Let's use the slope-point form to find the equation:
[tex]\begin{gathered} y-4=-2(x-(-3)) \\ \rightarrow y-4=-2(x+3) \\ \rightarrow y-4=-2x-6 \\ \rightarrow y=-2x-2 \\ \end{gathered}[/tex]Thereby, the equation of the line is:
[tex]y=-2x-2[/tex]Ten less than a number cubed is negative seven
We have
less than means subtract from
number cubed means elevate a number to power 3
therefore
Ten less than a number cubed is negative seven
is
[tex]x^3-10=-7[/tex]
Launch Problem The barista at Kellie's Coffee needs to make 10 12-ounce iced coffees. Each iced coffee is made with 2 ounces of oat milk, 8.2 ounces of cold brew coffee and 1.8 ounces of hazelnut flavoring. How much of each ingredient will be necessary to make the order of iced coffees? 2. How many ounces of cold brew coffee will be needed to make the order of iced coffee?
we have,
for 1 iced coffee:
2 ounces of oat milk
8.2 ounces of cold brew coffee
1.8 ounces of hazelnut.
then
answer 1:
for 10 iced coffee, we will need
2 x 10 = 20 ounces of oat milk
8.2 x 10 = 82 ounces of cold brew coffee
1.8 x 10 = 18 ounces of hazelnut flavoring
answer 2:
82 ounces of cold brew coffee are needed
The image represents a Biased Sample Population Sample. true or false
ANSWER:
True
STEP-BY-STEP EXPLANATION:
The sample is said to be biased when there is a difference between the sample data and the data for the entire population.
In this case, the sample and the population have different values, which means that the sample does have bias.
find the missing length, assume that segments that appear to be tangent are tangent.
Since the side that measures 16 is tangent to the circle, it is perpendicular to the side that measures 12.
IT makes a right triangle.
Since it is a right triangle we can apply the Pythagorean theorem:
c^2 = a^2 + b^2
Where:
c= hypotenuse (longest side )= ?
a & b =the other 2 legs of the triangle.
Replacing:
?^2 = 12 ^2 + 16^ 2
Solve for the missing side:
?^2 = 144+256
?^2 = 400
?=√400
? = 20
In a survey of 52 pet owners, 26 said they own a dog, and 14 said they own a cat. 13 said they own botha dog and a cat? How many owned a dog but not a cat?
From the given data we know that
[tex]26[/tex]owners own a dog, but out of those,
[tex]13[/tex]own both a cat and a dog.
Therefore, the number of pet owners that own only a dog is
[tex]26-13.[/tex]Answer:
[tex]13.[/tex]What is the area of sector GHJ, given that θ= π/3 radians? Express your answer in terms of π and as a decimal rounded to the nearest tenth.
Answer:
[tex]\text{area of sector=4.7 square }\imaginaryI\text{nches}[/tex]Step-by-step explanation:
The area of a sector when the angle is measured in radians is represented by:
[tex]\text{ area of sector= }\frac{1}{2}r^2\theta[/tex]The given theta is pi/3, and the radius is 3 inches.
[tex]\begin{gathered} \text{ area of sector=}\frac{1}{2}*3^2*\frac{\pi}{3} \\ \text{ area of sector=}\frac{3}{2}\pi \\ \text{ Convert as a decimal rounded to the nearest tenth:} \\ \text{ area of sector= 4.7 square inches} \end{gathered}[/tex]Circle 1 is centered at (-4, -6) and has a radius of 9 centimeters. Circle 2 is centered at (4, 2) and has a radius of 6 centimeters. What is the scale factor?Which translation rule will translate Circle 1 to Circle 2?
For this type of problem we first notice that the center of the first circle has coordinates (-4,-6) and the center of the second one has coordinates (4,2) then all point of circle 1 (x,y) are translated according to the rule (x+8,y+8).
For the scale factor, we notice that the radius of circle 1 is 9 cm and the radius of circle 2 is 6cm then the scale factor is (2/3).
Use the graph to answer the question about discontinuity refer to image
Given the graph of the function
We will check the discontinuity of the function at x = -3
So, as shown in the graph :
as the function reach to x = -3 from the right and the left , the value of the function = -1
But at x = -3 , the function does not have a value
So, there is a discontinuity at x = -3, but can be removed if f(-3) = -1
So, the answer is : option A
There is a discontinuity that can be removed by defining f(-3) = -1
Simplify the expression 3^2/ 3^1/4 to demonstrate the quotient of powers property. Show any intermittent stepsthat demonstrate how you arrived at the simplified answer.
We are given a quotinet of two power expressions to be used to demonstrate the quotient property of powers:
[tex]\frac{3^2}{3^{\frac{1}{4}}}=3^2\cdot3^{-\frac{1}{4}}=3^{(\frac{8}{4}-\frac{1}{4})}=3^{\frac{7}{4}}[/tex]ANother way of doing it is to represent 3^2 as 3 to the power 8/4 so as to have the same radical expression.
Recall that fractional exponents are associated with radicals, and in this case the power "1/4" represents the fourth root of the base "3". That is:
[tex]3^{\frac{1}{4}}=\sqrt[4]{3}[/tex]So we also write 3^2 with fourth root when we express that power "2 = 8/4":
[tex]3^2=3^{\frac{8}{4}}=\sqrt[4]{3^8}[/tex]So now, putting that quotient together we have:
[tex]\frac{\sqrt[4]{3^8}}{\sqrt[4]{3}}=\sqrt[4]{\frac{3^8}{3}}=\sqrt[4]{3^7}=3^{\frac{7}{4}}[/tex]So we see that we arrived at the same expression "3 to the power 7/4"
in both cases. One was using the subtraction of the powers as the new power for the base 3, and the other one was using the radical form of fractional powers.
Find the inverse of the function below and sketch by hand a graph of both the function and is inverse on the same coordinate plane. Share all steps as described in the lesson to earn full credit. Images of your hand written work can be uploaded. f(x)=(x+3)^2 with the domain x \geq-3
In order to find the inverse of f(x), let's switch x by f^-1(x) and f(x) by x in the function, then we solve the resulting equation for f^-1(x).
So we have:
[tex]\begin{gathered} f(x)=(x+3)^2 \\ x=(f^{-1}(x)+3)^2 \\ \sqrt[]{x}=f^{-1}(x)+3 \\ f^{-1}(x)=-3+\sqrt[]{x} \end{gathered}[/tex](The domain of f(x) will be the range of f^-1(x), so the range of f^-1(x) is y >= -3)
In order to graph the function and its inverse, we can use some points that are solutions to each one.
For f(x), let's use (-3, 0), (-2, 1) and (-1, 4).
For f^-1(x), let's use (0, -3), (1, -2) and (4, -1).
Graphing f(x) in red and f^-1(x) in blue, we have:
Graphing it manually, we have:
Solve triangles using the law of cosines . Find BC
The cosine rule states that:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]For the given triangle:
a= BC
b=AC=12
c=AB=9
∠A=87º
Replace the known measures on the formula:
[tex]BC^2=12^2+9^2-2(9\cdot12\cdot\cos 87)[/tex]Solve the exponents and the multiplication on the last term:
[tex]\begin{gathered} BC^2=144+81-216\cos 87 \\ BC^2=213.695 \end{gathered}[/tex]-Apply the square root to both sides of the expression:
[tex]\begin{gathered} \sqrt[]{BC^2}=\sqrt[]{213.695} \\ BC=14.618 \\ BC\approx14.62 \end{gathered}[/tex]The length of side BC is 14.62units
Draw an angle in standard position inQuadrant I that has legs of 6 inches and 8inches.
Given:
There is an angle lying in quadrant II that has legs of 6 inches and 8 inches
The drawing of the angle will be as follows:
As shown in the figure the angle x lying in the quadrant II
And the legs of the right-angle triangle = 6 inches and 8 inches
Note: the legs can be reversed, which gives us another possible solution.
what is the volume of the sphere with a radius of 2 inches ?
The volume of a sphere is
[tex]\text{volume}=\frac{4}{3}\pi^{}^{}r^3[/tex]Therefore,
[tex]\begin{gathered} \text{volume}=\frac{4}{3}\times3.14\times2^3 \\ \text{volume}=33.4933333333=33.49\text{ cubic inches} \end{gathered}[/tex]hich is the better buy? 2-quart carton of orange juice for $4.48 7-cup carton of orange juice for $3.64
According to the given data we have the following:
2-quart carton of orange juice=$4.48
7-cup carton of orange juice=$3.64
In order to find out what is the better choice to buy we would have to make the calculate the unit price.
2-quart carton of orange juice=$4.48,
Then unit price=$4.48/2
unit price=$2.24
7-cup carton of orange juice=$3.64
Then unit price=$3.64/7
unit price=$0.52
Therefore as the unit price of the 7-cup carton of orange juice is $0.52 and is lower than the unit price of $2.24 of the 2-quart carton of orange juice, hence, the better choice would be buying the 7-cup carton of orange juice.
bea earned $ 11,700.00 commission for selling a house calculated at 6/100 of the selling price. what was the selling price of the house?
Given:
Commision earned = $11,700
The commission was calculated at 6/100 of the selling price.
To find the selling price of the house, we have the equation:
[tex]11700=\frac{6}{100}S[/tex]Where S represents the selling price of the house.
Let's solve for S.
Multiply both sides of the equation by 100:
[tex]\begin{gathered} 11700(100)=\frac{6}{100}S\ast100 \\ \\ 1170000=6S \end{gathered}[/tex]Divide both sides of the equation by 6:
[tex]\begin{gathered} \frac{1170000}{6}=\frac{6S}{6} \\ \\ 195000=S \\ \\ S=195000 \end{gathered}[/tex]Therefore, the selling price of the house is $195,000
ANSWER:
$195,000
I need help with Number 5 please tell me what to put in the box
The price of a pair of tires is $130.56. We want to know the price of ten tires. Ten tires, is the same as five pairs of tires, then, since we know the price of a pair the price of five pairs will be just five times the price of the pair.
The price of five pairs is:
[tex]5\times130.56=652.80[/tex]$652.80.
1. Name one of the segments shown2.calculate their midpoint and lengths(as decimal rounded to the nearest tenth)3.identify all parallel segments
For naming a segment, we have to know its extrem points. If those extreme points are A and B, we name the segment as:
[tex]\bar{AB}[/tex]We are going to take as an example the segment with extreme points I and C, shown at the left above part of the image, so its name will be:
[tex]\bar{IC}[/tex]Solve the equation. Round your answer to the nearest hundredth.-4 = -1.5j + 3+ 32
Given the equation :
-4 = -1.5 j+ 32
combine like terms
-4 - 32 = -1.5 j
-36 = -1.5j
OR can be written
-1.5 j = -36
Divide both sides by -1.5
[tex]j=\frac{-36}{-1.5}=\frac{36}{1.5}=\frac{36\cdot10}{1.5\cdot10}=\frac{360}{15}=24[/tex]so, the value of j = 24
Determine whether each linear relationship is a direct variation. If so, state the constant of proportionality. (Example 4) 4. Pictures, x 3 4 5 6 51 Minutes, 185 235 285 335 Profit, y 24 32 40 48 Cost, y 60 100 140 180 7. 6. Game, X 2 5 20 5 15 10 Year, x Polnts, y 4 1 5 6 7 25 50 12.5 37.5 Helght, y
table 4 . Direct Variation, constant of proportionality =8
Table 5: No. There is not a direct variation, for the growth is not at a constant factor.
1) To state whether there is a direct variation, we need to examine each row to stat how it increases or decreases
2) So for table 4
x y
3 24
4 32
5 40
6 48
For this, we can write a linear function y=8x
Yes. Direct Variation. Constant of proportionality 8
Table 5
x y
185 60
235 100
285 140
335 180
No. There is not a direct variation, for the growth is not at a constant factor.
Table 6
x y
5 12.5
10 25
15 37.5
20 50
We can set a linear function for that y=5/2 x
Yes. Direct Variation. Constant of proportionality 5/2 (2.5)
Table 7
x y
2 4
3 5
4 6
5 7
There is not a direct variation, for the growth is not at a constant factor.
-8.2d + 28.1 = 3.6d is the solution Positive or Negative?
The given expression : -8.2d + 28.1 = 3.6d
Simplify the expression for the d :
-8.2d + 28.1 = 3.6d
Subtract 3.6d on both side of the equation
-8.2d -3.6d + 28.1 = 3.6d -3/6d
-11.8d + 28.1 = 0
Subtract 28.1 on both side :
-11.8d + 28.1 - 28.1 = -28.1
-11.8d = -28.1
Multiply both side by ( -1)
(-1) ( -11.8d) = (-1)(-28.1)
11.8d = 28.1
Divide both side by 11.8
11.8d/11.8 = 28.1/11.8
d = 2.38
Answer : d = 2.38
Hi! I need some help with this question!I am pretty sure my answer is correct , but I just need to check in overall and review the question!Thank you!
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
Verify each table
Remember that
In a proportional relationship, the linear equation passes through the origin (0,0)
we have that
Am B and C passes through the origin
so
I will check table D
we have the points
(10,30) and (15,45)
Find the slope
m=(45-30)/(15-10)
m=15/5
m=3
Find the equation in slope intercept form
y=mx+b
we have
m=3
point (10,30)
substitute
30=3(10)+b
b=0
y=3x
Verify with this equation for the other points
For x=100
y=3(100)=300 ----> is ok
For x=200
y=3(200)=600 ----> is ok
that means
table D is proportional
Verify table C
we have
(0,0) and (1,3)
m=(3-0)/(1-0)
m=3
Find the equation in slope intercept form
y=mx+b
we have
m=3
point (0,0)
y=3x
Verify the other points
For x=2
y=2(3)=6
6 is not equal to 9
that means
table C is not proportiona
answer is C
Evaluate the following expression given.
In order to evalute this function, we must substitute x=-2 into the equation. It yields
[tex]\frac{4(-2)+3(-2)+2(-2)+(-2)}{-2}[/tex]By computing the porduct we have
[tex]\frac{-8-6-4-2}{-2}[/tex]which is equat to
[tex]\begin{gathered} \frac{-20}{-2} \\ \sin ce\text{ minus times minus is plus, we have} \\ \frac{10}{2} \end{gathered}[/tex]Finally, the evaluations gives 5.
I need help with my math
Given an expression
[tex]\begin{gathered} y+\frac{3}{8}\text{ = }\frac{-2}{3}\text{ } \\ \text{collect like terms} \\ y=\text{ }\frac{-2}{3}\text{ - }\frac{3}{8} \\ y\text{ = }\frac{-16-9}{24} \\ \text{LCM = 24} \\ y=\text{ }\frac{-25}{24} \\ y=\text{ -1}\frac{1}{4} \end{gathered}[/tex]A small car has a tire with a 15-inch diameter. A mountain bike has a tire with a 27-inch diameter. How much father than the small car does the mountain bike have to drive for its tire to complete one revolution?
Answer:
The mountain bike will travel 37.7 inches farther than the small car in one complete revolution.
[tex]37.7\text{ inches}[/tex]Explanation:
The distance a tire travel in one complete revolution is equal to the circumference of the tire.
The circumference can be calculated using the formula;
[tex]C=2\pi r=\pi d[/tex]Where;
C = Circumference
r = radius of tire
d = diameter of the tire
For the small car with tire of diameter 15 inches, the distance travelled in one revolution is;
[tex]\begin{gathered} C_1=\pi d_1=\pi(15)=15\pi \\ C_1=47.12\text{ inches} \end{gathered}[/tex]For the mountain bike with tire of diameter 27 inches, the distance travelled in one revolution is;
[tex]\begin{gathered} C_2=\pi d_2=\pi(27)=27\pi_{} \\ C_2=84.82\text{ inches} \end{gathered}[/tex]The difference between the distance travelled in one complete revolution is;
[tex]\begin{gathered} \Delta C=C_2-C_1=84.82-47.12 \\ \Delta C=37.70\text{ inches} \end{gathered}[/tex]Therefore, the mountain bike will travel 37.7 inches farther than the small car in one complete revolution.
[tex]37.7\text{ inches}[/tex]evaluate and express answer in standard form.
4.56×3.6
________
0.12
The value of the given expression in the standard form is 1.368×10².
We are given a mathematical expression. The expression consists of two arithmetic operations. First of all, two numbers are multiplied by each other, and then their result is divided by the third number. Let the mathematical expression be denoted by the variable "E". The expression is given below.
E = (4.56×3.6)/0.12
First, we will multiply the numbers in the numerator.
E = 16.416/0.12
Now we will divide the numerator by the denominator.
E = 136.8
Hence, the value of the expression is 136.8. Now we need to convert the resulting number into standard form. The standard form is given below.
E = 1.368×10²
To learn more about expressions, visit :
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3/5 of a number is 18. What is the number
Let
x -----> the number
we have that
(3/5)x=18
solve for x
x=18*5/3
x=30
the number is 30Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.Find the lateral area for the regular pyramid.L. A. =Find the total area for the regular pyramid.T. A. =
Answer
LA = 4√10
TA = 4 + 4√10
Step-by-step explanation
To find the Lateral Area (LA) of the pyramid, first, we need to calculate its slant height (s).
Considering the right triangle formed inside the pyramid, we can apply the Pythagorean theorem to find the length of s, as follows:
[tex]\begin{gathered} s^2=3^2+1^2 \\ s^2=9+1 \\ s=\sqrt{10} \end{gathered}[/tex]Now, we can calculate the lateral area as follows:
[tex]\begin{gathered} LA=\frac{1}{2}\times P\operatorname{\times}s \\ \text{ where P is the perimeter of the base of the pyramid. Substituting }P=4\times2\text{ and }s=\sqrt{10}: \\ LA=\frac{1}{2}\operatorname{\times}4\operatorname{\times}2\operatorname{\times}\sqrt{10} \\ LA=4\sqrt{10} \end{gathered}[/tex]To find the total area (TA) of the pyramid, first, we need to calculate the area of its base (B). In this case, the base is a square, then its area is:
[tex]\begin{gathered} B=b^2\text{ \lparen where b is the length of each edge\rparen} \\ B=2^2 \\ B=4 \end{gathered}[/tex]Finally, the total area is calculated as follows:
[tex]\begin{gathered} TA=B+LA \\ TA=4+4\sqrt{10} \end{gathered}[/tex]For each line the SLOPE between the 2 points given - simplify each fraction to prove that the lines have a CONSTANT rate of change : 1) Point T : 2) Point R : 3) Point S : 4) Slope of TR : 5) Slope of RS : 6) Slope of TS : 7) Describe the SLOPE of the line : 8) Therefore the CONSTANT RATE OF CHANGE IS ...?
the point T on the line is T(-7,6)
point R = R(-3,0)
point S = S(1,-6)
the slope of TR is
[tex]\begin{gathered} m=\frac{6-0}{-7-(-3)} \\ m=-\frac{6}{4} \\ m=-\frac{3}{2} \end{gathered}[/tex]slope of RS,
m = (0 - (-6))/(-3-1)
= - 6/4
= -3/2
slope of TS
m = (-6-6)/ 1-(-7)
= -12/ 8
= -3/2
the slope of the line or the constant rate of change is m = -3/2
Wallpaper was applied to one rectangular wall of a large room. The dimensions of the wall are shown below. I will send the graph.
Given:
Wallpaper was applied to one rectangular wall of a large room. The dimensions of the wall is 42 feet and 25.5 feet.
Total cost of wallpaper was $771.12
Required:
What was the cost, in dollars, of the wallpaper per square feet.
Explanation:
We know the area of rectangle is length multiplied by breadth.
Here, we have
[tex]\begin{gathered} A\text{rea of wall =}42\times25.5 \\ =1071 \end{gathered}[/tex]Now,
The cost of wallpaper per square feet is
[tex]\begin{gathered} =\frac{771.12}{1071} \\ =0.72 \end{gathered}[/tex]Answer:
Hence, $0.72 is the answer.
Solve the Exponential Function: [tex]x^2 * 2 - 2^x = 0[/tex]
Given the equation of the exponential function:
[tex]x^2\cdot2-2^x=0[/tex]We will solve the equation using the graph
the graph of the function is as shown in the following picture:
The solution to the equation will be the values of (x) at the point of intersection with the x-axis
As shown, there are 3 points of x-intercepts
So, the solution to the equation will be:
[tex]x=\mleft\lbrace-0.58,1,6.32\mright\rbrace[/tex]