The product of two expressions can be calculated using distributive property as,
[tex](2x^3y+5xy^4)(3x^2)=2x^3y\times3x^2+5xy^4\times3x^2[/tex](Distributive property (A+B)C=AC+BC) )
[tex]\begin{gathered} (2x^3y+5xy^4)(3x^2)=6x^{3+2}y+15x^{1+2}y^4 \\ =6x^5y+15x^3y^4 \end{gathered}[/tex]Therefore, the product of the expressions is,
[tex]6x^5y+15x^3y^4[/tex]Given the polynomial expression 3x2 + 3bx - 6x - 6b, factor completely.
(3x-6)(x - b)
(x-2)(x + b)
3(x-2)(x + b)
3(x + 2)(x + b)
The factors of the given polynomial is 3(x-2)(x+b). Therefore, option C is the correct answer.
The given polynomial expression is 3x² + 3bx - 6x - 6b.
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The factors of given polynomial can be find using grouping method, that is
(3x² + 3bx) - 6x - 6b
=3x(x+b)-6(x+b)
=(x+b)(3x-6)
=3(x-2)(x+b)
The factors of the given polynomial is 3(x-2)(x+b). Therefore, option C is the correct answer.
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Find the exact value by using ahalf-angle formula.[?] --cos 75°
Answer::
[tex]\cos 75\degree=\frac{\sqrt[]{2-\sqrt[]{3}}}{2}[/tex]Explanation:
By the half-angle formula:
[tex]\cos \mleft(\frac{\theta}{2}\mright)=\pm\sqrt[]{\frac{1+\cos\theta}{2}}[/tex]Let θ=150°, therefore:
[tex]\begin{gathered} \cos (\frac{150\degree}{2})=\sqrt[]{\frac{1+\cos150\degree}{2}} \\ \cos (150)\degree=-\cos (180\degree-150\degree)=-\cos 30\degree \\ \implies\cos (\frac{150\degree}{2})=\sqrt[]{\frac{1+\cos150\degree}{2}}=\sqrt[]{\frac{1-\cos30\degree}{2}} \end{gathered}[/tex]Now, cos 30 = √3/2, thus:
[tex]\begin{gathered} =\sqrt[]{\frac{1-\frac{\sqrt[]{3}}{2}}{2}} \\ \text{Multiply both the denominator and numerator by 2} \\ =\sqrt[]{\frac{2-\sqrt[]{3}}{4}} \\ =\frac{\sqrt{2-\sqrt[]{3}}}{\sqrt{4}} \end{gathered}[/tex]The exact value of cos 75° is:
[tex]\cos 75\degree=\frac{\sqrt[]{2-\sqrt[]{3}}}{2}[/tex]Solve the equation 20 +7k = 8(k + 2).
[tex]k=4[/tex].
Step-by-step explanation:1. Write the expression.[tex]20 +7k = 8(k + 2)[/tex]
2. Solve the parenthesis on the right hand side of the equation.[tex]20 +7k = 8k+16[/tex]
3. Subtract 20 from both sides of the equation.[tex]-20+20 +7k = 8k+16-20\\ \\7k = 8k-4[/tex]
4. Subtract 8k from both sides of the equation.[tex]7k-8k = 8k-4-8k\\ \\-k = -4[/tex]
5. Multiply both sides by "-1".[tex](-1)-k = -4(-1)\\ \\k=4[/tex]
6. Verify.[tex]20 +7(4) = 8((4) + 2)\\ \\20 +28 = 8(6)\\ \\48=48[/tex]
7. Express the result.[tex]k=4[/tex].
Answer:
k = 4
Step-by-step explanation:
a) Simplify both sides of the equation.
20 + 7k = 8(k + 2)
20 + 7k = (8)(k) + (8)(2)
20 + 7k = 8k + 16
7k + 20 = 8k + 16
b) Subtract 8k from both sides.
7k + 20 − 8k = 8k + 16 − 8k
−k + 20 = 16
c) Subtract 20 from both sides.
−k + 20 − 20 = 16 − 20
−k = −4
Divide both sides by -1.
-k/-1 = -4/-1
k = 4
5 A salesman sold $1,500 worth of
merchandise and received $75 in
commission for the sale.What percent of the sale was commission
Answer:20%
Step-by-step explanation:
1500/75=20(%)
Which expression shows 42+6 rewritten as a product of the greatest common factor and sum of two numbers with no common factor?
Answer:
7(1 + 6)
Step-by-step explanation:
the graph of each function is shown. write the function in factored form . do not include complex numbers
We can see from the picture that the function f(x) has roots in x = -5 and x = 5. Using sintetic division with x = 5, we get:
then, we can write the function as:
[tex]f(x)=(x-5)(2x^3+11x^2+8x+15)[/tex]since we know that another root is x = -5,we can use again the sintetic division on the right factor:
therefore, the function in factored form is:
[tex]f(x)=(x-5)(x+5)(2x^2+x+3)[/tex]What I need to know is that what is 3.5x2
Answer:
7
Step-by-step explanation:
Just add 3.5 twice which is the same as multiplying it by 2
Answer:
7
Step-by-step explanation:
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Find the domain and range of the function represented by the graph.
543
domain: -4 ≤ x ≤ 2.
O domain: -4 < x <2.
O domain: -4 ≤ x ≤ 4.
O domain: -4 <
2
range: -4 Sy≤4
range: -4
range: -4 Sy≤2
x < 4. range: -4
Answer:
c
Step-by-step explanation:
c
Write the fraction as a percent.34/100
Answer:
34%
Explanation:
To write the fraction as a percent we need to divide 34 by 100 and then multiply by 100%, so
34/100 x 100 = 0.34 x 100% = 34%
Therefore, 34/100 as a percent is 34%
Let Events A and B be described as follows:• P(A) = buying popcorn• P(B) = watching a movieThe probability that you watch a movie this weekend is 48% The probability of watching amovie this weekend and buying popcorn is 38%. If the probability of buying popcorn is 42%,are watching a movie and buying popcorn independent?
Solution:
Given that;
[tex]\begin{gathered} P(A)=42\%=0.42 \\ P(B)=48\%=0.48 \\ P(A\cap B)=38\%=0.38 \end{gathered}[/tex]To find out if watching a movie and buying a popcorn are independent, the formula is
[tex]\begin{gathered} P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0.38}{0.48}=0.79166 \\ P(A|B)=0.79\text{ \lparen two decimal places\rparen} \end{gathered}[/tex]From the deductions above;
Hence, the answer is
[tex]No,\text{ because }P(A|B)=0.79\text{ and the }P(A)=0.42\text{ are not equal}[/tex]I am stuck on the graphing portion of this question, would it be formatted like A or like B?
To determine which option is a representation of the graph we need to make the numer line analysis; to make it we need to notice that the functions has zeros at the points:
[tex]\begin{gathered} x=2 \\ x=4 \\ x=-3 \\ x=0 \end{gathered}[/tex]once we know this we divide the number line in the following intervals:
now we need check the sign of the function in each interval, to do this we choose a value in them.
For the first interval let's take x=-4, then we have:
[tex]\begin{gathered} f(-4)=-(-4)^3(-4-2)^2(-4-4)(-4+3) \\ f(-4)=-(-64)(36)(-8)(-1) \\ f(-4)=(64)(36)(8) \\ f(-4)=18432 \end{gathered}[/tex]From the last expression we notice that the value of the function is positive at this point. Hence the firts interval have positive values for the function.
For the second interval let's take x=-1, then we have:
[tex]\begin{gathered} f(-1)=-(-1)^3(-1-2)^2(-1-4)(-1+3) \\ f(-1)=-(-1)(9)(-5)(2) \\ f(-1)=-90 \end{gathered}[/tex]From the result we conclude that the function is negative in this interval.
For the third interval, let's take x=1, we have:
[tex]\begin{gathered} f(1)=-(1)^3(1-2)^2(1-4)(1+3) \\ f(1)=-(1)(1)(-3)(-4) \\ f(1)=12 \end{gathered}[/tex]From the result we conclude that the function is positive in this interval.
For the fourth interval, let's take x=3. then we have:
[tex]\begin{gathered} f(3)=-(3)^3(3-2)^2(3-4)(3+3) \\ f(3)=-(27)(1)(-1)(6) \\ f(3)=162 \end{gathered}[/tex]Then the function is positive in this interval.
Finally, for the fifth interval let's take x=5, then we have:
[tex]\begin{gathered} f(5)=-(5)^3(5-2)^2(5-4)(5+3) \\ f(5)=-(125)(9)(1)(8) \\ f(1)=-9000 \end{gathered}[/tex]Then the function is negative in the last interval.
Hence the line analysis is:
The y-intercept of the function happens when x=0, then we have that:
[tex]\begin{gathered} f(0)=-(0)^3(0-2)^2(0-4)(0+3) \\ f(0)=0 \end{gathered}[/tex]Therefore the y-intercept of the function is 0.
Once we know the information from the line analysis and the y-intercept of the function we conclude that the sketch of the graph is option B.
Two graphs of the function (with different values for the y-axis) are shown below:
This graphs confirm that option B is an approximate sketch of the graph.
11 ^ (5/16) + 4 ^ (1/16)
Answer:
3.20611579...
Step-by-step explanation:
What is the slope of the line through (-4,2) and (3, -3)? Choose 1 answer: А) 7 5 (В 7 5 5 7 1 D 5 7
slope = (change in y)/ change in x
[tex]undefined[/tex]The mean height of an adult giraffe is 19 feet. Suppose that the distribution is normally distributed with standard deviation 0.9 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(19,0.9)b. What is the median giraffe height? 19 ft.c. What is the Z-score for a giraffe that is 22 foot tall? d. What is the probability that a randomly selected giraffe will be shorter than 18.9 feet tall? e. What is the probability that a randomly selected giraffe will be between 19.6 and 20.1 feet tall? f. The 70th percentile for the height of giraffes is ft.
You are an apprentice plumber for Pointer Plumbing. You are earning an annual salary of $21,060. You are married and claim 3 allowances. What amount in withheld from your weekly pay for federal income tax?
If you are an apprentice plumber earning an annual salary of $21,060, and you lay claim to 3 allowances, the amount that will be withheld from your weekly pay for federal income tax is: $7.
How much will be witheld from your weekly pay?To obtain the correct amount to be paid, we need to use the table provided by the IRS. First note that there are 52 weeks in a year, so we need to divide your annual earnings by the total number of weeks in a year.
So, 21060/52 = $405
When we look at the table to see the chart for a person who has a weekly wage of 400 - 410, and lays claim to three allowances, we will see that the right amount that such an individual is meant to pay is $7.
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Find the x-and y-intercepts.21x + 3y = -63
to find the x intercept, we need to replace y by 0, so we get
[tex]\begin{gathered} 21x+3\cdot0=-63 \\ 21x=-63 \\ x=\frac{-63}{21}=-3 \end{gathered}[/tex]to find the y-intercept we need to replace x by 0
[tex]\begin{gathered} 21\cdot0+3y=-63 \\ 3y=-63 \\ y=\frac{-63}{3}=-21 \end{gathered}[/tex]the angle t is an acute angle and sin t and cost t are given. Use identities to find tan t , csc t, sec t, and cot t. where necessary, rationalize demonstrations.sin t= 7/25, cos t= 24/25
Answer:
tan t = 7/24
csc t = 25/7
sec t = 25/24
cot t = 24/7
Explanation:
From the question, we're told that sin t = 7/25 and cos t = 24/25. Since we know the identities of sine and cosine to be as follows we can go ahead and determine tan t as shown below;
[tex]\begin{gathered} \sin t=\frac{opposite}{\text{hypotenuse}}=\frac{7}{25} \\ \cos t=\frac{adjacent}{\text{hypotenuse}}=\frac{24}{25} \\ \therefore\tan t=\frac{opposite}{\text{adjacent}}=\frac{7}{24} \end{gathered}[/tex]Let's go ahead and find cosecant t (csc t);
[tex]\csc t=\frac{1}{\sin t}=\frac{1}{\frac{7}{25}}=1\times\frac{25}{7}=\frac{25}{7}[/tex]For sec t, we'll have;
[tex]\sec t=\frac{1}{\cos t}=\frac{1}{\frac{24}{25}}=1\times\frac{25}{24}=\frac{25}{24}[/tex]For cot t;
[tex]\cot t=\frac{1}{\tan t}=\frac{1}{\frac{7}{24}}=1\times\frac{24}{7}=\frac{24}{7}[/tex]How many gallons of a 60% antifreeze solution must be mixed with 80 gallons of 20% antifreeze to get a mixture that is 50% antifreeze?
Given
gallons which have 20% antifreeze solution = 80
Final concentration = 50% antifreeze solution
Find
Number of galloons with 60% antifreeze solution
Explanation
Let the number of gallons with 60% antifreeze solution = x
According to question
0.6x+0.2(80) = 0.50(x+80)
0.6x+16=0.5x+40
0.1x=24
x=240
Final Answer
Hence 240 gallons of 60% antifreeze solution will be required
17. What is the value of x in the rhombusbelow?AC(x+ 40)B3x⁰D
ANSWER
x = 35 degrees
EXPLANATION
Given tthat
[tex]\begin{gathered} \text{ m Follow the steps below to find the value of xRecall, that the sum of m[tex]\text{ m < C + m Therefore, x is 35 degrees
In 2016, there were 35,867 burger restaurants worldwide, with 13,232 of them located in a country. Determine the percent of burger restaurants in that country in 2016Approximately what percent ?
we have that
35,867 ------> represents 100%
Applying proportion
Find out how much percentage represents 13,232
100/35,867=x/13,232
solve for x
x=(100/35,867)*13,232
x=36.89% ------> 37%
in the diagram below AD||EH I=54 and FBC=44. find CGH
Given,
angle I = 54 degrees
angle FBC = 44 degrees
Recall, the sum of the angles in a triangle is 180 degrees. This means that for triangle BIC,
angle B + angle I + angle BCI = 180 degrees
54 + 44 + angle BCI = 180
angle BCI + 98 = 180
angle BCI = 180 - 98 = 82(sum of angles in a triangle)
Since lines AD and EH are parallel,
angle BCI and angle FGI are corresponding angles(They have similar positions and lie on the same side of the transversal, CI)
Thus,
angle FGI = 82(corresponding angles)
angle CGH and angle
angle CGH and angle FGI are vertically opposite angles. Vertically opposite angles are equal. Thus,
angle CGH = 82 degrees
The reason is 'vertically opposite angles'
Write the equation in standard form for the circle passing through (2,3) centered at the origin
Given
coordinates (2, 3) and centre points (0,0)
Find
Equation of a circle
Explanation
As we know the standard equation for a circle with centre (h , k ) and r is a radius
[tex](x-h)^2+(y-k)^2=r^2[/tex]since, center is (0 , 0) , the equation becomes
[tex]x^2+y^2=r^2[/tex]Now, we find the value of radius , it is can find by using the pythagoras theorem,
[tex]r^2=2^2+3^2=4+9=13[/tex]so,
[tex]x^2+y^2=13[/tex]Final Answer
The equation for a circle passing through (2, 3) is
[tex]x^2+y^2=13[/tex]Create a graph system of linear equations that model this situation.
x represents the number of packages of coffee sold
y represents the number of packages of pastry sold
We were the cost of a package of coffee is $6 and the cost of a package of pastry is $4. If the total amount made from selling x packages of coffee and y packages of pastry is $72, then the equation representing this scenario is
6x + 4y = 72
Also, we were told that she sold 2 more packages of coffee than pastries. This means that
x = y + 2
Thus, the system of linear equations is
6x + 4y = 72
x = y + 2
We would plot these equations on the graph. The graph is shown below
The red line represents x = y + 2
The bu line represents x = y + 2
P(6,23), Q (13,28)
Distance=?
