(04.06 MC) In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB. Graph of two intersecting lines. One line f of x is solid and goes through the points 0, 4, and 4, 0 and is shaded above the line. The other line g of x is solid, and goes through the points 0, negative 1 and 2, 5 and is shaded in below the line. The graph represents which system of inequalities? y ≤ −3x − 1 y ≤ −x − 4 y ≥ −3x + 1 y ≤ −x − 4 y ≤ 3x − 1 y ≤ −x + 4 y ≤ 3x − 1 y ≥ −x + 4
Answers
Answer:
(D)y ≤ 3x − 1 y ≥ −x + 4
Step-by-step explanation:
The line f(x) is solid and goes through the points (0, 4) and (4, 0) and is shaded above the line.
The line that satisfies the point (0,4) and (4,0) is y=-x+4
Since it is shaded above the line, we have the inequality sign ≥.
Therefore, one of the lines is y≥-x+4
In the equation of the line y=3x-1
When x=0, y=3(0)-1=-1
When x=2, y=3(2)-1=5
Since it is shaded below the line, we have the inequality sign ≤ .
Therefore, the other line is y≤3x-1.
The correct option is D.
In this exercise we want to mark the correct alternative that corresponds:
The correct option is D.
The line f(x) is solid and goes through the points (0, 4) and (4, 0) and is shaded above the line. The line that satisfies the point (0,4) and (4,0) is:
[tex]y=-x+4[/tex]
Since it is shaded above the line, we have the inequality sign ≥. Therefore, one of the lines is :
[tex]y\geq -x+4[/tex]
In the equation of the line:
[tex]y=3x-1[/tex]
When: [tex]x=0, y=3(0)-1=-1[/tex]
When: [tex]x=2, y=3(2)-1=5[/tex]
Since it is shaded below the line, we have the inequality sign ≤ . Therefore, the other line is:
[tex]y\leq 3x-1.[/tex]
The correct option is D.
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Related Questions
TWO MINUTES HURRY HELP ME PLEASE
Answers
Answer:
x=-1
Step-by-step explanation:
Answer: x. = -1
Step-by-step explanation:
The Surface Area of a square pyramid is 3600 ft. The slant height is 80 feet and the base is 20 feet. At most how many 1 foot cubic
blocks can be stuffed in the pyramid?
Answer:
Answers
Answer:
10,583 flexible cubes
9915 rigid cubes
Step-by-step explanation:
The equation for the surface area of a square pyramid is area of base plus perimeter of base multiplied by the slant height
Surface area = A + 1/2·p·s
The volume of the pyramid = 1/3×A×h
Where:
A = Area of the base = 20 × 20 = 400 ft²
h = The height of the pyramid = √((slant height)² - ((base side length)/2)²)
h = √(80² - (20/2)²) = 30·√7
The volume of the pyramid = 1/3*400*30·√7 = 4000·√7 ft³ = 10,583.005 ft³
If the cubes are flexible, approximately 10,583 cubes
For rigid cubes we have
Given that the height of the pyramid = 30·√7
The slope of the pyramid = 30·√7/10 = 3·√7
So an increase in height of 1 foot gives a reduction in width of 2/(3·√7)
The bottom can hold 400 cubes
The next layer can hold 19×19 = 361
3rd 361
4th 361
5th 324
6th 324
7th 324
8th 324
9th
Continuing, we get a total of about 9915 rigid cubes in the pyramid.
find the geometric mean of 64 and 49
Answers
Answer:
i think 56..?
Step-by-step explanation:
The geometric mean of 64 and 49 is 56.
What is geometric mean?The geometric mean is a mean or average of the data sets using their product. The formula to calculate geometric mean is [tex]\sqrt{a*b}[/tex]
How to find geometric mean?To find the geometric mean of 64 and 49 we have to put these values in the above formula. So,
Geometric Mean=[tex]\sqrt{64*49}[/tex]
=[tex]\sqrt{3136}[/tex]
=56
Hence the geometric mean of 64 and 49 is 56.
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An equation is written to represent the relationship between the temperature in Alaska during a snow storm, y, as it relates to the time in hours, x, since the storm started. A graph of the equation is created. Which quadrants of a coordinate grid should be used to display this data? please help.
Answers
Answer:
the first and fourth quadrants
Step-by-step explanation:
We have that the time found hours is given on the x-axis and that the temperature is represented on the y-axis.
Let's first analyze time:
Time cannot be negative, therefore, the x coordinate cannot be negative therefore, for the x axis, we can use the first and fourth quadrants
Second let's analyze the temperature:
The temperature can be negative, therefore, the coordinate and can be positive or negative therefore, that for the y axis, we can use all four quadrants.
If we combine the two previous conditions, we can deduce that we can only use the first and fourth quadrants to represent the required data.
Sphere A has a diameter of 2 and is dilated by a scale factor of 3 to create sphere B. What is the ratio of the volume of sphere A to sphere B?
A 2:6
B 4:36
C 1:3
D 1:27
Answers
Answer:
1:27
Step-by-step explanation:
I will use solve in terms of pi
Know that Original volume * scale factor cubed = new volume.
The scale factor is 3 and 3^3 is 27,
Therefore the ratio is 1:27
Scaled figures are zoomed in or zoomed out (or just no zoom) versions of each other. The correct option is D.
What are Scaled figures?Scaled figures are zoomed in or zoomed out (or just no zoom) versions of each other. They have scaled versions of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.
So, if a side of a figure is of length L units, and that of its similar figure is of M units, then:
[tex]L = k \times M[/tex]
where 'k' will be called a scale factor.
The linear things grow linearly like length, height etc.
The quantities which are squares or multiple linear things twice grow by the square of the scale factor. Thus, we need to multiply or divide by k²
to get each other corresponding quantities from their similar figures' quantities.
So the area of the first figure = k² × the area of the second figure
Similarly, increasing product-derived quantities will need increased power of 'k' to get the corresponding quantity. Thus, for volume, it is k cubed. or
The volume of the first figure = k³ × volume of the second figure.
It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.
Given that the diameter of sphere A is 2 units, it is dilated by a scale factor of 3 to create sphere B. Therefore, the diameter of sphere B is,
Diameter of sphere B = 3 × Diameter of sphere A
= 3 × 2 units
= 6 units
Now, the ratio of diameters of the sphere and the volume of the sphere can be written as,
[tex](\dfrac{\text{Diameter of sphere A}}{\text{Diameter of sphere B}})^3 = \dfrac{\text{Volume of sphere A}}{\text{Volume of sphere B}} \\\\\\(\dfrac{2}{6})^3 = \dfrac{\text{Volume of sphere A}}{\text{Volume of sphere B}}\\\\\\\dfrac{\text{Volume of sphere A}}{\text{Volume of sphere B}} = \dfrac{1}{27}[/tex]
Hence, the correct option is D.
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what are the roots of the polynomial equation x⁴+x³=4x²+4x? use the graphing calculator and a system of equations.
-2,-1,0,2
-2,0,1,2
-1,0
0,1
Answers
Answer: A
Step-by-step explanation:
What is the measure of circumscribed ∠X? 45° 50° 90° 95° please answer asap
Answers
Answer:
90°
Step-by-step explanation:
Data provided in the question
Angle V = right angle = 90°
YX and WX = tangents,
And YV and WV = radii
So, we can say that
Angle Y = 90°
And,
Angle W = 90°
Now as we know that sum of four interior angles is 360°
So,
the equation is
V + Y + W + X = 360°
90° + 90° + 90° + X = 360°
270° + X = 360
Therefore,
X = 360° - 270°
= 90°
Answer:
c. 90
Step-by-step explanation:
What is the product?
Answers
Answer:
B
Step-by-step explanation:
3•(-6)=-18
3•(-11)=-33
3•(-14)=-42
3•(-9)=-27
Answer:
B. [ -18 -33]
[ -42 -27]
you have to distribute the x3 to all four numbers in the matrix
Timothy has a fenced-in garden in the shape of a rhombus. The length of the longer diagonal is 24 feet, and the length of the shorter diagonal is 18 feet. A rhombus is shown. Diagonals are drawn from each point to the opposite point and intersect at a point in the middle. The distance from the top point to the middle point is 12 feet. The distance from the right point to the middle point is 9 feet. What is the length of one side of the fenced-in garden? 12 ft 15 ft 21 ft 108 ft
Answers
Answer: b) 15 ft
Step-by-step explanation:
The diagonals intersect at a right angle (one of the properties of a rhombus).
Use Pythagorean Theorem to find the length of the side.
9² + 12² = c²
81 + 144 = c²
225 = c²
15 = c
Answer:
i got b!
Step-by-step explanation:
15 feet (:
in an abc triangle, the hypotenuse is 10 and the other sides are x, the measurement of angle B is 90 deg, what is the value of x
Answers
Answer:
x = [tex]5\sqrt{2}[/tex].
Step-by-step explanation:
The question says that the hypotenuse is 10, while the other two sides are both x. That means that the triangle is a 45-45-90 angle.
Because this is a 45-45-90 triangle, the proportions of the side lengths are 1-1-sqrt(2).
Since the hypotenuse is 10, and the side length is x, we can make a proportion.
[tex]\frac{10}{\sqrt{2}} =\frac{x}{1}[/tex]
[tex]x\sqrt{2}[/tex] = 10
x = [tex]\frac{10}{\sqrt{2} }[/tex]
x = [tex]\frac{10 * (\sqrt{2} )}{(\sqrt{2})(\sqrt{2} ) }[/tex]
x = [tex]\frac{10\sqrt{2} }{2}[/tex]
x = [tex]5\sqrt{2}[/tex]
Hope this helps!
Which equations represent the line that is parallel to 2x-7y=9 and passes through the point
(5-3) ? Select two options.
Answers
Answer:
e. 2x - 7y = 31.
Step-by-step explanation:
If you want a line parallel to the equation, the line must have the same slope.
2x - 7y = 9
-7y = -2x + 9
y = 2/7x - 9/7
You are looking for a line where the slope is 2/7.
a. Slope is 7/2.
b. Slope is -7/2.
c. Slope is 7/2.
d. Slope is...
y + 2 = 3/4x + 3
y = 3/4x + 1
Slope is 3/4.
e. Slope is -2/-7, which is 2/7. Just make sure to check whether it passes through (5, -3) by substituting those points into the equation.
2 * 5 - 7 * -3 = 31
10 --21 = 31
10 + 21 = 31
And there's your answer: e.
Hope this helps!
Simplify: -(-x + 1) -x − 1 x − 1 -x + 1 x + 1
Answers
Answer:
x -1
Step-by-step explanation:
-(-x + 1)
Distribute the minus sign
- 1 * -x + -1 (-x)
x -1
Steps to solve:
-(-x + 1)
~Distribute the negative sign
(- * -x) + (- * 1)
~Simplify
x - 1
Best of Luck!
******WHO ANSWERS WILL BE MARK AS BRAINLIEST******
Which equation can be used to solve for a?
tan50=a/3
cos50=3/a
sin 50=a/3
tan50=3/a
Answers
Answer:
Tan 50 =3/a is the ans
Step-by-step explanation:
Feel very happy to help u
Answer:
tan 50=3/a
Step-by-step explanation:
Using the trigonometric ratio, tan(tita)=opposite/adjacent.
Opposite is the side with only 90°. Adjacent is the side with two angles.
If the dimensions of a rectangular prism are 39 mm × 12 mm × 15 mm, then what is the surface area
Answers
Answer:
[tex]\huge\boxed{SA=2466\ (mm^2)}[/tex]
Step-by-step explanation:
The formula of a Surface Area of a rectangular prisms:
[tex]SA=2(lw+lh+wh)[/tex]
l - length
w - width
h - height
We have:
[tex]l=39mm;\ w=12mm;\ h=15mm[/tex]
Substitute:
[tex]SA=2\bigg((39)(12)+(39)(15)+(12)(15)\bigg)\\\\SA=2(468+585+180)\\\\SA=2(1233)\\\\SA=2466\ (mm^2)[/tex]
Help! I'm confused on this. It's not factorable right? What would my answer be? Factor [tex]xy+8y-2x-16[/tex].
Answers
Answer:
(y-2)(x+8)
Step-by-step explanation:
xy + 8y - 2x - 16= (xy +8y) - (2x+16) =y(x+8) - 2(x+8) =(y-2)(x+8)As you can see it is factorized
Determine if the equation defines y as a function of x: y2 = x2. yes or no
Answers
Answer:
no it's not, since y has two functions , a positive and negative in terms of x.
Here are 4 fractions labelled A,B,C,D. A is 3/4 B is 5/6 C=16/25 D=9/15 Using the label A,B,C,D, Write the fractions in order of size starting with the smallest fraction
Answers
Answer:
Starting with the smallest, we will have; D , C, A, B
Step-by-step explanation:
Given;
A = 3/4
B = 5/6
C = 16/25
D = 9/15
Convert the fractions to decimal, to determine their sizes;
A = 3/4 = 0.75
B = 5/6 = 0.833
C = 16/25 = 0.64
D = 9/15 = 0.6
From the decimal form of the fractions, it be observed that,
B > A > C > D
Starting with the smallest, we will have; D , C, A, B
Peter deposited $5000 in a bank paying 5% interest compounded yearly. Find the balance in his account after 3 years.
Answers
Answer:
5750
Step-by-step explanation:
[tex]\frac{5}{100}[/tex]×5000=250
250×3=750
5000+750=5750
Simplify the expression.
Write your answer without negative exponents.
Answers
Answer: [tex]\frac{5a^2}{-10a^4b^9}[/tex]
Step-by-step explanation:
Any negative exponent can be moved to the other side of the fraction as a positive exponent.
Thus, simply move the negative exponents to get: 5a^2/b*b^8*-10a^4. Then, use the exponent rule to get 5a^2/-10a^4b^9
Hope it helps <3
3. A un hombre le pagan doble el tiempo que trabaja por encima de las 40 horas. La
pasada semana, él trabajó 47 horas y recibió un cheque de $648.00. ¿Cuál es su
salario regular por hora?
Answers
Answer: Su salario regular por hora es $12
Step-by-step explanation:
Hola, para resolver este problema debemos plantear una ecuación:
A el hombre le pagan doble el tiempo que trabaja por encima de las 40 horas, el trabajo 47, o lo que es equivalente = 40+7.
Las primeras 40 horas recibió su salario regular por hora (x) y las otras 7 recibió el doble (2x). LA suma de esos productos da un total de $648.
Matemáticamente hablando:
40 x+ 7 (2x) = 648
Resolviendo para x (salario regular por hora)
40x +14x =648
54x =648
x = 648/54
x = 12
which equation represents a line that is parallel to the y axis, is perpendicular to the x-axts, and has an undefined slope?
o v = 2 + + 3
Answers
Answer:
x=7/2
Step-by-step explanation:
Answer:
X=7/2
Step-by-step explanation:
3х
Which expression is equivalent to X+ 1 divided by x + 1?
3х 1
X+1 x+1
1
3х
х+ 1 x+1
3х
х+1
1
Х+ 1
х+1 x+1
3х 1
Answers
Answer:
first option
Step-by-step explanation:
Given
[tex]\frac{3x}{x+1}[/tex] ÷ x + 1 = [tex]\frac{3x}{x+1}[/tex] ÷ [tex]\frac{x+1}{1}[/tex]
To perform the division
Leave the first fraction, change division to multiplication and turn the second fraction upside down, that is
= [tex]\frac{3x}{x+1}[/tex] × [tex]\frac{1}{x+1}[/tex]
Option A is correct, (3x/x+1).(1/x+1) is the equivalent expression of the expression 3x/x+1 divided by x+1.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 3x/x+1 divided by x+1.
We need to find the equivalent expression of it.
3x/x+1 divided by x+1 can be mathematically written as below
(3x/x+1)/x+1
(3x/x+1) is the numerator and x+1 is in denominator
(3x/x+1)/(x+1/1)
When a fraction is divided by another fraction the denominator is multiplied to numerator as a reciprocal.
(3x/x+1).(1/x+1)
Hence, Option A is correct, (3x/x+1).(1/x+1) is the equivalent expression of the expression 3x/x+1 divided by x+1.
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What is the value of x?
Answers
Answer:
The answer is option C.
Step-by-step explanation:
Angles in a triangle add up to 180°
To find x add up all the angles in the triangle and subtract it from 180°
Thus
x + 95 + 57 = 180
x = 180 - 152
x = 28°
Hope this helps
Which expression is equal to the expression below?
(7•2)7
Answers
Answer:
C. 7⁷ × 2⁷
Step-by-step explanation:
The exponent is outside of the brackets, so we distribute the exponent to all the terms inside the brackets.
(7 × 2)⁷
7⁷ × 2⁷
Answer:
c. [tex]7^7[/tex]· [tex]2^7[/tex]
Step-by-step explanation:
please mark me brainliest!
For every 10 minutes that Tia plays on the computer, she plays outside
for 19 minutes. What is the ratio of minutes Tia plays on the computer
to minutes she plays outside?
Answers
Answer: 10:19
Step-by-step explanation:
Time she plays on computer = 10 minutes
Time she plays outside = 19
Ratio will be 10:19
Hannah wants to display all the possible outcomes when rolling two fair 6-sided dice. By drawing a sample space, find the probability of the scores on the two dice adding to 11.
Answers
Answer:
1/18
Step-by-step explanation:
First list all the 2 answers that may add up to 11:
5 and 6
6 and 5
There are no more.
Next how many possible outcomes can se get?:
6 x 6 = 36
Thus, the probability = 2/36 = 1/18
The odds of the two dice's results adding up to 11 are 1/18.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
given, Hannah wants to display all the possible outcomes when rolling two fair 6-sided dice.
From the general formula of probability:
Probability = desired outcomes / total possible outcomes
in our case desired outcome = scores on the two dice adding to 11
the desired outcome is getting 6, 5 and 5,6
thus desired outcome = 2
since the dice is 6-sided
total outcome = 6*6 = 36
probability = 2/36
Probability = 1/18
therefore, the probability of the scores on the two dice adding to 11 is 1/18.
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PLZ HELP ME PLZZZ I NEED HELP
Answers
Answer:
y = 40.5 cm
Step-by-step explanation:
The total area of the shape is 792 cm²
let's find the area of the four parallelograms
To do that we should calculate the area of the rhombus inside and then substract it from the total area
The area of a rhombus is given by the formula:
A = [tex]\frac{d*d'}{2}[/tex] where d and d' are the diametersLet A be the area of the shape , A' the area of the rhombus and A" the area of the four parallelograms
A"= A - A' A" = A -[tex]\frac{d*d'}{2}[/tex] A" = 792- [tex]\frac{18*7}{2}[/tex] A" = 729 cm²Let a be the area of the single parallelogram
a = A"/4 since the parallelograms are congruent a = 729/4 a = 182.25 cm²the area of a parallelogram is fiven by the formula :
A = b*h b is the base (here y/2) and h the height (here 18/9)let's find y
a = [tex]\frac{y}{2}[/tex] * 9182.25*2 = y*9 364.5 = y*9 y = 364.5/9 y = 40.5What is the equation of the translated function, g(x), if
f(x)=x²?
O g(x) = (x-4)2 + 6
O g(x) = (x + 6)2 - 4
O g(x) = (x - 6)2 - 4
O g(x) = (x + 4)2 + 6
Answers
Answer:
the answer is (x+6)2-4
The correct equation of the translated function, g(x) is,
⇒ g(x) = (x + 4)² 6
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
here, we have,
Given that:
The function is,
,⇒ f (x) = x²
Here, f(x) has vertex point is (0,0)
and g(x) vertex point is (-4,6)
Hence, The general form of equation with vertex is
⇒ y = a (x - h)² + k
where (h, k) are the vertex.
So, the equation of g(x) form is
⇒ g(x) = (x + 4)² + 6
Therefore, Option D is correct.
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YOU GET 10 POINTS HELP HELP HELP HELP ME ME ME ME WITH THE CORRECT ANWSERS
Answers
Answer:
The third choice.
Step-by-step explanation:
This is a linear function.
The equation is y = (x - 5)(5x + 4) - 5x^2.
y = 5x^2 - 25x + 4x - 20 - 5x^2
y = 5x^2 - 5x^2 - 21x - 20
y = -21x - 20
That means this is a linear function, with a linear term of -21x and constant term of -20.
Hope this helps!
Answer:
Step-by-step explanation:
(Help Please It would be greatly appreciated) Which of these are true statements about the sine function? Choose all that are correct.
Answers
Answer:
A is wrong
B is correct
C is correct
D is wrong
E is wrong
F is correct
Step-by-step explanation:
Here, we want to select the correct options about the sine function.
A. is wrong
Let’s use a case of 30 degrees angle
Sin(-30) = -0.5
Sin(30) = 0.5
B is correct
sin(-30) = -0.5
-sin(30) = -0.5
C. C is correct
Sine function is an odd function.
By mathematical definition, we say a function is odd if for any value x of the function; f(-x) = -f(x)
This is obtainable and clear about the sine function from earlier options
D. Is wrong
E. is wrong
F. is correct
The period of the sine function is 2 pi
The period of a function is the time distance between two peaks or crests