Reduce the expression by cancelling the common factors.
= 32/37
In decimal;
0.864
Which expressions are equivalent to_____? Check all that apply.
Option 1. [tex](-2)(5x) + (-2)(-\frac{3}{4})[/tex] and option 4.[tex]-10x + \frac{3}{2}[/tex] are equivalent to [tex]-2(5x-\frac{3}{4} ).[/tex]
Step-by-step explanation:
Step 1:
The given expression is expanded as follows.
The -2 is multiplied with the 5x and then the -2 is multiplied with the [tex]-\frac{3}{4}[/tex].
So the expression becomes as follows;
[tex]-2(5x-\frac{3}{4} ) = (-2)(5x) + (-2)(-\frac{3}{4}).[/tex]
This is the first option given so the first expression is equivalent.
Step 2:
[tex]-2(5x-\frac{3}{4} ) = (-2)(5x) + (-2)(-\frac{3}{4}) = -10x + \frac{6}{4} = -10x + \frac{3}{2} .[/tex]
Of the other four options, only the fourth expression has the fraction [tex]\frac{3}{2}[/tex] so the fourth expression is also equivalent.
Expressions 1 and 4 are equivalent to the given expression.
What is 8.40 in word form
Answer:
Step-by-step explanation:
8.40 ×10°
Answer:
eight and four tenths
Step-by-step explanation:
What makes the ratio equivalent to 11:44
Answer:
1:4
Step-by-step explanation:
1:4=11:44
In △ABC , line AB is extended up to point E and line BC is extended up to D . The measure of some of the angles is given as; ∠BAC=70° and ∠EBC=120° .
Answer:
[tex]\angle ACD = 130 ^\circ[/tex].
Step-by-step explanation:
[tex]\angle ABC[/tex] and [tex]\angle EBC[/tex] are supplementary angles. Their sum should be [tex]180^\circ[/tex]. [tex]\angle EBC = 120^\circ[/tex] [tex]\implies \angle ABC = 180^\circ - \angle EBC = 180^\circ - 120^\circ = 60^\circ[/tex].
The sum of the three angles in triangle [tex]\triangle ABC[/tex]: [tex](\angle ABC + \angle BAC + \angle ACB)[/tex] should be equal to [tex]180^\circ[/tex].
[tex]\angle ABC = 60^\circ[/tex] and [tex]\angle BAC = 70^\circ[/tex] [tex]\implies \angle ACB = 180^\circ - \angle ABC - \angle ACB = 180^\circ - 70^\circ - 60^\circ = 50^\circ[/tex].
[tex]\angle ACB[/tex] and [tex]\angle ACD[/tex] form another pair of supplementary angles. Their sum should also be [tex]180^\circ[/tex]. [tex]\angle ACB = 50^\circ[/tex] [tex]\implies \angle ACD = 180^\circ - \angle ACB = 180^\circ - 50^\circ = 130^\circ[/tex].
Answer:
sum should also be . .
Step-by-step explanation:
It takes Dan 32 minutes to complete 2 pages of math homework. At this rate, how
many pages does he complete in 200 minutes?
Answer:
12.5 pages
Step-by-step explanation:
32/2= 16 min per page
200/16= 12.5 pages
or
200/x = 32/2
200/32= 6.25
6.25*2= 12.5
Answer:
Step-by-step explanation:
12.5
because you divide and then multiply it by 2
PLEASE ANSWER THIS QUICKLY I NEED THIS DONE BY 3:45!!!!!
A kitchen scale shows the weight of a piece of fruit is 2 pounds. The actual weight of the fruit is 1.6 pounds. What is the percent error for the kitchen scale?
The percent error in the kitchen scale's measurement is found using the formula ((Measured Value - Actual Value) / Actual Value) × 100%, resulting in a 25% error when comparing the scale's reading of 2 pounds to the actual weight of 1.6 pounds.
Explanation:The question asks to find the percent error for a kitchen scale when measuring the weight of a piece of fruit. The percent error is a way of comparing the accuracy of a measurement to the actual value, and it's calculated using the formula: Percent Error = ((|Measured Value - Actual Value|) / Actual Value) × 100%. In this case, the measured value is 2 pounds and the actual value is 1.6 pounds.
First, subtract the actual value from the measured value: 2 - 1.6 = 0.4 pounds. Then, divide this difference by the actual value: 0.4 / 1.6 = 0.25. Finally, multiply by 100% to find the percent error: 0.25 × 100% = 25%.
Therefore, the percent error for the kitchen scale is 25%. This calculation helps in understanding the accuracy and reliability of measurements taken by the scale.
Find x and y on a 30 60 90 triangle number 9
Answer:
x=12, y=[tex]12 \sqrt{3} [/tex]
Step-by-step explanation:
Please see attached picture for full solution.
sinθ= opp/hyp
cosθ= adj/hyp
One container is filled with a mixture that is 30% acid. A second container is filled with a mixture that is 50% acid. The second container is 50% larger than the first, and the two containers are emptied into a third container. What percent of acid is the third container?
Answer:
42% acid
Step-by-step explanation:
Suppose that these two storage containers are filled to complete capacity?
That makes the second container have 3 volume parts and the first container having 2 volume parts.
v*(1.50)= (3/2)*v
First Container 2v 30% acid
Second Container 3v 50% acid
The mixture of all of this is in the third container. Two parts plus three parts is 5 parts for the mix volume.
=(2*30+3*50)/5
=210/5
=42
So,
42 % Acid, mixture
Final answer:
After calculating the quantities of acid from both containers and their total volume, the final acid concentration in the mixture in the third container is found to be 42%.
Explanation:
The student has asked about finding the percentage of acid in a third container after mixing two solutions with different acid concentrations. This question involves proportion and percentage calculations, which are commonly covered in high school mathematics.
To find the final concentration of acid in the third container, we can use the formula final concentration = (quantity of acid in container 1 + quantity of acid in container 2) / total volume. Assume the first container has a volume of V liters. Since the second container is 50% larger, it has a volume of 1.5V liters.
Acid in the first container = V liters × 30% = 0.3V liters
Acid in the second container = 1.5V liters × 50% = 0.75V liters
Total volume = V + 1.5V = 2.5V liters
Thus, the final concentration of acid = (0.3V + 0.75V) / 2.5V = 1.05V / 2.5V = 42%.
The final acid concentration in the third container is 42%.
A table representing the function f(x) = 2(three-halves) Superscript x is shown below. A 2-column table has 4 rows. The first column is labeled x with entries (0, 1, 2, 3). The second column is labeled f (x) with entries 2, 3, 4.5, 6.75. What is true of the given function? The function increases at a constant additive rate. The function increases at a constant multiplicative rate. The function has an initial value of 0. As each x value increases by 1, the y values increase by 1.
Answer:
The function increases at a constant multiplicative rate.
Step-by-step explanation:
I had it
The correct conclusion about the function is 2: "the function increases at a constant multiplicative rate".
Given information:
The value of function f(x) is shown in the below table:
x 0 1 2 3
f(x) 2 3 4.5 6.75
So, the value of x changes from 0 to 3, and the value of function f(x) changes from 2 to 6.75.
Following observations can be made using the given values:
The function starts with an initial value of 2.The value of function increases with a constant multiplicative rate. The constant rate is 1.5 times. The increase of value of function is not constant as it is multiplicative.From the above conclusions and the given options, it can be said that the correct option is 2.
Therefore, the correct conclusion about the function is 2: "the function increases at a constant multiplicative rate".
For more details, refer to the link:
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what’s the hypotenuse?
Answer:
c = 10 feet
Step-by-step explanation:
Use the Pythagorean theorem: a^2 + b^2 = c^2
Step 1: Plug in the information
(6)^2 + (8)^2 = c^2
36 + 64 = c^2
100 = c^2
sqrt(100) = sqrt(c^2)
10 = c
Answer: c = 10 feet
will your balance increase on your credit card from month to month if you have a balance, but no new charges?why?
Answer:
yes (if no payments are made)
Step-by-step explanation:
If you have no new charges and you make no payments, you will incur interest costs every month.
Hence yes, you balance will increase by amount of interest owed.
Solve the value of y.
I believe that y=17.8
I hope that helps you!
The path of a ball kicked from the ground can be modeled by the equation y=−1/3(x−3)(x−21), where x and y are measured in feet. The x-axis represents the ground. How far does the ball land from where it is kicked?
The ball lands
feet from where it is kicked.
Answer:
The ball lands 18 feet from where it is kicked.
Step-by-step explanation:
Given : The path of a ball kicked from the ground can be modeled by the equation [tex]y=-\frac{1}{3}(x-3)(x-21)[/tex], where x and y are measured in feet. The x-axis represents the ground.
To find : How far does the ball land from where it is kicked?
Solution :
According to question,
The value of y is zero as it is kicked from ground.
So, [tex]0=-\frac{1}{3}(x-3)(x-21)[/tex]
Applying zero product property,
[tex]a\cdot b\cdot c=0\Rightarrow a=0\text{ or }b=0\text{ or }c=0[/tex]
i.e. [tex]-\frac{1}{3}\cdot (x-3)\cdot (x-21)=0[/tex]
[tex]x-3=0[/tex]
[tex]\Rightarrow x=3[/tex]
[tex]\text{ or }x-21=0[/tex]
[tex]\Rightarrow x=21[/tex]
The distance the ball land from where it is kicked is d=21-3=18.
Therefore, the ball lands 18 feet from where it is kicked.
The ball lands 18 feet from where it is kicked.
To find out how far the ball lands from where it is kicked, we need to determine the horizontal distance traveled by the ball when it hits the ground again. The x-axis represents the ground, so we are looking for the x-coordinate of the point where the ball lands, which is when y = 0.
Given the equation of the path of the ball:
[tex]\[ y = -\frac{1}{3}(x - 3)(x - 21) \][/tex]
We set y to 0 to find the x-coordinates where the ball touches the ground:
[tex]\[ 0 = -\frac{1}{3}(x - 3)(x - 21) \][/tex]
This equation can be factored to:
[tex]\[ 0 = (x - 3)(x - 21) \][/tex]
Setting each factor equal to zero gives us two solutions for x:
[tex]\[ x - 3 = 0 \quad \text{or} \quad x - 21 = 0 \][/tex]
[tex]\[ x = 3 \quad \text{or} \quad x = 21 \][/tex]
These solutions represent the x-coordinates where the ball is kicked (x = 3) and where it lands (x = 21). To find the distance between these two points, we subtract the smaller x-coordinate from the larger one:
[tex]\[ \text{Distance} = 21 - 3 = 18 \text{ feet} \][/tex]
However, since the ball is kicked from the ground and lands back on the ground, the distance it travels horizontally is the absolute value of the difference between the two x-coordinates:
[tex]\[ \text{Horizontal distance} = |21 - 3| = |18| = 18 \text{ feet} \][/tex]
a bakery uses 3/5 a cup of sugar for each cookies.How many batches of cookies can they make with 9 cups of sugar?
Answer:
12
Step-by-step explanation:
divide 9 by 3/5 or .75
Find the square root of 60 accurate to one decimal place (and two decimal places)
The specific answer is
7.74596669241
Please help me with this problem, The answer is 192 but how do you solve it??
Answer:
192
Step-by-step explanation:
You can form a rectangle from sides 15 and 3, another rectangle with dimensions 10 and 9, another rectangle with dimensions 6 and 5, and a triangle with sides 9 and 6 (all formed by extending lines inside the figure, don't want to go into detail). Add all the areas and the answer would be 192:
15*3 =45
10*9=90
6*5=30
0.5*9*6=27;
45 + 90 +30 + 27 = 192 units squared
Which of the following sets does not contain any irrational numbers?
{-5.12,pi,30}
{square root of 80, 100, 6.56}
{ 9/2 , square root of 100, 5.123}
{5.123..., 1/2 , -65}
Answer:
{ 9/2 , square root of 100, 5.123}
Step-by-step explanation:
The answer would be an option (D) {5.123..., 1/2, -65}. This set does not contain any irrational numbers.
What are real numbers?Real numbers are defined as the value of a continuous quantity that can represent a distance along a line of a real number in mathematics. Rational and irrational numbers are both real numbers. Rational numbers such as integers (-7, 0, 4), fractions(5/2,7/2, 4.2), and irrational numbers such as √5, π, etc., are all real numbers.
According to the given options
(A) {-5.12,pi,30}
Here the irrational number is pi
(B) {square root of 80, 100, 6.56}
Here the irrational number is the square root of 80 i.e. (√80)
(C) { 9/2, square root of 100, 5.123}
Here the irrational number is the square root of 100i.e. (√100)
(D) {5.123..., 1/2, -65}
Here this set does not contain any irrational numbers
Hence, the answer would be option (D) {5.123..., 1/2, -65}. This set does not contain any irrational numbers.
Learn more about irrational numbers here:
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A cylinder has a base diameter of 8 inches and a height of 7 inches. What is its volume in cubic inches, to the nearest tenths place?
Answer:
351.9 cubic in
Step-by-step explanation:
The volume of a cylinder is hr²π.
r is half the diameter, so 8/2 is 4.
Plug in your h and r and get:
7 * 4² * π
7 * 16 * π
112π
Multiply the π and you'll get about 351.9 cubic in
The volume of the cylinder is 352 cu.inches.
What is a Cylinder?A cylinder is a three-dimensional figure, it is made up of parallel circular discs of the same radius.
The cylinder consists of two circular bases, connected by a curved surface at a fixed distance.
A cylinder has a base diameter of 8 inches and a height of 7 inches.
The volume is the space occupied by a three-dimensional object.
The volume of the cylinder is given by the formula
V = πr²h
Here, r is the radius of the base,
h is the height of the cylinder.
The volume is determined in cubic units.
The value of r = diameter / 2
r = 8/2 = 4 inches
h = 7 inches.
Substituting these values in the formula to determine the volume,
Volume = (22/7) * 4² * 7
Volume = (22/7) * 16 * 7
Volume = 22 * 16
Volume = 352 cu.inches
To know more about Cylinder
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21, 28, and 36 units is a triangle
Answer:
Yes, it could be a triangle.
Step-by-step explanation:
If the Pythagorean Theorem is satisfied, then these three side lengths represent a right triangle:
21^2 + 28^2 = 36^2 => 1225 = 1296 FALSE; we don't have a right triangle here.
However, the sum 21 + 28 is greater than 36, so we could indeed construct a triangle from these 3 side lengths. It just wouldn't be a right triangle.
The smalltown Zoo has 2 African elephants. An elephant eats 230 pounds of food per day. How many pounds of food are needed to feed the elephants for an entire week?
Answer:
3,220
Step-by-step explanation:
3220 is how much food you will need for both elephants
tan x= 3÷5 nearest tenth
Answer:
17.0°
Step-by-step explanation:
We want to solve
[tex] \tan(x) = \frac{3}{10} [/tex]
We take inverse tangent of both sides using a scientific calculator to get:
[tex]x = { \tan}^{ - 1} ( \frac{3}{10} )[/tex]
[tex]x = 16.6992[/tex]
We round to the nearest tenth to get;
[tex]x = 17.0 \degree[/tex]
Therefore the value of x is 17.0°
The reference angle for 305
Answer:
55°
Step-by-step explanation:
The angle 305° is in the fourth quadrant
To find the related acute angle ( the reference angle ) subtract from 360°
reference angle = 360° - 305° = 55°
Which quadrilateral is a trapezoid?
Answer:
Look for the parallelograms , or squares , or rectangles . Those quadrilaterals are usually trapezoids .
Step-by-step explanation:
Answer:
You cna have trapezoid and isosceles trapezoid both have either inward end lengths and parallel lines so some look like a flat roof with identical slant. one going one way and the other slant going the other.
Step-by-step explanation:
A line goes through the points (-1,9) and (1,1).Write the equation of this line in point slope form using one of these points.
Answer:
y-9= -4(x+1)
Step-by-step explanation:
First, you should know what the format for point slope form is. y-y1=m(x-x1). Now, fill in the points to the x1 and y1 variables. It doesn't matter what ordered pair you use. If the number you fill in is negative, for example, -1, change it to a positive 1. If you're plugging in a positive number such as 9, it becomes -9. Now, it may look like this: y-9=m(x+1). However, you still need to find slope. You can use the expression y-y1/x-x1. 9-1=8. -1-1= -2. So, your slope is 8/-2. However, you can simplify this to -4. Now, plug in -4 to your equation to have your final answer: y-9=-4(x+1).
Kris is staining 30 wooden rectangular fence pieces. The fence pieces are different sizes, and Kris wants
to determine the approximate number of square feet of paint she will need. She decides to take a sample
of 4 fence pieces and calculate the mean of the areas instead of calculating the area of each fence piece.
Which is a true statement about this problem?
A. The sample size is 30,
B. The population is the 4 fence pieces
C. The mean area of the 4 fence pieces is a parameter
D. The mean area of the 4 fence pieces multiplied by 30 would be similar to the total area.
Answer:
D
Step-by-step explanation:
Hey! Some easy points people. Is this a polygon and what shapes would be a polygon and why?
HELP ME PLEASE BE QUICK
Answer:
Radius is 5/2 or 2.5 inches
Step-by-step explanation:
C = 2πr
5π/2π = 2πr/2π
5/2 = r
Answer: Radius is 5/2 or 2.5 inches
Solve the equation:
12/x = 3/2
Hence the value of x is 8
Answer:
8
Step-by-step explanation:
12/x = 3/2
(x)(12/x)=3/2x
12=3/2x
(12)(2/3)=x
8=x
Challenge: Find the area of the polygon.
space.
2.4 m
0.4 m
0.4
m
0.4 m
1.0
ms
W 90
Your answer
Answer:
[tex]3.6 {m}^{2} [/tex]
Step-by-step explanation:
The area of a rectangle is length times width.
We divide the polygon into 4 rectangles:
The area of the first rectangle is :
[tex]0.4 \times 0.4 = 0.16 {m}^{2} [/tex]
The area of the second rectangle is
[tex]2.4 \times 0.6 = 1.44 {m}^{2} [/tex]
The area of the 3rd rectangle is
[tex]1.6 \times 1 = 1.6 {m}^{2} [/tex]
The area of the fourth rectangle is
[tex]0.4 \times 1 = 0.4 {m}^{2} [/tex]
Putting all together, the area of the polygon is;
0.16+1.44+1.6+0.4=3.6m²
Ian is going to use a computer at an internet cafe. The cafe charges an initial fee to
use the computer and then an additional price per minute of usage. It is known that
the total charge to use a computer for 5 minutes would be $6 and that the additional
rate per minute of use is $0.40. Write an equation for the function C(t),
representing the total cost of using a computer for t minutes at the internet cafe.
Answer:
C(t) = 6 + .4t
Step-by-step explanation:
Since there is a constant rate of 6 for the first 5 minutes, that would be a value itself. After that, it would always differ by .4 every minute, making this the function.