Answer:
Δ = 349
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 ) , then the discriminant is
Δ = b² - 4ac
9x² + 5x - 9 = 0 ← is in standard form
with a = 9, b = 5 , c = - 9 , then
b² - 4ac
= 5² - (4 × 9 × - 9)
= 25 - (- 324)
= 25 + 324
= 349
Antonia earns $6 per hour helping her grandmother. Write and solve an equation to find how many hours she needs to work to earn $48.
Answer:
48 = 6h
48 = 6 x 8
48 = 48
Step-by-step explanation:
Let e equal her earning and h equal the amount of hours worked. You would divide 48 by 6 to find that she works 8 hours.
Please help with this problem!
(WILL MAKE BRAINLIEST)
Answer:
the third, and fourth options
Step-by-step explanation:
hope it helps
Answer:
3rd n 4th
hope this helps you!!!
please help this is homework and I don’t know how to do it!!!
Step-by-step explanation:
you don't understand what the multiplication or division with 10 (or a higher power of 10) does ?
or you don't know. what 10² means ?
this means 10 to the power of 2 or 10 squared and is simply 10 multiplied with itself 2 times : 10×10.
and 10×10 is ... 100.
as you can imagine, this is not restricted to the number 2 (and 10). "power of" can be any number and just indicates how often the base number is multiplied with itself.
a surcharge case is "power of 0", which is simply 1.
now that we understand that, let's have a quick look at how the numbers we are dealing with (in daily life as well as in class and in science) are actually built :
when I write e.g the number
1234
then this actually means
4×10⁰ + 3×10¹ + 2×10² + 1×10³
when I multiply this now by e.g. 10 this becomes
4×10⁰×10 + 3×10¹×10 + 2×10²×10 + 1×10³×10 =
4×10¹ + 3×10² + 2×10³ + 1×10⁴
as you can see, the previous "single" position 4 now becomes a 40.
and the result looks in short form :
12340
so, a multiplication by 10 adds a 0 at the low end of the number.
a multiplication by 10² or 100 (= 10×10) adds then 2 0s at the low end. and so forth.
a division by 10 does the opposite and removes a 0 at the low end of the number.
but what if we don't have any 0 at this position of the number ? then we enter the system of the decimal point.
because on the right side of the decimal point we continue to countdown the exponent of 10 below 0.
the first position right of the decimal point stands for 10^‐1, the second position for 10^‐2, and so forth. and that is nothing else than tenths, hundredths, thousandths, ...
so, in short, a multiplication by 10 moves the decimal point one position to the right. and if we run out of written positions, then we can simply assume an infinite sequence of 0s continuing further to the right.
and a division by 10 moves the decimal point one position to the left. and if we run out of written positions, then we can simply assume an infinite sequence of 0s continuing further to the left too that are then showing up on the right side of the decimal point.
now, I think we covered all the basics and we can look at the question here :
10² × 18.72
10² = 100 = 10×10
so, we are multiplying twice by 10 and move the decimal point therefore 2 positions to the right.
the result is then
1872
as a little guide : when it is clear that the number has to get bigger by the operation (like a multiplication by 10 or 100), you need to move the decimal point in the direction that makes the number bigger (which is to the right).
and if the operation is clearly trying to make the number smaller, then you have to move the decimal point in the direction to make the number smaller (to the left).
YES I WILL GIVE BRAINLIST
Which of the following systems of equations has exactly one solution?
Question 1 options:
2x+y=10y=−2x+8
2x+4y=102(x+2y)=10
2(2x+1)=yy=2x+8
y=10−2xy=−2x+7
Which of the following systems of equations has infinitely many solutions?
Question 4 options:
2x+7x+y=6y=9x+6
y=5x+7y=2x+8
y=x+42y=2x+8
7x−y=10y=6x+8
Answer:
Question 1) Option C: 2(2x+1) = y, y = 2x + 8.
Question 4) Option C: y = x + 4, 2y = 2x + 8
Step-by-step explanation:
Definitions:Perpendicular LinesThe graph of perpendicular lines will show an intersection of two lines at a single point, forming 90° adjacent angles. Since perpendicular lines intersect at exactly one point, then it means that they will have one solution. Additionally, perpendicular lines have negative reciprocal slopes for which multiplying the slopes of both lines result in a product of -1.
Coinciding LinesLines that have the same slope and y-intercept. Therefore, they are equivalent equations that will result in an infinitely many solutions. The graph of these lines will coincide on top of each other, as if they are the same line. The systems of linear equations that result in an infinitely many solutions are dependent and consistent. They are dependent if they have an infinite number of solutions, and consistent because they have at least one solution.
Parallel linesParallel lines have the same slope. A systems of linear equations whose graph involve parallel lines have no solution, as there is no point of intersection between those two lines. Therefore, parallel lines have no solution, making it an inconsistent system.
Question 1:We must transform these equations in its slope-intercept form, y = mx + b, which will allow us to easily determine the type of lines a given system has based on their slopes.
Option A:Equation 1: 2x + y = 10
Equation 2: y = −2x + 8
Transform Equation 1 to slope-intercept form:
2x + y = 10
Subtract 2x from both sides:
2x - 2x + y = - 2x + 10
y = -2x + 10 ⇒ This is the slope-intercept form of Equation 1.
Since Equations 1 and 2 have the same slope, but different y-intercepts, then it means that they are parallel lines that have no point of intersection.
Option B:
Transform both equations to slope-intercept form:
Equation 1: 2x + 4y = 10
[tex]\large\bf\sf{y\:=\:-\frac{1}{2}x\:+\:\frac{5}{2}}[/tex] ⇒ This is the slope-intercept form of Equation 1.
Equation 2: 2(x+2y) = 10
Distribute 2 into the parenthesis:
2(x+2y) = 10
2x + 4y = 10 ⇒ It is clear at this point that this equation matches Equation 1. Thus, the slope-intercept form of Equation 2 will be the same:
[tex]\large\bf\sf{y\:=\:-\frac{1}{2}x\:+\:\frac{5}{2}}[/tex] ⇒ Slope-intercept form of Equation 2.
It turns out that Equations 1 and 2 are equivalent, as they have exactly the same slope and y-intercept. Therefore, they have coinciding lines and have infinitely many solutions.
Option C:Transform both equations to slope-intercept form:
Equation 1: 2(2x+1) = y
y = 4x + 2 ⇒ Slope-intercept form of Equation 1.
Equation 2: y = 2x + 8
Option D:Equation 1: y = 10 − 2x
y = − 2x + 10 ⇒ This is the slope-intercept form of Equation 1.
Equation 2: y = −2x + 7
Since Equations 1 and 2 have the same slope, but different y-intercept, then it means that they are parallel from each other.
Answer for Question 1:Out of all the given four options, Option C seems to be the correct answer, since the given system has varying slopes and y-intercept. Therefore, the correct answer for Question 1 is Option C: 2(2x+1) = y, y = 2x + 8.
Question 4:For Question 4, I will not elaborate as thoroughly as in Question 1 since I'll be using the same techniques.
Option A)Equation 1: 2x+ 7x + y = 6
Combine like terms:
2x+ 7x + y = 6
9x + y = 6
Subtract 9x from both sides:
9x - 9x + y = - 9x + 6
y = - 9x + 6 ⇒ Slope-intercept form of Equation 1.
Equation 2: y = 9x + 6
Option A Explanation:
Equations 1 and 2 have different slopes and the same y-intercept. This implies that they will have a point of intersection = one solution. However, they don't have perpendicular lines because their slopes are not negative reciprocal of each other. Hence, Option A is not a valid answer for question 4.
Option B)Equation 1: y = 5x + 7
Equation 2: y = 2x + 8
Option B explanation:
Similar to Option A, Equations 1 and 2 have different slopes and varying y-intercepts. Since they are not parallel from each other, and do not have coinciding lines, then Option B is not a valid answer for question 4.
Option C)Equation 1: y = x + 4
Equation 2: 2y = 2x + 8
Transform Equation 2 to Slope-intercept form:
Divide both sides by 2 to isolate y:
[tex]\displaytext\mathsf{\frac{2y}{2}\:=\:\frac{2x\:+\:8}{2}}[/tex]
y = x + 4 ⇒ This is the slope-intercept form of Equation 2.
