To calculate the quadratic equation below:
[tex]6x^2+23x+7[/tex]Step 1: break the expression into groups
[tex]\begin{gathered} 6x^2+23x+7 \\ 6x^2+2x+21x+7 \end{gathered}[/tex]Step 2: factor out 2x, and 7 from first and second
[tex]2x(3x^{}+1)+7(3x+1)[/tex]Step 3: Factor out common fact
[tex](3x+1)(2x+7)[/tex]Hence the final answer = (3x+1)(2x+7)
what is the probability of landing on a 5 and then later on a 5 as a fraction or whole number
probabilities of landing on 5 = favorable outcome / total outcomes
total outcomes = 3 ( 5 , 4 and 3)
Favourable outcomes = 1 ( 5)
P = 1/3
Probability of of landing on 5 two times
1/3 x 1/3 = 1/9
Arianna filled up her car with gas before embarking on a road trip across the country. Let G represent the number of gallons of gas remaining in her gas tank after driving for t hours. A graph of G is shown below. Write an equation for G then state the x- intercept of the graph and determine its interpretation in the context of the problem.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
G = gallons remaining in the tank
t = hours
equation = ?
x- intercept of the graph = ?
Step 02:
We must analyze the graph to find the solution.
point 1 ( 0 , 15) x1 = 0 y1 = 15
point 2 (12 , 0) x2 = 12 y2 = 0
slope formula
[tex]m\text{ = }\frac{y2\text{ -y1}}{x2-x1}=\frac{0-15}{12-0}=\frac{-15}{12}=-1.25[/tex]slope-intercept form of the line
y = mx + b
m = -1.25
b = y-intercept = 15
G = -1.25x + 15
x- intercept of the graph = 12
After 12 hours there is no gas left in the tank.
The answer is:
G = -1.25x + 15
x- intercept of the graph = 12
After 12 hours there is no gas left in the tank.
Find the area of a regular hexagonwith a side length of 8 cm. Round tothe nearest tenth.а8 cm[?] cm2
We are asked to determine the area of a regular hexagon given a side of 8 cm. To do that we will use the following formula:
[tex]A=\frac{3\sqrt[]{3}}{2}a^2[/tex]Where:
[tex]\begin{gathered} A=\text{ area} \\ a=\text{ length of the side} \end{gathered}[/tex]Now, we plug in the values:
[tex]A=\frac{3\sqrt[]{3}}{2}(8cm)^2[/tex]Solving the operations:
[tex]A=166.3cm^2[/tex]Therefore, the area of the hexagon is 166.3 square centimeters.
Can I get an answer please? (also let me know if you need more than this image)
A' ( 0,0)
B' (4,0)
C' (4, 8)
D' (0,8)
Given the transformation rule, we want to get the coordinates of the transformed point
The transformation rule is that;
(x,y) to (x,2y)
Thus we have;
A (0,0) to (0 , 2(0))
A' (0,0)
For B (4,0)
WE have
(4, 2(0)) = (4,0)
For C (4,4)
WE have;
(4, 2(4)) = (4,8)
For (0,4)
We have
(0, 2(4)) = (0,8)
Use the diagram as a reference to answer the question below
Let us draw out the triangle below:
Given that
[tex]\arctan \frac{\sqrt[]{3}}{3}=\beta[/tex]Using the trigonometric identity for tan 30, where
[tex]\tan 30=\frac{\sqrt[]{3}}{3}[/tex]Therefore,
[tex]\beta=30\degree[/tex]The sum of angles in a triangle is 180°.
Therefore,
[tex]\begin{gathered} \alpha+\beta+90=180\degree \\ \therefore \\ \alpha+30+90=180 \\ \alpha=180-90-30 \\ \alpha=60\degree \end{gathered}[/tex]To get the sides of the triangle, let us apply the Trigonometric ratios:
Using the Sine Trig. ratio,
[tex]undefined[/tex]Caculate the arc length of GH in terms of pie
Here, we want to calculate the arc length GH in terms of pi
What we will do here is to use the formula for the length of an arc
However, looking at the central angle, we can see it is 60
60 is actually 1/6 of the angle at the center which is 360
Thus, we have the arc length as 1/6 of the length of the circumfrence of the circle
Mathematically, we have this as;
[tex]\begin{gathered} GH\text{ = }\frac{1}{6}\text{ }\times\text{ 2}\times\text{ }\pi\times\text{ r} \\ \\ r\text{ is radius = 10}mm \\ \\ GH\text{ = }\frac{1}{6}\times2\times\pi\times10 \\ \\ GH\text{ = }\frac{10}{3}\pi\text{ mm} \end{gathered}[/tex]que fracción falta en 3/4+ ? = 4/5
Respuesta: 1/20
Explicación:
Si tenemos 2 números que sumados dan c, entonces c menos uno de los números es igual al otro.
Si a + b = c, entonces b = c - a
Esto significa que la fracción que falta puede ser calculada de la siguiente forma:
[tex]\frac{4}{5}-\frac{3}{4}=\frac{4\cdot4-5\cdot3}{5\cdot4}=\frac{16-15}{20}=\frac{1}{20}[/tex]Por lo tanto, la fracción que falta es 1/20
Ellie is building a dollhouse. She has boards that are two different lengths. One long board is 7 inches longer than the total length of three of the short boards. Draw a picture showing how the short and long boards are related.
Ellie is building a dollhouse and she has four boards according to the question.
One long board is 7 inches longer than THE TOTAL LENGTH of three of the short boards.
Therefore, if she has boards A, B, C and D then board A equals the addition of boards B, C and D plus an additional 7 inches. We can put this into pictures as shown below;
From the pictures shown, whatever are the lengths of b, c and d, e simply add them up and add 7 to the result to derive the length of a.
B = b
C = c
D = d
A = (b + c + d) + 7
how to solve 5u+27+4u=9
Given equation is
[tex]5u+27+4u=9[/tex]Now, we keep all the terms with u in the left hand side and the terms without u in the right hand side. It follows
[tex]\begin{gathered} 5u+4u=9-27 \\ 9u=-18 \\ u=-2 \end{gathered}[/tex]Hence, the solution is u=-2.
Which of the following represents another way to write the function rule f(x) = 3 +11.f(1) = 4 2.f(y) = 3x + 1 3.y - 3x+1 4.x=3y+1
A common notation which is used to represent functions is the following:
[tex]y=f(x)[/tex]Then, the function f(x)=3x+1 can also be written as:
[tex]y=3x+1[/tex]Therefore, the answer is that of the 3rd option.
a grocery store sells chicken for $3.30 per pound. what would be the cost of 2 1/2 pounds of chicken
hello
the store sells chicken for $3.30 per pound
1 pound = $3.30
would would be the cost of 2 1/2 pound
let x represent the cost of 2 1/2 pound
[tex]\begin{gathered} 1\text{ pound = \$3.30} \\ 2\frac{1}{2}pound\text{ }=\text{ x} \\ \text{1 pound = \$3.30} \\ \frac{5}{2}\text{ pound = x} \\ cross\text{ multiply and make x the subject of formula} \\ 2.5\text{ }\times\text{ 3.30 }=\text{ 1 }\times\text{ x} \\ x\text{ = 8.25} \end{gathered}[/tex]the cost of 2 1/2 pound chicken is $8.25
The annual interest rate for Jack's savings account increased from 2.1% to 3.2%. Complete parts (a) and (b) below.a. Describe the change as an absolute change in terms of percentage pointsThe annual interest rate increased by percentage points.(Type an integer or decimal rounded to the nearest tenth as needed.)b. Describe the change as a relative change in terms of a percentageThe annual interest rate increased by %.(Type an integer or decimal rounded to the nearest tenth as needed.)
Step 1
Given;
[tex]\begin{gathered} \text{Initial annual interest;2.1\%} \\ \text{Current annual interest=3.2\%} \end{gathered}[/tex]Step 2
Describe the change as an absolute change in terms of percentage points. Absolute change is given as;
[tex]\text{Current annual interest}-\text{Initial annual interest}[/tex][tex]\begin{gathered} 3.2-2.1=1.1\text{ \%}^{} \\ \end{gathered}[/tex]The annual interest rate increased by 1.1 percentage points.
Step 3
Describe the change as a relative change in terms of a percentage.
[tex]Relative\text{ change in \%=}\frac{Absolute\text{ c}hange}{\text{initial annual interest}}\times100[/tex][tex]\begin{gathered} Relative\text{ change in \%=}\frac{1.1}{2.1}\times100=52.38095 \\ Relative\text{ change in \%}\approx52.4 \end{gathered}[/tex]The annual interest rate increased by 52.4 % to the nearest tenth.
Assume that the figures shown to the right are similar. Given the lengths of sides and measures of angles in the figure, what information is known About the right figure?
2/3x - 9 = 6explain work
Here, we are to solve for the value of x in the given euation;
2/(3x-9) = 6
We can solve this by making a cross multiplication
2/(3x-9) = 6/1
The cross-multiplication would yield;
2 * 1 = 6 * (3x-9)
2 = 6(3x-9)
opening the bracket, we have
2 = 18x - 54
Collect like terms;
54 + 2 = 18x
18x = 56
divide both sides by 18
18x/18 = 56/18
x = 28/9
x = 3 1/9
If terminal side of angle t goes through (-5/13,12/13) what is sin(t)
Given the point P(-5/13,12/13)
the angle t is
then
since we know x and y values (-5/13,12/13) we can solve theta
where
Opp = -5/13
Adj = 12/13
[tex]tan(\theta)=\frac{Opp}{Adj}[/tex][tex]tan(\theta)=\frac{\frac{-5}{3}}{\frac{12}{13}}[/tex][tex]tan(\theta)=\frac{-5*13}{3*12}[/tex][tex]tan(\theta)=\frac{-65}{36}[/tex][tex]\theta=ArcTan(\frac{-65}{36})[/tex][tex]\theta=61.02°[/tex]Adding the 90° of the first quadrant
The angle t is
[tex]t=61.02+90[/tex][tex]t=151.02[/tex]to rads
[tex]t=\frac{151.02\pi}{180}[/tex]then sin t
[tex]sin(t)=0.48450[/tex]A sample of 394 people is selected. The people are classified according to place of residence ("urban", "suburban", or "rural"). They are also classified accordingto highest educational degree earned ("no college degree", "two-year degree", "Your-year degree", or "advanced degree“). The results are given in thecontingency table below.No college degree Two-year degree Four-year degree Advanced degreeUrban50152045Suburban23481543Rural46272240
Class: Place of residence is rural
Class frequency: (46+27+22+40) =135
n: 394 people is selected
Relative frequecy of people in the sample whose place of residence is rural:
[tex]=\frac{135}{394}\approx0.34[/tex]Below, the two-way table is given for a classof students.FreshmenSophomoreJuniorsSeniorsTotalMale4622Female 3463TotalIf a student is selected at random, find theprobability the student is a senior.P( Senior ) = [?]%Round to the nearest whole percent.
EXPLANATION
In a two-way table probability, we need to examine the relationship between two categorical variables. In this case, we have a conditional probability.
We first need to fill in the total quantities in the boxes:
Now, in order to get the number of students we need to apply the following equation:
[tex]P(senior)=\frac{Desired\text{ outcomes}}{All\text{ the possible outcomes}}[/tex]Where the desired outcomes represent the total number of studentes in the column "Seniors" and all the possible outcomes is equal to the total number of students.
Plugging in the terms into the equation:
[tex]P(senior)=\frac{5}{30}[/tex]Simplifying:
[tex]P(senior)=\frac{1}{6}[/tex]Rounding to the nearest whole percent:
[tex]P(senior)=17\text{ \%}[/tex]In conclusion, the solution is 17%
What is the scientific notation of the following number? 367 x 10^-3 *
the given number is
367 x 10^-3
the scientific notation of this number will be
3.67 x 10^-1
thus, the answer is 3.67 x 10^-1
The Tabular Method is used to divide the polynomials shown below. Write the number of terms of the divisor.
Answer:
2
Explanation:
The divisor of the expression is (x + 1). Then, the terms of the divisor are the parts that are separated by the signs '+' or '-'. Therefore, in this case, there are 2 terms, x and 1.
So, the answer is 2.
Efgh is a rectangle . EA is 12 inch. Find the length of the diagonal EH
ANSWER
line EH is 24 in (option B)
EXPLANATION
Since EF || GH, and EG || FH
line EH = EA + AH
But EA and AH are equal
Then, EH = 12 + 12 = 24 in
Hence, line EH is 24 in
2L + 2W =PSolve for w
Answer:
[tex]W=\frac{P}{2}-L[/tex]Explanation:
Given the equation
[tex]2L+2W=P[/tex]To solve for W, first subtract 2L from both sides
[tex]\begin{gathered} 2L+2W-2L=P-2L \\ \\ 2W=P-2L \end{gathered}[/tex]Next, divide both sides by 2
[tex]\begin{gathered} \frac{2W}{2}=\frac{P-2L}{2} \\ \\ W=\frac{P}{2}-L \end{gathered}[/tex]it takes Abbas 12 minutes to eat a pizza, and it takes Mashi 6 minutes to eat the same size pizza. Working together, how many of these pizzas could they polish off in 24 minutes if they can continue eating pizza at the same rate?
Given:
Abbas takes 12 minutes to eat a pizza and Mashi takes 6 minutes to eat same size pizza.
Abbas will eat 2 pizza in 24 minutes and Mashi eats 4 pizza in 24 minutes .
[tex]\text{Total number of pizza they polish off in 24 minutes }=2+4[/tex][tex]\text{Total number of pizza they polish off in 24 minutes }=6[/tex]A test is graded on a scale from O to 100. Your friend says that if you score a 78, your percentile rank must be 78. Is your friend correct?
Percentile rank refers to the percentage of scores that are equal to or less than a given score.
A percentile rank of 78 means that 78% of the scores fall at or below a given score.
Then, if if you score a 78 in a test graded from 0 to 100, it doesn't mean that the percentile rank is 78; to find the percentile rank you need to compare your score with the score of the other students that presented the test.
Answer: Your friend is not correctHi I will be late ⏰ if we are ok weQuestion 5
SOLUTION:
Case: Differentiation
Method:
[tex]\begin{gathered} h(t)=10+50t+\frac{1}{2}at^2 \\ h^{\prime}(t)=50+2\times\frac{1}{2}at^{2-1} \\ h^{\prime}(t)=50+at \\ But \\ h^{\prime}(1.25)=9.75 \\ h^{\prime}(1.25)=50+1.25a \\ 9.75=50+1.25a \\ 1.25a=9.75-50 \\ 1.25a=-40.25 \\ a=\frac{-40.25}{1.25} \\ a=-32.2ft\text{ /}s^2 \end{gathered}[/tex]Final answer:
a = -32.2 ft per sq seconds
Sanjay is making punch. He uses 1/3 cup of pineapple juice for every 3/4 cup of orange juice. How many cups of pineapple juice does he need if he uses 3 cup of orange juice.
Step
The question involve a direct proportion because when quantity inrease, the other increase.
Concept:
Find the constant of proportionality by dividing one quantity by the other.
Step 2
Find constant of proportionality K for 1/3 cup of pineapple juice for every 3/4 cup of orange juice.
[tex]\begin{gathered} k\text{ = }\frac{1}{3}\text{ }\frac{.}{.}\text{ }\frac{3}{4} \\ k\text{ = }\frac{1}{3}\text{ }\times\text{ }\frac{4}{3} \\ k\text{ = }\frac{4}{9} \end{gathered}[/tex]Step 3
Use can use the direct proportion method
Let P represent the number of cups of pineapple juice
[tex]\begin{gathered} \frac{\frac{1}{3}}{\frac{3}{4}}\text{ = }\frac{P}{3} \\ \text{Cross multiply} \\ \frac{3}{4}P\text{ = }\frac{1}{3}\text{ }\times\text{ 3} \\ \frac{3P}{4}\text{ = 1} \\ 3P\text{ = 4} \\ P\text{ = }\frac{4}{3} \end{gathered}[/tex]Final answer
[tex]\begin{gathered} \frac{4}{3}\text{ cups of pineapple juice is n}eeded\text{ for 3 cups of orange juice.} \\ \frac{4}{3}\text{ cups of Pineapple juice} \end{gathered}[/tex]1. congruent circles2. tangent circles3. concentric circleswhat best describes the circles shown
A.) Two circles are congruent if they have the same size. The size can be measured as the radius, diameter or circumference. They can overlap.
Among the given figures, this best describes what congruent circles are,
B.) When two circles touch one another at exactly one point, then we say that the two circles are tangent to one another.
Among the given figures, this best describes what tangent circles are.
C.) Concentric circles are circles with a common center.
Among the given figures, this best describes what concentric circles are,
Find the slope of the line satisfy Ming the following conditions
The slope of an horizontal line is always zero.
This comes from the fact that the slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]and if two points lie on a horizontal line this means that their y components are equals and then the numerator is zero.
Therefore the slope is zero.
reflect triangle ABC over the line Y equals to translate the image right three and up to. Then what are the coordinates of the verticals in the image
ANSWER
[tex]\begin{gathered} A^{\prime}^{\prime}(-2,4) \\ B^{\prime}^{\prime}(-3,7) \\ C^{\prime}^{\prime}(0,6) \end{gathered}[/tex]EXPLANATION
First, let us find the coordinates of the vertices of the triangle:
[tex]\begin{gathered} A(-5,2) \\ B(-6,-1) \\ C(-3,0) \end{gathered}[/tex]Now, we have to reflect the points over the line y = 2.
To do this, find the distance between the y-coordinate of each vertex and y = 2 and add it to 2. That becomes the new y-coordinate of the point while its x-coordinate remains the same.
Therefore, the coordinates become:
[tex]\begin{gathered} A(-5,2)\rightarrow A^{\prime}(-5,(2-2)+2)\Rightarrow A^{\prime}(-5,2) \\ B(-6,-1)\rightarrow B^{\prime}(-6,(2-(-1)+2)\Rightarrow B^{\prime}(-6,5) \\ C(-3,0)\rightarrow C^{\prime}(-3,(2-0)+2)\Rightarrow C^{\prime}(-3,4) \end{gathered}[/tex]Now, we have to translate the points 3 units right and 2 units up. To do that, add 3 units to the x-coordinates and add 2 units to the y-coordinates of A'B'C':
[tex]\begin{gathered} A^{\prime}(-5,2)\rightarrow A^{\prime}^{\prime}(-5+3,2+2)\rightarrow A^{\prime}^{\prime}(-2,4) \\ B^{\prime}(-6,5)\rightarrow B^{\prime}^{\prime}(-6+3,5+2)\rightarrow B^{\prime}^{\prime}(-3,7) \\ C^{\prime}(-3,4)\rightarrow C^{\prime}^{\prime}(-3+3,4+2)\rightarrow C^{\prime}^{\prime}(0,6) \end{gathered}[/tex]That is the answer.
How would I solve this problem, and with which theorem would it be solved with?
Given:
[tex]\begin{gathered} m\text{ }\angle RST=(3x-2)^0 \\ m\text{ }\angle TSK=(2x+22)^0 \end{gathered}[/tex]The angles form a linear pair.
Required:
[tex]m\angle RST\text{ = ?}[/tex]From the linear pair theorem:
The Linear Pair Theorem states that two angles that form a linear pair are supplementary; that is, their measures add up to 180 degrees.
Applying this theorem, we have:
[tex]m\text{ }\angle RST\text{ +m }\angle TSK\text{ = 180}[/tex]Substituting we have:
[tex]\begin{gathered} (3x-2)\text{ + (2x + 22) = }180 \\ \text{Collect like terms} \\ 3x\text{ + 2x -2 + 22 = 180} \\ 5x\text{ = 180-20} \\ 5x\text{ = 160} \\ \text{Divide both sides by }5 \\ \frac{5x}{5}=\frac{160}{5} \\ x\text{ = 32} \end{gathered}[/tex]The required angle is:
[tex]\begin{gathered} m\angle RST\text{ = 3x -2} \\ \text{Substituting} \\ =\text{ 3(32)-2} \\ =\text{ }96-2 \\ =\text{ 94} \end{gathered}[/tex]Name of the theorem: linear pair theorem:
Describe the effect of the transformation (x,y) → (x,y+4)
The image's been translated 4 units up.
Since this Geometric Transformation, described is a Translation.
Then We can say that the Image moved 4 units up, for it is +4 and this figure has not been translated horizontally.
Pre-Image Image
(x,y) (x, y+4)