The age of the man whose normal pressure measures 128 mmHg is approximately 38 years.
How do we determine the age of the man using a quadratic equation?The quadratic formula can be used to determine the age of a man whose normal blood pressure measures 128 mmHg. This can be expressed mathematically as:
[tex]\mathbf{ \dfrac{-b \pm\sqrt{b^2 - 4ac}}{2a}}[/tex]
From the given equation:
P = 0.006A² - 0.02A + 120
where;
P = 128128 = 0.006A² - 0.02A + 120
= 0.006A² - 0.02A + 120 - 128
= 0.006A² - 0.02A - 8
where:
a = 0.006 , b = - 0.02, and c = -8[tex]\mathbf{ \dfrac{-(-0.02) \pm\sqrt{(-0.02)^2 - 4(0.006)(-8)}}{2(0.006)}}[/tex]
[tex]\mathbf{ = \dfrac{(0.02) \pm 0.43863}{0.012}}[/tex]
= 38.2195 or -34.8862
Taking the positive integer value, the age of the man whose normal pressure measures 128 mmHg is approximately 38 years.
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For the data that are shown on the graph below, which best describes within which range of x-values extrapolation occurs?
On a graph, points are at (0, 15), (1, 17), (3, 18), (4, 20) and (6, 22).
A) x greater-than 6
B) x less-than 0 and x greater-than 6
C) x less-than 0 and x greater-than 10
D) x greater-than-or-equal-to 0 and x less-than-or-equal-to 6
The range of x-values extrapolation occurs in between x < 0 and x > 6
We have given that,
On a graph, points are at (0, 15), (1, 17), (3, 18), (4, 20) and (6, 22).
What is the range?
The Range is the difference between the lowest and highest values.
Therefore we can conclude that the,
range of x-values extrapolation occurs in between x < 0 and x > 6.
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Find the midpoint of CD.
M = (¹2
X1+X2 Y1+Y2
Y₁+Y2)
2 1
C = (10,-1) and D = (-6,3)
([? ],[ ])
Answer:
Step-by-step explanation:
C=(10,-1)
D=(-6,3)
[tex]mid~point~x=\frac{10+(-6)}{2} =\frac{10-6}{2} =\frac{4}{2} =2\\y=\frac{-1+3}{2} =\frac{2}{2} =1[/tex]
mid point=(2,1)
The midpoint of line segment CD is M = (2, 1).
We have,
To find the midpoint of the line segment CD, we can use the midpoint formula:
M = ((X₁ + X₂)/2, (Y₁ + Y₂)/2)
Given C = (10, -1) and D = (-6, 3), we can substitute the values into the formula:
M = ((10 + (-6))/2, (-1 + 3)/2)
= (4/2, 2/2)
= (2, 1)
Therefore,
The midpoint of line segment CD is M = (2, 1).
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A, B & C form the vertices of a triangle.
CAB = 90°, ABC = 30° and AC = 9.3.
Calculate the length of AB rounded to 3 SF.
The length of AB = 18.6 .
What is a Triangle ?A triangle is a polygon with three sides , angles and vertices.
It is given that ABC is a triangle such that
CAB = 90°
ABC = 30° and
AC = 9.3.
AB = ?
As the triangle is a right angled triangle
Trigonometric ratios can be used.
sin x = Perpendicular / base
sin 30 = AC / AB
(1/2) = 9.3 / AB
AB = 9.3 /0.5
AB = 18.6
Therefore the length of AB = 18.6 .
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If 5 cups of flour are needed to make 40 biscuits how much flour is needed to make 18 cups of the same kind of biscuit express your answer in mixed fraction
Answer:
[tex]2\frac14[/tex]
Step-by-step explanation:
Note: 18 cups of biscuit?
Anyway:
Since 5 cups of flour = 40 biscuits, 1 biscuit = [tex]\frac{1}8[/tex] cups of flour
18 biscuits = [tex]\frac{18}{8}=\frac94=2\frac14[/tex]
HELP ME ANSWER THIS PLEASE
The table does not represent a function.
What is a function?
A function is a relationship that maps elements of the domain into elements of the range. Such that each element of the domain can be mapped into only one element of the range.
Here we have a table.
If you look at the table, you can see that the element of the domain:
x = -18
Is being mapped into two different values in the range.
Into y = -10 and y = 21.
From that, we conclude that this table does not represent a function.
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Solven/6 =24/36, for the unknown quantity,n.
n=192
n=144
n=108
n=4
Answer:
n = 4
Step-by-step explanation:
[tex]\frac{n}{6} =\frac{24}{36}[/tex]
cross multiply
24*6 = 144
n * 36 = 36n
144 = 36n
divide both sides by 36
n = 4
answer is D
n=4
simplify the fraction on the right to get 4/6
n/6 = 4/6
since denominators are same, you can cancel those
therefore, your answer will be n=4
Use a truth table to decide whether each argument is valid or invalid If a person is on this reality show, they must be self-absorbed. Laura is notself-absorbed. Therefore, Laura cannot be on this reality show.
The arguments are valid therefore F F →T
What is a truth table?A truth table is a mathematical table which shows the truth values for a given set of arguments and tells if the argument is valid or invalid.
Analysis:
Argument 1( P)= if a person is on this reality show(true) T
Argument 2(Q) = the person is self absorbed true(T)
Laura is not self absorbed = False(≈Q)
Laura wont be on the reality show = False(≈P)
So she can only be on the reality show if she is self absorbed else she cannot.
so F F → T
Which means that the argument is valid.
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What is the height of a cylinder with a volume of 384 pi cubic inches and a radius of 8 inches? Round to the nearest tenth of an inch.
inches
Answer: 1.9 inches
Step-by-step explanation:
- the equation to find the volume of a cylinder is V = π r^2 h
- so we can just change this equation around to H = V / π r^2
- so H = 384/ π 8^2 = 1.91 or 1.9
hope this helps :)
If $200 is put in the bank and each year the account earns 5% simple interest,
then how much interest will be earned in two years?
$10
$20
$30
$100
Work Shown:
i = P*r*t
i = 200*0.05*2
i = 20
A quick mental shortcut is to double the 5% interest to get 10%, since this occurs over 2 years. Then taking 10% of something is the same as moving the decimal point one spot to the left. So we go from 200 to 20
Question 12 of 21
What is the domain of the exponential function shown below?
f(x) = 5.3x
Answer: All real numbers
Step-by-step explanation:
I assume you meant [tex]y=5.3^x[/tex].
In this case, the domain is the set of real numbers, as is with most standard exponential functions.
Which the most accurate statement about progress monitoring?
a. Progress monitoring is a useful way to ensure children are participating in targeted, purposeful, and meaningful math instruction and allows for the teacher to identify the skills children may need additional support in.
b. Incorporating children's individual differences into lesson planning is not necessary since the curriculum includes all the skills children need to learn in the order they need to learn them.
c. Progress monitoring is about administering formal assessments at the beginning and end of the year.
Answer:
progress monitoring is used to access students academic and social emotional behaviour as EB progress examine rate of improvement and evaluate effectiveness of introduction are invention it is typical use with both individual students and small groups
Which two points are on the graph of y=x - 4?
(4.0), (1, 3)
(0.-4). (4.1)
(1.5), (0, -4)
(1.-3), (-1,-5)
Answer: (1.-3), (-1,-5)
Step-by-step explanation:
Substituting the x coordinates into the equation, we get that the result is equal to the y coordinate of the points.
Thus, the points lie on the line.
Type the correct answer in each box. Use numerals instead of words.
What is the equation of the quadratic function shown in the graph?
The equation of the quadratic function shown in the graph y - 8 = -2(x + 1)².
How to illustrate the graph?The vertex of this parabola is (-1, 8). It opens downward, so the x² term has a negative coefficient. The zeros are (-3, 0) and (1, 0), and the y-intercept is (0, 7).
Through the vertex form of the equation of a parabola we get:
y - (8) = a(x - (-1)) + 7, or.y - 8 = a(x + 1)².
Find coefficient a by substituting the coordinates (-3, 0) in this equation:
0 - 8 = a(-3 + 1)^2, or
-8 = a(-2)² or a = -2
The desired equation is y - 8 = -2(x + 1)^2
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What is the solution, if any, to the inequality |3x|≥0?
all real numbers
A.all real numbers
B.no solution
C.x20
D.x≤0
The inequality is all real numbers.
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
|3x|≥0
3x = 0
Divide both sides of the equation by the coefficient of variable
x= 0/3
x=0 = RHS
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Find an equation of each line given one point and the slope : (4, 8); slope 8
Step-by-step explanation:
in such a case the easiest approach might be using the point-slope form of a line equation :
y - y1 = m(x - x1)
with m being the slope, and (x1, y1) being a point on the line.
so, in our case that would be
y - 8 = 8(x - 4)
simplified this would be
y - 8 = 8x - 32
y = 8x - 24
FYI - this would be then the slope-intercept form (-24 would be the intercept point on the y-axis).
Evaluate 2 p-q when p=17 and q=3.
Final answer:
The value of the expression is 31.
Step-by-step explanation:
Substitution is a process of putting the values of variable in the expression.
Given: p=17 and q=3
To find: value of 2p-q
We will substitute the values and simplify.
Putting the values of variables in the expression as
2p-q = 2x17-3 =34-3 = 31
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[tex]\large\text{Hey there!}[/tex]
[tex]\large\textbf{What does your current question look like?}[/tex]
[tex]\mathsf{2p - q}[/tex]
[tex]\large\textbf{How will we make the question easier to solve?}[/tex]
[tex]\mathsf{2p - q}[/tex]
[tex]\mathsf{= 2(17) - 3}[/tex]
[tex]\mathsf{= 34 - 3}[/tex]
[tex]\mathsf{= 31}[/tex]
[tex]\large\textbf{What is the \boxed{overall} answer?}[/tex]
[tex]\large\boxed{\mathsf{17}}\large\checkmark[/tex]
[tex]\large\text{Good luck on your assignment \& enjoy your day!}[/tex]
Question 4 of 5
Select the correct answer.
On a number line, point A is at -3.4 and point C is at 0.6. Point C divides AB in a ratio such that AC to CB is 4:7. What is the length of
AB?
O
AB = 4.2 units
AB = 11 units
AB= 2.8 units
AB= 7.6 units
Answer:
AB = 11 units
Step-by-step explanation:
a given ratio also tells us how many equally sized units there are in the whole (in this case the line).
the ratio 4:7 tells us therefore, that from the whole line 7 ratii units (of 7+4 = 11 ratio units) are on the side of CB.
4 ratio units (of the 11 ratio units) are on the side of AC.
AC is the distance between A and C.
that is
0.6 - -3.4 = 0.6 + 3.4 = 4 line units
aha ! the distance is 4 units on the number line, and the ratio tells us that AC is 4 ratio units.
so, line unit and ratio units are 1:1 the same.
that means that CB with 7 ratio units is then also 7 line units long.
so, the whole line AB is then 4 + 7 = 11 line units long.
Answer:
11 units
Step-by-step explanation:
correct on plato
Find the value of 5y-3 given that -3y-8=7. Simplify your answer as much as possible. Find the value of 5y - 3 given that -3y - 8 = 7 . Simplify your answer as much as possible .
Answer:
-28
Step-by-step explanation:
Find 5y-3 , given -3y - 8 = 7.
First, we will multiply -3y - 8 = 7 by [tex]-\frac{5}{3}[/tex] to get 5y first.
[tex]-\frac{5}{3} (-3y-8)=-\frac{5}{3} (7)\\5y+\frac{40}{3} =-\frac{35}{3} \\[/tex]
Now we will get the constant on the left side of the equation to 3.
[tex]5y+\frac{40}{3} -\frac{40}{3} =-\frac{35}{3} -\frac{40}{3} \\5y=-25\\5y-3=-25-3\\5y-3=-28[/tex]
The difference of a number and 8 is the same as 38 less the number. Find the number.
System A
−10x−4y=0
−2x+7y=8
System B
−10x−4y=8
−2x+7y=0
1) How can we get System B from System A?
(Choice C, Checked, Correct)
CORRECT (SELECTED)
Swap only the right-hand sides of both equations
2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
CORRECT (SELECTED)
No
For the given systems we have:
1) Swap the right sides of both equations in system A.
2) No, the systems are not equivalent systems.
How can we get System B from System A?
The two systems are:
A:
-10x - 4y = 0
-2x + 7y = 8
B:
-10x - 4y = 8
-2x + 7y = 0
Notice that the only different thing between the systems is that the right sides are inverted. So, if we invert the right side of A, we will get system B.
2) Are the systems equivalent?
No, the systems are not equivalent because to go from system A to system B we only modified the right side of system A, the systems would be equivalent only if modifying both sides of A gave system B, but this is not the case.
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If....................
Answer:
C - 22
Step-by-step explanation:
Put in '3 ' for 'x' in both of the equations....then multiply the results together
f(3) = 3 (3)^2 - 5 = 22
g(3) = -1
22 * -1 = -22
To solve for f(3)g(3):
* We know fg(x) means we need to multiply f with g replacing all x's with the x-value given
Replace all x's with 3Solve for f(3)g(3)[tex](3(3)^{2}-5)(-2(3)+5)\\(3(9)-5)(-6+5)\\22 * -1\\-22[/tex]-22 is the answer
Hope it helps!
how to convert each rate to a unit rate
Answer:
If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.
Step-by-step explanation:
The diameter of a proton is about 1.9 cross times 10 to the power of short dash 15 end exponent meters. A hydrogen atom has an overall length of 100,000 times (or 1 cross times 10 to the power of 5 times) the diameter of a proton.
What is the length of the hydrogen atom, in meters, if it were written in scientific notation?
A. 1.9 x 10 (15 exponent)
B. 1.9 x 10 (-15 exponent)
C. 1.9 x 10 (-8 exponent)
D. 1.9 x 10 (-12 exponent)
Using scientific notation, the measure is given as follows:
[tex]1.9 \times 10^{-10}[/tex]
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
The diameter of a proton, in scientific notation, is given by:
[tex]1.9 \times 10^{-15}[/tex].
The hydrogen atom has an overall length of 100,000 = 10^5 times the diameter of the proton, hence the length is given by:
[tex]L = 100000 \times 1.9 \times 10^{-15} = 10^5 \times 1.9 \times 10^{-15} = 1.9 \times 10^{5 - 15} = 1.9 \times 10^{-10}[/tex]
For the above length, I applied the multiplication of factors with the same base and different exponents, where we keep the base and add the exponents.
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Use the demoivres theorem
The value of the given complex number is -1
De'moivres theorem
Given the polar form of a complex number expressed as:
[tex](cos\theta + isin\theta)^n\\[/tex]
This can also be expressed according to the de moivre's theorem as;
[tex]=(cos\theta + isin\theta)^n\\\\=(cosn\theta+isinn\theta)[/tex]
Given the expression below;
[tex](cos\frac{\pi}{6} + isin\frac{\pi}{6} )^{18}\\(cos18\cdot\frac{\pi}{6} + isin18\cdot\frac{\pi}{6} )\\(cos3\pi + isin3\pi)\\=-1[/tex]
Hence the value of the given complex number is -1
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tommy starts walking from school to home at the same time that his dad starts walking home to school the both depart at 300pm tommy is walking at a speed of 1.35meters pr second and his dad is walking at a speed of 1.65 meters per second. the distance between home and school is 720 meters at what time wil they meet
Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.
Given that:-
Tommy starts walking from school to home at the same time that his dad starts walking home to school they both depart at 300pm Tommy is walking at a speed of 1.35meters per second and his dad is walking at a speed of 1.65 meters per second. the distance between home and school is 720 meters at what time will they meetThe time will be calculated by using the relative speed concept.
Relative speed = Speed of father - Speed of Tommy
Relative speed = 1.65 - 1.35
Relative speed = 0.3 meter per second
Relative speed = Distance / Time
0.3 = 720 / Time
Time = 720 / 0.3
Time = 2400 seconds = 2400/ 60 = 40 minutes
We know that both departed at 3 pm they will meet at 3:40 pm.
Therefore Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.
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Answer:
They will meet at 3:04 p.m
Step-by-step explanation:
Since they are walking toward each other, that means we should add their speed together:
speed = 1.35 m/s + 1.65 m/s
= 3 m/s
Now that we have found the speed, we can calculate the time:
time = 720 meters / 3 m/s
= 240 seconds
= 4 minutes ( 240 seconds is 4 minutes)
What number am I? If you divide me by 8, the quotient is 3.
Answer:
24
Step-by-step explanation:
[tex]8 * \frac{x}{8}=3 * 8[/tex]
x = 24
Answer:
24
Step-by-step explanation:
Let the number we are looking for = [tex]x[/tex].
∴ According to the question:
[tex]x[/tex] ÷ 8 = 3
• Multiply both sides by 8:
[tex]x[/tex] = 8 x 3
[tex]x[/tex] = 24
how many solutions does equation 6x + y = -1 and -6x - 4y =4 have
Answer:
There are no solutions.
Step-by-step explanation:
When you solve for x in the first equation, you get x = (-1-y)/6. Plugging this value for x into the second equation gives you -4y = 4 + y, which has no solutions.
A pizza place has pizzas in 2 different sizes, with 8 different flavors for the crust, and 8 different toppings.
How many one-topping pizzas can be ordered?
Use multiplication:
[tex]2\text{ sizes}*8\text{ flavors}*8\text{ toppings}=\large\boxed{128\text{ pizzas}}[/tex]
This question is basically the same as the other question of yours that I answered, so the explanation is very similar:
You can imagine the possibilities as leaves on a tree. Your tree has 2 large branches to represent the two possible sizes. Each of those branch off into 8 smaller branches, each representing a crust flavor. Each one of the smaller branches has 8 leaves to represent a different topping. Each leaf is a combination of a size, a crust flavor, and a topping, so it represents a complete pizza. Your job is to calculate the number of leaves.
A box contains 240 lumps of sugar. Fie lumps are fitted across the box and the were three layers. How many lumps are fitted along the box?
Answer:
v240
Step-by-step explanation:
What is the length of the unknown leg in the right triangle? a right triangle has a side with length 20 meters, hypotenuse with length 25 meters, and side labeled b.
The length of the unknown leg of the triangle is 15 m.
Length of one leg = 20 m
Length of the hypotenuse= 25m
As it is a right angled triangle we can use pythogoras theorem.
Let the unknown length be y
(20) (20) + y(y) = (25) (25)
400 + y(y) = 625
[tex]y^{2}[/tex]= 225
y = √225
y = 15
The length of the unknown leg is 15 m.
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