Okay, here we have this:
[tex]x^2+2x-7=0[/tex]We will solve using the general formula, then we obtain:
[tex]\begin{gathered} x_{1,2}=\frac{-2\pm\sqrt[]{2^2-4\cdot1\cdot(-7)}}{2\cdot1} \\ =\frac{-2\pm\sqrt[]{4+28}}{2} \\ =\frac{-2\pm\sqrt[]{32}}{2} \\ =\frac{-2\pm4\sqrt[]{2}}{2} \end{gathered}[/tex]Let's separate the solutions:
[tex]\begin{gathered} x_1=\frac{-2+4\sqrt[]{2}}{2} \\ =\frac{2(-1+2\sqrt[]{2})}{2} \\ =-1+2\sqrt[]{2} \end{gathered}[/tex][tex]\begin{gathered} x_2_{}=\frac{-2-4\sqrt[]{2}}{2} \\ =\frac{2(-1-2\sqrt[]{2})}{2} \\ =-1-2\sqrt[]{2} \end{gathered}[/tex]Finally we obtain that the roots are: -1+2√2 and -1-2√2.
The same set of data has been fit using two different functions. The following images show the residual plots of each function. A residual plot where the points are scattered around the x-axis with no pattern.© 2018 StrongMind. Created using GeoGebra. A residual plot where the points are scattered in a u-shape.© 2018 StrongMind. Created using GeoGebra. Which function is a better fit for the data, and why?Select the option that correctly answers both questions.
Answer:
Function B, because the points have more variation around the x-axis.
Step-by-step explanation:
Remember that if the points in a residual plot are randomly dispersed around the horizontal axis, a regression model is appropriate for the data. Therefore, the function that is the best fit for the data is function B, because the points have more variation around the x-axis.
The population of a small town in central Florida has shown a linear decline in the years 1985-1997. In 1985 the population was 46000 people. In 1997 it was 38080 people.
Given:
(1985,46000)
(1997,38080)
(a)
General linear equation is:
[tex]y=mx+c[/tex]here y represent the population and x represent time so equation is:
[tex]p=mt+c[/tex][tex]\begin{gathered} \text{slope}=m \\ m=\frac{p_2-p_1_{}}{t_2-t_1} \end{gathered}[/tex][tex]\begin{gathered} (p_1,t_1)=(1985,46000) \\ (p_2,t_2)=(1997,38080) \end{gathered}[/tex]
slope is:
[tex]\begin{gathered} m=\frac{p_2-p_1}{t_2-t_1} \\ m=\frac{38080-46000}{1997-1985} \\ m=\frac{-7920}{12} \\ m=-660 \end{gathered}[/tex]So equation is:
[tex]\begin{gathered} p=mt+c \\ p=-660t+c \end{gathered}[/tex]Point (1985,46000)
[tex]\begin{gathered} p=-660t+c \\ p=46000 \\ t=1985 \\ p=-660t+c \\ 46000=-660(1985)+c \\ c=46000+1310100 \\ c=1356100 \end{gathered}[/tex]So equation is:
[tex]\begin{gathered} p=mt+c \\ p=-660t+1356100 \end{gathered}[/tex](b)
population in 2000.
[tex]t=2000[/tex][tex]\begin{gathered} p=mt+c \\ p=-660t+1356100 \\ t=2000 \\ p=-660(2000)+1356100 \\ p=36100 \end{gathered}[/tex]so population in 2000 is 36100.
For / (x) = 4x+1 and g(x)=x2-5, find
We need to find g(x)/f(x) so we will put them over each other as a fraction
[tex]\frac{g(x)}{f(x)}=\frac{x^2-5}{4x+1}\text{ , x}\ne\frac{-1}{4}[/tex]In any algebraic fraction, denominators can not be zero, so we avoid any values make it equal to zero like -1/4 in our question
Find the slope of the tangent line to f(x) when x= -3. Two points on the line tangent to f(x) at x = -3 are: (-4,-7) and (1,3).
When x = -3, the line that's tangent to f(x) is shown in the given image. So, in order to find the slope of f(x) at x = -3, we need to find the slope of that line.
The slope of a line is given by the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]Now, notice that the points (-4,-7) and (1,3) belong to the tangent line. Therefore, we can use them to find the slope:
y₂ = 3
y₁ = -7
x₂ = 1
x₁ = -4
So, we have:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-7)}{1-(-4)}=\frac{3+7}{1+4}=\frac{10}{5}=2[/tex]Therefore, the slope is 2.
I need to know if it’s A b c or D
The value of x is 1.
Step - by - Step Explanation
What to find? The value of x.
Given:
From the diagram,
• Inscribed angle = 70°
,• arc length = 141x - 1
The formula we can use to solve the given problem is;
[tex]\text{Inscribed angle =}\frac{1}{2}(\text{ length of arc)}[/tex]Substitute the values into the formula.
[tex]70=\frac{1}{2}(141x\text{ - 1)}[/tex]Simplify the above.
To simplify, first multiply both-side of the equation by 2.
[tex]70\times2=\cancel{2}\times\frac{1}{\cancel{2}}(141x-1)[/tex]140 = 141x - 1
Add 1 to both-side of the equation.
140 + 1 = 141x -1 + 1
141 = 141x
Divide both-side of the equation by 141.
[tex]\frac{\cancel{141}x}{\cancel{141}}=\frac{141}{141}[/tex]x = 1
POS The radius of a cylindrical box of oatmeal is 5 centimeters. The height of the box is 18 centimeters. 5 cm 18 cm QATMEAL Which measurement is closest to the total surface area of the oatmeal box in square centimeters? A 597 cm2 B 361 cm? C 314 cm? D 723 cm?
Explanation
Step 1
to find the area, imagine the unfolded cylindrical box
Let
length=18 cm
width=2*pi*radius
radius= 5 cm
[tex]\begin{gathered} \text{width}=2\cdot\pi\cdot5\text{ cm} \\ \text{width}=10\cdot\pi\cdot\text{cm} \\ \text{width}=31.4\text{ cm} \end{gathered}[/tex]Step 2
now, the total area would be
[tex]\begin{gathered} \text{total area= area of the rectangle+twice area of the circle} \\ \text{replacing} \\ \text{total area=(length}\cdot widht9+2(\pi\cdot radius^2) \\ \text{total area=(18 cm}\cdot31.4\text{ cm)+2(3.14}\cdot25cm^2) \\ \text{total area=565.2 cm}^2+157.07cm^2 \\ \text{total area=722.27 cm}^2 \\ \text{rounded} \\ 723cm^2 \end{gathered}[/tex]I hope this helps you
For any number a, |a|=A-1B. sqrt a^2C. 1D. a^2
EXPLANATION
The module of any number, as in this case |a|, is the same number with positive sign, in this case the appropiate option is sqrt(a^2) ---> OPTION B.
5.1234 to the thousandths 6.6666 to the thousandths
Answer:
[tex]\begin{gathered} 5.1234\approx5.123 \\ 6.6666\approx6.667 \end{gathered}[/tex]Explanation:
We want to round up the given number to the nearest thousandths.
[tex]5.1234[/tex]To the nearest thousandth which is also to 3 decimal place, we have;
[tex]\approx5.123[/tex]Also;
[tex]6.6666[/tex]To the nearest thousandth, we have;
[tex]6.667[/tex]Note that numbers from 5 above will be rounded up, while numbers below 5 will be rounded down.
.Jeremy needs to mail five Christmas packages to his family. The first two weigh 3 pounds each and theother three weigh 2 pounds each. If two-day shipping costs $0.37 per ounce and ground shippingcosts $0.30 per ounce, how much will he save by shipping all of his packages by ground rather thantwo-day?
We know that
• The first two weigh 3 pounds.
,• The other three weigh 2 pounds,.
,• Two-day shipping costs $0.37 per ounce.
,• Ground shipping costs $0.30 per ounce.
We also know that 1 pound is equal to 16 ounces.
So, the weights are
[tex]3\cdot16=48[/tex][tex]2\cdot16=32[/tex]So, the cost of each package of 48 ounces is
[tex]48\cdot0.37=17.76[/tex]Therefore, each 3 pounds package costs $17.76 with two-day shipping.
