y-6 = -5/3 (x+2) is the point - slope equation of the line through (-2 , 6 ) ( 1 , 1 ) using exact numbers.
What is point - slope equation ?For linear equations, the typical form is y-y1=m(x-x1). It highlights the line's slope and a line point (that is not the y-intercept).
The two approaches for determining the equation of a line given a point and its slope are as follows:
(a). Input the slope and the (x, y) point values into the equation y = mx + b, then solve for b using the substitution technique
b) Point-slope form: (x 1, y 1), where (y 1, x 1) is the point and (m, the slope) is the specified slope.
CalculationFirst you need to find the slope, (y2-y1)/(x2-x1). This is (1-6)/(1-(-2)) or -5/3
Now that you know the slope you can use that for the point-slope equation
The point-slope equation is y-y1 = m(x-x1). If we start with y-6, the x value is -2 (from our point (-2,6)
y-6 = -5/3 (x-(-2))
or, y-6 = -5/3 (x+2)
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3) Calculate the volume
4 cm
5 cm
3 cm
9 cm
Answer:
57cubic sm
Step-by-step explanation:
4 x 3= 12
5 x 9= 45
12 + 45 = 57
200,000 divided by 2,800
A rectangle has a length of 17 inches less than 7 times its width. If the area of the rectangle is 2204square inches, find the length of the rectangle.
SOLUTION
We are told that the length of the rectangle is 17 inches less than 7 times its width.
Now, let the letter L represent the length and the letter w represent the width of the rectangle.
This statement can be represented algebraically as
[tex]L=7w-17[/tex]So, Area =
[tex]\text{Area = L x w}[/tex]We are also told the Area A of the rectangle = 2204. Now
[tex]\begin{gathered} 2204=L\times w \\ \\ 2204=(7w-17)\times w \end{gathered}[/tex]We have to find the width, then we find the length L
[tex]\begin{gathered} 2204=(7w-17)\times w \\ 2204=7w^2-17w \\ 7w^2-17w-2204=0 \\ \\ \text{Solving the quadratic equation } \\ \\ w=19\text{ or w = -16.57} \end{gathered}[/tex]Since the width cannot be negative, w = 19 inches
The length becomes
[tex]\begin{gathered} L=7w-17 \\ L=7\times19-17 \\ L=133-17 \\ L=116\text{ inches } \end{gathered}[/tex]A sinking fund is established to discharge a debt of $70,000 in 10 years. if deposits are made at the end of each 6-month period and interest is paid at the rate of 9%, compounded semiannually, what is the amount of each deposit? (round your answer to the nearest cent.)
The amount of each deposit is $210000
What is compound interest?Compound interest is when you reinvest your income. Compound interest distinctively means "interest on interest" and is the reason so many investors are so successful.
The computation of the each deposit is shown below:
Given that
Future value be $70,000
Time period = 10 × 2 = 20
And, the rate = 9% ÷ 2 = 4.5%
Now the formula is as follows
= (Future value × rate of interest) ÷ (1 + rate of interest)^time period - 1
= ($70,000 × 4.5) ÷ (1 + 0.025)²⁰⁻¹
= $315,000 ÷ 1.5
= $210000
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Find the slope of a line that is a) parallel and b) perpendicular to the given line.– 3x – 4y = 1
The line is:
[tex]-3x-4y=1[/tex]Which is equivalent to:
[tex]\begin{gathered} \Rightarrow4y=-3x-1 \\ \Rightarrow y=-\frac{3x}{4}-\frac{1}{4} \end{gathered}[/tex]Thus, the slope of the line is equal to -3/4
a) Every line parallel to that one has the same slope, then the answer is -3/4
b) On the other hand, if m_1 and m_2 are the slopes of two perpendicular lines, then:
[tex]m_1\cdot m_2=-1[/tex]Therefore, since the slope of our line is equal to -3/4, the slope of any line perpendicular to that one is:
[tex]\begin{gathered} m_1\cdot(-\frac{3}{4})=-1 \\ \Rightarrow m_1=\frac{4}{3} \end{gathered}[/tex]Hence, the answer is 4/3
F(2-k)=8-5(2-k) evaluating functions
Answer:
f = 5k−2/−k+2
8. If two lines are cut by a transversal so that consecutive interior angles are (congruent, supplementary, complementary), then the lines are parallel
Supplementary angles add up to 180°
If two lines are cut by a transversal so that consecutive interior angles are ( supplementary,, then the lines are parallel
wich equation is proportional?y=2x-6y=-1/4x
Circle describe and correct each error.X-int = (0,-2)Y-int = (-4,0)
First, we solve for y in the expression:
[tex]\begin{gathered} 4x+2y=-8\Rightarrow2y=-4x-8 \\ \\ \Rightarrow y=-2x-4 \end{gathered}[/tex]So, the y-intercept is (0, -4).
