~Given:
The right triangle ABC,
Use the Pythagorean theorem to find the length of the third side
\(\begin{gathered} AC=\sqrt[]{20^2+21^2} \\ AC=\sqrt[]{841} \\ AC=29 \end{gathered}\)The triangle DEF IS,
Use Pythagorean theorem.
\(\begin{gathered} DF^2=DE^2+EF^2 \\ 58^2=40^2+EF^2 \\ EF^2=1764 \\ EF=42 \end{gathered}\)It is also observed that sides of the triangles DEF are multiple sides of triangle ABC,
\(\begin{gathered} DE=40=2\times AB \\ EF=42=2\times BC \\ DF=58=2\times AC \end{gathered}\)Therefore,
\(\Delta ABC\text{ \textasciitilde }\Delta DEF\)Factor the quadratic expression completely.
-7x^2-24x-9
Answer:
(7x+3)(-x-3)
Step-by-step explanation:
-7x²-24x-9 would be the same thing as (7x+3)(-x-3) because 7x*-x=-7x², +3*-3=-9, and 7x*-3 - 3x = -24x
Suppose that 17 inches of wire costs 85 cents. At the same rate, how many inches of wire can be bought for 65 cents?
Answer:
13 inches
Step-by-step explanation:
17=85
1=85/17
1=5
Now
For 65 cents,
65=nx5
65/5=n
n=13 inches
Answer: 13 inches
Step-by-step explanation:
To solve this problem you would need to make a ratio.
A Ratio can be the symbol, : , / or the word to.
In this case you would need to do the problem as shown:
17/85 = x/65
First you would need to cross multiply, then flip the equation. And should end up with something like this:
85x =1105
Then Divide both sides by 85.
85x/85 = 1105/85
Answer:
X= 13
9 less than the quotient of 2 and x.
the answer is 2/x-9
Answer:
\( \dfrac{2}{x} - 9\)
Step-by-step explanation:
the quotient of 2 and x:
\( \dfrac{2}{x} \)
9 less than the quotient of 2 and x:
\( \dfrac{2}{x} - 9\)
27,813 students took the ACET this year. If only 2,836 students were admitted into the Ateneo among those students, what is the Ateneo’s acceptance rate? a. 7.5% b. 10.2% c. 13.4% d. 9.0%
If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.
How the rate is determined:The rate is the ratio of one value, expression, measurement, or quantity compared to another.
The rate represents the quotient of the numerator and the denominator.
The rate is expressed as a percentage by multiplication with 100.
The number of students who took the ACET this year = 27,813
The number of students who were admitted into the Ateneo = 2,836
The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)
= 10.2%
Thus, we can conclude that the acceptance rate or percentage is Option B.
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Jason can peel 15 potatoes in 25 minutes. Janette can peel 8 potatoes in 1/10 hour. If they start peeling at the same time how many
minutes will it take them to peel 406 potatoes?
9514 1404 393
Answer:
210 minutes
Step-by-step explanation:
Jason's rate of peeling is ...
(15 potatoes)/(25 minutes) = 15/25 potatoes/minute = 3/5 potatoes/minute
Janette's rate of peeing potatoes is ...
(8 potatoes)/(6 minutes) = 4/3 potatoes/minute
Their combined rate is ...
(3/5 +4/3) = (9 +20)/15 = 29/15 . . . . potatotes/minute
Then the time required for 406 potatoes is ...
(406 potatoes)/(29/15 potatoes/minute) = (406×15/29) minutes
= 210 minutes
Help Please!!!
That partitions the segments into a ratio of 3 to 2
let's say the segment with A(-5 , -8) and B(10 , 7) gets partitioned by point C
\(\textit{internal division of a line segment using ratios} \\\\\\ A(-5,-8)\qquad B(10,7)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{2}\implies \cfrac{A}{B} = \cfrac{3}{2}\implies 2A=3B\implies 2(-5,-8)=3(10,7)\)
\((\stackrel{x}{-10}~~,~~ \stackrel{y}{-16})=(\stackrel{x}{30}~~,~~ \stackrel{y}{21}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-10 +30}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-16 +21}}{3+2} \right)} \\\\\\ C=\left( \cfrac{ 20 }{ 5 }~~,~~\cfrac{ 5}{ 5 } \right)\implies C=(4~~,~~1)\)
Answer:
( 4, 1 )
Step-by-step explanation:
5. Lisa has a cubed-shaped box with a
volume of 512 cm. If Lisa fills the box
with 1-cubic centimeter blocks, how
many blocks make up each layer?
Answer:
64
Step-by-step explanation:
\(\sqrt[3]{512} = 8\\8x8 = 64\)
Someone help what would be the evaluation of this?
What is the slope of a line that is perpendicular to the line y = 1/6 x + 4? The slope of the line is .
Answer:
-6
Step-by-step explanation:
The slope of a perpendicular line has the slope of the opposite and reciprocal of the current line. We would get -1/6 and then -6.
What is the average rate of change for this quadratic
function for the interval from x=2 to x = 4?
A. 12
B. -6
C. -12
D. 6
-10-
Click here for long description
SUBMIT
The average rate of change of the function over the interval is -6
Finding the average rate of changeFrom the question, we have the following parameters that can be used in our computation:
The graph
The interval is given as
From x = 2 to x = 4
The function is a quadratic function
This means that it does not have a constant average rate of change
So, we have
f(2) = -3
f(4) = -15
Next, we have
Rate = (-15 + 3)/(4 - 2)
Evaluate
Rate = -6
Hence, the rate is -6
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which of the following must be true to prove abc = def by the aas the theorem
In 1–2 sentences, explain how a fossil is found.
Please hurry!!!
a fossil is usually found by digging underground
.
Answer: a fossil is usually found under layers and layers of rock. you can find one by digging deep enough
Need help! 37 points.
Answer:
c and d
Step-by-step explanation:
cause
Answer:
C & D
Step-by-step explanation:
Because all the others are going like 4,12, u get what i mean, and the other go by, 5,10,15,20 thats what they mean by propertional realtionship lol, hope this helps l
Please help ASAP! Thank you
Answer:
a. lines intersecting at a single point
b. one solution
Step-by-step explanation:
a. The equations can be rewritten as:
y = -5x+23 and y = -1/6x+1
Comparing the equations with standard equation: y=mx+c, where m is the gradient of the line formed by the linear equation.
Since the gradient of the lines are different then the lines cannot be parallel and will intersent at one point.
b. The equation will have one solution as below.
The equations can be rewritten as:
5x+y=23
5x+30y=30
Subtracting both equation will result in,
29y=7
=> y=7/29
Hence x= 660/29
I need this answer!!!
Answer:
2 feet per second
Step-by-step explanation:
6/3 is 2
PLEASE HELP!
What is the weight of 7 bags, each weighing 7 kg?
Hey!
There are 7 bags, and all 7 of them weigh 7 kg.
To find the weight, multiply 7 * 7 (amount of bags * current known weight)
7 * 7 = 49
The 7 bags weigh 49 kg.
I will give brainleist pls
Answer:
C
Step-by-step explanation:
We can immediatly rule out A and B because the Quotient is bigger than the Divisor.
We can then rule out D because 2,016 does not round to 2,200.
The answer is C. 2,184 can round to 2200 and the Divisor is bigger than the quotient.
Answer:
C
Step-by-step explanation:
This is quite simple as we can find the answer out on the first hint itself. The first hint says the divisor, 2 number in the equation or number you are dividing by, can be rounded to 50, which means it is in the range of 45-54. We can see the only divisor in that range is C. To go with the other hints, though, the dividend, first number, can be rounded to 2,200 which means it is in the range of 2,151-2,250. All of them pass that, so on to the next hint. It says the quotient, number you get as answer, is smaller than the divisor, which we found is in the range of 45-54. Answer choices A and B do not follow this as the divisors of their equation are obviously smaller than the quotient, so we can conclude C to be our answer
Please help 18points
Mofor has homework assignments in five subjects. He only has time to do two of
them.
The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.
If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:
1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.
2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.
3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.
The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.
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Jeffrey needs $200 to buy a new iPod. Right now, he has $75. What percent of the $200 does he have?
PLEASE HELPPP
Answer:
40%
Step-by-step explanation:
Answer:
If you need help on further questions like this, divide what he has to what he needs or his goal
in order to get 37.5% you have to divide 75/ 200
You will get 0.357 and that is 37.5% this is ABOUT 40% but I reccomend putting 37.5% to be safe.
Find the compound ratio of 2:3 and 5:4
The compound ratio of natural number ratios 2 : 3 and 5 : 4 is equal to 5 : 6.
How to determine a compound ratio
Herein we must determine a compound ratio, that is, the product of two ratios, whose definition is shown below:
For a : b and c : d, where a, b, c, d are natural numbers, the compound ratio is equal to (a · c) / (b · d).
If we know that a : b = 2 : 3 and c : d = 5 : 4, then the compound ratio is equal to:
r = (2 · 5) : (3 · 4)
r = 10 : 12
Finally, we simplify the resulting expression:
r = 5 : 6
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help needed brainliest will be given for attempt
What is an example of how public conduct, even outside of the office itself, can affect one’s job?
Answer:
What is an example of how public conduct, even outside of the office itself, can affect one’s job?
Step-by-step explanation:
help ASAP DUE in 10 minutes do not spam or you will get reported A farmer wants to increase the area of his rectangular pen but keep the pen a rectangular shape. He decides to add 5.7 yards of fencing to the width of the pen, but the length will remain 9.5 yards. The new area will be 77.9 square yards.
Answer:
The one you have selected is correct. 9.5(w+5.7)=77.9
Step-by-step explanation:
Area is length x width, but the length is the same. So, the 9.5 is not in the parentheses. The existing width (w) is having 5.7 yards added on before being multiplied for area calculations. Because of the order of operations, (w+5.7) must be in parentheses so it is done before multiplication.
Answer:
9.5(w+5.7)=77.9
Step-by-step explanation:
took the test
Find the area of the figure shown
Answer:
21.75 m^2
Step-by-step explanation:
area of a triangle =base*height/2
=8.7 * 5/2
=43.5/2
=21.75 m^2
Answer:
21.75m^2
Step-by-step explanation:
5x8.7= 43.5
43.5/2 = 21.75
the following pair of triangles are similar. find the value of x 10 x x+2 x+14
The numerical value of x in the similar pair of triangle is 10.
What is the numerical value of x?A ratio is simply the relation between two amounts showing how many times a value is contained within another value.
From the diagram,
Side A of the small triangle = 10
Side B of the small triangle = x + 2
Side A of the Big triangle = 10 + x
Side B of the big triangle = x + 14
Hence;
Ratio of Side A to Side B of the small triangle = 10 / x + 2
Ratio of Side A to Side B of the Big triangle = 10 + x / x + 14
Since the triangle area similar, equate the two ratio and solve for x.
10 / ( x + 2 ) = ( 10 + x ) / ( x + 14 )
Cross multiply
10( x + 14 ) = ( 10 + x )( x + 2 )
Expand using FOIL method
10x + 140 = 10x + 20 + x² + 2x
10x + 140 = x² + 12x + 20
x² + 12x + 20 = 10x + 140
x² + 12x + 20 - 10x - 140 = 0
x² + 2x - 120 = 0
Factor the left side of the equation
( x - 10 )( x + 12 ) = 0
Hence;
x - 10 = 0 and x + 12 = 0
x = 10 and x = -12
Since the dimension of the triangle cannot be negative,
x = 10
Therefore, the value of x is 10.
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4 divided by 0.572 whats the answer
Answer:
6.993006
Step-by-step explanation:
repeated
Simplify to a single trig function or constant with no fractions.
We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.
The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:
cosec(t) = 1/sin(t)
tant(t) = sin(t)/cos(t)
Substituting these expressions into the original expression, we get:
cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))
The sin(t) term in the numerator and denominator cancel out, leaving:
cosec(t)tant(t) = 1/cos(t)
Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:
cosec(t)tant(t) = 1/sec(t)
Therefore, we can simplify cosec(t)tant(t) to sec(t).
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Convert 25.0 miles per hour to meters per second. Round the answer to the nearest tenth. (1 mile = 1,609 meters and 1 hour = 3,600 seconds)
A. 10 m/s
B. 11 m/s
C. 11.1 m/s
D. 11.2 m/s
E. 11.17 m/s
\(3x² -10 = -37\)
\( {3x}^{2} - 10 = - 37 \\ = > {3x}^{2} = - 37 + 10 \\ = > {3x}^{2} = - 27 \\ = > {x}^{2} = \frac{ - 27}{3} \\ = > {x}^{2} = - 9 \\ = > x = \sqrt{ - 9} \\ = > x = - 3 \: \: or \: \: \: 3\)
Answer:x = -3 or 3
Hope it helps.
Do comment if you have any query.
Using the image below, answer the following questions. Be sure to answer all three questions, in order.A. Do RS and UV have equivalent slopes? Yes or noB. What is the slope of SQC. Name a segment that has an undefined slope.
A. Do RS and UV have equivalent slopes?
Let's determine their slopes.
Slope of RS:
\(\text{ Slope of RS = }\frac{\text{ Rise}}{\text{ Run}}\text{ = }\frac{\text{ 6 units}}{\text{ 6 units}}\text{ = 1}\)Slope of UV:
\(\text{ Slope of UV = }\frac{\text{ Rise}}{\text{ Run}}\text{ = }\frac{\text{ 3}}{\text{ 3}}\text{ = 1}\)Therefore, the answer is YES. They have the same slopes.
B. What is the slope of SQ.
Given:
Point 1 = Point Q = (-2, 1)
Point 2 = Point S = (-8, 1)
Let's determine the slope.
\(\text{ Slope = m = }\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{\text{ 1-1}}{-8\text{ - (-2)}}\text{ = }\frac{0}{-8+\text{ 2}}=\frac{0}{-6}\text{ = 0}\)Therefore, the slope of SQ is 0.
C. Name a segment that has an undefined slope.
Vertical lines are said to have an "undefined slope," as their slope appears to be some infinitely large, undefined value.
In the given figure, segments QR and TU are vertical lines.
Therefore, segments QR and TU have an undefined slope.