Distributive property:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]Multiplication of powers with the same base:
[tex]a^m\cdot a^n=a^{m+n}[/tex]For the given expression:
[tex]\begin{gathered} (x^2+3)(x^3-5)=x^2\cdot x^3+x^2\cdot(-5)+3\cdot x^3+3\cdot(-5) \\ \\ =x^{2+3}-5x^2+3x^3-15 \\ =x^5-5x^2+3x^3-15 \\ =x^5+3x^3-5x^2-15 \end{gathered}[/tex]Answer is the second option
What is the value of f(3) on the following graph?
Answer
f(3) = -2
Explanation
We are asked to find the value of f(3) from the graph.
This means we are looking for the value of f(x) or y on the graph, at a point where x = 3.
From the graph, we can see that at the point where x = 3, y = -2
Hence, f(3) = -2
Hope this Helps!!!
Solve the triangle: a = 25, C = 25, B = 25°. If it is not possible, say so.A=25*,b= 25, C = 250A=77.5*,b=10.8, C = 77.5eA=77.5', b = 24.1, C = 77.5This triangle is not solvable.
We will have the following:
First:
Since we have that sides a & c have the same length by theorem angles A & C are equal, so the following is true:
[tex]A+B+C=180\Rightarrow2A+B=180[/tex][tex]\Rightarrow2A=180-25\Rightarrow A=77.5[/tex]so, angles A & C have a measure of 77.5°.
*Second: We determine the measurement f the segment b, that is:
[tex]\frac{b}{\sin(25)}=\frac{25}{\sin(77.5)}\Rightarrow b=\frac{25\sin (25)}{\sin (77.5)}[/tex][tex]\Rightarrow b=10.8219807\Rightarrow b\approx10.8[/tex]So we will have that the measurements are:
A = 77.5°
b = 10.8
C = 77.5°
[Option B]
5. What is the range of the graph?8all real numbers{y 1-1 sys1)(XI-15x51){x | xs-1 or x 21)
The correct option is option D
For more comprehension,
Option D is :
[tex]undefined[/tex]can you help me on the part 2 Heads in a Row:
Given:
Flipping a coin twice.
Required:
We need to find the likelihood of flipping heads twice in a row.
Explanation:
The sample space = All possible outcomes.
The sample space, S= {TT,TH,HT,HH}
[tex]n(S)=4[/tex]Let A be the event of flipping heads twice..
The favorable outcomes = flipping heads twice.
The favorable outcomes ={HH}
[tex]n(A)=1[/tex]Consider the probability formula.
[tex]P(A)=\frac{n(A)}{n(S)}[/tex][tex]P(A)=\frac{1}{4}[/tex][tex]P(A)=0.25[/tex]The probability of flipping heads twice in a row is 0.25 which is a close value to the number 0.
This event happens least likely.
Final answer:
Flipping heads twice in a row is the least likely.
The probability of flipping heads twice in a row is 0.25.
find the value or measure. Assume all lines that appear to be tangent are tangent. mPM=
Segments that crosses around a circle
MN ^2 = OP • ON
mm
then 59° = (
Simplify the following sum of polynomials completely ( - 12s raise to power 2 + 10s - 3) + ( 2s raise to power 2 - 12s - 2)
ANSWER
[tex]-10s^2-2s-5[/tex]EXPLANATION
Given
[tex]\mleft(-12s^2+10s-3\mright)+\mleft(2s^2-12s-2\mright)[/tex]removing the brackets, we have;
[tex]-12s^2+10s-3+2s^2-12s-2[/tex]collecting like terms, we have
[tex]\begin{gathered} -12s^2+2s^2+10s-12s-3-2 \\ \end{gathered}[/tex]adding similar terms, we have;
[tex]-10s^2-2s-5[/tex]The solution is
[tex]-10s^2-2s-5[/tex]Question 6 What is the factored form of the expression below? 7 - 16 O OD (x-8)(x - 8) (x - 4)(x + 4) (x - 4)(x - 4) (x-8)(x + 8) Oo
If :
[tex]x^2-16[/tex][tex]\begin{gathered} \sqrt[]{x^2}=x \\ \sqrt[]{16}=4 \end{gathered}[/tex]Then:
[tex]x^2-16\text{ =(x-4)(x+4)}[/tex]Answer: ( x - 4 ) ( x + 4 )
Identify the minimum from the tableType your answer as an ordered pair (x,y)
By definition, a function is a relation in which each input value has one and only one output value.
The input values are also known as x-values and the output values are also called y-values.
By definition, the Minimum is the lower point of the function.
Having the table shown in the exercise, you can identify the following points:
[tex]\begin{gathered} (-2,10) \\ (-1,8) \\ (0,6) \\ (1,4) \end{gathered}[/tex]You can identify that the lower y-value of all those points is:
[tex]y=4[/tex]Therefore, you can determine that the lower point of the function is:
[tex](1,4)[/tex]The answer is:
[tex](1,4)[/tex]1) The weights of a particular group of show dogs are normally distributed with a mean of 16.6 kg and astandard deviation of 2.2 kg. If a random show dog is selected from the group, what is the probability thatit would weigh less than 15.5 kg?
In order to determine the probability, first use the followinf formula to calculate the Z factorr:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]where:
x: specific value from the data = 15.5 kg
σ: standard deviation = 2.2 kg
μ: mean = 16.6 kg
replace the previous values to find the Z factor:
[tex]Z=\frac{15.5\operatorname{kg}-16.6\operatorname{kg}}{2.2\operatorname{kg}}=0.5[/tex]Next, search the corresponding value of the probability in a table of Normal distribution.
The correspondinf value of the probability for Z = 0.5 is P = 19.15%
This can be noticed in the following graph.
1. Abby baked 2-dozen brownies. She took 1 dozen to her scout meeting. Her family ate 8, and she put the rest in a container in the refrigerator. How can Abby find the number of brownies left in the refrigerator?
The number of brownies left in the refrigerator is 4.
How to calculate the value?It's important to note that 1 dozen = 12
In this case, Abby baked 2-dozen brownies, she took 1 dozen to her scout meeting and her family ate 8, and she put the rest in a container in the refrigerator.
Therefore, the remaining amount will be:
= 2 dozens - 1. dozen - 8
= (2 × 12) - 12 - 8
= 24 - 12 - 8
= 4
There'll be 4 left. This illustrates the concept of subtraction.
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Look at the first Model It. In the first place-value chart, why is the thousandths column for the decimal 5.67 empty?
The thousandths column for the decimal 5.67 is empty because there's no thousandth value in the decimal.
What is a place value?Place value is the value provided by a digit in a number based on its place in the number. For example, 7 hundreds or 700 is the place value of 7 in 3,743. Place value is the value provided by a digit in a number based on its place in the number.
In this case, the decimal that's given is illustrated as 5.67. It should be noted that 6 is the tenths value and 7 is the hundredth value. Therefore, there is no thousandth value. This is why it's empty.
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Find the circumference of each circle .(use 22/7 as an approximation for PI
Let us find the circumference of each circle.
The circumference of a circle is given by
[tex]C=2\pi r\: \: or\: \: C=\pi D[/tex]Where r is the radius and D is the diameter of the circle.
Circle 1:
Here we are given the diameter of the circle
D = 21 cm
[tex]C=\pi D=\frac{22}{7}\cdot21=22\cdot3=66\operatorname{cm}[/tex]So, the circumference of the circle is 66 cm.
Circle 2:
Here we are given the diameter of the circle
D = 91 ft
[tex]C=\pi D=\frac{22}{7}\cdot91=286\: ft[/tex]So, the circumference of the circle is 286 ft.
Circle 3:
Which answer shows how to solve the given equation using the quadratic formula? 22 - 3. - 4= 0 3+, 22-4(2)(-4) 2(2) -(-3)=1/(-3)2-4(2)(-4) 2(2) 4+/(-3) -4(2)(-4) 2 3+1/32-4(-3)(-4) 2(2)
hello
the question here is a given quadratic equation and we're required to use quadratic formula to solve it.
[tex]2x^2-3x-4=0[/tex]now, to solve this, let's bring out quadratic formula first
[tex]x=-b\pm\frac{\sqrt[]{b^2-4ac}}{2a}[/tex]now from our equation given, we can easily identify a, b and c.
[tex]\begin{gathered} 2x^2-3x-4=0 \\ a=2 \\ b=-3 \\ c=-4 \end{gathered}[/tex]next we plug in the variables into the equation and solve
[tex]undefined[/tex]please help me work through this, thank you! it specifies to round to 2 decimal places
Since they will collide the time taken for both to reach the intersection is the same.
Let the time taken by t.
