What is the slope of the line that contains these points?х: 5 6 7 8y: -5 -6 -7 -8
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Answer
Explanation
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex](x₁, y₁) and (x₂, y₂) are picked from the table using
Related Questions
5. If Ms. Yamagata uses 18-inch tiles, what are the least number of tiles that she needs to buy to cover the floor? A. 30 B. 45 C. 68 D. 102
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We will have the following:
*First: We determine the area:
[tex]A=7.5\cdot9\Rightarrow A=67.5[/tex]So, there is an area of 67.5 square feet, now we take that to square inches:
[tex]\Rightarrow A=67.5\cdot144\Rightarrow A=9720[/tex]So, there is an area of 9720 square inches in that bathroom.
*Second: We will determine the number of 18-inch tiles that can be accommodated in the length and width:
**Length: We take into account that for each foot there are 12 inches and that each tile has a side length of 8 inches, so:
[tex]L=\frac{9\cdot12}{18}\Rightarrow L=6[/tex]So, in the length, we can accommodate 6 18-inch tiles.
**Width:
[tex]W=\frac{7.5\cdot12}{18}\Rightarrow W=5[/tex]So, in the width, we can accommodate 5 18-inch tiles.
*Third: We determine the number of tiles we will need by multiplying the number of tiles that can be accommodated in the length times the tiles that can be accommodated on the width, that is:
[tex]t=6\cdot5\Rightarrow t=30[/tex]So, she will need 30 18-inch tiles.
Hot Air Balloon Tours, Inc. must pay the bank $23,515.27 in interest 200 days after making a loan of $328,120 to purchase hot air balloons. What is the interest rate? Round to the nearest tenth of a percent
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To solve this problem we will use the formula for compound interest:
[tex]P_N=P_0\cdot(1+\frac{r}{k})^N\text{.}[/tex]Where:
• P_N is the balance in the account after N years,
,• P_0 is the starting balance of the account (also called an initial deposit, or principal),
,• r is the annual interest rate in decimal form,
,• N in years,
,• k is the number of compounding periods in one year.
In this problem, we have:
• P_0 = $328,120,,
,• interest P_N - P_0 = $23,515.27 → ,P_N = $351,635.27,,
,• N = ,200 days = ,200/365,
,• k = 1.
From the formula above, we have:
[tex]\begin{gathered} (\frac{P_N}{P_0})^{\frac{1}{N}}=1+r \\ r=(\frac{P_N}{P_0})^{\frac{1}{N}}-1. \end{gathered}[/tex]Replacing the data of the problem, we get:
[tex]r=(\frac{351,635.27}{328,120})^{\frac{365}{200}}-1\cong0.1346\cong13.5％.[/tex]Answer
The annual interest is 13.5%.
May I please get help with this. For I am confused as I have tried many times and many ways to get the correct answers but still could not find the right answers or how to plot it in the graph
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From the graph, the point marked with a large dot is located at (-7, -6)
Translation 5 units to the right transforms the point (x, y) into (x+5, y). Applying this rule to the point, we get:
(-7, -6) → (-7+5, -6) → (-2, -6)
Translation 7 units up transforms the point (x, y) into (x, y+7). Applying this rule to the point, we get:
(-2, -6) → (-2, -6+7) → (-2, 1)
In the final figure, the point is (-2, 1)
Find the sum and classify the polynomial based on degree and number of terms.
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We need to simplify the given expression as follows:
[tex]\begin{gathered} 3n^2(5n^2-2n+1)+(4n^2-11n^4-9) \\ =(15n^4-6n^3+3n^2)+(4n^2-11n^4-9) \\ =4n^4-6n^3+7n^2-9 \end{gathered}[/tex]Now, to determine the degree of the polynomial we need to find the term which has the biggest exponential term. In this case, it is 4n^4. So, the expression is a 4th-degree polynomial.
Then, the answer is option C. 4th degree polynomial with 4 terms
how do you solve for x in the following problem? 4x + 16 equals 24
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Let's begin by listing out the information given to us:
[tex]\begin{gathered} 4x+16=24 \\ \text{Subtract 16 from both sides, we have:} \\ 4x+16-16=24-16_{} \\ 4x=8 \\ \text{Divide both side by 4, we have:} \\ \frac{4x}{4}=\frac{8}{4}\Rightarrow x=2 \\ x=2 \end{gathered}[/tex]Write an equation that describes the following relationship: y varies inversely as the cube root of x and when x=64, y=2
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Since y varies inversely as the cube root of x then:
[tex]\begin{gathered} y=\frac{k}{\sqrt[3]{x}}, \\ \text{where k is the constant of proportionality.} \end{gathered}[/tex]Now, to determine the value of k, we use the fact that when x=64, y=2:
[tex]2=\frac{k}{\sqrt[3]{64}}.[/tex]Solving the above equation for k we get:
[tex]\begin{gathered} \frac{k}{\sqrt[3]{64}}\times\sqrt[3]{64}=2\times\sqrt[3]{64}, \\ k=2\sqrt[3]{64}, \\ k=2\cdot4=8. \end{gathered}[/tex]Therefore:
[tex]y=\frac{8}{\sqrt[3]{x}}\text{.}[/tex]Answer:
[tex]y=\frac{8}{\sqrt[3]{x}}\text{.}[/tex]0.6(x-2)=0.3x+5-0.1x
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First, we have to use the distributive property.
[tex]\begin{gathered} 0.6(x-2)=0.3x+5-0.1x \\ 0.6x-1.2=0.3x+5-0.1x \\ \end{gathered}[/tex]Then, we reduce like terms.
[tex]0.6x-1.2=0.2x+5[/tex]Now, we subtract 0.2x from each side.
[tex]\begin{gathered} 0.6x-0.2x-1.2=0.2x-0.2x+5 \\ 0.4x-1.2=5 \end{gathered}[/tex]Then, we add 1.2 on each side.
[tex]\begin{gathered} 0.4x-1.2+1.2=5+1.2 \\ 0.4x=6.2 \end{gathered}[/tex]At last, we divide both sides by 0.4.
[tex]\begin{gathered} \frac{0.4x}{0.4}=\frac{6.2}{0.4} \\ x=15.5 \end{gathered}[/tex]Therefore, the solution to the equation is x = 15.5.Find the distance between the points (0, 10) and (–9, 1).A. 14.21B. 12.73C. 16.23D. 20.22
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We have the next formula to calculate the distance between 2 points
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]in our case
(0,10)=(x1,y1)
(-9,1)=(x2,y2)
we substitute the values
[tex]d=\sqrt[]{(1-10)^2+(-9-0)^2}[/tex]then we simplify
[tex]d=9\sqrt[]{2}=12.7279[/tex]Therefore the correct choice is B. 12.73
(3х2 - 10x + 4) + (10х2 – 5х +8) can we this as a performance as a operation
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Starting with the expression:
[tex](3x^2-10x+4)+(10x^2-5x+8)[/tex]Ignore the parenthesis, since their coefficients are equal to 1:
[tex]=3x^2-10x+4+10x^2-5x+8[/tex]Use the commutative property of addition to change the order of the terms without changing the result of the sum. Bring like terms together:
[tex]=3x^2+10x^2-10x-5x+4+8[/tex]Add like terms:
[tex]=13x^2-15x+12[/tex]Therefore:
[tex](3x^2-10x+4)+(10x^2-5x+8)=13x^2-15x+12[/tex]4: Random numbers are useful for ______ real-world situations that involve chance.
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Real world situations that involve chance can be modeled by the use of random numbers.
The answer is option A.
Represent the expression “A number, x, decreased by the sum of 2x and 5* algebraically. A. (2x + 5) - x B. x - (2x + 5) C. x - 2x + 5 D. (x + 2x) - 5
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We are given the following word problem
"A number, x, decreased by the sum of 2x and 5"
We are asked to translate the word problem into an algebraic expression.
Sum of 2x and 5 means (2x + 5)
Now we need to subtract (decrease) this sum (2x + 5) from x
So, the algebraic expression becomes
[tex]x-(2x+5)_{}[/tex]Therefore, the correct algebraic expression is option B
Evaluate the expression 6c-d when c=2 and d=10 I need help?
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To evaluate the expression 6c - d, in case c = 2 and d = 10, we can proceed as follows:
We need to substitute the value of c and d in the expression, that is
c = 2, d = 10
Then
6c - d
6 x (2) - 10
12 - 10 = 2
So, the evaluation of the expression 6c - d when c =2 and d = 10 is 2.
Find all real solutions of the equation by using the square root method.(3c+4)2−37=0 c= Leave answers that include radicals as a single fraction, and separate multiple solutions with commas.
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Given the equation in the question expressed as:
[tex](3c+4)^2-37=0[/tex]Add 37 to both sides of the equation
[tex]\begin{gathered} (3c+4)^2-37+37=0+37 \\ (3c+4)^2=37 \end{gathered}[/tex]Take the square root of both sides
[tex]\begin{gathered} \sqrt{(3c+4)^2}=\sqrt{37} \\ 3c+4=\sqrt{37} \end{gathered}[/tex]Subtract 4 from both sides
[tex]\begin{gathered} 3c+4-4=\sqrt{37}-4 \\ 3c=\sqrt{37}-4 \end{gathered}[/tex]Divide both sides of the resulting equation by 3
[tex]\begin{gathered} \frac{3c}{3}=\frac{\sqrt{37}-4}{3} \\ c=\frac{\sqrt{37}-4}{3} \end{gathered}[/tex]Algebra 1Simplify each expression by using the Distributive Property and combine like terms to simplify the expression.-(3n-5)-7n
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-(3n-5)-7n
Apply the distributive property to distribute the negative sign:
-(3n)-(-5)-7n
-3n+5-7n
Combine like terms ( the ones with "n")
-3n-7n+5
-10n+5
Find the length of the segment that starts at (3,4)and goes to (8,7).
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To find the length of a segment delimited by two points we need to find the distance between said points. This is done by using the following expression:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]We then need to apply the coordinates of the given points:
[tex]\begin{gathered} d=\sqrt[]{(8-3)^2+(7-4)^2} \\ d=\sqrt[]{5^2+3^2} \\ d=\sqrt[]{25+9=\sqrt[]{36}} \\ d=6 \end{gathered}[/tex]The segment has a length of 6 units.
Just give best explanation and give answer to both questions
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If the two triangles are similar then their angles have the same measure. This also implies that the quotient between a side of one triangle and its corresponding side in the other one is the same for the three pairs of sides. The sides of the large triangle are 9, 2+y and 12 and their corresponding sides in the small triangle are 3, 2 and x. Then since the quotient between corresponding sides is always the same we get:
[tex]\begin{gathered} \frac{9}{3}=\frac{2+y}{2}=\frac{12}{x} \\ 3=\frac{2+y}{2}=\frac{12}{x} \end{gathered}[/tex]So for x we get:
[tex]3=\frac{12}{x}[/tex]We multiply both sides by x and we get:
[tex]\begin{gathered} 3\cdot x=\frac{12}{x}\cdot x \\ \\ 3x=12 \end{gathered}[/tex]And we divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{12}{3} \\ x=4 \end{gathered}[/tex]Then for y we get:
[tex]3=\frac{2+y}{2}[/tex]We can multiply both sides by 2:
[tex]\begin{gathered} 3\cdot2=\frac{2+y}{2}\cdot2 \\ 6=2+y \end{gathered}[/tex]And we substract 2 from both sides:
[tex]\begin{gathered} 6-2=2+y-2 \\ y=4 \end{gathered}[/tex]So x=4 and y=4. Then the answer to part 1 is option A and the answer to part 2 is option B.
Find the pattern in each sequence and use it to list the next two terms. a. 5, 17, 29, 41, b. 18, 14, 10, 6, c. -9,4,-8,5, -7,6,
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Given:
The objective is to find the pattern and list out the next two terms in the sequence.
Explanation:
a)
The given sequence is 5, 17, 29, 41....
Let's find the difference between the two successive terms of the sequence.
[tex]\begin{gathered} d=17-5=12 \\ d=29-17=12 \\ d=41-29=12 \end{gathered}[/tex]Thus, the common difference between each successive terms is 12.
Then, the next two terms can be calculated as,
[tex]\begin{gathered} 41+12=53 \\ 53+12=65 \end{gathered}[/tex]Hence, the next two terms are 53 and 65.
b)
The given sequence is 18, 14, 10, 6...
Let's find the difference between the two successive terms of the sequence,
[tex]\begin{gathered} d=14-18=-4 \\ d=10-14=-4 \\ d=6-10=-4 \end{gathered}[/tex]Thus, the common difference between each successive terms is -4.
Then, the next two terms can be calculated as,
[tex]\begin{gathered} 6-4=2 \\ 2-4=-2 \end{gathered}[/tex]Hence, the next two terms are 2 and -2.
c)
The given sequence is -9, 4, -8, 5, -7, 6.
Here it can be observed that starting from -9, the alternate numbers are increasing.
Then, the next number can be calculated by find the difference between those sequence provided with alternae places.
[tex]\begin{gathered} d=-8-(-9)=1 \\ d=-7-(-8)=1 \end{gathered}[/tex]Thus, the common difference between each successive terms is 1.
Similarly, the commo difference between the series present inside is,
[tex]\begin{gathered} d=5-4=1 \\ d=6-5=1 \end{gathered}[/tex]Then, the next two number will be,
[tex]\begin{gathered} -7+1=-6 \\ 6+1=7 \end{gathered}[/tex]Hence, the two numbers are -9, 4, -8, 5, -7, 6, -6, 7.
how can you figure out how many squares are in figure 50??
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The pattern followed in numbering the squares is such that, each number of squares is added to itself and then two squares are added at the edge of it, one square at either end.
Hence, one square would be
1 = 1 + 1 + 2
2 = 2 + 2 + 2
And so on
This can be expressed in algebraic form as follows;
When x is the number given, the number of squares in it becomes
x = x + x +2
x = 2x + 2
So if x is 50, then the number of squares is now,
x(50) = 2(50) + 2
x(50) = 100 + 2
x(50) = 102
Therefore in figure 50 you have 102 squares.
For the graph shown, identify a) the point(s) of inflection and b) the intervals where the function is concave up or concave down X . 110 ! a) The point(s) of inflection is/are (Type an ordered pair. Use a comma to separate answers as needed.)
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We have the following:
Therefore:
a.
The point (0,5)
b.
therefore:
Concave up:
[tex](-4,0)[/tex]Convace down:
[tex](-2,\frac{3}{2})[/tex]a.
(0,5)
Consider the right triangle shown below.Suppose the hypotenuse of this right triangle is r=7 cm long.Suppose that sin(θ)=0.629.y is how many times as large as r? ____times as large What is the value of y?y=Suppose that cos(θ)=0.778.x is how many times as large as r? ______times as large What is the value of x?x=
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y is 0.629 times as large as r
x is 0.778 times as large as r
y = 4.403
x = 5.446
Explanations:From the right-angled triangle shown:
The opposite is the side facing the angle θ
Opposite = y
The Hypotenuse is the longest side of the triangle
Hypotenuse = r
The Adjacent is the third side
Adjacent = x
Suppose sinθ = 0.629
r = 7
[tex]\begin{gathered} \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ 0.629\text{ = }\frac{y}{r} \\ 0.629\text{ = }\frac{y}{7} \\ y\text{ = 7(0.629)} \\ y\text{ is 0.629 times as large as r} \\ y\text{ = }4.403 \end{gathered}[/tex]Suppose that cos θ = 0.778
and r = 7
[tex]\begin{gathered} \cos \theta\text{ = }\frac{Adjacent}{\text{Hypotenuse}} \\ 0.778\text{ = }\frac{x}{r} \\ 0.778\text{ = }\frac{x}{7} \\ x\text{ = 0.778(7)} \\ x\text{ is 0.778 times as large as r} \\ x\text{ = }5.446 \end{gathered}[/tex]The veterinarian weighed Oliver’s new puppy, Boaz, on a defective scale. He weighed pounds. However, Boaz weighs exactly pounds. What is the percent of error in measurement of the defective scale ? Round your answer to the nearest whole number.
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It is given that Boaz weight is 36 pounds on a defective scale and exact weight is 34 pounds.
To determine the percent of error in measurement of the defective scale
[tex]PE=\frac{approxvalue-exactvalue}{\text{exactvalue}}\times100[/tex][tex]PE=\frac{36-34}{34}\times100=\frac{2}{34}\times100=5.882[/tex]Hence the percent error in measurement of the defective scale is 6.
The length of the rectangle is 9 feet and width of the rectangle is three fourths of the length. Which represents the width of the rectangle?
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Explanation
This is the given rectangle:
The width of the rectangle is:
[tex]W=\frac{3}{4}L=\frac{3}{4}\times9[/tex]Answer
The correct answer is option 1: 9 x 3/4
What is the distance from point P(- 1, 1) to the line y = -2x + 4? Round to the nearest tenth.
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Line equation: y = -2x + 4, Point (-1,1)
We have to write the equation in the standard form:
y = -2x + 4
-2x - y + 4 = 0
Now we can see the values of a, b, c and x0 and y0 to use the formulas
a = -2
b = -1
c = 4
x0 = -1
y0 = 1
Distance = abs(ax0 + by0 + c)/sqrt(a^2 + b^2) = abs(-2(-1) -1 (1) + 4)/sqrt((-2)^2 + (-1)^2) =
D = abs(2 - 1 + 4)/sqrt(4 + 1) = abs(5)/sqrt(5) = 5/2.236067 = 2.2360
Rounding to nearest tenth: Distance = 2.2
Answer: Distance is 2.2
[tex]d\text{ = }\frac{\mathrm{abs}(ax_0+by_0+c)}{\sqrt[]{a^2+b^2}}[/tex]Which transformation can NOT be used to prove that ABC is congruent toA DEF?ÁO A. rotationB. reflectionC. dilationD. translation
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If two triangles are congruent, it means that the lengths of their corresponding sides and angles are equal. Thus, the triangles have equal sizes. Transformations involing rotation, reflection and translation does not change the size of the triangle but dilation does. It increases or decreases it. Thus, the correct option is
C. dilation
For each ordered pair (x,y) determine whether it is a solution to the inequality y<-3x-6
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We have 4 ordered pairs (x,y), for which we must satisfy that the following inequality is satisfied:
[tex]y<-3x-6[/tex]What we must do to solve this is to replace the variables "x" and "y" in the inequality and verify that it is fulfilled.
First-order pair
[tex]\begin{gathered} (7,-27) \\ -27<-3\cdot(7)-6 \\ -27<-21-6 \\ -27=-27 \end{gathered}[/tex]This order pair is not a solution to the inequality
Second-order pair
[tex]\begin{gathered} (-9,25) \\ 25<-3\cdot(-9)-6 \\ 25<27-6 \\ 25>21 \end{gathered}[/tex]This order pair is not a solution to the inequality
Third-order pair
[tex]\begin{gathered} (6,-26) \\ -26<-3\cdot(6)-6 \\ -26<-18-6 \\ -26<-24 \end{gathered}[/tex]This order pair is a solution to the inequality
Fourth-order pair
[tex]\begin{gathered} (-3,-2) \\ -2<-3\cdot(-3)-6 \\ -2<9-6 \\ -2<3 \end{gathered}[/tex]This order pair is a solution to the inequality
Finally, we have that only the following ordered pair are a solution for the inequality:
[tex]\begin{gathered} (6,-26) \\ (-3,-2) \end{gathered}[/tex]Which expression is equivalent to 18-2V14r8 67704, if x + 0? O A. 12.142 OB. 3.42 O C.3.147 OD. 3.02 Reset Next
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We will simplify the expression thus:
[tex]\frac{18x^2\sqrt[]{14x^8}}{6\sqrt[]{7x^4}}[/tex][tex]\frac{18x^2\times\sqrt[]{14}\times x^{8\times\frac{1}{2}}}{6\times\sqrt[]{7}\times x^{4\times\frac{1}{2}}}[/tex]Simplifying further will give us:
[tex]\begin{gathered} \frac{3x^2\times\sqrt[]{2}\times x^4}{x^2} \\ \frac{3\times\sqrt[]{2}\times x^4}{1} \\ =3x^4\sqrt[]{2} \\ \text{The correct answer is option B.} \end{gathered}[/tex]determine the axis of symmetry of the quadratic functionA) y = 2B) x = 2C) x = 0D) y = 1
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SOLUTION:
Case: Axis of symmetry of quadratic function
Given: A graph with a turning point
Required: To find the axis of symmetry of the quadratic function
Method:
Use a vertical on the divide the graph into two equal parts
Final answer:
The axis of symmetry is at x=2
Explain how you know whether a relationship between two quantities is or is not a function
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In order to know whether a relationship is a function or not, follow these steps:
1. Identify the input values, usually grouped as the values for the independent variable "x"
2. Identify the output values, usually grouped as the values for the dependent variable "y"
3. If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.
Find the length of the 3rd side using the simplest radical form
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Given a right angled triangle, we shall solve for the unknown side by applying the Pythagoras' theorem which is;
[tex]c^2=a^2+b^2[/tex]Where c is the hypotenuse (side facing the right angle) and then a and b are the other two sides.
Substituting for the given values, we shall now have the following;
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=5^2+5^2 \\ c^2=25+25 \\ c^2=50 \end{gathered}[/tex]Take the square root of both sides;
[tex]\begin{gathered} \sqrt[]{c^2}=\sqrt[]{50} \\ c=\sqrt[]{50} \end{gathered}[/tex]We can now re-arrange the the right side of the equation;
[tex]\begin{gathered} c=\sqrt[]{2\times25} \\ c=\sqrt[]{2}\times\sqrt[]{25} \\ c=5\sqrt[]{2} \end{gathered}[/tex]ANSWER:
The third side of the triangle would now be;
[tex]5\sqrt[]{2}[/tex]I need help on this math question and I NEED IT NOWWW
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The triangle contains two right triangles. The base of each right triangle is equal. Given that the length of the base of the triangle is 10, the base of each right triangle is
10/2 = 5
The diagram of the right triangle is shown below
We would find x by appying the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the diagram,
hypotenuse = 13
one leg = 5
other leg = x
By applying the pythagorean theorem,
13^2 = 5^2 + x^2
169 = 25 + x^2
Subtracting 25 from both sides of the equation, we have
169 - 25 = 25 - 25 + x^2
x^2 = 144
x = square root of 144
x = 12