Answer:
The correct answers are:
Question 4: the first step Keisha should take is: log to the power of x equals log 9.
Question 5: step 4 could be n ln 2 equals ln 86
Question 6: the exact solution is x=ln(7)
Step-by-step explanation:
Ok,
Question 4: the equation that shows the first step Keisha should take is:
[tex]7^{x}=9[/tex]
[tex]log(7^{x} )=log(9)[/tex]
[tex]x(log(7))=log(9)[/tex] (applying the properties of logarithms)
[tex]x=\frac{log(9)}{log(7)} =1.129[/tex]
Solution: the first step Keisha should take is: log to the power of x equals log 9.
Question 5: Her first three steps are:
[tex]2^{n}-3=83[/tex]
[tex]2^{n}-3+3=83+3[/tex] (adding 3 to both sides)
[tex]2^{n}=86[/tex]
[tex]2^{n}-3+3=83+3[/tex]
[tex]nln(2)=ln(86)[/tex]
Solution: step 4 is: [tex]nln(2)=ln(86)[/tex] (applying the properties of logarithms)
Question 6: The exact solution of 2 e to the power of x equals 14 is:
[tex]2e^{x}=14[/tex]
[tex]\frac{2e^{x} }{2} =\frac{14}{2}[/tex] (dividing both sides by 2)
[tex]e^{x}=7[/tex]
[tex]xln(e)=ln7[/tex] (ln(e)=1)
[tex]x=ln(7)[/tex]
Solution: [tex]x=ln(7)[/tex]
For Keisha's equation, the first step involves taking the logarithm of both sides, and for Mary's equation, the fourth step involves taking the natural logarithm. The exact solution for the third equation is x = ln 7.
Question 4:
Keisha is solving the equation [tex]\(7^x = 9\)[/tex]. The correct first step is:
[tex]\[ \log(7^x) = \log(9) \][/tex]
So the correct option is:
[tex]\[ \text{log } 7^x = \text{log } 9 \][/tex]
Question 5:
For Mary's equation [tex]\(2^n - 3 = 83\)[/tex], Step 4 involves taking the natural logarithm:
[tex]\[ n \ln 2 = \ln 86 \][/tex]
So the correct option is:
[tex]\[ n \ln 2 = \ln 86 \][/tex]
Question 6:
The equation [tex]\(2e^x = 14\)[/tex] can be solved by taking the natural logarithm:
[tex]\[ x = \ln \left(\frac{14}{2}\right) \][/tex]
Simplifying this gives:
[tex]\[ x = \ln 7 \][/tex]
So the correct option is:
[tex]\[ \ln 7 \][/tex]
The diagram below shows the dimensions of Tessa’s garden.
C) Tessa decided that she liked the shape of her garden but wanted to have 2 times the area. She drew a design for a garden with every dimension multiplied by 2. Explain the error in Tessa’s design.
Answer:
Tessa's mistake was to have multiplied each dimension by two instead of multiplying by a square root of two.
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z -----> the scale factor
x ----> the area of the enlarged garden
y ----> the area of the original garden
[tex]z^{2}=\frac{x}{y}[/tex]
we have that
If Tessa multiplies each dimension by 2, then the scale factor equals 2.
[tex]z=2[/tex]
substitute
[tex]2^{2}=\frac{x}{y}\\\\ 4=\frac{x}{y}\\\\x=4y[/tex]
The area of the enlarged garden will be equal 4 times the area of the original garden
so
If Tessa wanted to have twice as much surface, she must multiply each dimension by a square root of 2.
therefore
Tessa's mistake was to have multiplied each dimension by two instead of multiplying by a square root of two
how to find volume of cube?
Answer:
V=a3
Step-by-step explanation:
To find the volume of any cube you need to know the length, width and height. The formula to find the volume multiplies the length by the width by the height. The good news for a cube is that the measure of each of these dimensions is exactly the same. Therefore, you can multiply the length of any side three times.
Measure a side of the botom and then multiply it by 2 (That's the area), then multiply the result with the height: Area X Height = Volume. :)
hope you understand my answer LoL
A sphere has a diameter of 15inches. what is the volume of the sphere rounded to the nearest tenth? use 3.14 for pi. A:441.6in 3 B:1766.3in 3 C3532.5 in 3 D: 14,230.0 in 3
Answer: B.
Step-by-step explanation:
Diameter = Radius divided by 2.
The volume formula of a sphere is V = 4/3 π r^3.
Radius of this problem = 7.5.
So, V = 4/3 π (7.5) ^3.
Once you "plug in" the radius and solve the equation, you get an answer of 1,766.3, rounded to the nearest tenth.
Don't forget the inches cubed!
The answer is B. 1766.3
What is the effect on the volume of a sphere if the radius is divided by 3?
For this case we have by definition, that the volume of a sphere is given by:
[tex]V = \frac {4} {3} \pi * r ^ 3[/tex]
Where:
r: It is the radius of the sphere
If the radius is divided by 3 we have:
[tex]\frac {r} {3}:[/tex]
[tex]V = \frac {4} {3} \pi * (\frac {r} {3}) ^ 3\\V = \frac {4} {3} \pi * \frac {r ^ 3} {27}\\V = \frac {4} {81} \pi * r ^ 3[/tex]
ANswer:
the volume decreases considerably because the denominator increases
Will give brainliest
Answer:
quadratic: y = x^2 + 4x + 4
Step-by-step explanation:
Notice that each y value is the square of an integer.
4 = 2^2
9 = 3^2
16 = 4^2
etc.
This is a quadratic equation.
The first ordered pair is (0, 4). 4 is 2^2, so add 2 to x and rthen square the quantity. (0 + 2)^2 = 2^2 = 4. This also works for the other values of x.
The equation is
y = (x + 2)^2
y = x^2 + 4x + 4
Answer: quadratic: y = x^2 + 4x + 4
A freight carrier charges $0.57 for a package weighing up to one ounce. A company is shipping a package weighing 224 grams what is the cost to ship the package in dollar and cents?
Answer:
$ 4.50
Step-by-step explanation:
Given:
Charges of shipping package up to 1 ounce= $0.57
charges of shipping package of 224 grams=?
Converting grams into ounces
1 gram = 0.035274 ounces
224 grams = x ounces
By cross-multiplication we get
224(0.035274)= x ounces
7.90137= x
224 grams= 7.90137 ounces
Now finding charges of shipping package of 7.90137 ounces
Charges of shipping package up to 1 ounce= $0.57
charges of shipping package of 7.90137 ounces= $ x
By cross-multiplication we get
$x= 7.90(0.57)
= 4.50
Hence the cost to ship the package in dollar and cents is $4.50
i.e. 4 dollars and 50 cents!
How do i do mean and median
To find median your numbers have to be in numerical order from smallest to largest and the value that occurs more often and if no number is repeated then there is not median aka (mode)
To find mean you need to add all the number and divide the numbers that you add.
To find median you put the numbers least to greatest. Then, cross the numbers until you find an one number and that's it. If they are two numbers that left, you can add together and divide by two.
I hope this help you. :)
Find the mean of the following data set.
8, 5, 15, 12, 10
50
10
12.5
14
8+5+15+12+10= 50 / 5 = 10
5 4/5 b+6 3/4 −(2 11/15 +7 7/12 )
The value of the given expression is equal to the [tex]\frac{29b}{5}-3\frac{17}{30}[/tex].
We have given that,
[tex]5\frac{4}{5}b+6\frac{3}{4}-\left(2\frac{11}{15}+7\frac{7}{12}\right)[/tex]
We have to determine the,
[tex]=\frac{29}{5}b+6\frac{3}{4}-\left(2\frac{11}{15}+7\frac{7}{12}\right)[/tex]
What is the expression?The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols. The expression consists of unknown variables.
