The height of a tree is x feet. If it grows ½ times the original height, choose the correct expression that denotes the situation.
Answers
ANSWER
1.5(x)
EXPLANATION
The tree is originally x feet tall. If it grows 1/2 this height it means that now it is 1/2x taller, or we can express this as a decimal, 0.5x. If we add these two heights we'll have the new height of the tree:
[tex]x+0.5x=(1+0.5)x=1.5x[/tex]Related Questions
find the solution to the following system by substitution x + y = 20 y = 3x 8
Answers
Based on the substitution method, the solution of the system of the equation is x = 3 and y = 17.
Substitution method:
Substitution method is the way of finding the value of any one of the variables from one equation in terms of the other variable.
Given,
Here we have the system of equations
x + y = 20
y = 3x + 8
Now we need to find the solutions for these equation using the substitution method.
From the given details we know that the value of y is defined as 3x + 8.
So, we have to apply these value on the other equation in order to find the value of x,
x + (3x + 8) = 20
4x + 8 = 20
4x = 20 - 8
4x = 12
x = 3
Now apply the value of x into the other equation in order to find the value of y,
y = 3(3) + 8
y = 9 + 8
y = 17
Therefore, the solution of the equation is x = 3 and y = 17.
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Exercise 1: What's In2.Mark’s temperature goes 1.5°C higher from the normal body temperature. What is Marks temperature now?A. 38.5°CB. 37.5°CC. 36.5°CD. 36.5C
Answers
The normal body temperature of a human is 37°C.
If Mark's temperature goes 1.5°C higher than that temperature, his new temperature will be:
[tex]\Rightarrow37+1.5=38.5°C[/tex]OPTION A is the correct option.
A reflection across which line(s) carries the trapezoid onto itself?
Answers
If we reflect about x =2, it is a mirror image on each side ( left and right). There is no other line where we can have a mirror image on each side.
2. Given: ZMOP is a right angle RP I OP Prove: MO || RP
Answers
Given that;
[tex]\begin{gathered} \measuredangle MOP\text{ is a right angle.} \\ \measuredangle MOP=90^0 \end{gathered}[/tex]And;
[tex]\vec{RP}\perp\vec{OP}[/tex]Since line RP is perpendicular to line OP, Angle RPO must be a right angle.
[tex]\measuredangle RPO=90^0[/tex]Recall that for two parallel lines intersected by a straight line, Same side interior angles are supplementary.
[tex]A+B=180^0[/tex]So, for line MO to be parallel to line RP, the sum of angle MOP and angle RPO must be equal to 180 degree.
[tex]\measuredangle MOP+\measuredangle RPO=90+90=180^0[/tex]Since the sum of angle MOP and angle RPO is equal to 180 degree, then line MO is parallel to line RP.
[tex]\begin{gathered} \text{ Since} \\ \measuredangle MOP+\measuredangle RPO=180^0 \\ \text{Then;} \\ MO\Vert RP \end{gathered}[/tex]Proved
Of the twenty-two students in a classroom, ten are transfer students, seven are nursing students, four are AAS students and one student is undecided.If three students are chose randomly, without replacement, find the probability that all three students are nursing students.
Answers
Given that:
• There are a total number of 22 students in the classroom.
,• 10 of them are transfer students.
,• 7 are nursing students.
,• 4 are AAS students.
,• 1 student is undecided.
,• Three students are chosen randomly.
Since you need to find the probability that all three students that are chosen randomly are nursing students, you need to set up that this is:
[tex]P(A)[/tex]Where Event A is that one of the students is a nursing student.
Therefore, the probability that three of the chosen students are nursing students can be set up as:
[tex]\begin{gathered} P=P(A)\cdot P(A)\cdot P(A)=P(A)^3 \\ \\ P=P(A)^3 \end{gathered}[/tex]Knowing that the total number of students is 22 and 7 of them are nursing students, you know that:
[tex]P(A)=\frac{7}{22}[/tex]Therefore:
[tex]P=(\frac{7}{22})^3[/tex][tex]P=0.0322[/tex]Hence, the answer is:
[tex]P=0.0322[/tex]There is $1.90 in a jar filled with quarters, dimes, and nickels. There are 2 more quarters than dimes and there are 2 more nickels than quarters. How many of each coin are there? quarters dimes [ ) nickels Enter the number that belongs in the green box.
Answers
5 quarters, 3 dimes, 7 nickels
Explanations:Let the number of quarters in the jar = q
Let the number of dimes in the jar = d
Let the number of nickels in the jar = n
1 quarter = $0.25
1 dime = $0.1
1 nickel = $0.05
The jar is filled with quarters, dimes, and nickels, totaling $1.90
This can be represented mathematically as:
0.25q + 0.1d + 0.05n = 1.90.........(1)
There are two more quarters than dime:
q = d + 2..............(2)
There are two more nickels than quarters
n = q + 2..............(3)
make d the subject of the formula in equation (2)
d = q - 2............(4)
Substitute equations (3) and (4) into equation (1)
0.25q + 0.1(q - 2) + 0.05(q + 2) = 1.90
0.25q + 0.1q + 0.05q - 0.2 + 0.1 = 1.90
0.4q - 0.1 = 1.90
0.4q = 1.90 + 0.1
0.4q = 2.0
q = 2.0/0.4
q = 5
n = q + 2
n = 5 + 2
n = 7
d = q - 2
d = 5 - 2
d = 3
There are 5 quarters, 3 dimes, 7 nickels
which ordered pair is a solution of 6X + 7 < 21
Answers
Substitute 2 for x and 1 for in the inequality to verify that ordered pair satisfy the inequality or not.
[tex]\begin{gathered} 6\cdot2+7\cdot1<21 \\ 12+7<21 \\ 19<21 \end{gathered}[/tex]The inequality is trus so point (2,1) satisfy the inequality.
Substitute 4 for x and 1 for y in the inequality to verify that ordered pair satisfy the inequality or not.
[tex]undefined[/tex]-10 is no less than 2 times a number plus 14
Answers
Let the number be x.
Then according to the question,
[tex]\begin{gathered} -10\ge2x+14 \\ -10-14\ge2x \\ -24\ge2x \\ x\ge-12 \end{gathered}[/tex]Thus, the number should be greater than or equal to -12.
A bakery makes and sells hot cocoa bombs during the holidays. The first 12 hot cocoa bombs of an order cost is $4.00 each. Each of the next 6 hot cocoa bombs cost $3.50 each. For orders exceeding 18, the cost drops to $3 each. The function C(x) represents the bakery's pricing.
Answers
Solution
Step 1
Given data for C(x), the bakery's pricing
[tex]\begin{gathered} F\text{or this range 0}\leq x\leq12ofhotcocoabombs\text{ we use C(x) =4x} \\ \text{For this range }1218,ofhotcocoabombs\text{ we useC(x) = }3x+15 \end{gathered}[/tex]Required
Step 1
To find the cost of 8 hot cocoa bombs
[tex]\begin{gathered} C(8)\text{ lies in the range 0}\leq x\leq12 \\ \text{Hence we use 4x where x = 8} \\ \text{The cost of 8 hot cocoa bombs = 4(8) = \$32} \end{gathered}[/tex]Step 2
To find the cost of 18 hot cocoa bombs
[tex]\begin{gathered} C(18)\text{ lies in the range 12}Step 3To find the C(30)
[tex]\begin{gathered} C(30)\text{ lies in the range x}\ge18 \\ \text{Hence we use 3x +15, where x = 30} \\ C(30)\text{ = 3(30) + 15 = 90 + 15 = \$105} \\ \end{gathered}[/tex]Step 4
What C(30) represents.
C(30) represents the cost of ordering 30 hot cocoa bombs which is $105
9. If L 1 equals 120 then what is the measure of its supplement <2=
Answers
Supplementary angles are angles whose addition sums up to 180 degrees.
Therefore, if angle 1 measures 120, then its supplement which is angle 2, must mean both add up to 180.
Hence, you have
Angle 1 + Angle 2 = 180
120 + Angle 2 = 180
Subtract 120 from both sides of the equation
Angle 2 = 180 - 120
Angle 2 = 60 degrees
By definiton, two angles are complimentary angles if they both add up to 90 degrees. Hence if angle L5 equals 50 degrees, then its compliment would be derived as 90 - 50 which equals 40. The compliment of angle L5 which is 50 degrees, equals 40 degrees.
Find LM if LN = 137mm.
Answers
Each n in the model represents the same value. 136.5 What is the value of n? there are 7 N's in the problem
Answers
The value of n must be 136.5/7
n = 136.5/7
n = 19.5
Result n = 19.5
Rob earns $4200 per month at his new job. He pays the following taxes: 6.2% for social security 1.45% for Medicare 16% for federal income tax • 5.5% for state income tax Calculate his annual net income.
Answers
Answer:
$35,708.4
Explanation:
His net income will be the total that he earns less the taxes.
So, we need to calculate how much money does Rob pays for each tax.
Therefore, 6.2% of 4200 is equal to:
[tex]4200\times6.2\text{ \% =4200 }\times\frac{6.2}{100}=260.4[/tex]It means that Rob pays $260.4 each month for social security,
In the same way, 1.45% of 4200 is equal to:
[tex]4200\times1.45\text{ \% = 4200}\times\frac{1.45}{100}=60.9[/tex]16% of 4200 is equal to:
[tex]4200\times16\text{ \% = 4200}\times\frac{16}{100}=672[/tex]5.5% of 4200 is equal to:
[tex]4200\times5.5\text{ \% = 4200}\times\frac{5.5}{100}=231[/tex]Now, we can calculate the net income per month as:
$4200 - $260.4 - $60.9 - $672 - $231 = $2975.7
Finally, his annually net income will be the net income per month multiplied by 12 months:
$2975.7 x 12 = $35,708.4
So, the answer is $35,708.4
Please help and answer this question ASAP! :)
Answers
Answer:
Odd, Even, Even, Neither=========================
The difference between odd and even functions is that:
f(-x) = f(x) for even functions,f(-x) = - f(x) for odd functions.Let's test this property for the given functions.
Function f(x)f(-4) = - f(4) = 8 and f(-2) = - f(2) = 1, so this is an odd functionFunction g(x)g(4) = g(-4) = -4 and g(2) = g(-2) = 2, so this is an even functionFunction j(x)j(2) = j(-2) = 2 and j(1) = (j-1) = - 4, so this is an even functionFunction k(x)k(-4) = 9, k(4) = 1 and k(-2) = 4, k(2) = 0, since each value is different this is neither odd nor even functionA truck carries 4 chairs and tables. The table weighs 35 pounds. The total weight of the chairs and tables is 63 pounds. How much does each chair weigh?
Answers
The weight of each chair is 7 pounds.
What is basic arithmetic?Specific numbers and their computations employing a variety of fundamental arithmetic operations are at the center of arithmetic mathematics. Algebra, on the other hand, deals with the limitations and guidelines that apply to all other types of numbers, including whole numbers, integers, fractions, functions, and so on. Arithmetic math serves as the foundation for algebra, which always adheres to its definition. A large range of subjects fall within the broad definition of mathematics, which encompasses a very broad range of topics. Beginning with the fundamentals like addition, subtraction, and division of numbers, they then move on to more complicated topics like exponents, variations, sequence, progression, and more. This part does touch on some of the mathematical formulas and mathematical sequence. Four essential mathematical operations—addition, subtraction, multiplication, and division—are covered in basic arithmetic.
Total weight = 63 pounds
Weight of the table = 35 pounds
Weight if 4 chairs = 63 - 35
= 28 pounds
Weight of one chair = 28/4
= 7 pounds
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I need some help with this! I know about the trig identitys and stuff like that, but I just get a little confused on how to apply sometimes.
