Answer:
CONSIDER THE POINTS (1,4) and (2,7)
[tex]m = \frac{y1 - y2}{x1 - x2} \\ [/tex]
m=(7-4)/(2-1)
=3/1
m=3x
c=1
y=3x+1
the answer is option A
Answer:
y=3x+1
Step-by-step explanation:
here is your answer
Round 9.107 to the nearest tenth.
Answer:
9.1
Step-by-step explanation:
Answer:9.1
Step-by-step explanation: simply remove the 2 digits after 1 as the tenth place is always one digit after the point
Given tan t = 2/3 and that pi <= t <= 3pi/2. Find exact value for each of the following:
a) sec t
b) cos t
c) sin t
d) csc t
e) cot t
well, first off let's notice something about angle "t", is between π and 3π/2, or namely the III Quadrant, where both "x" or adjacent side as well as "y" or opposite side are negative.
something else noteworthy is that, the hypotenuse is just a radius length and thus is never negative.
[tex]tan(t)=\cfrac{2}{3}\implies tan(t)=\cfrac{\stackrel{opposite}{-2}}{\underset{adjacent}{-3}}\qquad \textit{let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c =\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{(-3)^2+(-2)^2}\implies c = \sqrt{9+4}\implies c = \sqrt{13}[/tex]
[tex]\rule{34em}{0.25pt}\\\\ sec(t)=\cfrac{\stackrel{hypotenuse}{\sqrt{13}}}{\underset{adjacent}{-3}}~\hfill cos(t)=\cfrac{\stackrel{adjacent}{-3}}{\underset{hypotenuse}{\sqrt{13}}}\implies \cfrac{-3\cdot \sqrt{13}}{\sqrt{13}\cdot \sqrt{13}}\implies \cfrac{-3\sqrt{3}}{13}[/tex]
[tex]sin(t)=\cfrac{\stackrel{opposite}{-2}}{\underset{hypotenuse}{\sqrt{13}}}\implies \cfrac{-2\cdot \sqrt{13}}{\sqrt{13}\cdot \sqrt{13}}\implies \cfrac{-2\sqrt{13}}{13} \\\\\\ csc(t)=\cfrac{\stackrel{hypotenuse}{\sqrt{13}}}{\underset{opposite}{-2}}~\hfill cot=\cfrac{\stackrel{adjacent}{-3}}{\underset{opposite}{-2}}\implies \cfrac{3}{2}[/tex]
how do you solve 8/14 = 2/x
Answer:
x = 3 1/2
Step-by-step explanation:
8/14 = 2/x
Using cross products
8*x = 14*2
8x = 28
Divide by 8
8x/8 = 28/8
x = 7/2
x = 3 1/2
Solve for x in this inequality. Show all your work and
graph your solution.
4(x-3)<2x-4
Answer:
x<4
Step-by-step explanation:
To solve for x in the inequality equation, the terms should be rearranged such that x is on one side and integers are on the other side.
First, expand 4(x-3).
This will obtain:
[tex]4x - 12 < 2x - 4[/tex]
Now, shift x terms and integers on each side.
[tex]4x - 2x < - 4 + 12[/tex]
After simplifying, it will get:
[tex]2x < 8[/tex]
Finally, we can solve for x.
[tex]x < 4[/tex]
We can also draw the respective graph (please don't mind my drawings), where the area shaded in green is the range.
A computer company invested a total of $242 million in research and development in its scanners and video digitizers. If the amount the company spent on research and development on scanners was $95 million more than was spent on research and development on its video digitizers, how much in fact did the company spend on research and development on its scanners?
Answer:
$168,500,000
Step-by-step explanation:
Given that :
Total amount spent on both scanner and video digitizer research and development = $242,000,000
Let :
amount spent on scanner = x
Amount spent on video digitizer = y
Total amount spent, c = x + y
x = y + 95,000,000
Hence,
242000000 = y + 95,000,000 + y
242000000 - 95000000 = 2y
147,000,000 = 2y
y = $73,500,000
Hence, amount spent on scanners :
$73,500,000 + $95,000,000
= $168,500,000
how to get the interval?
Step-by-step explanation:
Decide on the number of classes.
Determine the range, i.e., the difference between the highest and lowest observations in the data.
Divide range by the number of classes to estimate approximate size of the interval
hope it helps.
stay safe healthy and happy...find the equation of the line that is parallel to y=2x+5 and contains the point (2, -4)
Answer:
Step-by-step explanation:
y + 4 = 2(x - 2)
y + 4 = 2x - 4
y = 2x - 8
Help plzz
7. Patrick wants to buy a new computer. He already has $275 saved and plans to save $125 each month. The price of
the computer is currently $1,850, but Patrick expects the price to drop by $100 each month. Patrick wants to
determine the number of months he will need to save
a) Ifx represents the number of months, then write an equation to represent A, the total amount Patrick saves
b) Ifx represents the number of months, then write an equation to represent the cost of the computer.
c) Use your equations from part "" and part to determine how many months he will need to save before he can
buy the computer. Show your work or explain how you got your answer.
d) If the price of the computer does not drop as expected, then how many months will it take Patrick to buy the
computer at its original cost? Show your work or explain how you got your answer.
Answer:
A) A = 275 + 125x
B) 1850 - 100x
C) 7 months
D) 13 months
Step-by-step explanation:
He has $275 saved.
He plans to save $125 each month.
We are told that the computer is currently $1,850
And the price drops $100 each month.
Thus;
A) If x represents the number of months, then equation of the amount he will save is;
A = 275 + 125x
B) If x represents the number of months, then equation to represent the total cost is;
1850 - 100x
C) To find the Number of months he will need to save, we will equate gotten in question A to the equation gotten in question B. Thus;
275 + 125x = 1850 - 100x
Rearranging;
125x + 100x = 1850 - 275
225x = 1575
x = 1575/225
x = 7 months
D) If the price doesn't drop like he is anticipating, then the cost will still be $1850. Thus;
275 + 125x = 1850
125x = 1850 - 275
125x = 1575
x = 1575/125
x = 12.6 months
Approximating to the nearest whole number gives 13 months
A household aquarium tank in the shape of a rectangular prism has a base length of 242424 inches (\text{in})(in)(, start text, i, n, end text, )and a base width of 15\,\text{in}15in15, start text, i, n, end text. The height of the water is 12\,\text{in}12in12, start text, i, n, end text above the base. During cleaning, 900900900 cubic inches of water is removed. What is the absolute value of the change in the height of the water in inches
Answer:
The absolute change in the height of the water is 9.5 inches
Step-by-step explanation:
Given
[tex]l =24in[/tex] --- length
[tex]w = 15in[/tex] --- width
[tex]h =12in[/tex] --- height
[tex]V_1 = 900in^3[/tex] --- the volume removed
Required
The absolute change in the height of the water
First, calculate the base area (b):
[tex]b = l * w[/tex]
[tex]b =24in * 15in[/tex]
[tex]b =360in^2[/tex]
The height of the water that was removed is:
[tex]H = \frac{V_1}{b}[/tex] i.e. the volume of the water removed divided by the base area
[tex]H = \frac{900in^3}{360in^2}[/tex]
[tex]H = \frac{900in}{360}[/tex]
[tex]H = 2.5in[/tex]
The absolute change in height is:
[tex]\triangle H = |h - H|[/tex]
[tex]\triangle H = |12in - 2.5in|[/tex]
[tex]\triangle H = |9.5in|[/tex]
[tex]\triangle H = 9.5in[/tex]
Help fast please??!!
Answer:
104.6
just use the cone formula and add the two together.
Jeanette uses more yarn to knit a poncho than she uses to knit a scarf. Write an inequality to represent the amount of yarn Jeanette uses to knit a poncho (p), and explain how to represent the inequality on a number line.
Answer:
[tex]p > s[/tex]
Step-by-step explanation:
Given
[tex]p \to poncho[/tex]
[tex]s \to scarf[/tex]
Required
The inequality
From the question, we understand that;
the number of p used is more than the number of s
more than means greater than.
So, the inequality is:
[tex]p > s[/tex]
To represent this on a number line.
First, we identify the position of s (i.e. scarf)
[tex]p > s[/tex] implies that p is any point to the right of s
1. Two numbers, which differ by 3, have a product of 88.
Find them.
Answer:
Let x be one of the numbers
then since they differ by 3... Let (x-3) be the 2nd Number
Their product is 88
(x-3)x = 88
x²-3x =88
x² - 3x - 88=0
Solving The quadratic eqn
x=11 or x = -8.
To check this answer
since the Numbers are x and x-3
x= 11
x-3 = 11 - 3 = 8
(x-3)x = 8x11 = 88.
Or When x=-8
(x-3) = -8 - 3 = -11
x= -8
(x-3)x = -8 x - 11 = 88.
Have a great day!
Answer:
First Set: [11, 8], Second Set: [-8, -11]
Step-by-step explanation:
The first number will be x. The second number is x-3. So now make an equation: x(x-3)=88 because their product equals 88. So now solve.
Solving:
[tex](x)(x-3)=88[/tex]
[tex]x^{2}-3x-88=0[/tex]
Now you can factor:
[tex](x-11)(x+8)=0[/tex]
[tex]x=11, x=-8[/tex]
Now plug in each number for x for the following equation:
[tex](x)(x-3)=88[/tex]
[tex](11)(11-3)=88[/tex]
[tex]88=88[/tex]
This is true.
[tex](-8)(-8-3)=88[/tex]
[tex]88=88[/tex]
This is true.
Both are true. So now you have two sets of answers.
Your welcome!
Find the value of c that makes x^2–6x + c a perfect square trinomial and write as a binomial squared.
Answer: 9
Step-by-step explanation:
Given
The function is [tex]x^2-6x+c[/tex]
To make it a perfect square, compare it with [tex](a-b)^2=a^2+b^2-2ab[/tex]
Here,
[tex]x=a,\\-6x=-2ab\\\\\therefore b=3[/tex]
So, c must be square of b i.e. 9
[tex]x^2-6x+c\Rightarrow x^2-6x+9\\\Rightarrow (x-3)^2[/tex]
Therefore, value of c is 9.
If f(x) = x2 – 1, and
g(x) = x + 2, then
f(g(x)) = [ ? ]x2+[ ]x+]
Answer:
f(g(x)) = x^2+4x+3
Step-by-step explanation:
f(x) = x^2 – 1
g(x) = x + 2
f(g(x))=g(x)^2-1=(x+2)^2-1=x^2+4x+4-1=x^2+4x+3
What is the length of leg s of the triangle below?
45
3
1072
90°
45
$
The length of the leg is 9.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
From the triangle,
S = length of the leg.
Now,
Applying the Pythagorean theorem.
√18² = 3² + s²
18 = 9 + s²
s² = 18 - 9
s² = 9
s = 9
Thus,
The length of the leg is 9.
Learn more about the Pythagorean theorem here:
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I need help solving this quick pleaseeeeeee
Answer:
Step-by-step explanation:
angle 1 and angle 2 add to 180 degree because they are supplementary angel and in supplementary angle sum of two angles is 180 degree
angle 1 and angle 3 is equal as they are vetically opposite angles and vertically opposite angles are always equal.
angle 3 and 4 add to 180 degree because they are supplementary angle and in supplementary angle sum of two angles id 180 degree.
angle 2 and angle 4 are equal because they are vertically opposite angles and vertically opposite angles are always equal.
Find the surface area of the space figure represented by the net.
90 cm2
69 cm2
75 cm2
96 cm2
1) An average soccer ball has a mass of .4 kg. If a soccer ball is kicked with a force of 750 Newtons, what is the acceleration of the soccer ball after it has been kicked?
2) If a tiger runs at a speed of about 12.3 m/s, how far will it travel in 25 seconds?
Answer:
1) 187.5ms^2
1) 187.5ms^22) 307.5m
Step-by-step explanation:
1) You can use the formula:
Force = Mass x Acceleration
750 = 4 x a
750 = 4a
750/4 = a
187.5ms^2
2)
For every one second it travels 12.3 meters therefore you can just do 12.3x25 = 307.5m
A store sells dolls for $10 each. They charge a one time shipping fee of $5. Write an equations that gives the number of dolls, d, if the store made $100.
Answer: 100 = 10d + 5
Step-by-step explanation:
Dolls are sold for $10 each so when checking the total amount made from the sale of d dolls you will multiply d by the price of each doll:
= 10 * d
= 10d
There is a $5 charge for shipping but this is one time so it is added to the total price of d dolls:
= 10d + 5
The total made was $100 so the equation above should equal $100:
100 = 10d + 5
Mrs. Tatum needs to share 4 fluid ounces of red paint equally among 5 art students. How many ounces of red paint will each student get?
Answer: [tex]\dfrac{4}{5}\ \text{ounces}\ \text{or}\ 0.8\ \text{ounces}[/tex]
Step-by-step explanation:
Given
There is 4 fluid ounces of red paint which needs to be shared among 5 students
So, division operation is needed to deduce the ounces of red paint each student will get
Each student get
[tex]\Rightarrow \dfrac{4}{5}\ \text{ounces}\ \text{or}\ 0.8\ \text{ounces}[/tex]
The value of the expression StartFraction 2 x squared Over x EndFraction plus x (100 minus 15 x) when x = 5 is.
Answer:
C. 135
Step-by-step explanation:
The value of the expression when x = 5 is 135.To find the value of the expression when x = 5, substitute the value of x into the expression and perform the calculations:
Expression: [tex](2x^2 / x) + x(100 - 15x)[/tex]
Now, replace x with 5:
[tex](2 * 5^2 / 5) + 5(100 - 15 * 5)[/tex]
Calculate the values within the parentheses first:
[tex](2 * 25 / 5) + 5(100 - 75)[/tex]
Now, perform the arithmetic inside each set of parentheses:
[tex](50 / 5) + 5(25)\\50 / 5 = 10[/tex]
Now, continue:
10 + 5 * 25 = 10 + 125 = 135
So, the value of the expression when x = 5 is 135.
To know more about expression :
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Please help me ASAP tysm
Can someone help me please
Answer:
1) B/second one
2) ???
3) C/third one
Step-by-step explanation:
1) Factoring out a number means taking out the number both sets have in common (23) so it becomes (59+21)*23.
2) What's in the sets???
3) Replace x with 8 to get 18-8=10
Which describes 9 and -9?
Answer:
opposite of each other
Hope this helps!
please help with number 5 (20 pts) those who answer all on the screen gets brainliest
Answer:
True
Step-by-step explanation:
This is an Isosceles triangle because it has two equal sides.
A bag contains 4 red marbles, 8 blue marbles and 2 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be red?
Tina has a greenhouse in which she grows strawberries. The sprinkler system in the greenhouse sprays a fine mist to ensure the strawberries get enough water. The strawberries are watered for a total of 2 hours and 45 minutes every day and the temperature in the greenhouse is kept constant at 25 °C. The clock below shows the time each morning when the sprinkler system is switched off
Answer:
a) 9:11 am
b) 77°F
Step-by-step explanation:
a) From the clock shown in the image attached, we can see that the time that the sprinkler system is switched off is at 11:56 am. Since the strawberries are watered for a total of 2 hours and 45 minutes every day, the time that the sprinkler is switched on can be gotten by subtracting 2 hours 45 minutes from 11:56 am. Hence:
Time sprinkler system is switched on = 11:56 am - 2 hours 45 minutes = 9:11 am
b) Temperature in °Farenheit = (1.8 * temperature in degree Celsius) + 32°
Temperature in °Farenheit = (1.8 * 25°) + 32° = 45° + 32°
Temperature in °Farenheit = 77°F
On George's block, the ratio of cars to houses is 8 to 5. There are 32 cars, how many houses are there?
Answer:
Step-by-step explanation:
20 houses
Answer:
20
Step-by-step explanation:
You would set it up as 8:5=32:x. Since you are multiplying the number of cars by 4, you should do the same with houses. This gives 32:20, meaning there are 20 houses on the block.
**You may want to revise multiplying and dividing with ratios. I'm always happy to help!
7X^2+20x=24
X=?
Please answer to 2 d.p
Answer:
0.76
or
-0.76
hope this helps
Is this correct? I don’t think it is at all lol. Help me please!
Keith's bank account starts with $250 and he adds $150 to it every month. If m is the number of months that have passed, then the amount of money (in dollars) in his account is given by
250 + 150m
Victoria's account starts with $2000 and she removes half of it each month. So after m months, her account has a value of
2000/2^m
If you were to plot these amounts, then
(a) Keith's account's value is indeed linear - TRUE
(b) Keith is constantly adding money to his account, so its value is increasing - FALSE
(c) Victoria's account's value involves an exponential expression - TRUE
(d) Victoria is removing money, so the value is decreasing - TRUE
Your answers are correct except for (c).