rectangle rstw has diagonals RT and SW that intersect at Z. If RZ= 5x+8 and SW= 11x-3 find the value of x.
Answers
Answer:
19
Explanation:
We know that the diagonals of a rectangle are always equal, therefore RT = SW.
So if RZ = 5x + 8 and SW = 11x - 3, lets's go ahead and find x as shown below;
[tex]\begin{gathered} 2(5x+8)=11x-3 \\ 10x+16=11x-3 \\ 16+3=11x-10x \\ 19=x \\ \therefore x=19 \end{gathered}[/tex]
Related Questions
what are the coordinates of the focus of the conic section shown below (y+2)^2/16-(x-3)^2/9=1
Answers
Given the function of the conic section:
[tex]\mleft(y+2\mright)^2/16-\mleft(x-3\mright)^2/9=1[/tex]This conic section is a hyperbola.
Use this form below to determine the values used to find vertices and asymptotes of the hyperbola:
[tex]\frac{(x-h)^2}{a^2}\text{ - }\frac{(y-k)^2}{b^2}\text{ = }1[/tex]Match the values in this hyperbola to those of the standard form.
The variable h represents the x-offset from the origin b, k represents the y-offset from origin a.
We get,
a = 4
b = 3
k = 3
h = -2
A. The first focus of a hyperbola can be found by adding the distance of the center to a focus or c to h.
But first, let's determine the value of c. We will be using the formula below:
[tex]\sqrt[]{a^2+b^2}[/tex]Let's now determine the value of c.
[tex]\sqrt[]{a^2+b^2}\text{ = }\sqrt[]{4^2+3^2}\text{ = }\sqrt[]{16\text{ + 9}}\text{ = }\sqrt[]{25}[/tex][tex]\text{ c = 5}[/tex]Let's now determine the coordinates of the first foci:
[tex]\text{Coordinates of 1st Foci: (}h\text{ + c, k) = (-2 + 5, 3) = 3,3}[/tex]B. The second focus of a hyperbola can be found by subtracting c from h.
[tex]\text{ Coordinates of 2nd Foci: (h - c, k) = (-2 - 5, 3) = -7,3}[/tex]Therefore, the conic section has two focus and their coordinates are 3,3 and -7,3.
In other forms, the foci of the hyperbola is:
[tex]\text{ }(h\text{ }\pm\text{ }\sqrt[]{a^2+b^2},\text{ k) or (-2 }\pm\text{ 5, 3)}[/tex]Therefore, the answer is letter B.
Answer :It's A lol
Step-by-step explanation:
write the vertex form equation of the parabola with, vertex: (10,9), passes through: (12,-7)
Answers
Th equation of a parabola in its vertex form is;
y = a(x-h)² + k
(h,k) are the coordinates of the vertex and a is a constant
(h, k) = (10, 9)
substitute the above into the equation
y = a(x- 10)² + 9 -------------------(1)
Next is to find the value of a
substitute x=12 and y= -7 into equation (1)
-7 = a (12 - 10)² + 9
-7 - 9 = 4a
-16 = 4a
a = -4
The equation of the parabola will be formed by substituting a = -4 in equation (1)
y = -4(x - 10)² + 9
Jess's age is six years less than three times Ethan's age. The product of their ages is 45. What are their ages? Hint: Write an equation to represent the product of their ages, using x to represent Ethan's age, then solve this quadratic equation. Connect each person to their correct age.
Answers
Jess's age is six years less than three times Ethan's age. The product of their ages is 45. What are their ages?
Hint: Write an equation to represent the product of their ages, using x to represent Ethan's age, then solve this quadratic equation. Connect each person to their correct age.
Let
x ------> Ethan's age
y -----> Jess's age
we have that
y=3x-6 -------> equation A
xy=45 ------> equation B
substitute equation A in equation B
x(3x-6)=45
solve for x
3x^2-6x=45
3x^2-6x-45=0
Solve using the formula
so
a=3
b=-6
c=-45
substitute
[tex]x=\frac{-(-6)\pm\sqrt[]{-6^2-4(3)(-45)}}{2(3)}[/tex][tex]\begin{gathered} x=\frac{6\pm\sqrt[]{576}}{6} \\ \\ x=\frac{6\pm24}{6} \end{gathered}[/tex]the solutions for x are
x=5 and x=-3 (is not a solution)
Find the value of y
y=3(5)-6
y=9
therefore
Ethan's age is 5 years
Jess's age is 9 years
The following hyperbola has a horizontal transverse axis: (x + 2) (w+7)=11617
Answers
for the given hyperbola
[tex]\frac{(x+2)^2}{16}-\frac{(y+7)^2}{17}=1[/tex]We have the following graph. Visually we can see that this hyperbola does have a transverse axis, however you can do all the calculations to check it
[tex]\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1 \\ h=-2 \\ k=-7 \\ a^2=16 \\ b^2=17 \\ c^2=16+17 \\ c=\sqrt[]{33}=5.7 \\ f_1=(h-c,k) \\ f_1=(-2-5.7,-7) \\ f_2=(-7.7,-7) \\ f_2=(3.7,-7) \\ y=-7\to\text{ is the ecuation of the transversal axis} \end{gathered}[/tex]As we can see y = -7 is a line parallel to the x axis, turning the transversal axis horizontal.
That is, this hyperbola does have a horizontal transverse axis and the answer is TRUE
Short steps pleaseFind the mean and variance of the binomial experiment in which n 5 and p 0.7. a. Mean b. Variance
Answers
Given
n= 5
p = 0.7
Find:
a. mean
b. variance
sol:
Mean d
[tex]\begin{gathered} mean\text{ =n}\times\text{p} \\ \\ \text{ = 5}\times\text{0.7} \\ \\ \text{ =3.5} \end{gathered}[/tex][tex]\begin{gathered} variance=np(1-p) \\ \\ =\text{ }5\times0.7(1-0.7) \\ \\ =3.5(0.3) \\ \\ =1.05 \\ \\ \end{gathered}[/tex]What polynomial identity should be used to prove that 40 = 49 − 9?
a
Difference of Cubes
b
Difference of Squares
c
Square of a Binomial
d
Sum of Cubes
Answers
A polynomial identity that should be used to prove that 40 = 49 − 9 is: B. Difference of Squares.
What is a polynomial function?A polynomial function is a mathematical expression which comprises variables (intermediates), constants, and whole number exponents with different numerical value, that are typically combined by using the following mathematical operations:
AdditionMultiplication (product)SubtractionIn Mathematics, the standard form for a difference of two (2) squares is modeled or represented by this mathematical expression:
a² - b² = (a + b)(a - b).
Where:
a and b are numerical values (numbers or numerals).
Given the following equation:
40 = 49 − 9
40 = 7² - 3³
40 = (7 + 3)(7 - 3).
40 = (10)(4)
40 = 40 (proven).
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To graph the inequality y>-3x-4, you would draw a dashed line.O A. TrueO B. False
Answers
True.
Since it is strictly greater
Daisy is buying a video game in the shop. The price before tax is $21, and after sales tax is $24.74. What is the sales tax plied to the video game? Round to the nearest hundredth
Answers
Recall that:
[tex]\text{salesprice}=\text{originalprice+taxes.}[/tex]Therefore Daisy pays:
[tex]24.74-21=3.74\text{ dollars}[/tex]in taxes for the videogame.
Now, recall that to determine the percentage that a represents from b we use the following expression:
[tex]\frac{a}{b}\cdot100.[/tex]Therefore, the sales tax applied to the videogame is:
[tex]\frac{3.74\text{dollars}}{21\text{dollars}}\cdot100\approx17.81[/tex]percent.
Answer: The tax applied to the videogame is 17.81%, in this case, the sales tax is 3.74 dollars.
Frank uses 27/5 tablespoons of pista extract to make 9 servings of a recipe. How many tablespoons of pista extract does each serving need?
Answers
Answer: 3/5 tablespoons.
Use the standard algorithm to solve the equation 36 x 25 =
Answers
Answer: 900
Step-by-step explanation:
Column method
there are 12 questionsI got 7 right what did I make?
