Given:
f(x) is an exponential function.
f(4) = 7.
f(5.5) = 53.
Since f(x) is an exponential function, f(x) can be expressed as,
[tex]f(x)=ab^x[/tex]Here, a and b are constants.
Hence, we can write
[tex]\begin{gathered} f(4)=ab^4----(1) \\ f(5.5)=ab^{5.5}\text{ ------(2)} \end{gathered}[/tex]Divide equation (2) by (1).
[tex]\frac{f(5.5)}{f(4)}=\frac{ab^{5.5}}{ab^4}[/tex]Substitute f(4) = 7 and f(5.5) = 53 in the above equation.
[tex]\begin{gathered} \frac{53}{7}=\frac{b^{5.5}^{}}{b^4} \\ \frac{53}{7}=b^{5.5-4} \\ \frac{53}{7}=b^{1.5} \\ \frac{53}{7}=b^{\frac{3}{2}} \\ b=(\frac{53}{7})^{\frac{2}{3}} \\ b=3.855 \end{gathered}[/tex]Now, the value of a can be obtained as,
[tex]\begin{gathered} f(4)=ab^4 \\ 7=a(\frac{53}{7})^{\frac{2}{3}} \\ a=\frac{7}{(\frac{53}{7})^{\frac{2}{3}}} \\ =1.815 \end{gathered}[/tex]Will mark as brainlist
Which of the following best represents R= A - B ?
Please help, it’s due soon!
Answer: I would say it is C
Step-by-step explanation: If you think about it, if you have a pencil and the pencil is in A form, and you have to put it to B form, it kinda makes sence. BUT, I honestly don't know, so don't trust me...
GL LUCK THO AND GOD BLESS
The answer is 78 ft provided by my teacher, I need help with the work
ok
To solve this problem, I'll use trigonometric functions,
The trigonometric function that relates the opposite side and the hypotenuse is sine
Formula
sin 48 = Opposite side / hypotenuse
hypotenuse = 105 ft
opposite side = H
Substitution
sin 48 = H/105
Solve for H
H = 105*sin 48
Simplification
H = 105*0.743
Result
H = 78 ft
What is a possible step when solving for x? Sey. 51x + 2x = 37
Solving for x, the value of x is 37/53
Algebraic expression: what is it?An expression that has been created utilizing integer variables, constants, and algebraic operations is known as an algebraic expression. As an illustration, the algebraic expression 3x2 2xy + c
Given,
51x + 2x = 37
To resolve the x equation
51x + 2x = 37
Including the xs
53x = 37
53 divided between the two sides
53x/53 = 37/53
x = 37/53
As a result, by solving for x in the subsequent steps, we obtain:
x = 37/53
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Write the curve equation associated to those parametric equations.x(θ) = 3 cos θy(θ) = 6 sin θ
We want to rewrite the following parametric equations
[tex]\begin{gathered} \begin{cases}x={3\cos\theta} \\ y={6\sin\theta}\end{cases} \\ \frac{\pi}{2}<\theta<\frac{3\pi}{2} \end{gathered}[/tex]as one equation. Using the following property
[tex]\sin^2\theta+\cos^2\theta=1[/tex]We can eliminate the parameter theta adding the square of the coordinates
[tex]\begin{gathered} \sin^2\theta+\cos^2\theta=1 \\ 6^2(\sin^2\theta+\cos^2\theta)=6^2 \\ 6^2\sin^2\theta+6^2\cos^2\theta=6^2 \\ (6\sin\theta)^2+(6\cos\theta)^2=6^2 \\ (6\sin\theta)^2+(2\cdot3\cos\theta)^2=6^2 \\ (y)^2+(2x)^2=6^2 \\ y^2+4x^2=36 \\ \frac{x^2}{9}+\frac{y^2}{36}=1 \end{gathered}[/tex]And this is the standard equation of an ellipse
[tex]\frac{x^{2}}{9}+\frac{y^{2}}{36}=1[/tex]The constrain
[tex]\frac{\pi}{2}<\theta<\frac{3\pi}{2}\implies x<0[/tex]tells us that x can only assume negative values, therefore, the graph is only the left side of the ellipse.
What is the slope of a line perpendicular to the line whose equation is x+4y=16. .
Answer:
The slope is [tex]-\frac{1}{4}[/tex].
Step-by-step explanation:
This is the slope formula equation.
[tex]y=mx+b[/tex]
[tex]x+4y=16[/tex]
First, you divide the entire equation by 4 to get rid of the 4 in 4y.
[tex]\frac{x}{4} +y=4[/tex]
Then, you subtract [tex]\frac{x}{4}[/tex] on both sides.
[tex]y=-\frac{x}{4} +4[/tex]
In front of the x should be and invisible 1. So this should be your slope.
[tex]m=-\frac{1}{4}[/tex]
The total profit from the Spanish club fundraiser varies directly with the number of dinner tickets sold. If the sale of 14 tickets results in a profit of $175, how many tickets must be sold to reach the fundraising goal of $600?
Spanish club has 48 tickets which must be sold to reach the fund-raising goal as profit of $600.
What is profit?
In mathematics, the term profit can be explained as the amount which is on the standard cost price. For the profit, the amount of the commodity can be designed by the shopkeeper which is bigger amount as per the cost price.
According to the question, the total profit from the Spanish club fundraiser varies directly with the number of dinner tickets sold.
If the sale of 14 tickets results in a profit of : $175.
Therefore, Profit in 1 ticket = 175/14 = 12.5 dollars
Let us assume 'x' tickets are sold in order to reach the fund-raising goal of $600.
x = (14/175)(600) = 48
x = 48 tickets
Hence, 48 tickets must be sold to reach the fund-raising goal as profit of $600.
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Which point lies on the graph of the equation 7x-3y=9
Answer:
Slope:
7/3
y-intercept:
(0, −3)
Step-by-step explanation:
Describe the similarity transformation that maps the preimage to the image. I need help with question 4
The coordinates of the vertices of the original shape are given to be:
[tex]\begin{gathered} L\Rightarrow(6,6) \\ M\Rightarrow(0,4) \\ N\Rightarrow(0,6) \end{gathered}[/tex]The transformed shape coordinates are given to be:
[tex]\begin{gathered} L^{\prime}\Rightarrow(7,2) \\ M^{\prime}\Rightarrow(4,1) \\ N^{\prime}\Rightarrow(4,2) \end{gathered}[/tex]On observation, the shapes show a dilation and a shift in position.
The image has a scale factor of 1/2, meaning it is reduced by 1/2. Therefore, the original coordinates will be reduced to give:
[tex]\begin{gathered} L^{\doubleprime}\Rightarrow\frac{1}{2}(6,6)=(3,3) \\ M^{\doubleprime}\Rightarrow\frac{1}{2}(0,4)=(0,2) \\ N^{\doubleprime}\Rightarrow(0,6)\Rightarrow(0,3) \end{gathered}[/tex]The translation of the initial image can be gotten by subtracting the corresponding coordinates:
[tex]\begin{gathered} L^{\prime}-L^{\doubleprime}=(7-3,2-3)=4,-1 \\ M^{\prime}-M^{\doubleprime}=(4-0,1-2)=4,-1 \\ N^{\prime}-N^{\doubleprime}=(4-0,2-3)=4,-1 \end{gathered}[/tex]All the differences are the same. This means that the image moves to the right by 4 units and down by 1 unit.
The dilation rule with a scale factor of k is given to be:
[tex](x,y)\to(kx,ky)[/tex]The translation rule for a units to the right and b units down is given to be:
[tex](x,y)\to(x+a,y-b)[/tex]Combining both rules, we have:
[tex](x,y)\to(kx+a,ky-b)[/tex]Given:
[tex]\begin{gathered} k=\frac{1}{2} \\ a=4 \\ b=1 \end{gathered}[/tex]Therefore, the transformation is given to be:
[tex]\Rightarrow(\frac{1}{2}x+4,\frac{1}{2}y-1)[/tex](d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
In triangle XYZ, measure of angle X=152, y=15, z=19. Find x to the nearest thousandth.
In triangle XYZ, measure as shown below
Step 1: Using Cosine rule
[tex]\begin{gathered} x^2=y^2+z^2\text{ - 2yz CosX} \\ x^2=15^2+19^2\text{ - 2(15)(19)Cos 152} \\ x^2=\text{ 225+361-570 cos 152} \end{gathered}[/tex][tex]\begin{gathered} x^2=\text{ 586-570(-0.88295)} \\ x^2=586\text{ + 503.28} \\ x^2=\text{ 108}9.28 \\ x\text{ = }\sqrt[]{1089.28} \\ x\text{ = 33.004} \end{gathered}[/tex]Hence the value of x = 33.004
Write the augmented matrix for the system of linear equations. (Do not perform any row operations.)X- y + 4z = 46x - 8y +Z = -14x +y0:
For you to input the information in a Matix you only have to consider the coefficients corresponding to each variable in each equation, in this case the matrix is:
1 -1 4 : 4
6 -8 1 : -1
4 1 0 : 0
This is the matrix for the given equations
Complete the function for this graph.Enter the correctsymbol, + or -y = [?][x
Given:
The graph of modulus function is given.
The modulus function is defined as,
[tex]\begin{gathered} |x|=x,\text{ for x}\ge0 \\ =-x\text{ for x<0} \end{gathered}[/tex]For the given graph,
[tex]\begin{gathered} \\ \text{The graph of function is} \\ y=-|x| \end{gathered}[/tex]P (8, 4) is a point on a circle, centre O.
The tangent at P intersects the axes at points A and B.
a) Find the gradient, m, of the tangent.
Your final line should say, m =...
(2)
b) Find the equation of the tange the
form y = mx + c where m and c are integers. (1)
y =
X +
c) Find the coordinates of point A.
d) Work out the length of AB,
giving your answer in the form a√5 where a is an integer.
(1)
B
P (8,4)
A
5 (2)
Total marks: 6
The equation of tangent is y = -2x + 20. The slope of the tangent line is negative 2. And coordinate of point A is (10, 0). And the length of AB is 22.36 units.
What is the equation tangent line to circle?The equation of the circle with center at origin and radius r is given as,
x² + y² = r²
The slope of the tangent line to the circle at points (8, 4) is given as,
2x + 2y (dy/dx) = 0
dy / dx = - 8 / 4
m = - 2
Then the equation of the line is given as,
y = -2x + c
The equation is passing through (8, 4), then we have
4 = -2(8) + c
c = 4 + 16
c = 20
The equation is y = -2x + 20. Then the x-intercept is given as,
y = 0
-2x + 20 = 0
2x = 20
x = 10
Then the length of the line is given as,
AB² = (10 - 0)² + (0 - 20)²
AB² = 100 + 400
AB = √(500)
AB = 22.36 units
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If $8^7)^2 = 2^y, what number is y?
The value of y based on the information given about the expression (8^7)² = 2^y is 21.
How to illustrate the information?It should be noted that based on the information, the power rule will be essential. This will be illustrated thus:
(8^7)² = 2^y
It should be noted that 8 = 2 × 2 × 2 = 2³
Therefore, 8^7 = 2^(3 × 7) = 2^21
Therefore, the value of y is 21.
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See question below. I am not sure how to set this up.
Answer and Explanation:
Let x represent the number of hours Sandy needs to work.
We can go ahead and set up the required inequality as shown below;
[tex]150<10x+20<200[/tex]Let's go-ahead and determine x by splitting the compound inequality above as shown below;
[tex]\begin{gathered} 150<10x+20 \\ 150-20<10x \\ 130<10x \\ x>\frac{130}{10} \\ x>13 \end{gathered}[/tex][tex]\begin{gathered} 10x+20<200 \\ 10x<180 \\ x<\frac{180}{10} \\ x<18 \end{gathered}[/tex][tex]13We can see from the above that Sandy needs to work between 13 and 18 hours to be able to meet her goal.Explain why a V-shaped graph does not represent a linear function.
A V-shaped graph belongs to an absolute value function or a piecewise function, never to a linear function (these are graphed only with a single line).
Why a V-shaped graph does not represent a linear function?This is really trivial question.
A linear function has a graph that is a straight line.A V-shaped graph is not a straight line, is a V.So the answer is really trivial, as you can see.
But let's explain it a little bit more.
The only functions that have V-shaped graphs are piecewise functions (formed of two linear equations) or absolute value equations, neither of these are exactly linear (but they are made of "linear like parts").
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I need help with this practice problem solvingI will send you another pic… it is a graph, please use the graph to answer this.
Before we can proceed in graphing the complex number, let's get the sum of the two given complex numbers first.
[tex](2-3i)+(-1-i)[/tex]When adding complex numbers, simply combine similar terms like real-to-real and complex-to-complex only.
So, we have:
[tex]\begin{gathered} =(2+(-1))+(-3i+(-i)) \\ =(2-1)+(-3i-i)_{} \\ =1+(-4i) \\ =1-4i \end{gathered}[/tex]Hence, the sum of the two complex numbers is 1 - 4i.
When plotting a complex number in the plane, the real number acts as the x-coordinate and the complex number acts as the y-coordinate.
Hence, the x-coordinate is 1 while the y-coordinate is -4.
Here's the graph of the sum.
Find the equation of the quadratic function whose graph is shown below. Given two points. Vertex= (-5,-5) Passes Through (-7,3)
Solving the Question
We're given:
Vertex= (-5,-5)Passes Through (-7,3)One of the forms of a quadratic equation is vertex form:
[tex]y=a(x-h)^2+k[/tex]
a = vertical stretchh = horizontal translationk = vertical translation(h,k) is the vertexPlug in the vertex:
[tex]y=a(x-h)^2+k\\y=a(x+5)^2-5[/tex]
Plug in the given point and solve for a:
[tex]3=a(-7+5)^2-5\\3=a(-2)^2-53=4a-5\\8=4a\\a=2[/tex]
Plug 2 into the equation as a:
[tex]y=2(x+5)^2-5[/tex]
Answer[tex]y=2(x+5)^2-5[/tex]
What is the dividend when the divisor is 8 and the quotient is 96 with a remainder of 3?
The dividend when the divisor is 8 and the quotient is 96 with a remainder of 3 is 771.
What is a dividend?The dividend in mathematics is the value that is divided by another value to obtain the result. The dividend is the starting point for any division method. The dividend is one of four critical components of the division process. It is the whole that is to be divided into equal parts.
A divisor of an integer n, also known as a factor of n, is an integer m that can be multiplied by another integer to produce n. In this case, n is also said to be a multiple of m.
In this case, the dividend will be:
= (96 × 8) + 3
= 768 + 3
= 771
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hello I am needing help how to solve the attached photo
For this question, we can see our function has two variables ("x" and "y"). So all we h=need to do is to substitute the different values of "x" to get the corresponding values of "y". So, let's calculate as follows:
Once we got all y-values we can finish our table as follows:
And that is our final answer.
5. Which of the equations show x and y DIRECTLY proportional to each relationship? For every one that does provide the constant of proportionality
A direct proportional relation can always be express as an equation of the form:
[tex]y=kx[/tex]where k is the constant of proportionality. (This means that y has to be the result of multiplying a number by x)
Now, let's see at the option we have.
a)
Solving the equation for y we have:
[tex]\begin{gathered} 2x+2y=0 \\ 2y=-2x \\ y=-\frac{2}{2}x \\ y=-x \end{gathered}[/tex]Since we can write the equation in the form as a direct proportional relationship we conclude that option a shows a directly proportional relationship and that the constant is -1.
b)
For this case we have the equation:
[tex]x=.125y[/tex]From it we already can see that this means that x is directly proportional to y and that the constatn of porportionality is 0.125.
Now if we want we can solve the equation for y, then we have:
[tex]\begin{gathered} y=\frac{1}{.125}x \\ y=8x \end{gathered}[/tex]this equation shows that y is directly proportional to x and that the constant of proportionality is 8.
