the right answer is 44.
Answer:
44 degrees.
Step-by-step explanation:
We are asked to find the measure of angle Q using law of cosines.
Law of cosines:
[tex]c^2=a^2+b^2-2ab\times cos(C)[/tex]
Upon substituting our given values in above formula we will get,
[tex]24^2=20^2+34^2-2\times 20\times 34\times cos(Q)[/tex]
[tex]576=400+1156-1360\times cos(Q)[/tex]
[tex]576=1556-1360\times cos(Q)[/tex]
[tex]576-1556=1556-1556-1360\times cos(Q)[/tex]
[tex]-980=-1360\times cos(Q[/tex]
Upon dividing both sides of our equation by -1360 we will get,
[tex]\frac{-980}{-1360}=\frac{-1360\times cos(Q}{-1360}[/tex]
[tex]0.7205882352941176=cos(Q)[/tex]
Now we will use arccos to solve for the measure of angle Q.
[tex]cos^{-1}(0.7205882352941176)=Q[/tex]
[tex]43.896932391182=Q[/tex]
[tex]Q\approx 44[/tex]
Therefore, the measure of angle Q is 44 degrees.
Which are the solutions of x2 = –13x – 4? 0, 13 0, –13
Answer:
Option 3 and 4 - 0,-13
Step-by-step explanation:
Given : Expression [tex]x^2=-13x-4[/tex]
To find : What are the solutions?
Solution :
The quadratic formula of the quadratic equation [tex]ax^2+bx+c=0[/tex] is
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Comparing with general equation, [tex]x^2+13x+4=0[/tex]
where, a=1 ,b=13, c=4
Substitute in the formula,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-13\pm\sqrt{13^2-4(1)(4)}}{2(1)}[/tex]
[tex]x=\frac{-13\pm\sqrt{169-16}}{2}[/tex]
[tex]x=\frac{-13\pm\sqrt{153}}{2}[/tex]
[tex]x=\frac{-13+\sqrt{153}}{2},\frac{-13-\sqrt{153}}{2}[/tex]
The value of x is [tex]x=-0.315,-12.68[/tex]
Approximately the solution of the expression is x=0,-13.
EASSSSSSSSSSSSSSSSSSY
A salad recipe calls for 1 3/4 cups of chopped tomatoes. The recipe calls for 4 1/7 times as many cups of lettuce as tomatoes. How many cups of lettuce do you need for this recipe?
4 1/7 cups
4 3/28 cups
7 1/4 cups
7 1/7 cups
The opening balance of one of the 31-day billing cycles for Lorenzo's credit card was $4100, but after 15 days Lorenzo made a payment of $2300 to decrease his balance, and it stayed the same for the remainder of the billing cycle. If his credit card's APR is 24%, how much more in interest would he pay for the billing cycle with the previous balance method than with the adjusted balance method? A.$83.57
B.$46.88
C.$36.69
D.$120.26
Solution:
Adjusted Balance method
Amount in Lorenzo credit card in the beginning of month= $ 4100
Payment made = $ 2300
Amount in Lorenzo credit card after 15 days = $ 4100 -$ 2300= $ 1800
APR= 24 %
Monthly APR = [tex]\frac{24\times 31}{365}=2.038[/tex]%
2.03% of 1800=$ 36.54
Previous Balance method:
Amount possessed at the beginning of the month= $ 4100
APR= 24 %
Monthly APR = [tex]\frac{24\times 31}{365}=2.038[/tex]%
2.038% of 4100=$ 83.23
The interest that Lorenzo would pay for the billing cycle with the previous balance method than with the adjusted balance method
= $ 83.23 - $ 36.54
= $ 46.69→→ option (B)
Find the average rate of change for the given function from x = −1 to x = 2.
Graph of f of x equals negative three x plus 2
Answer:
Average rate of change: [tex]-3[/tex]
Step-by-step explanation:
We are asked to find average rate of change for our given function [tex]f(x)=-3x+2[/tex].
We will use average rate of change formula to solve our given problem.
[tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]
Upon substituting our given values in above formula, we will get:
[tex]\text{Average rate of change}=\frac{f(2)-f(-1)}{2-(-1)}[/tex]
[tex]\text{Average rate of change}=\frac{(-3(2)+2)-(-3(-1)+2)}{2-(-1)}[/tex]
[tex]\text{Average rate of change}=\frac{(-6+2)-(3+2)}{2+1}[/tex]
[tex]\text{Average rate of change}=\frac{(-4)-(5)}{3}[/tex]
[tex]\text{Average rate of change}=\frac{-4-5}{3}[/tex]
[tex]\text{Average rate of change}=\frac{-9}{3}[/tex]
[tex]\text{Average rate of change}=-3[/tex]
Therefore, the average rate of change for our given function from [tex]x=-1[/tex] to [tex]x=2[/tex] is [tex]-3[/tex].
The area of circle z is 64 pi ft^2
What is the value of r?
we know that
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
where
r is the radius of the circle
In this problem we have
[tex]A=64\pi \ ft^{2}[/tex]
substitute in the formula and solve for r
[tex]64\pi=\pi r^{2}[/tex]
Simplify
[tex]64=r^{2}[/tex]
Square root both sides
[tex]r=8\ ft[/tex]
therefore
the answer is
The value of r is [tex]8\ ft[/tex]
Find the measure of z.
Which type of light is most likely to cause burns?why?
Simplify
2x x y x 3
To simplify 2x * y * 3, multiply the coefficients (2 and 3) and the variables (x and y) separately, resulting in the simplified expression 6xy.
Explanation:To simplify the expression 2x * y * 3, we can multiply the coefficients and the variables separately. The coefficients are 2 and 3, so their product is 2 * 3 = 6. The variables are x and y, so their product is xy. Putting it all together, the simplified expression is 6xy.
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Solve for x: 14 = 0.1x 14 140 1.4 .14
The value of x that satisfies the equation 14 = 0.1x is 140.
Explanation:To solve the equation 14 = 0.1x, we can start by dividing both sides of the equation by 0.1 to isolate x. This gives us 14/0.1 = x, which simplifies to 140 = x. So, the value of x that satisfies the equation is 140.
What is the answer to the question above? I need help with it.
Determine which equations below, when combined with the equation 3x minus 4y equals 2, will form a system with no solutions. choose all that apply.
Find the value of x in the triangle shown below
How do I do this?
Find the inverse function for
\(\large\bf{f(x)= \sqrt{2x-6}}\)
I found that it was
\(\large\bf{\color{Red}{y=\frac{1}{2}x^{2} + 3}}\)
but I am to restrict the function would it be \(\bf{x \ge 0}\)?
what translation rule can be used to describe the result of the composition of (x,y) --> (x - 9,y - 2) and (x,y) --> (x + 1, y - 2) ? PLEASE HELPPPPP!!!!!
we know that
the rule of the translation A is
[tex](x,y)-----> (x-9,y-2)[/tex]
that means
the translation is [tex]9[/tex] units to the left and [tex]2[/tex] units down
the rule of the translation B is
[tex](x,y)-----> (x+1,y-2)[/tex]
that means
the translation is [tex]1[/tex] unit to the right and [tex]2[/tex] units down
therefore
the rule of the composition A+B is
[tex](x,y)-----> (x-9+1,y-2-2)[/tex]
[tex](x,y)-----> (x-8,y-4)[/tex]
that means
the translation is [tex]8[/tex] units to the left and [tex]4[/tex] units down
so
the answer is
[tex](x,y)-----> (x-8,y-4)[/tex]
The translation rule that describes the result of the composition of the transformations (x, y) --> (x - 9, y - 2) and (x, y) --> (x + 1, y - 2) is (x, y) --> (x - 8, y - 4). This rule is obtained by sequentially applying each transformation to (x, y).
Explanation:When we talk about compositions of translations in geometry, what we are doing is carrying out one translation after the other. So, if we have two translations: (x, y) --> (x - 9, y - 2) and (x, y) --> (x + 1, y - 2), we perform these operations sequentially.
First, we apply the transformation (x,y) --> (x - 9, y - 2). Then we take these new coordinates and apply the second transformation (x,y) --> (x + 1, y - 2). The result of this composition is (x - 9 + 1, y - 2 - 2) = (x - 8, y - 4), as you add (or subtract) the changes introduced by each translation.
So, the translation rule that can be used to describe the result of the composition of these transformations is: (x, y) --> (x - 8, y - 4).
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Make t the subject of the formula 2(t-5) = y
Add.
(2x + 5) + (3x - 7)
A) x - 2
B) x + 2
C) 5x - 2
D) 5x + 2
Answer:
C) 5x - 2
Step-by-step explanation:
When parentheses are preceded by a + sign, they may be immediately removed. Two additions and one subtraction are called for here: 2x + 5 + 3x - 7. This is 5x - 2.
(2x + 5) + (3x - 7)
2x + 5 + 3x - 7
2x + 3x - 7 + 5
5x - 2.
Hope this helps!!!
1. Which statement about subatomic particles is not true?
Protons and electrons have opposite charges.
Neutrons have no electrical charge.
Protons and neutrons have the same charge.
Protons and neutrons have nearly the same mass.
2.
Which term describes the sum of the number of protons and neutrons in an atom?
mass number
nuclear charge
atomic charge
atomic number
3.
Which is not part of John Dalton’s atomic theory?
All elements are composed of atoms.
Atoms are made up of smaller particles.
Atoms of different elements have different masses.
4.
All atoms of the same element have the same mass.
Dalton’s model of an atom is best described as _____.
a scoop of chocolate chip ice cream
a solar system
a cloud
a solid sphere
5.
Who provided the first evidence that atoms contain subatomic particles?
J. J. Thomson
Ernest Rutherford
John Dalton
6.
Which statement about electrons and atomic orbitals is not true?
An atom’s lowest energy level has only one orbital.
An electron has the same amount of energy in all orbitals.
An electron cloud represents all the orbitals in an atom.
An orbital can contain a maximum of two electrons.
7.
How is heavy water different from normal water?
A hydrogen atom in heavy water has an extra proton.
A hydrogen atom in heavy water has an extra neutron.
An oxygen atom in heavy water has an extra neutron.
An oxygen atom in heavy water has an extra proton.
8.
What experimental evidence did Thomson use to support his hypothesis that atoms are made up of even smaller, charged particles?
The glowing beam was always deflected by charged plates.
Identical particles were produced no matter which metal he used.
The particles all had the same mass as a hydrogen atom.
9.
Atoms may emit light energy when _____.
electrons move to a higher energy level
protons move to a higher energy level
protons move to a lower energy level
electrons move to a lower energy level
10.
Which term describes the region in which an electron is most likely to be found?
isotope
path
orbital
cloud
11.
According to Dalton, if 2 grams of element X combine with 4 grams of element Y to form compound XY, how many grams of element X would combine with 28 grams of element Y to form the same compound?
28
14
7
56
12.
An electron is a particle with a _____.
positive charge, found outside the nucleus
negative charge, found in the nucleus
positive charge, found in the nucleus
negative charge, found outside the nucleus
13.
The glow of a neon light is caused by electrons emitting energy as they _____.
move from higher to lower energy levels
collide with the nucleus
move from lower to higher energy levels
collide with other electrons
14.
To find the number of neutrons in an atom, subtract its _____.
atomic number from its mass number
mass number from its atomic number
isotope number from its atomic number
15.
Which is the best analogy describing the location of an electron in an atomic orbital?
pins on a map plotting your location every minute of a school day
the path of a bee moving from flower to flower in a garden
free-thrown basketballs bouncing on a basketball court
Answer:
12 is a negative charge outside the nucleu
Step-by-step explanation:
The sum of twice a number and 17 less than the number is the same as the difference between -5 and the number. What is the number?
What is the length of leg s of the triangle below
Answer: The correct option is (B) 3.
Step-by-step explanation: We are given to find the length of the leg s in the triangle shown in the figure.
From the figure, we note that
the given triangle is a right-angled one, where
length of the hypotenuse, H = √18 units,
length of one leg, P = 3 units
and
length of the other leg, s = B =?.
From Pythagoras theorem, we have
[tex]H^2=P^2+B^2\\\\\Rightarrow (\sqrt{18})^2=3^2+B^2\\\\\Rightarrow 18=9+B^2\\\\\Rightarrow B^2=18-9\\\\\Rightarrow B^2=9\\\\\Rightarrow B=3.[/tex]
Thus, the length of the leg s is 3 units.
Option (B) is CORRECT.
Find the missing side length.
chelsea is 4 years older than her brother. translate the verbal description into an equation. use the verbibale c to represent chelsea age and b to represent her brothers age
Rhea is a freelance writer. She works for multiple clients and has several sources of income. Some of her clients pay her more than $600 for her work. These clients always send a specific form to her where she has to report her gross payments. What form do you think the clients are sending to Rhea?
Factor the expression. X^4+6x^2-7 completely. Show work!
What is the first step in solving a quadratic equation of the form given below? (ax + b)2 = c
Answer:
The answer on apex is: Take the Square Root of both sides.
Step-by-step explanation:
what is 31590 rounded to the nearest thousand
Wendi worked for $6 an hour for the first month she was on the job. She was then given a raise to $6.24 an hour. What was the percent of her wage increase?
Explain how proving two triangles congruent can help prove parts of the triangle congruent.
what is the coefficient in the expression x / 3 + 7
Answer:
The coefficient of x is [tex]\frac{1}{3}[/tex]
7 is a constant
Step-by-step explanation:
[tex]\frac{x}{3} +7[/tex]
We need to find the coefficient of each term in the given expression
x/3 can be written as 1/3 times x
The coefficient is the number with the variable x
The coefficient of x is [tex]\frac{1}{3}[/tex]
7 is a constant
When washing your hands, the correct amount of time to scrub your hands is approximately: select one:
a. 30 seconds.
b. 5 seconds.
c. 10-15 seconds.
d. 1 minute?