let's rewrite:
[tex]n^2+7n+15=5[/tex]as:
[tex]n^2+7n+10=0[/tex]The factors of 10 that sum to 7 are 2 and 5, therefore:
[tex]n^2+7n+10=(n+2)(n+5)[/tex]Which statement best compares the slopes and y intercepts of the two functions Function 1 has a greater slope and greater y-intercept than Function 2.Function 2 has a greater slope and greater y-intercept than Function 1.Function 1 has a greater slope and leşser y-intercept than Function 2. Function 2 has a greater slope and lesser y-intercept than Function 1.
From function 1:
[tex]\begin{gathered} y=\frac{1}{3}x+2 \\ m=\text{slope}=\frac{1}{3} \\ b=y-\text{intercept}=2 \end{gathered}[/tex]For function 2:
[tex]\begin{gathered} (x1,y1)=(-3,-3) \\ (x2,y2)=(3,0) \\ m=\frac{0-(-3)}{3-(-3)}=\frac{3}{6}=\frac{1}{2} \\ \text{ Using the point slope equation:} \\ y-y1=m(x-x1) \\ y+3=\frac{1}{2}(x+3) \\ y=\frac{1}{2}x+\frac{3}{2} \\ y=\frac{1}{2}x-\frac{3}{2} \end{gathered}[/tex]Therefore: Function 2 has a greater slope and lesser y-intercept than Function 1.
Danielle bought a set of mixing bowls yesterday. They originally cost 23 dollars. She had a coupon for 5 percent off and the sales tax rate is 5 percent . How much did the mixing bowls cost?
Danielle bought a set of mixing bowls yesterday.
The original cost was $23.
She had a coupon for 5% off
Let us find 5% of 23 and then subtract it from the original cost.
[tex]\frac{5}{100}\times\$23=\$1.15[/tex]So, the cost after 5% off will be
[tex]\$23-\$1.15=\$21.85[/tex]But there is also 5% sales tax, that she has to pay so we need to find out 5% of 21.85 and add to it.
[tex]\frac{5}{100}\times\$21.85=\$1.09[/tex]So, the final cost is
[tex]\$21.85+\$1.09=\$22.94[/tex]Therefore, the mixing bowls cost $22.94.
Don is a barangay scholar in a college. To keep his scholarship, he needs to maintain a grade point average of 90 per semester. The following are his grades in the first semester: 85, 84, 90, 88, 89, 90, 92, 89, and 90. Will Don be able to reach the required grade for his scholarship?
Answer:
• 2. Median = 89
,• 3. Mode = 90
,• 4. Mean = 89
Explanation:
Don's grades in the first semester are as follows:
[tex]85,84,90,88,89,90,92,89,90[/tex]Part 1
The grades arranged from the least to the greatest are:
[tex]84,85,88,89,89,90,90,90,92[/tex]Part 2
The middle grade in the set of Don's grade is 89.
Thus, the median grade = 89.
Part 3
The grade that occurs most frequently is 90.
Thus, the mode = 90.
Part 4
To find the mean grade, sum up the grades and divide by 9.
[tex]\begin{gathered} Mean=\frac{84+85+88+89+89+90+90+90+92}{9}=\frac{797}{9}=88.56 \\ \approx89 \end{gathered}[/tex]Part 5
A valid basis on whether Don maintained his scholarship is the mean. This is a result of the fact that he needs to maintain a grade point average of 90 per semester.
By definition, the word average implies the mean.
Geometry how to combine the like terms. -2x+3y-5x—8y+9y
Answer:
The expression in the question is given below as
[tex]-2x+3y-5x—8y+9y[/tex]Step 1:
Collect the similar terms and then add and substract them
Similar terms are ( -2x and -5x)
The similar terms also are (+3y ,-8y +9y)
By rearranging the terms, we will have
[tex]\begin{gathered} -2x+3y-5x—8y+9y \\ =-2x-5x+3y-8y+9y \end{gathered}[/tex]Step 2:
By simplifying the terms, we will have
[tex]\begin{gathered} -2x-5x+3y-8y+9y \\ =-7x-5y+9y \\ =-7x+4y \end{gathered}[/tex]Hence,
The final answer = -7x +4y
What is the x-intercept of: 3y+x=6?
The x-intercept is the value of x when y=0, is the point of the function where the line intersects with the x-axis.
