Answer:
19°
Step-by-step explanation:
In triangle ABC, ∠A=120°, a=8, b=3.
Use the sin rule:
[tex]\dfrac{a}{\sin \angle A}=\dfrac{b}{\sin \angle B}\\ \\\dfrac{8}{\sin 120^{\circ}}=\dfrac{3}{\sin \angle B}\\ \\8\sin \angle B=3\sin 120^{\circ}\\ \\8\sin \angle B=3\cdot \dfrac{\sqrt{3}}{2}\\ \\\sin \angle B=\dfrac{3\sqrt{3}}{16}\approx 0.3248\\ \\\angle B\approx 18.95^{\circ}\approx 19^{\circ}[/tex]
Michael has a recipe that requires 3/4 cup of flour,and he wants to make 1/2 the recipe. How much flour does he need?
Answer:
Michael will use 3/8 cup of flour.
Step-by-step explanation:
Half of a Fraction:
1. Reduce fraction to its lowest terms.
2. If the numerator is an even number than divide the numerator by 2.
Example: 4/5 divided in half would be 2/5.
3. If the numerator is an odd number than multiply the denominator by 2.
Example: 1/3 divided in half would be 1/6.
3/4 cup of flour divided in half would be 3/8 because the numerator 3 is an odd number so the denominator of 4 would be multiplied by 2 equaling 8.
If m+p+k=70, p=2m, and k=2p, then m =
m=10 as p=2m and k=2p=4m
Answer:
10
Step-by-step explanation:
Between x = 2 and x = 3, which function has a larger average rate of change than f(x) = 2x has?
Answer:
x=2
Step-by-step explanation:
Answer:
C) h(x)=[tex]4^{x-1}[/tex]
Step-by-step explanation:
-p+60 = = h + 10,000
In the equation above, h is a constant. If p = 10 is a solution to the equation, what is the value
of h?
By substituting p = 10 into the equation -p + 60 = h + 10,000 and solving for h, we find that the constant h is -9,950.
The solution cam be solved as:
To find the value of constant h when p = 10 is a solution to the equation -p + 60 = h + 10,000, we substitute p = 10 into the equation and solve for h.
-p + 60 = h + 10,000
-10 + 60 = h + 10,000
50 = h + 10,000
h = 50 - 10,000
h = -9,950
The value of h is therefore -9,950.
what is value of x-(3x+5) when x=-2
Answer:
2
Step-by-step explanation:
3 * -2 = -6
-6 +5 = 1
-2 * -1 = 2
the value would be two
( − 2 7 ) ( 5 − 8 ) Please solve .
Answer:
81
Step-by-step explanation:
We have to solve the following multiplication: (−27) (5−8)
First, we are going to simplify the second parenthesis, before performing the multiplication:
(−27) (5−8) = (−27)(-3) = 81.
The result is positive given that minus times minus equals plus.
Step 1: Solve the second parentheses
( − 2 7 ) ( 5 − 8 )
5 - 8 = -3
(-27)(-3)
Step 2: Multiply -27 by -3. Since these are both negative the answer will be positive
-27 * -3 = 81
Hope this helped!
~Just a girl in love with Shawn Mendes
1/3 2/5 4/7 least to greatest
1.Change them all to having common denominators so it’s easier to compare the numerators
1/3=35/105 *35
2/5=42/105 *21
4/7=60/105 *15
2.Compare and order
3. Answer from smallest to largest =
1/3,2/5,4/7
Hope this helps :)
Find the value of y (Angle A and angle B are congruent)
A) 64
B) 68
C) 71
D) 82
Answer:
The value of y is 64 ⇒ first answer
Step-by-step explanation:
* Lets study the figure to solve the question
- The figure is a polygon of 5 sides
- It has five interior angles and five exterior angles
- The sum of its interior angles depends on the number of its sides
- We can find the sum of the measures of its interior angles from this
rule ⇒ the sum = (n - 2) × 180°, where n is the number of its sides
- The sum of the measures of its exterior angles is 360°
(fixed for any polygon)
- The sum of the measure of an interior angle and its exterior angle
is 180°
∵ m∠A = m∠B
∴ The exterior angle of ∠A = the exterior angle of ∠B
∵ The exterior angle of ∠B is y°
∴ The exterior angle of ∠A is y°
∵ The measure of the interior angle of the exterior angle x° is 90°
∴ 90° + x° = 180° ⇒ subtract 90 from both sides
∴ x° = 90°
∵ The polygon has five exterior angles
# Angle of measure 75 , angle of measure 67 , y° , y° , x°
∴ 75° + 67° + y° + y° + x° = 360° ⇒ sum of the exterior angles
∵ x° = 90°
∴ 75° + 67° + y° + y° + 90° = 360° ⇒ simplify
∴ 232 + 2y° = 360° ⇒ subtract 232 from both sides
∴ 2y° = 128 ⇒ divide both sides by 2
∴ y° = 64°
* The value of y is 64
Answer:
The correct answer is option A. 64
Step-by-step explanation:
From the figure we can see a pentagon.
Sum of angles of a pentagon is 540
To find the value of m<B
From the figure we get, Angle A and angle B are congruent
m<A = m<B and one angle is 90°
Other two angles are,
180 - 75 = 105° and 180 - 67 = 113°
Also we can write,
105 + 113 + 90 + m<A + m<B = 540
308 + m<A + m<B = 540
m<A + m<B = 540 - 308 = 232
2m<B = 232
m<B = 232/2 = 116
To find the value of y
From figure we get,
<B + y = 180
y = 180 - <B
= 180 - 116 = 64
Therefore the correct answer is option A. 64
If f(x)=3x2-2 and g(x)=4x+2 what is value of (f+g)(2)
The value of (f+g)(2) is 20.
The expression (f+g)(2) represents the sum of the functions f(x) and g(x) evaluated at x = 2.
To find the value of (f+g)(2), we need to first find the values of f(2) and g(2), and then add them together.
Given that f(x) = 3x^2 - 2 and g(x) = 4x + 2, we can find the values of f(2) and g(2) as follows:
1. Substitute x = 2 into f(x):
f(2) = 3(2)^2 - 2
= 3(4) - 2
= 12 - 2
= 10
2. Substitute x = 2 into g(x):
g(2) = 4(2) + 2
= 8 + 2
= 10
Now, we can find the value of (f+g)(2) by adding f(2) and g(2):
(f+g)(2) = f(2) + g(2)
= 10 + 10
= 20
Therefore, the value of (f+g)(2) is 20.
25 Kaia ate 3/6 of a banana. Zoie ate an equivalent amount. Which
fraction shows how much of a banana Zoie ate? Circle the
letter of the correct answer.
A:1/3 B:2/3 C:5/8 or D:1/2
از
Landon chose A as the correct answer. How did he get
that answer?
Answer: D:1/2
Step-by-step explanation: 3/6 simplifies to 1/2, making them equal. Landon got his answer by simplifying the problem incorrectly. 1/3 is equal to 2/6
Final answer:
Kaia ate 3/6 of a banana, which simplifies to 1/2. Zoie ate an equivalent amount, so the fraction that shows this is 1/2, represented as option D:1/2. Landon incorrectly chose 1/3 which is not equivalent to 1/2.
Explanation:
Kaia ate 3/6 of a banana, which is an equivalent fraction to 1/2 when reduced (because 3/6 = 1/2). If Zoie ate an equivalent amount, then we are looking for a fraction that is also equivalent to 1/2. Among the options provided: A:1/3, B:2/3, C:5/8, and D:1/2, the correct answer is D:1/2. Landon chose A:1/3 as the correct answer, which is incorrect because 1/3 is not equivalent to 1/2.
To understand why 3/6 is equivalent to 1/2, we can divide the numerator and the denominator by their greatest common factor, which in this case is 3. Doing so, we simplify 3/6 as: 3÷3 / 6÷3 = 1/2, thus, showing that 3/6 and 1/2 represent the same quantity.
which statement best describes the association between variable X and variable Y?
*weak negative association
*moderate negative association
*moderate positive association
*weak positive association
Answer:
Weak negative association
Step-by-step explanation:
because it is widely scattered, it is weak but in general it is negative
Answer:
weak negative association
Step-by-step explanation:
The association is negative because when variable x increase, variable y decrease.
Given that many points, like x = 1, x = 2, et cetera, have more than 1 y-value associated and those values are spread, the association is weak.
how does f(x)=9^x change over the interval from x=8 to x=10
Answer:
Step-by-step explanation:
9^8 to 9^10 involves a change (multiplication) of 9^8 by 9^2 (which is 81).
Over the given interval, f(x) increases by 81.
HOW MANY TRIANGLES CAN BE CONSTRUCTED WITH THE FOLLOWING MEASURES?
AB = 7.6 cm, AC = 5.4 cm, and m/_ABC = 50°.
Answer:
No triangle can be constructed with given measures.
Step-by-step explanation:
Refer the following figure.
AB = c = 7.6 cm
AC = b = 5.4 cm
∠ABC = B = 50°
Sine rule is given by [tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
Substituting
[tex]\frac{5.4}{sin50}=\frac{7.6}{sinC}\\\\sinC=1.078[/tex]
Value of sinC is more than 1, which is not possible.
Hence no triangle can be constructed with given measures.
solve using the substitution method 3m-n=18 and 2m+n=-7
Answer:
m = 11/5, n= -57/5
Step-by-step explanation:
3m-n=18 and 2m+n=-7
Solve one of the equations for n
2m +n = -7
Subtract 2m from each side
2m-2m +n = -7 -2m
n = -7-2m
Substitute this into the first equation
3m -n =18
3m - (-7-2m) = 18
Distribute the minus sign
3m +7+2m = 18
Combine like terms
5m +7 = 18
Subtract 7 from each side
5m+7-7 = 18-7
5m = 11
Divide by 5
m = 11/5
Substitue this back into the equation for n
n = -7-2m
=-7 -2(11/5)
=-7-22/5
-35/5 -22/5
=-57/5
To solve the system using substitution, solve the first equation for n, substitute it into the second, and solve for m, which gives m = 11/5. Then, substitute m back into the expression for n to get n = -57/5.
To solve the system of equations using the substitution method, you can solve one of the equations for one variable and then substitute that expression into the other equation. Let's start with the two given equations:
3m - n = 18
2m + n = -7
First, solve the first equation for n:
n = 3m - 18
Now substitute this expression for n into the second equation:
2m + (3m - 18) = -7
Combine like terms:
5m - 18 = -7
Add 18 to both sides:
5m = 11
Divide by 5:
m = 11/5
Next, substitute the value of m back into the expression for n:
n = 3(11/5) - 18
n = 33/5 - 90/5
n = -57/5
Therefore, the solution to the system using the substitution method is m = 11/5 and n = -57/5.
Find the value of x.
Answer:
The value of x is 4√5 ⇒ 1st answer
Step-by-step explanation:
* Lets revise the rules in the right angle triangle when we draw the
perpendicular from the right angle to the hypotenuse
- In triangle ABC
# Angle B is a right angle
# The hypotenuse is AC
# BD ⊥ AC
∴ (AB)² = AD × AC
∴ (BC)² = CD × AC
∴ (BD)² = AD × CD
∴ BD × AC = AB × BC
* Lets use one of these rules to solve the problem
- y is the perpendicular from the right angle to the hypotenuse
- x is one leg of the right angle
∵ The length of the hypotenuse = 5 + 11 = 16 units
∵ The part nearest to x = 5
* Lets use the rule (AB)² = AD × AC
∴ x² = 5 × 16 = 80 ⇒ take √ for both sides
∴ x = √80 = 4√5 units
May someone please help me get this question?? It would mean a lot to me if you could stop by and answer this for me >~<
Answer: Less than 1 bag.
Step-by-step explanation:
Take the total number of bags and divide it by them between the 12 yards.
7.5/12 is equal to 0.625 which is less than 1 bag.
Hope this helps!
select all possible choices-
Which expressions are equivalent to the expression 4a – 6b + 3c?
a) a + 3(a − 2b + 3c)
b) 4a + 3(2b + c)
c) 2(2a − 3b + c) + c
d) 2(2a − 3b) + 3c
I know B is on possible choice for this and maybe d almost certain
c) and d)
c) 4a-6b+2c+c
d) 4a-6b+3c
The histogram shows the weekly attendance of participants in a school's study skills program. What was the highest weekly attendance recorded for the program?
A.
8
B.
12
C.
16
D.
18
That would be on the 5th week. There were 18 students that attended (D.)
Hope this helped!
Answer: It is 18
Step-by-step explanation: Hope this helps :D
Factor completely 2x2 + 2x − 24.
2x^2 + 2x - 24
= 2x^2 + 8x - 6x -24
= 2x(x + 4) -6(x + 4)
= (x+4)(2x-6)
Answer:
.
Step-by-step explanation:
The trick here is to notice that all 3 terms can be div. by 2:
2(x^2 + x - 12)
Note that -12 factors into -3 * 4 or -4 * 3. Thus,
x^2 + x - 12 = (x-4)(x+3), and so 2x2 + 2x − 24 = 2(x-4)(x+3).
10 points help please!?
Answer:
[tex]\large\boxed{\sqrt{80}=4\sqrt5}[/tex]
Step-by-step explanation:
Method 1:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (-4, 1) and (4, 5). Substitute:
[tex]d=\sqrt{(4-(-4))^2+(5-1)^2}=\sqrt{8^2+4^2}=\sqrt{64+16}=\sqrt{80}[/tex]
[tex]\sqrt{80}=\sqrt{16\cdot5}=\sqrt{16}\cdot\sqrt5=4\sqrt5[/tex]
Method 2:
Look at the picture.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=8,\ leg=4,\ hypotenuse=x[/tex]
Substitute:
[tex]x^2=8^2+4^2\\\\x^2=64+16\\\\x^2=80\to x=\sqrt{80}\\\\x=4\sqrt5[/tex]
Find the volume of the cylinder in terms of pi.
Answer:
[tex]\large\boxed{V=81\pi\ in^3}[/tex]
Step-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
We have r = 3in and H = 9in. Substitue:
[tex]V=\pi(3^2)(9)=\pi(9)(9)=81\pi\ in^3[/tex]
The Pythagorean Theorem says that in a right triangle, a2 + b2 = c2 , where a and b are the lengths of the legs, and c is the length of the hypotenuse. If b = 2, what is the length of side a in terms of c? Remember, “in terms of c” means that the variable c will appear in your answer.
Answer: [tex]a=\sqrt{c^2-4}[/tex]
Step-by-step explanation:
You know that the Pythagorean Theorem is:
[tex]a^2+b^2=c^2[/tex]
Where "a" and "b" are the legs and "c" is the hypotenuse.
Then, since you need to find the length of side "a" in terms of the hypotenuse "c", you need to solve for "a":
Subtract b² from both sides of the equation:
[tex]a^2+b^2-b^2=c^2-b^2[/tex]
[tex]a^2=c^2-b^2[/tex]
And finally, you need to apply square root to both sides of the equation:
[tex]\sqrt{a^2}=\sqrt{c^2-b^2}\\\\a=\sqrt{c^2-b^2}[/tex]
Then:
[tex]a=\sqrt{c^2-2^2}\\\\a=\sqrt{c^2-4}[/tex]
Answer:
Final answer is [tex]a=\sqrt{c^2-4}[/tex].
Step-by-step explanation:
Given that b=2. Now using Pythagorean theorem, we need to find the value of a in terms of c.
So let's plug b=2 into formula :
[tex]a^2+b^2=c^2[/tex]
[tex]a^2+2^2=c^2[/tex]
[tex]a^2+4=c^2[/tex]
[tex]a^2=c^2-4[/tex]
Take square root of both sides and use principle root as side length can't be negative.
[tex]a=\sqrt{c^2-4}[/tex]
Hence final answer is [tex]a=\sqrt{c^2-4}[/tex].
15 points!!! The triangle ABC is dilated with respect to the point O(8,-3) and the scale factor 3 to a new triangle A'B'C'. What are the coordinates of B?
(24,-9)
(24,-3)
(12,-9)
(-4,-3)
Answer:
(-4,-3)
Step-by-step explanation:
we know that
The distance OB is equal to
(8-4)=4 units
To find the new distance OB', multiply the distance OB by the scale factor
so
OB'=OB*3
OB'=4*3=12 units
The x-coordinate of point B' is equal to
8-12=-4
The y-coordinate of point B' is the same that B -3
the coordinates of point B'are (-4,-3)
I NEED HELP IN 2 QUESTIONS, PLEASE HELP AND SHOW YOUR WORK!
Which expression best represents the area of the rectangle? ( The longer side is x+12, and the shorter side is x-5)
A) x2 + 7x + 60
B) x2 + 17x + 60
C) x2 − 7x + 7
D) x2 + 7x − 60
Multiply: (2x − 5)(3x2 − 4x + 2)
A) 6x3 − 23x2 + 24x − 10
B) 6x3 − 7x2 + 24x − 10
C) 6x3 − 23x2 + 16x − 10
D) 6x3 − 7x2 + 16x − 10
Answer:
Q1. D) x² + 7x - 60Q2. A) 6x³³ - 23x² +24x - 10Step-by-step explanation:
Q1.The formula of an area of a rectangle:
[tex]A=l\times w[/tex]
l - length
w - width
We have l = x + 12 and w = x - 5. Substitute:
[tex]A=(x+12)(x-5)[/tex] use FOIL (a + b)(c + d) = ac + ad + bc + bd
[tex]A=(x)(x)+(x)(-5)+(12)(x)+(12)(-5)[/tex]
[tex]A=x^2-5x+12x-60[/tex] combine like terms
[tex]A=x^2+7x-60[/tex]
Q2.[tex](2x-5)(3x^2-4x+2)[/tex] use the distributive property a(b + c) = ab + ac
[tex]=(2x-5)(3x^2)+(2x-5)(-4x)+(2x-5)(2)\\\\=(2x)(3x^2)+(-5)(3x^2)+(2x)(-4x)+(-5)(-4x)+(2x)(2)+(-5)(2)[/tex]
[tex]=6x^3-15x^2-8x^2+20x+4x-10[/tex] combine like terms
[tex]=6x^3+(-15x^2-8x^2)+(20x+4x)-10\\\\=6x^3-23x^2+24x-10[/tex]
Adrianna has fabric that is 3/4 yard long. How many 1/8 yard long pieces will she have???
Answer:
6
Step-by-step explanation:
If x is the number of 1/8 yard long pieces, then the total length is x * 1/8. We know that the total length is 3/4 yards. Therefore:
x * 1/8 = 3/4
Divide:
x = (3/4) / (1/8)
To divide a fraction, multiply by its reciprocal:
x = (3/4) * (8/1)
x = 24/4
x = 6
She has 6 pieces.
Answer:
Adrianna will have 6 1/8 yard pieces.
Step-by-step explanation:
[tex]1/8*2/1=2/8 \\2/8=1/4\\So\\6/8=3/4[/tex]
Help me solve this math problem!
Answer:
4x + y = 32
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
First obtain the equation in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (7, 4) and (x₂, y₂ ) = (5, 12)
m = [tex]\frac{12-4}{5-7}[/tex] = [tex]\frac{8}{-2}[/tex] = - 4, thus
y = - 4x + c ← is the partial equation of the line
To find c substitute either of the 2 points into the partial equation.
Using (7, 4), then
4 = - 28 + c ⇒ c = 4 + 28 = 32
y = - 4x + 32 ← in slope- intercept form
Add 4x to both sides
4x + y = 32 ← in standard form
There were 15 girls and 25 boys in the Science club. What percent of the members were girls?
Answer: 37.5
Step-by-step explanation:
15 15 3
___ = ___ = ___ = 0.375 = 37.5
15+25 40 8
A pair of equations is shown below:
y = 6x − 4
y = 5x − 3
Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)
Part B: What is the solution to the pair of equations? (4 points)
Answer:
The solution to the pair of equations is [tex]x=1,y=2[/tex]
Step-by-step explanation:
The given equations are:
[tex]y=6x-4[/tex]
[tex]y=5x-3[/tex]
To solve the pair of equations graphically, we need to graph the two equations. Their point of intersection is the solution to the pair of equations.
The functions are in the form;
[tex]y=mx+b[/tex]
where m=6 is the slope and b=-4 is the y-intercept of [tex]y=6x-4[/tex].
and where m=5 is the slope and b=-3 is the y-intercept of [tex]y=5x-3[/tex].
The two equations have been graphed in the attachment.
They intersected at (1,2).
The solution to the pair of equations is [tex]x=1,y=2[/tex]
If one side of a square notebook measures 20 cm, what is the area of the front cover of the notebook?
40 cm2
80 cm2
200 cm2
400cm2
Answer:
400cm
Step-by-step explanation:
Answer:
it is 400cm2
Step-by-step explanation:
i know things
The perimeter of the rectangle is 28 units.
What is the value of w?
Step-by-step explanation:
The formula of a perimeter of a rectangle:
[tex]P=2l+2w[/tex]
We have P = 28. Substitute:
[tex]28=2l+2w[/tex]
Solve for w:
[tex]2l+2w=28[/tex] subtract 2l from both sides
[tex]2w=28-2l[/tex] divide both sides by 2
[tex]w=14-l[/tex]
Where [tex]0<l<14[/tex]
Answer:
answer is w = 14