We repeat the process for the other packages.
[tex]32\cdot0.37=11.84[/tex]Therefore, each 2 pounds package costs $11.84 with two-day shipping. So, the total is
[tex]2(17.76)+3(11.84)=35.52+35.52=71.04[/tex]Sending all packages with two-day shipping costs $71.04.
We repeat all the process for ground shipping.
[tex]2\cdot48\cdot0.30=28.8[/tex][tex]3\cdot32\cdot0.30=28.8[/tex]Both services cost $28.8 each, so the total is $57.6.
IF we compare both services, we have
[tex]71.04-57.6=13.44[/tex]Therefore, he will save $13.44.Q. A student earned a grade of 80% on a math test that had 30 problems. How manyProblems on this test did the students answer correctly
In order to calculate how many answers the student did correctly, we just need to find 80% of 30, that is, the product of 80% and 30.
Knowing that 80% corresponds to 0.8, we have:
[tex]80\text{\% of }30=0.8\cdot30=24[/tex]So the students answered 24 questions correctly.
A company sells a product for $72 each. The variable costs are $15 per unit and fixed costs are $29,697 per month
Step 1
Given;
Step 2
A)
[tex]\begin{gathered} Revenue=\text{ Number of units sold }\times\text{ cost per unit} \\ Let\text{ each quant}\imaginaryI\text{ty of good sold be x} \\ cost\text{ per unit= \$72} \\ TR=72\times x=72x \\ \end{gathered}[/tex][tex]\begin{gathered} B)\text{ }total\text{ cost=f}\imaginaryI\text{xed cost + var}\imaginaryI\text{able cost} \\ TC=29697+15x \end{gathered}[/tex]C)At breakeven, TR = TC
[tex]\begin{gathered} 72n=29697+15x \\ 72x-15x=29697 \\ 57x=29697 \\ x=\frac{29697}{57}=521 \end{gathered}[/tex]the number of units needed to breakeven is 521
D) To calculate the TR, we substitute 521 for n in the given function for TR as seen below:
[tex]\begin{gathered} TR=72x \\ TR=72(521)=\text{ \$}37512 \end{gathered}[/tex]TR = $37512
Answers;
[tex]\begin{gathered} A)\text{ 72x} \\ B)\text{ 29697 +15x} \\ C)\text{ 521 units} \\ D)\text{ \$37512} \end{gathered}[/tex]
to which set or sets of numbers does the number 5 belong?A. rational numbers only b. integers c. integers and rational numbers or D. integers,whole numbers, and rational numbers
5 belongs to the set of integers, whole numbers and rational numbers, so the answer is D.
Describe the association represented in the graph.no associationstrong, negativestrong positive D weak, negative.
Given:
the scatter plot is shown in the graph
We will Describe the association represented in the graph.
As shown, when drawing a line of best fit of the points, the line will be with a negative slope that will be a strong negative
So, the answer will be: strong, negative
what is 80% of 685?
To know the percentage of a quantity, we have to divide the percentage we want to know (in this case 80%), over 100%. Then, that part has to be multiplied by that result as it is the part that corresponds to 80%.
0. Dividing 80% over 100%
[tex]\frac{80}{100}=0.8[/tex]2. Multiplying by the quantity
[tex]0.8\times685=548[/tex]Answer: 548
The formula for finding the distance traveled, base on the speed and time, is D= RT, whereD is distanceR is rateT is timeUnits must be consistent. If the unit for D is miles and the unit for T is minutes, what must the units for R be?_______Solve this formula for R.R=______If a bicyclist rides for 140 minutes at an average speed of 14 miles per hour, how far was the ride, to 1 decimal place?_______ miles.At what speed must a bicyclist ride to cover 60 miles in 1.5 hours, to 1 decimal place?______ miles/hour
Given:
a)
The formula for finding the distance traveled, based on the speed and time, is D= RT, where D is distance, R is rate and T is time.
The unit for D is miles and the unit for T is minutes.
b)
A bicyclist rides for 140 minutes at an average speed of 14 miles per hour.
c)
A bicyclist ride to cover 60 miles in 1.5 hours.
Required:
a)
We need to find the units fir R.
b)
We need to find the distance.
c)
We need to speed.
Explanation:
a)
The given formula is
[tex]D=RT[/tex]Divide both sides of the equation by T.
[tex]\frac{D}{T}=\frac{RT}{T}[/tex][tex]\frac{D}{T}=R[/tex]Substitute D =miles and T= minutes in the formula.
[tex]miles=R\times minutes[/tex][tex]\frac{miles}{minutes}=R[/tex]We can rewrite miles by the hour. since 60 minutes = one hour
[tex]60\text{ }\frac{miles}{hour}=R[/tex]The most common unit of speed is miles/ hour.
Answer:
The unit of R is miles/hour.
b)
T =140 minutes and R =14 miles per hour.
Convert the minutes onto hours.
Divide 140 by 60 to convert units.
[tex]T=\frac{140}{60}hours[/tex][tex]T=\frac{7}{3}hours[/tex]Consider the formula.
[tex]D=RT[/tex]Substitute R =14 and T=7/3 in the formula.
[tex]D=14\times\frac{7}{3}[/tex][tex]D=32.7miles[/tex]Answer:
The bicycle was ridden 32.7 miles.
c)
D =60 and T =1.5
Consider the formula.
[tex]D=RT[/tex]Substitute D =60 and T =1.5 in the formula.
[tex]60=R\times1.5[/tex]Divide both sides by 1.5.
[tex]\frac{60}{1.5}=R\times\frac{1.5}{1.5}[/tex][tex]40=R[/tex]Answer:
The speed of the bicycle is 40 miles/hour.
Final answer:
How do I solve angle measurements and find the value of x on a polygon
ANSWER and EXPLANATION
We want to find out how to find the measurement of angles in a regular polygon.
To do this, first we have to know the total angle in the entire polygon.
To find this, we use the formula:
Total Angle = 180(n - 2)
where n = number of sides of the polygon
Now, after finding that total angle, we can find the individual angles in the polygon by dividing that total angle by the number of angles in the polygon.
For example, consider the diagram below:
Let us take that as a regular pentagon with 5 sides.
This means that n = 5.
Therefore, the total angle in the pentagon is:
Total Angle = 180(5 - 2)
Total Angle = 180 * 3 = 540 degrees.
Now, there are 5 angles in the polygon. Therefore, the value of x is:
[tex]x\text{ = }\frac{540}{5}=108^o[/tex]That is how to find the individual angles in a polygon.
Which equation is parallel to the above equation and passes through the point (35, 30)?Group of answer choicesy=5/7x +79y=5/7x +30y= 5/7x +10y= 5/7x + 5
Notice that all the options contain the term
[tex]\frac{5}{7}x[/tex]Setting x=35, we obtain
[tex]\frac{5}{7}(35)=5\cdot5=25[/tex]Finally,
[tex]30=25+5[/tex]Then, the answer is
[tex]\begin{gathered} y=\frac{5}{7}x+5 \\ \text{set x=35} \\ \Rightarrow y=\frac{5}{7}\cdot35+5=25+5=30 \end{gathered}[/tex]Option D is the answer, y=5x/7+5.
Notice that all the options have the same slope as that of the line y=5x/+10
If u= {1,2,3,4,5,6,7,8,9} a = the event of drawing an odd B= the event of drawing prime number Find p( A unión b)
Using venn diagrams:
Therefore, the union will be given by:
[tex]P(A\cup B)=\mleft\lbrace1,2,3,5,7,9\mright\rbrace[/tex]es? Explain your reasoning.
35. MP MODELING REAL LIFE A planet orbiting a star
at a distance such that its temperatures are right for
liquid water is said to be in the star's habitable zone. The
habitable zone of a particular star is at least 0.023 AU
and at most 0.054 AU from the star (1 AU is equal to the
distance between Earth and the Sun). Draw a graph tha
represents the habitable zone.
the distanco
♥it must orbit in a zone where liquid water is possible♥
What is the length of the dotted line in the diagram below? Round to the nearesttenth.
From the given figure
The rectangle has a width of 3 and its length is the hypotenuse of a right triangle with legs 5 and 7
Then we will find at first the hypotenuse of the triangle using the Pythagoras Theorem
[tex]\begin{gathered} L=\sqrt[]{7^2+5^2} \\ L=\sqrt[]{49+25} \\ L=\sqrt[]{74} \end{gathered}[/tex]Now, to find the dotted line we will do the same with the length and the width of the rectangle
[tex]\begin{gathered} D=\sqrt[]{L^2+W^2} \\ L=\sqrt[]{74},W=3 \\ D=\sqrt[]{(\sqrt[]{74})^2+(3)^2} \\ D=\sqrt[]{74+9} \\ D=\sqrt[]{83} \\ D=9.110433579 \end{gathered}[/tex]Round it to the nearest tenth
The length of the dotted line is 9.1
. Find the value of each expression. Show your work. (a) 1.42 (b) 300 = 2(0.5 +4.5) ? 3 ) te) -23
For the first expression, we have 1.4², this can be expressed as 1.4×1.4 and then we get:
[tex]1.4^2=1.4\times1.4=1.96[/tex]For the second expression, 300 ÷ 2(0.5 + 4.5)² we must start by solving the sum inside the parenthesis, then we get:
300 ÷ 2(0.5 + 4.5)² = 300 ÷ 2(5)²
Then, solve the exponent on the right of the division symbol:
300 ÷ 2(5)² = 300 ÷ 2×25
Now, solve the multiplication
300 ÷ 2×25 = 300 ÷ 50
Now, we can solve the division
300 ÷ 50 = 6
Then, 300 ÷ 2(0.5 + 4.5)² = 6
For the last expression, we must start with the exponent:
[tex]\begin{gathered} \frac{1}{3}\div2(\frac{1}{2})^3 \\ \frac{1}{3}\div2\times\frac{1}{2^3} \\ \frac{1}{3}\div2\times\frac{1}{8}^{} \end{gathered}[/tex]Now we can solve the multiplication:
[tex]\frac{1}{3}\div2\times\frac{1}{8}^{}=\frac{1}{3}\div\frac{2}{8}^{}[/tex]In order to divide one fraction by another one we just have to keep the first fraction unchanged, change the ÷ for a × and flip the second fraction, like this:
[tex]\frac{1}{3}\div\frac{2}{8}^{}=\frac{1}{3}\times\frac{8}{2}=\frac{1\times8}{3\times2}=\frac{8}{6}=\frac{4}{3}[/tex]Then, the value of the last expression is 4/3
What is the variable term in 2x+3?
In the expression
[tex]undefined[/tex]write each ratio as a fraction in its simplest form12/10
The given ratio is,
[tex]\frac{12}{10}[/tex]Taking 2 as common from both 12 and 10 we have,
[tex]\frac{12}{10}=\frac{6\times2}{5\times2}=\frac{6}{5}[/tex]As there is no common factor between 6 and 5. it cannot be simplified further as fraction.
Thus, the answer is 6/5
a. Use symbols and proper notation to name the angle shown on thegraph. Write all three correct names.
The correct names are:
∠RST (the three points involved with the vertex at the middle)
∠TSR (same as the previous name, but with other order)
∠S (the letter of the vertex)
Find the surface area of the pyramid. Round your answer to the nearest hundredth.
Okay, here we have this:
Considering the provided information, we are going to calculate the surface area of the pyramid, so we obtain the following:
Let's use the following formula to find the surface area:
Surface area=Area of the base+1/2*Perimeter of the base*Slant Height
Replacing:
Surface area=(12.2ft¨* 12.2 ft)+1/2 * (12.2 ft * 4) * 9.5ft
Surface area=148.84 ft² + 1/2 * 48.8 ft * 9.5 ft
Surface area=148.84 ft² + 231.8 ft²
Surface area=380.64 ft²
Finally we obtain that the correct answer is the first option.
Find all the roots of the following equations2x^3+x^2-7x-2=0
Let's begin by listing out the information given to us:
2x³ + x² - 7x- 2 = 0
We will proceed to factorise, we have:
(x + 2)(2x² − 3x - 1) = 0
We will proceed to equate the factors to zero, we have:
x + 2 = 0⇒ x = -2
⇒ x = -2
2x² − 3x - 1 = 0
We will use the quadratic formula, we have:
[tex]\begin{gathered} 2x^{2}-3x-1=0 \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ a=2,b=-3,c=-1 \\ x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(2)(-1)}}{2(2)} \\ x=\frac{3\pm\sqrt[]{9+8}}{4}=\frac{3\pm\sqrt[]{17}}{4} \\ x=\frac{3\pm\sqrt[]{17}}{4}\Rightarrow x=\frac{3+\sqrt[]{17}}{4},\frac{3-\sqrt[]{17}}{4} \\ x=\frac{3+\sqrt[]{17}}{4},\frac{3-\sqrt[]{17}}{4} \end{gathered}[/tex]
A hot air balloon is sitting on the ground. Hot air was added causing the balloonto ascend at a rate of 4 feet per second for 60 seconds.A. Use integers to write an expression to determine the location of the airballoon relative to its starting location.
Since the rate in which the balloon ascends is constant this means that we can represent its altitude (the location relative to its starting point) as a linear function.
A linear funtion is given by:
[tex]y=mx+b[/tex]where m is the slope or rate of change and b is the y-intecept (the value of y when x=0).
In our case let x be the time it passes since the balloon started ascending and let y be its altitude. With this definition for the variables we conclude that in our case the rate of change is 4 and, since the ballon started on the ground, the valur of b is zero. Therefore the expression we need is:
[tex]y=4x[/tex]Note:
It is important to notice that this expression is only valid for:
[tex]0\leq x\leq60[/tex]This comes from the fact that that the balloon ascends at that rate for 60 seconds and the fact that the time can't be negative.
Answer: The answer to that would be y=4 x 60 or just write it as y= 240
But in expression form it would be 0<_x<_60
Hope this helps.
which one of the following options is true when considering the expansion of the binomial expression (x+y)^4?A) The sum of the exponents of each term of the expansion of (x+y)^4 is 5.B) The expansion of (x+y)^4 will yield 4 termsC) The last term of the expansion of (x+y)^4 is y^4D) The coefficients of the expansion of (x+y)^4 are: 1,4,4,1.
Given:
[tex](x+y)^4[/tex]To Determine: The binomial expansion of the given
Solution
Using binomial expansion formula below
[tex](x+y)^n=\sum_{k\mathop{=}0}^n(^n_k)x^{n-k}y^k[/tex]PERCENT PROBLEMS The local toy store manager found all the wrong percents marked on the following toys. The ball is 35% off, the game system is 45% off, the doll and airplane are both 65% off. Find the sale prices if the dump truck's sale price was the original price of the doll and the ball. The original price of the game system was $280 more than the sale price of the dump truck and $10 less than the original price of the airplane. to spe PLATTEGRONY
The sale prices of the toys obtained from their original prices and the percentage discounts are;
Toy [tex]{}[/tex] The selling price of the
Truck [tex]{}[/tex] $16.99
Ball [tex]{}[/tex] $11.04
Doll [tex]{}[/tex] $5.95
Game system [tex]{}[/tex] $192.97
Airplane [tex]{}[/tex] $107.41
What is a percentage?A percentage is the expression of a ratio or fraction between two quantities in which the denominator of the fraction is 100.
From the a similar question online, we have;
The price of the truck = $16.99
The original price of the doll = $16.99
Original price of the ball = $16.99
Original price of the game system = $280 + $16.88 = $296.88
Original price of the airplane = $296.88 + $10 = $306.88
The sale prices are therefore;
Sale price of the ball = $16.99 - 35% × $16.99 ≈ $11.04
Sale price of the doll = $16.99 - 65% × $16.99 ≈ $5.95
Sale price of the game system = $296.88 - 35% × $296.88 ≈ $192.97
Sale price of the airplane = $306.88 - 65% × $306.88 = $107.41
Learn more about percentages here:
https://brainly.com/question/24339661
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what is 12/1020 in algorithm
Answer:
12/1020=
0 R 12
Step-by-step explanation: