Answer:
20
Step-by-step explanation:
Since this is a ratio problem we first plug in all that we know
14:x
21:30
Now we find a way to get from 21 to 30
The ratio 14:21 can be simplified if we divide each by 7 give us 2:3
Now we plug the new ratio in
2:x
3:30
We get from 3 to 30 by multiplying by 10 so we also multiply 2 by 10 and we get 20
What is nature of root equation?
The nature of root equation is depends of their types.
(1) When D=0, the roots in this situation are x = -b/2a.
(2) When D>0, the roots are real and unequal.
(3) When D<0, the roots are imaginary and unequal.
The type of roots depends on the discriminator:
We will talk about the following scenarios involving the nature of roots in accordance with the discriminates value.
Case: D=0
The roots of the quadratic equation ax^2 + bx + c = 0 are real and equivalent if the discriminate is equal to zero (b^2 - 4ac = 0), a, b, and c are real values, and a(0) . The roots in this situation are x = -b/2a. The X axis is the only location at which the equation's graph meets it.
Case: D>0
The roots of the quadratic equation ax2 + bx + c = 0 are real and unequal if the discriminate is bigger than zero (b2 - 4ac > 0), a, b, and c are real integers, and a0. The X-axis is intersected by the equation's graph twice.
Case: D<0
When a, b, and c are real numbers and the discriminate is smaller than zero (b2 - 4ac 0), the roots of the quadratic equation ax2 + bx + c = 0 are imaginary and unequal. There are conjugate pairings of roots. The equation's graph does not extend to the X-axis.
Case: D > 0 and perfect square
The roots of the quadratic equation are real, unequal, and rational if D > 0 and a perfect square.
Case: D < 0 and perfect square
The roots of the quadratic equation are real, unequal, and irrational if D > 0 and not a perfect square.
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if 4x ≤ g(x) ≤ 2x4 − 2x2 + 4 for all x, evaluate lim x→1 g(x).
The value of expression lim x→1 g(x) is 4.
In mathematics, a limit is a point at which a function becomes close to producing the desired result for the given input values. Limits are necessary for calculus and mathematical analysis and are also needed to establish integrals, derivatives, and continuity. It is used during the analysis process and continually thinks about how the function will act in a particular situation. The idea of the limit of a topological net broadens the definition of the limit of a sequence and relates it to the limit and direct limit in the theory category.
Given expression,
[tex]4x\leq g(x)\leq2x^{4}-2x^{2} +4[/tex]
For x → 1
4x = 4(1)
= 4
[tex]2x^{4}-2x^{2} +4[/tex] = 2(1)-2(1)+4
= 4
Hence, the value of lim x→1 g(x) is 4.
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You want to construct an open-top box that is 6 inches deep, with a square base. It must have a volume of 864 cubic inches. You have one big piece of cardboard. You will start by cutting it down to a square, and then you will cut smaller squares out of each corner and fold up the sides.
The statements that are true are the volume of the box is v = lwh = 864 in³ and the volume can be expressed in an equation as v = 6x² = 864in³
Volume of a SquareThe volume of a square box is equal to the cube of the length of the side of the square box. The formula for the volume is V = l³, where "l" is the length of the side of the square box.
In the given problem, the volume of the box is 864 cubic inches.
However, we have to remember that the box isn't a square, but rather the base has a square shape.
The volume of the figure is
v = l * w * h
l = lengthw = widthh = heightIf we divide the volume by the height, we will have the area of the figure
Area = volume / height
Area = 864 / 6
Area = 144 square inches
Since the base has a square shape;
A = l²
144 = l²
l = √144
l = 12 in
The side length is 12 inches.
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How do you tell if the function is increasing or decreasing?
A function is increasing if the function value increases on increasing the input value and the function is decreasing if the function value decreases on increasing the input value.
We know that a function is a relation between input and output values where each input has exactly one output.
Consider a function y = f(x)
For a given function if the value of y increases on increasing the value of x, then the function is called as an increasing function
If the y-value decreases on increasing the value of x, then the function is called as a decreasing function.
Another method is that if a function f(x) is differentiable on an open interval, we calculate the derivative of function f(x)
If the derivative f′(x) > 0 on an open interval, then function f(x) is increasing on that interval.
If the derivative f′(x) < 0 on an open interval, then function f(x) is decreasing on that interval.
