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Explanation:
2x + 4y < 16 solves to y < -0.5x+4 when you isolate y. The inequality sign does not change direction because we divided both sides by a positive value (in this case, 4).
The graph of y < -0.5x+4 will be the same as the graph of 2x+4y < 16
To graph y < -0.5x+4, we graph y = -0.5x+4 which is a straight line that goes through the two points (0,4) and (2, 3). This is the boundary line of the inequality shaded region. The boundary line is a dashed line because we are not including points on the boundary that are part of the solution set. We only include these boundary points if the inequality sign has "or equal to".
We then shade below the dashed boundary line to indicate points below the boundary line. The shading is done downward due to the "less than" sign.
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Perhaps another method to find what direction we shade is we can try out a point like (0,0). The point cannot be on the boundary line.
Plug those coordinates into either equation. I'll pick the second equation
y < -0.5x+4
0 < -0.5*0+4
0 < 0+4
0 < 4
The last inequality is true, so the first inequality is also true when (x,y) = (0,0). Therefore, the point (0,0) is in the shaded region. The point (0,0) is below the boundary line y = -0.5x+4
So this is another way to see that the shaded region is below the boundary line.
A gardener has 100 feet of fencing in order to enclose a rectangular garden. The equation A(x)=x(50−x) gives the area of the garden whose width is x feet. What is a reasonable domain for this function? Explain.
Answer:
the answer is a
Step-by-step explanation:
A reasonable domain would be
−∞<x<∞
because
A(x)
is defined for all real numbers.
36.Find the following using suitable identities.
a) (7a – 4b) (7a + 4b)
b) 501 x 502
Would appreciate if you send a pic of the solutions<3
Answer:
1) [tex]49 {a}^{2} - 16 {b}^{2} [/tex]
2) [tex]251502[/tex]
Step-by-step explanation:
a) Question :-[tex](7a - 4b)(7a + 4b)[/tex]
Identity used here :-[tex](a + b)(a - b) = {a}^{2} - {b}^{2} [/tex]
So,
[tex](7a + 4b)(7a - 4b)[/tex]
[tex]=> {(7a)}^{2} - {(4b)}^{2} [/tex]
[tex]=> 49 {a}^{2} - 16 {b}^{2} [/tex]
b) Question :- [tex]501 \times 502[/tex]
Identity used here :-[tex](x + a)(x + b) = {x}^{2} + (a + b)x + ab[/tex]
So,
[tex]501 \times 502 = (500 + 1)(500 + 2)[/tex]
[tex] = > {(500)}^{2} + (1 + 2)500 + 1 \times 2[/tex]
[tex] = > 250000 + 1500 + 2[/tex]
[tex] = > 251502[/tex]
6 1 + 4 7 =start fraction, 1, divided by, 6, end fraction, plus, start fraction, 7, divided by, 4, end fraction, equals
9514 1404 393
Answer:
1 11/12
Step-by-step explanation:
[tex]\dfrac{1}{6}+\dfrac{7}{4}=\dfrac{2}{12}+\dfrac{21}{12}=\dfrac{2+21}{12}\\\\=\boxed{\dfrac{23}{12}=1\dfrac{11}{12}}[/tex]
Two pet stores offer customers the opportunity to donate money, in dollar increments, to the local humane society at the register. The dot plots below show the amounts donated last week.
The variability at each pet store is 1.4. The difference between the mode amount donated at each pet store is approximately how many times the variability?
A. 3
B. 4
C. 2
D. 5
A rectangle has an area of 12x²+17x-5mm². For what value of x is the rectangle a square? What is the area of a square? Justify your answer and show your work. A=12x²+17x-5mm²
Answer:
23mm
528 mm^2
Step-by-step explanation:
The area of a rectangle is given as the product of its length and width.
Given that 12x²+17x-5mm² is the area
factorize
12x²+17x-5 = 12x²+20x -3x-5
= 4x(3x+5)-1(3x+5)
= (3x+5)(4x-1)
For the rectangle to be a square, it means that the sides 3x+ 5 and 4x - 1 are equal. Hence
3x + 5 = 4x -1
collect like terms
3x - 4x = -5 -1
-x = -6
x = 6
substitute into the sides
3x + 5 = 3(6) + 5 = 23
4x -1 = 4(6) - 1 = 23
The area of the square which is a product of the sides
= 23 * 23
= 529
what is this equal to
[tex] \frac{a + 8}{2} = \frac{a - 4}{8} [/tex]
What would be the first step in solving the equation 7/9x + 34 = 174?
Answer:
[tex] \frac{7}{9} x + 34 = 174 \\ => \frac{7x}{9} = 174 - 34 \\ = > \frac{7x}{9} = 140 \\ = > 7x = 140 \times 9 \\ = > 7x = 1260 \\ = > x = \frac{1260}{7} = 180 \\ { \huge{ \pink{x = 180}}}[/tex]
❤️❣️❤️Find the measure of the arc.
A
146°
E
B
MABC = [ ? 1°
Answer:
i get mABC = 270°
Step-by-step explanation:
This is fairly straight forward once you the right angle symbol for the arc AC. Also realizing the 148° for mAB is not needed for this question. The 148° for mAB would be useful if you wanted to calculate arc mBC.
Remember there are 360° in a circle.
The arc mAC is 90°
The arc mABC is the rest of the circle. is the arc from A to B to C
arc ABC + arc AC is the full circle 360°
mABC + mAC = 360° mAC = 90°
mABC + 90° = 360° - 90° from both sides
mABC = 360° - 90°
mABC = 270°
The angle ∠ABC in the given circle will be 270°.
What is an angle?
An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
Angle is very useful to measure any angular rotational motion for example if you have to find out the rotation among the circle then it cannot measure in length parameter such that meter inch so it will be measured as an angle in a unit of degree or radian.
In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.
Now since we know that the angle of complete rotation is 360°.
Now ∠ADC + ∠ABC = 360
Given that ∠ADC = 90°
∠ABC = 360° - 90° = 270°
Hence, 270° will be the correct answer.
For more about the angle
brainly.com/question/13954458
#SPJ5
Find two integers whose sum is -2 and product is -80
Answer:
-10 and 8
Step-by-step explanation:
-10 + 8 = -2
-10 x 8 = -80
Answer:
x = -10 and y = 8
x = 8 and y = -10
Find WX please help is very much appreciated
Answer:
WX = 6
Step-by-step explanation:
1. Approach
First, one must find the value of the variable (x). This can be done by using the Tangent-Line-intersection-theorem (many people refer to it by another name, but the theory is the same). This theory essentially states that when two lines are tangent to a circle and are non-parallel, the distance between the point of tangency, and the point of intersection of those two lines are the same for each line. After finding the value of (x), one can substitute it back into the given equation for the value of (WX), and solve it.
2. Finding (x)
The two segments; (WX) and (XY) are tangent to the given circle. Meaning that they only make contact with the circle at a single point. The space between their point of tangency and the point at which they intersect will be equal. Essentially meaning that the length of (WX) and the length of (XY) are the same. Therefore the equation
(XY) = (XW)
Can be formed. Substitute in the given values;
7x - 29 = 2x + 16
Inverse operations,
7x - 29 = 2x + 16
-2x -2x
5x - 29 = 16
+29 +29
5x = 45
/5 /5
x = 9
3. Solve for (WX)
Now substitute back in to find the length of (WX)
7x = 29
x = 5
7(5) - 29
35 - 29
6
------------Need help ----------
Y=3x-2
Answer: -8, -5, -2, 1, 4
Step-by-step explanation:
Y=3x-2
- Plug in the number for x.
x = -2, y = 3x - 2= 3(-2) - 2 = - 6 - 2= - 8
x = -1, y = 3x - 2= 3(-1) - 2 = - 3 - 2= - 5
x = 0, y = 3x - 2= 3(0) - 2 = 0- 2= - 2
x = 1, y = 3x - 2= 3(1) - 2 = 3 - 2= 1
x = 2, y = 3x - 2= 3(2) - 2 = 6 - 2= 4
Jose's gas tank is 1/5 full. After he buys 9 gallons of gas, it is 7/10 full. How many gallons can Jose's tank hold?
Answer:
18 gallonsStep-by-step explanation:
Let the capacity of tank is x
1/5x + 9 = 7/10x2/10x + 9 = 7/10x5/10x = 91/2x = 9x = 18 gallons11x - ? = 19x what is the missing number?
Answer:
8x !
Step-by-step explanation:
Answer:
8x
Step-by-step explanation:
The average length of a female dolphin is about 179 inches What is the length in feet and inches pleaseee help me I have been stuck on this questions for about 20 mins !
Please help will give brainliest
Answer:
(5j + 4k)2
2(5j + 4k)
Step-by-step explanation:
Only choices where it distributes 10j + 8k
Answer: 2(5j+ 4K) and (5j+4k)2
Hope this helps!
Step-by-step explanation:
Zander read 13 3/4pages in 1/4 of an hour. Sydney read 43 1/3 pages in 2/3 of an hour. At these rates, would Zander or Sydney read more pages in 1 hour?
Answer:
At these rates Sydney read 10 pages per hour more than Zander.
Step-by-step explanation:
Zander read [tex]13\frac{3}{4}[/tex] pages in [tex]\frac{1}{4}[/tex] of an hour.
Therefore, pages read by Zander in 1 hour = [tex]\frac{\text{Total pages read}}{\text{Total time taken}}[/tex]
= [tex]\frac{13\frac{3}{4}}{\frac{1}{4}}[/tex]
= [tex]\frac{55}{4}\times \frac{4}{1}[/tex]
= 55 pages per hour
Sydney read [tex]43\frac{1}{3}[/tex] pages in [tex]\frac{2}{3}[/tex] of an hours.
Pages read by Sydney in 1 hour = [tex]\frac{43\frac{1}{3}}{\frac{2}{3} }[/tex]
= [tex]\frac{130}{3}\times \frac{3}{2}[/tex]
= 65 pages per hour
Therefore, number of pages read more by Sydney as compared to Zander,
= 65 - 55
= 10 pages per hour
At these rates Sydney read 10 pages per hour more than Zander.
Which is the most appropriate unit to measure the amount of liquid in bottle A) fluid ounces B) cubic centimeters C) ounces D) cubic feet
Answer:
a
Step-by-step explanation:
Answer:
A) Fluid ounces
Step-by-step explanation:
PLEASE HELP:). The branch of an isosceles triangle is 2.5 times longer than the base and the circumference of the triangle is 60 cm. Find the lengths of the midpoints of the triangle.
Answer:
Step-by-step explanation:
2.5x + 2.5x + x = 60
x= 10
2.5x = 25
the sides of the triangle are 25, 25, 10
I don't know what you mean by "midpoints of the triangle".
Area of composite shapes!!
Find the area
Its geometry
Due Tomorrow
Plz HURRY
Offering brainliest
Which inequality is a true statement?
Select each correct answer.
-5 = -7
ロ-5<-7
-5 > -7
0-5 > -7
-5 < -7
Answer:
-5 > -7 and 0-5>-7 are both true statements the rest aren't.
Step-by-step explanation:
9 less than m squared
Answer: b = m
(3 + m)(3 - m)
Step-by-step explanation:
Please help will give brainliest
Three bags of chips and sodas cost $12.50. Four bags of chips and two sodas cost $10.00. What is the cost of each item? ASAP pls!
Step-by-step explanation:
3c + 3s = 12.50
4c + 2s = 10.00
3S = 12.50-3c
s = 4.17 - c
4c + 2 (4.17-c) = 10.00
2c + 8.34 = 10.00
2c = 1.66
chips = 0.83
soda = 3.34
Please help me with the questions please ASAP
Answer:
x = 20
Step-by-step explanation:
You can solve this problem using similar triangles; you know the triangles are similar due to the AAA property because of the Corresponding Angles Theorem.
To find x, you need to identify what sides 8 and x correspond to:
8 corresponds to 14 (6 + 8)
x corresponds to (x + 15)
Now, you need to find the scale factor by dividing 14 by 8:
14 ÷ 8 = 7/4
At this point, you can write and solve an equation for x:
7/4x = x + 15
3/4x = 15 (subtract x from both sides)
x = 20 (multiply both sides by 3/4)
I need the answer for this. Please help
Y=8/10+22
The diameter of a circle is 4 yards. What is the circle’s area?
Use 3.14 for pi
Answer:
12.566 yd
Step-by-step explanation:
i honestly just need help and nones helping 6th grade work
The cost of making a shirt is half of what the shirt normally sells for. Today, the shirt is in a 15 percent discount from its normal price. What is the current price of the shirt?
Answer:
.85 times the cost to make the shirt
Step-by-step explanation:
Let x represent cost to make the shirt.
Today, the shirt is in a 15 percent discount from its normal price.
Discount = 15/100 * x = 0.15x
Current cost = Original cost - discount
Current cost = x - 0.15x = 0.85x
The answer is;
.85 times the cost to make the shirt
PLEASE HELP PLEASEEEE!!! Number 3
Answer in terms of A and B