The solving in the below shows similarity in triangles ΔAED ≈ΔBEC By SSS criteria.
What are the four traits of triangles that are similar?The sizes of similar triangles vary while having the same shape. The comparable angles in identical triangles are equal. The ratio of the corresponding sides of comparable triangles is the same. The ratio of any pair of corresponding sides' squares to any similar triangle's area is the same.
According to given information:Two triangles are comparable if they fall under one of the headings below: Angles in two comparable pairs are equal. Three pairs of corresponding sides make up the ratio. The comparable angles amongst two pairs of adjacent sides are proportional and equal.
Given that ΔAED ≈ΔBEC & AC = BD.
as ΔAED ≈ΔBEC, AD = BC .................(1)
Now in ΔABD and ΔBAC,
AD = BC
(corresponding sides of similar triangles) [from (1)]
AB = AB
(common side)
AC = BD
(given)
∴ ΔABD ≈ΔBAC (By SSS criteria)
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The function f is given by f(x)= (x-2) (x+4) . Without using graphing technology, answer the following questions.
1. What are the x-intercepts of the graph representing f?
2. What are the x- and y-coordinates of the vertex of the graph?
3. What is the y-intercept?
Answer:
Step-by-step explanation:
1. What are the x-intercepts of the graph representing f? They are the points on the horizontal axis where the graph touches or crosses the axis. Note that on this axis, y = 0.
2. What are the x- and y-coordinates of the vertex of the graph? Since the function is written as the product of two binomials, we can take these coordinates directly from the binomials: (x - 2) yields x = 2 and (x + 4) yields x = -4.
3. What is the y-intercept? Multiply out these binomials. We get:
f(x) = x^2 + 2 - 8. When x = 0, y = -8. The y-intercept is (0, -8).
1) The x-intercepts of the graph representing f are; 2 and 4
2) The x- and y-coordinates of the vertex of the graph are; (1, -5)
3) The y-intercept is at; (0, -8)
We are given the function; f(x) = (x - 2)(x + 4)
1) The x-intercepts of a graph are the points where the graph crosses the x-axis. The x-intercepts are the value of x when f(x) = 0. Thus, the x-intercepts here are 2 and 4.
2) The vertex is the lowest point of the graph in this case as the parabola opens upwards.
Let us expand the function to get;
f(x) = x² - 2x + 4x - 8
f(x) = x² + 2x - 8
where; a = 1, b = 2, c = -8
Formula for the x-coordinate of the vertex is;
x = -b/2a
x = -2/2(1)
x = 1
Thus;
y = (1 - 2)(1 + 4)
y = -5
x- and y-coordinates of the vertex of the graph are; (1, -5)
3) The y-intercept is the point at which x = 0. Thus;
y = 0² + 2(0) - 8
y = -8
The y-intercept is (0, -8).
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Which undefined term can contain parallel lines?
line
plane
point
ray
Is (3,6) a solution to this system of equations?
y=2x+1
y=4x+6
Step-by-step explanation:
y = 2x + 1 -------- (I)
y = 4x + 6 --------(ii)
from eqn (I)
y = 2x + 1
sub y = 2x + 1 in eqn (ii)
2x + 1 = 4x + 6
2x - 4x = 6 - 1
-2x = 5
x = -5/2
sub x = -5/2 in eqn (I)
y = 2(-5/2) + 1
y = -5 + 1
y = -4
Therefore, (x, y) = (-5/2, -4)
What is the inverse of 9 by 7?
-9/7 is the inverse of 9/7.
-9/-7 = 9/7
9/7 + (-9/7) = 0
-9/7 is consequently the additive opposite of -9/-7.
By merely switching the integer's sign, you can add the original number and the additive inverse to produce a result equal to 0. The value that, when added to the original number, results in zero is known as a number's additive inverse. It is what we add to a number to make it equal to zero. Considering that an is the starting number, its additive inverse will be a minus one, or -a, such that;
a+(-a) = a – a = 0
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What is the rule for quadrant 4?
All points in Quadrant IV have a positive x-coordinate and a negative y-coordinate.
The fourth quadrant, indicated as Quadrant IV, is in the bottom right quadrant. The x-axis in this quadrant has positive values, whereas the y-axis has negative numbers.
A two-dimensional Cartesian system's axes split the plane into four infinite areas called quadrants, each of which is limited by two half-axes. These are frequently numbered from first to fourth.
A quarter of a circle; a 90° arc. the region enclosed by an arc and two radii are drawn one to each extreme. As a mechanical component, anything is shaped like a quarter of a circle.
All Quadrant I points have two positive coordinates.
Quadrant II points all have a negative x-coordinate and a positive y-coordinate.
All Quadrant III locations have two negative coordinates.
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ANSWER SOON PLS Which of these sets of ordered pairs would define a line with a negative slope? A. (2, 3) and (7, 6) B. (2, 3) and (-4, -1) C. (5, 5) and (0, 1) D. (3, 6) and (5, 1)
Answer:
D
Step-by-step explanation:
Answer:
Step-by-step explanation:
e:f =2:5 f:g=3:4 work out e:g in simpliest form
After a work out, the simplest form of e:g is 3:10.
What is a ratio?Ratio is an expression which shows the relationship between two numbers or variables. It can generally be expressed in two forms, viz; a:b or a/ b.
To work out the simplest form of e:g as required in the question,
e/ f = 2/ 5
2f = 5e ........... 1
f/g = 3/ 4
3g = 4f ........... 2
From equation 1,
f = 5e/2
substitute the value of f in equation 2
3g = 4(5e/2)
3g = 10e
Therefore, e:g is given as;
3/ 10 = e/ g
3:10 = e: g
Thus in its simplest form, e:g = 3:10
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Plz, help me with this question!
Answer:
Rectangle
Step-by-step explanation:
If the base is a square that means the cross-section can also be a square.
A designer is planning a trail mix box that is shaped like a rectangular prism. The front of the box must have the width and height shown. Volume of the box must be 162 cubic inches. What must be the depth, d, of the box?
Answer:
The box must be 2.4 in deep.
Step-by-step explanation:
Front dimensions are 9 in by 7.5 in. Find the area of the front: it is
A = (9 in)(7.5 in) = 67.5 in^2. One way to complete this work would be to divide the given volume by this area, 67.5 in^2.
A slightly different approach follows:
The volume must be 162 in^2. Given V = (width)(height)(depth),
V
(depth) must be -----------------------
(width)(height)
In this particular case,
162 in^3
(depth) must be ----------------------- = 2.4 in
(7.5 in)(9 in)
The box must be 2.4 in deep.
Solve the inequality. Graph the solution. -3y<-14
Answer:
y > 14/3
Step-by-step explanation:
-3y<-14
Divided both sides by -3. Because divided by a negative number, the < will switch to the >
y > 14/3
A rectangular con lot of land is 0.4 kilometer long and 0.07 kilometer wide. What is its area in square kilometers?
Answer: 0.28 Km^2
Step-by-step explanation:
A= L x W
=0.4x0.7
=0.28
expressions equivalent to -2(x-5)
Answer:
-2x + 10
Step-by-step explanation:
Apply the distributive law: a(b - c) = ab - ac
-2(x - 5 ) = -2x - ( -2) x 5
= - 2x - ( - 2 ) x 5
- ( -2 ) x 5 = 10
= -2x + 10
In its prime, Mr. Ford's 2002 Focus would get 36 miles/gallon. Mr. Ford starts a road trip to San Bernardino, Barstow, Kingman, Winona, and Flagstaff, AZ. He starts with 13.2 gallons of gas in his gas tank. a) Write a slope-intercept equation that models how much gas remains in his tank after each mile of of travel(hint: g/mi)
Given :
Mr. Ford's 2002 Focus would get 36 miles/gallon.
He starts with 13.2 gallons of gas in his gas tank.
To Find :
Write a slope-intercept equation that models how much gas remains in his tank after each mile of of travel(hint: g/mi).
Solution :
Let, required equation is :
y = mx + c
Here, y is gas remains in gallons.
Here, m is slope i.e. miles travelled per gallon.
So, m = -36 ( since gas is decreasing )
Initially distance travelled is 0 i.e. putting x = 0
y = c = 13.2
Therefore, y = -36x + 13.2 this is the required equation.
Which graph represents the function?
f(x)=3√x + 2
What does * mean after a word?
that usually means that word has a definition that will be given at the bottom of the page or in the glossary depending on what type of book or excerpt of text you have.
hope this helps!
HELP
i been trying for a while and cant get it
The ordered pair for the function y = -(x/3) + 2 is (-3, 3), (0, 2), (3, 2) and (6, 0)
What is an equation?An equation is used to show the relationship between numbers and variables.
The standard form of a linear equation graph is:
y = mx + b
Where m is the slope of the line and b is the y intercept.
Given the function:
y = -(x/3) + 2
At x = -3:
y = -((-3)/3) + 2 = 3
At x = 0:
y = -(0/3) + 2 = 2
At x = 3:
y = -(3/3) + 2 = 1
At x = 6:
y = -(6/3) + 2 = 0
The value of y when x = -3 is 3
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i need help with B) C) and D)
Please Help me!!!
Answer:
b is the right answer
Step-by-step explanation:
The probability of winning a coupon at the grocery store checkout is 2/25. What is the probability of not winning?
The probability of not winning the coupon at the grocery store given the probability of winning the coupon is 23/25.
What is the probability?Probability determines the likelihood of the occurence of an event. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability of not winning the coupon = 1 - probability of winning
1 - 2/25 = 23/25.
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Solve the following system of equations.
5x - 4y= -16
2x+9y=-17
Answer:
Im kind of confused if I rewrite or find the y and x intercept to this equation but I hope this helps.
if you can please give me brainliest.
A soft drink company is conducting research to select a new design for their can. A sample of 9 participants has been selected. Instead of a typical taste test with two different sodas, they give each participant the same soda twice. One drink is served in a predominantly red can, the other in a predominantly blue can. The order the two cans are used is chosen randomly. Participants are asked to rate each drink on a scale of 1 to 10. The mean difference between the rating of the red and blue can for the 9 participants is -0.56 with standard deviation 2.19. Researchers would like to determine whether or not the mean difference in ratings between the red and blue can is 0.
The p-value for this hypothesis test is 0.4676. Select the correct decision below.
a. Reject the null hypothesis.
b. Fail to reject the null hypothesis.
c. Reject the alternative hypothesis.
d. Accept the null hypothesis.
Answer:
Option B
Step-by-step explanation:
The p value is greater than 0.05.
Hence there are not enough evidences to reject the null hypothesis.
Basically no effect is observed when p>0.05
Hence, the test results are statistically significant
Option B is correct
Need this for a homework assignment, have been stuck for an hour and a half.
find the slope. please help
Match each object which the characteristics.
Answer:
Ray goes with horizon
Line goes with a broom handle
Parallel lines goes with rows of seats on a plane
Line segment goes with a sun ray
Point goes with cookie crumb
Perpendicular lines goes with the letter T
Step-by-step explanation:
Not sure how to explain it
An object is placed at a certain distance on the principal axis of a concave mirror. The image is formed at a distance of 30cm from the mirror. Find the object distance if radius of curvature R=15cm.
Answer:
Object distance, u = -6 cm
Step-by-step explanation:
Given that,
The radius of curvature, R = 15 cm
The radius of the mirror, f = -7.5 cm
We need to find the object's distance from the mirror. The mirror's formula is used to find the object distance such that,
[tex]\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}\\\\\dfrac{1}{u}=\dfrac{1}{f}-\dfrac{1}{v}\\\\\dfrac{1}{u}=\dfrac{1}{(-7.5)}-\dfrac{1}{30}\\\\u=-6\ cm[/tex]
So, the object distance is 6 cm.
y=-5 8x+5y=-17 substitution
[tex]8x+5y=-17[/tex] when y is -5
Substitute for y with given value:
[tex]8x+5(-5)=-17[/tex]
[tex]8x-25=-17[/tex]
Add 25 to both sides:
[tex]8x-25+25=-17+25[/tex]
[tex]8x=8[/tex]
Divide both sides by 8:
[tex]\dfrac{8x}{8} =\dfrac{8}{8}[/tex]
[tex]\fbox{x = 1}[/tex]
What is 26633646376+63761876784
Answer:63,761,876,784
Step-by-step explanation:
A new surgery is successful 70% of the time , if the results of 8 such surgeries are randomly sampled, what is the probability that more than 5 of them are successful?
Answer:
P (x>5) = 0.5324014=0.523
Step-by-step explanation:
Here success = p= 0.7 and failure = q= 1-p= 1-0.7 = 0.3
Number of surgeries= n= 8
Applying the binomial distribution
( p+q) ^n= nC x p^x . q^n-x
More than 5 means 6,7, and 8
( p+q) ^8= 8C 5 (0.7)^5 . (0.3)^3
=56* 0.16807*0.027
= 0.254121
( p+q) ^8= 8C 6 (0.7)^6 . (0.3)^2
= 28* 0.1177* 0.09
= 0.296604
( p+q) ^8= 8C 7 (0.7)^7 . (0.3)^1
= 8* 0.0824* 0.3
= 0.19776
( p+q) ^8= 8C8 (0.7)^8 . (0.3)^0
= 1* 0.05765* 1
=0.05765
Adding the above all probabilities gives
P (x>5) = P (x=6) + P(x=7) + P(x=8)
= 0.296604+0.19776+0.05765
= 0.5324014
ASAP
HELP JUST THE ANSWER
Answer:
40:15 simplified is, (i divided by 5) 8:3
Ratio is when you have a number to a number just put them together but put a colon between them to make it a ratio, thats all ;D. It's basically a fraction.
But you can also simplify ratios just like fractions because they are fractions!
Answer:
D. 8:3
Step-by-step explanation:
40/15
Simplify:
8/3
25 less than the sum of a number and 5 results in 15 what is the number
The number is 35.
What is an equation?
An equation is a statement of equality between two expressions. It uses the equal sign (=) to show that the expressions on either side of the sign have the same value.
For example 2x+3=5y-7z, and x+y=5 are examples of equations.
In solving your problem,
25 less than the sum of a number and 5 results in 15, can be written as an equation like this:
let x be the number we want to find.
x + 5 =15+25 (25 less than the sum of x+5)
x + 5 = 40
then
x=40-5
x=35
So the number is 35.
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Y = -17.5x + 2.7x + 14.1 - 11.9x
Answer:
y=-26.7x+14.1
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
y=−26.7x+14.1
Step-by-step explanation:
y=−17.5x+2.7x+14.1−11.9x
y=−26.7x+14.1
Solve for x:
Step 1: Flip the equation.
−26.7x+14.1=y
Step 2: Add -14.1 to both sides.
−26.7x+14.1+−14.1=y+−14.1
−26.7x=y−14.1
Step 3: Divide both sides by -26.7.
x=−0.037453y+0.52809
Solve for y:
y=−26.7x+14.1