The error is that you are given the wrong y-intercept and the wrong x-intercept; they are swapped in the place of writting.
On a cold day in new york, a street vendor sold 35 cups of hot chocolate and her entire stock of hot cider. if the ratio of cider to hot chocolate is 8:5, how many cups of cider did she sell?
Using the concept of ratio and proportion, the vendor sold 56 cups of hot cider.
How does a ratio operate?The word "proportion" often denotes a portion, share, or sum that is in comparison to a whole. Two ratios are in proportion when they are equal, according to the proportional idea. When an equation or a statement to that effect is used, two ratios or fractions are equal.
Define ratio.A percentage is a mathematical comparison of two numbers. In terms of proportion, two sets of given numbers are said to rise or decrease in the same ratio if they are directly proportionate to one another.
Cider supplied by the street seller for value = x for 35
= x/35
The cider's ratio is 8:5,
x/35 :: 8:5,
x = [35(8)]/ 5
=56.
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Aiden ran a total of 8 miles over the course of 2 track practices. How many track practices would it take for Aiden to run 16 miles? Assume the relationship is directly proportional.
Answer:
4
Step-by-step explanation:
8 miles over 2 practices so double that
Students in mrs smiths class must complete at least 40 math problems for homework every week. the table shows the progress of four students on Wednesday. Which list shows the names of students in order from the greatest amount of homework complete to the least amount of homework completed? A Katie, Jonah, D’Angelo. Grace B D’Angelo, grace, Jonah, Katie C Katie, Jonah, grace, D’Angelo D Jonah, Katie, D’Angelo, grace
Answer: the anwser is B
Step-by-step explanation:
Answer:
Grace, jonah,D'angelo,then Katie.
First,Grace because she finished it 100%
Next,it's Jonah because he finished it 2/3 the way meaning about around 70% of the work.
Then, D'angelo because he completed five more than Katie.
Last,Katie because she was less than jonah.She had 40 but D'angelo had five more than her
Which of the following equations is equivalent to 4x + 2y = 12? A. 2y = -4x + 12 B. y=-2x + 6 C. y = 2X - 6 D. y = 8x + 24
Let's find the equivalent equation to:
4x + 2y = 12
2y = 12 - 4x
Dividng by 2 at both sides:
2y/2 = 12/2 - 4x/2
y = 6 - 2x
We can see that choices B and C are not correct because the signs.
If we multiply by 2 at both sides, we have:
2y = 12 - 4x
We can see that if we change the order at the right side of the equation, we have:
2y = -4x + 12
I think now you are ready to select the correct choice, Deppreso.
0.08 is 30%?TrueFalse
A number can be expressed in percent form or in decimal form.
For example, 0.3
Find the equation of the line passing through the given pair of points. Write the equation in slope-intercept form.(-4,-2), (3,7)
Equation of a line in slope intercept form:
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
To find the slope use the two given points in the next formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{points: }(-4,-2)(3,7) \\ \\ m=\frac{7-(-2)}{3-(-4)} \\ \\ m=\frac{7+2}{3+4}=\frac{9}{7} \end{gathered}[/tex]Use the slope and one of the points to find the y-intercept:
[tex]\begin{gathered} y=mx+b \\ (3,7) \\ \\ 7=\frac{9}{7}(3)+b \\ \\ 7=\frac{27}{7}+b \\ \\ 7-\frac{27}{7}=b \\ \\ b=\frac{49-27}{7} \\ \\ b=\frac{22}{7} \end{gathered}[/tex]Then, the equation of the line passing through the given pair of points is:
[tex]y=\frac{9}{7}x+\frac{22}{7}[/tex]What is the measure of angle X to the nearest degree?
Using a trigonometric relation we will see that the correct option is B, 24°.
What is the measure of angle X?On the image we can see a right triangle, where the length of the hypotenuse and of one leg (the opposite cathetus to angle X) are known.
We can use the trigonometric relation:
sin(a) = (opposite cathetus)/(hypotenuse)
Then we can write:
sin(X) = 9/22
If we apply the inverse sine function in both sides, we will get:
X = Asin(9/22) = 24.15°
Then the correct option is B.
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Find the GCF and LCM for 24 & 30.
GCF-
LCM-
Answer:
The GCF of 24 & 30 would be 6. The LCM of 24 & 30 would be 120.
Step-by-step explanation:
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5.
Write the equation for this line
Answer:
y = 3x - 6 is the correct equation. The slope is 3, and the y-intercept is at -6.
Last year the book fair sold 200 bookmarks compared to the 180 sold this year. What is the percent of change in the number of bookmarks sold?
Answer:
Step-by-step explanation:
1. Subtract 200 from 180
200 - 180 = 20
2. Divide the difference of the number of bookmarks by last years
20 / 200 = 0.1
3. Multiply 0.1 by 100 to get the percentage
0.1 x 100 = 10 %
4. Since this is a reduction in number of bookmarks sold, then it would be a -10% change in the number of bookmarks sold.
a frame is 9 inch wide and 6 inch tall. if it is reduced to a width of 3 inch the how tall will it be?
The height of the frame will remain the same.
The height of the frame is 6 inch
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
A frame:
The frame can be considered as a rectangle.
Wide = 9 inch
Height = 6 inch
_______
| |
| | 6-inch (height)
| |
|_______|
9-inch (wide)
If wide = 3 inches the height remains the same.
Thus,
The height of the frame will remain the same.
The height of the frame is 6 inch
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Annie purchased a season pass for the new aquarium at a cost of $110. if she uses the pass 10 times this year , what is the unit rate in cost per visit?
If she uses the pass 10 times this year then the unit rate in cost per visit is $11 unit per visit.
In the given question,
Annie purchased a season pass for the new aquarium at a cost of $110.
If she uses the pass 10 times this year then we have to find the unit rate in cost per visit.
We have to find the unit rate.
Unit rate means finding the value of one object, that means we have to find the cost of one visit.
The cost of season pass is $110.
She visit aquarium 10 times.
We find the unit rate cost per visit by dividing the total cost of season pass for the new aquarium by total times she visits in the new aquarium.
10 times = $110 cost
Divide by 10 on both side
10/10 times = $110/10 cost
1 times = $11 cost
Hence, if she uses the pass 10 times this year then the unit rate in cost per visit is $11 unit per visit.
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Find the domain and range and intercepts.g of x = 3 / x-4
a) Domain; all real numbers except 4
b) Range; all real numbers except y = 0
c) Y-intercept = -0.75
d) x-intercept does not exist
Here, we want to find the domain, range and intercepts
The domain refers to the possible x-values
From the question, the function will hold for all values of x, except x = 4, where we will have an undefined expression
Thus, the domain is all real numbers, except x= 4
For the range, we are referring to the possible y-values
From the given equation the possible y values are all real numbers except y = 0
To find the intercepts, let us write g(x) as y
The equation is thus;
[tex]\begin{gathered} y\text{ = }\frac{3}{x-4} \\ \end{gathered}[/tex]To get x-intercept, substitute y = 0
By doing this, we have no x-intercept
To get the y-intercept, we simply substitute x = 0
That means;
[tex]\begin{gathered} y\text{ = }\frac{3}{0-4} \\ y\text{ = }\frac{3}{-4} \\ y\text{ = -0.75} \end{gathered}[/tex]Enter the value of 5.6( 7+13)
Answer:
112
Step-by-step explanation:
According to pemdas we do what’s in parentheses first and then multiply
5.6(7+13)
5.6(20)
112
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-7t-8=10+2t solve for t
Answer:
t= -2
Step-by-step explanation:
Hope this helps!!
Answer:
t = -2
Step-by-step explanation:
-7t - 8 = 10 + 2t
Subtract 10 from both sides
-7t - 18 = 2t
Add 7t to both sides
-18 = 9t
Divide both sides by 9
-2 = t
What is the equation for the line in slope-intercept form?
Answer:
y = -2x - 4
Step-by-step explanation:
Slope intercept form : y = mx + b
Where
m = slopeb = y intercept Finding Y - InterceptThe y intercept is the point where the line crosses the y axis.
Here, just by looking at the graph we can say that the y intercept is at (0,-4) because that is where the line passes the y intercept.
This means that b = - 4
Finding the slopeWe can find the slope using the following formula
Slope = (y2-y1)/(x2-x1)
Where, (x1,y1) and (x2,y2) are any given points on the line
The points used can vary however I have chosen (0,-4) and (-2,0)
Defining our variables we get (x1,y1) = (0,-4) and (x2,y2) = (-2,0)
So we have x1 = 0 , x2 = -2 , y1 = -4 and y2 = 0
We now plug this in to the formula
Slope = (y2-y1)/(x2-x1)
==> plug in x1 = 0 , x2 = -2 , y1 = -4 and y2 = 0
Slope = (0-(-4))/(-2-0)
==> remove parenthesis
Slope = (0+4)/(-2-0)
==> simplify addition and subtraction
Slope = 4/-2
==> simplify fraction
Slope = -2
So the slope or "m" is -2
Plugging the y intercept and slope into y intercept formAgain we have y = mx + b
m = slope so m = -2 and b = y intercept so b = -4
Plugging this in, we acquire y = -2x - 4
one angle of a triangle mesures 24 more than the smallest angle in the triangle. the third angle measures twice the measure of the smallest angle
What is the measure of the smallest angle?
24
39
52
54
The answer, the measure of the smallest angle is 39° in the triangle.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angle of triangle = 180
Let x be the smalletst angle
2nd angle will be x+24
and 3rd angle will be 2x
So sum of all angles x+2x+x+24=180
4x=180-24
x=156/4
x=39
Hence the measure of the smallest angle will be 39°
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question 1A.) 4, 8, 12B.)6, 10, 26C.) 2, 6, 22D.) 1, 2, 6
Answer
Option C is correct.
a₁, a₂ and a₃ = 2, 6 and 22 respectively.
Explanation
We have been told that
a₀ = 1
And any term after that is given as
[tex]a_{i+1}=4a_i-2[/tex]So,
a₁ = 4a₀ - 2
a₁ = 4 (1) - 2
a₁ = 4 - 2
a₁ = 2
a₂ = 4a₁ - 2
a₂ = 4 (2) - 2
a₂ = 8 - 2
a₂ = 6
a₃ = 4a₂ - 2
a₃ = 4 (6) - 2
a₃ = 24 - 2
a₃ = 22
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If a loan is taken out for $278 at 10% and costs the borrower $174.12 in simple interest, how many years was the loan for? ROUND YOUR ANSWER TO THE NEAREST WHOLE YEAR
Data:
Loan=$278 at 10%
A simple interest is calculated for payments on the initial capital.
If the total interest was $174.12.
If the interest is on a year. You calculated the interes of one year. The 10% of $278:
[tex]278\cdot\frac{10}{100}=27.8[/tex]In a year the interest is $27.8.
Then, $174.12 divided into $27.8 is the number of years of the loan:
[tex]\frac{174.12}{27.8}=6.26\approx6[/tex]Then, the loan was for 6 yearsIf z=13 which equation is true?
A) 3z + 16 = 55
B) 2(23 + z) = 70
C) 3( 18 + z) = 85
D) 2z - 5 = 20
360 2 kg G 10. A yogurt tub contains 1 liter of yogurt. Nancy and her friends' eat 425 milliliters of yogurt. How much yogurt is left? Datab 425 s 75 you
The amount of 1 litre is equivalent yo 1000 milliliter.
Determine the amount yogurt left by subtraction of 425 from 1000.
[tex]1000-425=575[/tex]So 575 milliliter of yogurt is left.