product means multiplication:
So the product of Pf and EP is PF.EP
that expression is equal to AP.
So, the correct formula is:
PF.EP =AP
y = - (x + 3)^2 + 5 Step 1: Identify the constants a, h, and k. O a = 0, h = 3, and k = 5 a = -1, b = 3, and k = 5 a = -1.b = -3. and k = -5 a.-1, b=-3 and k=5
We can express the equation of a parabola in the form:
[tex]y=a(x-h)^2+k[/tex]Let's identify the constants a,h and k for our case:
[tex]y=-(x+3)^2+5[/tex]As you can see, the term on the parentheses has a minus sign, which means that this term is being multiplied by a -1, hence:
a= -1
Inside the parentheses, there's a 3 that is being added to x instead of being subtracted, this means that h is -3, because x-(-3)=x+3
h= -3
And as we can see, 5 is added to the first term, then:
k=5
A 12 ft lamppost makes a shadow x ft long when the angle of elevation is 30 degrees. Find x. Round your answer to the nearest hundredth.
We can find the length of x using the tangent trig ratio given to be:
[tex]\tan \theta=\frac{\text{opp }}{adj}[/tex]From the diagram provided, we have that:
[tex]\begin{gathered} \theta=30\degree \\ opp=12\text{ ft} \\ adj=x \end{gathered}[/tex]Therefore, we can substitute these values into the ratio and solve for x. This is shown below:
[tex]\begin{gathered} \tan 30=\frac{12}{x} \\ \therefore \\ x=\frac{12}{\tan 30} \\ x=20.78\text{ ft} \end{gathered}[/tex]Therefore, the value of x is 20.78 ft.
What is the magnitude of a vector whose terminal point is at (7,-5)?
Solution
Step 1:
The magnitude of a vector is the length of the vector itself.
Given a bi-dimensional vector, the magnitude of the vector is given by:
[tex]\text{v = }\sqrt{v_x^2+v_y^2}[/tex]Step 2:
where
Vx is the x-component of the vector
Vy is the y-component of the vector
Step 3:
The vector in the problem is ( 7 , -5 )
Where
[tex]\begin{gathered} v_x\text{ = 7} \\ v_y\text{ = -5} \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} \text{v = }\sqrt{7^2\text{ + \lparen-5\rparen}^2} \\ \text{v = }\sqrt{49\text{ + 25}} \\ \text{v = }\sqrt{74} \\ \end{gathered}[/tex]Final answer
[tex]\begin{gathered} Magnitude\text{ of the vector is} \\ \sqrt{74}\text{ or 8.6} \end{gathered}[/tex]Mia by eight apples and four mangoes for $.34 find the cost of single apples
Given:
Isabella bought 2 apples and 4 mangoes for 28 cents. Mia bought 8 apples and 4 mangoes for 34 cents.
Required:
We need to find the cost of single apple.
Explanation:
First of all let assume a as a apple and m as a mango so now the equations are as
[tex]\begin{gathered} 2a+4m=28 \\ 8a+4m=34 \end{gathered}[/tex]now use substitution method
[tex]4m=28-2a[/tex]put this in another equation and we get
[tex]\begin{gathered} 8a+28-2a=34 \\ 6a=6 \\ a=1 \end{gathered}[/tex]Final answer:
So the cost for single apple is 1 cent.
Graph triangle DEF with vertices D(2,4) E(6,4) and F(4,8) and it’s image after a dilation centered at the origin with a scale factor of 3/2. Then, find the difference between the area of the image and the area of the preimage.The graphing part I got correct. I’m just confused on how to find the difference between the area of the image and the preimage.
We have to find the difference between the area of the image and the pre-image.
When we scale a figure with a scale factor k, the the area of the image figure will be k² times the area of the pre-image figure.
We will prove this by calculating both areas with the traditional method: the area of a triangle is equal to half the product of the base and the height.
We can identify the base and the height in the graph of both figures as:
We then can calculate the area of the pre-image as:
[tex]A=\frac{bh}{2}=\frac{4\cdot4}{2}=\frac{16}{2}=8[/tex]and the area of the image as:
[tex]A^{\prime}=\frac{b^{\prime}h^{\prime}}{2}=\frac{6\cdot6}{2}=\frac{36}{2}=18[/tex]Then, the difference in the area between the image and the pre-image is:
[tex]d=A^{\prime}-A=18-8=10[/tex]NOTE: we can now test that the relation between the areas is k²:
[tex]\begin{gathered} k=\frac{3}{2} \\ A^{\prime}=k^2\cdot A \\ A^{\prime}=(\frac{3}{2})^2\cdot8=\frac{9}{4}\cdot8=\frac{72}{4}=18 \end{gathered}[/tex]Answer: the difference of areas between the image and the pre-image is 10 square units.
Translate and solve:Five less than two-thirds of a number is three. Find the number.
Let the number be x
step 1: Two-thirds of the number x is
[tex]\frac{2}{3}x[/tex]step 2: Five less than two-thirds of the number is
[tex]\frac{2}{3}x-5[/tex]step 3: Equals 3
[tex]\frac{2}{3}x-5=3[/tex]step 4: Solve for x
[tex]\begin{gathered} \frac{2}{3}x-5=3 \\ \text{collect like terms} \\ \frac{2}{3}x=3+5 \\ \frac{2}{3}x=8 \\ \text{Multiply both sides by the denominator 3} \\ \frac{2x}{3}\times3=8\times3 \\ 2x=24 \\ x=\frac{24}{2}=12 \end{gathered}[/tex]Therefore, the number is 12
A triangular pyramid is sliced by a plane parallel to the base. What is the shape of the cross-section?choice:rectangletrianglestarsquare
Answer:
triangle
Explanation:
The base of a triangular pyramid is a triangle, so if this figure is sliced by a plane parallel to the base, the cross-section will have the shape of the base. Then, cross-section is also a triangle.
So, the answer is triangle
The function is defined as follows for the domain given. h(x) = 1 - 2x; domain = \{- 3, - 2, 1, 5\} Write the range of h using set notation. Then graph h.
Given: The function below
[tex]\begin{gathered} h(x)=1-2x \\ Domain:\lbrace-3,-2,1,5\rbrace \end{gathered}[/tex]To Determine: The range and the graph of h9x)
Solution
Please note the ddomain is the input of the function. Let us use the values of x (domain) to get the range as shown below
[tex]\begin{gathered} h(x)=1-2x \\ x=-3 \\ h(-3)=1-2(-3) \\ h(-3)=1+6=7 \end{gathered}[/tex][tex]\begin{gathered} x=-2 \\ h(-2)=1-2(-2) \\ h(-2)=1+4=5 \\ x=1 \\ h(1)=1-2(1) \\ h(1)=1-2=-1 \end{gathered}[/tex][tex]\begin{gathered} h(5)=1-2(5) \\ h(5)=1-10=-9 \end{gathered}[/tex]Hence, the range is {7, 5, -1, -9}
Let use the domain, the set of x-values to plot a graph against the corresponding y- values
The table of values showing x-values and corresponding y-values is
The graph of the domain and the range values is as shown below
Convert the following radian or degree measures to the other form
Solution
For this case we need to take in count that:
[tex]\pi=180[/tex]Then we can do this:
[tex]\frac{\pi}{5}=36\text{degrees}[/tex]And we can convert -155° on this way:
[tex]\frac{x}{-155}=\frac{\pi}{180}[/tex]Solving for x we got:
[tex]x=-155\cdot\frac{\pi}{180}=-\frac{31}{36}\pi[/tex]identify the constant of variation.7y-4x=0
We have the following equation given:
[tex]7y-4x=0[/tex]We can solve for y like this:
[tex]7y=4x[/tex][tex]y=\frac{4}{7}x[/tex]And if we compare with the general formula:
[tex]y=kx[/tex]With k the constant of variation we see that the answer is k= 4/7
Draw an angle in standard position such that the terminal side passes through the given point. (-4, -3)
Explanation
We are told to draw the angle in the standard position that passes through the point (-4, -3)
In this case,
[tex]\begin{gathered} x=-4 \\ y=-3 \end{gathered}[/tex]solve the following variation: interest varies jointly with time and principle of the interest is 1,000 when the time is 10 years and the principle is 6,000. then find the equation of the variable
Interest varies jointly with time and principle
let I = interest
time = t
Principle = P
Mathematically:
[tex]\begin{gathered} I\text{ }\alpha\text{ tP} \\ I\text{ = ktP} \\ where\text{ k = constant of proportionality} \end{gathered}[/tex]when interest = 1000
time = 10 years
Principal = 6000
We will substitute these values in the formula we got above to get k:
[tex]\begin{gathered} 1000\text{ = k}\times10\times6000 \\ 1000\text{ = 60000k} \\ divide\text{ both sides by 60000:} \\ \frac{1000}{60000}\text{ = }\frac{60000k}{60000} \\ k\text{ = 1/60} \end{gathered}[/tex]To get the equation of the variable, we will substitute the value of k in the formula:
[tex]\begin{gathered} I\text{ = }\frac{1}{60}\times t\times P \\ \\ Equation\text{ of the variable:} \\ I\text{ = }\frac{tP}{60} \end{gathered}[/tex]find the axis of symmetry, the max or min, y and x intercepts, the domain, and the range of y=(x+2)^2-9
The quadratic equation is
[tex]y=x^2+4x-5[/tex]The solutions to the question can all be gotten from the graph of the quadratic equation;
The axis of symmetry is the point on the x-axis that divides the vertex of the parabola into two equal parts.
Therefore, the axis of symmetry occurs at x = -2
The graph curves downwards, hence it has a minimum point.
The minimum point occurs at y = -9
The y-intercept is the point where the curve cuts the y-axis when x = 0
Thus, the y-intercept occurs at y = -5
The x-intercept is the point where the curve cuts the x-axis at y = 0. The x-intercept also means the root of the equation
The x-intercept occurs at x = -5 and x = 1.
The domain of the equation is the set of all real values of x that will give real values for y.
Hence, the domain is from minus infinity to plus infinity. All real values of x satisfy the equation.
Domain =
[tex](-\infty,+\infty)[/tex]The range of a quadratic graph is the set of all real values of y that you can get by inputting real values of x
The graph ranges from y greater than or equal to -9
Therefore, the range is ;
[tex]y\ge-9[/tex]What do they mean to write 5 less than r as an expression
What do they mean to write 5 less than r as an expression?
Explanation:
From the given data,
[tex]r-5[/tex]Thus, the expression is (r-5)
Hey :)
[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
Put a minus sign between 5 and r. And put 5 after the minus.
[tex]r-5[/tex]. This is what the expression is. If you do everything correctly, then ur answer should be [tex]r-5[/tex].
So, the calculations showed that the answer is x=5. I hope i could provide a good explanation and a correct answer to you. Thankyou for taking the time to read my answer.
here for service,
silennia[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
Estimate the area of a triangle with a base of 4.23 inches and a height of 7.8 inches.A) 16 in^2B) 32 in^2C) 14 in^2D) 28 in^2
Formula of area of a triangle ( A ):
[tex]A=\frac{b\cdot h}{2}[/tex]where b is the base and h is the height.
Procedure:
0. Replacing the values given
[tex]A=\frac{4.23\cdot7.8}{2}[/tex]2. Simplifying
[tex]A=\frac{32.99}{2}[/tex][tex]A\approx16.50[/tex]Answer: A) 16 in^2
Which of the following values would complete the ordered pair if the point is on the graph of f(x) = -2x + 3?(-1____)-40 15
An ordered pair is a pair of values called the input and output, or just the x and the y on your graph. The input is your x and the output is your y.
When you're given a function, as long as you have a value for your x, you can always easily determine your value of y. Hence, you input -1 and whatever the result is, you have your y value.
The function is given as
f(x) = -2xof y
Kuta Software - Infinite Algebra 2 Name Solving Multi-Step Equations Solve each equation. 2-12=2+5v 1) 4n - 2n = 4
The volume of a soup can is 125.6 cubic inches the diameter of the can is 8 inches what is the height of the soup can
Okay, here we have this:
Considering the provided information, we are going to calculate the requested height of the cylinder, so we obtain the following:
Then to find the requested height we will clear the height of the formula for the volume of a cylinder, therefore we have:
V=h * π * r^2
h=V/(π * r^2)
Replacing with the given values:
h=V/(π * (d/2)^2)
h= 125.6 in^3/(π * (8in/2)^2)
h= 125.6 in^3/(π * (4in)^2)
h= 125.6 in^3/(π * 16in^2)
h= 125.6 in^3/(3.14 * 16in^2)
h= 125.6 in^3/(50.24 in^2)
h= 2.5 inches
Finally we obtain that height of the soup can is 2.5 inches.
Convert: 176 ounces=pounds
EXPLANATION
The relationship between ounces and pounds is 1 pound is equivalent to 16 ounces.
Therefore, we can apply the unit method to get the amount of pounds, as follows:
[tex]Weight\text{ in pounds=176 ounces*}\frac{1\text{ pound}}{16\text{ ounces}}=[/tex]Simplifying:
[tex]Weight\text{ in pounds=11 pounds}[/tex]In conclusion, the solution is 11 pounds.
A class has 12 boys and 21 girls. The class as a whole has a GPA (grade point average) of 2.96, and the boys have a GPA of 2.40. What is the GPA of the girls? (Round your answer to two decimal places.)
Given data:
A class has 12 boys and 21 girls.
The GPA of the whole class is 2.96.
The GPA of the boys is 2.40.
to find the GPA of girls,
let x be the GPA of girls.
Then,
(12+21)(2.96) = 12(2.40) + 21x
33(2.96) = 28.8 + 21x
97.68 = 28.8 + 21x
68.88 = 21x
x = 68.88/21
x = 3.28.
Carrie and Steve agree to a $149,000 mortgage at 5.5% annual interest for 30 years. They have a monthly payment of $846.01 and the interest paid in month one is $682.92. Assuming they only make the minimum payment in month one, what do you know about their loan?
They make the minimum payment in month one, which is just the interest from the value of the mortgage. That means that the initial $149.000 has no change, if the value of the mortgage has no change, and the interest neither, then the interest in month two will be $682.92.
In the standard equation for a conic section Ax? + Bxy + Cy? + Dx +Ey + F = 0, if B2 - 4AC > 0, the conic section in question is a circle.TrueFalse
If B² -4AC > 0, the conic is a hyperbola. If B² -4AC < 0, the conic is a circle, or an ellipse. If B² - 4AC = 0, the conic is a parabola.
So in this case the conic section in question is a hyperbola. Therefore it is false.
Solve 5c^2 + 5c = 36 by completing the square. If there are multiple answers, list them separated by a comma (e.g. there is no real solution, enter Ø. Enter an exact answer. Provide your answer below:
First, completing the square, we have:
[tex]undefined[/tex]Heather dropped a water balloon over the side of her school building from a height of 80 feet.The approximate height of the balloon at any point it's fall can be represented by the following quadratic equation: h=16t^2+80. About how long did it take for the balloon to hit the groundA. 1.73B.2.24C.2.45D.2.83
Here, we want to know the time it took the ballon to reach the ground from the given height
Now, the height on the ground is at 0 ft
Thus, at this point, h= 0
Which of the following equations is equivalent to v = logx? O A. r=10 O B. v=107 O c. v=x 710 O D. r= 1,10
Given the equation :
[tex]v=\log x[/tex]The given equation is equivalent to :
[tex]x=10^v[/tex]Find the quotient. 5 3 2 = 7 8 12 3 5 2 = 7 8 12 (Type a whole number, fraction, or mixed number.)
Step 1
Write your question.
[tex]\begin{gathered} 2\frac{3}{8}\text{ }\frac{.}{.}\text{ 7}\frac{5}{12} \\ \end{gathered}[/tex]Step 2
Convert all mixed fractions to improper fractions.
[tex]=\text{ }\frac{19}{8}\text{ }\frac{.}{.}\text{ }\frac{89}{12}[/tex]Step 3
Change division to multiplication and invert the fraction.
[tex]\begin{gathered} =\text{ }\frac{19}{8}\text{ x }\frac{12}{89} \\ =\text{ }\frac{19\text{ x 3}}{2\text{ x 89}} \\ =\text{ }\frac{57}{178} \end{gathered}[/tex]Student in a limnology class took water from a lake to determine the temperature at different depths. Which of the following techniques for gathering data do you think was used
The Experiment is the best way to determine the temperatures at different depths. This is because to do a measurement of the temperature it's necessary that the student introduce a thermometer into the water by himself, and determine how the temperature is changing while He is go down with the thermometer into the water of the lake.
All the previous description is the description of an Experiment.
How many liters each of a 50% acid solution and a 75% acid solution must be used to produce 70 liters of a 70% acid solution? (Round to two decimal places if necessary.)
We can express this as a system of equations.
Let x be the liters of the 50%-acid solution and y the liters of the 75%-acid solution.
We then need 2 equations to solve this.
One equation is the total amount of liters (70 liters) that is equal to the sum of the amount of each solution:
[tex]x+y=70[/tex]The second equation is the final concentration, that is a weighted average of the concentration of each solution:
[tex]0.5\cdot x+0.75\cdot y=0.7\cdot70=49[/tex]Then, we can solve this by substitution:
[tex]x+y=70\longrightarrow y=70-x[/tex][tex]\begin{gathered} 0.5x+0.75y=49 \\ 0.5x+0.75(70-x)=49 \\ 0.5+52.5-0.75x=49 \\ -0.25x=49-52.5 \\ -0.25x=-3.5 \\ x=\frac{3.5}{0.25} \\ x=14 \end{gathered}[/tex]Then, we can calculate y as:
[tex]y=70-x=70-14=56[/tex]Answer: we need 14 liters of the 50% acid solution and 56 liters of the 75% acid solution.
help me graph a consistent dependent system of linear equations
Let's start with some definitions. First, a sistem of linear equations means that each equation of the system can be graphed as a line and can be written as follows:
[tex]y=a+bx[/tex]The solutions of a system of linear equations is the interception of the lines of each equation.
If the system is consistent, it means that it has at least one solution.
If the system is dependent, it means that it has infinite solutions.
Graphically, the system has no solution if the lines are parallel (they have the same slope) and they don't itnercept each other, so they have different y-intercepts.
The system will have only one solution when the lines have different slopes.
And the system will have infinite solutions if the lines have the same slope and the same y-intercept, meaning they are the same.
So, a consistent dependent system of linear equations have infinite solutions by definition, meaning the lines are the same, which can be represented graphically by two lines that are together:
In the graph above, we can see an example of this, where the lines are together.
A translation 1 unit down and 6 units left maps L onto L'. If the coordinatesof L are (-2, 6), what are the coordinates of L'?
Translation
We are given the rule for a translation: 1 unit down and 6 units left. It can be written as:
(x,y) --> (x - 6 , y -1 )
We need to subtract 6 units to the x-coordinate and subtract 1 unit to the y-coordinate.
The point L=(-2,6) will map to L' when applied the translation described above.
The coordinates of L' are:
L' = (-2-6 , 6 - 1 ) = (-8 , 5)
The coordinates of L' are (-8,5)
