Which graph correctly represents
x + 2y ≤ 4?
Step-by-step explanation:
[tex]x + 2y \leq 4[/tex]
To graph this inequality we replace <= symbol with = sign
[tex]x + 2y =4[/tex]
subtract x on both sides
[tex]2y =-x+4[/tex]
divide both sides by 2
[tex]y= \frac{-1}{2} x +2[/tex]
Graph the equation using a table
LEts assume some number for x and find out y
x [tex]y= \frac{-1}{2} x +2[/tex]
-2 3
0 2
2 1
Now graph the equation using points (-2,3) (0,2)(2,1)
use solid line for graphing
Now use test point (0,0) for shading
[tex]x + 2y \leq 4[/tex]
[tex]0 + 2(0) \leq 4[/tex]
[tex]0 \leq 4[/tex] true
So we shade the region that contains (0,0)
the graph is attached below
What are the vertex, focus, and directrix of the parabola with the equation x^2+8x+4y+4=0
Answer:
Vertex=(-4,3)
Focus=(-4, 2)
Directrix: y=4
Step-by-step explanation:
Given the equation
[tex]x^2+8x+4y+4=0[/tex]
we have to find the vertex, focus, and directrix of parabola.
[tex]x^2+8x+4y+4=0[/tex]
[tex]y=\frac{-x^2}{4}-2x-1[/tex]
[tex]h=\frac{-b}{2a}=\frac{2}{2(\frac{-1}{4})}=-4[/tex]
Now, k can be calculated by putting x=4 and y=k in given equation
[tex]k=-1-\frac{16}{4}-2(-4)=-1-4+8=3[/tex]
The vertex is (h,k) i.e (-4,3)
[tex]y=\frac{-x^2}{4}-2x-1[/tex]
[tex]y=\frac{1}{4}(-x^2-8x-4)[/tex]
[tex]=\frac{1}{4}(-x^2-8x-16+16-4)[/tex]
[tex]y=\frac{1}{4}(-(x+4)^4+12)[/tex]
[tex]y=\frac{-1}{4}(x+4)^2+3[/tex]
which is required vertex form [tex]4p(y-k)=(x-h)^2[/tex]
gives p=-1
Focus=(-4, 3+(-1))=(-4,2)
Now directrix can be calculated as
y=3-p=3-(-1)=4
The key idea of the transformation called a reflection is _____.
the object moves the plane a certain angle measure
the object moves in a straight line movement
the object and its image have opposite orientations
the rotating of a plane about a fixed point
Answer: The object and its image have opposite orientations
Step-by-step explanation:
A reflection is a type of rigid transformation in which the preimage is flipped across a line of reflection to produce the image, such that the figure and its image have opposite orientations.
Since, it preserves distance.
Therefore, the points of the image have the same distance from the line as the points of pre-image on the opposite side of the line.
Hence, the right option is "the object and its image have opposite orientations".
The original value of the car is $18,000 it depreciates by 15% every year what is the value of the car after three years
Russells previous test scores are 70,74,87,85 what score does he need to get an average of 80
Answer:
84 is the score that you Russell needs on the next test to achieve an average of at least 80.
Step-by-step explanation:
Russell's test scores are: 70,74,87 and 85
Average of the test scores = A = 80
Let thescore needed to achieve an average of 80 be x
Average = [tex]\frac{\text{Sum of terms}}{\text{Number of terms}}[/tex]
[tex]A=\frac{70+74+87+85+x}{5}[/tex]
[tex]80=\frac{70+74+87+85+x}{5}[/tex]
[tex]70+74+87+85+x=400[/tex]
[tex]x=400-(70+74+87+85)=84[/tex]
84 is the score that you Russell needs on the next test to achieve an average of at least 80.
