Answers
Answer:
20°,70°
Step-by-step explanation:
X+y+90=180
X+y=90
20+y=90
y=70°
2x+180-40=180
2x=40
X=20°
The measures of angles of the triangle is x = 20° and y = 70°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , let the side be represented as BD , which cuts AC at point D
And , the measure of BD = measure of DC ( given )
And , the measure of ∠ABC = 90°
The measure of ∠BDA = 40°
So , the measure of angle ∠BDC = 140° ( angles on a straight line )
Now , the measure of angle ∠DBC = measure of ∠BCD ( given )
So , the measure of x = ( 180 - 140 ) / 2
x = 20°
And , the measure of y = 180° - 40° - 70°
y = 70°
Hence , the angles of triangle are x = 20° and y = 70°
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Related Questions
On this assignment I am just writing about what the student did wrong. Please help me. LOOK AT THE PICTURE ABOVE ^^^^^^^^^^^^^^^^^^^^^^^^^
QUESTIONS:
1. What math did Ann do well?? EXPLAIN
2. What mistake has Ann made? EXPLAIN
Answers
ann made a rectangle with the
right perimeter & area
ann doesn't try any other
rectangles to see if their areas are
different.
splitting the land , ann confuses perimeter and area
mapmathshellorg
Please help. Will mark brainliest. Please choose one answer
Which of the following is the most reasonable estimate of the correlation coefficient? Image is provided
0.5
0.7
0.9
1.0
Answers
The most reasonable estimate of the correlation coefficient is 0.9
What is the correlation coefficient?The correlation coefficient gives an estimate of how strong is the linear relationship between two variables.
The correlation coefficient, r, is given by the formula;
[tex]r = \dfrac{\sum(x_i-\overline x)\cdot (y_i-\overline y)}{\sqrt{\sum (x_i-\overline x)^2\sum(y_i-\overline y)^2} }[/tex]
Where;
[tex]x_i[/tex] = The ith x-value
[tex]\overline x[/tex] = The mean (average of the x-values)
[tex]y_i[/tex] = The ith y-value
[tex]\overline y[/tex] = The mean (average of the y-values)
The give points on the scatter plot graph are;
(8, 9), (6, 9), (6, 6), (5, 5), (4, 5), (3, 4), (3, 3), (2, 4), (1, 2), (1, 3)
Plotting the above points on MS Excel gives;
The equation of the regression line is; y = 0.9407·x + 1.3313
The square of the correlation coefficient, R² = 0.8322
Therefore, R = √(0.8322) ≈ 0.9122
The option that is the most reasonable estimate of the correlation coefficient is therefore; 0.9
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Preston goes to the movies with $15 in his wallet. He buys
a ticket for $6.50 and two snacks for $1.75 each. How
much money does he have left?
Select the correct expression.
OA. 15-6.5-1.75
OB. 15-(6.5+ 2.1.75)
O C. 15-2(6.5+ 1.75)
OD. 15-6.5+2.1.75
Answers
Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)
What is an Algebraic Expression?
An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression. For example, 3x² − 2xy + c is an algebraic expression.
Given,
Total money Preston have = $15
He buys the ticket for = $6.50
And, two snacks = $1.75 each
so the cost of two snacks is = 1.75 * 2 = $3.5
Total cost for ticket and snacks = $3.5 + $6.50 = $10
Now, he spent money on snacks and ticket $10 and he have total money $15 so,
Preston left with = $15 - $10
= $5
Therefore, Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)
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Sam spends exactly £20 on petrol. The petrol costs £1.45 per litre. Work out the number of litres of petrol she buys.
Answers
Answer: 13,8 litres
Step-by-step explanation:
£1.45 ------------ 1 L
£20 ------------- ?
?= [tex]\frac{20 *1}{1.45} = 13,79310345 L[/tex] = 13,8 L
Can someone help solve this the first problem is below in the picture. Can you put it in interval notation, regular notation, graph it on a number line, and set builder
Answers
The solution to the system of inequalities is -6 < x [tex]\leq[/tex] -3
What is an Inequality?Inequality shows the relationship between two values in an algebraic expression that are not equal. Inequality signs can indicate that one variable of the two sides of the inequality is greater than, greater than or equal to, less than, or less than or equal to another value.
