$120
Explanation
remember
[tex]75\text{ \% =}\frac{75}{100}=0.75[/tex]it means you can find 75 % of any value, just by doing th product of the number and 0.75
[tex]\begin{gathered} 160\cdot0.75=120 \\ \end{gathered}[/tex]Hence, 75% is $120 ,
the discount is 120,the new price is 40
the money you save is the difference, it is 120
I hope this helps you
A train travels 165 km in 1.5 hours.
How far will the train travel in 2.2 hours if it maintains the same speed?
[tex]\huge\red{\mid{\underline{\overline{\textbf{EQUATION AND ANSWER}}}\mid}}[/tex]
_________________
Let's solve this equation using rates,
_________________DefinitionsUnit Rate - A unit rate means a rate for one of something.
Cross Multiplication - In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.
_________________
Now that we understand the definition we can further solve this equation
[tex]\large\red{\mid{\underline{\overline{\textbf{Values}}}\mid}}[/tex]
[tex]165[/tex] [tex]km[/tex] ⇒ [tex]1.5[/tex] [tex]hr[/tex]
[tex]x\\[/tex] [tex]km[/tex] ⇒ [tex]2.2[/tex] [tex]hr[/tex]
Now we will use cross-multiplication to solve this equation
[tex]\large\red{\mid{\underline{\overline{\textbf{Equtation}}}\mid}}[/tex]
[tex]165 \cdot 2.2\\x\cdot1.5[/tex]
Once solving this equation we get
[tex]1.5x=363[/tex] [tex]km[/tex]
Divide both sides by [tex]1.5[/tex]
[tex]x=242[/tex] [tex]km[/tex]
[tex]\large\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}[/tex]
A train travels 165 km in 1.5 hours. How far will the train travel in 2.2 hours if it maintains the same speed?The train would've traveled a total of 242 km in 2.2 hours.
Have a good day!what digit is in the
So, let's turn the notation from mixed number to fraction:
[tex]1\frac{11}{100}\text{ = }\frac{100}{100}+\frac{11}{100}=\text{ }\frac{111}{100}[/tex]As you can see, the whole becomes 100/100 and then you just add the numerators.
Answer: 111/100
Which of the following proportions can be used to solve the problem below?Suppose you are using a photocopier to reduce the size of a picture that is 10 inches wide by 12 inches long. If you reduce the picture so that it is 9 inches wide, how long will it be?
We are asked to determine the length of a picture that is originally 10 inches wide and 12 inches long.
By reducing it we must keep the same proportion between length and width. Therefore, the ratio between length and width must remain the same. The ratio between width and length is:
[tex]\frac{10}{12}[/tex]Now, we set this equal to the ratio of the reduced picture:
[tex]\frac{10}{12}=\frac{9}{x}[/tex]Therefore, the right proportion is B
please help me!!!!!!
I attach the table with the results organized correctly.
The correct option is 1.
A multivitamin tablet contains 12.5mg of calcium how much calcium does a bottle of 40 tablets contain write your answer in grams
One multivitamin tablet contains 12.5mg.
Therefore, 40 tablets will contain
[tex]40\times12.5=500[/tex]40 tablets will contain 500mg.
In grams:
By conversion,
[tex]1g=1000mg[/tex]Hence, 500mg can be converted as
[tex]\frac{500}{1000}=0.5[/tex]Hence, there are 0.5g of calcium in
The exit is exactly half way between the Ferris wheel and where you parked your car. Give the coordinates of your parking spot.
GIven data :
The coordinates of ferris wheel is, (2,7).
The coordinates of exit is (4,0).
they have given exactly half way so let us use the midpoint formula,
the mid point formula is,
[tex](\frac{x_1+x_2}{2},\frac{y_1,y_2}{2})\ldots(1)[/tex]take the coordinates as
[tex]\begin{gathered} (x_1,y_1)=(2,7) \\ (x_2,y_2)=(4,0) \end{gathered}[/tex]let us subsitute in eqiuation (1),
[tex]\begin{gathered} (\frac{2+4_{}}{2},\frac{7_{}+0_{}}{2}) \\ (\frac{6}{2},\frac{7}{2}) \\ (3,3.5) \end{gathered}[/tex]thus the coordinates of parking spot is (3,3.5).
solve for x 3/5x-1/3x =4
Answer:
3/5x times 3 = 9/15. 1/3x times 5 =5/15. 9/15x-5/15x=(4/15x)
Step-by-step explanation:
(5x 10-6)(3x 10-4)(5x 10-6) (3 x 10 - 4) =PLS HELP IT’S DUE TNNNN !
we can multiply the normal numbers on the one hand and the scientific notation on the other hand
so
[tex]\begin{gathered} (5\times3)(10^{-6}\times10^{-4}) \\ (15)(10^{-6+(-4)}) \\ =15\times10^{-10}=1.5\times10^{-9} \end{gathered}[/tex]In the news you hear “ tuition is expected to increase from the current cost of $1,050 to $2,050 over the next ten years.” This represents a __% increase from the current tuition.
According to the information given in the exercise, the tuition is expected to increase from $1,050 to $2,050 over the next ten years.
Then, you need to use the following formula in order to solve this exercise:
[tex]Percentage\text{ }Increase=\frac{Final\text{ }value-Initial\text{ }value}{|Initial\text{ }value|}\cdot100[/tex]In this case:
[tex]\begin{gathered} Initial\text{ }value=1,050 \\ Final\text{ }value=2,050 \end{gathered}[/tex]Therefore, substituting these values into the formula and evaluating, you get:
[tex]\begin{gathered} PercentageIncrease=\frac{2,050-1,050}{|1,050|}\cdot100 \\ \\ PercentageIncrease=95.24 \end{gathered}[/tex]Hence, the answer is: 95.24% increase.
Please help me with the last part of the question thanks
There is a direct proportion between two values when one is a multiple of the other.
In this case, we have:
[tex]1\text{ hour = 60 minutes}[/tex]This means that to convert hours to minutes, the multiplier is always 60.
The equation of a direct proportion is:
[tex]undefined[/tex]What is the lateral surface area of the square pyramidrepresented by this net?11 ft8 ftEnter your answer in the box.11 ft11 ftA8 ft다ft?111 ft
Surface area of a square pyramid is given as:
[tex]\begin{gathered} \text{Surface area = }Area\text{ of base + }\frac{1}{2}PS \\ \text{where P = perimeter of base} \\ S\text{ = slant height} \end{gathered}[/tex][tex]\begin{gathered} \text{Area of base = area of square} \\ \text{Area of base = }(length)^2 \\ \text{length = 8 }ft \\ \text{Area of base = 8}^{\text{ 2}}=64ft^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Perimeter of base = 4(length)} \\ \text{Perimeter of base = 4(8) = 32 ft} \end{gathered}[/tex][tex]\begin{gathered} \text{slant height = }11\text{ ft} \\ \\ \text{The surface area = 64 + }\frac{1}{2}(32\times11) \\ \\ \text{The surface area = 64 + }\frac{1}{2}(352) \end{gathered}[/tex][tex]\begin{gathered} \text{The surface area = 64 + 176} \\ \text{The surface area = }240ft^2 \end{gathered}[/tex]How do I find all possible rational zeros in a polynomial function?f(x) = x^4-2x^3-4x^2+2x+3
The factors are 1 , -1 twice and 3
Here, we want to find the rational roots of;
[tex]f(x)\text{= }x^4-2x^3-4x^2+2x+3[/tex]We can start here by trying out simple numbers if we cannot factorize the polynomial at a go
The given polynomial here can be factorized
We can express it as;
[tex]x^4-2x^3-4x^2+2x+3\text{ = (}x-1)(x+1)^2(x-3)[/tex]So what we have here is to simply equate individual linear factor to zero
Thus, we have the factors as;
1 , -1 twice and 3
which is a better buy? 20 items for $5.99 or 30 items for $7.99
Answer:
Step-by-step explanation:
Obisouly 20 items for $5.99
A painter has three partially filled paint cans. One contains1 7/8 gallons, the second contains1 1/5 gallons, and the third contains1 3/4 gallons. Which answer is closest to the total amount of paint?
Explanation
Step 1
convet the mixed numbers into simple fractions
remember
[tex]a\frac{b}{c}=\frac{(a\cdot c)+b}{c}[/tex]then
[tex]\begin{gathered} 1\text{ }\frac{7}{8}=\frac{(1\cdot8+7)}{8}=\frac{15}{8} \\ 1\frac{1}{5}=\frac{(1\cdot5+1)}{5}=\frac{6}{5} \\ 1\frac{3}{4}=\frac{(1\cdot4+3)}{4}=\frac{7}{4} \end{gathered}[/tex]Step 2
now, make the sum to find the total amount
[tex]\begin{gathered} \text{total amount= }\frac{15}{8}+\frac{6}{5}+\frac{7}{4} \\ \text{total amount=}\frac{(15\cdot5\cdot4)+(6\cdot8\cdot4)+(7\cdot5\cdot8)}{160} \\ \text{total amount=}\frac{300+192+280}{160} \\ \text{total amount=}\frac{772}{160} \\ \text{total amount=}\frac{193}{40} \end{gathered}[/tex]I hope this helps you
16 The water level of a river was measured each day during a two-week period. The graph models the linear relationship between the water level of the river in feet and the number of days the water level was measured. Water Level of River 28 20 16 Water Level (0) 3 4 6 8 10 12 14 Number of Days Which statement best describes the y-intercept of the graph?
From the graph, it can be observed that line intersect the y-axis at (0,16) and after that level of water increases with increase in number of days.
So 16 feet represents the initial water level of the river. The correct answer is,
The initial water level was 16 ft.
hi my name is Shila and I'm trying to explain how to solve this problem to my daughter but a but confused can you direct me please?
As given by the question
There are given that the point
[tex]\frac{8}{6}[/tex]Now,
First, break the point
So,
[tex]\frac{8}{6}=\frac{4}{3}[/tex]According to the above point, there are showing 3 in the denominator
So, between 0 and 1 divide 3 parts in the number line
Then,
16. Solve this system: y = 3x+1 y= 5x-3
y=3x+1 (1)
y=5x-3 (2)
To solve this system, we can use the equalize method:
3x+1=5x-3
3+1=5x-3x
4=2x
x=4/2
x=2
Now, substitung x=2 in y=3x+1
y=3(2)+1
y=6+1
y=7
Then, the solution to this system of equation would be: (2, 7)
Judy is buying 6 pint of ice cream for her party at $3.45 each if she has a $20 bill does she have enough to buy the ice cream
the cost of the ice cream is,
3.45 $
also, she has only 20 $
SO, the number of icecreams bought by
Evaluate the function when x= -2,0, and 5 h(x)= -2x+9
Given:
a function is given as h(x) = -2x + 9
Find:
we have to evaluate the function at x = -2 , 0 and 5.
Explanation:
when x = -2
h(-2) = -2(-2) + 9 = 4 + 9 = 13
when x = 0
h(0) = -2(0) + 9 = 0 + 9 = 9
when x = 5
h(5) = -2(5) + 9 = - 10 + 9 = -1
Therefore, the values of given function h(x) are 13, 9 , -1 at x = -2, 0 , 5 respectively.
what value of y will make the equation true? √34 × √y = 34
Clear y from the equation to find its value
[tex]\begin{gathered} \sqrt[]{34}\cdot\sqrt[]{y}=34 \\ \sqrt[]{y}=\frac{34}{\sqrt[]{34}} \\ \sqrt[]{y}=\sqrt[]{34} \\ y=(\sqrt[]{34})^2 \\ y=34 \end{gathered}[/tex]The value of y that will make the equation true is 34.
Answer:
The value of y=√34 will make the equation true.
Step-by-step explanation:
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The given expression is:-
√34 x √y =34
Putting the value of y=√34 will satisfy the equation.
√34 x √34 =34
34 = 34
Therefore the value of y=√34 will make the equation true.
To know more about equations follow
brainly.com/question/2972832
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Can you help me find the angles of x°, R, Q, and P?
SOLUTION
Using the theorem
The sum of angles in a triangle is 180°
Then we have
[tex]P^0+Q^0+R^0=180^0[/tex]from the diagram in the questions
[tex]\begin{gathered} P=x-11 \\ Q=3x+6 \\ R=x \end{gathered}[/tex]Substituting the parameters we have
[tex]\begin{gathered} (x-11)^0+(3x+6)^0+x^0=180^0 \\ \text{ Remove the parenthesis} \\ x-11+3x+6+x=180^0 \\ \text{ Rearrange the expression} \\ x+3x+x+6-11=180^0 \end{gathered}[/tex]Simplify the equation above
[tex]\begin{gathered} 5x-5=180^0 \\ 5x=180+5 \\ 5x=185 \\ \text{Divide both sides by 5} \\ x=\frac{185}{5} \end{gathered}[/tex]Therefore
[tex]x=39^0^{}[/tex]Hence
The value of x is 39°
Suppose that you decide to buy a car for $32,635, including taxes and license fees. You saved $9,000 for a down payment and can get a four year car loan at 6.31%. Find the monthly payment and the total interest for the loan. Equation below.
SOLUTION:
Step 1:
In this question, we are given the following:
Suppose that you decide to buy a car for $32,635, including taxes and license fees.
You saved $9,000 for a down payment and can get a four-year car loan at 6.31%.
Find the monthly payment and the total interest for the loan.
Step 2:
In this question, we are given:
Cost of the car = $ 32, 635
Down payment = $ 9000
Principal on the Car loan = $ ( 32,635 - 9,000 ) = $ 23, 635
Rate = 6. 31%
Using the PMI Formulae, we have that:
3. *Which of the following equations has x intercepts at 4 and -2? (A) y = 3x^2 - 10x - 8 (B) y = x^2 + 2x - 8 (C) y = 3x^2 – 2x – 8 (D) y = x^2 - 2x - 8
Given data:
The x-intercepts given are 4 and -2.
Substitute 0 for y in the first option.
[tex]\begin{gathered} 0=3x^2-10x-8 \\ 3x^2-12x+2x-8=0 \\ 3x(x-4)+2(x-4)=0 \\ x=4,\text{ -}\frac{2}{3} \end{gathered}[/tex]Substitute 0 for y in the second option.
[tex]\begin{gathered} 0=x^2+2x-8 \\ x^2+2x-8=0 \\ x^2+4x-2x-8=0 \\ x(x+4)-2(x+4)=0 \\ (x-2)(x+4)=0 \\ x=2,\text{ -4} \end{gathered}[/tex]Substitute 0 for y in the third option.
[tex]\begin{gathered} 0=3x^2-2x-8 \\ 3x^2-2x-8=0 \\ 3x^2-6x+4x-8=0 \\ 3x(x-2)+4(x-2)=0 \\ (x-2)(3x+4)=0 \\ x=2,\text{ -}\frac{4}{3} \end{gathered}[/tex]Substitute 0 for y inlast option.
[tex]\begin{gathered} 0=x^2-2x-8 \\ x^2-4x+2x-8=0 \\ x(x-4)+2(x-4)=0 \\ (x-4)(x+2)=0 \\ x=4,\text{ -2} \end{gathered}[/tex]Thus, option (D) is correct.
Simplify each expression by distributing8(x + 5)
ok
8(x + 5) Just multiphy 8 by each term
8x + 40 This is the result
If 8 more than twice a number is 14, what is 8 times the number?
Let the unkonwn number be
[tex]=x[/tex]Twice the number means
[tex]\begin{gathered} =2\times x \\ =2x \end{gathered}[/tex]8 more than twice the number means the sum of twice the number and 8
[tex]=2x+8[/tex]8 more than twice a number is 14, will be represented below as
[tex]2x+8=14[/tex]collect similar terms from the equation above to get
[tex]\begin{gathered} 2x+8=14 \\ 2x=14-8 \\ 2x=6 \\ \text{divide both sides by 2} \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}[/tex]8 times the number will then be,
[tex]\begin{gathered} =8\times x \\ =8\times3 \\ =24 \end{gathered}[/tex]Hence,
The correct answer is OPTION C
The equation ^2 − 4 − 4^2 + 13 = 0 will produce a hyperbola. How can we tell by simply observing the equation?In what directions do the branches of this hyperbola open? How do you know? Explain. Sketch a graph of this hyperbola, clearly indicating how you have determined thekey characteristics (center, vertices, eccentricity, foci). Give the domain and range of this hyperbola.
we have the equation
[tex]^2−4−4^2+13=0[/tex]Group similar terms and move the constant to the right side
[tex](^2−4)−4^2=-13[/tex]Complete the square
[tex]\begin{gathered} (y^2-4y+2^2-2^2)-4x^2=-13 \\ (y^2-4y+2^2)-4x^2=-13+2^2 \\ (y^2-4y+2^2)-4x^2=-9 \end{gathered}[/tex]Rewrite as a perfect square
[tex](y-2)^2-4x^2=-9[/tex]Divide both sides by -9
[tex]\begin{gathered} \frac{(y-2)^2}{-9}-\frac{4x^2}{-9}=\frac{-9}{-9} \\ \\ -\frac{(y-2)^2}{9}+\frac{x^2}{\frac{9}{4}}=1 \\ \\ \frac{x^{2}}{\frac{9}{4}}-\frac{(y-2)^{2}}{9}=1 \\ \end{gathered}[/tex]The coordinates of the center are (0,2)
The transverse axis is on the x-axis
a^2=9/4 -----------> a=3/2
b^2=9 -----------> b=3
The vertices are --------> (0+1.5,2) and (0-1.5,2)
so
Vertices at (1.5,2) and (-1.5,2)
Find out the value of c
c^2=a^2+b^2
c^2=(9/4)+9
c^2=45/9
c=√5
Find out the coordinates of the foci
(0+√5,2) and (0-√5,2)
using a graphing tool
The domain is the interval (-infinite, -1.5) U (1.5, infinite)
The range is the interval (-infinite, infinite)
Share it: Due:Friday, Aug 28, 2020, 12:00 AM How is comparing and ordering rational numbers different from comparing and ordering integers? Be specific.
hello
to compare or know the difference between rational numbers and integers
rational numbers are numbers in which are expressed as fractions of two integers eg a/b where b is a non zero number
integers are whole numbers in mathemathics without the expression in fraction or rather they're expressed in fractions but the denominator must be equal to 1
now when we want to compare and order integers, they're prefereably done using the number line system.
for an integer
[tex]\begin{gathered} in\text{ the number line system} \\ -3>\text{ }-4 \\ 2\text{ }<\text{ 3} \end{gathered}[/tex]while in rational numbers,
[tex]\begin{gathered} \frac{1}{2}\text{ }>\text{ }\frac{1}{4} \\ -\frac{2}{3}\text{ <}\frac{1}{2} \end{gathered}[/tex]If the measures of the angles of a triangle arerepresented by 2x, 3x - 15, and 7x +15, the triangleis1) an isosceles triangle2) a right triangle3) an acute triangle4) an equiangular triangle
Answer
Option 1 is correct.
The triangle is an isosceles triangle.
Explanation
Noting that the sum of angles in a triangle is 180°.
We can solve for each of the angles in this triangle to obtain the type of triangle it is.
The angles of the triangle are 2x, (3x - 15) and (7x + 15)
2x + 3x - 15 + 7x + 15 = 180°
2x + 3x + 7x - 15 + 15 = 180°
12x = 180°
Divide both sides by 12
(12x/12) = (180°/12)
x = 15°
We can then solve for the measures of the three angles now
2x = 2 (15°) = 30°
3x - 15 = 3 (15°) - 15° = 45° - 15° = 30°
7x + 15 = 7 (15°) + 15° = 105° + 15° = 120°
So, the angles of the triangle are 30°, 30° and 120°
A tringle that has two of its angles equal to each other is called an isosceles triangle.
Hope this Helps!!!
How to write a rule for the nth term of the geometric seq
The nth term of a geometric sequence is expressed as:
[tex]a_n=ar^{n-1}[/tex]were:
• a is the first term
,• r is the common ratio
,• n is the number of terms
If the 2nd term a₂ = 28, then;
[tex]\begin{gathered} 28=ar^{2-1} \\ ar=28 \end{gathered}[/tex]If the 5th term a₅ = 1792, then;
[tex]\begin{gathered} 1792=ar^{5-1} \\ ar^4=1792 \end{gathered}[/tex]Take the ratio of both equations to have:
[tex]\begin{gathered} \frac{ar^4}{ar}=\frac{1792}{28} \\ r^3=64 \\ r=\sqrt[3]{64} \\ r=4 \end{gathered}[/tex]Substitute r = 4 into any of the equations to have:
[tex]\begin{gathered} ar=28 \\ 4a=28 \\ a=\frac{28}{4} \\ a=7 \end{gathered}[/tex]Determine the rule for the nth term of the geometric sequence. Recall that;
[tex]\begin{gathered} a_n=ar^{n-1} \\ a_n=7(4)^{n-1} \end{gathered}[/tex]This gives the nth term of the geometric sequence
Chris earns $298.65 each week. The federal government withholds 17% ofthat for federal income tax. How much is withheld from her pay annuallyfor federal income tax?a. $15,529.80b. $50.77c. $2,640.07d. $2,963.77
Remember that
1 year=52 week
so
17%=17/100=0.17
Multiply $298.65 by 0.17
$298.65*0.17=$50.7705
Multiply by 52
$50.7705*52=$2,640.07
the answer is option C