Statement. (Reasons are in boldfaced words)
1. H is the midpoint of AD. By given.
2. AD bisects GC. By given.
3. HA = HD. By definition of midpoint.
4. GH = CH. By definition of the bisector.
5. Angles AHG and DHC are congruent. By vertical angles theorem.
6. AG = DC. They are the height of the figure.
7. Triangles GHA and CHD are congruent. By Side-Angle-Side postulate of congruence.
At the beginning of a snowstorm, Hassan had 2 inches of snow on his lawn.
The snow then began to fall at a constant rate of 2.5 inches per hour.
Assuming no snow was melting, how much snow would Hassan have on his
lawn 5 hours after the snow began to fall? How much snow would Hassan
have on his lawn after t hours of snow falling?
Hassan will have 14.5 inches of snow on his lawn after 5 hours of snow falling.
How to find amount snow ?Individual ice crystals that make up snow develop while suspended in the atmosphere, typically within clouds, before falling and accumulating on the ground, where they go through additional changes.
It starts out as frozen crystalline water that forms in the atmosphere under favourable conditions, grows to millimetre size, precipitates and builds up on surfaces, then undergoes a metamorphosis in place, and finally melts, slides, or sublimates away.
2 inches of snow on the lawn
Rate of snow falling = 2.5 inches per hour
Snow did not melt
Let y = height of snow on the lawn
Let t = time in hours
y = 2 + 2.5t
To find how much snow is on the lawn after 5 hours of snowing, substitute t = 5 into the found equation and solve for y:
⇒ y = 2 + 2.5(5)
⇒ y = 2 + 12.5
⇒ y = 14.5 inches
Therefore, Hassan will have 14.5 inches of snow on his lawn after 5 hours of snow falling.
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What is the point slope form of the line with slope -1/4 that passes through the
point (9, 2)?
Answer:
[tex]y - 2 = - \frac{1}{4} (x - 9)[/tex]
Write the product using exponents.3.3.3.3Using exponents, the product is
In the product
3×3×3×3
you have 4 threes, then it's equivalent to the next expression:
[tex]3\cdot3\cdot3\cdot3=3^4[/tex]How many units are in a hundred?
Solution
There are 100 units
[tex]100\text{ units}[/tex]Brief Explanation
[tex]\begin{gathered} 1\text{ unit}=1unit \\ \\ 1tens=10units \\ \\ 1hundred=10tens=10(10)units \\ \\ 1hundred=100units \end{gathered}[/tex]write an expression for the perimeter of the bedroom shown below
In this case, we'll have to carry out several steps to find the solution.
Step 01:
perimeter = ?
x + 4 = width
2x - 3 = length
Step 02:
perimeter = 2* width + 2*lenght
perimeter = 2 * (x + 4) + 2 * (2x -3)
= 2x + 8 + 4x - 6
= 6x + 2
The answer is:
The perimeter of the bedroom is 6x - 2
Evaluate the expressions. 0 3 9 Х Ś ? (-2) =
Question:
Solution:
Every number different from zero, with zero power, is always equal to 1. Then we can conclude that:
[tex]3(\frac{4}{9})^0\text{ = 3(1) = 3}[/tex]and
[tex](-2)^0\text{ = 1}[/tex]A box contains five cards lettered A,A,B,C,D. If one card is selected at random from the box and NOT replaced, what is the probability that Jill will draw an A and then a C?
A box contains five cards lettered A,A,B,C,D. If one card is selected at random from the box and NOT replaced, what is the probability that Jill will draw an A and then a C?
step 1
Find the probability that Jill draw an A
P=2/5
step 2
Find the probability that jill draw a C
P=1/4
therefore
the probability that Jill will draw an A and then a C is
P=(2/5)(1/4)
P=2/20
P=1/10 or 10%Please help me solve this problem
Answer:
The amount invested at an 8% rate would be $184
The amount invested at a 3% rate would be $69
Step-by-step explanation:
The amount invested at an 8% rate would be $184 because 2,300 x 0.08 (8% in a decimal form) x 1 (since it was after 1 year) would come to 184.
The amount invested at an 3% rate would be $69 because 2,300 x 0.03 (3% in a decimal form) x 1 (since it was after 1 year) would come to 69.
help meeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeee pleaseeeeeee
Answer: 10.8 seconds
Step-by-step explanation:
[tex]-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]
The graph below has the same shape as the graph of G(x) = {4, but it isshifted two units to the right. Complete its equation. Enter exponents usingthe caret (-); for example, enter x4 as x^4. Do not include "G(X) =" in youranswer.5.G(X) =
ANSWER:
[tex]G(x)=(x-2)^4[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]G(x)=x^4[/tex]In a function, to move it to the right or to the left we must add if we want to move to the left and we must subtract if we want to move to the right.
But we must add or subtract within the exponent, since it moved 2 to the right we must subtract 2 units, just like this:
[tex]G(x)=(x-2)^4[/tex]if a_1=2 and a_n=2a_n-1 find the first five terms of the sequence
Answer:
a1 = 2, a2 = 4, a3 = 8, a4 = 16, and a5 = 32
Explanation:
Given the first term and the nth term of the sequence as;
[tex]\begin{gathered} a_1=2 \\ a_n=2a_{n-1} \end{gathered}[/tex]Since the first term is given already to be 2, let's go ahead and find the 2nd term;
[tex]\begin{gathered} a_2=2a_{2-1} \\ a_2=2a_1 \\ a_2=2\ast2 \\ \therefore a_2=4_{} \end{gathered}[/tex]The 3rd term will be;
[tex]\begin{gathered} a_3=2a_{3-1} \\ =2a_2 \\ =2\ast4 \\ \therefore a_3=8 \end{gathered}[/tex]The 4th term can be found as follows;
[tex]\begin{gathered} a_4=2a_{4-1} \\ =2a_3 \\ =2\ast8 \\ \therefore a_4=16 \end{gathered}[/tex]The 5th term can found as follows;
[tex]\begin{gathered} a_5=2a_{5-1} \\ =2a_4 \\ =2\ast16 \\ \therefore a_5=32 \end{gathered}[/tex]Write an equation of the form y = mx for the line shown below. If appropriate,use the decimal form for the slope.(4,3)
SOLUTION
Step 1 :
In this question, we are expected to find the equation of the line,
y = m x + c
where y = dependent variable,
x = dependent variable,
m = gradient of the line
c = intercept on the y - axis.
Step 2 :
We are given that :
[tex]\begin{gathered} \text{The gradient of the line, } \\ m\text{ }=\text{ }\frac{y_2-y_1}{x_{2_{}}-x_1} \\ \text{where (x }_{1\text{ , }}y_{1\text{ }}\text{ ) = ( 4, 3)} \\ (x_{2\text{ , }}y_2\text{ ) = ( -4 ,- 3 )} \\ \text{Then we have that :} \\ m\text{ = }\frac{(\text{ -3 - 3 ) }}{-\text{ 4 - 4}} \\ m\text{ = }\frac{-6}{-8} \\ m\text{ =}\frac{3}{4} \end{gathered}[/tex]Step 3 :
Since ( x 1, y 1) = ( 4, 3 ) and
[tex]\begin{gathered} \text{the gradient m = }\frac{3}{4}\text{. } \\ y-y_{1\text{ }}=m(x-x_1) \\ y\text{ - 3 =}\frac{3}{4}\text{ ( x - 4 )} \\ \text{simplifying further, we have that:} \\ 4\text{ y - 12 = 3 x - }12 \\ 4y\text{ - 3x - 12 + 12 = 0} \\ 4\text{ y - 3 x = 0} \\ \operatorname{Re}-\text{arranging the equation, we have that:} \\ 4\text{ y = 3 x } \end{gathered}[/tex]CONCLUSION:
The final answer is :
[tex]y=\text{ }\frac{3}{4}\text{ x }[/tex]help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
2.5
Step-by-step explanation:
[tex]h(t)=213 \\ \\ \implies -16t^2 +126t=213 \\ \\ 16t^2-126t+213=0 \\ \\ t=\frac{-(-126) \pm \sqrt{(-126)^2-4(16)(213)}}{2(16)} \\ \\ t \approx 2.46, 5.42[/tex]
If we consider the graph, since height can't be negative, we only consider the first root.
Someone please help me
Answer:
3. Texas (1), timeline (2), tryouts (3), two-step (4)
4. wail (1), waved (2), wriggled (3), write (4)
Step-by-step explanation:
3. All start with T
go onto the next letter
Texas
Two-step
Tryout
Timeline
Therefore,
Texas (1)
Timeline(2)
Tryout(3)
two-step (4)
4. Same process as before, we are going to the third letters for wail and waved, the fourth letter for wiggled and write.
Wriggled
Write
Wail
Waved
g comes before t
i comes before v
Therefore,
wail (1)
waved (2)
wriggled(3)
write(4)
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
What is the equation of the line that passes through the points (4,7) and (-3,7)
Answer: y-7 =0
Step-by-step explanation: after applying m=y1-y2/x1-x2 you get 0/-7 which means that the slope is 0
What the answer to this problem f(x)=-4x^2+12x-9
We are given the function;
[tex]f(x)=-4x^2+12x-9[/tex]The input of this function as it is, is x. To evaluate the function at any given output we would simply replace/substitute the value of x with the value provided.
If for example, we are given the function and we have to evaluate its value at f(3), what we will simply do is replace x with two in the function. This is shown below;
[tex]\begin{gathered} f(x)=-4x^2+12x-9 \\ f(3)=-4(3)^2+12(3)-9 \\ f(3)=-4(9)+36-9 \\ f(3)=-36+36-9 \\ f(3)=-9 \end{gathered}[/tex]Therefore, the value of the function at f(3) is -9.
This is basically the procedure we shall use when evaluating a function at any given output value.
Use the graph to answer the question.Identify the domain of the graphed function.
The domain of the graphed function is [-2, 1) U (5, 9]
STEP - BY - STEP EXPLANATION
What to find?
The domain of the graph function.
What are domains?
Domains are sets of x- values for which the function is defined.
Observe from the graph given, the function are defined for set of all x - values between -2 and 1 with -2 included.
Also the function is also defined for a set of all x-values between 5 and 9 with 9 included.
This can be represented using interval notation as [-2, 1) U (5, 9].
Therefore, the correct option is A.[-2, 1) U (5, 9].
Determine the equivalent system for the given system of equations.4x − 5y = 23x − y = 8
Solution:
Given:
[tex]\begin{gathered} 4x-5y=2 \\ 3x-y=8 \end{gathered}[/tex]Two systems of equations are equivalent if they have exactly the same solution set.
Hence, we determine the solution to the system of equations.
[tex]\begin{gathered} 4x-5y=2\ldots\ldots.\ldots.\ldots.\ldots.(1) \\ 3x-y=8\ldots\ldots.\ldots\ldots\ldots\ldots..(2) \\ \\ m\text{ ultiplying equation (2) by 5} \\ 5(3x-y)=5(8) \\ 15x-5y=40 \\ \\ \text{Solving both equations (1) and the newly formed equation (2) simultaneously,} \\ 4x-5y=2\ldots\ldots\ldots\ldots(1) \\ 15x-5y=40\ldots\ldots\ldots.\mathrm{}(2) \end{gathered}[/tex]
Subtracting equation (1) from equation (2),
Equation (2) - equation (1) becomes;
[tex]undefined[/tex]Jada drank 12 ounces of water from her bottle. This is 60% of the water the bottle holds. How much water does the bottle hold?
Jada's water bottle holds 20 ounces of water.
Let the water bottle holds x ounces of water.
She drank 12 ounces of water.
this is equivalent to 60%
Hence 60% of x = 12
or, 0.6x = 12
or, x = 20 ounces
Therefore the bottle holds 20 ounces of water.
The English word percentage which refers to fractions with a denominator of 100, was derived from the Slang term "per centum," which means "by the hundred."
In other words, it is a connection where it is always assumed that the value of the whole is 100. The proportion of each reading to the total value is represented by the actual number whenever we have two or more readings that sum up to 100.
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Assume the cost of a taxi is one dollar per ride and $2.30 per mile what function represents your total cab fare be sure to indicate any domain restrictions.
The total cost of a taxi is given by the sum of a fixed amount of $1.00 per ride and an additional amount of $2.30 per mile driven. Then, the total cost f in function of the total number of miles driven x is given by:
[tex]f(x)=1+2.3x[/tex]Notice that, since there is no sense in considering "negative miles driven" the domain of this function is given by:
[tex]\mleft\lbrace x\in\mathfrak{\Re }\mright|x\ge0\}[/tex]This is equivalent to state "x is a real number greater than or equal to 0"
describe the translation of the point to its image: (-4,-6) to (-6,-12)
We want to translate from point (- 4, - 6) to (- 6, - 12)
If we translate a point with coordinates, (x, y) by c units to the left and d units downwards, the new coordinates would be (x - c, y - d)
Looking at the given points,
- 4 - 2 = - 6
- 6 - 6 = - 12
Thus, the point was translated by 2 units to the left and 6 units downwards
you buy rice at 0.71 Uptown one batch of fried rice requires 10 lb of rice how much does a rice for one batch cost
Consider one pound of rice costs $0.71. Then, for 10 lb of rice, you have:
cost of 10 lb of rice = 0.71 x 10 = $7.1
Hence, 10 lb of rice cost $7.1
Find the arc length of the semicircle.
Either enter an exact answer in terms of π or use 3.14 point, 14 for π and enter your answer as a decimal.
