Step-by-step explanation:
It is important to remember that when we graph a linear equation, we get a line and when we graph a quadratic equation, we get a parabola.
Then, given a system of a quadratic equation and a linear equation, there are three possibles cases for the solution:
- If the line and the parabola never intersect, then there is no real solution.
- If the line just touches the parabola, then there is one real solution.
- If the line and the parabola intersect at two points, then there Two real solutions.
Then the system of a quadratic equation and a linear equation may have: no intersections points, one intersection point or two intersection points.
Write the equation of the graph
The sum of the exterior angles of a polygon is always 180 degrees. True False
Answer:True
Step-by-step explanation:
Answer:
The sum of the exterior angles of a polygon is always 180 degrees.
Step-by-step explanation:
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F (- 12) = 2/3(-12)+7
F (- 12) = 2/3(-12)+7
F (- 12) = 2(-4) + 7
F(-12) = -8 + 7
F(-12) = -1
Barbie is analyzing a circle, y2 + x2 = 16, and a linear function g(x). Will they intersect?
Answer:
Yes,they will intersect at (0.686,3.941) and (2.914,-2.741)
Step-by-step explanation:
Given the values that represent the function g(x) you can plot them directly on a graph tool and plot the function y²+x²=16 then visualize
You can also determine the equation of the linear function as then graph both equations on the graph tool
Finding gradient m
Given (0,6) and (1,3)
m=change in value of y/change in value of x
[tex]m=\frac{3-6}{1-0} =\frac{-3}{1} =-3[/tex]
Finding the equation of the linear function
Taking points (2,0) and (x,y)
[tex]m=\frac{y-0}{x-2} \\\\-3=\frac{y-0}{x-2} \\\\\\-3(x-2)=y-0\\\\\\-3x+6=y-0\\\\\\y=-3x+6[/tex]
From the graph,they intersect at
(0.686,3.941) and (2.914,-2.741)
Answer:
Yes, at positive x coordinates
A computer manufacturer had net sales of $380 million with returns equal to 1/80 of gross sales . Find gross sales rounded to the nearest million given that net sales equals gross sales less returns .
Answer:
4.75 is the answer
Step-by-step explanation:
The Gross sales were 393 million.
It is required to find the gross sales rounded to the nearest million
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Let gross sales = x millions
Returns = 1/80xmillions
x-1/80x=380
29x/30=380
x=380*30/29
x=393.10≈393
Therefore, the Gross sales were 393 million.
Learn more about arithmetic here:
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Kite ABCD is rotated 180° clockwise about the origin and then reflected over the Y axis followed by reflection over the X axis. What is the location of point a after the transformations are complete? (5,-1), (-5,1), (-5,-1), (5,1)
Answer:
(-5, 1)
Step-by-step explanation:
We are given a kite on the graph which is rotated 180° clockwise about the origin and then reflected over the Y axis followed by reflection over the X axis.
We are to find the coordinates of point A after the complete transformation.
A (-5, 1)
When a point is rotated 180° clockwise about the origin, the signs of its coordinates change.
A (-5, 1) ---> A' (5, -1) - after clockwise rotation of 180 degrees about origin
Then this point A' is reflected over the Y axis where the y coordinate remains the same but x coordinate changes its sign.
A' (5, -1) ---> A'' (-5, -1) - after reflection through y axis
Now this point A'' is reflected over the X axis where the x coordinate remains the same while y coordinates changes its sign.
A'' (-5, -1) ---> A''' (-5, 1) - after complete transformation
Answer:(-5, 1)
Step-by-step explanation:
90 points?with explanation
A transversal is a line that passes through two lines (as shown above) on the same plane.
N is the transversal since it passes through line L and M at two distinct points.
Answer:
A transversal is a line that passes through two lines (as shown above) on the same plane.
N is the transversal since it passes through line L and M at two distinct points.
Step-by-step explanation:
Find the distance between the points (-2, 4) and (4, -6).
0 212
2/(10)
O2V(34)
Answer:
2[tex]\sqrt{34}[/tex]
Step-by-step explanation:
Calculate the distance (d) using the distance formula
d = √(x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 2, 4) and (x₂, y₂ ) = (4, - 6)
d = [tex]\sqrt{(4+2)^2+(-6-4)^2}[/tex]
= [tex]\sqrt{6^2+(-10)^2}[/tex]
= [tex]\sqrt{36+100}[/tex]
= [tex]\sqrt{136}[/tex] = [tex]\sqrt{4(34)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{34}[/tex] = 2[tex]\sqrt{34}[/tex]
What is the slope of the line trated in the picture below?
Note: One scale is equivalent to 1.
11
Answer:
-2 = m
Step-by-step explanation:
y = -2x + 2; your y-intercept is [0, 2] and your x-intercept is [1, 0] (not all the time your x-intercept will be an endpoint). Simply do rise\run until you hit another endpoint. As you can see, you go two blocks south then go one block over east. Do you understand?
The perimeter of an equilateral triangle is 18y-6. What is the length of one side of the triangle
Answer:
An equilateral triangle has all sides equal.
If perimeter = 18y -6 then one side = (18y -6) / 3 =
6y -2
Step-by-step explanation:
Answer:
54
Step-by-step explanation:
18y-6
y=18/6
y=3
18*3=54
What are the coordinates of the center and length of the radius of the circle whose equation is X^2+6x+4y=23?
The center of the circle is (-3, -9/2) and the radius is sqrt(41)/2.
Explanation:To find the coordinates of the center and length of the radius of the circle, we need to rewrite the equation of the circle in the standard form (x-h)^2 + (y-k)^2 = r^2. First, complete the square for the x and y terms by adding and subtracting the necessary constants:
x^2 + 6x + 4y = 23
x^2 + 6x + 9 + 4y + 9 = 23 + 9 + 9
(x + 3)^2 + (y + 9/2) = 41/4
Therefore, the center of the circle is (-3, -9/2) and the radius is sqrt(41/4), which simplifies to sqrt(41)/2.
Convert the radian measure to degree measure. Use the value of π found on a calculator, and round answers to two decimal places.
eleven pi divided by four
Answer: 495 degrees
Step-by-step explanation:
[tex]\frac{11\pi }{4}[/tex] · [tex]\frac{180}{\pi }[/tex]
[tex]\frac{1980}{4}[/tex]
495 degrees
The students at Midtown Middle school sold flowers as a fundraiser in September and October. In October, they charged $1.50 for each flower. The October price was a 20% increase of the September price.
Part A
What was the price of the flowers in September?
Enter your answer in the box.
$
Part B
The seventh-grade class earned 40% of the selling price of each flower.
In September, they sold 900 flowers.
In October, they sold 700 flowers.
Select a choice from each drop-down menu to make a true statement.
The seventh-grade class earned more money in by
Save
Answer:
[tex]\boxed{\text{A. \$1.25; B. September by 4.7 \%}}[/tex]
Step-by-step explanation:
Part A. Price of flowers in September
Let x = price of flowers in September.
Then 1.2x = price of flowers in October
1.2x = $1.50
[tex]x = \dfrac{\$1.50 }{1.20} = \$1.25\\\\\text{The price of flowers in September was }\boxed{\textbf{\$1.25}}[/tex]
Part B. Seventh-grade class
40 % of September price = 0.40 × $1.25 = $0.50
40 % of October price = 0.40 × $1.50 = $0.60
In September
[tex]\text{Earnings} = \text{900 flowers} \times \dfrac{\$0.50}{\text{1 flower} } = \$450[/tex]
In October,
[tex]\text{Earnings} = \text{700 flowers} \times \dfrac{\$0.60}{\text{1 flower} } = \$430\\\\\text{Difference} = \$450 - \$430 = \$20[/tex]
The class earned $20 more in September.
Compared with October earnings,
[tex]\text{\% Difference} = \dfrac{\text{Difference}}{\text{October earnings}} \times 100\%\\\\\text{\% Difference} = \dfrac{\$20}{\$430} \times 100\% = 4.7 \%\\\\\text{The class made more money in } \boxed{\textbf{September}} \text{ by } {\boxed{\mathbf{4.7 \%}}[/tex]
The answer above me deserves brainliest !! They did so well!!!
20 Points!!
Solve 2(4 x + 3) < 5 x + 21.
A) { x | x < 9}
B) { x | x > -5}
C) { x | x > -9}
D) { x | x < 5}
Answer:
D
Step-by-step explanation:
8x-5x<21-6
x<15÷3
x<5
Answer:
D) { x | x < 5}
Step-by-step explanation:
2(4 x + 3) < 5 x + 21
Distribute
8x +6 < 5x+21
Subtract 5x from each side
8x-5x+6 < 5x-5x+21
3x+6 < 21
Subtract 6 from each side
3x+6-6<21-6
3x <15
Divide each side by 3
3x/3 <15/3
x < 5
In △ABC, a=26, b=19, and c=17.2. Identify m∠C rounded to the nearest degree.
The figure shows triangle A B C. The length of segment A B is c units. The length of segment A C is b units. The length of segment B C is a units.
Answer:
41°
Step-by-step explanation:
∠C is opposite of side c.
Using law of cosines:
c² = a² + b² − 2ab cos C
17.2² = 26² + 19² − 2(26)(19) cos C
cos C = 0.750
C ≈ 41°
Answer:
The answer is 41 degrees
What is the value of y in the equation 3 (3y - 9) = 0
Answer:
y=3
Step-by-step explanation:
3 (3y - 9) = 0
Divide each side by 3
3/3 (3y - 9) = 0/3
3y -9 = 0
Add 9 to each side
3y -9+9 = 0+9
3y =9
Divide by 3
3y/3 = 9/3
y =3
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Solve (x-3)^2 = 49. Select the values of x
Answer:
x = -4, 10
Step-by-step explanation:
We take the square root and use the fact of "plus-minus" and find two values of x. The process of solving this equation is shown below:
[tex](x-3)^2 = 49\\\sqrt{(x-3)^2}=\sqrt{49}\\ x-3=+-7\\x=3+7=10\\x=3-7=-4[/tex]
Hence the two values of x are -4 and 10
Note: both (-7)^2 and (7)^2 are 49 . So we took "plus-minus" values of [tex]\sqrt{49}[/tex]
Answer: -4 and 10
Step-by-step explanation:
b and c
the second and and the third option
the middle two
25 points? last one..Lol
Answer:
38
Step-by-step explanation:
The 38-deg angle and and angle 6 are vertical angles, so they are congruent.
m<6 = 38 deg
Angles 6 and 4 are corresponding angles of parallel lines cut by a transversal, so they are congruent.
m<4 = m<6 = 38 deg
Answer:
38
Step-by-step explanation:
< 6 = 38 vertical angles
< 6 = <2 alternate interior angles
<2 = <4 vertical angles
<4 = 38
The perimeter of a rectangle is greater than or equal to 74 meters.
If the length is 25 meters, the minimum width of the rectangle is ______ meters.
Answer:
12
Step-by-step explanation:
First, multiply the length by two then, subtract the total by the sum, last divide by two.
(25 * 2)
(74 - 50)
(24/2)
Answer = 12
Answer:
w>/=12
Step-by-step explanation:
2(25)+2w>/= 74
50+2w>/=74
-50 -50
2w>/=24/2
w>/=12
help pleaseeeee picture attached
Answer:
The diagonal of the base is 4√5 centimeters.
The area of a base is 40 square centimeters.
The area of a lateral side between the bases is about 126.5 square centimeters.
Step-by-step explanation:
The lenghts of two sides of a right triangle are 5 inches and 8 inches. What are the difference between the two possible lenghts of the third side of the triangle? Round your answer to the nearest tenth
See the attached picture:
A rectangular swimming pool is 15 meters long, 13 1 2 meters wide, and 1 1 2 meters deep. What is its volume?
Answer: 1439
Step-by-step explanation:
Volume= Length* breadth* height
= 15*1312*112
= 1439
find an equation of the line passing through the given points. Use function notation to write the equation (-4,-5) and (-8,-6)
5.Find the roots of the parabola given by the following equation.
2x2+ 5x - 9 = 2x
6.Solve the inequality and graph the solution on a number line.
–3(5y – 4) ≥ 17
Answer:
Part 5) The roots are x=-3 and x=1.5
Part 6) The solution on a number line is the shading area below of the line y=-1/3 (close circle)
Step-by-step explanation:
Part 5) Find the roots of the parabola given by the following equation
[tex]2x^{2} +5x-9=2x[/tex]
we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]2x^{2}+5x-2x-9=0[/tex]
[tex]2x^{2}+3x-9=0[/tex]
so
[tex]a=2\\b=3\\c=-9[/tex]
substitute in the formula
[tex]x=\frac{-3(+/-)\sqrt{3^{2}-4(2)(-9)}} {2(2)}[/tex]
[tex]x=\frac{-3(+/-)\sqrt{81}} {4}[/tex]
[tex]x=\frac{-3(+/-)9} {4}[/tex]
[tex]x=\frac{-3(+)9} {4}=1.5[/tex]
[tex]x=\frac{-3(-)9} {4}=-3[/tex]
therefore
The roots are x=-3 and x=1.5
Part 6) Solve the inequality and graph the solution on a number line.
[tex]-3(5y-4)\geq 17[/tex]
Solve for y
[tex]-15y+12\geq 17[/tex]
Subtract 12 both sides
[tex]-15y\geq 17-12[/tex]
[tex]-15y\geq 5[/tex]
Multiply by -1 both sides
[tex]15y\leq -5[/tex]
Divide by 15 both sides
[tex]y\leq -1/3[/tex]
The solution is the interval -----> (-∞, -1/3]
All real numbers less than or equal to negative one third
The solution on a number line is the shading area below of the line y=-1/3 (close circle)
The graph in the attached figure
what is the simplify of the expression where possible (r3s2t)4
Answer:
The simplification of the given expression (r3s2t)4 is:
r¹²s⁸t⁴
Step-by-step explanation:
Given expression:
(r³s²t)⁴
power of '4' on the whole term will be applied to individual terms after we open the brackets. In this case the power on the whole term will be multiplied to the power of each individual term:
= (r³)⁴(s²)⁴(t1)⁴
= r³ˣ⁴ s²ˣ⁴ t¹ˣ⁴
= r¹²s⁸t⁴
The length of a rectangle is 8 1/2
inches and the width
3 1/4
inches. What is the ratio, using whole numbers, of the length to the width?
13:34
34:13
17:13
1311
Answer:
34/13
Step-by-step explanation:
The length-to-width ratio here is:
8.5 / 3.25
which can be reduced by dividing numerator and denominator both by 0.25:
8.5/0.25
--------------- = 34/13
3.25/0.25
Is (0,0) a solution to this system?
ys x2 - 4
y> 2x-1
Answer:
C
Step-by-step explanation:
Ok, so to do this, we are just going to plug in (0,0) and see it it checks out.
Let's take the first question. y[tex]y\geq x^{2} -4[/tex]
When we plug (0,0) into this, we get the following
[tex]0\leq 0^{2} -4[/tex]
[tex]0\leq 0-4[/tex]
[tex]0\leq -4[/tex]
This is false.
Let's check the other equation:
[tex]0>2(0)-1\\0>0-1\\0>-1[/tex]
This is true.
So the correct answer is C
Find the value of x for which m||n
A:38 B:62 C:103 D:150
Answer:
I think the answer is B= 62
Step-by-step explanation:
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Part of the population of 7000 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 8 of them are infected. How many elk are likely to be infected
Answer:
1120
Step-by-step explanation:
8/50=x/7000
50x=56000
Divide 50 on both sides
1120
Answer:
1120
Step-by-step explanation:
8/50=x/7000
50x=56000
Divide 50 on both sides
1120
Which property was used to write the equation in step 2?
Answer:
Distributive property.
For this case we have that by definition, the distributive property establishes that:
[tex]a (b + c) = ab + ac[/tex]
So, if we have:
[tex]5 (x-7) = 55[/tex]
When applying distributive property to the terms within the parenthesis we have:
[tex]5x-35 = 55[/tex]
The distributive property was used to write the second step.
Answer:
Distributive property