Answer:
x< 3
7x<21
Divide each term in 7x<21 by 7.
Cancel the common factor of 7.
Divide 21 by 7.
The result can be shown in multiple forms.
Inequality Form:
x< 3
Interval Notation:
(−∞, 3)
A playground slide is 14. 5 feet long with an 8. 5-foot tall ladder. A playground slide is 14. 5 feet long and has an 8. 5 foot tall ladder. The angle formed by the ladder with the ground is 90 degrees. The angle formed by the slide with the ground is x. What is the measure of the angle that the slide makes with the ground, x, to the nearest degree?.
The angle made by the slide of length 14.5 ft with the ground is 36°
The length of the slide = 14.5ft
The length of the ladder = 8.5 ft
The angle made by the ladder and ground = 90°
The angle formed by the slide can be found using the Pythagoras theorm,
sinθ = O / H
where θ is the angle made by the slide
O is the side opposite to the angle of the slide
H is the side that is hypotenuse with the slide
Let us rearrange the above equation in order to get the angle of the slide,
θ = sin⁻¹ (O/H)
Let us substitute the known values in the above equation, we get
θ = sin⁻¹ (8.5 / 14.5)
= sin⁻¹ (0.586)
≈ 36°
Thus, the angle of the slide is 36°
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Is 48 a factor of 8?
No, number 48 is not the factor of 8 , 48 is a multiple of 8.
As given in the question,
Given number is equal to ,
48.
Factors are those numbers which divide the given number completely without leaving any remainder.
The factors of the number 48 are equal to:
1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Multiple of 8 are equal to :
8, 16, 24, 32, 40, 48, .....
48 is not considered as a factor of 8 it the multiple of the number 8.
8 is the factor of the given number 48.
Therefore, number 48 is not the factor of 8 , it is considered as the multiple of 8.
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A hotel has four elevators. One of them
is a freight elevator. When pressing the
button, one of the elevators randomly
services your floor. If you use the
elevators seven times, what is the
probability that you use the freight
elevator exactly four times?
O 57.68%
O 5.768%
O 68%
O 5.6%
On solving the provided question, we can say that probability, P( use the freight elevator exactly four times) = 4/7 *100 = 57.1428571429 %
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
the favorable out come is 4 times
total outcomes = 7 times
Probability, P( use the freight elevator exactly four times) = 4/7 *100 = 57.1428571429 %
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Can someone explain how to solve this
Answer:
(-(11 w^2 - 13))
Step-by-step explanation:
Simplify the following:
2 w^2 - 13 w^2 + 13
Grouping like terms, 2 w^2 - 13 w^2 + 13 = (-13 w^2 + 2 w^2) + 13:
(-13 w^2 + 2 w^2) + 13
2 w^2 - 13 w^2 = -11 w^2:
-11 w^2 + 13
Factor -1 out of -11 w^2 + 13:
Answer: (-(11 w^2 - 13))
In a group consisting of 21 people from small towns and 28 people
from cities, 15 of the small-town residents and 21 of the city
residents exercise regularly. What is the probability that a person
selected at random from this group exercises regularly, given that the
person comes from a small town?
Enter your answer as a fraction, a decimal value accurate to two
places, or a percent accurate to the nearest whole number.
Answer:
31%
Step-by-step explanation:
21 s - 15 exercise
28 c - 21 exericse
15/49 = 31%
Answer:
85Step-by-step explanation:
21 + 28 = 49
49 + 15 = 64
64 + 21 = 85
Have a Nice Day : ) if Incorrect sorry.
Sean deposits $275 each month into his savings. He started with $1000 in the account.
The slope of the line will be
In 10 months the savings will be at
The graph of this line will
y = savings and x = months
Type the equation WITH NO SPACES
(positive or negative)
dollars (type the number)
(increase or decrease)
4
The slope of the line will be,In 10 months the savings will be at,The graph of this line will positive slop.
What is positive slop?Sean deposits $275 each month into his savings. He started with $1000 in the account.
The slope of the line will be In 10 months the savings will be at ,The graph of this line will y = savings and x = months
When two variables have a positive slope, it implies that they are positively correlated; that is, when x rises, y rises as well, and when x falls, y falls as well. A line on a line graph that has a positive slope rises as the line advances from left to right.Positive slopes are founded on the idea that when x rises, y rises as well, making the ratio of y/x positive. Negative slopes are founded on the idea that when x rises, y falls. This results in a negative change in y and a positive change in x, which yields a negative result.The slope of the line will be,In 10 months the savings will be at,The graph of this line will positive slop.
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Evaluate each expression when X=3/4 and y=2.5
1. 8x
2. y2
3. 10/y
Answer:
1. 6
2. 5
3. 4
Step-by-step explanation:
For each expression, Substitute the variable for what is given in the statement.
1. 8×(3/4)=6
2. 2.5×(2)=5
3. 10/2.5=4
What kind of function is an exponential function?
An exponential function is a function in which the variable (usually represented by "x") is the exponent, rather than the base.
The most common form of an exponential function is f(x) = b^x, where b is a positive constant known as the base of the function.
Exponential functions can take many different forms, but they all have one thing in common: the variable is in the exponent. In most cases, the base of the function is a positive constant, and the exponent is the input variable. Exponential functions can also be used to model a wide variety of real-world phenomena, such as population growth, compound interest, and decay of radioactive materials.
The graph of an exponential function is always a smooth curve that increases or decreases at an increasing rate. The slope of the curve increases as x increases, which means that the rate of change of the function also increases as x increases.
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Pls help 4 cups of flour are mixed with 24 cups of sugar. How many cups of flour should be used if 84 cups of sugar are used?
The amount of flour needed for 84 cups of sugar will be 14 cups of flour.
How to measure quantity?A property that can be measured like, mass, length, time, volume, and pressure. A unit is a standard quantity against which a quantity is measured for example, gram, metre, second, litre, pascal, which are units of the preceding quantities.
To measure the quantity of cups of flour needed to mix 84 cups of sugar;
24 cups of sugar = 4 cups of flour
84 cups of sugar = ? cups of flour = 84/24 x 4
for 84 cups of sugar = 3.5 x 4 = 14 cups of flour.
It will take 14 cups of flour to mix 84 cups of sugar.
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1. Which ordered pairs are solutions of the
inequality 5y - 3x ≤ 7?
A. (0,0)
B. (3,5)
D. (1, 2.5)
(C.) (-2,-5)
E. (5,-3)
Graph
The ordered pairs (0,0), (- 2, - 5), (5, - 3) are solutions of the inequality 5y - 3x ≤ 7.
What is inequality?A linear inequality is one that would result in a linear equation if we were to substitute the equals relation for the inequality. When solving the inequality, the direction of an inequality is reversed when we multiply or divide both sides by a negative value.The collection of all solutions makes up the solution set for an inequality.
Here,
Now, in order to determine which ordered pairs are a solution, we need to substitute the coordinate points into the left side of the inequality and check against right side for the validity.
A. (0,0)
5(0) - 3(0) = 0 ≤ 7
So, (0,0) is a solution.
B. (3, 5)
5(5) - 3(3)= 25 - 9 = 16 ≥ 7
So, (3, 5) is not a solution.
C. (1,2.5)
5(2.5) - 3(1)= 12.5 - 3 = 9.5 ≥ 7
So, (1,2.5) is not a solution.
D. (- 2, - 5)
5(-5) - 3(-2) = - 25 + 6 = - 19 ≤ 7
So, (- 2, - 5) is a solution.
E. (5, - 3)
5(-3) - 3(5) = - 15 - 15 = -30 ≤ 7
So, (5, - 3) is a solution.
Hence, the ordered pairs (0,0), (- 2, - 5), (5, - 3) are solutions of the inequality 5y - 3x ≤ 7.
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The cost of 1 cap and 1 wallet is
£28.
The cost of 2 caps and 1 wallet is
£45.
a) How much does 1 cap cost?
b) How much does 1 wallet cost?
Answer:
cap: 17, wallet: 11
Step-by-step explanation:
45 - 28 = 17
45 - (17 x 2) =
45 - 34 = 11
could also do:
28 - 17 = 11
Hope this helps have a good day
What is the exponential form of 64 *?
The exponential form of 64 is 2^6.
A food delivery driver is 4 3/4 miles west of a city's library when he receives a call to pick up food from a restaurant. The restaurant is 1.5 miles east of the library. Assume the driver takes the most direct route to the restaurant. How will the driver drive to the restaurant? Select from the drop-down menus to correctly complete the statement.
If a food delivery driver is 4 3/4 miles west of a city library when he gets a call to pick up food from a restaurant, the mixed fraction is 4.75 miles, and the overall distance is 6.25 miles.
What is a fraction?The numerator, which is the portion of a fraction that is at the top, and the denominator, which is the portion that is at the bottom, are its two constituent parts.
It is given that:
A food delivery driver is 4 3/4 miles west of a city library when he receives the call to pick up food from a restaurant.
The restaurant is 1.5 miles east of the library.
The mixed fraction can be written as:
4 3/4 = 19/4 = 4.75
Total = 4.75 + 1.50 = 6.25 miles
Thus, If a food delivery driver is 4 3/4 miles west of a city library when he gets a call to pick up food from a restaurant, the mixed fraction is 4.75 miles, and the overall distance is 6.25 miles.
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Solve for x.
2(x−3 1/2)=10 3/4
Enter your answer as a mixed number in simplest form in the box.
Answer:
x = 71/8
Step-by-step explanation:
Solve for x:
2 (x - (3 + 1/2)) = 10 + 3/4
Put 3 + 1/2 over the common denominator 2. 3 + 1/2 = (2×3)/2 + 1/2:
2 (x - (7/2)) = 10 + 3/4
2×3 = 6:
2 (x - (1/2 6 + 1/2)) = 10 + 3/4
6/2 + 1/2 = (6 + 1)/2:
2 (x - (7/2)) = 10 + 3/4
6 + 1 = 7:
2 (x - 1/2 7) = 10 + 3/4
Put each term in x - 7/2 over the common denominator 2: x - 7/2 = (2 x)/2 - 7/2:
2 ((2 x)/2 - 7/2) = 10 + 3/4
(2 x)/2 - 7/2 = (2 x - 7)/2:
2 (1/2 (2 x - 7)) = 10 + 3/4
(2 (2 x - 7))/2 = 2/2×(2 x - 7) = 2 x - 7:
(2 x - 7) = 10 + 3/4
Put 10 + 3/4 over the common denominator 4. 10 + 3/4 = (4×10)/4 + 3/4:
2 x - 7 = ((4×10)/4 + 3/4)
4×10 = 40:
2 x - 7 = 40/4 + 3/4
40/4 + 3/4 = (40 + 3)/4:
2 x - 7 = ((40 + 3)/4)
40 + 3 = 43:
2 x - 7 = 43/4
Add 7 to both sides:
2 x + (7 - 7) = 43/4 + 7
7 - 7 = 0:
2 x = 43/4 + 7
Put 43/4 + 7 over the common denominator 4. 43/4 + 7 = 43/4 + (4×7)/4:
2 x = (43/4 + (4×7)/4)
4×7 = 28:
2 x = 43/4 + 28/4
43/4 + 28/4 = (43 + 28)/4:
2 x = ((43 + 28)/4)
43 + 28 = 71:
2 x = 71/4
Divide both sides by 2:
x = (71/2)/4
4×2 = 8:
Answer: x = 71/8
Identify the center of dilation. plss
So on solving the provided question we cans say that rom the graphs Area 0f triangle = 1/2 AB = 1/2 . 250 . 200 = 25000sq units
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle.
Here,
Given :
from the graph we can say that -
B = 250
A = 200
Area 0f triangle = 1/2 AB = 1/2 . 250 . 200
Area = 25000sq units
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What is the range of f(x) = |x| − 5?
Answer:
from -5 to infinity
Step-by-step explanation:
Hope this helps.
A cubical box of cardboard has an edge 4.8 m long. how many closed cuboidal boxes of dimension 24 cm×12cm×10cm can be made out of it
Answer
38,400
Step by Step Explanation
Firstly we have to get the volume of the cube box in cm³ which is 480³ = 110,592,000
Secondly we have to get the volume of the cuboid in cm³ too which is 24×12×10 = 2,880
And lastly, 110,592,000/2,880 = 38,400
The number of closed cuboidal boxes is 38400.
Side of the Cubical Box, a = 4.8 m
Using the formula,
Volume of a cube: V = a³
V1 = a³
V1 = (4.8)³
V1 = 110.59 m³
Dimension of Cuboidal Boxes,
Length, l = 24 cm
Breadth, b = 12 cm
Height, h = 10 cm
Using the formula,
Volume of cuboid : V = l × b × h
V2 = l × b × h
V2 = 24 × 12 × 10
V2 = 2880 cm³ or 0.0028m³
Number of closed cuboidal boxes,
[tex]=\frac{Volume of cube}{Volume of cuboid}[/tex]
[tex]= \frac{110.59}{0.0028}[/tex]
[tex]= 38400[/tex]
Hence, there are 38400 closed cuboidal boxes.
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Which of the following is logically equivalent to~ (~p⇒q)?p ∧qp ∧~ q~p ∧q~ p ∧~q
p ∧qp ∧~ q~p ∧q~ p ∧~q is logically equivalent to~ (~p⇒q) for the given question
If p → q
and q →r , then you can use the law of transitivity to conclude
q→r.
That is a basic law of sillogisms.
An example will help you to understand the transivity law:
Make p, stand for 3 > 3/4, q stand for 3/4 > 15 / 20, the you can conclude that 3 > 15 / 20.
3 > 3/4
3 /4 > 15 / 20
Then, 3 > 15 /20.
This is, from the fact that you know that 3 is gretar than 3/4 and that 3/4 is greater than 15/20, you can conclude that 3 > 15 / 20. That is transitivity and is a law of logic, which you can use to get conclusions.
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The formula for the area of a square is A = s^2 where s is the side length. A square garden has a side length of x^4y. What is the area of the garden?
Why is a line of longitude called a meridian Class 6?
A line of longitude is called a meridian because it connects the North and South poles and forms a circle around the Earth, like the sun's meridian path during the day.
A line of longitude is an imaginary line that circles the Earth and runs in a north-south direction. It is measured in degrees and divides the Earth into two equal halves, the Eastern Hemisphere and the Western Hemisphere. This line is called a meridian because it is derived from the Latin word meridies which means mid-day or noon. The sun's path across the sky during the day follows a meridian from the North Pole to the South Pole, and this is what inspired the term "meridian" to describe the line of longitude.
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Determine the type of dilation shown and the scale factor used.
Enlargement with scale factor of 1.5
Enlargement with scale factor of 2.5
Reduction with scale factor of 1.5
Reduction with scale factor of 2.5
The figure's scale factor and type of dilatation are
enlargement using a 2.5 scale factorFinding the type of dilatationWhat are scale factors?Scale factors are applied to alter the size of the image. The circumstance of increase is frequently referred to as enlargement or magnification.
Given that the preimage is smaller than the image, the situation is enlargement. This implies that the scale factor will also be higher than 1.
Establishing a baseline, say side 8 and side 20 in the preimage and the image respectively. Then, assuming the factor is k, get the factor.
8k = 20
k = 20/8
k = 2.5
The scale factor is 2.5
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Write the quadratic equation whose roots are -3 and 6, and whose leading coefficient is 4
The quadratic equation whose roots -3 and 6 and leading coefficient 4 is 4x²-12x-72 = 0
What is quadratic equation?A quadratic equation is an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is y = ax^2 + bx + c, where a, b, and c are numbers and a cannot be 0. Examples of quadratic equations include all of these: y = x² + 3x + 1 , y = x²+x-1
If the root of the quadratic equation are -3 and 6
then, x = -3 and x= 6
therefore x+3 = 0 and (x-6) = 0
(x+3)(x-6) = 0
with leading coefficient 4,
then 4( x+3) ( x-6) = 0
4 ( x²-6x+3x-18) = 0
4( x²-3x-18) = 0
open the parentheses,
4x²-12x-72 = 0
Therefore, the quadratic equation with root -3 and 6 and leading coefficient 4 is 4x²-12x-72 = 0
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(40 PTS, HELP ME) In the following diagram, A || B.
Use complete sentences to explain how the special angles created by the intersection of A and B by D can be used to solve for x.
Solve for x, showing all of your work
The answer is 24
What are supplementary angles?Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°.
Given here: A || B.
Now if transversal D intersects A and B we have
If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary, i.e. they add up to 180°. When two lines intersect each other, then the opposite angles, formed due to intersection, are called vertical angles or vertically opposite angles.
Thus we have 4x+5+3x+7=180
7x=168
x=24
Hence, The value of x is 24
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Solve for y
x = x (2x - 4) + y
The first x is squared I just can’t put a square in brainly
Answer:
y = −x^2 + 4x
Step-by-step explanation:
x^2 = x (2x - 4) + y
Let's simplify it and we get
x^2 = 2x^2 - 4x + y
Now, we want to get the y by itself
x^2 = 2x^2 - 4x + y
-x^2 = -4x + y
-x^2 + 4x = y
So, our answer is y = −x^2 + 4x
what is the answer please i need help -2.6f+0.4f-14-4
Answer: [tex]-2.2f-18[/tex]
Step-by-step explanation:
[tex]-2.6f+0.4f-14-4=f(-2.6+0.4)+(-14-4)=-2.2f-18[/tex]
A recipe uses 4 cups of milk to make 24 servings. If the same amount of milk is used for each serving, how many servings can be made from two gallons?.
The servings can be made from two gallons is 192 serving
From the question, we know that 4 cups of milk equals to 24 servings.
4 cups = 24 serving
To solve total serving which can be made from two gallons of milk, we have to convert unit from gallon into cup, so it can be multiplied with the amount of serving
1 gallon equals to 4 quarts .....(1)
1 quart equals to 2 pints ..........(2)
From info no. 1 and 2, we can know that
1 gallon = 4 x 2 = 8 pints ..........(3)
Next, 1 pint equals to 2 cups ...........(4)
Since 1 gallon equals to 8 pints from information no. 3, we combine information no. 3 and information no. 4 to convert gallon to cup.
1 gallon = 8 x 2
= 16 cups ....................(5)
For 2 gallon, we just simply multiply info no 5
2 gallon = 16 x 2 cups
= 32 cups .................(6)
In the case of 4 cups can make 24 serving, Total number of serving can be calculated with info no. 6
Number of serving = 32 / 4 x 24 = 8 x 24 = 192 serving
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What happens when you take the absolute value of a complex number?
The origin in the complex plane is represented by the number 0. Therefore, the separation between a complex number and the complex plane's origin (zero) equals its absolute value.
What happens when you calculate a number's absolute value?A number, variable, or expression is enclosed in two vertical bars to represent an absolute value in mathematics, as in the following example: A number's absolute value is always either positive or zero when calculated. The absolute value remains the same whether the initial value is already positive or zero.The origin in the complex plane is represented by the number 0. Therefore, the separation between a complex number and the complex plane's origin (zero) equals its absolute value.You won't have a solution if your absolute value expression is set to a negative quantity.To learn more about absolute value refer to:
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Solve the system of linear equations by elimination.
-5x+12y=8
2x-8y=0
Answer:
x = -4
y = -1
Step-by-step explanation:
-5x+12y=8
2x-8y=0
We multiply the first equation by 2 and the second equation by 5
-10x + 24y = 16
10x - 40y = 0
-16y = 16
y = -1
Now put -1 back in for y and solve for x
-5x + 12(-1) = 8
-5x - 12 = 8
-5x = 20
x = -4
Let's check
-5(-4) + 12(-1) = 8
20 - 12 = 8
8 = 8
So, x = -4 & y = -1 is the correct answer.
I kinda need help :<
For each coordinate grid, identify a pair of congruent figures. Then determine a congruence transformation that maps the pre-image to the congruent image.
The coordinates of the vertices of △ABC are A(-4,1), B(-2,4), C(-2,0), △CDE are C(-1,-1), D(1,1), E(4,-1), and △IHG are I(2,3),H(4,0), G(4,4).
The transformation is △ABC reflected with the line y =2 and shifted 6 units right sides.
What are the vertices of a triangle?
A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.
There are three triangles. The vertices of △ABC are A(-4,1), B(-2,4), C(-2,0).
The vertices of △CDE are C(-1,-1), D(1,1), E(4,-1). The vertices of △IHG are I(2,3),H(4,0), G(4,4).
The △ABC is congruent with △IHG.
The difference between the x-coordinate of A and I is (2 - (-4)) = 6
The difference between the x-coordinate of B and H is (4 - (-2)) = 6
The difference between the x-coordinate of C and G is (4 - (-2)) = 6
The sum of the y-coordinate of A and I is (3+1) = 4
The sum of the y-coordinate of B and H is (4 + 0) = 4
The sum of the y-coordinate of C and G is (4 + 0) = 4
The midpoint of y-coordinate of △ABC and △IHG is 4/2 = 2
The △ABC is reflected by y = 2 and shifted 6 units right side.
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Determine the domain of the graph
You need to look at the graph and identify where the x-axis is located.
In this graph Domain is {-2,2,4,6}
How to determine the domain of a graph?To determine the domain of a graph, you need to look at the graph and identify where the x-axis is located.
The domain of a graph is the set of all possible x-values for which the graph is defined.
In other words, it is the set of all x-values that the graph will plot.
For example, if the x-axis of the graph is between 0 and 10, then the domain of the graph is the set of all numbers between 0 and 10, including 0 and 10.
The domain of a sine wave graph is all real numbers. This is because the sine wave graph is periodic and repeats itself over and over again.
In this graph domain is {-2,2,4,6}
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