1. For what equation is x = 5 a solution?
A 2 + x = 3
C X/2 10
B 3x = 15
D x - 7 = 12
Answers
Related Questions
Please help!! I am terrible at math and I cannot fail this class!!
Answers
Don't worry, just write it out.
\($\frac{15xy^7z^4}{5x^6yz^{16}} = \frac{15}5 \cdot \frac x{x \cdot x \cdot x \cdot x \cdot x \cdot x} \cdot \frac{y \cdot y \cdot y\cdot y\cdot y \cdot y \cdot y}{y} \cdot \frac{z^4}{z^{16}}$\)
Note that the top x cancels with one of the bottom x's, and on the other fraction, the bottom y cancels with one of the top y's. For the z's, using the same reasoning, the four z's on the top cancel with four on the bottom, leaving 16 - 4 = 12 z's on the bottom. So you get
\($3 \cdot \frac1{x \cdot x \cdot x\cdot x\cdot x} \cdot (y \cdot y \cdot y \cdot y \cdot y \cdot y) \cdot \frac 1{z^{12}}$\)
which is
\($3 \cdot \frac1{x^5} \cdot y^6 \cdot \frac 1{z^{12}}$\)
\($= \boxed{\textbf{D) }\frac{3y^6}{x^5z^{12}}}$\)
Given: Circle O with diameter CDC (-7, -1) and D (1,2)Create the equation of this circle,+-:: (2+3):: (y – 1):: (y + 1):: 25:: 100
Answers
Explanation
The equation of a circle with center (h,k) and radius r units is given by:
\((x-h)^2+(y-k)^2=r^2\)then
Step 1
find the diameter of the cirlce:
to do this, we can use the distance between two points formula:
if
\(\begin{gathered} A\mleft(x_1,y_1\mright) \\ B(x_2,y_2) \end{gathered}\)the distance from A to B is
\(\begin{gathered} d_{AB}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \end{gathered}\)so,let
distance CD=
\(\begin{gathered} CD=\sqrt[]{(1-(-7))^2+(2-(-4))^2} \\ CD=\sqrt[]{(8)^2+(6)^2} \\ CD=\sqrt[]{64+36} \\ CD=\sqrt[]{100} \\ CD=10 \end{gathered}\)hence, the diameter of the circle is
\(\begin{gathered} \text{diameter}=10 \\ w\text{e know also} \\ \text{diameter}=2\cdot\text{raidus} \\ \frac{\text{diamteter}}{2}=radius \\ \text{replace} \\ \frac{10}{2}=\text{ radius} \\ \text{radius}=5 \end{gathered}\)Step 2
find the center of the circle:
the center of the circle is the midpoint of CD
so
\(\text{midpoint}=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)replace
\(\begin{gathered} \text{midpoint}=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \text{midpoint}=(\frac{-7+1}{2},\frac{-4+2_{}}{2}) \\ \text{midpoint}=(\frac{-6}{2},\frac{-2}{2}) \\ \text{midpoint}=(-3,-1) \\ \end{gathered}\)so, the center of the circle is (-3,-1)
Step 3
finally, replace in the formula to get the equation of the circle
let
\(\begin{gathered} center=\mleft(-3,-1\mright) \\ radius=5 \end{gathered}\)replace
\(\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (x-(-3))^2+(y-(-1))^2=5^2 \\ (x+3)^2+(y+1)^2=25 \end{gathered}\)therefore, the answer is
\((x+3)^2+(y+1)^2=25\)I hope this helps you
8th grade math, please help.
Answers
Answer:
140 degrees
Step-by-step explanation:
because they're congruent
what is 7.5% of 180 dollars? please provide step by step answer
Answers
Answer:
13.5
Step-by-step explanation:
7.5 percent *180=
(7.5:100)*180=
(7.5*180):100=
1350:100= 13.5
Moussa decides to estimate the volume of a coffee cup by modeling it as a right cylinder. He measures its height as 7.7 cm and its radius as 3.2 cm. Find the volume of the cup in cubic centimeters. Round your answer to the nearest tenth if necessary.
Answers
Answer:
247.7 cm³
Step-by-step explanation:
V = πr²h
V = 3.14159 × (3.2 cm)² × 7.7 cm
V = 247.70808 cm³
Answer: 247.7 cm³
What is the complete factorization of the polynomial below?
O A. (x+2)(x+)(**)
OB. (x-2)(x+)(x-)
C. (x-2)(x+)(x+1)
OD. (x+2)(x+1)(x-1)
Answers
The complete factorization of the polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)
What is an equation?
An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.
A polynomial is an expression consisting of coefficients and variables forming an equation.
Given the polynomial:
x³ + 2x² -x - 2
Factorizing:
= (x + 2)(x² - 1)
= (x + 2)(x + 1)(x - 1)
The polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)
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Find the value of , and in the identity
+ 5 − + 4 ≡ 2 2 + − 10
Find the value of and in the identity
4 3 + + 5 + ≡ 22 + 28
Answers
y = 10x + 8 in the second identity. Substituting this into the equation:4(3x + 5) + 10x + 8 ≡ 22x + 28. Simplifying: 22x + 28 ≡ 22x + 28.
This equation is true for all values of x, so there are infinite solutions.
What is an equation?A mathematical statement that affirms the equality of two expressions, usually separated by an equal sign, is recognized as an equation. In other words, an equation is a statement that two expressions are the same.
Equations can be used to solve problems, find unknown values, or describe relationships between quantities.
To find the values of x and y in the first identity:
x + 5 − y + 4 ≡ 2(2x + y) − 10
Simplifying the left-hand side:
x + 5 − y + 4 = x + y + 9
Substituting this into the original equation:
x + y + 9 ≡ 2(2x + y) − 10
Expanding the right-hand side:
x + y + 9 ≡ 4x + 2y - 10
Simplifying the right-hand side:
x + y + 9 = 4x + 2y - 10
Solving for x:
3x = -19
x = -19/3
Substituting this into the original equation and solving for y:
-19/3 + y + 9 - y + 4 ≡ 2(2(-19/3) + y) − 10
-5/3 ≡ -38/3 + 2y - 10
-5/3 ≡ -48/3 + 2y
43/3 ≡ 2y
y = 43/6
Therefore, x = -19/3 and y = 43/6 in the first identity.
To find the values of x and y in the second identity:
4(3x + 5) + y ≡ 22x + 28
Expanding the left-hand side:
12x + 20 + y ≡ 22x + 28
Simplifying:
y - 10x ≡ 8
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Which polynomials are in standard form?
Choose all answers that apply:
А
5 - 2x
B
24 – 8x2 – 16
523 + 4x4 – 3x + 1
D
None of the above
Answers
The point stated to prove this point is:
Brady has $20,000 in student loans with 3.3% interest that he plans to pay off in 5 years. Find the total cost of repayment.
Answers
The total cost of repayment over 5 years is $23,300.
What is the total cost of repayment?A loan repayment refers to the act of paying back money previously borrowed from a lender.
To get total cost of repayment, we must principal amount, the interest rate and the duration of the loan.
The formula to get total cost of repayment is given by \(Total Cost of Repayment = Principal + Interest\)
Interest = Principal * Interest Rate * Time
Given:
Principal amount is $20,000
Interest rate is 3.3%
Duration is 5 years.
Interest = $20,000 * 0.033 * 5
Interest = $3,300
Total Cost of Repayment = Principal + Interest
= $20,000 + $3,300
= $23,300.
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i need help with my homework please check work when done I NEED HELP WITH THE QUESTION IN BLUE
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Amount invested by Katelyn = $4000
rate = x%
time = x + 2 years
n = number of times compounded
n = annually = 1
We need to find the function that models the total amount
To find the function, we will apply the compound interest formula:
\(\begin{gathered} $$FV\text{ = P(1 +}\frac{r}{n})^{nt}$$ \\ \\ P\text{ = 4000} \\ t\text{ = x + 2} \\ n\text{ = 1} \\ \text{ r = x\% = x/100} \\ FV=\text{ total amount } \end{gathered}\)substitute the values into the formula:
\(\begin{gathered} FV=\text{ 4000\lparen 1 + }\frac{\frac{x}{100}}{1})^{1\times(x\text{ + 2\rparen}} \\ \\ FV=\text{ 4000\lparen1 + }\frac{x}{100})^{x+2} \end{gathered}\)\(FV=\text{ 4,000\lparen}\frac{100+\text{ }x}{100})^{x\text{ +2}}\text{ }\)let the function that represents the total amount = f(x)
\(f(x)=\text{ 4000\lparen}\frac{\text{ }x+\text{ 100}}{100})^{x\text{ +2}}\text{ }\)Find k such that the line y = 3x+3 is tangent to the graph of the function below.
Find \( k such that the line \( y=3 x+3 is tangent to the graph of the function below. \[ y=k \sqrt{x} \] \( k= "
Answers
The value of \( k \) that makes the line \( y = 3x + 3 \) tangent to the graph of the function \( y = k\sqrt{x} \) is 0.
To find the value of \( k \) such that the line \( y = 3x + 3 \) is tangent to the graph of the function \( y = k\sqrt{x} \), we need to set the slopes of the two functions equal to each other.
The slope of the line \( y = 3x + 3 \) is simply the coefficient of \( x \), which is 3.
To find the slope of the function \( y = k\sqrt{x} \), we can differentiate it with respect to \( x \). Applying the power rule, we get:
\[ \frac{dy}{dx} = \frac{k}{2\sqrt{x}} \]
For the line and the function to be tangent, their slopes should be equal. So we can set:
\[ 3 = \frac{k}{2\sqrt{x}} \]
We want to find \( k \), so let's solve this equation for \( k \). We can start by squaring both sides to eliminate the square root:
\[ 9 = \frac{k^2}{4x} \]
Multiplying both sides by 4x, we have:
\[ 36x = k^2 \]
Now, we can solve this equation for \( k \) by taking the square root of both sides:
\[ k = \sqrt{36x} \]
We want to find the value of \( k \) such that the line is tangent, which means it touches the curve at a single point. In this case, the line will be tangent when the discriminant of the quadratic equation is zero.
\[ 36x = 0 \Rightarrow x = 0 \]
Substituting this value of \( x \) back into the equation for \( k \), we get:
\[ k = \sqrt{36 \times 0} = \sqrt{0} = 0 \]
Therefore, for the line \( y = 3x + 3 \) to be tangent to the graph of the function \( y = k\sqrt{x} \), the value of \( k \) is 0.
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What are the first 10 digits after the decimal point when the fraction $\frac17$ is written in base 16?
Answers
Answer:
The amswer is "2,4,9....."
Step-by-step explanation:
\(x=\frac{1}{7}\\\\x_d=0.\overline{142857}\\\\x_h=0.\overline{249}\\\\\)
by leave you to work out the other 7 digits:
\(\to \frac{1}{7}\approx \frac{a}{16}\\\\a= \text{first hex digit}\\\\a=floor(\frac{16}{7})=2\\\\\)
\(\to \frac{1}{7}- \frac{a}{16}\approx \frac{b}{16^2}\\\\b= \text{second hex digit}\\\\b=floor(\frac{16^2}{7} -16a)=4\\\\\)
\(\to \frac{1}{7}- \frac{a}{16}-\frac{b}{16^2} \approx \frac{c}{16^3}\\\\c= \text{third hex digit}\\\\c=floor(\frac{16^3}{7} -16^2a-16b)=9\\\\\)
Discuss how well you data on resistivity (obtained based on the Eqn. 3) agrees with the given values. Discuss the sources of experimental error.
Eqn.3) rho = (slope)A = (slope)Ï(d/2)2
Answers
Based on the equation 3, the data on resistivity agrees well with the given values. However, there may be some sources of experimental error that can affect the accuracy of the data. These sources of error which include Measurement, Human, Random errors.
1. Measurement errors: These can occur due to the inaccuracy of the measuring instruments used in the experiment. For example, if the instrument used to measure the slope is not calibrated correctly, it can lead to inaccurate results.
2. Human errors: These can occur due to the mistakes made by the experimenter. For example, if the experimenter does not read the measurements correctly, it can lead to inaccurate results.
3. Random errors: These can occur due to the uncontrollable factors that can affect the experiment. For example, if there is a change in temperature during the experiment, it can affect the resistivity of the material.
Overall, it is important to consider these sources of experimental error in order to obtain accurate data on resistivity.
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2. The Population of Brownsville is 20,000 in year 2010. Using the function P(t)= (20,000) (1.15)
what is the population in 2012?
Answers
Given:
The Population of Brownsville is 20,000 in year 2010.
Consider the population function
\(P(t)=20000(1.15)^t\)
To find:
The population in 2012.
Solution:
The population function of Brownsville is
\(P(t)=20000(1.15)^t\)
The Population of Brownsville is 20,000 in year 2010.
So, the given function P(t) represents the population of Brownsville after t years of 2010.
2012 is 2 years after 2010.
Putting t=2 in P(t), we get
\(P(2)=20000(1.15)^2\)
\(P(2)=20000(1.3225)\)
\(P(2)=26450\)
Therefore, the Population of Brownsville is 26,450 in year 2012.
Analyze the expression and then choose the sentences describing whether the binomial theorem can be used to factor it. Check all that apply.
x^3 – 24x^2 + 192x – 512
A.) The value of n is 3, and the first and last terms are perfect cubes.
B.) The middle terms do not take into account the coefficients from Pascal’s triangle.
C.) The exponents on each term follow the pattern for a binomial expansion.
D.) The sign of the constant must be positive in the binomial expansion. The signs are all reversed.
E.) The expression can be factored using the binomial theorem.
F.) The expression cannot be factored using the binomial theorem.
Answers
Answer:
-The middle terms do not take into account the coefficients from Pascal’s triangle.
-The exponents on each term follow the pattern for a binomial expansion.
-The expression cannot be factored using the binomial theorem.
The statements that apply for the expression are A , D and E
What is Binomial Theorem ?Binomial theorem explains how to expand the algebraic statement (x + y)ⁿ to a sum of terms using individual exponents of variables x and y.
The expression given is
x³ – 24x² + 192x – 512
as the first and the last term is a perfect cube
In general (a-b)³ = a³ - 3a²b +3ab²-b³
here a = x and b = 8
(x-8)³ = x³ +3 *x*8² -3 *8*x² -8³
(x-8)³ = x³ – 24x² + 192x – 512
Therefore it can be factorized using Binomial Theorem , n = 3 and the factors follow the rule for binomial expansion so the statements that are correct are A , C and E
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The graph of $f(x)$ is shown below.
For each point $(a,b)$ on the graph of $y = f(x),$ the point $\left( 3a - 1, \frac{b}{2} \right)$ is plotted to form the graph of another function $y = g(x).$ For example, $(0,2)$ lies on the graph of $y = f(x),$ so $(3 \cdot 0 - 1, 2/2) = (-1,1)$ lies on the graph of $y = g(x).$
(a) Plot the graph of $y = g(x).$ Include the diagram in your solution.
(b) Express $g(x)$ in terms of $f(x).$
(c) Describe the transformations that you would apply to the graph of $y = f(x)$ to obtain the graph of $y = g(x).$ For example, one transformation might be to stretch the graph horizontally by a factor of $5.$
Answers
Answer:
See attached
Step-by-step explanation:
The graph of both f(x) and g(x) attached
g(x) obtained from f(x) by x→ 3x - 1 and y → y/2 transformation rule
The transformation to get g(x) would be:
Vertical compression by a factor of 2Horizontal shrink by a factor of 3f(x) is the blue graph
g(x) is the red graph
Answer:
Step-by-step explanation:
ask the message board ! :)
the length of a rectangle is 15 cm more than the width. a second rectangle whose perimeter is 72 cm is 5cm wideer but 2cm shorter than the first rectangle. what are the dimensios of each rectangle?
Answers
the dimensions of each rectangle is 72.
What is perimeter?In geometry, a shape's perimeter is referred to as its total length. The perimeter of a form is determined by adding up the lengths of all of its sides and edges. Linear measurements like centimeters, meters, inches, and feet are used to indicate its dimensions.
EXPLANATION :
The length of a rectangle is 15 cm more than its width.
L - W = 15
Compared to the first rectangle, which has a circumference of 72 cm, the second is 2 cm smaller and 5 cm wider.
2(L-2) + 2(W+5) = 72
Simplify to get 36 L + W + 3 and 36 L + W, which equals 33 by multiplying L - 2 + W + 5 by 2.
Here, combine the two equations and apply elimination.
L - W = 15 \sL + W = 33
Using the initial length, L 2L = 48 L = 24 cm, we may find W = 24 - 15 W = 9 cm, so removing W. Second rectangle width: initial width 24 - 2 = 22 cm; second rectangle length: 9 + 5 = 14 cm.
Calculate the second rectangle's perimeter using the following equation: 2(22) + 2(14) = 44 + 28 = 72
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I need help with something maybe if I can send a picture of it it will be easier
Answers
Answer:
sure send it and I will do my best to help you..
calculate the correlation coefficient between X and Y
for:
the translate for the last sentence is: 0
otherwise
Answers
The correlation coefficient (r) can be calculated by using the following formula: r = (nΣXY - (ΣX)(ΣY)) / sqrt((nΣX² - (ΣX)²)(nΣY² - (ΣY)²))where X and Y are the variables, n is the number of observations, ΣXY is the sum of the products of paired scores, ΣX is the sum of X scores, ΣY is the sum of Y scores, ΣX² is the sum of squared X scores, and ΣY² is the sum of squared Y scores.
Given the value, it is mentioned that X and Y are uncorrelated.
The formula to calculate the correlation coefficient is:r = (nΣXY - (ΣX)(ΣY)) / sqrt((nΣX² - (ΣX)²)(nΣY² - (ΣY)²))where X and Y are the variables, n is the number of observations, ΣXY is the sum of the products of paired scores, ΣX is the sum of X scores, ΣY is the sum of Y scores, ΣX² is the sum of squared X scores, and ΣY² is the sum of squared Y scores.
When X and Y are uncorrelated, it means that the covariance between the two is zero, which means ΣXY = 0.
Using this information in the formula for correlation coefficient, we get:r = 0 / sqrt((nΣX² - (ΣX)²)(nΣY² - (ΣY)²))This simplifies to r = 0.
Summary:Thus, the correlation coefficient between X and Y is 0 when X and Y are uncorrelated.
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Solve for x, worth 10 points
Answers
Answer: x=22
Step-by-step explanation:
Since the angles are corresponding angles, use x+14=5x-74. You get 36=36 meaning it is right when you substitute the value for x.
x+14=5x-74
-x on both sides
14=4x-74
+74 on both sides
88=4x
Divide both sides by 4
x=22
the graphs below represent four polynomial functions which one of these functions has zeros of 2 and 3
Answers
The curve is passing through (0, 2) and (0, -3).
The zeroes of the polynomial function are 2 and -3.
The number of zeroes is 2. Then the degree of the polynomial will be 2. So, the function is a quadratic function.
The zeroes of the function represent the x-intercepts. Then the curve is passing through (0, 2) and (0, -3).
Thus, the correct option is B.
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The residents of a clty voted on whether to raise property taxes. The ratio of yes votes to no votes was 3 to 2. If there were 2570 total votes, how many yes votes were there?
Answers
There were 1542 yes votes
Explanation:Parameters:
Total votes = 2570
Ratio of yes votes to no votes = 3:2
Sum of ratios = 3 + 2 = 5
The given statement means if 2570 was divided into 5, yes votes take 3 part of the votes, and no votes take the remaining 2.
So
Yes Votes = (3/5)*2570
= 1542
No Votes = (2/5)*2570
= 1028
what are the 2 clsest integers to 300
Answers
Answer:
299 and 301
Step-by-step explanation:
An integer is colloquially defined as a number that can be written without a fractional component.
Therefore the two closest integers to 300 are 299 and 301.
Use this graph to answer the following two questions.
Answers
Can someone help me with this I do not know where to start.
Answers
Answer:
Try and start at the line?
Step-by-step explanation:
Cynthia invests some money in a bank which pays
5% compound interest per year
She wants it to be worth over £8000 at the end of 3 years
What is the smallest amount, to the nearest pound, she can invest?
Answers
Answer:
£1200
Step-by-step explanation:
£8000 divide by 5% = 400
£400 times 3 = £1200
Help yalll I really need help major time
Answers
Answer:
Annalise is correct because the outputs are closest when x = 1.35
Step-by-step explanation:
The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.
Multiply using the rule for the product of the sum and difference of two terms. (6x+5)(6x-5)
Answers
The product of (6x+5)(6x-5) is 36x^2 - 25.
To find the product of (6x+5)(6x-5), we can use the rule for the product of the sum and difference of two terms, which states that the product of (a+b)(a-b) is equal to a^2 - b^2.
In this case, the terms are (6x+5) and (6x-5), where a = 6x and b = 5. Applying the rule, we have:
(6x+5)(6x-5) = (6x)^2 - 5^2
Simplifying further:
(6x)^2 - 5^2 = 36x^2 - 25
Therefore, the product of (6x+5)(6x-5) is 36x^2 - 25.
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The agricultural company "Cultivos Mediterráneos, S.L." uses a production function
Y = (L1/2 + K1/2) ^2, where K is the number of tractors employed, and L the number of workers,
where Y is the number of cultivated tasks. Price of capital is r and price of labor is w.
a) Find PMgL and PMgK.
b) Find the conditional demands of K and L.
c) Find an expression for the minimum cost.
d) If w=2 and r=1, write the minimum cost function, and find CMg and CMe.
Answers
a. = 1 + (L/K)^(1/2)
b. The conditional demand of K is K = L * (w - 1)^2, and the conditional demand of L is L = K * (r - 1)^2.
c. Cost = wKr^2 - 2wKr + wK + rw^2L - 2rL + L
d. CMe = Cost / Y = (4K + 3L) / ((L^(1/2) + K^(1/2))^2)
a) To find the marginal product of labor (PMgL) and the marginal product of capital (PMgK), we need to take partial derivatives of the production function with respect to labor (L) and capital (K), respectively.
PMgL = ∂Y/∂L
= 2(L^(1/2) + K^(1/2)) * (1/2) * L^(-1/2)
= (L^(1/2) + K^(1/2)) / L^(1/2)
= 1 + (K/L)^(1/2)
PMgK = ∂Y/∂K
= 2(L^(1/2) + K^(1/2)) * (1/2) * K^(-1/2)
= (L^(1/2) + K^(1/2)) / K^(1/2)
= 1 + (L/K)^(1/2)
b) To find the conditional demands of K and L, we set the marginal products equal to their respective prices.
PMgL = w
1 + (K/L)^(1/2) = w
(K/L)^(1/2) = w - 1
(K/L) = (w - 1)^2
PMgK = r
1 + (L/K)^(1/2) = r
(L/K)^(1/2) = r - 1
(L/K) = (r - 1)^2
The conditional demand of K is K = L * (w - 1)^2, and the conditional demand of L is L = K * (r - 1)^2.
c) The minimum cost expression is obtained by substituting the conditional demands of K and L into the cost function.
Cost = wL + rK
Cost = w(K * (r - 1)^2) + rL * (w - 1)^2
Cost = wKr^2 - 2wKr + wK + rw^2L - 2rL + L
d) If w = 2 and r = 1, we can substitute these values into the minimum cost function.
Minimum Cost Function:
Cost = 2K - 2K + 2K + 4L - 2L + L
Cost = 4K + 3L
To find CMg (the marginal cost) and CMe (the average cost), we take the partial derivatives of the minimum cost function with respect to K and L.
CMg = ∂Cost/∂K = 4
CMe = Cost / Y = (4K + 3L) / ((L^(1/2) + K^(1/2))^2)
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Terrance invested money in a technology stock whose growth is modeled by the function f(x) = 0.01(2)x, where x represents a number of days.
Find the approximate average rate of change from day 3 to day 8.
A) 0.496
B) 2.016
C) 2.48
D) 5
Answers
Answer:
use d e s m o s it helps with calculations and stuff
Step-by-step explanation: