Step-by-step explanation:
the area of a triangle is
baseline × height / 2
now we also know that
the height in that triangle is twice its baseline.
so,
height = 2×baseline
so, for the given area we have
49 = baseline × 2 × baseline / 2 = baseline²
baseline = 7 ft.
therefore,
height = 2×baseline = 2×7 = 14 ft.
and now we run into a problem. as we don't have any further information about the triangle, the lengths of the sides cannot be determined.
the reason is that the height can be placed anywhere on the baseline (from the left end point all the way over to the right end point). all these triangles created by the moving height have the same area (49 ft²), but different lengths of the legs.
the lengths of the legs are calculated via Pythagoras, because the height splits the main triangle into 2 smaller right-angled triangles.
so, if I assume e.g. an isoceles triangle (both legs are equally long), then I know that the height splits the triangle into 2 equal triangles and the baseline in half.
then I can calculate :
leg² = (baseline/2)² + height² = 3.5² + 14² =
= 12.25 + 196 = 208.25
(each) leg = 14.43086969... ft
if I assume the height is at an endpoint of the baseline then the whole triangle is by itself a right-angled triangle.
and the height is one leg and the other leg is again via Pythagoras
leg² = baseline² + height² = 7² + 14² = 49 + 196 = 245
leg = 15.65247584... ft
all the possible solutions for the leg lengths are between 14 ft (the height) and 15.65247584... ft.
Which operation would you do first in the following equation?
10-4÷1x 5
A scale drawing is to be made of a rectangular plot of land that is 120yd x 53yd. If it is drawn to a scale of 1in.:5yd, what are the dimensions of the drawing
The dimensions of the drawing of the rectangular plot using the scale of 1in.:5yd is; 24 inches by 10.6 inches
How to represent Scale Drawings?
We are told that the dimensions of the rectangular plot of land is 120yd x 53yd.
Now, you want to draw this rectangular plot on a scale of 1 inch : 5 yards. This means that 1 inch will represent 5 yards.
Thus, for the side of 120 yards, using the scale gives us;
1/5 * 120 = 24 inches
For the side of 53 yards, using the scale gives us;
1/5 * 53 = 10.6 inches
Thus, the dimensions of the drawing of the rectangular plot using the scale of 1in.:5yd is; 24 inches by 10.6 inches
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Please helppppppppp!!!!!!!!!
Answer:
Rate of change in y is -6
-3-6 = -9
-9-6=-15
-15-6=-21
Rate of change in x is 1
1+1=2
2+1= 3
3+1 = 4
4-1=5
........And so on
using a property of operations, what can you say about the sum of two expressions
Answer: Using a property of operations, what can you say about the sum of two expressions, Then the temperature changed more on Day 2.
Step-by-step explanation:
Using a property of operations, what can you say about the sum of the two expressions.
Let us assume the table of values is : Sunrise (F) = -11.31 -7.69
Sunset (F) = 13.49 25.25
Day 1 and Day 2
Sunrise Temperature (F) = -11.31 -7.69 (eq-1)
Sunset Temperature (F) = 13.49 25.25 (eq-2)
The sum of the two equations are:
Sunrise Temperature (F) = -11.31 -7.69
(F) = -19
Sunset Temperature (F) = 13.49+ 25.25
(F) = 38.74
Which day saw the greatest variation in temperature? Describe your thinking. To do this, we only compute the absolute difference in daily temperatures between the times of sunrise and sunset.
So, we can write
Day 1 = |-11.31 - 13.49|
Day 1 = 24.8
Day 2 = |-7.69 - 25.25|
Day 2 = 32.94
So, 32.94 is greater than 24.8
Therefore, Day 2 is greater than the Day 1
Hence, the temperature changed more on Day 2.
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A box of cereal can be purchased in the large size, which is 15 ounces for $3.14, or the family size, which is 24 ounces for $5.34. Which size box of cereal has the lowest price per ounce, and what is the amount?
a -Large size at $0.21 per ounce
b-Large size at $0.22 per ounce
c-Family size at $0.21 per ounce
d-Family size at $0.22 per ounce
Given the values that we have here for the large sizes and the family size of cereal the one that has the lowest price per ounce is that of the Large size at $0.21 per ounce
How to solve for the sizes of the cerealsFor the family size
We would first have to divide 5.34 by 24
= 5.34 / 24
= 0.22 per dollar
For the large size we have
15 ounces for $3.14
= 3.14 / 15
= 0.21 dollars
Hence we can see that the size of the cereal that is the lowest price per ounce is given as Large size at $0.21 per ounce
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someone help me please!!
Answer: Distance point is 8.
Step-by-step explanation:
You would do 2 by the power of 2 and double that (8)
What does x equal if log (1+3 x)=3 ?
The required value of x using the properties of exponents and logarithm is 6.362.
What are the various properties of the logarithm?
Out of several properties of logarithms, some of the main properties are given below:
Product Rule
log (ab) = log a + log b
Change of base
log ₇ x = log x / log 7
Power Rule
log a² = 2 log a
Quotient Rule
log (a / b) = log a - log b
Solving the given equation for x
We are given a logarithmic expression: log (1 + 3x) = 3
On applying exponent both sides, we get,
e^[log (1 + 3x)] = e^3
Using the properties of exponents and logarithm, we get,
1 + 3x = 20.0855
3x = 19.0855
x = 6.362
Hence, the required value of x can be 6.362.
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You owe $1,032.56 on a credit card with an 11.25% APR. The minimum due is $67.00
and you pay it at the beginning of the month. How much interest is accrued by the end of the month?
Interest accrued at the end of the month is $1.41.
What is the interest on credit card?Credit cards impose interest on any sums that you don't pay by the due date each month. Interest accrues everyday when you hold a balance from month to month based on the so-called Daily Periodic Rate (DPR). DPR is only another term for your daily interest charge.
Step 1: Make the initial payment of $882 ($1,032 - $150).
Step 2: $882 times 1.00938 is $890.27
Step 3: Pay $1,032 multiplied by 1.00938 ($1,041.68) at the conclusion.
Step 4. $1,041.68 - $150= $891.68
The interest for the first month is $1.41.
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How many 1/3 ounce spoonfuls of salt are in a filled 4 3/4 ounce Salt shakers
Answer:15 spoonfuls
Step-by-step explanation:
Three points of a parrallelogram are (4,3)(-4,3)(-4,3) and (2,-3) what are the coordinates of the 4th point that would complete the parallelogram
The fourth point of the parallelogram is (10, -3).
What is Parallelogram?
A Parallelogram is a quadrilateral with opposite sides parallel.
Given that;
Three points of a parallelogram are (4,3), (-4,3) and (2,-3).
Now, Take Two points at one diagonal of parallelogram are (4, 3) and
(2, -3).
Let fourth point of a parallelogram is (x, y).
Take (-4,3) and (x, y) on the another diagonal of a parallelogram.
Since, Midpoint of both diagonal is same.
Hence, Midpoint of (4, 3) and (2, -3) is calculated as;
(4+2/2, 3+(-3)/2) = (6/2, 0/2) = (3, 0)
So, Midpoint of (4, 3) and (2, -3) = (3, 0)
And, Midpoint of (-4,3) and (x, y) = (-4+x/2, 3+y/2)
Since, Midpoint of both diagonal is same.
Hence, (-4+x/2, 3+y/2) = (3, 0)
Equating coordinates we get;
⇒-4+x/2 = 3
⇒ -4 + x = 6
⇒ x = 6 + 4
⇒ x = 10
And, 3+y/2 = 0
⇒3 + y = 0
⇒y = -3
So, The fourth point of the parallelogram is (10, -3).
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Using complete sentences describe the transformation from the parent function f(x)= |x| to g(x)=-2 |x+3|
Answer:
The transformation from the parent function is a translation of 3 units left, a vertical stretch of scale factor 2, and a reflection in the x-axis.
Step-by-step explanation:
Given function:
[tex]\text{g}(x) = -2|x+3|[/tex]
Parent function:
[tex]\text{f}(x) = |x|[/tex]
A parent function is the simplest form of a family of functions.
The graph of g(x) is related to the graph of f(x) by a series of transformations. To determine the series of transformations, work out the steps of how to go from f(x) to g(x).
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]
[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]
[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]
[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]
[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]
Step 1
Translation left by 3 units:
[tex]\implies f(x+3) =|x+3|[/tex]
Step 2
Stretch in the direction of the y-axis (vertically) with scale factor 2:
[tex]\implies 2f(x+3) =2|x+3|[/tex]
Step 3
Reflection in the x-axis:
[tex]\implies -2f(x+3) =-2|x+3|[/tex]
Conclusion
The transformation from the parent function is a translation of 3 units left, a vertical stretch of scale factor 2, and a reflection in the x-axis.
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Point t is on line segment \overline{su} su . given st=3x+2,st=3x+2, tu=3x+4,tu=3x+4, and su=5x+9,su=5x+9, determine the numerical length of \overline{su}. su .
Given that Point T is on line segment SU, T is collinear with S and U, and the numerical length of SU is 24.
Since Point T is on line segment SU, then S, T, and U are collinear.
Collinear points refers to the points that lies on the same straight line.
IF S, T, and U are collinear, then the sum of the numerical length of ST and the numerical length of TU is equal to the numerical length of SU.
ST + TU = SU
Given:
ST = 3x + 2
TU = 3x + 4
SU = 5x + 9
Substitute the expressions in the equation and solve for x.
ST + TU = SU
3x + 2 + 3x + 4 = 5x + 9
3x + 3x - 5x = 9 - 2 - 4
x = 3
Substitute the value of x in the expression for SU.
SU = 5x + 9
SU = 5(3) + 9
SU = 24
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given that x is a number that is not negative, kelvin conjectured that x2>x 1. which value is a counterexample to kelvin's conjecture? −12 negative one half −2 negative 2 0 0 5
0 is a counterexample to Kelvin's conjecture.
Firstly rewriting the expression -
x²>x + 1
Now, we will use hit and trial method to find the counterexample to Kelvin's conjecture.
We can not use first two options, because question mentions that x is not negative. So, starting our hit and trial method from 0.
We will keep the value in expression to find the result -
0²>0 + 1
0 > 1
This contradicts or opposes Kevin's statement, as 0 is not greater than 1.
Trying the second number -
5²>5 + 1
25 > 6
This is in accordance with Kevin's conjecture or conclusion, as 25 is greater than 6.
Hence, 0 is the value which is a counterexample to Kelvin's conjecture.
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The complete question is -
Given that x is a number that is not negative, Kelvin conjectured that x^2>x+1 .
Which value is a counterexample to Kelvin's conjecture?
−12
−2
0
5
Evvie has these dight card 4 5 0 8 2 she makes them into 6 digit number larger than 300.000 and smaller than 400.000
Step-by-step explanation:
500.000 evvie was on the digit card
Old McDonald had a farm. And on that farm he had 38 animals, some
horses and some chickens. Altogether, there were 94 animal legs in the
farm. Solve for the number of Horses and Chickens.
Answer:
Heya, your answer would be 52 horses, and 42 chickens.
Step-by-step explanation:
By doing the long, long and I mean long process of adding 2 + 2 or 4 + 4 (due to the fact chickens have 2 legs and horses have 4), we get to 52 horse legs, and 62 chicken legs.
Adieu
Answer:
There are 9 horses and 29 chickens.
Step-by-step explanation:
a = animals
a = 38
h = horses
c = chickens
l = legs
l = 94
Equation 1: h + c = 38
Horses have 4 legs. Chickens have 2 legs.
Equation 2: 4h + 2c = 94
Manipulate the equations so that one of the coefficients are the same.
We will multiple Equation 1 by 2 so that both equations have 2c.
Equation 1: 2h + 2c = 76
Equation 2: 4h + 2c = 94
Subtract Equation 1 from Equation 2.
Equation 2 - Equation 1
(4h + 2c) - (2h + 2c) = 94 - 76
(4h - 2h) + (2c - 2c) = 94 - 76
2h = 18
h = 9
Substitute h into either equation to solve for c.
Equation 1: 2h + 2c = 76
Equation 1: 2(9) + 2c = 76
Equation 1: 18 + 2c = 76
Equation 1: 2c = 76 - 18
Equation 1: 2c = 76 - 18
Equation 1: 2c = 58
Equation 1: c = 29
Equation 2: 4h + 2c = 94
Equation 2: 4(9) + 2c = 94
Equation 2: 36 + 2c = 94
Equation 2: 2c = 94 - 36
Equation 2: 2c = 58
Equation 2: c = 29
There are 9 horses and 29 chickens.
If you can't help me with that answer then can you help me with this one please?
Answer:
73° & 107°
Step-by-step explanation:
1. Those angles are supplementary, so they add up to 180 degrees.
2. (8x - 20) + (8x + 8) = 180
3. You need to add both 8x's together to make 16x. Do the same with -20 & 8. That makes -18. This is binomial addition.
4. 16x - 18 = 180
5. Add 18 to both sides
6. 16x = 198
7. Divide both sides by 16
8. x = 12.375
9. Plug in your x for both angles.
Is the expression 33x33^7 equivalent to (33x33)^7? Explain.
Answer:
Step-by-step explanation:
no because perenthesis
Answer:
No it is not equivalent because the parenthesis
Step-by-step explanation: When it comes to parenthesis you have to do the problem in them, so you would do 33x33 rather than the whole problem at once. no idea if that makes sense bff it sounded right in my head
Can somebody simplify this? (−8) × (-6) − (−5)²
Answer:
23Step-by-step explanation:
Can somebody simplify this?
(−8) × (-6) − (−5)² =
48 - 25 =
23
Solve the equation.
1/3 (
(9x + 3) = 3x + 1
Answer: x=0
Step by step explanation:
1/3 (9x+3) =3x+1
=3x+1=3x+1
=3x-3x=1-1
=0x=0
So x=0
I hope this helps you! Have a nice day!!!!
Which graph represents the inequality 3y - 5x≤-6?
Answer: Graph A represents the given inequality 3y−5x>−6. Option A is correct.
From the graphs, the graph is to choose which best describes the inequality 3y−5x>−6
Step-by-step explanation: hope this helps
Graph A represents the inequality 3y - 5x≤-6. Correct option is A. The inequality 3y - 5x ≤ -6 represents a linear inequality in two variables, y and x.
To graph this inequality, we can rearrange it into slope-intercept form (y = mx + b), where m is the slope, and b is the y-intercept.
Let's rearrange the given inequality:
3y - 5x ≤ -6
First, add 5x to both sides of the inequality:
3y ≤ 5x - 6
Now, divide both sides by 3 to isolate y:
y ≤ (5/3)x - 2
Now, you have the inequality in slope-intercept form:
y ≤ (5/3)x - 2
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What is 0.00784 rounded to 2 significant figures? Pls I need this quick
The answer would be 0.0078
The decimal number 0.00784 rounded off to 2 decimal places is 0.
What is rounding off of numbers?We round off numbers to make them easier to remember and it also keeps its value approximately to the place it has been rounded off.
To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.
Given, 0.00784 and we have to round off to two significant figures means
the number will have 2 digits after the decimal place.
Now, 0.00784
= 0.00780.
= 0.0078.
= 0.0080.
= 0.008.
= 0.010.
= 0.01.
= 0.00.
= 0.
So, 0.00784 rounded off to 2 decimal places is 0.
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This year, a small business had a total revenue of $14,200. If this is 29% less than their total revenue the previous year, what was their total revenue the previous year?
The total revenue the previous year is $20,000
How to calculate the total revenue ?This year the total revenue of the small business is $14,200
This amount is 29% less than the total revenue in the previous year
Therefore the total revenue in the previous year can be calculated as follows
100 - 29
= 71
= 71/100
= 0.71
Total revenue= 14,200/0.71
= 20,000
Hence the total revenue the previous year is $20,000
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What is the solution of the system?
4 x+2 y=4
6 x+2 y=8
(F) (-2,2)
(G) (2,-2)
(H) (1,2)
(I) (-1,2)
For the system of equations 4 x+2 y = 4 and 6 x+2 y = 8, the solution is (2, - 2).
We are given the system of equations as:
4 x+2 y = 4 … (1)
6 x+2 y = 8 … (2)
We need to solve it to find the value of x and y.
Subtracting equation (1) form equation (2), we get that:
6 x - 4 x + 2 y - 2 y = 8 - 4
Combining the like terms, we get that:
2 x = 4
x = 4 / 2
x = 2
Now put it in equation (1) to get the value of y
4 (2) + 2 y = 4
8 + 2 y = 4
2 y = - 4
y = - 2
(x, y) = (2, - 2)
Therefore, we get that, for the system of equations 4 x+2 y = 4 and 6 x+2 y = 8, the solution is (2, - 2).
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The midpoint of BC is M(5, 2). One endpoint is B(8, 0). Find the coordinates of the other endpoint C. Write the coordinates as decimals or integers. C = (, ) Submit
The coordinate of point C from the given expression is (2, 4)
Midpoint of coordinatesThe formula for calculating the midpoint of coordinates is given by the equation shown below:
Midpoint = {(x₁+x₂)/2, (y₁+y₂)/2}
Given the following parameters
Midpoint = M(5, 2)
B(8, 0)
Required
Coordinate point C
Substitute the given parameters
5 = (8+x₂)/2
5(2) = 8+x₂
10 = 8+x₂
x₂ = 2
Similarly
2 = (0+y₂)/2
2(2) = 0+x₂
4 = 0 +y₂
y₂ = 4
Hence the coordinate of point C from the given expression is (2, 4)
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Explain why the expansion at the right of log₄√t/s is incorrect. Then do the expansion correctly.
The correct expansion of log₄√t/s is 1/2 log₄(t/s).
Logarithms is another way of writing exponents. Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only. Understanding logs is not so difficult. To understand logarithms, it is sufficient to know that a logarithmic equation is just another way of writing an exponential equation.
Logarithm and exponent are inverse forms of each other. One can understand this from the section below. Initially, a mathematician named John Napier introduced logarithms for making calculations in a simple way and this concept is quickly adopted by other scientists, engineers, etc.
Given that, log₄√t/s and we have to expand this logarithmic function having base 4 accordingly. So, let's proceed to solve this logarithmic expansion.
log₄√t/s = log₄((t/s)^(1/2))
= log₄((t/s)^(1/2))
Apply log rule, logₐ(xᵇ) = b.logₐ(x), assuming x ≥ 0
= 1/2 log₄(t/s)
Hence, log₄√t/s = 1/2 log₄(t/s) is the correct expansion.
Therefore, 1/2 log₄(t/s) is the required answer.
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-5x^2-2x^3-4x write the polynomial in standard form then identify the polynomial by the number of terms
Answer: - 2x³ - 5x² - 4x, trinomial
Step-by-step explanation:
When writing a polynomial, the standard form is to have the terms ordered from highest power to lowest power. 3 > 2, so we will reorder them as so;
- 5x² - 2x³ - 4x ➜ - 2x³ - 5x² - 4x
To identify the polynomial, we will look at the number of terms. This polynomial has three terms, so it is a trinomial.
- 2x³ - 5x² - 4x
[1] - 2x³
[2] - 5x²
[3] - 4x
4 1/4 *-1/2= I really help on this it's for homework and I don't know if our teacher will be helping with it so please please please will somebody help me please.
Eli takes a typing test and types all 240 words in 1/12 hour. he takes the test a 2nd time and types all the words in 1/15 hour. was he faster or slower on the 2nd attempt.
Answer: he was faster the second time
Step-by-step explanation:
1/15 is a smaller fraction and 1/12, 1/15 of an hour is 4 minutes and 1/12 of an hour is 5 minutes, so he took it in 4 minutes the second time which was quicker
So basically what you have to do is subtract the above ground level (1) with ground level (4) and you’ll get 3 which is negative bc it counts as below ground level . Now that the car rises 13 meters subtract 13-3= 10 and add it with the other ground level 6 meters . 10-6=4
Rollercoaster Car is at 4 m above the ground by using integer concept.
As per the question statement, Rollercoaster Car that goes above and below the ground.
Before solving the question, we need to know the concept of integer operations on a number line.
Here the car is [tex]1 meter[/tex] above the ground level and then goes 4 meter down.
So the position is [tex]1-4=-3 meter[/tex] or 3 meter below the ground level.
Now it rises 13 meter above the ground. So now the position is [tex]-3+13 = 10 meter[/tex] or 10 meter above the ground.
Now it again falls by 6 meter so position is [tex]10-6 = +4 meters[/tex] or 4 meters above the ground.
Therefore the final position is 4 meters above the ground level.
Integers: a number without a fraction (no decimals). Includes the digits 1, 2, 3, etc., in counting, zero {0}, and the antithesis of the numerals "-1, -2, -3,... " We can classify them all in the following order: {..., -3, -2, -1, 0, 1, 2, 3, ...}To learn more about integers and its operations, click on the link given below:
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-46 decreased by the difference between -23 and -61
When -46 decreased by the difference between -23 and -61, the number becomes -18.
What is the value of the subtraction?
Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign that is used to represent subtraction is -.
According to mathematical rules, when two negative signs are multiplied by each other, the number becomes positive.
The difference between -23 and -61: -61 - (-23)
-61 + 23 = -38
-46 - (-38)
-46 + 28 = -18
Here is the complete question:
-46 decreased by the difference between -23 and -61. What is the value of the number?
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