Answer:
He would to jog 5 miles to go direct to his home
Step-by-step explanation:
* Lets explain how to solve the problem
- Charlie jogs 3 miles south and then 4 miles west
- We need to know if Charlie were to jog straight home, without
changing direction how far he have to jog
- Remember: the East-west line is perpendicular to the north-south line
∵ He jogs 3 miles south
∵ He jogs 4 miles west
∵ South ⊥ west
- We can consider that the west and east distance with the straight
distance to home formed a right triangle its legs are the south and
west distance and the straight distance is its hypotenuse
∴ By using Pythagoras Theorem we can find the straight distance
- Remember: In Pythagoras Theorem [tex]c=\sqrt{a^{2}+b^{2}}[/tex]
where c is the hypotenuse , a and b are the legs of the right Δ
∴ The straight distance = [tex]\sqrt{(3)^{2}+(4)^{2}}\sqrt{9+16}=\sqrt{25}=5[/tex]
∴ He would to jog 5 miles to go direct to his home
Martin recently celebrated his son's birthday of his son just turned 1 years old how many minutes has his son been alive assume that the year is 365 days long no leap year
Answer:
Hos son is alive for 525600 mins
Step-by-step explanation:
365 x 24 hrs=8760 hrs
8760 hrs x 60 min= 525600 mins
Multiplication is the process of multiplying. The number of minutes for which Martin's son is live is 525,600 minutes.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given that Martin recently celebrated his son's birthday of when he turned 1 years old. Therefore, the number of minutes for which Martin's son is live is,
Number of minutes
= Number of days in a year × Number of hours in a day × Number of minutes in an hour
= 365 days × 24 hours × 60 minutes
= 525,600 minutes
Hence, the number of minutes for which Martin's son is live is 525,600 minutes.
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supplement of angle z. z=42.1°
Answer:
137.9°Step-by-step explanation:
Supplementary angles add up to 180 °.
x + z = 180° → x = 180° - z
180° - 42.1° = 137.9°
On a construction project, poured concrete is given 1,000 hours to dry completely.
What is the result when this time is converted into days?
Use 24 hours = 1 day.
Enter your answer in the boxes.
days,
hours
Answer:
41.6 days.
Step-by-step explanation:
1000 divided by 24 is 41.6 repeating
what is the greatest common factor of 150, 275 and 420
Answer:
I believe the answer is 5!
Step-by-step explanation:
Will mark brainest! Write an equation in slope intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation, (-3,6) y=1/3x-5
(Write an equation for the perpendicular line in slope-intercept form)
Juwad picked 30 bags of apples on Monday and sold them at his fruit stand for $3.45 each. The following week he picked and sold 26 bags.
a. How much money did Juwad earn in the first week?
b. How much money did he earn in the second week?
c. How much did Juwad earn selling bags of apples these two weeks?
d. Extension: Each bag Juwad picked holds 15 apples. How many apples did he pick in two weeks? Write an expression to represent this problem.
Answer:
Step-by-step explanation:
a. So since it doesn't say anything else after Monday for that week we assume he only got the apples Monday. Now, if you're having trouble figuring out how much he got from selling all 30 try thinking about selling one at a time. one is 3.45, two is 6.90 and so on. So you multiply the amount by how many there are. so 30*3.45.
b. Second week is similar, 26*3.45
c. it wants to know how much in total, so just add the two results. 30*3.45 + 26*3.45.
d. So, each bag has 15. You can use similar thinking. one bag is 15, two is 30 and so on. Writing an expression means putting a variable in. let's say x is the number of bags. To find the number of apples you multiply it by 15. so 15x. Now, to find how many apples were gotten int he two weeks we want x to equal the total number of bags, which is 30+26.
If there was something you didn't understand let me know and I will explain it.
Answer:
a. [tex]\$103.5[/tex]
b. [tex]\$89.7[/tex]
c. [tex]\$193.2[/tex]
d. Expression: [tex]15(30+26)[/tex]
He picked 840 apples in two weeks.
Step-by-step explanation:
We know that he sold each bag for $3.45.
a. Let be "x" the amount of money Juwad earned in the first week. To find its value we need to multiply the price of one bag by the number of bags he sold the first week.
Since he sold 30 bags that week,we get:
[tex]x=(\$3.45)(30)=\$103.5[/tex]
b. In the second week Juwad sold 26 bags.
Let be "y" the amount of money Juwad earned in the second week.
We must multiply the price of one bag by 26 bags in order to find the value of "y". This is:
[tex]y=(26)(\$3.45)=\$89.7[/tex]
c. The amount of money he earned selling bags of apples those two weeks is:
[tex]total\ earned=x+y\\\\total\ earned=\$103.5+\$89.7\\\\total\ earned=\$193.2[/tex]
d. We already know that he picked 30 bags of apple in the first week and 26 in the second week.
Since each bag holds 15 apples, we can wrie the following expression to represent the number of apples he picked in two weeks:
[tex]15(30+26)[/tex]
Evaluating the expression, we get:
[tex]15(56)=840[/tex]
He picked 840 apples in two weeks.
Is the statement (35)4 = (34)5 true?
Answer:
No.
Step-by-step explanation:
35(4) = 140
34(5) = 170
140 does not equal 170, therefore it is NOT TRUE
-4 or -5 which is smaller
Answer: -5!
Step-by-step explanation:
Imagine a number line with negatives on the left and positives on the right. The bigger the number is, the more to the right it would be on a number line.
-5 is more to the left than -4. Hope this helps!
If 24 extra large cans of soup will serve 96 people, how many cans should Ann buy to serve 28 people?
Answer:
She should buy a total of 25, so one more can
Omar writes a number that is greater than 271,680 but less than 276,108. What number could he have written? Use <,>, or = to justify your answer
Answer:
276,108>x>271,680
Un agricultor tiene un terreno cuadrado dedicado al cultivo de hortalizas. Para ampliarlo, quiere comprar el terreno adyacente, que mide de largo lo que mide el lado de su terreno actúa, y de ancho 10 metros. De esa manera, con los dos terrenos juntos, dispondría de 600 metros cuadrados cuanto mide el lado del terreno
Answer: 20 meters.
Step-by-step explanation:
The formula for calculate the area of a square is:
[tex]A=s^2[/tex]
Where "s" is the side length of the square:
The formula for calculate the area of a rectangle is:
[tex]A=lw[/tex]
Where "l" is the lenght and "w" is the width.
Based on the information provided, you know the sum of the areas of the square land and the adjacent land is 600 m². This is:
[tex]A_1+A_2=600\\\\s^2+lw=600[/tex]
Knowing that the width of the adjacent land is 10 meters:
[tex]s^2+10l=600[/tex]
Since the lenght of the adjacent land and the side lenght of his actual land are equal:
[tex]l=s[/tex]
You can substitute this into [tex]s^2+10l=600[/tex]:
[tex]s^2+10s=600\\\\s^2+10s-600=0[/tex]
Applying the Quadratic formula, you get:
[tex]s=\frac{-b\±\sqrt{b^2-4ac} }{2a}\\\\s=\frac{-10\±\sqrt{(10)^2-4(1)(-600)} }{2(1)}\\\\s_1=20\\\\s_2=-30[/tex]
Since the side lenght cannot be negative, you can determine that this is:
[tex]s=20\ m[/tex]
what is the length of BC in the right triangle below?
Answer:
E:75
Step-by-step explanation:
[tex]\sqrt{21^{2} +72^{2}}[/tex]
Answer : The length of BC in the right triangle is, 75
Step-by-step explanation :
Using Pythagoras theorem in ΔBAC :
[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]
[tex](BC)^2=(AB)^2+(AC)^2[/tex]
Given:
Side AB = 21
Side AC = 72
Now put all the values in the above expression, we get the value of side BC.
[tex](BC)^2=(21)^2+(72)^2[/tex]
[tex]BC=\sqrt{(21)^2+(72)^2}[/tex]
[tex]BC=\sqrt{441+5184}[/tex]
[tex]BC=\sqrt{5625}[/tex]
[tex]BC=75[/tex]
Therefore, the length of BC in the right triangle is, 75
Point G is on line segment FH. Given FH = 4x, GH = x, and FG = 2x + 10,
determine the numerical length of FG.
Answer:
30 units
Step-by-step explanation:
If point G is on line segment FH, then point G lies between points F and H.
Segment Addition Postulate states that given 2 points F and H, a third point G lies on the line segment FH if and only if the distances between the points satisfy the equation FG + GH = FH.
By segment addition postulate,
[tex]FG+GH=FH[/tex]
Given
FH = 4x,
GH = x,
FG = 2x + 10,
then
[tex]4x=x+2x+10\\ \\4x=3x+10\\ \\4x-3x=10\\ \\x=10\\ \\FG=2x+10=2\cdot 10+10=30\ units[/tex]
Answer:
FG=11
Step-by-step explanation:
100 POINTS AND BRAINLEST
Note: Enter your answer and show all the steps you use to solve this problem in the space provided.
6×5+3×8
Hey!
-----------------------------------------------
PEMDAS stands for the steps in solving an equation.
P - Parenthesis
E - Exponent's
M - Multiply
D - Divide
A - Addition
S - Subtract
-----------------------------------------------
Expression:
= 6 × 5 + 3 × 8
Multiply first since its the first step in this equation:
= (6 × 5) + (3 × 8)
Simplify:
= 30 + 24
Answer:
= 54
-----------------------------------------------
Hope This Helped! Good Luck!
*Further simplification is in bold*
Answer:
54
Step-by-step explanation:
1- 6x5+3×8= Work out the division and multiplication at each side from left to right. First do the times always. so for example 2×2=4; so 6×5= 30 and 3x8= 24
2- 30+ 24= Work out the sum. Then do the sum for example 3+2=6. So in this case 30+24; you can do as 30+20=50+4= 54
3- 30+24= 54
Feel free to ask more questions.
i have no idea what this means
Answer: square root is a number that can be multiplied by itself to get that number in that radical aka checked half box.
Step-by-step explanation: square root of 18 is
Approx: ~4.2
Since that approx multiplied by itself is 19. Search up place values. Numbers after the decimals start from, tenths place, hundredths, thousands place and so on. This one asked for the tenths place. 0.2 the 2 is in the tenths place
A line passes through (0, –7) and has a slope of -2/3. What is the equation of the line in slope-intercept form
Answer:
the required equation is y = ( -2/3 )x -7
Step-by-step explanation:
Given :-
the line passes through the point ( 0 , -7 )
)and slope of the line is ( -2/3 )
• To form an equation when one point and it's slope is given ,
• To form an equation when one point and it's slope is given , we use ;
• To form an equation when one point and it's slope is given , we use ;( y - y1 ) = m ( x - x1 )
• To form an equation when one point and it's slope is given , we use ;( y - y1 ) = m ( x - x1 )Where , x and y are variables
• To form an equation when one point and it's slope is given , we use ;( y - y1 ) = m ( x - x1 )Where , x and y are variablesand x1 and y1 are the points where the line meet !
• To form an equation when one point and it's slope is given , we use ;( y - y1 ) = m ( x - x1 )Where , x and y are variablesand x1 and y1 are the points where the line meet ! and m is slope of the tangent !!
y1 = -7
x1 = 0
So, putting all the values in the equation we get ,
[tex](y - ( - 7)) = \frac{( -2 )}{3} (x - 0) \\ \\ y + 7 = \frac{ - 2}{3} x \\ \\ 3y + 21 = - 2x \\ \\ 3y = - 2x - 21[/tex]
[tex]3y = - 21 - 2x \\ \\ y = \frac{ - 2}{3} x - \frac{21}{3 } \\ \\ y = \frac{ - 2}{3} x - 7[/tex]
• Slope intercept form of the equation
• Slope intercept form of the equation y = mx + c
• Slope intercept form of the equation y = mx + c Where , m is slope of the line
• Slope intercept form of the equation y = mx + c Where , m is slope of the line and c is y intercept !!
[ also , we can directly put the value of c = -7 and m = ( -2/3 ) from given ]
Hence , here m = (-2/3 ) and c = -7
So, the required equation is y = ( -2/3 )x -7
A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 180 lb and each box of books weighs 40 lb. The maximum capacity of
the elevator is 850 lb. How many boxes of books can the delivery person bring up at one time?
Answer:
The delivery person can bring up max 16 boxes at one time.
Step-by-step explanation:
The elevator can only hold max 850 lbs, and the delivery man weighs 180 lbs.
850-180=670
That means the delivery man can have up to 670 lbs of boxes on the elevator.
670/40=16.75
Which means that the delivery man can hold up to 16 boxes max at one time.
With the delivery person's weight and the maximum capacity of the elevator considered, the maximum number of 40 lb boxes of books the delivery person can bring up at once is 16.
Explanation:This question is about problem-solving and arithmetics. In this context, the maximum weight the elevator can carry is 850 lb. The delivery person's weight of 180 lb must be included in this maximum. To figure out how many boxes of books at 40 lb each the delivery person can carry, one would have to subtract the delivery person's weight from the total maximum weight and then divide this total by the weight of each box.
By doing the subtraction, 850 lb (maximum capacity) - 180 lb (weight of delivery person) = 670 lb. This is the total weight of boxes that can be carried. Then, divide this remaining weight by the weight of each box: 670 lb / 40 lb = 16.75 boxes. Since one cannot have 0.75 of a box, the maximum number of boxes that can be carried at one time is 16.
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The Bake Star Bakery uses 21 cups of raisins to make 4 servings
of trail mix. How many cups of raisins are in each serving?
Answer:
5.25 cups of raisins in each cup.
Step-by-step explanation:
Divide 21 cups of raisins by 4 servings to get 5.25 cups of raisins per serving.
What is the price per pound if you buy 14.5 pounds for $25.52
Answer:
Each pound costs $1.76. Hope this helps :)
Help with Tuesday plz!!!!!!!!!!!!!!!
Answer:
120cm^3
Step-by-step explanation:
4*5*6=120
***urgent***
Write a definition for the geometric terms.
A. right angle
B. vertical angles
C. complementary angles
Answer:
Step-by-step explanation:
right angle: an angle of 90°
vertical angles: each of the pairs of opposite angles made by two intersecting lines.
complementary angles: either of two angles whose sum is 90°.
A water tank leaks 5 gallons of water each day. What integer represents the change in the number of gallons of water in the tank after 7 days?
The change in the number of gallons of water in the tank after 7 days is 35 gallons.
Explanation:The water tank leaks 5 gallons of water each day. To find the change in the number of gallons of water in the tank after 7 days, we multiply the amount leaked per day (5 gallons) by the number of days (7). The expression for the change in gallons can be written as:
Change in gallons = amount leaked per day × number of days
Change in gallons = 5 × 7
Change in gallons = 35 gallons
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Final answer:
The integer representing the change in the number of gallons of water in the tank after 7 days is -35, as the tank loses 5 gallons per day.
Explanation:
If a water tank leaks 5 gallons of water each day, the total amount of water it would lose in seven days is calculated by multiplying the daily water loss by the number of days. The calculation steps are:
Determine the daily water leakage: 5 gallons per day.
Multiply the daily leakage by the number of days: 5 gallons/day × 7 days.
Calculate the total leakage over seven days: 35 gallons.
As water is being lost from the tank, the change in the number of gallons in the tank after 7 days would be represented by a negative integer, since it is a decrease in the volume of water. Therefore, the integer representing the change in the water level is -35.
Simple problem; I keep on getting it wrong, not sure what I'm doing wrong.
Answer: [tex]\bold{\dfrac{1}{70}}[/tex]
Step-by-step explanation:
PEMDAS states to do parentheses first, then multiplication and division, and lastly subtract.
[tex]\bigg(3\dfrac{1}{3}-1\dfrac{5}{6}\bigg)\div2\dfrac{1}{7}-1\dfrac{1}{3}\cdot2.4\\\\\\\text{Step 1: Subtract}\ 3\dfrac{1}{3}\ and\ 1\dfrac{5}{6}\quad \longrightarrow \quad \dfrac{10}{3}\bigg(\dfrac{2}{2}\bigg)-\dfrac{11}{6}\quad =\dfrac{9}{6}\quad =\dfrac{3}{2}\\\\\implies \quad \dfrac{3}{2}\div2\dfrac{1}{7}-1\dfrac{1}{3}\cdot2.4[/tex]
[tex]\text{Step 2: multiply}\ \dfrac{3}{2}\ and\ 2\dfrac{1}{7}\quad \longrightarrow \quad \dfrac{3}{2}\times \dfrac{15}{7}\quad =\dfrac{45}{14}\\\\\implies \dfrac{45}{14}-1\dfrac{1}{3}\cdot 2.4\\\\\\\\\text{Step 3: multiply}\ 1\dfrac{1}{3}\ and\ 2.4\quad \longrightarrow \quad \dfrac{4}{3}\times 2\dfrac{4}{10}\quad =\dfrac{4}{3}\times \dfrac{12}{5}\quad =\dfrac{16}{5}\\\\\implies \dfrac{45}{14}-\dfrac{16}{5}[/tex]
[tex]\text{Step 4: subtract}\ \dfrac{45}{14}\ and\ \dfrac{16}{5}\quad \longrightarrow \quad \dfrac{45}{14}\bigg(\dfrac{5}{5}\bigg)-\dfrac{16}{5}\bigg(\dfrac{14}{14}\bigg)\quad =\dfrac{1}{70}\\\\\implies \large\boxed{\dfrac{1}{70}}[/tex]
what type of number is 15/10
Answer:
An improper fraction
Step-by-step explanation:
15/10 is 1 and 1/2, but it's a bigger number over a smaller number.
Answer:
Rational Number.
Step-by-step explanation:
It is a rational number because it is written as a/b where a and b are integers.
This one can simplify to 3/2.
what is the measure of pheta
Answer:
The answer is C
Step-by-step explanation:
A recipe calls for 1 1/2 cups of flour, 3/4 cup of white sugar, and 1/8 cup of brown sugar. Which of the following mixing bowls can you use to make the recipe: 2-cup, 3-cup, or 4-cup? Justify your answers.
Answer:
So if I'm going to add this numbers i need them to share a denominator
1 1/2 = 1 4/8 1/8 stays the same 3/4 - 6/8 6/8 + 1/8 = 7/8
7/8 + 1 4/8 = 1 11/8 = 2 3/8 so 3 cups would be the best estimate because the 3/8's are important for the exact mesurement
Hope this helps : )
To determine which mixing bowl to use for combining[tex]\frac{11}{2}[/tex]cups of flour, [tex]\frac{3}{4}[/tex] cup of white sugar, and [tex]\frac{1}{8}[/tex] cup of brown sugar, their volumes need to be added, resulting in a total of 2.375 cups. The suitable bowl size is the 3-cup bowl, as it is larger than the combined ingredient volume.
The student's question relates to determining which size of mixing bowl is required to accommodate the ingredients for a recipe, based on their total volume. To solve this problem, we should add the volumes of flour, white sugar, and brown sugar together:
[tex]\frac{3}{4}[/tex] cup white sugar
[tex]\frac{1}{8}[/tex]cup brown sugar
By converting these measurements to a consistent unit (cups) and adding them, we get:
1.5 cups (flour) + 0.75 cups (white sugar) + 0.125 cups (brown sugar) = 2.375 cups
Since the total volume of the ingredients is 2.375 cups, the smallest bowl that can be used is the one that holds more than 2.375 cups. Therefore, the 3-cup bowl will be sufficient for mixing the ingredients.
6. Tyrone weighed 1 box of macaroni and found it weighed.64 pounds. He then decides that
100 boxes of macaroni would weigh 640 pounds. Decide if Tyrone was correct or incorrect and
explain why or why not.
A. He was correct since.64 x 100 = 640
B. He was not correct since .64 x 100 = 64
C. He was not correct since .64 x 100 = 6.4
Answer:
B. He was not correct since .64 x 100 = 64
Step-by-step explanation:
100 x .64
400 + 6000 = 6400
Add your decimal by moving it to the left twice.64.
The question asks if Tyrone's estimation that 100 boxes of macaroni, each weighing .64 pounds, would total 640 pounds. The estimation is correct as the multiplication .64 x 100 equals 640.
Explanation:The subject of this question is Mathematics and it is a middle school level problem. The question revolves around the concept of simple multiplication and estimation. If Tyrone estimated that 100 boxes of macaroni would weigh 640 pounds based on the fact that one box weighs .64 pounds, he is correct.
This is affirmed by conducting the simple multiplication calculation: .64 (the weight of a single box) multiplied by 100 (the number of boxes) equals 640.
The mathematical representation of this can be expressed as .64 x 100 = 640. Therefore, Tyrone's estimation is correct.
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Solve the system using multiplication for the linear combination method.
6x - 3y = 3
-2x + 6y = 14
What is the solution to the system?
(2, 1)
o (2, -3)
(2, -1)
10 (2, 3)
0
0
Answer:
(2, 3)
Step-by-step explanation:
[tex] -2(2) + 6(3) = 14 \\ \\ -4 + 18 = 14 \\ \\ \\ 6(2) - 3(3) = 3 \\ \\ 12 - 9 = 3[/tex]
I am joyous to assist you anytime.
Morgan invested $4,200 into two accounts. One account paid 4% interest and the other paid 7.5% interest. She earned 7% interest on the total investment. How much money did she put in each account?
Answer:
The amount invested at 4% was $600
The amount invested at 7.5% was $3,600
Step-by-step explanation:
Let
x ----> the amount invested at 4%
$4,200-x -----> amount invested at 7.5%
we know that
The total interest earned is equal to the interest earned by the amount invested at 4% plus the interest earned by the amount invested at 7.5%
Remember that
[tex]4\%=4/100=0.04[/tex]
[tex]7.5\%=7.5/100=0.075[/tex]
[tex]7\%=7/100=0.07[/tex]
so
The linear equation that represent this situation is
[tex]0.04x+0.075(4,200-x)=0.07(4,200)[/tex]
Solve for x
[tex]0.04x+315-0.075x=294[/tex]
[tex]0.075x-0.04x=315-294[/tex]
[tex]0.035x=21[/tex]
[tex]x=\$600[/tex]
[tex]\$4,200-x=\$3,600[/tex]
therefore
The amount invested at 4% was $600
The amount invested at 7.5% was $3,600
Final answer:
Morgan invested $600 in the account with 4% interest and $3,600 in the account with 7.5% interest by setting up a system of equations and solving for both variables.
Explanation:
Calculating Investment Distribution
To find out how much money Morgan put in each account, we need to set up a system of equations. Let's designate x as the amount put into the account with 4% interest, and y as the amount put into the account with 7.5% interest. We know the total investment is $4,200, so our first equation is x + y = 4200.
Morgan earned 7% interest on the total investment. The interest from each account can be represented as 0.04x for the 4% account and 0.075y for the 7.5% account. The total interest earned is 7% of $4,200, which is $294. This gives us the second equation: 0.04x + 0.075y = 294.
To solve the system, we can use the substitution or elimination method. If we solve the first equation for y, we get y = 4200 - x. Substitute this into the second equation to get: 0.04x + 0.075(4200 - x) = 294. Now solve for x:
0.04x + 315 - 0.075x = 294-0.035x = 294 - 315-0.035x = -21x = 600So Morgan invested $600 in the 4% account. Now we can find y:
y = 4200 - xy = 4200 - 600y = 3600Therefore, Morgan invested $3,600 in the 7.5% account.
angle P and angle Q are supplementary angles. if angle P measures 4x + 1 and angle Q measures 9x -3, what is the measurement of angle Q
Answer: Angle Q= 123
Step-by-step explanation:
4x+1+9x-3=180
X=14
9(14)-3=123
The measurement of angle Q is 123 degrees if angle P and angle Q are supplementary angles.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
It is given that:
Angle P and angle Q are supplementary angles. if angle P measures 4x + 1 and angle Q measures 9x -3,
As we know the sum of the supplementary angles is up to 180 degrees
Angle P + Angle Q = 180
4x + 1 + 9x - 3 = 180
13x - 2 = 180
13x = 180 + 2
13x = 182
x = 182/13
x = 14
The measurement of the angle Q = 9x - 3
The measurement of the angle Q = 9(14) - 3
The measurement of the angle Q = 126 - 3
The measurement of the angle Q = 123 degrees
Thus, the measurement of angle Q is 123 degrees if the angle P and angle Q are supplementary angles.
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