Answer:
[tex]a_n=78-6n[/tex]
[tex]a_{14}=78-6(14)[/tex]
Step-by-step explanation:
To solve this, we are using the formula for the nth term of an arithmetic progression:
[tex]a_n=a_1+(n-1)d[/tex]
where
[tex]a_1[/tex] is the first term of the progression
[tex]d[/tex] is the difference
[tex]n[/tex] is position of the term in the progression
We know for our problem that the bottom row contains 72 bricks, so [tex]a_1=72[/tex]. We also know that each row above decreases by 6 bricks, so the difference is -6 ([tex]d=-6[/tex]).
Replacing the values:
[tex]a_n=72+(n-1)(-6)[/tex]
[tex]a_n=72-6n+6[/tex]
[tex]a_n=72-6n+6[/tex]
[tex]a_n=78-6n[/tex]
Where [tex]n[/tex] is the row
Since we want to now the number of bricks in the 14th row, [tex]n=14[/tex]:
[tex]a_{14}=78-6(14)[/tex]
[tex]a_{14}=78-84[/tex]
[tex]a_{14}=-6[/tex]
Since bricks can't be negative, we can conclude that this is an impossible real-life situation.
Please include work in the answer.
The answer is 3. You would just match up the sides and combine the common things. 3z times z is 3z^2 because it would be the same number twice, not times two. Then 9 times 8 is 72. Z times 8 is 8z because it would be 8 times whatever number the variable was. Then lastly it’s 9 times 3 z. You’ll multiply the 9 times 3 to get 27. Then it would be 27z. 27z and 3z^2 cannot be added together because they are preforming different things. One is multiplying by the variable another is multiplying by 3 and the the variable to the 2nd power.
Fishing rods are discounted at 50% off the regular price of $25. How much money will be saved?
Answer:
$12.50
Step-by-step explanation:
I NEED HELP asap would be nice thanks
The Answer is B
Hope this helps :)
Solve: a^2+4(3+a)
a=5
Answer:
57
Step-by-step explanation:
[tex] {a}^{2} + 4(3 + a)[/tex]
[tex] {5}^{2} + 4(3 + 5)[/tex]
[tex]25 + 12 + 20[/tex]
[tex]57[/tex]
x/8 = 13. what does X equal?
Answer:
x equal 104
Step-by-step explanation:
since 8 needs to go into something 13 times we can multiply
8 x 13 to get
104
104 divided by 8
equals 13
Answer:
x=104
Step-by-step explanation:
x/8 = 13
Multiply each side by 8
x/8 *8 = 13*8
x = 104
Tell whether the lines for.the pair of equations are parallel, perpendicular, or neither y = - 4/5x + 3; 4x - 5y = -15
Answer:
The lines are neither parallel nor perpendicular
Step-by-step explanation:
The first step is to re-write the equations in slope-intercept form. The first equation is given as;
y = -4/5x + 3
This equation is already in slope-intercept form. Its slope is -4/5
The second equation is given as;
4x - 5y = -15
We solve for y;
-5y = -4x - 15
y = 4/5x + 3
The slope of the line is thus 4/5
Parallel lines have equal or identical slopes. The slopes of the two lines are not equal implying that the lines are not parallel. Two lines are said to be perpendicular if the product of their slopes is equal to -1.
The product of the slopes of the two lines is;
(-4/5) * (4/5) = -16/25 ≠ -1
The two lines are not perpendicular
By comparing the slopes of the given equations, y = -4/5x + 3 and 4x - 5y = -15, we find that they are negative reciprocals of each other, indicating that the lines are perpendicular.
To determine whether the given pair of equations represent lines that are parallel, perpendicular, or neither, we need to compare their slopes. The slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept.
The first equation is already in slope-intercept form: y = -4/5x + 3, so its slope is -4/5.
To put the second equation into slope-intercept form, we solve for y:
4x - 5y = -15
-5y = -4x - 15
y = (4/5)x + 3
The slope of the second line is 4/5.
Since the slopes of the two lines are negative reciprocals of each other, the lines are perpendicular.
HELPP!! In the 30-50-90 triangle below, side s has a length of and side q has a length of
Answer:
(B) is the homogeneous mixture
How many solutions does the equation -2y+2y+3=3have?
Cancel 3 on both sides
-2y + 2y = 0
Simplify -2y + 2y to 0
0 = 0
Since both sides are equal, there are infinitely many solutions;
= Infinitely Many Solutions
Simplify: |5-11|
16
-16
6
-6
Subtract 11 from 5 to get -6.
Because the equation is in between two vertical lines, this means the absolute value, which is a positive value, so -6 becomes positive 6.
The answer is 6
When you went to sleep, the temperature was −2.8°C.
When you woke up, the temperature was 1.4°C.
Which expression and statement describes the situation?
A. 1.4<-2.8,so 1.4°C is cooler than −2.8°C.
B. -2.8>1.4,so −2.8°C is warmer than 1.4°C.
C. 1.4=1/2(-2.8),so 1.4°C is half as cold as −2.8°C
D. 1.4>-2.8,so 1.4°C is warmer than −2.8°C
D
The larger the number the warmer it is
Answer:
D
Step-by-step explanation:
Which expression represents the distance between point (0,a) and point (a,0) on a coordinate grid?
You can always compute the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] using the pythagorean theorem:
[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
In your case, we have
[tex]d = \sqrt{(0-a)^2+(a-0)^2} = \sqrt{2a^2}=a\sqrt{2}[/tex]
Answer:
[tex]\sqrt{2}a[/tex]
Step-by-step explanation:
We are asked to find the distance between point (0,a) and point (a,0) on a coordinate grid.
We will use distance formula to solve our given problem.
The distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex], where D represents distance between two points.
Let point [tex](0,a)=(x_1,y_1)[/tex] and point [tex](a,0)=(x_2,y_2)[/tex].
Substitute the values in distance formula:
[tex]D=\sqrt{(0-a)^2+(a-0)^2}[/tex]
[tex]D=\sqrt{(-a)^2+(a)^2}[/tex]
[tex]D=\sqrt{a^2+a^2}[/tex]
[tex]D=\sqrt{2a^2}[/tex]
Factor out perfect square:
[tex]D=\sqrt{2}a[/tex]
Therefore, the distance between two points would be [tex]\sqrt{2}a[/tex].
What is the approximate area of the triangle below?
a)72.8 sq. cm.
b)111.9 sq. cm.
c)142.0 sq. cm.
d)164.7 sq. cm.
Answer:
Option a)72.8 sq. cm.
Step-by-step explanation:
step 1
Find the measure of the third internal angle of the triangle
Remember that
the sum of the internal angles of a triangle must be equal to 180 degrees
so
95°+35°+A=180°
A=180°-95°-35°
A=50°
step 2
Applying the law of sines
Find the length side opposite to the angle of 35 degrees
14/sin(50°)=b/sin(35°)
b=[14/sin(50)]*sin(35)
b=10.48 cm
step 3
Applying the law of sines find the area of the triangle
A=(1/2)(14)(10.48)sin(95°)=73.10 cm²
therefore
The approximate area of the triangle below is 72.8 sq. cm
Answer:
72.8 sq. cm
Step-by-step explanation:
Given:
two angles and a side of a triangle that are 95°, 35° and 14 cm receptively
Area of triangle=?
Finding 3rd angle
=180-(95+35)
= 180-130
=50
Area of triangle can be calculated by using ASA i.e.
Area= a^2sinBsinC/2sinA
Putting values of a=14, B=95, C=35 and A=50, we get
Area= 14^2(sin95)(sin35)/2(sin50)
=98(0.74591)
=73.099
Closest option is a)72.8 sq. cm!
From the equation, find the axis of symmetry of the parabola.
y = 2x2 + 4x - 1
a. X=3
C. X=-3
b. x=-1
X = 1
Answer:
B. x= -1
Step-by-step explanation:
axis of symmetry is: [tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-4}{2(2)} \\x=\frac{-4}{4}\\x=-1[/tex]
The axis of symmetry for the given parabola equation y = 2x²+ 4x - 1 is x = -1.
The axis of symmetry of a parabola in the form y = ax² + bx + c can be found using the formula x = -b/(2a). For the given equation y = 2x² + 4x - 1, we can identify a as 2 and b as 4. Substituting these values into the formula for the axis of symmetry gives us x = -4/(2²) = -1.
Determine the direction that this parabola opens y=x^2-6x
Answer:
the graph of the parabola opens upwards.
Step-by-step explanation:
For any quadratic equation of the form
[tex]ax ^ 2 + bx + c[/tex] is true that:
if the main coefficient "a" is negative then the graph of the parabola opens downwards.
If the main coefficient "a" is positive, the parabola opens upwards
In this case the parabola is [tex]y=x^2-6x[/tex]
Note that [tex]a=1[/tex] and [tex]a>0[/tex] therefore the graph of the parabola opens upwards.
Please help I’m confused!! I will mark brainliest
Hello There!
“A” 2g+17
“B” 18h-3
Have A Great Day!
Answer:
A) 2g + 17
B) 18h - 3
Step-by-step explanation:
Hello! The reasoning for A is 2 x g + 17 would be the algebraic expression for "the sum of 2 times g and 17.
the reasoning for B is the same reason as a it is the algebraic expression for "the product of 18 and h.
I hope this helped you good luck!
PLEASE GIVE A BRAINLIEST IT WOULD MEAN A LOT!
:)
Find the area of the triangle in terms of x
Answer:
4x + 16
Step-by-step explanation:
Area of a triangle is:
A = ½ bh
Here, b = x+4 and h = 8:
A = ½ (x + 4) (8)
A = 4x + 16
The area of the given triangle with sides 5x,8, and x+4 is 4x + 16.
We have given the diagram.
In the diagram we have,
base(b) = x+4 and height(h) = 8
We have to determine the area of the triangle
What is the area of a triangle?[tex]A = 1/2\times b\times h[/tex]
Where b is the base and h is the height of the triangle
Use the given values in the above formula we have,
[tex]A = 1/2(x + 4) (8)\\\\A = 4x + 16[/tex]
Therefore the area of the triangle is 4x + 16.
To learn more about the area of the triangle visit:
https://brainly.com/question/21735282
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Question 18.
A population of students in a summer program for students in
grades kindergarten to grade 8 is surveyed. Which statement
demonstrates sampling variability?
A.
In one random sample chosen from the population, the
mean age was 9.4 years. In another random sample, the
mean age was 9.8 years.
B. In one random sample chosen from the population, the
mean age was identical to that from another random sample.
C. The mean age of the population is 8.8 years, and the mean
age from a random sample was 9.2 years.
D.In one random sample chosen from the population, the
mean age was 9.4 years.
Answer: c
Step-by-step explanation:
sampling variability is the difference between the measured value of the random sample and the mean age of the population
Option A demonstrates sampling variability because the mean age changes between two random samples chosen from the same population, illustrating the concept of sampling variability in statistics.
Explanation:The subject of this question is a concept in statistics known as sampling variability. Sampling variability refers to the idea that the statistics of a random sample of a population (like mean, median, etc.) will vary from one sample to another. In essence, if we were to keep pulling samples from the same population, it's expected that our sample statistics will not always be the same.
In this context, the statement that demonstrates sampling variability is Option A: 'In one random sample chosen from the population, the mean age was 9.4 years. In another random sample, the mean age was 9.8 years.'. This demonstrates sampling variability because the mean age changes (varies) depending on the sample chosen from the population.
Learn more about Sampling Variability here:https://brainly.com/question/35495533
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Help please I can’t solve please
Answer:
d = 52 inC = 6π mm²Step-by-step explanation:
The formula of a circumference:
[tex]C=2\pi r=d\pi[/tex]
r - radius
d - diameter
We have [tex]C=52\pi\ in[/tex].
Calculate the diameter using [tex]C=d\pi[/tex]:
[tex]d\pi=52\pi[/tex] divide both sides by π
[tex]d=52\ in[/tex]
-------------------------------------------------------------------------
If a circle inscribed in a square, then the diameter of a circle and a side of a square are congruent (have the same length).
We have the area of the square:
[tex]A=36\ mm^2[/tex]
The formula of an area of a square:
[tex]A=s^2[/tex]
s - side
Substitute:
[tex]s^2=36\to s=\sqrt{36}\\\\s=6\ mm[/tex]
The formula of a circumference [tex]C=d\pi[/tex]
d - diameter
d = s → d = 6 mm
Substitute:
[tex]C=6\pi\ mm[/tex]
solve the system of equations below. -3x+6y=9
5x+7y=-49
A. (1,-2)
B.(-2,-7)
C.(-7,-2)
D.(-2,1/2)
[tex]
-3x+6y=9 \\
5x+7y=-49 \\ \\
-15x+30y=45 \\
15x+21y=-147 \\ \\
51y=-102 \\
\underline{y=-2} \\ \\
-3x+6\cdot(-2)=9 \\
-3x-12=9 \\
-3x=21 \\
\underline{x=-7} \\ \\
\boxed{(-7, -2)}
[/tex]
The answer is C.
Hope this helps.
r3t40
Answer:
(-7, -2) is the correct answer
3. What’s the answer to this question asap!
Because you are required to get a positive number of centimetres we use positive value of x.
[tex]
\mid6.75-x\mid<0.25 \\
6.75-x<0.25\Longrightarrow x>6.5
[/tex]
The answer is B: The length of a part must be greater than 6.5 cm.
Need to find the value of y
Answer:
√55
Step-by-step explanation:
Notice that the small triangle in the bottom corner shares an angle with the overall triangle. Also, they are both right triangles. Therefore, they are similar triangles.
Notice that the large triangle at the top shares an angle with the overall triangle and is also a right triangle. Therefore it is also similar to the overall triangle and the smaller triangle.
Writing a proportion between the small and large triangles:
y / 11 = 5 / y
y² = 55
y = √55
45% as fraction in the simplest form
Answer:9/20
Step-by-step explanation: 45/100=9/20, 45÷5=9, 100÷5=20 both the denominater and the numerator are divisible by 5.
To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100. 45% can be written as the ratio 45 to 100 or 45/100. Notice however that 45/100 is not in lowest terms so we need to dive both the numerator and denominator by the greatest common factor of 45 and 100 which is 5.
45 ÷ 5 = 9
100 ÷ 5 = 20
Therefore, 45% can be written as the fraction 9/20.
Cecile drew a 4-sided figure. It had 2 sides that were 3.4 centimeters long and 2 sides that were 3.3 centimeters long. It had at least 3 right angles. Which best describes the figure she drew?
square
rectangle that is not a square
quadrilateral that is not a parallelogram
trapezoid
answer would be the second one: Rectangle that is not a square
Answer:
B.Rectangle that is not a square.
Step-by-step explanation:
We are given that Cecile drew a 4-sides figure. it means a quadrilateral.It had 2 sides that were 3.4cm long and 2 sides that were 3.3 centimeters long.
We are given that a quadrilateral had atleast 3 right angles.
If a quadrilateral had 3 right angles then the IV angle of quadrialteral is also right angle.
In quadrlateral ABCD
[tex]\angle A=90^{\circ}[/tex]
[tex]\angle B=90^{\circ}[/tex]
[tex]\angle C=90^{\circ}[/tex]
[tex]\angle A+\angle B+\angle C+\angle D==360^{\circ}[/tex]
By angle sum property of quadrilateral
[tex]90+90+90+\angle D=360[/tex]
[tex]270+\angle D=360[/tex]
[tex]\angle D=360-270=90^{\circ}[/tex]
Hence, IV angle of quadrilateral is also right angle.
Given two sides of quadrilateral are equal and other two sides of quadrilateral are equal.Therefore, the given quadrilateral can be rectangle not square because in square four sides are of equal lengths.
Hence, the given quadrilateral can be rectangle but not square.Therefore, option B is correct.
The shed in Adam’s backyard is shown below. Which correctly describes the dimensions of the figures that make up the shed? a rectangular prism measuring 5 feet by 6 feet by 8 feet and a triangular prism with the dimensions of 3 feet by 5 feet by 8 feet a rectangular prism measuring 3 feet by 5 feet by 8 feet and a triangular prism with the dimensions of 5 feet by 6 feet by 8 feet a rectangular prism measuring 5 feet by 6 feet by 8 feet and a triangular prism with the dimensions of 3 feet by 5 feet by 6 feet a rectangular prism measuring 3 feet by 5 feet by 6 feet and a triangular prism with the dimensions of 5 feet by 6 feet by 8 feet
Answer:A
Step-by-step explanation:took the test
The correct option is a. A rectangular prism measuring 5 feet by 6 feet by 8 feet and a triangular prism with the dimensions of 3 feet by 5 feet by 8 feet describes the correct dimensions of the figures.
A rectangular prism has three dimensions: length, width, and height.
A triangular prism has three dimensions: the base of the triangular face, the height of the triangular face, and the length (or depth) of the prism.
Let's examine each option based on the given dimensions:
Option a is the correct answer. It logically fits the dimensions of the shed with a larger rectangular prism for the base and a reasonably proportioned triangular prism for the roof.
In figure, the dimensions of rectangular prism are 5 feet by 6 feet by 8 feet and the dimensions of triangular prism are 3 feet by 5 feet by 8 feet.
The complete question is
The shed in Adam’s backyard is shown below.
Which correctly describes the dimensions of the figures that make up the shed?
a. a rectangular prism measuring 5 feet by 6 feet by 8 feet and a triangular prism with the dimensions of 3 feet by 5 feet by 8 feet
b. a rectangular prism measuring 3 feet by 5 feet by 8 feet and a triangular prism with the dimensions of 5 feet by 6 feet by 8 feet
c. a rectangular prism measuring 5 feet by 6 feet by 8 feet and a triangular prism with the dimensions of 3 feet by 5 feet by 6 feet
d. a rectangular prism measuring 3 feet by 5 feet by 6 feet and a triangular prism with the dimensions of 5 feet by 6 feet by 8 feet
negative two and one thirds minus negative five
If your "and" means multiplication than:
[tex]-2\times\frac{1}{3}-(-5) \\
\frac{-2}{3}+5 \\
\frac{-2+15}{3} \\
\boxed{\frac{13}{3}\approx4.33\dots}
[/tex]
If it is a logical and than we are unable to solve the problem since you didn't provide any variables that would have a meaningful values.
