To obtain the surface area of a triangular prism, the formula to employ is:
[tex]\begin{gathered} A_{triangular\text{ prism}}=2A_B+(a+b+c)h \\ \text{where A}_B=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where s=}\frac{a+b+c}{2} \\ a,b\text{ and c are sides of the triangular prism and h is the height} \end{gathered}[/tex]From the image, a=18in, b=21in, c =15in and h=12in
We have to obtain the value of 's' first, from the equation:
[tex]\begin{gathered} s=\frac{a+b+c}{2} \\ s=\frac{18+21+15}{2} \\ s=\frac{54}{2} \\ s=27in \end{gathered}[/tex][tex]\begin{gathered} \text{Then, we obtain the value of A}_B \\ A_B=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A_B=\sqrt[]{27(27-18)(27-21)(27-15)} \\ A_B=\sqrt[]{27(9)(6)(12)} \\ A_B=\sqrt[]{17496} \\ A_B=132.27in^2 \end{gathered}[/tex]The final step is to obtain the area of the triangular, having gotten the values needed to be inputted in the formula;
[tex]\begin{gathered} A_{triangular\text{ prism}}=2A_B+(a+b+c)h \\ A_{triangular\text{ prism}}=(2\times132.27)+(18+21+15)12 \\ A_{triangular\text{ prism}}=264.54+(54)12 \\ A_{triangular\text{ prism}}=264.54+648 \\ A_{triangular\text{ prism}}=912.54in^2 \end{gathered}[/tex]Hence, the surface area of the triangular prism is 912.54 square inches
4.(02.02 MC)Demarcus will be 24 years old when he graduates. If the mean brweekly wage of his career is $2456.00, what will his lifetime earrings be when he retires at the of65 (1 point)O $100,79600$1.000 76.00$261896.00$5226,192.00
Given:
Weekly wage = $2456
A career starts 24 years and ends in 65 years.
Find-: Lifetime earring.
Sol:
Total years of working is:
[tex]\begin{gathered} =65-24 \\ =41 \end{gathered}[/tex]In one year 52 weeks
For 41 years total week is:
[tex]=41\times52[/tex]Lifetime earnings.
[tex]\begin{gathered} =41\times52\times2456 \\ =5236192.00 \end{gathered}[/tex]So lifetime earning is 5236192.00
Find the value of x in x + y = 9 and x - y = 2.5.553.5-5.5
Step 1
Given; Find the value of x in x + y = 9 and x - y = 2.
Step 2
Using the elimination method.
[tex]\begin{gathered} x+y=9 \\ + \\ x-y=2 \\ --------- \\ 2x\text{ +0=11} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} 2x=11 \\ x=\frac{11}{2} \\ x=5.5 \end{gathered}[/tex]Answer;
[tex]x=5.5[/tex]What is the measure of BOC I couldn’t figure this out.
The arc length formula is :
[tex]\text{arc}=r\theta[/tex]where r = radius and the angle is in radians
From the problem, the arc length is 21π units and the radius is 15 units.
Using the formula above :
[tex]\begin{gathered} 21\pi=15\theta \\ \theta=\frac{21\pi}{15} \\ \theta=\frac{7}{5}\pi \end{gathered}[/tex]ANSWER :
A.
The parent function of the graph of F(x) is the square root function, whichwas reflected across the x-axis. Which of the following is the equation of F(x)2O A. F(x) = -1O B. F(x) - Vx+1O C. F(x) -O D. F(X) ---
The rule of a reflection about the x-axis is given by
[tex]f(x)\longrightarrow-f(x)[/tex]in our case,
[tex]f(x)=\sqrt[]{x}[/tex]then, by reflecting this function about the x-axis, we get
[tex]f(x)=\sqrt[]{x}\longrightarrow F(x)=-\sqrt[]{x}[/tex]therefore, the answer is option D.
Solve x2 − 4x − 1 = 0 by completing the square.
Hello! To solve completing by the square, we have to follow some steps:
[tex]\begin{gathered} x^2-4x=1 \\ \end{gathered}[/tex]Now, we have to add the same value in both sides (square):
If we factorize the first part of this expression, we can obtain:
Notice that we obtained the same expression, and now we know the value of the square. So, let's rewrite the first expression and replace the squares by 4:
suppose there is a 1.2°F drop in temperature for every thousand feet that an airplane climbs into the sky. if the temperature on the ground is 56.9°F, what will be the temperature when the plane reaches an altitude of 8,000 ft?
We have a linear model, that relates temperature with altitude.
The first senctence gives us a clue about tha rate of change (the slope) of temperature in function of the altitude.
We can write the slope, in °F/1000 ft, as:
[tex]m=-1.2[/tex]The temperature on the ground, where h=0, is 56.9 °F, so we can write the equation of the line as:
[tex]T(h)=-1.2h+56.9[/tex]When the altitude is 8,000 ft, h=8 and T is:
[tex]T(8)=-1.2\cdot8+56.9=-9.6+56.9=47.3[/tex]The temperature at 8,000 ft will be 47.3 °F.
WILL GIVE BRAINLIEST write your answer as a simplified mixed number please show your work
Answer:
Step-by-step explanation:
Given equation...
[tex]-2\frac{1}{2}[/tex] ÷ [tex]\frac{3}{4}[/tex] =
Step One...
= [tex]\frac{-5}{2}[/tex] ÷ [tex]\frac{3}{4}[/tex]
Step Two...
= [tex]\frac{-10}{3}[/tex]
Step Three...
= -3[tex]\frac{1}{3}[/tex]
Hope this helps!
An uber charges a flat rate of $20 plus $2 per mile. Lyft charges a flat rate of $15 plus $4 per mile. Write an equation to find the number of miles m for which uber and lyft would cost the same amount.
if a= -3, find the value of a²
Answer:
a = 9
Step-by-step explanation:
[tex]a^{2}[/tex] = a*a
a = -3
-3 * -3 = 9
NOTE: 2 negative numbers multiplied by each other always equals a positive
So.... a = 9
question provided in picture only need assistance with part b
PART B
The probability is 1/2
STEP - BY - STEP EXPLANATION
What to find?
The probability of identical twins given that the twins consists of two boys.
Let A be the event of identical twins.
Let B be the event of having two boys as twins.
From the table given;
P(A) = 2/38
P(B)= 2/38
Recall the formula for a condititional probabibility
[tex]P(A\text{ \backslash{}B)=}\frac{P(A\text{ n }B)}{P(B)}[/tex]Note that:
P(A n B) =1/38
[tex]P(A\text{ \backslash B) =}\frac{\frac{1}{38}}{\frac{2}{38}}[/tex][tex]=\frac{1}{38}\times\frac{38}{2}[/tex][tex]=\frac{1}{2}[/tex]Therefore, the probability of identical twins given that the twins consists of two boys is 1/2
HELP QUICK PLS!!
State all integer values of x in the interval -4 ≤ x ≤ 3 that satisfy the following inequality:
-5x - 3 > 8
Answer:
[tex]-4 \leq x < -2.2[/tex]
Step-by-step explanation:
-5x - 3 > 8
-5x > 11
x < -11/5
We know that -4 ≤ x ≤ 3 and x < -11/5 (-2.2)
-4 <= x < -2.2
Joanne cannot decide which of two washing machines to buy. The selling price of each is $390. The first is marked down by 40%. The second is marked down by 10% with an additional 30% off. Find the sale price of each washing machine. Use pencil and paper. Explain why Joanne should buy the first washing machine rather than the second if the machines are the same except for the selling price.
Answer:
Joanne should definitely purchase the first one because it is much cheaper.
Step-by-step explanation:
So, to find the cost of each washing machine, we can simply turn the percentages into decimals and multiply to get our answer. Let's start with 40%. We bring the decimal back to spaces to get: 0.40. Then, we multiply it from the $390, because 40% 'of' means multiply:
0.40 x 390 = $156.
390 - 156 = $234
Now, the next one:
0.10 x 390 = $39
390 - 39 = $351
Then, we take 351 dollars and find the 30% off difference.
0.30 x 351 = 105.30
390 - 105.3 = $284.70
May I have Brainliest please? I am so close to getting my next ranking! I just need 3 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
The weights of the melons harvested from a patch are distributed normally. The mean weight is 6 pounds; the standard deviation is 0.25 pounds. Which is closest to the percent of melons that weigh 6.25 pounds or less?A) 34B) 68C) 84D) 98
As it is normally distributed, we can use Z to find the result.
Procedure
0. Finding the value of ,Z
[tex]Z=\frac{x-\mu}{\sigma}[/tex]1.2. Replacing the values given in the problem:
[tex]Z=\frac{6.25-6}{0.25}[/tex][tex]Z=\frac{0.25}{0.25}=1[/tex]2. As it is normally distributed:
[tex]P(x\le6.25)=P(Z\le1)[/tex]3. Using the normal standard table, we can conclude:
[tex]P(Z<1)=0.8413[/tex]As it is asking for a percentage, we multiply by 100.
Answer: C) 84%
17. P(-6, 16), Q(2, -4), R(-6, 14), S(-2, 4)Slope of PQ Slope of RSTypes of Lines
The formula for finding slope is expressed as
slope = (y2 - y1)/(x2 - x1)
where
y2 and y1 are final and initial values of the y coordinates respectively
x2 and x1 are final and initial values of the x coordinates respectively
Considering line PQ,
x1 = - 6, y1 = 16
x2 = 2, y2 = - 4
Slope = (- 4 - 16)/(2 - - 6) = - 20/8
Slope = - 2.5
Considering line RS,
x1 = - 6, y1 = 14
x2 = - 2, y2 = 4
Slope = (4 - 14)/(- 2 - - 6) = - 10/4
Slope = - 2.5
If the slope of two lines are equal, it means that they are parallel. We can see that the slopes of PQ and RS are equal. Thus,
Line PQ is parallel to line RS
2
While digging in his garden Will pushes a shiv into the ground with a force of 585 newtons at an angle of 80° with the ground
Force, F = 585 N
Angle, θ = 80°
The diagram that shows the resolution of the force into its rectangular component is drawn below
The magnitude of the horizontal component is:
[tex]\begin{gathered} F_x=585\sin 80 \\ F_x=585(0.9848) \\ F_x=576N \end{gathered}[/tex]The magnitude of the vertical component is:
[tex]\begin{gathered} F_y=585\cos 80 \\ F_y=585(0.174) \\ F_y=102N \end{gathered}[/tex]Therefore, the magnitudes of the horizontal and vertical components of the force are (576, 102)
Estimate the sum by rounding each number to the nearest hundredth: 0.087+0.043 that's my question
To round each number to the nearest hundredth, you need to look th
x = 3y + 18
5x+4y = -5
X =
y = 0
010
X
5
Answer:
Step-by-step explanation:
x = 3y + 18
5x+4y = -5
X =
y = 0
010
X
5
Beginning with the equation x=-27 write the new equation produced by dividing both sides by 3
Answer:
[tex]\frac{x}{3}=-9[/tex]
Explain step by step how to complete -0.7 = 9.1
Answer:
9.1.4 -0.7=9.1
Step-by-step explanation:
Step 1: Determine the Assessment Unit ID (AUID) of the waterbody of interest.
Step 2: Express the quadratic equation in standard form
4.An image of a book shown on a website is 1.5
inches wide and 3 inches tall on a computer monitor.
The actual book is 9 inches wide.
5.
be
di
a) What scale is being used for the image? Explain or
show your reasoning.
b) How tall is the actual book? Show your
calculations.
S
a. The scale that is being used for the image is: 1 inches to 6 inches or 1 inches = 6 inches.
b. The actual book is 18 inches tall.
What is an Image?An image is the new figure formed when an original figure is dilated, either by enlargement or by reduction. The image is a similar figure to the preimage (original figure).
Given the following:
Width of the image = 1.5 inchesHeight of the image = 3 inchesActual book width (preimage) = 9 inchesa. The scale being used = width of image : width of preimage (actual book)
Scale = 1.5 : 9
Scale = 1 : 6
This is, 1 inches to 6 inches or 1 inches = 6 inches.
b. Height of image = 3 inches
Height of actual book (preimage) = 3 × 6 = 18 inches.
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112+18x14+14-14=
OA) 12
O B) 18
O C) 116
O D)130
A mathematical "operation" is the process of calculating a value using operands and a math operator.
If the equation be 112 + 18 × 14 + 14 - 14 by simplifying the calculation, we get 364.
What is meant by mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.
A mathematical "operation" is the process of calculating a value using operands and a math operator. There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers. Image: The basic mathematical operation symbols. A set of numbers and operations make up a mathematical expression.
Let the equation be 112 + 18 × 14 + 14 - 14
= 112 + 252 + 14 - 14
Add and subtract (left to right)
112 + 252 + 14 - 14 = 364
Therefore, by simplifying the above calculation, we get 364.
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Rosalia went on a long bike ride. The table shows how long she biked and the distance she traveled. Determine whether the relationship between hours biked and miles traveled is proportional.
The rate of change is not the same for all the cases so,
The relationship between hours biked and the miles traveled is not proportional.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
From the table, we need to find the rate of change between two given hours and the miles traveled at that time.
Now,
Between 1 hour and 2 hours.
The rate of change.
= (26 - 12) / (2 -1)
= 14 / 1
= 14
Between 2 hours and 3 hours.
The rate of change.
= (30 - 26) / (3 - 2)
= 4 / 1
= 4
Between 3 hours and 4 hours.
The rate of change.
= (48 - 30) / (4 - 3)
= 18 / 1
= 18
We see that,
The rate of change is not the same for all the cases so,
The relationship between hours biked and the miles traveled is not proportional.
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Credit Card Statement Calculate the newPrevious Balance $120.00 balance on thisFinance Charge $15.00 account after theseNew Purchases $200.00 charges andPayments $(300.00) payments areCredits$0.00applied.A. $35.00B. $635.00C. $235.00D. $395.00
Previous Balance: $120
Finance Charge: $15
New Purchases: $200
Payments: $300
Recall this is a Credit Card Statement.
To find the new balance we must subtract the payments and add the charges:
New Balance = $120 - $300 + $15 + $200
New Balance = $35
Answer: A. $35.00
A merchant is bagging potatoes that he will sell for 5 a bag he want to take 400 for then how many bags should he prepare
The number of bags that the merchant should prepare if he wants to make 400 is; 80 bags
How to solve Algebra Word Problems?The method to solve algebra word problems is as follows;
1. Carefully read through the problem thoroughly, and try to know the meaning.
2. Use variables to denote unknown numbers.
3. Translate the remaining part of the problem into a mathematical expression.
4. Solve the problem.
We are told that the merchant sells 5 for a bag. Now, he wants to make 400. This means if the number of bags is x, then;
x = 400/5
x = 80 bags
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Determine if the triangles are congruent. If so, state which reason proves the triangles are congruent.
Group of answer choices
Not congruent
SAS
HL
SSA
The △ABC is congruent to triangle △ADE (△ABC ≅ △ADE) under (B) SAS condition.
What do we mean by the congruency of triangles?Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.
You can move, flip, twist, and turn these triangles to produce the same effect.
So, first label the two triangles as △ABC and △ADE.
Now, to prove that △ABC ≅ △ADE:
BA = DA (Given)
AC = ED (Given)
∠BAC = ∠ADE (Since, both lines are similar, so the angle between them will also be soililar and congruent.
So, we can say that △ABC ≅ △ADE is under SAS conditions.
Therefore, the △ABC is congruent to triangle △ADE (△ABC ≅ △ADE) under (B) SAS condition.
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Complete question:
Determine if the triangles are congruent. If so, a state which reason proves the triangles are congruent.
Group of answer choices
a. Not congruent
b. SAS
c. HL
d. SSA
What is the equation of the line in slope-intercept form?
Answer:
5/2; 5
Step-by-step explanation:
The first box is m, which is the slope. To find the slope you do rise over run, so basically the change in x and y. You move up 5 and over 2, so m would be 5/2.
The second box is b, which is the y-intercept. To find the y-intercept, you just find where the line crosses the y-axis. That would be 5
Asif can use the greatest common factor to rewrite 28+49 as (4+ ).
Answer:
7*(4 + 7)
Step-by-step explanation:
28 = 7 *4
49 = 7 * 7
GCF = 7
28 + 49 = (7*4) + (7*7)
= 7*(4 + 7)
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (suchas printing). The one-time fixed costs will total $30456. The variable costs will be $10 per book. The publisher will sell the finished product to bookstores at aprice of $21.75 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Let x be the number of books that need to be sold, then for the cost of the production and the profit to be the same we can set the following equation:
[tex]30456+10x=21.75x\text{.}[/tex]Subtracting 10x from both sides of the equation we get:
[tex]30456=21.75x-10x,[/tex]adding like terms we get:
[tex]30456=11.75x\text{.}[/tex]Dividing by 11.75 we get:
[tex]x=2592.[/tex]Then the producer must sell 2592 books.
Answer: 2592.
Katie’s hair is 4 ½ x + 1 inches long. She decides to get a haircut. The barber cuts ¼ x – 2 inches off her hair. Write an expression that would represent how long Katie’s hair is when she leaves the barbershop, if simplified.
Katie's hair is (17x/4 +3) inches long when she leaves the barber shop.
According to the question,
We have the following information:
Katie’s hair is 4 ½ x + 1 inches long.
The barber cuts ¼ x – 2 inches off her hair.
Now, the remaining length of her hair will be obtained by subtracting the length of hair cut from the original length.
So, we have the following expression:
([tex]4\frac{1}{2} x+1[/tex])-(x/4-2)
9x/2+1-x/4+2
9x/2-x/4+3
Taking 4 as the least common factor:
18x-x+12/4
17x+12/4
17x/4 + 12/4
17x/4 + 3 inches
Hence, Katie's hair is (17x/4 +3) inches long when she leaves the barber shop.
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48.06 ÷ 6 what is the anwser
Answer:
8.01 is the answer
Answer:
8.01
Step-by-step explanation: