Answer:
a) (2,9); b) no points of intersection
Step-by-step explanation:
a)
Set the two equations equal to each other
7x - 5 = -2x + 13
Rearrange collecting like terms and solve
9x = 18
x = 2
Sub in x = 2 into either of the equations and it should yield the same result
Eq.1 y = 7(2) - 5 = 9
Eq.2 y = -2(2) + 13 = 9
Therefore the point of intersection is (2,9)
The graph confirms this result (see graph 1 with red and blue lines)
b)
As the gradients are the same, we can tell straight away that the two lines should be parallel and never intersect, but we'll try to solve it algebraically using the same method as in part a.
3x - 1 = 3x + 2
When rearranging, the x's cancel out which can be seen when subtracting 3x from both sides
-1 = 2
This equation is clearly incorrect. This means that there are no values of x at which the two equations are equal. Graphically, this means that the two lines are parallel and there are no points of intersection (see graph 2 with purple and green lines)
The infield of a softball
diamond is shaped like a
square. If the distance
between bases is 60 feet,
Find the diagonal distance
From third base to First
base
1-84.9
2-11.9
3-12.5
Answer:
84.9
Step-by-step explanation:
The distance between first and third base makes the hypotonus of a triangle where the lengths of the legs are each 60 feet. To find the hypotonus, add (60)^2 + (60)^2 to get 3600 +3600 = 7200. Then square root 7200 to get the distance between first and third as 84.9
What is an equation of the line that passes through the points (-5, 1) and (5,5)
Answer:
Equation: y = 0.4x + 3.
Step-by-step explanation:
picture
how do i solve b^2-5b+3
Answer:
[tex]x {}^{2} - 5x = - 3 \\ x( x - 5) = - 3 \\ x = - 3 \\ x - 5 = - 3 \\ x = 2[/tex]
part one is the first pic the second part is the one that starts with the result.
What is the solution for the equation? 14. 8 = n minus 0. 3 n = negative 15. 1 n = negative 14. 5 n = 14. 5 n = 15. 1.
Answer:
Step-by-step explanation;
3, 4, 5), while (m, n) = (5,2) gives the ... x 2 + 29x + 210 = (x + 15)(x + 14) and x2 + 29x - 210 = (x + 35)(x - 6)
bra9inly pls help me on this question
Step-by-step explanation:
area of the trapezoid = area of the 2 triangles +
area of the rectangle
i) area of triangle on left:
a = ½ bh
a = ½ × 2 × 9
a = 9 in²
ii) area of triangle on right:
a = ½ bh
a = ½ × 2 × 9
a = 9 in²
iii) area of rectangle = length × width
a = l × w
a = 12 × 9
a = 108 in²
iv) area of trapezoid = 9 + 9 + 108
= 126 in²
hope this helps you!
-s.
tanya is 1.6m tall and sid is 2m tall find the ratio of tanya height to sid’s height
Answer:
4 : 5
Step-by-step explanation:
tanya : sid = 1.6 : 2 ( divide both parts by 0.4 )
= 4 : 5
Show working pls
Find the area of the following composite shapes
Answer:
112 sq cm
Step-by-step explanation:
Area of the square:
A = s^2
= 8^2
=64 sq cm
Area of a triangle:
A = 1/2•b•h
= 1/2•8•12
= 48 sq cm
Area of total shape:
A_square + A_triangle
= 64 + 48
= 112 sq cm
Jack read 9 books in 15 months. What was his rate of reading in months per book? Include units.
Your answer should be written in fraction form (mixed number)
Answer:
3/5 books
Step-by-step explanation:
Divide 9 by 15 to get 0.6
0.6=3/5
I need help with this question, how do I find the value of x??
Answer:
Im sure that you need to subtract so 140 minus 15 is 130
Answer: x is 20 degrees
Step-by-step explanation:
145 + 15 = 160
180 - 160 = 20
( straight line: 180 degrees )
Cone A and Cone B both have a height of 5 inches. The volume of Cone A
is 20.9 cubic inches. The volume of Cone B is 4 times the volume of Cone A.
About how many times longer is the diameter of Cone B than the diameter
of Cone A
Answer:
cone A= 20.9×5=104.5
cone B= 5×4=20
20×20.9=418
cone B -cone A = -313.5
What is the value of the rational expression 2x2+ 5x +9/x2+2x -1?
A.)-7
B.)-9
C.)9
D.)7
(Help Please.)
Answer:
hai
Step-by-step explanation:
Which is the equation of the following line.
Answer:
D
Step-by-step explanation:
D
0 is the y intercept and -4 is the slope.
Answer:
D. y = -4x
Step-by-step explanation:
First, find the slope:
m = (-8 - 0) / (2 - 0)
[tex]m = -\frac{8}{2}[/tex]
Use slope-intercept form:
[tex]y = -\frac{8}{2}x[/tex]
[tex]y = -4x[/tex]
Can someone plss help me with these questions!!
Answer:
1 year data analysis of input and output
Solve for a.
5a−12=3
Enter your answer in the box.
a =
[tex]5a - 12 = 3 \\ 5a = 3 + 12 \\ 5a = 15 \\ a = \frac{15}{5} \\ a = 3[/tex]
Answer:
[tex]a=3[/tex]
Step-by-step explanation:
Given the following question:
[tex]5a-12=3[/tex]
To solve this equation, we need to add 12 on both sides and then isolate the variable for a.
[tex]5a-12=3[/tex]
[tex]-12+12=0[/tex]
[tex]12+3=15[/tex]
[tex]5a=15[/tex]
[tex]\frac{5a}{5} =\div5[/tex]
[tex]15\div5=3[/tex]
[tex]a=3[/tex]
Hope this helps.
The scale for the drawing of a rectangular playing field is 2 inches=7 feet.
Find an equation you can use to find the dimensions of the actual field. What
are the actual dimensions? PLS HELP
Answers YAVE NO IDEA
Step-by-step explanation:
I DONT KNOWWWW
Please answer this for the love of God!! :(
Answer:
4(5x+4)
Step-by-step explanation:
The factors of 16 are: 1, 2, 4, 8, 16
The factors of 20 are: 1, 2, 4, 5, 10, 20x
Then the greatest common factor is 4.
Kindly solve the question
Answer:
in the picture
Step-by-step explanation:
in the picture
Answer:
6.4 = b and 7.8 = a
Step-by-step explanation:
Using the formula:
a^2 + b^2 = c^2
we can find the length of b
for the first triangle
now we just plug in the lengths.
5^2 + 4^2 = b^2
simplify into :
25 + 16 = b^2
add
41 = b^2
now in order to get rid of the ^2, we just find the square root of 41.
√41 ≈ 6.4
6.4 = b
Now we just need to solve for A
since we know
a^2 + b^2 = c^2 that must mean
c^2 - b^2 = a^2
so this is the formula we will be using.
now we just plug in the lengths of the second triangle into this equation.
10.5^2 - 7^2 = a^2
simplifies into
110.25 - 49 = a^2
subtract
61.25 = a^2
now we just find the square root of 61.25.
√61.25 = 7.8
7.8 = a
you can check this by putting it back in the formula
a^2 + b^2 = c^2
I will do this quickly (only for the second triangle)
we know
a = 7.8
b = 7
c = 10.5
7.8^2 + 7^2 = 10.5^2
simplifys into
60.84 + 49 = 110.25
60.84 + 49 ≈ 110
110.25 ≈ 110
110 = 110
which proves that this is correct.
please help (images below)
Answer:
2) D
because:
[tex] \frac{9}{1} \times 4 \\ 9 \times 4 \\ 36 \: is \: not \: equal \: to \: 4[/tex]
4) B
because:
[tex] \frac{5}{5} \times 8 \\ 1 \times 8 \\ 8 \: is \: equal \: to \: 8[/tex]
Two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. Use the data to determine which function is exponential, and use the table to justify your answer.
A. g(x) is exponential; an exponential function increases faster than a linear function.
B. g(x) is exponential; g(x) has a lower starting value and higher ending value.
C. f(x) is exponential; an exponential function increases more slowly than a linear function.
D. f(x) is exponential; f(x) increased less overall than g(x).
Answer:
the correct answer should be c
help me help me help me
Answer:
should be 67 Step-by-step explanation:
Answer:
They are Vertical angles, and it is 67 degrees
Step-by-step explanation:
Kyle types college reports for $1.70 per page. He also charges $6 to cover the cost of supplies. How many pages did he write if he charged $40.00? Write and solve an equation.
Answer:
$1.70p + $6 = $40.00
Step-by-step explanation:
$1.70p + $6 - $6 = $40.00 - $6
$1.70p = $34.00
$1.70p ÷ 1.70 = $34.00 ÷ 1.70
p = 20
He wrote 20 pages.
Find the domain for the expression:
y/y-5 + 1/y+8
Answer:
1/y+4
Step-by-step explanation:
1-5+1/y+8
1/y+(1-5+8)
1/y+4
[tex] \frac{y}{y} - 5 + \frac{1}{y} + 8 [/tex]
→[tex](1 - 5) + \frac{1}{y} + 8[/tex]
→[tex]-4 = \frac{ - 4}{1} = \frac{ - 4 \: • \: y}{y} [/tex]
→[tex] \frac{ - 4 \: • \: y + 1}{y} = \frac{1 - 4y}{y} [/tex]
→[tex] \frac{(1 - 4y)}{y} + 8[/tex]
→[tex]8 = \frac{8}{1} = \frac{8 \: • \: y}{y} [/tex]
→[tex] \frac{(1 - 4y) + 8 \: • \: y}{y} = \frac{4y + 1}{y} [/tex]
→[tex] \frac{4y + 1}{y} [/tex]
In a fruit punch drink, the 3 ingredients are apple juice, orange juice and cranberry juice. If 3/4 of the drink is apple juice and 1/10 is orange juice then write the ratio of cranberry juice to apple juice to orange juice in its simplest form.
Answer:
15/20 : 2/20 : 3/20 or you could put 3/4 : 1/10 : 3/20 but that's up to your teacher
Step-by-step explanation:
We know that there are 3 ingredients.
3/4 apple juice
1/10 orange juice
We want to know how much cranberry juice to apple juice to orange juice.
First, let's start with getting common denominators.
The LCD (least common denominator) between these two fractions is 40. (4 * 10)
So:
3/4 * 10/10 = 30/40
1/10 * 4/4 = 4/40
Now we know them with equal denominators. Now let's subtract them from the whole (40/40) to find out how much cranberry juice.
40/40 - 30/40 - 4/40 = 6/40
Cranberry juice = 6/40 of the whole.
Now we can find the ratio in its simplest form.
30/40 : 4/40 : 6/40
Can we simplify these fractions? yes.
The can all be simplified by 2
15/20 : 2/20 : 3/20
Since 2 can't be simplified by anything but 2 or 1, and 15 and 3 cannot be simplified by 2, this is your answer.
or you could put 3/4 : 1/10 : 3/20 but that's up to your teacher.
Please help me I’ll give 20 points :)
Answer:
B
Step-by-step explanation:
because when simplified we get b
Answer:
1. AStep-by-step explanation:
1.[tex] {x}^{2} - 4x - 12 \\ {x}^{2} + 2x - 6x - 12 \\ x(x + 2) - 6(x + 2) \\ (x - 6)(x + 2) \\ [/tex]
which represents a function HURRY PLSSS (90 POINTS)
Answer:
neither a or b
Step-by-step explanation:
a function has to have each X have a Y
a domain is paired with exactly one range value.
it has to pass the vertical line test
independent variable is X
dependant variable is Y
student name = x
colors/teachers is Y
so since there is the chance the students can have the same teacher and/or favorite color. then it is not a function
How much cubic centimeters of dirt must be removed when digging for a foundation of a building if the excavation is 32m long, 12m wide, and 8m deep
Answer:
3,072m
Step-by-step explanation:
32 × 12× 8= 3,072 (This is only you are multiplying them all)
If you are trying to find the area then its: 384m
Find x to the nearest tenth.
8
6
X
Answer:
x ≈ 5.3
Step-by-step explanation:
a²+b²=c²
c is always the hypotenuse in a right angle triangle.
6² + x² = 8²
36 + x² = 64
64 - 36 = 28
x² = 28
x = √28
Use calculator from here.
√28 = 5.29150262213
5.29150262213 ≈ 5.3
Because the number after 2, which is 9, is greater than 5, the nearest tenth is 5.3, not 5.2.
Question 1 (5 points)
Dilate the rectangle below by a scale factor of 2. If the current side lengths are 15
and 8, what are the side lengths on the new dilated rectangle?
In your answer, give the new side lengths for the dilated image and explain how you
calculated them.
Answer:
AB and CD would be 30
AC and BD would be 16
Step-by-step explanation:
The scale factor is what you multiply the sides by. Dilate means wider or larger so you multiply each side by the scale factor of 2 to get the higher scaled rectangle.
What is the value of the rational expression 6-x/ x+5 when x= 2
A.)4/7
B.)4/5
C.)8/7
D.)8/5
(Please do hurry.)
Answer:
A
Step-by-step explanation:
(6-2)/(5+2)
4/7
Answer:
4/7 6 -2/2+5 = 4/7
simple
Find at least five solutions to graph the linear equation 0x -
3y = 15
Answer:
Any points across y=5. ex: (-2,5) (0,5) (1,5), (3,5) (4,5)
Step-By-Step Solution
(3y=15)/3 divide all by 3
and get y=5
any 5 points that gave y=5 will work