The options that can help prove that the triangles EFG and JHG are congruent are determined as follows:
Two triangles are said to be congruent (or the same) if:
i) One of the triangles has the lengths of all its sides equal to the lengths of the sides of the other triangle.
This scenario is called the SSS scenario
ii) One of the triangles has the lengths of two of its sides equal to the lengths of two sides of the other triangle, and then both of the two triangles have an angle in common.
This scenario is called the SAS scenario
From the above explanations, we can tell that the two triangles EFG and JHG will be congruent under the scenarios SAS and SSS
Thus options B and C are correct
Solve 3n - 5p + 2n = 10p for n.
Solving for n ,
[tex]\begin{gathered} 3n-5p+2n=10p \\ \rightarrow3n+2n=10p+5p \\ \rightarrow5n=15p \\ \rightarrow n=\frac{15p}{5} \\ \\ \Rightarrow n=3p \end{gathered}[/tex]How to: determine if the side lengths could form a triangle. use an inequality to prove your answer
We need to simply use the triangle inequality Theorem, This theorem state that the sum of the two side lengths of a triangle must always be greater than the third side.
Now let's check from the given lengths
16 + 21 = 37 and 37 is less than 39 which is the third side
Hence, it cannot form a triangle
Julia has been measuring the length of her baby's hair. The first time it was 6 cm long and after one month it was 2 cm longer. If the hair continues to grow at this rate, determine the function that represents the hair growth and graph it.
Given that,
The length of baby's hair at first time = 6cm
After a month, the length was 2 cm longer = 6 + 2 = 8 cm
As mentioned in the question, the hair continues to grow at this rate. Therefore, after two months, the length would be = 8 + 2 = 10 cm
It results in a sequence with a common difference of 2,
6, 8, 10, 12, ............
If a sequence has a common difference, it is called an arithmetic sequence. In such sequences, the nth term is calculated as:
an = a1 + (n-1)*d
Here,
a1 = first term = 6
d = common difference = 2. (8-6 or 10 - 8 = 2)
Now, put all the values in the equation,
an = a1 + (n-1)*d
an = 6 + (n-1)*2
an = 6 + 2n - 2
an = 2n + 4
an = 2(n+2)
Hence, the function that represents growth is an = 2(n+2).
By varying the value of 'n', you can get the values of 'an'. Both will generate ordered pairs that will help you in plotting. For example:
n = 1
an = 2(n+2) = 2(1+2) = 2 (3) = 6
=> ordered pair (1, 6)
n = 2
an = 2(n+2) = 2(2+2) = 2 (4) = 8
=> ordered pair (2, 8)
n = 3
an = 2(n+2) = 2(3+2) = 2 (5) = 10
=> ordered pair (3, 10)
n = 4
an = 2(n+2) = 2(4+2) = 2 (6) = 12
=> ordered pair (4, 12)
With the ordered pairs, you can plot the graph.
whats the absolute value between the points -45 and -11
For two real numbers u and v, |u-v| is the absolute value between the points:
|-45-(-11)|=|-34|=34
I need help with homework I got the picture with the questions and will send it to you
3a.
DVA + AVB = 180 (straight line), so
75 + Angle AVB = 180
Angle AVB = 180 - 75
Angle AVB = 105 degrees
3b.
Angle DVC and Angle BVA are vertical angles.
Vertical angles form when we have a geometrical "X".
Vertical angles are equal so,
DVC = BVA
60 = 60
BVA = 60 degrees
3c.
BVC and CVD are in a straight line, so
BVC + CVD = 180
2x + 35 + 3x + 45 = 180
Let's solve for x:
5x + 80 = 180
5x = 100
x = 100/5
x = 20
Angle BVC = 2x + 35 = 2(20) + 35 = 40 + 35 = 75 degrees
Angle CVD = 3x + 45 = 3(20) + 45 = 60 + 45 = 105 degrees
what can you prove congruent from your given
Answer:
a. line OL bisects angle MLN
b. triangle MLO is congruent to triangle OLN
c. line OL proves that they are congruent through reflexive property.
Step-by-step explanation:
hope this helps!
What is numeral value of 3/4 + 5/8
The given expression is
[tex]\frac{3}{4}+\frac{5}{8}[/tex]We have to sum these fractions with the cross-rule. The image below shows this method.
Select the equation that represents the graph of the line. 3+ 2 1- -5 -4 -3 -2 -1 1 2 3 4 5 -3+ -4- -57 o y = 1 / 2 x + 2 O'y=x-1 o y = 1 / 2 x - 1 O y=x+2
First, we have to find the slope with the formula below.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the points (0, -1) and (2, 0).
[tex]m=\frac{0-(-1)}{2-0}=\frac{1}{2}[/tex]Once we have the slope, we use the slope-intercept formula to find the equation.
[tex]y=mx+b[/tex]Where m = 1/2, and b = -1.
[tex]y=\frac{1}{2}x-1[/tex]Hence, the answer is the third choice.An item is regularly priced at $95. It is on sale for 60% off the regular price. How much (in dollars) is discounted from the regularprice?
We have to find the 60% of $95. Doing so, we have:
60/100*$95
0.6*$95 (Dividing)
$57 (Multiplying)
The discount is $57
The Voronoi diagram below shows the locations of the four post offices P_{1} , P_{2} P_{3} , and P_{4}in a city.y(km)8P_{3}P2r (km)6P_{1}PKatie's apartment lies inside the shaded circle shown on the diagram.(a) Write down the post office nearest to Katie's apartment.P is located at coordinates (3-6), and the edge between P and P_{i} has the equation y = - 5/3 * x = 16/3(b) Determine the location of PPa is located at coordinates (1.7).3(c) Find the gradient. A. of the edge between P, and P.
Given -
Voronoi diagram:
To Find -
(a) Write down the post office nearest to Katie's apartment.
(b) Determine the location of P4
(c) Find the gradient k. of the edge between P3 and P4
Step-by-Step Explanation -
(a)
We can see from the voronoi diagram that the center of the x-axis where the circle covers is where Katie's apartment is located.
It is located near P4.
So,
P4 is nearest to Katie's apartment.
(b)
The location of P4:
(2, -3)
(c)
[tex]k\text{ = }\frac{Y_2\text{ - Y}_1}{X_2\text{ - X}_1}\text{ = }\frac{7}{50}[/tex]Final Answer -
(a) The post office nearest to Katie's apartment = P4
(b) The location of P4 = (2, -3)
(c) The gradient k of the edge between P3 and P4 = 7/50
Linda must choose a number between 55 and 101 that is a multiple of 3,5, and 9. Write all the numbers that she could choose.
We will have the following:
*The LCM of the numbers given (3, 5 & 9) is 72. [This is the value to chosse]. We will have that 90 is also a multiple of 3, 5 & 9 [This is other value that can be chosen].
You pick a card at random. Without putting the first card back, you pick a second card at rando 4 5 6. What is the probability of picking an odd number and then picking an odd number? Simplify your answer and write it as a fraction or whole number.
Given data:
The three numbers on the cards are 4, 5, 6.
The probability of picking an odd number and then picking an odd number is,
[tex]\begin{gathered} P=\frac{1}{3}\times\frac{0}{2} \\ =0 \end{gathered}[/tex]Thus, the probability of picking an odd number and then picking an odd number is 0.
Without graphing, find the slope of the line that goes through each pair of coordinate points. (0,5) and (8,2 ) [Choose ] (2,-1) and (6, 1) [ Choose ] (-3,-2) and (- 1,-5) [ Choose]
Answers:
(0,5) and (8,2 ) = 2/3
(2,-1) and (6, 1) = 1/2
(-3,-2) and (- 1,-5) = -3/2
Explanation:
The slope of a line that goes through two points (x1, y1) and (x2, y2) can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, the slope of a line that goes through (0,5) and (8,2) is equal to:
[tex]m=\frac{2-0}{8-5}=\frac{2}{3}[/tex]The slope of a line that goes through (2, -1) and (6, 1) is:
[tex]m=\frac{1-(-1)}{6-2}=\frac{1+1}{4}=\frac{2}{4}=\frac{1}{2}[/tex]The slope of a line that goes through (-3, -2) and (-1, -5) is:
[tex]m=\frac{-5-(-2)}{-1-(-3)}=\frac{-5+2}{-1+3}=-\frac{3}{2}[/tex]Therefore, the answers are:
(0,5) and (8,2 ) = 2/3
(2,-1) and (6, 1) = 1/2
(-3,-2) and (- 1,-5) = -3/2
The five‐number summary of a distribution consists of(a) mean, median, standard deviation, and two quartiles.(b) minimum, maximum, mean, median, and standard deviation. (c) minimum, maximum, median, and two quartiles(d) mean, standard deviation, correlation, and two quartiles
The five-number summary of a distribution consists of
1)The minimum(smallest observation)
2)The maximum ( Largest observation)
3)median
4)Two quartiles( The first quartile and the third quartile)
That is option C
A trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts. Write a proportional equation where r represents the amount of raisins, and p represents the amount of peanuts.
A trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts. Write a proportional equation where r represents the amount of raisins, and p represents the amount of peanuts.
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where
k is the constant of proportionality
In this problem we have
p=kr
step 1
Find the value of k
k=p/r
we have the ordered pair (4,6)
substitute
k=6/4
k=1.5
therefore
the proportional equation is
p=1.5rHi, can you help me answer this question please, thank you!
Given that
[tex]\begin{gathered} \mu_1=sample\text{ of soda in the coke can} \\ \mu_2=sample\text{ of soda in the pepsi can} \end{gathered}[/tex]Therefore, in the first statement, we are to test how accurate the companies package these cans.
Mathematically it can be expressed as,
[tex]H_0\colon\mu_1\leq\mu_2[/tex]In the second statement, we wish to test the claim that the mean of the amount of liquid in coke cans is greater than the amount of liquid in pepsi cans. This can be expressed mathematically as,
[tex]H_a\colon\mu_1>\mu_2[/tex]Hence, the correct option is Option 1.
The following two-way table describes student'safter school activities. Find the probability that arandomly selected student is in sports.GradeMusic/DramaWorkSports20Sophomore73Junior2013255SeniorP(Sports) = [? ]%25
Solution
The Probability that a random selected students is in sports is
[tex]P(Sports)=\frac{65}{Total}=\frac{65}{20+20+25+7+13+5+3+2+5}=0.65=65\%[/tex]The answer is 65%
I need to know the system of equation in the photo
Solution:
The graph has a solution (4,-1);
That is, the system of equation must satisfy x=4 as y=-1.
LINE 1 has its y-intercept;
[tex]\begin{gathered} (0,1) \\ \end{gathered}[/tex]LINE 2 has its y-intercept as;
[tex](0,-5)[/tex][tex]\begin{gathered} x+2y=2 \\ 2y=-x+2 \\ y=-\frac{1}{2}x+\frac{2}{2} \\ y=-\frac{1}{2}x+1 \\ \\ x-y=5 \\ y=x-5 \end{gathered}[/tex]Thus, the system of equation that satisfy the graph is;
[tex]\begin{gathered} x-y=5 \\ x+2y=2 \end{gathered}[/tex]4y-3x=-16 I need help with this problem and the problem in the picture please help me this work is already late I need to turn it in
Answer
x = 1.6
y = -2.8
Explanation
The question wants us to solve the simultaneous equation
4y - 3x = -16
8x - 4y = 24
Adding the two equations, we have,
4y - 3x + 8x - 4y = -16 + 24
5x = 8
Divide both sides by 5
(5x/5) = (8/5)
x = 1.6
If x = 1.6,
8 (1.6) - 4y = 24
12.8 - 4y = 24
-4y = 24 - 12.8
-4y = 11.2
y = -2.8
Hope this Helps!!!
A rectangle is inscribed with its base on the -axis and its upper corners on the parabola y = 7 - x ^ 2 What are the dimensions of such a rectangle with the greatest possible area?
The width = 3.06
The height = 4.66
Explanation:The rectangle is inscribed with its base on the -axis and its upper corners on the parabola
Width = 2x
Height = 7 - x²
Area of the inscribed rectangle:
Area = width x height
A = 2x (7 - x²)
A = 14x - 2x³
Take the derivative of the area (A) and equate to zero
A' = 14 - 6x²
0 = 14 - 6x²
6x² = 14
x² = 14/6
x² = 2.33
x = √2.33
x = 1.53
The width = 2x
The width = 2(1.53)
The width = 3.06
Substitute x = 1.53 into the equation y = 7 - x² to solve for the height
y = 7 - 1.53²
y = 4.66
The height = 4.66
Banana Cupcakes
makes 10 cupcakes
1 cup granulated sugar
cup vegetable oil
1 large egg
4 tablespoons sour cream
2 medium-sized ripe bananas, mashed
1 cups all-purpose flour
1 teaspoon baking soda
teaspoon salt
1 teaspoon vanilla extract
pinch of nutmeg
You will use the recipe above to answer the following questions:
This recipe serves 10, but you need to serve 30. What number will you need to multiply the amount of each ingredient by to adjust the recipe? How did you determine this number?
How much vegetable oil do you need for 30 cupcakes?
How much flour do you need for 30 cupcakes?
What is the difference in the amount of vanilla extract you would need for 30 cupcakes?
What is the difference in the amount of salt you would need for 30 cupcakes?
In the real world, even though you make adjustments to a recipe to accommodate the number of people you need to serve, you sometimes round the amount of an ingredient instead of using an exact amount. Which ingredient would it make more sense to round rather than coming up with the exact amount? Why?
For 30 cupcakes we need 3 cups of vegetable oil, and 3 cups of flour, for 30 cupcakes we need 3 teaspoons of vanilla, the difference is 3 - 1 = 2.
Here we have a recipe that works for 10 serves.
Then, if we want to make 30 servings, we need to use that recipe 3 times. (because x*10 = 30, then x = 30/10 = 3)
This would be equivalent to multiplying each ingredient by 3.
for 30 cupcakes we need:
3 cups of vegetable oil.
3 cups of flour.
(because for each one of these ingredients we needed only 1 cup to make 10 cupcakes).
for 10 cupcakes we need 1 teaspoon of vanilla.
for 30 cupcakes we need 3 teaspoons of vanilla, the difference is 3 - 1 = 2.
So the difference is 2 teaspoons.
Hence, for 30 cupcakes we need 3 cups of vegetable oil, and 3 cups of flour, for 30 cupcakes we need 3 teaspoons of vanilla, the difference is 3 - 1 = 2.
To learn more about differences from the given link
https://brainly.com/question/18218045
#SPJ1
+ Type a messageSend2Help Mark use completing the square with the algebra tiles to convert this standard form equation to vertexform. Draw the tiles using this method and show the algebraic steps that take you from this equation to itsequivalent vertex form. Then state the vertex.014Show Your WorkCorrect answer y=xThis assignment has been submitted and is no longer editable.Client time: 5/13/2021, 6:06:10 PM (America/Los_Angeles)Server time: 5/13/2021, 6:06:10 PM (-70.44)Missing.omeos StommKB
From the image.
we have
1 y
1 x^2
6 x
8 (1squares)
We can write the standard equation as
[tex]y=x^{2^{}}+\text{ 6x +8}[/tex]But we need to express it in vertex form y = a(x-h)^2 + k where (h,k) is the vertex
to complete the squares we need to express the equation as
y = (x^2+6x+8+__)-___
to complete the square we need to add +1 inside the parenthesis and -1 outside
y = (x^2+6x+8+1)-1
We can express the equation
y = (x+3)^2 -1
[tex]y=(x+3)^2-1[/tex]A box contains different colored paper clips. The probability of drawing two red paper clips from the box without replacement is 1/7, and the probability of drawing one red paper clip is 2/5.What is the probability of drawing a second red paper clip, given that the first paper clip is red?1/65/142/32/35
SOLUTION
The probability of two red paper clips without replacement means
The probability of drawing the first and the probability of drawing the second one. This is represented as
[tex]P(R_{1st}\cap R_{2nd})[/tex]And this was given as
[tex]\frac{1}{7}[/tex]So
[tex]P(R_{1st}\cap R_{2nd})=\frac{1}{7}[/tex]Probalilty of drawing one red paper clip is
[tex]P(R_{1st})=\frac{2}{5}[/tex]Now the probability of drawing a second red paper clip, given that the first paper clip is red becomes
[tex]\begin{gathered} P(R_{1st}/R_{2nd})=\frac{P(R_{1st}\cap R_{2nd})}{P(R_{1st})} \\ \\ P(R_{1st}/R_{2nd})=\frac{\frac{1}{7}}{\frac{2}{5}} \\ \\ =\frac{5}{14} \end{gathered}[/tex]A local diner purchased a jukebox for $9400 the business makes a down payment of $1000 and agrees to 36 monthly payments of $275 each estimate the annual percentage rate to the nearest 10th of a percent
Given:-
Jukebox for $9400.
Payment done is $1000.
Agrees to make down payment for 36 months each month of $275.
To find
In a survey, 315people said they drivetheir car to work. Thisrepresents 90% of thepeople surveyed.How many peoplewere surveyed?
We know that 90% is equivalent to 315 people and we want to know how many people are equivalent to 100%. So, using the rule of three, we get:
90% ------------------- 315
100% ------------------ X
Where X is the number of people surveyed.
Solving for X, we get:
[tex]X=\frac{100\cdot315}{90}=350[/tex]Therefore, 350 people were surveyed.
Answer: 350 people
f(x) = 6x^4 + 6Use the limit process to find the slope of the line tangent to the graph of f at x = 2. Slope at x= 2:__Find an equation of the line tangent to the graph of f at x = 2:__
The given function is
f(x) = 6x^4 + 6
The formula for the limit is shown below
[tex]\begin{gathered} f^{\prime}(x)\text{ = }\lim _{h\to0}\text{ }\frac{f(x\text{ + h) - f(x)}}{h} \\ \text{Substituting x = x + h into the function, we have} \\ f^{\prime}(x)\text{ = }\lim _{h\to0}\text{ }\frac{6(x+h)^4+6-(6x^4+6)}{h} \\ f^{\prime}(x)\text{ = }\lim _{h\to0}\text{ }\frac{6(h^4+4h^3x+6h^2x^2+4hx^3+x^4)+6-6x^4-6}{h} \\ f^{\prime}(x)\text{ = }\lim _{h\to0}\text{ }\frac{6h^4+24h^3x+36h^2x^2+24hx^3+6x^{4\text{ }}-6x^4\text{ + 6 - 6}}{h} \\ f^{\prime}(x)\text{ = }\lim _{h\to0}\text{ }\frac{h(6h^3+24h^2x+36hx^2+24x^3)}{h} \\ h\text{ cancels out} \\ \end{gathered}[/tex]Evaluating the limit at h = 0, we would substitute h = 0 into 6h^3 + 24h^2x + 36hx^2 + 24x^3
It becomes
6(0)^3 + 24(0)^2x + 36(0)x^2 + 24x^3
The derivative is 24x^3
f'(x) = 24x^3
This is the slope of the tangent line is at x = 2
By substituting x = 2 into f'(x) = 24x^3, it becomes
f'(2) = 24(2)^3 = 192
To find the y coordinate of the point, we would substitute x = 2 into
f(x) = 6x^4 + 6
y = 6(2)^4 + 6 = 102
Thus, the x and y coordinates are (2, 102) and the slope is 192
The equation of the line in the point slope form is
y - y1 = m(x - x1)
Thus, the equation of the tangent is
y - 102 = 192(x - 2)
1. Determine the difference inclock 12 arithmetic bystarting at the first numberand countingcounterclockwise on theclock the number. Of unitsgiven by the second number 1-11=?
Given:
The identity element is P.
Required:
Determine the inverse if exist of
(a) P (b) Q (c) R
Explanation:
We know that the inverse is the element when combined on the right or the left through the operation, always gives the identity element as the result.
We can see in the first row the identity element P is getting by the operation of P and P. Thus the Inverse of P is itself.
In the second and third rows, the identity element is P is getting by the operation of Q and R.
Thus the inverse of Q is R and the inverse of R is Q.
Both are inverse of each other.
Final Answer:
The Inverse of the following are as:
(a) P = P
(b) Q = R
(c) R =Q
What are the new coordinates of the point (-2,1) after undergoing the transformation?
Given the following rule of a transformation:
[tex]P(x,y)\rightarrow P^{\prime}(x+2,2y)[/tex]We will find the new coordinates of the point (-2,1) after undergoing the transformation.
[tex](-2,1)\rightarrow(-2+2,2(1)=(0,2)[/tex]So, the answer will be the last option (0, 2)
complete the sentence to make it true 0.5 is 1/100 of?
to find 0.5 is 1/100 of what ?
[tex]50\times\frac{1}{100}=0.5[/tex]the answer is 50.
In 6-13 round each number to the place of the underlined digit
6. 32.7
7. 3.25
8. 41.1
9. 0.41
10. 6.1
11. 6.1
12. 184
13. 905.26
1) Considering that the underline marks the place to be rounded off we can do the following:
Note that if the number is greater than or equal to 5 then we will round it up.
If the number is lesser than 5 it will be rounded down.
Based on that we can round like this.
6. 32.7
7. 3.25
8. 41.1
9. 0.41
10. 6.1
11. 6.1
12. 184
13. 905.26
2)
