Answer:
g(x) = 4 - x^2
at x-intercept, y=0
0=4-x^2
x^2=4
x = ± 2
=> two x- intercepts, (-2,0) and (2,0)
at y-intercept, x = 0
g(x) = y = 4 - 0 = 4
y-intercept = (0,4)
The x-intercept is ( ±2 , 0 ) and y- intercerpt is (0,4).
What is an intercept?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis.
This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.
g(x) = 4 - x²
At x-intercept, y = 0
0=4-x²
x² = 4
x = ± 2
Two x- intercepts, (-2,0) and (2,0)
at y-intercept, x = 0
g(x) = y = 4 - 0 = 4
y-intercept = (0,4)
Therefore, the x-intercept is ( ±2 , 0 ) and y- intercerpt is (0,4).
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Can you answer this math homework? Please!
Step-by-step explanation:
[tex]x + 3y = 7 \\ 2x + 4y = 8 \\ x = 7 - 3y \\ 2(7 - 3y) + 4y = 8 \\ 14 - 6y + 4y = 8 \\ 14 - 2y = 8 \\ - 2y = - 6 \\ y = 3 \\ x = 7 - 3(3) \\ x = 7 - 9 \\ x = - 2[/tex]
Answer:
2x+3y=7x4
x+4y=8x3
8x+12y=27
3x+12y=24
8x-3x =5x
+12y-+12y=0
27-24=3
5x/5 3/5x
answer = x = 3/5
y=1.85
Find the circumference of the circle. Then, find the length of each bolded arc. Use appropriate notation
Answer:
[tex]\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: } \frac{3\pi}{2}\text{ mi}[/tex]
Step-by-step explanation:
The circumference of a circle with radius [tex]r[/tex] is given by [tex]C=2\pi r[/tex]. The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle [tex]\theta^{\circ}[/tex] is equal to [tex]2\pi r\cdot \frac{\theta}{360}[/tex].
Formulas at a glance:
Circumference of a circle with radius [tex]r[/tex]: [tex]C=2\pi r[/tex] Length of an arc with central angle [tex]\theta^{\circ}[/tex]: [tex]\ell_{arc}=2\pi r\cdot \frac{\theta}{360}[/tex]Question 1:
The radius of the circle is 12 m. Therefore, the circumference is:
[tex]C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}[/tex]
The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:
[tex]\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}[/tex]
Question 2:
In the circle shown, the radius is marked as 2 miles. Substituting [tex]r=2[/tex] into our circumference formula, we get:
[tex]C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}[/tex]
The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:
[tex]\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}[/tex]
what is the solution to the equation?
[tex] \frac{2 }{x} - \frac{x}{x + 5} = \frac{10}{ {x}^{2} + 5x } [/tex]
a. 0
b. 2
c. 0 and 2
d. no solution
Answer:
Hello,
answer B
2
Step-by-step explanation:
[tex]\dfrac{2}{x} -\dfrac{x}{x+5} =\dfrac{10}{x^2+5x} \\\\we\ suppose\ x\neq 0\ and\ x\neq -5\\\\\text{Reducing to the same denominator}\\\dfrac{2(x+5)-x^2}{x(x+5)} =\dfrac{10}{x^2+5x} \\\\Simplify\ by\ x^2+5x\\\\2x+10-x^2=10\\\\-x^2+2x=0\\\\-x(x-2)=0\\\\roots\ are\ 2 \ and\ 0\ (to\ be\ excluded)\\\\Root=2\\[/tex]
please help me asap:)
will give brainliest to the correct answer
Answer:
A=29.12ft^2
Step-by-step explanation:
first, find the area of the triangle and semicircle separately, then add them together to find the total area of the figure:
area of a triangle: 1/2bh
1/2(6)(8)=24ft^2
area of a circle: πr^2
(**we're using 3.14 instead of pi, and it's a semicircle)
1/2(3.14)(4)^2
1/2(3.14)(16)
1/2(50.24)
25.12ft^2
total area of the figure:
24+25.12=29.12ft^2
Answer: 49.12 ft²
Step-by-step explanation:
This figure is composed of
a half-circlea right triangleFirst, find the area of the half-circle.
The area of a full circle is π · r², but since it's only half a circle, we divide that by half, resulting in (π · r²)/2
π = pi ≈ 3.14r = radius = 8/2 = 4 ftTherefore, the area of the half-circle is:
(3.14 · 4²)/2 = (3.14 · 16)/2 = 50.24/2 = 25.12 ft²
Second, find the area of the right triangle.
The area of a triangle = ½bh.
b = base length = 6 fth = height = 8 ftTherefore, the area of the triangle is:
½ · 6 · 8 = ½ · 48 = 24 ft²
Add the two areas together:
24 + 25.12 = 49.12 ft²
Find the length of the hypotenuse of a right angle triangle if remaining side are 3 cm and 4 cm.
Answer:
5 cm
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
let h be the hypotenuse , then
h² = 3² + 4² = 9 + 16 = 25 ( take the square root of both sides )
h = [tex]\sqrt{25}[/tex] = 5
Fine the angle of the triangle using sides
Answer:
35.54
Step-by-step explanation:
use inverse tan
soh cah toa
we have both opposite and adjacent so we are using tangent
[tex]tan^{-1} (\frac{5}{7} )[/tex]
put that into a calculator and it would give you approximately 35.54 degrees
Use the coordinates of the labeled point to find the point-slope equation of
the line.
(2, -1)
Answer: (C) [tex]y+1=-2(x-2)[/tex]
Step-by-step explanation:
Slope: y = mx +b
By looking at the graph we can see that the slope has a rise of 2 and a run of -1 (aka. -2x) We can also tell that this has a y-intercept of 3
So our slope is: y = -2x + 3
Now you just have to find the answer that matches.
Evaluate w+(-x) - 2/3 where w = -5/9 and x = 4/3
Answer:
-23/9 or -2 5/9
Step-by-step explanation:
w+(-x) - 2/3
Let w = -5/9 and x = 4/3
-5/9+(- 4/3) - 2/3
Get a common denominator of 9
-5/9 - 4/3 *3/3 - 2/3 *3/3
-5/9 - 12/9 - 6/9
-23/9
-2 5/9
Answer:
-2 5/9
Step-by-step explanation:
Can y’all help me with this answer ASAP
Answer:
sqrt(24)
Step-by-step explanation:
The number is slightly less than 5
We know that 5^2 =25
sqrt(25) = 5
so the number has to be less that sqrt(25)
The only number less than sqrt(25) is sqrt(24) and sqrt(20)
sqrt(20) is too far away to be slightly less than 5 so it must be sqrt(24)
357 students went on a field trip. Eight
buses were filled and 5 students traveled
in cars. How many students were in each
bus?
Answer:
There were 44 students in each bus.
Step-by-step explanation:
357 - 5 = 352
352/8 = 44
Answer:
Step-by-step explanation:
Total students = 357
Total buses filled = 8
No of students traveled in car = 5
Remaining students = 357 - 5 = 352
Students in each bus = 352 ÷ 8 = 44 students
There are a total of 12 boys in a chess club. If the ratio of boys to girls in the chess club is 3 to 5, what is
the total number of boys and girls in the chess club?
==================================================
Explanation:
b = number of boys = 12g = number of girls = unknownThe ratio of boys to girls is 3 to 5, which means,
b/g = 3/5
12/g = 3/5 ... plug in b = 12
12*5 = g*3 ... cross multiply
60 = 3g
3g = 60
g = 60/3 .... divide both sides by 3
g = 20 is the number of girls
b+g = 12+20 = 32 total students in the chess club.
Which table of ordered pairs represents a proportional relationship?
-3
y
3
2
1
-5
1
O
داده |
-5
oh w
х
-2
-4
-6
-5
-7
-9
立
-2
-3
y у
0
-1
Answer:
second x -1,-3,-5 y 1 3 5 for proportional relation
Would kindly appreciate the help please !
Answer:
cannot be determined
Step-by-step explanation:
We do not know if any of the angles are equal and are only given two sides.
We cannot determine if the two triangles are similar
Solve for 4
NEED HELP ASAP
Answer:
32 = <4
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
15+17 = <4
32 = <4
Me ajudem pfvr!!!!....
pleaseee help mee helpp meeee
Answer:
i can help you i know this answer
Simplify: 45 ÷ 3 + 2 × 8 - 12 + 42
Answer:
61
Step-by-step explanation:
45/3 = 15
2*8 = 16
15+16-12+42 = 61
Answer:
15 + 16 + 30
and that is in total 61
Step-by-step explanation:
45/3 = 15
2×8 = 16
-12 + 42 = 30
you simplify an expression by calculating the part expressions, to be left only with the main terms and main operations.
PLS HELP!
When rolling a single number cube, what are the odds, in simplest form, in favor of rolling a 4 or a 5? A. 1:1 B. 1:2 C. 1:3 D. 1:5
Answer: 1:3
Step-by-step explanation:
The odds are 2/6 because you’re given 2 choices from the 6 side die you can then simplify that fraction to 1:3
Which of these is an example of an output?
A
swiping on phone screen
B
the notification sound of a text message
C
typing on a keyboard
D
talking into a microphone
Answer:
d talking into microphone
Find the value of the indicated angle. Justify your answer.
Answer:
x=15
Step-by-step explanation:
The first triangle
90+2x+4x=180
90+6x=180
6x=90
x=15
AABC is a right triangle in which zB is a right angle, AB = 1, AC = 2. and BC = V3.
COS Cx sin A =
The value of COS Cx sin A by the given data is V3/4.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
Trigonometric ratio can be defined in terms of ratios of perpendicular, bases and hypotenuse. These are defined only in right angled triangles (triangles whose one angle is of 90 degree measure).
We are given that;
AB = 1, AC = 2 and BC = V3
Now,
To find the value of cos C x sin A, we need to use the trigonometric ratios of the right triangle.
We know that cos C = adjacent/hypotenuse = AB/AC = 1/2 and sin A = opposite/hypotenuse = BC/AC = V3/2.
cos C x sin A = (1/2) x (V3/2) = V3/4.
Therefore, by the trigonometric ratio the answer will be V3/4.
Learn more about trigonometric ratios;
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What is the graph of the solution set of the inequality?
Answer:
The Tasty Beans Coffee House being planned for the corner of SE 12th and Main will ruin a perfectly nice neighborhood. Besides the fact that Tasty Beans already has coffee shops all over the city, it will pull business away from local coffee houses that have been here for decades. In addition, there is already a parking problem on that street, and the new business will just add to the congestion. They're planning a drive-up window, too, and that will mean a steady stream of traffic in a very high-volume area. Ask anyone walking down the street, and they'll tell you this is a bad idea. I speak for my whole neighborhood when I say, "Go away, Tasty Beans!"
Step-by-step explanation:
The value of a jewel in 2015 was $17500. The jewel was purchased in 2008, and its value appreciated 2.5%
each year. What was the initial value of the jewel when it was first bought? Round to two decimal places
Answer:
$14722.14
Step-by-step explanation:
We are given that
In 2015
The value of jewel=$17500
Rate of appreciation, r=2.5%
We have to find the initial value of the jewel when it was first bought.
Time, n=7 years
Final value=[tex]Initial\;value (r/100+1)^n[/tex]
Using the formula
[tex]17500=Initial\;value(2.5/100+1)^7[/tex]
[tex]17500=Initial\;value(1.025)^7[/tex]
[tex]Initial\;value=\frac{17500}{(1.025)^7}[/tex]
Initial value=$14722.14
Hence, the the initial value of the jewel when it was first bought=$14722.14
Find the sum of first five multiple of 5
Answer:
75
Step-by-step explanation:
The first five multiples of 5 are 5, 10, 15, 20, and 25. The sum of the first five multiples of 5 is 75.
find the missing length indicated
Answer:
119?
Step-by-step explanation:
18 Ib. Then her dog loses another 1 lb. Finally, it
Cece dog
gains lb. What is the total change in her dog's weight? how your work. Pleasss help
Answer:
17 lb I guess 8 don't think the question is full
Step-by-step explanation:
the question is half
Which polynomial represents the sum below?
7x9.5x*-**8
5x 0.9x**
A. 5x10.7x8 + 5x5.9x+16
B. 5x10 + 7x8 + 5x5 + 8x+ 16
C. 12x18+1474+8x+ 16
D. 12/16 + 4X4+ 7x+ 16
what is the answer to this problem
9514 1404 393
Answer:
5.7·10^-3
Step-by-step explanation:
The expanded scale shows point P lies 7/10 of the way between 5 and 6 times 10^-3. Its value is 5.7·10^-3.
a polyhedron has 6 faces and 6 vertices. how many edges does it have?
Answer:
a polygon has 3 or more sides
The table shows values for functions f(x) and g(x)
X
f(a) = 2-2
g(x) = -22
-3
18
6
-2
4.
4
-1
2
2
0
0
1
2
2.
44
3
6
18
What is the solution to f(x) = g(x) ?
Select each correct answer.
Answer: When f(x)=g(x) , x equal to -2 or -1
Step-by-step explanation:
