Answers
Given:
The function is given as
[tex]f(x)=-3x-2[/tex]Required:
We want to find the value of
[tex]f(-7)[/tex]Explanation:
[tex]f(-7)=-3(-7)-2=21-2=19[/tex]Final answer:
19
Related Questions
Select the expression equivalent to:(4x + 3) + (-2x + 4)A: 2x + 7B: -2x + 12C: -8x + 12D: 6x + 7
Answers
(4x + 3) + (-2x + 4)
Eliminating the parentheses:
4x + 3 - 2x + 4
Reordering:
4x -2x + 3 + 4
2x + 7
How to solve this problem step by step in depth. I have no idea how to solve this
Answers
Answer
[tex]f^{-1}(x)=\frac{-1}{5}x-\frac{4}{5}[/tex]Explanation
The given function is
[tex]f(x)=-5x-4[/tex]Let y = f(x), this implies
[tex]y=-5x-4[/tex]Now, make x the subject of the formula
[tex]\begin{gathered} y=-5x-4 \\ 5x=-y-4 \\ \text{To get x, we divide both sides by 5} \\ \frac{5x}{5}=\frac{-y-4}{5} \\ \\ x=\frac{-y-4}{5} \end{gathered}[/tex]Since f(x) = y, then x = f⁻¹(y)
[tex]\begin{gathered} f^{-}^{1}\mleft(y\mright)=\frac{-y-4}{5} \\ \therefore f^{-1}(x)=\frac{-x-4}{5} \end{gathered}[/tex]The above inverse function can be rewritten as follows
[tex]\begin{gathered} f^{-1}(x)=\frac{-x}{5}-\frac{4}{5} \\ f^{-1}(x)=\frac{-1}{5}x-\frac{4}{5} \end{gathered}[/tex]according to a census, there were 66 people per square mile (population density) in a certain country in 1980. By 2000, the # of people per square mile had grown to 76. This information was used to develop a linear equation in slope intercept form, given below, where x is the time in years and y is the population density. Think of 1980 as year zero. what is the population density expected to be in 2018? y = 1/2x + 66
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Determine the value of x for taking 1980 as 0.
[tex]\begin{gathered} x=2018-1980 \\ =38 \end{gathered}[/tex]The equation is y = 1/2x + 66.
Substitute the value of x in the equation to determine the population density in 2018.
[tex]\begin{gathered} y=\frac{1}{2}\cdot38+66 \\ =19+66 \\ =85 \end{gathered}[/tex]So population density in year 2018 is 85.
Answer: 85
As we learn more about lines, we will occasionally have to consider perfectly vertical lines as a special case and treat them differently. Think about applying what you have learned in the last couple of activities to the case of vertical lines. What is the same? What is different?
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If the line of the graph is vertical then the slope of the graph is zero. The coordinate of the y-value will never change on vertical lines.
What are vertical lines?The vertical line is a line that is parallel to the y-axis. A vertical line can be defined as a line on the coordinate plane where all the points on the line have the same x-coordinate. A form of test employed in relation is the vertical line test. Any kind of vertical line equation lacks a y-intercept. The vertical line test is used to determine whether or not the given relation is a function. The vertical line is another name for the vertical bar. A mathematical sign is an upright slash. Depending on the context, it may be used to represent a certain kind of logic or an operation. The vertical line is the line that runs along the y-axis.
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If Rosa is at most 27 years old. What symbol does at most refer to less than greater than less than or equal to greater than or equal to
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The correct answer is less than or equal to because at most 27 years means that Rosa's highest age is 27.
5. Determine the value of each variable for parallelogram INDY that has diagonals that intersect at P.IP = 3x, DP = 6x-2, NP = 3y, and YP = 7x - 2.
Answers
Given the INDY
The diagonals has intersected at the point P
IP = 3x, DP = 6x - 2
NP = 3y , YP = 7x - 2
So, IP = DP
[tex]6x-2=3x[/tex]Solve for x :
[tex]\begin{gathered} 6x-2=3x \\ 6x-3x=2 \\ 3x=2 \\ \\ x=\frac{2}{3} \end{gathered}[/tex]And : NP = YP
[tex]3y=7x-2[/tex]substitute with the value of x :
[tex]\begin{gathered} 3y=7\cdot\frac{2}{3}-2=\frac{23}{3}-2=\frac{17}{3} \\ \\ y=\frac{17}{9} \end{gathered}[/tex]So, the answer is :
[tex]\begin{gathered} x=\frac{2}{3} \\ \\ y=\frac{17}{9} \end{gathered}[/tex]5. In a 45-45-90 right triangle if the hypotenuse have length "x V 2", the leg 2 pointshas length IOхO 2xO x 2XV3
Answers
Given data:
In a right angle triangle hypotenues is given that is
[tex]H=x\sqrt[]{2}[/tex]Now, by the Pythagorean theorem we have
[tex]\text{Hypotenues}^2=Perpendicular^2+Base^2[/tex]So, by the hit and trial method
Let , perpendicular = base = x we get
[tex]\begin{gathered} H^{}=\sqrt[]{x^2+x^2} \\ H=\sqrt[]{2x^2} \\ H=x\sqrt[]{2} \end{gathered}[/tex]Thus, the correct option is (1) that is x
solve equation 10 - 25x = 5 what is the value of x
Answers
ANSWER
x = 1/5
EXPLANATION
We are given the equation:
10 - 25x = 5
To find the value of x, first we subtract 10 from both sides of the equation:
10 - 25x - 10 = 5 - 10
10 - 10 - 25x = 5 - 10
-25x = -5
Now, divide both sides by 5:
=> x = -5 / -25
x = 1/5
That is the value of x.
1/ (gg^2 e^5)^2 Write your answer with only positive exponents
Answers
ANSWER
[tex]\frac{1}{g^6e^{10}}[/tex]EXPLANATION
In the denominator, we have the product of g and g². The product of two powers with the same base is the base raised to the sum of the exponents,
[tex]\frac{1}{(gg^2e^5)^2}=\frac{1}{(g^{2+1}e^5)^2}=\frac{1}{(g^3e^5)^2}[/tex]Now, we also have the power of a product. The exponents can be distributed into the multiplication,
[tex]\frac{1}{(g^3e^5)^2}=\frac{1}{(g^3)^2(e^5)^2}[/tex]And finally, for both g and e, we have the power of a power. The result is the base raised to the product of the exponents,
[tex]\frac{1}{(g^3)^2(e^5)^2}=\frac{1}{g^{3\cdot2}e^{5\cdot2}^{}}=\frac{1}{g^6e^{10}}[/tex]Hence, the simplified expression is,
[tex]\frac{1}{g^6e^{10}}[/tex]what is 8q= 96 what is it?
Answers
To find the value of q, divide both sides of the equation by 8:
[tex]\begin{gathered} 8q=96 \\ \Rightarrow\frac{8q}{8}=\frac{96}{8} \end{gathered}[/tex]Simplify both members of the equation:
[tex]\begin{gathered} \Rightarrow q=\frac{96}{8} \\ \Rightarrow q=12 \end{gathered}[/tex]Therefore:
[tex]q=12[/tex]_________ ____________ allows us to derive new facts quickly from those we know. (spelling counts)
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Derived Facts allows us to derive new facts quickly from those we know.
What is a derived fact?
Derived facts are math facts that are derived from known facts. For example, if we know the doubles fact, 3+3=6, then we can derive the answer to 3+4 by using the 3+3 fact and adding 1 to it. So a derived fact strategy is the mental process of deriving a new fact from a known fact.
What is a related fact example?
We say: Two plus One equals Three. We can also use these same three numbers in our math fact: 2, 1, and 3 to make a related fact. This time our math fact will read: 1 + 2 = 3 because we added 1 and then 2 to get a total of 3.
