how do I solve for x intercepts of this equation. I'm having trouble solving it.[tex]y = 2x ^{2} + 12x + 13[/tex]
To find the x-intercepts of this equation, substitute y by 0 at first
[tex]0=2x^2+12x+13[/tex]Now we need to factor this equation into 2 factors
We need 2 numbers their sum = 12 (the middle term)
But we can not find them mentally, then we will use the formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]a is the coefficient of x^2
b is the coefficient of x
c is the numerical term
a = 2, b = 12, c = 13
Let us substitute them in the rule to find x
[tex]\begin{gathered} x=\frac{-12+\sqrt[]{(12)^2-4(2)(13)}}{2(2)} \\ x=\frac{-12+\sqrt[]{144-104}}{4} \\ x=\frac{-12+\sqrt[]{40}}{4} \end{gathered}[/tex]We will simplify the root
[tex]x=\frac{-12+2\sqrt[]{10}}{4}[/tex]Divide up and down by 2 to simplify the fraction
[tex]x=\frac{-6+\sqrt[]{10}}{2}[/tex]The 2nd root will be the same number but a different middle sign
[tex]x=\frac{-6-\sqrt[]{10}}{2}[/tex]The x-intercepts are
[tex](\frac{-6+\sqrt[]{10}}{2},0)\text{and(}\frac{-6-\sqrt[]{10}}{2},0)[/tex]- 3/4 m - 1/2 = 2 + 1/4 m2345
12 posters for 36 students 21 poses for 36 students
In order to find Lorenzo's speed in miles per hour, we need to convert from yard to mile and from second to hour. The rates are:
1 yard = 1/1760 miles
1 second = 1/3600 hours
So we have that:
[tex]\text{speed}=5\frac{yards}{\sec ond}=5\frac{\frac{1}{1760}miles}{\frac{1}{3600}hour}=5\frac{3600}{1760}\frac{miles}{hour}=10.227\text{ miles/hr}[/tex]Lorenzo can ride 10.227 miler per hour.
i have an answer in mind i just need to make sure its correct
The names of the angles are ; ∠XYZ , ∠ ZYX or ∠1
Here, we want to give three different ways in which we can name the angle
To name the angle, we can use the two end points and the location of the angle itself as angle
This can be ∠ZYX or ∠XYZ
Lastly, we can make use of the labeling on the angle itself
The name can be ∠1
write a recursive rule for the sequence -10,-3,4,11
Let the given sequence is -10,-3,4,11
The objective is to write recursive rule for the sequence.
In the given sequence each number has an equal difference between them
[tex]\begin{gathered} -3-(-10)=7 \\ 4-(-3)=7 \\ 11-4=7 \end{gathered}[/tex]So, consider the terms as,
[tex]\begin{gathered} a_1=-10 \\ a_2=-3 \\ a_2=a_1+7 \\ a_3=a_2+7 \\ a_4=a_3+7 \end{gathered}[/tex]Hence the recursive series is
[tex]a_n=a_{n-1}+d[/tex]Marcia sells lemonade for $2 per cup and candy for $1.50 per candy bar. She earns $425 selling lemonade and candy bars. If marcia sold 90 bars of candy, which equation could be used to figure out how many cups of lemonade she sold?
Answer: 145 cups of lemonade
Step-by-step explanation:
hope it helped :)
For almost all mortgage lenders, a home buyer must put down a certain percentage ofthe selling price towards the sale and financing of a home. Different banks and differentkinds of loans have set standards. Based on the given information, solve the problems.A buyer decides to put a contract on a house he/she would like to purchase. For eachscenario given, find the amount of down payment, the loan amount, the realestate commission, and tax assessment.#1 Selling price is $250,000.00 10% down payment would be $______ the real estate commissionthe seller would pay (at 6% commission) would be $______ and the amount for the mortgage(selling price - down payment) would be $______ House assesses for $245,000.00 and the taxrate is $1.15 per $100.00 of assessed value so taxes on the house would be $_____ for theyear#2 Selling price is $195,000.00 10% down payment would be $______ the real estate commissionwould be (at 6%) $______ and the mortgage amount would be for $_______ House assesses for$189,000.00 and the tax rate is $1.09 per $100.00 so the real estate taxes for the yearwould be $______
Answer:
(1)
• 10% down payment would be $25,000.
• The real estate commission would be $15,000.
• The amount for the mortgage would be $225,000.
• Taxes on the house would be $2817.50 for the year.
(2)
• 10% down payment would be $19,500.
• The real estate commission would be $11,700
• The amount for the mortgage would be $175,000.
• Taxes on the house would be $2060.10 for the year.
Explanation:
Part 1
The selling price is $250,000.00.
[tex]\begin{gathered} \text{ Down Payment}=10\%\text{ of }250,000 \\ =0.1\times250,000 \\ =25,000 \end{gathered}[/tex]• 10% down payment would be $25,000.
[tex]\begin{gathered} \text{ Real Estates Commission}=6\%\text{ of }250,000 \\ =0.06\times250,000 \\ =15,000 \end{gathered}[/tex]• The real estate commission the seller would pay (at 6% commission) would be $15,000.
[tex]\begin{gathered} \text{ Mortgage Amount}=\text{ Selling Price}-\text{ Down Payment} \\ =250,000-25,000 \\ =225,000 \end{gathered}[/tex]• The amount for the mortgage would be $225,000.
[tex]Tax=\frac{1.15}{100}\times245,000=2817.50[/tex]• Taxes on the house would be $2817.50 for the year.
Part 2
The selling price is $195,000.00.
[tex]\begin{gathered} \text{ Down Payment}=10\%\text{ of }195,000 \\ =0.1\times195,000 \\ =19,500 \end{gathered}[/tex]• 10% down payment would be $19,500.
[tex]\begin{gathered} \text{ Real Estates Commission}=6\%\text{ of }195,000 \\ =0.06\times195,000 \\ =11,700 \end{gathered}[/tex]• The real estate commission the seller would pay (at 6% commission) would be $11,700.
[tex]\begin{gathered} \text{ Mortgage Amount}=\text{ Selling Price}-\text{ Down Payment} \\ =195,000-19,500 \\ =175,500 \end{gathered}[/tex]• The amount for the mortgage would be $175,000.
[tex]Tax=\frac{1.09}{100}\times189,000=2060.10[/tex]• Taxes on the house would be $2060.10 for the year.
Jackson types 120 words in 2 minutes. Enter the number of words Jackson types in 4 minutes at this ratewords
if in 2 minutes Jackson Typed 120 words, in 4 minutes will type twice the amount. SO
[tex]w=120\cdot2=240[/tex]he will type 240 words in 4 minutes
???????????????????
Given,
g(x) = - x^2
now, in part (b), we have to find g(-2)
It can be done by replacing the value of x with -2, so
g(x) = - x^2
g(-2) = - (-2)^2
g(-2) = - 4
Part d:
g(m) = ?
So, here we will put the 'm' value in place of x.
g(x) = - x^2
g(m) = - (m)^2
g(m) = -m^2
Question 7 using radians, find the amplitudeand period of each function and graph it
Given:
y = 4 sin 4θ
The amplitude is 4.
Period:
[tex]\begin{gathered} P=\frac{2π}{B};\text{ }hence: \\ \\ P=\frac{2π}{4}=\frac{π}{2} \end{gathered}[/tex]The period is π/2.
Graph:
6/2(1+2)help me with math problem
Calculate the volume of the rectangular prism.A. 179 cm³B. 187 cm³C. 189 cm³D. 198 cm³
ANSWER
[tex]C.\text{ }189\text{ }cm^3[/tex]EXPLANATION
We want to calculate the volume of the rectangular prism.
The volume of a rectangular prism is given by:
[tex]V=L*W*H[/tex]where L = length
W = width
H = height
Therefore, the volume of the rectangular prism is:
[tex]\begin{gathered} V=9*7*3 \\ \\ V=189\text{ }cm^3 \end{gathered}[/tex]The answer is option C.
Solve |x| < 12 a{ x| x < -12 or x > 12}b { x|-12 < x < 12} c{-12, 12}Pllzzzzz alot of points
We need to solve the inequality:
[tex]|x|<12[/tex]Find the probability of X successes, using Table B in Appendix A of the textbook or some other method.n = 10, p = 0.3, X = 7
SOLUTION
The probability is a binomial probability
The probability is given as
[tex]\text{nCxp}^xq^{n-x}[/tex]Where p= proability of succes=0.3
q=probability of failure=1-p=1-0.3=0.7
n=10, x=7
Then, substitute the parameters into the formula
[tex]10C_7(0.3)^7(0.7)^3[/tex][tex]\begin{gathered} 10C_7=120 \\ 120\times2.187\times10^{-4}\times0.343 \end{gathered}[/tex]Then we have
[tex]\begin{gathered} 9.0017\times10^{-3} \\ 0.0090017 \end{gathered}[/tex]The probability of x-success is 0.009
Select the following that are true.Select one or more:a.If a quadrilateral is a square, then it is a rectangle.b.If a quadrilateral is a square, then it is a parallelogram.c.If a quadrilateral is a rhombus, then it is a parallelogram.d.If a quadrilateral is a rectangle, then it is a rhombus.e.If a quadrilateral is a square, then it is a rhombus.f.If a quadrilateral is a parallelogram, then it is a rectangle.
a. One of the properties of squares is all sides are congruent (they have the same length) and this is not a property of rectangles. But the square is a special rectangle since it fits in the properties of rectangles, but rectangles are not squares. In this case, this is TRUE.
b. A parallelogram is a quadrilateral with two pairs of opposite parallel sides and the opposite sides are congruent. The square fits into this description, so this is TRUE.
c. A rhombus has four equal opposite parallel sides, so we can say it fits into the parallelogram definition. This is TRUE.
d. As we said in part a, a rectangle doesn't have all of its sides congruent, but the rhombus does. Then, this is FALSE.
e. Squares have four equal opposite parallel sides, and rhombus too. Then, a square is a rhombus. This is TRUE.
f. Not all parallelograms have the properties of rectangles, then this is FALSE.
Look again at the table of refrigerator sizes and prices. Is the relation a function?A. The relation is not a function. All input values are paired with only oneoutput value.B. The relation is not a function. Some of the input values are paired withmore than one output value.C. The relation is a function. The input values are paired with more than oneoutput value.D. The relation is a function. All input values are paired with only one outputvalue.HINTSUBMIT
B. The relation is not a function. Some of the input values are paired with
more than one output value.
Explanation
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Step 1
Identify the input values and compare with the outputs
as we can see one input is related to TWO outputs, for example
[tex]\begin{gathered} 1.7\rightarrow80 \\ 1.7\rightarrow79 \end{gathered}[/tex]hence, the relation is not a function
B. The relation is not a function. Some of the input values are paired with
more than one output value.
I hope this helps you
Please just put the answer for this question On D
Answer
The liters of air takes in during 150 seconds is 25 liters
Step-by-step explanation:
A man takes in 5 liters of air in 30 seconds
Firstly, we need to find the rate
Given:
Volume = 5 liters
time = 30 seconds
Rate =?
Volume = rate x time
5 = rate * 30
rate = 5/30 liters / second
Find the volume of air takes in during 150 seconds at the same rate
Volume = rate * time
Volume = 5/30 * 150
Volume = 5 * 150 / 30
Volume = 25 liters
Hence, the liters of air takes in during 150 seconds is 25 liters
A sales person is given a choice of two salary plans. Plan 1 is a weekly salary of 700 plus 4% commission of sales. Plan 2 is a straight commission of 12%Of sales. How much in sales must he make in a week for both plans to result in the same salary?
Let 's' represent the amount of sales.
Plan 1:
[tex]\text{ \$700 + (4\% of s)}[/tex][tex]\begin{gathered} \text{ \$700+(}\frac{\text{4}}{100}\times s) \\ \text{ \$700+(0.04}\times s)=\text{ \$700}+0.04s \end{gathered}[/tex]Plan 2:
[tex]12\text{ \% of s}[/tex][tex]\begin{gathered} \frac{12}{100}\times s \\ 0.12\times s=0.12s \end{gathered}[/tex]Equating the two plans together and solving for the amount of sales,
[tex]\begin{gathered} \text{Plan 2=Plan 1} \\ 0.12s=\text{ \$700+0.04s} \\ \end{gathered}[/tex]Collecting like terms,
[tex]\begin{gathered} 0.12s-0.04s=\text{ \$700} \\ 0.08s=\text{\$700} \end{gathered}[/tex]Divide both sides by 0.08,
[tex]\begin{gathered} \frac{0.08s}{0.08}=\frac{\text{ \$700}}{0.08} \\ s=\text{ \$8750} \end{gathered}[/tex]Hence, the amount of sales is $8,750.
one-half of a number y is more than 22
1) Writing that statement as an inequality we have:
[tex]\begin{gathered} \frac{y}{2}>22\text{ } \\ Multiplied\text{ by 2 on both sides} \\ y>44 \end{gathered}[/tex]2) Hence, we can say that if one-half of a number y is more than 22
then y > 44
I need help with math please
1. 92 .
2. 7
3. >=<
4. -
5. 8x3=24
Step-by-step explanation:
hey ms or mr can you please help me out?
B'C' = 3BC
Explanations:Note:
When a figure is dilated by a scale factor, a similar figure of the same shape but of different size is formed.
When a triangle ABC is dilated by a scale factor of 3, the vertices of the image of ΔA'B'C' formed will have a distance from the center of dilation that is three times that of the vertices of ΔABC
Therfore:
A'B' = 3AB
B'C' = 3BC
A'C' = 3AC
The correct choice is option B
That is, B'C' = 3BC
i need help with this
graphing the points
answer: (- 8, 6)
What transformations were applied to the toolkit function to create the new function?
The parent functions is f(x) = 1/x
We have 1/(x+2) -1
The 1/(x+2) is f(x+2) which is a horizontal translation left 2 units
Then we have -1 which is f(x+2) -1 which is a vertical translation down 1 unit
The total transformation is a horizontal translation left 2 units and a vertical translation down 1 unit
Answer: left 2 units down 1 unit
The Hudson family is saving for a
family vacation to Disney World.
They determine that the trip will
cost $3,200. Mr. and Mrs.
Hudson have already set aside
$1,500 for the trip. If they leave
in 16 weeks, then how much
will they need to save
each week?
The amount of money that Hudson will need to save each week is $106.25.
How to calculate the value?From the information, they determine that the trip will cost $3,200. Mr. and Mrs. Hudson have already set aside $1,500 for the trip.
Let the amount saved each week be represented as w.
Based on the information given, this will be illustrated as:
1500 + 16w = 3200
Collect like terms
16w = 3200 - 1500
16w = 1700
Divide
w = 1700 / 16
w = 106.25
The amount is $106.25.
Learn more about money on:
brainly.com/question/24373500
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For f(x) = 2x and g(x) = x,find f (g(2))
2. Find each of the following products of monomials. (a) (3x?) (10x) (b) (-2x)(-9x) (c) (4x+y)(8x*y) (d) (5x) (e) (-41)(-151") 2 (f) (7x)(5xy^) ** | (12x) (h) (2xP)(5x)(-6x4)
In order to solve the products between the followings monomials you take into account that the multiplication is in between coefficients, and also you take into account that it is necessary to multiply the involved signs.
a)
[tex](3x^3)(10x^4)=(3)(10)x^{^{3+4}}=30x^7[/tex]when the product is between the same variable but different exponents, you sum the exponents
b)
[tex](-2x^5)(-9x)=(-2)(-9)x^{5+1}=18x^6[/tex]where you have used that minus multiplied by minus is equal to positive
c)
[tex](4x^2y)(8x^5y^3)=(4)(8)x^{2+5}y^{1+3}=32x^7y^4[/tex]where you sum the exponents of x and y
d)
[tex](5x^4)^2=(5)^2(x^4)^2=25x^{4\cdot2}=25x^8[/tex]In the case in which you have a variable with an exponent, power to another exponent, these exponents must be multiplied. The coeeficient also has to be exponentiated
e)
[tex](-4t^2)(-15t^5)=(-4)(-15)t^{2+5}=60t^7[/tex]f)
[tex](7x)(5xy^4)=35x^2y^4[/tex]g)
[tex](\frac{2}{3}x^4)(12x)=\frac{2\cdot12}{3}x^5=8x^5[/tex]f)
[tex](2x^2)(5x)(-6x^4)=(2)(5)(-6)x^{2+1+4}=-60x^7[/tex]where you multiply all coefficientes and signs, and sum the exponents of x
how many kiloliters are in 32,500 centiliters325 kl3,250,000,000 kl32.5 kl0.325 kl
0.325 kl
Explanation:We need to convert from centiliters to Kiloliters:
[tex]\begin{gathered} 1liter=100^{}\text{centiliter} \\ 1\text{ kilo = 1000} \\ 1\text{ kiloliter = 1000liter} \\ 1\text{ kiloliter = 100000 centiliter} \end{gathered}[/tex][tex]\begin{gathered} 100000\text{ centiliter = }1\text{ kiloliter} \\ 32500\text{ centiliter = }\frac{\text{32500(1)}}{100000} \\ \text{= }\frac{32500}{100000} \\ 32500\text{ centiliter }=\text{ 0.325 kl} \end{gathered}[/tex]Part 2: Write limits given outputs.Use the graph of the function to write limit equations given limit values.Use the graph to write a limit equation for f(x) that satisfies each given condition. (2 points for each)a. b. c. d. e. Are there other values than what you chose for x where the limit of the function approaches 4? Is the graph continuous at these points? Explain your reasoning. (4 points)
a) From the graph, we see that the function takes the value y = 4 when x = 4, so we have:
[tex]\lim _{x\rightarrow4}f(x)=4.[/tex]b) We see that the curve tends to -∞ when x approaches zero from the left, so we have:
[tex]\lim _{x\rightarrow0^-}f(x)=-\infty.[/tex]c) We see that curve increases without limit when x tends to infinity, so we have:
[tex]\lim _{x\rightarrow\infty}f(x)=\infty.[/tex]d) From the graph, we see that the function tends to y = 0 when x approaches zero from the right, so we have:
[tex]\lim _{x\rightarrow0^+}f(x)=0.[/tex]e) Yes, there are two possible values of x for the limit of the function approaching 4:
• x = 2,
,• x = 4.
By definition, a function is continuous when its graph is a single unbroken curve.
We see that at the points x = 2 and x = 4 the curve is a single unbroken curve, so we conclude that the function is continuous at those points.
Answers
a, b, c, d
[tex]\begin{gathered} \lim _{x\rightarrow4}f(x)=4 \\ \lim _{x\rightarrow0^-}f(x)=-\infty \\ \lim _{x\rightarrow\infty}f(x)=\infty \\ \lim _{x\rightarrow0^+}f(x)=0 \end{gathered}[/tex]e. Yes, there are two possible values of x for the limit of the function approaching 4:
• x = 2,
,• x = 4.
By definition, a function is continuous when its graph is a single unbroken curve.
We see that at the points x = 2 and x = 4 the curve is a single unbroken curve, so we conclude that the function is continuous at those points.
See question below as I tried to ask another tutor
Given the word problem, we can deduce the following information:
1. The formula V=2.5r can be used to estimate the maximum safe velocity,v, in miles per hour, at which a car can travel if it is driven along a curved radius of curvature r in feet.
2. The radius of curvature is 280 feet.
To determine the maximum safe speed, we use the given formula as shown below:
[tex]V=2.5r[/tex]where:
V= Maximum safe velocity in miles per hour
r=radius of curvature = 280 feet
We plug in what we know:
[tex]\begin{gathered} V=2.5r \\ =2.5(280) \\ Calculate \\ V=700\text{ }\frac{miles}{hour} \end{gathered}[/tex]Therefore, the maximum safe speed is 700 miles per hour.
Multiply the following [tex] \sqrt{ - 15} \times \sqrt{ - 15} [/tex]
Answer: -15
Given:
[tex]\sqrt[]{-15}\times\sqrt[]{-15}[/tex]Since the radical rule states that:
[tex]\begin{gathered} \sqrt[]{a}\sqrt[]{a}=a \\ \Rightarrow\sqrt[]{-15}\times\sqrt[]{-15}=-15 \end{gathered}[/tex]Therefore, the answer is -15.