Therefore, if the output value of function increases on increasing the input value then the function is an increasing function and if the output value of function decreases on increasing the input value then the function is an decreasing function.
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Tonya and Jill each opened savings accounts. Tonya started with $60 and deposited $20 each month.Jill started with $20 and deposited $40 each month. If they each continue to make deposits at the same rate when will they have the same amount of money
Two months would pass before they received the same sum of money.
What does same rate mean in math?In mathematics, equivalence is a relationship that states that two quantities have the same value or that two mathematical expressions reflect the same mathematical object. A = B is the symbol for the equality of A and B, and it is also pronounced as A = B.
Briefing:Total amount saved = amount started with + (amount deposited per month x number of months)
Amount saved by Tonya = $60 + $20m
Amount saved by Jull = $20 + $40m
The two aforementioned equations would be equivalent if they both saved the same amount of money:
60 + 20m = 20 + 40m
Take the below actions to find the value of m:
60 - 20 = 40m - 20m
40 = 20m
m = 40 / 20
m = 2
In the calculation that shows how much money Tonya has overall saved, replace m with:
$60 + $20(2)
$60 + $40 = $100
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Please help... I suck at thissss
How do you solve inequalities Grade 7?
A system of inequalities can be solved by subtracting, adding, multiplying, or dividing both sides of the inequalities until a single variable is left on its own.
What is an inequality?In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Greater than (>).Greater than or equal to (≥).Less than (<).Less than or equal to (≤).For instance, the following inequality can be solved as follows;
0.75 < -1.5n
0.75 + 1.5n < 0
1.5n < -0.75
Next, we would divide both sides of the inequality by 1.5 as follows:
n < -0.75/1.5
n < -0.5
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pls i really need help with this question
Answer:
1282 miles
Step-by-step explanation:
You have a rectangle with sides 365 and 276 miles, and you want to know the perimeter. (This is an approximation of the state of Wyoming.)
PerimeterThe perimeter of a rectangle is the sum of its side lengths. The formula is ...
P = 2(L +W)
ApplicationP = 2(365 +276) = 2(641)
P = 1282
The perimeter of Wyoming is about 1282 miles.
y varies jointly as x and z. If y = -40 when x = -2 and z = -1, what is the variation equation?
Answer:
-20
Step-by-step explanation:
if y varies jointly as x and z, then y = k * x * z
where k is the variation constant.
-40 = k * -2 * -1
-40 =2k
k = -20
x³ + 3x² + 3x +5=0
What is the rational roots of this polynomial equation?
Answer:
x=-³√4-1
Step-by-step explanation:
x³+3x²+3x+5=0
(x+1)³+4=0
(x-1)³=-4
x+1=-³√4
x=-³√4-1
A man i four time a old a hi on. In 5 year’ time he will be three time a old a hi on. What i the preent age of the on in year?
The present age of the Son will be 10 years and Father's present age will be 40 years.
We will solve this problem with the concept of age.
Age is referred to as the length of time that a person or item has been alive. Problems based on age generally consist of information about the ages of two or more people and a relation between their ages in the present or future or past. Using this information it is asked to calculate the ages of one or more people in the present past or future.
The important thing to keep in mind while solving problems of ages.
If the present age is y, then n times the present age = ny.
If the present age is x, then age n years later/hence = x + n.
If the present age is x, then the age n years ago = x – n.
The ages in a ratio a: b will be ax and bx.
If the current age is y, then 1/n of the age is y/n.
According to our problem:
Let the present age of the son = x
The present age of the father = 4x
After 5 years
Son age = x+5.
Father age = 4x+5
According to the condition =
4x+5 = 3(x+5)
4x+5 = 3x + 15
x = 10
Therefore the present age of the son will be x = 10 years and the father will be 4x= 40 years.
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PLS HELP WHO EVER ANSWERD FIRST WILL GET THE BRAINLIEST PLS
Leo is a salesperson. Let y represent her total pay (in dollars). Let x represent the number of items she sells. Suppose that x and y are related by the equation y=32x+1900.
What is Leo's total pay if she doesn’t sell any items?
A. $19
B. $3,200
C. $32
D. $1,900
Explain your work pls
What is negative infinity?
The negative infinity, which is smaller than any real number, is the idea of infinity. For the representation of negative infinity, use the sign "-∞".
Given that,
We have to find what is negative infinity.
We know that,
The negative infinity, which is smaller than any real number, is the idea of infinity. For the representation of negative infinity, use the sign "-∞".
