Adam and Kevin are standing 35 metres apart, on opposite sides of a flagpole. From Adam’s position, the angle of elevation of the top of the flagpole is 36°. From Kevin’s position, the angle of elevation is 50°. How high is the flagpole?
Isaac made all these rectangles with 24cm lengths of string. This implies that the perimeter of all these rectangles are equal
Final answer:
When Isaac uses 24cm of string to make rectangles, no matter the individual dimensions, the sum of the length and width of these rectangles must always be 12 cm. This is a direct result of the fixed perimeter, which requires that the combined measurements of length and width halves the total perimeter to maintain the consistent total string usage.
Explanation:
Isaac made all these rectangles with 24cm lengths of string, which implies that the perimeter of all these rectangles is equal. The observation about the sum of the length and the width of these rectangles is that regardless of the individual measurements of the length and width, their sum must always be half the total perimeter of the rectangle. Given a fixed perimeter of 24cm, the formula for the perimeter of a rectangle (P) is
P = 2(l + w),
where l is the length and w is the width. Since the perimeter is given as 24cm, this simplifies to
24 = 2(l + w), or 12 = l + w.
This equation means that the sum of the length and width of the rectangles must always equal 12 cm. This is because the total loop made by the string when forming the rectangle has to be divided into four edges, two lengths, and two widths, which totals the provided 24cm of string. Therefore, if we adjust either the length or the width, the other measurement must adjust in such a way that their sum remains constant at 12 cm to maintain the total perimeter as 24cm.
Find two numbers if their sum is 3 and their difference is 21
PLZ HELP!!!!
Triangle GHI is similar to triangle JKL. If JP = 26, MH = 36 and PK = 16 then GM =
A.
44.3
B.
58.5
C.
86
D.
117
If you were solving a system of equations and you came to a statement like 4 = 4, what do you know about the solution to the system? (1 point) The solution is (4, 4) The solution is x = 4 and y = 4 There is no solution There are infinitely many solutions
Answer:
There are infinitely many solutions.
Step-by-step explanation:
While solving a system of equations, if we get a true statement like 1=1, then there will be "infinitely many solutions" and if we get a false statement like 1=2, then there will be "no solution".
Here the statement is 4=4, which is a true statement.
So, there are infinitely many solutions.
What is the area of this polygon?
Enter your answer in the box.
Batman is 4 times robins age. The sum has f their ages is equal to 45. How old is Batman and robin?
Answer:
Robin is 9 years old and Batman is 36 years old
Step-by-step explanation:
Batman: 4x
Robin: x
4x + x = 45
5x = 45
x= 9
Juanita is making bread.She needs 3 1/2 cups of flour.Juanita only has a 1/4-measuring cup.How many 1/4 cups of flour will Juanita use to prepare he bread?
Eliza paints a circle on her bedroom wall as part of a mural. After she paints it, she decides that she wants a much bigger circle. So, she multiplies her original radius by four and repaints the circle. Which statement best describes Eliza's solution?
a.) The area of the new circle is two times larger.
b.) The area of the new circle is four times larger.
c.) The area of the new circle is eight times larger.
d.) The area of the new circle is 16 times larger.
Answer: d.) The area of the new circle is 16 times larger.
Step-by-step explanation:
Let the radius of the original circle be r.
Then the area of the original circle will be :-
[tex]\text{A}_1=\pi r^2[/tex]
When she multiplies her original radius by four and repaints the circle.
The new radius = [tex]R=4r[/tex]
Then the area of the new circle will be :-
[tex]\text{Area}=\pi R^2\\\\\Rightarrow\ \text{Area}=\pi (4r)^2\\\\\Rightarrow\ \text{Area}=\pi (16r^2)\\\\\Rightarrow\ \text{Area}=16\pi r^2\\\\\Rightarrow\ \text{Area}=16(\pi r^2)\\\\\Rightarrow\ \text{Area}=16A_1[/tex]
Hence, The area of the new circle is 16 times larger.
Jackson's kitten weighted 2 pounds and 3 ounces. A month later the kitten weighted 56 ounces. How much weight did the kitten gain in that month?
1 pound= 16 ounces
***Need answered ASAP***... PLEASE
What happens to the temperature of the remaining liquid when some if the liquid evaporates?
A. Increases
B. decreases
C. Does not change
D. The change cannot be determine
PLEASE FULL ANSWERS! need all the help I can get
Bill and Greg are walking in opposite directions with speeds of 45 and 75 feet per minute. When they started, the distance between them was 20 feet. What will be the distance between them in 2.5 min?
Answer:
The distance between them in 2.5 min will be 320 ft
Step-by-step explanation:
Let
x--------------> Bill distance after 2.5 min------- > speed 45 ft/min
y--------------> Greg distance after 2.5 min------> speed 75 ft/min
z-------------> distance between them in 2.5 min
we Know that
z=x+y+20
Remember that
To find the distance multiply the speed by the time
so
x=45*2.5=112.5 ft
y=75*2.5=187.5 ft
therefore
z=x+y+20-----------> 112.5+187.5+20=320 ft
Final answer:
Bill and Greg's total distance apart after 2.5 minutes is 320 feet, calculated by adding their initial distance of 20 feet to the distance they covered in 2.5 minutes at their combined speed of 120 feet per minute.
Explanation:
Bill and Greg are walking away from each other with speeds of 45 and 75 feet per minute, respectively.
Since they are moving in opposite directions, their relative speed is the sum of their individual speeds, which is 45 + 75 feet per minute, or 120 feet per minute.
To find the distance between them after 2.5 minutes, we multiply their relative speed by the time elapsed. Therefore, the distance is:
Distance = Speed × Time = 120 feet/minute × 2.5 minutes = 300 feet.
We must also include the initial distance between them, which was 20 feet, so the total distance after 2.5 minutes is:
Total distance = Initial distance + Distance covered in 2.5 minutes = 20 feet + 300 feet = 320 feet.
A piece of wire 32cm Long is cut into two parts. Each part is bent to form a square. Given that the total area of the two squares is 34cm square, find the perimeter of each square
The possible perimeters for the squares are 20 cm and 12 cm, depending on how the wire is cut.
Let's denote the length of one part of the wire as x and the length of the other part as 32−x. Each part is bent to form a square.
The perimeter (P) of a square is given by 4 × side length.
The side length of the first square ([tex]S_1[/tex] ) is x/4, and the side length of the second square ([tex]S_2[/tex] ) is (32−x)/4.
The total area of the two squares is given as [tex]34cm^2[/tex] , so we can write the equation:
[tex]S^2_1 + S^2_2 = 34[/tex]
Substitute the expressions for [tex]S_1 and S_2[/tex] :
[tex](\frac{x}{4})^2 + (\frac{(32-x)}{4})^2 =34[/tex]
Now, solve for x:
[tex]\frac{x^2}{16} + \frac{(32-x)^2}{4} =34[/tex]
Multiply both sides by 16 to get rid of the denominators:
[tex]x^2 +(32-x)^2=544[/tex]
Expand and simplify:
[tex]x^2+1024-64x+x^2 =544[/tex]
Combine like terms:
−64x+480=0
Divide the entire equation by 2 to simplify:
−32x+240=0
Now, factor the quadratic equation:
(x−20)(x−12)=0
So, x=20 or x=12.
If x=20, the lengths of the two parts are 20 cm and
32−20=12 cm.
If x=12, the lengths of the two parts are 12 cm and
32−12=20 cm.
Now, we can find the perimeter of each square by multiplying the side length by 4:
For x=20, the perimeter is [tex]4 \times \frac{20}{4} = 20 cm[/tex]
For x=12, the perimeter is [tex]4 \times \frac{12}{4} = 12 cm[/tex]
So, the possible perimeters for the squares are 20 cm and 12 cm, depending on how the wire is cut.
help me please !!! Surface area
a sperm whale can stay underwater 7 times longer than a sea cow can.how long can a sperm whale stay underwater?
The sperm whale's underwater duration is seven times that of the sea cow, showcasing remarkable breath-holding abilities, likely adapted for deep-sea foraging and hunting.
The relationship between the underwater durations of a sperm whale and a sea cow suggests that the sperm whale's capability is sevenfold that of the sea cow. Let's denote the sea cow's duration as "x." Accordingly, the sperm whale's underwater duration would be 7 times x.
In practical terms, if we assume the sea cow can stay submerged for 10 minutes (x = 10), then the sperm whale, being seven times more proficient, can stay underwater for 7 times 10, which is 70 minutes (7x = 7 * 10 = 70). This sevenfold difference implies a significant contrast in their breath-holding abilities.
The numerical representation extends universally; if the sea cow can endure underwater for "x" units of time, the sperm whale can endure for 7 times "x" units of time. This relationship showcases the remarkable adaptation of the sperm whale to extended submersion, likely linked to its deep-sea foraging behavior and hunting strategies.
In essence, the sperm whale can stay underwater for a duration that is seven times longer than that of the sea cow, highlighting its remarkable breath-holding capacity.
A sperm whale can stay underwater for 7 times longer than a sea cow, so it can stay underwater for 7 times the duration of a sea cow.
If a sperm whale can stay underwater 7 times longer than a sea cow, we can express this relationship as:
Time a sperm whale can stay underwater = 7 * Time a sea cow can stay underwater
So, if we let the time a sea cow can stay underwater be represented by 'x', then the time a sperm whale can stay underwater is:
7 * x
Therefore, a sperm whale can stay underwater for 7 times longer than a sea cow, which means it can stay underwater for 7x.
PLEASE HELP ASAP
The solutions to a certain quadratic equation are x=-4 and x=3. Write the equation in standard form below.
First correct answer will receive brainiest !!
Convert the rectangular coordinates (4, –4) into polar coordinates.
On which triangle can the law of cosines be applied once to find an unknown angle measure? Law of cosines: a2 = b2 + c2 – 2bccos(A)
options are in the pics
Answer: The correct option is 4.
Explanation:
The formula of law of cosine is,
[tex]a^2=b^2+c^2-2bc\cos(A)[/tex]
Where a,b,c are sides of the triangle and A is the interior angle of vertex A.
Reason for correct option:
From the above formula we can easily conclude that to find an unknown angle measure we need the length of all sides of the triangle.
In figure 4 all sides are given, so the correct option is 4.
Reason for incorrect option:
In figure 1,2 and three all sides are not known, so we can apply the cosine rule to mind the unknown angle measure.
Therefore option 1,2 and 3 are incorrect.
what is y−2=−3(x−7) written in standard form?
a square parking lot has an area of 225 yards.There is a sidewalk along one side of the parking lot.How long is the sidewalk
Answer: 56.25
Step-by-step explanation:
Since there are four sides to a square and the area is 225 yards you would -
225 yards/ 4 sides
= 56.25 yards per side
Mitsu borrowed $1,250. She made 36 payments of $45.15 each. How
much did she pay in interest?
a. $375.40
b. $162.54
c. $1,625.40
d. $37.54
If f(x)=4^x-1+6 and g(x)=2x-5, what is (f-g)(x)?
A. (f-g)(x)=4^x-1-2x-1
B. (f-g)(x)=4^x-1-2x+11
C. (f-g)(x)=4^x-1-2x-11
D. (f-g)(x)=4^x-1-2x+1
Answer:
B is correct.
Step-by-step explanation:
Leonardo da Vinci drew a portrait of a young woman. The portrait is shaped like a rectangle. It is 13.5 inches long and 10 inches wide. What is the length of a diagonal that connects one corner of the portrait to the other? Round the answer to the nearest tenth of an inch.
WZ←→ is tangent to circle O at point B.
What is the measure of ∠OBZ?
80º
90º
160º
180º
Answer:
The correct option is 2.
Step-by-step explanation:
Given information: WZ is tangent to circle O at point B.
According to the tangent of circle theorem: The tangent line is perpendicular to the radius at the point of tangency. It means the angle formed on the point of tangency by tangent and radius is a right angle.
Since WZ is tangent to circle O at point B and OB is radius, therefore
[tex]\angle OBZ=90^{\circ}[/tex]
Therefore correct option is 2.
The measure of angle ∠OBZ is 90°, as the tangent line to a circle at a point is perpendicular to the radius at that point.
Explanation:The question regards the measure of angle ∠OBZ where WZ↔ is tangent to circle O at point B. By a well-known theorem in geometry, a line tangent to a circle is perpendicular to the radius drawn to the point of tangency. Therefore, the measure of angle ∠OBZ, which is formed by the radius OB and the tangent line at B, must be 90°.
The solution for the following system of equations is shown on the graph. What is the solution? y = 3x - 5 y = 1 3 x + 3 A) (3, 3) B) (3, 4) C) (4, 3) D) (4, 6)
Answer:3,4.b
Step-by-step explanation: Took the test.
Solve 3x+11= k for x.
A. x=3k-11
B. x=k-11
C. k+11
x=———
3
D. k-11
x= ———
3
Answer: the correct option is (D) [tex]x=\dfrac{k-11}{3}.[/tex]
Step-by-step explanation: We are given to solve the following equation for the value of x :
[tex]3x+11=k~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given equation for x, we need to take x on one side and all other terms on the other side of the equality.
The solution of equation (i) is as follows :
[tex]3x+11=k\\\\\Rightarrow 3x=k-11\\\\\Rightarrow x=\dfrac{k-11}{3}.[/tex]
Thus, the required value of x is [tex]x=\dfrac{k-11}{3}.[/tex]
Option (D) is CORRECT.
The amount of trout y (in tons) caught in a lake from 1995 to 2014 can be modeled by the equation y = -0.08x2 + 1.6x + 10, where x is the number of years since 1995. When were about 15 tons of trout caught in the lake? The year and the year .
About 15 tons of trout were caught in the lake in the years 1999 and 2011.
To determine the years when about 15 tons of trout were caught in the lake, we need to solve the equation [tex]\( y = -0.08x^2 + 1.6x + 10 \) for \( y = 15 \).[/tex]
The equation becomes:
[tex]\[ 15 = -0.08x^2 + 1.6x + 10 \][/tex]
Subtract 15 from both sides to set the equation to zero:
[tex]\[ 0 = -0.08x^2 + 1.6x - 5 \][/tex]
This is a quadratic equation in the form of [tex]\( ax^2 + bx + c = 0 \)[/tex], where:
- ( a = -0.08 )
- ( b = 1.6 )
- ( c = -5 )
We solve this quadratic equation using the quadratic formula [tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \):[/tex]
First, calculate the discriminant [tex]\( \Delta = b^2 - 4ac \):[/tex]
[tex]\[ \Delta = (1.6)^2 - 4(-0.08)(-5) \][/tex]
[tex]\[ \Delta = 2.56 - 1.6 \][/tex]
[tex]\[ \Delta = 0.96 \][/tex]
Now, calculate the two possible values of ( x ):
[tex]\[ x = \frac{-1.6 \pm \sqrt{0.96}}{2(-0.08)} \][/tex]
Calculate [tex]\( \sqrt{0.96} \):[/tex]
[tex]\[ \sqrt{0.96} \approx 0.9798 \][/tex]
Now solve for ( x ):
[tex]\[ x_1 = \frac{-1.6 + 0.9798}{-0.16} \][/tex]
[tex]\[ x_1 = \frac{-0.6202}{-0.16} \][/tex]
[tex]\[ x_1 \approx 3.88 \][/tex]
[tex]\[ x_2 = \frac{-1.6 - 0.9798}{-0.16} \][/tex]
[tex]\[ x_2 = \frac{-2.5798}{-0.16} \][/tex]
[tex]\[ x_2 \approx 16.12 \][/tex]
Since ( x ) is the number of years since 1995:
For [tex]\( x_1 \approx 3.88 \):[/tex]
[tex]\[ \text{Year} = 1995 + 4 = 1999 \][/tex]
For [tex]\( x_2 \approx 16.12 \):[/tex]
[tex]\[ \text{Year} = 1995 + 16 = 2011 \][/tex]
Therefore, about 15 tons of trout were caught in the lake in the years 1999 and 2011.
Which professional needs the knowledge of statistics and geometry in order to comprehend maps, graphs and charts? Pilot, banker, fashion designer, or an architect?
Answer:
The correct answer is pilot. I took the test
Step-by-step explanation:
What is the slope of this skateboard ramp if it rises 1.2 meters above the ground and runs 4 meters horizontally at the base?
Final answer:
The slope of the skateboard ramp, calculated using the rise over run formula, is 0.3. This is found by dividing the rise of 1.2 meters by the run of 4 meters.
Explanation:
The slope of a ramp is calculated as the rise divided by the run. To find the slope of the skateboard ramp, which rises 1.2 meters above the ground and runs 4 meters horizontally at the base, you would use the formula:
Slope (m) = Rise / Run
Here, the rise is the height the ramp rises above the ground, which is 1.2 meters, and the run is the distance along the ground, which is 4 meters horizontally. By substituting the given rise and run into the formula, you obtain:
Slope (m) = 1.2 m / 4 m = 0.3
So, the slope of the skateboard ramp is 0.3.