Option C explanation:
Equations 1 and 2 are equivalent, as they have exactly the same slope and y-intercept. They also have coinciding lines, having infinitely many solutions.
Therefore, Option C is the correct answer for Question 4.Option D)
Equation 1: 7x − y = 10
y = 7x - 10 ⇒ This is the slope-intercept form of Equation 1.
Equation 2: y = 6x + 8
Option D explanation:
Similar to Option B, Equations 1 and 2 have different slopes and varying y-intercepts. Since they are not parallel from each other, and do not have coinciding lines, then Option D is not a valid answer for question 4.
Juana buys a computer for $785.00. Her local sales tax is 6.85%. How much does Juana pay for the computer, including tax?
Answer:
838.7725
Step-by-step explanation:
Divide x5+15x4+54x3−25x2−75x−34 by x+8
Step-by-step explanation:
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
x+8x5+15x4+54x3-25x2-75x-34
Divide the highest order term in the dividend x5 by the highest order term in divisor x.
x4x+8x5+15x4+54x3-25x2-75x-34
Multiply the new quotient term by the divisor.
x4x+8x5+15x4+54x3-25x2-75x-34+x5+8x4
The expression needs to be subtracted from the dividend, so change all the signs in x5+8x4
x4x+8x5+15x4+54x3-25x2-75x-34-x5-8x4
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x4x+8x5+15x4+54x3-25x2-75x-34-x5-8x4+7x4
Pull the next terms from the original dividend down into the current dividend.
x4x+8x5+15x4+54x3-25x2-75x-34-x5-8x4+7x4+54x3
Divide the highest order term in the dividend 7x4 by the highest order term in divisor x.
On dividing, x⁵+15x⁴+54x³−25x²−75x−34 by x+8, Quotient is x⁴+7x³−2x²−9x−3 and Remainder is -10.
What is an Expression?An expression is a mathematical statement which consists of variables, constants and mathematical operators.
Dividend is x⁵+15x⁴+54x³−25x²−75x−34
Divisor is x+8
After division, the solution is attached in the image.
Quotient is ( x⁴+7x³−2x²−9x−3)
Remainder is -10
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The sum of two numbers is 110.The larger number is 2 less than 7 times the smaller.Find the Large number
Answer:
The larger number is 96.
Step-by-step explanation:
[tex]let \: the \: two \: numbers \: be \: a \: and \: b \\ a + b = 110 \\ let \: a \: be \: the \: larger \: number \\ a = 7b - 2 \\ we \: can \: get \: the \: value \: of \: b \: by \: substituting \: the \: value \: above \: for \: a \: in \: eq \: 1 \\ 7b - 2 + b = 110 \\ 8b - 2 = 110 \\ 8b = 110 + 2 \\ 8b = 112 \\ b = \frac{112}{8} \\b = 14\\ calculate \:the \: value \: of \: a \: using \: the \: equation \: above \\ a + b = 110 \\ a = 110 - 14 \\ a = 96 \\ hence \: the \: large \: number \: is \: 96[/tex]
if x = 5 find the value of a) x² b) (x + 3)²
Answer:
x=5a)x²
5²=25
b] (x+3)²
(5+3)²
(8)²=64
Mr. Walker asked his students to use the associative property to find an expression that is equivalent to (13 + 15 + 20) + (20 + 47 + 18). The expressions that four students created are shown in the table below.
Expressions Generated by Students
Student
Expression
Jeremy
(20 + 13 + 15) + (20 + 47 + 18)
Layla
(20 + 47 + 18) + (13 + 15 + 20)
Keith
(13 + 20) + (20 + 47 + 18) + 15
Melinda
(13 + 15 + 20 + 20) + (47 + 18)
How many of the students correctly applied only the associative property to rewrite the expression?
one
two
three
four
Mark this and return
Answer:
Jeremy
Step-by-step explanation:
You need to add 20+13+15=48 Then you add 20+47+18=85.
If angle 3 = 81, what is angle 4?
Answer:
99 degrees
Step-by-step explanation:
Angle 3 and 4 added together is 180 degrees since it is a straight line.
if you know angle 3 is 81 degrees, then angle 4=180-81=99
Answer:
99 is the measure of angle 4
Step-by-step explanation:
Two parralel lines cut by a transversal.
This is all you gotta remember
Alternate interior angles (4 and 6, 3 and 5) are congruent (equal)
Altenrate exterior angles (1 and 7, 2 and 8) are congruent (equal)
Corresponding angles (2 and 6, 3 and 7, 1 and 5, 4 and 8) are congruent (equal)
Same side interior angles (3 and 6, 4 and 5) are supplementary (equal to 180 if added up)
Same side exterior angles, (2 and 7, 1 and 8) are supplementary (Equal to 180 if added up)
Same line, opposite transversal (4 and 3, 5 and 6, 8 and 7, 1 and 2) are also supplementary.
Decrease 80 in the ratio 3 : 4
Answer:
60
Step-by-step explanation:
A decrease in the ratio 3 : 4 implies that
new value : old value = 3 : 4
x : 80 = 3 : 4
x/80 = 3/4
x = 3/4 * 80
= 3 * 20
= 60
The graph represents the distance a car traveled over time.
What is the constant of proportionality K.
Answer:
K=2/5
Step-by-step explanation:
So, I’m assuming that by constant of proportionality you mean slope of the line. To do that, you just figure out how y changes with x. The easiest way to do this is rise over run (y over x). If you look at the graph, there is a point that pass through (0,0) and another that passes through (5,2) so if you count how many spaces we moved up then how many spaces we moved right, you will get the slope of the line. Spaces moved up are 2-0=2 and spaced moved right are 5-0=5. Use rise over run which is going to be 2/5. So, K=2/5.
What are the coordinates of point P?
O (-4, 3)
O (-3, 4)
0 (3,-4)
O (4, -3)
P
Answer:
A
Step-by-step explanation:
crawl before you walk.
Which of these are ways to measure a resting heart rate?
Select all that apply.
Answer:
Place the index and middle fingers on the neck to the side of the windpipe to find the pulse.
Place two fingers between the bone and the tendon over the radial artery of the wrist to find the pulse.
Step-by-step explanation:
I did a test and that was a correct answer.
Mr. Green’s hobby was restoring old houses. He recently purchased an old rundown house that needed a lot of repair, especially with the plumbing. The kitchen faucet dripped all day and night. It intrigued Mr. Green how much water dripped from this faucet in one day, but he surely didn’t want to sit and watch the faucet drip all day. So he figured that if he could discover how much water dripped within a certain time span, he could calculate the dripping rate for any time span. In his first observation he noted that 6 ounces of water dripped in 10 minutes.
A) Using Mr. Green’s observation, can you help him figure out how much water would have dripped in only 5 minutes?
Answer:
3 ounces of water
Step-by-step explanation:
If 6 ounces of water dripped in 10 minutes, then that means that in HALF the time (5 minutes), HALF the amount of water would drip, which is 3 ounces.
What is the range of the function graphed below
4223422222222222222222222222
Answer:
-3<y<=3
Step-by-step explanation:
The function ranges from - 3 to 3,but 3 is included
what is 846837947+858
Answer:
846,838,805
Step-by-step explanation:
Add 846837947+858
what each word means, in your own words
Please help at least by defining in your own words 3 or more.
Rotation
Transformation
Translation
Dilation
Angle of Rotation
Line of Reflection
Rotation - Rotation is a plane transformation that rotates every point in a figure through a given angle and direction on a fixed point.
Transformation - Transformation is a process that alters the shape and or position of a point, a line, or a geometric figure.
Translation - Translation occurs when a figure is relocated from one position to another without changing its size, shape, or orientation.
Dilation - Dilation is a transformation that alters the size of a figure, whether enlarging or shrinking it, but it has no effect on the shape of the figure.
Angle of Rotation - Angle of Rotation is the amount that a figure is rotated about a fixed point referred to as the point of rotation.
Line of Reflection - Line of Reflection is a transformation in which each point in a shape appears at an equal distance on the opposite side of a given line.
Hope this helps!!
What is the equation of the line perpendicular to y = -4x + 3 that goes through (8, -3)?
what is 10 feet then half that length again
Answer:
5 feet?
Step-by-step explanation: 10 divided by 2 = 5
Answer:
5 feet :D
Step-by-step explanation:
Well the answer would be 5 feet due to finding the half of a number you divide it by 2. 10 divided by 2 would be 5, so the answer is 5.
2^-3 x 3^-2
what’s the answer?
Answer:
1/72Step-by-step explanation:
[tex]2^{-3} * 3^{-2} =[/tex][tex]1/2^3 * 1/3^2 =[/tex][tex]1/8*1/9=[/tex][tex]1/72[/tex][tex]\\ \sf\longmapsto 2^{-3}\times 3^{-2}[/tex]
[tex]\\ \sf\longmapsto( \dfrac{1}{2})^3\times( \dfrac{1}{3})^2[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{8}\times \dfrac{1}{9}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{72}[/tex]
What is an equation in point-slope form of the line shown in the graph, using the point (1, 5)?
Answer:
The point-slope form is
y
+
6
=
1
5
(
x
−
4
)
or
y
+
5
=
1
5
(
x
−
9
)
, depending on which point you use. If you solve for
y
to get the slope-intercept form, both equations will convert to
y
=
1
5
x
−
34
5
Step-by-step explanation:
can you Solve for c?
Answer:
[tex]3\sqrt{2}[/tex] or [tex]\sqrt{18}[/tex]
Step-by-step explanation:
Use 45-45-90 triangle theorem
3*[tex]\sqrt{2}[/tex]
what is the square root of 0.09 as a fraction
[tex]\\ \rm\bull\rightarrowtail 0.09[/tex]
[tex]\\ \rm\bull\rightarrowtail \dfrac{9}{100}[/tex]
Find square root
[tex]\\ \rm\bull\rightarrowtail \sqrt{\dfrac{9}{100}}[/tex]
[tex]\\ \rm\bull\rightarrowtail \dfrac{3}{10}[/tex]
[tex]\\ \rm\bull\rightarrowtail 0.3[/tex]
The solution of the square root of 0.09 as a fraction is,
⇒ 3 / 10
We have to given that,
To find value of the square root of 0.09 as a fraction.
Now, We can write it as,
⇒ √0.09
⇒ √9 / 100
⇒ √(3/10)²
⇒ 3/10
⇒ 0.3
Therefore, The solution of the square root of 0.09 as a fraction is,
⇒ 3 / 10
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Pizza is sold at a restaurant in 3 sizes: small (S), medium (M), and large (L). Customers can choose from 4 toppings to be used on a 1-topping pizza. The 4 toppings are green peppers (G), ham (H), pepperoni (P), and olives (O).
A customer plans to order a large or medium 1-topping pizza with any topping except pepperoni (P).
This sample space shows all the types of 1-topping pizzas. Which outcomes in this sample space show the types of pizza the customer may order?
Select all correct outcomes
Using the given sample space, it is found that the types of pizza the customer may order is: {MG, MH, MO, LG, LH, LO}
The sample space is the set that contains all possible outcomes.
In this problem:
The pizza is large or medium, hence the first letter has to be M or L.The topping is any except pepperoni, hence, the second letter is G, H or O.Thus, the possible outcomes are: {MG, MH, MO, LG, LH, LO}
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two friends A and b invest some money in a buisness in the ratio 13:12. they make a profit of 542600. How much should b receive as profit if the profit is proportional to the investment
Answer:
Step-by-step explanation:
What is a real number.
Answer:
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
Can you solve for x plz?
Answer:
x=25
Step-by-step explanation:
4x+50=150
4x=100
x=25
What is the length of side x?
Answer:
21
Step-by-step explanation:
10.5 ÷ 3 = 3.5
3.5 × 6 = 21
The average third grader student can read 60 words in five minutes what is the average reading rate per minute
Answer:
12 words a minute
Step-by-step explanation:
To find the answer all you need to do is divide 60/5
Answer:
12
Step-by-step explanation:
60 divided by 5