Answers
We know that the segment DP is an angle bisector of angle BDC; this means that angle 1 has to be half angle BDC, that is:
[tex]m\angle1=\frac{1}{2}m\angle BDC[/tex]Plugging the expresions given for each angle we have:
[tex]\begin{gathered} 6x+6=\frac{1}{2}(15x) \\ 12x+12=15x \\ 15x-12x=12 \\ 3x=12 \\ x=\frac{12}{3} \\ x=4 \end{gathered}[/tex]Therefore, the value of x is 4
Related Questions
Circle terms and simplify the expression50+3(-10)+2(-20)
Answers
The given expression is
[tex]50+3(-10)+2(-20)[/tex]First, we solve the products.
[tex]50-30-40[/tex]Then, we sum.
[tex]-20[/tex]Therefore, the answer is -20.The cost of a pound of nails increased from $2.04 to $2.51. What is the percent of increase to the nearest whole-number percent?The percent of increaseis
Answers
In order to determine the percent of increase, proceed as follow:
Subtract 2.04 to 2.51:
2.51 - 2.04 = 0.47
Next, consider that the x percent of 2.04 is 0.47, then, you can write:
(x/100)*(2.04) = 0.47
by solving for x, you get:
x = (0.47/2.04)*(100)
x = 23
Hence, the percent of increase is approximately 23%
A triangle has a 45 degree angle, a 624 degree angle, and a side 5 feet in length.Select True or False for each statement about this type of triangle.TrueFalseThe triangle must be a scalene triangle.The triangle must be an acute triangle.The triangle must contain another angle that is 623 degrees.
Answers
The addition of the three angles of a triangle is equal to 180°, then the measure of the third angle is:
x = 180° - 45° - 62.5°
the Panthers baseball team needs new equipment They plan to purchase bats that cost $60 each and gloves that cost $25 each. The number of bats will purchase is half the number of gloves they will purchase If they have $700 how many of each can they buy? what is the problem asking you to find?
Answers
Answer:
Bats = 6.32 or 6 units.
Gloves = 12.73 or 12 units.
The problem asks you to find the number of bats and gloves that the Baseball team can buy with 700$.
Answer:
According to the problem:
Costs:
Bats (B) = $60/unit
Gloves (G) = $25/unit
Relation (The number of bats will purchase is half the number of gloves):
B = G/2
And, since the total amount they have is $700:
[tex]700=60\cdot B+25\cdot G[/tex]We can use the relation B = G/2 to find G.
[tex]\begin{gathered} 700=60\cdot\frac{G}{2}+25\cdot G \\ 700=30\cdot G+25\cdot G \\ 700=55\cdot G \\ \frac{700}{55}=G \\ G=12.73 \end{gathered}[/tex]The number of gloves is 12.73 or 12 (since it is not possible to buy 0.72 gloves).
The number of bats can be found using the relation:
[tex]\begin{gathered} B=\frac{G}{2} \\ B=\frac{12.73}{2} \\ B=6.36 \end{gathered}[/tex]The number of bats they can buy is 6.36 or 6 (since it is not possible to buy 0.36 baths).
In summary,
They can buy:
Bats = 6.32 or 6 units.
Gloves = 12.72 or 12 units.
solve for x: 13x=130
Answers
x = 10
Explanations:The given equation is:
13x = 130
Divide both sides by 13:
[tex]\frac{13x}{13}=\frac{130}{13}[/tex]x = 10
what is 3/5 as an equation or fraction?use an equation to write each fraction or product as a multiple of a unit fraction 3/5
Answers
Answer:
Writing as a multiple of a unit fractions, we have;
[tex]\frac{3}{5}=3\times\frac{1}{5}[/tex]Explanation:
Given the fraction;
[tex]\frac{3}{5}[/tex]A unit fraction is of the form;
[tex]\frac{1}{n}[/tex]where n is a positive integer.
Writing as a multiple of a unit fractions, we have;
[tex]\frac{3}{5}=3\times\frac{1}{5}[/tex]x2 + 5x – 9 = 5Which of the following values of x satisfies the equationabove?A. 7 B. 3 C. –2 D. –7
Answers
The easiest way to answer this is to plug in all of the given choices to see which of them will satisfy the given equation.