Answers
we have that
Let
x ------> the distance in miles from a point on the ground (the red line)
In the right triangle of the figure
sin(6.5)=7,000/x
solve for x
x=7,000/sin(6.5)
using a calculator
x=61,835.70 ft
Convert to miles
Remember that
1 mile=5,280 ft
so
61,835.7 ft=61,835.7/5,280=11.71 miles
therefore
the answer is 11.71 milesAlyssa will correctly label the numbers 48.4, 48482, 48.09, and 48on the number line below.
Answers
The numbers under consideration are:
[tex]48.4,\text{ 48}\frac{1}{2},\text{ 48.09, 48}\frac{3}{5}[/tex]Converting all the numbers to decimal:
[tex]\begin{gathered} 48\frac{1}{2}=\text{ 48+0.5 = 48.5} \\ 48\frac{3}{5}=\text{ 48 + }0.6\text{ = 48.6} \end{gathered}[/tex]Therefore, the numbers can be written as:
48.4, 48.5, 48.09, and 48.6
Out of these numbers, only 48.6 is closest to 49
[tex]48\frac{3}{5}\text{ is closest to 49}[/tex]NEED ASAP ILL GIVE BRAINLIEST IF CORRECT
Answers
answer: 8 square root(y^5)
because your base in the fraction is y and so you can subtract the exponents.
numerator exponent - denominator exponent so it’s:
7/8 - 1/4 that gives you 5/8 and so it’s
y^(5/8) and if you write that in the radical form it’s numerator as exponent and denominator as your radical base. therefore the final answer would be:
8 square root(y^5) . so your first option at the top
An envelope is 15 centimeters wide, and it measures 17 centimeters along the diagonal. The envelope is __ centimeters tall.
Answers
An envelope is rectangular in shape.
Given the width = 15cm, and diagonal = 17cm
Let h represent the tall length of the envelope
Applying Pythagoras theorem, we have
[tex]\begin{gathered} 17^2=15^2+h^2 \\ 289=225+h^2 \\ h^2=289-225 \\ h^2=64 \\ h=\sqrt[]{64} \\ h=8\operatorname{cm} \end{gathered}[/tex]The envelope is 8cm tall
Given four numbers P, Q, R and S. The first three numbers form an arithmetic sequence while the last three form a geometric sequence. If the sum of the first and the fourth number is 16 and the sum of the second and the third number is 12, find these four numbers.
Answers
The most appropriate choice for arithmetic and geometric series will be given by-
P = 0, Q = 4 , R = 8, S = 16 or P = 15, Q = 9, R = 3, S = 1 are the required numbers
What is arithmetic and geometric series?
Arithmetic series are those series whose difference between two consecutive terms are same.
Geometric series are those series whose ratio between two consecutive terms are same.
Here,
P, Q and R forms an Arithmetic sequence
Let P = a - d , Q = a, R = a + d, Where a is the first term of the Arithmetic sequence and d is the common difference of the sequence.
Let S = b
Q, R and S forms a Geometric sequence
[tex]\frac{a + d}{a} = \frac{b}{a +d}[/tex]
[tex](a + d)^2 = ab\\a^2 + d^2 + 2ad = ab\\[/tex] ............... (1)
Now the sum of first and fourth number is 16
a - d + b = 16
b = 16 - a + d
Putting the value of b in (1),
[tex]a^2 + d^2 + 2ad = a(16 - a +d)\\a^2 + d^2 + 2ad = 16a -a^2+ad\\a^2+a^2 + d^2+2ad - ad - 16a = 0\\2a^2 + ad+d^2 -16a = 0[/tex]............ (2)
Sum of second and third number is 12
[tex]a + a + d = 12\\2a +d = 12\\d = 12-2a[/tex]
Putting the value of d in (2)
[tex]2a^2 + a(12 - 2a)+(12 - 2a)^2-16a = 0\\2a^2 + 12a - 2a^2+144-48a+4a^2 - 16a = 0\\4a^2-52a+144=0\\4(a^2-13a+36)=0\\a^2 -13a+36=0\\a^2-9a-4a+36=0\\a(a - 9)-4(a-9)=0\\(a-4)(a-9) = 0\\[/tex]
[tex]a - 4 = 0[/tex] or [tex]a - 9 = 0[/tex]
[tex]a = 4[/tex] or [tex]a = 9[/tex]
When a = 4,
[tex]d = 12 - 2\times 4\\d = 12 - 8\\d = 4[/tex]
[tex]b = 16 - 4+4\\b = 16[/tex]
P = 4 - 4 = 0
Q = 4
R = 4 + 4 = 8
S = 16
When a = 9,
[tex]d = 12 - 2\times 9\\d = 12 - 16\\d = -6[/tex]
[tex]b = 16 - 9-6\\b = 1[/tex]
P = 9 - (-6) = 15
Q = 9
R = 9 + (-6) = 3
S = 1
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What is the equation of the line below in slope-intercept form?(4 Points)x-3y = 6y =- 2y = 3x - 2y = - ** - 2y = -3x - 2
Answers
Let's make y the subject of the equation.
[tex]\begin{gathered} x-6=3y \\ y=\frac{x-6}{3} \\ y=\frac{1}{3}x-\frac{6}{3} \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]The correct option is A
This not a test btw ! But can you please help me with this !
Answers
Using elimination:
[tex]\begin{gathered} (A)-3(B)\colon \\ 6x+12x-3y+3y=-4-15 \\ 18x=-19 \end{gathered}[/tex]Therefore, the answer is:
B) Multiply A by 1 and B by -3
A boat is heading towards a lighthouse, whose beacon-light is 140 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 10∘∘ . What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest tenth of a foot if necessary.
Answers
see the figure below to better understand the problem
we have that
tan(10∘)=140/x -----> by TOA
solve for x
x=140/tan(10∘)
x=794 ft
therefore
The answer is 794 feetAnswer:
Step-by-step explanation:
tan 10=140/x
x=140 / tan 10
x=794
Question 17
2(h - 6) + 20 = -4
Answers
Which equation has at least one solution? Mark all that app A. 2x-1= 2 B. 3 y + 1) = 3y 1 C. 5p - (3 + p) = 6p + 1 D. 4/5m=1-1/5m E. 10 +0.5w =1/2w - 10 F. 4a + 3(a - 2) = 8a - (6 + a) Answer Choices:
Answers
Let's check the options
A.
2x - 1 = 2
2x= 3
x= 3/2=1.5
option A has atleast one solution
B
3y+ 1 = 3y
option B has no solution
C.
5p - (3 + p) = 6p + 1
5p - 3 - p = 6p + 1
4p - 6p = 1 + 3
-2p = 4
p =-2
option C has atleast one solution
D.
4/5 m = 1- 1/5 m
4/5 m + 1/5m = 1
1m = 1
m = 1
Option D has atleast one solution
E.
10 + 0.5w = 1/2w - 10
0.5 w - 1/2 w = -10 - 10
option E has no solution
F.
4a + 3(a-2) = 8a - (6+a)
4a +3a - 6 = 8a -6 - a
7a -6 = 7a - 6
option F has many solution. Hence it also has atleast one solution
Therefore;
option A, C, D and F has atleast one solution
A school bus with the football team left Jefferson HighSchool and drove at an average speed of 48 mph. A schoolbus with the cheerleading squad left 2 hours later and wasable to catch up to the football team after 6 hours. Whatwas the speed of the bus carrying the school's cheerleadingsquad?
Answers
Given data
A school bus with the football team from Jefferson High School drove at an average speed of 48mph
Another school bus with the cheerleading squad left 2 hours later and caught with the football team after 6 hours.
Required
To find the speed of the bus carrying the Cheerleading squad.
Step 1
Determine the distance the bus carrying the football team had travelled in the first 2 hours
Speed is given as
[tex]\begin{gathered} \text{speed =}\frac{dis\tan ce}{time} \\ \text{where sp}eed\text{ = 48mph} \\ \text{time = 2 hours} \\ \text{distance = sp}eed\text{ x time} \\ \text{distance = 48 x 2 =96miles} \end{gathered}[/tex]Step 2
Determine of the distance covered by the bus with the football team in the next 6 hours and find the total distance in 8 hours
[tex]\begin{gathered} \text{Distance = sp}eed\text{ }\times\text{ time} \\ where \\ \text{speed = 48mph} \\ \text{time = 6 hours} \\ \text{Distance = 48 }\times\text{ 6 = 288 miles} \end{gathered}[/tex]The total distance in 8 hours covered by the bus = 288 + 96 = 384miles
Step 3
Determine the speed of the bus carrying the Cheerleaders
The total distance to be covered by the Cheerleaders is 384 miles
The total time of their journey to catch with the bus carrying the Football team is 6hours
Hence the speed of the bus required is given as
[tex]\begin{gathered} \text{Speed = }\frac{dis\tan ce}{time} \\ \text{speed = }\frac{384}{6} \\ \text{speed = 64mph} \end{gathered}[/tex]Therefore, the speed of the bus carrying the school's Cheerleaders squad is 64mph
ok my question is math algebra. consider the linear equation y-1=0 and grapthe two points
Answers
To find:
We need to find two points on the linear equation y-1=0 and to plot those points on graph.
Step by step solution:
We know that:
General coordinate of any two points on line y = 1:
= (x, 1)
So let us assume any two random points on the line:
= (1,1) and (2,1)
We will now mark them on the graph:
Find the sum of the arithmetic series 31+37 +43 +49 +... where n=8,OA. 416B. 1668OC. 832D. 834Reset Selection
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given details
[tex]\begin{gathered} a_1=31 \\ n=8 \\ d=37-31=6 \end{gathered}[/tex]STEP 2: Write the formula for finding sum of arithmetic series
STEP 3: Find the sum of the series
By substitution,
[tex]\begin{gathered} S_8=\frac{8}{2}[2(31)+(8-1)6] \\ S_8=4(62+42) \\ S_8=4(104)=416 \end{gathered}[/tex]Hence, the sum is 416
At a birthday party, guests ate 452 plates ofchocolate cupcakes and 2/3 plates of cherrycupcakes. How many did the guests eat altogether?If 5 plates of chocolate cupcakes and 5 plates ofcherry were made, how much of each are left?
Answers
Given
[tex]\begin{gathered} \text{Ate 4}\frac{5}{12}\text{Plates of chocolate cupcakes} \\ \text{And} \\ \text{Ate 2}\frac{1}{3}\text{plates of cherry} \end{gathered}[/tex]We are to add them together to know the total
[tex]4\frac{5}{12}+2\frac{1}{3}=6\frac{5+4}{12}=6\frac{9}{12}=6\frac{3}{4}[/tex]The final answer
[tex]6\frac{3}{4}[/tex]4. Which inequality is represented by the graph?8642S-6428X4-6laO4x - 2y > 12O4x - 2y < 12O4x + 2y > 12O4x + 2y < 12
Answers
Hello there. To solve this question, we'll have to remember some properties about inequalities and its graphs.
First, we have to determine the equation of the line. For this, we have to find, by inspection, two points contained in that line:
We can easily find the points (0, -6) and (2, -2).
With this, we can find the equation of the line using the point-slope formula:
[tex]y-y_0=m\cdot(x-x_0)[/tex]Where (x0, y0) is a point of the line, as well as (x1, y1) and the slope m is given by:
[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]Plugging the coordinates of the points, we get:
[tex]m=\frac{-2-(-6)}{2-0}=\frac{-2+6}{2}=\frac{4}{2}=2[/tex]Such that:
[tex]\begin{gathered} y-(-6)=2\cdot(x-0) \\ y+6=2x \end{gathered}[/tex]Rearranging it in the ax + by = c form,
[tex]2x-y=6[/tex]Multiply both sides of the equation by a factor of 2
[tex]4x-2y=12[/tex]Finally, notice that the values of y in the shaded region are greater than the values in the line, which means that the inequality we're looking for is:
[tex]4x-2y>12[/tex]All the point (x, y) satisfying this inequality are contained in the shaded region.