What are the 3 phases of multiplication fact mastery?
Phase 1: Modeling or counting to find the answer.
Phase 2: Deriving answers using reasoning strategies based on known facts.
Phase 3: Efficient production of answers (Mastery).
Hence the answer is Derived Facts allows us to derive new facts quickly from those we know.
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write an equation of the line that satisfies the given conditions. give the equation (a) in slope intercept form and (b) in standard form. m=-7/12 ,(-6,12)
Answers
Given the slope of the line:
[tex]m=-\frac{7}{12}[/tex]And this point on the line:
[tex](-6,12)[/tex](a) By definition, the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
In this case, you can substitute the slope and the coordinates of the known point into that equation, and then solve for "b", in order to find the y-intercept:
[tex]12=(-\frac{7}{12})(-6)+b[/tex][tex]12=\frac{42}{12}+b[/tex][tex]\begin{gathered} 12=\frac{42}{12}+b \\ \\ 12=\frac{7}{2}+b \end{gathered}[/tex][tex]\begin{gathered} 12-\frac{7}{2}=b \\ \\ b=\frac{17}{2} \end{gathered}[/tex]Therefore, the equation of this line in Slope-Intercept Form is:
[tex]y=-\frac{7}{12}x+\frac{17}{2}[/tex](b) The Standard Form of the equation of a line is:
[tex]Ax+By=C[/tex]Where A, B, and C are integers, and A is positive.
In this case, you need to add this term to both sides of the equation found in Part (a), in order to rewrite it in Standard Form:
[tex]\frac{7}{12}x[/tex]Then, you get:
[tex]\frac{7}{12}x+y=\frac{17}{2}[/tex]Hence, the answers are:
(a) Slope-Intercept Form:
[tex]y=-\frac{7}{12}x+\frac{17}{2}[/tex](b) Standard Form:
[tex]\frac{7}{12}x+y=\frac{17}{2}[/tex]find the shaded area to the nearest tenth, use 3.14 for pi. help pls due tmrw
Answers
The area of the shaded region inside the circle is 49.04cm².
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle.
In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
So, the shaded area is:
We can easily tell that the diameter of the circle here is 12cm.
So, the radius will be 6cm.
Now, calculate the area of a circle as follows:
A = πr²
A = 3.14(6)²
A = 3.14(36)
A = 113.04cm²
Now, the area of the smaller square:
A = s²
A = 2²
A = 64²
Area of the shaded region:
113.04 - 64
49.04 cm²
Therefore, the area of the shaded region inside the circle is 49.04cm².
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3. If the mZLKI - 174º and KR bisects LLKI, then find the mLLKR.
R
E
K
87°
1740
0740
90°
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1:
[tex]undefined[/tex]Answer:
87°
Step-by-step explanation:
Angle bisector:Angle bisector is a ray that divides an angle into two congruent angles.
∠LKR = ∠LKJ ÷ 2
= 174° ÷ 2
= 87°
Use the value of x to find the measure of Angle 1.x=25 5x-5 2x+10
Answers
Given:
• x = 25
,• ∠1 = 5x - 5
,• ∠2 = 2x + 10
Let's find the measure of angle 1.
To find the measure of angle 1, substitute 25 for x in (5x - 5) and evaluate.
We have:
m∠1 = 5x - 5
m∠1 = 5(25) - 5
m∠1 = 125 - 5
m∠1 = 120
Therefore, the measure of angle 1 is 120 degrees.
ANSWER:
∠1 = 120°
1 What is the image of (12,-8) after a dilation by a scale factor of 4 centered at the origin? 12.4) b 18-32) 13,-2)
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A dilation of a point by a factor of 4 means that its coordinates will be multiplied by 4, so the image of the point (x,y) after the dilation will be (4x,4y). With this in mind, let's solve the problem:
[tex]H\text{ = }(12\cdot4,-8\cdot4)=(48,-32)[/tex]The answer is (48,-32).
. Find the value of the variables in the rhombus below. B A 0
Answers
As the triangles are congruent and isosceles we get that
[tex]\begin{gathered} B=37=A=D \\ C=180-2\cdot37=106 \\ 24=4x-4 \\ 4x=28\rightarrow x=\frac{28}{4}=6 \end{gathered}[/tex]Find the X-Intercept and the y-intercept of 4x- 5y = 15X-Intercept:???Y-intercept: ???help
Answers
The y-intercept is (0,-3) while the x-intercept is (18.75,0)
Here, we want to find the x and y-intercepts of the given line
Firstly, we have to rewrite the equation of the line in the standard form
We have this as;
[tex]\text{y = mx + b}[/tex]m is the slope and b is the y-intercept
Rewriting the given equation, we have this as;
[tex]\begin{gathered} 5y\text{ = 4x-15} \\ y\text{ =}\frac{4}{5}x-\frac{15}{5} \\ \\ y\text{ = }\frac{4}{5}x\text{ - 3} \end{gathered}[/tex]We have the y-intercept as -3
In the coordinate form, this is (0,-3)
To get the x-intercept, we set the y value to zero
We have this as;
[tex]\begin{gathered} 0\text{ = }\frac{4}{5}x-15 \\ 15\text{ = }\frac{4x}{5} \\ \\ 4x\text{ = (15}\times5) \\ 4x\text{ = 75} \\ x\text{ = }\frac{75}{4} \\ x\text{ = 18.75} \end{gathered}[/tex]The x-intercept is 18.75 which in the coordinate form is (18.75,0)
x Michael uses synthetic division to divide f(x) by g(x), his last line of work 0/3is shown. How would he write his answer of f(x) divided by g(x). *7 0 24 0 07x^2+24Х
Answers
We know that the last line of the synthetic division is 7
Write 3 equivalent ratios for 5:8
Answers
Given data:
The given ratio is a=5:8.
Multiply 2 on numerator and denominator both.
[tex]\begin{gathered} a=\frac{2(5)}{2(8)} \\ =\frac{10}{16} \end{gathered}[/tex]Multiply 3 on numerator and denominator both.
[tex]\begin{gathered} a=\frac{3(5)}{3(8)} \\ =\frac{15}{24} \end{gathered}[/tex][tex]\begin{gathered} a=\frac{4(5)}{4(8)} \\ =\frac{20}{32} \\ \end{gathered}[/tex]2. Identify the vertex from the quadratic function y=-5(x-6)^2+8 *2 points(-5, 6)(-6,8)(6,8)(8,6
Answers
Answer
2) Option C is correct.
The vertex of the quadratic function is at
x = 6, y = 8.
In coordinate form, the vertex = (6, 8)
4) Option A is correct.
-3 stretches the graph and reflects it about the x-axis.
Explanation
2) We are told to find the vertex of the quadratic function. The vertex of a quadratic function is the point at the base of the curve/graph of the function. It is the point where the value of the quadratic function changes sign.
The x-coordinate of this vertex is given as
x = (-b/2a)
The y-coordinate is then obtained from the value of the x-coordinate.
The quadratic function for the question is
y = -5 (x - 6)² + 8
We first need to put the quadratic function in the general form of
y = ax² + bx + c
So, we first simplify the expression
y = -5 (x - 6)² + 8
= -5 (x² - 12x + 36) + 8
= -5x² + 60x - 180 + 8
y = -5x² + 60x - 172
So,
a = -5
b = 60
c = -172
For the vertex
x = (-b/2a)
= [-60/(2×-5)]
= [-60/-10]
= 6
So, if x = 6.
y = -5x² + 60x - 172
y = -5(6²) + 60(6) - 172
y = -5(36) + 360 - 172
y = -180 + 360 - 172
y = 8
So, the vertex of the quadratic function is at
x = 6, y = 8.
In coordinate form, the vertex = (6, 8)
Option C is correct.
4) y = -3(x²)
The graph of x² is a parabola, but multiplying the function x² by -3 transforms the graph.
The 3, because it is greater than 1, stretches or enlarges the graph.
And the minus sign in front of the 3, ,that is, -3 reflects the graph about the x-axis.
So, altogether, -3 stretches the graph and reflects it about the x-axis.
Option A is correct.
Hope this Helps!!!
Person A went to the store and bought some books at $12 each and some DVDs at $15 each. The bill (before tax) was less than $120. Which inequality represents the situation if x=books and y=DVDs?A) 12x+15y = 120B) 12x+15y < 120C) 12x+15y >-D) none of the above
Answers
Since the cost of each book is $12, and x is the number of books, the total cost of books will be 12x.,
Similarly, since the cost of each DVD is $15, and y is the number of DVDs, the total cost of DVDs will be 15y.
Thus, the total cost of books and DVDs will be 12x + 15y.
We know that the total cost was less than $120, so this expression should be less than 120.
Thus, the inequality is:
[tex]12x+15y<120[/tex]Which corresponds to alternative B.
To check wether the amount in the alternatives can be purchased, we just need to substitute x and y and check wether the inequality is valid:
A
[tex]\begin{gathered} 12\cdot5+15\cdot5<120(?) \\ 60+75<120(?) \\ 135<120\to invalid \end{gathered}[/tex]B
[tex]\begin{gathered} 12\cdot6+15\cdot2<120(?) \\ 72+30<120(?) \\ 102<120\to valid \end{gathered}[/tex]C
[tex]\begin{gathered} 12\cdot2+15\cdot6<120(?) \\ 24+90<120(?) \\ 114<120\to valid \end{gathered}[/tex]D
[tex]\begin{gathered} 12\cdot0+15\cdot10<120(?) \\ 0+150<120(?) \\ 150<120\to invalid \end{gathered}[/tex]E
[tex]\begin{gathered} 12\cdot8+15\cdot0<120(?) \\ 96+0<120(?) \\ 96<120\to valid \end{gathered}[/tex]Thus, the amounts that could have been purchased are thouse in alternatives B, C and E.
Sketch vector v. Be sure to number your axes. Then find the magnitude of vector v. Show all work.
Answers
Step 1
Sketch the vector V.
[tex]v=-2i\text{ +5j}[/tex]Step 2
Find the magnitude of the vector. The magnitude of a vector is given as;
[tex]\begin{gathered} |v|=\sqrt{(i)^2+(j)^2} \\ i=-2 \\ j=5 \\ \left|a+bi\right|\:=\sqrt{\left(a+bi\right)\left(a-bi\right)}=\sqrt{a^2+b^2} \end{gathered}[/tex][tex]\begin{gathered} |v|=\sqrt{(-2)^2+(5)^2} \\ |v|=\sqrt{4+25} \\ |v|=\sqrt{29} \end{gathered}[/tex]Therefore, the magnitude is given as;
[tex]|v|=\sqrt{29}[/tex]which figure can we transformee into figure k by a reflection across the x-axis and dilation of 1/2.
Answers
The rule for reflecting a point through the x-axis is (x, -y) and to dilation is (1/2x, 1/2y):
Now, let's se what figure can be transformed into figure K:
J
(8, 4), reflecting through x-axis (8, -4), dilation (4, -2) --> This point meets figure K
Let's prove with another point of J:
(4, 4) ---> (4, -4) ---> (2, -2) --> This point also meets figure K
Then we can say that figure J can be transformed into figure K
differentiatey = 3x√x⁴-5
Answers
Given:
[tex]y=3x\sqrt{x^4-5}[/tex]Required:
We need to differentiate the given expression.
Explanation:
Consider the given expression.
[tex]y=3x\sqrt{x^4-5}[/tex][tex]y=3x(x^4-5)^{\frac{1}{2}}[/tex]Differentiate the given expression with respect to x.
[tex]Use\text{ }(uv)^{\prime}=uv^{\prime}+vu^{\prime}.\text{ Here u=3x and v=}(x^4-5)^{\frac{1}{2}}.[/tex][tex]y^{\prime}=3x(\frac{1}{2})(x^4-5)^{\frac{1}{2}-1}(4x^3)+(x^4-5)^{\frac{1}{2}}(3)[/tex][tex]y^{\prime}=\frac{3x(4x^3)}{2\left(x^4-5\right)^{\frac{1}{2}}}+3(x^4-5)^{\frac{1}{2}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+3(x^4-5)^{\frac{1}{2}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+\frac{3(x^4-5)^{\frac{1}{2}}(x^4-5)^{\frac{1}{2}}}{(x^4-5)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+\frac{3(x^4-5)}{(x^4-5)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+\frac{3x^4-15}{(x^4-5)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{6x^4+3x^4-15}{\left(x^4-5\right)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{9x^4-15}{\left(x^4-5\right)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)}{\left(x^4-5\right)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)}{\sqrt{x^4-5}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)}{\sqrt{x^4-5}}\times\frac{\sqrt{x^4-5}}{\sqrt{x^4-5}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)\sqrt{x^4-5}}{x^4-5}[/tex]Final answer:
[tex]y^{\prime}=\frac{3(3x^4-5)\sqrt{x^4-5}}{x^4-5}[/tex]Someone help how do I find if it’s a function
Answers
To know if this is a function, simply perform a vertical line test on it.
If it passed the vertical line test then it is a function but if it fails it then it is not a function
In the graph given, if you draw a vertical point at any point, we woulld not have two points on the vertical line, hence it is a function
which portion must be true?
Answers
The two figures are similar
Using the similarity theorem
The only true proportion is
[tex]\frac{8}{2}\text{ = }\frac{x}{y}[/tex]Is the line through points P(3, -5) and 2(1, 4) parallel to the line through points R(-1, 1) and S(3,Explain.
Answers
As given by the question
There are given that the two-point;
[tex]\begin{gathered} P(3,\text{ -5) and Q(1, 4)} \\ R(-1,\text{ 1) and S(3, -3)} \end{gathered}[/tex]Now,
First, find the slope of both of the lines from the point
Then,
For first line:
[tex]\begin{gathered} PQ(m)=\frac{y_2-y_1}{x_2-x_1} \\ PQ(m)=\frac{4_{}+5_{}}{1_{}-3_{}} \\ PQ(m)=\frac{9}{-2} \\ PQ(m)=-\frac{9}{2} \end{gathered}[/tex]Now,
For the second line:
[tex]\begin{gathered} RS(m)=\frac{y_2-y_1}{x_2-x_1} \\ RS(m)=\frac{-3_{}-1_{}}{3_{}+1_{}} \\ RS(m)=-\frac{4}{4} \\ RS(m)=-1 \end{gathered}[/tex]Since both slopes are different, they are not parallel lines, which means parallel lines have the same slope.
Hence, the correct optio
Caleb is renting a kayak for 14.50 per half hour. how much would it cost Caleb to rent the kayak for 5 minutes
Answers
Answer:
It would cost Caleb approximately $2.4 to rent kayak for 5 minutes
Explanation:
Given that Caleb is renting a kayak for $14.40 per half hour.
This means he rents it for 30 minutes, as 30 minutes is half an hour.
In an equation form, we can write as:
$14.40 = 30 minutes
So that:
1 minute = $(14.50/30)
= $0.48
This mean he rents at $0.48 per minute
For 5 minutes, it would cost him:
$0.48 * 5 = $2.4 approximately.
A committee must be made up of two students from grades 9, 10, or 11, and another two students from grade 12. How many different committees can be made? Explain and show all of your work.
Answers
to make the committee