Midpoint=?
Answer:
Step-by-step explanation:
distance between the two points:
[tex]\sqrt{ (x_2-x_1)^{2} +(y_2-y_1)^2[/tex]
[tex]\sqrt[/tex](13-6)²+(28-23)²
√(7)²+(5)²
√49+25
√74
distance: 8.6cm
midpoint=
[tex](\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )[/tex]
(6+3/2,23+28/2)
(19/2,51/2)
(9.5,25.5)
Choose all equivalent expression ( s). (4) ^ (3z ^ 2); (4) ^ (- 3x ^ 2); (1/4) ^ (3z ^ 2); (pi/4) ^ (3x)
Among the given options, no one is an equivalent expression.
What is an equivalent expression?
Expressions are said to be equivalent if they do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
In the given options no one satisfies the property of an equivalent expression.
Therefore, among the given options, no one is an equivalent expression.
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Why is a third-degree polynomial function with a negative leading coefficient not appropriate for modeling non-negative real-world phenomena over a long period of time?
Given:
A third-degree polynomial function with a negative leading coefficient not appropriate for modeling non-negative real-world phenomena over a long period of time.
Explanation:
Because a third-degree polynomial function with a negative leading coefficient is always going to turn negative as the independent variable increases.
That is, the end behavior of the graph will always be negative on the right.
Final Answer:
Because a third-degree polynomial function with a negative leading coefficient is always going to turn negative as the independent variable increases.
That is, the end behavior of the graph will always be negative on the right.
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately
σ
=
50.2
. You would like to be 90% confident that your estimate is within 1.5 of the true population mean. How large of a sample size is required?
Using the sample size relation with the standard normal distribution, the required sample size is 3032 samples.
What is Normal distribution ?
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Using the sample size relation with the standard normal distribution, the required sample size is 673 samples.
n = [(Z* × σ) / ME]²
ME = margin of error
Z* = Z critical at 90% = 1.645
Substituting the values into the equation :
n = [(Z* × σ) / ME]²
n = [(1.645 × 50.2) / 1.5]²
n = (82.6/ 1.5)²
n = 55.06
n ≈ 3032
Therefore, the Number of samples required is 3032 samples.
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Graph this steph function on the coordinate grid please help I don’t understand!
Given:
[tex]f(x)=\begin{cases}{-5\text{ }if\text{ }-5Required:
We need to graph the given step function.
Explanation:
From the given data we have, -5,-1, and 2 are the respective values of y.
[tex]-5The draw annulus to denote the points do not lie on the line since there is a symbol '<'.
Final answer:
The next model of a sports car will cost 11.5% less than the current model. The current model costs $59,000. How much will theprice decrease in dollars? What will be the price of the next model?
we are given that a car cost $ 59000 and the price will decrease by 11.56%, therefore, the amount it will decrease is equivalent to:
[tex]59000\times\frac{11.56}{100}=6820.4[/tex]Therefore, the price will decrease by $6820.4. The total price will be then:
[tex]59000-6820.4=52179.6[/tex]Therefore, the price will be $52179.6
The first three terms of a sequence are
given. Round to the nearest thousandth
(if necessary).
4, 8, 12,..
Find the 40th term
Answer:
Step-by-step explanation:
Recall the formula for an arithmetic sequence: [tex]a_{n} =a_{1} +d(n-1)[/tex]
Where d is the common difference and a_1 is the first term of the sequence.
You are given :
a_1=4
a_2=8
a_3=12
Next is to find the common difference d.
To find the common difference, take the next term and subtract it from the current term.
a_2-a_1=8-4=4
Let try the next term start at a_2
a_3-a_2=12-8 =4
Do you see the pattern?
The patter is going up by 4 each time. So the common difference is 4 i.e d=4
Now we just need to plug into the generalize formula above and get
[tex]a_{n}=4+4(n-1)[/tex]
The question asked for the 40th term. Plug 40 into the formula and you will get:
[tex]a_{40}=4+4(40-1)=160[/tex]
I hope this helps!