Answer:
A is the Answer
Step-by-step explanation:
Since the population is being split up into 2 divisions out of 5,000.
This means District X and Y must add up 5000.
[tex]x + y = 5000[/tex]
District X and Y must differ no more than 500 people.
So this means that X and Y total people difference cannot be over 500 people. So the equation for this is
[tex]x - y \leqslant 500[/tex]
A shows this so A is the answer.
1. Which of the following is an algebraic expression?
a. X+5= 7
b. 5-2x = 3
C. 5x +4- 2x
d. -2 = 3x + 1
1.
C. 5x + 4 - 2x is an algebraic expression
Find the perimeter of the polygon
Answer:
Answer 60
Step-by-step explanation:
The distance from an exterior point to the incircle is equal to the tangent length in both cases.
So the 19 is made up of 9 and 10.
The length of the other portion of the tangent from the end of 19 to the tangent point on the right is also 10.
By a similar argument the lower length of the line to the tangent point is 11.
So you have
9 + 9 + 10 + 10 + 11 + 11
18 + 20 + 22 = 60.
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Answer:
a. (0,-5)
Step-by-step explanation:
please help me i will give 20 points for this question
Answer:
1. a. 2
b. -½
c. y - 3 = -½(x - 8) => point-slope form
y = -½x + 7 => slope-intercept form
2. a. -1
b. 1
c. y - 5 = 1(x - 3) => point-slope form
y = x + 2 => slope-intercept form
Step-by-step explanation:
1. (8, 3) and (10, 7):
a. The gradient for the line joining the points:
Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (8, 3) = (x_1, y_1) [/tex]
[tex] (10, 7) = (x_2, y_2) [/tex]
Plug in the values
Gradient = [tex] \frac{7 - 3}{10 - 8} [/tex]
Gradient = [tex] \frac{4}{2} [/tex]
Gradient = 2
b. The gradient of the line perpendicular to this line = the negative reciprocal of 2
Negative reciprocal of 2 = -½
c. The equation of perpendicular line if it passes through the first point, (8, 3):
Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).
Where,
(a, b) = (8, 3)
Slope (m) = -½
Substitute (a, b) = (8, 3), and m = -½ into the point-slope equation, y - b = m(x - a).
Thus:
y - 3 = -½(x - 8) => point-slope form
We cam also express the equation of the perpendicular line in slope-intercept form by rewriting y - 3 = -½(x - 8) in the form of y = mx + b:
Thus:
y - 3 = -½(x - 8)
y - 3 = -½x + 4
y - 3 + 3 = -½x + 4 + 3
y = -½x + 7
2. (3, 5) and (4, 4):
a. The gradient for the line joining the points:
Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (3, 5) = (x_1, y_1) [/tex]
[tex] (4, 4) = (x_2, y_2) [/tex]
Plug in the values
Gradient = [tex] \frac{4 - 5}{4 - 3} [/tex]
Gradient = [tex] \frac{-1}{1} [/tex]
Gradient = -1
b. The gradient of the line perpendicular to this line = the negative reciprocal of -1
Negative reciprocal of -1 = 1
c. The equation of perpendicular line if it passes through the first point, (3, 5):
Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).
Where,
(a, b) = (3, 5)
Slope (m) = 1
Substitute (a, b) = (3, 5), and m = 1 into the point-slope equation, y - b = m(x - a).
Thus:
y - 5 = 1(x - 3) => point-slope form
We can also express the equation of the perpendicular line in slope-intercept form by rewriting y - 5 = 1(x - 3) in the form of y = mx + b:
Thus:
y - 5 = 1(x - 3)
y - 5 = x - 3
y - 5 + 5 = x - 3 + 5
y = x + 2
The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.
Answer:
59.04°
58.31 inches
Step-by-step explanation:
The solution triangle is attached below :
Since we have a right angled triangle, we can apply trigonometry to obtain the angle ladder makes with the ground;
Let the angle = θ
Tanθ = opposite / Adjacent
Tanθ = 50/30
θ = tan^-1(50/30)
θ = 59.036°
θ = 59.04°
The length of ladder can be obtained using Pythagoras :
Length of ladder is the hypotenus :
Hence,
Hypotenus = √(adjacent² + opposite²)
Hypotenus = √(50² + 30²)
Hypotenus = √(2500 + 900)
Hypotenus = 58.309
Length of ladder = 58.31 inches
Answer:
59°
58.3 inches
Step-by-step explanation:
Here is the full question :
A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.
Please check the attached image for a diagram explaining this question
The angle the ladder makes with the ground is labelled x in the diagram
To find the value of x given the opposite and adjacent lengths, use tan
tan⁻¹ (opposite / adjacent)
tan⁻¹ (50 / 30)
tan⁻¹ 1.667
= 59°
the length of the ladder can be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
√(50² + 30²)
√(2500 + 900)
√3400
= 58.3 inches
Write an equation in standard form of the line that passes through the given point and has the given slope (-8,0); m= -4 PLEASE HELP NEED DONE ASAP WILL GIVE BRAINLIEST
Answer:
4x+y=-32
Step-by-step explanation:
given,
slope (m) = -4
point: (-8,0)
as we know the slope intercept form of the line is, y=mx+b, b=y-mx, now we put x=-8, y=0 to find b [because the point is given (-8,0) so it must satisfy the equation]
so,
b = 0-(-4)×(-8) = -32
y=mx+b
or, y=-4x-32
or, 4x+y=-32
(this is the standard form of the line)
Using the equation y - y1 = m(x - x1)
y - 0 = -4(x - (-8))
y = -4(x + 8)
y = -4x - 32
3. JK is tangent to circle L. Find JL to two decimal places.
Answer:
14.32
Step-by-step explanation:
Since this is a right triangle, we can us the Pythagorean theorem
a^2 + b^2 = c^2
3^2 + 14^2 = JL ^2
9+196 = JL ^2
205 = JL ^2
Taking the square root of each side
sqrt(205) = JL
14.31782106 = JL
To 2 decimal places
14.32
The amount of money Aria has in the bank after T years is determined by the equation A = 1,000 · 1.0512^T. After how many years will Aria have $2,000 in the bank?
(1) 12.9 (2) 13.9
(3) 14.9
(4) 15.9
Answer:
Step-by-step explanation:
You are given most of the equation that you need to solve. To find the number of years it will take to have 2000, sub in 2000 for A and solve:
[tex]2000=1000(1.0512)^t[/tex] and begin by dividing away the 1000 on both sides to get
[tex]2=(1.0512)^t[/tex] now we have to take the natural log of both sides:
[tex]ln(2)=ln(1.0512)^t[/tex]. Taking the natural log allows us to bring the t down out front:
ln(2) = t ln(1.0512) and now divide both sides by ln(1.0512):
[tex]\frac{ln(2)}{ln(1.0512)}=t[/tex] and do this on your calculator to get
t = 13.9 years
Answer:
T = 13.9
Step-by-step explanation:
A = 1,000 · 1.0512^T
Let A = 2000
2000 = 1,000 · 1.0512^T
Divide each side by 1000
2000/1000 = 1,000/1000 · 1.0512^T
2 = 1.0512^T
Take the log of each side
log 2 = log 1.0512^T
We know log a^b = b log a
log 2 = T log 1.0512
Divide each side by log 1.0512
log 2 / log 1.0512 = T
T=13.88172
Rounding to the nearest tenth
T = 13.9
AXYZ has side lengths that measure 20 centimeters each. Which of the
following best describes this type of triangle?
A. Scalene triangle
B. Right triangle
C. Obtuse triangle
D. Equilateral triangle
Step-by-step explanation:
The triangle is equilateral (OPTION D) because any triangle that has 3 equal side lengths is an equilateral triangle.
if x^2=y^2+z^2
what does x equal?
Answer:
[tex]\displaystyle x = \sqrt{y^2 + z^2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertyAlgebra i
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle x^2 = y^2 + z^2[/tex]
Step 2: Solve for x
[Equality Property] Square root both sides: [tex]\displaystyle x = \sqrt{y^2 + z^2}[/tex]y= -(x+3)^2 -5
What is the leading coefficient?
How do you find the vertex?
Answer:
To find the leading coefficient, first expand the function:
[tex]y= -(x+3)^{2} -5\\\\y=-(x^{2} +6x+9)-5\\\\y=-x^{2} -6x-9-5\\\\y=-x^{2} -6x-14[/tex]
The leading coefficient is the coefficient of the highest-order term, which, in this case, would be the -1 from -x².
To find the vertex: see image below
Vertex = (-3, -5)
10.
Define an operation ★ on the set of real numbers as follows:
a ★ b = 0.5ab
If 0.1 ★ b = 10, then evaluate bb.
a. 500
b. 200
c. 20
d. 50
Please explain how you got your answer.
If a ★ b = 0.5ab, then
0.1 ★ b = 0.5 (0.1) b = 0.05b = 10
==> b = 10/0.05 = 200
A person can run 3 miles per minute. (Convert to miles per hour to decide.)
O True
O False
it depends upon a persons pace a average pace is 9-10 mins
one class collects 8 1/4 pounds of recyclable materials. Another class collects 1 1/2
Step-by-step explanation:
what to find then??.........
Helpppppppppppppppppppppppp im not smart pls don't just say some bull i need help ill just get it deleted
Answer:
a. 6m
b. m-2
c. 5(m-2)
d. 6m +5m -10= 56
E. 11m=66
divide by 6: m=6
Maple Granola= 6$
Apple Granola= 4$
Solve the square of this equation with explanation as I don’t understand please
===========================================================
Explanation:
Cut the x coefficient (10) in half to get 10/2 = 5. Then square this to get 5^2 = 25.
We'll add 1 to both sides so that the "24" turns into "25", thereby completing the square
x^2 + 10x + 24 = 0
x^2 + 10x + 24+1 = 0+1
x^2 + 10x + 25 = 1
Notice on the left hand side we have something of the form A^2+2AB+B^2 where A = x and B = 5. We can factor this into (A+B)^2, which is the whole reason why we completed the square. You can use the FOIL rule to see how (A+B)^2 expands out into A^2+2AB+B^2. Factoring reverses this process.
This means x^2+10x+25 factors to (x+5)^2 and we now have these steps
(x+5)^2 = 1
x+5 = sqrt(1) or x+5 = -sqrt(1)
x+5 = 1 or x+5 = -1
x = 1-5 or x = -1-5
x = -4 or x = -6 are the two solutions
------------------
Let's check x = -4 to see if it works or not
x^2 + 10x + 24 = 0
(-4)^2 + 10(-4) + 24 = 0
16 - 40 + 24 = 0
-24 + 24 = 0
0 = 0
We get a true equation. That confirms x = -4 is a solution.
If we tried x = -6, then,
x^2 + 10x + 24 = 0
(-6)^2 + 10(-6) + 24 = 0
36 - 60 + 24 = 0
-24 + 24 = 0
0 = 0
That x value is confirmed as well.
In order to solve the following system of equations by addition, which of the
following could you do before adding the equations so that one variable will
be eliminated when you add them?
-2x + 4y = 10
3x - 2y = -7
A. Multiply the top equation by 2 and the bottom equation by 3.
B. Multiply the bottom equation by 2.
C. Multiply the top equation by -3.
O D. Multiply the top equation by 3 and the bottom equation by -2.
Answer:
Multiply the bottom equation by 2
two triangles are similar what is x
Answer:
x = 10
Step-by-step explanation:
smaller triangle / bigger triangle = 20 / 28
hence,
3x / (4x+2) = 20/28
28(3x) = 20(4x+2)
84x = 80x + 40
4x = 40
x = 10
Can someone please do this for me please
Answer:
r=-11
Step-by-step explanation:
7r+2=5(r-4)
7r+2=5r-20
2r=-22
r=-11
Please Help
The students in a high school are being randomly split into focus and accountability groups that meet each morning for the first fifteen minutes of the school day. Each group contains four students, selected regardless of gender or grade level.
In order to explore the composition of the groups with regard to grade level, you have decided to conduct a simulation using colored discs. Since the number of students in each grade level is about the same, you put the same number of four different colored discs in a bag: red, blue, green, and yellow. You decide that red (r) represents the freshmen, blue (b) represents the sophomores, green (g) represents the juniors, and yellow (y) represents the seniors.
Next, you randomly select one disc from the bag, record the color, and put the disc bag in the bag. You do the same thing three more times to represent one group. Then, you complete this entire process twenty-five times, as shown below.
Based on the results of the simulation, the chances of a group having at least one senior is:
likely
unlikely
neither unlikely or likely
19/25 which is likely
count the ones with y and put that over 25
For the Parabolay = (x + 7)2 – 3. the equation for the Line Of Symmetry is
Answer:
Hello
Step-by-step explanation:
Axis of symmetry is vertical:
x=-7 (since (-7,-3) is the vertex)
Answer:
x = -7
Step-by-step explanation:
y = (x+7)^2 -3
This is in vertex form
y =a(x-h)^2+k where (h,k) is the vertex and the line of symmetry for a vertical parabola is x=h
y = (x- -7)^2 -3
x = -7
What is the estimated value of 2v12 . 3V5 / V30 . V36
Answer:
the correct answer is b and I know this because I just had it
NOW ASAP I NEED HELP ON THIS FAST PLEASEEEEEEEEEEEEE
Answer:
fourth time ...
same problem...
the red line crosses a corner of a box at (4,20) and (2,10)
20/4 = 5
and
10/2 = 5
the slope , constant, gradient for this relationship is "5"
Step-by-step explanation:
Same promblem as first but different angles
If two parallel lines are intersected by a transversal, then internal opposite angles are equal.
So, x° = 61°
=> x = 60
Because they are internal opposite angles.
600 becomes 720 in 2 years when the interest is simple if the rate of interest is increased by 2% then what will be the total amount.
Hi
So: 720 -600 = 120
120 for two years makes 120/2 = 60 in a year .
60 from 600 is 600/60 = 10
Interest is 10 %
If interest in 2% more, then it's 12%.
I'm sure you can count 12% simple interest for two years, so I let you try.
good luck.
Solve the following given problem
Answer:
The radius is 3.5cm
Step-by-step explanation:
Given
[tex]V = 192.5cm^3[/tex]
[tex]h = 5cm[/tex]
Required
The volume (V)
The volume of the vase is:
[tex]V = \pi r^2h[/tex]
So, we have:
[tex]192.5 = 22/7 * r^2 * 5[/tex]
Divide by 5
[tex]38.5 = 22/7 * r^2[/tex]
Multiply by 7/22
[tex]12.25= r^2[/tex]
Take positive square roots
[tex]r = 3.5[/tex]
Convert 75 mg into gram
Answer:
[tex]{ \tt{1 \: mg = 1 \times {10}^{ - 3} \: g}} \\ { \tt{75 \: mg = (75 \times 1 \times {10}^{ - 3} ) \: g}} \\ { \bf{ = 75 \times 10 {}^{ - 3} \: grams}} \\ { \bf{ = 0.075 \: grams}}[/tex]
Five cups of rice will server 8 people. Exactly how many cups of rice are needed to server 14 people?
Answer:
8.75 cups
Step-by-step explanation:
We can write a ratio to solve
5 cups x cups
---------- = -----------
8 people 14 people
Using cross products
5*14 = 8x
70 = 8x
Divide by 8
70/8 = 8x/8
8.75=x
Step-by-step explanation:
8 people => 5 cups
1 person => 5/8 cups
14 people => 5/8 ×14 = 35/4 cups
ig so this is correct I can give u 93.69% guarantee
Please help simple alebgra! Write an equation representing the translation of f(x) = 7x + 3 down 4 units.
Will mark brainliest!
9514 1404 393
Answer:
g(x) = 7x -1
Step-by-step explanation:
The y-coordinate of a function tells how many units the function value lies above the x-axis. Translating that value down 4 units is the same as subtracting 4 from the function value.
g(x) = f(x) -4
g(x) = 7x +3 -4
g(x) = 7x -1
-x/c=6.5
I need to solve for x first then c
Answer:
[tex]x = -6.5c[/tex]
[tex]c = -\frac{x}{6.5}[/tex]
Step-by-step explanation:
In both cases, you are simply isolating the variable you are trying to solve for:
[tex]\frac{-x}{c} = 6.5[/tex]
Solve for x. Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. First, multiply c to both sides, and then divide -1 from both sides:
[tex]\frac{-x}{c} = 6.5\\\frac{-x}{c} * c = 6.5 * c\\-x = 6.5c\\\frac{-x}{-1} = \frac{6.5c}{-1}\\x = -6.5c[/tex]
Solve for c. Isolate the variable, c. Note the equal sign, what you do to one side, you do to the other. Multiply -1/x to both sides of the equation:
[tex]\frac{-x}{c} = 6.5\\\frac{-x}{c}(c)) = 6.5(c) \\-x = 6.5c\\\frac{-x}{6.5} = \frac{6.5c}{6.5}\\c = -\frac{x}{6.5}[/tex]
Answer:
x = -6.5c
-x/6.5 = c
Step-by-step explanation:
-x/c=6.5
Multiply each side by -c
-x/c * -c=6.5*-c
x = -6.5c
-x/c=6.5
Multiply each side by c
-x/c *c=6.5*c
-x = 6.5c
Divide each side by 6.5
-x/6.5 = 6.5c/6.5
-x/6.5 = c
