Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
[tex](0,7),(-13,-97)[/tex]
Equation Form:
[tex]x=0,y=7\\x=-13,y=-97[/tex]
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-(8*x+7)=0
Equation of a Straight Line
Solve y-8x-7 = 0
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.'
n this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-8x-7 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 7/1 so this line "cuts" the y axis at y= 7.00000
y-intercept = 7/1 = 7.00000
Calculate the X-Intercept :
When y = 0 the value of x is 7/-8 Our line therefore "cuts" the x axis at x=-0.87500
x-intercept = 7/-8 = -0.87500
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 7.000 and for x=2.000, the value of y is 23.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 23.000 - 7.000 = 16.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 16.000/2.000 = 8.000
Geometric figure: Straight Line
Slope = 16.000/2.000 = 8.000
x-intercept = 7/-8 = -0.87500
y-intercept = 7/1 = 7.00000
Pull out like factors :
-x2 - 5x - 7 = -1 • (x2 + 5x + 7)
Trying to factor by splitting the middle term
2.2 Factoring x2 + 5x + 7
The first term is, x2 its coefficient is 1 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant 1 • 7 = 7
Step-2 : Find two factors of 7 whose sum equals the coefficient of the middle term, which is 5 .
-7 + -1 = -8
-1 + -7 = -8
1 + 7 = 8
7 + 1 = 8
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Find the Vertex of y = -x2-5x-7
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens down and accordingly has a highest point (AKA absolute maximum) . We know this even before plotting "y" because the coefficient of the first term, -1 , is negative (smaller than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -2.5000
Plugging into the parabola formula -2.5000 for x we can calculate the y -coordinate :
y = -1.0 * -2.50 * -2.50 - 5.0 * -2.50 - 7.0
or y = -0.750
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = -x2-5x-7
Axis of Symmetry (dashed) {x}={-2.50}
Vertex at {x,y} = {-2.50,-0.75}
Function has no real roots
Solve Quadratic Equation by Completing The Square
3.2 Solving -x2-5x-7 = 0 by Completing The Square .
Multiply both sides of the equation by (-1) to obtain positive coefficient for the first term:
x2+5x+7 = 0 Subtract 7 from both side of the equation :
x2+5x = -7
Now the clever bit: Take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4
Add 25/4 to both sides of the equation :
On the right hand side we have :
-7 + 25/4 or, (-7/1)+(25/4)
The common denominator of the two fractions is 4 Adding (-28/4)+(25/4) gives -3/4
So adding to both sides we finally get :
x2+5x+(25/4) = -3/4
Adding 25/4 has completed the left hand side into a perfect square :
x2+5x+(25/4) =
(x+(5/2)) • (x+(5/2)) =
(x+(5/2))2
Things which are equal to the same thing are also equal to one another. Since
x2+5x+(25/4) = -3/4 and
x2+5x+(25/4) = (x+(5/2))2
then, according to the law of transitivity,
(x+(5/2))2 = -3/4
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x+(5/2))2 is
(x+(5/2))2/2 =
(x+(5/2))1 =
x+(5/2)
Q. If the word problem is asking you to find the space inside the circle, which formula should you use?
answer choices
Answer:
The last option: bottom right
Step-by-step explanation:
Explain three key differences between index funds and mutual funds
The three main differences are management style, investment objective and cost — and index funds are the clear winner.
Sure hope this helps you and pls mark me brainiest!
The main difference between index funds and mutual funds is that index funds seek market-average returns whereas mutual funds tries to outperform the market.
What is index funds?"Index funds are investment funds that follow a benchmark index, such as the S&P 500 or the Nasdaq 100."
What is mutual funds?"A mutual fund is a professionally managed investment fund that pools money from many investors to purchase securities. "
"If a mutual fund is active, then it has high fees than index fees."
"The performance of index fund is predictable whereas the performance of active mutual fund is not predictable."
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please help I am confused
Answer: -5
Step-by-step explanation:
Opposite sides of a parallelogram are parallel, and thus have equivalent slopes.
