Answers
The area of a triangle is given by the formula:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ \text{ Where b is the base and} \\ h\text{ is the height of the triangle} \end{gathered}[/tex]From the information given you know that the measure of the height of the triangle EFG is 16 cm but the measure of the base of the triangle is unknown.
To find the measure of the base, you can first find the measure of the middle of the segment EG using the Pythagorean theorem, since the triangle formed by the vertices F, G, and EG/2 form a right triangle. Graphically,
The formula of the Pythagorean Theorem is
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where c is the hypotenuse and} \\ a,b\text{ are the sides of the triangle} \end{gathered}[/tex]So, you have
[tex]\begin{gathered} a=16 \\ b=\frac{EG}{2} \\ c=20 \\ (16)^2+b^2=(20)^2 \\ 256+b^2=400 \\ \text{ Subtract 256 from both sides of the equation} \\ 256+b^2-256=400-256 \\ b^2=400-256 \\ b^2=144 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{b^2}=\sqrt[]{144} \\ b=12 \\ \text{ Then} \\ \frac{EG}{2}=12 \end{gathered}[/tex]Then, the measure of the segment EG, that is, the measure of the base of the triangle EFG is
[tex]\begin{gathered} \frac{EG}{2}=12 \\ \text{ Multiply by 2 on both sides of the equation} \\ \frac{EG}{2}\cdot2=12\cdot2 \\ EG=24 \end{gathered}[/tex]Finally, the area of triangle EFG will be
[tex]\begin{gathered} b=24\operatorname{cm} \\ h=16\operatorname{cm} \\ A=\frac{b\cdot h}{2} \\ A=\frac{24\operatorname{cm}\cdot16\operatorname{cm}}{2} \\ A=\frac{384\operatorname{cm}^2}{2} \\ A=192\operatorname{cm}^2\text{ } \end{gathered}[/tex]Therefore, the area of the triangle EFG is 192 square centimeters.
Related Questions
-Describe the expression.Suvolino bolo2 * 5+7(3 + 13)+Which of the following describes(7 in the expression above?A. factor(B, sumC. quotientD. product
Answers
Answer
A. factor
Explanation
The given expression is 2 x 5 + 7(3 + 13)
In the expression given, '7' represents a factor because after adding 3 and 13, you would need to multiply it by 7.
Hence, the correct option is:
A. factor
4x = -3x - 7 need help
Answers
Solve the equation for x, solve the operations between similar terms.
[tex]\begin{gathered} 4x=-3x-7 \\ 4x+3x=-7 \\ 7x=-7 \\ x=-\frac{7}{7} \\ x=-1 \end{gathered}[/tex]x has a value of -1.
Add 7 3/10 simlify the answer and write it as a mixed number ?17/3011 7/2511 7/3011 17/30
Answers
To add mixed numbers first, we can add the whole numbers:
[tex]7+4=11[/tex]Now, we can add the fractions. For this, we can find the lowest common denominator (LCD) of both denominators. The LCD is the lowest number that is evenly divisible by both numbers. Since the denominators of the fractions are 10 and 15, the LCD is 30 because 30 is the smallest number that is divisible by 10 and 15. Then, we have:
[tex]\begin{gathered} \frac{3}{10}+\frac{4}{15}=\frac{3\cdot3}{10\cdot3}+\frac{4\cdot2}{15\cdot2} \\ \frac{3}{10}+\frac{4}{15}=\frac{9}{30}+\frac{8}{30} \\ \frac{3}{10}+\frac{4}{15}=\frac{9+8}{30} \\ \frac{3}{10}+\frac{4}{15}=\frac{17}{30} \end{gathered}[/tex]Therefore, the result of adding the given mixed numbers is:
[tex]$$\boldsymbol{7\frac{3}{10}+4\frac{4}{15}=11\frac{17}{30}}$$[/tex]If the product of the extremes is 8,then the geometric mean is..
A. 2
B. 4
C. 2/2
Answers
Answer: THE ANSWER TO THAT IS C
Step-by-step explanation:
Jan made a mixed vegetable soup using tomatoes and carrots. Forty percent of the
tomatoes. If she used a total of 50 tomatoes, how many carrots should she use?
Answers
Jan should use 75 carrots for mixed vegetable soup.
Let us assume the total number of tomatoes and carrots be x. So, as per the mentioned information, the equation will be -
40%×x = 50
Converting percentage to fraction
40/100×x = 50
x = 50×100/40
Cancelling zero and performing division
x = 5×25
Performing multiplication
x = 125
Total number of vegetables = number of tomatoes + number of carrots
125 = 50 + Number of carrots
Number of carrots = 125 - 50
Performing subtraction
Number of carrots = 75
Therefore, Jan should use 75 carrots.
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The complete question is -
Jan made a mixed vegetable soup using tomatoes and carrots. Forty percent of the mixed vegetables were tomatoes. If she used a total of 50 tomatoes, how many carrots should she use?
Answer:
Step-by-step explanation:
75 carrots should be used
John ordered a large three topping pizza for $7.50 and a large 8 topping pizza for $10. Write an equation in slope intercept form to describe the situation.
Answers
Explanation
Step 1
[tex]\begin{gathered} \text{large pizza(3 toppings)}\rightarrow7.5 \\ \text{large pizza( }8\text{ toppings)}\rightarrow10 \\ \text{then we have 2 points of the line} \\ (3,7.5) \\ (8,10) \end{gathered}[/tex]Step 2
find the slope
the slope is given by:
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]Let
P1(3,7.5)
P2(8,10)
replace
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{10-7.5}{8-3}=\frac{2.5}{5}=0.5 \\ \text{slope}=0.5 \end{gathered}[/tex]Step 3
usin P1 (3,7.5) ans m= 0.5 find the equation
[tex]\begin{gathered} y-y_1=m(x-x_0) \\ \text{replace} \\ y-7.5=0.5(x-3) \\ y-7.5=0.5x-1.5 \\ y=0.5x-1.5+7.5 \\ y=0.5x+6 \end{gathered}[/tex]I hope this helps you
A line has a slope of 8 and passes through the point (0,5). What is its equation inslope-intercept form?Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
The form of the equation of the line in slope-intercept form
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept
The y-intercept is the value of the y-coordinate when the x-coordinate is equal to zero
Therefore in our case
m=8
b=5
We substitute the values
[tex]y=8x+5[/tex]ANSWER
y=8x+5
The mean output of a certain type of amplifier is 129 watts with a variance of 100.
If 96 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 0.9 watts? Round your answer to four decimal places.
Answers
The probability is given by -0.001, that the mean of the sample would differ from the population mean by less than 0.9 watts.
What is normal probability distribution?
Normal distribution also known as the Gaussian probability, ia a probability distribution that is symmetric about the mean, showing that data bear the mean are more frequent in occurrence than data far from the mean.
In a set with mean μ and standard deviation (which is the square root of the variance) σ , the z score of a measure X is given by:
Z =X-μ/σ
we have given μ =129
σ = [tex]\sqrt{100}[/tex] n = 96
This is the pvalue of Z when X = 129+1.7 =130.7 subtracted by the pvalue of Z when X = 129 - 1.7 = 127.3
When X = 130.7
Z =X-μ/σ
Z = 130.7-129/10
Z = 0.17 pvalue = 0.1699
When X = 127.3
Z =X-μ/σ
Z = 127.3-129/10
=-0.17 pvalue
0.1699 - 0.1700 = -0.001
Hence the probability is -0.001
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Identify the independent and dependent variables
the amount of gasoline in a car's fuel tank and the amount of time spent driving
Answers
Answer:
The independent variable is the time spent drive and the dependent variable with the amount of gas in the tank
Step-by-step explanation:
Does the gas in the tank depend on the time driving or does the time driving depend on the amount of gas in the car.
The amount of gas is the tank is determined by how much time the car is driven.
Solve the following proportion for y.y/5 = 7/8Round your answer to the nearest tenth.
Answers
The given proportion is expressed as
y/5 = 7/8
If we crossmultiply, it becomes
y * 8 = 7 * 5
8y = 35
y = 35/8
y = 4.375
Rounding to the nearest tenth,
y = 4.4
Help please this one is tricky
Answers
B; False
Here, we want to establish if there is a relationship between two variables
From the question, it was stated that at higher speeds, the ticket fee to be paid will be higher
So, what this mean is that the amount of ticket fee to be paid is a factor of the speed at which she was traveling
This directly makes the speed the independent variable while the ticket fee (value depends on the speed of travel) represents the dependent variable
Hence, we can establish that that the ticekt fee is a function of the speed and not the other way round
This makes the correct option FALSE
Factor completely the trinomial 10x^2 + 19x + 7
Answers
From the problem :
[tex]10x^2+19x+7[/tex]Factor completely :
We need to find the factors of 10 and 7
We have :
10 = 1 x 10
10 = 2 x 5
7 = 1 x 7
We will do trial and error, The sum of the product of the factors must be equal to the middle term which is 19
Let's say for 10 = 1 x 10 and 7 = 1 x 7
(1 x 7) + (1 x 10) = 17 not equal to 19
(7 x 10) + (1 x 1) = 71 not equal to 19
try the other factors of 10.
10 = 2 x 5 and 7 = 1 x 7
(2 x 7) + (5 x 1) = 19 Equal to 19
Now we have the factors, let's arrange in this way :
[tex](O+I)(I+O)[/tex]O will be the outer and I will be the inner.
O is the paired factors of 10 and 7
For O, we have 2 and 7
For I, we have 5 and 1
This will be :
[tex](2x+5)(x+7)[/tex]The answer is (2x + 5)(x + 7)
Which describes the pedestrian crossing sign shown?
The sign is a trapezoid because exactly one pair of opposite sides is parallel.
The sign is a parallelogram because both pairs of opposite sides are parallel.
The sign is a kite because both pairs of opposite sides are congruent.
The sign is a parallelogram because at least one pair of opposite sides is parallel
Answers
The sign is a parallelogram because both the pairs of the opposite sides are parallel.
A parallelogram is a quadrilateral with two sets of parallel sides. A parallelogram has opposing sides that are the same length and angles that are the same size. the internal angles on the same side that are in addition to the transversal. The sum of all interior angles is 360 degrees.
Characteristics of a parallelogram:
The contrasting sides are parallel and congruent.Angles that diverge line up.The following angles act as a fallback.If any one of the angles is a right angle, then all the angles will be at right angles.Split in half are the two diagonals.Each diagonal divides the parallelogram into two equal and congruent triangles.A parallelogram's diagonals are equal to the sum of its squares.To learn more about parallelogram visit :
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Answer:
B
Step-by-step explanation:
cual es el valor absoluto de -x+2
Answers
The absolute value of -x+2 is 2-|x-2|.
What is the Absolute Value ?
The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is indicated by the symbol |x|.
Since the absolute value is isolated, we set it equal to the positive and negative of the constant
Therefore,
|(-x+2)| =
for x < 2, -(-x + 2)
for x ≥ 2, (x + 2)
Hence, This is so that no matter the value of x, the value of the function is always greater or equal to 0.
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A recipe for 2 dozen whole-wheat requires 600g of flour. How many muffins can be made with 900g of flour?
Answers
when we have a proportion it is defined as
[tex]\frac{a}{b}=k\cdot\frac{c}{d}[/tex]what this means is that we have a constant of proportionality which means that is the same term
[tex]\frac{8}{9}=\frac{16}{17}[/tex]there is not a proportion between both sides menaning that the expression is false.
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
How many squares will it take to fill up the large empty square?
A. 5
B. 10
C. 25
D. 50
Answers
You can use the Pythagorean theorem on the triangle formed in between the the squares to find that the large empty square has a length of 5 on each side.
To find the area, multiply length by with: 5 x 5=25.
3b(u - 8) - n(u – 8) =
Answers
Answer:
3bu - 24b -nu + 8n
Step-by-step explanation:
Expanded
Write the linear equation that gives the rule for this table.
x y
3 13
4 14
5 15
6 16
Answers
To get y, you always need to add 10.
A packet of carrot seeds has a germination rate of 92%. In other words, the probability of any
seed sprouting is 0.92. How many seedlings would you expect in a row of 50 seeds?
Answers
The number of constructive seedlings in a row of 50 seeds is 46.
What is probability of a given event and how can it be analyzed?
Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability generally refers to the degree to which something is likely to occur. Utilize probability to ascertain how likely something is to occur. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty. Every event's probability in a sample space is one.
Given, the germination rate of the seeds to seedlings is = 92%
Therefore, the probability of any seed sprouting is 0.92.
Hence the required number of seedlings can be expected in a row of 50 seeds = 50*0.92 = 46 seeds
Thus, the number of constructive seedlings in a row of 50 seeds is 46.
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What is this number in standard form?
(5 × 1, 000) + (7 × 10) + (8 × 1) + (4 × ) + (1 × 1.000)
Answers
16,518
(or 1.6518 x 10⁴)
7 • 10 = 70
8 • 1 = 8
1 • 1.000 = 1
Then you add the answers together.
You put 4 x but you didn’t put whatever you had to multiply it by. So multiply and add the answer too. And that will be your answer
What is the product of 4 1/5 * 5 ³/7? 22 4/5 20 3/35 20 31/35 22
Answers
The answer is 75
Plea helpppppp asap, Ik This is easy for you guys but yeah I’m just stupiad
Answers
Answer:
Figure 3
Step-by-step explanation:
That is a trapezoid, not a parallelogram.
Ms. U.S. Bonds invested a total of $4500, some at 9% per year and the rest at 6% per year. The return for the 9% investment exceeds that from the 6% investment by $180. How much did she Invest at each rate
Answers
Using simple interest, the amounts she invested are given as follows:
$3,000 at 9%.$1,500 at 6%.Simple InterestSimple interest is used when there is a single compounding per time period, usually measured in years.
The amount of money after t periods in is modeled by:
A(t) = P(1 + rt)
The interest accrued after t periods is modeled by:
I(t) = Prt
In which:
P is the initial amount.r is the interest rate, as a decimal.She had two investments, investing a total of $4500, hence:
[tex]P_1 + P_2 = 4500[/tex]
The return for the 9% investment exceeds that from the 6% investment by $180, hence:
[tex]I_2 = 0.06(4500 - P_1)[/tex][tex]I_1 = 0.09P_1[/tex][tex]I_2 = I_1 - 180[/tex]Then:
[tex]I_2 = 0.06(4500 - P_1)[/tex]
[tex]I_1 - 180 = 0.06(4500 - P_1)[/tex]
[tex]0.09P_1 - 180 = 0.06(4500 - P_1)[/tex]
[tex]0.15P_1 = 450[/tex]
[tex]P_1 = \frac{450}{0.15}[/tex]
[tex]P_1 = 3000[/tex]
Which is the amount invested at 9%, hence the amount invested at 6%, considering that a total of $4,500 was invested, is given by:
4500 - 3000 = $1,500.
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What is 8 1/3 times 6 2/5
Answers
Answer:53.312
Step-by-step explanation: 8.33 x 6.40
How to do because I dont know need help ASAP 20 points
Answers
Some arithmetic sequences could be easier to write as functions. As long as I know what value "n" has, I can find out any term in a particular Sequence whenever I need to. You might choose the implicit term over the prior term of a Sequence if it is known.
What is meant by Arithmetic Sequences?The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values.
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Some arithmetic sequences could be easier to write as functions. You are aware of the prior term.
Consider that we only have the numbers (...,4,...) from an arithmetic sequence with a common difference of 5.
The complete question is:
You are given the first four terms of an arithmetic sequence. Under what conditions might a recursive formula be preferred over the explicit formula? Under what conditions might an explicit formula be preferred over the recursive formula?
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Roland's farm land is assessed at 1.5 million dollars and the improvements for $500,000.
At a tax rate of 4 mills, how much are Rolan's monthly taxes?
Answers
At a tax rate of 4 mills, Rolan's monthly taxes are $667.00.
