-8x ≤ 38
-8 is multiplying on the left, then it will divide on the right. Remember that when you divide by a negative number, the sign changes.
x ≥ 38/(-8)
x ≥ -19/4
The first term of a geometric sequence is 1/2 and the sum of the first two terms is 3/5.Work out the sum of the first 10 terms of the sequence.Give your answer as a decimal correct to 3 significant figures.
The formula for calculating the sum of the terme in a geometric sequence is expressed as
Sn = a1(1 - r^n)/(1 - r)
where
Sn is the sum of the first n terms
a1 is the first term
r is the commin ration
n is the number of terms
From the information given,
a1 = 1/2
when n = 2, S2 = 3/5
Thus,
3/5 = 1/2(1 - r^2)/(1 - r)
Cross multiply. It becomes
3/5 x 2 = (1 - r^2)/(1 - r)
(1 - r^2) can be expressed as (1 - r)(1 + r)
Thus, the expression becomes
6/5 = (1 - r)(1 + r)/(1 - r)
6/5 = 1 + r
r = 6/5 - 1
r = 1/5
Next, we would calculate the sum of the first 10 terms, S10
In this case,
n = 10
S10 = 1/2(1 - (1/5)^10)/(1 - 1/5)
S10 = 1/2(1 - 1/25)/(4/5)
S10 = 0.625
the sum of the first 10 terms of the sequence is 0.625
Identify the translation of the triangle along the given vector.
Hello there. To solve this question, we'll have to translate the following triangle along the vector v:
In this case, we simply need to translate it (move it without changing none of its aspects), such that:
This is what we have in the second option. The other options shows some type of rotation of the triangles, so they cannot be a translation.
- 11.33< - 7.40 means that - 11.33 is located to the left of - 7.40 on the number line choose yes or no
The answer is yes
we can see it on the number line
Find the intercepts, if any, of the graph of x^2+y^2+4x-2y-11=0
Hello there. To solve this question, we'll have to remember some properties about finding the intercepts of a graph.
Given the function
x² + y² + 4x - 2y - 11 = 0
In this case, we want to determine the x, y intercepts, it is, when y = 0, x = 0, respectively.
Making y = 0, we find the x-intercepts
x² + 4x - 11 = 0
Solving this quadratic equation,
[tex]x=\frac{-4\pm\sqrt[]{4^2-4\cdot1\cdot(-11)}}{2\cdot1}=\frac{-4\pm\sqrt[]{60}}{2}=\frac{-4\pm2\sqrt[]{15}}{2}=-2\pm\sqrt[]{15}[/tex]The intercepts are (-2 - sqrt(15), 0) and (-2 + sqrt(15), 0)
Now, to find the y-intercepts, plug in x = 0:
y² -2y - 11 = 0
Same process, solving this quadratic equation:
[tex]y=\frac{-(-2)\pm\sqrt[]{(-2)^2-4\cdot1\cdot(-11)_{}}}{2\cdot1}=\frac{2\pm\sqrt[]{48}}{2}=\frac{2\pm4\sqrt[]{3}}{2}=1\pm2\sqrt[]{3}[/tex]The intercepts are (0, 1 - 2sqrt3) and (0, 1 + 2sqrt3)
Find the missing angle measures: 42 X В. A 9 A 10 B 11 C 12 S 13 T 14 X 40 48 57 41 1 76 ST 46
1) For those triangles, let's start by ∠A
The sum of the interior angles of a triangle is
The graph of g(x), shown below, is a vertical shift of the graph of f(x) = 3*.Write the equation for g(x).109-2A. g(x) = 3x+1B. g(x) = 3x - 1C. g(x) = 3x - 1D. g(x) = 3* + 1
Notice that the vertical shift corresponds to one unit. Then, the proper transformation g(x) is:
[tex]g(x)=3^x+1[/tex]Question. Vonna scored 27 goals at soccer practice. Her ratio of goals to misses was 3:7 how many times did she miss
We have
3 goals to 7 misses
27 goals to x
We will use the crossed multiplication by using the ratio given and the number of scored goals.
