Using the length of shadow, the height of the building to the nearest tenth is 23.4 metres.
How to find the height of the building?The length of a shadow of a building is 26 m.
The distance from the top of the building to the tip of the shadow is 35 m.
The height of the building can be found as follows:
This situation forms a right angle triangle.
Therefore, the length of the shadow is the adjacent side and the distance from the top of the building to the tip of the shadow is the hypotenuse side.
Hence, using Pythagoras theorem,
c² = a² + b²
35² - 26² = b²
1225 - 676 = b²
b² = 549
b = √549
b = 23.4307490277
Therefore, the height of the building is 23.4 m.
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what is the answer too 14:10=:55
Answer: Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Step-by-step explanation:
what percent of 51 is 127.5?20.67 is 42.5% of what?
a) We have to find what percent of 51 is 127.5.
As 127.5 is larger than 51, we expect a percentage larger than 100%.
We can find the percentage by dividing the part, 127.5, by the total, 51, and multiplying by 100%:
[tex]\frac{127.5}{51}\cdot100\%=2.5\cdot100\%=250\%[/tex]b) We have to find the value x of which 42.5% is equal to 20.67.
We can write this as:
[tex]\begin{gathered} x\cdot\frac{42.5}{100}=20.67 \\ x\cdot0.425=20.67 \\ x=\frac{20.67}{0.425} \\ x\approx48.63 \end{gathered}[/tex]Answer:
a) 127.5 is 250% of 51.
b) 20.67 is 42.5% of 48.63.
Find the 29th term of an arithmetic sequence with a1 = 2 and d =5
Arithmetic Sequence is a sequence of numbers such that the difference between each number is constant. The formula for the arithmetic sequence is given by;
[tex]a_n=a_1+(n-1)d[/tex]where An is the last term
A₁ is the first term
n is the number of terms (or number in the sequence)
d is the common difference
In our problem we are given the first term (a₁) = 2, a common difference of 5 (d = 5), and the number of terms which is 29 (n = 29).
Now in order to find the 29th term of the sequence (a₂₉), we just need to follow the formula;
[tex]\begin{gathered} a_{29}=a_1+(n-1)d_{} \\ a_{29}=2_{}+(29-1)5 \\ a_{29}=2_{}+(28)5 \\ a_{29}=2_{}+140 \\ a_{29}=142 \end{gathered}[/tex]Therefore the 29th term of the arithmetic sequence is 142.
Formula: an=a1 + (n-1) x d
a1=2
d=5
n=29
plug in the values: an= 2 + (29-1) x 5 = 142
SO THE ANSWER IS : 142
Is this the right answer to the question. Not 100% sure.
Answer:
Yes, you are correct. Lines l and m are parallel, so corresponding angles are congruent. It does follow that x = 60.
Find the quotient.0.56/−0.7
ANSWER
-0.8
EXPLANATION
The division between a positive number and a negative number gives as a result a negative number. With this in mind, we can do the division as if the numbers were both positive and then add the minus sign to the result:
Adding the minus sign, the result is -0.8
A scientist begins with 100 milligrams of a radioactive substance, which decays exponentially.after 9 hours 55mg of the substance remains How many milligrams will remain after 21 hours? Round the answer to the nearest whole number and include units
We have that the general expression for a function with exponential growth or decay is:
[tex]f(t)=ab^t[/tex]where 'a' represents the initial value, 'b' represents the growth or decay and t represents the time.
In this case, we have that a = 100, since that is the initial population (100 mg of radioactive substance). Also, since we have that after 9 hours, 55 mg of the substance remains, we have the following equation:
[tex]f(9)=55[/tex]now, given the exponential function, with a = 100, we have:
[tex]f(t)=100b^t[/tex]then, combining both expressions, we get:
[tex]f(9)=100b^9=55[/tex]solving for b, we have:
[tex]\begin{gathered} 100b^9=55 \\ \Rightarrow b^9=\frac{55}{100} \\ \Rightarrow b=\sqrt[9]{\frac{55}{100}}=0.935 \\ b=.935 \end{gathered}[/tex]then, the function is defined as follows:
[tex]f(t)=100\cdot(0.935)^t[/tex]finally, to find out how many milligrams will remain after 21 hours, we can make t = 21 and evaluate the function:
[tex]\begin{gathered} t=21 \\ \Rightarrow f(21)=100(0.935)^{21}=24.38 \\ f(21)=24.38mg \end{gathered}[/tex]therefore, there will be 24.38mg after 21 hours
Determine all solutions to the equation radical 2 times cosine 2 times x equals sine squared x plus cosine squared x on the interval [0, 2π).
Given
The equation,
[tex]\sqrt{2}\cos2x=\sin^2x+\cos^2x[/tex]To determine all the solutions in the interval [0, 2π).
Explanation:
It is given that,
[tex]\sqrt{2}\cos2x=\sin^2x+\cos^2x[/tex]Since
[tex]\sin^2x+\cos^2x=1[/tex]Then,
[tex]\begin{gathered} \sqrt{2}\cos2x=\sin^2x+\cos^2x \\ \Rightarrow\cos2x=\frac{1}{\sqrt{2}} \\ \Rightarrow2x=\cos^{-1}(\frac{1}{\sqrt{2}}) \\ \Rightarrow2x=\frac{\pi}{4} \\ \Rightarrow x=\frac{\pi}{8} \end{gathered}[/tex]Hence, the solutions of the given equation in [0, 2π) is,
[tex]a)\text{ }x=\frac{\pi}{8},\frac{7\pi}{8},\frac{9\pi}{8},\frac{15\pi}{8}[/tex]
Simplify the expression
10 - 2(-10x + 7)
Answer: 20x - 4
Step-by-step explanation:
10 - 2(-10x+7)
Distribute the -2:
10 + 20x -14
Combine Like Terms:
20x - 4
Solve each inequality.
1/2-2p>2/3
Answer:
our house and the only way I can see the only way I can see the only u new friends at the only way I can see the 77
The function g is defined as follows.
g(x)=x² +1
If the graph of g is translated vertically upward by 4 units, it becomes the graph of a function h.
Find the expression for h (x).
Answer:
Use that steps to find your answer
Answer:
h(x) = g(x) + 5 = x² + 5
Step-by-step explanation:
Since the graph is translated vertically upward by 4 units, there is no change in the x values; for the same x value the new y value is +4 times the old y value
As a first step in solving the system shown, Yumiko multiplies both sides of the equation 2x – 3y = 12 by 6. By what factor should she multiply both sides of the other equation so that she can add the equations and eliminate a variable?5x + 6y = 182x – 3y = 12factor:
Given the equations
[tex]\begin{cases}5x+6y=18 \\ 2x-3y=12\end{cases}[/tex]First, she multiplied the second equation by 6:
[tex]\begin{gathered} 6\cdot(2x-3y)=6\cdot12 \\ 6\cdot2x-6\cdot3y=6\cdot12 \\ 12x-18y=72 \end{gathered}[/tex]You have to determine the factor to multiply the equation 5x+6y=18 to be able to add both equations and eliminate one of the variables.
To do so, compare the coefficients of the like terms:
5x and 12x, "12" is not a multiple of 5, so there is no factor that when multiplied by 5x will give 12x as a product.
6y and 18y, 18 is a multiple of 6, if you multiply 6y by 3 the product will be 18y.
So, the factor you have to use to multiply the equation and eliminate one variable is 3.
The area of the scale model of a playground is 6 square yards. The scale model is enlarged by a scale factor of 3 to create the actual playground. What is the area of the actual playground?
The actual area of the playground is 54 square yards
How to determine the area?The given parameters are
Area of the scale model = 6 square yardsScale factor of dilation = 3The actual area of the playground is calculated as
Actual area = Area of the scale model * Scale factor of dilation^2
Substitute the known values in the above equation
So, we have
Actual area = 6 * 3^2
Evaluate the exponent
Actual area = 6 * 9
Evaluate the product
Actual area = 54
Hence, the value of the area is 54
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If a car will go 108 miles on a 6 gallon of gasoline in city driving. What is the rate in miles per gallon.
To find the rate in miles per gallon, divide the number of miles by the number of gallons of gasoline:
[tex]\frac{108\; \text{miles}}{6\; \text{gallons}}[/tex]Reduce the fraction by 6:
[tex]\frac{108}{6}=18\text{ miles per gallon}[/tex]The rate in miles per gallon is 18.
y=5x+50 in standard form
Answer:
-5x + y = 50
Step-by-step explanation:
to formula for standard form is Ax + By = C
the formula (y=5x+50) is in slope-intercept form, which is y=mx+b
to write (y=5x+50) in standard form, move the 'mx' (which in this case is 5x) to the other side of the '=' or also known as the equation:
y = 5x + 50
y - 5x = 5x - 5x + 50
y - 5x = 50
(here, we subtracted 5x on both sides of the equation to 'move it')
Ax = -5x
By = 1y = y
C = 50
so, to write it in the standard form:
-5x + y = 50
for each pair of equations decide whether the given value of x is a solution to one or both equations
Answers:
1. x = 2 is solution of both equations.
2. x = 3 is a solution of equation b.
3. x = -2 is solution of both equations.
4. x = -1 is solution of both equations.
5. x = -5 is solution of both equations.
Explanation:
To know if the value of x is a solution, we need to replace x with the given value. So:
1. Repalcing x by 2, we get:
a. x ( 2 + 3) = 10
2 ( 5) = 10
10 = 10
b. 2x + 3x = 10
2(2) + 3(2) = 10
4 + 6 = 10
10 = 10
The equality is true in both cases, so x = 2 is solution of both equations.
2. Replacing x by 3, we get:
a. x - 4 = 1
3 - 4 = 1
- 1 = 1
b. 4 - x = 1
4 - 3 = 1
1 = 1
Since -1 and 1 are distintc, x = 3 is a solution of equation b.
3. Replacing x by -2, we get:
a. 7x = -14
7(-2) = -14
- 14 = - 14
b. x(14) = - 28
(-2)(14) = - 28
- 28 = - 28
So, x = -2 is solution of both equations.
4. Replacing x by -1, we get:
a. x + 3 = 2
-1 + 3 = 2
2 = 2
b. 3 + x = 2
3 + (-1) = 2
2 = 2
So, x = -1 is solution of both equations.
5. Replacing x by -5, we get:
a. 3 - x = 8
3 - ( - 5) = 8
3 + 5 = 8
8 = 8
b. 5 - x = 10
5 - ( - 5) = 10
5 + 5 = 10
10 = 10
So, x = -5 is solution of both equations.
Hi can someone please explain this?
Image is attached
Answer:
B
Step-by-step explanation:
Since triangles BCD and PQR are similar, we can find BD through the three proportional sides. Line BD is to PR and option B is the only answer where BD and PR are both numerators/denominators in this case the denominators of the two fractions. Hope this helps!
help meeeeeeeeeeeeeeeeeeeeeee
thank you
The height of the object based on the information is 1963 feet.
How to calculate the height?It should be noted that a function is important to show the relationship between the variables given in the data.
In this case, the function given for the height of the object is given as:
h = 16t² + 1899
where t = time
When the time is 2 seconds, the height will be:
h = 16t² + 1899
h = 16(2)² + 1899
h = 64 + 1899
h = 1963
The height is 1963 feet.
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Solve the equation using the quadratic formula. 2y^2 + 4y + 1 = 0
Answer:
The solution to the quadratic equation is;
[tex]\begin{gathered} y=-1+\frac{\sqrt[]{2}}{2} \\ \text{and} \\ y=-1-\frac{\sqrt[]{2}}{2} \\ y=-1+\frac{\sqrt[]{2}}{2},-1-\frac{\sqrt[]{2}}{2} \end{gathered}[/tex]Explanation:
Given the quadratic equation;
[tex]2y^2+4y+1=0[/tex]Applying quadratic formula;
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Substituting the coefficients of the quadratic equation;
[tex]\begin{gathered} y=\frac{-4\pm\sqrt[]{4^2-4(2)(1)}}{2(2)} \\ y=\frac{-4\pm\sqrt[]{16^{}-8}}{4} \\ y=\frac{-4\pm\sqrt[]{8}}{4} \\ y=\frac{-4\pm2\sqrt[]{2}}{4} \\ y=\frac{-2\pm\sqrt[]{2}}{2} \end{gathered}[/tex]Therefore, the solution to the quadratic equation is;
[tex]\begin{gathered} y=-1+\frac{\sqrt[]{2}}{2} \\ \text{and} \\ y=-1-\frac{\sqrt[]{2}}{2} \\ y=-1+\frac{\sqrt[]{2}}{2},-1-\frac{\sqrt[]{2}}{2} \end{gathered}[/tex]he two-way table shows the number of students in a school who have rabbits and/or birds as pets:Have RabbitsDo Not Have RabbitsTotalHave Birds182240Do Not Have Birds253560Total4357100How many more students have rabbits than birds? (4 points)372225
The numbers we want to compare are ther number of students that have rabbits and the number of students that have birds.
The number of students that have rabbits is in the column "Have Rabbits" and, since we want all of them, we get the value from the row "Total", so the number is 43.
Similarly, the number of students that have birds is in the row "Have Birds" and, since we want all of them, we pick the number in column "Total", which is 40.
So, the number of students that have rabbits is 43 and the number of students that have birds is 40. Since 43 is 3 more than 40, there are 3 more students that have rabbits that students that have birds.
3 The table shows the average mass, in kilograms, of different sizes of cars and trucks. Size Small Car Large Car Large Truck Average Mass (kilograms) 1,354 1,985 2,460 Parta
The average mass of the large truck is 2460 kg and the average mass of the small car is 1354 kg.
Based on the given data, the mass of the large truck is 1106 kg.
Now, rounding off to the nearest hundred, the average mass of the larger truck is 2500 kg and the average mass of the small car is 1400 kg.
So, the larger truck is 1100 kg heavier than than the smaller car.
A store has clearance items that have been marked down by 40%. They are having a sale, advertising an additional 60% off clearance items. What percent of the original price do you end up paying?
Answer:
24 percent
Step-by-step explanation:
Let's say that there is a 100-dollar item. Mark that by 40 and you get 60. Marking that by 60 again gives you 24 dollars. 24 dollars is 24 percent of 100, so you only pay 24 percent of the original price.
Make the following conversions. Round your answers to 2 decimal places, where necessary.5 hours 10 minutes toa. Minutes: ? minb. Hours: ? hr
Let's do the math for this question.
A brick has dimensions of110. cm x 655 cm x 1330 cm.What is the volume of the brick in cubic meters?
Answer: We have to find the volume of the brick, the formula for the volume is as follows:
[tex]V=l\times w\times h\Rightarrow(1)[/tex]Identifying the known variables and plugging in the equation (1) gives the following answer:
[tex]\begin{gathered} l=110cm \\ w=655cm \\ h=1330cm \end{gathered}[/tex]The volume therefore is:
[tex]\begin{gathered} V=(110cm)\times(655cm)\times(1330cm) \\ V=95,826,500cm^3 \end{gathered}[/tex]Simplify: ✓- 72 O A - 6iva O B. 6iv 2 O c. 5i/3 OD. – 517 3
We want to simplify the following expression
[tex]\sqrt[]{\text{ -72}}[/tex]To do so we will use the following properties
[tex]\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}[/tex]and
[tex]\sqrt[]{\text{ -1}}=i[/tex]So we have that
[tex]\sqrt[]{\text{ -72}}=\sqrt[]{\text{ -1}\cdot72}=\sqrt[]{\text{ -1}}\cdot\sqrt[]{72}=\sqrt[]{72}i=\sqrt[]{8\cdot9}i=\sqrt[]{8}\cdot\sqrt[]{9}i=\pm3\cdot\sqrt[]{8}i=\pm3\cdot\sqrt[]{4\cdot2}i=\pm3\sqrt[]{4}\sqrt[]{2}i[/tex]which is equal to
[tex]\pm3\cdot2\sqrt[]{2}i=\pm6\sqrt[]{2}i[/tex]so options A and B are correct
given the function. calculate the following values.
Answer:
[tex]5, \sqrt{2}, 10[/tex]
Step-by-step explanation:
[tex]x=-7 \implies x<0 \implies f(-7)=5 \\ \\ x=0 \implies x \geq 0 \implies f(0)=\sqrt{2(0)^2+2}=\sqrt{2} \\ \\ x=7 \implies x \geq 0 \implies f(7)=\sqrt{2(7)^2+2}=10[/tex]
a hotel manager has 12 diferent promotional events,plans to run 4 weeks, how many events can she run
Answer: 3 per week.
Step-by-step explanation: 3 x 4 = 12.
(1 point)
Use the complete the square method to find the vertex of the following parabola:
y = x² + 16x +67
Step 1: Separate non-x-terms from x-terms
Manipulate the equation until all terms containing x are on one side of the equation, and all terms not containing x are
on the opposite side:
Step 2: Identify the value that completes the square
Step 3: Complete the Square
Step 4: Factor and solve for y
Step 5: Identify the vertex
= x² + 16x
Answer:
32
Step-by-step explanation:
Solve for x using the "Quadratic Formula". You MUST show every level of work (like you saw in the lesson) in order to receive full credit.
3x^2-5x+1
The solution to the quadratic equation 3x² - 5x + 1 using quadratic formula is; x = (5 + √13)/6 or (5 - √13)/6
How to use the quadratic formula?
The general form of a quadratic equation is given as;
ax² + bx + c = 0
The quadratic formula that is used to solve this is given by;
x = [-b ± √(b² - 4ac)]/(2a)
Now, we are given the quadratic equation as;
3x² - 5x + 1
Thus, using quadratic formula we have;
x = [-(-5) ± √((-5)² - (4 * 3 * 1))]/(2 * 3)
x = [5 ± √(25 - 12)]/6
x = (5 ± √13)/6
x = (5 + √13)/6 or (5 - √13)/6
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Translate "the sum of m and 2.33 multiplied by s is 52.25" into an algebraic equation. Do not solve the equation.
Answer:
[tex](m + 2.33) \times s = 52.25[/tex]
:)
Angela purchase a shirt for $14.65 a pair of jeans for $21.99 and she was charged $2.93 tax how much change should she receive if she paid with a $50 bill
The cost of the shirt = $14.65
The cost of the pair of jeans = $21.99
Tax = $2.93
Amount paid = $50
Change = Amount paid - (Cost of shirt + Cost of jeans + tax)
Change = 50 - (14.65 + 21.99 + 2.93)
Change = 50 - 39.57
Change = $10.43
