The two numbers are 80 and 8.
What is linear equation in two variables?An equation is said to be linear equation in two variables if it is written in the form of ax + by + c = 0, where a, b & c are real numbers and the coefficients of x and y, i.e. a and b respectively, are not equal to zero.
What is substitution method ?The substitution method can be defined as a way to solve a linear system algebraically. This method works by substituting one y-value with the other.
Let the two numbers be x and y.
According to the question.
x = 10y
And,
x - 10y = 72
Now, We have a linear equation in two variables. So, for finding the values of x and y we solve the above two equations by substitution method.
Substitute the value of x = 10y in x - y = 72
[tex]\implies 10y -y = 72 \\\implies 9y = 72\\\implies y = \frac{72}{9} \\\implies y = 8[/tex]
Therefore,
x = 10 × 8 = 80
Hence, the two numbers are 80 and 8.
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Which kinematics equation is a quadratic equation?
The mean of a set of credit scores is u=690 and o=14. Which credit score is within z-score of 3.3?
A)634
B)640
C)720
D)750
I think it is C
BMK ><
Answer:
c)720
Step-by-step explanation:
The mean of a set of credit scores is u=690 and o=14.
mean = 690 and standard deviation SD = 14
We use z- score formula
[tex]z=\frac{x-mean}{SD}[/tex]
z= 3.3 given
Plug in the values and find out x
[tex]3.3=\frac{x-690}{14}[/tex]
Multiply 14 on both sides
46.2 = x- 690
Now add 690 on both sides
x= 736.2
Credit score is 720 that comes under 736.2
So answer is 720
The absolute value function g(x) = |x + 7| − 4 is translated 5 units right and 2 units up to become g′(x). The quadratic function f(x), graphed below, is also moved 5 units right and 2 units up to become f′(x). Which of these two transformed functions has a range of y ≤ −2 and what is the vertex of this transformed function?
g′(x) has a range of y ≤ −2 and its vertex is at (−2, −2).
g′(x) has a range of y ≤ −2 and its vertex is at (2, −2).
f′(x) has a range of y ≤ −2 and its vertex is at (3, −2).
f′(x) has a range of y ≤ −2 and its vertex is at (−7, −6).
The difference between the squares of two consecutive numbers is 23. what are the two numbers?
(x+1)^2-x^2=23
x^2+2x+1-x^2=23
2x+1=23
2x=22
x=11
11^2 = 121
x+1 =12
12^2=144
144-121 = 23
Write a point-slope equation for the line that has slope 5 and passes through the point (6, 22). Do not use parenthesis on the y side.
(HELP ASAP) Kite EFGH is inscribed in a rectangle where F and H are midpoints of parallel sides.
The area of EFGH is 35 square units. What is the value of x?
4 units
5 units
6 units
7 units
The answer is 5 units on e2020.
What is the value of 3yx +2x when x=4 and y=-2
A.-28
B.-16
C.8
D.56
Write the equations in graphing form, then state the vertex of the parabola or the center and radius of the circle.
x^2+y^2+y+2=8
Julio has started his very own floral business. He sells centerpieces for $19.50 each. His fixed costs are $500 per month, and each centerpiece cost $8 to produce. What is your break-even point? a. Julio must sell approximately 18 centerpieces to break even. b. Julio must sell approximately 23 centerpieces to break even. c. Julio must sell approximately 44 centerpieces to break even. d. Julio must sell approximately 55 centerpieces to break even.
500= (19.50-8.00)x
500 = 11.50x
x=500/11.50=43.48
so he needs to sell approximately 44 centerpieces to break even
FIND THE MISSING VALUE. SHOW YOUR WORK.
c:
to find x multiply the side (24) by the tangent of the angle(13)
so 24 * tan(13) = 5.5408
D:
to find x
divide the side (10) by the sin of the angle (20)
10/sin(20) = 29.238
Round the answers as needed.
A tree casts a shadow of 26 meters when the angle of elevation of the sun is 24°. find the height of the tree to the nearest meter.
Using the trigonometric tangential function, the height of the tree casting a 26-meter shadow at an angle of elevation of 24° is approximately 11 meters.
Explanation:The given problem can be solved by applying trigonometric principles, specifically the tangent function. In this case, we know the shadow length (26m) and the angle of elevation of the sun (24°). The height of the tree is the side opposite the angle, and the shadow is the adjacent side. Thus, we can use the tangent equation (Tan θ = Opposite/Adjacent). So, Tan 24° = Height of the tree / 26m. By cross multiplying and evaluating Tan 24°, we get the height of the tree to be approximately 11 meters.
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give and example of a line that is parrallel to 9x+6y= -6
William buys a basket of lemons on sale for $11 before tax. The sales tax is 15%. What is the total price William pays for the basket of lemons?
How do you write 5/100 in decimal form?
what is the solution to 2sin^(2)x+sinx+1=0
a. 30 deg
b.150 deg
c.240 deg
d. 270 deg
e. 330 deg
what are the domain and range of the following functions? write your answer using inequality symbols if possible
Can someone help me with this math problem, please? Thanks!
A cylindrical tank standing upright (with one circular base on the ground) has a radius of 1212 cm for the base. how fast does the water level in the tank drop when the water is being drained at 2323 cm33/sec? note that the volume of a cylinder is v=πr2hv=πr2h where rr is the radius of the base and hh is the height of the cylinder.
To find the rate of change of height with respect to time, we use the formula dh/dt = dV/dt / (πr²) and substitute the given values for the rate of volume change and the radius.
We have the rate of volume change as 23 cm³/sec and the cylinder has a radius of 12 cm. Note that the typo '2323 cm³/sec' and '1212 cm' should be read as '23 cm³/sec' and '12 cm,' respectively.
The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. To find the rate at which the height h changes over time, we can take the derivative of the volume with respect to time, which gives us dV/dt = πr² dh/dt. We can solve this equation for dh/dt (the rate of change of height with respect to time) by dividing both sides by πr² and substituting the given values. Therefore, dh/dt = dV/dt / (πr²).
Substituting the values, we get:
dh/dt = 23 cm³/sec / (π * (12 cm)²)
Upon simplifying, we will obtain the rate at which the height of the water is decreasing in cm/sec.
Which value of m will create a system of parallel lines with no solution?
y = mx – 6
8x – 4y = 12
Answer:
answer is D ;)
Step-by-step explanation:
simplify each expression by destributing. math problem> 3(2y-7)
A basketball is thrown with an initial upward velocity of 23 feet per second from a height of 7 feet above the ground. The equation h=−16t2+23t+7h=−16t2+23t+7 models the height in feet t seconds after the basketball is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop? Select one: a. 1.29 seconds b. 1.44 seconds c. 1.70 seconds
Given the provided motion physics model and using the quadratic formula, it is determined that it would take approximately 3.79 seconds for the basketball to go into the hoop after it was thrown.
Explanation:The subject in consideration here is a problem related to quadratic equations in motion physics. The equation given in the question signifies a model of the height of the basketball as a function of time in the format of a quadratic equation. The equation is h = -16t² + 23t + 7.
With this equation, we can apply the quadratic formula to find the amount of time it takes for the ball to reach the hoop.
Upon using the quadratic formula, two solutions come up, t = 3.79 s and t = 0.54 s. The ball is at a height of 10 m at two times during its trajectory—once on the way up (as it rises) and once on the way down (as it falls). Since the question is about the time the ball goes into the hoop after reaching its maximum height and coming down, the larger value of t (3.79s) is considered as the valid solution.
Therefore, the time it takes for the basketball to go into the hoop after it was thrown is approximately 3.79 seconds which is not an offered option.
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Frank borrowed $400 from his neighbor. He made 3 payments of $65 each and another payment of $95. How much does Frank still owe?
What is the intersection of this sphere with the yz-plane? find an equation of the sphere with center (−3, 2, 9) and radius 6?
The equation of the sphere with center (-3, 2, 9) and radius 6 is (x + 3)² + (y - 2)² + (z - 9)² = 6². The intersection of this sphere with the yz-plane is described by the equation (y - 2)² + (z - 9)² = 27.
Explanation:The equation of a sphere with center (-3, 2, 9) and radius 6 is given by:
(x + 3)² + (y - 2)²+ (z - 9)² = 6²
To find the intersection of this sphere with the yz-plane, we need to set x = 0 in the equation:
(0 + 3)² + (y - 2)² + (z - 9)² = 6²
Simplifying this equation gives:
(y - 2)² + (z - 9)² = 27
So, the intersection of the sphere with the yz-plane is described by the equation (y - 2)² + (z - 9)² = 27.
A sixteen-sided number cube has the numbers 1 through 16 on each face. each face is equally likely to show after a roll. what is the probability that you will roll an even number or an odd prime number? round to the nearest thousandth.
a. 0.063
b. 0.813
c. 0.219
d. 0.875
Answer:
B. 0.813
Step-by-step explanation:
A sixteen-sided number cube has the numbers 1 through 16 on each face.
So, [tex]|\ S\ |=16[/tex]
Let us assume that, A be the event that the number will be an even number. So,
[tex]A=\left \{ 2,4,6,8,10,12,14,16 \right \}[/tex] and [tex]|\ A\ |=8[/tex]
Then,
[tex]P(A)=\dfrac{|\ A\ |}{|\ S\ |}=\dfrac{8}{16}[/tex]
Let us assume that, B be the event that the number will be an odd prime number.
[tex]B=\left \{3,5,7,11,13 \right \}[/tex] and [tex]|\ B\ |=5[/tex]
Then,
[tex]P(B)=\dfrac{|\ B\ |}{|\ S\ |}=\dfrac{5}{16}[/tex]
So the probability that you will roll an even number or an odd prime number will be,
[tex]P(A\cup B)=P(A)+P(B)-P(A\cup B)[/tex]
[tex]=\dfrac{8}{16}+\dfrac{5}{16}-0[/tex] ( as independent events)
[tex]=\dfrac{13}{16}[/tex]
[tex]=0.813[/tex]
The figure consists of a tangent and a secant to the circle. Solve for x.
A. 9.2
B. 7.7
C. 14.3
D. 85
Answer:
9.2
Step-by-step explanation:
We are given that a figure in which a tangent and a secant to the circle.
We have to find the value of x.
Length of tangent segment=x
Length of secant segment=12 +5=17 units
Length of external segment=5 units
We know that secant-tangent theorem
It states that product of length of secant segment and its external segment is equal to square of length of tangent segment.
[tex]x^2=17\times 5=85 [/tex]
[tex]x=\sqrt{85}=9.2 units[/tex]
Hence, the value of x=9.2
Tom is showing his work in simplifying (5.2 – 8.5) – 0.5 + 6.8. In which step did Tom make an error? Step 1:: (5.2 – 8.5) – 0.5 + 6.8 Step 2: 5.2 + (–8.5 – 0.5) + 6.8 (distributive property) Step 3: 5.2 – 9 + 6.8 Step 4: 5.2 + 6.8 – 9 (commutative property) Step 5: 12 – 9 = 3 Step 2; he wrote distributive instead of commutative Step 2; he wrote distributive instead of associative Step 4; he wrote commutative instead of associative Step 4; he wrote commutative instead of distributive
Answer:
B
Step-by-step explanation:
Step 2 he wrote distributive instead of associative
If one u.s. dollars equals 5.76 egyptian pounds and one u.s. dollar equals 0.56 british pound, how many egyptian pound equal one british pound?
How can 3.7=x+(-5) be solved for x in one step?Add 3.7 to both sides .Add 5 to both sides. Subtract 3.7 from both sides Subtract 5 from both sides
The first step to solve for x in the given algebra using properties of equality is; Add 5 to both sides.
How to Simplify Algebra?We want to simplify the algebraic expression;
3.7 = x + (-5)
When dealing with algebra like this, what we have to first do is to balance both sides of the equation.
To solve this particular algebra problem, we will use additional property of equality by adding 5 to both sides to get;
3.7 + 5 = x + (-5) + 5
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The first step to solving the expression 3.7 = x + (- 5) is,
''Add 5 to both sides''
The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to give that,
An algebraic expression to simplify,
⇒ 3.7 = x + (- 5)
Now, Simplify the expression by combining like terms as,
⇒ 3.7 = x + (- 5)
⇒ 3.7 = x - 5
Use the additional property of equality by adding 5 to both sides to get;
3.7 + 5 = x + (-5) + 5
8.7 = x
x = 8.7
So, the first step is, ''Add 5 to both sides''.
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Choose a number. add 5. multiply by -4. subtract 3. for each starting number what is your ending number ?
An airplane pilot over the Pacific sights an atoll at an angle of depression of 5. At this time, the horizontal distance from the airplane to the atoll is 4629 meters. What is the height of the plane to the nearest meter?
A. 403 m
B. 405 m
C. 4611 m
D. 4647 m
Rounded to the nearest meter, the height of the plane is approximately 405 meters.
So, the correct answer is B. 405 m.
To find the height of the plane, we can use trigonometry, specifically the tangent function.
Let's denote the height of the plane as h (in meters).
From the information given, we know that the angle of depression from the airplane to the atoll is 5 degrees, and the horizontal distance from the airplane to the atoll is 4629 meters.
Using the tangent function, we have:
tan(angle of depression) = height / horizontal distance
tan(5 degrees) = h / 4629
To find the value of h, we can rearrange the equation:
h = 4629 * tan(5 degrees)
Now, let's calculate the height of the plane:
h ≈ 4629 * 0.0874886635 ≈ 404.773 meters
Rounded to the nearest meter, the height of the plane is approximately 405 meters.
So, the correct answer is B. 405 m.
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