Which of the following equations represents a quadratic function?
y(y + 4)(y - 6) = 0
z2 + 2 = 3z(z2 - 1)
(2x - 3)(4x + 5) = 10x
(3b)(5b – 7)(b + 8) = 0
A quadratic equation is one in which the highest exponent of a variable is 2. We can solve this problem by expanding each choices then find which has highest exponent equal to 2.
y(y + 4)(y - 6) = 0 ---> By expansion we get y^3, therefore highest exponent is 3.
z2 + 2 = 3z(z2 - 1) ---> By expansion we get z^3, therefore highest exponent is 3.
(2x - 3)(4x + 5) = 10x ---> By expansion we get x^2, therefore highest exponent is 2.
(3b)(5b – 7)(b + 8) = 0 ---> By expansion we get b^3, therefore highest exponent is 3.
The answer to this problem is therefore:
(2x - 3)(4x + 5) = 10x
Vivian measured 2/5 cup of onions, 1/3 cup of celery, and 1/2 cup of carrots. How many cups of vegetables did Vivian measure out for her vegetable soup?
A game involves tossing a biased coin that has a 60% probability of landing on heads. If a player wins $50 when heads appears, what is the expected value of a player's winnings?
What is 2/3x = 4/15?
2/3x = 4/15 =
x = 4/15 / 2/3 = 4/15 x 3/2 = 12/30 = 2/5
x = 2/5
all i know is x=25 its hard for me to explain.
This net folds into the cube shown beside it. On the cube, which letter will be on the side opposite D?
Without more information or a diagram, it's hard to give a specific answer. However, on a cube net, the face opposite 'D' is likely the one not directly connected to 'D' on the plane of the net.
Explanation:Unfortunately, without a diagram or more context, it's difficult to provide a definitive answer to the question. However, typically on a cube net, sides that are opposite each other when the net is folded into a cube are adjacent (next to each other) on the net. For example, if 'D' were on a flat square in the center of the net, the squares directly connected to it (on the top, bottom, left, and right) on the plane of the net would end up being the sides adjacent to 'D' when the cube is formed. The square not connected directly to 'D' on the plane would be opposite 'D' once the cube is formed.
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a bowl contains 80 M&M candies If 15 are orange what fraction of the candies is NOT orange. Answer reduced to lowest terms
Find the factorization of the polynomial below.
2x²+7x+6
A. (2x+2)(x+4)
B. (2x+2)(x+3)
C. (2x+3)(x+1)
D. (2x+3)(2x+2)
Answer:
(2x+3)(x+2)
Step-by-step explanation:
i hope this helps
Find the critical value zα/2 that corresponds to a 98% confidence level.
A critical value is the point on the scale of the test statistic (z test in this case) outside which we reject the null hypothesis, and is taken from the level of significance of the test. The critical values can be obtained from the standard distribution tables for z and for this case, it is equivalent to:
critical value zα/2 at 98% confidence level = 2.326
Answer: 2.326
Answer:
2.33
Step-by-step explanation:
Find the length of the hypotenuse of a right triangle with legs of lengths 5 and 12. If necessary, round your answer to two decimal places
The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r. The equation solved for P is P = . What is the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years? $60 $80 $90 $100
we know that
The simple interest formula is equal to
[tex]I=Prt[/tex]
where
I represents simple interest
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=5\ years\\ P=?\\ I=\$40\\r=0.10[/tex]
[tex]I=Prt[/tex]
Solve for P
[tex]P=I/(rt)[/tex]
substitute the values
[tex]P=40/(0.10*5)=\$80[/tex]
therefore
the answer is
[tex]\$80[/tex]
For which value of m does the graph of y = 18x2 + mx + 2 have exactly one x-intercept?
Answer:
12
Step-by-step explanation:
Evaluate the function rule for the given value. Y=6*4 for x=-3
I need help please :( !!!
Rita is saving money to buy a game. So far she has saved $15, which is three-fifths of the total of the game. How much does the game cost?
15 /3 = 5. so each 1/5 is $5
5*5 = 25
so the game costs $25
Use the graph below to answer the following question:
What is the average rate of change from x = –4 to x = 1?
–3
–1
0
1
The average rate of change from x = –4 to x = 1 is 3.
Explanation:To find the average rate of change from x = –4 to x = 1, we need to calculate the change in y-values and divide it by the change in x-values. Given that the slope of the line is 3, we can use the formula for average rate of change: (change in y) / (change in x). In this case, the change in x is 1 - (-4) = 5, and the change in y is 3 * 5 = 15. Therefore, the average rate of change is 15 / 5 = 3.
Which statement is true about the discontinuation of the function F(x)? F(x)=x+1/6x^2-7x-3
what is the radius of a circle given by the equation x^2+(y-3)^2=21
Vera and her roommates ate 1 1/3 pints of ice cream on Friday night and 1 1/6 pints of ice cream on Saturday night. How many pints did they eat in all
1 1/3 + 1 1/6
add the 1 +1 = 2
add 1/3 + 1/6 ( find common denominator, which in this case is 6)
so 1/3 becomes 2/6
2/6 + 1/6 = 3/6 which reduces to 1/2
they ate 2 1/2 pints total
A triangle has a perimeter of 48" and the dimensions of each side are given as X + 3, 4x-1, 2X -3 solve for the value of X and determine the length of each side
how can exponential and logarithmic functions be created to use in real world situations?
1.Find the area of each triangle with the given heights and bases
a. h = 6 inches; b = 10 inches
b. h = 9 centimeters; b = 4 centimeters
c. h = 13 yards; b = 20 yards
Answer: 1.)
A. 30in^2
B. 18cm^2
C. 130yd^2
2.) The formula for the area of a triangle is half the base times the height. So 1/2 x 40 x 32 = 640cm^2
3.) 17 yards. The fence that enclose Sondra's backyard is a right triangle whose sides measuring 8 yards, 15 yards and 17 yards respectively.
4.) From the Pythagorean Theorem we know:
hypotenuse^2 = side^2 + side^2
hypotenuse^2 = 36 + 36
hypotenuse = square root (72)
hypotenuse = 8.48528... feet
5.) a. 5
b. √128
c. √221
Area of triangle are [tex]30inches^{2}[/tex] in part(a),
[tex]18[/tex] [tex]centimerters^{2}[/tex] in part(b) and [tex]130[/tex] [tex]yards^{2}[/tex] in part(c)
What is Triangle?
In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.
What is area?
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
According to questions, we have the following
In part (a.), h = [tex]6[/tex] inches; b = [tex]10[/tex] inches
In part (b.), h =[tex]9[/tex] centimeters; b =[tex]4[/tex] centimeters
In part (c.) h = [tex]13[/tex] yards; b = [tex]20[/tex] yards
We have to find the area of each triangle with the given heights and bases.
Now, Area of triangle in part a
[tex]=\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]
[tex]=\frac{1}{2}[/tex]×[tex]6[/tex]×[tex]10[/tex]
[tex]=30inches^{2}[/tex]
Area of triangle in part b
[tex]=\frac{1}{2}[/tex]×[tex]9[/tex]×[tex]4[/tex]
[tex]=18[/tex] [tex]centimerters^{2}[/tex]
Area of triangle in part c
[tex]=\frac{1}{2}[/tex]×[tex]13[/tex]×[tex]20[/tex]
[tex]=130[/tex] [tex]yards^{2}[/tex]
Hence, we can conclude that area of triangle are [tex]30inches^{2}[/tex] in part(a),
[tex]18[/tex] [tex]centimerters^{2}[/tex] in part(b) and [tex]130[/tex] [tex]yards^{2}[/tex] in part(c)
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Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: Two rectangular tiles, rectangle PQRS with vertices at P 5, 7. Q is at 9, 7. R is at 9, 12. S is at 5, 12 . Rectangle JKLM with vertices J 4, 5. K is at 6, 5. L is at 6, 10. M is at 4, 10. Which statement is correct?
Last year the profit for a company was $560,000. This year's profit decreased by 7.1%. Find this year's profit.
C =5/9(F-32). Covert 12 degrees Celsius to Fahrenheit. Round to nearest degree
Use the change of base formula to evaluate log4 20.