Hope this helps.
if f(x)=2(x)^2+5sqrt(x+2), complete the follwoing statement ( round your answer to the nearest hundreth) : f(0)=_____
Answer:
[tex]f(0)=7.07[/tex]
Step-by-step explanation:
We have the function [tex]f(x)=2(x)^2+5\sqrt{(x+2)}[/tex]
In this case we want to find the value of f0)
To find f(0) you must replace the x in the function with the number 0 and solve as shown below
[tex]f(0)=2(0)^2+5\sqrt{(0+2)}[/tex]
[tex]f(0)=0+5\sqrt{(0+2)}[/tex]
[tex]f(0)=5\sqrt{(2)}[/tex]
Therefore
[tex]f(0)=7.07[/tex]
Function g can be thought of as a scaled version of f(x)=x^2. Write the equation for g(x).
To write the equation for g(x) which is a scaled version of f(x)=x^2, we can use the general form of a quadratic function y=a(x-h)^2+k. The value of a determines the scaling factor.
Explanation:To write the equation for g(x) which is a scaled version of f(x)=x^2, we can use the general form of a quadratic function y=a(x-h)^2+k. The value of a determines the scaling factor. Since g(x) is a scaled version of f(x), a is the scaling factor. Therefore, the equation for g(x) is g(x)=a(x-h)^2+k, where a is the scaling factor, h is the x-coordinate of the vertex of f(x), and k is the y-coordinate of the vertex of f(x).
The scaled version of the function f(x) = x^2 is g(x) = a * x^2, where a is the scale factor determining the graph's stretch or compression.
If the function g is considered a scaled version of f(x) = x^2, it means that g will also be a quadratic function, but with a constant factor that scales or stretches the graph of f. The general form of a scaled quadratic function is g(x) = a * x^2, where a is the scale factor.
This scale factor a could be any real number. It determines whether the graph of g is narrower or wider compared to f. For example, if a is greater than 1, the graph of g will be narrower; if 0 < a < 1, the graph will be wider; and if a is negative, the graph will be reflected over the x-axis.
If angle PQR and angle RQS form a linear pair and angle PQR =5x+5 and angle RQS =11x-65 then angle PQR=?
Answer:
m<PQR = 80°
Step-by-step explanation:
Points to remember
Sum angles in a linear pair is 180
To find the value of x
It is given that, angle PQR and angle RQS are linear pairs, and
m< PQR =5x+5 and m<RQS =11x-65
m<PQR + m<RQS = 180
5x + 5 + 11x - 65 = 180
16x -60 = 180
16x = 180 + 60
16x = 240
x = 15
To find the value of angle PQR
m<PQR = 5x + 5
= 5*15 + 5
= 75 + 5 = 80
Therefore m<PQR = 80°
Alison is playing a video game. At the end of each level, the player is given either a bag of gold or a magic wand.
Alison says that the probability of getting a bag of gold is 30%. To test this, she plays the game 50 times and calculates the relative frequency of each outcome.
Outcome Bag of Gold Magic Wand
Relative frequency 0.32 0.68
Select from the drop-down menus to correctly complete each statement.
The relative frequency of getting a bag of gold is
30%.
Alison's claim about the theoretical probability is likely to be
.
Further, this means that the theoretical probability of getting a magic wand is most likely
.
Outcome Bag of Gold Magic Wand
Relative frequency 0.32 0.68
The relative frequency of getting a bag of gold is .......... reasonably close
.32 is close to 30% so
Alison's claim about the theoretical probability is likely to be 2............true
Further, this means that the theoretical probability of getting a magic wand is most likely 3............1 - 30% = 70%
Find x. Assume that segments that appear tangent are tangent.
a.
56
c.
32
b.
28
d.
20
Answer:
c. 32
Step-by-step explanation:
The problem states that we need to assume that segments that appear tangent are actually tangent. From the figure, the tangent segment is the one that measures [tex]x[/tex] while the radius measures 24. The key in this problem is that if a radius of a circle and a tangent line to that circle touch intersect at the same point, then they form a right angle there. Accordingly, we have a right triangle here, so using the Pythagorean theorem, we can find [tex]x[/tex]. Thus:
[tex]x=\sqrt{40^2-24^2} \\ \\ x=\sqrt{1600-576} \\ \\ \boxed{x=32}[/tex]