Answer:
28.26 units
Step-by-step explanation:
circumference equals 2r times pi. radius is 9 so the circumference is 2 x 9 x pi (which is 3.14). This would give is 56.52 but since its a half circle you divide it by two
find the 12th term of the geometric sequence 1,3,9,...
find the 12th term of the geometric sequence 1,3,9,...
we have
a1=1 ------> first term
a2=3
a3=9
Find the value of r (common ratio)
we have that
a2/a1=3/1=3
a3/a2=9/3=3
so
the common ratio is
r=3
we know that the general equation for a geometric sequence is
[tex]a_n=a_1\cdot r^{(n-1)}[/tex]we have
a1=1
r=3
substitute
[tex]\begin{gathered} a_n=1\cdot3^{(n-1)} \\ a_n=3^{(n-1)} \end{gathered}[/tex]Find the 12th term
so
For n=12
substitute in the equation
[tex]\begin{gathered} a_{12}=3^{(12-1)} \\ a_{12}=3^{(11)} \\ a_{12}=177,147 \end{gathered}[/tex]therefore
the answer is177,147help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 5.7 feet, Length = 10.5 feet
Step-by-step explanation:
Let the width be w. Then, the length is 2w-0.9.
[tex]w(2w-0.9)=59.85\\\\2w^2 -0.9w-59.85=0\\\\w =\frac{-(-0.9) \pm \sqrt{(-0.9)^2 -4(2)(-59.85)}}{2(2)}\\\\w =5.7\\\\\implies 2w-0.9=10.5[/tex]
Brian is sanatizing his pool and hot tub with a bag of 63 oz powdered sanatizer. If he used 1/3 of the bag on his pool and 1/7 of the bag on his hot tub how much is left in the bag?
Answer:
33 oz
Step-by-step explanation:
63x1/3=21
63x1/7=9
21+9=30
63-30=33
33 oz of powdered sanitizer is left in the bag.
I took 1/3 of 63 first, to show how much he used on the pool. Then I took 1/7 of 63 to show how much he used on the hot tub. I added the amount he used, and subtracted them from 63 to see how much was left. He had 33 oz left in the bag. Hope this helps! Good luck! :)
Let A={1,2,3,4,5,6} and B={4,6,8}. Which of the following is an element of A∩B?Select the correct answer below:3682
Given the following set:
A = {1,2,3,4,5,6}
B = {4,6,8}
∩ means "intersection" of two sets. In other words, the data that the two sets have in common.
Checking the given sets,
A = {1,2,3,4,5,6}
B = {4,6,8}
A∩B or A and B have a common data of 4 and 6. These two are the intersections of A and B.
Among the given choices, only Choice B is correct which is 6.
Therefore, the answer is CHOICE B : 6
pls help me i will fail if i get this wrong ):
The position of museum relative to hotel will be (9,1) as the starting position will be (0,0) that is her hotel then the position of coffee shop is (-2,4) and at the end position of museum is (7,5).
What is coordinate?A set of values indicating an exact position. On graphs, it is typically represented by a pair of numbers: the first number represents the distance along, and the second number represents the distance up or down. The location in the cartesian plane will be defined by the coordinate points. The distance between two points is known as the x-coordinate, or abscissa, and the distance between two points is known as the y-coordinate. To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to find the y-coordinate.
Here,
The starting coordinate=0,0
The second coordinate=-2,4
The ending coordinate=7,5
The required coordinate will be
=7--2-0,5-4-0
=9,1
The position of the museum in relation to the hotel is (9,1) because the starting point is (0,0) that is her hotel and the position of the coffee shop is (-2,4) and the position of museum is (7,5).
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A car travels at an average speed of 56 miles per hour. How many miles does it travel in 4 hours and 45minutes?
We can use the following formula to solve the exercise.
[tex]\text{ Distance }=\text{ Rate}*\text{ Time}[/tex]Then, we have:
[tex]\begin{gathered} \text{ Distance = ?} \\ \text{ Rate = 56 mph} \\ \text{ Time }=4\frac{3}{4}=\frac{4*4+3}{4}=\frac{19}{4}=4.75\text{ hours} \\ \text{ Because }\frac{45\text{ minutes}}{60\text{ minutes}}=\frac{45}{60}=\frac{15*3}{15*4}=\frac{3}{4} \end{gathered}[/tex]We replace the know values in the formula.
[tex]\begin{gathered} \begin{equation*} \text{ Distance }=\text{ Rate}*\text{ Time} \end{equation*} \\ \text{ Distance }=56\text{ mph}*4.75\text{ hours} \\ \text{ Distance }=266\text{ mi} \end{gathered}[/tex]AnswerThe car travels 266 miles in 4 hours and 45minutes.