Answer:
4/9
Step-by-step explanation:
The possibilities of transportation: (The first will be for morning, second will be for afternoon)
B, B
B, C
B, T
C, B
C, C
C, T
T, B
T, C
T, T
It is clearly seen that there are 9 transportation options.
(Using cab 1 time we have BC, CB, CT, TC. So four of the transportation methods use cab one time.)
Therefore, the probability that she will use a cab only once is 4/9.
Alvin and Simon shared £540 in the ratio 4:5
Alvin gave half of his share to Theo.
Simon gave a tenth of his share to Theo.
What fraction of the £540 did Theo receive?
Answer:
5/18
Step-by-step explanation:
540/9=60
60x4=240(Alvin's money)
60x5=300(simon's money)
Alvin gives half so you divide 240 by 2 which is 120
Simon gives a tenth so you divide 300 by ten which is 30
120+30=150
150/540=5/18 ( simpliest form)
Theo have 5/18 fraction of total amount of money.
Given that, Alvin and Simon shared £540 in the ratio 4:5.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Now, 4+5=9
So, share of Alvin = 4/9 × 540
= 4 × 60
= £240
Then Simon share = 540-240 = £300
Theo's share = 1/2 × 240
=£120
Theo's share 1/10 of 300
=1/10 × 300
=£30
Total Theo's share = 120+30 =£150
Now, fraction = 150/540
=5/18
Therefore, Theo have 5/18 fraction of total amount of money.
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Which inequality represents all values of x for which the product below is defined? √ x-4•√ x+1 a. x ≥ -1 b. x ≥ 4 c. x ≥ 0 d. x ≤ 4
The inequality that represents all x values is [tex]x \ge 4[/tex]
The expression is given as:
[tex]\sqrt{x - 4} \cdot \sqrt{x + 1}[/tex]
Set the radicands to >=0
[tex]x - 4 \ge 0[/tex] or [tex]x + 1 \ge 0[/tex]
Solve for x in both inequalities
[tex]x \ge 4[/tex] or [tex]x \ge -1[/tex]
When [tex]x \ge -1[/tex], the first radicand is irrational from some x values
Hence, the inequality that represents all x values is [tex]x \ge 4[/tex]
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Find the x intercept. y = x + 3 / x - 2
Answer:
(-3, 0).
Step-by-step explanation:
At the x intercept y = 0 so
(x + 3) / (x - 2) = 0
x + 3 = 0
x = -3.
x-intercept is at (-3,0).
the side of a square is 32/5, what is the area of the square
Answer: 1,024/25 or 40.96
Step-by-step explanation:
The length of one side of a square is 32/5, and all sides of a square have the same length, then all sides of the square have 32/5 as the length.
In order to get the area of the square, you need to multiply one side by another.
32/5 * 32/5 = 1,024/5 (fraction form)
32/5 = 6.4
6.4 * 6.4 = 40.96 (decimal form)
Connie started with___
in her saving account
Fill in the blank
Answer:
Connie started with $25 in her savings account.
Step-by-step explanation:
The y-intercept is the value of the function at time zero.
At x = 0, which is week zero, when Connie opened the account, the y value is 25. That means she opened the account with $25.
Answer: $25
Answer:
25
Step-by-step explanation:
I tried to answer this but not getting the right answer. Can someone help me plzzz
Answer: 17
Step-by-step explanation:
Use the Pythagorean theorem.
C^2 = A^2 + B^2
So, C is always the hypotenuse which is the longest side length and the side length diagonal of the right angle. Side "s" is the hypotenuse.
Square sides AB and BD
It looks like this:
C^2 = 8^2 + 15^2
8^2 = 64
15^2 = 225
225 + 64 = 289
the square root of 289 is 17
17 = s
Hi there I need help with this please
Answer:
4(x-6)=45
Step-by-step explanation:
x is the number
so a number decreased by six
x-6
all multiplied by 4
4(x-6)
is 45
4(x-6)=45
i need help please!!!!!!!!!!!!
Answer:
-1/2
Step-by-step explanation:
The line in slope-intercept form,
y = mx + b
has slope m.
In this case, m = -1/2
Slope = -1/2
Answer:
1. m=-1/2
Step-by-step explanation:
The line is given in slope-intercept form, or
y=mx+b
where m is the slope and b is the y-intercept.
Essentially, the number that is multiplied by x is the slope, and the number that is added or subtracted from the term with x is the y-intercept.
The equation of line is:
y= -1/2x+ 1/4
-1/2 and x are being multiplied (-1/2*x= -1/2x). 1/4 is being added onto the term with x (-1/2x).
Therefore, the slope must be -1/2 and the y-intercept is 1/4.
m= -1/2
b= 1/4
The slope is -1/2 and the first choice is correct.
If 28 g of cashew nuts contains 14 g of fats.
How many grams of fat are there in 42g of cashew nuts?
Answer:
21 g
Step-by-step explanation:
Use ration method
28:14 = 42:x
To find x,
(14 x 42) divided by 28, which equals 21g
Given: Z1 is complementary to 22.
What is the missing statement in step 3 of the proof?
22 is complementary to 23.
0 m21 = m22
Prove: mz1 = m 23
OmZ1 + m22 = 90°
OmZ2 = m23
VV
m22 + m23 = 180°
Statements
1. 21 is comp. to 22
2. 22 is comp. to 23
3. ?
4. m21-90°-m22
5 m22+m23-90°
6. m23-90°-m22
7. m 1 m3
1
2.
3
4
5
6.
7
Reasons
given
given
def. of comp. ZS
subtr. equality prop.
def. of comp. ZS
subtr. equality prop
trans. prop.
Answer:
Option (2)
Step-by-step explanation:
Statements Reasons
1). ∠1 is comp. to ∠2 1. Given
2). ∠2 is comp. to ∠3 2. Given
3). ∠1 + ∠2 = 90° 3. def. of comp. angles
4). m∠1 = 90° - ∠1 4. Subtr. equality property
5). m∠2 + m∠3 = 90° 5. def. of comp. angles
6). m∠3 = 90° - m∠2 6. subtr. equality property
7). m∠1 = m∠3 7. Transitive property
Option (2) will be the answer.
Both angle ∠1 and ∠3 are complementary to ∠2, therefore, ∠1 + ∠2 = 90°
and by properties of equality, ∠1 = ∠3.
Response:
The missing statement in step 3 is; m∠1 + m∠2 = 90°Which property or definition is used to find the missing statement?The completed two column proof is presented as follows;
Statements [tex]{}[/tex] Reasons
1. ∠1 is comp. to ∠2 [tex]{}[/tex] 1. Given
2. ∠2 is comp. to ∠3 [tex]{}[/tex] 2. Given
3. m∠1 + m∠2 = 90° [tex]{}[/tex] 3. Definition of complementary angles4. m∠1 = 90° - m∠2 [tex]{}[/tex] 4. Subtraction equality property
5. m∠2 + m∠3 = 90° [tex]{}[/tex] 5. Definition of complementary angles
6. m∠3 = 90° - m∠2 [tex]{}[/tex] 6. Subtraction equality property
7. m∠1 = m∠2 [tex]{}[/tex] 7. Transitive property
The missing statement in step 3 is therefore; m∠1 + m∠2 = 90°Details of the solution:
Given that ∠1 is complementary to ∠2, we have;
∠1 + ∠2 = 90°
Similarly, by definition of complementary angles, we have;
∠2 + ∠3 = 90°
Which gives;
∠3 + ∠2 = 90°
Therefore;
∠1 + ∠2 = ∠3 + ∠2
Subtracting ∠2 from both sides (subtraction property of equality), gives;
∠1 + ∠2 - ∠2 = ∠3 + ∠2 - ∠2
∠1 + 0 = ∠3 + 0
Which gives;
∠1 = ∠3
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A baker is folding up open-topped boxes to package up her baked goods. She has
flat, rectangular pieces of cardboard that are 10 inches by 6 inches. She wants to
maximize the volume of the box. What size squares should she cut from the corners
of the cardboard?
Answer:
She should cut 1.21 inches (or a square of area 1.46 inch²) from 4 corners to get the maximum volume
Step-by-step explanation:
Length = L = 10 inches
Width = W = 6 inches
Suppose x is cut from the 4 corners to make a box.
Dimensions of the Box:
L= 10 - 2x
W = 6 - 2x
H = x
Volume of the Box:
V = (L)(W)(H)
V = (10-2x)(6-2x)(x)
V = 4x³ - 32x² + 60x
For Maximum value:
[tex]\frac{dV}{dx}=0[/tex]
[tex]\frac{dV}{dx}=\frac{d}{dx}(4x^3-32x+60x)\\\frac{dV}{dx}=12x^2-64x+60\\12x^2-64x+60 = 0[/tex]
The values of x found are:
x= 4.12 , x = 1.21
If we put x= 4.12 in W= 6-2x , the value of width becomes negative, so that is not possible.
We discard 4.12. Now x=1.21
So,
If 1.21 inches are cut from 4 corners, or a square of 1.21*1.21 = 1.46 inch² is cut from 4 corners, we get the maximum value of V
FInd the circumference of this circle:
Diameter - 32
π = 22/7
Answer:
The circumference of circle is 101 units.
Step-by-step explanation:
Given that the diameter of circle is 32 units so you have to find radius by dividing it by 2 :
[tex]radius = diameter \div 2[/tex]
[tex]radius = 32 \div 2[/tex]
[tex]radius = 16 \: units[/tex]
Next, we have to apply circumference formula, C = 2×π×r where r represents radius which is 16 units :
[tex]c = 2 \times \pi \times r[/tex]
Let π = 22/7,
Let r = 16,
[tex]c = 2 \times \frac{22}{7} \times 16[/tex]
[tex]c = 32 \times \frac{22}{7} [/tex]
[tex]c = \frac{704}{7} [/tex]
[tex]c = 101 \: units \: (3s.f)[/tex]
__________________________________
Hey!!
Solution,
Diameter=32
Radius=32/2=16
Circumference of circle=?
Now,
Circumference of circle=2 pi r
=2*22/7*16
=100.57
hope it helps...
Good luck on your assignment
_________________________________
What is the general form of the equation of a circle with center at (a, b) and radius of length m? A. x2 + y2 − 2ax − 2by + (a2 + b2 − m2) = 0 B. x2 + y2 + 2ax + 2by + (a2 + b2 − m2) = 0 C. x2 + y2 − 2ax − 2by + (a + b − m2) = 0 D. x2 + y2 + 2ax + 2by + a2 + b2 = -m2
Answer:
A
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (a, b) and r = m , thus
(x - a)² + (y - b)² = m² ← in standard form
Expand the factors using FOIL and rearrange
x² - 2ax + a² + y² - 2by + b² = m² ( subtract m² from both sides )
x² + y² - 2ax - 2by + (a² + b² - m² ) = 0 ← in general form → A
Answer:
It's option A for plato
Step-by-step explanation:
A. x^2 + y^2 − 2ax − 2by + (a^2 + b^2 − m^2) = 0
A cone has a height of 7ft and a radius of 4ft which equation can find the volume of the cone v=1.3 (7.2)
Answer:
The volume of a cone is:
V=(hπr^2)/3, where h=height and r=radius
V=(7π4^2)/3
V=112π/3 ft^3
V≈117.29 ft^3 (to nearest hundredth of a cubic foot)
Step-by-step explanation:
the roots of the equation 7x^2 +x-1=0 are:
real and distinct
real and equal
not real
none of these
Answer:
Correct option: First one -> real and distinct.
Step-by-step explanation:
To evaluate the roots of the equation 7x^2 + x - 1 = 0, lets find the discriminant Delta using the Bhaskara's formula:
[tex]\Delta = b^{2} - 4ac[/tex]
Where a, b and c are coefficients of the quadratic equation (in this case, a = 7, b = 1 and c = -1)
So we have that:
[tex]\Delta = 1^{2} - 4*7*(-1) = 29[/tex]
To evaluate the roots of the equation, we have the following cases:
[tex]\Delta > 0[/tex] : Two roots real and distinct
[tex]\Delta = 0[/tex] : Two roots real and equal
[tex]\Delta < 0[/tex] : Two roots not real
In our case, we have [tex]\Delta > 0[/tex], so the roots are real and distinct.
Correct option: First one
The area of a rectangle is 54 5454 square meters. The width is 9 99 meters long. Which equation correctly relates the given information and the length, ℓ ℓell?
Answer:
it is longer than 1/3
Step-by-step explanation:
Help me please on this question
Answer:
Step-by-step explanation:
Given : QP║RT and QR║US
To prove: ∠1 ≅ ∠5
Statements Reasons
1). QP║RT 1). Given
2). QR║US 2). Given
3). ∠1 ≅ ∠2 3). Alternate angles
∠2 ≅ ∠5
4). ∠1 ≅ ∠5 4). Transitive property
Reasons for third step,
PQ║RT and QR is a transverse therefore, ∠1 and ∠2 will be alternate angles.
Similarly, QR║US and RT is a transverse therefore, ∠2 and ∠5 will be the alternate angles.
Line JK passes through points J(-4,-5) and K(-6, 3). If the equation of the line is written in slope-intercept form, y = mx + b,
what is the value of b?
-21
-4
11
27
Mark this and retum
Save and Exit
Nex
Answer:
A
Step-by-step explanation:
If the equation of the line is written in slope-intercept form, y = mx + b then the value of b will be -21; the correct answer is option A.
What is the slope of a straight line?Slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
This is because the more the height of the line to thee amount we walk or run on the horizontal axis, the more the slope is. That is why we took difference of horizontal axis in denominator and difference of vertical axis on numerator.
Formula for slope, thus, is;
Slope = (y₂ - y₁) / (x₂ - x₁)
Parameters;
J(-4, -5) and K(-6, 3)
= (3 - (-5)) / (-6 - (-4))
= (3 + 5) / (-6 + 4)
= 8 / -2
= -4
Substitute one of the coordinates into the formula to solve for b
y = mx + b
y = -4x + b
3 = -4(-6) + b
3 = 24 + b
3 - 24 = b
b = - 21
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Got a fairly simple looking system of equations, 2k+4y=20, and 3x+6y=30 Don't understand how to prove what values of k provide - 1 solution - no solutions - and many solutions
Answer:
2kx+4y=20 ⇒ kx+2y=10
3x+6y=30 ⇒ x+2y= 10
k is the coefficient of x, so it is the slope of the line
when k=1, both equations will be same, then there are many solutionswhen k=0 there is one solutionwhen k is anything different, then the lines will be parallel, so no solutionsAndrea's living room floor is a rectangle 12 feet by 15 feet. She wants to buy a rug that is geometrically similar to her living room floor. Which size of rug should she buy? *
Answer:
180 square feet
Step-by-step explanation:
A rug that is geometrically similar to her room floor is one that has the same size as her room floor.
The floor has dimensions 12 feet by 15 feet.
The area of the floor and hence, the rug is:
A = 12 * 15 = 180 square feet
She should buy a rug that is 180 square feet
A trail mix contains peanuts raisins and m&ms in the mix the amount of peanuts is three times the amount of m&ms;and the amount of raisins is two times the amount of m&ms.let m represent the amount of m&ms.write and simplify an expression for the total number of pieces of food in the trail mix
Answer:
6m
Step-by-step explanation:
m =number of M&M's
3m=number of peanuts
2m=number of raisins
m+3m+2m=total number of pieces of food=6m
Given ƒ(x) = 9x + 54, find x when ƒ(x) = 18. A) −6 B) −4 C) 3 D) 8
Answer:
-4 =x
Step-by-step explanation:
ƒ(x) = 9x + 54
Let f(x) = 18
18 = 9x+54
Subtract 54 from each side
18-54 = 9x + 54-54
-36 = 9x
Divide each side by 9
-36/9 = 9x/9
-4 =x
Answer: B
Step-by-step explanation:
Well, they told you what f(x) equals. So make the function of f(x) equal to the value they gave, 18
[tex]18=9x+54[/tex]
Subtract 54 from both sides to get:
[tex]-36=9x[/tex]
Divide both sides by 9 to get x = -4
Helpppppp meeeee please URGENT
True or False
Answer:
false
Step-by-step explanation:
you cant have same size without congruent
¿que es la trigonometria?
Answer:
I don't speak Spanish but I know what your asking. Trigonometry is a thing in physics.
Step-by-step explanation:
any help would be amazing, please?!!
Answer:
I think it's C
Step-by-step explanation:
Sorry if I'm wrong
can sumone help with this pls
Answer:
D
Step-by-step explanation:
The range means the possible values of the y coordinate which is y ≥ 1 in this function
Which of these questions can be answered with a simple yes or no?
O A. Is there an engineering school?
B. What dining options are offered on campus?
C. What sororities and fraternities are available?
D. How much is the tuition?
Please answer correctly !!!!!! Will mark brianliest answer !!!!!!!!!!
Answer:
see below
Step-by-step explanation:
g(x) = (x² - 2 * 1/2 x) - 6
= (x - 0.5)² - 0.25 - 6
= 1(x - 0.5)² - 6.25
11.A bus is going with speed of
18 m/s and suddenly bus driver
applied a break and it takes 3
second to stop completely.
Find out the value of
acceleration. *
Answer:
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me...
Answer:
-6m/s^2
Step-by-step explanation:
State your knowns
s=Not required
u=18m/s
v=0m/s
a=?
t=3 seconds
(by the way this is more a physics question)
Find an applicable suvat equation
v=u+at
Rearrange the equation
v-u=at
(v-u)/t=a
Substitute values
(0-18)/3=a
Evaluate
a=-6
State the answer
The value of acceleration is -6m/s^2
which law would you use to simplify the expression (p/q)^3
Answer:
Step-by-step explanation: