The value of b is 11.
From the question, we have
ax² + bx + c
using (0, 9)
substituting the value we get
9 = a(0)² + b(0) + c
c = 9
Therefore,
-1 = a(-1)² + b(-1) + c
-1 = a - b + 9
-1 - 9 = a - b
a - b = - 10
using (-2, -9)
-9 = a(-2)² + b(-2) + 9
-9 - 9 = 4a - 2b
-18 = 4a - 2b
2a - b = -9
combine the equation
a - b = - 10
2a - b = -9
solving the equations we get
a = 1
Then,
1 - b = -10
b = 1 + 10
b = 11
Hence, the value of b is 11.
Subtraction:
The process of removing items from a collection is represented by subtraction. Subtraction is represented by the minus sign. If, for instance, there are nine oranges stacked together (as shown in the above figure), and four of those oranges are then moved to a basket, the stack will contain nine minus four oranges, or five oranges. As a result, 9 minus 4 equals 5, or the difference between 9 and 4. Incorporating subtraction into other types of numbers is possible in addition to using it with natural numbers.
The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference. As the first integer to be subtracted from in a subtraction phrase, a minuend is the first number in the subtraction process.
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I need to know which point is the solution and I need a check for it to make sure it’s correct and the line on the graph
The system of equations are given as
[tex]\begin{gathered} y-2x=-4 \\ y=-x-1 \end{gathered}[/tex]The graph of the system of equations is
The point which is the solution is
[tex](1,-2)[/tex]I do not understand the problem on how to to write an equation.
Given a line passes through the point (-4,6) and has a slope of 3
We will write the equation of the line in point-slope from
The formula of the point-slope form will be as follows:
[tex]y-k=m(x-h)[/tex]Where (h, k) is the point that lies on the line and (m) is the slope
From the given:
m = 3
h = -4
k = 6
Substitute into the formula
so, the answer will be:
[tex]y-6=3(x+4)[/tex](linear approximation calc !) The radius of a disc is 24 cm if the radius has a maximum error of 0.2 cm. estimate the relative percentage air in the calculated area the area of a circle = pi r ^2
Given:
The radius of the circular disk is 24cm.
The radius has a maximum error of 0.2 cm.
To find:
The area
Explanation:
Using the area of the circle,
[tex]A=\pi r^2[/tex]The area of the disk is,
[tex]\begin{gathered} A=\pi\times24^2 \\ =576\pi cm^2 \end{gathered}[/tex]If the radius is increased from 24 by 0.02, then the radius becomes, r = 0.02
The change in the calculated area will be,
[tex]\begin{gathered} \Delta A=Area\text{ of the cirlce with radius of 24.02-Area of the circle with radius of 24} \\ =\pi\times24.02^2-\pi\times24^2 \\ =576.96\pi-576\pi \\ =0.96\pi cm^2 \end{gathered}[/tex]The relative percentage of area is,
[tex]\begin{gathered} \frac{\Delta A}{A}\times100=\frac{0.96\pi}{576\pi}\times100 \\ =0.0017\times100 \\ =0.17\text{ \%} \end{gathered}[/tex]Final answer:
The maximum error in area is,
[tex]0.96\pi cm^2[/tex]The relative percentage error in the area is 0.17%.
Measure the dimensions of all the walls of the bedroom in your home, in feet. Find the dimensions of any windows or doorways as well.
Explanation
we can fill up the dimensions as follow
A support cable runs from the top of a telephone pole to a point on the ground 42.7 feet from its base. Suppose the cable makes an angle of 29.6 with the ground (as shown in the following figure).(a) Find the height of the pole. (Round the answer to the nearest tenth.) feet (b) Find the length of the cable. (Round the answer to the nearest tenth.) feet
We will draw a sketch to see the position of the cable
From the figure, we can use the tangent ratio to find the height
[tex]\frac{h}{42.7}=tan(29.6)[/tex]By using the cross-multiplication
[tex]\begin{gathered} h=42.7tan(29.6) \\ \\ h=24.3\text{ feet} \end{gathered}[/tex]a) The height of the pole is 24.3 feet to the nearest tenth
To find the length of the cable we will use the cosine ratio
[tex]cos(29.6)=\frac{42.7}{L}[/tex]Switch L and cos(29.6)
[tex]\begin{gathered} L=\frac{42.7}{cos(29.6)} \\ \\ L=49.1\text{ feet} \end{gathered}[/tex]b) The length of the cable is 49.1 feet to the nearest tenth
Estimate the product by adjusting the larger factor to the compatible number 25 and then multiply. 27 x 8 = Think about counting by 25s.