[tex]\text{ x}^2\text{ + 5x - 9 = 5}[/tex]We get,
Choice A: 7
[tex]\text{ x}^2\text{ + 5x - 9 = 5}[/tex][tex]\text{ (7)}^2\text{ + 5(7) - 9 = 5}[/tex][tex]\text{ 49 + 35 - 9 = 5}[/tex][tex]\text{ 84 - 9 = 5}[/tex][tex]\text{ 75 }\ne\text{ 5}[/tex]Therefore, x is not equal to 7.
Choice B: 3
[tex]\text{ (3)}^2\text{ + 5(3) - 9 = 5}[/tex][tex]\text{ 9 + 15 - 9 = 5}[/tex][tex]\text{15 }\ne\text{ 5}[/tex]Therefore, x is not equal to 3.
Choice C: -2
[tex](-2)^2\text{ + 5(-2) - 9 = 5}[/tex][tex]\text{ 4 - 10 - 9 = 5}[/tex][tex]\text{ -15 }\ne\text{ 5}[/tex]Therefore, x is not equal to -2.
Choice D: -7
[tex](-7)^2\text{ + 5(-7) - 9 = 5}[/tex][tex]\text{ 49 - 35 - 9 = 5}[/tex][tex]\text{ 5 = 5}[/tex]Therefore, x = -7
The answer is letter D : -7
pat's pizza shack offers customers the choices of crust, sauce, and toppings shown below. if a 1-topping pizza is selected at random, what is the probability that it will be deep dish crust, with traditional sauce and green peppers?
Answers
Solution
For this case we can find the number of total combinations like this:
2* 3* 4= 24
Since we have two options for Crust , 3 for Sauce and 4 for Toppings
Then the probability would be given by:
1/24
i need help with my homewrok PLEASE CHECK WORK number 6
Answers
Given: The graph of an exponential function as shown in the image
To Determine: The equation of the given graph
Solution
The general equation of an exponential equation is
[tex]\begin{gathered} y=ab^x \\ a=vertical\text{ stretch} \\ b=common-ratio \end{gathered}[/tex]Let us pick a point from the graph and the value of common ratio to solve for a
Please note that the common ratio is 2 because the processing power doubles every year
So
[tex]\begin{gathered} Point:(0,60),b=2 \\ y=ab^x \\ 60=a(2)^0 \\ 60=a(1) \\ 60=a \\ a=60 \end{gathered}[/tex]Let us substitute a and b into the general equation would given us
[tex]y=60(2)^x[/tex]Hence, the equation is
y = 60 (2)ˣ
determine weather the degree of the function is even or odd and weather the function itself is even or odd.
Answers
Answer:
The function is odd.
Explanation:
A function is classified as odd if
[tex]f(x)=-f(-x)[/tex]Graphically, this means if a function has a positive value at x = a (to the right of the y-axis), then it must have a negative value at x = -a (to the left of the y-axis).
To prove that our function is odd, we take a few examples from the graph
[tex]\begin{gathered} f(2)=-f(-2)_{} \\ f(6)=-f(-6) \end{gathered}[/tex]and so on.
Hence, our function is odd!
A store has two types of nuts that they will mix together to make a mixture worth $5.91 per pound. If thestore uses 13 pounds of a nut that costs $3.10 per pound, how many of pounds of nuts that cost $7.50 perpound should be added to make the mixture?The store should addpounds of nuts worth $7.50 per pound (round to the nearest wholepound - NO COMMAS).
Answers
Given:
The cost of mixture per pound, M= $5.91.
The quantity of nuts taken first , n=13 pounds.
The cost of nuts per pound, which was taken first, N=$3.10.
The cost of nuts per pound taken second, P=$7.50.
Let p be the quantity of nuts taken second.
Hence, we can write,
[tex]M(n+p)=Nn+Pp[/tex]Now, put the values in the above equation.
[tex]\begin{gathered} 5.91\times(13+p)=3.1\times13+7.5\times p \\ 5.91\times13+5.91p=3.1\times13+7.5\times p \\ 5.91p-7.5\times p=3.1\times13-5.91\times13 \\ -1.59p=13(3.1-5.91) \\ -1.59p=13\times(-2.81) \\ -1.59p=-36.53 \\ p=\frac{-36.53}{-1.59} \\ p\cong23\text{ pounds} \end{gathered}[/tex]Therefore, 23 pounds of nuts that cost $7.50 per pound is added to make the mixture.
Suppose that the functions g and h are defined as follows.g(x) = -4+3x²h(x)=2-8x(a) Find(3)(-1).(b) Find all values that are NOT in the domain ofhIf there is more than one value, separate them with commas.
Answers
From the given functions :
[tex]\begin{gathered} g(x)=-4+3x^2 \\ h(x)=2-8x \end{gathered}[/tex]a. Find (g/h)(-1)
We need to find first the function (g/h) then substitute x = -1
[tex]\begin{gathered} (\frac{g}{h})(x)=\frac{-4+3x^2}{2-8x} \\ (\frac{g}{h})(-1)=\frac{-4+3(-1)^2}{2-8(-1)}=\frac{-1}{10} \end{gathered}[/tex]Therefore, the answer is -1/10
b. Find all values that are NOT in the domain.
Domain is the set of x values that will make the function (g/h)(x) be defined.
Note that the function will be UNDEFINED if the denominator is equal to 0.
Thus, we need to equate the denominator to 0. To get the values of x, which are NOT in the domain.
The denominator is 2 - 8x, let's equate it to 0, then solve for x :
[tex]\begin{gathered} 2-8x=0 \\ -8x=-2 \\ x=\frac{-2}{-8}=\frac{1}{4} \end{gathered}[/tex]Therefore, the values that are NOT in the domain is 1/4
(2x-1) (3x-1)=15my choices area)3b)0c)-6d)-1
Answers
(2x-1) + (3x-1) = 15
2x - 1 + 3x - 1 = 15
rearrange
2x + 3x - 1 -1 = 15
5x -2 = 15
5x = 15 + 2
5x = 17
Divide both sides by 5
x = 17/5
= 3.4
Rounding to 3
Option a)3
topic is hard for me to understand, help is appreciated
Answers
Answer:
Given vector v is,
[tex]\vec{v}=-24\vec{i}-7\vec{j}[/tex]$$=-24\vec{i}-7\vec{j}$$To find the unit vector that has the same direction as the vector v is,
Unit vector u is,
[tex]\vec{u}=\frac{\vec{v}}{\lvert\vec{v}\rvert}-----(1)[/tex]we have that,
To find a unit vector with the same direction as a given vector, we divide the vector by its magnitude.
The magnitude of a vector formula is used to calculate the length of a vector and is denoted by |v|. The magnitude of a vector is always a positive number or zero it cannot be a negative number.
[tex]\lvert x\vec{i}+y\vec{j}\rvert=\sqrt[]{x^2+y^2}[/tex]we get,
[tex]\lvert\vec{v}\rvert=\sqrt[]{24^2+7^2}[/tex][tex]=\sqrt[]{625}[/tex][tex]=25[/tex][tex]\lvert\vec{v}\rvert=25[/tex]Substitute the values in equation (1), we get
[tex]\vec{u}=\frac{-24\vec{i}-7\vec{j}}{25}[/tex][tex]\vec{u}=\frac{1}{25}(-24\vec{i}-7\vec{j})[/tex]Answer is:
[tex]\vec{u}=\frac{1}{25}(-24\vec{i}-7\vec{j})[/tex]Complete the square rational only:Solve the equation for all values of x by completing the square.x^2 + 4x + 3 = 0
Answers
Problem:
Solve the equation for all values of x by completing the square.
x^2 + 4x + 3 = 0
remember the following:
To solve
[tex]ax^2\text{ + bx +c= }0[/tex]by completing the square, we carry out the following steps:
1. Transform the equation so that the constant term, c, is only on the right-hand side. In our case:
[tex]x^2\text{ + 4x = -3}[/tex]2. If a , the leading coefficient (the coefficient of the term x^2), is not equal to 1, divide both sides by a. Notice that in our case a = 1. Then, we don't do this step.
3. Add (b/2a)^2 to the right and the left side of the equation, that is:
[tex]x^2\text{ + 4x + (}\frac{b}{2a})^2\text{= -3 + (}\frac{b}{2a})^2[/tex]in our case note that b = 4 and a = 1, so we have:
[tex]x^2\text{ + 4x + (}\frac{4}{2})^2\text{= -3 + (}\frac{4}{2})^2[/tex]this is equivalent to say:
[tex]x^2\text{ + 4x + (2})^2\text{= -3 + (2})^2\text{ = -3+4}[/tex]this is equivalent to say
[tex]x^2\text{ + 4x + (2})^2=1[/tex]this is equivalent to say:
[tex](x+2)^2=1[/tex]now, we take the square root of both sides of the equation
[tex]\sqrt[]{(x+2)^2}=\sqrt[]{1}[/tex]this is equivalent to say:
[tex]x+2^{}=\pm1[/tex]solve for x
[tex]x=\pm1\text{ - 2}[/tex]then, we have two solutions:
[tex]x=1-2\text{ = -1}[/tex]and
[tex]x=-1-2\text{ = -}3[/tex]the two roots(zeros) are x = -1 and x = -3
2n-5=11Two step equation
Answers
You have the following equation:
|2n + 5| = 11
In order to solve the previoues equation for n, you take into account that an equation with an absolute value has two solutions. In this case you have:
2n + 5 = 11
2n + 5 = - 11
That is, the equation must be solved for both cases.
For the first equation you have:
2n + 5 = 11 you add 5 both sides
2n = 11 - 5
2n = 6 divide by 2 both sides
n = 6/2
n = 3
For the second equation you have:
2n + 5 = -11 add 5 both sides
2n = -11 - 5
2n = -16 divide by 2 both sides
n = -16/2
n = -8
Hence, the solutions to the given equation are:
n = {3,-8}
Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 86 km slower than the other. If the two planes are 9450 h kilometers apart after 5 hours, what is the rate of each plane?
Answers
Let 'd' be the distance that the faster plane travels, then the distance that the slower plane travels is:
[tex]9450-d[/tex]Now, let 's' be the speed of the faster plane, then similarly, the speed of the slower plane is:
[tex]s-86[/tex]We have the following equation for the faster plane:
[tex]d=5\cdot s[/tex]and the equation for the slower plane is:
[tex]9450-d=5\cdot(s-86)[/tex]Now we can do the substitution d=5s on the second equation to find the value of s:
[tex]\begin{gathered} d=5s \\ \Rightarrow9450-5s=5\cdot(s-86)=5s-430 \\ \Rightarrow9450+430=5s+5s=10s \\ \Rightarrow10s=9880 \\ \Rightarrow s=\frac{9880}{10}=988 \\ s=988 \end{gathered}[/tex]We have that the speed of the faster plane is s=988 km/h. Now we can find the speed of the slower plane:
[tex]s-86=988-86=902[/tex]Finally, we can check the answer by finding the distance traveled:
[tex]\begin{gathered} 9450-d=5\cdot(902) \\ \Rightarrow d=9450-5\cdot(902)=9450-4510=4940 \\ \text{and} \\ d=5(988)=4940 \end{gathered}[/tex]Therefore, the speed of the faster plane is 988 km/h and the speed of the slower plane is 902 km/h
Tell whether a correlation is likely in thissituation. If so, tell whether there is acausal relationship. Explain yourreasoning.the age of your parents and the length ofyour hair
Answers
A correlation is not likely between the age of your parents and the length of your hair.
This is owing to the fact that the length of your hair is a factor entirely dependent on your individual biological composition and lifestyle choices.
The two polygons are similar. Write a proportion and solve for x. I just need help with 11 and 13
Answers
11)
Given data:
The given pair of traingles.
The expression for the ratio of the coorresponding sides is,
[tex]\begin{gathered} \frac{5}{x}=\frac{2}{1} \\ 5=2x \\ x=2.5 \end{gathered}[/tex]Thus, the value of x is 2.5.
13)
Given data:
The given pair of rectangles.
The expression for the ratio of the corresponding sides is,
[tex]\begin{gathered} \frac{3}{x}=\frac{4}{6} \\ 18=4x \\ x=\frac{18}{4} \\ =4.5 \end{gathered}[/tex]Thus, the value of x is 4.5.
g(x)=1/2x−4. Evaluate g(10) please help me
Answers
Hello there. To solve this question, we'll need to plug in the value of x to find the value of the function in that point.
Let g(x) = 1/(2x - 4).
To evaluate g(10), we need to plug in x = 10 to the function
g(10) = 1/(2*10 - 4)
Multiply the values
g(10) = 1/(20 - 4)
Subtract the values
g(10) = 1/16.
QUESTION 2
To calculate the average rate of change of the amount of money, we'll need to use the slope formula.
The slope m of a line passing through two points (x0, y0) and (x1, y1) is given by: m = (y1-y0)/(x1-x0)
As you can see on the graph, in the 0-th month, Sarah had $200 in her account. In the 12-th month, she had $500.
Which means we have the points (0, 200) and (12, 500)
Using the slope formula, we get:
AVG = (500 - 200)/(12-0)
Subtract the values
AVG = 300/12
AVG = 25
This is the average rate of change of the amount of money. If you wanted the instantaneous rate of change, we would be talking about derivatives. In this case, the values would be equal since we dealing with a line and the slope is the leading coefficient of the line equation.
Find the area of the pentagon in the diagram below. A 15 square inches B 20 square inches C25 square inches D 28 square inches
Answers
we divide the pentagon into two figures
Trapezium
trapezium area
[tex]\begin{gathered} A=\frac{(B+b)\times h}{2} \\ \\ A=\frac{(6+2)\times4}{2} \\ \\ A=16 \end{gathered}[/tex]the are of the trapezium is 16 square in
Triangle
triangle area
[tex]\begin{gathered} A=\frac{b\times h}{2} \\ \\ A=\frac{6\times3}{2} \\ \\ A=9 \end{gathered}[/tex]the area of the triangle is 9 square in
Total area
Sum the areas to find the area of the pentagon
[tex]\begin{gathered} 16+9 \\ =25 \end{gathered}[/tex]the pentagon area is 25 square inches
On a track for remote controlled racing cars, racing car A completes the track in 36 seconds, while racing carB completes in 24 seconded If they both start at the same time after how many seconded will they be side by side againConvert the answer to show how many minute and seconded it would take for them to be side by side again
Answers
Okay, here we have this:
Here we need to identify how many seconds will it take for the two cars to meet again, therefore for this we are going to find the least common multiple of the two numbers (36, 24):
To do this, we will first decompose each number, and then we will multiply each factor the greatest number of times that it occurs in any of the numbers:
36=2*2*3*3
24=2*2*2*3
LCM(36, 24)=2*2*2*3*3
LCM(36, 24)=72 seconds.
Finally we obtain that the two cars will take 72 seconds to meet again, this is equivalent to 1 minute and 12 seconds.
What is 38,050,000 expressed in scientific notation?А. 3.805 x 108ОООв. 0.3805 x10^8С. 0.38 х 10-8D. 3 805 x 107
Answers
By definition, Scientific Notation has the following form:
[tex]a\cdot10^b[/tex]Where "a" is a number greater than or equal to 1, but less than 10 and "b" is an Integer.
In this case, you have this number:
[tex]38,050,000[/tex]To express it in Scientific notation, follow these steps:
-The decimal point must be after the first digit (which must not be zero), so you must move de the decimal point 7 spaces to the left, so "b" will be positive.
-Then, the exponent "b" will be 7.
So, you get 38,050,000 expressed in scientific notation is :
[tex]=3.805\cdot10^7[/tex]Which best describes the figure that is represented by the following coordinates? A(-3,4), B(3, 4), (3,-2) and D(-3,-2) a trapezoid a parallelogram a rectangle a square
Answers
We have 4 points: A(-3,4), B(3, 4), C(3,-2) and D(-3,-2).
We can graph them in an xy-plane and join the points to draw the figure:
The 4 sides are equal in length (6 units) and the angles at each vertex are right angles, so the figure is a square.
Answer: square.
standard deviation of 0.37, 0.13, 0.06,0.15,0.29
Answers
A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. Tables of the standard normal distribution are frequently used to show different regions of the normal distribution.
How do I calculate standard deviation?First, determine the mean. Step 2: Calculate the square of each data point's variance from the mean. Add the values from Step 2 in Step 3. Divide by the total number of data points in step 4.
Mean = 0.37+0.13+0.06+0.15+0.29\s=1.00
It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.
Standard deviation is the square root of variance, which is the average squared deviations from the mean. Both metrics capture distributional variability, although they use different measurement units:
The units used to indicate standard deviation are the same as the values' original ones (e.g., minutes or meters).
The units used to express variation are substantially greater.
To learn more about standard deviation refer to:
https://brainly.com/question/475676
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you download 2 movies and 3 songs the next week you download 1 movie and 5 songs.what is the total cost of the downloads?
Answers
Price of downloads of number of movies and songs is given by function g(x) =2x and f(x) = (x/2) +2 respectively , then total cost of the downloads of total 3 movies and 8 songs is equal to 12 dollars.
As given in the function,
Price of downloads of number of movies represented by
g(x) = 2x
where x is the number of movies
Price of downloads of number of songs represented by
f(x) = (x /2) +2
where x is the number of songs
Total number of downloads
First week
Number of movies downloads = 2
Number of songs downloads =3
Next week
Number of movies downloads = 1
Number of songs downloads = 5
Total movies = 2+1
=3
Cost of downloads 3 movies
g(3)= 2(3)
=6
Total songs =3+5
= 8
Cost of downloads8 songs
f(8)= (8/2) +2
=6
Total cost of the downloads = 6 +6
= 12 dollars
Therefore, price of downloads of number of movies and songs is given by function g(x) =2x and f(x) = (x/2) +2 respectively , then total cost of the downloads of total 3 movies and 8 songs is equal to 12 dollars.
The complete question is :
The price for digital downloads of music is represented by the linear function f(x) shown on the graph. The price for digital downloads of movies is represented by g(x) = 2x, where x is the number of movies downloaded and g(x) is the total cost in dollars. Graph of a line with equation f of x equals one half times x plus 2. The x-axis is labeled Number of Songs, and the y-axis is labeled Price in Dollars.
You download 2 movies and 3 songs the next week you download 1 movie and 5 songs. What is the total cost of the downloads?
Learn more about total cost here
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identify the following sequence as geometric, arithmetic, or neither 25, 50, 75, 100
Answers
Arithmetic sequence.
Explanation:From the question, we are to determine whether 25, 50, 75, 100 is an arithmetic or geometric sequence:
An arithmetic sequence is identified by a common difference. First, let us check whether the sequence is arithmetic.
Determine the common difference:
[tex]\begin{gathered} d=100-75=75-50=50-25 \\ d=25 \end{gathered}[/tex]Since the sequence has a common difference, therefore the sequence is an arithmetic sequence.
One line passes through the points (-1, 6) and (2,0). A second linepasses through the points (-5, 5) and (-1,9).At what point do the two lines intersect?
Answers
First, locate the points of the first line and join them to form the line.
Do the same for the second line, the point where both lines cross each other is the point we are looking for:
Lines don't intersect
Sorry for the bad photo quality! I will write out what the question is asking (geometry)Write or draw a counter example to the following conditionals #18: if a polygon is a quadrilateral, then it has four right angles
Answers
The given statement is,
If a polygon is a quadrilateral, then it has four right angles.
To write a counterexample to the given statement:
The statement, "If a polygon is a quadrilateral, then it has four right angles" is not always possible.
Because rhombus is one such figure which has four sides and none of its angles are right angles.
Thus, a counterexample for the statement, "If a polygon is a quadrilateral, then it has four right angles" is Rhombus.
The exponential models describe the population of the indicated country, A, in millionthe greatest growth rate? By what percentage is the population of that country increaCountryhas the greatest growth rate.
Answers
We are given the following logistic growth function P(x)
[tex]P(x)=\frac{90}{1+271e^{-0.122x}}[/tex]The function P(x) models the percentage of Americans who have coronary heart disease.
Here x is the age.
Let us find the percentage of 55-years old who have some coronary heart disease.
Substitute x = 55 into the function
[tex]\begin{gathered} P(55)=\frac{90}{1+271e^{-0.122(55)_{}_{}}} \\ P(55)=\frac{90}{1+271e^{-6.71_{}}} \\ P(55)=\frac{90}{1+0.33} \\ P(55)=67.7\% \end{gathered}[/tex]Therefore, the percentage of 55-years old with some coronary heart disease is 67.7% (rounded to one decimal)