Given any three numbers a, b, and c.
By the distributive law, we must have:
a x (b + c) = (a x b) + (a x c)
Now to find 8 x78
8 x 78 = 8 x (70 + 8) = (8 x 70) + (8 x 8) = 560 + 64 = 624
an athlete eats 45 g of protein per day while training. how much protein will she eat during 23 days of training?
SOLUTION
From the question, the athlete eats 45 g of protein in a day. This means that in 23 days the athlete will eat
[tex]\begin{gathered} 23\times45\text{ g of protein } \\ =23\times45 \\ =1,035g \end{gathered}[/tex]Hence the answer is 1 035 g of protein, or 1.035 kg of protein.
Note that: To change grams to kilograms, we divide by 100.
Can someone help me with this math question. I just need to see the work.
pic of question below
The polar coordinates for each point are given as follows:
a. [tex](r, \theta) = \left(2\sqrt{5}, \frac{7\pi}{4}\right)[/tex]
b. [tex](r, \theta) = \left(6, \frac{\pi}{3}\right)[/tex]
Polar coordinatesSuppose we have a point with Cartesian coordinates given as follows:
(x,y).
The polar coordinates will be found as follows:
r² = x² + y².θ = arctan(y/x).For item a), the Cartesian coordinates are as follows:
(-4, 4).
Hence the polar coordinates will be given as follows:
r² = (-4)² + (4)² -:> r = sqrt(32) = 2sqrt(5).θ = arctan(-4/4) = arctan(-1) = -45º = 2pi - pi/4 = 7pi/4.For item a), the Cartesian coordinates are as follows:
(3, 3sqrt(3)).
Hence the polar coordinates will be given as follows:
r² = (3)² + (3sqrt(3))² = 9 + 27 = 36 -> r = sqrt(36) = 6.θ = arctan(3sqrt(3)/3) = arctan(sqrt(3)) = 60º = pi/3.More can be learned about polar coordinates at https://brainly.com/question/7009095
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Please fill in the blanks so that the following statement is trues
x-intercepts
1) In a quadratic equation, the Real solutions correspond to the points in which the parabola intercepts the x-axis.
2) Note that when the roots are not real solutions, then we'd have complex numbers and the parabola wouldn't intercept the x-axis.
3) Therefore, the answer is: x-intercepts
Jo started a business selling fishing supplies. He spent $5200 to obtain his initial supplies, and it costs him $350 per week for general expenses. He earns $750 per week in sales.
Create the linear function, in slope-intercept form, that represents the scenario.
The linear function is given by 5200+350x = 750x
What is linear function?
A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.
Amount spent to obtain merchandise = $5,200
Cost of general expenses = $350
Earnings from sales per week = $750
Now,
Let 'x' be the number of weeks taken to make profit
thus,
Total cost involved = $5,200 + ( $350 × x )
Total profit from sales = $750 × x
Now, the number of weeks after that the cost and earning will be equal, will be given by
5200+350x = 750x
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0.2x + 0.21x - 0.04 = 8.16Solve for "x".
Given the folllowing equation:
[tex]0.2x+0.21x-0.04=8.16[/tex]You need to solve for "x" in order to find its value. To do this, you can follow the steps shown below:
1. You can apply the Addition property of equality by adding 0.04 to both sides of the equation:
[tex]\begin{gathered} 0.2x+0.21x-0.04+(0.04)=8.16+(0.04) \\ 0.2x+0.21x=8.2 \end{gathered}[/tex]2. Now you need to add the like terms on the left side of the equation:
[tex]0.41x=8.2[/tex]3. Finally, you can apply the Division property of equality by dividing both sides of the equation by 0.41:
[tex]\begin{gathered} \frac{0.41x}{0.41}=\frac{8.2}{0.41} \\ \\ x=20 \end{gathered}[/tex]The answer is:
[tex]x=20[/tex]10. The graph shows the scores of an exam. About what percent of students scored above 86%?Distribution of Exam Scores20Percent1078808286889084Score11%18%6.5%
Answer
Option B is correct.
Percent of students that scored above 86% = 18%
Explanation
To find the percentage of students that scored above 86%, we will need to add the percent of the bars for all the scores greater than 86%.
For 87%, the bar is 8%
For 88%, the bar is 5.8%
For 89%, the bar is 2.2%
For 90%, the bar is 2%
So,
Percent of students that scored above 86% = 8 + 5.8 + 2.2 + 2 = 18%
Hope this Helps!!!
What is 5,435,778 expressed in scientific notation?A.5.435778 x 10*7B.5.435778 x 10*3C.5.435778 x 10*6D.5.435778 x 10*5
Given the number
[tex]5,435,778[/tex]We can express it in scientific notation below;
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.
Therefore, in the given question, we will have;
[tex]5,435,778=5.435778\times10^6[/tex]Answer: Option C
using the gcf and the distributive property find the sum of 34+51
it would be 75 ur welcome
SOMEONE PLS HELPPPPPPPP
Answer:
**NEED USEFUL ANSWER ASAP, H.W QUESTION**
Given that hotter blackbodies produce more energy than cooler blackbodies, why do cooler red giants have much higher luminosities than much hotter white dwarfs?
Step-by-step explanation:
The length of a rectangle is 5 ft less than double the width, and the area of the rectangle is 33f * t ^ 2 Find the dimensions of the rectangle. length___with____
The length of rectangle is : 6ft .
Width of rectangle is : 5.5ft .
What is an area of rectangle?The area of rectangle is :
A = l × w
Here given,
length is 5ft less than twice the width,
So the equation can be represented in terms of length as,
l = 2w - 5
Given area = 33sqft
By substituting value of length,
33 = (2w - 5) × w
By applying distributive property,
33 = 2w² - 5w
= 2w² - 5w - 33
By factoring the equation:
(2w - 11)(w + 3) = 0
To find value of zeros,
2w - 11 = 0
2w = 11
w = 5.5
Similarly,
w + 3 = 0
w = -3
Since width cannot be negative , the width will be:
the width = 5.5 ft.
Also find length by substituting value of width in equation,
33 = 5.5l
33/5.5 = l
l = 6 ft.
∴ The length = 6ft, and width = 5.5ft.
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Alejandra categorized her spending for this month into four categories: Rent, Food, Fun, and Other.The percents she spent in each category are pictured here.Food21%Rent30%Other31%Fun18%If Alejandra spent a total of $2500 this month, how much did she spend on Food?
she spent 525 on Food
she spent 750 on rent
she spent 775 on others
she spent 450 on fun
Explanation
to find the value of the percentage of any number just use this formula
[tex]\text{ percentage=}\frac{\text{ x\%}\cdot\text{ Number}}{100}[/tex]so
to find the values, apply the formula
Step 1
a) food :21 %
so
[tex]\begin{gathered} \cos t\text{ of food=}\frac{\text{ 21}\cdot2500}{100} \\ \cos t\text{ of food=}525 \end{gathered}[/tex]it means she spent 525 on Food
Step 2
b) Rent:30 %
so
[tex]\begin{gathered} \cos t\text{ of rent=}\frac{\text{ 30}\cdot2500}{100} \\ \cos t\text{ of rent=}750 \end{gathered}[/tex]it means she spent 750 on rent
Step 3
c)other:31 %
so
[tex]\begin{gathered} \cos t\text{ of other=}\frac{\text{ 31}\cdot2500}{100} \\ \cos t\text{ of other=}775 \end{gathered}[/tex]it means she spent 775 on others
Step 4
d)Fun:18 %
so
[tex]\begin{gathered} \cos t\text{ of fun=}\frac{\text{ 18}\cdot2500}{100} \\ \cos t\text{ of fun=}450 \end{gathered}[/tex]it means she spent 450 on fun
I hope this helps you
determine the value of x nodes following quadrilateral
The value of x nodes given quadrilateral is 80° which is determined by the measure of the supplemental interior angle.
What is the quadrilateral?A quadrilateral is a polygon with four sides. This also indicates that a quadrilateral has four vertices and four angles.
Exterior Angle is defined as an angle produced on the outside of a polygon by extending the sides of the polygon.
First, we have to find the measure of the supplemental interior angle
Here take the exterior angle1 = 100° and exterior angle2 = 60°, find its interior angles
⇒ 100 + int.1 = 180 ⇒ int.1 = 180 - 100 = 80°
⇒ 60 + int.2 = 180 ⇒ int.2 = 180 - 60 = 120°
Since the sum of all interior angles of a polygon = 360°
As per the given figure,
x + 80 + x + 120 = 360
2x = 360 - 200
2x = 160
x = 80°
Therefore, the value of x nodes given quadrilateral is 80°.
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Solve for x. Round to the nearest hundredth. Show all work.
The equation is given as,
[tex]3e^{5x}=1977[/tex]Transpose the term,
[tex]\begin{gathered} e^{5x}=\frac{1977}{3} \\ e^{5x}=659 \end{gathered}[/tex]Taking logarithm on both sides,
[tex]\ln (e^{5x})=\ln (659)[/tex]Consider the formula,
[tex]\ln (e^m)=e^{\ln (m)}=m[/tex]Applying the formula,
[tex]\begin{gathered} 5x=\ln (659) \\ x=\frac{1}{5}\cdot\ln (659) \\ x\approx1.30 \end{gathered}[/tex]Thus, the solution of the given exponential equation is approximately equal to,
[tex]1.30[/tex]Which x-value is in the domain of the function? Thank you!
Solution:
Given the function;
[tex]f(x)=4\cot(2x)+3[/tex]The graph of the function is;
ANSWER:
[tex]\frac{\pi}{3}[/tex]1. 9c-3c=48A) c=9B) c=3C) c=4D) C=8
To solve this equation, we need to subtract both, 9c - 3c:
[tex]9c\text{ - 3c = 6c = 48}[/tex]Dividing by 6 at both sides of the equation
[tex]\frac{6c}{c}\text{ = }\frac{48}{6}[/tex]Then
[tex]c\text{ = 8}[/tex]Then the answer C = 8. (Option D)
Identify the measurement that cannot be taken directly if you were constructing a two-
dimensional visual representation of the fish tank.
The measurement that cannot be taken directly in 2-D is depth
What do you mean by measurement?
Measurement is the quantification of an object's or event's properties for comparison with other objects or occurrences. Measurement, in other terms, is the act of establishing how large or little a physical amount is in comparison to a fundamental reference quantity of the same sort. The scope and use of measurement are context and discipline dependent. Measurements do not apply to nominal qualities of things or events in natural sciences and engineering, which is compatible with the recommendations of the International Bureau of Weights and Measures' International lexicon of metrology. However, measures in other domains, such as statistics and the social and behavioral sciences, can have numerous levels.
The measurement that cannot be taken directly in 2-D is depth
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Yesterday, Diane had c baseball cards. Today, she gave 6 away. Using c, write and expression for the number of cards Diane has left.
Answer:
The expression is c-6. She gave away 6 cards so subtract 6 from the original number which is c.
Find the domain of the rational function.f(x)=x−1/x+4
Given:
[tex]f(x)=\frac{x-1}{x+4}[/tex][tex]\begin{gathered} \text{Let, x+4=0} \\ x=-4 \end{gathered}[/tex]Domain:
[tex]-\infty<-4<\infty[/tex][tex](-\infty,-4)\cup(-4,\infty)[/tex]NEED TO FINISH BEFORE 9!!! PLEASE HELP!!!
A rational value that is less than zero is -√4.
An irrational value greater than five is 5 1/9.
A rational value between 10 and 20 is √225.
What are rational numbers and irrational numbers?A rational number is a number that can be expressed as a fraction of two integers. A rational number can either be a positive number, negative number, whole number, decimal or fraction. Examples of rational numbers are 100, -0.5.
A irrational number is a number that cannot be expressed as a fraction of two integers. An irrational number can either be a positive number, negative number, whole number, decimal or fraction. Examples of irrational numbers are 22/7, 1-/9.
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Which function rule would help you find the values in the table?J K2 -124 -246 -368 -48A k=-12jB k=-6jC k=j - 12D k=j - 6
Solution
As seen from the table
For each values of the table
We define the variation from K to J
[tex]\begin{gathered} K\propto J \\ K=cJ\text{ (where c is constant of proportionality)} \end{gathered}[/tex]When J = 2, K = -12
[tex]\begin{gathered} K=cJ \\ -12=c(2) \\ 2c=-12 \\ c=-\frac{12}{2} \\ c=-6 \end{gathered}[/tex]Therefore, the formula connecting them will be
[tex]k=-6j[/tex]Option B
a circular cylinder with a diameter of 12 cm and a height of 27 cm is filled with water. An aquarium is in the shaoe of a rectangular prism with the dimensions 35 cm 40cm by 42cm. what isvthe maximum number of full cylinders that can be poured into the fish tank without overflowing it?
Given data:
The diameter of cylinder is d=12 cm.
The height of the cylinder is h= 27 cm.
The dimension of the aquarium is V=(35 cm)(40 cm)( 42 cm).
The volume of the cylinder is,
[tex]\begin{gathered} V^{\prime}=\frac{\pi}{4}(d)^2h \\ =\frac{\pi}{4}(12cm)^2(27\text{ cm)} \\ =3053.628cm^3 \end{gathered}[/tex]The volume of the aquarium is,
[tex]\begin{gathered} V=(35\text{ cm)(40 cm)(42 cm)} \\ =58800cm^3 \end{gathered}[/tex]The number of cylinders that can be pour into aquarium is,
[tex]\begin{gathered} n=\frac{V}{V^{\prime}} \\ =\frac{58800}{3053.628} \\ =19.25 \end{gathered}[/tex]Thus, the number of cylinders that can be pour into aquarium is 19.25.
2. a) How many sets of opposite faces does this rectangular prism have? ____b) Why is the figure called a rectangular prism?
Answer:
a) 3 sets of opposite faces
b) The given figure is called a rectangular prism because its bases( the bottom face and the top face) are both rectangles.
Explanation:
a) Looking at the given rectangular prism and counting the faces, we can see that there are 6 faces in all. Out of the 6 faces of the rectangular prism, we can see that there are 3 pairs of opposite faces.
b) A prism is any 3-dimensional shape that has two identical shapes called bases facing each other.
If the two identical shapes facing each other are rectangles, then the prism is termed a rectangular prism.
Therefore, we can say that the given figure is called a rectangular prism because its bases ( the bottom face and the top face) are both rectangles.
h(x)= -1/2 (x+4)^2 +10Writing quadratics in standard form
`Answer:
h(x) = -x^2/2 - 4x + 32
Explanation:
The standard form of a quadratic equation is expresssed as
ax^2 + bx+c
Writing the given equation h(x)= -1/2 (x+4)^2 +10 in stabdard form will give;
h(x)= -1/2 (x+4)^2 +10
h(x)= -1/2 (x^2+8x+16)+40
h(x)= -x^2/2 - 4x - 8 + 40
h(x) = -x^2/2 - 4x + 32
Hence the equation in standard form is expressed as h(x) = -x^2/2 - 4x + 32
find the inverse function of g(x)= x-1÷x+5
1. replace g(x) with y:
[tex]y=\frac{x-1}{x+5}[/tex]2.Replace every x with a y and replace every y with an x
[tex]x=\frac{y-1}{y+5}[/tex]3. Solve for y:
[tex]\begin{gathered} (y+5)x=y-1 \\ yx+5x=y-1 \\ yx-y=-1-5x \\ y(x-1)=-1-5x \\ y=\frac{-1-5x}{x-1} \end{gathered}[/tex]4. Replace y with g−1(x) g− 1 ( x ):
[tex]g(x)^{-1}=\frac{-5x-1}{x-1}[/tex]Use the change of base formula and a calculator to evaluate the logarithm
The change of base formula states that:
[tex]\log _bx=\frac{\ln x}{\ln b}[/tex]this means that we can caculate any logarithm using the natural logarithm if we make the quotient of the natural logarithm of the original value and the natural logarithm of the original base.
In this case we have:
[tex]\begin{gathered} x=14 \\ b=\sqrt[]{3} \end{gathered}[/tex]Then, using the change of base formula, we have:
[tex]\log _{\sqrt[]{3}}14=\frac{\ln 14}{\ln \sqrt[]{3}}[/tex]Once we have the expression we just evaluate the expression on the right to get the appoximation we need:
[tex]\log _{\sqrt[]{3}}14=\frac{\ln14}{\ln\sqrt[]{3}}\approx4.804[/tex]find the sum of the first 44 terms of the following series. to the nearest integer 10,14,18,...
The first term is a=10.
The number of terms is n=44.
The common difference is d=4.
The formula for the sum of n terms is,
[tex]S=\frac{n}{2}\lbrack2a+(n-1)d\rbrack[/tex]Determine the sum of first 44 terms of the series.
[tex]\begin{gathered} S=\frac{44}{2}\lbrack2\cdot10+(44-1)4\rbrack \\ =22\cdot\lbrack20+172\rbrack \\ =22\cdot192 \\ =4224 \end{gathered}[/tex]So answer is 4224.
Find the point that partitions segment AB in a 1:3 ratio (_,_)Find the point that partitions segment AD in 1.1 ratio (_,_)
AB in 1:3 ratio, Find a pointwhere on one side there is 1/4 of AB and in the other side 3/4 of AB:
The variables x and y vary directly. Use values to write an equation that relates x and y. y=25;x=5And y=20;x=12
A lineal equation has the next form:
[tex]y=mx+b[/tex]where m is the slope and is calculated as follow:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For this case
y1=20
y2= 25
x1=12
x2= 5
so:
[tex]m=\frac{25-20}{5-12_{}}=\frac{5}{-7}=-\frac{5}{7}[/tex]then the equation will be:
[tex]y=(-\frac{1}{7})x+b[/tex]Using one of the points we calculate the b
we are going to use y=25 x=5
[tex]25=(-\frac{5}{7})5+b[/tex]Clearing the b we get:
[tex]25-\frac{25}{7}=b\Rightarrow\frac{200}{7}=b[/tex]b=200/7 or b=28.57
So the final equation is:[tex]y=-\frac{1}{7}x+\frac{200}{7}[/tex]A lineal equation has the next form:
[tex]y=mx+b[/tex]where m is the slope and is calculated as follow:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For this case
y1=20
y2= 25
x1=12
x2= 5
so:
[tex]m=\frac{25-20}{5-12_{}}=\frac{5}{-7}=-\frac{5}{7}[/tex]then the equation will be:
[tex]y=(-\frac{1}{7})x+b[/tex]Using one of the points we calculate the b
we are going to use y=25 x=5
[tex]25=(-\frac{5}{7})5+b[/tex]Clearing the b we get:
[tex]25-\frac{25}{7}=b\Rightarrow\frac{200}{7}=b[/tex]b=200/7 or b=28.57
So the final equation is:[tex]y=-\frac{1}{7}x+\frac{200}{7}[/tex]11. The population of the District of Columbia was approximately 572 thousand in 2000 and had been growing by about 1.15% per year.(a) Write an explicit formula for the population of DC t years after 2000 (i.e. t=0 in 2000), where Pt is measured in thousands of people.Pt = (b) If this trend continues, what will the district's population be in 2025? Round your answer to the nearest whole number. thousand people(c) When does this model predict DC's population to exceed 800 thousand? Give your answer as a calendar year (ex: 2000).During the year
Given:
Population in 2000 = 572 thousand
Rate of growth per year = 1.15%
Let's solve for the following:
(a) Explicit formula for the population years after 2000.
Where:
In year 2000, t = 0
To write the explicit formula, apply the exponantial growth function formula:
[tex]f(t)=a(1+r)^t[/tex]Where:
a is the initial amount
r is the growth rate.
Thus, we have:
[tex]\begin{gathered} P_t=572(1+\frac{1.15}{100}_{^{}})^t \\ \\ P_t=572(1+0.0115)^t \end{gathered}[/tex]Therefore, the explicit formula for the population years after 2000 is:
[tex]P_t=572(1.0115)^t[/tex](b) What will be the district's population in 2025.
Where:
In the year 2000, t = 0
In the year 2025, t will be = 25
To find the population in 2025, substitute 25 for t in the explicit formula for evalaute:
[tex]\begin{gathered} P_{25}=572(1.0115)^{25} \\ \\ P_{25}=572(1.330905371) \\ \\ P_{25}=761.28\approx761 \end{gathered}[/tex]The population in 2025 if the trend continues will be approximately 761 thousand.
(c) When does the model predict the population to exceeed 800 thousand.
Substitute 800 for Pt and solve for t.
We have:
[tex]\begin{gathered} P_t=572(1.0115)^t \\ \\ 800=572(1.0115)^t \end{gathered}[/tex]Divide both sides by 572:
[tex]\begin{gathered} \frac{800}{572^{}}=\frac{572(1.0115)^t}{572} \\ \\ 1.3986=1.0115^t \end{gathered}[/tex]Take the natural logarithm of both sides:
[tex]\begin{gathered} \ln (1.3986)=\ln (1.0115)^t \\ \\ \ln (1.3986)=t\ln (1.0115) \\ \\ 0.33547=0.01143t \end{gathered}[/tex]Divide both sides by 0.01143:
[tex]\begin{gathered} \frac{0.33547}{0.01143}=\frac{0.01143t}{0.01143} \\ \\ 29.3=t \\ \\ t=29.3\approx29 \end{gathered}[/tex]When t = 29, the year is 2000 + 29 = 2029
Therefore, using this model, DC's population will exceed 800 thousand in the year 2029.
ANSWERS:
[tex]\begin{gathered} (a)P_t=572(1.0115)^t \\ \\ (b)=761\text{ thousand people} \\ \\ (c)\text{ 20}29 \end{gathered}[/tex]**Determine the x-value at which the-following function touches but does not cross the x-axis:3x^3- 182 + 27x
Okay, here we have this:
We need to identify the x-value at which the-following function touches but does not cross the x-axis in the following function: 3x^3- 18^2 + 27x. So, considering that if is a zero with even multiplicity, the graph touches the x-axis and bounces off of the axis. And if it is a zero with odd multiplicity, the graph crosses the x-axis at a zero.
According with this let's