugar to make lemonade. She requires 5 cups of lemon juice if she uses 5 cups of sugar to produce a larger batch of lemonade.
What is the ratio?It is defined as the comparison of two quantities to ascertain how many times one yields the other. The ratio can be written as a fraction or as a sign: between two numbers.
It is given that, Kate uses 2 cups of sugar and 1 cup of lemon juice to make lemonade. If she uses 10 cups of sugar to create more lemonade.
The ratio of lemon juice to sugar is 1:2.
For 10 cups of sugar, the number of cups of lemon juice needed as,
We have to maintain the ratio as 1:2.So for 10 cups of sugar, the ratio is maintained as,
=5:10
=1:2
Thus, she needs 5 cups of juice to make lemonade.
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