The solutions of the equation x² – 5x – 24 = 0 will be 8 and -3. Then the correct option is D.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The quadratic equation is given below.
x² – 5x – 24 = 0
Then the factor of the equation will be
x² – 5x – 24 = 0
x² – 8x + 3x – 24 = 0
x(x – 8) + 3(x – 8) = 0
(x – 8)(x + 3) = 0
x = 8, -3
Then the correct option is D.
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HELP, PLATO!!!!!!!
David proved the Law of Cosines with reference to ∆ABC using a different method. Arrange the steps of his proof in the correct sequence.
Answer:
the law of cosines with ABC
A school administrator bought 6 desk sets. Each set consists of one table and one chair. He pald $48.50 for each chair. If he pald a total of $663 for the 6 sets, the cost of each table Is
4 rows with circles and triangles, left to right. Row 1, circle, triangle, 2 circles, triangle. Row 2, triangle, circle, 2 triangles, circle, triangle. Row 3, circle, 2 triangles, circle, triangle. Row 4, triangle, 2 circles, 2 triangles. The ratio of the number of circles to the number of triangles in simplest form is . The number of circles that need to be added to make the ratio 1 : 1 is .
The ratio of circle to triangles is; 3:4 and the number of circles which should be added to make the ratio 1:1 is; 3.
What is the ratio of circles to triangles?It follows from the task content that the total number of circles and triangles in all 4 rows and can be counted and concluded as; 9 and 12 respectively.
Hence, the ratio of circles to triangles is 9 to 12 and in its simplest form is; 3:4.
However, to make the ratio 1:1, the number of circles and triangles must be equal. Hence, 3 circles must be added to make the ratio 1:1.
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RSTU is an isosceles trapezoid with bases RS and TU.
Find x and m/S if m/R=4x +11 and m/T=2x-5.
[tex]\angle R[/tex] and [tex]\angle S[/tex] are supplementary by the same-side interior angles theorem, and [tex]\angle S \cong \angle T[/tex] because of the properties of an isosceles trapezoid, meaning that [tex]\angle R[/tex] and [tex]\angle T[/tex] are supplementary.
[tex]4x+11+2x-5=180\\\\6x+6=180\\\\6x=174\\\\x=\boxed{29}\\\\\implies m\angle S=m\angle T=2(29)-5=\boxed{53^{\circ}}[/tex]
Which expression represents the distance Kelli traveled downstream?
0.1(x – 5)
0.1(x + 5)
The distance that Kelli can swim will be about 6.11 kilometers per hour.
How to calculate the distance?Here is the complete question:
Solve the equation x – 5 = 0.1(x + 5) for x. Round your answer to the nearest hundredth. Kelli can swim about km/hour.
To solve for x, you need to follow SADMEP. SADMEP is subtraction, addition, division, multiplication, exponents, and parentheses.
It follows the same rules as PEMDAS, but SADMEP is only used when solving algebraic equations.
x - 5 = 0.1(x + 5) (use the distributive property)
x - 5 = 0.1x + 0.5 (subtract 0.1x to both sides)
0.9x - 5 = 0.5 (add 5 to both sides)
0.9x = 5.5 (divide both sides by 0.9)
x = 6.11 km/hour.
Therefore, Kelli can swim about 6.11 kilometers per hour.
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Answer:
It's the first one for upstream and the other one for downstream
Step-by-step explanation:
Clasify each polynomial based on the number of terms it contains
Answer:
Monomial - one term
Binomial - two terms
Trinomial - three terms
Polynomial - any polynomial with more than three terms
Brainliest, please :)
NO LINKS!!!! What is the transformation of f (x)= x^3:
PART 4:
THIS IS NOT MULTIPLE CHOICE!!!!
10. f(x)= (x+5)^3
11. f(x)= (1/5x)^3
12. f(x)= (-x)^3
Answer:
10. Left 5
11. Horizontal stretch by a factor of 5
12. Horizontal reflection
Step-by-step explanation:
Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Identify the transformations that take the parent function to the given function.
Question 10
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(x+5)^3[/tex]
Comparing the parent function with the given function, we can see that 5 has been added to the x-value of the parent function.
Therefore, the transformation is:
[tex]f(x+5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units left}[/tex]
Question 11
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=\left(\dfrac{1}{5}x\right)^3[/tex]
Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by ¹/₅.
Therefore, the transformation is:
[tex]y=f\left(\dfrac{1}{5}x\right) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{\frac{1}{5}}[/tex][tex]\textsf{As }\dfrac{1}{\frac{1}{5}}=5 \implies \textsf{horizontal stretch by a factor of 5}[/tex]
Question 12
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(-x)^3[/tex]
Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by -1.
Therefore, the transformation is:
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
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The value of [tex]\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)-\sin ^{-1}\left(\frac{1}{2}\right)[/tex] is
Answer:
[tex]\displaystyle \frac{\pi}{6}[/tex]
Explanation:
According to the unit circle, [tex]\displaystyle \frac{\pi}{3}[/tex] and [tex]\displaystyle \frac{\pi}{6}[/tex] are the radian measures you are looking for because all y-coordinates are associated with the sine function, so when evaluating, you will arrive at this:
[tex]\displaystyle \boxed{\frac{\pi}{3}} = \frac{\pi}{3} - \frac{\pi}{6}[/tex]
I am joyous to assist you at any time.
A certain 90-mile trip took 2 hours. Exactly 1/3 of the distance traveled was by rail and this part of the trip took 1/5 of the travel time. What was the average rate, in miles per hour, of the rail portion of the trip?
A. 71 B. 73 C. 74 D. 75
The average rate, in miles per hour, of the rail portion of the trip is; D: 75
How to calculate the average speed?Since exactly 1/3 of the distance travelled was by rail, then we can say that;
(1/3) * (90) = 30 miles
We are told that part of the trip took 1/5 of the travel time. Thus;
Time it takes to travel that distance is:
(1/5) * (2) = 2/5 of an hour
Average rate is;
30/(2/5) = 150/2 = 75 mph
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The equation y minus 1 = negative 7 (x minus 3). is written in point-slope form. What is the y-intercept of the line? –4 –2 20 22
Answer:
22
Step-by-step explanation:
Hello!
We can convert it into slope-intercept form.
Slope - Intercept Form: [tex]y = mx +b[/tex]
m = slopeb = y-interceptConverty - 1 = -7(x - 3)y = -7x + 21 + 1y = -7x + 22The y-intercept of the line is 22.
Giving brainliest!!!!!
I think it is 49123.52
Step-by-step explanation:
Analyze and sketch the polynomial functions and complete the charts below. State the degree and sign of the leading coefficient of the polynomial functions. Determine the end behavior of the graph of the functions. For 5b, write the polynomial function as a product of linear factors (in factored form).
a. f(x) = –7(x + 2)^3(x – 1)^2(x – 3) Zeros Multiplicity Crosses/Touches
Degree Sign
End behavior
b. m(x) = x^3 – 4x^2
Factored form: m(x) =
Degree Zeros Multiplicity Crosses/Touches
Sign End behavior
See below for the properties of the functions
How to analyze the functions?The function f(x)
We have:
f(x) = –7(x + 2)^3(x – 1)^2(x – 3)
From the graph, we have the following features:
Leading coefficient: Negative, because -7 is negativeZeros: x = -2 at multiplicity = 3, x = 1 at multiplicity = 2 and x = 3 at multiplicity = 1Crosses = 2Touches = 3End behavior = [tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:-\infty \:[/tex]The function m(x)
We have:
m(x) = x^3 - 4x^2
Factor out x^2
m(x) = x^2(x - 4)
Factor out x
m(x) = x(x)(x - 4)
From the graph, we have the following features:
Leading coefficient: PositiveZeros: x = 0 at multiplicity = 2, x = 4 at multiplicity = 1Crosses = 1Touches = 1End behavior = [tex]\mathrm{as}\:x\to \:+\infty \:,\:m\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:m\left(x\right)\to \:-\infty \:[/tex]Read more about functions at:
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Drag each label to the correct location on the chart. Not all labels will be used. Given: and are supplementary and are supplementary Prove: The two linear pairs and one supplementary angle with values of 1, 2, and 3 Statements Reasons 1. and are supplementary 1. given 2. and are supplementary 2. given 3. 3. congruent supplements theorem Complete the flow chart to show the proof. vertical angles theorem given congruent complements theorem congruent supplements theorem
Based on the Congruent Supplements Theorem, <1 = <3 are congruent, given that <1 and <2 and <2 and <3 are supplements.
What does the Congruent Supplements Theorem say?The Congruent Supplements Theorem shows that when two angles are considered to be supplements of a certain angle, then those two angles must be congruent.
Filling in the chart would therefore be:
<1 and <2 are
supplementary <1 = <3
GIVEN Congruent Supplements Theorem
<2 and <3 are
supplementary
GIVEN
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The graph of a system of inequalities is shown.
195
554-3-2-1
4
(5
-5-
-6
-7
-8
9
23 x
Which system is represented by the graph?
O
O
y> 2x
x+2y≤-8
y≥ 2x
x+2y<-8
y< 2x
x+2y²-8
y≤2x
x+2y>-8
Answer: Option (1)
Step-by-step explanation:
The line y = 2x is shaded above and is dotted, so it represents [tex]y > 2x[/tex].
This eliminates all the options except for option (1).
The graph of a system of inequalities is shown. The following system of inequations represents the graph:
y ≥ 2x;
x + 2y ≤ -8:
Inequality refers to a condition in which there's a lack of equivalency or aesthetics, frequently panning out in disparities or differences in chances, resources, treatment, or outcomes among individuals, groups, or associations. It encompasses various forms, including economic inequality, colonial inequality, and political inequality.
The blue region is on the left of the blue line of equation y = 2x so the region is represented by the line y ≥ 2x. The equality holds in this inequality as the region also includes the origin (0, 0).
The second option only has the inequality y ≥ 2x in its system of inequalities.
So, the correct answer is the second one. The system of inequation is
y ≥ 2x;
x + 2y ≤ -8:
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b) The resale value of a piece of industrial equipment has been found to behave according to the function V=700,000e-0.02t.
i) What was the original value of the piece of equipment
The original value of the piece of equipment is 700000
How to determine the original value?The resale value is given as:
V=700,000e^(-0.02t)
The original value is when t = 0.
So, we have:
V=700,000e^(-0.02 *0)
Evaluate the product
V=700,000e^0
This gives
V=700,000 * 1
Evaluate
V=700000
Hence, the original value of the piece of equipment is 700000
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If we approximate the function y=sin(x) with a0+a1 x a2 x^2 +a3 x^3, what is a0,a2,a2,a3?
The coefficients [tex]a_0,a_1,a_2,a_3[/tex] could be chosen to be the coefficients in the Maclaurin series of [tex]\sin(x)[/tex].
We have
[tex]y = \sin(x) \approx a_0 + a_1 x + a_2 x^2 + a_3 x^3 \\\\ \implies y(0) = 0 = a_0[/tex]
[tex]y' = \cos(x) \approx a_1 + 2a_2 x + 3a_3 x^2 \\\\ \implies y'(0) = 1 = a_1[/tex]
[tex]y'' = -\sin(x) \approx 2a_2 + 6a_3 x \\\\ \implies y''(0) = 0 = 2a_2[/tex]
[tex]y''' = -\cos(x) \approx 6a_3 \\\\ \implies y'''(0) = -1 = 6a_3[/tex]
It follows that [tex]a_0=0[/tex], [tex]a_1=1[/tex], [tex]a_2=0[/tex], and [tex]a_3 = -\frac16[/tex].
please help me with this math problem
will mark brainiest
Using the given exponential function, the age of the skull is 6,733 years old.
What is the exponential function for the skull's amount?It is given by:
[tex]N(t) = N(0)e^{-kt}[/tex]
In which:
N(0) is the initial amount.k is the decay rate.t is the time in years.In this problem, the parameters are given as follows:
N(t) = 0.51N(0), k = 0.0001.
Hence we solve for t to find the age.
[tex]N(t) = N(0)e^{-kt}[/tex]
[tex]0.51N(0) = N(0)e^{-0.0001t}[/tex]
[tex]e^{-0.0001t} = 0.51[/tex]
[tex]\ln{e^{-0.0001t}} = \ln{0.51}[/tex]
[tex]-0.0001t = \ln{0.51}[/tex]
[tex]t = -\frac{\ln{0.51}}{0.0001}[/tex]
t = 6,733 years old.
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HELP! ASAP!
F is a right angle, and segment (a)(f), BG, and CH are all parallel. Use this information to explain why ∆AFD ~ ∆BGD ~∆CHD. Support your answer using a postulate or theorem.
Use the diagram to answer each part of the question
By the corresponding angles theorem,
∠AFG, ∠BGD, and ∠CHD are congruent∠BAF, ∠CBG, and ∠DCH are congruentThus, triangles AFD, BGD, and CHD are similar by AA.
Given the figure, triangles AFD, BGD, CGD are similar by Angle-Angle-Angle (AAA) criterion for the similarity.
The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that “If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar”.
In the given question,
∠F = ∠G = ∠H = 90°
Let ∠D = x°
In triangle CHD,
∠H = 90°
∠D = x°
∠C = 180 - 90 - x = (90-x)°
In triangle BGD,
∠G = 90°
∠D = x°
∠B = 180 - 90 - x = (90-x)°
In triangle AFD,
∠F = 90°
∠D = x°
∠A = 180 - 90 - x = (90-x)°
In triangle AFD and BGD and CHD,
∠A = ∠B = ∠C
∠F = ∠G = ∠H
∠D = ∠D =∠D
triangle AFD and BGD and CHD are similar.
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have someone who can can help me with this I need help
Answer is underlined
BD: 16.8+50.4= 67.2 mm
LM: 4-2.6= 1.4 cm
Which statements are true about exponential functions? Check all that apply.
The domain is all real numbers.
The range always includes negative numbers.
The graph has a horizontal asymptote at x = 0.
The input to an exponential function is the exponent:
The base represents the multiplicative rate of change.
Answer:
edge 2023
Step-by-step explanation:
A D E (dudes above me right js making it easier)
If 2x/7 divided by 1=0 then what will be value of x is
The value of x = -3/2 .
What is an Equation ?An equation is a mathematical statement that relates unknown variable to constants to determine their value.
The equation given is
(2x+3 ) / 7 Divided by 1 = 0
2x +3 = 0
2x = -3
x = -3/2
Therefore the value of x = -3/2 .
The complete equation is
(2x+3)/7
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What is the value of x in the triangle?
The value of x in the right triangle is 4 units.
How to find the side of a right triangle?The side x of the right triangle can be found using trigonometric ratios.
Therefore,
sin 30° = opposite / hypotenuse
sin 30 = x / 8
1 / 2 = x /8
cross multiply
8 = 2x
divide both sides by 2
8 / 2 = 2x / 2
x = 4
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Given that the Earth orbits the Sun with an orbital velocity of about 29.8 km/s and a radius of 1 AU, use the equation above to estimate the total mass in the solar system inside the orbit of the Earth. Is this similar to the mass of the Sun? Remember to convert units to S.I. units of meters, kilograms, and seconds before proceeding so that your answer is in kg.
Answer:
I would like to use lb if that's ok
The question is down below
also I home school and have permission to post this question
Answer:
2448 ft²
Step-by-step explanation:
The surface area of the triangular prism is the sum of the areas of the triangular bases and the lateral area of the rectangular faces.
Base areaThe two right triangle bases together form a rectangle that is 24 ft wide and 18 ft tall. The total base area is ...
A = (24 ft)(18 ft) = 432 ft²
Lateral areaThe rectangular faces of the prism are each 28 ft wide and have a total width of 18 +24 +30 = 72 ft. Their total area is ...
LA = (28 ft)(72 ft) = 2016 ft²
Total surface areaThe sum of the base area and lateral area is ...
total area = (432 ft²) +(2016 ft²) = 2448 ft²
The surface area of the triangular prism is 2448 ft².
__
Additional comment
The area formula for the triangular base is ...
A = 1/2bh . . . . . . area of one triangle with base b and height h
Then the area of the two congruent triangular bases is ...
A = 2(1/2bh) = bh
This is the formula we used above. It skips the work of dividing by 2, then multiplying by 2 again.
Find the x-intercept of the graph of the linear equation y = −1
2
x + 3.
x-intercept
Answer:
there is no x-intercept
Step-by-step explanation:
The graph of the equation y = -1 is a horizontal line that passes through (0, -1). The line is parallel to the x-axis. It never intersects the x-axis. There is no x-intercept.
Your elderly neighbor places a bag of corn kernels on your doorstep each morning. The first day, the bag contained 1 kernel of corn, the second day it contained 2 kernels
of corn, 4 kernels of corn the third day, and so on. Each kernel of corn weighs 0.06 grams. How many kernels of corn will be in the bag on the 22nd day?
Answer:
2^25
Step-by-step explanation:
Given
On first day bag contained 1 kernels
on second bag contained 2 kernels of corn
on third day bag contained 4 kernels of corn
on n th day bag contains 2n-1 kernels of corn
thus on 26 th day bag contains 2^26= 2^25=33,554,432 kernel
Each kernel weigh 0.07 gm
Therefore 2^25 kernels weighs = 2^25 x 0.07
Therefore on 26 th day 2^25 kernel weighs 23,488.1024 kg
PLS ANSWERS QUCIK THANK YOU
Answer:
394.13cm²
Step-by-step explanation:
Formula: The area of a circle is found by A = πr²
Given:
radius is 11.2cm (shown in circle)π = 3.142Plug in:
A = πr² → A = (3.142)(11.2)²
→ A = (3.142)(125.44)
→ A = 394.13248
"2 decimal places", round up to 394.13
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5) Solve the simultaneous equations log(x+y)=0 Solve the simultaneous equations 2logx=log(y+1)
Answer:
(1,0)
Step-by-step explanation:
Since log (x+y) = 0 you should know x+y = 1
so y = (1-x)
then 2 logx = log (y+1)
log x^2 = log (1-x +1) = log (2-x)
x^2 = 2-x
x^2 + x-2 = 0
(x+2)(x-1) = 0 so x = -2 or +1
then y = 3 or 0
-2,3 and 1,0 since you cannot have a log of a negative number
the only answer is (1,0)
the data represented by the following stem-and-leaf plot range from to .
4|578
5|14
6|023
7|69
A. 45,76
B. 48,79
C. 45,79
D. 48,76
Considering the stem-and-leaf plot, the range of the data-set is given as follows:
C. 45,79
What is an stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
Considering the key format, the smallest value in this problem is 4|5 = 45, and the highest is 7|9 = 79, hence the range is given by:
C. 45,79
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Could someone help me out?
Limit, can be defined as the every nearby the value of a variable for a function exists, is called limits|
⇒ [tex]\lim_{h \to0 \zero} 46x^11+32xh^3+6x^15h+23[/tex]
When putting h = 0
⇒ [tex]46x^11+23[/tex]
Thus, the value of a function of its limit is given by [tex]46x^11+23[/tex]
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