Answer:
x
2
−4x−5=0
All equations of the form ax
2
+bx+c=0 can be solved using the quadratic formula:
2a
−b±
b
2
−4ac
. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x
2
−4x−5=0
This equation is in standard form: ax
2
+bx+c=0. Substitute 1 for a, −4 for b, and −5 for c in the quadratic formula,
2a
−b±
b
2
−4ac
.
x=
2
−(−4)±
(−4)
2
−4(−5)
Square −4.
x=
2
−(−4)±
16−4(−5)
Multiply −4 times −5.
x=
2
−(−4)±
16+20
Add 16 to 20.
x=
2
−(−4)±
36
Take the square root of 36.
x=
2
−(−4)±6
The opposite of −4 is 4.
x=
2
4±6
Now solve the equation x=
2
4±6
when ± is plus. Add 4 to 6.
x=
2
10
Divide 10 by 2.
x=5
Now solve the equation x=
2
4±6
when ± is minus. Subtract 6 from 4.
x=
2
−2
Divide −2 by 2.
x=−1
The equation is now solved.
x=5
x=−1
h(t) = 2t^{2}[/tex] − t; t = 2, t = 9 Determine the net change between the given values of the variable. Determine the average rate of change between the given values of the variable.
The average rate of change between the given values of the variable is 21
What is a function?A function can be defined as an expression or rule showing the relationship between a dependent and an independent variable.
Given the function;
h(t) = 2t^{2}[/tex] − t
For t =2
Substitute the value of t as 2 in the function, we have;
h(2) = 2 (2)² - (2)
Find the square
h(2) = 2(4) - 2
h(2) = 8 - 2
h(2) = 6
For t = 9
Substitute the value of t as 9 in the function, we have;
h(9) = 2(9)² - 9
Find the square
h(9) = 2(81) - 9
h(9) = 153
The average change = 153 - 6 = 147/ 9 -2 = 147/ 7 = 21
Thus, the average rate of change between the given values of the variable is 21
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what’s the midpoint of C(-3,-8) and D(-6.5, -4.5)
Answer: M(-4.75,-6.25)
Step-by-step explanation:
C(-3,-8) D(-6.5,-4,5)
Let the midpoint of C(-3,-8) and D(-6.5, -4.5) is M(x,y)
[tex]\displaystyle\\M(x,y)=(\frac{-3+(-6.5)}{2} ,\frac{-8+(-4.5)}{y} )\\\\M(x,y)=(\frac{-9.5}{2},\frac{-12.5}{2})\\\\M(x,y)=(-4.75,-6.25)\\\\Thus, \ M(-4.75,-6.25)[/tex]
A cargo van delivers only 50-pound and 80-pound packages. for each delivery trip, the van must carry at least 20 packages, and the total weight of the packages cannot exceed 1,500 pounds. write a system of inequalities to determine the maximum number of 80-pound packages that the van can carry per trip.
If a cargo van delivers only 50-pound and 80-pound packages and the total weight of the packages cannot exceed 1,500 pounds, then a system of inequalities to determine the maximum number of 80-pound packages that the van can carry per trip is x + y ≥ 20; 80x + 50y ≤ 1,500.
A system of inequalities is a term used in mathematics that is a set of two or more than two inequalities in one or more than one variable.
Consider,
the number of 80-pound packages = x
the number of 50-pound packages = y
As the van can carry a minimum of 20 packages, the sum of x and y can be given as,
x + y ≥ 20
The weight of 80-pound boxes can be given as 80x and the weight of 50-pound boxes can be given as 50x. As the total weight of the packages cannot be more than 1500 pounds,
80x + 50y ≤ 1500
If we consider x to be 19,18 or 17 and the remaining to be y, it will exceed the limit of 1500 pounds. If x is considered to be 16,
80(16) + 50 (4) = 1480
Hence, the maximum number of 80-pound packages that the van can carry per trip is 16.
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What’s the answer please help
Answer:
Step-by-step explanation:
where?
Solve for y;
7(3y - x) = -21
Organic hotdogs at the grocery store cost $2.00 each. at a major league baseball game, an organic hotdog cost $6.50. by what percent does the baseball field mark up its organic hotdogs?
The baseball field mark up its organic hotdogs from $2.00 to $6.50 each by 225%.
The markup on cost is defined as the amount added to the original cost of a product or service to arrive at the new selling price. It can also be a percentage of the original cost.
mark up = selling price - original price
If organic hotdogs at the grocery store cost $2.00 each and at a major league baseball game, an organic hotdog cost $6.50, then the mark up price is the difference between the two.
mark up = selling price - original price
mark up = $6.50 - $2.00
mark up = $4.50
To get the percentage of the mark up from the original price, divide the mark up price by the original selling price and multiply by 100%.
percent mark up = (mark up price/original price) x 100%
percent mark up = ($4.50/$2.00) x 100%
percent mark up = 2.25 x 100%
percent mark up = 225%
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Solve each system by substitution. Check your answers.
3c + 2d=2 , d=4
By substitution, the solution of the system of equations, 3c + 2d = 2 and d = 4, is (c , d) = (-2 , 4).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in variables c and d,
3c + 2d = 2 (equation 1)
d = 4 (equation 2)
Since the second equation is already expressed in d in terms of a constant, substitute the second equation to the first equation.
3c + 2d = 2 (equation 1)
3c + 2(4) = 2
3c + 8 = 2
Combining all terms containing the variable c on one side and the constants on the other side of the equality, and solving for c.
3c + 8 = 2
3c = 2 - 8
3c = -6
c = -6/3
c = -2
Hence, the solution of the given system of equations is (c , d) = (-2 , 4).
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Please give me the answer for a) and b)
Answer: a) y=x²+6x+2 b) x=-3-√7, -3+√7
Step-by-step explanation:
(0,2) (-6,2) (-3,-7)
a)
y=ax²+bx+c
(0,2)
x=0 y=2
⇒ 2=a(0²)+b(0)+c
⇒ 2=0+0+c
⇒ 2=c
(-6,2)
x=-6 y=2
⇒ 2=a(-6)²+b(-6)+2
⇒ 2=36a-6b+2
⇒ 2-2=36a-6b+2-2
⇒ 0=36a-6b
⇒ 0+6b=36a-6b+6b
⇒ 6b=36a
Divide both parts of the equation by 6:
b=6
(-3,-7)
⇒ -7=a(-3)²+6(-3)+2
⇒ -7=9a-18+2
⇒ -7=9a-16
⇒ -7+16=9a-16+16
⇒ 9=9a
Divide both parts of the equation by 9:
1=a
Hence,
y=x²+6x+2
b)
x²+6x+2=0
D=(-6)²-4*1*2
D=36-8
D=28
√D=√28
√D=√(4*7)
√D=2√7
x=(-6±2√7)/2
x=-3-√7
x=-3+√7
Which expression correctly represents "three less than the product of a number and two, increased by five"? 2 n minus 3 5 3 minus 2 n 5 3 minus (2 n 5) 2 (n minus 3) 5
Answer: 2n+5-3
Step-by-step explanation:
Break this quote down:
"three less than the product of a number and two, increased by five"
To this:
"three less than the product" ==> product-3
Now break this quote down
Product: "product of a number and two, increased by five"
To this:
"product of a number and two" ==> 2*n
"increased by five" ==> +5
"product of a number and two, increased by five" ==> 2*n+5
Product: 2*n+5
Product-3: 2*n+5-3=2n+5-3
In the final round of a singing competition, the audience voted for one of the two finalists, Luke or Sean. Luke received 25% more votes than Sean received. Altogether, the two finalists received 5175 votes. How many votes did Luke receive?
Based on the number of votes that the two finalists received, the number of votes that Luke received was 2,875 votes
What number of votes did Luke receive?Assuming that the number of Sean's votes could be shown as x, the expression for the votes would be:
x + (x + 25%) = 5,175
2.25x = 5,175
x = 5,175 / 2.25
= 2,300 votes
Luke's votes were:
= 2,300 x (1 + 25%)
= 2,875 votes
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Question 7: Luna has consumed 900 calories so far today. She has also burned 500 calories in dance class. She wants to keep her daily calorie total to 1,500 calories per day. How many calories does she have left to consume for the day? Is 1,200 a viable solution to this problem?
No; 1,200 is more than the 500 she burned dancing.
No; 1,200 will cause her to exceed 1,500.
Yes; 1,200 is less than 1,500.
Yes; 1,100 is less than 1,500.
1,200 is not a viable solution to this problem as B.
No; 1,200 will cause her to exceed 1,500
How to calculate the value?It should be noted that Luna has consumed 900 calories so far today and has also burned 500 calories in dance class.
Therefore, the amount left will be:
= 1500 - (900 - 500)
= 1500 - 400
= 1100
Therefore, 1,200 is not a viable solution to this problem
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Find the sum.
(3x² + x + 5) + (2x² + x - 2)
Answer:
5X2 + 2X + 3 orr 10x + 2
Step-by-step explanation:
Point N is the midpoint of FG. If FN = 2x, what expression represents FG?
The line segment FG can be represented as expression 4x whose midpoint is N
We are provided with that Point N is the midpoint of FG and FN = 2x and We need to find expression that represents FG
As N is the midpoint of line segment FG than FN = NG
Also it could be written as FG = FN + NG because FG is the broken into two different line segment FN and NG because of the midpoint N
Therefore, FN = 2x which means FN= NG=2x
So, we can write an expression that could represent FG
FG = FN + NG
FG = 2x + 2x
FG = 4x
Hence, The line segment FG can be represented as expression 4x
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Position and label triangle JKLon the coordinate plane so that its base JL is a units long, vertex K is on the y-axis, and the height of the triangle is b units.
ΔJKL has been drawn such that its base JL is a unit long, vertex K is on the y-axis, and the height of the triangle is b units.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.
The right angle triangle JKL with base JL and perpendicular KJ has been drawn.
Height = KJ = a
Since J(0,0) so K(0,a)
Hence "ΔJKL has been drawn such that its base JL is a unit long, vertex K is on the y-axis, and the height of the triangle is b units".
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which number falls between -25/4 and -400% on a number line
The number falls between [tex]-\frac{25}{4}[/tex] and - 400 % is [tex]-\frac{43}{8}[/tex] = 5.375
first we convert fraction into decimal number
[tex]-\frac{25}{4}[/tex] = - 6.25
and for remove percentage we divide by 100
- 400 % = - 4
from choose the option,
[tex]-\frac{43}{8}[/tex] = 5.375
- 720 % = - 7.2
[tex]-\frac{20}{3}[/tex] = - 6.6
then, choose [tex]-\frac{43}{8}[/tex]
therefore, number lies between [tex]-\frac{25}{4}[/tex] and - 400 % is [tex]-\frac{43}{8}[/tex] = 5.375
A fraction is any number of the form a/b where both “a” and “b” are whole numbers and b≠0. On the other hand, a rational number is a number which is in the form of p/q where both “p” and “q” are integers and q≠0.
Thus, a fraction is written in the form of m/n, where n is not 0 and m & n are whole (or natural numbers). For example, 12/23, 10/32, 12/10, 4/21. A rational number can also be written in the form of a/b, where b is not 0 and a & b are integers. For example, 15/7, -18/13, 3/-7, -6/-12.
All fractions can be termed as rational numbers; however, all rational numbers cannot be termed as fractions. Only those rational numbers in which ‘p’ and ‘q’ are positive integers are termed as fractions. Let a/b be any fraction. Now, a and b are natural numbers. Since all natural numbers are also integers, a and b are also integers. Thus, the fraction a/b is the quotient of 2 integers such that b ≠ 0. Hence, a/b is a rational number. One of the examples in which a number is a rational number but not a fraction is:
Consider the fraction 12/-32. It is a rational number but not a fraction because its denominator (n) is not a natural number.
A fraction is expressed in the form of the ratio of whole numbers, a/b and b≠0.
A rational number is also expressed in the form of a ratio, p/q, where numerator and denominator are integers and q≠0.
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Evaluate each expression for the given values of the variables.
-5(x + 2y) + 15(x + 2y) ; x=7 and y=-7
The result of the expression -5(x+2y)+15(x+2y) for the variable x=7 and y= -7 is -70
Given,
The expression = -5(x+2y)+15(x+2y)
The value of the variables
x=7 and y= -7
Substitute the values in the expression
-5(7+2(-7))+15(7+2(-7))= -5(7-14)+15(7-14)
=-5(-7)+15(-7)
=35-105
=-70
Hence, the result of the expression -5(x+2y)+15(x+2y) for the variable x=7 and y= -7 is -70
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13. Which of these descriptions could the equation 16x - 17 = 26 represent
Check all that apply.
W 910/1
A The difference between sixteen times a number and seventeen is 26.
B. The difference between seventeen times a number and sixteen is 26.
When sixteen times a number is decreased by seventeen, the result
is 26.
riew
b. When seventeen times a number is decreased by sixteen, the result
is 26.
The sum of sixteen times a number and seventeen is 26.
The sum of seventeen times a number and sixteen is 26.
When seventeen times a number is increased by sixteen, the result
is 26.
H. When sixteen times a number is increased by seventeen, the result
is 26.
Answer:
when sixteen times a number is decreased by seventeen the result is 26
The difference between two numbers is 30. The sum of two-third of the first number and one-eleventh of the second number is 5. Find the product of the two numbers.
Answer:
26 and 32 are the two numbers, the product is 832
Step-by-step explanation:
How are previously decided court cases similar to theorems?
Determine whether each sequence is arithmetic or geometric. Then identify the common difference or common ratio. 1620,540,180,60,20, . . . .
The sequence 1620,540,180,60,20, . . . .. is a geometric sequence with common ratio 1/3.
To determine whether the sequence is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.
If it is an arithmetic sequence, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric sequence, then:
a(n) = a(n-1) . r
where r is the common ratio.
The given sequence is:
1620,540,180,60,20, . . . .
In this sequence:
a(1) = 1620
a(2) = 540
a(3) = 180
First we check the difference between 2 consecutive terms:
a(2) - a(1) = 540 - 1620 = -1080
a(3) - a(2) = 180 - 540 = -360
Since the difference is not constant, then the sequence is not an arithmetic one.
Now we check the ratio,
a(2) : a(1) = 540 : 1620 = 1/3
a(3) : a(2) = 180 : 540 = 1/3
and so on
Since the ratio of consecutive terms are constant, then the given sequence is a geometric sequence. Furthermore, its ratio, r = 1/3
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7(x-3)=9x-3
Please help!!
Answer:
x=-9
Step-by-step explanation:
x=-9
Thank you so much!
HELPPPPPPPP, Unidenifined Slope
Answer: f = 10
Step-by-step explanation:
An undefined slope means it's graphed as a straight vertical line. There is no change in x, so the x value will be the same for both points.
Here, f = x as coordinate points are written as (x, y);
f = 10
Why is the opposite of the reciprocal of 5 the same as the reciprocal of the opposite of 5 ?
Yes, the opposite of the reciprocal of 5 is same as the reciprocal of the opposite of 5 ,both are equals to (-1/5).
As given in the question,
Given number is 5
Case 1 : First find reciprocal of 5
Reciprocal of 5 =1/5
Then, opposite of the reciprocal of 5 =(-1/5)
Case 2. First find the opposite of 5
Opposite of 5 =-5
Reciprocal of the opposite of 5 =(1/ -5)
=(1/-5) × (-1/-1)
=(-1/5)
Therefore, the opposite of the reciprocal of 5 is same as the reciprocal of the opposite of 5 ,both are equals to (-1/5).
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Find the value of $A$ if the $4$-digit number $3A5A$ is divisible by $15$.
The value of A in the 4-digit number, 3A5A is 5.
What is the value of A?The 4-digit number provided in the question has to be a multiple of 15 given the information in the question. A multiple of a number is divisible by that number. A multiple of 10 is 100 because when 100 is divided by 10 , the value gotten is 10.
A multiple of a number is the product of an integer and that number. For example, a multiple of 2 is 100. This is because 2 multiplied by 50 is equal to 100.
The multiplies of 15 either have a unit value of 5 or 0.
If A is 5, the number becomes 3555.
3555 / 15 = 237
If A is 0, the number becomes 3050
3050 / 15 = 203.33
Thus, the value of A is 5 because 3555 is divisible by 15.
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9) Cell phone company A charges $20 per month plus $0.05 per text
message. Cell phone company B charges $10 per month
per text message. Is there any number of text
plus $0.07
messages that will
result in the exact same charge from both companies?
The number of the text messages where it will result in the exact same charge from both companies is 500 messages
What is number system?Number systems are mathematical systems that allow computers to understand and express numbers in various ways. A number is a mathematical value that is used to count and measure items as well as execute arithmetic calculations.
Natural numbers, whole numbers, rational and irrational numbers, and so on are all types of numbers. Similarly, different number systems with differing properties exist, such as the binary number system, the octal number system, the decimal number system, and the hexadecimal number system.
Let the number calls be x where the messages will result in the exact same charge
So, Cell phone company A charges $20 per month plus $0.05 per text
message is 20 + 0.05x
And, Cell phone company B charges $10 per month plus $0.07 per text message is 10 + 0.07x
As we want the numbers to be equal, following equation is obtained
20 + 0.05x = 10 + 0.07x
Lets find x
20 + 0.05x = 10 + 0.07x
0.07x - 0.05 = 20 -10
0.02x = 10
x = 10/0.02
x = 500
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Escalators consist of steps on a continuous loop that is driven by a motor. At the top and bottom of the platform, the steps collapse to provide a level surface for entrance and exit.
a. What is the relationship between the treads of the ascending stairs?
The climbing steps have parallel planes for the treads. Although each step may appear to be a line, it is actually a plane.
Considering it as a staircase; a moving stairway that transports people between levels of a building or structure is known as an escalator. It is made up of a motor-driven chain of individually connected steps on a track that cycles along a pair of tracks that maintain them horizontal.
The climbing stair treads are parallel planes. Each step appears to be a line, but it is actually a plane.
The top two steps of the inclination are on the same plane. They are parallel.
These tires are twisted. They are neither parallel, nor do they share the same plane.
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6266226ghsgjshss if she cut
Answer:
Step-by-step explanation:
solve by factoring
you get x=3/2
There are 5 children and 3 adults going on a trip. What fraction of the people going on the trip are ADULTS
answer=
Children =5
Adults = 3
3/8 are adults
If (3/5 - 1/8 i ) - (7/10 + 1/6 i )
Answer:
-1/10 - 7i/24
Step-by-step explanation:
10. Hypoglycemia (low blood sugar) and hyperglycemia (high blood sugar) are potentially dangerous and
occur when a person's blood sugar fluctuates by more than 38 mg from the normal blood sugar level of
88mg. Write and solve an absolute value inequality to describe blood sugar levels that are considered
potentially dangerous.
We get the absolute value inequality as | x - 88 | > 38.
We are given that:
Hypoglycemia (low blood sugar) and hyperglycemia (high blood sugar) are potentially dangerous and can occur when a person's blood sugar fluctuates by more than 38 mg from the normal blood sugar level of 88mg. We need to write an inequality for it.
We know that the blood sugar level should not be less than:
88 mg - 38 mg = 50 mg
Also, the blood sugar level should not be higher than:
88 mg + 38 mg = 126 mg
The inequality then will become:
50 mg ≤ Blood sugar level ≤ 126 mg.
The absolute value inequality will be:
| x - 88 | > 38
Therefore, we get the absolute value inequality as | x - 88 | > 38.
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