Look closely at this representation of infinity: opposite-pointing zip lines that travel along positive and negative infinity. To get closer to negative infinity on the zip line, they must turn left. On a number line, numbers move closer to positive infinity as they advance to the left and negative infinity as they move to the right. Positive infinity is always larger than any number, while negative infinity is always smaller.
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What is example of distributive?
An example of distributive property is 3 × (4 + 7) = (3 × 4) + (3 × 7).
Distributive Property is a property of multiplication and it is related with the distribution of numbers.
It states that the product of three numbers do not change even if the distribution of numbers are changed.
The distributive property of multiplication states that:
a × (b + c) = (a × b) + (a × c).
Let us verify it with help of an example.
3 × (4 + 7) = (3 × 4) + (3 × 7)
Taking L.H.S
3 × (4 + 7) = 3 × 11 = 33
Taking R.H.S
(3 × 4) + (3 × 7) = 12 + 21 = 33
Therefore, L.H.S = R.H.S
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The length of segment ef is 8 units and the length of segment ed is 10 units. Find the length of segment fa. Explain or show your reasoning.
If the length of segment ef is 8 units and the length of segment ed is 10 units. The length of segment fa is 6 units.
How to find the length of segment?Using Pythagoreans theorem formula to find the length of segment
c² = √a² + b²
Where:
c = Length
a = 10 units
b = 8 units
Let plug in the formula
c² = √10² - 8²
c² = √100 - 64
c² = √36
c = 6 units
Therefore we can conclude that the length is 6 units.
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How do you know what method SSS SAS ASA AAS to use when proving triangle congruence?
The method to use when proving triangle congruence depends on the information given about the triangles.
What is triangle congruence?Triangle congruence is a doctrine of mathematics which states that two triangles are congruent when all the corresponding sides and angles of both triangles have the same measure. This means that the two triangles are of the same size and shape, and each of their sides and angles correspond to each other in terms of size and measure. Triangle congruence is an important theorem in geometry, and is often used for solving various problems in mathematics.
If two triangles have three pairs of corresponding congruent sides, then the Side-Side-Side (SSS) method can be used. If two triangles have two pairs of corresponding congruent angles and a pair of corresponding congruent sides, then the Angle-Side-Angle (ASA) method can be used. If two triangles have two pairs of corresponding congruent sides and a pair of corresponding congruent angles, then the Side-Angle-Side (SAS) method can be used. If two triangles have three pairs of corresponding congruent angles, then the Angle-Angle-Side (AAS) method can be used.
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Two dice are (hkv-fhyp-che) thrown at the same time. Find the probability of getting
(i) the same number on both dice.
(ii) different numbers on both dice.
(1) 6/36
(2) 30/36
There are six possible outcomes. The probability of obtaining any side/number is 1/6,
Then for 2 dies it’s 2/36
Total possible outcomes=total numbers of the first die (6)× total numbers of the second die(6)= 36
The outcomes of rolling two dice are below:
1 2 3 4 5 6
1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
2 (2, 1) (2, 2)(2, 3)(2, 4)(2, 5)(2, 6)
3 (3, 1) (3, 2)(3, 3)(3, 4)(3, 5)(3, 6)
4 (4, 1) (4, 2)(4, 3)(4, 4)(4, 5)(4, 6)
5 (5, 1) (5, 2)(5, 3)(5, 4)(5, 5)(5, 6)
6 (6, 1) (6, 2)(6, 3)(6, 4)(6, 5)(6, 6)
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What are the slope and y value at the y-intercept of the line y 3x 5?
The slope is 3 and the y-intercept is −5 of the equation y = 3x - 5.
The line with m as the slope, m, and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope.
Slope-intercept form,
y = mx + c
Given equation,
y = 3x-5
Slope, m = 3
y-intercept, c = -5
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State the domain of the function y = 3x+1.
The domain of the function y = 3x+1 is the set of all real values
How to determine the domain?From the question, we have the following parameters that can be used in our computation:
Function: y = 3x + 1
The above function is a linear function
A linear function can take any real number as its input
This means that the domain of the function contains all real values
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4 of 64 of 6 Questions
Question
A new doughnut shop lost $624 during its first 13 days of business. If it lost the same amount of money each day, what was the loss each day?
Which choice shows the correct quotient and answer?
(−624)÷13=−48; The doughnut shop lost $48 each day.
(−624)÷13=8,112; The doughnut shop made a profit of $8,112 each day.
(−624)÷13=48; The doughnut shop made a profit of $48 each day.
(−624)÷13=−611; The doughnut shop lost $611 each day.
If a new doughnut shop lost $624 during its first 13 days of business. If it lost the same amount of money each day, the loss each day is: A. (−624)÷13=−48; The doughnut shop lost $48 each day.
How to find the loss per day?Given data:
Amount lost = $624
Days of business = 13 days
Now let determine the amount that the doughnut shop lost per day
Loss per day = Amount lost / Days of business
Loss per day = - $624/13 days
Loss per day = -$48
Therefore we can conclude that the correct option is A
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What are the possible rational zeros of f x 2x3 − 15x2 9x 22 2 points?
The possible rational zeros of f(x) = [tex]2x^{3} - 15x^{2} +9x-22[/tex] are ±1, ±2, ±11, ±22, ±1/2, ±11/2.
What is mean of rational zero ?
A rational zero is a rational number, which is a number that can be written as a fraction of two integers. An irrational zero is a number that is not rational, so it has an infinitely non-repeating decimal.
By Rational Zero Theorem,
If P(x) is a polynomial with integer coefficients and if is a zero of P(x) (P( ) = 0),
then p is a factor of the constant term of P(x)
q is a factor of the leading coefficient of P(x)
Possible value of rational zero is p/q
Given, f(x) = [tex]2x^{3} - 15x^{2} +9x-22[/tex]
Here, constant term, p = +22
Leading coefficient, q = +2
The factors of the constant term +22 are ±1, ±2, ±11, ±22.
Therefore , The possible rational zeros of f(x) = [tex]2x^{3} - 15x^{2} +9x-22[/tex] are ±1, ±2, ±11, ±22, ±1/2, ±11/2.
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a batch of 200 iron rods consists of 50 oversized rods, 50 undersized rods and 100 rods of the desired length. if two rods are drawn at random without replacement, what is the probability of obtaining (a) two rods of the desired length, (b) exactly one of the desired length, (c) none of the desired length? show all steps and clearly write out your formulas and assumptions
(a) The probability of obtaining two rods of the desired length is (100/200) * (99/199) = 0.495.
This can be found by using the formula for independent events:
P(A and B) = P(A) * P(B)
Since the two draws are of rods without replacement,
the probability of the first-rod being of the desired length = 100/200 (there are 100 desired-length rods out of a total of 200).
The probability of the second-rod being of the desired length = 99/199 (since one of the desired length rods has already been drawn). Multiplying these two probabilities gives us the answer.
(b)The probability of obtaining exactly one rod of the desired length
=(100/200) * (100/199) + (100/200) * (100/199)
= 0.990.
This can be found by using the formula for the union of two events: P(A or B) = P(A) + P(B).
Since the two draws are rods without replacement, the first draw has a probability of 100/200 of being of the desired length (there are 100 desired-length rods out of a total of 200).
The probability of the second draw being of the desired length is 100/199 (since one of the desired length rods has already been drawn). Adding these two probabilities gives us the answer.
(c) The probability of obtaining none of the desired length is (50/200) * (50/199) = 0.015.
This can be found by using the formula for independent events
: P(A and B) = P(A) * P(B).
Since the two draws are of rods without replacement, the probability of the first-rod being of the undersized length is 50/200 (there are 50 undersized rods out of a total of 200).
The probability of the second-rod being of the undersized length is 50/199 (since one of the undersized rods has already been drawn). Multiplying these two probabilities gives us the answer.
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How to solve x3 6x2 11x 6 0?
The solutions of the cubic equation x³ + 6x² + 11x + 6 = 0 will be -1, -2, and -3.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The equation is given below.
x³ + 6x² + 11x + 6 = 0
Factorize the equation, then we have
x³ + 6x² + 11x + 6 = 0
x³ + x² + 5x² + 5x + 6x + 6 = 0
x²(x + 1) + 5x(x + 1) + 6(x + 1) = 0
(x + 1)(x² + 5x + 6) = 0
(x + 1)[x² + 3x + 2x + 6] = 0
(x + 1)(x + 3)(x + 2) = 0
x = -1, -2, -3
The solutions of the cubic equation x³ + 6x² + 11x + 6 = 0 will be -1, -2, and -3.
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What is the median of the following set of scores 18 16 12 14?
The median of the set of numbers 18, 16, 12, and 14 is 15. This is the average of the two middle numbers in the ordered set, and it is not affected by extreme values or outliers.
The median of a set of numbers is the value that is exactly in the middle of the set when it is ordered from least to greatest. In this case, the set of numbers is 18, 16, 12, and 14. When we order this set from least to greatest, we get 12, 14, 16, and 18. There are four numbers in this set, so the median is the average of the two middle numbers. The two middle numbers in this set are 14 and 16, so the median is (14 + 16) / 2 = 15.
To find the median, we first need to arrange the numbers in order from least to greatest. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. In this case, there are four numbers in the set, so the median is the average of the two middle numbers.
In summary, the median of the set of numbers 18, 16, 12, and 14 is 15. This is the average of the two middle numbers in the ordered set, and it is not affected by extreme values or outliers.
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Simplify quantity 9 x squared plus 12 end quantity over 6 (5 points)
By distributing the division, we will get the simplified expression:
(3/2)*x² + 2
How to simplify the quantity?Here we have the following quadratic expression:
(9x² + 12)/6
Remember that the division is distributive, then we can rewrite:
(9x² + 12)/6 = 9x²/6 + 12/6
Now we can just simplify the two fractions.
(9x² + 12)/6 = (9/6)*x² + 2
= (3/2)*x² + 2
This is the most we can simplify the given expression.
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Which of the following equations has no real roots a X² 4x 3 √ 2?
The equation that has no real roots is 3x² + 4√3x + 4.
Option D is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
If the discriminant of the equation is less than zero the equation has no real roots.
Discriminant < 0
D < 0
D = b² - 4ac
Now,
The equation is in the form of ax² + bx + c
x² - 4x + 3√2 = 0
D = (-4)² - 4 x 1 x 3√2 = 16 - 12√2 > 0
x² + 4x - 3√2 = 0
D = 16 + 12√2 > 0
x² - 4x - 3√2 = 0
D = 16 + 12√2 > 0
3x² + 4√3x + 4 = 0
D = 16 - 48 = 32 < 0
Thus,
The equation 3x² + 4√3x + 4 has no real roots.
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The complete question is:
Which of the following equations has no real roots
a. x² - 4x + 3√2 = 0
b. x² + 4x - 3√2 = 0
c. x² - 4x - 3√2 = 0
d. 3x² + 4√3x + 4 = 0
Are these parallel, perpendicular, or neither y= --2x+4 and -5x+10y=5
NEED HELP ASAP!!!!
Mel slides down waterslide A,
and Victor slides down waterslide B. After 2 seconds, Mel was 50 feet in
the air, and after 5 seconds, she was 35 feet in the air. After 1 second, Victor was 60 feet in the air, and
after 4 seconds, he was 50 feet in the air. Who was descending at a
faster rate?
Mel: (2, 50) and (5, 35)
Victor: (1, 60) and (4, 50)
Mel's rate of change is
second.
That means that her height in the air decreases
feet every
Victor's rate of change is
second.
That means that his height in the air decreases _
feet every
DONE
Intro
0 000
Answer:
Step-by-step explanation:
answer:
Mel was descending at a faster rate
Mel's rate of change is negative. That means that your height in the air decreases 5 feet every second.
Victor's rate of change is negative. That means that his height in the air decreases 3.33 feet every second.
Answer:
Mel (2, 50) and (5, 35)Victor (1, 60) and (4, 50)
Step-by-step explanation:
Edge 2020.
What is the nature of the roots of the quadratic equation 4x² 4 √ 3x 3 0?
The roots of the quadratic equation 4x² + 4√3x - 3 = 0 are two distinct imaginary roots.
To find the roots of a quadratic equation, we have to use the quadratic formula. The formula is x = [-b ± √(b² - 4ac)]/2a. In this case, a = 4, b = 4√3, and c = -3. Plugging in the values, we get x = [-4√3 ± √(4√3² - 4*4*(-3))]/8. Simplifying and solving, we get x = [-2i ± √12]/4. Since both solutions contain an imaginary component, this means that the roots of the equation are two distinct imaginary roots.
x = [-4√3 ± √(4√3² - 4*4*(-3))]/8
x = [-4√3 ± √(48)]/8
x = [-2i ± √12]/4
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need a quick answer
Answer:
-14
Step-by-step explanation: