Answer:
x = ± 10
Step-by-step explanation:
Given
y = x² - 100 ← a difference of squares , that is
y = x² - 10² = (x - 10)(x + 10)
To find the x- intercepts let y = 0 , that is
(x - 10)(x + 10) = 0
Equate each factor to zero and solve for x
x - 10 = 0 ⇒ x = 10
x + 10 = 0 ⇒ x = - 10
Volume of rectangular cuboid is 8000cm. Length= 4x Width= 2x Height= 1x Find it's height, width and length.
Answer: 40 cm, 20 cm, 10 cm
Step-by-step explanation:
Given
Volume of rectangular cuboid is [tex]8000\ cm^3[/tex]
Length of cuboid is [tex]4x[/tex]
width of cuboid is [tex]2x[/tex]
Height of cuboid is [tex]x[/tex]
Volume of cuboid is given by
[tex]\Rightarrow \text{Volume}=\text{length}\times \text{width}\times \text{height}[/tex]
[tex]\Rightarrow V=4x\cdot 2x\cdot x\\\Rightarrow 8000=8x^3\\\Rightarrow x^3=1000\\\Rightarrow x=10\ cm[/tex]
Length =40 cm
width =20 cm
Height =10 cm
3 qp 4P 62 Ling, Mandy and Selvi share a sum of money. The ratio of Ling's share to Mandy's share to Selvi's share is 9:4:6. Mandy receives $72. How much money do the 3 girls receive altogether? L:M:S 4p=872 9:4:6 lp = 72:3 3 = 24 The girls received & 96 altogether. 19 = $72 +$24 =896
Answer:7+7=0
Step-by-step explanation: bc im smart
find the surface area _______ square inches
Need help FAST NO LINKS please!!!
Answer:
x=√30
Step-by-step explanation:
Because the triangle is equilateral and is cut by the bisector, both triangles are 30-60-90 triangles. Therefore, to find side x, you multiply the short side by √3. This means that side x is √10*√3=√30 units.
what is the difference between 3,0 and 3,-2
Answer:
if these are points on a graph, then the point (3,-2) has y-value 2 below the point at (3,0).
Step-by-step explanation:
Which triangle is a translation of the gray triangle
Answer:
Triangle DEF
Step-by-step explanation:
Hi there!
A translation of a shape occurs when all the coordinates of the original image is shifted up, down, left or right by an equal value.
Triangle ABC is a reflection of the grey triangle across the y-axis. We know this because the y-axis acts like a line of symmetry between the two shapes.
Triangle DEF appears as if it's been shifted. Therefore, triangle DEF is a translation of the grey triangle.
I hope this helps!
What is the equation of the line that is parallel to the line x = -2 and passes through the point (5.4)?
Lines parallel to each others only occur when two slopes of equations are same. The definition of parallel lines is:
[tex] \large \boxed{m_1 = m_2}[/tex]
We are given the equation of a line which is x = -2. For x = a, the equation forms a verical line and has an undefined slope. These below are basic that you may need to learn when learning about the line graph:
y = a —> horizontal line; slope is 0.x = a —> vertical line; slope is undefined.For y = a, any a-values would have same x-values. For example, if we are given y = 2 then any domains or x-values can have the range of 2.For x = a, any a-values would have same y-values or range.Back to the question. We want to find the equation of a line that is parallel to the line x = -2 and passes through (5,4) point. Recall the definition of parallel line that both slopes of equations must equal. Since x = a for any a-values would give an undefined slope. That means our parallel would be x = b.
Because the line passes through (5,4) - for any a-values from x = a would give out the set of all real numbers for range. Therefore the equation of a line is x = 5.
Answer
The equation of a line that is parallel to x = -2 and passes through (5,4) is x = 5.I hope this helps! If you have any doubts or questions, don't hestitate to ask in comment! Good luck on your assignment and have a great day!
1. Pick two animals to be in a race and answer the following questions.
a. Suppose two animals are in a race. Choose two animals from Table 1 and calculate the speed of each animal in yards per second. (6 points)
Example: Kangaroo – 30 miles/hour multiply by 1760 (conversion to yards) divided by 3600 (conversion to seconds). So the speed of a Kangaroo is 14.67 yd/sec.
b. You decide how much of a head start (in yards) the faster animal will offer the slower animal. For each animal, write an equation relating speed (v), distance from the starting line (d), and time (t). (6 points)
Formula:
c. Graph the two equations on the same coordinate plane. (4 points)
d. How long will it take the faster animal to overtake the slower animal? How many yards from the starting line are the animals when the faster animal overtakes the slower animal? (3 points)
e. Reduce the head start by half and repeat parts (c) and (d) from above. (9 points)
(c)
(d) How long will it take the faster animal to overtake the slower animal? How many yards from the starting line are the animals when the faster animal overtakes the slower animal?
2. Pick a third animal and answer the following questions.
a. Choose a third animal. Calculate its speed in yards per second. Compare its speed with the speed of the two animals you chose in Activity 1. (6 points)
b. Decide which two animals should get head starts and how much of a head start each should get. Write three equations relating distance from the starting line to time. (10 points)
c. Graph all three equations on the same coordinate plane. (6 points)
Part B: Which Community Garden Plan? (50 possible points)
The Community Garden Club would like to plant a garden on a small lot in a local neighborhood. One community member, Nancy, suggests a square garden while another member, Juan, suggests a rectangular garden. You will be in charge of determining which of the two gardens would cover the most area while using the least amount of fencing to surround it. You should show all calculations, and give complete explanations.
1. Nancy’s plans for a square garden include an area of (x2 + 12x + 36) m2. Write expressions for the length and width of this square garden. (8 points)
2. The plans for the square garden shows a length of 12 m. What is the width of the square garden? Using the area from problem 1, what is the value of x? What is the total area of this square garden? (9 points)
3. Juan’s plans include a rectangular garden with an area of (x2 + 14x + 24) m2. Write expressions for the length and width of the rectangular garden. (8 points)
4. The plans for the rectangular garden shows a length that is 6 m. longer than the length of the square garden. What is the width of the rectangular garden? How much shorter is the width of the rectangular garden than the square garden? (9 points)
5. Write expressions for the perimeter of each garden in terms of x. Then find each perimeter for the x-values calculated in the previous questions. (8 points)
6. The Community Garden Club would like the garden that covers the most area possible while requiring the least amount of fencing needed to completely surround it. Which garden plan should they choose? Explain your reasoning using the information you calculated for each garden plan. (8 points)
This project can be submitted electronically. Check the Project page in the online course for more detailed instructions.
Answer:
You can pick a Hare and a Tortoise LOL
Step-by-step explanation:
find the cost of tiling a rectangular floor 10m by 14m if square tiles with side 1m are used. The price of a tile is $5.20
Answer:
$728.00
Step-by-step explanation:
10m*14m=140m
140*$5.20=$728.00
what is the order of the numbers from least to greatest?
Answer:
-2 3/4, -2, -1 1/2, -0.8, -1/3, 0.2
Step-by-step explanation:
The bigger the negitive, the smaller the number, it's the opposite for the positives
I made a mistake while solving the inequality below. What mistake did I make? Explain what I should’ve done instead.
Answer:
Mistakes:
Used addition
Didn't flip inequality form
Corrections:
Divide each term
Instead of a positive value it should be negative
flip the direction of the inequality form
Step-by-step explanation:
[tex] - 9x \div - 9 \leqslant 90 \div – 9 [/tex]
cancel the common factor
[tex] \times \leqslant 90 \div - 9[/tex]
Divide 90 by – 9
Answer is:
[tex] \times \leqslant - 10[/tex]
Hope this helps!
A prism is unfolded. Which of the following faces can be considered a base?
Check all that apply.
A. G
В. С
C. А
D. D
Answer:
Well, if we fold it into a shape, we find out it's a pentagon prism. Thats as far as I can explain it, but I think that G, C, and A are the answers. I may be wrong though! Heart it if it was helpful! Thanks!
Step-by-step explanation:
The middle two answer choices
Why is this? Because the base faces are the nonrectangular portions of the pentagonal prism. Think of a room that has 5 sides. The floor and ceiling are both pentagons, so they are the base faces. The five walls are rectangles.
The area of the pathway is square, and its area is 196 square cm. Find the length of the pathway.
Answer:
14 cm
Step-by-step explanation:
Use the formula for the area of a square, a = s², where s is the side length of the square.
Plug in 196 as the area, then solve for s.
a = s²
196 = s²
14 = s
So, the length of the pathway is 14 cm
help the volume of the roller is 576cm. Calculate the height and area of the roller if its radius is 8cm.
Answer:
143.7cm^2
Step-by-step explanation:
Given data
Volume= 576cm^3
Radius= 8cm
The expression for the volume of cylinder is
V= πr^2h
substitute
576= 3.142*8^2*h
576= 3.142*64*h
576= 201.088h
h= 576/201.088
h=2.86cm
The formula for finding the lateral area of a right circular cylinder is:
A=2πrh
substitute
A= 2*3.142*8*2.86
A= 143.7cm^2
Hence the area is 143.7cm^2
A bag contains 28 marbles. The theoretical probability of randomly drawing a
blue marble is 3/7. Find the number of blue marbles in the bag.
Answer:
12
Step-by-step explanation:
Probability = Expected outcome/Total outcome
GIven
Total outcome = 28marbles
probability of randomly drawing a blue marble = 3/7
Substitute
3/7 = number of blue marbles/28
Cross multiply
7N = 3* 28
N = 3*4
N= 12
Hence there 12 blue marbles in the bag
Do anyone know what it is
What is the base of the expression 1113?
3
11
12
21
Answer:
7
Step-by-step explanation:
I just guessed 7 and believe me its right
The Malcolms are taking a trip. Midville is 214 miles
from their home. Walesburg is 3 times as far.
How far is Walesburg from their home?
Answer:
642 miles
Step-by-step explanation:
Distance of Midville from their home = 214 miles
Walesburg is 3 times as far.
How far is Walesburg from their home?
Distance of Walesburg from their home = 3 × Distance of Midville from their home
= 3 × 214 miles
= 642 miles
Distance of Walesburg from their home = 642 miles
Y= -2/5x-10
What is the slope of a line perpendicular to y =
What is the slope of line JK?
Answer:
perp. just switch from -2/5 to positive 5/2
Step-by-step explanation:
Answer:
m2 =5/2
Step-by-step explanation:
m1=-1/m2
m2=-1/m1
y=-2/5x-10
m1=-2/5
m2= -1/-2/5
m2=5/2
y=5/2x-10 ⊥ y=-2/5x-10
Y is inversely proportional to x, when Y = 2, x = 4.
Find the constant of proportionality.
For full credit, write a proportion and show work.
PLEASE HELP I WILL MAKE BRANILIST OR WHATEVER PLEASE
Answer:
Constant of proportionality is y divided by x. y is 2 and x is 4. 2 divided by 4 is 1/2.
Let me know if that is correct.
Step-by-step explanation:
Suppose that the dollar cost of producing x ratios is c(x)=800+40x-0.2x^2. Find the average cost per radio of producing the first 40 radios.
Answer:
24radios
Step-by-step explanation:
Given that the dollar cost of producing x ratios is c(x)=800+40x-0.2x^2. Find
Average cost is expressed as dC(x)/dx
dC(x)/dx = 40-0.4x
C'(x) = 40 - 0.4x
If x = 40
C'(40) = 40 - 0.4(40)
C'(40) = 40 - 16
C'(40) = 24
Hence the average cost per radio of producing the first 40 radios is 24radios
Which statement is true?
(1) B and C have the same zeros.
(2) A and B have the same y-intercept.
(3) B has a minimum and C has a maximum.
(4) C has a maximum and A has a minimum.
AGE NO.:
DATE:
simplify!
12 / 24 - 3/216 +5600 -5554
Use calculator for the solving:
12 / 24 - 3/216 +5600 -5554 = ?
Answer: 46.4861111111
Hopefully it's correct :)
-3(-7 - x) = 1/2 (x + 2)
Answer:
x=-8
Steps:
Simplify-
−3(−7−x)= x+2/2
Simplify-
−3(−7−x)= 1+ x/2
Multiply both sides by 2-
−6(−7−x)=2+x
Expand-
42+6x=2+x
Subtract 2 from both sides-
42+6x−2=x
Simplify-
6x+40=x
Subtract 6x from both sides-
40=x−6x
Simplify-
40=−5x
Divide-
-40/5=x
Simplify-
-8=x
Switch sides-
x=-8
I believe this is correct, if not let me know and I will fix it.
Simplify (1+ 3) (2-3)
Step-by-step explanation:
[tex] \sqrt{3} - 1[/tex]
Answer:
-1 + √3
Step-by-step explanation:
use the F.O.I.L method to solve this.
"firsts"
1 * 2 = 2
"outsides"
1 * -√3 = -√3
"insides"
√3 * 2 = 2√3
"lasts"
√3 * - √3 = -3
so you get:
2 - √3 + 2√3 - 3
combine like terms
-1 + √3
what's the answer? help asap
plssssss
Please show full explanation!
Answer:
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
Given,
[tex]3x - 2y = 5[/tex]
[tex]xy = - 2[/tex]
Now,
[tex](3x - 2y) {}^{2} = (5) {}^{2} \\ [/tex]
Use the algebraic identity ⇻ (a - b)² = a² - 2ab + b²
[tex](3x - 2y) {}^{2} = (5) {}^{2} \\ 3x {}^{2} - 2 \times 3x \times 2y + 2y {}^{2} = 5 {}^{2} \\ 9 {x}^{2} - 12xy + 4y {}^{2} = 25 \\9x {}^{2} + 4y {}^{2} = 25 + 12xy \\ 9x {}^{2} + 4 {y}^{2} - 1 = 24 + 12xy[/tex]
✐ So, the value of 9x² + 4y² - 1 is 24 + 12xy
Now,
xy = - 2
So, 12xy = 12 × - 2 = - 24
•°• 24 + 12xy
= 24 + (-24)
= 24 - 24
= 0
⎆ The value of 9x² + 4y² - 1 is 0.ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
# ꧁❣ RainbowSalt2²2² ࿐
find the Midpoint M of the segment joining the points S=(-7,-8) an T= (3,-4)
Answer:
[tex]( -2 ,\:-6) [/tex]
Step-by-step explanation:
Given points are: [tex] S=(-7,-8)=(x_1, \:y_1) \:\&\:T= (3,-4)=(x_2, \:y_2) [/tex]
Midpoint of segment ST
[tex]M=( \frac{x_1+x_2}{2} ,\:\frac{y_1+y_2}{2}) [/tex]
[tex]M=( \frac{-7+3}{2} ,\:\frac{-8+(-4)}{2}) [/tex]
[tex]M=( \frac{-7+3}{2} ,\:\frac{-8-4}{2}) [/tex]
[tex]M=( \frac{-4}{2} ,\:\frac{-12}{2}) [/tex]
[tex]M=( -2 ,\:-6) [/tex]
Suppose a ship's load has 10 containers in each row from one side to the other, 15 containers in each row from front to back, and 8 layers of containers. How many containers are in the whole load?
Answer:
1200 Containers
Step-by-step explanation:
According To The Question, We Have
10 Containers in each Row from one side to other ( 10 length )15 Containers in each Row From front Side To Back (15 Breadth)8 layers of Containers (8 Height)By All this Data We Found That, Basically A Big Size Cuboid is Formed Here.
Now, For The Total Numbers Of Containers = 10×15×8 = 1200 Containers
A pair of shoes is 60% off if the sale price is now $33 find the original price
Answer:
$82.5
Step-by-step explanation:
40%-33
10%-8.25
100%-82.5
What is the rule for the reflection ?
Answer:
This idea of reflection correlating with a mirror image is similar in math.
This complete guide to reflecting over the x axis and reflecting over the y axis will provide a step-by-step tutorial on how to perform these translations.
First, let’s start with a reflection geometry definition
Math Definition: Reflection Over the X Axis
A reflection of a point, a line, or a figure in the X axis involved reflecting the image over the x axis to create a mirror image. In this case, the x axis would be called the axis of reflection.
Math Definition: Reflection Over the Y Axis
A reflection of a point, a line, or a figure in the Y axis involved reflecting the image over the Y axis to create a mirror image. In this case, theY axis would be called the axis of reflection.
What is the rule for a reflection across the X axis?
The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.
