The concept of factoring quadratic equations simply is one of the ways to solve for the zeroes of the quadratic equation.
What is quadratic equations by factoring?The concept of factoring quadratics is a technique which is characterized by expressing the quadratic equation ax2 + bx + c = 0 as a product of its associated linear factors as (x - f)(x - g), in which case, f and g are the roots of the quadratic equation ax2 + bx + c = 0.
Factoring is an important concept that helps express equations of any type in simpler forms The mode of operation of the factoring works such that, the polynomial is rewritten in a simpler form and consequently, expressed as a product of it's linear factors.
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someone explain, i did a and its just 12x + 36 but for part b I don't understand half a thing, I did something I did in a, I did x^2 + 12x + 36 -144 but then the answer was wrong someone please help me I have final exam tmrw and I'm gonna do really bad :(
Answer:
a. x²
b. 144 cm²
Step-by-step explanation:
You want to know an expression for the area of the four white triangles in the given figure, and you want to know that area when x = 12 cm.
a. Triangle areaIf you draw horizontal and vertical lines through the middle of the figure, you can see that for each white triangle there is a matching shaded triangle. That is, the shaded area is equal to the white area.
The shaded area is the square of the length of the side of the shaded square, so is ...
shaded area = x²
The white area is the same, so is ...
white area = x²
b. Area for x=12 cmUsing x = 12 cm, the formula from part (a) tells us ...
white area = (12 cm)² = 144 cm²
The total area of the four white triangles is 144 cm².
__
Additional comment
The relation between the side lengths of the shaded area and the side length of the total area is ...
2x/√2 = x+6
This has one solution: x = 6/(√2 -1) ≈ 14.485281 (cm).
The figure cannot be drawn to scale for any other value of x, so it is impossible for x=12 cm, unless the outside length is (x+4.97056...)
If you take the white triangles to be isosceles right triangles, each will have an area of A = 1/2bh = 1/2(x/√2)(x/√2) = x²/4. The four of them will have an area of 4(x²/4) = x². If you take the white area to be the overall area less the area of a square of side length x, then the area of the four triangles will be (x+6)² -x² = 12x+36. You will notice that these expressions give different values of the area of the white triangles when x=12. (See the previous comment about the value of x.)
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Determine the y-intercept of -5x+7y=8
Answer:
The y-intercept of -5x+7y=8 is (0,8/7)
Step-by-step explanation:
The y-intercept of a linear equation is the point where the graph of the equation crosses the y-axis. In this equation, when x = 0, the equation becomes 7y = 8, so the y-intercept is (0, 8/7).
Answer:I hope this helps
Step-by-step explanation:
-5x+7y=8
To find the -intercept, substitute x=0 something like this
-5 times 0+7y=8
Solve the equation for Y which is something like
y=8/7 this your answer for the y intercept.
How do you solve the midline theorem of a triangle?
The midline theorem claims that cutting along the midline of a triangle creates a segment that is parallel to the base and half as long.
The condition for the midline theorem is that the two triangles must have the same size and shape, so all three sides have the same length, and all three angles have the same measure.
For the theorem, we draw a line through two points on either side of the triangle and then we prove that the line divides the sides into equal halves. Once proven that the sides are in two equal halves using congruency it is proved that the base and midline are parallel.
Since the base and midline are parallel to each other using the SAS rule of congruency therefore according to the theorem the segment is half as long as the base.
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What is sum of angles of a triangle class 7?
According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.
The smallest polygon with three sides and three interior angles is a triangle.
A triangle is a three-sided polygon that consists of three vertices, three sides, and three angles. Three types of triangles—scalene, isosceles, and equilateral—can be distinguished based on the length of their sides.
It can be an acute-angled, obtuse-angled, or right-angled triangle depending on the size of its angles. A triangle's internal angles add up to 180 degrees. Two more terms—altitude and triangle median—are introduced to you in this essay.
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Afia chool i plotted at -8, -3 on a coordinate plane. Her babyitter houe i located at 8 , -3. What i the ditance between Afia chool and her babyitter houe?
The distance between Afia's school and her babysitter's house is 16 units.
Distance is a measurement of how far away two things or locations are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.
The distance between two points in a coordinate plane can be found using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.
In this case, the coordinates of Afia's school are (-8, -3) and the coordinates of her babysitter's house are (8, -3).
Plugging these values into the distance formula:
d = √((8 - (-8))^2 + (-3 - (-3))^2)
d = √((8 + 8)^2 + (0)^2)
d = √(16^2)
d = √(256)
d = 16 units
Therefore, the distance between Afia's school and her babysitter's house is 16 units.
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If point (x, y) is reflected over the x-axis, the resulting point is (-x, y)
The given statement "If point (x, y) is reflected over the x-axis, the resulting point is (-x, y)" is true.
What is the reflection on x-axis?When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).
The given statement is "If point (x, y) is reflected over the x-axis, the resulting point is (-x, y)".
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Therefore, the given statement is true.
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Here are the first four terms of a sequence.
28 23 18 18
Find the nth term of the sequence.
Answer:
8, 3
Step-by-step explanation:
28, 23, 18, 13
Subtract each term from the next term.
23 - 28 = -5
18 - 23 = -5
13 - 18 = -5
All differences are equal. When all differences are equal, you have an arithmetic sequence. The equal differences are called the "common difference." To find a new term, add the common difference to the previous term.
13 + (-5) = 13 - 5 = 8
8 + (-5) = 8 - 5 = 3
Answer: 8, 3
Which of the following statement is correct regarding Sampling Distributions?a. The sampling distribution of the sample mean will be approximately normal.b. The mean of the sampling distribution of the sample mean will be equal to the population mean.c. Both A and B.d. None of the above.
Hence option b is the correct option i.e The sample mean's sampling distribution will be roughly normal.
The appropriate response to the question about Sampling Distributions is The sample mean will have a sampling distribution mean that is identical to the population mean.
The sampling distribution must then resemble the normal distribution as the sample size grows.
According to this, if the sample size is large enough, the sampling distribution of the mean will always be normally distributed. The sampling distribution of the mean will be normal regardless of whether the population has a normal, Poisson, binomial, or any other distribution.
A bell-shaped, symmetrical distribution known as a normal distribution has fewer observations the farther out from its center.
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Is 4x an exponential function?
Yes, 4x is an exponential function. An exponential function is one where there is a constant being raised to a variable.
Exponential functions involves exponents. An exponential function has a constant as its base and a variable as its exponent but not the other way round. if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function. The exponential function is a type of mathematical function which are helpful in finding the growth or decay of population, money, price that are growing or decay exponentially. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. it can be extended to the complex numbers or generalized to other mathematical objects like matrices.
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evaluate the integral (v3 to 1) 5 arctan 1/x dx
After integrating the expression [tex]$$I=\int_1^{\sqrt{3}} 5 \arctan \left(\frac{1}{x}\right) d x$$[/tex] we will get the value as: [tex]$I=\left(\frac{5 \sqrt{3}}{6}-\frac{5}{4}\right)^\pi+\frac{5}{2} \ln |2|$[/tex]
Integration by parts, also known as partial integration, is a technique used in calculus and more widely in mathematical analysis to determine the integral of a function's product in terms of the integral of the product of the function's derivative and antiderivative.
The integration of the result of two functions is the integration by parts. Typically, the two functions are shown as f(x) and g. (x). The first function, f(x), is chosen from the two functions in such a way that its derivative formula exists, while the second function, g(x), is chosen in such a way that its integral formula exists.
∫ f(x).g(x).dx = f(x) ∫ g(x).dx - ∫(f'(x) ∫g(x).dx).dx + C
We have, [tex]$$I=\int_1^{\sqrt{3}} 5 \arctan \left(\frac{1}{x}\right) d x$$[/tex]
We know that
[tex]\frac{1}{x}=arccot(x) \\I=5 \int_1^{\sqrt{3}} arccot(x) dx[/tex]
Integrating by parts
[tex]$$\int f g^{\prime}=f g-\int f^{\prime} g$$[/tex]
let us assume that,
[tex]$\quad f=\cot ^{-1}(x) \quad g^{\prime}=1$[/tex]
[tex]$I=5 \int_1^{\sqrt{3}} \cot ^{-1}(x) d x$[/tex]
[tex]$I=5\left[x \cot ^{-1}(x)-\int \frac{-x}{x^2+1} d x\right]$[/tex]
[tex]$I=5\left[x \cot ^{-1}(x)+\frac{1}{2} \ln \left|x^2+1\right|\right]_1^{\sqrt{3}}$[/tex]
[tex]$I=5\left[\left(\sqrt{3} \cot ^{-1}(\sqrt{3})+\frac{1}{2} \ln |4|\right)-\left(\cot ^{-1}(1)+\frac{1}{2} \ln |2|\right)\right]$[/tex]
[tex]$I=5\left[\frac{\sqrt{3} \pi}{6}+\ln 2-\frac{\pi}{4}-\frac{1}{2} \ln |2|\right]$[/tex]
[tex]$I=\left(\frac{5 \sqrt{3}}{6}-\frac{5}{4}\right)^\pi+\frac{5}{2} \ln |2|$[/tex]
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The correct question should be:
Evaluate the integral [tex]$$I=\int_1^{\sqrt{3}} 5 \arctan \left(\frac{1}{x}\right) d x$$[/tex]
Can the sides of a triangle have lengths 4 7 and 8?
It is possible to construct a triangle with lengths of its sides 8cm, 7cm and 4cm because the sum of two sides of a triangle is greater than the third side.
Now, According to the question:
We know that:
What is triangle inequality rule?
The triangle inequality theorem states that for any given triangle, the sum of the two sides is always greater than the third side. The Triangle is a polygon with three line segments as its boundaries.
Suppose A, B and C are three sides of a triangle, then by using triangle inequality rule, A + B > C then A, B and C make a triangle.
We have the sides:
4 , 7 and 8
4 + 7 > 8
It is possible to construct a triangle with lengths of its sides 8cm, 7cm and 4cm because the sum of two sides of a triangle is greater than the third side.
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Suppose f(x) is a function such that if p
Of(x) can be odd or even.
Of(x) can be odd but cannot be even.
Of(x) can be even but cannot be odd.
Of(x) cannot be odd or even.
Answer:
Step-by-step explanation:
In rectangular park that is 63 yards by 16 yards, a dog began in the northwest corner and ran south along the length of the park. Then the dog ran east along the width to the southeast corner. Finally, the dog ran back to the northwest corner. How far did the dog run?
If in rectangular park that is 63 yards by 16 yards, a dog began in the northwest corner and ran south along the length of the park and Finally, the dog ran back to the northwest corner. The dog ran 65 yards.
What is distance?Distance can be defined as how far an object is from another object.
Using the Pythagoreans theorem to find the distance
c² = √a² + b²
Let plug in the formula
c² = √63² + 16²
c² = √3,969 + 256
c = √4,225
c = 65 yards
Therefore the distance is 65 yards.
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please what is 4 times 5
_
12
Answer:20
Step-by-step explanation: 5+5+5+5
Answer:
4 times 5 is equal to 20.
Step-by-step explanation:
What is 4/3 as an exponent?
Answer:
4/3 as an exponent is 4 to the 3rd power ( so four with a three right above it a little)
Step-by-step explanation:
Please please please help me!!!! 20+ points! Thank you :)
Answer:
m∠1 = 32
Step-by-step explanation:
∠WXZ = 115
m∠2 = m∠1 + 51
x + x + 51 = 115
2x + 51 = 115
2x = 64
x = 32
A square pyramid is shown. What is the surface area?
A square based pyramid, with bases labeled 3.5 centimeters and side length of triangle labeled 7 centimeters.
(4 points)
30.625 cm2
61.25 cm2
19.25 cm2
49.625 cm2
The surface area of the square pyramid is B)61.25[tex]cm^2[/tex]
What is surface area of square pyramid?
The term "square pyramid" also refers to a polyhedron having a square base and four triangular faces. Where the four faces come together is known as the apex. The pyramid's faces connect the base and the tip. The calculation for the square pyramid's surface area adds the areas of the four triangular faces and the base.
Here the given measures are base = 3.5 cm and height = 7cm.
Now using surface area formula then
Surface area of the square pyramid = Base area + 2bl square unit.
Base area = 3.5 × 3.5 = 12.25[tex]cm^2[/tex]
=> Surface area = 12.25+ 2×3.5×7
=> Surface area = 12.25+49
=> Surface area = 61.25[tex]cm^2[/tex]
Hence the surface area of the square pyramid is B)61.25[tex]cm^2[/tex]
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The sum of two numbers is 10. The larger number is 4 times the smaller number.
The system of equations used to represent this scenario is y = –x + 10 and y = 4x.
What is the larger number?
he system of equations used to represent this scenario is y = –x + 10 and y = 4x, where x and y are the two numbers.
To find the larger number, we can solve the system of equations by setting y = 4x in the first equation and solving for x.
y = –x + 10
4x = –x + 10
3x = 10
x = 10/3
So the smaller number is 10/3. To find the larger number, we know that it is 4 times the smaller number, which is 4(10/3) = 40/3.
Therefore, the larger number is 40/3.
Answer:
The larger number = 8
Step-by-step explanation:
Below is the system of equations:
y = -x + 10
y = 4x
Since both equations equal "y", we can set them equal to each other:
4x = -x + 10
4x + x = 10
5x = 10
x = 2
This means that at x = 2, the y-values of both equations are the same and is when the criteria of "the sum of two numbers are 10 and the larger number is 4 times the smaller number" is met
"x" is the smaller number. To find the bigger number, input "x" into either one of the equations in the system:
y = 4(2) = 8
solve the system. 3x + y = 10 y = 6x + 1
ann and byron positioned themselves 35m apart on one side of a stream
Ann and Byron set up shop 35 meters apart on one side of a creek, with the height of the cliff on the other side of the stream being 106.73 meters.
what is triangle ?Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners.
given
consider the triangles ABC and ACD
from the figure
∠DAC = 36°
∠CAB = 68°
AD = 35 m
we have to find the height of the cliff i.e. he length BC
i.e. the length BC
cosθ = adjacent side / hypotenuse
cos36° = 35 / AC
AC = 43.21 m
tan68° = BC / 43.21
BC = 43.21 * 2.47 = 106.73 m
Ann and Byron set up shop 35 meters apart on one side of a creek, with the height of the cliff on the other side of the stream being 106.73 meters.
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the admision to a local fair is $10 each for adult and $6 for each child. Each ride costs $1.50 for an adult and $1 for a child.
An adult and child will each go on 7 ride. How much more did the adult spend?
The cost of admission for an adult is $10 and for a child is $6
The cost of each ride for an adult is $1.50 and for a child is $1
The adult will spend $10 for admission + $1.5 x 7 rides = $17.5
The child will spend $6 for admission + $1 x 7 rides = $13
The adult spent $17.5 - $13 = $4.5 more than the child.
Find an equation for the perpendicular bisector of the line segment whose endpoints are (−2,−9) and (−6,7)
Answer: y = 1/4x +1
Step-by-step explanation:
First, we can find the midpoint of the line segment using the average of x and y coordinates of the endpoints:
M(x,y) = ((-2 + (-6))/2 , (-9 + 7)/2)
M(x,y) = (-4, -1)
To find the slope of the perpendicular bisector, we have to take the negative reciprocal of the slope of the line segment which is (y2-y1)/(x2-x1) = (7-(-9))/(-6-(-2)) = -16/4 = -4
Slope of the perpendicular bisector = -1/slope of the line segment = -1/(-4) = 1/4
Now we can use the point-slope form to find the equation of the line:
y - y1 = m(x - x1)
y - (-1) = 1/4(x + 4)
y = 1/4x +1
so the equation of the perpendicular bisector of the line segment whose endpoints are (-2,-9) and (-6,7) is y = 1/4x +1
Find the exact volume of a waffle ice cream cone with a 3-in. diameter and a
height of 15 inches.
Answer:
Step-by-step explanation: v = 1/3π[tex]r^{2}[/tex]h
[tex]\frac{1}{3}[/tex]π([tex]1.5^{2}[/tex]) x 15
[tex]\frac{1}{3}[/tex]π x 2.25 x 15
=35.34291
17 7/9 divided by 0. Please hurry I have to get this done soon. Thank uu :D
Answer:undefined
Step-by-step explanation:
I’ll give brainliest please help! Using point slope form find the equation of the line with the given slope that passes through the given point
Answer:
Below
Step-by-step explanation:
Point -4, 6 slope = - 3
Point slope form of the line : ( y-y1) = m (x - x1)
(y-6) = -3 (x - -4)
y - 6 = -3 (x+4)
A store sells peanut butter in 28-ounce jars for $4.29 and in 16 ounce jars for $2.49. Find the price per ounce for each size jar and determine which jar is the better buy. Explain.
By finding the unit rates for the two jars, we will see that the better option is the 28-ounce jar.
Which size of jar is the better buy?To find wich option is the better buy, we need to find the unit rate for each of these jars.
To get the unit rate, we need to take the quotient between the cost of each jar and the volume of peanut butter that each jar has.
We know that the jar of 28 ounces has a cost of $4.29, then its unit rate is:
U = ($4.29)/28 oz = $0.153 per oz.
This means that with this jar, each ounce costs $0.153
For the 16 ounce jar, the cost is $2.49, then the unit rate is:
U' = $2.49/16 oz = $0.156 per oz.
So here the cost per ounce is larger, then the better option is the 28-ounce jar.
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What is the coefficient of x² in 3x³ 2x² x 1?
So on solving the provided question we can say that here, coefficient of x² in 3x³+ 2x² -x+ 1 is 2
What is the coefficient?A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include: The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.
here,
coefficient of x² in 3x³+ 2x² -x+ 1 is 2
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Which could be the measures of the three angles of an acute triangle.A. 40, 90, 50B. 45, 45, 90C. 25, 25, 130D. 70, 80, 30
Answer:
Option D
Step-by-step explanation:
Remember that the sum of all angles in ANY triangle is 180 degrees. Also, remember that an acute triangle has angles that are all less than 90 degrees. So not only do our options have to add up to 180 degrees, but they also have to be less than 90 degrees in order for the triangle to be acute.
We can immediately exclude options A, B, and C because all three options have angles greater than 90 degrees, which means the triangle isn't acute.
Your answer is option D or "70, 80, 30." Since...
70 + 80 + 30 = 180
70 < 90
80 < 90
30 < 90
Hope this helps.
p:q=2/3:5/6 and q:r=3/4:1:2,find p:q:r
Answer:
p:q:r = 12:15:10
Step-by-step explanation:
Given p:q = (2/3):(5/6) and q:r = (3/4):(1/2), you want p:q:r.
Integer ratiosWe can turn each ratio into a ratio of integers by multiplying by the least common denominator.
p:q = 4:5 . . . . . . . multiply the given ratio by 6
q:r = 3:2 . . . . . . . multiply the given ratio by 4
Now, we need to have q be represented in each ratio by the same number. That number will be the least common multiple of its representations in these ratios: LCM(5, 3) = 15.
Multiplying the first ratio by 3, we have ...
p : q = 12 : 15
Multiplying the second ratio by 5 gives ...
q : r = 15 : 10
Ratios of all threeNow, we can write the ratio of interest:
p : q : r = 12 : 15 : 10
<95141404393>
To find the quotient of 14 and 8, consider that some number times 8 equals 14. Since 14 is equivalent to Response area, that number must be Response area. Then 14÷8=Response area, because of the inverse relationship between multiplication and division.
Since 14 is equivalent to 8x, that number must be 14 ÷ 8. Then 14 ÷ 8 = x, because of the inverse relationship between multiplication and division.
How to use inverse relationship of division?There are 4 basic mathematical operations which are addition, subtraction, division and multiplication.
Multiplication and division are inverse operations because multiplication undoes division and also division undoes multiplication.
We want to find the quotient of 14 and 8. This is expressed as 14 ÷ 8.
Now, we are told to consider that some number times 8 equals 14. Let the number be x and as such we have;
8x = 14
Now, since 14 is equal to 8x, then that number must be gotten by using the inverse relationship by multiplying both sides by 1/8 to get;
x = 14/8
Finally, 14÷8 = x because of the inverse relationship between multiplication and division.
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