x² + 7x + 12 = 0
Using the factorisation method
Find two numbers such that its product gives 12 and its sum gives 7
The two numbers are 3 and 4
Replace 7 in the equation by those two numbers and then factorise
That is;
x² + 3x + 4x + 12 = 0
x(x+3) + 4(x+3) = 0
(x+3)(x+4) = 0
Either x+3 = 0 or x+4 =0
Either x = -3 or x= -4
The table below gives the material of each item in Maria’s jewelry box. These are the only items in Maria’s jewelry box. Give the contra positive
The contra positive of the conditional statement is given as follows:
If an item is not made from copper, then it is not a pendant.
How to find the contra positive of a conditional statement?A conditional statement is modeled as follows:
p -> q.
In which:
p is the hypothesis.q is the conclusion.Hence the statement is read as:
If p then q.
The contra positive of the statement is given by:
~q -> ~p.
Hence it is read as:
If not q, then not p.
In the context of this statement, the hypotheses and the conclusion are given, respectively, by:
p: Item is a pendant.q: Item is made from copper.Hence the contra positive of the statement is:
If an item is not made from copper, then it is not a pendant.
What is the missing information?The statement is missing and is given as follows:
"If an item is a pendant, then the item is made from copper".
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Finding Slope From Two Points
Find the slope of the line through each pair of points.
1) (19,-16), (-7, -15)
The slope of a line from given points (19,-16), (-7, -15) is - 1/26
Slope :
In Mathematics, Slope of a line defined as the direction of the line and the change in y-coordinate with respect to x - coordinate. Slope of a line is denoted by 'm'
The formula for slope of a line which passes through the points (x₁, y₁) and (x₂, y₂) is given by Slope (m) = (y₂– y₁)/(x₂ – x₁)
Here, we have pair of points (19,-16), (-7, -15)
Take (x₁, y₁) = (19,-16) and (x₂, y₂) = (-7, -15)
Slope (m) = [-15 -(-16) ] / [ -7 -19 ]
= [ - 15+16] / [ -26 ]
= [ 1 ] / [ -26 ]
= - 1/26
Therefore,
The slope of line from given points (19,-16), (-7, -15) is - 1/26
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Suppose that the function f is defined, for all real numbers, as follows.
f(x)= {5x-4 if x≤1
-x+4 if x>1
Graph the function f. Then determine whether or not the function is continuous.
Answer:
F(x)
Step-by-step explanation:
hope it helps
Given the function [tex]f(x) = \left \{ {{5x-4, \ \ \ x\leq 1} \atop {-x+4, \ \ \ \ \ x > 1}} \right.[/tex], the function is not continuous at x = 1.
A function is said to be continuous if it can be drawn without picking up the pencil. Otherwise, a function is said to be discontinuous.
Given function,
[tex]f(x) = \left \{ {{5x-4, \ \ \ x\leq 1} \atop {-x+4, \ \ \ \ \ x > 1}} \right.[/tex]
We need to check the continuity of the function f(x) at x = 1. At all other points, it is continuous.
f(x) at x = 1 : 5x - 4 = 5*1 - 4 = 5 - 4 = 1
f(x) at x < 1 : 5x - 4 = 5*1 - 4 = 5 - 4 = 1
f(x) at x > 1 : -x + 4 = -1 + 4 = 3
Since, f(x) at x < 1 ≠ f(x) at x > 1, therefore, f(x) is not continuous at x = 1.
The same is also visible from the graph attached below. There is a disruption at x = 1, the graph is not a smooth line.
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2) At a party, Karen notices the amount songs being played. The chart shows wh she figured out. Number of hours 50 Number of songs VSJ 3 4 5 6 60 80 A. 85 C. 100 After five hours, how many songs were played? 120 B. 90 D. 110
Answer:
C. 100
Step-by-step explanation:
If 60 songs are played in 3 hours, 80 songs in 4 hours, and 120 songs in 6 hours, you want to know the number played in 5 hours.
Linear functionConsidering the rate of change of songs per hour, we find ...
hours 3-4: 80-60 = 20 songs, over the 1-hour period
hours 4-6: 120 -80 = 40 songs, over the 2-hour period
It appears that the number of songs being played is steady at 20 songs per hour. Then 5×20 = 100 songs were played in 5 hours.
Find the total cost of 12 boxes of cookies if each box costs $3.
each box costs $3 : The cost of one box = $3
12 boxes of cookies : The total number of boxes = $12
For the total cost of 12 boxes : Multiply the cost of one box by the number of boxes
The total cost of 12 boxes = 12 x $3
The cost of 12 boxes = $36
The cost of 12 boxes of cookies ia $36
Answer : $36
A basketball player scores 14, 16, 20, 5, 22, 30, 16, and 28 points during a
tournament. Make a box-and-whisker plot for the points scored by the player.
The diagram attached shows the box-and-whisker plot for the points scored by the player.
How to Make a Box-and-whisker Plot for a Data Set?A box-and-whisker plot displays the maximum and minimum data values, the upper and lower quartiles, and the median of the data. They are called the five-number summary.
Given the data for the number of points scored by a basketball player is: 14, 16, 20, 5, 22, 30, 16, and 28, the five-number summary for the data would therefore be:
Minimum: smallest data point, which is 5.First Quartile: center of the first part of the data set when ordered, which is 15.Median: The middle data point, which is 18.Third Quartile: center of the second part of the data set, which is, 25Maximum: this represents the highest data point, which is, 30The box-and-whisker plot is shown below.
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Instructions: For the following sequence, state the common ratio, identify which is the explicit form and which is the recursive form of the rule.
Given that the series is 1, 3, 9, 27, ............
The common ratio will be
[tex]Common\text{ ratio=}\frac{2nd\text{ term}}{1st\text{ term}}=\frac{3}{1}=3[/tex]So the common ratio is 3.
The explicit formula uses starting term and the recursive formula uses the previous term.
As
[tex]\begin{gathered} Explicit\text{ form} \\ a_n=3^{n-1} \\ Recursive\text{ form} \\ a_n=a_{n-1}\times3 \end{gathered}[/tex]These are the required forms.
(5)(3) - (2-7) divided by 4?
Answer:
Step-by-step explanation:
Answer:
[tex]{ \tt{(5)(3) - (2 - 7) \div 4}}[/tex]
- We are going to simplify the expression using BODMAS
B stands for BracketsO stands for OfD stands for DivisionM stands for MultiplicationA stands for AdditionS stands for Subtraction- From our expression, relating it to BODMAS, Brackets come first, so let's first operate the brackets
[tex] = { \tt{(5 \times 3) - ( \frac{2 - 7}{4}) }} \\ \\ = { \tt{15 - ( - \frac{5}{4} )}} \\ \\ = { \tt{15 + 5 \div 4}}[/tex]
- Then in our last expression, Division comes next
[tex] = { \tt{15 + \frac{5}{4} }} \\ [/tex]
- Then addition comes last
[tex] = { \tt{ \frac{65}{4} }} \\ [/tex]
- Simplifying our answer into mixed fraction and decimal format;
[tex] = { \tt{16 \frac{1}{4} \: \: or \: \: 16.25}}[/tex]
[tex]{ \boxed{ \delta}}{ \underline{ \mathfrak{ \: \: beicker}}}[/tex]
If f(x) = -x-11, find -3f(5) x f(2)
Given the function :
[tex]f(x)=-x-11[/tex]we need to find the value of 3f(5) x f(2)
so, to find the value of f(5), substitute with x = 5 at the given function
And to find the value of f(2) , substitute with x = 2 at the given function
so,
[tex]\begin{gathered} f(5)=-5-11=-16 \\ \\ f(2)=-2-11=-13 \\ \\ 3f(5)\cdot f(2)=3\cdot-16\cdot-13=624 \end{gathered}[/tex]need help!! algebra 1
Answer:
Step-by-step explanation:
6a) f(1)=-3
b) x=-5 x=-1 x=1
:]
I need help with this question please?
[tex]t=100 \left(1-\frac{V}{50} \right)^2\\\\\frac{t}{100}=\left(1-\frac{V}{50} \right)^2[/tex]
Since time is positive, we take the positive square root.
[tex]\frac{\sqrt{t}}{10}=1-\frac{V}{50}\\\\\frac{\sqrt{t}}{10}-1=-\frac{V}{50}\\\\50-5\sqrt{t}=V\\\\\therefore f^{-1}(V)=\boxed{50-5\sqrt{V}}[/tex]
NEED HELP ASAP‼️‼️‼️‼️‼️‼️‼️‼️‼️
simplify 3xy³ + x²y⁵ over xy²
PLEASE SEND QUICK DUE IN 10-15 MINUTES ‼️‼️‼️
Answer:
[tex]4xy^3[/tex]
Step-by-step explanation:
3xy^3 + x^2y^5/xy^2
A pizza shop specializes in deep-dish pizzas. They sell a 14 -inch pizza that is 3 inches deep and a 16-inch pizza that is 2 inches deep. The 14 -inch pizza is cut into 8 slices and the 16-inch pizza is cut into 7 slices, and each slice is sold for the same price. If you are purchasing one slice of pizza, which size should you choose to get the most food? Show all of your work to justify your response.
Answer:
The 14-inch pizza cut into 8 slices.
Explanation:
The deep-dish pizza forms a cylindrical shape.
To make comparisons, we find the volume of each slice of pizza in each case.
[tex]\text{Volume of a cylinder=}\pi r^2h[/tex]Case 1
A 14-inch pizza that is 3 inches deep.
Radius = 14/2 = 7 inches
Height = 3 inches
[tex]\begin{gathered} \text{The volume of the full pizza}=\pi\times7^2\times3 \\ =147\pi\text{ cubic inches} \end{gathered}[/tex]Since it is cut into 8 slices:
[tex]\begin{gathered} \text{The volume of one slice=}\frac{147\pi}{8} \\ =18.375\pi\text{ cubic inches} \end{gathered}[/tex]Case 2
A 16-inch pizza that is 2 inches deep.
Radius = 16/2 = 8 inches
Height = 2 inches
[tex]\begin{gathered} \text{The volume of the full pizza}=\pi\times8^2\times2 \\ =128\pi\text{ cubic inches} \end{gathered}[/tex]Since it is cut into 7 slices:
[tex]\begin{gathered} \text{The volume of one slice=}\frac{128\pi}{7} \\ \approx18.285\pi\text{ cubic inches} \end{gathered}[/tex]Conclusion
The volume of a slice of pizza in the first case (the 14 -inch pizza cut into 8 slices) is larger, therefore it should be chosen to get the most food.
show each quadratic equation by factoring (show your solution)
7x^2+25x+12
PLEASE HELP
Answer:or a polynomial of the form
a
x
2
+
b
x
+
c
, rewrite the middle term as a sum of two terms whose product is
a
⋅
c
=
7
⋅
−
12
=
−
84
and whose sum is
b
=
25
.
7
x
2
−
3
x
+
28
x
−
12
Factor out the greatest common factor from each group.
Tap for more steps...
x
(
7
x
−
3
)
+
4
(
7
x
−
3
)
Factor the polynomial by factoring out the greatest common factor,
7
x
−
3
.
(
7
x
−
3
)
(
x
+
4
)
Step-by-step explanation:
Question 7Simplity 663x - 5) + (2x - 1). Show each step on a separate line and tell what you did in that step. Write your answer in factored form.
The expression is given as
[tex]6(3x-5)+5(2x-1)[/tex]STEP 1
Expand the first parenthesis by multiplying all the terms there by 6.
[tex]18x-30+5(2x-1)[/tex]STEP 2
Expand the second parenthesis by multiplying all the terms there by 5.
[tex]18x-30+10x-5[/tex]STEP 3
Collect the like terms.
[tex]18x+10x-30-5[/tex]STEP 4
Perform the arithmetic operations (addition and subtraction) to get the final answer.
[tex]28x-35[/tex]The final answer is 28x - 35
7. Are the lines represented by the equations below parallel, perpendicular, or neither?
Justify your answer with words and numbers. (3 points)
- 3x + 6y = 12
y =
3x + 10
The two lines are neither parallel nor perpendicular.
What is condition for perpendicular, parallel?
if two given lines are parallel, perpendicular, or neither, we need to compare their slopes. For this, we need to make sure that their equations are in the form y = mx + b. This represents the equation of a straight line in the slope-intercept form, where m is the slope and b is the y-intercept.
If the given lines have the same slope, they’re parallel to one another. On the other hand, if they have slopes that are opposite reciprocals, i.e., the slopes have opposite signs and are flipped fractions of one another, they are perpendicular to each other. Else, they are neither.
The given lines are
- 3x + 6y = 12 or, y = (1/2)x + 2 ... (1)
y = - 3x + 10 ... (2)
The gradient of the lines (1) and (2) are 1/2 and (- 3) respectively.
Since the gradients are not equal, the lines are not parallel and also since (1/2) × (- 3) ≠ - 1, the lines are not perpendicular to each other.
Hence we can conclude that the given two lines are neither parallel nor perpendicular.
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what is the result of processing the set of numbers in a domain called
Answer:
the output
Step-by-step explanation:
output
I need help solving for x assume that lines which appear tangent are tangent
SOLUTION:
Case: Secant secant theorem
Secant-Secant Power Theorem: If two secants are drawn from an external point to a circle, then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant
Method:
[tex]\begin{gathered} 7(7+x+6)=8(8+x+2) \\ 7(x+13)=8(x+10) \\ 7x+91=8x+80 \\ 91-80=8x-7x \\ x=11 \end{gathered}[/tex]Final answer:
x = 11
mr. Smith took out a 54200 car loan at 10.2% compounded annually what would the interest be after 4 years
The compounded loan means that in the first year the 10.2% of interest is add to the initial 54200 and that value generate the next year the 10.2%
then in the first year the interest will be:
You use a rule of three:
[tex]\text{1st}=\frac{54200\cdot10.2}{100}=5528.4[/tex]As the first year the interest is 5528.4
To the second year that sum is added to the 54200 to get the interest:
[tex]54200+5528.4=59728.4[/tex][tex]2nd=\frac{59728.4\cdot10.2}{100}=6092.3[/tex]Third year:
[tex]59728.4+6092.3=60820.7[/tex][tex]3rd=\frac{60820.7\cdot10.2}{100}=6203.7[/tex]Fourth year:
[tex]60820.7+6203.7=67024.4[/tex][tex]4th=\frac{67024.4\cdot10.2}{100}=6836.5[/tex]After 4 years:
[tex]67024.4+6836.5=73860.9[/tex][tex]=\frac{73860.9\cdot10.2}{100}=7533.8[/tex]After 4 years the interest will be: 7533.8you have 27 teaspoons of peppercorns you need 0.25 teaspoons make one serving of beef brisket how many servings can you make
Given:
Total Number of teaspoons of peppercorns = 27
Amount of teaspoons you need for one serving of brief brisket = 0.25
Let's find the amount of servings can be made.
To find the amount of servings that can be made, apply the formula:
[tex]\text{Number of servings = }\frac{TotalNumber\text{ of teaspoons}}{Teaspooons\text{ for one brisket}}\text{ }[/tex]Thus, we have:
[tex]\begin{gathered} \text{Number of servings = }\frac{27}{0.25} \\ \\ \text{Number of servings = }\frac{27}{\frac{25}{100}} \\ \\ \text{Number of servings = }\frac{27}{25}\ast100=1.08\ast100=108 \end{gathered}[/tex]Therefore, 108 servings can be made.
ANSWER:
108
what is 42/100 of x over 35?
The value of x in 42/100 of x over 35 based on the computation is 14.7.
How to calculate the fraction?It should be noted that a fraction simply means a number that's not a whole number.
Based on the information, we want to calculate 42/100 × x/35. This will be illustrated thus:
= 42/100 × x/35.
Cross multiply
(100 × x) = (42 × 35)
100x = 1470
Divide through by 100
100x / 100 = 1470 / 100
x = 14.7
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Solve each problem below by writing an equation that matches the situation. Then solbe your equation to find the solution to the problem. (It's been almost a day and these two questions baffled me.)
Step 1:
Let the number of hours = m
Flat fee = $25
Fees charge per hour = $30
Step 2:
Money Ronnie made from his first customer = $175
Write an equation.
30m + 25 = 175
Step 3:
Solve the equation.
[tex]\begin{gathered} 30m\text{ + 25 = 175} \\ 30m\text{ = 175 - 25} \\ 30m\text{ = 150} \\ \text{Divide through by 30} \\ m\text{ = }\frac{150}{30} \\ \text{m = 5 hours} \end{gathered}[/tex]Final answer
5 hours
For which value of x is therelation not a function?{(3, 1), (x, 0),(9,5),(12, 6)}A) 1. B)3C) 8. D)6
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
Here the domain of the relation is {3,x,9,5}.
The given relation is a function only if x not takes any of the value 3, 9 or 5.
So, option B is correct.
Find the perimeter of the figure shown. Round your answer to the nearest centimeter. This is for problem number 9
helppppppppppppp!!!!!!!!!!!!
The height of a trapezoid can be expressed as x - 4, while the bases can be expressed as x + 4 and x + 9. If the area of the trapezoid is 99 cm², find the length of the larger base.
Answer: 19 cm
Step-by-step explanation:
Substituting into the formula for the area of a trapezoid,
[tex]\frac{1}{2}(x-4)(x+4+x+9)=99\\\\\frac{1}{2}(x-4)(2x+13)=99\\\\(x-4)(2x+13)=198\\\\2x^2 +5x-250=0\\\\(2x+25)(x-10)=0\\\\x=-12.5, 10[/tex]
However, as x must be positive (since length must be positive), x=10. This means the length of the longer base is 19 cm.
a survey was given to people who owned a certain type of car.what percent of the people surveyed were completely satisfied with the car.blue:compleletely satisfiedpurple: somewhat satisfiedgreen:not satisfied
The percent of people that were completely satisfied (%PS) can be calculated with the formula:
[tex]\text{ \%PS=}\frac{PS}{TP}\times100\text{\%}[/tex]Where PS is the number of persons that were completely satisfied and TP is the total number of persons, in this case, the total number of persons is the sum of each number of persons from each category:
[tex]TP=160+740+1100=2000[/tex]And as we can see from the figure, the number of completely satisfied people is 1100, then the percent of people that were completely satisfied is:
[tex]\begin{gathered} \text{\%PS=}\frac{PS}{TP}\times100\text{\%} \\ \text{\%PS=}\frac{100}{2000}\times100\text{\%} \\ \text{\%PS=}0.55\times100\text{\%}=55\text{\%} \end{gathered}[/tex]The percent of people that were completely satisfied is 55%
You just have to divide 1100 by the total people which is 2000, and then just multiply by 100, and that's it
Hello what is ALL of the answers to this question
Answer
The function that describes the height of the rocket in terms of the is
[tex]h(t)=-16t^2+224t+68[/tex]
WILL MARK BRAINLIEST PLS HELP
⇒For m=2 and n=-3 in the equation 3m-4n In the place of m plug in 2 and in the place of n plug in -3 and simplify.
[tex]=3(2)-4(-3)\\=6+12\\=18[/tex]
Option C is the answer.
Find and simplify each of the following for f(x) = 4x2 - 5x + 7.(A) f(x + h)(B) f(x +h)-f(x)f(x+h) – f(x)(C)h
(A) f(x+h)
[tex]\begin{gathered} f(x+h)=4(x+h)^2\text{ - 5(x + h) + 7} \\ =\text{ 4(x + h)(x + h) - 5x - 5h + 7} \\ =4(x^2+2xh+h^2)\text{ - 5x - 5h + 7} \\ =4x^2+8xh+4h^2\text{ - 5x - 5h + 7} \end{gathered}[/tex](B) f(x + h) - f(x)
[tex]\begin{gathered} =4x^2+8xh+4h^2\text{ - 5x - 5h + 7 - }(4x^2\text{ - 5x + 7)} \\ =4x^2+8xh+4h^2-5x-5h+7-4x^2\text{ + 5x - 7} \\ =4x^2-4x^2-5x+5x+7-7+8xh+4h^2\text{ - 5h} \\ \text{ = 0 + 0 + 0 + 8xh + 4h}^2\text{ - 5h} \\ =8xh+4h^2\text{ - 5h} \end{gathered}[/tex](C)
[tex]\begin{gathered} =\text{ }\frac{f(x+h)\text{ - f(h)}}{h} \\ =\text{ }\frac{8xh+4h^2\text{ - 5h}}{h} \\ =\text{ }\frac{8xh}{h}\text{ + }\frac{4h^2}{h}\text{ - }\frac{5h}{h} \\ =\text{ 8x + 4h - 5} \end{gathered}[/tex]