The system of linear equations,
x + 4 > -2 or -4x [tex]\geq[/tex] 12
from first inequality,
x + 4 > -2
making x stand alone,
x > -2 -4
x > -6
from second inequality,
-4x [tex]\geq[/tex] 12
divide both sides bu -4
x [tex]\leq[/tex] 12/-4
x [tex]\leq[/tex] -3
The combined inequality is -6 < x [tex]\leq[/tex] -3
In conclusion, -6 < x [tex]\leq[/tex] -3 is the solution for the set of inequalities.
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Activity 8. Counting the roots of polynomial equation
by inspection determine the number of real roots of each polynomial equation. Roots multiply n are counted n times
1. (x-4)(x+3)^2(x-1)^3=0
2. X^2(x^3-1)=0
3. X(x+3)(x-6)^2=0
4. 3x(x^3-1)^2=0
5. (x^3-8)(x^4+1)=0
patulong po plss.
Answers
The number of real roots found are-
1. (x-4)(x+3)^2(x-1)^3=0 ; 6 real roots.
2. X^2(x^3-1)=0 ; 3 real roots.
3. X(x+3)(x-6)^2=0 ; 4 real roots.
4. 3x(x^3-1)^2=0 ; 3 real roots.
5. (x^3-8)(x^4+1)=0 ; 1 real roots.
Define the term roots of polynomial?If a root is not imaginary (defined as a number as in form a + bi, whereby I is a number which is not on any real number line, which is why the name imaginary), it is said to be real.Consider the given cases-
1. (x-4)(x+3)^2(x-1)^3=0,
Put each equals zero.
x – 4 = 0 or (x + 3)^2 = 0 or (x – 1)^3 = 0,
Thus,
x = 4
x = –3 twice
x = 1 thrice
All are real numbers, thus given polynomial has 6 real roots.
2. x^2(x^3-1)=0
Put each equals zero.
x² = 0
x³ – 1 = x³ – 1³ = (x – 1)(x² + x + 1) = 0
The quadratic expressions has 2 imaginary roots.
Use the discriminant formula to find-
D = b² – 4ac = 1² – 4(1)(1) = 1 – 4 = –3 < 0.
Thus, roots that are not real.
So, the real roots of this polynomial : 0(twice) and 1.
Hence, thus given polynomial has 3 real roots.
3. x(x+3)(x-6)^2=0
Put each equals zero.
x = 0
x = 3
x = 6 twice
Hence, thus given polynomial has 4 real roots.
4. 3x(x^3-1)^2=0
Put each equals zero.
3x = 0 and x = 0
(x^3 – 1)² = [(x – 1)(x² + x + 1)]² = (x – 1)²(x² + x + 1)² = 0,
Here, only two roots are real
The quadratic expression do have unreal roots, thus 1 twice are the real roots.
Hence, thus given polynomial has 3 real roots..
5. (x^3-8)(x^4+1)=0
Put each equals zero.
x³ – 8 = x³ – 2³ = (x – 2)(x² + 2x + 4) = 0
There is only one real root i.e, 2, the quadratic expression do have imaginary roots
Check using the discriminant formula
D = b² – 4ac = 2² – 4(1)(4) = 4 – 16 = – 12 < 0.
x⁴ + 1 = 0 has imaginary roots.
Hence, thus given polynomial has 1 real roots..
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Just 2 questions.
Explaining the Converse of the Pythagorean Theorem
Task 1
Part A
The Pythagorean Theorem states that for any given right triangle, a2 + b2 = c2. Using the Pythagorean Theorem, what should be the relationship between the areas of the three squares?
Task 2
Part E What does this show about the relationship between the two triangles?
Answers
The Pythagorean Theorem indicates the following relationship between the squares and triangles.
Part A
The relationship between the areas of the squares is that the area of the large square is the sum of the areas of the other two squares.Part E
The point that the length c on one triangle is equal to the length n on the other triangle and that the other two sides of both triangles are congruent, the two triangles are congruent by SSS congruency rule.What is the Pythagorean Theorem?Pythagoras theorem can be stated as follows; The square of the length of the hypotenuse side of a right triangle is equal to the sum of the squares of the other two sides.
Part A
The possible squares in the question are the three squares arranged on the three sides of the triangle, and having a side length which is the same as the length of the side of the triangle to which the square is attached
The relationship between the three squares of side length a, b, and c according to Pythagorean theorem is; a² + b² = c²
Therefore, the area of the largest square that is located on the hypotenuse side of the triangle is equal to the sum of the areas of the other two squares.
Part E
The length of the sides of the triangles, obtained from a similar question on the site are; a, b, and c and a, b, and n
It was shown that c² = n²
Therefore;
c = n
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R is inversely proportional to A.
R = 12 when A = 1.5
a) Work out the value of R when A = 5.
b) Work out the value of A when R = 9
Answers
The value of R when A equal 5 is 3.6 and the value of A when R equal 9 is 2 as R is varies inversely to A.
What is the value of R when A equal 5 and value of A when R equal 9?Proportional relationships are relationships between two variables where their ratios are equivalent.
If R is inversely proportional to A.
R ∝ 1/A, then
R = k/A
Where k is the proportionality constant.
Given that;
R = 12 A = 1.5Proportionality constant k = ?First, we determine the proportionality constant.
R = k/A
Plug in R = 12 and A = 1.5 and solve for k
k = R × A
k = 12 × 1.5
k = 18
a) The value of R when A = 5 will be;
R = k/A
R = 18 / 5
R = 3.6
b) The value of A when R = 9
R = k/A
R × A = k
A = k/R
A = 18 / 9
A = 2
Therefore, the value of A when R equal 9 is 2.
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Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on.
Answers
Answer:
For part a you would decompose the fraction into two independent fractions with the following form:
() = ()/( x^2+5)(x ^2+3x−4) = (Ax + B)/(x^2+5) + (Cx + D)/(x ^2+3x−4)
Combining these fractions we get:
((Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5))/( x^2+5)(x ^2+3x−4) = ()/( x^2+5)(x ^2+3x−4)
Thus we can say: (Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5) = ()
You then simplify the equation on the left by combining like terms and solve the system of equations that arise corresponding with ().
You would follow a similar process for part b as well.
Step-by-step explanation:
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease y=210(1.092)^x
Answers
The change y=210(1.092)^x represent exponential growth
The percentage rate of increase is 9.2 percent increase
How to determine exponential growthExponential functions are functions that consist of three part say c(b)^d
the part that says whether the function is growth or decay is b
b is called the base function and it is used as follows to determine growth or decay function
b < 1 gives a decay functionb > 1 gives a growth functionComparing with the given function 1.092 > 1 hence a growth function
The percentage is solved as follows
1.092 * 100 = 109.2%
109.2% is also referred to as 9.2 percent increase since it is an increment of 9.2%. this is shown below
100% + 9.2% = 109.2%
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best ontime airlines: hawaiian airlines topped the list of the most punctual u.s. airlines for full-year 2014, according to data released by the bureau of transportation statistics. the on-time arrival performance was 91.9% another aviation data service believes that this percentage now is even higher. the team of researchers chose 130 randomly selected flights and find that 120 of the flights arrived on time. can a hypothesis test be used to determine whether the proportion of hawaiian airlines flights that arrive on-time is higher than 91.9%? group of answer choices yes, because the sample is random. thus, it is representative of the population of flights for the airlines. yes, because the sample is random and (130)(0.923) and (130)(0.077) are both at least 10. this means the normal model is a good fit for the sampling distribution. yes, because the sample is random and (130)(0.919) and (130)(0.081) are both at least 10. this means the normal model is a good fit for the sampling distribution.
Answers
1.because sample is random and (130)
(0.923) and (130)(0.077) are both at least 10.
This means the normal model is a good fit for the sampling distribution.
Consider the provided information.
130 randomly selected flights and find that
120 of the flights arrived on time.
n=130
The on-time arrival performance was 91.9%
p=0.923 and q=1-0.923=0.077
np = 130 x 0.923
np = 120 ≥ 10
nq = 130 × 0.077
nq = 10 = 10
Hence, Yes, because sample is random and
(130)(0.923) and (130)(0.077) are both at least 10. This means the normal model is a good fit for the sampling distribution.
2.because sample is random and (130)
(0.919) and (130)(0.081) are both at least 10.
This means the normal model is a good fit for the sampling distribution.
Consider the provided information.
130 randomly selected flights and find that
120 of the flights arrived on time.
n=130
The on-time arrival performance was 91.9%
p=0.919 and q=1-0.919=0.081
np = 130 x 0.919
np = 119.5 ≥ 10
nq = 130 × 0.081
nq = 10.5 ≥ 10
Hence, Yes, because sample is random and
(130)(0.919) and (130)(0.081) are both at least 10. This means the normal model is a good fit for the sampling distribution.
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37=18q+1 show work pls
Answers
Answer:
37=18q+1
subtract 1 on both sides
then divide both sides by 18
q=2
Step-by-step explanation:
Answer:
q = 2Step-by-step explanation:
[tex]\sf 37=18q+1[/tex]
[tex]\sf 18q+1=37[/tex]
Subtract 1 from both sides:-
[tex]\sf 18q+1-1=37-1[/tex]
Simplify:-
[tex]\sf 18q=36[/tex]
Divide both sides by 18:-
[tex]\sf \cfrac{18q}{18}=\cfrac{36}{18}[/tex]
[tex]\sf q=2[/tex]
_____________________
Hope this helps!
Have a great day!
The system of conics has two solutions.
(x−4)^2 + (y+1)^2 = 9
(x−4)^2/9 + (y+1)^2/81 = 1
What are the solutions to this system of conics?
Answers
The system of equations has its solutions to be (1, -1) and (7, -1)
How to solve the system of equations?The system of equations is given as
(x−4)² + (y+1)² = 9
(x−4)²/9 + (y+1)²/81 = 1
Make (y + 1)² the subject in the equation (x−4)² + (y+1)² = 9
So, we have
(y+1)² = 9 - (x−4)²
Substitute (y+1)² = 9 - (x−4)² in (x−4)²/9 + (y+1)²/81 = 1
This gives
(x−4)²/9 + [9 - (x−4)²]/81 = 1
Split
(x−4)²/9 + 9/81 - (x−4)²/81 = 1
Collect the like terms
(x−4)²/9 - (x−4)²/81 = 1 - 9/81
Evaluate the like terms
[9(x−4)² - (x−4)²]/81 = 72/81
So, we have
9(x−4)² - (x−4)² = 72
Evaluate the difference
8(x−4)² = 72
Divide by 8
(x−4)² = 9
Take the square roots
x - 4 = ±3
So, we have
x = 4 ± 3
Evaluate
x = 1 or 7
Substitute x = 1 or 7 in (y+1)² = 9 - (x−4)²
(y + 1)² = 9 - (1−4)² or (y + 1)² = 9 - (7−4)²
This gives
(y + 1)² = 0 or (y + 1)² = 0
This gives
y + 1 = 0
Evaluate
y = -1
Hence, the solution is (1, -1) and (7, -1)
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a) Work out the gradient of the line y=5x-3 (1)
Gradient = (Answer here)
b) Work out the gradient of the line 3y-12x+7=0 (1)
Gradient = (Answer here)
Answers
Answer:
5 and 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the gradient and c the y- intercept )
(a)
y = 5x - 3 ← is in slope- intercept form
with gradient m = 5
(b)
3y - 12x + 7 = 0 ( add 12x to both sides )
3y + 7 = 12x ( subtract 7 from both sides )
3y = 12x - 7 ( divide through by 3 )
y = 4x - [tex]\frac{7}{3}[/tex] ← in slope- intercept form
with gradient m = 4
Write down the two district properties between parellelograml and trapezium
Answers
You can see pic..
Pls help due today!!!!!
Answers
Karama can paint a staircase banister in 50 minutes. Find the rate per minute at which Karama can paint banisters
Answers
The rate per minute at which Karama can paint banisters is 0.02.
In the given question,
Karama can paint a staircase banister in 50 minutes.
We have to find the rate per minute at which Karama can paint banisters.
Since we have to find the rate per unit. Rate per unit means how much Karama can paint in one minute.
To find the rate per unit we divide 1 by 50.
As we know that Karama can paint one staircase banister in 50 minute.
So we can write it as
50 minute = 1 staircase banister paint
Now in 1 minute.
1 minute = 1/50 staircase banister paint
Simplifying
1 minute = 0.02 staircase banister paint
Hence, the rate per minute at which Karama can paint banisters is 0.02.
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In a shop the price of a radio is reduced by one third. if the original price of the radio is two thousand four hundred naira,what is the reduced price
Answers
If the original price of the radio is 2,400 Naira and it is reduced by one third, then the discounted price is 1,600 Naira.
A store usually provides discount of some items to attract more customers and make greater sales.
Suppose the original price is p, the discount rate is d%, and the discounted price is q, then the discounted price can be calculated as:
q = (1 - d%) x p
Parameters given in the problem:
p = 2,400 Naira
d = 1/3
Hence,
q = (1 - 1/3) x 2400
q = 2/3 x 2400 = 1600
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Characterize the slope of the line in the graph.
• A. Zero
• B. Negative
• C. Undefined
• D. Positive
Answers
Answer: C Undefined
Step-by-step explanation:
A vertical line never moves left and right, so the run is 0. Because the quotient of a number divided by 0 is undefined, the slope of a vertical line is always undefined.
The slope is positive
D.Positive
Lora's phone records data for screen time each week. Last week, she used 840 minutes. This week, Lora used 504 screen time minutes on the phone. Calculate the percent decrease in screen time this week.
17%
34%
40%
67%
Answers
The percent decrease in screen time this week is 40%. Therefore, option C is the correct answer.
Given that, last week, Lora used 840 minutes. This week, Lora used 504 screen time minutes on the phone.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Now,
Difference=840-504
= 336
Percentage decrease = Difference in value/Original value ×100
= 336/840 ×100
= 0.4 ×100
= 40%
The percent decrease in screen time this week is 40%. Therefore, option C is the correct answer.
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answer the questions below about the following function
what is the domain of f(x)
what is the range of f(x)
what is the x-intercept of f(x)? enter your answer as an ordered pair. if no x-intercept exists, enter none
what it the equation of the vertical asymptote
Answers
Domain of the function is, (0, ∞).
Range of the function is, (-∞, ∞).
x - intercept of the function is, (1, 0).
Vertical asymptote of the function is, None.
What is domain and range?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
First to find the domain of the function,
Since, all input values shown on the x-axis make up a graph's domain.
We can see that values of x values are from 0 to ∞.
Hence, the domain is (0, ∞).
Now to find the range.
Since, the y-axis on a graph represents the possible output values, or range.
The y - axis having the values from -∞ to ∞.
Hence, the range of the function is, (-∞, ∞).
x - intercept is the point where function crosses the x - axis.
Here function crosses x - axis at (1, 0).
Hence, the x - intercept is (1, 0).
A graph's vertical asymptote is the vertical line at x = a where the graph trends toward positive or negative infinity as the inputs go closer to a.
So, the vertical asymptote is x = 0.
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The art teacher gave each student half of a sheet of paper. Then she asked the students to colored one one fourth of their pieces of papper. what do the number represent? what information was given?
Answers
The number 1/8 represent the fraction of full sheet of paper the teacher asked each student to color.
The information given are;
Paper given to each student by the teacherPart the teacher asked each student to colorWhat fraction of paper did the student colored?The information given are
The full sheet of paper = xPaper given to each student by the teacher = 1/2xPart the teacher asked each student to color = one fourth of their pieces of papper= 1/4 of 1/2x
= 1/4 × 1/2x
= 1/8x
So therefore, the student colored 1/8 of the original piece of paper.
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Complete both transformations below. Then enter the final coordinates of the figure. A (1.-2)
B (4,-1)
C (5.-3)
1) < -2.4 >
2) Dilate K = 3
Answers
Applying the transformation rule (x - 2.y + 4) and using the scale factor k = 3 for dilation gives
preimage translation image Dilation image
A (1.-2) A' (-1, 2) A'' (-3, 6)
B (4,-1) B' (2, 3) B'' (6, 9)
C (5.-3) C' (3, 1) C'' (9, 3)
What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Translation refers to a type of transformation that involve a linear movement.
