[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x}{2},\stackrel{y}{-10})~~ \textit{we know } \begin{cases} x=2\\ y=-10 \end{cases}\implies -10=k2\implies \cfrac{-10}{2}=k\implies -5=k \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=-5x~\hfill[/tex]
Write and solve a real-world problem for 9 divided by 1/8. Then explain the meaning of the quotient.
Answer:
Mike went 9 miles on 1/8 of a tank of gas, how many miles can he go with his full tank.
Then to solve this, we would divide 9 by 1/8
9 ÷ 1/8 = 72
A mosaic is made from 25 pieces each piece is a parallelogram as shown in the figure what is the total area of the mosaic?
Answer:
Step-by-step explanation:
Unless there is something special about this, the answer is 25 times the area of 1 parallogram.
Area of 1 parallelogram = Base * Height
Base = B = 5.3 cm
Height = H = 3.3 cm
Area = B*H
Area = 5.3 * 3.3
Area = 17.49
There are 25 pieces.
Total Area = 25 * 17.49
Total Area = 437.25 cm^2
True or False. You have to flip the inequality symbol in this problem:
-3x < 15
True
False
You can multiply both sides of an inequality by the same, nonzero number, but if this number is negative, you have to flip the sign.
In this case, in order to solve for x, you have to divide by -3 (i.e. multiply by -1/3), so yes, you must switch the sign:
[tex]-3x<15 \implies x>-5[/tex]
Alternatively, you may add 3x to both sides:
[tex]0<3x+15[/tex]
Subtract 15 from both sides:
[tex]3x>15[/tex]
And divide both sides by 3:
[tex]x>5[/tex]
The sign switch here was hidden behind the fact that we switched the two sides of the inequality
What is the value of k?
Please answer ASAP, Thank you :)
Answer:
k = 10
Step-by-step explanation:
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ZYM is an exterior angle of the triangle and
∠'s YZX and ZXY are the 2 opposite interior angles, hence
4k + 5 + 6k + 10 = 115
10k + 15 = 115 ( subtract 15 from both sides )
10k = 100 ( divide both sides by 10 )
k = 10
Answer:
k=10
Step-by-step explanation:
∠ZYX= 180-115= 65 these are supplementary angles adding up to 180°.
The interior angles in the triangle should add up to 180°
Adding the values and then equating to 180° we get the following equation.
65+(4k+5)+(6k+10)=180°
simplifying we get: 80+10k=180
10k=180-80
10k=100
k=10
what is the experimental probability of rolling a sum of 7 or 11?
Answer:
1/6
Step-by-step explanation:
The sum is a 7 in 6 of the 36 outcomes and hence the probability of rolling a 7 is 6/36 = 1/6.
The function k(x) = (g x h)(x) is graphed below, where g is an exponential function and h is a linear function. If h(x) = x + 1, which option below give the formula for g? h(x) = 2x h(x) = –2x h(x) = –2–x h(x) = 2–x
Answer:
The graph of your question is attached in the picture below.
g(x) = 2^(-x)
Step-by-step explanation:
First of all, we use a graphing tool to plot each of the equations.
If we multiply in the plotter each graph, we can easily see which is the correct option.
h(x) =x+1
g(x) = 2^-x
Answer:
h(x)=-2^-x
Step-by-step explanation:
There are 4 pennies, 2 nickels, 5 dimes, and 5 quarters in a jar. The probability that a random selected coin is a penny is 1/4. Is this experimental or theoretical probability
Answer:
Theoretical
Step-by-step explanation:
There are 4 pennies out of 16 coins, so the probability is 4/16, which reduces to 1/4. This is based on the beginning situation, not on the results of an experiment, so it is the theoretical probability. Theoretically, you have a 1/4 chance of pulling a penny, but that isn't necessarily what will happen.
Now I need help with this one please I’m really bad at math
Please help. I would really appreciate it.
[tex]f(x) = 3 {x}^{2} + 5x + 1 \\ \\ \frac{f(x + h) - f(x)}{h} \\ \\ \frac{(3(x + h)^{2} + 5(x + h) + 1) - (3 {x}^{2} + 5x + 1 }{h} \\ \\ \frac{(3( {x}^{2} + 2xh + {h}^{2}) + 5x + 5h + 1) - 3 {x}^{2} - 5x - 1}{h} \\ \\ \frac{3 {x}^{2} + 6xh + 3 {h}^{2} + 5x + 5h + 1 - 3 {x}^{2} - 5x - 1 }{h} \\ \\ \frac{6xh + 3 {h}^{2} + 5h}{h} \\ \\ \frac{h(6x + 3h + 5)}{h} \\ \\ = 6x + 3h + 5[/tex]
Does the rule y=-3*2^x represent a linear or an exponential function?
Answer:
its exponential because the parent function is y=(a)(b)^x
Step-by-step explanation:
Final answer:
The rule y = -3 ∙ 2ˣ defines an exponential function due to the term 2ˣ, where the base 2 is a constant raised to the variable power x, leading to a rapid change in y values as x changes.
Explanation:
The rule y = -3 ∙ 2ˣ represents an exponential function, not a linear function. In a linear function, the variable x is raised to the first power and appears in the form y = mx + b, where m and b are constants, and the graph is a straight line. In contrast, an exponential function is of the form y = a ∙ bˣ, where a and b are constants, and b is the base raised to the power of x.
The presence of the term 2ˣ indicates that as x increases, the value of y changes at an exponential rate. This is characterized by a curve that shows a rapid increase or decrease in value rather than a constant rate of change. Additionally, since the base b (which is 2 in this case) is a positive number other than 1, and it is raised to the power of x, this confirms the exponential nature of the function.
A solid is composed of squares and equilateral triangles. It’s net is shown below:
The area of each triangle is 4 square units. The surface area of the triangular prism is __ square units. (Input whole number only)
PLEASE ANSWER QUICKLY!
Answer:
35 square units
Step-by-step explanation:
The surface area of the given solid will be the sum of areas of all of its sides. From the given figure we can see that the sides(faces) of the solid are:
2 Equilateral Triangles3 SquaresThe Area of each triangle is 4 square units. So we need to calculate the area of the squares.
Side length of square = 3 units
Area of square = Length² = 3² = 9
Surface Area of Given Solid = Area of 2 Triangles + Area of 3 Squares
= 2(4) + 3(9)
= 8 + 27
= 35 square units
Surface Area of Given Solid = 35 square units
Answer:
The surface area of the triangular prism is 35 square units
Step-by-step explanation:
It is given that,A solid is composed of squares and equilateral triangles
The area of each triangle is 4 square units
To find the surface area of solid
From the figure we get,
Surface area = Area of 2 triangle + area of 3 squares
There are 2 triangles with area = 4 square units
Area of 2 triangle = 2 * 4 = 8 square units
There are 3 squares with side = 3 units
Area of 1 square = 3 * 3 = 9 square units
Area of 3 squares = 3 * 9 = 27 square units
Surface area = 8 + 27 = 35 square units
The surface area of the triangular prism is 35 square units
Find the center, vertices, and foci of the ellipse with equation 2x2 + 8y2 = 16.
A) Center: (0, 0); Vertices: the point zero comma negative two square root two and the point zero comma 2 square root two ; Foci: Ordered pair 0 comma negative square root 6 and ordered pair 0 comma square root 6
B) Center: (0, 0); Vertices: (-8, 0), (8, 0); Foci: Ordered pair negative 2 square root 15 comma 0 and ordered pair 2 square root 15 comma 0
C) Center: (0, 0); Vertices: (0, -8), (0, 8); Foci: Ordered pair 0 comma negative 2 square root 15 and ordered pair 0 comma 2 square root 15
D) Center: (0, 0); Vertices: the point negative square root six comma zero and the point square root six comma zero ; Foci: Ordered pair negative square root 6 comma 0 and ordered pair square root 6 comma 0
Step-by-step explanation:
i think its B I'm not really sure
On average, how much more is the total cost of owning a cat for 10 years than owning a small dog for 10 years?
Answer:
Its 960
Step-by-step explanation:
Although the total cost depends on various factors, generally, owning a small dog tends to be more expensive than owning a cat, mostly due to additional expenses like training, grooming, and potential healthcare costs.
Explanation:The question is about the average total cost difference between owning a cat and a small dog for a decade. This can be a complex calculation as different cost factors need to be considered, such as food, vaccinations, regular vet care, grooming etc. However, with the given information, we are unable to compute the exact difference. At this stage, a proper figure cannot be provided due to lack of the essential data about the yearly costs for each pet. However, on average, it is generally considered that owning a small dog can be more expensive than owning a cat due to additional expenses like training, grooming, and potentially higher healthcare costs.
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What does alabama have that most students would like to have
4 a’s and only 1 b :)
4 is a and only 1 b , your welcome
mari is standing 50 feet from the base of a building. From where he stands, the angle formed between the top of the building and the ground at his feet is 60°.
Answer:
Your answer will be...
Step-by-step explanation:
50 square root of 3 ft
Miranda spent 1/5 of her time cooking pasta. If she spent 2 hours cooking, did Miranda spend more than, less than, or equal to 2 hours cooking pasta? Explain.
Step-by-step explanation:
Less than 2 hours. Since 100 percent of her time is 2 hours and she only spent 20 percent of 2 hours, which is less than 100 percent, it is less than
Answer:
more
Step-by-step explanation:
1/5 times 2 is equal to 3
a rectangular metallic block is 16 cm long . 8 cm broad and 4 cm thick . If it is melted and converted into a cube , find the surface area of the cube
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Answer:
384 cm²
Step-by-step explanation:
Calculate the volume of metal in the block
V = 16 × 8 × 4 = 512 cm³
Then the volume of the cube = 512 cm³
That is
s³ = 512 ← s is length of side of cube, hence
s = [tex]\sqrt[3]{512}[/tex] = 8 cm
The cube has 6 square faces, hence
surface area = 6 × 8² = 6 × 64 = 384 cm²
write an integer to represent 30 meters below sea level. explain the meaning of 0 in this situation
LMK ASAP...... 10 POINTS
Answer: The correct answer is 15 according to my work that I have done.
Step-by-step explanation:
* Here is all the all information you'll need just in case.
* Hopefully this helps:) Mark me the brainliest:)!!
∞ 234483279c20∞
Answer:
The correct answer is option 3
arc length = 7.5π
Step-by-step explanation:
It is given a circle with central angle ADC = 45° and radius = 30 cm
To find the length of arc ABC
From the figure we can see that the central angle of arc ABC = 45°
Therefore the arc length = (45/360) * Circumference
To find the circumference
Circumference = 2πr = 2 * π * 30 = 60π
To find the arc length
Arc ABC = (45/360) * 60π= 7.5π
Therefore arc length = 7.5π
The correct answer is option 3
Your mission is to dilate the rectangle shown below by a scale factor of 2.
Answer:
The dimensions of the dilated rectangle are 30 cm x 16 cm
Step-by-step explanation:
we know that
To find the dimensions of the dilated rectangle, multiply the original dimensions by the scale factor
so
Let
A'B'C'D'------> the dilated rectangle
z-------> the scale factor
we have
z=2
A'B'=AB*z=15*2=30 cm
B'D'=BD*z=8*2=16 cm
The dimensions of the dilated rectangle are 30 cm x 16 cm
A used car dealer estimates that 40% of his customers will buy sedans. If he sells 26 sedans, about how many total cars would he expect to sell?
Answer:
10.4, or 10 if rounding.
Step-by-step explanation:
26 * .4 = 10.4
A car dealer expected to sell 10.4 ≈ 10 sedans.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
A used car dealer estimates that 40% of his customers will buy sedans.
If he sells 26 sedans,
total cars he would have expected to sell,
= 26 x 40/100
= 10.4
≈ 10
Therefore, he expected 10 sedans to sell.
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a store increased its prices on computers by 12%. If p represents the regular price of computers, what expression could be used to find the new prices of computers?
Answer:ayy but imma rapper follow me on souncloud kid ice pvt
Step-by-step explanation:
To find the new prices of computers after a 12% increase, use the expression p + 0.12p or 1.12p.
Explanation:To find the new prices of computers after a 12% increase, you can use the expression p + 0.12p. This expression represents the regular price p plus 12% of p. Simplifying this expression, we get 1.12p as the new prices of computers.
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Betsy spent 26 days traveling in Europe. How many hours did she spend traveling in Europe.
For the function F(x) = 1/x, whose graph is shown below, what is the relative value of F(x) when the value of x is close to zero?
A - Either a very large positive or very large negative number
B.A very small positive number
C. Only a very large positive number
D.Only a very large negative number
E.Either a very small positive or very small negative number
can someone help me out asap 13
Answer:
180m^2
Step-by-step explanation:
5 x 3 x 12 = 180m^2
Answer:
I believe the answer is 150m
Step-by-step explanation:
On Tuesday the Baker makes a total of 60 muffins. How many blueberry muffins does the baker make on Tuesday.
Answer:
60
Step-by-step explanation:
This question is super common sense which probably makes you
want to rethink the simple answer. Very plainly it says: Tuesday the Baker makes a total of 60 muffins. It doesn't tell us what "kind" of muffins they
are or are not. So then it asks how many "blueberry" muffins does the Baker bake on Tuesday.
They are only giving us one number that the Baker bakes on Tuesday and that number is 60
Which of these is a complex number?
A.
B.
C.
D.
Answer:
option D
[tex]\frac{8}{3} + \sqrt{\frac{-7}{3} }[/tex]
Step-by-step explanation:
Given in the question are 4 number
5√1/3 - [tex]\frac{9}{\sqrt{7} }[/tex]
2 - [tex]\frac{1}{\sqrt{11} }[/tex]
9 + [tex]3\sqrt{\frac{5}{2} }[/tex]
[tex]\frac{8}{3} + \sqrt{\frac{-7}{3} }[/tex]
A Complex Number is a combination of a Real Number and an Imaginary Number
Examplea + ib
where a is real number
b is imaginary number
i is 'lota' which is √-1
So according to the definition above[tex]\frac{8}{3} + \sqrt{\frac{-7}{3} }[/tex] is complex number in which
[tex]\frac{8}{3}[/tex] is real part
[tex]\sqrt{\frac{7}{3} } \sqrt{-1}[/tex] = [tex]\sqrt{\frac{7}{3} } i[/tex] is the imaginary part
Answer:
D. 8/3+ sqrt-7/3
Step-by-step explanation:
A landscape architect wishes to enclose a rectangular garden on one side by a brick wall costing $24 per foot and on the other three sides by a metal fence costing $8 per foot. If the area of the garden is 800 ft, find the dimensions of the garden minimizing the cost. (Let x be the length of the brick wall and y be the length of an adjacent side in feet.)
Answer:
x = 20 feet, y = 40 feet
Step-by-step explanation:
See attached photo for solution
The length of the brick wall is 20 ft and the length of an adjacent side is 40 ft and this can be determined by forming the linear equation in two variables.
Given :
A brick wall costs $24 per foot and on the other three sides by a metal fence costs $8 per foot.The area of the garden is 800 [tex]\rm ft^2[/tex].Let 'x' be the length of the brick wall and 'y' be the length of an adjacent side in feet. Then the area of the garden is:
xy = 800 --- (1)
The perimeter of the rectangular garden will be:
Perimeter = 24x + 8x +2(8)y ---- (2)
Now, solve equation (1) for y.
[tex]y = \dfrac{800}{x}[/tex] --- (3)
Now, put the value of 'y' in equation (2).
[tex]\rm P=32x+16\times \dfrac{800}{x}[/tex]
Now, for minimizing cost differentiate the perimeter with respect to 'x'.
[tex]\rm P'=32-16\times \dfrac{800}{x^2}[/tex]
Now, equate the above equation to zero.
[tex]0=32-16\times \dfrac{800}{x^2}[/tex]
[tex]\dfrac{800}{2}={x^2}[/tex]
x = 20
Now, put the value of 'x' in the equation (3).
[tex]y = \dfrac{800}{20}[/tex]
y = 40
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The vertex form of the equation of
a parabola is y = 2(x +4)^2 - 7.What is the standard form of the equation?
Answer:
The standard form of the equation is y = 2x^2 + 16x + 25
Step-by-step explanation:
To find the standard form, first square the parenthesis.
y = 2(x + 4)^2 - 7
y = 2(x^2 + -8x + 16) - 7
Now distribute the 2
y = 2(x^2 + 8x + 16) - 7
y = 2x^2 + 16x + 32 - 7
Now combine like terms
y = 2x^2 + 16x + 32 - 7
y = 2x^2 + 16x + 25
In an experiment, the one variable that is changed by the person doing the experiment is called the Question 2 options: controlled variable testing variable independent variable dependent variable
Answer: Independent Variable
Step-by-step explanation:
The independent (or manipulated) variable is something that the experimenter purposely changes or varies over the course of the investigation. The dependent (or responding) variable is the one that is observed and likely changes in response to the independent variable.