Solve the equation for all values of x by completing the square. 5x^2-70x=-230
Solve this ASAP please
Answer:
[tex]x=7 + \sqrt{3}[/tex]
[tex]x=7 - \sqrt{3}[/tex]
Step-by-step explanation:
Given equation:
[tex]5x^2-70x=-230[/tex]
Divide both sides by 5:
[tex]x^2-14x=-46[/tex]
Square half of the coefficient of [tex]x[/tex]: [tex](-14 \div 2)^2=49[/tex]
and add this to both sides:
[tex]x^2-14x+49=-46+49[/tex]
Factor the left side and simplify the right side:
[tex](x-7)^2=3[/tex]
Square root both sides:
[tex]x-7=\pm\sqrt{3}[/tex]
Add 7 to both sides:
[tex]x=7 \pm \sqrt{3}[/tex]
[tex]\sf x=\pm \sqrt{3}+7[/tex]
solving step wise:
[tex]\sf 5x^2-70x=-230[/tex]
divide the following by 5
[tex]\sf x^2-14x=-46[/tex]
completing square
[tex]\sf (x-\dfrac{14}{2})^2-(\dfrac{14}{2})^2 =-46[/tex]
should look like this
[tex]\sf (x-7)^2-49=-46[/tex]
simplify by changing sides
[tex]\sf x-7=\pm \sqrt{3}[/tex]
final answer:
[tex]\sf x=\pm \sqrt{3}+7[/tex]
You are going to the mall with your
friends, and you have $200 to spend.
you find a store that has all jeans for
$25 and all shirts for $10. you buy a
total of 14 items. how many of each
item did you buy?
Answer:3 jeans and 11 shirts with 15 dollars leftover
Step-by-step explanation:
3x25=75
11x10=110
110+75=185
200-185=15
25x4 will make the leftover money higher, so 3 and 11
ANSWER NOW NEEDS TO BE DONE WITHIN 90 MIN!!!!
What percent of the students received a score below 64, if the mean grade on a test was 70 and the standard deviation was 6.
Using the normal distribution, it is found that 15.87% of the students received a score below 64.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem, the mean and the standard deviation are given by, respectively: [tex]\mu = 70, \sigma = 6[/tex].
The proportion of students who received a score below 64 is the p-value of Z when X = 64, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{64 - 70}{6}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
Hence, 15.87% of the students received a score below 64.
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I need help please with these 2 problems
Step-by-step explanation:
1a) =>3(3x+1)/4(3x+1)=3/4
b) => 2x(x+5)/(x+5)²=2x/x+5
2) a raph restriction means that the graph stops where the restriction says. But because the y's are the output of the x's, they only give u the x restriction and then you can calculate the point by finding the y coordinate. This may sound weird but here is an example:
[1,3] => this means the graph will only show between the points 1 and 3 (on the x-as). Both points are included in the graph.
[1,3[ => this means the raph will only show between the points 1 and 3 but 1 is still a part of the graph but not 3 so up till every little number but just not 3.
hope u get it lol
help i’ll mark brainlist
Please help me with this please and thank you
Answer:
b. [tex]3^{-x}[/tex]
Step-by-step explanation:
(-2, 9)
[tex]f(-2)=3^{-(-2)} =3^{2} =9[/tex]
(-1, 3)
[tex]f(-1)=3^{-(-1)} =3^{1} =3[/tex]
(0 1)
[tex]f(0)=3^{0} =1[/tex]
Hope this helps
Write the equation of a line that passes through the point (-4,-5) and is perpendicular to the line y= -1/2x+5
Answer:
Step-by-step explanation:
First let us determine the perpendicular line by remembering that a perpendicular line that intersects with the current line must have the opposite reciprocal slope as it. Meaning... the current slope is -1/2 and the opposite reciprocal is +2 or 2.
To clarify...
*opposite= the opposite sign ex. the opposite of +3 is -3 and the opposite of -1 is +1
*reciprocal=put simply, the reciprocal is the flipped version of the current number ex. the reciprocal of 1/2 is 2/1 or 2 and the reciprocal of 3 or 3/1 is 1/3
After we determine the slope of the perpendicular line, we are also know the point it must pass through.
Given that, we can find the equation.
Using y=mx+b
Plug in known varibles
y=-5
x=-4
m=2
b=?
-5=2(-4)+b
b=3
So now that we have b, we can put the equation in standard form.
y=2x+3
Hope this helps!!!
The number of points scored by two basketball teams in each teams' latest
10
games are listed below. Compare and contrast the measures of central
tendency for the data sets.
Team one: {54, 47, 62, 59, 49, 51, 54, 60, 57, 53}
Team two: {63, 57, 49, 52, 61, 43, 51, 53, 56, 48}
Answer:
See below.
Step-by-step explanation:
Arranging the data in ascending order:
Team one: { 47, 49, 51, 53, 54, 54, 57, 59, 60, 62}
Team two: {43, 48, 49, 51, 52, 53, 56, 57, 61, 63}
The mean for team one = sum of the scores / 10 =
= 546/10 = 54.6.
The median for team 1 = 54.
The mean for team two = sum of the scores / 10 =
= 533/10 = 53.3.
The median for team 2 = 52.5.
Team 1 has a higher mean than team 2: 54.6 - 53.3 = 1.3 higher.
In both cases, the mean is greater than the median though the difference is < 1 in both cases. So in both cases the distribution of the scores is close to symmetrical, with team 1 being slightly more symmetrical.
A sample of 100 students was randomly selected from a middle school in a large city. These participants were asked to select their favorite type of pizza: pepperoni, cheese, veggie, or Hawaiian. pizza preference and gender were recorded for each participant. The results of the survey are summarized in the table
The variables of the hypothesis test include the favorite type of pizza and the gender
The null hypothesis is Favorite pizza and gender are independent
How to determine the null hypothesis?
From the complete question, the variables that are measured are:
Favorite type of pizzaGenderThe null hypothesis of a test used the equality statement.
So, the null hypothesis would be
Favorite pizza and gender are independent
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71-2x + 2
y2= -x+8
Albert created this table of solutions for the equations.
X
-2
0
4
N
S
yu
2 | 2
6
10
y2
10
8
6
4
Which point is a solution to the system of equations?
А.
(-2,-2)
B. (0,8
C.
(2,6
Cinem
D. (10,4)
in
Answer:
(2,6)
Step-by-step explanation:
y1 = y2
2x + 2 = - x + 8
2x + x = 8 - 2
3x = 6
x = 2
y1 = y2 = 6
Determine the value of k so that the relation {(2, 5), (k, 0), (–9, 2), (0, –9)} can be a function
Step-by-step explanation:
in a function every valid values of x has exactly one assigned y value.
in an ordered pair the first number is x, the second number is y.
the y in (k, 0) is therefore 0.
and this y is different to all other y values in the relation.
therefore, k must be different to all other defined x values (otherwise it would give an x value a second y value, which would make this a not-function).
so, k must be an integer not out of {-9, 0, 2}
A frame contains 4 pounds of gold. suppose gold is worth $1,277 per ounce. how much would the gold in the frame be worth?
Answer:
$81,728
Step-by-step explanation:
For reference: 1 pound = 16 ounces.
Therefore, 4 pounds of gold must be 16 * 4 = 64 ounces.
Since each ounce is $1,277, we must have the total cost of the gold to be $1,277 * 64 = $81,728.
The key word here is "per", which means to multiply.
Answer:Answer:5,108
Step-by-step explanation:
90 pounds =. Ounces
I need help
Answer:
1440 ounces
Step-by-step explanation:
there are 16 ounces in a pound so multiply 90 by 16 and you get 1440 hope this helps!
Jasmin rakes at two different houses. it takes her 2 1/3 hours to rake leaves at the first. it takes her 1/2 of that time to rake at the second house. how long does it take jasmin to rake at the second house?
Answer:
Jasmin rastrilla en dos casas diferentes. le toma 2 1/3 horas rastrillar las hojas al principio. le toma 1/2 de ese tiempo rastrillar en la segunda casa. ¿Cuánto tiempo tarda el jazmín en rastrillar en la segunda casa?
Step-by-step explanation:
Rhys's house had a temperature of 12°C. He put the heating on and the temperature rose by 8°C. As he was still co Rhys decided to light a fire which increased the temperature by a further 13°C. What was the temperature in the hou now?
Answer:
this is very easy.
Step-by-step explanation:
if he started at a temperature of 12, then added 8 and added 13 onto that? the sum of those numbers would be 33. so 33 degrees Celsius
An observer at the top of a building sees a car on the road below. the angle of depression to the car is 28 degrees. If the car is about 50m from the building when it is seen, how tall is the building?
Answer:
Step-by-step explanation:
The height of the building is: 26.585 m.
What is angle of Depression?The angle formed by the line of sight and the horizontal plane for an object below the horizontal.
Given:
angle of depression= 28 degree,
distance between car and building= 50m
using trigonometry,
tan 28= P/B
0.5317= P/50
P= 26.585 m
Hence, the height of the building is 26.585 m.
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Help please I'ma giving alot of points if you say something else just to get the points I will report
Answer:
Read the explanation
Step-by-step explanation:
look at the photo
Hello people ~
factorise: : x^2 – 21x + 108
[tex]\\ \rm\rightarrowtail x^2-21x+108[/tex]
Use midterm splitation[tex]\\ \rm\rightarrowtail x^2-12x-9x+108[/tex]
[tex]\\ \rm\rightarrowtail x(x-12)-9(x-12)[/tex]
[tex]\\ \rm\rightarrowtail (x-9)(x-12)[/tex]
Done!
A cube has a side length of 5 inches. What is the surface area, in square inches of the cube?
Answer:
A=6a2=6·52=150in²
Step-by-step explanation:
Agustin says that he can hold his breath for 90 seconds. And, he says that he did this 5 times this week. He used fractions and multiplication to calculate how many minutes he held his breath this week.
Answer:
7.5 minutes
Step-by-step explanation:
90 seconds is equivalent to 1.5 minutes
1.5×5=7.5
How to write expressions as the sine, cosine, or tangent of a single angle
find the missing side of the parallelogram. keep answer in simplest form
Area of parallelogram is Base×height
10×18=15× x
x= 12
hope it helps
Answer:
x = 12
Step-by-step explanation:
So, area of a parallelogram is base times height.
In this picture, one of the base, height pair is 18 and 10.
18 * 10 = 180
The other base, height pair is 15 and x.
So, 15 and x should equal to 18 * 10.
Then, 15x = 180.
Divide both sides by 15, and you get 15x/15 = x and 180/15 = 12.
So, x = 12
please help! pleaseeeeee
Answer:
D-27 cm
Step-by-step explanation:
we are given that the top is 8cm
one side is 3..the 2 sides are the same length so total of 6
the bottom is 5, we know the top is 8 so 8-5 =3
the 2 breaks are 1 each
so we do
8 + 5+ 6+ 2+3 =24
Can you pls help me with this
The function f(x)=4x^(5)-2x^(3)+8x is:
Answer:
C. Odd
Step-by-step explanation:
If you reflect this function across the y-axis it is not symmetrical, therefore it is not an even function
But, if you rotate this function by 180 degrees, it is unchanged, therefore it is and odd function
Tim wants to buy soda. He can choose a 6-pack of 0.355-liter cans or a 2-liter bottle. Which statement is true?
A. The 6-pack contains 0.130 liters more soda.
B. The 2-liter bottle contains 0.130 liters more soda.
C. The 2-liter bottle contains 0.645 liters more soda.
D.The 6-pack contains 0.645 liters more soda.
The true statement is that the 6-pack contains 0.130 litres more soda.
He can choose a 6-pack of 0.355-liter cans or a 2-liter bottle.
6 pack of 0.355-liter cans. Therefore, let's establish the following proportion.
Proportional relationship1 pack = 0.355 litre can
6 pack = ?
cross multiply
volume of soda = 6 × 0.355 = 2.13 litres
The 6-pack of 0.355-liter cans contains 2.13 litres of soda.
difference = 2.13 - 2.00 = 0.13 litres
Therefore, the 6-pack contains 0.130 litres more soda
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PLSSSSSS HELP ME WITH THISS!!!
Answer:
Her total would be $59 so, we would be a dollar extra.
The answer is Yes, the total will be $59.
Step-by-step explanation:
$58 - $18.50 = You need to earn $39.5.
Garden = $6.50 per hour
Cakes = $5.25 per hour
$6.50 X 3 hours = $19.50
$5.25 X 4 hours = $21
$21 + $19.50 = $40.50 totall
$18.50 + $40.50 = $59