You have the following product:
27 x 8
To estimate the product by rounding 27 to 25, you consider that 25 x 8 is the same as adding 25 eight times.
Then, you have:
25 x 8 = 25 + 25 + 25 + 25 + 25 +25 + 25 +25
25 x 8 = 50 + 50 + 50 + 50 each pair of 25's add up 50
25 x 8 = 100 + 100 each pair of 50's add up 100
25 x 8 = 200
Hence, an estimation of the given product is 200, by considering 27 rounded to 25.
Hi, simplify the following rational expression, if possible: x + 2/ x^2 = 4x + 4
Given:
[tex]\frac{x+2}{x^2-4x+4}[/tex]To simplify the given rational expression, we first factor x^2-4x+4 by applying Perfect Square Formula as shown below:
[tex]\begin{gathered} a^2-2ab+b^2=(a-b)^2 \\ \end{gathered}[/tex]Hence,
[tex]x^2-4x+4=x^2-2x(2)+2^2=(x-2)^2[/tex]Now, we simplify the given expression:
[tex]\frac{x+2}{x^{2}-4x+4}=\frac{x+2}{(x-2)^2}[/tex]Therefore, the answer is:
[tex]\frac{x+2}{(x-2)^{2}}[/tex]4. Write the equation of the line in SLOPE-INTERCEPT FORM that passes through the given points(4,2) and (0,6)
The slope intercept form equation is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The formula for determining slope is expressed as
slope, m = (y2 - y1)/(x2 - x1)
From the information given,
y2 = 6, y1 = 2
x2 = 0, x1 = 4
Slope, m = (6 - 2)/(0 - 4) = 4/- 4
m = - 1
We would determine the y intercept, c by substituting m = - 1, y = 6 and x = 0 into the slope intercept equation. It becomes
6 = - 1 * 0 + c
6 = c
c = 6
The equation would be
y = - x + 6
solve for C -3 (C + 5)- (c-3)=32
Given the equation:
[tex]-3(c+5)-(c-3)=32[/tex]To find the value of 'c', the first step to do is to get rid of the parenthesis. We can do this using the distributive property on both cases:
[tex]\begin{gathered} -3(c+5)-(c-3)=32 \\ \Rightarrow-3\cdot c+(-3)\cdot5-c-(-3)=32 \\ \Rightarrow-3c-15-c+3=32 \end{gathered}[/tex]Now that we don't have any parenthesis in our equation, we start moving similar terms: we leave on the left the terms with the variable 'c' and we move the rest of the terms to the right side with it's sign changed:
[tex]\begin{gathered} -3c-15-c+3=32 \\ \Rightarrow-3c-c=32+15-3 \end{gathered}[/tex]We can make the operations on each side since now we have the similar terms apart:
[tex]\begin{gathered} -3c-c=32+15-3 \\ \Rightarrow-4c=47-3=44 \\ -4c=44 \end{gathered}[/tex]Finally, we move the -4 that is multiplying the 'c' to the other side doing its opposite operation:
[tex]\begin{gathered} -4c=44 \\ \Rightarrow c=\frac{44}{-4}=-11 \\ c=-11 \end{gathered}[/tex]therefore, c=-11
Solve on the interval [0,27): RCŨsx+c05X +1 = ] T O 3 A. X= 27,x = x=57 4. 4 O B. X = 27,X = O c. X= 7T,X = 1 47T 3 T D. X= ET 6 6 NAMAN
ANSWER:
C.
[tex]x=\pi,x=\frac{2\pi}{3},x=\frac{4\pi}{3}[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]2cos^2x+3cosx\: +1\: =\: 0[/tex]Using the substitution method, we can calculate the value of x, like this:
[tex]\begin{gathered} u=\cos x \\ \text{ therefore:} \\ 2u^2+3u+1=0 \\ 3u=2u+u \\ 2u^2+2u+u+1=0 \\ 2u(u+1)+u+1=0 \\ (u+1)(2u+1)=0 \\ u+1=0\rightarrow u=-1 \\ 2u+1=0\rightarrow2u=-1\rightarrow u=-\frac{1}{2} \\ \text{ replacing:} \\ \cos x=-1\rightarrow x=\cos ^{-1}(-1)\rightarrow x=\pi \\ \cos x=-\frac{1}{2}\rightarrow x=\cos ^{-1}(-\frac{1}{2})\rightarrow x=\frac{2\pi}{3},\frac{4\pi}{3} \end{gathered}[/tex]The edge of a cube measures 11 m. Find the surface area.
In order to determine the surface area of the cube, use the following formula:
[tex]S=6a^2[/tex]where a is the length of the side of a cube a = 11 m.
Replace the value of a into the formula for S:
[tex]S=6(11m)^2=726m^2[/tex]Hence, the surface area of the given cube is 726m^2
Find the probability of the event.If a single die is tossed once, find the probability of the following event. Rollinga 3 or a 5
ANSWER
1/3
EXPLANATION
If we have a fair die, the probability of rolling any of the numbers is the same. In this case, we want to know the probability of rolling a 3 or a 5, which is the sum of the probabilities of rolling each of these values,
[tex]P(3)=P(5)=\frac{1}{6}[/tex]So,
[tex]P(3or5)=P(3)+P(5)=\frac{1}{6}+\frac{1}{6}=\frac{2}{6}=\frac{1}{3}[/tex]Hence, the probability of rolling a 3 or a 5 is 1/3
what expression is equivalent to 2y+7
The expression which is equivalent to the given expression (3y - 4) (2y + 7) + 11y - 9 is 6 y²+ 24y- 37
Define an expression.A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.
A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities.
Presented expression = (3y - 4) (2y + 7) + 11y - 9
Solving the expression we get= 6y²+21y-8y-28+11y-9
= 6y²+24y-37
There for the correct response is that the given expression is equivalent to = 6y²+24y-37
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Convert 57•F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas.C=5/9 (F-32)F= 9/5 C+32
ANSWER
[tex]13.9°C[/tex]EXPLANATION
We want to convert 57°F to degrees Celsius.
To do this, apply the formula:
[tex]C=\frac{5}{9}(F-32)[/tex]where F = temperature in Fahrenheit
Therefore, 57°F to degrees Celsius is:
[tex]\begin{gathered} C=\frac{5}{9}(57-32) \\ \\ C=\frac{5}{9}*25 \\ \\ C=13.9°C \end{gathered}[/tex]That is the answer.
Factor 64x3 + 27.(4x – 3)(16x2 – 12x + 9)(4x + 3)(16x2 - 12x + 9)(4x + 3)(16x2 + 12x + 9)(4x - 3)(16x2 + 12x + 9)
Answer
Option B is correct.
64x³ + 27 = (4x + 3) (16x² - 12x + 9)
Explanation
We are told to factorize
64x³ + 27
To do this, we use the factorization of (x³ + y³) as a guide. First of,
(x + y)³ = (x + y) (x + y)² = (x + y) (x² + 2xy + y²)
(x + y)³ = x³ + y³ + 3x²y + 3xy²
So, we can write
x³ + y³ = (x + y)³ - 3x²y - 3xy² = (x + y)³ - 3xy(x + y)
= (x + y) [(x + y)² - 3xy]
= (x + y) (x² + y² + 2xy - 3xy)
= (x + y) (x² - xy + y²)
So, comparing (64x³ + 27) with (x³ + y³), we can see that
64x³ = (4x)³
27 = (3)³
(64x³ + 27) = (4x)³ + 3³
x³ + y³ = (x + y) (x² - xy + y²)
(4x)³ + 3³ = (4x + 3) [(4x)² - (4x × 3) + 3²]
= (4x + 3) (16x² - 12x + 9)
Hope this Helps!!!
use the functions f (×) and g (×) to complete the comparison statements using <,>,or =.F(x)= -×-5
First Question:
f(3) = (-3)-5 (Replacing x in the equation)
f(3) = -8 (Operating integers)
From the table we see that g(3) = 8, therefore, f(3)< g(3)
Second Question:
The slope of f is the coefficient of x in the equation, so, the slope of f is -1.
Using the slope formula for g(x) with points (0,2) and (3,8) we find that:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{8-2}{3-0}=\frac{6}{3}=2[/tex]The slope of g is 2.
Therefore, the slope of f is less (<) than the slope of g
Third Question:
The y-intercept of f is the value next to the term -x, so, it is equal to -5
The y-intercept of g can be found with the point (0,2), when x=0, y is equal to 2, then the y-intercept is 2.
Therefore, the y-intercept of f is less(<) than the y-intercept of g.
describe and correct the error solution error a student made when graphing a linear equation y equals -3 / 4 x - 6
we have two points (0, 6) and (4, 3)
this can be represented as (x, y)
the equation of a straight line is
y = mx + c
slope = m = y2 - y1/ x2 - x1
x1 = 0, y1 = 6, x2 = 4 and y2 = 3
slope = 3 - 6 / 4 - 0
slope = -3/4
slope = -3/4
from the equation of a straight line
(y - y1) = m(x - x1)
y1 = 6 and x1 = 0
y - 6= -3/4(x - 0)
y - 6 = -3/4x + 0
y = -3/4x + 6
the error he made was that he used - 6 instead of +6 in the final answer
Assume that the random variable X is normally distributed , with mean = 80 and standard deviation = 15. Compute the probability P(X > 92) .
Assume that the random variable X is normally distributed , with mean = 80 and standard deviation = 15. Compute the probability P(X > 92) .
step 1
Find z score
z=(92-80)/15
z=0.8
step 2
using the z-score table
For z=0.8
P=0.7881
therefore
answer is
P=0.7881Evaluate 10y-15 for y=5
10 y - 15
y = 5
We replace 5 in the expression
10 * 5 - 15 =
50 - 15 = 35
____________________
Answer
35
Use the Distributive Property
solve the equation.
- 6(x + 3) = 30
Answer: X = -2
Step-by-step explanation:
-6 time x is -6x and -6 times 3 is -18
Now you have -6x + -18 = 30
Add the now add 18 to both the -18 and 30 now your left with -6x = 12
And at last divide both -6 and 12 to -6
And you have X = -2
Answer: -8
Step-by-step explanation:
-6(x + 3) =30
-Distribute -6 and x = -6x
-Distribute -6 and 3 = -18
-6x -18 = 30
+18 +18. Take away 18 on both sides of the equation
_________
-6 / -6x = 48/-6 Divide -6 on both sides to get x by itself
X = -8
Final Answer : -8
This is non graded algebra 1 I need help on question 10
An exponential decay function can be generically written as:
[tex]y=a\cdot b^x[/tex]The conditions for this function are:
1) The y-intercept is 4.
2) The values of y decrease by a factor of one half as x increases by 1.
The y-intercept corresponds to the value of y when x = 0, so we can express it as:
[tex]\begin{gathered} y=a\cdot b^x \\ 4=a\cdot b^0 \\ 4=a\cdot1 \\ a=4 \end{gathered}[/tex]This condition let us find the value of a.
The next condition will be used to find the value of b.
As x increases by 1, y decreases by one half.
We can write this as a quotient between consecutive values of y:
[tex]\begin{gathered} \frac{y(x+1)}{y(x)}=\frac{1}{2} \\ \frac{4\cdot b^{x+1}}{4\cdot b^x}=\frac{1}{2} \\ b^{x+1-x}=\frac{1}{2} \\ b^1=\frac{1}{2} \\ b=\frac{1}{2} \end{gathered}[/tex]Then, we can write the function as:
[tex]y=4\cdot(\frac{1}{2})^x[/tex]Answer: y = 4*(1/2)^x
indicate whether (2, 7) is a solution of the given system.y is greater than or = -x+1Y is less than 4x+2
In order to determine if the point (2, 7) is a solution to the given system of inequalities we just have to replace 7 for y and 2 for x and see if the two inequalities are met, like this:
For y ≥ -x + 17 ≥ -2 + 1
7 ≥ -1
As you can see, 7 is greater than -1 then the first inequality is met.
For y < 4x + 27 < 4(2) + 2
7 < 8 + 2
7 < 10
As you can see, the second inequality is also met, then (2, 7) is a solution for the system of inequalities.
Simplify: 7a + 2a - a + 6b - 5b
We must simplify the following expression:
[tex]7a+2a-a+6b-5b[/tex]From the expression, we see that we have terms with variable a and terms with variable b. In order to simplify the expression, we add the terms with a together (which sums up 8a), and we do the same for the terms with b (which sums up 1b):
[tex]\begin{gathered} 7a+2a-a+6b-5b \\ =(7a+2a-a)+(6b-5b) \\ =8a+b \end{gathered}[/tex]The solution is: 8a+b
the odds against (E) are 23:77 Find the probability of (not E) :
We can rewrite the question as the probability of getting the event E is 23:77. Find the probability of getting the event not E.
The number 23:77 is a ratio and is it equivalent to:
[tex]\frac{23}{77}[/tex]To get the probability of the event not-E, we can proceed as follows:
[tex]1-\frac{23}{77}=\frac{77}{77}-\frac{23}{77}=\frac{53}{77}\approx0.7013[/tex]So the probability for the event not-E is about 53/77 or 0.7013 (or a little more than 70%).
Question 5 of 15, Step 1 of 14/15CorrectIfy is inversely proportional to x and y = -71 when x = 16, find yifx = 7. (Round off your answer to the nearest hundredth.)
Answer:
[tex]y=-31.06[/tex]Step-by-step explanation:
Since y and x are inversely proportional, we'll have that:
[tex]y=\beta x[/tex]For a given betha value. Since we have a pair of x and y values, we can plug them in the formula and find our particular value of betha, as following:
[tex]\begin{gathered} y=\beta x\rightarrow-71=\beta\times16\rightarrow\beta=-\frac{71}{16} \\ \end{gathered}[/tex]This way, our formula would be:
[tex]y=-\frac{71}{16}x[/tex]Plugging in x = 7,
[tex]\begin{gathered} y=-\frac{71}{16}x\rightarrow y=-\frac{71}{16}(7)\rightarrow y=-\frac{497}{16} \\ \\ \Rightarrow y=-31.06 \end{gathered}[/tex]Which expression represents the distance between point (0, a) and point (a,0) on a coordinate grid?
2a
Ο Ο Ο Ο
2a
O
Answer:
Explanation:
To determine the distance between two points on a coordinate grid, use the formula below:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Hello may you please check me work for number 5
Surface area of a rectangular prism:
[tex]SA=2(wl+hl+hw)[/tex]Substitute 1.2 for all of the variables in the formula:
[tex]SA=2[(1.2)(1.2)+(1.2)(1.2)+(1.2)(1.2)][/tex]Using a calculator, you should get an answer of:
[tex]SA=8.64\text{ }yd[/tex]The answer is that the surface area of this shape is 8.64 yards.
Use the expressions from the previous questions to determine Mary’s age.
The age of Mary is 15 years old.
To solve this, we have three expressions:
[tex]\begin{gathered} M=J+5 \\ J=T-28 \\ T=3H-1 \end{gathered}[/tex]Where M is the age of Mary, J is the age of Jacob, T is the age of Uncle Tim and H is the age of Henry
Also teh problem give us an additional info, the age of Henry is 13. With this, we can replace the value of H in the thrid equation:
[tex]\begin{gathered} \begin{cases}H=13 \\ T=3H-1\end{cases} \\ \text{Then:} \\ T=3\cdot13-1=39-1=38 \\ T=38 \end{gathered}[/tex]Now we can replace T in the second equation:
[tex]\begin{gathered} \begin{cases}T=38 \\ J=T-28\end{cases} \\ \text{Then:} \\ J=38-28=10 \\ J=10 \end{gathered}[/tex]Finally, we can replace J in the first equation to get the age of Mary:
[tex]\begin{gathered} \begin{cases}J=10 \\ M=J+5\end{cases} \\ \text{Then:} \\ M=10+5=15 \end{gathered}[/tex]Thus, the age of Mary is 15 years old.
Pleaee help me draw this. Construct a tangent to the circle from point R.
solution
For this case the tangent line to the circle and the point should be:
The reason is because the tangent line and the point needs to touch the circle just one time
can you please help me with the work sheet and get all the answers and thank you
ANSWER
[tex](x+2)(x-4)[/tex]EXPLANATION
7) Given;
[tex]f(x)=x^2-2x-8[/tex]Using factors of 2 and -4;
[tex]\begin{gathered} \lparen x^2+2x-4x-8) \\ \left(x^2+2x\right)+\left(-4x-8\right) \\ \end{gathered}[/tex]Factorise;
[tex]\begin{gathered} x\left(x+2\right)-4\left(x+2\right) \\ \end{gathered}[/tex]Factor out the common term;
[tex]\begin{gathered} x(x+2)-4(x+2) \\ (x+2)(x-4) \end{gathered}[/tex]The graphical solution is attached.