Answer:
x1=4
x2=-8
Step-by-step explanation:
x^2+6x-16=0
a=1 b=6 c=-16
D=b^2 - 4ab= 36+64=100
D>0, 2 sqrt
x1= -b+sqrt{D} /2= -6+10/2= 4
x2= -b-sqrt{D} /2= -6-10/2= -8
(That's what we were taught!)
Write a formula for the function in the image below.
The vertex form of a quadratic function is:
[tex]f(x)=a(x-h)^2+k[/tex]Where (h, k) is the vertex. Looking at the graph, the vertex is at (-1, 2), then:
[tex]\begin{gathered} h=-1 \\ k=2 \\ \Rightarrow f(x)=a(x+1)^2+2 \end{gathered}[/tex]Finally, to find "a" we use the fact that 1 is the y-intercept of the graph (where the function is evaluated at x = 0). Then:
[tex]\begin{gathered} f(0)=1\Rightarrow a(0+1)^2+2=1 \\ a=1-2 \\ \Rightarrow a=-1 \end{gathered}[/tex]The final form of the function is:
[tex]f(x)=-(x+1)^2+2[/tex]There are 152 students at a small school and 45 of them are freshmen. What fraction of the students are freshmen? Use "/" for the
fraction bar. Do not use spaces in your answer.
use the quadratic formula to solve the equation2x^2-1=11xthe solution(s) are/is x=?
Answer:
[tex]\begin{gathered} x=\frac{1}{4}(11-\sqrt[]{129}) \\ \\ x=\frac{1}{4}(11+\sqrt[]{129}) \end{gathered}[/tex]Explanation:
To solve the equation we first subtract 11x from both sides to write
[tex]2x^2-11x-1=0[/tex]Now we use the quadratic formula in which a = 2, b = -11, and c = -1
[tex]x=\frac{11\pm\sqrt[]{11^2-4(2)(-1)}}{2\cdot2}[/tex][tex]x=\frac{11\pm\sqrt[]{11^2-4(2)(-1)}}{2\cdot2}[/tex]which gives
[tex]\begin{gathered} x=\frac{1}{4}(11-\sqrt[]{129}) \\ x=\frac{1}{4}(11+\sqrt[]{129}) \end{gathered}[/tex]which are our solutions!
A hoverboard manufacturer has just announced the Glide 5 hoverboard. The accounting department has determined that the cost to manufacturer the Glide 5 hoverboard is y = 42.96x + 32976. The revenue equation is y = 88.76x. What is the break even point for the - Glide 5 hoverboard? The break even point for the Glide 5 hoverboard is
The break-even point for the glide 5 hoverboard is 36670.4.
What is the break-even point?In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even." Although opportunity costs have been paid and capital has received the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."The break-even threshold is reached when overall costs and total revenues are equal, leaving your small firm with no net benefit or loss. In other words, you've achieved the point in production where the revenue from a product equals the cost of manufacture.Given that:
Cost function: - y = 25.42x + 23452Revenue function: - y = 70.52xWe know that at break-even:
Cost price = Revenue priceNow,
70.52x = 25.42x + 23452By subtracting "25.42x" from both sides, we get:
70.52x - 25.42x = 25.42x + 23452 - 25.42x45.1x = 23452x = 23452/45.1Then,
y = 70.5270.52*52036670.4Therefore, the break-even point for the glide 5 hoverboard is 36670.4.
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Problem Solving
20. A city is building 3 parks in a new subdivision. Each park
will be 1.25 acres. How many total acres will the 3 parks
be?
According to the solving all three parks will cover surface of 37.5 acres in total.
How much area of land is in acres?The imperial and US customary systems both utilize the acre as a unit of land area. An acre is approximately equal to approximately 4,047 [tex]m^{2}[/tex].
How much area will 3 parks cover?Area covered by 3 parks can be calculated by multiplying the area of one park by three.
so, area covered by 3 parks=3×1.25
area covered by 3 parks=3.75
As you know multiplication is the repeated addition so we can obtain the same results by adding 1.25 three times to itself.
These three parks will cover total area of 3.75acres.
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m^3n^-6p^0 i dont understand how to solve this problem it has exponents
ANSWER:
[tex]\frac{m^3}{n^6}[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]m^3n^{-6}p^0\:\:[/tex]We simplify as follows:
[tex]\begin{gathered} a^{-b}=\frac{1}{a^b}\rightarrow n^{-6}=\frac{1}{n^6} \\ \\ p^{0}=1 \\ \\ \text{ We replacing:} \\ \\ m^3n^{-6}p^0\:\:=m^3\cdot\frac{1}{n^6}\cdot\:1=\frac{m^3}{n^6} \end{gathered}[/tex]sketch the graph of each equation y= -5x
Step 1
To graph the function y= -5x
we set x=1 and y=0 individually.
[tex]\begin{gathered} when\text{ x= 1} \\ y=-5x \\ y=-5(1) \\ y=-5 \\ \text{coordinate points are (1,-5)} \\ \end{gathered}[/tex][tex]undefined[/tex]Two planes fly in opposite directions. One travels 450 mi/h and the other 550 mi/h. How long will it take before they are 4,000 mi apart? The planes must fly Answer hours before they will be 4,000 mi apart.
Given,
The speed of first plane is 450 miles per hour.
The speed of second plane is 550 miles per hour.
The total distance between plane required is 4000 miles.
As, the planes are moving in opposite direction, then distance cover by both is must be added.
Number of distance both plane becomes apart in one hour is,
[tex]\text{Number of distance = 450+550=1000 miles.}[/tex]The Number of hours required to complete 4000 miles is,
[tex]\text{Time=}\frac{4000}{\text{1}000}=4\text{ hours}[/tex]Hence, it will take 4 hours before they are 4,000 miles apart.
When point A'(-2,4) is reflected over they-axis, where is the image A"?(2,-4)(2,4)(4,-2)
Answer:
Explanation
Given a coordinate (x, y), If this coordinate reflected over y axis, the resulting coordinate will be expressed as (-x, y). Note that only the sign of the x coordinate axis was
resents "three lessWrite the expression -- 5x(4 + 3x) using words,the sum of negative five times a number andfour minus three times the numberthe product of negative five times a numberand the quantity four plus three times thenumberthe product of three times a number plus thequantity four and five times the numberpresents "thetwo less than theDONE
Given:
[tex]=-5x(3x+4)[/tex]Sol:.
The product of negative five times a number and the quantity four plus three times the number.
Which graph represents the equation X =2?
ANSWER and EXPLANATION
We are given x = 2.
To plot the graph of x = 2, it is important to note that the value of x does not change for this equation.
x is always 2 regardless of the value of y.
This means that we are going to plot a straight line that will straight up (and down as well) at x = 2.
The graph therefore is:
28. A man spends 1/5 of his income on Food and 1/3 of the remainder on his car. If he then has #286.00 left, what is his income? A. #612.86 B. #686.83 C. #536.25 D. #2,145 E. #4,290 als
Answer:
4,290
Step-by-step explanation:
286.00 x 3 x 5 = 4,290
3. For the polynomial: ()=−2(+19)3(−14)(+3)2, do the following:A. Create a table of values that have the x-intercepts of p(x) in the first column and their multiplicities in the second column.B. State the degree and end behavior for p(x). C. Hand sketch a rough graph of p(x). You should have the x-int labeled, but you do not need tick marks for all numbers in between.
Part A. We are given the following polynomial:
[tex]\mleft(\mright)=-2\mleft(+19\mright)^3\mleft(-14\mright)\mleft(+3\mright)^2[/tex]This is a polynomial of the form:
[tex]p=k(x-a)^b(x-c)^d\ldots(x-e)^f[/tex]The x-intercepts are the numbers that make the polynomial zero, that is:
[tex]\begin{gathered} p=0 \\ (x-a)^b(x-c)^d\ldots(x-e)^f=0 \end{gathered}[/tex]The values of x are then found by setting each factor to zero:
[tex]\begin{gathered} (x-a)=0 \\ (x-c)=0 \\ \text{.} \\ \text{.} \\ (x-e)=0 \end{gathered}[/tex]Therefore, this values are:
[tex]\begin{gathered} x=a \\ x=c \\ \text{.} \\ \text{.} \\ x=e \end{gathered}[/tex]In this case, the x-intercepts are:
[tex]\begin{gathered} x=-19 \\ x=14 \\ x=-3 \end{gathered}[/tex]The multiplicity are the exponents of the factor where we got the x-intercept, therefore, the multiplicities are:
Part B. The degree of a polynomial is the sum of its multiplicities, therefore, the degree in this case is:
[tex]\begin{gathered} n=3+1+2 \\ n=6 \end{gathered}[/tex]To determine the end behavior of the polynomial we need to know the sign of the leading coefficient that is, the sign of the coefficient of the term with the highest power. In this case, the leading coefficient is -2, since the degree of the polynomial is an even number this means that both ends are down. If the leading coefficient were a positive number then both ends would go up. In the case that the leading coefficient was positive and the degree and odd number then the left end would be down and the right end would be up, and if the leading coefficient were a negative number and the degree an odd number then the left end would be up and the right end would be down.
Part C. A sketch of the graph is the following:
If the multiplicity is an odd number the graph will cross the x-axis at that x-intercept and if the multiplicity is an even number it will tangent to the x-axis at that x-intercept.
7 1/3 × 2 2/11 3/5 × 6 2/34 1/5 × 1 1/14
It is easier to perform the operations if you convert the mixed fractions into improper fractions.
For point 1. Make the mixed fractions improper first
[tex]7\frac{1}{3}=\frac{3\cdot7+1}{3}=\frac{21+1}{3}=\frac{22}{3}[/tex][tex]2\frac{2}{11}=\frac{11\cdot2+2}{11}=\frac{22+2}{11}=\frac{24}{11}[/tex]Now, the multiplication of fractions is done like this
[tex]\frac{a}{b}\cdot\frac{c}{d}=\frac{a\cdot c}{b\cdot d}[/tex]Then, you have
[tex]7\frac{1}{3}\cdot2\frac{2}{11}=\frac{22}{3}\cdot\frac{24}{11}=\frac{528}{33}=16[/tex]For point 2.
[tex]6\frac{2}{3}=\frac{3\cdot6+2}{3}=\frac{18+2}{3}=\frac{20}{3}[/tex]Now multiplying the improper fractions you have
[tex]\frac{3}{5}\cdot6\frac{2}{3}=\frac{3}{5}\cdot\frac{20}{3}=\frac{60}{15}=4[/tex]Finally for point 3.
[tex]4\frac{1}{5}=\frac{5\cdot4+1}{5}=\frac{20+1}{5}=\frac{21}{5}[/tex][tex]1\frac{1}{14}=\frac{14\cdot1+1}{14}=\frac{14+1}{14}=\frac{15}{14}[/tex]Now multiplying the improper fractions you have
[tex]\begin{gathered} 4\frac{1}{5}\cdot1\frac{1}{14}=\frac{21}{5}\cdot\frac{15}{14}=\frac{315}{70}=\frac{35\cdot9}{35\cdot2}=\frac{9}{2} \\ 4\frac{1}{5}\cdot1\frac{1}{14}=\frac{9}{2} \end{gathered}[/tex]15÷6%=
A. 1004
B. 100
C. 24
D. 24
10 in.What is the volume of atriangular pyramid that is10 in. tall and has a basearea of 9 square in.?9cubic inchesVolume of a pyramid: V = {Bh (Where "B" is the area of the pyramid's base.)=
You have to calculate the volume of a pyramid with a height of 10in and a base area of 9 in²
The volume of a pyramid is equal to one third the product of the area of the base (B) and the height (h), following the formula:
[tex]V=\frac{1}{3}Bh[/tex]Replace the values on the formula and calculate the volume:
[tex]\begin{gathered} V=\frac{1}{3}\cdot9\cdot10 \\ V=30in^3 \end{gathered}[/tex]The volume is equal to 30 cubic inches.
Justin and poor friends are going to a movie each person buys a movie ticket that costs one 50 less than the square of $3 of the friends bought a bag of popcorn and a small soda that cost $2.25 more than the score of $2 right expression that can be used to find the total amount that Justin is trying to at the movies
Answer:
4(3² - 1.5) + 3(2² + 2.25)
Explanation:
First, they buy 4 tickets that cost $1.50 less than the square of $3. So, we can express that as follows:
4 x (3² - 1.5)
Then, they buy 3 bags of popcorn and a small soda that cost $2.25 more than the square of $2, so the expression for this is:
3 x (2² + 2.25)
Therefore, the numerical expression that can be used to find the total amount is the sum of the expression above:
4 x (3² - 1.5) + 3 x (2² + 2.25)
4(3² - 1.5) + 3(2² + 2.25)
So, the answer is:
4(3² - 1.5) + 3(2² + 2.25)
Solve for z. 24z - 48 = 16z + 112
Answer: z = 20
Explanation:
The given equation is
24z - 48 = 16z + 112
Subtracting 16z from both sides of the equation, we have
24z - 16z - 48 = 16z - 16z + 112
8z - 48 = 112
Adding 48 to both sides, we have
8z - 48 + 48 = 112 + 48
8z = 160
Dividing both sides by 8,
8z/8 = 160/8
z = 20
-1514,2 – 30r2y3 + 45ryjent of517is 3(x^3)y + 6x(y^2) - 3.1. Whe3(x^3)y - 6x(y^2) +9Res-3(x^3)y + 6x(y^2) - 33(x^2)y + 5x(y^2) - 93(x^3)y + 5x(y^2) + 3
To find the quotient of the first part, we can start by noticing that all the factors on the denominator are present in all terms of the numerator, so we can factor those out and cancel with the denominator ones:
[tex]\frac{15x^4y^2-30x^2y^3+45xy}{5xy}=\frac{5xy\cdot3x^3y+5xy\cdot(-6xy^2)+5xy\cdot9}{5xy}=\frac{5xy\cdot(3x^3y-6xy^2+9)}{5xy}=3x^3y-6xy^2+9[/tex]So, the first dropdown option is
[tex]3x^3y-6xy^2+9[/tex]Also, this is the quotient, so we will use it for the second part.
The second part says that if we divide by one of the options (let's call it a), we will get:
[tex]\frac{3x^3y-6xy+9}{a}=x^3y-2xy^2+3[/tex]As we can see, no terms on the final result has fractional coefficient, so the number a has to be a common factor of all the terms coefficients. the coefficients are 3, -6 and 9, so the only common factors are 1 and 3, so the answer should be 3:
[tex]\frac{3x^3y-6xy+9}{3}=\frac{3(x^3y-2xy+3)}{3}=x^3y-2xy^2+3[/tex]So, the second dropdown option is 3.
What is the GCF of 42 and 70
To find the GCF of 42 and 70,
List the prime factors of each numbers,
The prime factors of 42 and 70 is
[tex]\begin{gathered} 42\Rightarrow2\times3\times7 \\ 70\Rightarrow2\times5\times7 \end{gathered}[/tex]42 and 70 share the common factors below
[tex]2\text{ and 7}[/tex]Multiply the common factors to find the GCF
The GCF of 42 and 70 will be
[tex]\text{GCF}=2\times7=14[/tex]Hence, the GCF of 42 and 70 is 14
What is 120 plus 5% sales tax
Answer:
126
Step-by-step explanation:
Hello!
Since you are adding 5% of 120 to 120, we can simply find 105% of 120.
To do that, we can multiply 120 by the number value of the percentage.
Find the Total Price105% of 1201.05 * 120126The total price after the sales tax is 126.
A motor scooter travels 22 mi in the same time that a bicycle covers 8 mi. If the rate of the scooter is 6 mph more than twice the rate of the bicycle, find both rates.The scooter’s rate is ____ mph. (Type an integer or a decimal)
Let's use the variable x to represent the speed of the scooter and y to represent the speed of the bicycle.
For a same time t, the scooter travels 22 mi and the bicycle travels 8 mi, so we can write the following equation:
[tex]\begin{gathered} distance=speed\cdot time\\ \\ 22=x\cdot t\\ \\ t=\frac{22}{x}\\ \\ 8=y\cdot t\\ \\ t=\frac{8}{y}\\ \\ \frac{22}{x}=\frac{8}{y} \end{gathered}[/tex]Then, if the rate of the scooter is 6 mph more than twice the rate of the bicycle, we have the following equation:
[tex]x=2y+6\\[/tex]Using this value of x in the first equation, let's solve it for y:
[tex]\begin{gathered} \frac{22}{2y+6}=\frac{8}{y}\\ \\ 22y=8(2y+6)\\ \\ 22y=16y+48\\ \\ 6y=48\\ \\ y=8\text{ mph} \end{gathered}[/tex]Now, calculating the value of x, we have:
[tex]\begin{gathered} x=2y+6\\ \\ x=16+6\\ \\ x=22\text{ mph} \end{gathered}[/tex]Therefore the scooter's rate is 22 mph and the bicycle's rate is 8 mph.
is the number 6.35 a whole number and a integer
Natural numbers are all numbers 1, 2, 3, 4… They are the numbers you usually count and they will continue on into infinity. This includes all numbers that can be written as a decimal.
Hence, 6.35 is a natural number. It is natural number, whole number, integer, and rational number.
Brookner's Grocery Store sells bars of chocolate in cartons. There are 39 bars of
chocolates in each box. There are 25 boxes in each carton. Last weekend
Brookner's Grocery sold 48 cartons of chocolates. How many bars of chocolate did
the Brookner's Grocery sell last weekend? Explain your thinking.
Course ListScore! OU TUUTUTZu anisweredQuestion 11In A XYZ, the sum of the measures of ZX and Y are 55°. What is the measure of ZZ?ZZ=?
To solve that question we must remember that the sum of all internal angles of a triangle is 180°, we can say that
[tex]\angle X+\angle Y+\angle Z=180[/tex]That's a rule! it's always true.
The problem says that
[tex]\angle X+\angle Y=55[/tex]Then let's use it in our equation!
[tex]\begin{gathered} \operatorname{\angle}X+\operatorname{\angle}Y+\operatorname{\angle}Z=180 \\ \\ 55+\operatorname{\angle}Z=180 \end{gathered}[/tex]Now we can solve it for Z
[tex]\begin{gathered} 55+\angle Z=180 \\ \\ \angle Z=180-55 \\ \\ \angle Z=125° \end{gathered}[/tex]Therefore the measure of Z is 125°
write a quadratic fuction f whose zeros are -3 and -13
The zeros of a quadratic function are the points where the graph cuts the x axis.
If one zero is - 3, it means that
x = - 3
x + 3 = 0
Thus, one of the factors is (x + 3)
If another zero is - 13, it means that
x = - 13
x + 13 = 0
Thus, one of the factors is (x + 13)
Thus, the quadratic function would be
(x + 3)(x + 13)
We would open the brackets by multiplyingeach term inside one bracket by each term inside the other. Thus, we have
x * x + x * 13 + 3 * x + 3 * 13
x^2 + 13x + 3x + 39
x^2 + 16x + 39
Thus, the quadratic function is
f(x) = x^2 + 16x + 39
Kui Software tinite Algebra 2 Compound Inequalities Solve each compound inequality and graph its solution. Name Samanthace ballos Date valgan 1) n+15-3 or-in- Perut k 2) ohs- n2-3-1
n<4 or n>8
10) Let's solve that compound inequality:
12 + 4n> 44 or 10 -12n> -38
2) Solving each one separately
12 + 4n > 44 Subtracting 12 from both sides
4n > 44 -12
4n > 32 Divide both sides by 4
n> 8
10 -12n> -38 Subtracting 10 from both sides
-12n > -38 -10
-12n > -48 Divide both sides by -1 and flipping the sign
n < 4
3) Graphing the solution, we have:
Notice that for that, we'll use open dots since 4 and 8 are not included.
If RT = 36, RS = 2x + 3 and ST = 7x + 6, find RSand ST.
We know that RT=36 and that RS=2x+3 and ST=7x+6. We notice that
[tex]RT=RS+ST[/tex]Then, plugging the corresponding values and expressions we have
[tex]36=(2x+3)+(7x+6)[/tex]Solving this equation for x,
[tex]\begin{gathered} 36=(2x+3)+(7x+6) \\ 36=2x+3+7x+6 \\ 36=9x+9 \\ 36-9=9x \\ 27=9x \\ x=\frac{27}{9} \\ x=3 \end{gathered}[/tex]Then te value of x is 3.
Once we have the value of x we are able to find the value of RS and ST, we just have to substitute said value in the expressions. Then
[tex]\begin{gathered} RS=2(3)+3=6+3=9 \\ ST=7(3)+6=21+6=27 \end{gathered}[/tex]Therefore RS=9 and ST=27.
Plot the Trapezoid ABCD with vertices A(-8,-4),B(-5, -1), C(0, -2), and D(-4,-8) in the x-axis.
Let's begin by listing out the information given to us:
ABCD is a trapezoid
A (-8, -4); B (-5, -1); C (0, -2); D (-4, -8)
We will proceed to plotting this points on a Cartesian plane, we have:
Given Z VYX is bisected by YW, mZ VYX =(6r-18), and m2 VYW = 36. What is the value of r? A. 15 B. 30 C. 36 D. 72
A) 15
1) Let's sketch that
According to the Bisector Theorem, the bisected line equally divides the angle. So we can write:
∠VYW≅∠WYX
And:
6r-18 = 36+36
6r -18 = 72
6r= 90
r= 15