[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{1}y^2\stackrel{\stackrel{b}{\downarrow }}{-7}y\stackrel{\stackrel{c}{\downarrow }}{-9}=0 \qquad \qquad y= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ y= \cfrac{ - (-7) \pm \sqrt { (-7)^2 -4(1)(-9)}}{2(1)} \implies y = \cfrac{ 7 \pm \sqrt { 49 +36}}{ 2 } \\\\\\ y= \cfrac{ 7 \pm \sqrt { 85 }}{ 2 }\implies y= \begin{cases} \frac{ 7 + \sqrt { 85 }}{ 2 }\\[1em] \frac{ 7 - \sqrt { 85 }}{ 2 } \end{cases}[/tex]
is 4/5 equivalent to 16/20
Answer:
yes
Step-by-step explanation:
you have to divide by the top and bottom to get the answer to the lowest number
Answer:
yes
Step-by-step explanation:
Check by changing to a common denominator
Identify a pattern in each list of numbers. Then use this pattern to find the next number.
5, 12, 33, 96, 285, ___
=====================================================
Explanation:
The given sequence is 5, 12, 33, 96, 285, ...
The jump from 5 to 12 is +7The jump from 12 to 33 is +21The jump from 33 to 96 is +63The jump from 96 to 285 is +189The sequence of increases is: 7, 21, 63, 189
Then notice,
The jump from 7 to 21 is "times 3"The jump from 21 to 63 is also "times 3"The jump from 63 to 189 is also "times 3".Assuming this pattern keeps up, the next increment will be 189*3 = 567
We add this increment to the last term of the original sequence
285+567 = 852
The sequence is now 5, 12, 33, 96, 285, 852, ...
Perform the indicated operation
7 1/8 ∙ 5 2/3
Evaluate h(r) given that h(t) = 6 - 18t. h(r) =
This problem is related to the formation of a function. We need to know how an function is formed. Here it is given that there is a function which is affected by the value of t. Which means the value of t in the function decides the value of that function.
Similarly we have to write the function as the variable r so that the value of function is related to the value of r.
h(r)=6-18r ; where 6 is the constant and 18r is the variable in the function.
Hence, the required function is h(r)=6-18r.
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one cubic foot holds 7.48 gallons of water and one gallon of water 8.33 pounds. How much does 5.1 cubic ft of water weigh in pounds? In tons?
The 5.1 cubic ft of water weighs 317.77 pounds
The weight of 5.1 cubic ft of water in tons is 0.16 tons
Calculating weightFrom the question, we are to calculate how much 5.1 cubic ft of water weigh in pounds
From the given information,
"one cubic foot holds 7.48 gallons of water"
Therefore,
5.1 cubic ft of water = 5.1 × 7.48 gallons of water
= 38.148 gallons of water
Also,
"one gallon of water 8.33 pounds"
That is,
38.148 gallons of water = 38.148 × 8.33 pounds
= 317.77 pounds
Thus, 5.1 cubic ft of water weigh 317.77 pounds
For the weight in tons
NOTE: 1 pounds = 0.0005 tons
∴ 317.77 pounds = 0.0005 × 317.77 tons
= 0.158886 tons
≈ 0.16 tons
Hence, the weight of 5.1 cubic ft of water in tons is 0.16 tons
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refer to the number line. find the coordinate of point C that is 7/8 of the distance from m to j. m = 2 , j=18
The coordinate of point C that is 7/8 of the distance is 14
How to find the coordinate of point C that is 7/8 of the distance?The given parameters are
C =7/8 from m to j
While the points are
M = 2
J = 18
The coordinate of point C that is 7/8 of the distance is calculated as
C = 7/8 * (J - M)
This gives
C = 7/8 * (18 - 2)
Evaluate
C = 14
Hence, the coordinate of point C that is 7/8 of the distance is 14
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According to the bar chart, Alphabet's revenue in 2011 was 37,905 million dollars. Write Alphabet's 2011
revenue in ordinary notation.
thirty-seven billion nine hundred five million
Answer:
hskekndndndokn jskjskiwijsnjskjskiwijsn kkskskskjd kdkdkdndndn
Step-by-step explanation:
There are 2 triangles and 8 circles. What is the simplest ratio of triangles to total shapes?
Answer:
1 : 5
Step-by-step explanation:
Circles + Triangles = Total shapes
8 + 2 = 10
Number of triangles : Total shapes
2 : 10
Both can be divided(simplified) by 2
= 1 : 5
Hope this helped! ^^
Please list the intercepts I need help!
Answer:
{(5,1),(5,0),(1,0),(0,-3),(-3,0),(-4,-3),(2,5)}
Step-by-step explanation:
This is all I could get from the cropped out picture of the graph
Lucia walked of the length of the Tremont Trail before
stopping for a rest. How far had Lucía walked on the trail?
Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail
We are told in the question that
Linda walked 3/4 of the length of the Tremont Trail before stopping for a rest.
From the question, the length of the Tremont Trail = 3 1/2 miles
Hence, the distance (how far )Linda has walked =
3/4 of 3 1/2 miles
= 3/4 × 3 1/2 miles
= 3/4 × 7/2 miles
= 21/8 miles
= 2 5/8 miles or 2.625 miles
Therefore, Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail.
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Amelia went on a walk that was miles long. She stopped to have lunch
15
4
when she had walked of the way.
12
25
How far, in miles, did Amelia walk before lunch?
Give your answer as a fraction in its simplest form.
4
Amelia went on a walk that was, She stopped to have lunch [tex]\frac{15}{4}[/tex] miles
when she had walked of the way [tex]\frac{12}{25}[/tex] miles. Amelia walk before lunch in
[tex]\frac{3}{25}[/tex] miles.
What do you mean by miles?The mile is a customary unit of measurement in the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is often referred to as the international mile or statute mile to distinguish it from other miles. In 1959, the statute mile was formally redefined with respect to SI units as precisely 1,609.344 meters. This resulted in a standardization of the statute mile between the British Commonwealth and the United States.
The unqualified term "mile" is typically understood to refer to the current international mile. The international mile may also be referred to as a land mile or a statute mile when it has to be distinguished from nautical mile.
The term "statute mile" in British English can apply to either the current international mile or any other variation of the English mile since the 1593 Act of Parliament, which established it as 1,760 yards. However, in American law, a statute mile is equivalent to a US survey mile. If it is obvious from the context, as in a discussion of the 2nd-century Antonine Itinerary that the distances are described in terms of miles rather than Roman miles, the qualifier to describe the type of mile being used may be omitted. Foreign and historical units that are translated into English as miles typically employ a qualifier to describe the kind of mile being used.
Now from the above given question:
She stopped to have lunch in [tex]\frac{15}{4}[/tex] miles
She had walked of the way in [tex]\frac{12}{25}[/tex] miles
[tex]\frac{15}{4}-\frac{12}{25} = \frac{60}{100}- \frac{48}{100} = \frac{12}{100}[/tex][tex]=\frac{3}{25}[/tex].
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Find f(a + 7).
f(x) = x² + 5
hi
f(a+7)
f(x) =x²+5
by remplacing X by (a+7) :
then f(a+7) = (a+7)²+5
= a² +2*a*7 +49 +5
= a² +14a +54
If it is given that m ∠ J K L = m ∠ X Y Z and m ∠ X Y Z = m ∠ Q R S , then concluding that m ∠ J K L = m ∠ Q R S is an example of:
Concluding that m∠ J K L = m ∠ Q R S is an example of: substitution property of equality
What is Substitution Property of Equality?The substitution property of equality states that 'If a variable x is equal to another variable y, then x can be substituted in place of y in any equation/expression and y can be substituted in place of x in any equation/expression.
Now, we are told that m ∠ J K L = m ∠ X Y Z and m ∠ X Y Z = m ∠ Q R S.
Thus, concluding that m ∠ J K L = m ∠ Q R S is an example of: substitution property of equality
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maths geometry
i just need 4)
i’ve worked everything else out
Step-by-step explanation:
good job then !
the first thing I see in the graphic is that
BG is half of BD (as a major definition of diagonals in a parallelogram).
BD on the other hand is the Hypotenuse (the side opposite of the 90° angle at A) of the triangle ABD.
to be able to use Pythagoras to get BD, I need to find the length of AB.
this I get from the triangle ABE. this is also a right-angled triangle. AE = 4cm. the angle B1 = 50°. the angle A = 90°.
so, the angle E1 = 180 - 90 - 50 = 40° (remember, the sum of all angles in a triangle is always 180°).
now we use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with a, b, c being the sides of the triangle, and A, B, C being the corresponding opposite angles.
so, we have here
AE / sin(50) = AB / sin(40)
4 / sin(50) = AB / sin(40)
AB = 4×sin(40) / sin(50) = 3.356398525... cm
so (Pythagoras),
BD² = AB² + AD² = 3.356398525...² + 9² =
= 11.26541106... + 81 = 92.26541106...
BD = 9.60548859... cm
BG = BD/2 = 4.802744295... cm
and now look at that.
because of the fact that I did not have to go through the other points, I chose the first approach that went through my mind.
and it showed that your teacher created an impossible (contradicting) scenario :
the angle of B1 does not fit to the ratios of the various line segments.
as you correctly calculated CD as 3 cm, that must mean that AB is also 3 cm.
that makes
BD² = 9² + 3² = 81 + 9 = 90
BD = 9.486832981... cm
BG = BD/2 = 4.74341649... cm
PLEASE, USE THIS VALUE.
there is a difference to my previous calculation. and the reason for this is : the 50° for B1 are not correct.
with AE = 4, AB = 3 and then BE = 5, we get
AE / sin(B1) = BE / sin(A)
4 / sin(B1) = 5 / sin(90) = 5
sin(B1) = 4/5 = 0.8
B1 = 53.13010235...°
and not 50° !!!!
The number of students at Jefferson School is even.
The number has three digits.
The digit in the tens place is 4.
Write three numbers that could be how many students
there are at Jefferson School.
school
There are a total of 36 possible answers in digit .
What is digits in math?
A digit is a part of a set that, when taken as a whole, makes up a numeration system. A digit is a number in that particular circumstance. The members of the set 0 through 9 make up the digits of the decimal (base-10) Arabic numbering system.Let's assign three blanks for each digit of the unknown number. But let's fill in the tens digit because it is already specified.
_ 4 _
The last digit should be even to make it even. The possible digits for this are 2, 4, 6, and 8. The first digit could be any digit from 1 to 9. Therefore, the possible answers are
142 242 342 442 542 642 742 842 942
144 244 344 444 544 644 744 844 944
146 246 346 446 546 646 746 846 946
148 248 348 448 548 648 748 848 948
Therefore, there are a total of 36 possible answers.
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Given: Triangle ABC
Prove: mA = 64°
A
(4x)
B
(90)
C
(x+10)
For the given triangle ABC, the value of angle A = 64°.
What is defined as the triangle?A triangle is a two-dimensional closed shape. It has three sides and is a polygon. Straight lines make up all of the sides. The vertex is the intersection of two straight lines. As a result, the triangle does have three vertices. Each vertex creates an angle.A triangle is made up of three angles. These angles are made up of two triangle sides meeting at a main point recognized as the vertex. The total of all 3 interior angles is 180 degrees.For the given ΔABC;
∠A = 4x
∠B = 90
∠C = x + 10
By the sum of angles of triangle property;
∠A + ∠B +∠C = 180
Substitute the values;
4x + 90 + x + 10 = 180
Simplifying the equation;
5x = 180 - 100
5x = 80
x = 16
Put the value of x in angle A.
∠A = 4x
∠A = 4×16
∠A = 64°
Therefore, the value of angle A is found as 64°.
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In a room, 9 students have glasses on, while 15 do not. Give the percentage of students wearing glasses. (Round to the nearest tenth of a percent)
Work Shown:
9+15 = 24 students total
9 have glasses, so 9/24 = 0.375 = 37.5% of the class wears glasses.
Whats 21 - 20 x 2? (Hint: the most used number and the last number)
Answer:
-19Step-by-step explanation:
Whats 21 - 20 x 2?
remember PEMDAS21 - 20 x 2 =
21 - 40 =
-19
26. Julie says that sin A/cos A = tan A and sin B / cos B = tan B. Use the triangle shown to prove
Julie's statements true or false. Make sure you enter your work
-confused as to what this even means.
Julie is correct because:
[tex]\frac{\sin A}{\tan A}=\frac{a/c}{b/c}=a/b=\tan A \\ \\ \frac{\sin B}{\cos B}=\frac{b/c}{a/c}=b/a =\tan B[/tex]
The product of a number x and 0.28 is 13.44 which equation matches this statement
Answer:
x · 0.28 = 13.44
Equation: X multiplied by 0.28 = 13.44.
How to solve: Divide 13.44 ÷ 0.28 = 48.
Multiply to check. 48 x 0.28 = 13.44.
Give me a crown.
Use inductive reasoning to predict the next line in this sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct.
9*9+7=88
98*9+6=888
987*9+5=8888
9876*9+4=88888
Make a conjecture by predicting the correct numbers in the line below.
blank * 9 +3 =
The number predicted is 98765 and using calculator gives 888888 which confirms it is correct.
Given data
9*9+7=88
98*9+6=888
987*9+5=8888
9876*9+4=88888
How to predict the correct numbersUsing inductive reasoning and the given data as the premise we can see that the number multiplying 9 is gotten by adding a new digit which is a lesser digit of the preceding number while counting backwards.
Using the last operation as instance we have that
9876*9+4=88888
the last digit that joined is 6, and this number is the next digit after 7 while counting backwards. Also the number 4 added is the next after 5 while counting backwards.
so we can predict the next row by counting backwards in the two occasions as follows:
counting backwards after 6 is 5 therefore we have 98765
counting backwards after 4 is 3 therefore we have 3
arranging the numbers into row gives
98765 * 9 + 3
adding with a calculator gives
98765 * 9 + 3 = 888888
The number predicted is 98765
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Rewrite -4/15 as an equivalent fraction
[tex](\frac{-4}{5} )[/tex] in the form of Equivalent Fraction can be written as [tex]\frac{-4x}{15x}[/tex], where "x" is any integer.
As per the question statement, we are provided with a fraction, [tex](\frac{-4}{5} )[/tex].
We are required to rewrite the above mentioned fraction in the form of a general Equivalent Fraction.
To solve this question, we need to know what an equivalent fraction is.
Equivalent fractions are those fractions that have different numerators and denominators but are equal to the same value, when simplified.
For example, [tex](\frac{1}{2}, \frac{2}{4}, \frac{3}{6}, \frac{4}{8})[/tex] all equate to [tex]\frac{1}{2}[/tex] when simplified.
Now, for this case, equivalent fractions of [tex](\frac{-4}{5} )[/tex] are [tex](\frac{-8}{30}, \frac{-12}{45}, \frac{-16}{60},...)[/tex], where
[tex]\frac{-8}{30}=\frac{(-4)*2}{15*2}\\\frac{-12}{45}=\frac{(-4)*3}{15*3}\\ \frac{-16}{60}=\frac{(-4)*4}{15*4}[/tex]
i.e., the equivalent fractions of [tex](\frac{-4}{5} )[/tex] are in the form of [tex]\frac{-4x}{15x}[/tex], where "x" can be any integer, (...-6, -5, -4, -3, -2, -1, 2, 3, 4, 5, 6...)
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April wants to borrow $200 from her father and is willing to pay $9 in Interest. Her father wants to charge an interest rate of 6%. How long can April keep the money?
Answer:
principle (p)= $200
interest (I) =$9
Rate (R) = 6%
time (T)= ?
we know,
Time(T) = I×100÷P×R
= 9×100÷ 200×6
= 3÷4 years
Pls Help me please!!
Simplify 2.67 + (−8.9).
Answer:
-6.23 is the answer
HOPE IT'S HELPS YOUAnswer:
-6.23
Step-by-step explanation:
The solution will be,
→ 2.67 + (−8.9)
→ 2.67 - 8.9
→ -6.23
So, the answer is -6.23.
Solve for x in the inequality 2|x + 1| < 8
After solving the inequality we get the value of x as x ∈ (₋5,3)
Given the inequality is 2 |x + 1| < 8
Divide both sides of the inequality by the coefficient of variable.
|x + 1| < 8/2
Reduce the fraction
|x + 1| < 4
Now convert the absolute inequality to standard inequality.
₋4 < x₊1 < 4
separate compound inequalities into system of inequalities.
x ₊ 1 > ₋4 (1)
x ₊ 1 < 4 (2)
for (1) x ₊ 1 > ₋4
rearrange variables to the left side of the equation.
x > ₋4 ₋1
calculate the sum.
x > ₋5
for (2) x ₊ 1 < 4 (2)
rearrange the terms.
x < 4 ₋ 1
x < 3
therefore ₋5 < x < 3
Hence we get the value ranging from (₋5 , 3)
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Consider the following sequence. -5,5,15,25,35. Write an explicit formula for the sequence.
This sequence's explicit formula is [tex]a_n=-5+(n-1)*10[/tex]
What is a sequence?
A sequence is indeed an acknowledged group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has individuals. The length of the series is the number of components (potentially infinite).The convergence features of sequences can be used to analyze functions, spaces, as well as other mathematical structures in a variety of mathematical fields. In particular, sequences serve as the foundation for series, which are crucial to analysis and differential equations.The common distinction is equal to:
10
The sequence's total is equal to:
40
This sequence's explicit formula is:
[tex]a_n=-5+(n-1)*10[/tex]
This sequence's recursive formula is:
[tex]a_n=a_((n-1))+10[/tex]
Next terms:
-5,5,15,25,35,45,55,65,75,85,95...
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Convert the following temperatures from Fahrenheit to Celsius or vice versa.
C= F-32/1.8
F = 1.8C+32
a. 50°F
b. 75°C
c. -40°C
Answer:
10°C
Step-by-step explanation:
c = [tex]\frac{F - 32}{1.8}[/tex] Plug in 50 for F and solve for C
c = [tex]\frac{50-32}{1.8}[/tex]
C = [tex]\frac{18}{1.8}[/tex] Divide
c = 10
What is the factored form of x2−9
Answer:
(x+3)(x-3)
Step-by-step explanation:
When factoring x^2-9 you'd look for square multiples of -9.
Because 3×3 is 9, 3 is your square. You can't just use (x+3) because your outcome is a -9. Which is why your answer would be (x+3)(x-3)
(100 points!) What is the slope-intercept form for the following equation?
x + 5y = 12
Questions:
x= 5y + 12
y= -1/5x + 12/5
x + 5y = 12x
5y= −x + 12
Answer:
the slope intercept form is 5y= -x+12