Answer:
B. 8 in^2.
Step-by-step explanation:
Let the width be x inches, then the length = x + 2 inches.
So by The Pythagoras theorem:
(√20)^2 = x^2 + (x + 2)^2
x^2 + x^2 + 4x + 4 = 20
2x^2 + 4x - 16 = 0
x^2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2, -4 (we ignore the negative so x = 2)
So the area = 2 * (2 + 2)
= 8 in^2.
Answer:
B
Step-by-step explanation:
L = W + 2
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
(W + 2)2 + W2 = [tex]\sqrt{20} ^{2[/tex]
2[tex]w^{2}[/tex] + 4W + 4 = 20
2[tex]w^{2}[/tex] + 4W − 16 = 0
W = 2 or W = −4
And,
L = W + 2
L = 2 + 2
L = 4
Therefore,
A = LW = (4)(2) = 8
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.
WILL CROWN BRAINLIEST, 5/5 RATING, AND LIKE!
A bag contains 2 white marbles and 7 purple marbles. Two marbles are drawn at random. One marble is drawn and not replaced. Then a second marble is drawn.
a. What is the probability of selecting a purple marble and then a white marble?
b. What is the probability of selecting two white marbles?
c. Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row? Show your work
Hey there!
If we have two white marbles and seven purple marbles, our first probability is out of nine.
First of all, we have the probability of selecting a purple marble, 7/9.
Now, if we do not replace it, there are only eight marbles left. Therefore, getting a white marble is 2/8, or 1/4.
We multiply these probabilities together to get our answer to a.
7/9(1/4)= 7/36
a. 7/36
Now, let's do b. We have 2/9, and then 1/8, giving us 1/36.
b. 1/36
Now, let's calculate selecting two purple to help us with C.
We have 7/9, and then 6/8, or 3/4.
7/9(3/4)= 7/12
Since there is a majority of purple marbles, there is a C) greater probability of selecting two purple marbles in a row.
I hope this helps!
Answer:
A. 7:9 B. 1:4 C. Purple
Step-by-step explanation:
A. Because there are 7:9 B. Because 1:4 C. Because Purple has more
The library is 5 miles from the post office. How many yards is the library from the post office?
Answer:
8800
Step-by-step explanation:
a yard is equals 3 feet a mile is 5 280
Answer: 8800 yards
Step-by-step explanation:
1 mile = 1760 yards
1760 yards x 5 miles = 8800 yards
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]
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]
After 3 months 5004 deposited in a savings account with simple interest had earned 162.63 in interest. What was the interest rate
Answer:
13%
Step-by-step explanation:
Please use the $ sign.
The simple interest formula is i = p*r*t, where p is the principal amount, r is the interest rate as a decimal fraction, and t is the time in years. Here, t = 1/4 year; r is unknown, p is $5004 and i is $162.63.
Writing this out with the given info, we get:
$162.63 = $5004*r*(1/4).
We can solve this for r by multiplying both sides by 4/$5004:
(4/$5004)($162.63) = (4/$5004)($5004)*r*(1/4) = r
Evaluating r, we get (4)($162.63)/$5004 = 0.13
The interest rate, r, is 0.13, or 13%.
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.
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.
Triangle ABC and triangle CFG are similar right triangles. Which proportion can be used to show that the slope of AC is equal to the slope of CG? A) 0 − 2 3 − 0 = 2 − 6 9 − 3 B) 0 − 2 3 − 0 = 6 − 2 9 − 3 C) 2 − 0 3 − 0 = 6 − 2 9 − 3 D) 3 − 0 2 − 0 = 9 − 3 6 − 2
Answer:
C
Step-by-step explanation:
proportion can be used to show that the slope of AC is equal to the slope of CG
Slope of AC = (2-0)/(3-0) = 2/3
Slope of CG = (6-2)/(9 -3) = 2/3
So answer is :
C)
2 − 0 6 − 2
------------ = -----------
3 − 0 9 − 3
Answer:C
Step-by-step explanation:
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.
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]
Box A has a volurme of 12 cublic meters. Box B is similar to box A. To create Box B, Box A's dimensions were multiplied by five. What is the volume of Box B?
A) 60 m^3
B)300 m^3
C) 1,500 m^3
D) 7,500 m^3
Answer:
C) 1,500 m³Step-by-step explanation:
[tex]k - \text{scale of similar}[/tex]
[tex]\text{If}\ AB\sim CD\ \text{in scale}\ k,\ \text{then}\ \dfrac{length_{AB}}{length_{CD}}=k[/tex]
[tex]\text{If}\ A\sim B\ \text{in scale}\ k,\ \text{then}\ \dfrac{area_A}{area_B}=k^2[/tex]
[tex]\text{If}\ A\sim B\ \text{in scale}\ k,\ \text{then}\ \dfrac{volume_A}{volume_B}=k^3[/tex]
[tex]\text{We have}\ B\sim A\ \text{in scale}\ k=5.\ V_A=12\ m^3,\ \text{therefore}\\\\\dfrac{V_B}{V_A}=k^3\to\dfrac{V_B}{12}=5^3[/tex]
[tex]\dfrac{V_B}{12}=125[/tex] multiply both sides by 12
[tex]V_B=1500\ m^3[/tex]
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).
Can someone help with this plz
For this case we must simplify the following expression:
[tex]\sqrt {\frac {16} {25}}[/tex]
We can rewrite 16 as:[tex]2 ^ 4 = 2 * 2 * 2 * 2[/tex]
We can rewrite 25 as:[tex]5 ^ 2 = 5 * 5[/tex]
[tex]\sqrt {\frac {2 ^ 4} {5 ^ 2}} =\\\frac {\sqrt {2 ^ 4}} {\sqrt {5 ^ 2}} =[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
Then, rewriting the expression:
[tex]\frac {2 ^ 2} {5} =\\\frac {4} {5}[/tex]
Answer:
[tex]\frac {4} {5}[/tex]
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]
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
Simplify 4 to the 4th over 4 to the 6th
Answer:
3/5^3 = 27
125
= 0.216
Step-by-step explanation:
Power: 3
5
^ 3 = 33
53
= 27
125
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
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
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]
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:
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:
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!
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.
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
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
What is the probability that the person is from California, given that the person prefers brand A? Round your answer to two decimal places
HELP!!!!!!!!!
Answer: D. 0.53
Step-by-step explanation:
From the given picture, the number of persons from California and prefers brand A = 90
The total numbers of persons prefer brand A = 170
The probability that the person is from California, given that the person prefers brand A will be :-
[tex]\dfrac{\text{Persons from California and prefers brand A}}{\text{Persons prefer brand A}}\\\\=\dfrac{90}{170}=0.529411764\approx 0.53[/tex]
Hence, The probability that the person is from California, given that the person prefers brand A = 0.53
Answer:
D 0.53
Step-by-step explanation:
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
Rectangle ABCD is rotated 360 around the orgin. What is the coordinate of C’
Answer:
-4,4
Step-by-step explanation:
I just answered it on edge and got it right trust me
The coordinate of the point C' after the rotation of 360 degrees will be the same as the coordinate of C.
What is a transformation of a shape?A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
Rectangle ABCD is rotated 360 around the origin.
If any object is rotated by 360 degrees about the origin. Then the position of the object does not change.
Then the coordinate of the point C' after the rotation of 360 degrees will be the same as the coordinate of C.
More about the transformation of the shape link is given below.
https://brainly.com/question/27224339
#SPJ6
Select the correct location on the number line. Which point on the number line represents the approximate volume of a cylinder with a radius of 4 units and a height of 4 units? Use 3.14 for π.
Answer:
the answer is 37.7 so the point closest to 40.
Step-by-step explanation:
Answer: the one between 30 and 40
Step-by-step explanation: