Answer:
[tex]\boxed{x=\frac{4\pm\sqrt{2}}{2}}[/tex]
Step-by-step explanation:
Part 1: Rewriting equation to match ax² + bx + c = 0 (quadratic function)
The given equation is not written in quadratic form. To rewrite the equation:
All values need to be on the left side of the equation and set equal to zero.To overcome this difficulty, follow these mathematical steps:
[tex]2x^2=8x-7\\2x^2-8x=-7\\2x^2-8x+7=0[/tex]
Subtract 8x from both sides of the equation to rearrange it to the left side. Then, add 7 to rearrange it as well. Finally, set the three values on the left of the equation equal to zero.
Part 2: Using the quadratic formula
The quadratic formula is defined as [tex]\boxed{x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} }[/tex].
Using the parent quadratic function, the values are easy to find in the given equation. [tex]\boxed{a=2, b=-8, c=7}[/tex]
Substitute these values into the quadratic formula and solve for x.
[tex]x=\frac{8\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)} \\\\x=\frac{8\pm\sqrt{64-4(14)}}{4}\\\\x=\frac{8\pm\sqrt{64-56}}{4} \\\\x=\frac{8\pm\sqrt{8}}{4}\\\\x= 2\pm\frac{\sqrt{8}}{4}\\ \\x=2\pm\frac{\sqrt{2}}{2}[/tex]
Part 3: Solving for x with the values from the quadratic formula
Now that x is set equal to the simplified version of the equation, the operations have to be followed through with.
This equation will have two zeros/roots to solve for by setting x equal to zero.
Operation 1: Addition
[tex]x=2+\frac{\sqrt{2} }{2}\\\\x=\frac{4+\sqrt{2}}{2}[/tex]
Operation 2: Subtraction
[tex]x=2-\frac{\sqrt{2}}{2}\\ \\x=\frac{4-\sqrt{2}}{2}[/tex]
Because both values are the exact same (minus the operations), the roots can be simplified even further to one value:
[tex]\boxed{x=\frac{4\pm\sqrt{2}}{2}}[/tex]
Tanisha lives in an apartment and pays the following expenses each month: electric bill, $42.42; TV streaming services, $27.99; and rent, $587.70. Estimate her total expenses for the month by first rounding each value to the nearest tens place.
A) $670
B) $ 650
C) $659
D) $660
Answer:
It is C
Step-by-step explanation:
42.60=43.00
587.70=588.00
27.99=28.00
Please thank you! I will give brainleist to the first correct answer if it lets me
Answer:
x=10 y=12
Step-by-step explanation:
just multiply 15 and 18 by 1/3 because both triangle are similar.
Answer:
x = 10; y = 12
Step-by-step explanation:
find the scale factor ratio using corresponding sides: 9 / 6 = 3/2 so the ratio is 3:2
from large triangle to small triangle you will get:
1. 15 / x
2. 18 / y
to implement the ratio, set the side length ratio equal to the scale factor:
1. [tex]\frac{15}{x}[/tex] = [tex]\frac{3}{2}[/tex]
2. [tex]\frac{18}{y}[/tex] = [tex]\frac{3}{2}[/tex]
cross multiply:
1. 30 = 3x
2. 36 = 3y
divide:
1. x = 10
2. y = 12
how do you find y=-4x+3 on a table
☆*☆=3x, if x is even and negative OR ☆*☆=4x, if x is odd. Following the rule above, what is the value of ☆ - 23 ☆?
A. 92
B. -92
C. 529
D. -529
Answer:
okay... Thanks have a great day!
Hi could somebody help me
Assuming both vertical lines are parallel and assuming I'm supposed to find all the unmarked angles...
Angle C:
Supplementary Angles.
x+36=180
180-36=x
x=144
Angle B:
Corresponding Angles.
Angle B ≅ Angle C
144
Angle A:
360 degrees in a quadrilateral
36+144+81+x=360
261+x=360
x = 99
Hope it helps <3
WILL GIVE BRAINLEIST!!!!!
Find the surface area of the right triangular prism shown below.
Answer:
144 units²
Step-by-step explanation:
Surface area of a traingular prism is given as:
Area = 2(B.A) + P*L
Where,
B.A = base area of the triangular prism = ½*b*h
b = base of the triangular base = 4 units
h = height of the triangular base = 3 units
Base Area (B.A) = ½*4*3 = 2*3 = 6 units²
P = Perimeter of triangular face = sum of all sides the triangle = 3 + 4 + 5 = 12 units
L = length or height of prism = 11 units
Plug in all values into the formula for surface area of triangular prism = 2(B.A) + P*L
[tex] Area = 2(6) + 12*11 [/tex]
[tex] = 12 + 132 [/tex]
[tex] Surface Area = 144 [/tex]
Surface area of the triangular prism = 144 units²
In the picture down below
Answer:
b
Step-by-step explanation:
The answer is b because we are looking for opposites
The opposite of +x is -x
While the opposite of -3 is +3
with this, we can switch them around.
this gives us the inverse of 3-x
Are these fractions equivalent or
nonequivalent?
Answer:
no
Step-by-step explanation:
there is no factor to convert one into the other.
moreover, 19 is prime and 9 is not, so no way.
what is the domain of the function represented by the graph.?
Answer:
all real numbers
Step-by-step explanation:
There is nothing on the graph to indicate the function is undefined for any values of x. The domain is all real numbers.
Answer:
Domain is all real numbers.
Step-by-step explanation:
The domain of a quadratic function in standard form is always all real numbers, meaning you can substitute any real number for x.
Find the ratio in which the line joining the points (2, 4, 16) and (3, 5, -4) is divided by the plane 2x – 3y+ z+ 6 = 0. Also find the co-ordinates of the point of division
Answer:
Step-by-step explanation:
let the plane intersects the join of points in the ratio k:1
let (x,y,z) be the point of intersection.
[tex]x=\frac{3k+2}{k+1} \\y=\frac{5k+4}{k+1} \\z=\frac{-4k+16}{k+1} \\\because ~(x,y,z)~lies~on~the~plane.\\2(\frac{3k+2}{k+1} )-3(\frac{5k+4}{k+1} )+\frac{-4k+16}{k+1} +6=0\\multiply~by~k+1\\2(3k+2)-3(5k+4)+(-4k+16)+6(k+1)=0\\6k+4-15k-12-4k+16+6k+6=0\\-7k+14=0\\k=2\\x=\frac{3*2+2}{2+1} =\frac{8}{3} \\y=\frac{5*2+4}{2+1}= \frac{14}{3} \\z=\frac{-4*2+16}{2+1} =\frac{8}{3}[/tex]
point of intersection is (8/3,14/3,8/3)
and ratio of division is 2:1
Triangle TQRS Find the value of x.
O x = 2
O x = 3
O x= 33
O x= 52
Answer:
x=3
Step-by-step explanation:
To solve for x, we will follow the steps below:
First note that exterior angle =two opposite interior angle
From the diagram below
(25x) ° + (57 + x)° = (45x)°
25x° + 57° + x° = 45x°
next step is to collect the like term
45x° - 25 x° - x° = 57°
19x° = 57°
Divide both-side of the equation by 19
19x°/ 19 = 57° /19
On the left-hand side of the equation 19 will cancel out 19 leaving us with just x° while on the right-hand side of the equation 57 will be divided by 19
x = 3
On the coordinate plane below, Point P is located at (2,-3), and point Q is located at (-4,4).
Find the distance between points P and Q Round your answer to the nearest whole number.
Answer:
9
Step-by-step explanation:
We can use the distance formula
d = sqrt ( ( y2-y1)^2 + ( x2-x1) ^2)
d = sqrt ( ( 4- -3)^2 + ( -4 -2) ^2)
= sqrt ( ( 7^2 + ( -6)^2)
= sqrt( 49+ 36)
= sqrt(85)
9.219544457
Rounding to the nearest whole number
= 9
Help me with this please I have no idea what to do. It says solve for a if the line through the two given points has the given slope a, 3) and (-3, - 1), m = -2
Answer:
a=-5
Step-by-step explanation:
When you do this every time the slope will go down 2 and over 1 which is rise over run or slope. You can see the y coordinates go down 4 points and every time is should go down 2 so you will know that it would have gone down 2 times so a+2 should equal -3 so if we subtract 2 from both sides we would get a=-5 and that is our answer.
Answer:
a = - 5
Step-by-step explanation:
Calculate the slope m using the slope formula and equate to - 2
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, - 1) and (x₂, y₂ ) = (a, 3)
m = [tex]\frac{3+1}{a+3}[/tex] = [tex]\frac{4}{a+3}[/tex] = - 2 ( multiply both sides by a + 3 )
- 2(a + 3) = 4 ( divide both sides by - 2 )
a + 3 = - 2 ( subtract 3 from both sides )
a = - 5
If point Q is reflected across x = 1, what are the coordinates of its reflection image?
Answer:
(-1, -2) last answer
Step-by-step explanation:
x = 1 is a vertical line
Answer:
(-1, -2)
Step-by-step explanation:
This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.
Find the area of this shape.
4 cm
2 cm
4 cm
4 cm
-
1
5.75 cm
1
1
The area of the shape is __
square centimeters.
Answer:
shape AREA= 35cm^2
Step-by-step explanation:
you should know that this shape is a combination of triangle and trapezoid. therefore you have to find the area of each shape and add them.
A=h/2(b1 + b2) for trapezoid
A=2/2((4+4)+4)
A=1*12
A=12cm^2
A=bh/2. for TRIANGLE
A=1/2((4+4)*5.75)
A=1/2(46)
A=23cm^2
shape AREA= triangle AREA + trapezoid AREA
shape AREA=12cm^2 + 23cm^2
shape AREA= 35cm^2
Can someone pls help will mark u as brainliest
Answer:
9*((2-1)/9)
or
2 -1
9
2-9 =-7
9. 9
9× -7
9
=-7
2- 3
9. -3
=(1.22222222222)
or
11/9
or
1*(2/9)
Please answer it now in two minutes
Answer:
59.0
Step-by-step explanation:
Given a right angled triangle, ∆XYZ, to know which trigonometric ratio formula to apply in finding the measure of angle X, note the following:
Opposite side to angle X = 6
Hypotenuse = 7
Therefore, we would apply the following trigonometric ratio formula to solve for m<X:
[tex] sin X = \frac{6}{7} [/tex]
[tex] sin X = 0.8571 [/tex]
[tex] X = sin^{-1}(0.8571) [/tex]
[tex] X = 58.99 [/tex]
[tex] m < X = 59.0 [/tex] (rounded to nearest tenth)
Previous problem : From Andy's house to Billy's hometown you can travel by 3 roads. And to get from Billy's hometown to Willie's house you can travel by 5 roads. How many possible ways are there to travel from Andy's house to Willie's house? From Dan's ranch one road is built to get to Andy's house and two roads are built to get to Willie's house (see previous problem). How many way are there now to get from Andy's house to Willie's house?
Answer:
Andy's house to Billy's hometown 15 ways
Andy's house to Willie's hometown 2 ways.
Step-by-step explanation:
Andy's house to Billy's hometown there are 3 roads. There 5 road from billy's hometown to Willie's house . In total there will be 15 ways to travel which is calculated by 3 * 5. For traveling to Willie's hometown there will be two ways. There are two roads that are built to get to Willie's house.
The Department of Health in the United Kingdom wants to know whether the healthcare system is achieving its goals in Scotland. Much information about healthcare comes from patient records, but that source doesn't allow us to compare people who use health services with those who don't. Therefore, the Department of Health conducted the Scotland Health Survey, which was used to interview a random sample of 34,572 people who live in Scotland.
Part A: What is the population for this sample survey? What is the sample? (4 points)
Part B: The survey found that 70% of males and 87% of females in the sample had visited a general practitioner at least once during the past year. Do you think these estimates are close to the truth about the entire population? Explain. (6 points)
Answer:
A. the population for this sample survey is 34,572 people, and the sample is the people who live in Scotland.
B. The estimates are close to the truth about the entire population.
Step-by-step explanation:
A. According to the given data we have that it was used to interview a random sample of 34,572 people who live in Scotland, therefore, the population for this sample survey is 34,572 people, and the sample is the people who live in Scotland.
B. The estimates are close to the truth about the entire population becuase a large sample was conducted, hence we can make an aproximation that represents the population parameter.
what is the product of (-a+3)(a+4)?
[tex](-a+3)(a+4)=-a^2-a+12[/tex].
Hope this helps.
Answer:
-a²-a+12
Step-by-step explanation:
-a²+3a-4a+12
-a²-a+12
A group of dragons and sheep are randomly divided into 2 equal rows. Each animal in one row is directly opposite an animal in the other row. If 75 of the animals are dragons, and the number of sheep opposite sheep is 10 more than the number of dragons opposite dragons, find the total number of animals in the group.
Answer:
Total number of animals in the group = 170
Step-by-step explanation:
Let the number of sheep = a
Number of dragons in the group = 75
Number of dragons opposite dragons = 37
Number of sheep opposite to the dragon = 1
Number of sheep left = a - 1
Number of sheep opposite to sheep = [tex]\frac{(a-1)}{2}[/tex]
Since. number of sheep opposite to sheep is 10 more than of dragons opposite dragons,
[tex]\frac{(a-1)}{2}[/tex] = 37 + 10
[tex]\frac{(a-1)}{2}=47[/tex]
a - 1 = 94
a = 95
Then total number of animals in the group = Total number of sheep + Total number of dragons
= 95 + 75
= 170
Therefore, total number of animals in the group are 170.
The population of a certain type of seahorse grew by 13% from year to year.
Should the be modeled linear function or Exponential function ?
Answer: Exponential function
Step-by-step explanation:
A linear function is the form[tex]f(x)=mx+c[/tex] , where m is the constant rate of change of y with respect to x and c is the y-intercept.
An exponential growth function is in the form [tex]f(x)=A(1+r)^x[/tex], where r is the rate of growth (generally in percent) and A is initial value.
If the population of a certain type of seahorse grew by 13% from year to year, then the rate of growth is 13% .
Hence it is an exponential equation.
The points (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0) forms a quadrilateral of type:
Answer:
A square.
Step-by-step explanation:
Jack challenged Jill to a race around a curve of a track. Jack took lane 8 with Jill at lane 1. If the radius of lane 1 is half of lane 8, what is the distance in metres Jack has to run if Jill ran a distance of 50m?
Answer:jac ganko
Step-by-step explanation:
(1/16)^(x+3) = (1/4)^(x+1)
Answer:
x=-5
Step-by-step explanation:
The answer is x = -5. The explanation and answer is in the image below.
What steps do you use to solve a system of two equations using elimination? For example:
7x +2y = -32
-3x+2y = -70
Answer:
Step-by-step explanation:
eliminate either vraible, here it is easy to eleimate y, by just subtacting, then solve for x. When you get the value of x, plug in one of the equation and find y. ther you go
Answer:
x= 3.8
y= -29.3
Step-by-step explanation:
I need help with this
Answer:
86.55 ft
Step-by-step explanation:
First find the perimeter for 3 sides of the rectangle that are solid
24+15+24 = 63
The we find the circumference for 1/2 of the circle
C = pi d
The diameter is 15 and pi = 3.14
But we only want 1/2
1/2 C = 1/2 pi d
= 1/2 ( 3.14) * 15
=23.55
Add the lengths together
23.55+63 =86.55 ft
11. How many kilometers is it from the main gate to Manatee Springs? (Hint: To convert from
yards to kilometers, multiply by 0.0009144). Round answer to the nearest hundredth kilometer.
Manatee Springs
Elephant
House
3,500 yds
4,200 yds
Train Depot
2,000 yds
Bird Sanctuary
Main Gate
(SHOW WORK)
Answer:
6 km
Step-by-step explanation:
Let us assume the following items
the Point at Train depot = T
The Point at Main gate = M
The Point at Bird sanctuary = B
The Point at Elephant house = E
The Point at manatee Springs = S
As we can see that there are two triangles namely TMB and TSE.
Mentioned that
MTB = ∠STE
∠TMB = ∠TSE
∠TBM = ∠TES.
According to the Angle-angle-angle (AAA similarity)
So, the triangles TMB and TSE are the same.
[tex]\frac{TM}{TS} = \frac{TB}{TE} \\\\ \frac{TM}{4,200} = \frac{2,000}{3,500}[/tex]
So, the TM is 2400 yds
Now the Distance between Main gate M and manatee Spring S is
MS = MT + TS
= 2,400 + 4200
= 6600 yds
Now the MS is
= 6600 × 0.0009144 km
= 6.035 km
≅ 6 km
What is the volume of a cylindrical garbage pail with a radius of 10 centimeters and a height of 50 centimeters?
Answer:
500[tex]\pi[/tex] or around 1570
Step-by-step explanation:
The formula for a volume of a cylinder is [tex]r^{2}h\pi[/tex]
The cylindrical garbage pain has a volume of 15700 cm².
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
The given cylindrical garbage has a radius(r) = 10 cm and a height(h) of
50 cm.
∴ The volume of the cylindrical garbage is = π(10)²×50 cm².
= 5000π cm².
= 15700 cm².
learn more about cylinders here :
https://brainly.com/question/16134180
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NEED HELP ASAP I DONT GET THIS
Answer:
x = 60
Step-by-step explanation:
In a circle, the sum of the angles that meet at a point is 360 degrees. So now that we have the total, we can subtract all the given information in the picture. We have 84, 75, 68, and x + 73. Now let us set up and equation for this problem.
360 = 84 + 75 + 68 + x + 73
Now combine like terms.
360 = x + 300
Now subtract 300 on both sides.
x = 60
And this is the value of x.
Answer:
50 degrees
Step-by-step explanation:
84 + 75 + 68 = 227
227 - 360 = 133
133 - 73 = 50
The answer is 50 degrees.