What is the mill rate?The amount of tax due per $1 of a property's assessed value is known as the mill rate. The word mill comes from the Latin millesimum, which means thousandth. In terms of property tax, 1 mill is the amount of property tax levied per $1,000 of the assessed value of a property. Divide the mill rate by 1,000 and multiply the assessed value of the property to determine the property tax.Given:
Assessed value = 1.5 million dollars
Amount for Improvements = $500,000
Tax rate = 4 mills
Total assessment of the property = Assessed value + Improvements
= 1,500,000 + 500,000
= $2,000,000
Multiply these 2 million by 4 mills then divide by 1000.
(2,000,000 × 4)/1000
= $8000 in annual taxes
To calculate the monthly tax amount divide by 12.
$8000/12 = $667.00
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Decrease £50 by 60%
need help asap!! imma be posting a lot
Answers
When £50 is decreased by 60%, the remaining value is £20.
What is a percentage?A percentage refers to the ratio of a variable expressed as a fraction of 100.
Percentages show the proportional value contained in another.
We use the percent sign (%) to denote percentages, which may be increases or decreases.
Initial value = £50
Percentage decrease = 60%
Percentage change = 40% (1 - 60%)
In monetary terms, the final value after the percentage decrease = £20 (£50 x (1 - 60%).
Thus, when £50 is reduced by 60% the value left is only 40% of the former deal, which is £20.
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what is the solution to the equation below? (round your answer to two decimal places.) 6•inx=9.1
Answers
ANSWER
B. x = 4.56
EXPLANATION
To solve this equation, first, we have to divide both sides by 6,
[tex]\begin{gathered} \frac{6\cdot\ln x}{6}=\frac{9.1}{6} \\ \\ \ln x=\frac{9.1}{6} \end{gathered}[/tex]Then apply the base exponent rule of logarithms,
[tex]a^{\log_ab}=b[/tex]So, in this case, we have to raise e to each side of the equation,
[tex]\begin{gathered} e^{\ln x}=e^{9.1/6} \\ \\ x\approx4.56 \end{gathered}[/tex]Hence, the solution is x = 4.56, rounded to two decimal places.
A triangle has side lengths of (5k-3) centimeters, (k+1) centimeters, and (m-7) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answers
The expression for the perimeter of the triangle is 6k + m -9.
How to calculate perimeter of the triangle?
In mathematics, the perimeter of any closed shape means addition of all the sides. Therefore, triangle has three sides and their addition represents the perimeter. It can be measured in different units like meters, centimeters, etc.
According to the question, the given parameters for the triangle is as written below:
The side lengths are: (5k - 3); (k + 1) and (m - 7)
Now, the perimeter of a triangle is addition of all the sides. That means,
Perimeter of a triangle = 5k - 3 + k + 1 + m - 7 = 6k + m - 9
Hence, the expression for the perimeter of the triangle is 6k + m -9.
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Classify each polynomial by degree and number of terms 1. X^3 + 5x 2. X^2 - 2x - 1 3. 5x^4 4. 6x^5 - 3x^2 + 7x + 9 5. -11x - 5 6. 4x^2 + 10THESE ARE THE OPTIONS Degree Name using degree 0 Constant1 Linear2 quadratic3 Cubic4 quartic5 quintic6 6th degree
Answers
1)
[tex]\begin{gathered} x^3\text{ + 5x} \\ \text{cubic , 2 terms} \end{gathered}[/tex]2) The term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second degree
[tex]\begin{gathered} x^2-2x-1 \\ \text{quadratic, 3 terms} \end{gathered}[/tex]3) of or relating to the fourth degree. a quartic polynomial or equation.
[tex]\begin{gathered} 5x^4 \\ \text{quartic, 1 term} \end{gathered}[/tex]4) quintic : a polynomial or a polynomial equation of the fifth degree.
[tex]\begin{gathered} 6x^5-3x^2\text{ + 7x + 9} \\ qu\text{intic , 4 terms} \end{gathered}[/tex]5)
[tex]\begin{gathered} =11x\text{ - 5} \\ L\text{inear , 2 terms} \end{gathered}[/tex]6)
[tex]\begin{gathered} 4x^2\text{ + 20} \\ \text{quadratic, 2 terms} \end{gathered}[/tex]