May I please get help finding this. I can’t seem to get the correct solution for the length.
Answers
Triangle ABE is similar to traingle ACD; in similar triangles, corresponding sides are always in the same ratio:
[tex]\frac{DC}{EB}=\frac{AC}{AB}[/tex]Use the equation above to find the length of x:
[tex]\begin{gathered} \frac{x}{4}=\frac{6+9}{6} \\ \\ \frac{x}{4}=\frac{15}{6} \\ \\ x=4\cdot\frac{15}{6} \\ \\ x=\frac{60}{6} \\ \\ x=10 \end{gathered}[/tex]Then, the length of x is 10
Related Questions
Suppose f(x)=5x+6 . Describe how the graph of g compares with the graph of f . g(x)=f(x+5)
Answers
g(x) = f(x) + 5 relates to f(x) by shifting f(x) 5 units up.
What is a function?The link between two independent variables and one dependent variable is described by a mathematical expression, rule, or law (the dependent variable).
An example of a rule is a function, which produces one output for a single input. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. We can infer that y is a function of x because x is the input value.
The function is given as:
f(x) = 5x+6
g(x) = f(x)+5
this gives,
g(x) = 5x+6+5
g(x) = 5x+11
g(x) = f(x) + 5 relates to f(x) by shifting f(x) 5 units up.
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Find the measure of angle R, given that the largest triangle is a right triangle.A)27B)18C)72D)45
Answers
we know that
The central angle is 90 degrees
so
18+R=45 degrees
R=45-18
R=27 degreesWhich point on the number line below best represents V30?
Answers
We should try different squared numbers that are bigger and smaller than 30 as:
[tex]\begin{gathered} \sqrt{16}=4 \\ \sqrt{25}=5 \\ \sqrt{36}=6 \end{gathered}[/tex]Since 30 is between 25 and 36, the square root of 30 is going to be between 5 and 6. So the point that best represents the square root of 30 is M.
Answer: Point M
write each ratio as a fraction in its simplest form12/10
Answers
The given ratio is,
[tex]\frac{12}{10}[/tex]Taking 2 as common from both 12 and 10 we have,
[tex]\frac{12}{10}=\frac{6\times2}{5\times2}=\frac{6}{5}[/tex]As there is no common factor between 6 and 5. it cannot be simplified further as fraction.
Thus, the answer is 6/5
find the area of each Lister answer exact form and approximate form
Answers
In the given circle, The diameter of the circle is 8 in
Radius is the half of the diameter,
Radius = Diameter/2
Radius = 8/2
Radius = 4 in
Area of the circle with radius r is express as :
[tex]\text{ Area of Circle =}\Pi(radius)^2[/tex]Substitute the value of radius = 4in
[tex]\begin{gathered} \text{ Area of Circle =}\Pi(radius)^2 \\ \text{ Area of Circle =}\Pi\times4\times4 \\ \text{ Area of Circle = 50.27 in}^2 \end{gathered}[/tex]Area of the circle is 50.27 in²
Answer : Area of the circle is 50.27 in²
Find the equation of a line in the form y=Mx+b MATH HW
Answers
Using y=mx+b form first we calculate the slope.
We'll use points (0,-8) and (-8,0).
[tex]\begin{gathered} m=(-8-0)\div(0--8) \\ m=-\frac{8}{8} \\ m=-1 \end{gathered}[/tex]Next we calculate our b intercept
[tex]\begin{gathered} 0=-1(-8)+b \\ b=-8 \end{gathered}[/tex]So the equation is y=-x-8
Ava solved the compound inequality +7
Answers
Tell me if the inequalities are correct
x/4 + 7 < -1 2x - 1 >= 9
x/4 < -1 - 7 2x >= 9 + 1
x/4 < -8 2x >= 10
x < -32 x >= 10/2
x >= 5
The second option is the correct one
If you are rolling two dice (numbered 1-6), what is the probability that the first die shows an odd number and the second die shows a number larger than 4?
Answers
Since we have two dices and we want to know the events where the first one shows an odd number and the second die shows a number larger than 4, we have that the following results are the ones that fit the requirement:
[tex](1,5),(1,6),(3,5),(3,6),(5,5),(5,6)[/tex]Now, we know that the sample space has 6x6=36 possible outcomes, therefore, the desired probability is:
[tex]P(\text{odd,x}>4)=\frac{6}{36}=\frac{1}{6}[/tex]therefore, the probability is 1/6
describe the transformations that occur from the parent function f(x) = x2 to the function g(x) =2(x+1)^2-7
Answers
we have
f(x)=x^2
this is a vertical parabola with vertex at (0,0)
and
we have
g(x)=2(x+1)^2-7
this is a vertical parabola with vertex at (-1,-7)
so
the transformation of f(x) to g(x) is equal to
(0,0) ------> (-1,-7)
the rule of the translation is equal to
(x,y) --------> (x-1, y-7)
that means ------> the translation is 1 unit at left and 7 units down
and we have a second transformation
(x,y) -------> (ax, y)
the factor a is 2
therefore
First transformation
x^2 --------> 2x^2
second transformation
2x^2---------> 2(x+1)^2-7
I will show you the pic .
Answers
we have the equation
(2/3)x+5=1
step 1
multiply by 3 both sides
2x+15=3
step 2
subtract 15 both sides
2x=3-15
2x=-12
step 3
divide by 2 both sides
x=-12/2
x=-6
What is the image of (-4, 8) after a dilation by a scale factor of centered at the
1/4
origin?
Answers
The image of the given point (-4, 8) is (1,-2).
The coordinates of the point are (4,-8).
Point is dilated by a scale factor of k centered at the origin.
When an image is subjected to dilation:
Upon dilation, with a scale factor of k centered at the origin, then the rule of dilation is defined as:
(x , y) → (kx , ky)
Using the above rule, we get
(-4 , 8) is dilated by a scale factor of 1/4 centered at the origin
(-4, 8) → (-4 x 1/4, 8 x 1/4)
(-4, 8) → (-1, 2)
Therefore, the image of the given point (-4, 8) is (1,-2).
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In AVWX, XV W X and m_W = 27°. Find mZX.
Answers
We will solve as follows:
From the information given we can deduce that the triangle is Isosceles. We also have from theorem that angles that are opposite to congruent sides are also congruent, therefore angle
Using this, and the fact that the sum o all internal angles of a triangle add to 180°, the following is true:
[tex]V+W+X=180[/tex]Now, we replace the values we know:
[tex]27+27+X=180\Rightarrow X=126[/tex]So, the value of angle
D1 ptsQuestion 3The bill of a white pelican can hold about 550 cubic inches of water,Nigel, the pelican from Finding Nemo, scoops up 160 cubic inches ofwater. Write an inequality that represents how much more waterNigel cal add to his bill.
Answers
let the additional water that is needed to add in the bill is x
[tex]\begin{gathered} 160+x\leq550 \\ x\leq550-160 \\ x\leq390 \end{gathered}[/tex]so, Nigel can add 390 cubic inches of water to the bill of a white pelican.
PLEASE HELP!!!!!!!!
Choose the two graphs that preserve congruence.
Answers
The two graphs that reserve congruence are in the option A and option D
What is congruency?Congruent refers to something that is "absolutely equal" in terms of size and shape.
The shapes hold true regardless of how we rotate, flip, or turn them.
Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another. We will see that they will superimpose, or be positioned entirely on top of, one another. This demonstrates the congruence of the two circles.
The images on the graphs in the options A and options D both maintains congruence, The sizes are identical and has a rigid transformation
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xP(x)00.2510.320.0530.4Find the mean of this probability distribution. Round your answer to one decimal place.
Answers
Given:
The probability distribution table values are given.
To find:
The mean
Explanation:
Using the mean formula,
[tex]\mu=\sum_{\text{ }}^{\text{ }}x\cdot P(x)[/tex]Substituting the given values we get,
[tex]\begin{gathered} \mu=0(0.25)+1(0.3)+2(0.05)+3(0.4) \\ =0+0.3+0.1+1.2 \\ =1.6 \end{gathered}[/tex]Therefore, the mean for the given data is 1.6.
Final answer:
The mean for the given data is 1.6.
Suppose that tan(x)csc(x)=1/f(x).Write f(x) in terms of sin(x) and cos(x).f(x)=
Answers
Trigonometry
We are given the equation:
[tex]\tan (x)\csc (x)=\frac{1}{f(x)}[/tex]It's required to write f(x) in terms of the sine and cosine functions.
Taking the reciprocal of both sides of the equation:
[tex]f(x)=\frac{1}{\tan (x)\csc (x)}[/tex]Recall:
[tex]\begin{gathered} \tan (x)=\frac{\sin (x)}{\cos (x)} \\ \text{csc(x)}=\frac{1}{\sin (x)} \end{gathered}[/tex]Substituting:
[tex]f(x)=\frac{1}{\frac{\sin(x)}{\cos(x)}\frac{1}{\sin (x)}}[/tex]Simplifying:
[tex]f(x)=\frac{1}{\frac{1}{\cos(x)}}=\cos (x)[/tex]Thus:
f(x)= cos(x)
Complete the following by filling in the missing terms in the sequence
Answers
Let's begin with the first sequence:
[tex]?,2,6,18,54,\text{?}[/tex]We can see each term of the sequence after the 2 is the previous term multiplied by 3. So the missing terms would be 2/3 and 54*3:
[tex]\frac{2}{3},2,6,18,54,162.[/tex]For the second sequence, we have:
[tex]?,?,17,12,7,2.[/tex]We can see that after the 17, each term is the previous one minus 5. So the sequence is:
[tex]27,22,17,12,7,2.[/tex]The third and fourth sequences are written correctly in the image.
For the fifth sequence, the only information we have to determine the ruele it's following is that the next number after 9 is 16, and the 1 that is before the number before the 9.
One possible rule would be to consider the sequence
[tex]x_n=n^2\text{.}[/tex]This way, if we start from n=0 we get:
[tex]0,1,4,9,16,25,[/tex]which fits the numbers we were given perfectly.
16) A bottle of high blood pressure medication contains 90 tablets. Each tablet contains 150 mg of the active ingredient. How many grams of the active ingredient are in the entire bottle? Hint: 1 gram = 1,000 mg
Answers
One tablet contains 150 mg of the active ingredient. Then, 90 tablets contain
[tex]90\text{ tablets }\cdot\frac{150\text{ mg}}{1\text{ tablet}}=13500mg_{}[/tex]1 gram is equivalent to 1,000 mg, then 13500 mg is equivalent to
[tex]13500\text{ mg}\cdot\frac{1\text{ gram}}{1000\text{ mg}}=13.5\text{ grams}[/tex]There are 13.5 grams of the active ingredient in the entire bottle
Find an equation for the perpendicular bisector of the line segment whose endpoints are (-2,1) and (-6,5)
Answers
Here, we want to find the equation of the perpendicular bisector of th line segment with the given endpoints
We start by calculating the slope of the line segment
Mathematically, we can have that as;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ m\text{ = }\frac{5-1}{-6-(-2)}=\text{ }\frac{4}{-4}\text{ = -1} \end{gathered}[/tex]So, we have the slope of the line as -1
Mathematically, the slopes of two lines which are perpendicular to each other have a product of -1
Thus;
[tex]\begin{gathered} m_2\text{ }\times\text{ (-1) = -1} \\ \\ m_2\text{ = 1} \end{gathered}[/tex]Now, we need the midpoint segment coordinates as it is the point through which the perpendicular bisector will pass through
We can get these coordinates using the mid-point formula
That will be;
[tex]\begin{gathered} (x,y)\text{ = (}\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}) \\ \\ (x,y)\text{ = (}\frac{-2-6}{2},\frac{1+5}{2}) \\ \\ (x,y)\text{ = (-4,3)} \end{gathered}[/tex]So we use the point-slope formula to get the equation
That will be;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3\text{ = 1(x+4)} \\ y-3\text{ = x + 4} \\ y\text{ = x + 4 + 3} \\ y\text{ = x + 7} \end{gathered}[/tex]The maximum value in this range is: Use the range rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls.
Answers
Answer:
The maximum value in the range is 8.113
1 girl in 10 births is a significantly low number of girls.
Explanation:
Note that the range rule of thumb says that the range of about 4 times the standard deviation.
We'll use the below formula to determine the standard deviation;
[tex]\begin{gathered} \sigma=\sqrt[]{\lbrack\sum^{}_{}x^2\cdot P(x)\rbrack-\mu^2} \\ \text{where }\mu=\text{ population mean} \end{gathered}[/tex]Let's go ahead and determine the mean as seen below;
[tex]\mu=\sum ^{}_{}\lbrack x\cdot P(x)\rbrack[/tex][tex]\begin{gathered} \mu=(0\cdot0.005)+(1\cdot0.12)+(2\cdot0.039)+(3\cdot0.113)+(4\cdot0.196)+(5\cdot0.235)+(6\cdot0.209) \\ +(7\cdot0.113)+(8\cdot0.036)+(9\cdot0.016)+(10\cdot0.026) \end{gathered}[/tex][tex]\begin{gathered} \mu=0.12+0.078+0.339+0.784+1.175+1.254+0.791+0.288+0.144+0.26 \\ \mu=5.233 \end{gathered}[/tex]Let's now determine the below;
[tex]\begin{gathered} \sum ^{}_{}x^2\cdot P(x)=(0^2\cdot0.005)+(1^2\cdot0.12)+(2^2\cdot0.039)+(3^2\cdot0.113)+(4^2\cdot0.196)+(5^2\cdot0.235) \\ +(6^2\cdot0.209)+(7^2\cdot0.113)+(8^2\cdot0.036)+(9^2\cdot0.016)+(10^2\cdot0.026) \end{gathered}[/tex][tex]\begin{gathered} \sum ^{}_{}x^2\cdot P(x)=0.012+0.156+1.017+3.136+5.875+7.524+5.537+2.304+1.296+2.6 \\ =29.457 \end{gathered}[/tex]So the standard deviation will be;
[tex]\sigma=\sqrt[]{29.457-5.233^2}=\sqrt[]{29.457-27.384}=\sqrt[]{2.073}=1.44[/tex]Let's determine the maximum and minimum value of the distribution as seen below;
[tex]\begin{gathered} Maximum\text{ value = }\mu+2\sigma=5.233+2(1.44)=5.233+2.88=8.113 \\ \text{Minimum value }=\mu-2\sigma=5.233-2(1.44)=5.233-2.88=2.353 \end{gathered}[/tex]We can see from the above that the number of girls born among 10 children should be between the range of 2.353 and 8.113, therefore 1 girl in 10 births is a significantly low number of girls.
The maximum value in this range is 8.113
Complete the equation describe how x and y are related
Answers
From the given equation and the given table, let the missing are m and b
[tex]y=mx+b[/tex]To find them use two points from the table
Let us use point (0, -2)
[tex]\begin{gathered} x=0,y=-2 \\ -2=m(0)+b \\ -2=0+b \\ -2=b \end{gathered}[/tex]Substitute b in the equation by -2
[tex]\begin{gathered} y=mx+(-2) \\ y=mx-2 \end{gathered}[/tex]Now, use the point (1, 1) to find m
[tex]\begin{gathered} 1=m(1)-2 \\ 1=m-2 \end{gathered}[/tex]Add 2 to both sides
[tex]\begin{gathered} 1+2=m-2+2 \\ 3=m \end{gathered}[/tex]Substitute m by 3 in the equation, then
The equation is
[tex]\begin{gathered} y=3x-2 \\ y=3x+(-2) \end{gathered}[/tex]The answer is y = 3x + (-2)
The missings are 3
(6x 2 +3x 3 +7x)−(x+3× 2 +2x 3
Answers
Given
[tex](6x^2+3x^3+7x)-(x+3x^2+2x^3\text{)}[/tex]To solve this question, let's observe the following steps
Step 1: Remove the parentheses (Brackets). So that we will obtain=>
[tex]6x^2+3x^3+7x-x-3x^2-2x^3[/tex]The next step is to collect like terms
[tex]3x^3\text{ }-2x^3\text{ + }6x^2-3x^2\text{ +}7x\text{ - x}[/tex]Then we will proceed to simplify further
[tex]x^3+3x^2\text{ + 6x}[/tex]May you help me with this
Answers
Given the function
[tex]h(x)=2x^2-3x+5[/tex]Set x=-3 and solve for h(-3) as shown below
[tex]\begin{gathered} x=-3 \\ \Rightarrow h(-3)=2(-3)^2-3(-3)+5=18+9+5=32 \\ \Rightarrow h(-3)=32 \end{gathered}[/tex]Therefore, the answer is 32
Question 4 of 10Select the correct product of the exponential expression.35A. 5.5.5B. 3.5C. 15D. 3.3.3.3.3SUBMIT
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You have the following expression:
[tex]3^5[/tex]it means that the number 3 is multipled by itself five times (because of the exponent), then, the previous expression can be written as follow:
[tex]3^5=3\cdot3\cdot3\cdot3\cdot3[/tex]Please help 50 points!
1. A cylindrical jar has a radius of 6 inches and a height of 10inches. The jar is filled with marbles that have a volume of 20 in3. Use 3.14 for pi. Show work. Complete sentences.
What is the volume of the jar?
Answers
The volume of the jar is 1130.4 in³. The number of marbles that is filled the jar is 56.
What is the cylindrical shape?
The three-dimensional shape of a cylinder is made up of two parallel circular bases connected by a curved surface. The right cylinder is created when the centers of the circular bases cross each other. The axis, which represents the height of the cylinder, is the line segment that connects the two centers.
Given that the radius of cylindrical jar is 6 inches and the height is 10 inches.
The volume of a cylindrical shape is [tex]\pi r^2h[/tex].
Where r is the radius of the cylinder and h is the height of the cylinder.
Given that, the radius of the cylindrical jar is 6 inches and height is 10 inches.
The volume of a cylindrical shape is 3.14 × 6² × 10 = 1130.4 in³.
The number of marbles by which the jar can be filled is 1130.4/20 = 56.52 = 56 (approx.)
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You'll have to make a series of transformations to make this parabola fit the bridge. Describethem
Answers
The transformations are as follows:
- There is firstly a vertical reflection
- There is a vertex shift from (0,0) to the (-2, 3) position (approximate)
- There is also a horizontal compression of the parabola.
using the points that are given, what is the slop of this line?
Answers
Solve the equation. – 4y - 37 = 6y + 13 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. y= (Type an integer or a simplified fraction.) B. The solution is all real numbers. C./ There is no solution.
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solve for y:
add 4y to both sides:
[tex]\begin{gathered} -4y-37+4y=6y+13+4y \\ -37=10y+13 \end{gathered}[/tex]Subtract 13 from both sides:
[tex]\begin{gathered} -37-13=10y+13-13 \\ -50=10y \end{gathered}[/tex]Divide both sides by 10:
[tex]\begin{gathered} \frac{10y}{10}=-\frac{50}{10} \\ y=-5 \end{gathered}[/tex]if the spinner was fair and spun 300 times,each outcome would be expected to be observed_____times.
Answers
ANSWER
Each outcome would be expected to be observed 75 times.
EXPLANATION
We have to find the theoretical probability of each outcome. If the spinner is fair, each outcome is equally probable. If we were to spin it 300 times, and the spinner has 4 sections, we would expect that each outcome to be observed:
[tex]\frac{300}{4}=75[/tex]75 times each section.
Given the following piecewise function, evaluate f(-1).f(x) =3x +4. X < -1-8x +8 x> -1
Answers
We have the expression:
[tex]3x+4\text{ if x}\leq-1[/tex]So, when x=-1 we need to use this expression, so lets plot -1 on it:
[tex]3(-1)+4=-3+4=1[/tex]so f(-1)=1.
