To multiply 64 × 8.32 use the logarithm equation 2)㏒64 + ㏒8.32
To answer the question, we need to know what logarithm of a number is
What is the logarithm of a number?The logarithm of a number x is the power to base 10 of that number.
So, logarithm of x to base 10 is written as ㏒x.
Since we want to multiply 64 × 83.2, we convert this to logarithmic equation using the addition rule of logarithm.
Addition rule of logarithm㏒ab = ㏒a + ㏒b
So, 64 × 8.32 to logarithm is ㏒(64 × 8.32) = ㏒64 + ㏒8.32
So, to multiply 64 × 8.32 use the logarithm equation 2)㏒64 + ㏒8.32
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How much would you
have to
deposit today to have an
accumulated amount of
$20,000 in 20 years
if yearly
interest is 4.75% compounded
continuously?
Determine which expressions represent purely real numbers and which expressions represent non-real complex numbers. -i^2+i^3 7-5i √ 6 0+9i √(-5)^2 -12 2 -7i^2
purely real number
non-real complex number
Purely real numbers are in the form of a+0i, while the Non-real complex numbers are in the form of a+bi.
What are Purely real numbers and Non-real complex numbers?Purely real numbers are in the form of a+0i, while the Non-real complex numbers are in the form of a+bi.
The given expressions can be simplified in the following manner,
[tex]-i^2+i^3 = -(\sqrt{-1})^2+(\sqrt{-1} \times \sqrt{-1} \times \sqrt{-1}) = 1 -i[/tex] 7-5i [tex]\sqrt{-6} = \sqrt{-1 \times 6} = \sqrt{-1} \times \sqrt{6} = 0+ i\sqrt{6}[/tex]i⁶ = (i²)³ = (-1)³ = -1 = -1 +0i0+9i [tex](\sqrt{-5})^2 = (\sqrt{-1 \times 5})^2 = -1 \times 5 = -5+0i[/tex] -12 = -12+0i[tex]2 -7i^2 = 2-7(-1) = 2+7 = 9+0i[/tex]Purely real numbers (a+0i)
-1 +0i-5+0i-12+0i9+0iNon-real complex number (0+bi)
1-i7-5i0+i√60+9iLearn more about Purely real numbers and Non-real complex numbers:
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Answer:
Step-by-step explanation:
go to BYJU's learning app and get to expert answer
Dusan says that ∆XYZ ~ ∆TUV because two pairs of angles are congruent. Is he correct? If not, why? Yes, he is correct. No, because two pairs of congruent angles cannot prove similarity. No, because the third angle measure cannot be determined. No, because there is only one set of congruent angles.
Answer:
No, because there is only one set of congruent angles.
Step-by-step explanation:
I took the instruction, and this was the right answer!
Answer:
D
Step-by-step explanation:
Please help me with this math word problem! Please...
Let the price of an adult ticket is x and a child ticket is y .
from the question ,
[tex]6x + 2y = 124 \: \: ...(i) \\ \\ 3x + 5y = 100 \: \: ...(ii)[/tex]
Multiply 2 in eq (ii)
[tex]6x + 10y = 200 \: \: ...(iii)[/tex]
On adding eq (iii) and (i)
[tex]6x + 10y = 200 \\ \\ 6x + 2y = 124[/tex]
we get ,
[tex]8y = 76 \\ \\ y = \frac{76}{8} \\ \\ y = 9.5[/tex]
putting y in eq (i)
[tex]6x + 2y = 124 \\ \\ 6x + 2 \times 9.5 = 124 \\ \\ 6x + 19 = 124 \\ \\ 6x = 124 - 19 \\ \\ 6x = 105 \\ \\ x = \frac{105}{6} \\ \\ x = 17.5[/tex]
The value of x = 17.5 and y = 9.5
Hence , The price of an adult ticket is 17.5 and the price of a child ticket is 9.5 .Questions in the attached file.
The area of the triangle based on the information given will be 4 units square
How to calculate the triangle?It should be noted that the area of a triangle is calculated by using the formula:
= 1/2 × base × height
Therefore, the area of the triangle will be:
= 1/2 × base × height
= 1/2 × 2 × 4
= 4 units²
In conclusion, the area of the triangle given will be 4 units square.
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Flying with the wind, a plane flew 1,200 mi in 4 h. Against the wind, the plane required 6 h to fly the same distance. Find the rate of the plane in calm air and the rate of the wind.
Answer:
Rate of plane = 250 mph
Rate of wind = 50 mph
Step-by-step explanation:
Let the speed of the plane in calm air be x mph& speed of the wind be y mphSpeed of plane with wind = (x + y) mphSpeed of plane against wind = (x - y) mphFormula relating speed, time and distance is given as: speed*time = distanceAccording to the first condition: (x+y)*4 = 1200-> x + y = 300 (1)According to the second condition: (x-y)*6= 1200-> x - y = 200 (2)Adding equations (1) & (2), we find:2x = 500-> x = 250 (Dividing 500 by 2)-> y = 50 (Plugging x = 250 in eq 1)Rate of plane = 250 mphRate of wind = 50 mphI can’t solve this problem
Answer:
f(-2) = -8f(-1) = -5f(0) = 0f(1) = 7Step-by-step explanation:
f(w) = [tex]w^{2}[/tex] + 6w
w = -2f(w) = f(-2) = [tex](-2)^{2}[/tex] + 6*(-2) = 4 - 12 = -8
w = -1f(w) = f(-1) = [tex](-1)^{2}[/tex] + 6*(-1) = 1 - 6 = -5
w = 0f(w) = f(0) = [tex]0^{2}[/tex] + 6*0 = 0 + 0 = 0
w = 1f(w) = f(1) = [tex]1^{2}[/tex] + 6*1 = 1 + 6 = 7
Please help me with this
what is the positive solution of x²-36=5×
Answer:
I'm assuming the x at the end is a variable
9, -4
Step-by-step explanation:
If we replace x with 9, we get 81-36=45 which is 45=45 so 9 is one solution.
If we replace x with -4, we get 16-36=-20 which is -20=20 so -4 is the other solution
So, the solutions are 9 and -4.
Hope this helped you! If there is a mistake in my answer, please tell me and I will correct it as soon as possible.
pls help me with this 10 ponits
Answer:
I believe it is B
Step-by-step explanation:
A triangular pane of glass has a height of 36 inches and an area of 396 square inches. What is the length of the base of the pane?
The length of the base of the pane is blank
inches.
Answer:
see the attachment photo!
Which is the graph of Y=Vx-5-1
Answer:
^^
Step-by-step explanation:
Answer:
Slope: 1
y-intercept: (0, -6)
Choose ALL the numbers that round down when rounding to the nearest hundred! Is it!: 47,035, 3,140, 76,654, 1,298, 607,882, 8,560?
Answer:
The answer is:
the first one
second one
:D
Step-by-step explanation:
in this case, any number in the tens place less than five will make the number round down
round 18.159 to the nearest tenth
Answer:
18.2
Step-by-step explanation:
A tenth is the first decimal, on the right of your unit. 5 to the sky (round up) 4 to the floor (round down)
18.159
To find:The nearest tenth of 18.159
Solution:First value right to the decimal place is tenths place. If the value given in hundredths place is 5 or more round up, if not keep it as it is.
So here the value in hundredths place is 5, so we'll have to add 1 to the tenths place.
18.159
= 18.2 ( nearest tenth )
1. Roll a standard die. Amanda wins if the result is prime or 1. Beto wins
if the result is composite
Answer:
What is the question?
Step-by-step explanation:
prime: 1, 2, 3, 5
composite: 4, 6
Beto has 2/6 = 1/3 chance of winning
Amanda has 4/6 = 2/3 chance of winning
According to the fundamental theorem of algebra, which polynomial function has exactly 6 roots? f (x) = 5 x superscript 4 baseline 10 x squared 2 f (x) = 5 x superscript 5 baseline 3 x superscript 4 baseline 12 x cubed 7 x squared minus 2 x 15 f (x) = 6 x superscript 5 baseline x cubed minus 4 x squared x minus 5 f (x) = 7 x superscript 6 baseline 3 x cubed 12
The polynomial function has exactly 6 roots is f(x) = 7x⁶ + 3x³ + 12. Then the correct option is D.
What is Algebra?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
According to the fundamental theorem of algebra.
The polynomial function has only exactly 6 roots.
The roots are the value of the variables in the polynomial at which the value of the polynomial is zero.
If the degree of the variable is n then the number of the roots will be n or less than n.
If the number of the roots are 6, then the degree of the variable will be 6 in the polynomial.
Then the polynomial function has exactly 6 roots is f(x) = 7x⁶ + 3x³ + 12.
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3 What is the solution to ža>-16? o a O a>-21 a 21 O a
Answer: The answer is the first option: [tex]a > -21\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] × [tex]a > -16[/tex]
[tex]\frac{3}{4}a\cdot \frac{4}{3} > -16\cdot \frac{4}{3}[/tex]
[tex]\frac{3}{4}\cdot \frac{4}{3}a > -16\cdot \frac{4}{3}[/tex]
[tex]a > -16\cdot \frac{4}{3}[/tex]
[tex]a > \frac{-16\cdot 4}{3}[/tex]
[tex]a > \frac{-64}{3}[/tex]
Find the value of x. Round to the nearest 10th.
The area is 34 in²
Answer:
12
Step-by-step eplanation:
Three trends each have a balance of $5,000 on their credit cards with a 25%APR. They've
decided that they will not make any other purchases on the cards until they pay of the debt
and make varying amounts of monthly paymentes
• Sharon can only make the credit card minimum payment, $150 per month
• Ceollia can set aside $400 per month to pay back her dett
• Alexander can pay $800 per month for his credit card
After 5 months, how much will each person have paid in interest so far and how large will
their remaining balance be? Use the formulas below to calculate their interest and balance
for each month
Hint Credit card interest is typically compounded daily so n=365Time here is in years, so
make sure you use a fraction for your t value. Need to show monthly interest and balance paid monthly for first 5 months on each person.
here i hope this exaple helps but for the time being while i solve it heres this example
if you currently owe $500 on your credit card throughout the month and your current APR is 17.99%, you can calculate your monthly interest rate by dividing the 17.99% by 12, which is approximately 1.49%. Then multiply $500 x 0.0149 for an amount of $7.45 each month.
Let f(x) = x² + 4x - 6 and g(x) = x + 2, find (f • g)(x).
Answer:
(f.g)(x) = (f×g)(x)
= (x² + 4x - 6) × ( x + 2)
= x^3 + 2x^2 + 4x^2 + 8x - 6x - 12
= x^3 + 6x^2 + 2x -12
Complete the Proof Statements Reasons 1. ABCD is a given AC BD 2. AD BC 3. 4. AABC=ABAD 5 ZDAB=LCBA 6. 7. ABCD is a rectangle 1. 2. 3. 4. 5. 6. 7. Congruent supp. angles are right angles 8. Given: ABCD is a parallelogram AC = BD Prove: ABCD is a rectangle SSS Triangle Congruence Theorem mZDAB = 90° m/CBA = 90° Reflexive Property of Congruence ZDAB and ZCBA are supplementary Definition of Rectangle O B CPCTC If the quad is a both pairs of opposite sides are congruent Consecutive angles in a are supplementary AB = AB
1) ABCD is a parallelogram, [tex]\overline{AC} \cong \overline{BD}[/tex] (given)
2) [tex]\overline{AD} \cong \overline{BC}[/tex] (if the quadrilateral is a parallelogram, both pairs of opposite sides are congruent)
3) [tex]\overline{AB} \cong \overline{AB}[/tex] (reflexive property of congruence)
4) [tex]\triangle ABC \cong \triangle BAD[/tex] (SSS Triangle Congruence Theorem)
5) [tex]\angle DAB \cong \angle CBA[/tex] (CPCTC)
6) [tex]\angle DAB[/tex] and [tex]\angle CBA[/tex] are supplementary (consecutive angles in a parallelogram are supplementary)
7) [tex]m\angle DAB=90^{\circ}, m\angle CBA=90^{\circ}[/tex] (congruent supplementary angles are right angles)
8) [tex]ABCD[/tex] is a rectangle (definition of rectangle)
All the missing statements with the respective reasons are given below.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Statement 1.
ABCD is a parallelogram,
AC ≅ BD
Reason: Given.
Statement 2.
AD ≅ BC
Reason: if the quadrilateral is a parallelogram, both pairs of opposite sides are congruent.
Statement 3. AB ≅ AB
Reason: reflexive property of congruence.
Statement 4. ΔABC ≅ ΔBAD.
Reason: SSS Triangle Congruence Theorem
Statement 5. ∠DAB ≅ ∠CBA
Reason: CPCTC
Statement 6. ∠DAB and ∠CBA are supplementary
Reason: consecutive angles in a parallelogram are supplementary.
Statement 7. m∠DAB = 90° and m∠CBA = 90°
Reason: congruent supplementary angles are right angles.
Statement 8. ABCD is a rectangle.
Reason: definition of a rectangle.
Therefore, all the required points are given above.
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Which equation can we use to find the length of the side labeled x?
Answer:
(D) sIn(30°) = 5/x
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between sides and trig functions for a right triangle. Here, the hypotenuse and the side opposite the angle are marked. The relevant relationship is ...
Sin = Opposite/Hypotenuse
Filling in figure values, we have ...
sIn(30°) = 5/x
comparing -4 to -5 integers
what they have in common is that there both Intergers but What's different is that there -1 off
Find the distance between points (3,6) and (9,2)
Answer:
A=(3,6)
B =(9,2)
The distance between AB=√(9-3)^2+(2-6)^2
=3√13
Below is a right cone with a radius of 3 cm and a slant height of 7.6 cm. Find both the volume and surface area of the cone. Round
everything to the nearest hundredth. Use 3.14 for .
Note: The slant height is different than the actual height of the cone.
Answer:
Surface Area: 99.852
Volume: 71.592
What is the distance between the following points?
Answer:
7.615773105864
Step-by-step explanation:
[tex]\text{let A and B be the points of coordinates} \ A\left( 3,-9\right) \text{and} \ B\left( 6,-2\right)[/tex]
[tex]AB=\sqrt{\left( 6-3\right)^{2} +\left( -2-(-9)\right)^{2} }[/tex]
[tex]=\sqrt{\left( 3\right)^{2} +\left( 7\right)^{2} }[/tex]
[tex]=\sqrt{58} =7.615773105864[/tex]
Write the quadratic equation whose roots are 2 and 3, and whose leading coefficient is 3. (Use the letter x to represent the variable.)
The quadratic equation whose roots are 2 and 3, and whose leading coefficient is 3 will be 3x² - 15x + 18 = 0.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have
Then the quadratic equation whose roots are 2 and 3, and whose leading coefficient is 3.
Then the factor or the quadratic equation will be
(x - 2) and (x - 3)
Then the equation will be
3(x - 2)(x - 3) = 0
3(x² -2x -3x + 6) = 0
3(x² - 5x + 6) = 0
3x² - 15x + 18 = 0
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Ryder found the volume of the figure below by using the steps shown. A rectangular prism with a length of 40 millimeters, width of 30 millimeters, and height of 5 millimeters. A rectangular pyramid with a base of 30 millimeters by 40 millimeters and a height of 95 millimeters. Total Volume = B h + one-half B h Equals 5 (40) (3) + one-half (40) (30) (95) Equals 6,000 + 57,000 Equals 63,000 cubic millimeters What mistake, if any, did Ryder make? Ryder determined the volume correctly. Ryder used the wrong formula for the total volume. Ryder used the wrong height for the pyramid. Ryder did not apply the order of operations correctly.
Answer:
B. Rider used the wrong formula for the total volume.
Step-by-step explanation:
I did the quiz
Answer: B
Step-by-step explanation: I did the quiz, sis, trust me.
Given that 5 cos (x+8.5)° - 1 = 0
0° ≤x≤ 90, calculate correct to the nearest degree, the value of x.
Answer:
x = 70
Step-by-step explanation:
To solve for x, use inverse operations to undo the operations performed on x.
__
5cos(x +8.5)° -1 = 0 . . . . given
5cos(x +8.5)° = 1 . . . . . . add 1
cos(x +8.5)° = 1/5 . . . . . divide by 5
x° +8.5° = arccos(1/5) . . . . take the inverse cosine
x° = arccos(1/5) -8.5° ≈ 70° . . . . evaluate the expression
The value of x is 70.
"solve for the following trig ratios using the unit circle":
1. tan(1755 degrees)
i have no idea how to do this. like do i use estimation orrrr.???
=========================================================
Explanation:
The goal is to get that 1755 degree angle between 0 and 360, so we can refer to the unit circle later.
Subtract off 360 from this until we get to that target
1755 - 360 = 13951395 - 360 = 10351035 - 360 = 675675 - 360 = 315Or a shortcut could be
1755 - 4*360 = 315The angles of 1755 degrees and 315 degrees are coterminal. They point in the same exact direction which is directly southeast in quadrant IV.
Now use the unit circle (see below) to find that
sin(315) = -sqrt(2)/2cos(315) = sqrt(2)/2Dividing those two items and simplifying gets us
tan(315) = sin(315)/cos(315) = -1
Then we go from tan(315) = -1 to tan(1755) = -1