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Given that the triangles are similar, we can express a proportion between their sides. DE and XY are corresponding sides. EF and YZ are corresponding sides. Let's define the following proportion.
[tex]\begin{gathered} \frac{XY}{DE}=\frac{YZ}{EF} \\ \frac{10}{5}=\frac{14}{2x-1} \end{gathered}[/tex]Now, we solve for x
[tex]\begin{gathered} 2=\frac{14}{2x-1} \\ 2x-1=\frac{14}{2} \\ 2x=7+1 \\ x=\frac{8}{2} \\ x=4 \end{gathered}[/tex]Hence, the answer is x = 4.Related Questions
help please A sandwich shop has three kinds of bread, seven types of meat, and four types of cheese. How many different sandwiches can be made using one type of bread, one meat, and one cheese?
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Types of combinations of
Bread, Meat , CHeese
How many combinations of B M CH can be made.
There are 3, 7 and 4 types of food , respectively
Made a tree of possibilities
Then, for every 3 , there are 7 possibilities. Multiply both
3 x 7 = 21
And for every 7 , there are 4 possibilities . Multiply then
3x 7 x 4 = 84 possible type of sandwiches
The table below shows the relationship between the number of hours a student studied and theirgrade on a certain test.
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It is necessary to adjust the given points of the graph to a line. The general form of the equation of a line is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept of the line.
To calculate the slope m, use the following formula:
[tex]undefined[/tex]Write the tangent ratios for LP and 4Q. If needed, reduce!P12R160Not drawn to scaletan P=tan Q =
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Given: The right triangle PQR as shown
To Determine: The tangents of P and Q
Solution
Given a right triangle, the tangent of any angle can be determine
Note that the side facing the right angle is the hypothenuse, the side facing the angle is the opposite and the other side is the adjacent.
Determine the opposite and the adjacent for angle P in the triangle PQR given
[tex]\begin{gathered} Note; \\ tan\theta=\frac{opposite}{adjacent} \\ tanP=\frac{16}{12} \\ tanP=\frac{4}{3} \end{gathered}[/tex]For lunch, Kile can eat a sandwich with either ham or a bologna and with or without cheese. Kile also has the choice of drinking water or juice with his sandwich. The total number of lunches Kile can choose isA. 12B. 8C. 4D. 6
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Okay, here we have this:
She can eat the following options:
Sandwich with ham with or without cheese. Two choices.
Sandwich with bologna with or without cheese. Other two choices
This mean that she can eat:
Sandwich with ham with cheese with water or juice. Two options.
Sandwich with ham without cheese with water or juice. Two options.
Sandwich with bologna with cheese with water or juice. Two options.
Sandwich with bologna without cheese with water or juice. Two options.
Finally we obtain a total of: 2+2+2+2=8 options of lunches.
Thw
Evaluate the function f(p) = p2 + 3p + 1 for p = -2.
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The result of the function f(p) = [tex]p^2[/tex] + 3p + 1 for p = -2 is -1
The function is
f(p) = [tex]p^2[/tex] + 3p + 1
The function is the expression that represents the relationship between the one variable and another variable. If one variable is dependent variable then the another variable will be independent variable.
The values of p = -2
Substitute the value of p in the function and find the solution
f(p) = [tex]p^2[/tex] + 3p + 1
f(-2) = [tex](-2)^2[/tex] + 3×-2 + 1
f(-2) = 4 - 6 + 1
f(-2) = -1
Hence, the result of the function f(p) = [tex]p^2[/tex] + 3p + 1 for p = -2 is -1
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pets : | bird | cat | dog | snake |frequency: | 3 | 5 | 11 | 1 |which of the following statments does NOT reflect the distribution of the data?a. one-fourth of the pets are catsb. snakes represent 10% of the pets on the farmc. the number of biirds and snakes on the farm make up 20% d. more than half of the pets on the farm are dogs
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SOLUTION:
Case: Interpreting from tables
The total number of pets is 20
Checking the options
Option A.
One-fourth of the pets are cats
[tex]\frac{1}{4}\times20=5\text{ }pets[/tex]This is TRUE from the table
Option B
Snakes represent 10% of the pets on the farm
[tex]\begin{gathered} 10\%\times20 \\ \frac{10}{100}\times20=2\text{ }pets \end{gathered}[/tex]This is FALSE from tables as there is only 1 snake
Option C
The number of biirds and snakes on the farm make up 20%
[tex]\begin{gathered} 20\%\times20 \\ \frac{20}{100}\times20=4\text{ }pets \end{gathered}[/tex]This is TRUE from the table
Option D
More than half of the pets on the farm are dogs
[tex]\frac{1}{2}\times20=10\text{ }pets[/tex]This is TRUE from the table
Let f(x)=5x.Let g(x)=5x−7.Which statement describes the graph of g(x)with respect to the graph of f(x)? g(x)is translated 7 units down fromf(x).g(x)is translated 7 units left fromf(x).g(x)is translated 7 units right from f(x).g(x)is translated 7 units up fromf(x).
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Given
[tex]\begin{gathered} f(x)=5x \\ g(x)=5x-7 \end{gathered}[/tex]According to rules of transformation:
f(x)+c shift c units up and f(x)-c shift c units down.
For the given function g(x) = 5x-7, 7 is being subtracted from 5x.
Where 5x is represented by f function.
Therefore, we could apply the rules of transformation f(x)-c shift c units down.
Here the value of c is 7.
Answer: g(x) is translated 7 units down from f(x)
food cost for your restaurant is about $.38 on the dollar. that means for every dollar in sales, you spend 38 cents in food cost.figure out the food cost for the following days’ sales:monday:$3,459.00tuesday:$2,976.81wednesday:$3,185.32thursday:$3,562.91friday:$4,582.13saturday:$4,820.36
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The Solution.
Monday's sales is $3459.00
The food cost for Monday is
[tex]\text{ Food cost = 0.38}\times3459=\text{ \$1314.42}[/tex]Tuesday's sales is $2976.81
The food cost for Tuesday is
[tex]\text{Food cost = 0.38}\times2976.81=\text{ \$}1131.19[/tex]Wednesday's sales is $3185.32
The food cost for Wednesday is
[tex]\text{ Food cost = 0.38}\times3185.32=\text{ \$}1210.42[/tex]Thursday's sales is $3562.91
The food cost for Thursday is
[tex]\text{Food cost = 0.38}\times3562.91=\text{ \$}1353.91[/tex]Friday's sales is $4582.13
The food cost for Friday is
[tex]\text{Food cost = 0.38}\times4582.13=\text{ \$}1741.21[/tex]Saturday's sales is $4820.36
The food cost for Saturday is
[tex]\text{Food cost = 0.38}\times4820.36=\text{ \$}1831.74[/tex]Graph the equation and find the x-coordinate of the x-intercept:1.5x - 3y = 7Round to the nearest hundredth
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We can begin by finding the x-intercept. This is the point at which the graph crosses the horizontal axis. This point is given when the y-value of the function is 0, then, we can solve the equation for y = 0 and find the value for x:
[tex]\begin{gathered} 1.5x-3y=7\to y=0 \\ 1.5x-3\cdot(0)=7 \\ 1.5x=7 \\ x=\frac{7}{1.5} \\ x\approx4.67 \end{gathered}[/tex]The x value of the x-intercept of the equation is approximately 4.67.
This is a linear equation, to build the graph we just need 2 points and join them with the line.
The x-intercept is the point (4.67, 0). Another easy point to find and build the graph can be the y-intercept, which is given when x = 0. Replacing in the equation:
[tex]\begin{gathered} 1.5x-3y=7\to x=0 \\ 1.5\cdot(0)-3y=7 \\ -3y=7 \\ y=\frac{-7}{3} \\ y\approx-2.33 \end{gathered}[/tex]With this, the other point we can use to graph the equation is (0, -2.33).
Drawing both points on a cartesian plane:
Both points (x and y-intercepts) are drawn in red.
b. (-4,-1) Y= 4/3 x + 6What’s the equation of the line in standard form
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When two lines are perpendicular, the slopes of the lines m1 and m2 are related such that
m1m2 = -1
from the given equation comparing with tyhe general form of the equation of a line (y = mx + c)
m1 = 4/3
The slope of the perpendicular line is -3/4
The equation of the line
y- -1 = -3/4(x - -4)
y + 1 = -3/4(x + 4)
y + 1 = -3x/4 - 3
Subtract 1 from both sides
y + 1 - 1 = -3x/4 - 3 - 1
y = -3x/4 - 3 - 1
y = -3x/4 - 4
This is the standard form of the equation
true or false 16/24 equals 30 / 45
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True.
Given:
The equation is, 16/24 = 30/45.
The objective is to find true or false.
The equivalent fractions can be verified by, mutiplying the denominator and numerator of each fraction.
The fractions can be solved as,
[tex]\begin{gathered} \frac{16}{24}=\frac{30}{45} \\ 16\cdot45=24\cdot30 \\ 720=720 \end{gathered}[/tex]Since both sides are equal, the ratios are equivalent ratios.
Hence, the answer is true.
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
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The required equation has the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p is 230p – 1010 = 650p – 400 – p.
What is an equivalent expression?Equivalent expressions are even though they appear to be distinct, their expressions are the same. when the values are substituted into the expression, both expressions produce the same result and are referred to be equivalent expressions.
We have the given expression below:
⇒ 2.3p – 10.1 = 6.5p – 4 – 0.01p
Convert the decimal into a fraction to get
⇒ (23/10)p – (101/10) = (65/10)p – 4 – (1/100)p
⇒ (23p – 101)/10 = (650p – 400 – p) /100
⇒ 230p – 1010 = 650p – 400 – p
As a result, the equation that has the same answer as 230p – 1010 = 650p – 400 – p.
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The table shows the total cost c for the number of aquarium tickets purchased t. Write an equationthat can be used to find the cost c oft aquarium tickets. Use the equation and complete the table tofind the cost of 7 tickets.7Number of Tickets, tCost, cWrite an equation3$29.2510 12$97.50 $117.00(Use the operation symbols in the math palette as needed. Use integers or decimals for any numbers in the equatioDo not include the $ symbol in your answer.)
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We can model the cost and number of tickets by a linear equation of the form
[tex]c=mt+b[/tex]Where c is the cost, t is the number of tickets.
m is the slope of the equation and b is the y-intercept.
First, let us find the slope which is given by
[tex]m=\frac{c_2-c_1}{t_2-t_1}[/tex]You can take any two pairs of values from the table.
[tex]m=\frac{117-97.50}{12-10}=\frac{19.5}{2}=9.75[/tex]The slope is 9.75 and the equation becomes
[tex]c=9.75t+b[/tex]Now we need to find the y-intercept (b)
Choose any one pair of values from the table and substitute them into the above equation and solve for b.
Let's choose (12, 117)
[tex]\begin{gathered} c=9.75t+b \\ 117=9.75(12)+b \\ 117=117+b \\ b=117-117 \\ b=0 \end{gathered}[/tex]The y-intercept is 0 so the equation is
[tex]c=9.75t[/tex]Now to find the cost of 7 tickets, simply substitute t = 7 into the above equation
[tex]\begin{gathered} c=9.75t \\ c=9.75(7) \\ c=68.25 \end{gathered}[/tex]Therefore, the cost of 7 tickets is $68.25
Graph the reflection of the polygon in the given line #5 Y=2
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We have the next image
the line of reflection is the line in red
the original polygon ABCD is the one in blue
the reflected polygon A'B'C'D' is the one in green
How do I simplify my answer of 42i^2+32i+6 when the original problem was (2-6i)(3-7i)
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Given problem is
[tex](2-6i)(3-7i)[/tex]Now,
[tex]\begin{gathered} (2-6i)(3-7i)=42i^2-14i-18i+6 \\ =42i^2-32i+6 \end{gathered}[/tex]We know that
[tex]i^2=-1[/tex]Using this face,
[tex]\begin{gathered} 42i^2-32i+6=-42-32i+6 \\ =-32i-36 \end{gathered}[/tex]Hence, the simplified form is
[tex]-32i-36[/tex]Write an equation in slope-intercept form for the line through (-1, 1) and (0,3).
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The slope intercept form of a line can be written as:
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
We have two points of the line: (-1,1) and (0,3).
Knowing that for x=0, the value of y=3 tells us that the y-intercept b is b=3:
[tex]\begin{gathered} y=mx+b \\ 3=m\cdot0+b \\ 3=b \end{gathered}[/tex]Using the other point and replacing the values of x and y in the equation we can calculate the value of the slope m:
[tex]\begin{gathered} y=mx+3 \\ 1=m\cdot(-1)+3 \\ 1-3=-m \\ -2=-m \\ m=2 \end{gathered}[/tex]Then, with m=2 and b=3, the equation becomes:
[tex]y=2x+3[/tex]Answer: y=2x+3
Find an equation of the line. Write the equation using function notation.Through (4, - 7); perpendicular to 6y=x- 12The equation of the line is f(x)=..
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To determine the equation of the line you need to determine its slope first.
You know that the line 6y=x-12 is perpendicular to the line you have to determine, two lines that are perpendicular, their slopes are opposite reciprocals. For example, let "m" represent the slope of one of the lines and "n" represent the slope of the perpendicular line, you can express their relationship as follows:
[tex]m=-\frac{1}{n}[/tex]To determine the slope of the given line, you have to write it in slope-intercept form:
[tex]y=mx+b[/tex]Where
m represents the slope
b represents the y-intercept
Given the line:
[tex]6y=x-12[/tex]-Divide both sides by 6
[tex]\begin{gathered} \frac{6y}{6}=-\frac{x}{6}=-\frac{12}{6} \\ y=-\frac{1}{6}x-2 \end{gathered}[/tex]The slope of this line is the coefficient of the x-term, n=-1/6
Its opposite reciprocal is:
[tex]\begin{gathered} m=-\frac{1}{n} \\ m=-(-\frac{1}{\frac{1}{6}}) \\ m=-(-1\cdot6) \\ m=-(-6) \\ m=6 \end{gathered}[/tex]The slope of the line you have to determine is m=6
Now that you have the slope of the line, using the point-slope form, you can determine the equation of the line:
[tex]y-y_1=m(x-x_1)[/tex]Where
m represents the slope of the line
(x₁,y₁) represent the coordinates of one point of the line
Replace the formula with m=6 and (x₁,y₁)=(4,-7)
[tex]\begin{gathered} y-(-7)=6(x-4) \\ y+7=6(x-4) \end{gathered}[/tex]The next step is to write the equation in slope-intercept form:
-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} y+7=6\cdot x-6\cdot4 \\ y+7=6x-24 \end{gathered}[/tex]-Pass "+7" to the right side of the equation by applying the opposite operation "-7" to both sides of it:
[tex]\begin{gathered} y+7-7=6x-24-7 \\ y=6x-31 \end{gathered}[/tex]Finally, write the equation of the line using function notation:
[tex]f(x)=6x-31[/tex]Look at the photograph and if you need anything let me know
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Observe that the triangles have one pair of congruent angles, and two pair of congruent sides. This means we can demonstrate the congruence using SAS postulate, that is, Side-Angle-Side.
Therefore, the answer is the first option.
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, the team observes that the angle of elevation to the top of the mountain is 32o. From a point 2,000 feet closer to the mountain along the plain, the team finds that the angle of elevation is 35o. How tall (in feet) is the mountain? Round to two decimal places.
___________
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To calculate the angle of elevation, just measure the angle formed by the line of sight and the level plain. The elevation of the peak is 10406.58 feet at its highest point.
This is further explained below.
What is the height of the mountain?Where
<A=30
AB=2000
<A B C=180-33
<A B C=147
<B C A=180-<A-<A B C
< B C A=180-30-147
<BCA=3
To begin, the side length BC may be calculated by using the following formula:
[tex]\frac{B C}{\sin A}=\frac{A B}{\sin C}[/tex]
So, we have:
B C=sin A *(A B/sin C)
B C=sin (30) *2000/sin (3)
B C=19107.3
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Find x, for which 7x+8=4x-10
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We are given the equation 7x+8=4x-10 and we want to find the value of x, such that the equality holds. To do so, we will start with the equation and the solve it for x. That is, we will apply mathematical operations on both sides of the equation, so we end up "ilosating" the x on one side of the equality sign. We start by
[tex]7x+8=4x\text{ - 10}[/tex]First, we subtract 4x on both sides, so we get
[tex]\text{ -10=(7x-4x)+8=3x+8}[/tex]Now, we subtract 8 on both sides, so we get
[tex]3x=\text{ -10-8=-18}[/tex]Finally, we divide both sides by 3, so we get
[tex]x=\frac{\text{ -18}}{3}=\text{ -6}[/tex]so x=-6.
Under certain conditions, the velocity of a liquid in a pipe at distance r from the center of the pipe is given by V = 400(3.025 x 10-5--2) where Osrs5,5x10 -3. Writeras a function of V.r=where the domain is a compound inequality(Use scientific notation. Use integers or decimals for any numbers in the expression.)Le
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Solving the equation for r:
[tex]\begin{gathered} V=400(9.025\cdot10^{-5}-r^2) \\ r^2=9.025\cdot10^{-5}-\frac{V}{400} \\ r=\sqrt[]{9.025\cdot10^{-5}-\frac{V}{400}} \end{gathered}[/tex]With the first equations, we can establish some limits for V:
With the lowest value for r (r=0):
[tex]\begin{gathered} V=400(9.025\cdot10^{-5}-0^2) \\ V=400(9.025\cdot10^{-5}) \\ V=3.61\cdot10^{-2} \end{gathered}[/tex]With the highest value for r (r=9.5x10^-3)
[tex]\begin{gathered} V=400(9.025\cdot10^{-5}-(9.5\cdot10^{-3})^2) \\ V=400(9.025\cdot10^{-5}-9.025\cdot10^{-5}) \\ V=400(0) \\ V=0 \end{gathered}[/tex]According to the radius range, velocity can be between 0 and 3.61x10^-2
It is also necessary to check the domain of the function considering it is a square root. The argument of an square root cannot be less than 0. Then:
[tex]\begin{gathered} 9.025\cdot10^{-5}-\frac{V}{400}\ge0 \\ 9.025\cdot10^{-5}\ge\frac{V}{400} \\ V\leq400(9.025\cdot10^{-5}) \\ V\leq3.61\cdot10^{-2} \end{gathered}[/tex]This is the same limit for velocity obtained before. Then, we can say for velocity that:
[tex]0\leq V\leq3.61\cdot10^{-2}[/tex]23,000,000 in scientific notation.
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Answer:
2.3 x 10⁷
Explanation:
A number is said to be in scientific notation when it is written in the form:
[tex]\begin{gathered} A\times10^n \\ \text{where:} \\ \text{A is between 1 and 10} \\ n\text{ is an integer} \end{gathered}[/tex]Given the number: 23,000,000
The number has 8 digits before the decimal point.
Therefore, in standard notation we have:
[tex]23,000,000=2.3\times10^7[/tex]Supposed g is a one-to-one function with the following valuesg(-7)= -6g(11)= -1
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Given:
The function g(x) is one-one.
[tex]g(-7)=-6[/tex][tex]g(11)=-1[/tex]Required:
We need to find the values of the inverse image of the function g(x).
Explanation:
Recall that the image of distinct elements of the function is distinct.
There exist an inverse of g(x) since g(x) is one to one.
The inverse image of the given can be written as follows.
Consider the equation
[tex]g(-7)=-6[/tex][tex]g^{-1}g(-7)=g^{-1}(-6)[/tex][tex]g^{-1}(-6)=-7[/tex][tex]g(11)=-1[/tex][tex]g^{-1}g(11)=g^{-1}(-1)[/tex][tex]g^{-1}(-1)=11[/tex]Final answer:
[tex]g^{-1}(-6)=-7[/tex][tex]g^{-1}(-1)=11[/tex]In which of the following triangles does m
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Okay let's analyze each triangle
In triangles A, B, and D the angle
creat an espression that includes the zero property of exponents the multiplication property of exponents and the power of a power property of exponents
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All in one, or one expression for each property?
a) Zero property
[tex]\text{ (x + y)}^0\text{ = 1}[/tex]b) Multiplication property
[tex]\text{ x}^2\cdot x^5=x^{2+5}=x^7[/tex]c) Power property
[tex]\text{ (x}^2)^3=x^{2\cdot3}=x^6[/tex]d) All in one (this is the expression)
[tex]\mleft\lbrace\text{(x}^0)(x^3)\mright\rbrace\text{ }(x^2)^5[/tex][tex]\text{ }\mleft\lbrace1(x^3\mright)\}(x^{10})[/tex]
Graph the line with the given slope m and y-intercept b.
m = 4,b=-5
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The graph of the linear equation can be seen in the image at the end.
How to graph the linear equation?
The general linear equation is.
y = m*x + b
Where m is the slope and b is the y-intercept.
Here we know that m = 4 and b = -5, so we have:
y = 4*x - 5
To graph this line, we need to find two points.
Evaluating in x = 0 we get:
y = 4*0 - 5 = -5
Evaluating in x = 2 we get:
y = 4*2 - 5 = 8 - 5 = 3
So we have the points (0, -5) and (2, 3), so now we need to graph these points and connect them with a line, the graph can be seen below:
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Use a calculator to evaluate the expression. (Do not round until the final answer. Then round to three decimal places as needed.)
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2.303
1) For the following expression:
[tex]\frac{\ln30+\ln15}{\log_{10}30+\log_{10}15}[/tex]We can simplify that and then round it off to the nearest thousandth:
2) Let's rewrite them simplifying using the logarithm property of multiplication:
[tex]\begin{gathered} \frac{\ln30+\ln15}{\log_{10}30+\log_{10}15}= \\ \frac{\ln(30\cdot15)}{\log_{10}30+\log_{10}15}= \\ \frac{\ln(30\cdot15)}{\log_{10}(30\cdot15)}= \\ \frac{\ln(450)}{\log_{10}(450)}= \end{gathered}[/tex]Note that the base of the Natural Log is the Euler's number "e" so let's move on now using the calculator, finally:
[tex]\frac{\ln(450)}{\log_{10}(450)}=\frac{6.10924}{2.65321}=2.30258\ldots\approx2.303[/tex]Note that only at the last step we have rounded it off. And that's the
answer
Pls help with my hw pls
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Convert to fractional Notation 4 19/100
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to solve this we need to convert the number 4 to a fraction with denominator 100 and add both fractions
to do that we can multiply 4 and 1 by 100, like this:
[tex]\frac{4\cdot100}{1\cdot100}=\frac{400}{100}[/tex]now we can add the fractions
[tex]\frac{400}{100}+\frac{19}{100}=\frac{419}{100}[/tex]So the answer is: 419/100
Use the times and corresponding closing prices of the stock to create coordinate pairs. Let X represent the number of weeks since the first at a point, and Y represent the closing price of each time. So, X equals zero represents the data point from five years ago. There are 52 weeks in a year, and you can write the time for each closing price recorded in terms of weeks that have passed since five years ago, when X equals zero. Fill in the table to represent your data as coordinate pairs
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Combining both tables we get:
