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)
Find the value of x for which ABCD must be a parallelogram.
Can someone explain this to me?
p-p-p-q-q-q =?
its urgent
Hey there!
Let's combine like terms:
p-p-p-q-q-q
p-p-p=-p
-p-p-q-q-q
-p-3q
Remember, like terms are from the same "family"
So p's are from the p family, and q's are from the q family.
Hope everything is clear.
Let me know if you have any questions.
#LearningDoesn'tEnd
the temperature is falling at rate of 3 degrees per hour. if the temperature at 12 midnight is "-2°c," what will be the temperature at 5:00 am
Answer:
- 17° C
Step-by-step explanation:
the temperature falls at 3° per hour
midnight → 5.00 am is 5 hours , then
5 × - 3 = - 15 ← falls 15° in the 5 hours
temperature at 5..00 am = - 2 - 15 = - 17° C
Answer:
-17
Step-by-step explanation:
as it is falling by three so at 5am it will reach -17
PLEASE HELP ME IM NOT GOOD AT MATH
Veronica rolls a six-sided die 28 times.
How many times should she expect the die to land on an even number?
Enter your answer as a number, like this: 42
Answer:
14
Step-by-step explanation:
There are 3 even and 3 odd sides meaning its a 50/50 chance for either to happen each time you roll. This means half of the results are expected to be odd and even.
Find the measure of angle GHI.
Answer:
119 is correct answer.
Step-by-step explanation:
angle GHI+90+151=360 (being complete turn angle)
angle GHI =360-119
angle GHI =119
I AM BEGGING. PLEASE HELP
Answer:
84cm³Step-by-step explanation:
Volume of the right triangular prism:
Note: V=l*w*h
L=3cm
W=4cm
H=7cm
Then, multiply.
3*4*7=84
84cm³
Therefore, the correct answer is 84cm³.
I hope this helps you! Let me know if my answer is wrong or not.
What is the value of `x` in the solution of the system of equations?`3x-2y=6``\ \ x+2y=10`
Answer:
x = 4
Step-by-step explanation:
3x - 2y = 6 → (1)
x + 2y = 10 → (2)
add (1 ) and (2) term by term to eliminate y
(3x + x) + (- 2y + 2y) = 6 + 10 , that is
4x = 16 ( divide both sides by 4 )
x = 4
Find the surface area and volume of the figure.
(Round to the nearest teeth as needed)
Answer:
Volume;
Let's find the volume of the hemisphere above,
Formula for hemisphere volume:
V = 2/3πr
Where pi(π) is 22/7 or 3.14, and 'r' is the radius.
(extra info:) D/2 = radius
So, diameter in this case is 6,
6/2 = 3 is the radius.
Replace values:-
V = 2/3πr
V = 2/3 x 3.14(3)
V = 2/3 x 9.42
V = 18.84/3
V = 6.28 feet is the volume for the hemisphere.
Now the cylinder's volume,
Cylinder volume formula:
V = π[tex]r^{2}[/tex]h
Where pi(π) is 22/7 or 3.14, 'r' is the radius which is being squared, and 'h' is the height.
Replace values (we figured out radius is 3);
V = π[tex]r^{2}[/tex]h
V = 3.14(3^2) x 10
V = 3.14(9) x 10
V = 28.26 x 10
V = 282.6 feet is the volume of the cylinder.
Add our volumes:-
6.28 + 282.6
= 288.88 feet is our volume.
Surface area;
Now the surface area formula of the cylinder is:
SA = 2πrh(lateral area) + 2π[tex]r^{2}[/tex](area of circle)
Replace values:
SA = 2πrh + 2π[tex]r^{2}[/tex]
SA = 2(3.14) x 10 + 2(3.14) x 3^2
SA = 6.28 x 10 + 6.28 x 9
SA = 62.8 + 56.52
SA = 119.32 is the surface area of the cylinder.
Now the surface area formula of the hemisphere;
SA = 3πr²
Replace values;
SA = 3πr²
SA = 3(3.14) x 3^2
SA = 9.42 x 9
SA = 84.78 is the surface area of the hemisphere.
Add the areas;
119.32 + 84.78
= 204.1 feet is the surface area.
i need helppppppppppppppppppppppppppppppppppppppp
There are 14 white cabbages and x purple cabbages in a box.
A cabbage is selected at random.
The probability of taking a white cabbage from the box is 0.56.
Find the value of x.
Answer:
x = 11
Step-by-step explanation:
Given:
14 = number of white cabbagesx = number of purple cabbagesP(W) = 0.56⇒ total number of cabbages = 14 + x
[tex]\mathsf{Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ outcomes}}[/tex]
[tex]\sf \implies P(W)=\dfrac{number \ of \ white \ cabbages}{total \ number \ of \ cabbages}[/tex]
[tex]\sf \implies 0.56=\dfrac{14}{14+x}[/tex]
[tex]\sf \implies 0.56(14+x)=14[/tex]
[tex]\sf \implies 7.84+0.56x=14[/tex]
[tex]\sf \implies 0.56x=6.16[/tex]
[tex]\sf \implies x=11[/tex]
i need help. please
Answer:
[tex]V=\pi r^2h=\pi *6^2*19[/tex] ≈ [tex]2148.8[/tex]
Let me know if you found this helpful! It means a lot!
A circle has a radius of 9 cm and a sector of the circle has an arc length of 9. 7cm
Answer:
S = R θ where θ is in radians
If θ = 2 pi then S = 2 pi R the circumference of the circle
θ = S / R = 9.7 / 9 = 1.08 rad
Since 1 rad = 360 / (2 pi) = 57.3 deg
the angle included = 1.08 rad * 57.3 deg/rad = 61.9 deg
ST is parallel to RU in the figure. What is m<3 if m<1 =49
Answer:
49
Step-by-step explanation:
M<1 = M<2 - Corresponding angles are congruent
M<2 = M<3 - Vertical angles
Answer:
6) 49°
7) 30°
Step-by-step explanation:
6)Where a transversal crosses parallel lines, alternate exterior angles are congruent. Angles 1 and 3 are alternate exterior angles, hence congruent.
∠3 = 49° . . . . . . . same as ∠1
__
7)Angles 5x and x are a linear pair, so supplementary. Angle 'a' corresponds to angle x, so is congruent to it.
5x +x = 180°
x = 180°/6 = 30°
a = 30° . . . . . . . . same as x
One of the acute angles in a right triangle measures 62°. What is the measure of the other acute angle in the triangle?
Answer: 28 degrees
Step-by-step explanation:
In a right triangle, the two acute angles are complementary, so the other acute angle measures 90-62=28 degrees.
The sides of a square are 12 feet long. Find the new side
length after it is increased by 40%.
Answer:
16.80 ft long
Step-by-step explanation:
X= 15+yx+2y =51solve the system using elimination
Answer:
Im not going to give u an answer, but i will help u get the answer.
Step-by-step explanation:
there is a algebra problem solver called symbolab it really helps
Consider the enlargement of the triangle and use the measurements to calculate the scale factor. 2 triangles have corresponding side lengths of 8 centimeters and 64 centimeters. scale factor =
The scale factor when a triangle of 8cm side is enlarged to a triangle of 64cm side is 8.
Side of the first triangle = 8cm
Side of the second triangle = 64cm
What is a scale factor?A scale factor is a number by which the size or dimension of an object is enlarged or diminished.
For example, if an equilateral triangle with a side x is dilated by a scale factor of 2, the enlarged size of the side will be 2a.
So, scale factor = side of the second triangle/ corresponding side of the first triangle.
Scale factor = 64/8
Scale factor = 8
Therefore, The scale factor when a triangle of 8cm side is enlarged to a triangle of 64cm side is 8.
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Answer:
8 I did the assignment
Step-by-step explanation:
16=2(-8t-1)(t-2) solve for t
hi there! so here's my answer
[tex] \rm \tiny\color{green}t = \frac{10}{9} \\ \\ \tt \: in \: alternative \: form \\ \\ \color{yellow} \rm \: t = 1 \frac{1}{9} \: \: \: or \: \: t = 1.1[/tex]
Step-by-step explanation:
[tex] \color{gray} \tt \: 16 = 2( - 8t - 1) \times (t - 2)[/tex]
calculate the difference[tex]\color{gray} \tt \: 16 = 2(- 9)(t - 2)[/tex]
multiplying an odd number of negative terms makes the product negative[tex]\color{gray} \tt \: 16=^ \ 2*9(t-2)[/tex]
multiply the numbers[tex]\color{gray} \tt \: 16=-18 (t-2)[/tex]
distribute - 18 trough the parentheses[tex]\color{gray} \tt \: 16 = - 18t + 36[/tex]
move the variable to the left hand side and change its sign[tex]\color{gray} \tt \:16+18t=36[/tex]
move the constant to the right-hand side and change its sign[tex]\color{gray} \tt \:18t=36-16 [/tex]
substract[tex]\color{gray} \tt \:18t=20 [/tex]
by both sides of the equation by 18[tex] \:\rm \tiny\color{green}t = \frac{10}{9} \\ \\ \tt \: in \: alternative \: form \\ \\ \color{yellow} \rm \: t = 1 \frac{1}{9} \: \: \: or \: \: t = 1.1[/tex]
hope it helps
solve pls brainliest
Answer:
No, No, Yes, Yes, Yes.
Step-by-step explanation:
A integer is a whole number. 1, 2, 3, etc.
Answer:
Only -46 is an integer number and others are not.
Step-by-step explanation:
An integer is a whole number but not a fractional number that can be positive, negative, or zero.
In this chart -46 is an integer cause it is a whole number and -1/2, 57.68, 24/6, 9/3 are not integers cause they are a fraction.
Dion bought 3 pounds of oranges and 2 pounds of grapefruit . Write an expression to represent the amount of money Dion spent on fruit. Then evaluate the expression. How much did Dion Spend?
Fruit Prices: Lemons : $0.79
Oranges : $ 0.99
Limes : $ 1.09
Grapefruit : $ 1.59
The expression to represent the amount of money Dion spent on fruit is 3x + 2y.
The amount of money Dion spent is $6.15
How to represent mathematical expression?Expression are numbers, symbols and operators grouped together that show the value of something.
Dion bought 3 pounds of oranges and 2 pounds of grapefruit.
The expression to represents the amount of money Dion spent on fruit is as follows:
let
x = cost of each pounds of oranges
y = cost of each pounds of grapefruit
Therefore,
total cost = 3x + 2y
Let's evaluate the expression
total cost = 3(0.99) + 2(1.59)
total cost = 2.97 + 3.18
total cost = 6.15 dollars
Therefore, Dion spent $6.15
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Please help me answer this question on congruent triangles. 30 points
Answer:
h = 24 cm
Step-by-step explanation:
Let [tex]x[/tex] = height of ΔCBD
Let [tex]h[/tex] = height of ΔABE
As ΔABE ~ ΔCBD then AE : CD = [tex]h[/tex] : [tex]x[/tex]
Given:
AE = 20 cmCD = 10 cm[tex]\implies 20 : 10 = h : x[/tex]
[tex]\implies \dfrac{20}{10}=\dfrac{h}{x}[/tex]
Cross multiply:
[tex]\implies 20x=10h[/tex]
Simplify:
[tex]\implies 2x=h[/tex]
As we are told that [tex]x+h=36 \ \sf cm[/tex]
[tex]\implies h=36-x[/tex]
Equate the two equations for [tex]h[/tex] and solve for [tex]x[/tex]:
[tex]\implies 2x=36-x[/tex]
[tex]\implies 3x=36[/tex]
[tex]\implies x=12[/tex]
Since [tex]h=2x[/tex] then
[tex]\implies h=2 \cdot 12[/tex]
[tex]\implies h=24 \ \sf cm[/tex]
hi, please answer the question, show your work
Step-by-step explanation:
3200 = 100%
2848 = ?%
2848 ÷ 3200 then × 100
= 89%
so 2848 = 89%
Answer:
89%
Step-by-step explanation:
3200/2848=0.89
To turn into a percentage multiply by 100
So 0.89*100=89%
Solve the following proportions
Answer:
[tex]6.5 \times 12.4 = 40.3 \: m \\ \frac{80.6}{40.3} = 2[/tex]
Miki, a resident of kyoto, earns an annual salary of ¥6,760,950. if the japanese government levies a 29.12% income tax on miki’s tax bracket, what is her yearly take-home pay, to the nearest whole yen? a. ¥4,792,161 b. ¥4,643,510 c. ¥4,439,195 d. ¥4,364,869
The amount of yearly take-home pay of Miki, a resident of Kyoto after the payment of income tax is ¥4,792,161.
What do you mean by percentage?
Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the percentage symbol '%'.
Miki, a resident of kyoto, earns an annual salary of ¥6,760,950. The Japanese government levies a 29.12% income tax on miki’s tax bracket.
The amount of tax Miki pay to the government as income tax is,
[tex]I=\dfrac{29.12}{100}\times6760950\\I=1968788.64[/tex]
Miki, earns an annual salary of ¥6,760,950. Thus, her yearly take-home pay after the deduction of income tax is,
[tex]M=6760950-1968788.64\\M=4792161.36\\M\approx4792161[/tex]
Thus, the amount of yearly take-home pay of Miki, a resident of Kyoto after the payment of income tax is ¥4,792,161.
Learn more about the percentage here;
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Answer:
A
Step-by-step explanation:
:) good luck
What is the square root of 81
Answer: 9
Step-by-step explanation:
9*9 = 81
Answer:
9
Step-by-step explanation:
9*9=81
Find the sine ratio for ∠D.
a. 7/25
b. 24/7
c. 25/24
d. 24/25
Answer:
sin ∠D = 24/25
Step-by-step explanation:
sin = opposite / hypotenuse
Looking at ∠D, the opposite side is 24, hypotenuse is 25
Therefore sin = 24/25
You pay 3. 5% annual simple interest for 12 years on a loan and you pay $1512 in interest. How much is the principal
Answer:
P = $1,064.79
Step-by-step explanation:
the equation we will use is P = A / (1 + rt), where P=principle, A=amount payed, r=rate(interest), and t=time. first convert the rate into a decimal (0.035) and then plug in the numbers into the equation P = 1512 / ( 1 + (0.035 × 12)) = 1064.79
200 divided by 5 what is the answer
Answer:
40
Step by Step:
200/5 = 40
Giving Brainliest
A spy realizes his cover is blown and flees toward his secret evacuation spot at a speed of 60 mph. Two hours later, a special agent in a helicopter starts chasing the spy. The special agent travels the same route at a speed of 90 mph.
A What distance does the spy cover in t hours?
B What distance does the special agent cover in t hours?
C How fast is the distance between them reducing
D How far apart are the spy and special agent when the chase begins?
E How long does it take the special agent to catch the spy?
F At what speed should the special agent chase the spy if the evacuation spot is 240 miles from the setting point
The distance covered by the spy in t hours will be 60t while the special agent's distance is 90t.
How to calculate the distance?The distance covered by the spy in t hours will be calculated thus:
= 60 × t
= 60t
The distance covered by the special agent in t hours will be:
= 90 × t
= 90t
The difference in the distance between them every hour will be:
= 90t - 60t
= 30t
The distance between the spy and special agent when the chase begins will be:
= (2 × 60mph) - 0
= 120m - 0
= 120m
The time taken to catch the spy will be:
120 + 60t = 90t
90t - 60t = 120
30t = 120
t = 120/30 = 4
The special agent will catch the spy in 4 hours.
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Answer:
A: 60t
B: 90t
C: 30 mph
D: 120 miles away
E: 4 hours
F: 120 mph
Step-by-step explanation: