Step-by-step explanation:
Part A:
4x² - 7x - 15
a, b, c = 4, -7, -15
ac = -60
factors that add up to -7 and multiply to -60 are (-12, 5)
rewrite equation
(4x² - 12x) + (5x - 15)
factor out GCF from both groups
4x(x - 3) + 5(x - 3)
(4x+5)(x-3)
Part B:
Using the factored form from the previous part we can set both factors equal to 0 to solve for x.
4x+5 = 0
4x = -5
x = -5/4
x-3 = 0
x = 3
the two x-intercepts are -5/4 and 3
Part C:
Since the leading coefficient is positive, the right side of the function will be going up or to positive infinity as x goes towards positive infinity. Since the degree is even both sides go in the same direction so on the left side it also goes towards positive infinity as x goes towards negative infinity.
Given:
p: Angles XYZ and RST are vertical angles.
q: Angles XYZ and RST are congruent.
Which statement is logically equivalent to p → q?
A. If angles XYZ and RST are congruent, then they are vertical angles.
B. If angles XYZ and RST are not vertical angles, then they are not congruent.
C. If angles XYZ and RST are not congruent, then they are not vertical angles.
D. If angles XYZ and RST are vertical angles, then they are not congruent.
Answer:
C
Step-by-step explanation:
The contrapositive is always logically equivalent to the original statement.
Answer:
C
Step-by-step explanation:
Pls help asap ily
one hour after junior space cadet had left his house, his sister gwen discovered that he had forgotten his head. if junior was driving at a speed of 50 mph, and gwen drove at a speed of 75 mph, how many hours did it take gwen to restore junior's head to his shoulders?
Answer:
2 hours
Step-by-step explanation:
you can write two linear equations and then set them equal to each other to see when they intersect. so for the first equation which will be representing the junior space cadets distance from his house. this can be written as
d = 50t + 50
where t represents time and d represents distance. there is 50 being added to the equation since he had already been traveling for an hour
the second equation which will represent his sister Gwen can be represented as
d = 75t
Now we set them equal to each other
50t + 50 = 75t
50 = 25t
2 = t
sin theta / cos theta - cos theta/ sin theta
Answer:
tan theta - cot theta
Step-by-step explanation:
sin/cos = tan
cos/sin = cot
james brewer purchased 100 shares of stock for $73 a share. james also paid a $60 commission. what was the total purchase price for this transaction?
Answer:
$ 7360.00
Step-by-step explanation:
100 shares * $ 73/share + $60 = $ 7360
Based on the calculation below, the total purchase price for this transaction is $7,360.
How do we calculate the total purchase price of shares of stock?The total purchase price for this transaction can be calculated using the following formula:
Total purchase price = (Price per share * Units of shares purchased) + Commission ...................................... (1)
Substituting all the values into equation (1), we have:
Total purchase price = ($73 * 100) + $60 = $7,360
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What is the factored form of the expression?
24g2 – gh – 10h2
The factored form of the expression is 2(g-h)(12g+5h)
What is a Quadratic Expression ?A quadratic Expression is what can be written in the form of
ax²+bx +c
The given quadratic expression is
24g² -gh -10h²
10g² - 10h² +14g² -gh
10(g+h)(g-h) +14 g(g -h)
(g-h)(10 g +10h +14g)
2(g-h)(12g+5h)
Therefore the factored form of the expression is 2(g-h)(12g+5h).
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can someone please help meee
Answer:
with a line accross the points
On January 1, 2023, One of Mr. Cutter’s chickens flies away and lands on a Hawaiian Island. She
immediately begins laying and hatching eggs. The chicken population on the island begins to
triple every year. Write and graph a function that represents this situation. How many chickens
will be on the island on January 1, 2033?
Answer:
Step-by-step explanation:
Do you have any options or a graph?
PLSS HELP ITS ANGLESSS
Answer: D. 66°
Step-by-step explanation:
A triangle has 180° and we already have the numbers for two sides. We must find the answer that adds up to 180°.
A. 43° + 71° + 19°= 133°
B. 43° + 71° + 77°= 191°
C. 43° + 71°+ 114= 228°
D. 43° + 71° + 66°= 180°
With this information, we know that the answer is D. 66°.
I hope this helps! Pls give brainliest :)
What is the equation of the line?
y=13x
y=−13x
y = 3x
y=−3x
Hi!
I am not completely sure what you mean but if you are looking for the slope of a line here is the best way to find it.
Y=Mx+b
it look difficult but really it's quite easy and once you get it it's super memorable. Y will always be Y that doesn't change. The M is the slope of the line (don't let equations confuse you with different letters! the M might be different but it is always the letter next to x) and b is the y intercept (where the line crosses y). All you need to find the slope of a line is 3 points. I see here you have a graph. So what you do is count how much it's moving up each block on the graph. I would say your slope is about 1/3. Y is really easy! just find the point it crosses the y axis(horizontal axis or the one going up and down) for yours it's 0. So your answer is y=1/3x+0
Need help (pic included)
The value of the coefficient of xy is 0.
What is an algebraic expression?It is an expression made of numbers and letters where the numbers are called coefficient.
Analysis:
(ax+by)(cx-dy)
ac[tex]x^{2}[/tex] -adxy +bcxy -bd[tex]y^{2}[/tex]
But, ac = 18, ad=bc, bd = 50
18[tex]x^{2}[/tex] -xy(bc -ad) - 50[tex]y^{2}[/tex]
since bc = ad, the coefficient of xy = 0
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Is the following statement a good definition? Why? An integer is divisible by 100 if and only if its last two digits are zeros. No, it is not. When the definition is separated into two conditional statements, one of the statements is false. Yes, it is. When the definition is separated into two conditional statements, one of the statements is true. Yes, it is. When the definition is separated into two conditional statements, both of the statements are true. No, it is not. When the definition is separated into two conditional statements, both of the statements are false.
The given statement is An integer is divisible by 100 if and only if its last two digits are zeros.
The two conditional statements that can be made are:
1) If an integer is divisible by 100 its last two digits are zeros.
This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have the last two digits zeros.
What happen when last two digit of the number are 0?
2) If the last two digits of an integer are zeros, it is divisible by 100.
This is also true. If the last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.
Therefore, the two conditional statements that are formed are both true.
So, option A is the correct answer.
Yes, it is. When the definition is separated into two conditional statements, both of the statements are true.
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The given statement is An integer is divisible by 100 if and only if its last two digits are zeros.
What is Integers?An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.
The two conditional statements that can be made are:
1) If an integer is divisible by 100 its last two digits are zeros.
This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have the last two digits zeros.
2) If the last two digits of an integer are zeros, it is divisible by 100.
This is also true. If the last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.
Therefore, the two conditional statements that are formed are both true.
So, option A is the correct answer.
Yes, it is. When the definition is separated into two conditional statements, both of the statements are true.
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what odd 3 digit number has digits that are all the same and that add up to 9?
Answer:
3
Step-by-step explanation:
3 is an odd number and obviously the only odd (same) three digit that add up to 9
like and mark as BRAINIEST
Show work, can someone help me out having trouble with this problem
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: f = \cfrac{9}{a}+7[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \:a = \cfrac{9}{f - 7} [/tex]
[tex]\qquad \tt \rightarrow \:a(f - 7) = 9[/tex]
[tex]\qquad \tt \rightarrow \:(f - 7) = \cfrac{9}{a}[/tex]
[tex]\qquad \tt \rightarrow \:f = \cfrac{9}{a} + 7[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Question Progress
1/3 Marks
a)
By rounding to 1 significant figure, estimate the answers to these questions:
b)
247 × 201
756 x 8674
Homework Progress
c) 3025 × 2007
22/32 Marks
Part (a)
[tex]247 \approx 200\\\\201 \approx 200\\\\\implies 247 \times 201 \approx 200 \times 200=\boxed{40000}[/tex]
Part (b)
[tex]756 \approx 800\\\\8674 \approx 9000\\\\\implies 756 \times 8674 \approx 800 \times 9000 =\boxed{7200000}[/tex]
Part (c)
[tex]3025 \approx 3000\\\\2007 \approx 2000\\\\\implies 3025 \times 2007 \approx 3000 \times 2000=\boxed{6000000}[/tex]
What is the measure of x?
16
x=[?]
Give your answer in simplest form.
Answer: [tex]8\sqrt{5}[/tex]
Step-by-step explanation:
By the geometric mean theorem,
[tex]\frac{y}{16}=\frac{4}{y}\\\\y^{2}=64\\\\y=8[/tex]
Thus, by the Pythagorean thoerem,
[tex]8^2 +16^2=x^2\\\\320=x^2\\\\x=\boxed{8\sqrt{5}}[/tex]
Which of the following is the graph of the piecewise function h of x is defined as negative x squared plus 2 for x is less than or equal to negative 2, or one half times x for negative 2 is less than x is less than 2, or x squared minus 2 for x greater than or equal to 2.?
The attached graph represents the piecewise function h(x)
Complete questionWhich of the following is the graph of the piecewise function
[tex]h(x) = \left[\begin{array}{cc}-x^2 + 2 &x \le -2\\ \frac 12x&-2 < x < 2\\x^2 - 2&x \ge 2\end{array}\right[/tex]
How to determine the graph of the function?The function is given as:
[tex]h(x) = \left[\begin{array}{cc}-x^2 + 2 &x \le -2\\ \frac 12x&-2 < x < 2\\x^2 - 2&x \ge 2\end{array}\right[/tex]
The above means that the piecewise function has 3 domains
2 of which are quadratic functionsThe last one is a linear functionNext, we plot the graph using a graphing tool
See attachment for the graph of the piecewise function h(x)
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[tex]-2(bx - 5) = 16[/tex]
Answer:
bx=-3
Step-by-step explanation:
-2(bx-5)=16
Use distributive property.
-2bx+10=16
Now, subtract 10 from both sides.
-2bx=6
Divide -2 from both sides.
bx=-3
Hope this helps!
If not, I am sorry.
Determine f(4) for A piecewise function f of x in three pieces. The function is defined by part 1, which is x cubed for x less than negative 3, part 2, which is 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than or equal to 4, and part 3 which is 5 times x plus 4, for x greater than 4..
23
24
41
64
Answer:
23
Step-by-step explanation:
seen it before
cho tam giác DEF cân tại D có đường trung tuyến DI
a) Chứng minh tam giác DEI = tam giác DFI
b) Các góc DIE và góc DIF là góc gì
16
Select the correct answer from each drop-down menu.
4
Each participant tastes snack A and snack B and then chooses their favorite. Some participants have eaten snack A before and some have not
The results of the test are shown in a table. Using the data in a table, the company that makes snack A calculates probabilities related to a
random selected person.
Has Eaten Snack A
before
Prefers Snack A
144
2 Edmentum. All rights reserved.
Type here to search
Prefers Snack B
Has Not Eaten
108
Snack A before
Total
252
320
Complete the conclusions based on the data in the table.
92
O
228
Total
236
Given a person who has eaten snack A before, the customer will
Given a person who has not eaten snack A before, the customer will want to eat snack
Reset
336
572
Next
75°F Sunny A
ave & Exit
6:46 AM
6/30/2022
The conditional probability values are 0.57 and 0.43
Missing informationHas Eaten before Have not Total
Snack A 144 108 252
Snack B 92 228 320
Total 236 336 572
Using the data in a table, the company that makes snack A calculates probabilities related to a random selected person.
Given a person who has eaten snack A before, the customer will want to eat snack AGiven a person who has not eaten snack A before, the customer will want to eat snackHow to determine the probabilities?The required probabilities are conditional probabilities, and they are calculated using:
P(A | B) = P(A and B)/P(B)
Using the above formula, we have:
The probability that a customer eats snack A given that the customer has eaten snack A before, to be:
P = n(Have eaten snack A)/n(Snack A)
This gives
P = 144/252
Evaluate
P = 0.57
Also, we have:
The probability that a customer eats snack A given that the customer has not eaten snack A before, to be:
P = n(Have not eaten snack A)/n(Snack A)
This gives
P = 108/252
Evaluate
P = 0.43
Hence, the probabilities are 0.57 and 0.43
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it is about Name the property of the rational numbers in each of the following
The property of each given rational number operation are respectively; Commutative Property; Closure Property; Associative Property; Closure Property; Distributive Property
What is the property of the rational number?The main properties of rational numbers are:
Commutative property.Associative Property. Distributive Property.Closure property.a) The property used here is commutative property which says that;
a + b = b + a.
This tallies with the operation used on the rational numbers.
b) The property used here is called Closure Property. This is because for two rational numbers say a and b, the results of addition, subtraction and multiplication operations gives a rational number.
c) The property used here is called associative property because it states that; a * (b * c) = (a * b) * c.
d) The property used here is called Closure Property. This is because for two rational numbers say a and b, the results of addition, subtraction and multiplication operations gives a rational number.
e) The property used here is called distributive property because it states that; a * (b * c) = (ab * ac)
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The table below shows a relationship between x and y values. Which of the following equations describes this relationship?
Answer: C
Step-by-step explanation: Substitute the x’s into C’s equation.
2(0) is 0, 0+1 is 1 so the first row is correct. 2(2) is 4, 4+1 is 5, so the second row is correct. 2(4) is 8, 8+1 is 9, so the third row is correct. And lastly, 2(6) is 12, 12+1 is 13 so fourth row is correct as well. Assuming the rest of the rows follow this pattern, the correct answer should be C.
simplify (–2 – c )(–1)
The simplified expression of (-2 - c)(-1) is 2 + c
How to simplify the expression?We have:
(-2 - c)(-1)
Express as product
(-2 - c) * (-1)
Evaluate the product
2 + c
Hence, the simplified expression of (-2 - c)(-1) is 2 + c
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a store pays $736 for an oil painting and marks the price up by 22 3/8 %. wat is the amount of the markup?
Answer:
$ 164.68 markup
Step-by-step explanation:
22 3/8 % = 22.375 % which is .22375 in decimal
.22375 * $ 736 = $ 164.68
What is the quotient of 0.8449 ÷ 0.71?
Answer:
1.19
Step-by-step explanation:
1) Shift the decimals of both 0.8449 and 0.71 to the right by 2 decimal places. (This is needed to convert 0.71 to 71, since long division must divide by a whole number.)
84.49 ÷ 71
2) Use the algorithm method.
1 . 1 9
7 1 | 8 4 . 4 9
7 1 .
1 3 . 4
7 . 1
6 . 3 9
6 . 3 9
3) Therefore, 0.8449 ÷ 0.71 = 1.19.
1.19
John ordered a caramel tea and he was lucky enough it was 20% off so if the original price was $5.75 how much does it cost??
Find the HCF of
x
3
y
3
and
y
4
Answer:
y^3
Step-by-step explanation:
x^3 y^3 and y^4
y^3 * x^3 and y^3 * y
Can somebody help me, i would really appreciate it!!
It will take 5 seconds for the waste to hit the ground.
How many seconds will it take for the waste to hit the ground?We know that the bird releases the waste from a height of 400ft, so the height equation is:
[tex]h(t) = -16t^2 + 400[/tex]
The waste will hit the ground when its height is equal to zero, so we just need to solve the quadratic equation:
[tex]h(t) = 0 = -16t^2 + 400\\\\16t^2 = 400\\\\t^2 = 400/16 = 25\\\\[/tex]
Now we can apply the square root in both sides:
[tex]t = \sqrt{25} = 5[/tex]
It will take 5 seconds for the waste to hit the ground.
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What is the midpoint of the class interval 80-89?
The midpoint of the class interval 80-89 is 84.5.
What is mid point of a class interval?The mid point of a class interval is also called the class mark of the class interval.
The midpoint is defined as the average of the upper and lower class limits.
Therefore, the midpoint of the class interval 80-89 can be calculated as follows:
mid point = 80 + 89 / 2
mid point = 169 / 2
mid point = 84.5
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What is the length of line segment c d? round to the nearest tenth. 2.3 cm 4.0 cm 10.7 cm 18.6 cm
The value of CD is 10.7 cm , Option C is the right answer.
What is a Line Segment ?A line segment is a line of fixed measure.
From the figure , as Triangle ABC is a right angled triangle
sin 30 degree = (Perpendicular / Hypotenuse)
∠ B = 30° , AB= 10 cm
sin 30 = AC/10
AC = 5 cm.
To determine CD ,
In Triangle ADC ,
tan 25 = Perpendicular / Base
tan 25 = AC / CD
tan 25 = 5 / CD
CD = 5 / 0.4663
CD = 10.7 cm
Therefore the value of CD is 10.7 cm , Option C is the right answer.
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Answer: C
Step-by-step explanation: 10.7 cm