Applying the transformation rule (x - 2.y + 4 ) gives
A (1.-2) = (1 - 2, -2 + 4) = (-1, 2)
B (4,-1) = (4 - 2, -1 + 4) = (2, 3)
C (5.-3) = (5 - 2, -3 + 4) = (3, 1)
preimage image
A (1.-2) A' (-1, 2)
B (4,-1) B' (2, 3)
C (5.-3) C' (3, 1)
Dilation involves making the image bigger or smaller. In this case K > 1 hence the image is bigger
Using the scale factor k = 3 for dilation rule (kx, ky) gives
A' (-1, 2) = (-1 * 3, 2 * 3) = (-3, 6)
B' (2, 3) = (2 * 3, 3 * 3) = (6, 9)
C' (3, 1) = (3 * 3, 1 * 3) = ( 9, 3)
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Write an equation in standard form with an x-intercept of 4 and a y-intercept of 5.
Answers
Equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.
Given:
x - intercept = 4
y - intercept = 5
At x intercept y = 0 and at y intercept x = 0
(4,0) and (0,5)
slope = 5-0/0-4
= 5/-4
m = -5/4
substitute (4,0) and m value,
y = mx+c
0 = -5/4*4 +c
0 = -5 + c
c = 5
y = mx + c
y = -5/4(x) + 5.
Therefore equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.
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Complete the square to re-write the quadratic function in vertex form:
y = 7x²56x + 117
Answers
The answer to the given quadratic equation is y = ( x + 4 )²
How do we solve a question by completing the square method?A(x + m)2 + n is the formula for completing the square, where m is any real number and n is a constant factor.
The following straightforward formula can be used to finish the square instead of the intricate step-by-step procedure. Find the following in order to complete the square in the phrase ax2 + bx + c:
N = c - (b2/4a) and m = b/2a
Enter these numbers where they belong: ax2 + bx + c = a(x + m)2 + n. These equations are geometrically derived.
Given : A quadratic equation y = 7x² + 56x + 117
this can also written as y = x² + 8 x + 17
y = x² + 4² - 4² + 17
y = ( x + 4 )²
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if l || m, solve for x and y
I NEED HELP ASAP
Answers
3x=48
x=16
If x= 16°
8(16)-14+5y+16=180
130+5y=180
5y=50
y=5°
Write a polynomial of least degree with roots 1 and -9. un Write your answer using the variable x and in standard form with a leading coefficient of 1.
Answers
Answer:
y = x² +8x -9
Step-by-step explanation:
You want the least-degree polynomial with roots 1 and -9, written in standard form.
FactorsEach root p means there is a factor (x-p). The two roots make the factored form of the polynomial be ...
y = (x -1)(x +9)
Expanding this to standard form, we get ...
y = x² +8x -9
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Additional comment
A quadratic that has two roots, p and q, will have the standard form ...
y = (x -p)(x -q) = x² -(p+q)x +pq
That is, the linear term coefficient is the opposite of the sum of the roots, and the constant is their product. This means you can write down the equation directly from the roots:
y = x² -(1-9)x +(1)(-9) = x² +8x -9
Which of the following statements are true?
Corresponding angles of congruent figures are the same.
Corresponding angles of similar figures are the same.
Corresponding sides of congruent figures are the same.
Corresponding sides of similar figures are the same.
Answers
The statements that are true are:
Corresponding angles of congruent figures are the same.Corresponding sides of congruent figures are the same.What is Corresponding angles of congruent figures ?It should be noted that the two figures can be regrdedas as one that are similar in the case whereby their corresponding angles are congruent ,also their ratios of the lengths with respect to their corresponding sides would also be equal.
In conclusion, when two figures are similar then it can be concluded that their corresponding angles are congruent .
Hence, the second and third options are correct.
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Answer:
Corresponding angles of congruent figures are the same.
The corresponding sides of congruent figures are the same.
Step-by-step explanation:
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Answers
Answer:
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