[tex]x=\frac{27\text{ goals }\cdot7\text{ missed}}{3\text{ goals}}[/tex]we simplify
[tex]x=\frac{27\cdot7}{3}=63\text{ misses}[/tex]ANSWER
63 misses
I need help finding the perimeter and area. Can you help me?Even for the 2 I did can you double check them and see if I'm right and if I'm wrong then can you fix them and give me the answers. Thank you for your help!
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The perimeter of the figure is:
[tex]\begin{gathered} 24+\text{ 18 + 17 + 9 +7+9} \\ =\text{ 84 units} \end{gathered}[/tex]The area of the figure is calculated as thus:
[tex]\begin{gathered} (\text{ 18x 17) + ( 9 x 7)} \\ =\text{ }306+63 \\ =\text{ }369units^2 \end{gathered}[/tex]Sole the three Pythagorean theorem problems to figure out m
According to the Pythagorean Theorem, if A and B are the legs of a right triangle and C is the hypotenuse, then:
[tex]A^2+B^2=C^2[/tex]The legs of the first right triangle are 5 and x, and its hypotenuse is 13. Use the Pythagorean Theorem and solve for x:
[tex]\begin{gathered} x^2+5^2=13^2 \\ \Rightarrow x^2+25=169 \\ \Rightarrow x^2=169-25 \\ \Rightarrow x^2=144 \\ \Rightarrow x=\sqrt[]{144} \\ \Rightarrow x=12 \end{gathered}[/tex]The legs of the second right triangle are 8 and x+3. Replace x=12. Then, the legs have measures 8 and 15. Use the Pythagorean Theorem to find the hypotenuse y:
[tex]\begin{gathered} 8^2+15^2=y^2 \\ \Rightarrow64+225=y^2 \\ \Rightarrow289=y^2 \\ \Rightarrow y=\sqrt[]{289} \\ \Rightarrow y=17 \end{gathered}[/tex]The legs of the third right triangle have measures m and 2y-2x+10, and the hypotenuse has length 29. Replace x=12 and y=17. Then, the legs of the third right triangle are m and 20, and the hypotenuse has length 29. Solve for m:
[tex]\begin{gathered} m^2+20^2=29^2 \\ \Rightarrow m^2+400=841 \\ \Rightarrow m^2=841-400 \\ \Rightarrow m^2=441 \\ \Rightarrow m=\sqrt[]{441} \\ \Rightarrow m=21 \end{gathered}[/tex]Therefore, the solutions for x, y and m are:
[tex]\begin{gathered} x=12 \\ y=17 \\ m=21 \end{gathered}[/tex]Question 2 Find the 10th term of the sequence -2,-16, -128,-1024... Do not use spaces or commas in your answer.
The first term is -2, and the common ratio is 8.
The nth term of a geometric progression is;
[tex]\begin{gathered} T_n=ar^{(n-1)} \\ T_{10}=2\times(-8)^{10-1} \\ T_{10}=2\times(-8)^9 \\ T_{10}=2\times(-134217728) \\ T_{10}=-268,435,456 \end{gathered}[/tex]The 10th term is equal to -268,435,456
what percent tip was given if a customer left $5 on a bI'll that had a subtotal of $31.25m?
We will determine the percentage as follows:
[tex]x=\frac{5\cdot100}{31.25}\Rightarrow x=16[/tex]So, the percent that the tip represents is 16%.
Business math questions
ANSWER
1.) $28,044
2.) 8 years
EXPLANATION
Applying the Future Value formula
[tex]undefined[/tex]draw the image of figure after each translation number 9. four units left and 4 unit down number 10 five units right in three units up
The coordinates for the pre-image are P(1,3), Q(4,4), R(4,1), and S(1, -1).
The transformation is 4 units left, and 4 units down.
That means we must subtract 4 units to x-coordinates, and subtract 4 units from y-coordinates. So, the image has coordinates P'(-3,-1), Q'(0,0), R'(0, -3), and S'(-3, -5).
The image below shows the image and pre-image.
For the function f(x) = x² + 4x - 12 solve the following.
Substitute the given equation for f(x)
[tex]\begin{gathered} f(x)\ge0 \\ x^2+4x-12\ge0 \end{gathered}[/tex]Factor the left side of the inequality
[tex]\begin{gathered} (x-2)(x+6)\ge0 \\ \\ \text{separate each factor},\text{ and equate to zero to determine the intervals} \\ x-2=0 \\ x-2+2=0+2 \\ x\cancel{-2+2}=2 \\ x=2 \\ \\ x+6=0 \\ x+6-6=0-6 \\ x\cancel{+6-6}=-6 \\ x=-6 \end{gathered}[/tex]Test for each interval
[tex]\begin{gathered} \text{IF }x\le-6,\text{ substitute }x=-7 \\ x^2+4x-12\ge0 \\ (-7)^2+4(-7)-12\ge0 \\ 49-28-12\ge0 \\ 9\ge0 \\ x\le-6\text{ works in the original inequality} \\ \\ \text{IF }-6\le x\le2,\text{ substitute }x=0 \\ 0^2+4(0)-12\ge0 \\ -12\ngeq0 \\ -6\le x\le2\text{ does not work} \\ \\ \text{IF }x\ge2,\text{ substitute }x=3 \\ x^2+4x-12\ge0 \\ 3^2+4(3)-12\ge0 \\ 9+12-12\ge0 \\ 9\ge0 \\ x\ge2\text{ works} \end{gathered}[/tex]Therefore, the solution to the inequality is
[tex](-\infty,-6\rbrack\cup\lbrack2,\infty)[/tex]can you help me with this assignment on deltamath?reflect the figure over the line y= -3 by drawing a diagram
To reflect a figure over a horizontal line using a diagram you have to determine the distance of each point of the figure until the horizontal line.
Then, starting from the horizontal line, draw a vertical line with the same measure, this will help you determine the position of each vertex of the figure after the reflection:
Cómo representaría 500 pies bajo el nivel del mar? Texto de una sola línea.
Para representar 500 pies bajo el nivel del mar con una recta numérica. Como es altitud se suele dibujar una recta numérica vertical como la siguiente:
Al colocar la cantidad negativa nos indica que es menor a cero. Usualmente se considera que el nivel del mar está en el 0 de la recta numérica.
I been working I can’t seem to find the answer and I get it mixed up with algebra
A. 10.6
1) In this problem, we have a right triangle. We know two angles and one length of the hypotenuse. If we pay attention to that triangle, we can see that this is an isosceles triangle.
2) So, we can find the missing leg making use of the Pythagorean theorem or we can use trig ratios.
[tex]\begin{gathered} a^2=b^2+c^2 \\ 15^2=x^2+x^2 \\ 225=2x^2 \\ \frac{225}{2}=\frac{2x^2}{2} \\ x^2=112.5 \\ x\approx10.6 \\ \\ or \\ \\ \sin (45)=\frac{x}{15} \\ \frac{\sqrt[]{2}}{2}=\frac{x}{15} \\ 2x=15\sqrt[]{2} \\ x=\frac{15\sqrt[]{2}}{2} \\ x\approx10.6 \end{gathered}[/tex]Note that either way we can find the same result. So the answer is 10.6
A student is standing 20 feet away from the base of a tree. He looks to the top of the tree at a 50°angle of elevation. His eyes are 5 feet above the ground. Using cos 50° 0.64, what is the heightof the tree to the nearest foot?
Given:
Base distance = 20 ft.
Angle = 50
Ground height = 5 ft
Find-:
The height of the tree
Explanation-:
The height of the tree
The height of the tree is:
[tex]\text{ Height }=H+5\text{ ft}[/tex]Value of H is:
In triangle ABC
[tex]\begin{gathered} \text{ Angle }=50 \\ \\ \text{ Base }=20 \\ \\ \text{ Perpendicular }=H \end{gathered}[/tex]Trignometry formula is:
[tex]\tan\theta=\frac{\text{ Perpendicular}}{\text{ Base}}[/tex]The value of "H" is:
[tex]\begin{gathered} \tan50=\frac{H}{20} \\ \\ H=20\times\tan50 \\ \\ H=20\times1.19 \\ \\ H=23.83507 \\ \\ H\approx24 \end{gathered}[/tex]So the height of the tree is:
[tex]\begin{gathered} \text{ Height }=H+5 \\ \\ \text{ Height }=24+5 \\ \\ \text{ Height }=29\text{ feet} \end{gathered}[/tex]Height of the tree is 29 feet.
Could an even or an odd function be transformed into the other (even to odd or odd to even)? Why or why not? Give an example.
The even and odd functions are functions that satisfy particular symmetry operations with repcet to taking additive inverses. A function,
[tex]f(x)=x^n[/tex]is said to be, even, if n is an even integer and odd function when n is an odd integer.
Also, for a function if,
[tex]\begin{gathered} f(x)=f(-x)\rightarrow even \\ -f(x)=f(-x)\rightarrow odd \end{gathered}[/tex]An even or an odd function be transformed into the other.
The product of two odd functions is an even function.
The product of an even function and an odd function is an odd function.
The quotient of two odd functions is an even function.
which of the following
Explanation
Step 1
Let n represents the number
now, let's check the sentence
A number times 5 is 15
hence,
A number times 5= n times 5= 5n
is= "="
15= 15
therefore, rewriting we have
[tex]\begin{gathered} a\text{ number times 5 is 15} \\ 5n=15 \end{gathered}[/tex]A student takes 1/6 an hour to paint a picture frame how many pictures frame can the student paint in 4 hours A. 28 framesB.24 frame C.20 frame D. 2/3
A student takes 1/6 an hour to paint 1 picture frame. To find how many pictures frame can the student paint in 4 hours, we can use the next proportion:
[tex]\frac{\frac{1}{6}\text{hour}}{4\text{ hours}}=\frac{1\text{ picture frame}}{x\text{ picture frames}}[/tex]Solving for x,
[tex]\begin{gathered} \frac{1}{6}\cdot x=1\cdot4 \\ x=\frac{4}{\frac{1}{6}} \\ x=4\cdot6 \\ x=24 \end{gathered}[/tex]The student can paint 24 picture frames in 4 hours
2. The fastest car on Earth, called the Thrust SSC, could drive from San Jose to Los Angeles in 30 minutes. That is a distance of 564 km. What is the speed of the car?
speed = distance / time
speed = 564 km / 0.5 h
speed = 1128 km/h
or
distance = 564 000 m
time = 30 min = 1800 s
speed = 564000m/1800s
speed = 313.3 m/s
marcia wishes to make a bowl in the form of a solid hemisphere.The density of the clay being used to make the hemisphere is .065 pound per cubic inchb and costs clay costs $0.12 per pound. If the diameter of the sphere is 1.5 feet, what is ther coast of making 15 of these bowls to the nearest dollar?
Hemisphere volume = 4/6 •( π•radius^3)
If diameter= 1.5 feet, then
radius R= 0.75 feet= 9.6 inches
then Volume V = 4/6•(π•9.6^3) = 1853 cubic inches
O.88 cubic foots transform to cubic inches =
32 cm/ 2.5 cm = 12.8 inches
Also
Density = Volume / mass = 0.065
Then
mass= Volume/Density = 1853 / 0.065 = 28507 pounds
Then answer for price of 15 bowls is
= 28507x 0.12x 15 =
= $51313 dollars
To determine the value of tangent of 11 times pi over 12, which identity could be used?
SOLUTION:
[tex]tan\frac{11\pi}{12}=\frac{sin\frac{11\pi}{12}}{cos\frac{11\pi}{12}}[/tex]Using half-angle formulas;
[tex]\begin{gathered} sin\frac{11\pi}{12}=sin(\frac{\frac{11\pi}{6}}{2})=\sqrt{\frac{1-cos\frac{11\pi}{6}}{2}} \\ cos\frac{11\pi}{12}=cos(\frac{\frac{11\pi}{6}}{2})=\sqrt{\frac{1+cos\frac{11\pi}{6}}{2}} \end{gathered}[/tex]Dividing them, we can see that;
[tex]tan\frac{11\pi}{12}=\sqrt{\frac{1-cos\frac{11\pi}{6}}{1+cos\frac{11\pi}{6}}}[/tex]also; the other 2 options work too;
thus, the answer is;
I need help with this question for part a and b
ANSWERS
a) 0%
b) 30.23%
EXPLANATION
The life of the streetlights, X, is normally distributed with a mean of 400 days and a standard deviation of 40 days,
[tex]X=N(400,40)[/tex]a) We have to find what percentage of lamps will last longer than 600 days. This is the same as the probability that a lamp will last more than 600 days, written as a percentage. So we have to find,
[tex]P(X>600)[/tex]We have to standardize the variable to use the standard normal curve,
[tex]P(X>600)=P\mleft(\frac{X-\mu}{\sigma}>\frac{600-\mu}{\sigma}\mright)=P\mleft(Z>\frac{600-400}{40}\mright)=P(Z>5)[/tex]As expected, this probability is 0. So the percentage of lamps that last longer than 600 days is 0%.
Note that the mean life is 400 days, and 600 days is 200 days past that mean life. If the standard deviation is only 40 days, it is expected that no lamp could last longer than 600 days.
b) Now, we have to find the probability that a lamp lasts between 420 and 500 days. We can sketch the normal curve to understand what we are looking for,
A Z-table shows the probability that the variable is less than a value - i.e. the area under the curve to the left of the value. So, this probability is the probability that X is less than 500 minus the probability that X is less than 420,
[tex]P(420Use the same method we used before to standardize the variable,[tex]P(Z<\frac{500-400}{40})-P(Z<\frac{420-400}{40})=P(Z<2.5)-P(Z<0.5)[/tex]Find these two values in a Z-table,
So the probability is,
[tex]P(420Multiply by 100 to obtain the percentage.Hence, the percentage of the lamps that last between 420 and 500 days is 30.23%.
Miriam tiene dos cuerdas, una de 200 cm de longitud y otra de 60 cm. Quiere cortarlas para obtener trozos de igual longitud y que no sobre nada de cuerda.
¿Cuál es la longitud máxima de los trozos en que puede cortar las dos cuerdas?
20
cm
¿Cuántos trozos le saldrán de la cuerda de 200 cm?
trozos
¿Y de la cuerda de 60 cm?
trozos
La longitud máxima de cada partición es 20 centímetros. Existen 10 particiones de cuerda en la cuerda de 200 centímetros y 3 particiones de cuerda en la cuerda de 60 centímetros.
¿Cómo determinar la cantidad de segmentos de longitud máxima que se puede derivar de dos cuerdas?
Dimensionalmente hablando, la longitud de cada cuerda puede definirse como el producto de la longitud de cada partición (s), en centímetros, y el número de particiones (n). La longitud es máxima cuando el número de particiones es el menor posible. Asumiendo que el número de particiones es un número entero no negativo, se tiene que la longitud total es:
s · (n₁ + n₂) = 260 cm
s · n₁ = 200 cm
s · n₂ = 60 cm
Si el número de particiones es un número entero no negativo, entonces la longitud de cada segmento deber ser otro número enterno no negativo. Ahora, la descomposición factorial de 260, 200 y 60 es, respectivamente:
260 = 2² × 5 × 13
200 = 2³ × 5²
60 = 2² × 3 × 5
La longitud máxima es el máximo común divisor de los tres números:
L = 2² × 5
L = 20
La longitud máxima de partición es 20 centímetros.
Ahora, determinamos el número de particiones de cada cuerda:
Cuerda de 200 cm:
n₁ = 200 cm / 20 cm
n₁ = 10
Existen 10 particiones de cuerda.
Cuerda de 60 cm:
n₂ = 60 cm / 20 cm
n₂ = 3
Existen 3 particiones de cuerda.
Suma de las dos cuerdas:
n₁ + n₂ = 260 cm / 20 cm
n₁ + n₂ = 13
Para aprender más sobre el máximo común divisor: https://brainly.com/question/28313336
#SPJ1
1. f(x) = 5x^2 + 7x-3 Degree:Leading Coefficient:End Behavior:
f(x) = 5x^2 + 7x-3
The Degree of a polynomial is the highest degree of the polynomial's monomials.
In this case:
Degree: 2
The leading coefficient is the number next to the highest degree variable:
Leading coefficient = 5
End behavior: Degree is even and the leading coefficient is positive, so en behavior is:
f(x) ⇒ ∞ as x ⇒ -∞
f(x)= ∞ as x ⇒ ∞
what are the solutions to the quadratic equation below? 3x^2+16x+21=0
ANSWER:
C. x = -7/3 and x = -3
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]3x^2+16x+21=0[/tex]We solve for x:
[tex]\begin{gathered} 16x=7x+9x \\ \\ \left(3x^2+7x\right)+\left(9x+21\right)=0 \\ \\ x\left(3x+7\right)+3\left(3x+7\right)=0 \\ \\ \left(3x+7\right)\left(x+3\right)=0 \\ \\ 3x+7=0\rightarrow3x=-7\rightarrow x=-\frac{7}{3} \\ \\ x+3=0\rightarrow x=-3 \end{gathered}[/tex]Therefore, the correct answer is C. x = -7/3 and x = -3
Jamaal has 20 models of planes and cars. He has three times as many cars as planes. What is the ratio of his cars to total models?1:43:13:44:3
We know that
There are 20 models in total.
He has three times as many cars as planes.
The first statement can be expressed as
[tex]x+y=20[/tex]The second statement can be expressed as
[tex]y=3x[/tex]Where y represents cars and x represents planes.
Now, we combine the equations
[tex]\begin{gathered} x+y=20 \\ x+3x=20 \\ 4x=20 \\ x=\frac{20}{4} \\ x=5 \end{gathered}[/tex]Then, we find y
[tex]y=3\cdot5=15[/tex]As you can observe there are three times more cars than planes, which means the ratio is 3:1.I already graphed the first question, need number 2 please
For the equation y = 2x + 3, calculate the x and y intercepts
when y = 0
0 = 2x + 3
x = -3/2
x = -1.5
The x-intercept = (-1.5, 0)
when x = 0
y = 2(0) + 3
y = 3
The y-intercept = (0, 3)
Locate the points (-1.5, 0) and (0, 3) to graph the equation y = 2x + 3
For the equation y = -1/3 x + 2, calculate the x and y intercepts
when y = 0
[tex]\begin{gathered} 0=-\frac{1}{3}x+2 \\ \frac{1}{3}x=2 \\ x=6 \end{gathered}[/tex]The x-intercept = (6, 0)
when x = 0
y = -1/3 (0) + 2
y = 2
The y-intercept = (0, 2)
The graphs of the two equations are plotted using their x and y intercepts as shown below
y = 2x + 3 is plotted in red
y = -1/3 x + 2 is plotted in blue
The solution to the system of equations represented by the two lines is (-0.429, 2.143)