Answers
there are 12 questions
I got 7 right
the easiest way to solve this is by using a rule of three
Step 1
Let
[tex]12\text{ questiones }\Rightarrow100\text{ percent}[/tex]then
[tex]7\text{ questions }\Rightarrow x\text{ percent}[/tex]Step 2
do the relation and solver for x
[tex]\begin{gathered} \frac{12}{100}=\frac{7}{x} \\ 12\cdot x=100\cdot7 \\ 12\cdot x=700 \\ x=\frac{700}{12} \\ x=58.33 \\ \end{gathered}[/tex]so, you did the 58.33 %
Graph the exponential function.f(x)=4(5/4)^xPlot five points on the graph of the function,
Answers
We are required to graph the exponential function:
[tex]f(x)=4(\frac{5}{4})^x[/tex]First, we determine the five points which we plot on the graph.
[tex]\begin{gathered} \text{When x=-1, }f(-1)=4(\frac{5}{4})^{-1}=3.2\text{ }\implies(-1,3.2) \\ \text{When x=0, }f(0)=4(\frac{5}{4})^0=4\text{ }\implies(0,4) \\ \text{When x=1, }f(1)=4(\frac{5}{4})^1=5\implies(1,5) \\ \text{When x=2, }f(2)=4(\frac{5}{4})^2=6.25\implies(2,6.25) \\ \text{When x=3, }f(3)=4(\frac{5}{4})^3=7.8125\text{ }\implies(3,7.8125) \end{gathered}[/tex]Next, we plot the points on the graph.
This is the graph of the given exponential function.
if I may ask may you help me solve this
Answers
Explanation
In the image,
[tex]QT=18[/tex]We can see that line SQ is a perpendicular line that serves as the bisector of RT
This implies that;
[tex]RQ=QT=18[/tex]Since;
[tex]\begin{gathered} RQ+QT=RT \\ 18+18=RT \\ RT=36 \end{gathered}[/tex]Answer: 36
Tiffany deposited two checks into her bank account this month.One check was for $50, and the second check was for $22.Her balance at the end of the month was $306, and she made no withdrawals.Which expression shows Tiffany's balance at the beginning of the month?
Answers
Tiffany's balance at the beginning of the month = $229
Explanations:First Deposit = $50
Second Deposit = $22
End of the month balance = $306
Balance at the beginning of the month = End of the month balance - (First Deposit + Second deposit)
Balance at the beginning of the month = 306 - (50 + 22)
Balance at the beginning of the month = 306 - 77
Balance at the beginning of the month = $229
Suppose a charity received a donation of $19.4 million. If this represents 43% of the charity's donated funds, what is the total amount of its donated funds? Round your answer to the nearest million dollars.
Answers
Given :
a charity received a donation of $19.4 million
Which represents 43% of the charity funds
Let the total funds = x
So,
43% of x = 19.4 million
So,
[tex]\begin{gathered} 43\%\cdot x=19.4 \\ \\ 0.43\cdot x=19.4 \\ \\ x=\frac{19.4}{0.43}\approx45.12 \end{gathered}[/tex]Rounding to the nearest million ,
The answer is : total donated funds = 45 million
I have answer for the question it in the image but I don't know if it right and I don't know any other formulas to find the area of a triangle
Answers
Hello there. To solve this question, we'll have to remember which other formulas for area of triangles can be used.
Most specifically, it asks for a formula that works on an obtuse triangle, that is, a triangle that haves an angle that measures more than 90º.
Besides the formula BH/2, that refers to half of the product between the measurements of the base and the height of the triangle, of course, this height must be a projection perpendicular to the base, as in the following drawing:
Another formula that can be used is Heron's formula;
Knowing the measures of all the sides of the triangle (no matter if it is an obtuse, acute or right triangle), say a, b and c, Heron's formula states that the area S of the triangle is given by:
[tex]S=\sqrt{\rho\cdot(\rho-a)\cdot(\rho-b)\cdot(\rho-c)}[/tex]Where
[tex]\rho=\dfrac{a+b+c}{2}[/tex]is the semiperimeter of the triangle.
