The side AB = BD
7x + 10 = 9x - 2
SImplify for x :
Subtract 7x from both side :
7x + 10 - 7x = 9x - 7x - 2
10 = 2x - 2
Add 2 on both side :
10 + 2 = 2x - 2 + 2
12 = 2x
divide both side by 2 :
2x/2 = 12/2
x = 6
identifies the kind of symmetry the figure has below if any.
We are asked to identify the types of symmetries found in the given geometrical figure. Let's remember that asymmetry is a transformation that maps the figure onto itself. In this case the object has symmetry under reflections, also has symmetry under rotations around its center
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If the polynomial function be P(x) = [tex]x^4[/tex] − 3x³ + 2x² then Zeros exists at x = 0, 0, 1, 2.
What is meant by polynomial ?A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
An expression that consists of variables, constants, and exponents that exists combined utilizing mathematical operations like addition, subtraction, multiplication, and division exists directed to as a polynomial (No division operation by a variable).
Let the polynomial function be P(x) = [tex]x^4[/tex] − 3x³ + 2x²
P(x) = x²(x² - 3x + 2)
factoring the above polynomial function, we get
P(x) = x·x(x - 1)(x - 2)
Zeros exists at x = 0, 0, 1, 2
P(x) exists degree 4, so it will contain four roots. You only entered three which exists probably why it came up as wrong. The x² term contains a multiplicity of 2, so it counts twice.
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89, 81,96, 85, 93, 70, 66, 64, 68, 70MeanMedianMode(s)Range
Okay, here we have this:
Considering the provided data set, we are going to calculate the requested data, so we obtain the following:
Mean:
It corresponds to the result of adding all the data and dividing it by the amount of data, then we have:
Mean=(89+81+96+85+93+70+66+64+68+70)/10
Mean=782/10
Mean=78.2
Median:
First we will order the data from smallest to largest and the value that is in the center will be the median:
Sorted Data Set: 64, 66, 68, 70, 70, 81, 85, 89, 93, 96
Since 70 and 81 are in the middle, the median will be their average.
Median=(70+81)/2=151/2=75.5
Mode:
It is the data that is repeated the most, in this case it is 70 because it is twice
Range:
It is the difference between the smallest and largest value, then:
Range=96-64=32
Ashgn in a bakery yves these options,• Option : 12 cupcakes for $29Option B. 24 cupcakes for $561. Find each unit price, Just type the number in your answer. (Don't forget to divide tothe thousandths place to help you round to the hundredths place.)Option :Option :2. Which option is the best deal per cupcake and gives the lowest unit price. Type A or
1) To find each unit price, let's find out the unit rate. Setting a proportion.
Option A
cupcakes price
12 ------------------- 29
1 --------------------x
Cross multiplying it:
12x = 29 Divide both sides by 12
x =2.42
Each cupcake costs $ 2.42
Option B
24 ------------ 56
1 ------------ y
24y = 56
y =$2.33 per cupcake.
2) The best deal for buying cupcakes is found in Option B. Since the price is lower per cupcake
3) Hence, the answers are:
Option A = $2.42 per cupcake
Option B =$2.33 per cupcake
Best Deal: Option B
The longest side of a triangle is 5in longer than the shortest side. The medium side is 4 inches longer than the shortest side. If the perimeter of the triangle is 21 inches, what are the lengths of the three sides?
The perimeter of a triangle is given by the sum of all it is sides.
Now, we have the next measures:
- The longest side of a triangle is 5in longer than the shortest side.
- The medium side is 4 inches longer than the shortest side
Then, the perimeter is given by:
P = (s+5)+(s+4)+s
If the perimeter is P=21 inches:
21 = (s+5)+(s+4)+s
Solve for s:
21 = s+5+s+4+s
21 = 3s + 9
21-9 = 3s
12 = 3s
s = 12/3
s= 4
Therefore,
The shortest side of the triangle is 4 inches.
The medium side is s+ 4 = 4+ 4 = 8 inches
The longest side is s+5 = 4+5 = 9 inches
Just do all 25 points If can show how it works it will be better thanks
a) Given:
The length of the side of a square is,
[tex]\frac{1}{5}cm[/tex]To find:
The area of the square.
Explanation:
Using the formula of the area of the square,
[tex]\begin{gathered} A=a^2 \\ A=(\frac{1}{5})^2 \\ A=\frac{1}{25}cm^2 \\ A=0.04cm^2 \end{gathered}[/tex]Final answer:
The area of the square is,
[tex]0.04cm^2[/tex]In the national park, the ratio of black bear bears to grizzly bears is 3:1. If the park had 12 grizzly bears, how many black bears would it have?
The number of black bears in the national park is 36
Here, given the ratio of black bears to grizzly bears, and the number of grizzly bears, we want to find the number of blackbears the national park has
Let the number of black bears be x
what this mean is that the total number of bears in the park is (x + 12)
The total ratio of the two is 3 + 1 = 4
Matematically;
[tex]\begin{gathered} \frac{3}{4}\text{ }\times\text{ (x + 12) = x} \\ \\ 3(x\text{ + 12) = 4 }\times\text{ x} \\ \\ 3x\text{ + 36 = 4x} \\ 4x-3x\text{ = 36} \\ \\ x\text{ = 36} \end{gathered}[/tex]Quadrilateral OPQR is dilated by a scale factor of 2/3 to form quadrilateral O'P'Q'R'. What is the measure of side RO?
Divide side R'O' (8) by th scale factor (2/3)
8 : 2/3= 12
Solve this inequality X-1 less than or equal to 9
Solution of an inequality
We can express the solution (s) of inequalities in several forms.
Here we will use two of them: The set-builder notation and the interval notation.
Let's solve the inequality
x - 1 ≤ 9
Adding 1 to both sides of the inequality:
x ≤ 10
The solution in words is "all the real numbers less than or equal to 10"
In set-builder notation:
{x | x <= 10}
In interval notation: (-inf, 10]
Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.
What is Cost?This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.
In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.
Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.
Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.
The difference is however $2.79 - $2.36 = $0.43.
Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.
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The height of a triangle is 4x more than the base, and the area of the triangle is 6 square units. Find the length of the base. Let x =the length of the base.
Write a quadratic equation in factored form. Write entire equation
Answer:
The length of the base is:
3 unitsThe resulting quadratic is
x² - 3= 0Step-by-step explanation:
Base = x
Height = 4x
Area, A = 1/2* base * Height
A = (1/2) * (x) * (4x)
A = 2x² (1)
But, A = 6 (2)
Since (1) = (2);
2x²= 6
x²= 3
Resulting quadratic:
x² - 3= 0
For the difference between 2 squares:
a² - b² = (a-b)(a+b)
Using that identity, we can factorize our quadratic:
(x-3)(x+3) = 0
So, we have 2 roots:
x = 3 and x = -3
Now, noting that length must take a positive value, we go for the first:
x = 3
CONCLUSION:The length of the base is:
3 unitsThe resulting quadratic is
x² - 3= 0Graph a line that contains the point 2 (-5, -6) and has a slope of 3 Y 6 4 2 2 -6 -4 2 4 6 -4- -6-
the graph of a line passing through point
[tex](x_1,y_1)[/tex]with gradient m
is given by
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y+6=3(x+5) \\ \Rightarrow y+6=3x+15 \\ \Rightarrow y=3x+9 \end{gathered}[/tex]A diver starts out at 342 feet below the surface (or – 342 feet). She then swims upward 237 feet.Use a signed number to represent the diver's current depth.
Given:
A diver starts at 342 feet below the surface, which means -342 feet.
Now, she swims 237 feet upward.
It shows that she is moving in a positive direction.
So, the current depth of diver is,
[tex]-342+237=-105[/tex]The depth is -105 feet, which shows that the diver is still 105 feet below the surface.
What is the missing number 100 -11- missing number -12=9
Answer:
68
Step-by-step explanation:
100-68-12-11=9
12+11=23
100-23-9=68
What is the volume air enclosed in a pyramid-shape tent whose square base measures 8 dm by 8 dm and whose height is 6dm?
We have to calculate the volume of the pyramid with the following dimensions:
We can express and calculate the volume as:
[tex]\begin{gathered} V=\frac{1}{3}A_bh \\ V=\frac{1}{3}(8\cdot8)\cdot6 \\ V=\frac{64*6}{3} \\ V=128\text{ }dm^3 \end{gathered}[/tex]Answer: the volume is 128 dm³
What is the sign of when x > 0 and y < 0 ?
The number line always goes from negative to positive :
It increases from left to right
SInce negative is always on the left side of the zero
Snumber greater than zero are always positive
i.e. x > o
Help!!!! (Show ur work)
There are two questions
Answer:
Question 1: 3
Question 2: $120
Step-by-step explanation:
Set up a proportion
[tex]\frac{inches}{miles}[/tex] = [tex]\frac{inches}{miles}[/tex] fill in the numbers that you know and solve for the unknow.
[tex]\frac{5}{2}[/tex] =[tex]\frac{7.5}{m}[/tex] Cross multiply
5x =7.5(2)
5x = 15 Divide both sides by 5
x = 3
If we take 40% off that means that we leave 60% on
Percent means per hundred
[tex]\frac{60}{100}[/tex] When you divide by hundred, you move the decimal two places to the left.
200(.6)
$120.00
Solve 6 < x + 5 < 11
we have the following:
[tex]\begin{gathered} 6Find the midpoint M of the line segment joining the points C=(6,2) and D=(2,8).
Given
[tex]point\text{ C \lparen6,2\rparen and Point \lparen2,8\rparen}[/tex]Solution
Formula
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2}) \\ \end{gathered}[/tex][tex]\begin{gathered} x_1=6 \\ x_2=2 \\ y_1=2 \\ y_2=8 \end{gathered}[/tex]Now
[tex]\begin{gathered} M=(\frac{6+2}{2},\text{ }\frac{2+8}{2}) \\ \\ M=(\frac{8}{2},\frac{10}{\text{2}}) \\ \\ M=(4,5) \end{gathered}[/tex]The midpoint M of the line segment joining the points C=(6,2) and D=(2,8). is
[tex]M=(4,5)[/tex]Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it
So we need to solve the following equation for x:
[tex]\sqrt[]{x-2}+8=x[/tex]The first step would be substracting 8 from each side of the equation:
[tex]\begin{gathered} \sqrt[]{x-2}+8-8=x-8 \\ \sqrt[]{x-2}=x-8 \end{gathered}[/tex]The next step is to square
A bee produce 0,05 ml of honey per day, how many litres of honey can the bee produce in its lifetime if they live for 28 days?
Given:
A bee produce 0.05 ml of honey per day
We will find how many liters of honey can the bee produce in its lifetime if they live for 28 days
Let it produces x ml
So, using the ratio and proportions
[tex]\frac{0.05}{1}=\frac{x}{28}[/tex]Solve for x:
[tex]x=0.05\times28=1.4ml[/tex]Convert ml to liters
1 liter = 1000 ml
So, 1.4 ml = 0.0014 liters
So, the answer will be
The bee can produce honey in its lifetime = 0.0014 liters
Can you please help me
we have that
the area of parallelogram is equal to
A=b*h
we have
b=14 mm
Find the value of h
tan(60)=h/7 -----> by opposite side divided by the adjacent side
Remember that
[tex]\tan (60^o)=\sqrt[]{3}[/tex]so
h=7√3 mm
substitute
A=14(7√3 )
A=98√3 mm2Which of the following is a solution to the inequality below?
Answer:
q = -1
Step-by-step explanation:
We are given the inequality [tex]11-\frac{64}{q} > 60[/tex]
We want to find out which value of q is a solution to the inequality. In other words, which value of q makes the statement true?
We can substitute the values given for q into the inequality to see this.
Let's start with q=2.
Replace q with 2.
[tex]11-\frac{64}{2} > 60[/tex]
Divide 64 by 2.
64/2= 32
11 - 32 > 60
Subtract 32 from 60
11-32 = -21
-21 > 60
The inequality reads "-21 is greater than 60", which is false (negative numbers are less than positive ones).
This means q=2 is NOT an answer.
Next, let's try q=-2
[tex]11 - \frac{64}{-2 } > 60[/tex]
64/-2 = -32
11 - - 32 > 60
- - 32 means subtracting a negative, which is the same as adding 32 to 11.
11 + 32 > 60
43 > 60
This is also NOT true (it reads "43 is greater than 60").
So q=-2 is also NOT an answer.
Now, let's try q = -1
[tex]11-\frac{64}{q} > 60[/tex]
[tex]11-\frac{64}{-1} > 60[/tex]
64/-1=-64
11 - -64 > 60
11 + 64 > 60
75 > 60
This reads "75 is greater than 60".
This is a true statement, meaning q = -1 IS an answer.
We are technically done, but just to be sure, we can check q=1 as well.
[tex]11 - \frac{64}{q} > 60[/tex]
[tex]11 - \frac{64}{1} > 60[/tex]
11 - 64 > 60
-53 > 60
This reads "-53 is greater than 60", which is false.
So this confirms that q = -1 is the only option that is an answer.
Which statement best describes the growth rates of the functions below?
ANSWER:
D. the exponential function grows faster than the quadratic function over two intervals; 2 < x ≤ 4
STEP-BY-STEP EXPLANATION:
We can see from the graphs that the growth is the same from 0 to 2 and then the exponential function grows faster, therefore, strictly speaking, the correct answer is D. the exponential function grows faster than the quadratic function over two intervals; 2 < x ≤ 4
Find the equation of the line with the given properties. Express the equation in general form or slope-intercept form.
To asnwer this questions we need to remember that two lines are perpendicular if and only if their slopes fullfil:
[tex]m_1m_2=-1[/tex]Now to find the slope of the line
[tex]-7x+y=43[/tex]we write it in slope-intercept form y=mx+b:
[tex]\begin{gathered} -7x+y=43 \\ y=7x+43 \end{gathered}[/tex]from this form we conclude that this line has slope 7.
Now we plug this value in the condition of perpendicularity and solve for the slope of the line we are looking for:
[tex]\begin{gathered} 7m=-1 \\ m=-\frac{1}{7} \end{gathered}[/tex]Once we hace the slope of the line we are looking for we plug it in the equation of a line that passes through the point (x1,y1) and has slope m:
[tex]y-y_1=m(x-x_1)[/tex]Plugging the values we know we have that:
[tex]\begin{gathered} y-(-7)=-\frac{1}{7}(x-(-7)) \\ y+7=-\frac{1}{7}(x+7) \\ y+7=-\frac{1}{7}x-1 \\ y=-\frac{1}{7}x-8 \end{gathered}[/tex]Therefore the equation of the line is:
[tex]y=-\frac{1}{7}x-8[/tex]factor the trinomial6x² + 17x + 12
Answer: The factor of the above function is (2x + 3) (3x + 4)
We are given the below function
[tex]6x^2\text{ + 17x + 12}[/tex]This function can be factor using factorization method
The co-efficient of x^2 = 6
Multiply 6 by 12 to get the constant of the function
12 x 6 = 72
Next, find the factors of 72
Factors of 72 : 1 and 72, 2 and 36, 6 and 12, 9 and 8, 3 and 24
The only factor that will give us 17 when add and give us 72 when multiply is 8 and 9
The new equation becomes
[tex]\begin{gathered} 6x^2\text{ + 17x + 12} \\ 6x^2\text{ + 8x + 9x + 12} \\ \text{Factor out 2}x \\ 2x(3x\text{ + 4) + 3(3x + 4)} \\ (2x\text{ + 3) (3x + 4)} \end{gathered}[/tex]The factor of the above function is (2x + 3) (3x + 4)
Choose the scenarios that demonstrate a proportional relationship for each person's income.
Millie works at a car wash and earns $17.00 per car she washes.
Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.
Carla makes sandwiches at her job and earns $7.85 per hour.
Tino is a waiter and makes $3.98 per hour plus tips.
The scenarios that demonstrate a proportional relationship for each person's income are :
Millie works at a car wash and earns $17.00 per car she washes.Carla makes sandwiches at her job and earns $7.85 per hour.Consider the income as y in each scenario
Scenario 1
Millie works at a car wash and earns $17.00 per car she washes.
Consider the number of car she washes as x
y = 17x
y ∝ x
This is a proportional relationship
Scenario 2
Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.
The relationship will be
y = 25 +12.50x
where x is the number of hours
This is not a proportional relationship
Scenario 3
Carla makes sandwiches at her job and earns $7.85 per hour.
The relationship will be
y = 7.85x
y ∝ x
Where x is the number of hours
This is a proportional relationship
Scenario 4
Tino is a waiter and makes $3.98 per hour plus tips.
The relationship will be
y = 3.98x + tips
Where x is the number of hours
This is not a proportional relationship
Hence, the scenarios that demonstrate a proportional relationship for each person's income are
Millie works at a car wash and earns $17.00 per car she washes.Carla makes sandwiches at her job and earns $7.85 per hour.Learn more about proportional relationship here
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1. It is h before closing time at the grocery store. It takes about h for Jane to find 1 item on her shopping list. How many items can she find before the store closes? (a) Create a model or write an equation for the situation. (b) Find the solution. Explain what you did. (c) State the solution as a full sentence.
GIVEN
The time left before the store closes is 3/4 h while the time taken to find one item is 1/8 h.
QUESTION A
Let the number of items that can be gotten before the store closes be N.
The number of items can be calculated using the formula:
[tex]N=\text{ number of hours left}\div\text{ number of hours used to find one item}[/tex]Therefore, the equation to get the number of items will be:
[tex]N=\frac{3}{4}\div\frac{1}{8}[/tex]QUESTION B
The solution can be obtained by division.
Apply the fraction rule:
[tex]\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]Hence, the solution will be:
[tex]\begin{gathered} \frac{3}{4}\div\frac{1}{8}=\frac{3}{4}\times\frac{8}{1} \\ \Rightarrow\frac{3\times\:2}{1\times\:1}=6 \end{gathered}[/tex]The answer is 6.
QUESTION C
Jane can find 6 items before the store closes.
Jim can choose plan A or plan B for his long distance charges. For each plan, cost (in dollars)depende on minutes used (per month) as shown below.(a)If Jim makes 40 minutes of long distance calls for the month, which plan costs more? How much more does it cost than the other plan?(b) For what number of long distance minutes do the two plans cost the same?
Answer:
• Plan B, by $4
,• 140 minutes
Explanation:
Part A
From the graph, at 40 minutes, the costs of the plans are:
• Plan A: $4
,• Plan B: $8
[tex]\begin{gathered} \text{Difference}=8-4 \\ =\$4 \end{gathered}[/tex]Plan B costs more by $4.
Part B
The point where the costs are the same is the time at which the two graphs intersect.
When the number of minutes = 140 minutes
• Cost of Plan A = $14
,• Cost of Plan B = $14
Thus, the two plans cost the same for 140 minutes of long-distance call.
• If the time spent is less than this amount, Plan B costs more.
True or False? A circle could be circumscribed about the quadrilateral below.B82"O A. TrueA 105°98° cO B. False75%
Solution
For this case since we want to verify if a circle can be circumscribed in the quadrilateral we can use the following Theorem:
Theorem: If a quadrilateral is incribed in a circle then the opposite sides are supplementary
And we cna verify:
105+ 98= 203
82 +75= 157
Then we can conclude that the answer is:
False