Given:
[tex]\begin{gathered} x^2-3x+2=0 \\ x^2+2x-15=0 \end{gathered}[/tex]Required:
We need to find the solution by Vièta's theorem.
Explanation:
Compare 1st equation with
[tex]ax^2+bx+c=0[/tex]we get
[tex]\begin{gathered} a=1 \\ b=-3 \\ c=2 \end{gathered}[/tex]Vièta's theorem is
[tex]\begin{gathered} x_1+x_2=-\frac{b}{a} \\ x_1x_2=\frac{c}{a} \end{gathered}[/tex][tex]\begin{gathered} x_1+x_2=3 \\ x_1x_2=2 \end{gathered}[/tex]now solve this equation and we get
[tex]\begin{gathered} x_1=1 \\ x_2=2 \end{gathered}[/tex]because addition of 1 and 2 is 3 and multiplication is 2
Now for 2nd equation
[tex]\begin{gathered} a=1 \\ b=2 \\ c=-15 \end{gathered}[/tex]apply Vièta's theorem
[tex]\begin{gathered} x_1+x_2=-2 \\ x_1x_2=-15 \end{gathered}[/tex]by this
[tex]\begin{gathered} x_1=3 \\ x_2=-5 \end{gathered}[/tex]because addition of 3 and -5 is -2 and multiplication is -15
Assume the hold time of callers to a cable company is normally distributed with a mean of 4.0 minutes and a standard deviation of 0.4 minute. Determine the percent of callers who are on hold between 3.4 minutes and 4.5 minutes. % (Round to two decimal places as needed.)
According to the problem, we have
[tex]\begin{gathered} \mu=4.0\min \\ \sigma=0.4\min \end{gathered}[/tex]We have to find the percent of callers who are on hold between 3.4 minutes and 4.5 minutes.
First, we find the z-score
[tex]z=\frac{x-\mu}{\sigma}[/tex]For x = 3.4
[tex]z=\frac{3.4-4.0}{0.4}=\frac{-0.6}{0.4}=-1.5[/tex]For x = 4.5
[tex]z=\frac{4.5-4.0}{0.4}=\frac{0.5}{0.4}=1.25[/tex]The probability we have to find is
[tex]P=(3.4Using a z-table, we have[tex]\begin{gathered} P(3.4Then, we multiply by 100 to express it in percetange.[tex]0.2351\cdot100=23.51[/tex]Hence, the probability is 23.51%.how do you solve 4 1/4 + 7/8
The given expression is,
[tex]4\frac{1}{4}+\frac{7}{8}[/tex]So, this can be solved as,
[tex]\begin{gathered} \frac{4\times4+1}{4}+\frac{7}{8}=\frac{17}{4}+\frac{7}{8} \\ \rightarrow\frac{8\times17+4\times7}{8\times4}=\frac{164}{32}=\frac{41}{8} \end{gathered}[/tex]Explanations:
To solve the mixed fraction,
[tex]4\frac{1}{4}\rightarrow\frac{(4\times4)+1}{4}=\frac{17}{4}[/tex]So, now we are adding the terms, as given in the expression,
[tex]\frac{17}{4}+\frac{7}{8}=\frac{(8\times17)+(7\times4)}{4\times8}[/tex]Here we are employing the rule,
[tex]\frac{a}{b}+\frac{c}{d}=\frac{ad+cb}{bd}[/tex]Use substitution to solve the system of equations. y = x + 2 4x - 5y = 14 A. (-22,-24) C. (-4,-2)B. (-24, -22) D. (-14, -12)
Solve by substitution;
[tex]\begin{gathered} y=x+2---(1) \\ 4x-5y=14---(2) \\ \text{Substitute for the value of y into equation (2)} \\ 4x-5(x+2)=14 \\ 4x-5x-10=14 \\ \text{Collect like terms} \\ 4x-5x=14+10 \\ -x=24 \\ \text{Divide both sides by -1} \\ x=-24 \\ \text{Substitute for the value of x into equation (1)} \\ y=x+2 \\ y=-24+2 \\ y=-22 \end{gathered}[/tex]Sports Authority marks up New Balance sneakers $30 and sells them for $109. Markup is on cost. What are the cost and percent markup?
If Sports Authority marks up New Balance sneakers for $30 and sells them for $109, then the cost will be $79 while the percent markup will be 37.97%.
What is the cost and percent markup?The original cost of the product can be obtained by subtracting the markup price from the selling price as seen below.
Cost = selling price - markup
Cost = $109 - $30
Cost = $79
Thus, we arrive at the result that the cost of the product by Sports Authority is $79.
Next, we calculate the percent markup with the formula below:
Percent markup = Markup/cost × 100
Percent markup = 30/79 × 100
= 37.97%
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√64= A. 16 B. 8 C. 7 D. 9
Answer:
B. 8
Explanation:
[tex]64=8\times8[/tex]We can write this in index form as:
[tex]64=8^2[/tex]Therefore:
[tex]\sqrt[]{64}=\sqrt[]{8^2}[/tex]On the right-hand side, the square root sign cancels the square, so we have:
[tex]\sqrt[]{64}=8[/tex]The correct choice is B.
all i need is for question 14 to be answered please help
Given
The path of particle 1 is,
[tex]x(t)=3t-6,\text{ }y(t)=t^2-2t[/tex]And, the path of second particle is,
[tex]x(t)=\sqrt{t+6},\text{ }y(t)=-3+2t[/tex]To model the path of the two particles in cartesian form and to find whether, the two particles collide.
Explanation:
It is given that,
The path of the first particle is,
[tex]x(t)=3t-6,\text{ }y(t)=t^2-2t[/tex]That implies,
[tex]x=2t-6,\text{ }y=t^2-2t[/tex]Consider,
[tex]\begin{gathered} x=2t-6 \\ 2t=x+6 \\ t=\frac{x+6}{2} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} y=(\frac{x+6}{2})^2-2(\frac{x+6}{2}) \\ y=\frac{x^2+12x+36}{4}-\frac{2x+12}{2} \\ y=\frac{x^2+12x+36-2(2x+12)}{4} \\ y=\frac{x^2+12x+36-4x-24}{4} \\ y=\frac{x^2+8x+12}{4}\text{ \_\_\_\_\_\_\_\_\_\_\lparen1\rparen} \end{gathered}[/tex]Also, the path of second particle is,
[tex]x(t)=\sqrt{t+6},\text{ }y(t)=-3+2t[/tex]That implies,
[tex]x=\sqrt{t+6},\text{ }y=-3+2t[/tex]Consider,
[tex]\begin{gathered} y=-3+2t \\ 2t=y+3 \\ t=\frac{y+3}{2} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} x=\sqrt{t+6} \\ \Rightarrow x^2=(t+6) \\ \Rightarrow x^2=(\frac{y+3}{2})+6 \\ \Rightarrow x^2=\frac{y+3+12}{2} \\ \Rightarrow2x^2=y+15 \\ \Rightarrow y=2x^2-15\text{ \_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]Hence, y=(x^2+8x+12)/4, y=2x^2-15 are the paths of the two particles respectively.
The graph of the path of the two particles are,
From, this it is clear that the particle collide at the points (-2.686, -0.568) and (3.829, 14.324).
which number is divisible by "644532"
Answer:
2
Step-by-step explanation: 2 can be divided by 644532
The dimensions of a rectangular prism are measured in centimeters. What unit will the volume of the prism be measured in?centimeterssquare centimeterscubic centimetersmeters
Given:
The dimensions of a rectangular prism are measured in centimetres.
Required:
What unit will the volume of the prism be measured in?
Explanation:
The volume of the prism will be measured in square centimetres
Final Answer:
Square centimeters
Kindly assist in answering these questions
The point of origin on the graph is (0,0) and the constant of proportionality is equal to 3.
Equation of LineThe equation of a straight line is y=mx + c. y = m x + c m is the gradient and c is the height at which the line crosses the y -axis, also known as the y -intercept.
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x, y to form an algebraic equation, which is referred to as an equation of a line.
In the given question, we are asked to find several values relating to the graph attached.
5) The point of origin on the graph is at (0,0) because the graph passes through the center along the straight line.
6) The constant of proportionality (k) is the value before the variable x.
The equation of the line is y = 3x.
The constant of proportionality of the equation is equal to 3.
7) The value of the ratio k is given as y/x
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what is the area of the following Circle R equals 7
Answer: Area is 153.94
Step-by-step explanation:
Area = π r 2
Find the quotient.8 / (1 1/3) (Type a whole number or a fraction.)
In order to calculate the result of this division, let's first convert the mixed number 1 1/3 into a fraction:
[tex]1\frac{1}{3}=1+\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3}[/tex]Now, calculating the division, we have:
[tex]\frac{8}{\frac{4}{3}}=8\cdot\frac{3}{4}=2\cdot3=6[/tex]So the result is 6.
Hi, The area of a circle is 100 quare millimeters. The radius is 5.64 millimeters. what is the circumference?
The area A of a circle is given by
[tex]A=\pi r^2[/tex]where Pi is 3.1416 and r is the radius. In our case, we get
[tex]100\operatorname{mm}=\pi r^2[/tex]and we need to find r. In this regard, if we move Pi to the left hand side we get
[tex]\frac{100}{\pi}=r^2[/tex]then, r is given by
[tex]r=\sqrt[]{\frac{100}{\pi}}[/tex]Now, the circunference C is given by
[tex]C=2\pi\text{ r}[/tex]then, by substituting our last result into this formula, we have
[tex]C=2\pi\sqrt[]{\frac{100}{\pi}}[/tex]since square root of 100 is 10, we get
[tex]C=2\pi\frac{10}{\sqrt[]{\pi}}[/tex]we can rewrite this result as
[tex]\begin{gathered} C=\frac{2\pi\times10}{\sqrt[]{\pi}} \\ C=\frac{2\sqrt[]{\pi\text{ }}\sqrt[]{\pi}\times10}{\sqrt[]{\pi}} \end{gathered}[/tex]and we can cancel out a square root of Pi. Then, we have
[tex]C=2\sqrt[]{\pi}\times10[/tex]and the circunference is
[tex]C=20\text{ }\sqrt[]{\pi}\text{ milimeters}[/tex](x - 5) (4x - 5) = 0 there are two answers
The solutions are the values of x that makes the expression equal to zero:
x-5 =0
Add 5 to both sides
x=5
4x-5=0
Add five to both sides
4x=5
Divide both sides by 4
x= 5/4
x=1.25
name each angle pair as corresponding, alternate interior, alternate exterior, consecutive interior angle, or no relationship. identify the transversal that connects each angle pair.
tell whether you can prove that each quadrilateral is a parallelogram. Explain.
WE know that in any quadrilateral the interior sum of its angles is 360. The missing angle in this case is:
[tex]360-121-59-59=121[/tex]Now, we also know that if the oposite angles in a quadrilateral are equal then the quadrilateral is a parallelogram.
Therefore the figure shown is a parallelogram.
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ≤ x ≤ 9.
The average rate of change is given by the rate of change of both variables.
"Rate" refers to a division. We want to divide the change of y, Δy, by the change of x, Δx:
Δy/Δx
("Δ" means "change").
We want to analyze the change over the interval 3 ≤ x ≤ 9.
Step 1: change of x (Δx)The change from x = 3 and x = 9 is
Δx = 9 - 3 = 6
Step 2: change of y (Δy)We observe the right column of the table. When x = 3, y = 28 and when x = 9, y = 4.
The change from y = 28 to y = 4 is
Δy = 4 - 28 = -24
Step 3: rate of changeThen, the average rate of change is:
Δy/Δx = -24/6 = -4
Answer: -4
Find each unit price and decide which is the better buy. Assume that we are comparing different sizes of the same brand.Frozen orange juice:$1.57 for 14 ounces$0.57 for 4 ounces----------------------------Find the unit price of a frozen orange juice which costs $1.57 for 14 ounces.$ (blank) per ounce(Type a whole number or a decimal. Round to three decimal places as needed.)Find the unit price of a frozen orange juice which costs $0.57 for 4 ounces.$ (blank) per ounce(Type a whole number or a decimal. Round to three decimal places as needed.)Which is the better buy?A. $1.57 for 14 ouncesB. $0.57 for 4 ounces
The different sizes of the given brands are
Frozen orange juice:
$1.57 for 14 ounces
$0.57 for 4 ounces
The unit price of a frozen orange juice which costs $1.57 for 14 ounces is
1.57/14 = 0.112
The unit price of a frozen orange juice which costs $0.57 for 4 ounces is
0.57/4 = 0.1425
The better buy is the size that has the lowest cost per ounce. Looking at our calculations, the lowest cost per ounce is $0.112
Therefore, the frozen orange juice which costs $1.57 for 14 ounces is the better buy.
A hairdresser is considering ordering a certain shampoo. Company A charges $5 per 8 ounce bottle plus a $5 handling fee per order. Company B charges $2 per 8 ounce bottle plus a $23 handling fee per order. How many bottles must the hairdresser buy to justify using Company B?
For the shampoo:
Company A charges $5 per ounce bottle + $5 handling fee.
Company B charges $2 per ounce bottle + $23 handling fee.
Let C represent the total cost for the shampoo and x represent the number of bottles of shampoo then you can express the total cost for both companies as equations:
[tex]\begin{gathered} C_A=5x+5 \\ C_B=8x+23 \end{gathered}[/tex]For the hairdresser to justify using the shampoo of company C, the cost must be less than for company A, so that:
[tex]\begin{gathered} C_BNowWhat is the slope of the line shown below?(2,2), (-1,-4) A. 2 B-6. C.6. D-2
Solution
The slope is given by
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \Rightarrow m=\frac{-4-2}{-1-1}=\frac{-6}{-2}=3 \end{gathered}[/tex]Hence, the slope is 3
1/10+1/2=____ options 3/5
we are given the sum of the following fractions:
[tex]\frac{1}{10}+\frac{1}{2}[/tex]To sum these fractions we may multiply the numerator and denominator of the second fraction by 5, like this:
[tex]\frac{1}{10}+\frac{5}{10}[/tex]Since now they have the same denominator we can add the numerators and leave the same denominator, like this:
[tex]\frac{1}{10}+\frac{5}{10}=\frac{1+5}{10}=\frac{6}{10}[/tex]Now we can simplify the resulting fraction by dividing the numerator and denominator by 2:
[tex]\frac{6}{10}=\frac{3}{5}[/tex]Therefore, the sum of the two fractions is 3/5
Which point is on the circle centered at the origin with a radius of 5 units?Distance formula: Vx2 - xy)2 + (V2 - y2)?(2, 721)(2, 23)(2, 1)O (2,3)
To know if the point is on the circle, we mus calculate the distance between the point and the origin.
For the first option, we have:
- (2, √21)
and the origin
- (0, 0)
Then, we must replace the two points in the distance formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\begin{gathered} d=\sqrt[]{(0-2)^2+(0-\sqrt[]{21})^2} \\ d=\sqrt[]{4+21}=\sqrt[]{25}=5 \end{gathered}[/tex]Knowing that the distancie is 5 we can affirm that the point is on the circle because the radius is 5.
Finally, the answer is
[tex](2,\text{ }\sqrt[]{21})[/tex]A ball is thrown from an initial height of 6 feet with an initial upward velocity of 21 ft/s. The ball's heighth (in feet) after t seconds is given by the following,6+21 167Find all values of t for which the ball's height is 12 feet.Round your answer(s) to the hearest hundredth(If there is more than one answer, use the "or" button.)
The given expression in the question is
[tex]h=6+21t-16t^2[/tex]with the value of h given as
[tex]h=12ft[/tex]By equating both equations, we will have
[tex]\begin{gathered} 12=6+21t-16t^2 \\ 12-6-21t+16t^2=0 \\ 6-21t+16t^2=0 \\ 16t^2-21t+6=0 \end{gathered}[/tex]To find the value of t we will use the quadratic formula of
[tex]ax^2+bx+c=0[/tex]which is
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{where} \\ a=16 \\ b=-21 \\ c=6 \end{gathered}[/tex]By substitution, we will have
[tex]\begin{gathered} t=\frac{-(-21)\pm\sqrt[]{(-21)^2-4\times16\times6}}{2\times16} \\ t=\frac{21\pm\sqrt[]{441-384}}{32} \\ t=\frac{21\pm\sqrt[]{57}}{32} \\ t=\frac{21\pm7.5498}{32} \\ t=\frac{21+7.5498}{32}\text{ or t=}\frac{21-7.5498}{32} \\ t=\frac{28.5498}{32\text{ }}\text{ or }t=\frac{13.4502}{32\text{ }} \\ t=0.89\text{ or t=0.42} \end{gathered}[/tex]Alternatively, Solving the equation graphically we will have
Therefore,
The values of t( to the nearest hundredth) t= 0.89sec or 0.42sec
how many apples are in 4 dozen
There are 48 apples in 4 dozen
Explanations:1 dozen = 12
This means that:
1 dozen of apples = 12 apples
4 dozen = 12 x 4
4 dozen = 48 apples
X-1 what is the answer
Answer:
x - 1 = x - 1
Step-by-step explanation:
If you were expecting a singular solution, you won’t get it. You’ll likely instead get a lot of smart alecks snidely answer your question. Looks like you already have actually.
But they speak true. x – 1 on its own like that wont really get you anything. Now if you asked something along the lines of “What is x – 1 equal to if x is equal to 5?” then you’d get one solid definitive solution: 4.
Answer:
YES!!!!!
Step-by-step explanation:
LOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLLOLOLOLOLOLOLOLOL
[tex] log_{2 }(x - 6) + log_{2}(x - 4) = log_{2}(x) [/tex]x=8,3x=8No solution
Answer:
x=8,3
Explanation:
Given the expression:
[tex]\log _2\mleft(x-6\mright)+log_2\mleft(x-4\mright)=log_2\mleft(x\mright)[/tex]Applying the addition law of logarithm:
[tex]\log _2(x-6)(x-4)=log_2x[/tex]Next, cancel the logarithm operator on both sides:
[tex]\begin{gathered} (x-6)(x-4)=x \\ x^2-4x-6x+24=x \\ x^2-10x-x+24=0 \\ x^2-11x+24=0 \end{gathered}[/tex]We solve the resulting quadratic equation:
[tex]\begin{gathered} x^2-8x-3x+24=0 \\ x(x-8)-3(x-8)=0 \\ (x-3)(x-8)=0 \\ x-3=0\text{ or }x-8=0 \\ x=3\text{ or }x=8 \end{gathered}[/tex]The value of x is 3 or 8.
5. SOLVE THe linear equation : 13x – 5 + 171 = x
Answer:
x = -83/6 = -13.833
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
13*x-5+171-(x)=0
1.1 Pull out like factors :
12x + 166 = 2 • (6x + 83)
2.2 Solve : 6x+83 = 0
Subtract 83 from both sides of the equation :
6x = -83
Divide both sides of the equation by 6:
x = -83/6 = -13.833
Ready for me for a quadratic function with vertex (3,9)
We have to write an equation of a quadratic function that has a vertex at (3,9) and pass through the origin.
We can use the vertex form of the quadratic equation:
[tex]y=a(x-h)^2+k[/tex]where the vertex has coordinates (h,k).
In this case, (h,k) = (3,9).
From the formula we can see that the parameter a that can take any value and still have the same vertex. We will use the parameter "a" to make it pass through the origin.
The vertex form of the equation is then:
[tex]y=a(x-3)^2+9[/tex]As it pass through the origin, then the equation should be satisfied when x = 0 and y = 0:
[tex]\begin{gathered} 0=a(0-3)^2+9 \\ 0=a(-3)^2+9 \\ 0=a\cdot9+9 \\ -9=9a \\ -\frac{9}{9}=a \\ a=-1 \end{gathered}[/tex]Then, as a = -1, we can write the equation as:
[tex]y=-(x-3)^2+9[/tex]Answer: An example of quadratic function with vertex (3,9) that pass through the origin is y = -(x-3)² + 9.
Which equation could result from
performing the distributive property
to
8.53 – 2 (2x + 8) =?
-
A
О
4.52 + 16 = 11.5
B
O
4.5x + 27 = -9
С
O
4.5x - 16 = 11
D
-4.52 +27 = 45
C
1) The distributive property allows us to rewrite some product in factors.
2) Let's then examine that equation:
[tex]\begin{gathered} 8.5x-2(2x+8)=\text{?} \\ 8.5x-4x-16= \\ 4.5x-16 \end{gathered}[/tex]3) Then examining the options, the only option that displays the correct application of the Distributive Property on the left side is: C
a construction company orders tile flooring for the kitchen in three bathrooms of a new home the kitchen floor measures 48 square feet 2 bathrooms have floor that each Measure 30 and 1/2 square feet the third bathroom floor measures 42 1/2 square feet if the tile cost 2.39 per square foot what is that the least amount of money to the nearest cent the company spends on tile for all three bathrooms
We are not concerned with the tiles needed for the kitchen.
From the given information, there are two bathroom floors with the same measurement in terms of area. The area of each floor is 30.5 square feet
Area of both bathroom floors = 30.5*2 = 61 square feet
Area of the third bathroom = 42.5 square feet
Area of the three bathroom floors = 61 + 42.5 = 103.5 square feet
Given that the tile costs 2.39 per sqare foot, the least amount of money that the company would spend for all three tiles is
103.5 * 2.39 = 247.365
Rounding up to the nearest cent means rounding up to the nearest hundredth or 2 decimal places
Rounding up to the nearest cent, it becomes 247.37
Watch help videoA group of friends wants to go to the amusement park. They have no more than $305to spend on parking and admission. Parking is $19, and tickets cost $26 per person,including tax. Write and solve an inequality which can be used to determine p, thenumber of people who can go to the amusement park.<
p = number of people who can go to amusement park
Amount they want to spend is no more than $305. This means there expenses will be less than or equals to $305.
parking = $19
cost per person = $26
Therefore,
[tex]19+26p\leq305[/tex][tex]\begin{gathered} 26p\leq305-19 \\ 26p\leq286 \\ p\leq\frac{286}{26} \\ p\leq11 \end{gathered}[/tex]