The measure of angle J in the isosceles triangle is given as follows:
m<J = 31º.
What is an isosceles triangle?An isosceles triangle is a triangle in which:
Two of the angles have equal measures.Two of the sides have equal measures.In the context of this problem, the angles are given as follows:
118º. (angle H).x: angle J.x: angle I.Angles J and I are equal as the triangle is isosceles and the congruent angles are acute, that is, they cannot have measures above 90º.
The sum of the measures of the internal angles of a triangle is of 180º, hence we can solve for x as follows:
x + x + 118º = 180º
2x = 62º
x = 62º/2
x = 31º.
Hence the measure of angle J is of 31 degrees.
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Find the slope of the line that goes through the given points 9,7 and 8,7
we have the points
(9,7) and (8,7)
Note that: The y-coordinates of both points are equal
that means
we have a horizontal line
therefore
The slope is zerohelp meee pleaseeee pleasee
Answer:
Step-by-step explanation:
An architect is designing the roof for a house what is the height of the roof?
An architect is designing the roof for a house
what is the height of the roof?
From the diagram,
We have that tan 30 = h/ 12
0.5774 = h/ 12
cross-multiply,
h = 12 x 0.5774
h = 6.9288 feet
1. Is this figure a polygon?2. Is this polygon concave or convex?3. Is this polygon regular, equiangular, Equilateral, or none of these?4. What is the name of this polygon?
A polygon is a closed shape with straigh sides, then
2. Is the figure a polygon? YES.
Since the figure is a polygon
1a. Is this polygon concave or convex? It is concave. A concave polygon will always have at least one reflex interior angle, tha is, it has on interior angle greater than 180 degrees.
1b. Is this polyogn regular, equiangular, equilateral or none of these? The marks on the picture mean that all the sides have the same length. This is the definition of equilateral. Then the answer is equilateral.
1c. What is the name of this polygon? We can see it has 4 equal sides and is concave, then his name is Concave Equilateral Quadrilateral.
In a certain country, the probability that a baby that is born is a boy is 0.52 and the probably that a baby that is born is a girl is 0.48. A family has two children. If X is the number of girls born to a family, find the probability that the family has 0, 1, or 2 girls.(a) Draw a tree diagram showing the possibilities for each outcome.(b) Create the binomial distribution table for p(X)
Given:
The probability that a baby that is born is a boy is 0.52.
The probability that a baby that is born is a girl is 0.48.
To find:
The probability that the family has 0, 1, or 2 girls.
Explanation:
Using the binomial distribution,
[tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]Here,
[tex]\begin{gathered} n=2 \\ P(Birth\text{ of girls\rparen=}p=0.48 \\ P(B\imaginaryI rth\text{ of boys\rparen=}1-p=0.52 \end{gathered}[/tex]The probability that the family gets 0 girl child is,
[tex]\begin{gathered} P(X=0)=^2C_0(0.48)^0(0.52)^2 \\ =0.2704 \end{gathered}[/tex]The probability that the family gets 1 girl child is,
[tex]\begin{gathered} P(X=1)=^2C_1(0.48)^1(0.52)^1 \\ =0.2496 \end{gathered}[/tex]The probability that the family gets 2 girl children is,
[tex]\begin{gathered} P(X=2)=^2C_2(0.48)^2(0.52)^0 \\ =0.2304 \end{gathered}[/tex]So, the probability that the family has 0, 1, or 2 girls is,
[tex]\begin{gathered} P(E)=0.2704+0.2496+0.2304 \\ =0.7504 \end{gathered}[/tex]a) The tree diagram is,
b) The binomial distribution table for p(X) is,
what should be done to solve the following e q u a t i o n x + 8 equals 4
we have the equation
x+8=14
step 1
subtract 8 both sides
x+8-8=14-8
x=6
therefore the answer is the last option
Kathryn needs to include a scale drawing of a race car on her science science fair project. Her actual race car is 180 inches long and 72 inches tall. if she uses a scale factor of 1 inch= 8 inches, what will the dimensions of her scale drawing?
To find the scaled measures of the race car, you have to divide the original measures by the scale. This is:
[tex]\text{length}=\frac{182in}{8}=22.75in[/tex][tex]\text{height}=\frac{72in}{8}=9in[/tex]So the scaled measures of the race car are: length=22.75in and height=9in
Si A = 5x 2 + 4 x 2 - 2 (3x2), halla su valor numérico para x= 2.
Based on the calculations, the numerical value of A is equal to 12.
How to determine the numerical value of A?In this exercise, you're required to determine the numerical value of A when the value of x is equal to 2. Therefore, we would evaluate the given equation based on its exponent as follows:
Numerical value of A = 5x² + 4x² - 2(3x²)
Numerical value of A = 5(2)² + 4(2)² - 2(3 × (2)²)
Numerical value of A = 5(4) + 4(4) - 2(3 × 4)
Numerical value of A = 20 + 16 - 24
Numerical value of A = 36 - 24
Numerical value of A = 12
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Complete Question:
If A = 5x² + 4x² - 2(3x²), find its numerical value for x = 2.
Do 9 and 10 keep it 9th grade if you can Question 9-10
Given the formula for the volume of a cylinder:
[tex]V=\pi r^2h[/tex]You know that "r" is the radius of the cylinder and "h" is the height.
a. In order to solve the formula for "h", you can divide both sides of the formula by:
[tex]\pi r^2[/tex]As follows:
[tex]\frac{V}{\pi r^2}=\frac{\pi r^2h}{\pi r^2}[/tex][tex]h=\frac{V}{\pi r^2}[/tex]b. Having a cylindrical swimming pool, you know that:
[tex]\begin{gathered} r=12\text{ }ft \\ V=1810\text{ }ft^3 \end{gathered}[/tex]And, for this case:
[tex]\pi\approx3.14[/tex]Therefore, you can substitute values into the formula for the height of a cylinder found in Part "a" and evaluate:
[tex]\frac{V}{\pi r^2}=\frac{\pi r^2h}{\pi r^2}[/tex][tex]h=\frac{1810\text{ }ft^3}{(3.14)(12\text{ }ft)^2}[/tex][tex]h=\frac{1810\text{ }ft^3}{452.16\text{ }ft^2}[/tex][tex]h\approx4\text{ }ft[/tex]Hence, the answers are:
a.
[tex]h=\frac{V}{\pi r^2}[/tex]b.
[tex]h\approx4\text{ }ft[/tex]Find the distance d(P1, P2) between the given points P1 and P2: P1 =(0,0) P2 = (2,3)d(P1,P2) = (Simplify your answer using radical as needed)
Recall that given points (a,b) and (c,d) the distance between them would be
[tex]d=\sqrt[2]{(c\text{ -a\rparen}^2+(d\text{ -b\rparen}^2}[/tex]In our case we are given a=0,b=0,c=2,d=3. So the distance would be
[tex]d=\sqrt[2]{(2\text{ -0\rparen}^2+(3\text{ -0\rparen}^2}=\sqrt[2]{2^2+3^2}=\sqrt[2]{4+9}=\sqrt[2]{13}[/tex]so the distance between them is the square root of 13.
First find the circumference. Do you need to divided by two? Find X. Then show all work to calculate the composite perimeter.
We are given the radius of the circle =5
then the circumference is given by
[tex]C=2\pi *r[/tex][tex]C=2\pi *5[/tex][tex]C=10\pi[/tex]then the cicumference of the semicircle is
[tex]\frac{C}{2}=\frac{10\pi}{2}=5\pi[/tex]Now let's find X
given the radius=5
the diameter = 2r = 5*2 = 10 in
then X is given by
[tex]X=4+10+4.5[/tex][tex]X=18.5[/tex]now the lateral side of the rectangle is given by
12-5= 7 in
then
the composite perimeter is
[tex]P=\frac{C}{2}+4.5+7+X+7+4[/tex][tex]P=5\pi+4.5+7+18.5+7+4[/tex][tex]P=5\pi+41[/tex][tex]P=56.70\text{ in}[/tex]then the composite perimeter is 56.7 in
Use the appropriate differenatal formula to find© the derivative of the given function6)3(16) 96) = (x²-1) ²(2x+115
1) We need to differentiate the following functions:
[tex]\begin{gathered} a)\:f(x)=x\sqrt[3]{1+x^2}\:\:\:\:Use\:the\:product\:rule \\ \\ \\ \frac{d}{dx}\left(x\right)\sqrt[3]{1+x^2}+\frac{d}{dx}\left(\sqrt[3]{1+x^2}\right)x \\ \\ \\ 1\cdot \sqrt[3]{1+x^2}+\frac{2x}{3\left(1+x^2\right)^{\frac{2}{3}}}x \\ \\ \sqrt[3]{1+x^2}+\frac{2x^2}{3\left(x^2+1\right)^{\frac{2}{3}}} \\ \\ f^{\prime}(x)=\sqrt[3]{1+x^2}+\frac{2x^2}{3\left(1+x^2\right)^{\frac{2}{3}}} \end{gathered}[/tex]Note that we had to use some properties like the Product Rule, and the Chain Rule.
b) We can start out by applying the Quotient Rule:
[tex]\begin{gathered} g(x)=\frac{(x^2-1)^3}{(2x+1)} \\ \\ f^{\prime}(x)=\frac{\frac{d}{dx}\left(\left(x^2-1\right)^3\right)\left(2x+1\right)-\frac{d}{dx}\left(2x+1\right)\left(x^2-1\right)^3}{\left(2x+1\right)^2} \\ \\ Differentiating\:each\:part\:of\:that\:quotient: \\ \\ ------- \\ \frac{d}{dx}\left(\left(x^2-1\right)^3\right)=3\left(x^2-1\right)^2\frac{d}{dx}\left(x^2-1\right)=6x\left(x^2-1\right)^2 \\ \\ \frac{d}{dx}\left(x^2-1\right)=\frac{d}{dx}\left(x^2\right)-\frac{d}{dx}\left(1\right)=2x \\ \\ \frac{d}{dx}\left(x^2\right)=2x \\ \\ \frac{d}{dx}\left(1\right)=0 \\ \\ \frac{d}{dx}\left(2x+1\right)=2 \\ \\ Writing\:all\:that\:together: \\ \\ f^{\prime}(x)=\frac{6x\left(x^2-1\right)^2\left(2x+1\right)-2\left(x^2-1\right)^3}{\left(2x+1\right)^2} \\ \end{gathered}[/tex]Thus, these are the answers.
Solve the inequality 3.5 >b + 1.8. Then graph the solution.
Collect like terms
[tex]\begin{gathered} 3.5-1.8\ge b \\ 1.7\ge b \\ b\leq\text{ 1.7} \end{gathered}[/tex]Find the slope and y-intercept for each equation:2. 2x + 9y = 18
Step-by-step explanation:
we need to transform the equation into the slope-intercept form
y = ax + b
a is then the slope, abd b is the y-intercept (the y-value when x = 0).
2x + 9y = 18
9y = -2x + 18
y = -2/9 x + 2
so,
-2/9 is the slope
2 is the y-intercept
two slices of dans famous pizza have 230 calories how many calories would you expect to be in 5 slices of pizza
We can answer this question, using proportions. We can see it graphically as follows:
Then, we have that 5 slices will have 575 calories.
I need help with the question I post as a photo.
We will have the following:
*First:
[tex]3x+\frac{1}{4}-x+1\frac{1}{2}=2x+\frac{1}{4}+\frac{3}{2}[/tex][tex]=2x+\frac{7}{4}=2x+1\frac{3}{4}[/tex]So, the first one is not equivalent to the other expression.
*Second:
[tex]2(3x+1)=6x+2[/tex]So, the second one is equivalent to the other expression.
*Third:
[tex]3(x+1)-(1+x)=3x+3-1-x[/tex][tex]=2x+2[/tex]So, the third one is not equivalent to the other expression.
*Fourth:
[tex]4(x+1)-x-4=4x+4-x-4[/tex][tex]=3x[/tex]So, the fourth one is equivalente to the other expression.
*Fifth:
[tex]5.5+2.1x+3.8x-4.1=5.9x+1.4[/tex]So, the fifth one is equivalent to the other expression.
The figure below is made up of a triangle and a circle. The ratio of the area of the triangle to the area of the circle is 5:6. If 1/5 of the area of the triangle is shaded, what is the ratio of the shaded area to the area of the figure?
ANSWER
[tex]\begin{equation*} 1:10 \end{equation*}[/tex]EXPLANATION
The ratio of the area of the triangle to the area of the circle is:
[tex]5:6[/tex]Let the area of the triangle be T.
1/5 of the area of the triangle is shaded i.e. 1/5 T
The total area of the figure is the sum of the area of the triangle that is not shaded and the area of the circle.
The area of the triangle that is not shaded is:
[tex]\begin{gathered} T-\frac{1}{5}T \\ \frac{4}{5}T \end{gathered}[/tex]Let the area of the circle be C. The ratio of the area of the triangle to that of the circle is 5/6. This implies that:
[tex]\begin{gathered} \frac{T}{C}=\frac{5}{6} \\ \Rightarrow C=\frac{6T}{5} \end{gathered}[/tex]And so, the area of the figure is in terms of T is:
[tex]\begin{gathered} \frac{4}{5}T+\frac{6}{5}T \\ 2T \end{gathered}[/tex]Therefore, the ratio of the shaded area to the area of the figure is:
[tex]\begin{gathered} \frac{1}{5}T:2T \\ \Rightarrow\frac{1}{5}:2 \\ \Rightarrow1:10 \end{gathered}[/tex]That is the answer.
A rectangle has a length of 9 inches and a widt of 5 inches whose sides are changing. The length is increasing by 3 in/sec and the width is shrinking at 9 in/sec. What is the rate of change of the perimeter?
Given:
A rectangle has a length of 9 inches and a width of 5 inches whose sides are changing. The length is increasing by 3 in/sec and the width is shrinking at 9 in/sec.
To find:
The rate of change of the perimeter.
Solution:
It is known that the perimeter of the rectangle is twice the sum of length and width.
[tex]P=2(l+w)[/tex]DIfferentiate the perimeter with respect to t:
[tex]\frac{dP}{dt}=2(\frac{dl}{dt}+\frac{dw}{dt})[/tex]From the given information:
[tex]\begin{gathered} \frac{dP}{dt}=2(3-9) \\ =2(-6) \\ =-12 \end{gathered}[/tex]Thus, the perimeter of the rectangle is decreasing at the rate of 12 inches per second.
20 ping pong balls are numbered 1-20, with no repitition of any numbers. What is the probability of selecting one ball that is either odd or less than 5?
given 20 ping pong balls
numbered 1-20
odd numbers = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
total odd numbers = 10
numbers less than 5 = 1, 2, 3, 4
total numbers less than 5 = 4
since 1 and 3 are in both sides,
total number of porbabilities
= 10 + 4 - 2
= 12
the probability of selecting one ball
= 12/20
= 3/5
= 0.6
therefore the probabilty of selecting one ball that is either odd or less than 5 = 0.6
Box #1 options is: A.true B.false
Box #2 options are: A.true B.false
Box #3 options are: A.enough B.not enough
Answers:
falsetruenot enough=======================================================
Explanation:
Let's say the claim is [tex]\text{x}^2 \ge \text{x}[/tex] true for any real number x. It certainly works for things like x = 5 and x = 27.
A counter-example to show this isn't true is to use x = 0.5
So,
[tex]\text{x}^2 \ge \text{x}\\\\0.5^2 \ge 0.5\\\\0.25 \ge 0.5\\\\[/tex]
The last statement is false, which thereby proves the original claim doesn't work for x = 0.5; by extension, the overall claim of that inequality working for any real number is false.
As you can see, all we need is one counter-example to contradict the claim to prove it false.
Unfortunately one single example is not enough evidence to prove a claim true. Think of it like saying "it's much easier to knock down a sand castle than to build it up".
Instead, we need to use a set of clearly laid out statements and reasons based on previously established theorems.
Andy spent 1/3 of his money on pastries and 3/4 of his remaining money on 2 pies. Each pie costs 6 times as much as each pastry. if all pastries cost the same how many did he buy
Solve for x in 2(2-x)=4(-2+x)
Given the equation:
[tex]2(2-x)=4(-2+x)[/tex]First, we open the brackets
[tex]4-2x=-8+4x[/tex]Next, we collect like terms. (Bring terms containing x to the left-hand side)
[tex]\begin{gathered} -2x-4x=-8-4 \\ -6x=-12 \end{gathered}[/tex]Finally, we divide both sides by -6 (negative 6) to obtain x.
[tex]\begin{gathered} \frac{-6x}{-6}=\frac{-12}{-6} \\ x=2 \end{gathered}[/tex]The value of x is 2.
The midpoint of AB is M(4,1). If the coordinates of A are (2,8), what are thecoordinates of B?
The length of the hypotenuse in a 30°-60°-90° triangle is 6√10yd. What is thelength of the long leg?
In order to calculate the length of the long leg, we can use the sine relation of the 60° angle.
The sine relation is the length of the opposite side to the angle over the length of the hypotenuse.
So we have:
[tex]\begin{gathered} \sin (60\degree)=\frac{x}{6\sqrt[]{10}} \\ \frac{\sqrt[]{3}}{2}=\frac{x}{6\sqrt[]{10}} \\ 2x=6\sqrt[]{30} \\ x=3\sqrt[]{30} \end{gathered}[/tex]So the length of the long leg is 3√30 yd.
SOMEONE please help.
The class interval of the median is 1 ≤ x ≤ 2 and the mean of the distribution is 1.8
How to determine the class interval of the median class?From the question, we have
Number of students = 30
This represents the total frequency
So, we have
Total frequency = 30
The median position is then calculated as
Median = (Total frequency + 1)/2
Substitute the known values in the above equation
So, we have
Median = (30 + 1)/2
Evaluate
Median = 15.5th
The 15.5th element is located in the second class
i.e. the class with the interval 1 ≤ x ≤ 2
So, the class interval in this case is 1 ≤ x ≤ 2
The mean of the distributionTo do this, we start by calculating the average of the class interval
This is represented as
0 ≤ x ≤ 1 ⇒ 0.5
1 ≤ x ≤ 2 ⇒ 1.5
2 ≤ x ≤ 3 ⇒ 2.5
3 ≤ x ≤ 4 ⇒ 3.5
So, we have
x f
0.5 6
1.5 13
2.5 7
3.5 4
The mean is calculated as
Mean = ∑fx/∑f
So, we have
Mean = (0.5 * 6 + 1.5 * 13 + 2.5 * 7 + 3.5 * 4)/30
Evaluate
Mean = 1.8
Hence, the mean value is 1.8
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Question 9 (1 point) Jennifer is a car saleswoman. She is paid a salary of $2200 per month plus $300 for each car that she sells. Write a linear function that describes the relationship between the number of cars sold x and the monthly salary y. Then, graph the function to show the relationship.
Which transformations of quadrilateral PQRS would result in the imageof the quadrilateral being located only in the first quadrant of thecoordinate plane?
Given:
The quadrilateral PQRS is given.
The aim is to locate the given quadrilateral into first quadrant only.
The graph will be reflected across x=4 then the graph will not be located to the first quadrant.
Find the values of x and y
Since the "x" values are vertical angles, and so are the "y" values, you must make them equal. If this is confusing, look at steps below (The order of solving the "x" or "y" values don't matter. I will write both ways down (in point form --> [tex](x,y)[/tex] and as just "x=..." "y=..."
First step is to make the "y" values equal each other
[tex]5y = 7y-34\\-2y = -34\\2y = 34\\\\y=17[/tex]
Next to solve make the "x" values equal each other
[tex]8x+7 = 9x-4\\-x = -11\\x = 11[/tex]
Final Answer:
[tex](11,17)[/tex]
x = 11; y = 17
Hope this helps :)
4+4x=2x+8+2x-5 help please
Simplify the expression.
[tex]\begin{gathered} 4+4x=2x+8+2x-5 \\ 4x-2x-2x=8-5-4 \\ 0=-1 \end{gathered}[/tex]Thus, the equation is solved.
SKIPPYTHEWALRUS U CAN'T ANSWER THIS QUESTIONI NEED CORRECT ANSWER 100 POINTS ONLY ANSWER CORRECTLY
A line passes through the points (7,9) and (10,1). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answer:
y - 1 = -8/3(x - 10)
also valid:
y - 9 = -8/3(x - 7)
Step-by-step explanation:
Point-slope equation is a fill-in-the-blank formula that is sort of a shortcut for writing the equation of a line. Point-slope is named that bc you fill in a point and the slope.
Point-slope Eq:
y - Y = m(x - X)
fill in the slope for the m and fill in any point on the line for the X,Y.
First slope:
Slope is y-y over x-x
9-1 / 7-10
= 8/ -3
= -8/3
So slope is -8/3 fill that in for the m.
y -Y = -8/3(x-X)
Pick one of the points (either one it totally doesn't matter)
Let's use (10,1)
fill in 10 for X and 1 in place of Y.
the y in the very front stays a y and the first x in the parentheses stays an x, so there will be two variables in your completed answer.
y - 1 = -8/3(x - 10)
make sure the parentheses on the right is beside the -8/3 fraction and is NOT written on the bottom, beside the 3 only.