This is the answer we've been looking for.
Compute the square root of 532 to the nearest tenth. Use the "divideand average method.
Answers
ANSWER:
[tex]\sqrt[]{532}\cong23.065[/tex]STEP-BY-STEP EXPLANATION:
We have the following square root
[tex]\sqrt[]{532}[/tex]We calculate by means of the divide and average method.
The first thing is to look for exact roots between those two values
Step 1 estimate
[tex]\begin{gathered} \sqrt[]{539}<\sqrt[]{532}<\sqrt[]{576} \\ 23<\sqrt[]{532}<24 \\ \text{Estimate 23.5} \end{gathered}[/tex]Step 2 divide
[tex]\frac{532}{23.5}=22.63[/tex]Step 3 average:
[tex]\frac{23.5+22.63}{2}=\frac{46.13}{2}=23.065[/tex]Therefore:
[tex]\sqrt[]{532}\cong23.065[/tex]complete the square to writey= x2 + 4x +9 in graphing form.
Answers
In order to express y = x² + 4x +9 in graphing form and graphing it we can follow these steps:
1. complete squares to express the equation in the form y = (x - p)² + q
We have to add and subtract (b/2)² on the right, where b is the coefficient of the second term of the equation
y = x² + 4x +9 + (4/2)² - (4/2)²
y = x² + 4x +9 + (2)² - (2)²
We can gorup and factor some terms of the equation by applying the following formula:
(x + a)² = x² + 2ax + a²
then by writing 4x as 2×2x we get:
y = x² + 2×2x + (2)² - (2)² +9
y = (x + 2)² - (2)² + 9
y = (x + 2)² - 4 + 9
y = (x + 2)² + 5
For an equation of the form y = (x - p)² + q, the vertex is (q, p), then, the vertex of the parabola is (-2, 5)
2. Determine the x-intercepts by replacing 0 for y and solving for x, like this:
0 = (x + 2)² + 5
0 - 5 = (x + 2)² + 5 - 5
-5 = (x + 2)²
±√-5 = √(x + 2)²
±√-5 = x + 2
x = -2 ± √-5
As you can see, on the right side the argument of the square root is a negative number, which makes the solution of this equation a complex number, then which means that the parabola won't intercept the x-axis.
3. Find the y-intercept by replacing 0 for x:
y = (0 + 2)² + 5
y = (2)² + 5
y = 4 + 5
y = 9
Then, the y-intercept of this parabola is (0, 9)
By graphing the vertex (-2, 5) and the y-intercept (0, 9) and joining them with the parabola we get the following graph:
2/4 turn into decimal
Answers
Answer:
The decimal form of 2/4 is;
[tex]0.5[/tex]Explanation:
We want to turn the fraction to decimal.
[tex]\frac{2}{4}=0.5[/tex]it can be obtained by;
Therefore, the decimal form of 2/4 is;
[tex]0.5[/tex]Find equation of a parallel line and the given points. Write the equation in slope-intercept form Line y=3x+4 point (2,5)
Answers
Given the equation:
y = 3x + 4
Given the point:
(x, y ) ==> (2, 5)
Let's find the equation of a line parallel to the given equation and which passes through the point.
Apply the slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
Hence, the slope of the given equation is:
m = 3
Parallel lines have equal slopes.
Therefore, the slope of the paralle line is = 3
To find the y-intercept of the parallel line, substitute 3 for m, then input the values of the point for x and y.
We have:
y = mx + b
5 = 3(2) + b
5 = 6 + b
Substitute 6 from both sides:
5 - 6 = 6 - 6 + b
-1 = b
b = -1
Therefore, the y-intercept of the parallel line is -1.
Hence, the equation of the parallel line in slope-intercept form is:
y = 3x - 1
ANSWER:
[tex]y=3x-1[/tex]
The width of a rectangle measures (5v-w)(5v−w) centimeters, and its length measures (6v+8w)(6v+8w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answers
The most appropriate choice for perimeter of rectangle will be given by -
Perimeter of rectangle = (22v + 14w) cm
What is perimeter of rectangle?
At first it is important to know about rectangle.
Rectangle is a parallelogram in which every angle of the parallelogram is 90°.
Perimeter of rectangle is the length of the boundary of the rectangle.
If l is the length of the rectangle and b is the breadth of the rectangle, then perimeter of the rectangle is given by
Perimeter of rectangle = [tex]2(l + b)[/tex]
Length of rectangle = (5v - w) cm
Breadth of rectangle = (6v + 8w) cm
Perimeter of rectangle = 2[(5v - w) + (6v + 8w)]
= 2(11v + 7w)
= (22v + 14w) cm
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Complete Question
The width of a rectangle measures (5v−w) centimeters, and its length measures(6v+8w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
-Exponential and Logarithmic Functions- Solve the following, round the answer to the nearest hundredth.
Answers
Answer:
x = 1.70
Explanation:
We were given that:
[tex]\begin{gathered} 5^x=15.4 \\ \text{Take the natural logarithm of both sides, we have:} \\ \ln 5^x=\ln 15.4 \\ x\cdot\ln 5=\ln 15.4 \\ \text{Divide both sides by ''ln5'', we have:} \\ x=\frac{\ln 15.4}{\ln 5}=1.699 \\ x=1.699\approx1.70 \\ x=1.70 \\ \\ \therefore x=1.70 \end{gathered}[/tex]Therefore, x = 1.70
Select all of the expressions approval to c⁶/d⁶:
answers:
(cd-¹)⁶
c¹²d¹⁸/c²d³
c⁸d⁹/c²d³
c⁶d-⁶
c-⁶d⁶
(c‐¹d)-⁶
Answers
Answer:
is = c⁸d⁹/c²d³
hope it helps
mark me brainliest
Find two positive numbers whose difference is 14 and whose product is 1976
Answers
The positive numbers that the difference is 14 and the product is 1976 are 38 and 52.
How to find the positive numbers?The difference of the positive numbers is 14 and the products of the positive numbers is 1976.
The positive numbers are the numbers that are greater than zero.
Positive numbers includes fractions, In general, positive numbers are natural counting numbers.
Therefore,
let the numbers be x and y
Hence, the difference of the positive numbers is 14.
x - y = 14
The product of the positive numbers is 1976. Therefore,
xy = 1976
Make x the subject of the formula in equation(ii)
x = 1976 / y
Substitute the value of x in equation(i)
1976 / y - y = 14
14y = 1976 - y²
solve the quadratic equation formed.
y² + 14y - 1976 = 0
Hence,
y² - 38y + 52y - 1976
y(y - 38) + 52(y - 38)
(y - 38)(y + 52)
Therefore,
y = 38 and y = -52
The number is positive .
Therefore, we can only use 38.
y = 38
Substitute the value of y in equation(i)
x - 38 = 14
x = 14 + 38
x = 52
Therefore, the positive numbers are 38 and 52.
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13. The population of Maryland was 5.17 million in 1999, and it grew to 6.05 million in 2019.(a) Assuming that the population is growing exponentially, find the growth rate r for Maryland's population. Give your answer as a percentage, rounded to the nearest hundredth of a percent.r = %(b) Write an exponential model to describe the population of Maryland from 1999 onward (let t=0 in 1999).Pt = (c) What is Maryland's population expected to be in 2030? Round your answer to one decimal place. million people(d) When do you expect that Maryland's population will reach 7.5 million? Give your answer as a calendar year (ex: 1999).During the year
Answers
Answer:
a) r = 0.79%
b)
[tex]P_t=5.17(1.0079)^t[/tex]c) 6.6 million people
d) 2046
Explanation:
We'll use the below formula for exponential growth;
[tex]P_t=a(1+r)^t[/tex]where a = initial amount
r = growth rate
t = number of time intervals
a) From the question, we have that
a = 5.17 million
P(t)= 6.05 million
t = 20 years
Let's go ahead and substitute these values into our formula, and solve for r as shown below;
[tex]\begin{gathered} 6.05=5.17(1+r)^{20} \\ \frac{6.05}{5.17}=(1+r)^{20} \\ (1+r)=\sqrt[20]{\frac{6.05}{5.17}} \\ r=\sqrt[20]{\frac{6.05}{5.17}}-1 \\ r=0.00789 \\ r=0.79\text{\%} \end{gathered}[/tex]b) The exponential model can be written as shown below;
[tex]\begin{gathered} P_t=5.17(1+0.0079)^t \\ P_t=5.17(1.0079)^t \end{gathered}[/tex]c) When t = 31 years, let's go ahead and find P as shown below;
[tex]\begin{gathered} P_t=5.17(1.0079)^{31} \\ P_t=6.6\text{ million people} \end{gathered}[/tex]d) When P = 7.5 million, let's go ahead and solve for t as shown below;
[tex]\begin{gathered} 7.5=5.17(1.0079)^t \\ 1.45=(1.0079)^t \\ \log 1.45=\log (1.0079)^t \\ \log 1.45=t\times\log (1.0079) \\ t=\frac{\log 1.45}{\log (1.0079} \\ t=47.2\text{years} \\ \end{gathered}[/tex]So to get the particular year all we need to do is add 47 years to the initial year. That will us 1999 + 47 = 2046
The table shows the cost for a clothing store to buy jeans and khakis. The total cost for Saturday's shipment, $1,800, is represented by the equation 15x + 20y = 1,800. Use the x- and y-intercepts to graph the equation. Then interpret the x- and y-intercepts.
Answers
I have attached the question
Answers
The following are the primary factors that the Cvp analysis employs to determine if the sales price per unit and variable costs per unit are impacted
Describe CVP Analysis?This is the term used to describe the cost-volume-profit analysis, which is used to determine how changes in cost and volume might directly affect operating costs.With this in mind, it is clear that the primary component that businesses utilize in their CVP analyses to ensure that their operational costs don't fluctuate arbitrary is cost changes. Profit = revenue - costs is the fundamental CVP formula. Naturally, you must understand how to calculate your revenue in order to use this formula:(Retail price * Units Sold)Additionally, you must understand how to calculate your costs: fixed costs plus (unit variable cost x number of units). Y = a + bx is the cost volume formula. Y = Total expense = Total fixed expense (that is, a cost that does not vary in proportion to activity)B is the variable cost per unit of activity; this cost does vary in relation to activity. Contribution/Sales is the P/V ratio. It is employed to gauge the company's profitability. The surplus of sales over variable costs is known as contribution. In essence, the P/V ratio is utilized to assess the level of contribution provided at various sales volumes.To learn more about Cpv analysis refer
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It takes 6 eggs, 5 oz of cheese, and 2 oz of butter to make twoomelets. What is the cost per omelet if eggs cost $.99 per dozen,1 lb of cheese costs $4.29, and 1/2 lb of butter costs $1.25?a. $2.15b. $1.34c. $1.08d. $.31
Answers
Given:
It takes 6 eggs, 5 oz of cheese, and 2 oz of butter to make two
omelets
Eggs cost per dozen = $0.99
So, the cost of 6 eggs = 0.99/2 = 0.495
1 lb of cheese costs $4.29
1 lb = 16 oz
So, the cost of 5 oz =
[tex]\frac{5}{16}\cdot4.29=1.34[/tex]1/2 lb of butter costs $1.25
So, the cost of 2 oz =
[tex]\frac{2}{8}\cdot1.25=0.3125[/tex]So, the cost of two omelets = 0.495+1.34+0.3125 = 2.1475
So, the cost of one omelet = 2.1475/2 ≈ 1.08
So, the answer will be option c. $1.08
Joyce paid $154.00 for an item at the store that was 30 percent off the original price. What was the original price?
Answers
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Draw the image of the figure under thegiven transformation.8. reflection across the y-axis
Answers
Whne the coordinates are reflected over y -axis, then the coordinates are (x,y) = (-x,y)
.
The coodinates of A(3,0) and after reflection A'(-3,0)
The coordinates B(1,4) and after reflection B'(-1,0)
The coordinates C(5,3) and after reflection C'(-5,3)
Plot the image on the graph
