Answers
4. CE is a median of triangle ADF, BF is the midpoint of AC.
5. CE = 3√3 cm and AG = 18√3 cm
6. AM is a median of right triangle ABC.
Describe Triangle?In mathematics, a triangle is a geometric shape that consists of three line segments that intersect at three endpoints. These endpoints are called vertices, and the line segments are called sides.
Triangles are one of the most basic shapes in geometry and are used in many areas of mathematics, science, engineering, and everyday life. They can be classified based on the length of their sides and the measure of their angles.
4. CE is a median of triangle ADF.
BF is the midpoint of AC.
Since C is the midpoint of segment AD and E is the midpoint of segment FD, CE is a median of triangle ADF. This is because CE passes through D and divides the opposite side A F into two equal halves.
Similarly, since B is the midpoint of segment AC, BF is a midpoint of AC. This is because BF passes through A and divides the opposite side AC into two equal halves.
5. To find CE and AG, we can use the fact that BF = 24 cm. Let's start by finding CE.
Since BF is the midpoint of AC, we have:
AC = 2 BF = 2(24 cm) = 48 cm.
Since C is the midpoint of AD, we have:
AD = 2 CD = 2 CE (by definition of midpoint)
Therefore, CE = AD/2
To find AD, we can use the fact that E is the midpoint of FD, so:
FD = 2 FE = 2 FG (by definition of midpoint)
Since F is the midpoint of GE, we have:
GE = 2 GF (by definition of midpoint)
Therefore, AG = AE + GE = AE + 2GF
Now, since AM is a median of triangle ABC, we have:
AM² = (AB² + BC²)/2 - (AC²/4)
Since triangle ABC is a right-angled triangle with angle B = 90 degrees, we have:
AB² + BC² = AC²
Therefore, we can simplify the equation for AM² as follows:
AM² = AC²/2 - AC²/4
AM² = AC²/4
Substituting the value we found for AC, we get:
AM² = 48²/4 = 576
Therefore, AM = 24 cm.
Now, we can use the Pythagorean theorem to find AE:
AE² + EM² = AM²
AE² + (AC/2)² = AM²
AE² + 24² = 576
AE² = 576 - 576/4 = 432
AE = √432 = 12√3 cm
Finally, we can find AG as:
AG = AE + 2GF = AE + 2(AD/4) (since G is the midpoint of EF)
AG = 12√3 + AD/2
But we know that AD = 2CE, so:
AG = 12√3 + CE
Therefore, to find AG, we just need to add the value of CE that we found earlier:
AG = 12√3 + CE = 12√3 + (AD/2) = 12√3 + (CE/2) = 12√3 + 6√3 = 18√3 cm.
Therefore, CE = AD/2 = (AG - 12√3)/2 = (18√3 - 12√3)/2 = 3√3 cm.
So, CE = 3√3 cm and AG = 18√3 cm.
6. Statement: AM is a median of right triangle ABC.
A median of a triangle is a line segment that joins a vertex to the midpoint of the opposite side. In right triangle ABC, the median AM joins the right angle vertex A to the midpoint of the hypotenuse BC.
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4). Section AC's midpoint is B, and section BF's midpoint is BF. Because BF cuts through A and splits the opposing side AC into two equal halves, this is the case.
5). CE = AD/2 = (AG - 12√3)/2 = (18√3 - 12√3)/2 = 3√3 cm.
So, CE = 3√3 cm and AG = 18√3 cm.
6). The middle of the hypotenuse BC is connected to the right angle vertex A by the median AM.
Describe Triangle?One of the most fundamental geometric shapes, triangles are used frequently in mathematics, science, engineering, and daily living. They can be categorized based on the dimensions of their edges and sides.
4). ADF's triangle's middle is CE.
BF sits in the middle of AC.
Triangle ADF's median is CE because C is the midway of segment AD and E is the midpoint of segment FD. This is the case because CE passes through D and divides the opposite side A F into two equal halves.
BF functions as an AC midpoint in a manner similar to how B acts as the segment's halfway point. This is the case because BF cuts through A and divides the opposite side AC into two equal halves.
5). We can use the knowledge that BF = 24 centimeters to determine CE and AG. Let's begin by locating CE.
Because BF is AC's middle, we have:
AC = 2 BF = 2(24 cm) = 48 cm.
Since C is the midpoint of AD, we have:
AD = 2 CD = 2 CE (by definition of midpoint)
Therefore, CE = AD/2
To find AD, we can use the fact that E is the midpoint of FD, so:
FD = 2 FE = 2 FG (by definition of midpoint)
Since F is the midpoint of GE, we have:
GE = 2 GF (by definition of midpoint)
Therefore, AG = AE + GE = AE + 2GF
Now that triangle ABC's middle is AM, we have:
AM² = (AB² + BC²)/2 - (AC²/4)
Triangle ABC has a right angle of 90 degrees, so we have:
AB² + BC² = AC²
As a result, we can simplify the AM² equation as follows:
AM² = AC²/2 - AC²/4
AM² = AC²/4
When we substitute the AC number we discovered, we obtain:
AM² = 48²/4 = 576
Therefore, AM = 24 cm.
We can now determine AE using the Pythagorean theorem:
AE² + EM² = AM²
AE² + (AC/2)² = AM²
AE² + 24² = 576
AE² = 576 - 576/4 = 432
AE = √432 = 12√3 cm
Finally, we can find AG as:
AG = AE + 2GF = AE + 2(AD/4) (since G is the midpoint of EF)
AG = 12√3 + AD/2
But we know that AD = 2CE, so:
AG = 12√3 + CE
The value of CE that we previously discovered can therefore simply be added to obtain AG:
AG = 12√3 + CE = 12√3 + (AD/2) = 12√3 + (CE/2) = 12√3 + 6√3 = 18√3 cm.
Therefore, CE = AD/2 = (AG - 12√3)/2 = (18√3 - 12√3)/2 = 3√3 cm.
So, CE = 3√3 cm and AG = 18√3 cm.
6). AM is the middle of the right triangle ABC.
A line section connecting a triangle's vertex to the middle of the other side is the triangle's median. The median AM connects the right angle vertex A to the middle of the hypotenuse BC in the right triangle ABC.
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Related Questions
Solve
X =
4-x
(21/7) ¹-*
-x = 92x-1
Answers
Answer:
☆ -10 ☆ is your correct answer!
Given mn, find the value of x.
t
(9x+7)°
(10X-10)°
HURRY PLEASE!!
Answers
(9x+7=10x-10)
All terms are shifted to the left:
(9x+7-(10x-10))=0
Parentheses are used to compute terms: +(9x+7-(10x-10)), so:
9x+7-(10x-10)
the Function Domain determination
9x-(10x-10)
+7
We eliminate parenthesis.
9x-10x+10+7
All the numbers and variables are added together.
-
1x+17
Returning to the equation
+(-1x+17)
We eliminate parenthesis.
-1x+17=0
We shift every term that contains x to the left and every other term to the right.
-x=-17 \sx=-17/-1 \sx=+17
Relation of degrees of polynomials:How can you determine an equation's degree?
The degree of a term in the polynomial expression is expressed as a + b if a and b are the exponents of the many variables in a term.
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Answer:
the answer is Undefined
Step-by-step explanation:
therefore the value of x is basically 0
I do indeed hope this helps
The perimeter of a rectangular
playground is 86 feet. If the width
of the playground is 15 feet, find
the length.
Answers
Answer: length is 33ft
Step-by-step explanation:
Perimeter = length x2 + width x2 (add all sides of a rectangle)
width = 15ft
15 x 2 = 30 ft
86ft - 30 ft = 66 ft
66/2 = length of 1 side = 33 ft
The Area of a Rectangle is 40. The width is 2 less than 3
times the length. Find the width.
O 10
O 12
O 15
O 14
Answers
Answer:
Width = 10
Step-by-step explanation:
let length = X
width = 3X - 2
Area = length x width
40 = X x (3X - 2)
40 = 3X^2 - 2X
therefore 3X^2 - 2x - 40 = 0
3x^2 + 10x - 12x - 40 = 0
x(3x + 10) - 4(3x + 10) = 0
(x - 4) (3x + 10) = 0
(x - 4) = 0
x = 4
(3x + 10) = 0
3x = - 10
x = -10/3
Since the lenght can't be negative, we'll work with x = 4
Therefore the width = 3x - 2
Width = 3(4) -2
Width = 12 - 2
Width = 10
Help pls worth 10
points!!!
Answers
Please help, 20 points uwu
Answers
X = 1 , 4 are the value of x in logarithm.
A logarithm is defined simply?
A logarithm is a mathematical operation that raises a number to a given power in order to produce another number (see Section 3 of this Math Review for more about exponents).
As an example, the logarithm of 100 in base ten is 2, since ten times two equals 100: log 100 = 2, since 102 = 100. The four most prevalent kinds of logarithms are common logarithms with a base of 10, natural logarithms with a base of e 2.71828, binary logarithms with a base of 2, and logarithms with a base of 2.
2log₃(6x) - log₃(4x) - 2log₃(x + 2) = 0
log₃(9x/(x+ 2)²) = 0
exponential form using the definition of a logarithm. If x and b are positive real numbers and b≠1, then
logb(x) = y equivalent to [tex]b^{y}[/tex] = x
3⁰ = 9x/(x + 2)²
9x = 3⁰ (x + 2)²
9x = x² + 4x + 4
-x² + 5x = 4
Factor x out of -x²
x(-x) + x. 5 = 4
x(-x + 5) = 4
-x² + 5x - 4 = 0
- ( x - 4) ( x - 1) = 0
x = 4 , 1
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A gym teacher fills a basket with 70 balls. Some of the balls are rubber, and the rest are foam. He has four classes per day. Each class gets out 10 balls at random. At the end of class, they put the balls back in the basket for the next class to use. The first class pulls out 2 rubber balls and 8 foam balls. The second class pulls out 4 rubber balls and 6 foam balls. The third and fourth classes both pull out 3 rubber balls and 7 foam balls. About how many of the balls in the basket are rubber?
Answers
To estimate the number of rubber balls in the whole basket, we can multiply this proportion by the total number of balls. Therefore, We can estimate that there are about 21 rubber balls in the basket.
What is average proportion?An average proportion is the sum of a set of proportions divided by the number of proportions.
It represents the average or typical value of the proportions in the set, and can be used to estimate the overall proportion or percentage of a larger population.
To estimate how many of the balls in the basket are rubber, we can use the proportion of rubber balls that were drawn in each class to find the average proportion of rubber balls across all four classes.
We can then use this average proportion to estimate the number of rubber balls in the whole basket.
The total number of balls drawn from the basket is:
(2 + 8) + (4 + 6) + 2 x (3 + 7) = 40
The total number of rubber balls drawn is:
2 + 4 + 2 x 3 = 12
The proportion of rubber balls drawn in each class is:
Class 1: 2/10 = 0.2
Class 2: 4/10 = 0.4
Class 3: 3/10 = 0.3
Class 4: 3/10 = 0.3
The average proportion of rubber balls across all four classes is:
(0.2 + 0.4 + 0.3 + 0.3) / 4 = 0.3
Therefore, we can estimate that approximately 30% of the balls in the basket are rubber. To estimate the number of rubber balls in the whole basket, we can multiply this proportion by the total number of balls:
Number of rubber balls = 0.3 x 70 = 21.
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Factor 81+45. Write your answer in the form a(b+c) where a is the GCF of 81 and 45.
please us these thing (4e4) sumthing like that
Answers
Answer:
9 × ( 9 + 5 )
Hope this helps!
Step-by-step explanation:
The GCF of 81 and 45 is 9.
Classify each pair of lines as parallel, perpendicular, or neither.
2y = x and y = -2x + 6
y + 3x = 1 and 2y = -6(x - 1)
3y + 2x = -3 and 4y = 6x + 12
y + 2 = 5x and 5y - x = -2
Answers
The pairs of lines are classified as: perpendicular, parallel, neither, neither.
The slopes of the first pair of lines differ, making them neither parallel nor perpendicular. The slopes of the first and second lines are 1/2 and -2, respectively.
The second set of lines is perpendicular because the slopes of the first line, which is -3, and the second line, which is 1/3, are the opposites of each other.
The third set of lines have varying slopes and are neither equal nor perpendicular. The slopes of the two lines are -2/3 for the first line and 6/4 for the second, which reduces to 3/2.
To classify each pair of lines as parallel, perpendicular, or neither, we need to compare their slopes.
2y = x and y = -2x + 6
The first equation can be written in slope-intercept form as y = (1/2)x, which means its slope is 1/2. The second equation can be written in slope-intercept form as y = -2x + 6, which means its slope is -2. Since the slopes are negative reciprocals of each other, these lines are perpendicular.
y + 3x = 1 and 2y = -6(x - 1)
The first equation can be written in slope-intercept form as y = -3x + 1, which means its slope is -3. The second equation can be written in slope-intercept form as y = -3x + 3, which means its slope is also -3. Since the slopes are the same, these lines are parallel.
3y + 2x = -3 and 4y = 6x + 12
The first equation can be written in slope-intercept form as y = (-2/3)x - 1, which means its slope is -2/3. The second equation can be written in slope-intercept form as y = (3/2)x + 3, which means its slope is 3/2. Since the slopes are not equal and not negative reciprocals of each other, these lines are neither parallel nor perpendicular.
y + 2 = 5x and 5y - x = -2
The first equation can be written in slope-intercept form as y = 5x - 2, which means its slope is 5. The second equation can be written in slope-intercept form as y = (1/5)x - 2/5, which means its slope is 1/5. Since the slopes are not equal and not negative reciprocals of each other, these lines are neither parallel nor perpendicular.
Therefore, the pairs of lines are classified as follows:
perpendicular
parallel
neither
neither
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How many insects were consumed throughout the month by the pitcher plants?
Answers
Answer:
I think 15 I am sure
Step-by-step explanation:
The number of insects consumed by pitcher plants is essential for their survival and growth, and it is fascinating to observe this unique aspect of their carnivorous nature.
Pitcher plants are carnivorous plants that trap and digest insects to obtain nutrients. The exact number of insects consumed by pitcher plants in a month can vary depending on factors such as the species of pitcher plant, its size, and the local environment. However, studies have estimated that a single pitcher plant can consume anywhere from a few dozen to hundreds of insects per month.
The mechanism of the pitcher plant is quite interesting. Insects are lured into the plant by its color and sweet-smelling nectar. Once inside, the insect becomes trapped and is unable to escape due to the slippery inner walls of the pitcher. The plant then secretes digestive enzymes that break down the insect's tissues, allowing the plant to absorb the nutrients.
Interestingly, not all insects are consumed by pitcher plants. They tend to prefer smaller insects such as ants and flies, but larger insects such as bees and wasps may occasionally become trapped as well.
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12. An online clothing company sells custom sweatshirts. The company charges $6.50 for each sweatshirt and a flat fee of $3.99 for shipping.
a. Write a linear function in the form y = mx + b that represents the total cost, y, in dollars, for a single order of x sweatshirts.
b. Describe how the linear function would change if the shipping charge applied to each sweatshirt.
Answers
Answer:
a. y = 6.5x + 3.99
b. y = 10.49x
Step-by-step explanation:
a.
total cost = charge per shirt + flat rate of shipping
y = 6.5x + 3.99
b.
total cost = charge per shirt + shipping charge per shirt
y = 6.5x + 3.99x
y = 10.49x
If the shipping charge applies to every shirt, then the total cost is the cost of the shirts (6.5x) plus the cost of shipping multiplied by the number of shirts (3.99x)
Four times the sum of 5 and some number is 20. What is the number?
Answers
This is the answer to your problem
what is the rental price for a shirt that a store buys for $10 after a 30% mark up
3 reads strategy: annotate and think /show work
1r: what is the problem about
2r:what is the question asking to find
3r: connection/ number...
help with work
Answers
Answer:
retail price = $13.00
Step-by-step explanation:
10 x 1.30 = $13
In a parallelogram, the largest angle is 50° greater than the smallest angle. what is the size of each angle in the parallelogram
Answers
Answer:
Largest angles- 115
Largest angle- 115
Smallest angle-65
Smallest angle-65
Step-by-step explanation:
Angles of opposite sides in a parallelogram are equal.
Let the smallest angle be y.
Let the largest angle be y+50
y+50+y+50+y+y=360
100+4y=360
4y=(360-100)/4
y=65
Theyre four angles:
50+y(65)= 115
50+y(65)= 115
y=65
y=65
Answer: 65° and 115°.
Step-by-step explanation:
Let the smallest angle is x°
Hence the largest angle is x°+50°
The sum of the angles in a parallelogram that are adjacent to one side is 180 degrees.
Therefore
x°+(x°+50°)=180°
2x°+50°=180°
2x°+50°-50°=180°-50°
2x°=130°
Divide both parts of the equation by 2:
x°=65°
x°+50°=65°+50°
x°+50°=115°.
Musa has a glass that holds 250 ml of water. He drinks of these glasses of water. He fills his glass from a 2-litre bottle of water. Work out how much water is left in the bottle. Give your answer in millilitres.
Answers
Answer:
1750ml
Step-by-step explanation:
2L=2000ml
2000-250
1750ml
y = 4x
y=x-4
8x = y
y = 0.25x
-2x + 6 = y
Please answer it by saying if it represents a proportion or does not represent a proportion. Help Please…
Answers
*A proportional equation should be written or able to be written as y = kx.
*The line will go through (0, 0).
*There will be no y intercept.
y = 4x ✅ proportional in format y = kx
y = x - 4 ❌ is not in format y = kx
8x = y ✅ proportional can be written y = 8x
y = .25x ✅ proportional in format y = kx
-2x + 6 = y ❌ is not in format y=kx
What is the slope for the function with the greater slope? Mark all that apply
Answers
According to this partial W-2, how much money was paid in FICA taxes? Round answer to two decimal places. If answer doesn't have two decimal places include zeros so that it does have two decimal places. For the units use a word not a symbol. Be sure to attach your work to this question in order to receive credit for your answer.
1 wages, tips, other compensation
38,974
2 Federal income tax withheld
4,427.94
3 Social Security wages
38,974
4 Social security tax withheld
2,144.72
5 Medicare wages and tips
38,974
6 Medicare tax withheld
474.41
7 Social security tips
8 Allocated tips
9
10 Dependent care benefits
Answers
Answer: A: $2374.56
there
Step-by-step explanation:
FICA taxes is the Social Security and the Medicare added together
So you add 1924.48+450.08 and you get 2374.56
an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 190 engines and the mean pressure was 7.3 lbs/square inch. assume the variance is known to be 1. if the valve was designed to produce a mean pressure of 7.2 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? state the null and alternative hypotheses for the above scenario.
Answers
The hypothesis for the given scenario can be written as follows:
Null hypothesis
H_0: μ = 7.2
Alternative hypothesis
H_1: μ ≠ 7.2
Here, μ = Population mean
The mean pressure produced by the valve is not 7.2 lbs/square inch.
The given level of significance (α) = 0.05
The given population variance is known to be 1.
Need to determine if there is sufficient evidence to show that the valve does not perform to the given specifications if the valve was designed to produce a mean pressure of 7.2 lbs/square inch. That is, whether to reject or accept the null hypothesis with the given level of significance (α) = 0.05.
The sample mean pressure of 190 engines tested was 7.3 lbs/square inch. Mean pressure (μ) = 7.3 lbs/square inch, σ² = Variance = 1, n = Number of observations = 190
Significance level (α) = 0.05
Test Statistic: Z = (x - μ) / (σ / √n)
where x = Sample mean
The formula for the test statistic can be written as:
Z = (7.3 - 7.2) / (1 / √190)Z = 4.3588 (approx.)The calculated value of Z = 4.3588 is greater than the Z critical value at 0.05 level of significance.
Hence, there is sufficient evidence to reject the null hypothesis H_0. Therefore, we can conclude that the valve does not perform to the given specifications. The mean pressure produced by the valve is not 7.2 lbs/square inch.
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How do you combine like terms with distributive property?
Answers
Jessie has a square pyramid with a base side length of 15 inches and a height of 7 inches. Carl has a square pyramid with a volume of 1890 in^3.
Use the information to choose all the correct statements below:
A.
Jessie's pyramid has a volume of 35 in^3.
B.
Jessie’s pyramid has a volume of 525 in^3.
C.
Carl’s pyramid is 48 times larger than Jessie’s.
D.
Carl’s pyramid is 3.6 times larger than Jessie’s.
E.
Carl's pyramid is 36% larger than Jessie's.
May be more than 1 correct answer
Answers
The correct statements are:
B. Jessie’s pyramid has a volume of 525 in^3. (Using the formula for the volume of a pyramid, V = (1/3) * base area * height, we get V = (1/3) * 15^2 * 7 = 525 in^3.)
D. Carl’s pyramid is 3.6 times larger than Jessie’s. (Using the formula for the volume of a square pyramid, V = (1/3) * base area * height, we can find the base side length of Carl's pyramid: base side length = sqrt((3*1890)/(7*15^2)) ≈ 18.46 inches. Therefore, the ratio of volumes is (18.46/15)^2 * (7/7) ≈ 3.6.)
Answer:The correct statements are:
B. Jessie’s pyramid has a volume of 525 in^3. (Using the formula for the volume of a pyramid, V = (1/3) * base area * height, we get V = (1/3) * 15^2 * 7 = 525 in^3.)
D. Carl’s pyramid is 3.6 times larger than Jessie’s. (Using the formula for the volume of a square pyramid, V = (1/3) * base area * height, we can find the base side length of Carl's pyramid: base side length = sqrt((3*1890)/(7*15^2)) ≈ 18.46 inches. Therefore, the ratio of volumes is (18.46/15)^2 * (7/7) ≈ 3.6.)
Step-by-step explanation:
Please help me///////
Answers
Answer: Anything greater than 3
Step-by-step explanation:
The answer can be any number greater or equal to 3. This is because if you subtract 3 by 3 you get 0 and zero is still greater than -2 making the inequality true
help plsssss i dont understand
Answers
Answer:
f(x)= 3x+2
Step-by-step explanation:
math
:)
What is the value of u?
Answers
Answer:
union apparently
Answer:
u = 26.1°
Step-by-step explanation:
the 2 angles u and 44.1° combine to form the angle 70.2° , that is
u + 44.1° = 70.2° ( subtract 44.1° from both sides )
u = 26.1°
assuming the rest of your diet remains constant, how many days will it take you to lose 9 pounds? you must burn an extra 3500 calories to lose 1 pound of body weight
Answers
As per the given measurement, you would need to burn an extra 500 calories every day in order to lose 9 pounds in 63 days, assuming that the rest of your diet remains constant.
We know that in order to lose 1 pound of body weight, you need to burn an extra 3500 calories. Therefore, to lose 9 pounds, you would need to burn an extra 31,500 calories
=> (9 pounds x 3500 calories per pound).
If you divide this number by the number of days in which you want to achieve this goal, you'll find the amount of calories you need to burn each day. In this case, it would be:
31,500 calories / 63 days = 500 calories per day
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for a continuous function, if the second derivative at the critical points is negative, is the function quasi-concave?
Answers
For a continuous function, if the second derivative at the critical points is negative, then it not necessarily mean that it is quasi-concave.
A "continuous-function" is defined as a function in which small changes in the input result in small changes in the output, without any abrupt jumps or discontinuities.
A function is termed as "quasi-concave" if its upper contour sets are convex.
A function is termed as "quasi-convex" if its lower contour sets are convex.
The "Quasi-concavity" is a weaker condition than concavity, so it does not exhibit in a condition on the sign of "second-derivative".
Therefore, if a continuous function has a negative second derivative at its critical points, it does not necessarily mean that it is quasi-concave.
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Please help
Find the total area S₁ + S₂ under the normal distribution, where S, is the area to the left of z=-2.15
and S₂ is the area to the right of z =
= 1.62.
Answers
Answer:
the total area under the normal distribution is 0.0684.
Step-by-step explanation:
We can use a standard normal distribution table or a calculator to find the areas S₁ and S₂.
Using a standard normal distribution table or calculator, we find:
S₁ = 0.0158
S₂ = 0.0526
To find the total area S₁ + S₂, we simply add these two values:
S₁ + S₂ = 0.0158 + 0.0526 = 0.0684
Therefore, the total area under the normal distribution is 0.0684.
You are given an isosceles trapezoid ABCD with median XY. Complete the following.
Answers
The measures of the angle m∠DAB for the isosceles trapezoid is equal to 75°.
What is an Isosceles trapezoidThis is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.
The upper base angles m∠DAB and m∠ADC are equal, and angles m∠ADC and m∠DCB are supplementary, so we shall calculate for the angle m∠DAB by first evaluating for angle m∠ADC as follows:
m∠ADC + m∠DCB = 180° {opposite angles are supplementary}
m∠ADC + 105° = 180°
m∠ADC = 180° - 105° {subtract 105° from both sides}
m∠ADC = 75°
m∠ADC = m∠DAB = 75°
Therefore, the measures of the angle m∠DAB for the isosceles trapezoid is equal to 75°.
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Distribute this binomial into two binomials: (y + 3)². DO NOT SOLVE IT.
Answers
Answer:
y² + 6y + 9.
It can be expressed into two binomials like this.
Answer:
(y + 3)(y + 3)
Using (a+b)² = (a+b)(a+b)
What quadratic equation could be solved to find any solutions to the system of equations?
y = -5x + 6
y = x^2 + 7x - 11
Replace the values of a, b, and c, in the equation to formulate the correct equation.
0 = ax² + bx + c
Answers
The quadratic equation that could be solved to find any solutions to the system of equations [tex]$y = -5x + 6$[/tex] and [tex]$y = x^2 + 7x - 11$[/tex] is:
[tex]$x^2 + 12x - 17 = 0$[/tex].
What is quadratic equation?
A quadratic equation is a polynomial equation of degree 2, which means it involves an unknown variable (usually denoted as x) that is raised to the power of 2. The general form of a quadratic equation is given by:
a[tex]x^{2}[/tex] + bx + c = 0
where a, b, and c are constants, and a is not equal to 0.
The quadratic equation that could be solved to find any solutions to the system of equations
[tex]$y = -5x + 6$[/tex]
[tex]$y = x^2 + 7x - 11$[/tex]
is given by:
[tex]$x^2 + 12x - 17 = 0$[/tex]
Therefore, the quadratic equation that could be solved to find any solutions to the system of equations [tex]$y = -5x + 6$[/tex] and [tex]$y = x^2 + 7x - 11$[/tex] is:
[tex]$x^2 + 12x - 17 = 0$[/tex]
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