The sum of two real numbers is 18 and the product is 70. what are the two numbers?
How you know when there is only one solution triangle possible from a side-side-angle?
Answer:
There will be only on solution if either of these conditions is met:
the given angle is opposite the longest sidethe triangle is a right triangle (the ratio of the side opposite the angle to the other given side is equal to the sine of the angle)Step-by-step explanation:
Consider the SSA geometry with the angle placed in standard position at the origin and its adjacent given side (the second side of SSA) extending along the +x axis. Draw a circle having a radius equal to the length of the first side of SSA, centered on the vertex between the two segments on the +x axis.
There are three possibilities for the way this circle intersects the other ray of the angle (the ray that is not the x-axis):
the first side is as long or longer than the second side, so there is one point of intersection (one solution to the triangle, purple in the attachment)the first side is just long enough to be tangent to the other ray, so there is one point of intersection (one solution to the triangle, green in the attachment)the first side is between these lengths, so intersects the other ray in two places, giving two solutions to the triangle, red in the attachment.a bag contains 5 red marbles, 3 yellow marbles, and 2 blue marbles. Once a marble is drawn, it is not replaced.what is the probability of drawing a blue on the first draw and a second blue marble on the next draw ?
A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) represents any point on the directrix.
What are the steps required to find the equation of the parabola?
if M and N are midpoints in a diagram below, determine values for x and y
The sum of six consecutive odd numbers is 204. What is the fourth number in the sequence
Which of the following ordered pairs is a solution to the equation 2x+7y=8
Select one:
a. (3, -2)
b. (2, -3)
c. (-3, 2)
d. (0, 4)
find the value of x if f(x) equals 7 f(x) equals 4x minus 1
What polynomial identity should be used to prove that 20 = 36 − 16
Diffrence of squares is the correct answer just score pract q
Don is 6 feet tall. at a given time of day, he measures his shadow to be 13 feet long. at the same time, he measures the shadow length of a nearby tree to be 51 feet. how tall is the tree
The height of the tree maintaining the given ratio is 23.54 feet.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
Don height = 6 feet
His shadow = 13 feet
The ratio of height to shadow = 6/13
Tree height = x (let's say)
Tree shadow = 51 feet
Ratio = x/51
Both ratios must be the same, therefore,
x/51=6/13
x=23.54 feet
Hence "The height of the tree maintaining the given ratio is 23.54 feet".
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(06.06) Which of the following demonstrates the Commutative Property of Multiplication? 3(4a − 2) = 12a − 6 3(4a − 2) = (4a − 2) ⋅ 3 12a − 6 = (4a − 2) ⋅ 3 (3 ⋅ 4a) − 2 = 3(4a − 2)
The point (-2, 6) is on the line given by which of the equations below?
A.
y = 4x
B.
y = 2x
C.
y = 3x
D.
y = -3x
A rectangular flower garden has area 32 square feet. if the width of the garden is 4 feet less than the length, what is the perimeter, in feet, of the garden?
The perimeter of the garden is 24 feet.
What is a Rectangle?A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.
How to solve it?We have, an area is 32 and width is 4,
so, the length will be 32/4 = 8 feet.
The perimeter will be 2(8+4) = 2(12)= 24 feet.
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if a metal tool chest has the shape of a prism with a pentagonal base of 6194in squared in area, calculate the volume of the metal chest and pick where length c = 6 inches and length m = 19 inches
The volume of the metal tool chest is 37,164 cubic inches. To calculate the volume of the metal tool chest, we use the formula for the volume of a prism: Volume = Base area × Height
Given that the pentagonal base has an area of 6194 square inches, and the length c (which represents the height) is 6 inches, we can calculate the volume as follows:
Volume = 6194 in² × 6 in
Volume = 37,164 cubic inches
So, the volume of the metal tool chest is 37,164 cubic inches.
As for the lengths provided:
c = 6 inches (height)
m = 19 inches (unknown side length of the pentagon)
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What is 5.928301 to 2 decimal places?
Final answer:
To round 5.928301 to 2 decimal places, we observe the third decimal place. It's 8, so we round up, making the answer 5.93.
Explanation:
When rounding the number 5.928301 to 2 decimal places, we need to look at the third decimal digit to decide whether to round up or down. Since the third decimal digit (8) is greater than 5, we round up. Therefore, the number 5.928301 rounded to 2 decimal places is 5.93.
Rounding a number to two decimal places involves examining the third decimal digit to determine whether to round up or down. In the case of 5.928301, the third digit is 8, which is greater than 5. Consequently, rounding up is necessary. Thus, the rounded value of 5.928301 to two decimal places is 5.93, emphasizing the role of the third digit in the rounding decision.
Where do the following graphs intersect? Show how you can find the intersection point algebraically.
1) y-2x=3
2) y-3= x^2
A point on an ellipse is 11 units from one focus and 7 units from the other. What is the length of the major axis?
Find the circumference of a circle with radius of 18 in. Leave your answer in terms of π
Find the equation of the line perpendicular to -9x+4y=8 that contains the point (9,7)
Answer:
[tex]\[y=-\frac{4}{9}x+11\][/tex]
Step-by-step explanation:
Equation of the given line is [tex]\[-9x+4y=8\][/tex]
Slope of the line = [tex]\[\frac{9}{4}\][/tex]
Slope of the perpendicular line = [tex]\[-\frac{4}{9}\][/tex]
Equation of the line perpendicular to the given line is [tex]\[y=mx+c\][/tex]
[tex]\[y=-\frac{4}{9}x+c\][/tex]
But this line passes through (9,7)
Substituting the values in the equation:
[tex]\[7=-4+c\][/tex]
=> [tex]\[c=7+4=11\][/tex]
So the overall equation of the parallel line is given by [tex]\[y=-\frac{4}{9}x+11\][/tex]
What is
5.63×
10
−6
in decimal form?
a. 0.00000563
b. 0.000000563
c.5,630,000
d. 56,300,000
The length of a rectangle is eight times it's width. If the length was decreased by 10 meters and the width decreased by 2 meters the area would be decreased by 162 m. Find the original dimensions.
1. In how many different ways can 5 people be seated at a round table?
2. Each block on the grid is 1 unit by 1 unit. We wish to walk from A to B via 7 unit path but we have to stay on the grid. How many different paths can we take?
3. How many different "words" can be made from the given word by re-arranging the letters?
a) VECTOR
B) TRUST
Use the given graph to determine the limit, if it exists.
limf(x)
x-->2
Answer:
Step-by-step explanation:
4
The limit as x tends to 2 is -1
How to find the limit
The limit is sought by investigating the graph. More attention is directed to when the domain or the x-value is at 2.
It can be observed that at this point we have 2 open dots and one closed dot.
The closed dot implies there is a value for x = 2, hence we trace the y coordinate at this point.
Tracing the y coordinate shows that the value is -1
The distance from earth to the moon is about 22^4 miles. the distance from earth to neptune is22^7 miles. which distance is the greatest and by how much
Select the additive inverse of 51
PQRS is an isosceles trapezoid and m angle Q=127. Find M angle P.
Answer:
[tex]m<P=127\°[/tex]
Step-by-step explanation:
we know that
If the trapezoid PQRS is an isosceles trapezoid
then
[tex]PS=QR[/tex] ----> congruent sides
[tex]m<P=m<Q[/tex] -----> congruent angles
In this problem we have
[tex]m<Q=127\°[/tex]
therefore
[tex]m<P=127\°[/tex]
The range of a projectile fired at an angle θ with the horizontal and with an initial velocity of v 0 feet per second is r = 1 v 20 sin 2θ where r is measured in feet. a golfer strikes a golf ball at 120 feet per second. 32 ignoring the effects of air resistance, at what angle must the golfer hit the ball so that it travels 140 feet? (round answer to nearest angle.)
The area of a rectangular wall of a barn is 75 75 square feet. its length is 10 10 feet longer than the width. find the length and width of the wall of the barn.
First, represent the unknown width as 'x'. Then, because the length is 10 feet more than the width, represent the length as 'x + 10'. Since the area is 75 square feet, set up and solve the equation x*(x + 10) = 75 for 'x'. This will give the width and the length will be this width plus 10 feet.
Explanation:This problem can be solved using algebra. First, let's denote the width of the wall as x in feet. If the length of the wall is 10 feet longer than the width, then we can express the length as x + 10. We're told that the area of the rectangle formed by the wall is 75 square feet. The area of a rectangle is calculated by multiplying its length by its width. Therefore:
x*(x + 10) = 75
You can solve this quadratic equation for x. The positive solution will be the width of the wall and the length will be that value plus 10 feet.
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the leg of a right triangle is 5 units and the hypotenuse is 8 units.what is the length in units of the other leg of the triangle
The square of the hypotenuse is equal to the sum of the square of other two sides. The length in units of the other leg of the triangle is 6.2 units
What is Pythagoras theorem?The square of the hypotenuse is equal to the sum of the square of the other two sides.
Mathematically;
l^2 = a^2 + b^2
Given
l = 8 units
a = 5 units
Substitute
8^2 = 5^2 + b^2
64 - 25 = b^2
b^2 = 6.2units
Hence the length in units of the other leg of the triangle is 6.2 units
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The trigonometric form of a complex number is unique - True or false?
Answer with explanation:
let, Z= a + i b,be a complex number.
Where, a = r cos A
b= r sin A
[tex]a^2 + b^2=(r cos A)^2 +(r sin A)^2\\\\ a^2 + b^2=r^2(cos^2 A+sin^2 A)\\\\ a^2 + b^2=r^2\\\\r=\sqrt{a^2 + b^2}[/tex]
[tex]Z=r cos A + i r sin A\\\\Z=r(cos A + i sin A)\\\\ Z=re^{iA},\text{Where}, e^{i\alpha }=cos \alpha +i sin\alpha[/tex]
Now, if we replace A, by, 2 kπ + A,in the above equation,where k is any positive integer,beginning from ,0.k=0,1,2,3,4,....
[tex]Z=r cos (2k\pi +A) + i r sin(2k\pi + A)\\\\Z=r[cos (2k\pi +A) + i sin(2k\pi + A)]\\\\ Z=re^{i(2k\pi +A)}[/tex]
So, for different value of , k ,there will be Different Complex number.
→So,the Statement: The trigonometric form of a complex number is unique = False
The trigonometric form of a complex number is unique is a false statement. Check the reason why it is false below.
Why is the trigonometric form of a complex number not special?The trigonometric form of a complex number is commonly seen as the polar form of that number.
This is due to the fact that there are lots of infinite choices are often made for θ and as such the trigonometric form of a complex number is said to be not unique in any way.
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