Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (9, -2) and (4, 2).
Substitute:
[tex]m=\dfrac{2-(-2)}{4-9}=\dfrac{2+2}{-5}=-\dfrac{4}{5}[/tex]
Put the value of a slope and coordinates of first or second point to the equation of a line:
[tex](9,\ -2),\ m=-\dfrac{4}{5}\\\\y-(-2)=-\dfrac{4}{5}(x-9)\\\\\boxed{y+2=-\dfrac{4}{5}(x-9)}\\\\(4,\ 2),\ m=-\dfrac{4}{5}\\\\y-2=-\dfrac{4}{5}(x-4)}[/tex]
What is the intersection of the sets A= {2,3,4,7} and B= {2,5,7,13}
Answer: { 2 , 7 }
Step-by-step explanation:
The intersection of a set is what the sets have in common. From the given sets , the numbers common to the two are 2 and 7 , so the intersection of the sets will be { 2 , 7 }
Mr. Shively’s TV cabinet is 30 inches tall and 40 inches wide. Best Buy is selling 50 inch, 55 inch, 60 inch, and 65 inch TVs. Of those options, which one should he buy? Explain your answer using mathematics , please explain using Pythagorean theorem.
Answer:
He should buy a 50 inch TV
Step-by-step explanation:
Using Pythagorean theorem the TV cabinet has a diagonal of :
[tex]\sqrt{30^{2} + 40^{2} } = 50[/tex]
If 3x/5 = 3/2, then x = ?
Answer:
5/2
Step-by-step explanation:
3x/5=3/2
x=(3/2)/(3/5)
x=(3/2)(5/3)
x=5/2
331/3% as a fraction
Two parallel lines are cut by a transversal. Angle 1 measures (4x + 28)°, and the angle adjacent to the alternate exterior angle with angle 1 measures (14x + 8)°. What is the value of x?
Answer:
The value of x is 8
Step-by-step explanation:
In the figure below,
The alternate exterior angles are 1 and 2
Alternate Exterior Angles are a pair of angles that lie on the outer side of each of those two lines but on opposite sides of the transversal and they are equal
Also angle 2 and 3 are adjacent and supplementary angle and their sum is equal to 180 degrees
Given that
[tex]\angle 1 = (4x + 28)^{\circ}[/tex]
[tex]\angle 3 = (14x + 8)^{\circ}[/tex]
Now we know that
[tex]\angle 2 + \angle 3 = 180 ^{\circ}[/tex]
[tex]\angle 2 +(14x+8) = 180[/tex]
[tex]\angle 2 = 180 - 14x -8[/tex]
[tex]\angle 2 = 172 - 14x[/tex]
We also know that
[tex]\angle 1 = \angle 2[/tex]
[tex]4x + 28 = 172 -14x[/tex]
[tex]4x + 14x = 172 - 28[/tex]
[tex]18x = 144[/tex]
[tex]x =\frac{144}{18}[/tex]
x = 8
Now
[tex]\angle 1 = (4x+28)^{\circ} = (4(8) +28)^{\circ} = (32 +28)^{\circ} =(60)^{\circ}[/tex]
[tex]\angle 3= (14x+8)^{\circ} = (14(8) +8)^{\circ} = (112 +8)^{\circ} =(120)^{\circ}[/tex]
Answer:
The value of x is 8
Step-by-step explanation:
Which description is correct for the polynomial −5x2−3x+3 ?
quartic binomial
quadratic binomial
quadratic trinomial
cubic binomial
The correct description for the polynomial [tex]-5x^{2} -3x+3[/tex] is quadratic trinomial.
Explanation:
Option a: Quartic binomial
A polynomial with degree 4 is said to be quartic polynomial. Also, if the polynomial contains two terms then it is binomial.
Hence, the polynomial [tex]-5x^{2} -3x+3[/tex] is not quartic binomial.
Option b: Quadratic binomial
A polynomial with degree 2 is said to be quadratic polynomial. Also, if the polynomial contains two terms then it is binomial.
Hence, the polynomial [tex]-5x^{2} -3x+3[/tex] is not quadratic binomial.
Option c: Quadratic trinomial
A polynomial with degree 2 is said to be quadratic polynomial. Also, if the polynomial contains three terms then it is binomial.
Hence, the polynomial [tex]-5x^{2} -3x+3[/tex] is a quadratic trinomial.
Option d: Cubic binomial
A polynomial with degree 3 is said to be cubic polynomial. Also, if the polynomial contains two terms then it is binomial.
Hence, the polynomial [tex]-5x^{2} -3x+3[/tex] is a cubic binomial.
Thus, the polynomial [tex]-5x^{2} -3x+3[/tex] is quadratic trinomial.
Answer:
quadratic trinomial
Step-by-step explanation:
Which of the following sequences of transformations is used to obtain figure A’ B’ C’ D’ from figure ABCD?
Answer:
Last one
Step-by-step explanation:
Imagine it as a mirror or like a paper folding in half, then figure out the direction it shifts.
Tina has 18 sunflower seeds in 15 Daisy seeds she wants to distribute them equally into pots then planting them with no seeds left over what is the greatest number of pots Tina can use
Answer:11
Step-by-step explanation:
Add 18 and 15 then find the GCF
The maximum number of pots she can make is 15.
What is subtraction?The process of subtracting one number from another is known as subtraction.
Given that, Tina has 18 sunflower seeds and 15 daisy seeds.
Since Tina wants to distribute the sunflower seeds and daisy seeds equally in each pot, each pot must contain at least one daisy seed and one sunflower seed.
Therefore, if, she has 1 daisy seed and 1 sunflower seed in each pot, then she can make 15 pots, as there are only 15 daisy seeds.
Now, there are only 3 sunflower seeds left but she cannot use them to make a pot as there are no daisy seeds.
Hence, the maximum number of pots she can make is 15.
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Let g(x)=9x−10 and evaluate g(x+h)−g(x)/h
Answer:
[tex]\frac{g(x+h)-g(x)}{h}=9[/tex]
Step-by-step explanation:
we have
[tex]g(x)=9x-10[/tex]
To find out g(x+h) substitute the variable x by the variable (x+h) in the function g(x)
so
[tex]g(x+h)=9(x+h)-10[/tex]
[tex]g(x+h)=9x+9h-10[/tex]
Evaluate
[tex]\frac{g(x+h)-g(x)}{h}[/tex]
we have
[tex]g(x+h)=9x+9h-10[/tex]
[tex]g(x)=9x-10[/tex]
substitute in the expression
[tex]\frac{9x+9h-10-(9x-10)}{h}[/tex]
[tex]\frac{9x+9h-10-9x+10)}{h}[/tex]
[tex]\frac{9h}{h}[/tex]
[tex]9[/tex]
therefore
[tex]\frac{g(x+h)-g(x)}{h}=9[/tex]
The high temperature in Fairbanks, Alaska was 12.2 degrees, then that night it fell 48.4 degrees. The next morning, it rose 17.1 degrees. What was the temperature in the morning?
Answer:
The temperature next morning was - 19.1 degrees
Step-by-step explanation:
High temperature in Fairbanks, Alaska = 12.2 degrees
Temperature that night = 12.2 - 48.4
Temperature that night = -36.2 degrees
Temperature next morning = -36.2 + 17.1
Temperature next morning = -19.1 degrees
The temperature next morning was - 19.1 degrees
What is the simplified form for (2x^8)*3y^9*2x^4=
Answer:
12x12y9
Step-by-step explanation:
83.40 divided by 12
Answer:
3.33 or 10/3
Step-by-step explanation:
simplify by dividing 40/12 by 4:
10/3 or 3.33
The value of the answer on dividing 83.40 by 12 is 6.95, i.e. 83.40 ÷ 12 = 6.95.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.
Given:
83.40 divided by 12,
The above expression can be written as,
83.40 ÷ 12
Divide the term 83 by 12. You get a quotient of 6 and a reminder of 11 put the dot and then take the value of 4 down, the number will be 114 divided by 12. You will get 9 quotients and 6 as a reminder, Then drop the value 0 and the new number is 60, divide 60 by 12 you will get question 5 and the remainder zero.
Thus, 83.40 ÷ 12 = 6.95.
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evaluate log base 12 of y^2, given log base 12=16
The value of log base 12 of y² is evaluated by using the power rule of logarithms. Given that log base 12y equals 16, the value of log base 12 of y² is calculated to be 32.
The student asked to evaluate log base 12 of y², given that log base 12y = 16. From the given information, we have:
log12(y) = 16
Using the power rule of logarithms, which states that logb(xy) = y. logb(x), we can express the asked expression log12(y²) as:
log12(y²) = 2 . log12(y)
Since we are given that log12(y) = 16, we can substitute this value into our previous equation:
log12(y²) = 2 . 16 = 32.
Therefore, the value of log12(y²) is 32.
What is the equation of the line that passes through the point (-4, -3) and has a slope of 5?
y = 5x - 17
y = 5x - 11
y = 5x + 11
y = 5x + 17
Answer:
y = 5x + 17
Last choice
Step-by-step explanation:
The equation for a line can be written in the form y = mx + b. (This is called slope-intercept form).
"x" and "y" mean points on the line.
"m" means the slope of the line, which is how steep the line is.
"b" means the y-intercept, which is when the line hits the y-axis.
To write an equation in slope-intercept form, we need the slope and y-intercept.
We know the slope needs to be 5.
m = 5
We know one point on the line, (-4, -3). Points are written (x, y), so:
x = -4
y = -3
Substitute the numbers we know for "m", "x" and "y" into the equation for a line. Then, we can isolate 'b' to know what it equals.
y = mx + b
-3 = (5)(-4) + b Multiply to simplify
-3 = -20 + b Start isolating 'b'
-3 + 20 = -20 + 20 + b Add 20 to both sides to cancel out on the right.
-3 + 20 = b Solve the left side.
17 = b Answer
b = 17 Put variable on left side for standard formatting
Now that we know m = 5 and b = 17, rewrite the equation in the form y = mx + b.
y = 5x + 17
what is the mode of 23,95,100,23,100,100
Answer:
The number that occurs most often in a set of numbers
in this case, the number 100 occurs more than any other number in the set. This means that the mode for this set of data is 100.
Answer:
100
Step-by-step explanation:
Mode is the number that appears most often
Hence
In the given set of numbers
The mode is 100
A vehicle is moving in a straight line. The velocity Vms^-1 at time t seconds after the vehicle starts is given by V = A (t− 0.05t^2) for 0 ≤ t ≤ 15. What is the value of A?
Answer:
The value of A is [tex](-\infty, 0) \cup(0, \infty)[/tex]
Step-by-step explanation:
Given:
[tex]V = A (t- 0.05t^2)[/tex]
When velocity V= 0
we have
[tex]A (t- 0.05t^2) = 0[/tex]
[tex](t- 0.05t^2) = 0[/tex]
[tex]t = 0.05t^2[/tex]
t =0 , t = [tex]\frac{1}{0.05}[/tex]
t = 0 , t = 20
So when we draw a graph,The resulting graph will be a quadratic graph.
[tex]\frac{dv}{dt} = A[1 - 0.1t][/tex]
[tex]\frac{dv}{dt} = 0[/tex]
t=10 sec
At t=10, the velocity will be
[tex]v(10) = [10 -0.05(10)^2][/tex]
[tex]v(10) = [10 -5][/tex]
[tex]v(10) = 5A[/tex]
But according to the question A is not dependent on t
So A can be any value other than zero
Answer:
Step-by-step explanation:
Find the width of a rectangular patio with a length of 16 feet and an area of 200 square feet
Answer:
Step-by-step explanation:
You already know the area, so just reverse the steps. Example: 200ft divided by the length which is 16ft equals 12.5 feet
Jevon has money. Angie has twice as much money as Jevon. Kenny Has five dollars more than Angie. How much more money does each of them have if the sum of their treasure is $80?
Answer:
Money Jevon would be having = $15
Money Angie would be having = $30
Money Kenny would be having = $35
Step-by-step explanation:
Given:
Angie has twice as much money as Jevon
Kenny has $5 more than Angie.
The sum of their treasure = $80
To find how much money does each of them have.
Solution:
Let Jevon has money in dollars = [tex]x[/tex]
Angie having twice as much money as Jevon would have in dollars = [tex]2x[/tex]
Kenny having $5 more than Angie would have in dollars = [tex]2x+5[/tex]
The sum of their money will be given as:
⇒ [tex]x+2x+2x+5[/tex]
Combining like terms.
⇒ [tex]5x+5[/tex]
The sum of their treasure = $80
So, the equation to find [tex]x[/tex] would be given as:
[tex]5x+5=80[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by 5.
[tex]5x+5-5=80-5[/tex]
[tex]5x=75[/tex]
Dividing both sides by 5.
[tex]\frac{5x}{5}=\frac{75}{5}[/tex]
∴ [tex]x=15[/tex]
Thus,
Jevon has = $15
Angie has = [tex]2\times \$15[/tex] = $30
Kenny has = [tex]\$30+\$5[/tex] = $35
Can someone help me with the problem in the image
Answer:
PT=57
Step-by-step explanation:
If PT=7x+8 and TQ=9x-6 qnd we have that T is the midpoint of PQ.
Since T is the midpoint of PQ, [tex]PT=TQ[/tex]
We substitute into the equation to get:
[tex]7x+8=9x-6[/tex]
Group the similar terms to get:
[tex]8+6=9x-7x[/tex]
We simplify now to get:
[tex]14=2x[/tex]
Divide through by 2 to get:
[tex]x=7[/tex]
PT=7*7+8=49+8=57
Please help!!!!!!!!!
The fraction [tex]\frac{13}{50}[/tex] is spent on federal income taxes.
Step-by-step explanation:
Given,
Combined income of parents = $20,000
Amount paid in federal income taxes = $5200
Fraction = [tex]\frac{Amount\ paid\ in\ taxes}{Combined\ income}[/tex]
Fraction spent on taxes = [tex]\frac{5200}{20000}[/tex]
Fraction spent on taxes = [tex]\frac{52}{200}[/tex]
Fraction spent on taxes = [tex]\frac{13}{50}[/tex]
The fraction [tex]\frac{13}{50}[/tex] is spent on federal income taxes.
Keywords: fraction, division
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Two cards are drawn from a well a shuffled standard deck of match each scenario to its probability
You weren't being specific so I searched up the question.
The correct answer is:
A. 1/169 - The probability of drawing a king followed by a queen with a replacement.
B.1/442 - The probability of drawing a red ace followed by another red ace without replacement.
C.4/442 - The probability of drawing a 3 or 5 followed by 4 or 6, with replacement.
D.1/52 - The probability of drawing a spade followed by a jack of ant color with replacement.
Keep in mind this is not my answer since I got it from somebody else.
Answer:
Refer to the picture bellow
Step-by-step explanation:
which of the following is a correct interpretation of the expression -4 - (-7)
Answer:
The answer is 3
Step-by-step explanation:
i) -4 - (-7) = -4 + 7 = 7 - 4 = 3 .... since (minus) [tex]\times[/tex] (minus) = plus
Martha wants to make four necklaces that are the same length.She asked her friends to cut the string for the necklaces 15 paper clips long. Would all the lengths be the same? Explain your answer.
Answer:
No. All the lengths will not be the same.
Step-by-step explanation:
Martha wants to make four necklaces that are the same length. She asked her friends to cut the string for the necklaces 15 paper clips long.
We are asked whether all the four lengths will be of the same length or not.
If Martha uses the paper clips to measure the lengths of the cut pieces of strings, then all the lengths will not be the same because 15 is not divisible by 4.
The lengths maybe 4, 4, 4, and 3 paper clips of lengths. (Answer)
Length of each string is 3.75 paper clips
Given that;Number of neckless = 4
Length of string = 15 paper clips
Find:Length of each string
Computation:Length of each string = Length of string / Number of neckless
Length of each string = 15 / 4
Length of each string = 3.75 paper clips
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Mr. Pham has 410,000 in a retirement account that earns 3.85% simple interest each year. Find the amount earned each year by this investment
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$410000\\ r=rate\to 3.85\%\to \frac{3.85}{100}\dotfill &0.0385\\ t=years\dotfill &1 \end{cases} \\\\\\ I=(410000)(0.0385)(1)\implies I=15785[/tex]
In one city, there are four straight streets that form a square block. The length of each side of the block is 154 m. Find the perimeter of the square defined by this city block.
Final answer:
The perimeter of the square defined by the city block is 616 meters.
Explanation:
In order to find the perimeter of the square block, we need to know the length of each side. The question states that each side of the block is 154 m, so we can use this information to calculate the perimeter. The perimeter of a square is equal to four times the length of one side, so in this case it would be 4 * 154 m = 616 m. Therefore, the perimeter of the square defined by this city block is 616 meters.
4. Emily bought 3 shirts for $12.50 each and a pair of shorts for $20. She had a coupon for $3 off
her purchase, before sales tax. Sales tax is 6%. How much did Emily pay for the clothes after the
coupon and sales tax?
Answer: $57.77
Step-by-step explanation:
3 x 12.50 = 37.5 + 20 = 57.5
57.5- 3 = 54.5
54.5 x .06 = 3.27
54.5 + 3.27 = $57.77 is the answer
I know there are too many of them but I need help. Giving brainliest
total vol. = 24
If length x base x height = vol. of cuboid
then,
vol. of cuboid = width
base x height
24 / (4 x 2) =
24/8=
3ft
A house is worth 125,000 when it is 2 years old and 135,150 when it is 7 years old. According to this model, how much will the house be worth when it is 16 years old
Final answer:
The house will be worth $153,420 when it is 16 years old, calculated by finding the annual increase in value from the given data and projecting this increase over the relevant time period.
Explanation:
To calculate the worth of the house when it is 16 years old, we need to establish the rate at which the house's value is increasing over time, based on the information given for its value at 2 years and at 7 years. The house is valued at $125,000 when it is 2 years old and $135,150 when it is 7 years old, showing an increase of $10,150 over 5 years.
First, we find the annual increase in value by dividing the total increase by the number of years:
Annual increase = $10,150 / 5 = $2,030.
Next, we predict the value when the house is 16 years old by multiplying the annual increase by the number of years from the starting point (2 years old) to 16 years old:
14 years (from year 2 to year 16) × $2,030 annual increase = $28,420 increase since year 2.
Finally, we add this increase to the original value at year 2:
Projected Value at Year 16 = $125,000 + $28,420 = $153,420.
Hence, according to the model, the house will be worth $153,420 when it is 16 years old.
What percent of 500,000 equals 250,000?
Answer:
The answer is 50%. 50% of 500,000 is 250,000.
During the summer, a property owner will pay $24.72 plus $1.32 per hcf for Conservation Usage. The bill for Conservation Usage would be between or equal to $31.32 and $52.12. How many hcf can the owner use if she wants her usage to stay in the conservation range? Enter truncated values for answers. Example: Enter 8.93 as 8 and 6.34 as 6.
Answer:
The owner can use between 5 and 20 HCF to stay in the conservation range
Step-by-step explanation:
Let's calculate the number of HCF, this way:
Lower value = (31.32 - 24.72)/1.32 = 6.60/1.32 = 5
Upper value = (52.12 - 24.72)/1.32 = 27.4/1.32 = 20.76 = 20 as truncated value
The owner can use between 5 and 20 HCF to stay in the conservation range
The owner can use between 5 and 20 hcf to stay within the conservation range.
Explanation:To find the range for the number of hcf the owner can use, we need to subtract the base cost from the maximum and minimum bill amounts. The base cost is $24.72, so subtracting this from the maximum bill amount of $52.12 gives us $27.40. Similarly, subtracting the base cost from the minimum bill amount of $31.32 gives us $6.60. In order to determine the maximum and minimum number of hcf, we divide these amounts by the additional cost per hcf, which is $1.32.
The maximum number of hcf would be $27.40 divided by $1.32, which is approximately 20 hcf. The minimum number of hcf would be $6.60 divided by $1.32, which is approximately 5 hcf.
Therefore, the owner can use between 5 and 20 hcf to stay within the conservation range.
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