What are the zeros of the parabola in #1? (that is, at what points does the graph cross the x-axis?)
Picture is number one
The zeroes of the parabola is -1, -5.
What is parabola and zeroes of parabola?
A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
The equation of parabola can be expressed in two different ways, such as the standard form and the vertex form. The standard form of parabola equation is expressed as follows:
f(x) = y= ax2 + bx + c
To find zeroes of parabola
x = -b ±[tex]\sqrt{b^{2}-4ac } /2[/tex]
Given equation is
f(x) = [tex]x^{2} +6x+5[/tex]
a = 1, b = 6, c = 5
x = -6 ±[tex]\sqrt{36-4(5)}[/tex]/2
x = -6 ±[tex]\sqrt{16} /2[/tex]
x = -6 ± 4 /2
hence,
x = -6-4/2 and x = -6 +4/2
x = -5 or x = -1
To know more about parabola, visit:
https://brainly.com/question/18054637
#SPJ1
math help, will mark brainliest
Answer: 1 question Solve for x
x=
3
−y−2z−10
Solve for y
y=−3x−2z−10
Step-by-step explanation: Steps for Solving Linear Equation
3x+y+2z=−10
Subtract y from both sides.
3x+2z=−10−y
Subtract 2z from both sides.
3x=−10−y−2z
The equation is in standard form.
3x=−y−2z−10
Divide both sides by 3.
3
3x
=
3
−y−2z−10
Dividing by 3 undoes the multiplication by 3.
x=
3
−y−2z−10
one serving of a certain brand of yogurt contains 7g of fat. the low fat version contains 45.75% less fat per serving. how many grams of fat does one serving of the low fat yogurt contain?
The grams of fat that are contained in one serving of the low-fat yogurt are: 3.7968g.
How do we obtain the grams of fat for one serving of low-fat yogurt?To obtain the number of grams of fat that is contained in one serving of the low-fat yogurt, we need to first note the percentage content of the low-fat version of yogurt.
100 - 45.75% = 54.25% or 0.5425
Since one serving of the yogurt contains 7g of fat, then the low-fat serving will be equal to:
7g × 0.5425 = 3.7968
So, the total gram of fat for one serving of the low-fat yogurt is equal to:
3.7968g
Learn more about grams measurement here:
https://brainly.com/question/448721
#SPJ1
It is 163 cm from your eyes to your toes. You're standing 220 cm in front of a tall mirror. How far is it from your eyes to the image of your toes?
The distance between the eyes and the distance to the image of the toes will be 273.80 cm.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.
According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given that It is 163 cm from your eyes to your toes. You're standing 220 cm in front of a tall mirror.
The distance between the image of toes and eyes will be calculated as,
H² = P² + B²
H= √(P² + B²)
H = √(163² + 220²)
H = √(26569+48400)
H = √74969
H = 273.80 cm
Therefore, the distance between the eyes and the distance to the image of the toes will be 273.80 cm.
To know more about the Pythagorean theorem follow
https://brainly.com/question/343682
#SPJ1
A road has a speed limit sign at the beginning that is noticed by 84 % of people. 95 % of people who didn't notice the sign speed on the road. Of those who notice the sign, 75 % follow the speed limit.
How many percent of people speeding on this road noticed the sign? In other words, how many people on this road speed on purpose. Give your answer in percentage.
The percentage is the indicating hundredth thus the percentage of people speeding on this road who noticed the sign would be 84% - 75% = 9%.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
As per the given,
Percentage of people who notice the speed limit = 84%
The percentage of people who notice the sign and follow the speed limit is 75%.
Therefore, 84% - 75% = 9% are the percentage speeding and noticed.
Hence "The percentage is the indicating hundredth thus the percentage of people speeding on this road who noticed the sign would be 84% - 75% = 9%".
For more about the percentage,
brainly.com/question/13450942
#SPJ1
sry for the awful picture but i couldnt get it as a file
Check the picture below.
Write the word sentence as an equation. Then solve. The sum of a number y and −3 is −8. Equation: Solution: y=
Considering the definition of an equation and the way to solve it, the equation is y +(-3)=-8 and the solution is -5.
Definition of equationAn equation is an algebraic equality in which letters appear with unknown value.
In an equation appears:
The members, which are each of the expressions that appear on both sides of the equal sign The terms, which are the addends that form the members of an equation.The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Equation and solution in this caseBeing "y" a number, and knowing that sum of a number and -3 is -8, the equation in this case is:
y + (-3)= -8
Solving:
y -3= -8
y= -8 +3
y= -5
Finally, the number "y" is -5.
Learn more about equations:
brainly.com/question/4983716
brainly.com/question/13314678
#SPJ1
d/dx(e^x)=e^x prove
⇒[tex]\frac{d}{dx} (e^{x} )= e^{x} *\frac{d}{dx} (x)\\\frac{d}{dx} (e^{x} )=e^{x}*1\\\frac{d}{dx} (e^{x} )=e^{x}[/tex]
⇒Note this is all applied due to chain rule.
Please help me simplify
Answer: [tex]\frac{4\sqrt{x} }{t^2}[/tex]
Step-by-step explanation:
You can start by either applying the exponent to both the numerator and denominator (exponent rule), or make things simpler by dividing first. Doing the latter allows me to show both properties. Since the terms in the fraction are being multiplied, we can divide common terms which will leave us with [tex]\frac{16x}{t^4}[/tex] on the inside. Now that it is simplified, we can apply the exponent. We will end up with 4x^1/2 in the numerator and t^2 in the denominator. If the exponent seems daunting, it is also helpful to know that raising something to the exponent of 1/2 is basically taking the square root of it.
Minimizing Costs A pencil cup with a capacity of 20 in.3 is to be constructed in the shape of a rectangular box with a square base and an open top. If the material for the sides costs 12¢/in.2 and the material for the base costs 60¢/in.2, what should the dimensions of the cup be to minimize the construction cost?
The dimensions of the cup that minimize the construction cost are 2 x 2 x 5 in
How to determine the dimensions of the cup that minimize the construction cost?
Given: Capacity = 20 in³, cost of material for the side = 12¢/in² and cost of material for the base = 60¢/in²
In order to calculate the dimension of the cup
Let h and x represent the height and square base respectively
Thus, the capacity (volume) of the pencil cup is can be represented as:
V = x²h (where V = 20)
20 = x²h
h = 20/x²
At minimum cost, we have:
C(x) = 60x² + 12(4xh)
C(x) = 60x² + 48xh (put h = 20/x²)
C(x) = 60x² + 48x(20/x²)
C(x) = 60x² + 960/x
Differentiating with respect to x, we have:
C(x) = 120x - 960/x² (multiply through by x²)
120x³-960 = 0
120x³ = 960
x³ = 960/120
x³ = 8
x = ∛8 = 2 in
For the height:
h = 20/x²
h = 20/2²
h = 20/4 = 5 in
dimensions = 2 x 2 x 5 in
Therefore, the dimensions of the cup that minimize the construction cost are a 2 x 2 square base and height of 5 in
Learn more about capacity on:
https://brainly.com/question/13644646
#SPJ1
Raven is taking a math test.
The test lasts for 1 hour and 35 minutes.
If they finish the test at 1:20, what time did they start the test?
If they took 1 hour and 35 minutes to complete the test and finished at 1:20 they started at 11:45.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, The total time of the math test Raven took was 1 hour and 35 minutes.
Now he finishes the test at 1:20.
So, One hour before the time was 12:20.
20 minutes before that was exactly 12:00 and 15 minutes before that was
11:45 so a total of 1 hour and 35 minutes.
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ1
Please help me I’ll mark your answer brainly
The measure of angle B is x, while the measure of angle A is 2·x. The 70° measure of angle C and the angle sum property of the interior angles of a triangle indicates that angle B is [tex]36.\overline 6^{\circ}[/tex] and angle A is [tex]73.\overline 3^{\circ}[/tex]
What are the interior angles of a triangle?The interior angles of a triangle are the angles formed by the sides sides of the triangle.
The question can be solved by making use of the known properties of a triangle.
The angle sum property of the interior angles in a triangle gives;
The sum of the interior angles of a triangle is 180°
Therefore; x + 2·x + 70 = 180
3·x = 180° - 70° = 110°
[tex]x = \dfrac{110^{\circ}}{3} = 36\frac{2}{3} ^{\circ}[/tex]
The measure of angle A is 2·x
Which gives;
[tex]A = 2 \times 36\frac{2}{3} ^{\circ} = 73\frac{1}{3} ^{\circ} = 73.\overline 3^{\circ}[/tex]
Learn more about the angles of a triangle here:
https://brainly.com/question/68217
#SPJ1
15. Rachel Teeter has a monthly budget of $3000. She plans
to spend 34% for rent and utilities, 23% for food, 5% for
entertainment, 25% to pay off debt, and the remainder
will go into a savings account.
(a) What percent of the total budget will go into a savings
account?
Answer: 17%
Step-by-step explanation:
If you add up 34%, 23%, 5%, & 25% that would equal 83%, if you subtract the 83% from 100%, you would get 17%.The 17% is equivalent to 510. So Rachel Teeter will have $510 in her savings account.
Hailey used math to describe design in nature:
the number of legs insects and spiders have, the number of petals on flowers, and even the patterns of spots on some animals.
Math shows the world is designed, and that design is _______.
The math shows the world is designed, and that design is symmetry and spirals.
How is math found in nature What is the significance of mathematical patterns in nature?
Mathematics is seen in many beautiful patterns in nature, such as symmetry and spirals. Both are aesthetically appealing and proportional. Symmetry can be radial, where the lines of symmetry intersect a central point such as a daisy or a starfish.
Here,
If Hailey used math to describe the design in nature: the number of legs insects and spiders have, the number of petals on flowers, and even the patterns of spots on some animals. The math shows the world is designed, and that design is symmetry and spirals.
Hence, the math shows the world is designed, and that design is symmetry and spirals.
To learn more about the nature of maths from the given link
https://brainly.com/question/24730520
#SPJ1
To purchase $12,200 worth of restaurant equipment for her business, Linda made a down payment of $1600 and took out a business loan for the rest. After 3
years of paying monthly payments of $322.48, she finally paid off the loan.
(a) What was the total amount Linda ended up paying for the equipment
(including the down payment and monthly payments)?
$0
(b) How much interest did Linda pay on the loan?
$0
Step-by-step explanation:
To purchase $12,200 worth of restaurant equipment for her business, Linda made a down payment of $1600 and took out a business loan for the rest. After 3 years of paying monthly payments of $322.48, she finally paid off the loan.
(a) What was the total amount Linda ended up paying for the equipment
(including the down payment and monthly payments)?
How much on loan:
12,200 - 1,600 = $10,600 loan amount
How much paid on loan:
$322.48 * 3 years * 12 months = $11,608.28 amount paid on loan
Total paid:
= loan amount + amount paid on loan
$10,600 + $$11,608.28
= $22,208.28 paid overall
________________________________________
(b) How much interest did Linda pay on the loan?
= loan amount - amount paid on loan
= $11,608.28 - $10,600
= $1,009.28 paid in interest
A total of 600 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the
number of adult tickets sold. How many adult tickets were sold?
Answer:
150 adult tickets where sold
Step-by-step explanation:
If we multiply 150 times 3 that gives us 450, which acounts for all the students. And 150 is the number thats left of adults that adds up to 600.
A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions correctly. If a student guesses each question, what is the probability that the student will pass the test?
The probability that the student will pass the test, using the binomial distribution, is of:
0.172 = 17.2%.
What is the binomial distribution formula?The formula that gives the probability of x successes is presented as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters of the formula are listed as follows:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.In the context of this problem, the values of these parameters are given as follows:
n = 10, as there are 10 questions.p = 0.5, as each question has two outcomes, and the student will guess the answer at random.The probability of passing is given by:
P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{10,7}.(0.5)^{7}.(0.5)^{3} = 0.1172[/tex]
[tex]P(X = 8) = C_{10,8}.(0.5)^{8}.(0.5)^{2} = 0.0440[/tex]
[tex]P(X = 9) = C_{10,9}.(0.5)^{9}.(0.5)^{1} = 0.0098[/tex]
[tex]P(X = 10) = C_{10,10}.(0.5)^{10}.(0.5)^{0} = 0.0010[/tex]
Then:
P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.1172 + 0.0440 + 0.0098 + 0.0010 = 0.172 = 17.2%.
More can be learned about the binomial distribution at https://brainly.com/question/24756209
#SPJ1
What is the mode for test scores 84,76,95,66,87,91,79,88,81,87?
Answer: mode is 94
Step-by-step explanation:
To go to the theater you would pay $8.00 for each ticket you purchase. Which answer choice correctly represents the algebraic expression for the cost of t tickets?
A. 8t
B. 8 + t
C. 8 – t
D.
Answer:
Step-by-step explanation:
a
I need help with this assignment.
Answer: over budget by $64
Step-by-step explanation:
$99 coat
$75 Shoes
$240 tv
Total=414
total-budget=
Budget =$350
414-350
= 64
I need help with this problem. Please and thank you.
After solving the given equation for r, the value of r is √T/4π.
What are equations?A mathematical equation is a formula that utilizes the equals sign to signify the equality of two expressions. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.So, the formula equation is:
T = 4πr²Now, solve for r as follows:
T = 4πr²r² = T/4πr = √T/4πTherefore, after solving the given equation for r, the value of r is √T/4π.
Know more about equations here:
https://brainly.com/question/28937794
#SPJ13
Simplify
8(x + 3)^2/2(× + 3)
Answer:
[tex] = \frac{8(x + 3) {}^{2} }{2(x + 3)} = 4(x + 3) = 4x + 12[/tex]
Hopefully this will help u
(a)- domain and range of function
(b)- intercepts
(c)- horizontal asymptotes
(d)- vertical asymptotes
(e)- oblique asymptotes
Please Help me its a hard ;--;
Answer: y intercept: (0, -1/7)
Step-by-step explanation:
First you start with y = 10x - 1/7
Since your finding the y-intercept, you turn the 10x into a 0
So you would have y = -1/7
So y = -1/7
is your answer!
factorize 6x²y-10xy+15x-25
The factors of 6x²y-10xy+15x-25 are (3x-5)(2xy+5).
According to the question,
We have the following expression:
6x²y-10xy+15x-25
In this expression, we can not use any identity to solve it further.
Now, in order to find the factors of this expression, we will find the common terms from the first two terms and one common factor from the last two terms.
Taking 2xy as a common factor from first two terms and 5x as a common factor from the last two terms:
2xy(3x-5)+5(3x-5)
Taking (3x-5) as a common factor from the above expression:
(3x-5) (2xy+5)
Hence, the factors of 6x²y-10xy+15x-25 are (3x-5)(2xy+5).
To know more about factors here
https://brainly.com/question/11994048
#SPJ1
5. Given the following measurements in
parallelogram ABCD, find the PERIMETER of
CED.
AC 34 in. AB = 26 in. BD = 28 in.
P=
The Perimeter of triangle CED is 57 in.
What is a parallelogram?
A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.
Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.
Two parallel pairs of sides make up a parallelogram, a quadrilateral. Four right angles form a parallelogram called a rectangle.
Rhombus: An equal-length parallelogram with four sides.
The diagonals of a parallelogram bisect each other AC = 2 CE
Substitute AC= 34 into AC = 2CE =34 = 2CE
Calculate 34 = 2 CE=> CE = 17
The diagonals of a parallelogram bisect each other BD = 2DE
Substitute BD= 28 into BD = 2DE => 28 = 2DE
Calculate 28 = 2DE => DE = 14
Opposite sides of parallelogram are congruent AB = CD
Substitute AB = 26 into AB = CD => CD = 26
Perimeter of a triangle PΔCDE = CE + CD + DE
Substitute CE = 17, DE = 14, CD = 26.
PΔCDE = CE + CD + DE
PΔCDE = 17+ 26 + 14
PΔCDE = 57 in
To learn more about parallelogram from the link:
brainly.com/question/970600
#SPJ1
Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used are y(y - 5) = 750, y² - 5y = 750, and (y + 25)(y – 30) = 0.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Length = y
Width = y - 5
Area = 750
The area of a rectangle is written as,
Length x Width = Area
y x (y - 5) = 750
y² - 5y = 750
y² - 5y - 750 = 0
(y + 25)(y – 30) = 0
The equations that can be used are y(y - 5) = 750, y² - 5y = 750, and (y + 25)(y – 30) = 0.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ1
PLEASE HELP ME I NEED HELP ADDMEDIATLY
Store A sells 2 bags of chips for $2.50. Store B sells 3 bags of chips for $3.25. Which store offers the better deal? Show your work.
Answer:
Store B
Step-by-step explanation:
Store A: $2.50 ÷ 2 = $1.25
Store B: $3.25 ÷ 3 = $1.08 (to nearest cent)
Store B offers the better deal.
12) m/GOP = 80°, m/ROP
and m/ROG= 32x + 4. Find x.
R
Q
= 3 +59x,
G
The angular value of x is 3° as per the given the given information in the question.
What is meant by an angle?An angle in Euclidean geometry is the figure produced by two rays, called the sides of the angle, that have a common termination, called the vertex of the angle. Angles formed by two rays lie in the plane containing the rays. Angles are also generated by the intersection of two planes. These are referred to as dihedral angles. Two intersecting curves can also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
Given,
m ∠GQP=80
m ∠RQP=3+59x
m ∠RQG=32x+4
From the figure,
m ∠RQG+ m ∠GQP= m ∠RQP
32x+4+80°=3+59x
27x=81°
x=3°
Therefore, the value of x=3°
To know more about angle, visit:
https://brainly.com/question/28451077
#SPJ1
If CE and FH are parallel lines and m/CDG =
are parallel lines and m/CDG = 128°, what is mZHGD?