1) Examining the expressions, let's factorize them taking the LCM out of the parentheses
5a +10 The LCM 5,10 is 5
5(a +2)
16k +12 The LCM 16, 12 is 4
4(4k +3)
2) So the answers are 5(a +2) and 4(4k +3) notice that if we distribute those factors you'll get the initial form.
translating english Phrases to mathematical expression
the square of a number y subtracted by 1
The mathematical expression for the given English phrase is given by [tex]x^{2}-1[/tex]
What is a mathematical expression?
In mathematics, a mathematical expression is a combination of finite symbols that is well-formed according to rules depending on the context.
We are given an English phrase as the square of a number subtracted by 1
Let the given number be 'x'
The square of the number i.e. x will be [tex]'x^{2} '[/tex]
Now square of the number subtracted by 1 is [tex]x^{2}-1[/tex]
Hence the mathematical expression for the English phrase is [tex]x^{2} -1[/tex]
To learn more about mathematical expression please refer
https://brainly.com/question/723406
#SPJ13
help me please
thank you
Answer:
Domain: A, [1, 7]
Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Two pools are being filled with water. To start, the first pool has 1900 liters of water and the second pool had 1372 liters of water. Water is being added to the first pool at a rate of 31 liters per minute. Water is being added to the second pool at a rate of 42 liters per minute.Let x be the number of minutes water has been added(a) For each pool, write an expression for the amount of water in the pool after x minutes.Amount of water in the first pool (in liters) = Amount of water in the second pool (in liters) =(b) Write an equation to show when the two pools would have the same amount of water.
For the first pool, we start with 1900 liters, and add water at a rate of 31 liters per minute, So the equation for the total amount of water in liters in terms of minutes is given by:
Water in Pool 1 = 1900 + 31 x
The other pool (Pool 2) starts with 1372 liters and the rate of water added is 42 liters per minutes, then after "x" minutes of being filled at this rate be have:
Water in Pool 2 = 1372 + 42 x
(b) For this part of the problem, when we assume that both amounts of water are the same, we equal the amount of water on each pool, connecting them via an equal sign:
Water in Pool 1 = Water in Pool 2
1900 + 31 x = 1372 + 42 x
Write the expression as a single logarithm, and simplify the result, if possible.
To simplify the logarithmic expression, we need to remember some logarithm rules. Some of the rules are:
[tex]\begin{gathered} \log _b(x\cdot y)=\log _bx+\log _by \\ \log _b\frac{x}{y}=\log _bx-\log _by \end{gathered}[/tex]In the expression that we have, we can group it into (log₃ 54 + log₃ 10) - log₃ 20.
We can apply the logarithm product rule in this expression: log₃ 54 + log₃ 10. This becomes log₃ (54 x 10) = log₃ 540
[tex]\begin{gathered} \log _bx+\log _by=\log _b(x\cdot y) \\ \log _354+\log _310=\log _3(54\cdot10)=\log _3540 \end{gathered}[/tex]Then, we can apply the logarithm quotient rule in this expression log₃ 540 - log₃ 20. This becomes log₃ (540/20) = log₃ 27 which is equal to 3.
[tex]\begin{gathered} \log _bx-\log _by=\log _b\frac{x}{y} \\ \log _3540-\log _320=\log _3\frac{540}{20}=\log _327=3 \end{gathered}[/tex]The single logarithm is:
[tex]\log _3\frac{54\cdot10}{20}[/tex]which then simplified to:
[tex]\log _327[/tex]which is equal to 3.
6 4/5 divided by 3 2/9
Answer:
Step-by-step explanation:
[tex]6 \frac{4}{5}=\frac{34}{5}[/tex]
[tex]3 \frac{2}{9} = \frac{29}{9}[/tex]
[tex]\frac{34}{5} : \frac{29}{9} = \frac{34}{5}*\frac{9}{29} = \frac{306}{145} \\[/tex]
[tex]\frac{306}{145}=2\frac{16}{145} \\[/tex]
nevermind i dont nedd help
Answer:
question (a) equals 980
Step-by-step explanation:
question (a) would equal 980 because if they charge $490 for 20 yards, they would charge $980 for twice the amount of dirt, so it is twice the price
20 (x2) 40
------ = ------
490 (x2) 980
Find an equation for the linear function which has f(300)=1200 and f(800)=4300
f(x)=
The equation of the linear function is f(x) = (31/5)x - 660.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
We have,
Let the equation be:
f(x) y = ax + m
Now,
The linear function:
f(300) = 1200
f(800) = 4300
This can be written as:
1200 = 300a + m ____(1)
4300 = 800a + m ______(2)
From (1) we get,
m = 1200 - 300a _____(3)
Putting (3) in (2) we get,
4300 = 800a + 1200 - 300x
4300 = 500a + 1200
4300 - 1200 = 500a
3100 = 500a
a = 31/5
Now,
m = 1200 - 300a
m = 1200 - 300 x 31/5
m = 1200 - 60 x 31
m = 1200 - 1860
m = - 660
The equation can be written as:
f(x) = (31/5)x - 660
We can cross-check:
f(300):
= (31/5) x 300 - 660
= 31 x 60 - 660
= 1860 - 660
= 1200
Thus,
The equation of the linear function is f(x) = (31/5)x - 660.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ1
Please help with the Geometry question.
The numerical values of x and y are 16 and 63 respectively, where line m and n are parallel to each other.
What are the numerical values of x and y?From the diagram;
Angle (8x - 2)° as a vertical angle of (2y)° forms a same side exterior angle with ( 4x - 10 )°.
Note that, same side exterior angle are supplementary.
Hence;
(8x - 2)° + ( 4x - 10 )° = 180°
Solve for x
8x - 2 + 4x - 10 = 180
Collect like terms
8x + 4x - 10 - 2 = 180
12x - 12 = 180
12x = 180 + 12
12x = 192
x = 192/12
x = 16
Therefore, the numerical value of x is 16.
Next, angle (8x - 2)° forms a vertical angle with angle (2y)°.
Note that, vertical angles are equal.
Hence
(8x - 2)° = (2y)°
Plug in x = 16 and solve for y.
8x - 2 = 2y
8( 16 ) - 2 = 2y
128 - 2 = 2y
126 = 2y
2y = 126
y = 126/2
y = 63
Therefore, the numerical value of y is 63.
Learn more about vertical angles here: https://brainly.com/question/24460838
#SPJ1
Which is the graph of g(x) = (0.5)^x+3 -4?
The graph of the function g(x) = (0.5)ˣ +3 -4 is shown (refer the graph attached below.)
What do we mean by the graph of the functions?The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We could also say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function. To determine if a graph represents a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point. The graph is not a function if the vertical line touches it at more than one location.So, the graph of the function g(x) = (0.5)ˣ +3 -4 will be:
(Refer to the graph attached below.)Therefore, the graph of the function g(x) = (0.5)ˣ +3 -4 is shown.
Know more about the graph of the functions here:
https://brainly.com/question/24335034
#SPJ9
The correct question is given below:
What is the graph of g(x) = (0.5)^x+3 -4?
Suppose that an individual has a body fat percentage of 17.3% and weighs 151 pounds. How many pounds of his weight is made up of fat? Round your answer
to the nearest tenth.
14
Answer:26.1
Step-by-step explanation: This probably isn't the most efficient way to do it bus this is how I do percentages: Divide the number by 100 (151) and multiply it by the percentage (17.3) 151/100*17.3 is 26.123 and rounding it is 26.1
Consider the equation: 0=x^2– 10x + 101) Rewrite the equation by completing the square.Your equation should look like (x+ a)^2= b or (x – c)^2= d.
1) Considering the equation x²-10x +10 let's rewrite it completing the square
1.1 Let's divide the coefficient of the term 10x by 2. To find the most closer term of the perfect square. As 10 :2 = 5
Then:
(x-5)² =x²-10x +25
2) Since there was added 25 on the left side, we need to add 25 on the right side to keep this identity:
x² -10x +25 +10 = 0 +25
(x-5)² +10=25
(x-5)² =25-10
(x-5)² = 15
3) Since the question does not ask us to solve it. Then we can stop it here.
Please help:A rectangular flower bed is enlarged so that its area increases by 24 ft². The enlarged flower bed is a rectangle and its area is x^2 + 11x + 24 ft².Which expressions represent the dimensions of the flower bed before the increase?Enter your answers in the boxes. __ft by __ ft
Enlarged area = x^2 + 11x + 24 ft²
Original area =
a + 24 ft^2 = x^2 + 11x + 24 ft²
a = x^2 + 11x + 24 ft² - 24 ft^2
a = x^2 + 11x
Factored:
a = x (x + 11 )
Dimensions before the increase
x ft by (x-11) ft
The base of a right prism is a right triangle. The lengths of the legs of the right triangle are 4 centimeters and 8 centimeters. The height of the prism is 5 centimeters. What is the volume of the prism?
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are:
Triangular prism formula:
[tex]\text{Volume of Right Triangular prism = }\frac{1}{2}X\text{ a X b x h}[/tex], where b is the length of the base of the triangle, h is the height of the triangle and length is prism length.
where:
[tex]\begin{gathered} a\text{ = 4 cm} \\ b\text{ = 8 cm} \\ h\text{ = 5cm} \end{gathered}[/tex][tex]\text{Volume of the prism = }\frac{1}{2}X4X8X5=80cm^3[/tex]CONCLUSION:
The volume of the prism =
[tex]80cm^{3\text{ }}(OPTION\text{ A)}[/tex]2/5 x 3/7 in simple form
Answer:
2/5*3/7= 6/35
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeeeeeee
thank you
The function g(3) has a value of 0
How to evaluate the function?The given parameters are the graphs in the figure
From the question, we have the function definition to be g(3)
Next, we analyze the functions of the graphs
The function on the first graph is a function of f(x), while the second graph is a function of g(x)
This means that we use the second graph to calculate the value of the function g(3)
The function g(3) means the value of x is 3
On the second graph, we have
g(x) = 0 when x = 3
So, we have
g(3) = 0
Hence, the value of the function is 0
Read more about functions at
https://brainly.com/question/28532394
#SPJ1
wSubmit your answer as an exact fraction or a decimal rounded to thehundredths place.You're a player in a video game and have theoption to choose from 5 character options (elf,dwarf, human, ranger, wizard) and 4 weaponsoptions (axe, shield, spear, staff).What is the probability that you will not be aelf or use a axe?Show your work here
we know that
5 character options and 4 weapons options
so
Total outcomes =5*4=20
step 1
Not be an ef
P=16/20
step 2
use an axe
P=5/20 ------> (include 4/20 of the previous probabilty)
so
The probability is equal to
(16/20)+(5/20)-(4/20)=17/20
The answer is 17/20What number should be placed in the box to help complete the division calculation
There is the number 224 should be placed in the box.
What are Arithmetic operations?Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
What is the divisibility rule?The divisibility rule states that " Divisible By, implies that when two numbers are divided, the result would be a whole number.
As per the given division calculation,
It is 3200 and subtracted 226 - 224 to get 4, so if you try to divide 16 into 226 you will get 3 for the quotient, and then 224 for the product in the box. Then, subtract 226- 224 to go on with the division.
Hence, there is the number 224 should be placed in the box.
Learn more about the divisibility rule here:
brainly.com/question/10703980
#SPJ1
Dirt cut 4 ft deep from a section of land 38 ft by 66 ft is used to fill a section 22 ft by 25 to a depth of 6ft. How many cubic yards of dirt are left after the fill?
Given
Dirt cut 4 ft deep from a section of land 38 ft by 66 ft is used to fill a section 22 ft by 25 to a depth of 6ft
Answer
The volume of dirt removed from a section of land = 4 x 38 x 66 = 10032 cubic ft
Volume of another section in which dirt is filled = 22 x 25 x 6 = 3300 cubic ft
Dirt left = 10032 - 3300 = 6732 cubic ft
Now 1 cubic ft = 0.037 cubic yards
6732 cubic ft = 6732 x 0.037 = 249.08 cubic yards
I Need help with this question.
How do you rewrite -8 - 4 = -12 in two different ways?
Answer:
Step-by-step explanation:
-4 - 8 = -12
-4 + 12 = 8
Susan said, "Venus is more than twice as far from the sun as Mercury is."
Is Susan correct? If so, write yes. If she is wrong, rewrite the statement to make it true.
You could change more to less, change the planets-do whatever you need to do to
make a TRUE statement for Susan.
Answer:
Venus bigger then mercury so it would be no so just change her answer
Is the relationship between Climate Change and Forest Fires causal or it a correlation?
A well-known pizza franchise sells over 4×10 to the power of 11 pizzas age in the US well well-known fast food chain sells about 2×10 to the power of nine taco city in the US proximately how many times greater are there any pizza sales in that taco sales
A. create an expression to represent how many times greater the annual pizza sales are than the annual taco sales
Pizza sales are 200 times greater than taco sales.
What are exponent?Exponent tells us how many times a number is multiplied by itself.
For example : [tex]2 ^ 4 = 2 \times 2 \times 2 \times 2[/tex]. Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a \times a \times a \times..... \times a[/tex] (m times), a is the base and m is the index.
Here,
Number of pizzas sold = [tex]4 \times 10^{11}[/tex] pizzas
Number of Taco sold = [tex]2 \times 10^9[/tex] tacos
By the problem,
[tex]2 \times 10^9 \times x = 4 \times 10^{11}\\x = \frac{4 \times 10^{11}}{2 \times 10^9}\\ x = 2 \times 10^2\\x = 200[/tex]
Pizza sales are 200 times greater than taco sales.
To learn more about exponent, refer to the link :
https://brainly.com/question/11975096
#SPJ9
which inequality can be used to determine x the maximum number of outfits scarlett can purchase while staying within her budget?
Answer
Option C is correct.
The inequality that can be used to determine x, the maximum number of outfits Scarlett can purchase while staying within her budget is
640 ≥ 74.2x + 504.91
Hope this Helps!!!
What is the missing leg in the following expression below?
The figure shows a right triangle with a hypotenuse of lengths c = 65 and one of the legs of length a = 60.
The other leg can be calculated by using the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]Solving for b:
[tex]b=\sqrt{c^2-a^2}[/tex]Substituting:
[tex]b=\sqrt{65^2-60^2}[/tex]Calculating:
[tex]\begin{gathered} b=\sqrt{4225-3600} \\ \\ b=\sqrt{625}=25 \end{gathered}[/tex]The missing leg is 25
find the equation of the parabola with its focus at -5,0 and it's directrix y = 2
Recall that a parabola is a curve where any point is at an equal distance from the focus and the directrix, if (x,y) is a point on the parabola then:
[tex]\sqrt[]{(-5-x)^2+(y-0)^2}=2-y\text{.}[/tex]Solving for y we get:
[tex]\begin{gathered} (-5-x)^2+y^2=(2-y)^2, \\ (x+5)^2+y^2=4-4y+y^2, \\ -4y=(x+5)^2-4, \\ y=-\frac{1}{4}(x+5)^2+\frac{4}{4}, \\ y=-\frac{1}{4}(x+5)^2+1. \end{gathered}[/tex]Answer: Second option.
Where do the graphs of f of x equals cosine of the quantity x over 2 and g of x equals square root of 2 minus cosine of the quantity x over 2 intersect on the interval [0, 360°)?
Given the functions f(x) and g(x) defined as:
[tex]\begin{gathered} f(x)=\cos (\frac{x}{2}) \\ g(x)=\sqrt[]{2}-\cos (\frac{x}{2}) \end{gathered}[/tex]The intersection of the graphs will be at f(x) = g(x):
[tex]\begin{gathered} \cos (\frac{x}{2})=\sqrt[]{2}-\cos (\frac{x}{2}) \\ 2\cos (\frac{x}{2})=\sqrt[]{2} \\ \cos (\frac{x}{2})=\frac{\sqrt[]{2}}{2}=\frac{1}{\sqrt[]{2}} \end{gathered}[/tex]This is true for:
[tex]\begin{gathered} \frac{x}{2}=45\degree\Rightarrow x=90\degree \\ \frac{x}{2}=315\degree\Rightarrow x=630\degree \end{gathered}[/tex]But only x = 90° is within the interval [0°, 360°)
Answer: 90°
Convert the standard equation 9x + 3y =18 to slop intercept form.Covert the point slope equation y= 1/3 (x-3) -8 to slop-intercept form.
14.) Convert the standard equation 9x + 3y = 18 to slope-intercept form.
Converting the given equation into standard form means we will be transforming the given equation into the following form: y = mx + b.
We get,
[tex]9x+3y=18[/tex][tex]9x+3y-9x=18-9x[/tex][tex]\text{ 3y = 18 - 9x}[/tex][tex]\text{ }\frac{\text{3y}}{3}\text{ = }\frac{\text{18 - 9x}}{3}[/tex][tex]\text{ y = 6 - 3x}[/tex][tex]\text{ y =-3x + 6}[/tex]Therefore, the slope-intercept form of the equation 9x + 3y = 18 is y = -3x + 6.
15.) Covert the point slope equation y = 1/3 (x-3) - 8 to slope-intercept form.
From the point-slope equation y = 1/3 (x-3) - 8,
y = 1/3 (x-3) - 8
(y + 8) = 1/3(x - 3)
We get,
Slope = m = 1/3
x₁ = 3
y₁ = -8
To convert it to a slope-intercept form, let's first find the y-intercept (b).
Substitute m = 1/3 and x,y = 3, -8 in y = mx + b.
y = mx + b
-8 = 1/3(3) + b
-8 = 1 + b
-8 - 1 = 1 + b - 1
-9 = b
b = -9
Let's now complete the equation, substitute m = 1/3 and b = -9 in y = mx + b.
y = mx + b
y = (1/3)x + (-9)
y = 1/3(x) - 9
In summary,
The answer to question 14 is:
[tex]\text{ y =-3x + 6}[/tex]The answer to question 15 is:
[tex]y=\frac{1}{3}x-9[/tex]PHS AND FUNCTIONSg local maxima and minima of a function given the graph
A local minimum, also called a relative minimum, is a minimum within some neighborhood that need not be (but maybe) a global minimum
(a) The function h(x) has two local minimums. The values at which h has a local minimum is :
[tex]\text{0, 4}[/tex](b) The local minimum values of h:
[tex]=\text{ -2}[/tex]4x2 + 4x - 1, evaluate and fully simplify each of the - For the function f(0) following f(s + h) f(x + h) - f(5) h 10
Given the function f(x);
[tex]f(x)=-4x^2+4x-1[/tex]Evaluating the function f(x+h);
[tex]\begin{gathered} f(x+h)=-4(x+h)^2+4(x+h)-1 \\ f(x+h)=-4(x^2+2xh+h^2)^{}+4(x+h)-1 \\ f(x+h)=-4x^2-4h^2-8xh^{}+4x+4h-1 \end{gathered}[/tex]So;
[tex]f(x+h)=-4x^2-4h^2-8xh^{}+4x+4h-1[/tex]Evaluating the second function;
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-4x^2-4h^2-8xh^{}+4x+4h-1-(-4x^2+4x-1)}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{-4x^2-4h^2-8xh^{}+4x+4h-1+4x^2-4x+1}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{-4x^2+4x^2-4h^2-8xh^{}+4x-4x+4h-1+1}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{-4h^2-8xh^{}+4h}{h} \end{gathered}[/tex]simplifying further;
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-4h^2-8xh^{}+4h}{h}=-4h-8x+4 \\ \frac{f(x+h)-f(x)}{h}=-4h-8x+4 \end{gathered}[/tex]Therefore, we have;
[tex]undefined[/tex]Find the equation of the line through the points (3,6) and (-1, 1).
Let's begin by listing out the information given to us:
(x, y) at point 1 = (3, 6)
(x, y) at point 2 = (-1, 1)
The equation of a straight line is given by:
[tex]\begin{gathered} y=mx+b \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-6}{-1-3}=\frac{-5}{-4} \\ m=\frac{5}{4} \end{gathered}[/tex]Substitute the slope (m) into the equation, we have:
[tex]\begin{gathered} y=mx+b \\ m=\frac{5}{4} \\ y=\frac{5}{4}x+b \\ \text{Substitute the value of x \& y into the equation from (}3,6) \\ 6=\frac{5}{4}\cdot3+b\Rightarrow6=\frac{15}{4}+b \\ b=6-\frac{15}{4}=6-3\frac{3}{4} \\ b=2\frac{1}{4}=2.25 \\ \\ \therefore y=\frac{5}{4}x+2.25 \end{gathered}[/tex]