Answer:520
Step-by-step explanation:
Suppose the original prize is=x
If the discount is of 80%,the selling prize is of 20%
20% of x=112
20x/100=112
X=520
Its the original prize...
Answer:
£560
Step-by-step explanation:
80% off means that the sale price is 20% of the original price.
The original price is represented by 100%
Divide the sale price by 20 to find 1% then multiply by 100 to obtain the original price
original price = [tex]\frac{112}{20}[/tex] × 100 = £560
Jonathan makes a weekly allowance of $25. He also makes $9.50 an hour at his job. Because of his age, he can work no more than 20 hours a week.
a) Write a function for the amount of money he makes each week based on the amount of hours, h, he works.
b) What is the domain of the function for this situation?
c) Sketch the graph of the function over the domain you chose.f
Final answer:
Jonathan's weekly income is determined by a linear function M(h) = 9.5h + 25, with the domain being 0 ≤ h ≤ 20 to reflect his work hour limitations. A sketch of this function would show a linear increase from an initial allowance of $25, rising by $9.50 for each hour worked up to 20 hours.
Explanation:
Jonathan makes a weekly allowance of $25 and earns $9.50 per hour at his job, with a maximum work limit of 20 hours per week.
a) Function for Jonathan's weekly earnings:
The function M(h) = 9.5h + 25 represents the amount of money Jonathan makes each week, where h is the number of hours he works.
b) Domain of the function:
The domain of this function, considering Jonathan's work hour limitation, is 0 ≤ h ≤ 20. This range is because Jonathan cannot work more than 20 hours a week due to his age restrictions.
c) Sketch of the graph:
The graph would start at the point (0, 25), which represents Jonathan's weekly allowance without any worked hours. Then, it would rise linearly at a slope of $9.50 for each additional hour worked, up to the point (20, 215), which represents the maximum amount Jonathan can earn by working 20 hours plus his weekly allowance. Note: The actual graph is not displayed here but can easily be sketched using the described points and slope.
The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original number. What is the original number?
Answer:
53
Step-by-step explanation:
Let's make some equations.
The number is two-digit, so let's make it [tex]xy[/tex]
Also, the two digits add up to 8, so [tex]x+y=8[/tex]
Now the value of [tex]xy=10x+y[/tex]
and the value of [tex]yx=10y+x[/tex]
Since we know that when we reverse the digits the number is less than the resulting number by 18, we can formulate an equation.
[tex]10y+x=10x+y+18[/tex]
Solve this equation.
[tex]9y-9x=18[/tex]
[tex]9(y-x)=18[/tex]
[tex]y-x=2[/tex]
Now let's use the equation we made earlier.
Change [tex]x+y=8[/tex] into [tex]y=8-x[/tex]
Solve the system of equations.
[tex]y-x=2[/tex]
[tex]y=8-x[/tex]
[tex]8-x-x=2[/tex]
[tex]8-2x=2[/tex]
[tex]-2x=-6[/tex]
[tex]x=3[/tex]
[tex]y-3=2[/tex]
[tex]y=5[/tex]
So the original number is 53.
Answer:
C
Step-by-step explanation:
What is the approximate value of x in the equation below.
Answer: First Option
[tex]x= -3.396[/tex]
Step-by-step explanation:
We have the following expression
[tex]log_{\frac{3}{4}}25 = 3x -1[/tex]
To solve the equation add 1 to both sides of the equality
[tex]log_{\frac{3}{4}}25 +1= 3x -1+1[/tex]
[tex]log_{\frac{3}{4}}25 +1= 3x[/tex]
Divide between 3 to both sides of the equation
[tex]\frac{log_{\frac{3}{4}}25 +1}{3}= x[/tex]
[tex]x= \frac{-11.19 +1}{3}[/tex]
[tex]x= -3.396[/tex]
The answer is the first option
Do you think that there is a rule you could use to predict the number of times your heart would beat in 15 seconds after you did 100 jumping jacks? Explain your answer.
Answer:
Yes
Step-by-step explanation:
The more you jump, the higher your blood flow becomes, since your heart needs to pump more blood to the working areas. This really doesn't belong in math though.
Answer: yes
Step-by-step explanation: but i am not that sure how i can explain it, here look at the guys answer above. Also thank the guy above, not me.
which statement is true
2 Points
What is the vertex of the graph of the function below?
y = x2 + 10x + 24
O A. (-4,-1)
O B. (-5, -1)
O C. (-5,0)
O D. (4,0)
SUBMIT
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+10}x\stackrel{\stackrel{c}{\downarrow }}{+24} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{10}{2(1)}~~,~~24-\cfrac{10^2}{4(1)} \right)\implies (-5~,~24-25)\implies (-5~,~-1)[/tex]
The vertex of the quadratic function y = x² + 10x + 24 is located at point B. (-5, -1). This is found by using the formula -b/2a for the x-coordinate and substituting the x coordinate into the function for the y-coordinate.
Explanation:The vertex of a quadratic function (a function in the form of y=ax²+bx+c) is the point that represents the minimum or maximum of the function graph. In this case, we are looking to find the vertex of the function y = x² + 10x + 24. The formula to find the x-coordinate of the vertex of a quadratic function is -b/2a. In this function, a = 1 and b = 10, giving us -10/(2*1) = -5 for the x-coordinate of vertex. We then substitute -5 into the function for x to determine the y-coordinate, resulting in y = (-5)² + 10*-5 + 24 = -1. Therefore, the vertex of the function is (-5,-1). So, the correct choice is B. (-5, -1).
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choose all of the perfect squares 196 256 390 484 564
Answer:
{196, 256, 484}
Step-by-step explanation:
14² = 196;
16² = 256;
19² = 361; 390 lies between 361 and 400, and is thus NOT a perfect square;
20² = 400;
22² = 484
564 lies between the two perfect squares 23² and 24², but is itself NOT a perfect square.
Thus, the perfect squares are {196, 256, 484}
The perfect squares out of the numbers 196, 256, 390, 484, 564 are 196, 256, and 484. A perfect square is a number that can be expressed as an integer multiplied by itself.
Explanation:The perfect squares from the list you provided are: 196, 256, and 484. A perfect square is a number that can be expressed as the product of an integer with itself. For example, 256 is a perfect square because it can be expressed as 16 times 16, or 16^2. Similarly, 196 and 484 are perfect squares as they can be expressed as 14^2 and 22^2, respectively. On the other hand, numbers 390 and 564 are not perfect squares as they cannot be expressed as the product of an integer with itself.
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A company makes glass lawn ornaments with a radius of 9 inches. The glass to make the balls costs the company $0.03 per square inch. To the nearest cent, how much does the company pay for the glass to create one ornament?
Answer:
$7.63
Step-by-step explanation:
We are given:
r=9 icnhes
We have to find the area of the circular ornament first. The formula for area of circle is:
Area= πr^2
Putting the value of r
Area=3.14*(9)^2
=3.14*81
=254.34 Square inches
As the company pays $0.03 for 1 square inch, for 254.34 square inch the company will have to pay:
=254.34*0.03
=$7.6302
Rounding off to the nearest cent
The cost for one ornament = $7.63
Answer:
$30.52
Step-by-step explanation:
4 x 9^2 x 3.14 x 0.03 = around 30.52
for f(x) equal 3x+1 and g(x) equal x-6 find (f - g) (x)
Answer:
2x + 7
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x) = 3x + 1 - (x - 6) = 3x + 1 - x + 6 = 2x + 7
This photo 2 of This question read it and find out what is The difference in feet between The Minimum and Maximum heights of a car on The ferris wheel
Answer:
From the looks of things, it seems to be 140 ft, the maximum height being 150 ft and the minimum height being 10 ft. Find the difference, and that should be your answer :)
Answer:C 140
Step-by-step explanation:
Which makes the statement true?
Answer:
3/11 + 5 5/8 > 5 6/8
Step-by-step explanation:
find the LCD's for both sides of the comparison. After this, add fractions from the same side of the comparison. Then, you must compare the two and check your answer. Have a nice day!
What is the factored form of x^12y^18+1?
Answer:
[tex](x^{4}y^{6}+1)(x^{8}y^{12}-x^{4}y^{6}+1)[/tex].
Step-by-step explanation:
We want to expand: [tex]x^{12}y^{18}+1[/tex].
We can rewrite this as the sum of two cubes.
[tex](x^{4})^3(y^{6})^3+1=(x^{4}y^{6})^3+1^3[/tex].
Recall and use the sum of cubes identity: [tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
By comparing our newly rewritten expression to this identity, we have [tex]a=x^4y^6[/tex] and [tex]b=1[/tex].
We substitute into the identity to get:
[tex](x^{4}y^{6})^3+1^3=[x^{4}y^{6}+1][(x^{4}y^{6})^2-(x^{4}y^{6})(1)+1^2][/tex].
We now use this rule of exponents :[tex](a^m)^n=a^{mn}[/tex] to get;
[tex](x^{4}y^{6}+1)(x^{8}y^{12}-x^{4}y^{6}+1)[/tex].
Which of the following best describes a ratio?
A. An expression that contains a radical sign
B. The cross product of two fractions
C. A comparison of two numbers
D. The inverse operation for multiplication
The best way to describe a ratio is option c, which is 'A comparison of two numbers'.
What is Ratio?A ratio shows us the number of times a number contains another number. therefore, it helps us to compare two numbers.
Which of the following best describes a ratio?As we have already discussed the ratio is the comparison of two numbers for a particular.
Hence, the best way to describe a ratio is option c, which is 'A comparison of two numbers'.
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What is the ordered pair of M after point M (5,6) is rotated 90 clockwise
Final answer:
The ordered pair of M after rotating 90 degrees clockwise is (-6,5).
Explanation:
When a point undergoes a 90-degree clockwise rotation around the origin, a distinct transformation occurs. Specifically, the x-coordinate of the original point becomes the negative value of its original y-coordinate, and the y-coordinate takes on the positive value of the original x-coordinate. This geometric operation is fundamental in transforming coordinates.
Taking point M(5,6) as an example, after the 90-degree clockwise rotation, the new coordinates manifest as (-6,5). This rotation plays a crucial role in various mathematical and geometric applications, contributing to the understanding of spatial transformations and coordinate systems.
a scale drawing of a square has a side length of 2 cm. The drawing has a scale of 1cm : 8ft. Find the actual perimeter and area of the square
Answer: Area: 256 ft squared Perimeter: 64 feet
Step-by-step explanation: If the scale is 1 cm to 8 ft then if you multiply 1 cm by 2 you get 2 cm. Then you multiply 8 by 2 to get 16 feet. Once you get 16 feet, you can do 16 times 16 to find the area and 16 times 4 to find the perimeter.
What is 726,034 rounded to the nearest ten thousand
Answer:730000
Step-by-step explanation:
Follow below steps;
To round the number 726,034 to the nearest ten thousand, we must look at the thousands digit, which is 2. Since 2 is less than 5, we do not round up, and thus, leave the ten thousands place as it is.
The number 726,034 rounded to the nearest ten thousand is 720,000. We can see that the thousand's digit is less than 5, so we round down. This process aligns with the rounding rule stating that if the number you are rounding is followed by 0, 1, 2, 3, or 4, you round the number down.
What is the value of "c" in the quadratic equation 3x2 + 5x + 7 = 0?
Answer:
Last option: 7
Step-by-step explanation:
The Standard form of a quadratic equation is the following:
[tex]ax^{2}+bx+c=0[/tex]
Where "a" is the quadratic coefficient (This coefficient cannot be 0), "b" is the linear coefficient, "c" is the constant and "x" is the variable.
In this case you have the quadratic equation [tex]3x^2 + 5x + 7 = 0[/tex] which is written is Standarf form. Then, you can identify that:
[tex]a=3\\b=5\\c=7[/tex]
Therefore the value of "c" is 7.
Which set of side lengths forms a right triangle 2,3,13 4,6,10 9,12,18 15,36,39
Answer:
15,36,39
Step-by-step explanation:
primitive pythag: 5, 12, 13 *3
Answer:
The Answer is D
Step-by-step explanation:
1. What is the slope of the line?
2. What is the slope of the line?
Answer:
1/4
Step-by-step explanation:
Answer:
[tex]slope =\frac{1}{4}[/tex]
slope is undefined
Step-by-step explanation:
WE need to find the slope of two lines
to find out slope we use formula
[tex]slope =\frac{y_2-y_1}{x_2-x_1}[/tex]
To find slope we pick two points from the line
(-4,0) and (0,1) is (x1,y1) and (x2,y2)
[tex]slope =\frac{1-0}{0+4}=\frac{1}{4}[/tex]
[tex]slope =\frac{1}{4}[/tex]
To find slope we pick two points from the line
(1,0) and (1,1) is (x1,y1) and (x2,y2)
[tex]slope =\frac{1-0}{1-1}=\frac{1}{0}[/tex]
When denominator =0 then the slope is undefined
Where does the graph of y = –3x – 18 intersect the x-axis?
Question 16 options:
a)
(6,0)
b)
(-6,0)
c)
(0,-6)
d)
(0,6)
Answer:
b) (-6, 0)
Step-by-step explanation:
The quickest method to use is to put "0" in for y, then figure out which term for x would make the equation authentic, or genuine.
A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line? Select two options.
(–2, 0) and (2, 5)
(–4, 5) and (4, –5)
(–3, 4) and (2, 0)
(1, –1) and (6, –5)
(2, –1) and (10, 9)
[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{4}{5}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{5}{4}}\qquad \stackrel{negative~reciprocal}{+\cfrac{5}{4}\implies \cfrac{5}{4}}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-0}{2-(-2)}\implies \cfrac{5}{2+2}\implies \cfrac{5}{4} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-(-1)}{10-2}\implies \cfrac{9+1}{8}\implies \cfrac{10}{8}\implies \cfrac{5}{4}[/tex]
Answer: Im pretty sure it answer options 1 and 5
Step-by-step explanation: 1) (-2,0) and (2,5) 5) (2,-1) and (10,9)
its on edg.
State the various transformations applied to the base function ƒ(x) = x^2 to obtain a graph of the function g(x) = −2[(x − 1)^2 + 3].
(A) A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 2 units to the right, and a vertical shift downward of 6 units.
(B) A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units.
(C) A reflection about the y-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units.
(D) A reflection about the y-axis, a vertical stretch by a factor of 2, a horizontal shift of 2 units to the right, and a vertical shift downward of 6 units.
Answer: Option B
A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units.
Step-by-step explanation:
If the graph of the function [tex]g(x)=cf(h-h) +b[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.
If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c
If [tex]c <0[/tex] then the graph is reflected on the x axis.
If [tex]b> 0[/tex] the graph moves vertically upwards b units.
If [tex]b <0[/tex] the graph moves vertically down b units
If [tex]h> 0[/tex] then the graph of f(x) moves horizontally h units to the left
If [tex]h <0[/tex] then the graph of f(x) moves horizontally h units to the right
In this problem we have the function [tex]g(x) = -2((x - 1)^2 + 3)[/tex] and our parent function is [tex]f(x) = x^2[/tex]
therefore it is true that [tex]c =-2<0[/tex] and [tex]b =-6 <0[/tex] and [tex]h=-1<0[/tex]
Therefore the graph is reflected on the x axis, stretched vertically by a factor 2. The graph of f(x) moves horizontally 1 units to the right and shift downward of 6 units.
The answer is (B) A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units.
Final answer:
The correct transformations from f(x) = x² to g(x) = −2[(x − 1)² + 3] are a reflection about the x-axis, a vertical stretch by 2, a horizontal shift 1 unit to the right, and a vertical shift 3 units upwards, which is option (B) in the list provided.
Explanation:
The function g(x) = −2[(x − 1)² + 3] has undergone several transformations from the base function f(x) = x^2. These transformations include a reflection about the x-axis due to the negative sign in front of the equation, indicating that a flip has happened vertically. A vertical stretch by a factor of 2 is also evident from the coefficient 2 before the parenthesis.
The term (x - 1) inside the parenthesis indicates a horizontal shift of 1 unit to the right since we subtract from x to move the graph to the right. Lastly, the +3 at the end of the equation signifies a vertical shift of 3 units upwards, which is a change in the y-value of every point on the graph.
Therefore, the correct sequence of transformations to obtain g(x) from f(x) is: a reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift of 3 units upwards, which corresponds to option (B) provided by the student.
if a base of a parallelogram is 8 inches long and the altitude to the base is 10 inches what is the area of the parallelogram
Answer: [tex]80 in^2[/tex]
Step-by-step explanation:
The area of a parallelogram can be calculated with the following formula:
[tex]A=b*h[/tex]
Where "b" is the base and "h" is the height or altitude.
You know that the base of this parallelogram is 8 inches long and the altitude to the base is 10 inches, then:
[tex]b=8in\\h=10in[/tex]
You need to substutite these values into the formula.
Therefore, the area the parallelogram is:
[tex]A=(8in)(10in)\\\\A=80in^2[/tex]
What is the slope of the line that passes through (-2, 5) and (3, 9)?
Answer: 4/5
Step-by-step explanation:
1. you need to know the formula which is m = y2-y1/x2-x1
2. you plug in the numbers which would be 9-5/3-(-2)
3. you get your answer as 4/5
4. the answer is 4/5
Answer:
○ b ⅘
Step-by-step explanation:
-y₁ + y₂\-x₁ + x₂ = m
[tex] \frac{4}{5} = \frac{ -5 + 9}{2 + 3}[/tex]
I am joyous to assist you anytime.
drag each tile to the table to multiply each row heading by each column heading
Answer:
drag each result in the corresponding box according to the results
Step-by-step explanation:
Hello
The product of two or more powers of equal base "a" is equal to the power of base "a" with exponent equal to the sum of the respective exponents.
[tex]a^{m}*a^{n} =a^{n+m}[/tex]
Step 1
[tex]d*2d^{2}\\[/tex]
[tex]d*2d^{2}=(2*1)d^{(2+1)}\\d*2d^{2}=2d^{3} \\[/tex]
Step 2
[tex]-9*2d^{2}\\[/tex]
[tex]-9*2d^{2}=(-9*2)d^{(2+0)}\\-9*2d^{2}=-18d^{2} \\[/tex]
Step 3
[tex]d*11d\\[/tex]
[tex]d*11d=(1*11)d^{(1+1)}\\11*d^{2}=11d^{2} \\[/tex]
Step 4
[tex]-9 * 11d\\[/tex]
[tex]-9 * 11d = (-9*11)d^{1+0}=-99 d[/tex]
Step 5
[tex]d*-4=-4d[/tex]
Step 6
[tex]-9*-4 = ( -*- ) (9*4)= 36[/tex]
Step 7
Now, drag each result in the corresponding box .
Have a great day
Answer:
Your welcome :)
Step-by-step explanation:
what is the slope of the line shown below (-3,1) (5,1)
Answer:
A. 1/4
Step-by-step explanation:
The line is upwards so slope will be positive. (either A or C will be the answer)
Now to solve for slope to find out
Two coordinate points on graph (-3,-1) ad (5,1)
Slope = (y2 - y1)/(x2 - x1)
Slope = (1 + 1)/(5 + 3) = 2/8 = 1/4
Answer:
[tex]A.\frac{1}{4}[/tex]
Step-by-step explanation:
Hello, I think I can help you with this
The slope is the inclination of the line with respect to the abscissa axis, if you know two points it can be calculated using
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\[/tex]
where
[tex]P1(x_{1},y_{1})\\P2(x_{2},y_{2})[/tex]
Step 1
put the values into the equation
Let
[tex]P1(-3,-1) \\P2(5,1)\\\\m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} } \\m=\frac{1-(-1)}{5-(-3) } \\m=\frac{1+1}{5+3} \\m=\frac{2}{8} \\m=\frac{1}{4}[/tex]
Have a great day
Historians generally begin forming historical arguments in order to:
Answer:
D. offer possible answers to historical questions.
Step-by-step explanation:
An argument is a statement which a historian proposes. In order to back up the statement the historian provides proof. The argument is then read by other historians and the proof is analyzed. After the analysis if other historians come to the same conclusion which the statement points to then the argument is accepted.
So, this is the way to offer possible answers to historical questions.
the burj khalifa a building in dubai united arab emirates is about 828 meters tall
Answer:
true
Step-by-step explanation:
What is the value of x in the equation −x = 4 − 3x + 6?
5
10
−5
−10
−x = 4 − 3x + 6
Move the -3x to the other side and simplify 4+6.
2x= 10
Divide both sides by 2
x=5.
Answer: First option.
Step-by-step explanation:
Given the equation [tex]-x = 4- 3x + 6[/tex], you need to solve for the variable "x" to find its value.
Add the like terms on the right side of the equation:
[tex]-x = 10-3x [/tex]
Now you need to subtract 10 from both sides of the equation:
[tex]-x-10 = 10- 3x -10[/tex]
[tex]-x-10 =- 3x[/tex]
The next step is to add "x" to both sides of the equation:
[tex]-x-10+x = - 3x +x[/tex]
[tex]-10 = - 2x[/tex]
And finally, divide both side by -2:
[tex]\frac{-10}{-2}=\frac{-2x}{-2}\\\\x=5[/tex]
How many solutions can be found for the equation 3x − 2 = 3x + 5?
a)zero
b)one
c)two
d)infinitely manyHow many solutions can be found for the equation 3x − 2 = 3x + 5?
Answer:
Zero
Step-by-step explanation:
there is no solution the sides are uneven. if you solve for it 3x and 3x cancels out each other leaving you with -2=5
Answer:
Zero
Step-by-step explanation:
Periodt