graph: y = |x+2| + 1
To serve 1 person at a local restaurant, it takes 10 minutes. To serve 5 people, it takes 18
minutes. Write and solve an equation to find the number of minutes it will take to serve a party of 8.
Answer:
8 people=24 minutes
Step-by-step explanation:
(1,10)(5,18)=18-10/5-1= 8/4 =2
y-8=2(x-4)
Find(f-g)(x)if f(x)=/4x and g(x)=/16x
The composition (f - g)(x) has a value of (c) (f - g)(x) = -2√x
How to evaluate the composite function?The definitions of the functions are given as
f(x) = √4x and g(x) = √16x
Evaluate the square roots in the above equations
This gives
f(x) = 2√x and g(x) = 4√x
To find the composition (f - g)(x), we make use of
(f - g)(x) = f(x) - g(x)
Substitute the known values in the above equation So, we have the following equation
(f - g)(x) = 2√x - 4√x
Evaluate the like terms
This gives
(f - g)(x) = -2√x
Hence, the value of the composition is (c) (f - g)(x) = -2√x
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Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. She worked 71 hours over the last two weeks and had a total of $2,046 in sales before taxes.
Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?
Sandy earn 306.9 dollars in commission and 1739.1 dollars in hourly wages.
How to find Sandy hour wages and commission?Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales.
She worked 71 hours over the last two weeks and had a total of $2,046 in sales before taxes.
The amount she will earn in her hourly wages and commission is as follows:
amount earn in commission = 15% of 2046
amount earn in commission = 15 / 100 × 2046
amount earn in commission = 30690 / 100
amount earn in commission = 306.9 dollars
Therefore,
amount earn in hourly wages = 2046 - 306.9
amount earn in hourly wages = 1739.1 dollars.
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Write the equation of the line in fully simplified slope-intercept form.
Answer: y = -x - 8
Step-by-step explanation:
Slope-intercept form is given in y = mx + b where m is the slope and b is the y-intercept.
We can see our b, the y-intercept, is -8 since the line intercepts the y-axis at (0, -8).
For our slope, we can see that the line moves down one and right one for a slope of 1/1=1. Since it's moving downwards, the slope is -1.
Now, we will write the full equation:
y = -x - 8
Calculate the volume of each of the following prisms.
1)
length = 35
width = 14
height = 24
2)
length = 27
width = 14
height = 21
3)
length = 21
width = 21
Height = 21
Step-by-step explanation:
1.) The first shape is a parallelogram like prism, So we use Area of prism= Area of base shape*height
that is, Area of base shape= rectangle,L*B
35*14=490*height
490*24=11760 cm3
2.)A rectangle base prism,
Area of prism= Area of base shape*height
Area of Base shape=27*14
378cm2*21
7938cm3
3.)Square based prism,
Area of prism= Area of base shape*height
=21*21*21 (since all sides are the same)
=9261cm3
Simplify the experession
6²-3³)÷7
Answer:
9/7 or 1.285714
Step-by-step explanation:
Answer:9/7
Step-by-step explanation:
The equation a = 12850 + 530h gives a hiker's altitude a (in feet), h hours after beginning his hike.
A. At what rate, in feet per hour, is the hiker gaining altitude?
The rate of gaining altitude for the hiker is 530 feet per hour.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as g'(x) = (g(x + h) - g(x)) /(x + h - x).
Its geometric aspect is the slope of the function at a given point.
The given equation for hiker's altitude is as below,
a = 12850 + 530h
Here a is the altitude in feet and h is time in hours.
In order to find the rate of gaining altitude, the equation for altitude has to be differentiated with respect to hours as below,
a = 12850 + 530h
Differentiate the above equation w.r.t h as,
da/dh = 0 + 530
= 530
Hence, the rate of gaining altitude is 530 feet per hour.
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-10b+3 ≤-37
Compound inequalities
Differentiate the function with respect to x.
When we differentiate the given function with respect to x we get
(30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
what is Differentiation?
Differentiate is used for calculating rates of change.
How to Differentiate function?
Some of the formulas are; Power Rule: (d/dx) (xn ) = nxn⁻¹. Derivative of a constant, a: (d/dx) (a) = 0.
Here, we have
y = 2x⁵ + 2x⁴ / 5x² -3
when we differentiate a given function with respect to x, we get
dy/dx = {(5x² -3)(10x⁴ + 8x³)} - {(2x⁵ + 2x⁴)(10x -3)}/(5x -3)²
dy/dx = (30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
Hence, after differentiating the given function with respect to x, we get
(30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
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Write each number as a product using gcf as a factor sipping distributive property the numbers are 28 49 77 and 3 gcf
Using as a product using gcf as a factor sipping distributive property For the numbers 28 and 49, GCF is 77.
Define GCF.The biggest number that both numbers can be divided by to get the two numbers' largest common factor. The smallest number that is a multiple of both numbers is the least common multiple of the two numbers. The largest number that may divide evenly into two or more other numbers is known as the greatest common factor (GCF). This is also sometimes referred to as the highest common factor (HCF) or the greatest common divisor (GCD).
Given,
Factor sipping distributive property,
For the numbers 28 and 49
GCF:
28 + 49
7(4) + 7(7)
7(4+7)
7(11)
77
Using as a product using gcf as a factor sipping distributive property For the numbers 28 and 49, GCF is 77.
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If y varies directly as x, find the constant of variation k and the direct variation equation for the situation.
y=2 when x= 10
Variation refers to differences in characteristics between individuals of the same species or between different genera or species. The formula is y = 0.25x.
What is meant by variation equation?A variation is a relationship between one set of values for one variable and another set of values for another variable. Variation in direct. If m is a nonzero constant and b = 0, then the function y = mx (often written y = kx) is a direct variation of the equation y = mx + b. If y varies directly as x and y = 6 when x = 2, the constant of variation is k = 3. As a result, the equation for this direct variation is y = 3x.The direct variation equation is a two-variable linear equation given by y = kx, where k is the constant proportionality. In a coordinate plane, the direct variation graph is a straight line.Therefore,
y=0.25 x
the initial statement is y ∝ x
to convert to an equation multiply by k the constant of
⇒ y=k x
to find k use the given condition
y=0.5 when x=2
[tex]$y=k x \Rightarrow k=\frac{y}{x}=\frac{0.5}{2}=0.25$$[/tex]
the equation is y = 0.25x
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The variation equation is [tex]y=\frac{1}{5} x[/tex]
What do you mean by direct variation?If two quantities change by the same amount, they are said to follow a direct variation. As a result, when one quantity changes, the other follows suit, increasing when the first changes and decreasing when the first changes. To put it another way, two quantities are said to be directly proportional to one another if the ratio of the first to the second is a constant term. The coefficient or constant of proportionality is the name given to this constant quantity.The mathematical relationship between the two quantities in the direct variation formula makes it so that one of the variables is a constant multiple of the other. The sign "∝" is used to indicate that two quantities are directly proportional to one another or directly varying from one another. Assuming that x and y are two quantities that are directly varying, they are stated as follows: y∝ xThe direct variation formula is expressed as follows when the proportionality sign is omitted.Calculation
Given, y =2 and x=10
we know the direct relation in y∝ x
so, y = kx, where k is the proportionality constant
2= k*10
k = [tex]\frac{2}{10} =\frac{1}{5}[/tex]
Therefore, the direct variation equation for this situation is [tex]y=\frac{1}{5} x[/tex]
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18. How does the
product change when one of the factors in
a multiplication problem is doubled? Give
two examples to support your conclusion.
The product doubles when one of the factors in a multiplication problem is doubled
What is a product?A product in mathematics is the result of multiplication, or an expression that identifies the objects to be multiplied, known as factors. For instance, 30 is the sum of 6 and 5.
In mathematics, multiplying means adding equal groups. The number of things in the group grows as we multiply. A multiplication problem includes the two factors and the product.
For example, 2 × 3 = 6. When 2 is doubled, it becomes 4 and the product will be:
= 4 × 3 = 12
Therefore, the product doubles too.
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Find the value of x .. assume that segments that appear to be tangent are tangent .
We got x = 16.54 by using Pythagorean theorem .
What is the Pythagorean theorem in plain English?
According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.angle of semicircle is always be 90° .
18² = 7.1² + x²
324 = 50.41 + x²
x² = 324 - 50.41
= 273.59
x = √ 273.59
x = 16.54
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The population of a city can be modeled using the formula P=100,000e^(0.05t), where t is the number of years after 2012 and P is the city's population. Which of the following equations can be used to find the number of years after 2012 that the population will triple to 300,000?
Group of answer choices
t=3/(0.05e)
t=ln3/0.05
t=(ln200,000)/0.05
t=log3/0.05
The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B t = ln(3) / 0.05
Given,
The population of a city can be modeled using the formula P=100,000e^(0.05t)
t is the number of years after 2012
P is the population of the city
We have to find the equation that can be used to find the number of years after 2012 that the population will triple to 300,000.
Here,
Substitute 300000 in for P and solve for t
300000=100000e^0.05t
Divide both sides by 100000:
We get,
3 = e^0.05t
Multiply both sides by the natural log (ln)
Then,
ln(3) = 0.05t
Now, divide 0.05 on both sides to get t by its self
t = ln(3) / 0.05
Therefore,
The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B t = ln(3) / 0.05
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DD.1 alculate mean, median, mode, and range What is the mean? If the answer is a decimal, round it to the nearest tenth. 45 46 43 41 43
Answer:
The answer to your question is,
MEAN = 43.6
MEDIAN = 43
MODE = 43
RANGE = 5
Step-by-step explanation:
BC I know math :)
Anna makes a round pizza. She wants to put a cheese layer on the pizza. If the
pizza is 11 in in diameter, how many square cm of cheese layer does she need
to put on the pizza?
The number of square cm of cheese layers that Anna needs to put on the pizza is 30.25π square cm.
What is the area of a circle?
In geometry, the area of a circle is the space occupied by the circle.
To find the area of a circle having radius "r", we can use the formula.
Area of a circle = π×r².
In the given question, the diameter of the pizza is 11 cm.
so the radius will be = 11/2 = 5.5 cm.
Area of the pizza = π×r²
= π×(5.5)²
= 30.25π square cm.
Hence, the number of square cm of cheese layers that need to be put on the pizza is 30.25π square cm.
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The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 1, 4
3 1, 2, 6
4 1, 3, 7
5 1, 1
6 5
Key: 3|2 means 3.2
What is the mean, and what does it tell you in terms of the problem?
The mean is 38.5. It tell us that the average distance a heavy ball was thrown is 38.5 feet.
What is the mean?A stem-and-leaf plot is table that displays a data set in ascending order. used to display a dataset. A stem-and-leaf plot divides a number into a stem and a leaf. In this stem-and-leaf plot, the stem is the tens digit and the leaf is the units digit. For example, in the number 32, 3 is the stem 2 is the leaf.
The mean is a measure of the center of a dataset that is used to determine the average of a set of numbers
Mean = sum of numbers / total numbers in the data set
(20 + 21 + 24 + 31 + 32 + 36 + 41 + 43 + 47 + 51 + 51 + 65) / 12
462 / 12 = 38.5
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I need help with this problem. Please and thank you.
The correct option; B. Two irrational numbers, are the two roots found for the given quadratic equation.
What is defined as the discriminant?In mathematics, a discriminant is a parameter that can be determined for an object or system to help with its categorization or solution. The discriminant for the quadratic equation ax² + bx + c = 0 is b² - 4ac.If the discriminant is positive, the roots of such a quadratic or cubic equation having real coefficients are real and distinct, if the discriminant is zero, the roots are real with at least two equal, and if the discriminant is negative, the roots have included a conjugate pair of complex roots.For the given question;
The quadratic equation is give as;
x² + 5x + 3 = 0
discriminant D = b² - 4ac
b = 5, a = 1 and c = 3
D = 25 - 4(1)(3)
D = 25 - 12
D = 13
√D = √13
As, number is real, there will be two real roots.
As, root of discriminant √D = √13 is a irrational number, the solutions of the given quadratic equation will be two irrational number.
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Help please willing to give brainliest badge an points
10. Reduce the fraction 36/48 to its lowest terms.
O A. 114
O B. %
O C. 112/48
O D.34
Answer:
if D is 3/4 then it is the answer
Step-by-step explanation:
Because both 36 and 48 can be divided by 12 and 36/12 = 3 and 48/12=4 so the answer is 3/4
A cuboid box has a square base and a height of 0.8 m, as shown in the diagram below. If
the volume of the box is 0.288 m3
, calculate the total surface area of the box.
Answer:
c
Step-by-step explanation:
because the explanation its just c
Determine a so that A(t)=A0at describes the amount of nitrogen-16 left after t seconds, where A0 is the amount at time t=0. Round to six decimal places.
using the power rule of logarithm, the value of a is 1.1021.
In the given question we have to determine a so that [tex]A(t)=A_{0}a^t[/tex] describes the amount of nitrogen-16 left after t seconds, where [tex]A_{0}[/tex] is the amount at time t=0.
The given exponential function is [tex]A(t)=A_{0}a^t[/tex].
The amount of nitrogen-16 is approximately 7.13 seconds.
According to the question, [tex]A(t)=A_{0}/2[/tex] and t = 7.13 seconds.
Putting the value in the given function;
[tex]A_{0}/2=A_{0}a^{7.13}[/tex]
Divide by [tex]A_{0}[/tex] on both side, we get
[tex]1/2=a^{7.13}[/tex]
Taking In on both side
[tex]\text{In}(1/2)=\text{In}(a^{7.13})[/tex]
Using the power rule of logarithm
In(1/2)=7.13In(a)
Divide by 7.13 on both side
In(a)= -0.693/7.13
In(a)= -0.0972
Taking exponential on both side
[tex]e^{\text{In}(a)}= e^{-0.0972}[/tex]
a = 1.1021
Hence, the value of a is 1.1021.
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What value of k will translate the graph of f(x) = 5x + 6 down by 1 when replaced by f(x) + k?
Step-by-step explanation:
"down by one" means that the y values (the function result values) are all decreased by 1.
so, k = -1
Question 9 of 10
Solve (x-3)² = 5.
A. x=-3+√√5
B. x=3+√5
C. x = 8 and x = -2
OD. x=5± √√3
Answer:
B (x = 3 + √5)
Explanation:
x² + 9 = 5
Take square root of both sides
x + 3 = ± √5
Add 3 to both sides
x = 3 + √5 or x = 3 - √5
Find the value of x in the equation
4^x+16^x= 272
Answer:
x = 2
Step-by-step explanation:
The table shows the population of Center City in various years. Use the data from 1990 and 2005 to create a linear model that predicts the population of the city (y) in a given year (x). In which year was the actual population of Center City most different from the value predicted by this model?
Year
City Population
1985
194,957
1990
197,800
1992
199,532
2000
203,750
2005
206,561
2012
210,600
1985
1992
2000
2012
Answer:
g(x)=−x−5, find g(1)g(1)
Step-by-step explanation:
g(x)=−x−5, find g(1)g(1)
Answer: 2012
Step-by-step explanation: biggest shift in pop
Claire Russell is buying a car. Her November monthly interest was $210 % interest. What is Claire’s principal balance at the beginning of November? Use 360 days. (Use 360 days. Do not round the denominator in your calculation and round your final answer to the nearest dollar.)
The Claire's principal balance at the beginning of November is 32516.
Given that,
Vehicle purchase by Claire Russell. Her interest rate for the month of November was 210 percent at 7 3/4%. Employ 360 days. When calculating, do not round the numerator; instead, round your result to the nearest dollar.
We have to find how much was left on Claire's principal at the start of November.
We know that,
Principal= Interest / time× rate of interest
Here,
Interest is 210
Time is 30/360
Rate of interest is 0.0775
Principal = 210/(30/360)×0.0775
Principal= 210/ 0.00645833
Principal =32516
Therefore, The Claire's principal balance at the beginning of November is 32516.
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PLEASE HURRY I WANT TO FIISH MY TEST PLEASE ASAP!!!
Determine which integers in the set S:{−32, −8, 16, 32} will make the inequality one fourth times the difference of m and four is less than or equal to one eighth times the difference of m and sixteen false.
The integer in the set S:{−32, −8, 16, 32} will make the inequality one fourth times the difference of m and four is less than or equal to one eighth times the difference of m and sixteen false is 32
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, based on the information we will replace m with 32. This will be illustrated thus:
1/4(32 - 4) ≤ 1/8 (32 - 16)
= 1/4(28) ≤ 1/8(16)
= 7 ≤ 2
In this case, 7 isn't less than or equal to 2. Therefore, 32 is the correct integer.
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3. Simplify the expression.
(3-i)-(2+6i)
01-7i
0-1+7i
0-6i
05+ Si
Answer:(3-i) - (2 +6i)
Combine like terms:
3-2 = 1
-i - 6i = -7i
Combine to get 1 -7i
Step-by-step explanation: