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Cosine formula
[tex]\cos (angle)=\frac{\text{ adjacent side}}{\text{ hypotenuse}}[/tex]Considering angle R, the adjacent side has a length of 9 units, and the hypotenuse of the triangle has a length of 15 units. Substituting this information into the above formula:
[tex]\cos (m\angle R)=\frac{9}{15}=\frac{\frac{9}{3}}{\frac{15}{3}}=\frac{3}{5}[/tex]Related Questions
20 quarts=_ 20_×(1 quart) =_20_×(1\4 gallon) =_20/4_gallons =_5_gallons
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From the question, we are to convert 20 quartz to gallons.
Given
1 quartz = 1/4 gallons
20 quartz = x
Cross multiply and find x;
1 * x = 20 * 1/4
x = 20/4
x = 5
Hence 20 quartz is equivalent to 5 gallons
In 1906 Kennelly developed a simple formula for predicting an upper limit on the fastest time that humans could ever run distances from 100 yards to 10 miles. His formula is given by t= 0.0588s^(1.125) where s is the distance in meters and t is the time to run thatdistance in seconds.a. Find Kennelly's estimate for the fastest a human could possibly run 1609 meters.t= seconds (Round to the nearest thousandth as needed.)
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For this problem, we are given a formula that predicts the fastest a human can run a certain distance. We need to determine the time a human can run 1609 meters.
The formula is:
[tex]t=0.0588s^{1.125}[/tex]We need to replace s with 1609 and solve for t.
[tex]\begin{gathered} t=0.0588(1609)^{1.125}\\ \\ t=0.0588\cdot4049.26\\ \\ t=238.096 \end{gathered}[/tex]The fastest a human can run 1609 meters is 238.096 seconds.
A population of bacteria grows according to function p(t) = p. 1.42^t, where t is measured in hours. If the initial population size was1,000 cells, approximately how long will it take the population to exceed 10,000 cells? Round your answer to the nearest tenth.
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Given the function p(t) and the initial condition, we have the following:
[tex]\begin{gathered} p(t)=p_0\cdot1.42^t \\ p(0)=1000 \\ \Rightarrow p(0)=p_0\cdot1.42^0=1000 \\ \Rightarrow p_0\cdot1=1000 \\ p_0=1000 \end{gathered}[/tex]Therefore, the function p(t) is defined like this:
[tex]p(t)=1000\cdot1.42^t[/tex]Now, since we want to know the time it will take the population to exceed 10,000 cells, we have to solve for t using this information like this:
[tex]\begin{gathered} p(t)=1000\cdot1.42^t=10000 \\ \Rightarrow1.42^t=\frac{10000}{1000}=10 \\ \Rightarrow1.42^t=10 \end{gathered}[/tex]Applying natural logarithm in both sides of the equation we get:
[tex]\begin{gathered} 1.42^t=10 \\ \Rightarrow\ln (1.42^t)=\ln (10) \\ \Rightarrow t\cdot\ln (1.42)=\ln (10) \\ \Rightarrow t=\frac{ln(10)}{\ln (1.42)}=6.56 \end{gathered}[/tex]Therefore, it will take the population 6.56 hours to exceed 10,000 cells
1. On Monday, Mike's account balance shows $-135, on Tuesday, Mikequickly deposited $200. What is his new balance on Tuesday? Write anequation for the situation and find the answer. *
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Ok we need to write an equation for the situation and find the answer. So, let's do it:
Balance on tuesday=previus balance+deposit
Replacing we get:
Balance on tuesday=-135+200=$65
The new balance on tuesday is $65.
Each of the letters a through H has one of the 8 values listed. no 2 letters have the same value. The Simple arithmetic problems are clues for determining the value of each letter. Simply guess and check to find the values for letters a through H. You must use numbers listed below.
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We have the following:
Let's start from the number C, which has two numbers that when adding it gives a number and subtracting two other numbers gives the same number C
C = 9, therefore:
[tex]\begin{gathered} F-D=9 \\ F=14 \\ D=5 \\ G+B=9 \\ G=3 \\ B=6 \\ 5+E=6\Rightarrow E=1 \\ 6+H=14\Rightarrow H=8 \\ A-9=8\Rightarrow A=17 \end{gathered}[/tex]The width of a 2-by-4 piece of wood is actually 34 inches. Find the total width of 28 2-by-4s laid side-by-side. Simplify youranswer.o 126 inchesO 98 inches0784 inches844 inches
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The of one 2-by-4 piece of wood is 3.5 inches
To find the width of 28 pcs of wood, just multiply the number of wood to the actual width which is 3.5 inches
So we have :
[tex]28\times3.5=98[/tex]The answer is 98 inches
The radius of a circle is 6 kilometers. What is the area of a sector bounded by a 126° arc?Give the exact answer in simplest form. ____ square kilometers.
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It is given that the radius is 6 kilometers and the arc is 126 degrees.
The area of sector is given by:
[tex]\frac{126}{360}\times\pi\times6^2=39.5840\operatorname{km}^2[/tex]Therefore the area is 39.5840 square kilometers.
Find y if the line through (5, 1) and (6, y) has a slope of 3.
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Answer:
Y = 32
Step-by-step explanation:
Y = mx + c, with a slope of 3
Y = 3x + c
Substitute values:
1 = 3 (5) + c
1 = 15 + c
c = -14
Rewrite formula:
Y = 3x - 14
Y = 3 (6) + 14
Y = 18 + 14
Y = 32
Hope this helps :)
Answer:
y = 4
Step-by-step explanation:
y = mx + b is the slope intercept form of a line.
We need an m (slope and a b(y-intercept)
They give us the slope, so we have to find the b
slope = 3
y = 1
x = 5
We need and x and y on the line and the point (5,1) gives us that.
y = mx + b
1 = 3(5) + b
1 = 15 + b Subtract 15 from both sides of the equation
-14 = b
Now we have the m (slope of 3) and the b (the y-intercept of -14)
y = mx + b
y = 3x -14 Now plug is the x (6) from the point given and solve for its y
y = 3(6) -14
y = 18 - 14
y = 4
64 is 2/3percent of what number
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We have to find the number x for which 64 is the 2/3.
entionaction f(x) = 4.12x +12. If f(x) = -2(5)*, what is f(2)?A100B.20fC227-2050C. -20D. -50boioht of 144I
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Problem
We have the following expression given:
f(x)= -2(5)^x
And we want to find f(2)
Solution
so we can do the following:
f(2)= -2 (5)^2 = -2*25 = -50
15. When x =9, which number is closest to the value of y on the line of best fit in the graph below? 121917
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We have a scatter plot.
We have to find the closest value to y on the line of best fit when x = 9.
We can estimate a line of best fit by hand in the graph as:
Although we have a data point where x = 9 and y =9, the line of best fit is kind of in between the two groups of points.
When we draw the line like this, the estimated value from the line of best fit when x = 9 is y = 12, as we can see in the graph.
Answer: 12
Graph the following inequality.Note: To graph the inequality:Select the type of line below (solid or dashed).Plot two points on the line.Click on the side that should be shaded.
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Given:
[tex]-4x-y>2[/tex]Consider the line,
[tex]-4x-y=2[/tex]Find the points on the line,
[tex]\begin{gathered} x=0 \\ -4(0)-y=2\Rightarrow y=-2 \\ x=1 \\ -4(1)-y=2\Rightarrow y=-6 \\ x=-1 \\ -4(-1)-y=2\Rightarrow y=2 \end{gathered}[/tex]The graph of the line is,
Now, find the region for inequality.
Consider any point from the right and the left side of the line and check which side satisfies the inequality.
[tex]\begin{gathered} R=(2,0) \\ -4x-y>2 \\ -4(2)-0=-8\text{ >2 is not true.} \end{gathered}[/tex]And,
[tex]\begin{gathered} L=(-2,0) \\ -4x-y>2 \\ -4(-2)-0=8>2\text{ is true} \end{gathered}[/tex]Therefore, the graph of the inequality is,
Note that inequality does not contain boundary points.
Use the given information to answer the questions and interpret key features. Use any method of graphing or solving.
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A quadratic function describes the relationship between the number of products x and the overall profits for a company.
The roots of the quadratic function are given as x = 0 and x = 28. We also know the graph's vertex is located at (14, -40).
The quadratic equation can be written in terms of its roots x1 and x2 as:
[tex]f(x)=a(x-x_1)(x-x_2)[/tex]Substituting the given values:
[tex]\begin{gathered} f(x)=a(x-0)(x-28) \\ \\ f(x)=ax(x-28) \end{gathered}[/tex]We can find the value of a by plugging in the coordinates of the vertex:
[tex]f(14)=a\cdot14(14-28)=-40[/tex]Solving for a:
[tex]a=\frac{-40}{-196}=\frac{10}{49}[/tex]Substituting into the equation:
[tex]f(x)=\frac{10}{49}x(x-28)[/tex]The graph of the function is given below:
The company actually loses money on their first few products, but once they hit 28 items, they break even again.
The worst-case scenario is that they produce 14 items, as they will have a profit of -40 dollars. The first root tells us the profit will be 0 when 0 products are sold.
What tip will Brady get if a customer adds a 15% tip to his $18.52 meal cost?
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Brandy will get a tip of $2.778
Here, we want to get the amount of tip Brandy will get
In the question, the tip is 15% of $18.52
That will mathematically be;
[tex]\begin{gathered} \frac{15}{100}\text{ }\times\text{ \$18.52} \\ \\ =\text{ }\frac{277.8}{100}\text{ = \$2.778} \end{gathered}[/tex]An animal shelter spends $1.50 per day to care for each cat and $6.50 per day to carefor each dog. Gavin noticed that the shelter spent $97.00 caring for cats and dogs onMonday. Gavin found a record showing that there were a total of 18 cats and dogs onMonday. How many cats were at the shelter on Monday?
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4 cats and 14 dogs.
Explanation:
Data :
Amount of cats : c = ?
Cost per cats : $1.50
Amount of dogs : d = ?
Cost per dogs : $6.50
Total spent for dogs and cats : $97.00
Total number of dogs and cats : 18
Formulas:
1.50c + 6.50d = 97.00
c + d = 18
Solution:
c + d = 18 => c = 18 - d
1.50(18 -d) + 6.50d = 97.00
27 - 1.50d + 6.50d = 97.00
27 - 1.50d + 6.50d - 27 = 97 -
determine the volume of each rectangular or triangular prism round to the nearest tenth if necessary
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Determine the volume of each rectangular or triangular prism round to the nearest tenth if necessary
____________________
volume = base (B)* height (H)
_____________________
Base area
Triangle
B = b*h/2
Rectangle
B= L1*L2
__________________
volume = base (B)* height (H)
H= 15
Triangle case
B = 4.8 *9.6 /2
B = 46.08 / 2
B= 23.04
V= 23. 04* 15
V= 345.6 in ^3
Hello! I need some help with this homework question, please? The question is posted in the image below. Q15
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ANSWER:
A.
[tex]x=-1,-3,11[/tex][tex]f(x)=(x+3)(x-11)(x+1)[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)=x^3-7x^2-41x-33[/tex]To find the zeros of the function we must set the function equal to 0 in the following way:
[tex]x^3-7x^2-41x-33=0[/tex]We reorganize the equation in order to be able to factor and calculate the zeros of the function, like this:
[tex]\begin{gathered} x^3-7x^2-41x-33=0 \\ -7x^2=-8x^2+x^2 \\ -41x=-33x-8x \\ \text{ Therefore:} \\ x^3-8x^2+x^2-33x-8x-33=0 \\ x^3-8x^2-33x=-x^2+8x+33 \\ x(x^2-8x-33)=-(x^2-8x-33) \\ x^2-8x-33 \\ -8x=3x-11x \\ x^2+3x-11x-33 \\ x(x+3)-11(x+3) \\ (x+3)(x-11) \\ \text{ we replacing} \\ x(x+3)(x-11)=-1 \\ x(x+3)(x-11)+(x+3)(x-11)=0 \\ (x+3)(x-11)(x+1)=0 \\ x+3=0\rightarrow x=-3 \\ x-11=0\rightarrow x=11 \\ x+1=0\rightarrow x=-1 \end{gathered}[/tex]Therefore, the zeros are:
[tex]x=-1,-3,11[/tex]And in its factored form the expression would be:
[tex]f(x)=(x+3)(x-11)(x+1)[/tex]Find the area of the shaded part of the figure if a=6, b=7, c=4. (I need help on this)
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To obtain the area(A) of the shaded part of the figure, we will sum up the area of the triangle and the area of the rectangle.
Let us solve the area of the triangle(A1) first,
The formula for the area of the triangle is,
[tex]A_1=\frac{1}{2}\times base\times\text{height}[/tex]where,
[tex]\begin{gathered} base=b=7 \\ height=a=6 \end{gathered}[/tex]Therefore,
[tex]A_1=\frac{1}{2}\times7\times6=21unit^2[/tex]Hence, the area of the triangle is 21 unit².
Let us now solve for the area of the rectangle(A2)
The formula for the area of the rectangle is
[tex]A_2=\text{length}\times width[/tex]Where,
[tex]\begin{gathered} \text{length}=b=7 \\ \text{width}=c=4 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} A_2=7\times4=28 \\ \therefore A_2=28\text{unit}^2 \end{gathered}[/tex]Hence, the area of the rectangle is 28unit².
Finally, the total area of the shaded area is
[tex]\begin{gathered} A=A_1+A_2=21+28=49 \\ \therefore A=49unit^2 \end{gathered}[/tex]Hence, the area of the shaded part is 49unit² (OPTION A).
The figure below shows a striaght line AB intersected by another straight line t: Write a paragraph to prove that the measure of angle 1 is equal to the measure of angle 3. (10 points)
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Angles 1 and 3 are vertical angles, that is, are pairs of opposite angles made by intersecting lines. If 2 angles are vertical then they are congruent, in other words, they have the same measure.
use the information provided to write the equation of each circle. center: (12,-13)point on circle: (18, -13)
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Answer:
[tex](x-12)^2+(y+13)^2=36[/tex]Explanation:
Given:
• Center: (12,-13)
,• Point on circle: (18, -13)
First, we find the length of the radius.
[tex]\begin{gathered} r=\sqrt[]{(18-12)^2+(-13-(-13)_{})^2} \\ =\sqrt[]{(6)^2} \\ r=6\text{ units} \end{gathered}[/tex]The general equation of a circle is given as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Substituting the centre, (h,k)=(12,-13) and r=6, we have:
[tex]\begin{gathered} (x-12)^2+(y-(-13))^2=6^2 \\ (x-12)^2+(y+13)^2=36 \end{gathered}[/tex]The equation of the circle is:
[tex](x-12)^2+(y+13)^2=36[/tex]If a car in 3 hours travels 156 miles, what is the speed of the car in miles per hour?
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To calculate the speed a vehicle is traveling you have to use the following formula:
[tex]S=\frac{d}{t}[/tex]Where
S: speed
d: distance
t: time
The car traveled d=156miles in t=3hs
Its speed can be calculated as:
[tex]\begin{gathered} S=\frac{156}{3} \\ S=52 \end{gathered}[/tex]The car's speed was 52 miles per hour
Solve the system of two linear inequalities graphically. Graph the solution set of the first linear inequality? Type of boundary line? Two points on boundary line? Region to be shaded?
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Answer:
Explanation:
Given the below system of linear inequality;
[tex]\begin{gathered} y<3 \\ y\ge-5 \end{gathered}[/tex]The graph of the linear inequality y < 3 will be a graph with a dashed line with a y-intercept of 3 since the inequality is not with an equal sign as seen below;
The graph of the 2nd linear inequality y >= -5 will be a graph with a solid line with a y-intercept of -5 since it has both the inequality sign and an equality sign as seen below;
Find the sin t as a fraction in simplest terms
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We are asked to determine the sinT. To do that let's remember that the function sine is defined as:
[tex]\sin x=\frac{opposite}{hypotenuse}[/tex]In this case, we have:
[tex]\sin T=\frac{VU}{VT}[/tex]To determine the value of VU we can use the Pythagorean theorem which in this case would be:
[tex]VT^2=VU^2+TU^2[/tex]Now we solve for VU first by subtracting TU squared from both sides:
[tex]VT^2-TU^2=VU^2[/tex]Now we take the square root to both sides:
[tex]\sqrt[]{VT^2-TU^2^{}}=VU[/tex]Now we plug in the values:
[tex]\sqrt[]{(6)^2+(\sqrt[]{36^{}})^2}=VU[/tex]Solving the squares:
[tex]\sqrt[]{36+36}=VU[/tex]Adding the values:
[tex]\sqrt[]{2(36)}=VU[/tex]Now we separate the square root:
[tex]\sqrt[]{2}\sqrt[]{36}=VU[/tex]Solving the square root:
[tex]6\sqrt[]{2}=VU[/tex]Now we plug in the values in the expression for sinT:
[tex]\sin T=\frac{6\sqrt[]{2}}{6}[/tex]Now we simplify by canceling out the 6:
[tex]\sin T=\sqrt[]{2}[/tex]And thus we obtained the expression for sinT.
solve the proportion 4/3 is equal to 9 / X
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We need to solve for X.
The proportion is:
[tex]\frac{4}{3}=\frac{9}{X}[/tex]To solve for X, we cross multiply and then use algebra to solve. The process is shown below:
[tex]\begin{gathered} \frac{4}{3}=\frac{9}{X} \\ 4\times X=3\times9 \\ 4X=27 \\ X=\frac{27}{4} \end{gathered}[/tex]Find the radius of a circle in which a 24 cm chord is 4 cm closer to the center than a 16 cm chord. Round your answer to the nearest tenth.
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The diagram representing the scenario is shown below
A represents the center of the circle. It divided each chord equally. Thus, we have CB = 16/2 = 8 for the shorter chord and DE = 24/2 = 12 for the longer chord
Assuming the distance between the
A
Write the equation of the circle given the following graph.
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Given:
Equation of a circle on a graph with center(3, -2).
To find:
Equation of a circle.
Explanation:
General eqution of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]Solution:
From the graph, we can see that center is (3, -2) and radius equal 3.
So, equation of a circle is
[tex](x-3)^2+(y+2)^2=3^2[/tex]Hence, this is the equation of a circle.
Gretchen is planting a rectangular garden. she wants to use 9 square feet for tulips.if garden has length of 8 feet by 3 feet, how much room will she have left for rest of her flowers
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Given: the garden has a shape of a rectangle
The garden has a length of 8 feet by 3 feet
So, the area of the garden =
[tex]8\cdot3=24ft^2[/tex]she wants to use 9 square feet for tulips.
So, the remaining for rest of her flowers = 24 - 9 = 15 square feet
At Paul's Pet Palace, 3/16 of the animals are dogs and 5/24 of the animals are cats. What fraction of the animals are neither dogs nor cat?
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You have that 3/16 of the animals are dogs and 5/24 of the animals are cat.
To determine the fraction of animals that are neither dogs nor cat, consider the following:
If 3/16 are dogs, then 13/16 are other animals, but from this fraction, 5/24 are cats. Then, the subtraction 13/16 - 5/24 results in the fraction of animals that are neither dogs nor cat:
[tex]\frac{13}{16}-\frac{5}{24}=\frac{312-80}{384}=\frac{232}{384}[/tex]simplify the last fraction:
[tex]\frac{232}{384}=\frac{116}{192}=\frac{58}{96}=\frac{29}{48}[/tex]Hence, 29/48 of the animal are neither dogs nor cats
Suppose that the functions and g are defined for all real numbers x as follows. f(x) = x + 3; g(x) = 2x - 2 Write the expressions for (fg)(x) and (f - g)(x) and evaluate (f + g)(3)
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Solution
Given
[tex]\begin{gathered} f(x)=x+3 \\ \\ g(x)=2x-2 \end{gathered}[/tex]Then
[tex](f\cdot g)(x)=f(x)\cdot g(x)=(x+3)(2x-2)=2x^2+4x-6[/tex][tex](f-g)(x)=f(x)-g(x)=(x+3)-(2x-2)=x-2x+3+2=5-x[/tex][tex](f+g)(3)=f(3)+g(3)=(3+3)+(2(3)-2)=6+4=10[/tex]The mean of a population is 100, with a standard deviation of 15. The mean of
a sample of size 100 was 95. Using an alpha of .01 and a two-tailed test, what do
you conclude?
O Accept the null hypothesis. The difference is not statistically significant.
Reject the null hypothesis. The difference is statistically significant.
Accept the null hypothesis. The difference is statistically significant.
Reject the null hypothesis. The difference is not statistically significant.
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We conclude that Reject the null hypothesis. The difference is statistically significant.
Define integers.The symbol used to represent integers is the letter (Z). A positive integer can be 0 or a positive or negative number up to negative infinity. The three elements that make up an integer are zero, the natural numbers, and their additive inverse. It can be shown on a number line, but without the fractional portion. Z stands for it.
A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043
Given,
The mean of a population is 100, with a standard deviation of 15. The mean of a sample of size 100 was 95.
z = [tex]\frac{95-100}{15/10}[/tex]
z = 3.333
Using the p value technique, the value of p is 0.0009, and since p = 0.0009 0.01 the null hypothesis is rejected, the conclusion is made.
Reject the null hypothesis. The difference is statistically significant.
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