Answer:
Slope= -2
y-intercept= -4
Step-by-step explanation:
To find the slope and y-intercept of a given equation, first rearrange the equation such that it is in the slope-intercept form. In the slope-intercept form, the coefficient of y is 1 and the rest are moved to the left hand side of the equation.
[tex]\textcolor{steelblue}{\text{Slope-intercept form}}[/tex]
y= mx +c, where m is the slope and c is the y-interceptGiven equation: 6x +3y= -12
Let's leave the y term on the left of the equation and bring the rest to the right.
3y= -6x -12
To ensure that the coefficient of y is 1, divide both sides by 3.
y= -2x -4
The equation is now in the slope-intercept form.
The slope is the coefficient of x (the number that comes before x), thus the slope is -2. The y-intercept is -4.
which trig ratio
determine which trig ratio to use to solve for x
Answer:
Step-by-step explanation:
1.cos
2.sin
3.cos
4.tan
5.sin
6.tan
Step-by-step explanation:
remember the basic trigonometry setup ?
the norm circle (radius = 1) with a horizontal and a vertical line through the center of the circle.
and then there is an angle at the center indicated by the horizontal line and an inclined (by that angle) radius line connecting the center and the circle arc.
this inclined radius line is then the baseline (Hypotenuse) of a right-angled triangle, and the legs of that triangle are sine and cosine of the angle at the center (sine is the vertical leg, cosine is the vertical leg).
in essence (at least it works for me), when given such right-angled triangle problems, I always try to rotate and/or flip this triangle until it looks like the described situation above.
the only other thing to remember is that for triangles inside circles with a different radius than 1, everything is multiplied by the actual radius (it really happens also for the norm circle, but multiplying by 1 does not really change anything, right ?).
so, now for the given problems :
1)
x is the radius of the circle.
we can make 68° the defining angle of that trigonometric situation. so, the top right vertex would be the center of the circle with radius x.
then
30 = cos(68)×x
x = 30/cos(68)
= 80.08401488...
2)
60 is the radius of the circle.
x is the defining angle.
then
15 = sin(x)×60
sin(x) = 15/60 = 1/4
x = 14.47751219...°
3)
x is the radius of the circle.
22° is the defining angle.
then
14 = cos(22)×x
x = 14/cos(22)
= 15.0994864...
4)
the unnamed side is the radius of the circle. let's call it "s".
54° is the defining angle.
then
47 = cos(54)×s
x = sin(54)×s
x/47 = sin(54)×s / (cos(54)×s) = sin(54)/cos(54) = tan(54)
x = 47×tan(54) or 47×sin(54)/cos(54)
= 64.68995026...
5)
14 is the radius of the circle.
41° is the defining angle.
then
x = sin(41)×14
= 9.184826406...
6)
the unnamed side is the radius of the circle. let's call it "s".
x is the defining angle.
then
57 = cos(x)×s
9 = sin(x)×s
9/57 = sin(x)×s / (cos(x)×s) = sin(x)/cos(x) = tan(x)
x = 8.972626615...°
On average, Evie’s chicken lays 3 eggs every 15 days. At this rate, how many days will it take Evie’s chicken to lay 45 eggs?
Answer:
43 ffhfhfhfhfhfhchchchchchc
Answer:
It will take 225 days for Evie's chicken to lay 45 eggs
Step-by-step explanation:
What is the volume of this right prism? 1200 in³ 1800 in³ 2040 in³ 3600 in³ Right triangular prism. The height of the prism is labeled as 15 in. The base of the prism is a triangle with the base labeled as 30 in., the height labeled as 8 in., and the other 2 sides of the triangle labeled as 17 in.
Please help asap!!!
Volume of right prism is 1800 in³, So option 'B' is the correct answer to the following question.
Volume of right prismWhat information do we have?
Height of the prism is labeled = 15 in.
Base of the prism is a triangle with the base = 30 in
Height labeled = 8 in
Volume of right prism = Area of base triangle × Height
Volume of right prism = (1/2)(b)(h) × Height
Volume of right prism = (1/2)(30)(8) × 15
Volume of right prism = (30)(4) × 15
Volume of right prism = 120 × 15
Volume of right prism = 1800 in³
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Answer:
The answer is B. 1800 [tex]in^{3}[/tex]
Step-by-step explanation:
I took the test
Triangle ABC has side lengths 12, 16, and 20. Do
the side lengths form a Pythagorean triple?
Explain.
Answer:
no they dont form a Pythagorean triple
Step-by-step explanation:
a2 + b2 = c2
Find the perimeter.
Write your answer as a fraction or as a whole or mixed numbe
5 1 cm
10
5 cm
10
Bloc
5
cm
10
5 cm
10
Answer:
20 2/5 cm
Step-by-step explanation:
4 ( 5 1/10)
4 × 51/10
2×51/5
0.4x51
=20 2/5
Determine
the rotation around the origin that was performed to transform the preimage on the left to its image on the right.
Answer:
-90 degrees counter clock wise
Step-by-step explanation:
it goes the opposite of a clock so it would be called -90 degrees counter clockwise, you could also say 270 degrees clockwise if the other isnt an option.
Which statement describes the behavior of the function f (x) = startfraction 2 x over 1 minus x squared endfraction?
The statement that describes the behavior of the function f(x) = 2x/(1-x²) is given by: Option B: The graph approaches 0 as x approaches infinity
How to find the value of the function as x approaches infinity (+ve or -ve)?If limits exist, we can take limits of the function, where x tends to -∞ or ∞, and that limiting value will be the value the function will approach.
For the considered case, the function is:
[tex]f(x) = \dfrac{2x}{1-x^2}[/tex]
The missing options are:
The graph approaches –2 as x approaches infinity.The graph approaches 0 as x approaches infinity.The graph approaches 1 as x approaches infinity.The graph approaches 2 as x approaches infinity.So we need to find the limit of the function as x approaches infinity.
[tex]lim_{x\rightarrow \infty}f(x) = lim_{x\rightarrow \infty}\dfrac{2x}{1-x^2} = lim_{x\rightarrow \infty}\dfrac{2x/x^2}{1/x^2 - 1} = lim_{x\rightarrow \infty}\dfrac{2/x}{1/x^2 - 1}\\\\lim_{x\rightarrow \infty}f(x) = \dfrac{lim_{x\rightarrow \infty}(2/x^2)}{lim_{x\rightarrow \infty}(1/x^2 - 1)} = \dfrac{0}{0-1} = \dfrac{0}{-1} = 0[/tex]
Since the value of the function approaches 0 as x approaches infinity, so as its graph will do.
Thus, the statement that describes the behavior of the function f(x) = 2x/(1-x²) is given by: Option B: The graph approaches 0 as x approaches infinity
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2640 yards= ________ miles
complete each conversion
After converting yards to miles:
2640 yards = 1.5 miles
Given,
2640 yards= ________ miles
Now,
To convert to yard to miles the conversion factor is 0.000568182.
So,
1 yard ⇒ 0.000568182 miles
Multiply 2640 on both sides,
2640 yards ⇒ 1.5 miles.
Therefore 2640 yards is equivalent to 1.5 miles.
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Help please thank you
Answer:
[tex] = 2 \times 4 = 8 \\ = 5 \times 5 = 25 \ \\ \frac{1}{2} \times 5 \times 3 = 7.5 \\ 7.5 + 8 + 2.5 = 18[/tex]
( Pls help ASAP) Will give 20 points if you answer 2 questions))
Answer:
1. -3 2. y=-1
Step-by-step explanation:
put the equation below into vertex form.
y=(x+9)(x+25)
Answer:
Step-by-step explanation:
A puppy weighs 4 pounds. How many ounces does the puppy weigh?
Answer:
64 ounces
Step-by-step explanation:
Since 1 lb = 16 oz, just do 4 × 16 = 64
If puppy weighs 4 pounds then the weigh in ounces is 64 ounces.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
There are 16 ounces in a pound.
1 pound= 16 ounces.
Given that puppy weighs 4 pounds.
We have to find the wight in ounces.
To convert pounds to ounces, we need to multiply the weight in pounds by 16.
The puppy weighs 4 pounds x 16 ounces/pound
= 64 ounces
Hence, if puppy weighs 4 pounds then the weigh in ounces is 64 ounces.
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PLEASE HELP
One number is 4 more than another number. If the greater number is x, what is the other number?
Answer:
12
Step-by-step explanation:
it would be 12 if it is unknown so 12 because y and x are used for unknown numbers.
i hope i got it right just tell me if this is wrong, please
The expression for the smaller number is q = x - 4
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the greater number be p = x
Let the smaller number be q
If the greater number is x, then the other number must be 4 less than x.
We can express this algebraically as:
On simplifying the equation , we get
q = x - 4
Hence , the other number is x - 4.
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How many solutions are there for the quadratic equation?
f(x)=5x^2+3x+2
Answer:
2
Step-by-step explanation:
[tex]5x^2 +3x +2 = 0\\\\\text{Apply the quadratic formula,}~ x=\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\\text{In this case,}~a= 5, ~ b = 3~ \text{and}~ c = 2\\\\ \\x=\dfrac{-3\pm \sqrt{3^2 -4\cdot 5 \cdot 2}}{2\cdot 5}\\\\~~~=\dfrac{-3 \pm \sqrt{9-40}}{10}\\\\~~~=\dfrac{-3 \pm \sqrt{-31}}{10}\\\\~~~=\dfrac{-3 \pm i\sqrt{31}}{10}\\\\\text{So, there are 2 solutions,}~ x=\dfrac{-3 + i\sqrt{31}}{10}~ \text{and} ~x=\dfrac{-3 -i\sqrt{31}}{10}[/tex]
Another way to find the number of solutions is by looking at the highest exponent(Degree), which indicates the number of solutions.
[tex]\\ \rm\rightarrowtail 5x^2+3x+2=0[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm \sqrt{9-40}}{10}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm\sqrt{-31}}{10}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm\sqrt{31}i}{10}[/tex]
a 21ft ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 19ft from the base of the building. how high up the wall does the ladder reach
Answer:
According to the graph:
H^2 + 10^2 = 21^2
Solve as:
H = 18.19 feet
So the height is 18.19 feet
Electric guitar kits originally cost $d$ dollars online. You buy the kits on sale for $50\%$ of the original price, plus a shipping fee of $\$4.50$ per kit. After painting and assembly, you sell each guitar online for $\left(1.5d+4.5\right)$ dollars. Find your profit on each guitar sold.
let's keep in mind that Profit = Revenue - Costs.
so each guitar costs originally "d" dollars online.
you buy the kits at half price, 50% of the original price, well, the original price is "d", half "d" is just 0.5d, and there's a shipping charge of $4.50. So the Cost to get one kit alone for you is 0.5d + 4.50.
After some work, you resell the kits online for 1.5d + 4.5, so since that's the selling price that is your Revenue for one kit.
[tex]\stackrel{\textit{\Large Profit}}{\stackrel{Revenue}{(1.5d~~ + ~~4.50)}~~ - ~~\stackrel{Costs}{(0.5d~~ + ~~4.50)}}\implies 1.5d+4.5-0.5d-4.5 \\\\\\ 1.5d-0.5d+4.5-4.5\implies 1d\implies d[/tex]
PLEASE HELP! DUE TODAY! TY!
Use the diagram to find the value of x and the measure of Arc MR. (MR) =(3x+19)° and (LK) =189°
Work:
x =
(MR) =
Answer: x=12, (MR)=55
Step-by-step explanation:
Do we, as a society, rely on technology too much?
no. the word technology spans every invention ever created. we don't.
Answer:
Yes, We as a society rely too much on technology because it is the new thing that everyone wants or needs. Technology can buy your groceries and food with a single click.
Step-by-step explanation:
Christine went on a passenger train that traveled 80 miles in one hour. How many miles will it travel in six hours?
Answer:
480
Step-by-step explanation:
[tex]80*6[/tex] = 480
Answer:
She will travel 480 miles in 6 hours
Step-by-step explanation:
All you need to do is Multiply 80 by 6 to get an answer of 480.
Hope that helps!
PLEASE HELP ill like!!!!!! Its 20 points
Answer:
1. Degree= 6, trinomial
2. degree= 4, binomial
Step-by-step explanation:
1. The largest exponent is 6 making it the degree and there are three terms because (m^5n^2), (mn^2), (n^6).
2. Since (9a^2bc^2) has the more than 1 exponent, you add them and the degree is 4. There are two terms because (2a^3b), (9a^2bc^2).
Sam rode a bull for 8 seconds.
Maddie rode a bull for 2 fewer seconds than Sam did.
How long did Maddie ride her bull?
Answer:
is it 7?
Step-by-step explanation:
if he rode for 8 seconds and it says she rode for 2 seconds FEWER are you not subtracting from 8 to get 7?
[tex] { \alpha }^{2} \beta + \alpha { \beta }^{2} [/tex]
Please solve this
14x - 2x + 3
12x + 3
3 (4x + 1)
4x+ 1
1
-8
3(5x + 9)
3(5x + 9)
= 3(5x + 9)
= 5x + 9
= x+9
=x
Answer:
-1/4
Step-by-step explanation:
14x - 2x + 3 = 0
12x + 3 = 0
12x = -3
12x/12 = -3/12
x = -1/4
sandra calculated the missing side of one of these three triangles using the pythagrean therom which triangle is it
Answer:
right angled triangle
Step-by-step explanation:
the only triangle that this formula can be used to find a side is the right angled triangle
helppp plsss. i have to turn this in asap
Answer:
y= 2x-5
Step-by-step explanation:
The slope formula is m=(y2-y1)/(x2-x1)
-3-1 / 1-3 = -4/-2= 2=m
The Y interception- y=mx+b using coordinates (3,1)
1=2(3)+b
1=6+b (subtracting 6 on both sides to isolate b)
-5=b
plug it in
y=2x-5
Suppose a charity received a donation of $22.2 million. If this represents 34% of the charity’s donated funds, what is the total amount of its donated funds?
Answer:
ok so lets make this into a algrebra equation
22.2(mil)=0.34x
divide by 0.34
65294117.6471=x
x=65294118
Hope This Helps!!!
310, 304, 298, ...
Find the 47th term.
Answer:
The answer is 34
Step-by-step explanation:
Given;a₁ = 310a₂ = 304a₃ = 298n = 47To Find;a₄₇ = ?Formula;aₙ = a + (n – 1) × dNow,
Common Difference (d)
d = a₂ – a₁ = 304 – 310 = -6
d = a₃ – a₂ = 298 – 304 = -6
Here, common difference is same everywhere
So,
aₙ = a + (n – 1) × d
a₄₇ = 310 + (47 – 1) × (-6)
a₄₇ = 310 + 46 × (-6)
a₄₇ = 310 – 276
a₄₇ = 34
Thus, The 47th term of this sequence is 34.
There are 777 students in a class: 222 boys and 555 girls. If the teacher picks a group of 333 at random, what is the probability that everyone in the group is a girl?
The probability is 0.1429.
The probability that the first person chosen is a boy is 5/7. The probability that the second is a boy is 4/6; the third, 3/5; and the fourth, 2/4. Both the numerator and denominator decrease every time, because you lose a boy to choose from and you lose a student to choose from as well. This gives us:
5/7(4/6)(3/5)(2/4) = 120/840 = 0.1429.
The probability that everyone in the group is a girl is 2/7.
What is probability?Probability sampling is defined as a sampling technique in which the researcher chooses samples from a larger population using a method based on the theory of probability.
Total number of students in a class = 7
Number of boys students = 2
Number of girls students = 5
The probability that everyone in the group is a girl is;
[tex]\rm Probability =\dfrac{Total \ number \ of \ girls}{Total \ number \ of \ boys}\\\\Probability=\dfrac{2}{7}[/tex]
Hence, the probability that everyone in the group is a girl is 2/7.
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In creating a new scale for the mercury thermometer, Anders Celsius initially set the boiling point of water at _____. A. 0° b. 32° c. 100° d. 273°.
The thermometer is a device that is used to measure the temperature gradient. Anders needs to set the boiling point of water at 100° C.
What is a thermometer?
The thermometer is a device that is used to measure the temperature gradient or the temperature of a body/object.
The boiling point of water is 100°C, therefore, Anders needs to set the boiling point of water at 100° C.
Thus, Anders needs to set the boiling point of water at 100° C.
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help me plssss ‼️‼️‼️
teddy bears = 80
hope it helps..!!!