Each integer from -3 to 5 inclusive is placed in the diagram, with one number going into each box. If the sum of the numbers in each row is the same, what is that sum? (the diagram will be a screenshot) A. 0 b. 3 c. 5 d.6
Answers
Answer:
the correct solution is B:3
Answer:
Our solution is option b, or in other words 3.
Step-by-step explanation:
This is more of a " guess and try " question. Say that 3 is the solution. If that is so, let us prove it, by arranging the values such that their addition is equivalent to 3 in each row.
Take - 3 as the first value in the first row. What other combinations can go with this, but still meet our requirement of a total of 3? The other two numbers must have a sum of 6, so let's list all possibilities -
{ 5 and 1 }
{ 4 and 2 }
Let us try 5 and 1. We should receive the following table so far -
| - 3 | 5 | 1 |
| ? | ? | ? |
| ? | ? | ? | ...... Now for this second row let - 2 be the starting value. The only possible values in the row should have a sum of 5 to have a total of 3 -
{ 3 and 2 }
This is the only possibility we have here. Plug it into our table,
| - 3 | 5 | 1 |
| - 2 | 3 | 2 |
| ? | ? | ? | .... Let's begin with the value - 1 for the third row. The only remaining values that could fill this row are 0 and 4. { - 1, 0, and 4 } add to 3, and hence the sum of the number in each row is a constant, 3. It has been proved.
| - 3 | 5 | 1 |
| - 2 | 3 | 2 | - This is our table.
| - 1 | 0 | 4 |
Related Questions
Which statement is true regarding the graphed functions?
Answers
Answer:
C
Step-by-step explanation:
You can look them up in the graphs.
f(2) means "where is the blue graph when x=2?", and you can see it is at y=0.
Helen drives 195 miles in 3 hours.
a) What is her average speed in mph?
Matthew drives at an average speed of 62 mph for 5 hours.
b) How many miles does Matthew drive?
Answers
Answer:
a) What is her average speed in mph?
= 65 mph
b) How many miles does Matthew drive?
=310 miles
Step-by-step explanation:
The average speed in meters per hour (mph) of Helen is 65 miles per hour
Given:
Total distance = 195 miles
Time taken = 3 hours
Average speed = Total distance ÷ Time taken= 195 miles ÷ 3 hours
= 65 miles per hour
If Matthew drives at an average speed of 62 mph for 5 hours.
Total distance between traveled = Average speed × Time taken
= 62 mph × 5 hours
= 310 Miles
Therefore the total miles Helen traveled in 5 hours at the rate of 62 mph is 310 miles
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Gerald has a garden in the shape of a square. The area, in square feet,
of the garden is described by the expression below.
x^2 - 6x +9
What's the length, in square feet, of each side of the garden?
Answers
Answer:
x - 3
Step-by-step explanation:
We know that the area of a square is length times width.
We also know that a quadratic can be factored:
(x - 3)²
So if each side is (x - 3), then when we do length times width, we get x² - 6x + 9. So our answer is choice D.
HURRRYYYY FIRST GETS BRAINLLEST Janine wrote the numbers 1-100 and placed them in a bag. If she selects a number without looking, what is the probability that the number is even and greater than 80? Input your answer as a decimal or fraction.
Answers
Answer:
1/10 or ( 0.1 )
Step-by-step explanation:
no. of even no.s greater than 80 = 10
Total no.of numbers = 100
So P(no. of even no.s greater than 80) = 10/100 = 1/10
Answer:
There are 10 even numbers greater than 80.
So Probability of getting an even numbers greater than 80 is 10/100 (1/10)
Hope it helps you. Please mark Brainliest :)
Have a nice day PPLS!!!!!!!
Identify the domain of the function shown in the graph.
5
O A. -1 5x53
O B. 25x37
Ο Ο Ο
O C. All real numbers
D. X23
Answers
Answer:
[2, 6].
Step-by-step explanation:
Notice that there is a red line (graph) only for [2, 6]. Thus, the domain of this function is [2, 6].
given f(x) = 3/2x - 5 and g(x) = x^2 + 2x find x (the input) if g(x) = 0 ( the output 0 ) there are 2 answers
Answers
Answer:
x = 0 , x = -2
Step-by-step explanation:
The function given to us is:
f(x) = 3/2x - 5
g(x) = x² + 2x
We have to find the input x, for which the output of the function g(x) becomes 0.
It means that there is no use for the function f(x) in this question, so discard it
Substitute g(x) = 0 into the given equation of g(x):
g(x) = x² + 2x
0 = x² + 2x
Take x common from both the terms:
x(x+2) = 0
Thus, the values of x can be written as:
x = 0 , x + 2 = 0
x = 0 , x = -2
Determine the length of BC . ANSWERS: A) 12.25 units B) 24.71 units C) 19.00 units D) 5.57 units
Answers
Answer:
A) 12.25 units
Step-by-step explanation:
From Pythagorean theorem:
AB² + BC² = 25²6² + BD² = BC²19² + BD² = AB²Defining:
x = AB²y = BC²z = BD²The system of equations is:
x + y = 625 (eq. 1)
36 + z = y (eq. 2)
361 + z = x (eq. 3)
Replacing equation 3 into 1:
361 + z + y = 625
From equation 2:
z = y - 36
Replacing it into equation 1:
361 + y - 36 + y = 625
2y = 625 + 36 - 361
y = 300/2
y = 150
Finally:
BC = √y
BC = √150
BC = 12.25 units
1. Write the standard form of the line that passes through the given points. (7, -3) and (4, -8)
2. Write the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2 x + y = -5.
3. Write the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to 2x + y = -5
Answers
Answer:
1. [tex]-5x+3y+44=0[/tex]
2. [tex]2x+y-2=0[/tex]
3. [tex]2x+y-4=0[/tex]
Step-by-step explanation:
Standard form of a line is [tex]Ax+By+C=0[/tex].
If a line passing through two points then the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
where, m is slope, i.e.,[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex].
1.
The line passes through the points (7,-3) and (4,-8). So, the equation of line is
[tex]y-(-3)=\dfrac{-8-(-3)}{4-7}(x-7)[/tex]
[tex]y+3=\dfrac{-5}{-3}(x-7)[/tex]
[tex]y+3=\dfrac{5}{3}(x-7)[/tex]
[tex]3(y+3)=5(x-7)[/tex]
[tex]3y+9=5x-35[/tex]
[tex]-5x+3y+9+35=0[/tex]
[tex]-5x+3y+44=0[/tex]
Therefore, the required equation is [tex]-5x+3y+44=0[/tex].
2.
We need to find the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to [tex]2 x + y =-5[/tex].
Slope of the line : [tex]m=\dfrac{-\text{Coefficient of x}}{\text{Coefficient of y}}=\dfrac{-2}{1}=-2[/tex]
Slope of parallel lines are equal. So, the slope of required line is -2 and it passes through the point (0,2).
Equation of line is
[tex]y-2=-2(x-0)[/tex]
[tex]y-2=-2x[/tex]
[tex]2x+y-2=0[/tex]
Therefore, the required equation is [tex]2x+y-2=0[/tex].
3.
We need to find the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to [tex]2x + y =-5[/tex].
From part 2, the slope of this line is -2. So, slope of required line is -2 and it passes through the point (2,0).
Equation of line is
[tex]y-0=-2(x-2)[/tex]
[tex]y=-2x+4[/tex]
[tex]2x+y-4=0[/tex]
Therefore, the required equation is [tex]2x+y-4=0[/tex].
A random sample of 145 students is chosen from a population of 4,250 students. The mean IQ in the sample is 130, with a standard deviation of 7. Using a margin of error of 0.95%, what is the 90% confidence interval for the students' mean IQ score?
Answers
Answer:
Approximately, the 90% confidence interval for the students' mean IQ score is between 129.045 - 130.956
Step-by-step explanation:
The formula to use to solve this question is called the Confidence Interval formula.
Confidence interval =
x ± z × ( σ/ (√n) )
Where:
x = the sample mean = 130
z = the z-value for 90% confidence = 1.645
σ = standard deviation = 7
n = sample size = 145
130 ± 1.645 × (7/√145)
130 ± 0.9562687005
130 - 0.9562687005 = 129.0437313
130 + 0.9562687005 = 130.9562687005
Therefore, approximately, the 90% confidence interval for the students' mean IQ score is between 129.045 - 130.956
I need help I don't understand I was on a streak and now this stupid problem is just unsolvable I just want to finish this stupid work and play gtao
Answers
Explanation:
Area of rectangle A: 48
Area of rectangle B: 96
48/96 = 4/8 = 1/2
Ratio of the area of rectangle A and B is 1:2
Answer:
the ratio is 1:3
Step-by-step explanation:
In triangle FGH, the bisector of angle F also bisects the opposite side. The ratio of each half of the bisected side to each of the other sides is 1 : 2. What type of triangle is triangle FGH? Explain.
Answers
If the angle bisector also bisects the opposite side, then it's also a median *and* an altitude. The triangle is isosceles.
Draw the diagram: you have that altitude forming a pair of mirror-image right triangles. In each, the short side is 1 and the hypotenuse is 2. What does this tell you about the large triangle?
Then the rest you have to think... cuz it wasn't that hard.( If you still don't understand comment it, and then I will explain to you!)
HOPE IT HELP!
A car travels at 60 miles per hour. If d is the distance traveled and t is the time in hours: Write a function for the distance traveled d in t hours. What is the dependent variable? What is the independent variable? Make a table with at least 5 coordinate pairs. Graph the coordinate pairs and draw the function
Answers
Answer:
Step-by-step explanation:
d= distance
t= time
The independent variable is t, time. The distance the car travels depends on the time in hours spent travelling. The dependent variable is d, distance. Here is a table with 5 coordinate pairs that can be used.
(T) (D)
1 30
2 60
3 90
4 120
5 150
These are the coordinate pairs for the function. When we use division and determine the rate of change, we can determine that the average rate of speed (MPH) is 30 MPH.
Classify the object in real life by what type of polygon it is. State if it is concave or convex, and explain why. Also write the sum of the interior angles. If the polygon is regular what would the measure of the interior and exterior angles be? a. Stop sign b. Tripod c. Computer screen d. School crossing sign e. The dome of a capitol building f. A cell in a honeycomb g. Describe the difference between a concave and convex polygon. h. What is a regular polygon? i. How do you calculate the sum of the interior angles?
Answers
Answer:
see below for classification
concave: angles less than 180°
regular: sides and angles congruent
sum = 180°(n -2)
Step-by-step explanation:
A) The given shapes are classified and described in the attachment. (A polygon is a plane figure, so a "tripod" and a "dome" are not polygons.)
__
B) A convex polygon has interior angles that measure less than 180°. A concave polygon has one or more reflex angles.
__
C) A regular polygon has all angle measures congruent, and all side lengths congruent.
__
D) The sum of interior angles can be calculated from the formula ...
angle sum = 180° · (n -2) . . . . where n is the number of sides
Which of these phrases contain a variable? Check all that apply.
O A. The length of the hallway
O B. Twelve ounces of tea
O C. The weight of the wombat
O D. Seven cups of flour
Answers
Answer:
The length of the hall way
the weight of the wombat
The weight of the wombat
What is the volume of a cylinder, in cubic in, with a height of 11in and a base diameter
of 4in? Round to the nearest tenths place
Answers
Answer:
Volume ≈ 138.3
Step-by-step explanation:
[tex]V = \pi r^2 h\\h = 11in\\d = 4in \\r = d/2 = 4/2 = 2\\\\V= \frac{22}{7} \times 2^2 \times 11\\V = \frac{22}{7} \times 4 \times 11\\V = 22/7 \times 44\\\\V = 968/7\\\\V = 138.2857[/tex]
Answer:138.2
Step-by-step explanation: n(2)^2(11) = 138.2300768 = 138.2
Need help solving triangle in picture
Answers
Answer:
see explanation
Step-by-step explanation:
Using the sine ration on the left, right triangle
sin35° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{8.6}[/tex] ( multiply both sides by 8.6 )
8.6 × sin35° = a , thus
a ≈ 4.93 cm
a + b = 15.7, so
4.93 + b = 15.7 ( subtract 4.93 from both sides )
b = 10.77
-------------------------------------------------------------
Using the cosine ratio on the left, right triangle
cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{8.6}[/tex] ( multiply both sides by 8.6 )
8.6 × cos35° = y , so
y ≈ 7.04 cm
Using Pythagoras' identity on the right, right triangle
c² = b² + y² = (10.77)² + (7.04)² = 115.99 + 49.56 = 165.55
Take the square root of both sides )
c = [tex]\sqrt{165.55}[/tex] ≈ 12.87 cm
What is the initial value of the equation shown?
y = -7x - 6
-13
-7
-6
-1
Answers
Answer:
-6
Step-by-step explanation:
Just did the test and -6 was the right answer.
What is the volume of the pyramid
150ft^3
540 ft^3
432 ft^3
48 ft^3
Answers
Answer:
Option (4)
Step-by-step explanation:
To calculate the volume of a pyramid we use the formula,
V = [tex]\frac{1}{3}(\text{Area of the base})(\text{Height of the pyramid})[/tex]
Area of the square base = (Side)²
= (6)²
= 36 square ft
Height of the pyramid 'h' = [tex]\sqrt{l^{2}-(\frac{\text{Side length of the base}}{2})^{2}}[/tex] [By Pythagoras theorem]
h = [tex]\sqrt{5^{2}-3^{2}}[/tex]
h = [tex]\sqrt{16}[/tex]
h = 4 ft
Therefore, volume of the given pyramid = [tex]\frac{1}{3}(36)(4)[/tex]
= 48 cubic ft
Option (4). 48 ft³ will be the answer.
The product of the slopes of two non-vertical perpendicular lines is always -1. It is NOT possible for two
perpendicular lines to both have a positive slope because the product of two positives is positive. So for the product
of the slopes to be -1, one of the slopes must be positive and the other negative.
Please select the best answer from the choices provided
ОТrue
OFalse
Answers
Answer:
true
Step-by-step explanation:
"If A, then B" is the form of a
statement.
Answers
Answer:
Hello!
__________________
"If A, then B" is the form of a statement then it is conditional statement.
Hope this helped you!
:D
What is this expression in simplified form?
(8/10)(8/5)
OA 64/50
OB. 16/50
OC. 80/2
OD. 320/2
Answers
Answer:
A.64/50
Step-by-step explanation:
8/10*8/5
64/50
The least simplified form of the equation is 32/25
The simplified form of expression is option (D) 64/50 is the correct answer.
What is simplification of an expression?Simplification of an expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression. It involves, multiply out the brackets and then simplify the resulting expression by collecting the like terms.
For the given situation,
The expression is (8/10)(8/5)
The simplified form of expression is
⇒ [tex](\frac{8}{10} )(\frac{8}{5} )[/tex]
⇒ [tex]\frac{64}{50}[/tex]
Hence we can conclude that the simplified form of expression is option (D) 64/50 is the correct answer.
Learn more about simplification of an expression here
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Harold has $20.00 to spend. He decided to buy a shirt for $15.95 and spend the rest on packs of gum. If each pack of gum costs $1.99, how many packs of gum can Harold buy?
Answers
Answer:
2 or less packs
Step-by-step explanation:
15.99 + 1.99g < 20.00 where g is the number of packs of gum
Subtract 15.99 from each side
15.99 + 1.99g - 15.99 < 20.00-15.99
1.99g < 4.01
Divide by 1.99
1.99g/1.99 < 4.01/1.99
g < 2.015075377
Harold must buy whole packs so g =2 or less
I really don’t understand these 3 questions please help.
Answers
Answer:
90 degrees
Step-by-step explanation:
Because they are 90 degrees we know that they are similar.
Shape A can be transformed to shape B by a reflection in the x-axis followed by a translation (c, d) find the value of c and the value of d
Answers
Answer:
c = -6
d = -1
Step-by-step explanation:
In the picture attached, the question is shown.
Shape A is composed of the points:
(3, 2)
(5, 2)
(3, 5)
Reflection across the x-axis transforms point (x, y) into (x, -y). Applying this transformation to shape A:
(3, 2) → (3, -2)
(5, 2) → (5, -2)
(3, 5) → (3, -5)
Translation (c, d) transforms (x, y) into (x+c, y+d). The point (3, -2) in the pre-image (before translation) corresponds to point (-3,-3) in the image (after translation). Therefore:
(3, -2) → (3+c, -2+d) → (-3,-3)
3+c = -3
c = -3 -3 = -6
-2+d = -3
d = -3+2 = -1
What is one of the solutions to the following system? StartLayout Enlarged left-brace 1st Row y minus 3 = x 2nd row x squared minus 6 x + 13 = y EndLayout (–5, 2) (–2, 1) (2, 5) (8, 5)
Answers
Answer:
The solution of given equation is (2,5)
Step-by-step explanation:
The equations give to us are:
y - 3 = x
or
y = x + 3
y = x² - 6x + 13
We can find the solution of the given system of equations by substituting each point in both of the equations. The point which satisfies both of the equation will be the solution of the the system of given equation.
Substitute (2,5) in both equations
y = x+3
5 = 2+3
5 = 5
TRUE
y = x² - 6x + 13
5 = 2² -6(2) + 13
5 = 5
TRUE
Similarly, we can also check the rest of the points, which come as FALSE.
Therefore, the solution of given equation is (2,5)
Answer:
Answer is C
Step-by-step explanation:
Which of these tables represents a function
Answers
Answer:
W.
Step-by-step explanation
A function is a rule that assigns a set of inputs
(x-values) to a set of outputs (y-values) in such a way that each input has a different output.
An easy way to tell if a table is not a function is to look for any repeated x-values that correspond with different y-values.
The table y represent the function. Then the correct option is C.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
For the function, the necessary condition is given below.
For each value of y, there should be the single value of x.
In table y, the value dependent variable is difference for different value of x.
Then the correct option is C.
More about the function link is given below.
https://brainly.com/question/5245372
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Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range. y = negative 5 x squared + 3 x + 10
Answers
Answer:
Use a graphing calc.
Domain: All real numbers
Range: (negative infinity, 10.45]
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Edge 2021
Help, My parents can’t even help me. I’m really stuck. In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from 1 to 10, and one SuperBall is drawn (at random) from ten red balls numbered from 11 to 20. When you buy a ticket, you choose three numbers from 1 to 10, and one number from 11 to 20. If the numbers on your ticket match at least two of the white balls or match the red SuperBall, then you win a super prize. What is the probability that you win a super prize?
Answers
Answer:
This is an extremely easy question. Your correct answer is 1/7,200 or 0.01389%
Step-by-step explanation:
Since you have to choose the three numbers and one super ball to be able to win the lottery, your chances of getting 3 white numbers is 1/10 x 1/9 x 1/8 = 1/720
The chances of getting the super ball is 1/10
And the chances of winning the jackpot is 1/720 x 1/10 = 1/7,200 = 0.01389%
Select the correct answer (Ignore the one already clicked)
Answers
Work Shown:
x = number of weeks
y = number of tests
slope = rise/run
slope = (change in y)/(change in x)
slope = 27/36
slope = (9*3)/(9*4)
slope = 3/4
A slope of 3/4 means that there are 3 tests for every 4 weeks.
If I have 2 steel rods, one with 17% purity and one with 25% purity. How much should I take (in kgs) from each bar?
Answers
Answer:
250 kg of 17% and 150 kg of 25%
Step-by-step explanation:
For answering this, we do it by proportions.
take the difference
17% === 20% === 25%
3 5
Then ratio
17% :25% = 5:3
For 400 kg,
17% = 5/(5+3) * 400 = 250 kg
25% = 3/(5+3) * 400 = 150 kg.
Above is a mental method, no calculation or pencil need.
I will edit to give an algebraic method.
Algebraic method:
Given:
17% rods and 25% rods.
Need to make 400 kg of 20% rods.
Let
A=weight of 17% rods
B=weight of 25% rods
to make 20% rods, we need
( 0.17A + 0.25B ) / (A+B) = 0.20 ............(1)
But we know that
A+B=400 .............(2)
substitute
B=400-A in (1)
( 0.17A + 0.25 (400-A) ) / 400 = 0.20
Cross multiply and simplify
(0.17-0.25)A +100 = 80
-0.08A = -20
A = -20 / (-0.08)
A = 250 ...........(3) (17% rods)
substitute (3) in (2)
B = 400-250 = 150 (25% rods)
Same answer as mental calculations
Even simpler albebra, same answer!
Given:
17% rods and 25% rods.
Need to make 400 kg of 20% rods.
Let
W=weight of 25% rods
400-W = weight of 17% rods
To make 20% purity rods, we need to have 400*0.2=80 kg of pure metal, which is
0.25W + 0.17(400-W) = 80
Expand and simplify
0.25W + 68 - 0.17W = 80
0.08W = 80-68 = 12
W = 12/0.08 = 150 (25% rods)
400-W = 250 kg (17% rods)
Answer:
245432
Step-by-step explanation:
Angela uses cup of strawberries to make of a liter of smoothie. What is the unit rate in cups of strawberries per liter of smoothie?