The formula is
[tex]A=\frac{(a+b)\cdot h}{2}[/tex]To solve for b, first, we multiply the equation by 2
[tex]\begin{gathered} 2A=2\cdot\frac{(a+b)\cdot h}{2} \\ 2a=(a+b)\cdot h \end{gathered}[/tex]Then, we divide the equation by h
[tex]\begin{gathered} \frac{2A}{h}=\frac{(a+b)h}{h} \\ \frac{2A}{h}=a+b \end{gathered}[/tex]At last, we subtract a from each side
[tex]\frac{2A}{h}-a=a-a+b[/tex]Hence, the final expression is[tex]b=\frac{2A}{h}-a[/tex]Please help, disregard the option I chose because I'm not sure it's right :)
Consider that the graph of f(x) is the graph of a cubic function, that is, the graph of a 3 degree polynomial. If you apply first derivative to such a polynomial, the result is another polynomial of degree 2.
Now, take into account that the graph of a polynomial of degree 2 is a parabola. The parabola can open up or down. It depends of the leadding coefficient of the polynomial. In this case, due to the graph of f(x), the leadding coefficient is positive, which means that the parabola of f'(x) opens up.
Hence, you can conclude that the graph of f'(x) is option C.
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!
8 more than the product of 12 and 11.
Please Help
How long will it take until the diver enters the water? How do you know?
Given:
The equaiton that model height of the driver jumps from the ledge.
[tex]h=-t^2+8t+115[/tex]Requried:
We need to find the time taken by driver to enter the water.
Explanation
Kaylee drove 160 miles in 5 hours. If she continued at the same rate, how far would she travel in 17 hours?
The distance covered by Kaylee in 17 hours at the same rate is 544 miles.
According to the question,
We have the following information:
Distance covered by Kaylee = 160 miles
Time taken by Kaylee = 5 hours
We know that the following formula is used to find the speed:
Speed = distance/time
Speed = 160/5 mile/hour
Speed = 32 miles/hour
Now, we have to find the distance when time taken is 17 hours and the speed is the same.
Now, from the formula of speed, we can find the distance:
Distance = speed*time
Distance = 32*17
Distance = 544 miles
Hence, the distance covered by Kaylee in 17 hours is 544 miles.
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Which equation represents a line which is perpendicular to the line y=-5/4x-4?A. 4y−5x=−4B. 5x+4y=−8C. 4x−5y=15D.4x+5y=40
The slope of a line, m, comes in the equation as the coefficient of x.
In the given equation, m= -5/4. Two perpendicular lines have slopes that are the negative reciprocals of each other.
So, the slope of the perpendicular line will be +4/5.
Between the given options, letter c will be:
4x-5y=15
-5y=15-4x (divided by -5)
y=4/5x-3
Letter C
In a game, Billy must roll two dice. One die is astandard six-sided number die, and the otherdie has a different color on each side (red,blue, green, orange, yellow, and purple). Whatis the probability that Billy rolls a 3 and agreen?A 162% czB 12D1WIN
The probability of getting a 3 is:
[tex]P=\frac{1}{6}[/tex]The probability of getting green is:
[tex]P=\frac{1}{6}[/tex]Therefore the probability of getting a 3 and a green is:
[tex]P=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36}[/tex]Hence the answer is C.
Choose SSS, SAS, or neither to comparethese two triangles.A) SSSB) SASC) neither
Answer:
C. Neither
Explanation:
The SSS Congruence Rule states that if the three sides of a triangle are equal to the three sides of another triangle, then the two triangles are congruent.
The SAS Congruence Rule states that if the two sides and the included angle of one triangle are equal to the two sides and the included angle of another triangle, then the two triangles are congruent.
Notice that in the given triangles, there are two congruent sides and a non-included angle, since this does not satisfy any of the rules stated above, SSS Congruence rule or SAS Congruence rule, we'll choose "neither" as the correct answer.
18
If p percent of an adult's daily allowance of
potassium is provided by x servings of Crunchy
Grain cereal per day, which of the following
expresses p in terms of x ?
Express p in terms of x : p = 5x
What is Percent?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.
If 5% of an adult's daily potassium requirement is provided by each serving of Crunchy Grain cereal, then x servings will offer x times 5%.
Five times as many servings, or p, of potassium are required for an adult's daily requirement.
As a result,
p = 5x can be used to describe the proportion of potassium in an adult's daily allotment.
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Each n in the model represents the same value. 136.5 What is the value of n? there are 7 N's in the problem
The value of n must be 136.5/7
n = 136.5/7
n = 19.5
Result n = 19.5
can someone please help me find the value of X?
Answer:
x = 100degrees
Explanation:
Using the theorem;
The angle at the vertex is the half of the difference of its intercepted arcs
Angle at the vertex = 15 degrees
angle at the intercepted arcs = 70degrees and x degrees
According to the theorem;
15 = 1/2(x-70)
Cross multiply
15 * 2 = x - 70
30 = x - 70
Add 70 to both sides
30 + 70 = x - 70 + 70
100 = x
Swap
x = 100degrees
Hence the value of x is 100degrees
for each of the following polynomial functions, write the equation of a different polynomial function that has the same key characteristic. explain your thinking.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Draw the given graph.
STEP 2: Get the function plotted on the graph.
[tex]undefined[/tex]During Thanksgiving Break, 68% of a school's students ate green bean casserole. Out of 650 students, how many ate green bean casserole?
650 --- total
650*.68=442
442 students ate green bean casserole
.68 represents the percentage
so for example, if they asked me for 50% of 1000
we need to multiply 1000*0.5
if they asked for 60% we will multiply 1000*0.6
Andrea is buying some new shirts and sweaters. She is able to buy 3 shirts and 5 sweaters for $99 or she is able to buy 6 shirts and 4 sweaters for $90. How much does a shirt cost? How much does a sweater cost?
Given :
The cost of 3 shirts and 5 sweaters is $99 .
The cost of 6 shirts and 4 sweaters is $90.
To determine :
The sweater cost and shirt cost each.
Explanation :
Let the shirt cost be x.
Let the sweater cost be y.
Then the equation formed is
[tex]3x+5y=99\ldots\ldots\ldots\ldots\ldots\ldots..1[/tex][tex]6x+4y=90\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots2[/tex]Solve the equation 1 and 2 to find x and y with the help of elimination method.
Multiply by 2 in equation 1.
[tex]6x+10y=198\ldots\ldots\ldots\ldots\ldots\ldots.\ldots.\ldots3[/tex]Solve equation 2 and 3 by subtraction,
[tex](6x+10y-198)-(6x+4y-90)=0[/tex][tex]6y-198+90=0[/tex][tex]6y=108[/tex][tex]y=18[/tex]The value of y is 18 and now substitute the value of y in equation 2 to find x.
[tex]6x+4y=90[/tex][tex]6x+4\times18=90[/tex][tex]6x=90-72[/tex][tex]6x=18\Rightarrow x=3[/tex]The value of x is 3.
Answer :
The cost of shirt is 3 dollar .
The cost of sweater is 18 dollar.
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpointand y.)midpoint (-7.-21), endpoint (-13.-15)
Ok, we are going to use the midpoint formula
M = ( (x1 + x2) / 2 , (y1 + y2) / 2 )
(-7,-21)=((x1-13)/2 , (y1-15)/2 )
Break up this formula into two equations.
(x1-13)/2=-7 and (y1-15)/2=-21
Solve for x1 and y1 from the equations. So:
x1=(-7*2)+13
x1=(-14)+13=-1
y1=(-21*2)+15=(-42)+15=-27
So the other endpoint is (-1, -27).
Multiply. Write your answer in decimal form: (8 x 10^2)(4 x 10^2)
Answer:
32×10⁴
Step-by-step explanation:
open the bracket
8×4×10^(2+2)
32×10⁴
hope it helps
please mark brainliest
Answer the following.(a) An astronomer's infrared telescope is able to detect radiation with a wavelength of 1.96 x 10^-5 meters. Write this number in standardnotation(b) The diameter of Venus at its equator is approximately 12,100 kilometers. Write this number in scientific notation.(a) Imeters(b) kilometers
a)
We need to convert 1.96 x 10^-5 meters. into standard notation.
Now, on the scientific notation, the power of ten shows how many places the decimal point has been moved.
- If the exponent is positive then the decimal point has been moved to the left.
- If the exponent is negative, then the decimal point has been moved to the right.
In this case, the power is negative 5 . So, the decimal point has been moved 5 places to the right.
Hence:
1.96 x 10^-5 = 0.0000196
b)
a. Meters
First, we need to convert kilometers into meters using the rule of three:
If 1k = 1000 meters
Then 12,100k = x
Where x = (12,100k*1000m)/ 1k
x =12000000 meters
We need to convert from standard notation to scientific notation:
12000000.0 = 1.2x10^7 meters
The decimal point has been moved 7 places to the left, so the power of then is positive 7.
b) We need to convert 12,100 kilometers into scientific notation:
12,100 = 12,100.0
Converting into scientific notation
1.21x10^4 kilometers
The decimal point has been moved 4 places to the left. Hence, the power of the is positive 4.
The Oldest rocks on Earth are about 4 x 10^9 years old. For which of these ages could this be an approximation?
A. 3,862,100,000 years
B. 3.849999999x10^9 years
C. 0.000000004 years
D.4,149,000,000 years
E.3.45x10^9 years
Determine the measures of angles x, y, and z: x = 75°95°105°° y = 75°95°105°° z = 75°95°105°°
Consider the figure,
So, we have, Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.
So, here, [tex]<\text{AHB}+z=180[/tex]
Therefore, z can be calculated as,
[tex]z=180-<\text{AHB}=180-105=75[/tex]Now, the angles DHC and
simplify 5(3c-4d)-8c
Answer:
7c - 20d
Step-by-step explanation:
5(3c - 4d) - 8c ← distribute parenthesis by 5
= 15c - 20d - 8c ← collect like terms
= 7c - 20d
Identify an equation in point slope form for the line perpendicular to y=1/4 x-7that passes through -2,-6
The equation in the point slope form for the line perpendicular to y = (1/4)x-7 that passes through the point (-2,-6) is y+6 = -4(x+2)
The given equation of the perpendicular line
y = (1/4)x -7
The equation is in the slope intercept form of the line
y = mx+b
Where m is the slope of the line
By comparing the given equation with the slope intercept form
The slope of the line m = 1/4
The slope of its perpendicular line = -1/m
= -4
The point slope form is
[tex](y-y_1)=m(x-x_1)[/tex]
The point is given that (-2,-6)
Substitute these values in the equation
(y-(-6) = -4(x-(-2)
y+6 = -4(x+2)
Hence, the equation in the point slope form for the line perpendicular to y = (1/4)x-7 that passes through the point (-2,-6) is y+6 = -4(x+2)
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A set of four numbers that begins with the number 32 is arranged fromsmallest to largest. If the median is 35, which of the following could possiblybe the set of numbers?a) 32, 32, 36, 38b) 32, 35, 38, 41c) 32, 34, 36, 39d) 32, 36, 40, 44
Given the word problem, we can deduce the following information:
1. A set of four numbers that begins with the number 32 is arranged from
smallest to largest.
2. The median is 35.
To determine the possible set of numbers of which the median is 35, we first note that median is the number separating the other half of the ordered data sample from the lower half.
Now, we check the median of each choices:
For a) 32, 32, 36, 38:
[tex]Median=\frac{32+36}{2}=34[/tex]For b) 32, 35, 38, 41:
[tex]Median=\frac{35+38}{2}=36.5[/tex]For c) 32, 34, 36, 39
[tex]Median=\frac{34+36}{3}=35[/tex]For d) 32, 36, 40, 44:
[tex]Median=\frac{36+40}{2}=38[/tex]Therefore, the answer is: c) 32, 34, 36, 39
For the parabola given by 4y – 9 = x2 – 6x, find the vertex and focus.
Solution
Gievn the equation below
[tex]4y-9=x^2-6x[/tex]To find the vertex and focus of the given equation, we apply the parabola standard equation which is
[tex]4p(y-k)=(x-h)^2[/tex]Where p is the focal length and the vertex is (h,k)
Rewriting the equation in standard form gives
[tex]\begin{gathered} 4y-9=x^2-6x \\ 4y=x^2-6x+9 \\ 4y=x^2-3x-3x+9 \\ 4y=x(x-3)-3(x-3) \\ 4y=(x-3)^2 \\ 4(1)(y-0)=(x-3)^2 \end{gathered}[/tex]Relating the parabola standard equation with the given equation, the vertex of the parabola is
[tex]\begin{gathered} x-3=0 \\ x=3 \\ y-0=0 \\ y=0 \\ (h,k)\Rightarrow(3,0) \\ p=1 \end{gathered}[/tex]Hence, the vertex is (3,0)
The focus of the parabola formula is
[tex](h,k+p)[/tex]Where
[tex]\begin{gathered} h=3 \\ k=0 \\ p=1 \end{gathered}[/tex]Substitute the values of h, k and p into the focus formula
[tex](h,k+p)\Rightarrow(3,0+1)\Rightarrow(3,1)[/tex]Hence, the focus is (3, 1)
Select the correct answer.
What is the value of this logarithmic e ession?
log2 16 - log₂ 4
Answer:l og2(16)=x log 2 ( 16 ) = x in exponential form using the definition of a logarithm. If x x and b b are positive real numbers and b b does not equal ...
Step-by-step explanation:
Which expression is equal to -2i(4 - i)?
Answer:
-8i + 2i^2
I am new but I hope this helps you
Answer:
-8i+2i²
this looks like an equation in factorization
Find the second endpoint of the segment that has an endpoint at (9,5) and its midpointat (4, 2).
it
Questlon 5 Refer to the figure. HJ I JE. HII IE. HJ HI J H E Complete the explanation to show triangle EJH is congruent to triangle EIH. The two triangles given are _____triangles. The leg and hypotenuse of triangle EJH are congrue hypotenuse of triangle EIH. By the ______ Theorem the third side ma triangles are congruent by the____ Triangle Congruence Theorem.choice 1.acute,obtuse or right angleschoice 2.corresponding parts of congruent triangles, pythagorean,or side-angle-side triangle congruence.choice 3. side-side-side, side-angle-side,or angle-side-angle
In the given figure, we have two triangles △EJH and △EIH
We are given the following information
[tex]\begin{gathered} \bar{HJ}\perp\bar{JE} \\ \bar{HI}\perp\bar{IE} \\ \bar{HJ}\cong\bar{HI} \end{gathered}[/tex]This means that these two triangles are "Right Triangles"
Therefore.
Choice 1 = right angles
When the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.
Therefore,
Choice 2 = side-angle-side triangle congruence
Choice 3 = side-angle-side
Answer: choice 1 -Right Angle
Choice 2 -Pythagorean
Choice 3- Side-Side-Side
Step-by-step explanation:other guy is completely wrong lol
Given four numbers P, Q, R and S. The first three numbers form an arithmetic sequence while the last three form a geometric sequence. If the sum of the first and the fourth number is 16 and the sum of the second and the third number is 12, find these four numbers.
The most appropriate choice for arithmetic and geometric series will be given by-
P = 0, Q = 4 , R = 8, S = 16 or P = 15, Q = 9, R = 3, S = 1 are the required numbers
What is arithmetic and geometric series?
Arithmetic series are those series whose difference between two consecutive terms are same.
Geometric series are those series whose ratio between two consecutive terms are same.
Here,
P, Q and R forms an Arithmetic sequence
Let P = a - d , Q = a, R = a + d, Where a is the first term of the Arithmetic sequence and d is the common difference of the sequence.
Let S = b
Q, R and S forms a Geometric sequence
[tex]\frac{a + d}{a} = \frac{b}{a +d}[/tex]
[tex](a + d)^2 = ab\\a^2 + d^2 + 2ad = ab\\[/tex] ............... (1)
Now the sum of first and fourth number is 16
a - d + b = 16
b = 16 - a + d
Putting the value of b in (1),
[tex]a^2 + d^2 + 2ad = a(16 - a +d)\\a^2 + d^2 + 2ad = 16a -a^2+ad\\a^2+a^2 + d^2+2ad - ad - 16a = 0\\2a^2 + ad+d^2 -16a = 0[/tex]............ (2)
Sum of second and third number is 12
[tex]a + a + d = 12\\2a +d = 12\\d = 12-2a[/tex]
Putting the value of d in (2)
[tex]2a^2 + a(12 - 2a)+(12 - 2a)^2-16a = 0\\2a^2 + 12a - 2a^2+144-48a+4a^2 - 16a = 0\\4a^2-52a+144=0\\4(a^2-13a+36)=0\\a^2 -13a+36=0\\a^2-9a-4a+36=0\\a(a - 9)-4(a-9)=0\\(a-4)(a-9) = 0\\[/tex]
[tex]a - 4 = 0[/tex] or [tex]a - 9 = 0[/tex]
[tex]a = 4[/tex] or [tex]a = 9[/tex]
When a = 4,
[tex]d = 12 - 2\times 4\\d = 12 - 8\\d = 4[/tex]
[tex]b = 16 - 4+4\\b = 16[/tex]
P = 4 - 4 = 0
Q = 4
R = 4 + 4 = 8
S = 16
When a = 9,
[tex]d = 12 - 2\times 9\\d = 12 - 16\\d = -6[/tex]
[tex]b = 16 - 9-6\\b = 1[/tex]
P = 9 - (-6) = 15
Q = 9
R = 9 + (-6) = 3
S = 1
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What are the coordinates of M', the image of M (2,4), after a counterclockwiserotation of 90° about the origin?
If M(h,k) is rotated 90° counterclockwise about the origin, the new position would be M'(k, -h)
M(2, 4)-> M'(4, -2)
In science class, the students were asked to create a container to hold an egg they would then drop this container from a window that is 25 feet above the ground if the equation of the containers pathway can be modelled by the equation: H =-16t²+25Find is the maximum height of the container?
Answer:
25 feet
Explanation:
The equation that models the pathway of the container is:
[tex]h=-16t^2+25[/tex]The maximum height occurs at the axis of symmetry.
First, we find the equation of symmetry:
[tex]\begin{gathered} x=-\frac{b}{2a}where\begin{cases}a=-16 \\ b=0\end{cases} \\ x=-\frac{0}{2\times-16} \\ x=0 \\ \implies t=0 \end{gathered}[/tex]Next, determine the value of h at t=0.
[tex]\begin{gathered} h=-16(0)^2+25 \\ h=25\text{ feet} \end{gathered}[/tex]The maximum height of the container is 25 feet.