To calculate said point you have to replace the formula with y=0 and solve for x:
[tex]\begin{gathered} 3y+x=6 \\ 3\cdot0+x=6 \\ x=6 \end{gathered}[/tex]The coordinates for the x-intercept of the given function are (6, 0)
Complete the table about a retiree’s investments:a. 0.05xb. 0.05 + xc. 0.05 - x d. x —— 0.05
SOLUTION
From the first row, the 4th column was derived by
[tex]4x\times0.08=0.32x[/tex]Therefore, IRA becomes, we do the same pattern of multiplication
[tex]x\times0.05=0.05x[/tex]Hence, option A is the correct answer.
A team of nine artists created wall murals in 18 classrooms at a constant rate. How many classrooms can a team of 15 artists paint?
We know that 9 artists created 18 classrooms at a constant rate, and we want to know how many classrooms can a team of 15 artists paint. This can be represented as:
Where x represents the value of classrooms painted by 15 artists.
As we know, if we have more artists, they will paint more classrooms. So, the magnitudes are directly proportional. The proportion will become:
[tex]\frac{9}{15}=\frac{18}{x}[/tex]Now, we multiply means and extremes, to obtain:
[tex]\begin{gathered} 9\cdot x=15\cdot18 \\ 9x=270 \end{gathered}[/tex]Lastly, we divide by 9 to both sides, and we get:
[tex]x=\frac{270}{9}=30[/tex]This means that 15 artists will paint a total of 30 classrooms.
.Ms. Lee has a reward system in heri class. When all of her studentsbehave well she rewards them by| drawing stars on a chart Whenthe chart has 200 stars or more,I the class has a party right now theclass has 28 stars. Write and solvean inequality to find how manyI more times the class needs to berewarded to earn a party.
Given:
When all the students behave well then Ms. Lee reward them by drawing stars on a chart.
The chart has 200 or more starts the class has a party.
Now, the class has 28 stars.
The inequality is,
[tex]28+x\ge200[/tex]Now, solve the inequality,
[tex]\begin{gathered} 28+x\ge200 \\ x\ge200-28 \\ x\ge172 \end{gathered}[/tex]That means the class need 172 or more to be rewarded to earn a party.
What is the line's slope? - -2 2 -2 -4 - 6
Answer:
slope = -5
Explanation:
The slope of the line is defined as the rise / run. In the words, for each
I would like help in this project from question 2-5 and the other side from questions 1-5 also
1.
From the graph given us, the point of intersection of the 2 linear functions is where the salaries are equal.
We will find that to be Year 5
Therefore. at Year 5, both basketball & baseball players earn an equal salary of about $350,000
2.
The y-intercept refers to the point that the straight line touches the y-axis & is given by:
[tex]\begin{gathered} ForBasketballPlayers\colon \\ y-intercept=90 \\ \\ ForBaseballPlayers\colon \\ y-intercept=150 \end{gathered}[/tex]We will proceed to obtain the equation for the functions as shown below:
[tex]\begin{gathered} y=mx+b------------1 \\ m=\frac{y_2-y_1}{x_2-x_!}-----------2 \\ where\colon m=slope,b=y-intercept \\ \\ \text{For Basketball Players: we have these points lying on the straight line:} \\ (x,y)=\mleft(0,90\mright),(5,350) \\ m=\frac{350-90}{5-0}=\frac{260}{5}=52 \\ m=52 \\ \text{Substitute the value of ''m'' into equation 1, we have:} \\ y=52x+90 \\ \\ \text{For Baseball Players: we have these points lying on the straight line:} \\ (x,y)=(0,150),(5,350) \\ m=\frac{350-150}{5-0}=\frac{200}{5}=40 \\ m=40 \\ \text{Substitute the value of ''m'' into equation 1, we have:} \\ y=40x+150 \end{gathered}[/tex]Therefore,
For basketball players, the equation is: y = 52x + 90
For baseball players, the equation is: y = 40x + 150
3.
A = (46, 2000)
B = (37, 2000)
4.
The average Basketball player salary is $8.2 million as compared to that of $2 million from here
The average Baseball player salary is $4.17 million as compared to that of $2 million from here
Hence, the average Basketball player salary is 4 times larger than that we have here & the average Baseball player salary is 2 times larger than that we have here
5.
The average salary of Football players is $860,000 which is about 10 times smaller than that of the average Basketball player & about 5 times smaller than that of an average Baseball player
1. If the height of the box is 7 inches andthe area of the base is 18 inchessquared, what is the volume of the box?
Answer:
The volume of the box is;
[tex]126\text{ cubic inches}[/tex]Explanation:
Given that the height of the box is 7 inches and the area of the base is 18 inches squared;
[tex]\begin{gathered} h=7\text{ inches } \\ A=18\text{ inches squared.} \end{gathered}[/tex]Recall that the volume of the box can be calculated using the formula;
[tex]V=A\times h[/tex]Substituting the value of the height and area;
[tex]\begin{gathered} V=18\times7 \\ V=126\text{ cubic inches} \end{gathered}[/tex]Therefore, the volume of the box is;
[tex]126\text{ cubic inches}[/tex]What is the Midpoint for (-1,-6) and (-6,5) What is the Midpoint for (-3.1, -2.8) and (-4.92,-3.3)
The formula for determining midpoint is expressed as
Midpoint = (x1 + x2)/2 , (y1 + y2)/2
For the first question,
x1 = - 1, y1 = - 6
x2 = - 6, y2 = 5
Midpoint = (- 1 + - 6)/2 , (- 6 + 5)/2
Midpoint = (- 1 - 6)/2 , (- 1)/2
Midpoint = - 7/2, - 1/2
For the second question,
x1 = - 3.1, y1 = - 2.8
x2 = - 4.92, y2 = 3.3
Midpoint = (- 3.1 + - 4.92)/2 , (- 2.8 + 3.3)/2
Midpoint = (- 3.1 - 4.92)/2 , (0.5)/2
Midpoint = - 8.02/2 , 0.25
Midpoint = - 4.01, 0.25
Solve for x.Question options:A) 11 B) 13 C) 12 D) 10
Line YZ is the midsegment of triangle QRS because it connects the midpoints of lines QR and RS. We would solve for x by appying the midsegment theorem which states that the midsegment is half the length of the third side or base. This means that
YZ = 1/2(QS)
x + 2 = 1/2 * (3x - 8)
2(x + 2) = 3x - 8
By opening the parenthesis, we have
2x + 4 = 3x - 8
Collecting like terms, we have
3x - 2x = 4 + 8
x = 12
Option C is correct
15% of 80 is 60% of what number?
the unknown number is 20
Explanation:15% of 80 = 15% × 80
= 0.15 × 80
= 12
60% of a number
let the number = y
60% of y = 60% ×y
= 0.6 ×y
= 0.6y
15% of 80 = 60% of the number
12 = 0.6y
divide both sides by 0.6:
[tex]\begin{gathered} \frac{0.6y}{0.6}\text{ = }\frac{12}{0.6} \\ y\text{ = 20} \end{gathered}[/tex]Hence, the unknown number is 20
Question 4 Multiple Choice Worth 4 points)Order the set of numbers from least to greatest: 271 2 15.0 271.2 V6,2o vs. 2 2712o şi vs. 271232 273V5Please help!
In order to compare them, we have to make some calculations.
Number #1: 2.71... (periodic)
Number #2: 2 3/4
[tex]2+\frac{3}{4}=\frac{2\cdot4+3}{4}=\frac{8+3}{4}=\frac{11}{4}=2.75[/tex]Number #3: square root of 5
[tex]undefined[/tex]triangles and are isosceles. angle has a measure of 84 degrees and angle has a measure of 24 degrees. find the measure of angle .
Hi, can you help me answer this question please, thank you:)
Given:
The total number of people are T = 267.
Explanation:
(a)
Determine the total number of teens.
[tex]\begin{gathered} t=39+43+25 \\ =107 \end{gathered}[/tex]The probability for the person to be a teen is,
[tex]\begin{gathered} P(t)=\frac{107}{267} \\ =0.4007 \end{gathered}[/tex](b)
Determine the number of people like the vanilla.
[tex]\begin{gathered} v=22+43+44 \\ =109 \end{gathered}[/tex]Determine the propability for the person selected likes the Vanilla.
[tex]\begin{gathered} P(v)=\frac{109}{267} \\ =0.4082 \end{gathered}[/tex](c)
Determine the number of people that are teen or likes the vanailla.
[tex]\begin{gathered} v\text{ OR t=}22+43+44+39+25 \\ =173 \end{gathered}[/tex]Determine the probability for a selected person is a teen or like the vanilla.
[tex]\begin{gathered} P\text{ (v or t)=}\frac{173}{267} \\ =0.6479 \end{gathered}[/tex](d)
The number of person that is teen and likes strawberry best are 25.
Determine the probability for selected person is teen and likes strawberry best.
[tex]\begin{gathered} P\text{ (t and s)=}\frac{25}{267} \\ =0.0936 \end{gathered}[/tex](e)
Determine the number of persons that are children.
[tex]\begin{gathered} C=21+22+9 \\ =52 \end{gathered}[/tex]Determine the number person that are children and likes strawberry best.
[tex]\text{ C and s=}9[/tex]So probability for the person likes the strawbwerry given that person is children is,
[tex]\begin{gathered} P\text{ (s|C)=}\frac{P\text{ (s and c)}}{P\text{ (c)}} \\ =\frac{\frac{9}{267}}{\frac{52}{267}} \\ =\frac{9}{52} \\ \approx0.1731 \end{gathered}[/tex](f)
The number of persons who likes the strawberry best is,
[tex]\begin{gathered} s=9+25+25 \\ =62 \end{gathered}[/tex]Determine the probability for person is teen given that person likes strawberry best.
[tex]\begin{gathered} P\text{ (}t|s\text{)}=\frac{P\text{ (t and s)}}{P(s)} \\ =\frac{\frac{25}{267}}{\frac{62}{267}} \\ =\frac{25}{62} \\ =0.4032 \end{gathered}[/tex]Answer:
Is a teen: 0.4007
Likes vanilla the best: 0.4082
Is a teen or likes the Vanilla the best: 0.6479
Is a teen and likes the strawberry best: 0.0936
Likes strawberry the best GIVEN the person is child: 0.1732
Is a teen GIVEN that person likes the strawberry best: 0.4032
Simplify the expression2.5x + 4.3x - 5⅜b - ¾b
The expression given is:
[tex]2.5x+4.3x-5[/tex]We add like terms (if any) and then simplify.
There are two x's terms, so we add them up and keep "-5" as is.
Thus, we add
2.5x + 4.3x = 6.8x
So, the expression simplifies to:
[tex]\begin{gathered} 2.5x+4.3x-5 \\ =6.8x-5 \end{gathered}[/tex]The answer is:
6.8x - 5
find an equation of the circle that has center (6, -1) and passes through (1, -5)
an equation of the circle that has center (6, -1) and passes through (1, -5) is 17. one of two numbers and/or letters indicating a point's precise location on a map or graph: Zoom in on the map after entering the GPS coordinates.
What is meant by XY coordinates?The horizontal and vertical addresses of a point in any two-dimensional (2D) space, such as a sheet of paper or a computer display screen, are called the X and Y coordinates, respectively. These coordinates work as a pair to pinpoint a point's precise location.Use the formula (x a) 2 + (y b) 2 = r 2 to determine a circle's equation when you are aware of its radius and center. Here, stands for the circle's center, and is its radius.The equation of a circle has the following formula: (x – h)
2+ (y – k) (y – k)
2 = r2, where (h, k) denotes the circle's center's coordinates and r denotes the circle's radius.
(1-5)
2 +(5—1) (5—1)
2\s=(-4)
2+(-1)
2\s=16+1\s=17
To learn more about XY coordinates refer to:
https://brainly.com/question/28045011
#SPJ1
What is the measure of AngleJKL?
ANSWER
m∠JKL = 120º
EXPLANATION
By the exterior angle theorem, which states that the measure of the exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles:
[tex]\begin{gathered} m\angle JKL=m\angle KJH+m\angle JHK \\ m\angle JKL=96º+24º \\ m\angle JKL=120º \end{gathered}[/tex]What is the lowest common denominator of 1/3,1/8,and 1/12?
Answer:
24
Step-by-step explanation:
The denominators in these fractions are:
3, 8 and 12
The lowest common denominator is the least common multiple between 3, 8 and 12.
It can be found factoring the three numbers, simultaneously, into prime factors. So
3 - 8 - 12| 2
3 - 4 - 6| 2
3 - 2- 3 | 2
3 - 1 - 3 | 3
1 - 1 - 1
The lowest common denominator is 2³*3 = 24
Given △△ABC and its image under a dilation centered at the origin, find the scale factor.
Answer
Scale factor = 2
Step-by-step explanation
Dilation centered at the origin by a factor of k transforms the point (x, y) into (kx, ky).
Using a scale factor of 2 and applying this transformation to the vertex of triangle ABC, we get:
A(-3, 4) → (2 x -3, 2 x 4) → A'(-6, 8)
B(-3, 1) → (2 x -3, 2 x 1) → B'(-6, 2)
C(2, 0) → (2 x 2, 2 x 0) → C'(4, 0)
A punch recipe calls for 3/4 cup of pineapple juice how much pineapple juice is needed to make three batches of the punch
A punch recipe calls for 3/4 cup of pineapple juice how much pineapple juice is needed to make three batches of the punch
you can easily solve this by using a rule of three
If a shape is dilated by a scale factor of one-half, what is the resulting perimeter?The new perimeter is one-half the originalThe new perimeter is one-fourth the originalThe new perimeteris 2 times theoriginalThe new perimeteris 4 times theoriginal
If the scale factor is one half, then all sides of the dilated figure is one half of the side of original figure.
The perimeter is sum of all sides of figure. So if side is one half of the original sides, then perimeter is also one half of the original perimeter.
So correct answer is, The new perimeter is one-half the original.
On October 23, 2011, one Chinese yuan was worth 0.16 U.S.Dollars. On that date, how many yuan was 38.39 dollars worth? ROUND TO THE NEAREST HUNDREDTH OF A YUAN
Let x be the amount of yuan that 38.39 dollars was worth. Since the ratio of chinese yuan to dollars is 1 to 0.16, then:
[tex]\frac{x}{38.39\text{ dollars}}=\frac{1\text{ yuan}}{0.16\text{ dollars}}[/tex]Solve for x:
[tex]\begin{gathered} x=\frac{1\text{ yuan}}{0.16\text{ dollars}}\times38.39\text{ dollars} \\ =\frac{38.39}{0.16}\text{ yuan} \\ =239.9375\text{ yuan} \\ \approx239.94\text{ yuan} \end{gathered}[/tex]Therefore, the answer is: 239.94 yuan.
Let f(x)=(3)x−3. What is f(1)?
If [tex]f(x)=3x-3[/tex], then [tex]f(1)[/tex] is saying that your x-value is 1. So you substitute 1 in for x and clean it up:
[tex]f(1)=3(1)-3[/tex]
[tex]= 3-3[/tex]
[tex]= 0[/tex]
Find the volume of a right pyramid whose square base has size 6 meters long and his height is 4 meters.
Answer
Volume of the prism = 48 cubic meters
Explanation:
square base = 6 meters
Height = 4 meters
Volume = 1/3 area x height
Volume = 1/3 x (6)^2 x 4
Volume = 1/3 x 36 x 4
Volume = 36 x 4 / 3
Volume = 144/3
Volume = 48 cubic meters
Therefore, the volume of the prism is 48 cubic meters
The base of a right prism is a rhombus with diagonals of 6 and 8. If the altitude of the prism is 12, what is the total surface area of this prism?A. 240 units²B. 288 units²C. 264 units²D. 312 units²
Our prism has 6 faces. 2 equal basis and 4 equal sides. To calculate the area of the base, we just have to use the area formula since we already know the value for the diagonals. To calculate the area of the sides of our prism we have to calculate the side length of the rhombus.
A rhombus has the following properties:
Opposite angles are equal. All sides are equal and, opposite sides are parallel to each other. Diagonals bisect each other perpendicularly.
Since the diagonals bisect each other perpendicularly, half the diagonals and the side of the rhombus form a right triangle.
Using the pythagorean theorem, we can determinate the side length our rhombus.
[tex]\begin{gathered} (\frac{6}{2})^2+(\frac{8}{2})^2=s^2 \\ 3^2+4^2=s^2 \\ s=\sqrt{9+16} \\ s=5 \end{gathered}[/tex]The side length of our rhombus is equal to 5 units. Now that we have all the measures, we can calculate the total surface area. The area of a rhombus is equal to half the product of the diagonals.
[tex]A_b=\frac{6\times8}{2}=\frac{48}{2}=24[/tex]The sides of our prism are rectangles, therefore, the area is given by the product between its distinct sides.
[tex]A_s=12\times5=60[/tex]Since we have 4 sides and 2 basis, the total surface area is:
[tex]S=2A_b+4A_s=2(24)+4(60)=48+240=288[/tex]The surface area of our prism is equal to 288 units². The answer is option B.
A man leaves Miami to San Francisco if he leaves at 10:40 am. The trip takes 5 hours and 50 minutes and there is a difference of 3 hours less at what time he arrives in San Francisco?
Answer:
[tex]\text{ He arrives at 1:30 PM to San Francisco}[/tex]Step-by-step explanation:
Time at Miami: 10:40 AM.
If the trip takes 5 hours and 50 minutes, add up to the original time at Miami. It would be:
[tex]4\colon30\text{ PM }[/tex]Then, since there is a difference of 3 hours less in San Francisco:
[tex]1\colon30\text{ PM}[/tex]Translate to a proportion. Do not solve What is 34% of 75?
What is 34% of 75?
Apply proportion
75/100=x/34
x=(75/100)*34
x=25.5answer is75/100=a/34