Given:
[tex]F\left(x\right)=x^3+x^2+9x+9[/tex]To find:
The zeros
Explanation:
Factorizing by grouping method,
[tex]\begin{gathered} F\left(x\right)=x^3+x^2+9x+9 \\ =x^2(x+1)+9(x+1) \\ =(x+1)(x^2+9) \end{gathered}[/tex]The zeros are found by equating the factors with zero.
[tex]\begin{gathered} x+1=0 \\ x=-1 \end{gathered}[/tex]And we have,
[tex]\begin{gathered} x^2+9=0 \\ x^2=-9 \\ x=\pm\sqrt{-9} \\ x=\pm3i \end{gathered}[/tex]So, the zeros are,
[tex]-1,3i,-3i[/tex]Final answer:
The zeros are,
[tex]-1,3i,-3i[/tex]tameka built 1/2 of a shed on monday and 2/5 of the tuesday
Triangle ABC is similar to triangle DEF. Side AB is the longest side of ABC. It measures 12 centimeters. Side DE is the longest side of DEF. It measures 8 centimeters. What is the scale factor that takes DEF to ABC?
since these are similar triangles, all sides have a scale factor in order to become the other
since you are being asked for the scale factor from DEF to ABC, the equality should be like this
[tex]8x=12[/tex]solve for x
[tex]x=\frac{12}{8}=\frac{3}{2}[/tex]WHAT WOULD BE THE SCALE FACTOR THAT TAKES ABC TO DEF?
apply same procedure as before, but the initial value should be 12
[tex]\begin{gathered} 12x=8 \\ x=\frac{8}{12}=\frac{2}{3} \end{gathered}[/tex]Evaluate the quantity G(-7) given the following function.G(x) = x2 + 4x - 12G(-7)=exact number, no toleranceexact number, no tolerance
Explanation
Step 1
replace the value of x in the equation with the given value
[tex]\begin{gathered} G(x)=x^2+4x-12 \\ \text{then} \\ G(-7)=(-7)^2+4\cdot-7-12 \\ G(-7)=49-28-12 \\ G(-7)=9 \end{gathered}[/tex]I hope this helps you
points (k,-3) lies on the line whose equation is X-2y=-2 what is the value of k
(k,-3)
x-2y=-2
replace (x,y ) for (k,-3) and solve for k
k-2(-3)=-2
k+6 =-2
k= -2-6
k=-8
I need help on 3 questions-42 - 6n = -30
hello
the question given is an equation -42 - 6n = -30
step 1
collect like terms
[tex]\begin{gathered} -42-6n=-30 \\ -42+30=6n \\ 6n=-12 \end{gathered}[/tex]step 2
divide both sides by the coefficient of n
[tex]\begin{gathered} 6n=-12 \\ \frac{6n}{6}=-\frac{12}{6} \\ n=-2 \end{gathered}[/tex]from the calculations above, the value of n is equal to -2
Divide and simplify. Assume all variables result in non-zero denominators.
The simplified form of the given expression is [tex]\frac{4q^2+7q-15}{4q^2-13q-12}\div\frac{q^2-9}{16q^2+12q}=\frac{4q(4q-5)}{(q-3)(q-4)}[/tex]
In the given question we have to divide and simplify the given expression.
The given exression is [tex]\frac{4q^2+7q-15}{4q^2-13q-12}\div\frac{q^2-9}{16q^2+12q}[/tex].
As we know that when we change division sign into multiplication the fraction after the division change their position.
So the expression should be
[tex]\frac{4q^2+7q-15}{4q^2-13q-12}\div\frac{q^2-9}{16q^2+12q}=\frac{4q^2+7q-15}{4q^2-13q-12}\times\frac{16q^2+12q}{q^2-9}[/tex]...............(1)
Before simplifying the expression we firstly find the factor of each term seprately.
Firstly find the factor of [tex]4q^2+7q-15[/tex].
The multiplication of first and third variable is 60 so the possible factors are 12 and 5. So
[tex]4q^2+7q-15=4q^2+(12-5)q-15[/tex]
[tex]4q^2+7q-15=4q^2+12q-5q-15[/tex]
[tex]4q^2+7q-15[/tex] = 4q(q+3)-5(q+3)
[tex]4q^2+7q-15[/tex] = (4q-5)(q+3)
Now finding the value of [tex]4q^2-13q-12[/tex].
The multiplication of first and third term is 48, so the possible factors are 16 and 3.
[tex]4q^2-13q-12=4q^2-(16-3)q-12[/tex]
[tex]4q^2-13q-12=4q^2-16q+3q-12[/tex]
[tex]4q^2-13q-12[/tex] = 4q(q-4)+3(q-4)
[tex]4q^2-13q-12[/tex] = (4q+3)(q-4)
Now finding the factor of [tex]q^2-9[/tex].
Using the formula [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]q^2-9=(q)^2-(3)^2[/tex]
[tex]q^2-9[/tex] = (q-3)(q+3)
Now finding the factor of [tex]16q^2+12q[/tex].
[tex]16q^2+12q[/tex] = 4q(4q+3)
Putting the value of factors in equation 1
[tex]\frac{4q^2+7q-15}{4q^2-13q-12}\div\frac{q^2-9}{16q^2+12q}=\frac{(4q-5)(q+3)}{ (4q+3)(q-4)}\times\frac{4q(4q+3)}{(q-3)(q+3)}[/tex]
Simplifying
[tex]\frac{4q^2+7q-15}{4q^2-13q-12}\div\frac{q^2-9}{16q^2+12q}=\frac{(4q-5)}{ (q-4)}\times\frac{4q}{(q-3)}[/tex]
Hence, the simplified form of the given expression is
[tex]\frac{4q^2+7q-15}{4q^2-13q-12}\div\frac{q^2-9}{16q^2+12q}=\frac{4q(4q-5)}{(q-3)(q-4)}[/tex]
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Question 4 of attached screenshot, I have all relevant information if required
The derivative of the function is given as:
[tex]g^{\prime}(x)=\frac{x^2-16}{x-2}[/tex]It is also given that g(3)=4.
Note that the Slope of a Tangent Line to a function at a point is the value of the derivative at that point.
Substitute x=3 into the derivative:
[tex]g^{\prime}(3)=\frac{3^2-16}{3-2}=\frac{9-16}{1}=\frac{-7}{1}=-7[/tex]It follows that the slope of the tangent line at x=3 is -7.
Since it is given that g(3)=4, it implies that (3,4) is a point on the line.
Recall that the equation of a line with slope m, which passes through a point (x₁,y₁) is given by the point-slope formula as:
[tex]y-y_!=m(x-x_1)[/tex]Substitute the point (x₁,y₁)=(3,4) and the slope m=-7 into the point-slope formula:
[tex]\begin{gathered} y-4=-7(x-3) \\ \Rightarrow y-4=-7x+21 \\ \Rightarrow y=-7x+21+4 \\ \Rightarrow y=-7x+25 \end{gathered}[/tex]Hence, the equation of the tangent line to the graph of g at x=3 is y=-7x+25.
The required equation is y=-7x+25.
To determine the number of trout in a lake, a conversationist catches 141 trout, tags them and trows them back into the lake. Later, 45 trout are caught and 15 are tagged. How many trout would the conversationist expect to be in the lake???
4x – 2y = 20-8x + 4y = -40
We have the system of equations:
[tex]\begin{gathered} 4x-2y=20 \\ -8x+4y=-40 \end{gathered}[/tex]We can tell that the equations are linear combination of each other: if we multiply the first equation by -2 we get the second equation.
[tex]\begin{gathered} -2(4x-2y)=-2(20) \\ -8x+4y=-40 \end{gathered}[/tex]So in fact we have only one equation and two unknowns, so there are infinite solutions to this system.
We can write the solution as:
[tex]\begin{gathered} 4x-2y=20 \\ 2y=20-4x \\ y=10-2x \\ y=-2x+10 \end{gathered}[/tex]Answer: the system has infinte solutions, expressed in the line y=-2x+10.
What concentration of mixture would need to be added to protect the cars engine from the coolant boiling away at 230 F
The mixture should be at a concentration of 65.5% to protect the cars from the coolant boiling away at 230°F .
The given table has the concentration percentages and the boiling points of the antifreeze.
So the coolant boils away at 230F, so we need to find the concertation whose boiling point is higher than 230F .
From the table it is evident that the boiling point of 236 is good to protect the coolant as it is higher and closest to the given temperature.
Corresponding to the temperature we have , the percentage at 65.5%.
As 236F > 230F , so it is evident that we need the concentration of 65.5%.
1. a break will be needed for the x axis.
2. The graph of the table is attached below.
the red line indicates 230F, so the value above it is the required data.
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If you vertically compress the absolute value parent function, f(x) = lxl, by afactor of 5, what is the equation of the new function?OA. g(x) = 51x|OB. g(x)=x-51OC. g(x) = 15x|O D. g(x) = x
When the parent function f(x) = |x| is vertically compressed by a factor of 5 then we get the transformed function as g(x) = 1/5 |x| .
The given function is of the form f(x) = ·|x| .
Therefore we can say that this function will be vertically compressed.
From the properties of transformation of graphs we know that when a function is vertically compressed by a factor of a we get the transformed function as 1/a times the original function.
given function:
f(x) = |x|
vertically compressed by 5.
therefore new function = 1/5 |x|
Hence the transformed function is g(x) .
g(x) = 1/5 |x|
Let us take a few coordinates along the x-axis to get the values of the y and the graph of both modulus function pass through origin .
f(x) = |x|
at x = 10 , f(x) = 10
and g(x) = 2
Here we see that the function is compressed.
Therefore when the parent function f(x) = |x| is vertically compressed by a factor of 5 then we get the transformed function as g(x) = 1/5 |x| .
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I need to determine the measure in degrees of arc BC??
ANSWER:
120°
STEP-BY-STEP EXPLANATION:
We must calculate the area of the circle, using the following formula:
[tex]\begin{gathered} A=\pi\cdot r^2 \\ \text{ replacing} \\ A=\pi\cdot9^2 \\ A=81\pi \end{gathered}[/tex]We know that this area represents 360 °, we know the area of ABC, therefore we can calculate the amount in degrees that it represents in the following way:
[tex]\begin{gathered} \frac{360}{81\pi}=\frac{x}{27\pi} \\ x=\frac{360\cdot27\pi}{81\pi} \\ x=120 \end{gathered}[/tex]Therefore, the value of arc BC is equal to the angle of area ABC, that is, the arc of BC is equal to 120°
m/4.5 = 2/5 Solve using scale factorI'm not sure how to use scale factor can you help me please?
[tex]\frac{m}{4.5}=\frac{2}{5}[/tex]
so, m will be calculated as following
find the relation between 4.5 and 5
so,
[tex]\frac{5}{4.5}=\frac{5\cdot10}{4.5\cdot10}=\frac{50}{45}=\frac{5\cdot10}{5\cdot9}=\frac{10}{9}[/tex]so, 5 divided by (10/9) will be equal 4.5
so,
m will be equal to 2 divided by (10/9) =
[tex]\frac{2}{\frac{10}{9}}=2\cdot\frac{9}{10}=\frac{18}{10}=\frac{9}{5}=1.8[/tex]This method is called scale factor
Which mean , we have used the scale factor (10/9) to get m/4.5 from 2/5
So, the answer is m = 1.8
Divide:7/4 ÷ 8/732/4949/3217/3281/32
7/4 ÷ 8/7
To divide fraction multiply the first fraction by the reciprocal of the second fraction:
7/4 x 7/8 = (7x7) / (4x8) = 49/32
How do I solve this and what is the answer
The speed of the vehicle is modeled by
[tex]y=9x+3[/tex]To find the initial value from the linaer function.
If x<0, then the velocity becomes negative. But velocity of a vehicle can not be negative.
Therefore x assumes greater than or equal to 0.
Putting x=0, the value of y is 3.
Therefore, the initial value is 3
Hence the correct answer is (C)
In the diagram shown, it is known that line RP upside-down T line QS and line RP bisects
Since we know that RP is perpendicular to QS we know that the bisector gives us two right triangles. Furthermore, the bisector divides by two the angle of 104, then the angle SRP is equal to 52°.
Now, we know that the interior angles of any triangle add to 180°. Therefore:
[tex]\begin{gathered} m\angle S+52+90=180 \\ m\angle S=180-52-90 \\ m\angle S=38 \end{gathered}[/tex]If a seed is planted, it has a 80% chance of growing into a healthy plant. If 8 seeds are planted, what is the probability that exactly 3 don't grow?
Given that a seed that is planted has an 80% chance of growing into a healthy plant, and knowing that you have to find the probability that exactly 3 seeds of 8 seeds planted don't grow, you need to use this Binomial Distribution Formula:
[tex]P(x)=\frac{n!}{(n-x)!x!}\cdot p^x(1-p)^{n-x}[/tex]Where "n" is the number of trials, "x" is the number of successes desired, and "p" is the probability of getting a success in one trial.
In this case, you can identify that:
[tex]p=100\text{\%}-80\text{\%}=20\text{\%}=0.20[/tex][tex]\begin{gathered} n=8 \\ x=3 \end{gathered}[/tex]Now you can substitute values into the formula and evaluate:
[tex]P(3)=(\frac{8!}{(8-3)!3!})(0.20)^3(1-0.20)^{8-3}[/tex][tex]P(3)=\frac{57344}{390625}\approx0.1468[/tex]Hence, the answer is:
[tex]P(3)\approx0.1468[/tex]you previously learned that a unit rate is a rate in which the second quantity in the comparison is one unit, such as 4 ounces per 1 serving. Describe the relationship between ounces of salsa and small jars of salsa using a unite rate.
Suppose there are 81 ounces of salsa in 9 small jars of salsa. To find the unit rate, you have to divide the number of ounces by the number of jars, as follows:
[tex]\frac{81\text{ ounces of salsa}}{9\text{ small jars}}=\frac{81}{9}\frac{\text{ounces of salsa}}{\text{small jars}}=9\text{ }\frac{\text{ounces of salsa}}{\text{small jar}}[/tex]That is, there are 9 ounces of salsa per small jar.
find the angle theta with 0°
0.16 whole number , integer, rational number (can be more than one set)
Answer : 0.16 is a rational number
Rational number is a number such that can be expressed as the quotient or fraction of two integers
An integer is a number that can be written without a fractional component
0. 16 can be written as
16 / 100
16 and 100 are both integers but 0.16 is not an integer but a rational number
16 / 100 = 0.16. This means that fraction of two integers that does does not gives an integer is a rational number
Hence, 0.16 is a ratioanal number
From the top of a high diving board to the bottom of a pool is 1,154 centimeters. If the pool is 244 centimeters deep, estimate the distance from the high diving board to the surface of the pool by rounding each number to the nearest hundred.
So, from the top of the diving board to the bottom of a pool is 1,154. If we subtract this from the depth of the pool, we'll find the distance from the diving board to the surface of the pool.
So, 1,154 - 244 = 910cm. About 9 meters, 900cm.
Also, if we round each number to the nearest hundred, we'll have
1,100 - 200 = 900 cm.
For the side length of 15ft 6ft and x which is it? the leg or hypotenuse they all have this option presented 2 you
Since the side length of 15ft is opposite the right angle, then this side length of 15ft is the hypotenuse of the triangle.
The other sides are considered the legs of the triangle. Therefore, the side length of 6ft is one of the legs of the triangle.
Find the angles using the diagram below. Line ris // to lines, and line tis I toline s.S3225045tm21= 2m22= 4m3= 5
To begin answering the question, let us familiarize ourselves with some basic terms
Linear Pairs: Two adjacent angles are a linear pair when their noncommon sides are opposite rays.
If you know the measure of one angle in a linear pair, you can find the measure of the other because the sum of the measure of the two angles is 180 degrees.
Vertical angles: Vertical angles are a pair of opposite angles formed by intersecting lines.
Vertical angles are equal.
We can now apply this knowledege to find the required angles
To find the measure of angle 1 (m<1)
[tex]\begin{gathered} m<1\text{ and 25}^0\text{ are linear pairs} \\ so\text{ they add up to 180}^0 \\ \end{gathered}[/tex]This means that
[tex]\begin{gathered} m<1+25^0=180^0 \\ m<1=180^0-25^0 \\ m<1=155^0 \end{gathered}[/tex]Thus, m<1 = 155°
To find the measure of angle 2 (m<2)
[tex]\begin{gathered} m<2\text{ and 25}^0\text{ are vertical angles} \\ \text{This means that they are equal} \end{gathered}[/tex]Hence,
[tex]m<2=25^0[/tex]m<2 =25°
To get the measure of angle 3 (m<3)
Given: Line t is perpendicular to s
Wehen two lines are perpendicular to eachother, they meet at right angle
This means that
[tex]m<3=90^0[/tex]Thus,
m<3=90°
Hence, the summary of the solution is shown below
[tex]\begin{gathered} m\angle1\Rightarrow155^0 \\ m\angle2\Rightarrow25^0 \\ m\angle3\Rightarrow90^0 \end{gathered}[/tex]At Paesano's Pizza, the price of a large pizza is determined by P = 9+ 1.5x, where x represents the number of toppings added to a cheese pizza. Donna spent $13.50 on a large pizza. How many toppings did she get?
Let's evaluate the function for:
[tex]P(x)=13.50[/tex][tex]\begin{gathered} 9+1.5x=13.5 \\ \text{Solving for x:} \\ \text{Subtract 9 from both sides:} \\ 9+1.5x-9=13.5-9 \\ 1.5x=4.5 \\ \text{Divide both sides by 1.5:} \\ \frac{1.5x}{1.5}=\frac{4.5}{1.5} \\ x=3 \end{gathered}[/tex]She get 3 toppings
Abby's dog ate 0.75kg of food per day for one week. How much food
did Abby's dog eat?
Answer:
5.25 kg
Step-by-step explanation:
0.75kgx7(1week)=5.25
Answer:
5.25kg of food
Step-by-step explanation:
Identify the 2 statements below that are false explain why each of those statements is false.
The graph of the given expression would be
According to the graph, the parabola is concave down, the vertex has an x-value of 3, the intercepts are (2,0) and (4,0).
Hence, the false statements are B and D.These statements are false because the x-value of the vertex is 3, and the GCF is -3.Please help me with this i just need the A,B,C or D please be super fast for 5 starts
One can notice that the two lines are not the same, nor they are parallel lines. Therefore, there is a unique solution to the system of equations. Graphically, the solution is the intersection of both lines; in this case,
[tex](-4,-3)[/tex]The answer is (-4,-3), the first option.
A: 502° CB: 6, 681° CC: 6, 135°CD: 47° C
The idea behind the problem is solving an equation involving square roots. The equation I'm talking about is
[tex]358=20\cdot\sqrt[]{273+t}[/tex](I merely replaced v by 358; what we are supposed to do is to find t). Let's solve it:
1. 20 is multiplying at the right-hand side, let's send it to divide at the left:
[tex]\frac{358}{20}=\sqrt[]{273+t}[/tex]2. (this is the most important step) Take the power of 2 on both sides:
[tex](\frac{358}{20})^2=273+t[/tex]...........................................................................................................................................................
Comment: Remember that
[tex](\sqrt[]{273+t})^2=273+t[/tex]because square root and powering by two are inverse of each other.
...........................................................................................................................................................
3. Put the left-hand side in a calculator to get:
[tex]\frac{128164}{400}=273+t[/tex]4. Let's subtract 273 to the left-hand side:
[tex]320.41-273=t[/tex][tex]47.41\degree C=t[/tex]
Find the volume of the circular cone picture below use 3.14 for pie. round your answer to the nearest whole number.
To find:
The volume of the circular cone whose height is 69 meters and the radius of the cone is 21 meters.
Solution:
The formula used to find the volume of the cylinder with height h and the radius r is given below:
[tex]V=\frac{1}{3}\pi r^2h[/tex]Fro the given question, h = 69 and r = 21. So, the volume of the cone is:
[tex]\begin{gathered} V=\frac{1}{3}\times3.14\times(21)^2\times69 \\ =31849.02m^3 \end{gathered}[/tex]Thus, the volume of the cone to neart
Which of the following is equal to the fraction below?(6)711O A. 7."44O B. 711411O O C. 11.00O D.D.7744
given the fraction
[tex](\frac{7}{4})^{11}[/tex]power properties
where
[tex](\frac{a}{b})^n=\frac{a^n}{b^n}[/tex]then
[tex](\frac{7}{4})^{11}=\frac{7^{11}}{4^{11}}[/tex]then te correct answer is option B