Recall that for steady motion,
[tex]\begin{gathered} d=st \\ \text{ Where:} \\ d=\text{ the distance covered} \\ s=\text{ the speed} \\ t=\text{ the time} \end{gathered}[/tex]Substitute d = 4 and s = 442 into the equation:
[tex]\begin{gathered} 4=442t \\ \text{ Dividing both sides by }442,\text{ it follows that:} \\ t=\frac{4}{442} \end{gathered}[/tex]Therefore, the distance covered by the Coyote in this time is given by:
[tex]d=\frac{4}{442}\times481=\frac{74}{17}[/tex]Using the Pythagorean Rule, it follows that the distance between Road Runner and the Coyote along the diagonal is given by:
[tex]h=\sqrt{(\frac{74}{17})^2+4^2}[/tex]Since speed s for a body that travelled distance d in time t is given by:
[tex]s=\frac{d}{t}[/tex]it follows that the required speed is given by:
[tex]-\sqrt{(\frac{74}{17})^2+4^2}\times\frac{442}{4}=-65\sqrt{101}[/tex]Therefore, the required rate is -65√101 kph.
what is the value of the expression below when w=2 8w+10
Given the expression:
8w + 10
To find the value when w = 2, we need to substitute 2 for w in the expression.
Therfore, we have:
[tex]8(2)\text{ + 10}[/tex][tex]16\text{ + 10 = 26}[/tex]Therefore, the value of the expression when w = 2 is 26
ANSWER:
26
What is the solution set of x² + 5x - 5 = 0?
The solution of x² + 5x - 5 = 0 is :
x = 0.854 and -5.854 .
Solution:
Here given equation,
x2 + 5x - 5 = 0
To solve the given equation use quadratic formula,
Using the quadratic formula,
x = [-b ± [tex]\sqrt{b2 - 4ac}[/tex] ] /2a
Here,
a = 1, b = 5 and c = -5
By substituting,
x = [-5 ± [tex]\sqrt{52 - 4(1)(-5)}[/tex] ] /2(1)
= [-5 ± √[tex]\sqrt{25 + 20}[/tex]] /2
= [-5 ± √45] /2
= [-5 ± 6.708] /2
So,
x = (-5 - 6.708)/2
= -11.708/2
= -5.854
= (-5 + 6.708)/2
= 1.708/2
= 0.854
∴ the solutions of equation is : 0.854 and -5.854.
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Any equation that can be rearranged in standard form as follows, where x stands for, is referred to be a quadratic equation in algebra.
What constitutes the x2 + 5x - 5 = 0 solution set?
We must figure out the equation's answer. The answers to the problem are thus 0.854 and -5.854. x^2 + 5x - 5 = 0
It is impossible to factor a quadratic equation like this one. It can be resolved either by completing the square or by applying the quadratic formula.
x = (-b +-sqrt(b2 - 4ac))/2a is the quadratic formula, where an is the coefficient of the x2, b is the coefficient of the x, and c is the constant.
a = 1, b = 5, c = -5
x = (-5 +- sqrt(25+20))/2
x = (-5 +- sqrt(45))/2
x = (-5 + - 3 sqt 5))/2
x = (-5 + 3sqrt5)/2 as well as x = (-5 - 3sqrt5)/2.
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In 2012 the total population of individuals in the
United States who were between 14 and 17 years old
(inclusive) was about 17 million. If the survey results
are used to estimate information about summer
employment of teenagers across the country, which
of the following is the best estimate of the total
number of individuals between 16 and 17 years old in
the United States who had a summer job in 2012?
Answer:
Its B I'm not to good at explaining but I've done my math
Step-by-step explanation:
and its b just trust me
What is the domain, range, and function? {(-3, 3), (1, 1), (0, -2), (1,4), (5, -1)}
The domain are all the inputs, that is; the x-values
Domain = { -3, 0, 1, 5}
The range are all the output, that is the y-values
Range = { 3, 1, -2, 4, -1}
This is just a relation and not a function, as we have more than 2 same value of x
Vernon mixed 2 1/3 cups of water with 2 1/3 of white vinegar to make a cleaning solution.how much cleaning solution did he make
SOLUTION
Write out the information given
[tex]\begin{gathered} \text{Quantity of water=2}\frac{1}{3}cups\text{ } \\ \\ \text{Quantity of white vinegar=2}\frac{1}{3}cups \end{gathered}[/tex]The quantity of the cleaning solution will the sum of the quantity above
The number model will be
[tex]2\frac{1}{3}cups+2\frac{1}{3}\text{cups }[/tex]Then
[tex]\begin{gathered} 2\frac{1}{3}+2\frac{1}{3}=2\times(2\frac{1}{3})=2\times(\frac{7}{3})=\frac{14}{3} \\ \text{then} \\ \frac{14}{3}=4\frac{2}{3} \end{gathered}[/tex]hence the cleaning solution will be
[tex]4\frac{2}{3}[/tex]Answer: 4 2/3
Graph v (standard position) and find its magnitude. Show all work.
EXPLANATION
[tex]\mathrm{Computing\: the\: Euclidean\: Length\: of\: a\: vector}\colon\quad \mleft|\mleft(x_1\: ,\: \: \ldots\: ,\: \: x_n\mright)\mright|=\sqrt{\sum_{i=1}^n\left|x_i\right|^2}[/tex][tex]=\sqrt{2^2+5^2}[/tex][tex]=\sqrt{4+5^2}[/tex][tex]=\sqrt{4+25}[/tex][tex]=\sqrt{29}[/tex]Now, we need to graph the vector as shown as follows:
The force of gravity is 6 times greater on the earth than it is on the moon. What is the weight of a 150-pound man on the moon?
The force of gravity on the Earth is equal to 9.8m/s².
Now, if the force of gravity on the moon is 6 times lesser than Earth's gravity.
Then,
The weight of a 150-pound man on the moon is:
150-pound/ 6
= 25-pounds
Hence, the weight of the man is 25-pounds
What is the answer and how do I solve this
A parent absolute value function f(x) = |x| is plotted as
We can change the appearance of this absolute value function based on what we add to the absolute value function and the constant accompanied by it.
Let's start with shifting the plot from |x| to |x+1|. If we add +1 to x inside an absolute value function, the parent absolute value function will shift one unit to the left. This shifting is represented by the red dotted plot on the figure below.
We now multiply a constant -3 on the absolute value function |x+1|. Multiplying a negative number to the absolute value function results in mirroring the absolute value function via the x-axis. Then, the plot will be compressed by a factor of 1/3. We now have
Hence, the final plot for the given absolute value function y = -3|x+1| is
For her phone service, Mai pays a monthly fee of $19, and she pays an additional $0.04 per minute of use. The least she has been charged in a month is$70.28. What are the possible numbers of minutes she has used her phone in a month?
We have a phone service fee which can be divided in:
- A fixed fee of $19 per month.
- A variable fee of $0.04 per minute, so that the cost for m minutes is 0.04*m.
We can add the two fees to express the total cost in function of the minutes as:
[tex]C(m)=19+0.04m[/tex]For a month where the cost is C(m) = 70.28, we can calculate the minutes as:
[tex]\begin{gathered} C(m)=70.28 \\ 19+0.04m=70.28 \\ 0.04m=70.28-19 \\ 0.04m=51.28 \\ m=\frac{51.28}{0.04} \\ m=1282 \end{gathered}[/tex]Answer: if she pays at least $70.28, she has talked at least m = 1282 minutes per month.
Convert each slope-intercept or point slope equation into standard form.
y - 3 = 1/5(x + 6)
The Standard form of the equation will be as x - 5y = -21
What is Standard form of equation?The standard form of the equation is defined as; Ax + By = C
Where, A, B and C are integers.
Given that the equation in slope - intercept form is;
⇒ y - 3 = 1/5 (x + 6)
Now,
We need to convert the equation in standard form as;
⇒ y - 3 = 1/5 (x + 6)
Now Change into standard form as;
⇒ y - 3 = 1/5 (x + 6)
Then Multiply by 5 both side, we get:
⇒ 5( y - 3) = (x + 6)
⇒ 5y - 15 = x + 6
⇒ 5y = x + 21
Now Subtract 21 both side, we get:
⇒ 5y - 21 = x + 21 - 21
⇒ 5y - 21 = x
⇒ - 21 = x - 5y
⇒ x - 5y = -21
Therefore,
The Standard form of the equation will be as x - 5y = -21
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Write a mathematical sentence that expresses the information given below. Use b as your variable name. If necessary:
type < = to mean
or > = to mean .
If you need to show multiplication, do not use the letter x. Use the asterisk ( * ) symbol instead, or simplify your answer.
Emily has 300 books. If Frank were to double the number of books that he now owns, he would still have fewer than Emily has.
The number of books owned by frank is represented as b < 150
What is inequality?Inequality represents the form of writing expressions where the left hand side of the expression is not exactly equal to the right hand side of the expression
How to represent the required expressionInformation gotten from the data include
Emily has 300 books
Frank were to double the number of books that he now owns, he would still have fewer than Emily has.
Let the number of books owned by frank be b and from the information we have that:
2b < 300
b < 150
hence the number of books owned by frank, b less than 150
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GRAPH each triangle and CLASSIFY the triangle according to its sides and angles.
Answer:
[tex]\Delta CAT\text{ is an ISOSCELES triangle}[/tex]Explanation:
To properly classify the traingle, we need to get the length of the sides
To get the length of the sides, we need to get the distance between each two points using the distance between two points formula
Mathematically,we have the formula as:
[tex]D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where (x1,y1) refers to the coordiantes of the first point while (x2,y2) refers to the coordinates of the second point
let us get the coordinates of the individual points as seen from the plot shown
C (1,8)
A (5,10)
T (7,6)
So, let us find the distance between each two points
For AC, we have:
[tex]D\text{ = }\sqrt[]{(5-1)^2+(10-8)^2}\text{ = }\sqrt[]{20}[/tex]For AT, we have:
[tex]D=\sqrt[]{(7-5)^2+(6-10)^2\text{ }}\text{ = }\sqrt[]{20}[/tex]Lastly, for CT, we have:
[tex]D\text{ = }\sqrt[]{(7-1)^2+(6-8)^2\text{ }}\text{ = }\sqrt[]{40}[/tex]From our calculations, we can see that AC = AT
If we have a triangle which has two of its sides equal in length (the angle facing these sides would be same too), we call this an isosceles triangle
So, the class of triangle CAT is isosceles triangle
It is question 16 pls help
Answer: yes it is 16 i did my work let me know if you want me to show my work
Step-by-step explanation:
Using f(x) = 2x - 3 and g(x) = 5, find f(g(3)).7530None of the choices are correct.I don’t think my answer is right please help me thank you
As per given by the question,
There are given that function,
[tex]\begin{gathered} f(x)=2x-3,\text{ } \\ g(x)=5 \end{gathered}[/tex]Now,
Find the value of f(g(3)).
Then,
There are given that,
[tex]g(x)=5[/tex]And,
According to question, value of x is 3, that means g(3).
So,
Put the value of x in g(x).
Then,
[tex]\begin{gathered} g(x)=5 \\ g(3)=5 \end{gathered}[/tex]Now,
For find the value f(g(3));
Put the value of g(3) in the above condition,
f(g(3)).
So,
[tex]f(x)=2x-3[/tex]Instead of x in f(x), put the g(3).
Then,
[tex]\begin{gathered} f(g(3))=2x-3 \\ f(5)=2\times5-3 \\ f(5)=10-3 \\ f(5)=7 \end{gathered}[/tex]So, the value of f(g(x)) is 7.
Hence, the option first is correct.
Number 14. Need help finding the area of the shaded area. Forgot how to solve it. Please help.
To find the area of the shaded region we need to calculate the area of the square and subtract to it the area of the circle.
The area of a square is calculated as follows:
[tex]A=b^2[/tex]where b is the length of each side.
Substituting with b = 16 cm (given that the radius of the circle is 8 cm, then the length of the square's side is 2x8 = 16 cm):
[tex]\begin{gathered} A_1=16^2 \\ A_1=256\operatorname{cm}^2 \end{gathered}[/tex]The area of a circle is calculated as follows:
[tex]A=\pi r^2[/tex]where r is the radius of the circle.
Substituting with r = 8 cm, we get:
[tex]\begin{gathered} A_2=\pi\cdot8^2 \\ A_2=\pi\cdot64 \\ A_2\approx201\operatorname{cm}^2 \end{gathered}[/tex]Finally, the area of the shaded region is:
[tex]\begin{gathered} A_3=A_1-A_2 \\ A_3=256-201 \\ A_3=55\operatorname{cm}^2 \end{gathered}[/tex]Graph a right triangle with the two points forming the hypotenuse. Using the sides,find the distance between the two points in simplest radical form.
Answer:
Explanation:
Given the points:
[tex](7,-5)\text{ and }(2,-7)[/tex]The graphed right triangle is given below:
Using the sides, we then find the distance between the two points, d.
By the Pythagorean theorem:
[tex]\begin{gathered} d^2=[5-(-7)]^2+[7-2]^2 \\ d^2=[5+7]^2+5^2 \\ d^2=12^2+5^2 \\ d^2=144+25 \\ d^2=169 \\ d^2=13^2 \\ \implies d=13 \end{gathered}[/tex]The distance between the two poi