Step-by-step explanation:
(2x+3)(x+1)prime(2x+3)(4x-1)The Polynomial Is Prime (2x-7)(x+4)Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
The correct answer is 8.5 in.
What is Heron's formula in math?Heron's formula, formula credited to Heron of Alexandria for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides: Area = Square root of√s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.we know that
The formula of area of triangle is equal to
[tex]A = \frac{1}{2} (b) (h)[/tex]
We have
b = BC = 6 in
h = AD = x in
substitute
[tex]A = \frac{1}{2} (6) (x)[/tex]
[tex]A = 3x^{2} in^{2} ..................(1)[/tex]
Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.
Let a,b,c be the lengths of the sides of a triangle.
The area is given by:-
[tex]A = \sqrt{p(p-a) (p-b) (p-c)}[/tex] where p is half the perimeter
[tex]p = \frac{a +b+ c}{2}[/tex]
a = 9 in , b= 9 in, c = 6 in
[tex]p = \frac{9 + 9 + 6}{2} = 12 in[/tex]
Find the area
[tex]A = \sqrt{12( 12 - 9) (12-9) (12 - 6)}[/tex]
[tex]A = \sqrt{12 (3)(3)(6)}[/tex]
[tex]A = \sqrt{648}[/tex]
[tex]A = 25.46 in^{2}[/tex]
Substitute the value of the area in the equation 1 and solve for x
[tex]A = 3x in^{2}[/tex]
25.46 = 3x
x = 25.46/3
x = 8.5 in
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The complete question is -
HELP PLEASE! Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
A. 8 in.
B. 11.3 in.
C. 8.5 in.
D. 6.2 in.
Show your steps in evaluating each of the following expressions. The steps count 4 points each, the answer is 1 point.
The steps in evaluating each of the following expressions is shown below.
What is an expression?An expression can be defined as a mathematical equation which shows the relationship existing between two or more numerical quantities or variables.
How to evaluate the given expressions?15 - 35/7 - 2 + 3 - 4
15 - (35/7) - 2 + 3 - 4 (bracket and division)
15 - 5 - 2 + 3 - 4 (regroup)
15 + 3 - 5 - 2 - 4 (subtract and add)
18 - 11 = 7.
Expression 2.10 + 2(9 - 5) - 16/18
10 + (2 × 4) - 8/9 (bracket and division)
10 + 8 - 8/9 (add)
18 - 8/9 (subtract)
162/9 - 8/9 = 17 1/9 or 154/9.
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Complete Question:
Show your steps in evaluating each of the following expressions. The steps count 4 points each, the answer is 1 point.
A. 15 - 35/7 - 2 + 3 - 4
B. 10 + 2(9 - 5) - 16/18
find the slope of y=6x+2
Hello,
y = ax + b where a is the slope ! so here the slope is 6
find the values of A and B
please help giving brainliest
Answer:
A=3Bz/2
B=2A/3z
Step-by-step explanation:
if you need more explanation you can ask me :)
The box-and-whisker plots show the points scored in each Super Bowl by the AFC and NFC. About how many points higher is the upper quartile for the NFC than the AFC?
The upper quartile for NFC is 3 points higher than that of AFC.
What is the difference in the upper quartiles?A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%
On the box, the third line on the box represents the upper quartile. 75% of the scores represents the upper quartile.
Upper quartile for AFC : 26
Upper quartile for NFC : 23
Difference = 26 - 23 = 3
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Given y=-x^2 if the function is shifted 5 units up which equation describes the new function
The equation that describes the new function is y' = x^2 + 5
How to determine the new function?The function is given as:
y = x^2
Shifting the function up by 5 units, the rule is
(x, y) = (x, y + 5)
So, we have:
y' = x^2 + 5
Hence, the equation that describes the new function is y' = x^2 + 5
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A student scores 74, 87, 68, 63, 76 on his last five
exams. His teacher will drop the lowest grade to
compute the student's average. What is the
students average in the class?
Answer:
76.25
Step-by-step explanation:
This Stem-and-Leaf Plot represents the heights of the students on Ralph’s basketball team. One student’s height is missing from the plot. If the mean height of all the students on the team is 61 inches, what is the missing height?
A. 55 in.
B. 59 in.
C. 61 in.
D. 65 in.
The missing height is 65.
What is the missing height?
Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
Missing height = (mean x total number of students) - sum of existing heights
Sum of existing heights = (54 + 55 + 56 + 61 + 63 + 64 + 70 ) = 423
Missing height = (8 x 61) - 423 = 64
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Identify the distance between points (- 3, 0, - 7) and (- 8, - 9, - 11) , and identify the midpoint of the segmen for which these are the endpoints . Round to the nearest tenth, if necessary
The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).
What is the distance between the two points and what is the midpoint of the line segment?
First, we find the vector between the two points by vector sum:
[tex]\vec r = (-8, -9, - 11) - (- 3, 0, -7)[/tex]
[tex]\vec r = (- 5, - 9, - 4)[/tex]
The distance between the two points is found by the following Pythagorean expression:
[tex]d = \sqrt{(-5)^{2}+(-9)^{2}+(-4)^{2}}[/tex]
d ≈ 11.1
And the midpoint is found by linear algebra:
[tex]\vec m = 0.5\cdot (-3, 0, -7) + 0.5 \cdot (-8, -9, - 11)[/tex]
[tex]\vec m = (- 1.5, 0, - 3.5) + (- 4, - 4.5, -5.5)[/tex]
[tex]\vec m = (- 5.5, - 4.5, - 9)[/tex]
The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).
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Latoya, Kevin, and Milan have a total of $117 in their wallets. Milan has 4 times what Latoya has. Latoya has $9 less than Kevin. How much do they have in
their wallets?
Answer:
Step-by-step explanation:
Let Kevin have x dollars. Then Latoya has x - 9 dollars and Milan has 4(x - 9) dollars.
x + (x-9) + 4(x-9) = 177
7x - 40 = 177
7x = 217
x = 31
Kevin has $31
Latoya has 31 - 9= $22
Milan has 4*24 = $96
PLS HELP AND EXPLAIN . math related
Answer:
(0,0)
Step-by-step explanation:
The y-intercept (where the graph of the equation crosses the y-axis) occurs where x = 0. If you substitute 0 for x in the equation, y = 0. So the y-intercept is at (0,0).
18. In AABC, 44 is a right angle, and m4B 45°. What is the length of BC? If the answer is not an integer, leave it in simplest radical form. The
diagram is not drawn to scale.
054 ft
17√3 ft
17√2 ft
017
Answer:
17√3
Step-by-step explanation:
In a 45-45-90 triangle, the hypotenuse is √3 times larger than the legs.
17*√3 = 17√3
Other than translation, what transformation is used to create this frieze pattern?
180° rotation
vertical reflection
horizontal reflection
translation
Other than translation, the transformation that is used to create this frieze pattern is; B: Vertical Reflection
How to Identify the Transformation?Now, we see all the Frieze Patterns on top are being transformed using Translation as it is the exact same pattern throughout the top.
Now, for the bottom we see that is is simply a reflection of the one on top and so it is a vertical reflection because it is reflected across the x-axis.
A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis.
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A mass weighing 16 pounds is attached to a spring whose spring constant is 36 lb/ft. what is the period of simple harmonic motion?
The period of simple harmonic motion is T = 4.19 seconds:
For given question,
A mass weighing 16 pounds is attached to a spring whose spring constant is 36 lb/ft.
So, we have mass (m) = 16 pounds
spring constant (k) = 36 lb/ft.
Let T be the period of simple harmonic motion.
Using the formula for the period of simple harmonic motion,
⇒ T = 2π√(m/k)
⇒ T = 2 × π × √(16/36)
⇒ T = 2 × π × √(0.444)
⇒ T = 2 × π × 0.666
⇒ T = 1.333 × π
⇒ T = 4.19 seconds
Therefore, the period of simple harmonic motion is T = 4.19 seconds
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party planners recommend that, for every eight quests, two orders of appetizers be provided. which function reflects this ratio
The ratio guest to appetizers at the party was 4 guest per appetizer.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Ratio of guest to appetizers = 8 guest / 2 appetizers = 4 guest per appetizer.
The ratio guest to appetizers at the party was 4 guest per appetizer.
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Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?
AB = 25
27 < AB < 81
AB = 85
AB< 27 or AB > 81
Answer:27 < AB < 81
Step-by-step explanation:
Answer:
27 < AB < 81
Step-by-step explanation:
in a triangle the sum of any 2 sides must be larger than the third side.
that must be true for every pair of sides you pick.
simply because, if that is not fulfilled, the third side would be too long, and the other 2 sides cannot connect to the endpoints of the third side.
so,
AC + CB = 81 must be longer than AB. otherwise the triangle cannot "close".
AC + AB = 27 + AB must be longer than CB = 54.
so, AB must be longer than 27.
CB + AB = 54 + AB must be longer than AC = 27. but that is always true, as CB alone is already larger.
so only the other 2 conditions need to be true.
hence the answer.
In a bag are three red marbles and three white marbles. If
two marbles are taken from the bag at the same time,
what is the probability that both marbles will be red?
The probability is 1/5.
How to find the probability?
There are 3 red marbles and 3 white marbles, for a total of 6.
The probability that the first marble is red is:
P(red) = 3/6
The probability that the second marble is also red is:
P(red') = 2/5 (because now there are 2 red marbles and a total of 5).
The joint probability is:
P = (3/6)*(2/5) = 1/5
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A box of chocolates contains hard-centred and soft-centred chocolates in the ratio 5 : 2. If there are 49 chocolates in the box, how many are hard-centred and how many are soft- centred?
Hard-Centred___________ Soft-Centred__________
There will be total 14 hard centred and 14 soft centred choclates in the box.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that in the question hard-centred and soft-centred chocolates in the ratio 5 : 2
Hard centred/ Soft centred = 5/2
And total
Hard centred + Soft centred = 49
Now let say hard centred is H and soft centred S
H/S = 5/2 and H + S = 49
Now H = (5/2)S put into second equation
(5/2)S + S = 49
S(7/2) = 49
S = 14 now put into second equation
H + 14 = 49 = 35 hence hard centred will be 35 and soft centred will be 14.
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WILL MAKE BRAINLIEST!! Solve for b.
Answer: 98
Step-by-step explanation: 180 - 82 = 98
180 - 80 = 100, and 100 - 2 is 98.
I needed help solving this
Answer:
Answer C: m = 26, f = 22
there is a typo in answer D.
Step-by-step explanation:
There are 48 vehicles, so m + f = 48.
They have 140 wheels, so 2m+4f = 140.
You can rewrite the first as m = 48-f and then plug it into the second:
2(48-f) + 4f = 140 =>
96 - 2f + 4f = 140 =>
2f = 140 - 96 =>
2f = 44
f = 22
m = 48 - 22 = 26
Answer:
D
Step-by-step explanation:
Let m = motorcycles and c = cars
m + c = 48 2m + 4c = 140
m + c = 48 Multiple this equation through by -2
-2m -2c = -96 Add this to the second equation above
2m +4c = 140
2c = 44 Divide both sides by 2
c = 22. There are 22 cars. Plug this back into the top equation to find the number of motorcycles.
m + c = 48
m + 22 = 48 Subtract 22 from both sides
m = 26
Patient a weighs 135.8 pounds.patient b weighs 135 2/5 ibs. which patient has the greater weight or if their weights are equal
Answer:
patient A has the greater weight
Solve the following system of equations and show all work.
y = -x² + 4
y = 2x + 1
Answer:
Step-by-step explanation:
The ys have to have the same value. That allows you to equate the right side of each y to each other.
-x^2 + 4 = 2x + 1 Subtract the right side from the left side.
-x^2 + 4 - 2x - 1 = 2x-2x +1 - 1 Combine
-x^2 - 2x + 3 = 0 Multiply both sides by - 1
-1(-x^2 - 2x + 3) = 0*-1 Remove the brackets
x^2 + 2x - 3 Factor
(x - 1)(x + 3 )
x - 1 = 0
x = 1
x + 3 = 0
x = - 3
So the line goes through x = 1 or x = - 3
x = 1
y = 2x + 1
y = 2(1) + 1
y = 3
x = - 3
y = 2(-3) + 1
y = - 6 + 1
y = - 5
Does the graph confirm this? See below.
red: y = -x^2 + 4
green: y = 2x + 1
Yes the graph is in agreement.
Which expression is equivalent to -7(y - 2)
The expression equivalent to -7(y - 2) is -7y + 14
Which expression is equivalent to -7(y - 2)?
Given the expression; -7(y - 2)
We expand the expression by multiplying each element inside the parentheses the element out i.e -7
-7(y - 2)
[ -7 × y and -7 × -2 ]
-7y + 14
Therefore, the expression equivalent to -7(y - 2) is -7y + 14.
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Which equation could be used to find the length of the hypotenuse?
Triangle A B C. Side A C is 5 centimeters and side C B is 8 centimeters. Hypotenuse A B is labeled c.
5 squared + 8 squared = c squared
5 squared + c squared = 8 squared
c squared minus 5 squared = 8 squared
8 squared minus 5 squared = c squared
The equation which could be used to find the length of the hypothenuse is; 5 squared + 8 squared = c squared.
Which equation could be used to find the length of the hypothenuse?.It follows from the task content that the equation which could be used to find the length of the third side be determined.
Hence, since it follows from Pythagoras theorem that the square of the hypothenuse is equivalent to the sum of the squares of the two other sides of a right triangle.
Hence, the required equation is; 5 squared + 8 squared = c squared.
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Answer:
The answer is A
5 squared + 8 squared = c squared
Step-by-step explanation:
Write the factored form of an equation that has the zeros 4 and -7.
The factored form of the equation that has the zeros 4 and -7 is y = ( x - 4)( x + 7 ).
What is the factored form of an equation that has the zeros or roots 4 and -7?Roots are simply the points where the graph intercepts with the x-axis. ( y = 0 )
That is, y = 0 the roots
Given the roots of the equation;
4-7Now, at x = 4,
x = 4
x - 4 = 0
y = ( x - 4)
Also, at x = -7,
x = -7
x - ( - 7 ) = 0
x + 7 = 0
y = ( x + 7 )
Hence; for the equation with the given roots; 4 and -7 will be;
y = ( x - 4)( x + 7 ).
The factored form of the equation that has the zeros 4 and -7 is y = ( x - 4)( x + 7 ).
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If the length of one leg in this triangle is .find the length of the hypotenuse.
By Pythagorean theorem we find that the length of the hypotenuse is [tex]r = \sqrt{2}\cdot l[/tex].
How to find the length of the hypotenuse
In the image attached we have a right triangle with two legs of same length. The hypotenuse of right triangles can be found by Pythagorean theorem, whose form is:
[tex]r = \sqrt{l^{2}+l^{2}}[/tex]
[tex]r = \sqrt{2}\cdot l[/tex], where l is the length of the legs.
By Pythagorean theorem we find that the length of the hypotenuse is [tex]r = \sqrt{2}\cdot l[/tex].
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Need help on the Sin(4x) part of the question please!!
a. The equivalent expression for cos(4x) in terms of just x is 8cos⁴x - 8cos²x + 1
b. The equivalent expression for sin(4x) in terms of just x is 4sinxcos³x - 2sinxcosx
a. The equivalent trigonometric expression for cos(4x)To find the trigonometric expression for cos(4x)
cos(4x) = cos[2(2x)]
Now from trigonometric identities
cos2Ф = 2cos²Ф - 1
Let 2x = Ф.
So, cos(4x) = 2cos²2x - 1
Also, cos2x = 2cos²x - 1
So, substituting cos2x into cos4x, we have
cos(4x) = 2cos²2x - 1
cos(4x) = 2[2cos²x - 1]² - 1
cos(4x) = 2[4cos⁴x - 4cos²x + 1] - 1
cos(4x) = 8cos⁴x - 8cos²x + 2 - 1
cos(4x) = 8cos⁴x - 8cos²x + 1
So, the equivalent expression for cos(4x) in terms of just x is 8cos⁴x - 8cos²x + 1
b. The equivalent trigonometric expression for sin(4x)To find the expression for sin(4x)
sin(4x) = sin2(2x)
From trigonometric identities sin2Ф = 2sinФcosФ
Let 2x = Ф
So, sin(4x) = sin2(2x)
= 2sin2xcos2x
Since
sin2x = 2sinxcosx and cos2x = 2cos²x - 1Substituting these into the equation, we have
sin(4x) = 2sin2xcos2x
sin(4x) = (2sinxcosx)(2cos²x - 1)
sin(4x) = 4sinxcos³x - 2sinxcosx
So, the equivalent expression for sin(4x) in terms of just x is 4sinxcos³x - 2sinxcosx
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Total area=
Help me please! Thanks so much
The surface area of the oblique prism is equal to 485 square units.
How to find the surface area of an oblique prism
In this question we have an oblique prism with seven faces, consistiting in two regular hexagons and five parallelograms. The surface areas is the sum of these seven faces:
A = 2 · 50 + 5 · 11 · 7
A = 485
The surface area of the oblique prism is equal to 485 square units.
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An expression is shown below:
f(x) = 5x^2+ 2x - 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work.
(2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or
minimum? What are the coordinates of the vertex? Justify your
answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that
you can use the answers obtained in Part A and Part B to draw the
graph. (5 points)
(10 points)
Answer:
a: (-1,0) , (3/5,0)
b:(-0.2,-3.2). It will be a minimum
c: To graph, you would first find the vertex using (-b/2a) and then plug that back into the equation to find the y coordinate of the vertex. Once you have the vertex plotted, you can then find the x-intercepts. This can be found by factoring the equation and finding the zeros. These 3 points you plot are enough to graph the line.
Step-by-step explanation:
For showing work on part a:
Turn 5x^2+2x-3 into
(5x^2+5x) (-3x-3)
5x(x+1) -3(x+1)
Finally:
(5x-3)(x+1)
The zeros from that are -1 and 3/5
A _____ is an interval estimate of an individual y value, given values of the independent variables. Group of answer choices prediction interval confidence interval interval estimation regression
A confidence interval is an interval estimate of an individual y value, given values of the independent variables.
According to statement
we have to find a interval which give an estimate of an individual y value, given values of the independent variables.
Confidence interval tells that more than just the possible range around the estimate. It also tells about how stable the estimate is. A stable estimate is one that would be close to the same value if the survey were repeated.
So, A confidence interval is an interval estimate of an individual y value, given values of the independent variables.
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