Notice that the the constant of proportionality changes if we write the relation as x directly proportional to y or if we write it as y directly proportional to x. Either way the relation express the same and it is directly proportional.
c) and d)
For this equations that we have a division in which one of the variables is the divisor (or the denominator); this means that the equation show a relation between x and y but their are not directly proportional. In fact this means that the equations show an inversely proportional relations.
Mai drove 754 miles in 13 hours.
At the same rate, how many miles would she drive in 11 hours?
Answer:
At the same rate, she will travel 638 miles if she drives 11 hours.
Step-by-step explanation:
[tex]\frac{754 miles}{13 hours\\} = \frac{x}{11 hours}[/tex]
x=11*754/13
x=638
which inequality matches this situation : a number is at least 6a= x ≥ 6b= x > 6c= x ≤ 6d= x < 6
Answer:
a. x ≥ 6
Explanation:
If a number is at least 6, then, the number is greater than or equal to 6.
Since the symbol ≥ means greater than or equal, the correct answer is:
a. x ≥ 6
please help I'm really stuck on this question for home work
1) If the function g(x) =-2x² +3 is translated vertically upward then we need to add 7 units, to that.
2) So the function h(x) is going to
h(x) = g(x) +7
h(x) = -2x² +3 +7
h(x) =-2x² +10
What is the factored form of the polynomial?x^2 + 2x - 24
Let's try to factorize this polynomial
[tex]x^2+2x-24=(x+)(x-)[/tex]in the blank spaces we have to put numbers that multiplied are 24, and substracted are +2. So we have 6 and 4
[tex]x^2+2x-24=(x+6)(x-4)[/tex]So the factored form of the polynomial is (x+6)(x-4)
3. In the diagram show, EF and point A not on EF are
given. Point M, given by the ordered pair(−3, 1) is the
midpoint of AC. Find point C.
Step-by-step explanation:
Hello ,nice too meet you✨
2 The half-life of a substance is defined as the period of time it takes for the amount of the
substance to decay by half. The sequence shows the amount of a substance that will remain
after a certain number of half-lives have elapsed.
1, 1/2, 1/4, 1/8
Describe this sequence.
The given sequence is
1, 1/2, 1/4, 1/8......
we can see that the ratio of the consecutive terms is the same. We have
1/2/1 = (1/4)/(1/2) = (1/8)/(1/4) = 1/2
This means that it is a geometric sequence
To find the amount of the substance left after 21 half lifes, we would find the 21st term of the sequence. The formula for finding the nth term of a geometric sequence is
an = a1r^(n - 1)
a1 = 1
n = 21
r = 0.5
Thus,
a21 = 1 * 0.5^(21 - 1) = 0.5^20
a21 = 0.00000095367
a21 = 1/1048576
The answer makes sense in the problem context because it follows the common ratio that was established at the begining.
What is the slope of the line that passes through (2, 2) and (10, 6) ?
Enter your answer in the box.
Please help asap! I havn't got help all day
The slope of the line that passes through (2, 2) and (10, 6) is; 1/2.
What is the slope of a line which passes through points ( p,q) and (x,y)?The slope of parallel lines is the same. Slopes of perpendicular lines are negative reciprocals of each other. The slope of a line or straight object is the ratio of how much amount of rising occurs in correspondence to the increment in the run.
Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
We have been given that the line that passes through (2, 2) and (10, 6).
Let ( p,q) and (x,y) are (2, 2) and (10, 6) respectively.
Slope = [tex]m = \dfrac{y-q}{x-p}[/tex]
m = (2-6)/(2-10)
m = 4/8
m = 1/2
Then the slope is 1/2.
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. What is the number of terms in this expression? m + 4.6 5 Enter your answer in the box.
Question: What is the number of terms in this expression? m/5 + 4.6
Answer:
Two terms
Explanation:
Addition and subtraction separate terms but division and multiplication do not, so they are two terms in the below expression;
[tex]\frac{m}{5}+4.6[/tex]The terms are m/5 and 4.6