[tex]=\frac{29}{5}b+\frac{27}{4}-\left(2\frac{11}{15}+7\frac{7}{12}\right)[/tex]
[tex]=\frac{29}{5}b+\frac{27}{4}-\left(\frac{41}{15}+7\frac{7}{12}\right)[/tex]
[tex]=\frac{29}{5}b+\frac{27}{4}-\left(\frac{41}{15}+\frac{91}{12}\right)[/tex]
[tex]=\frac{29b}{5}+\frac{27}{4}-\frac{619}{60}[/tex]
[tex]=\frac{29b}{5}-\frac{107}{30}[/tex]
[tex]=\frac{29b}{5}-3\frac{17}{30}[/tex]
The value of the given expression is equal to the [tex]\frac{29b}{5}-3\frac{17}{30}[/tex].
To learn more about the expression visit:
https://brainly.com/question/723406
#SPJ2
Find the eighth term of the
geometric sequence, given the
first term and common ratio.
a1=6 and r=-1/3
Answer:
a(8) = -0.0027
Step-by-step explanation:
The most general formula for a geometric sequence is a(n) = a(1)*r^(n-1), where a(1) is the first term and r is the common ratio.
Here, the formula becomes a(n) = 6*(-1/3)^(n-1).
Substitute 8 for n to find the eighth term:
a(8) = 6*(-1/3)^(8-1), or a(8) = 6(-1/3)^7, or a(8) = -0.0027
The eighth term of the geometric sequence with the first term of 6 and a common ratio of -1/3 is -6/2187.
To find the eighth term of a geometric sequence, we can use the formula for the nth term of the sequence, which is given by an = a1rn-1, where a1 is the first term and r is the common ratio. In this case, the first term (a1) is 6 and the common ratio (r) is -1/3. To calculate the eighth term (a8), we substitute the values into the formula and get:
a8 = 6 ×(-1/3)8-1
a8 = 6 × (-1/3)7
a8 = 6 ×(-1/2187)
a8 = 6 ×(-1/2187) = -6/2187
Once we simplify, we find that the eighth term is -6/2187.
What type of triangle is shown?
equiangular triangle
acute triangle
right triangle
obtuse triangle
Answer:
right triangle
Step-by-step explanation:
We know that the total angles of the triangle are 180 degrees:
(x) + (4x-10) + (2x+15) = 180
7x - 10 + 15 =180
7x + 5 = 180
7x = 180 - 5
7x = 175
x = 175÷ 5 = 25
Now we calculate each angle
x=25
4x-10= (4*25) -10=100-10=90
2x+15=(2*25)+15=50+15=65
Because we have a right angle, then the triangle is right triangle
Answer:
right angle
Step-by-step explanation:
dont let the look of the triangle fool you
Type the correct answer in each box.
A circle is centered at the point (-7, -1) and passes through the point (8, 7).
The radius of the circle is _____
units. The point (-15, __) lies on this circle.
The radius of the circle is 17 uints and the point (-15,-16) or (-15,14) lies on the circle.
step by step explanation is here,
centre of circle(h,k)=(-7,-1)
if the circle passes through the point (8,7)
then the distance between (8,7) and (-7,-1) represents the radius.
so, r^2= (x2-x1)^2 + (y2-y1)^2
or, r^2=(-7-8)^2 +(-1-7)^2
or, r^2=(-15)^2 +(-8)^2
or, r^2=225+64
or, r^2=289
or, r=17 units
now the equation of circle is
(x-h)^2 +(y-k)^2 =r^2
or, (x+7)^2 +(y+1)^2 =289
or, x^2 +14x +49 + y^2 + 2y+ 1=289
or, x^2 + y^2 + 14x +2y-239=0
puttimg x=-15,
or, (-15)^2 + y^2 +14×(-15) + 2y -239=0
or, y^2 + 2y -239+225-210=0
or, y^2 + 2y -224=0
If you slove y, then you will get 14 and -16.
The radius of the circle is 17.
The point (-15, 14) lies on the circle.
Given that:
A circle is centered at the point (-7, -1) and passes through the point (8, 7).
That is:
Center of the circle = (-7, -1)
A point on the circle = (8, 7)
The equation of the circle is:
(x - a)² + (y - b)² = r²
Here (a, b) is the center and r is the radius.
Substituting the given center.
(x - -7)² + (y - -1)² = r²
(x + 7)² + (y + 1)² = r²
Substitute points (8, 7).
(8 + 7)² + (7 + 1)² = r²
r² = 289
r = 17
So, the radius of the circle is 17.
So, the equation of the circle is:
(x + 7)² + (y + 1)² = 289
Substitute x = -15.
(-15 + 7)² + (y + 1)² = 289
(y + 1)² = 225
y + 1 = 15
y = 14
Hence the radius is 17 and the point is (-15, 14).
Learn more about Circle here :
https://brainly.com/question/29288238
#SPJ2
Please help me with this question.
Step-by-step explanation:
First, reflect over the y-axis:
(1, -2) → (-1, -2)
Then, rotate 180° around the origin:
(-1, -2) → (1, 2)
Please answer right away
Answer:
independent
Step-by-step explanation:
Since no one else answered, figured you wouldn't mind if I do. :-), and you didn't use any CAPS.
How those two events (even and greater than 9) relate?
independent: YES. Can one happen without the other? Certainly. You see (1,1) is an even number that is not greater than 9. Equally, you see (6,5) which is greater than 9, but is not an even number.
inclusive: No, since there's a least one case where a pair number is not greater than 9. The opposite is also true... at least 1 number > 9 that is not even.
Mutually exclusive: No, since there numbers that are even AND greater than 9 (6,4) for example.
Conditional: No. Does one need the other to happen? Absolutely not.
Which number line represents this expression?
-8 + 5
PLEASE HELP ME!!!
I NEED THIS FINISHED NOW, PLEASE HELP ME!!!
I believe it’s the third one
How do I solve x² + 2x − 8 = 0?
explain please/step by step
Answer:
It's x = -4 , 2.
Step-by-step explanation:
x^2 + 2x - 8 = 0
The left side will factor to the form (x + a)(x + b).
We need 2 numbers (a and b) whose product = -8 and whose sum = +2.
These are a = 4 and b = -2, so the factors are
(x + 4)(x - 2) = 0
Now either x + 4 = 0 or x - 2 = 0,
giving x = -4, x = 2 (answer).
Answer:
-2 , 4
Step-by-step explanation:
Their are 4 ways you can solve this but I am going to factorise to solve
x² + 2x − 8 = 0
Factors = 4 , -2
Sum = 2
Product = -8
x ( x + 4 ) - 2 ( x + 4 ) = 0
( x - 2 ) ( x + 4 ) = 0
x = - 2 , 4
The base of a 13 foot ladder is 5 feet away from the wall. How far up the wall does the ladder reach?
using pythagoras theorem the height ladder reaches above the wall can be found as in picture the answer would be 12ft
Please help I don’t know how to do this!
Answer:c
Step-by-step explanation:
The answer is the top one.
Hope this helps!
Jason ate 1/2 of a whole pizza. The next day, he shared the remaining pizza between himself and 2 friends. What fraction of the original pizza did each of them get?
Answer:
1/6
Step-by-step explanation:
jason ate 1/2, so only 1/2 of the pizza is left.
1 ÷ 2 = 1/2
he split it equally between himself and 2 friends (3 people)
1/2 ÷ 3
= 1/2 × 1/3
=1/6
If a football team has a 90% chance of making a field goal for 3 points and a 35% chance of making a touchdown for 7 points, find the expected value of a touchdown.
PLEASE HELP!!!
2.7 points (my guess)
Answer: The expected value of touchdown is 2.45.
Step-by-step explanation:
Since we have given that
Probability of making a field goal for 3 points = 90%
Probability of making a touchdown for 7 points = 35%
So, Expected value of a touchdown would be
[tex]\sum xp(x)=7\times \dfrac{35}{100}=\dfrac{245}{100}=2.45[/tex]
Hence, the expected value of touchdown is 2.45.
3g+5+3g+5+3g+5 Simplify!!!!!! PLZZ
Answer:
9q + 15
Step-by-step explanation:
3g+5+3g+5+3g+5
Combine like terms
= 9q + 15
Answer:
15+9g
Step-by-step explanation:
im kinda stuck
35-x=29
Answer:
6
Step-by-step explanation:
first subtract 29 from 35, then you get the difference, which is 6!
Hello There!
We have an equation “35 - x = 29”
To solve this we can use addition.
29 plus some number = 35.
29+5 = 34 so add 1 more and you get 35.
X=6
Marco is carrying two cylinder-shaped cans. Each can has the same height
and cross-sectional area as the other. Which of the following best describes
the relationship between the cans according to Cavalieri's principle?
Answer:
Choice D
Step-by-step explanation:
The Cavalieri's principle states that if two or more solids have identical cross-sectional area as well as height, then the solids will have equal volume.
Therefore, the volumes of the cylinders are the same
Answer:
The volumes of the cylinders are the same.
Step-by-step explanation:
Find the value of each trigonometric ratio
:) Hope this answers your question :)
gema has 4
FT of wire how much wire does she need to wrap one meter of her garden?
Answer:
3.28 feet
Step-by-step explanation:
One meter equals to 3.28 feet.
The question isn't exactly clear what Gema wants to use her wire for, because "wrap one meter" isn't correct.
You wrap something around something else... and you can't wrap something around a meter. You can wrap around a square meter by doing the perimeter... but then you'd need more than meter to do the perimeter of a square meter (the perimeter can be around 4 meters).
So, assuming she has a length of 1 meter to cover, she would need 3.28 feet.
What are not possible partial products of 28×15 select all that apply
Answer:
420
Step-by-step explanation:
420 I think that’s what you wanna
Find the measure of BAD
Answer:
22.5°
Step-by-step explanation:
The inscribed angle theorem tells us that the measure of an inscribed angle is half of the central angle swept out by the same arc. Here, the arc BD sweeps out a central angle of 45°, so the measure of angle BAD must be half that, or 45/2 = 22.5°
If f(x) = -5x - 1 and g(x) =√x - 6 , what is (f * g)(2)
Answer:
(f * g)(2) = -11√2 +66
Step-by-step explanation:
Points to remember
Let f(x) and g(x) be the two functions, then (f * g) can be written as,
(f * g) = [f(x)][g(x)]
To find the value of (f * g)(2)
we have,
f(x) = -5x - 1 and g(x) =√x - 6
f(2) = -5*2 - 1 = -11
g(2) = √x - 6 = √2 - 6
(f * g)(2) = [f(2)][g(2)]
= -11 (√2 - 6)
= -11√2 +66
Therefore (f * g)(2) = -11√2 +66
The price of a train ticket from Austin to Phoenix is normally $142.00 however, the train company is offering a special 65% discount to children under age 12. What is the sale price of a ticket from Austin to Phoenix for someone under 12?
Can someone pls help me I don’t get this question
Answer:
The sale price of a ticket from Austin to Phoenix for someone under 12 is $49.70
Step-by-step explanation:
Let
x----> the sale price of a ticket from Austin to Phoenix for someone under 12
we know that
100%-65%=35%=35/100=0.35
so
x=0.35*($142.00)
x=$49.70
which inequality matches the graph?
Answer:
2x - 3y < 7
Step-by-step explanation:
The coordinate is on 0 and this number is LESS THAN 0.
PLEASE MARK ME AS BRAINLIEST BECAUSE I REALLY NEED IT :(